SUPERLUBRICITY
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SUPERLUBRICITY
Edited by Ali Erdemir Argonne National Laboratory Argonne, USA and Jean-Michel Martin Ecole Centrale de Lyon Lyon, France
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Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK First edition 2007 Copyright © 2007 Elsevier BV. All rights reserved no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email:
[email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13: 978-0-444-52772-1 ISBN-10: 0-444-52772-9 For information on all Elsevier publications visit our website at books.elsevier.com
Printed and bound in The Netherlands 07 08 09 10 11
10 9 8 7 6 5 4 3 2 1
Contents Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xv
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1 Superlubricity for Incommensurate Crystalline and Disordered Interfaces J.B. Sokoloff 1.1 Superlubricity for Incommensurate Interfaces . . . . . . . . . . . . . . . . 1.2 Superlubricity for Disordered Interfaces . . . . . . . . . . . . . . . . . . . 1.3 Friction Resulting from Multiscale Roughness . . . . . . . . . . . . . . . . 1.4 Superlubricity Resulting from Polymer Brushes . . . . . . . . . . . . . . . 1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 1 1 3 6 11 14 14
2 Superlubricity of Clean Surfaces . . . . . . . . . . . . . . . . . . M. Hirano 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Preliminaries: Tomlinson’s Picture . . . . . . . . . . . . . . . 2.3 The Criterion for the Occurrence of Tomlinson’s Mechanism . 2.4 Atomistic Origin of Friction . . . . . . . . . . . . . . . . . . . 2.4.1 Frictional Model . . . . . . . . . . . . . . . . . . . . . 2.4.2 Static Friction . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Dynamic Friction: Energy Dissipation . . . . . . . . . 2.5 Superlubricity . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Superlubricity and Adiabatic Motion of Atoms . . . . 2.5.2 Friction Diagram . . . . . . . . . . . . . . . . . . . . . 2.5.3 Superlubricity and High Dimensionality . . . . . . . . 2.5.4 Energy Recurrence Phenomena . . . . . . . . . . . . . 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 17 17 18 21 25 25 26 27 30 30 31 33 34 36 37
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3 Theoretical Studies of Superlubricity . . . . . . . . . . . . . . . . . . . C.E. Campañá and M.H. Müser 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Friction and Superlubricity . . . . . . . . . . . . . . . . . . . . 3.2.2 Dry Friction on Idealized Zero Temperature Analytic Models v
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3.2.3 Disorder, Symmetry and Dimensionality . . . . . . . . . . . . 3.2.4 Thermal and Quantum Effects . . . . . . . . . . . . . . . . . . 3.3 Computer Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Rough Interfaces, Elastic Solids and Superlubricity . . . . . . 3.3.2 Lennard-Jones Systems . . . . . . . . . . . . . . . . . . . . . 3.3.3 Adsorbed Layers, Confined Fluids and Boundary Lubrication 3.3.4 Solid Lubricants and Layered Structures . . . . . . . . . . . . 3.3.5 Metallic Contacts . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.6 Carbon Films and Hydrogen-Terminated Surfaces . . . . . . . 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
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44 46 47 47 50 51 52 53 54 54 55
Ab-initio Atomic Scale Study of Nearly Frictionless Surfaces . . . . . . . S. Ciraci, T. Yildirim, S. Dag and O. Gulseren 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Frictionless Sliding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 General Theoretical Arguments . . . . . . . . . . . . . . . . . . . 4.2.2 Recent Experimental Progress . . . . . . . . . . . . . . . . . . . . 4.3 Description of Theoretical Model . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Atomistic Models and Details for Ab-initio Calculations . . . . . 4.4 Superlow Friction Coefficient Between Hydrogenated Diamond Surfaces 4.4.1 Force Variations in the Sliding Friction of Two Hydrogenated Diamond Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Sliding Friction of Hydrogenated Diamond (001) Slabs . . . . . . 4.4.3 Effect of Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Ab-initio Study of Atomic-Scale Friction Between Cubic BN-Surfaces . 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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57 57 57 59 59 60 60 60 61
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63 63 67 68 75 75 76
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79 79 79 80 80 83 84 84 88 91 92 92 96 98 100
Molecular Dynamics Simulations of Tribology . . . . . . . . . . . . . J.D. Schall, P.T. Mikulski, G.M. Chateauneuf, G. Gao and J.A. Harrison 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 MD Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Outline of Method . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Simulation of Tribology . . . . . . . . . . . . . . . . . . . . 5.3 Reactive Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Covalent Potentials . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Development and Fitting of Bond-Order Potential . . . . . . 5.3.3 Covalent + Intermolecular Forces (AIREBO) . . . . . . . . 5.4 Recent MD Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Tribochemistry at the Sliding Interface . . . . . . . . . . . . 5.4.2 Intrafilm Tribochemistry . . . . . . . . . . . . . . . . . . . . 5.4.3 Self-assembled Monolayers . . . . . . . . . . . . . . . . . . 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 What Causes Low Friction; What Causes High Friction . . . . . . . . . . Y. Zhu and S. Granick 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Superlubricity in Boundary Lubrication . . . . . . . . . . . . . . . . . . 6.3 Controlling the Boundary Condition of Hydrodynamic Flow . . . . . . . 6.3.1 The Mechanism that Controls Slip in Low-viscosity Fluids . . . . 6.3.2 “Slip” at Partially-Wetted Surfaces with Roughness Varied . . . . 6.3.3 “Slip” Can Be Modulated by Dissolved Gas—at Both Wetted and Partially-Wetted Surfaces . . . . . . . . . . . . . . . . . . . . . . 6.4 Outlook—The Purposeful Reduction in Friction . . . . . . . . . . . . . . 6.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Frictional Dynamics at the Atomic Scale in Presence of Small Oscillations of the Sliding Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Jeon, T. Thundat and Y. Braiman 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Effect of Surface Roughness and Adsorbates on Superlubricity V.N. Samoilov, C. Yang, U. Tartaglino and B.N.J. Persson 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Clean Smooth and Rough Surfaces . . . . . . . . . . . 8.3.2 Dependence of the Friction on the Load . . . . . . . . 8.3.3 Role of Adsorbates . . . . . . . . . . . . . . . . . . . . 8.4 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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9 Atomic-Scale Investigation of Superlubricity on Insulating Surfaces E. Gnecco, A. Socoliuc and E. Meyer 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 The Tomlinson–Prandtl Model . . . . . . . . . . . . . . . . . . . . 9.3 The Superlubric Regime . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Experimental Evidence of Superlubricity: Quasistatic Case . . . . .
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9.5 Experimental Evidence of Superlubricity: Dynamic Case . . . . . . . . . . 9.6 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Superlubricity of Fullerene Intercalated Graphite Composite . . . . . . K. Miura and N. Sasaki 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Sliding of Graphite Flakes . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Sliding of Graphite Flakes over Graphite . . . . . . . . . . . . . 10.2.2 Lateral Force versus Load Acting between Graphite Surfaces . . 10.3 Superlubricity of a Graphite/C60 Monolayer Film/Graphite . . . . . . . 10.3.1 Structure of a Graphite/C60 Monolayer Film/Graphite System . 10.3.2 Ultralow Lateral Movement of C60 Molecules . . . . . . . . . . 10.4 Superlubricity of C60 (C70 ) Intercalated Graphite Composite . . . . . . 10.4.1 Preparation and Structure of C60 (C70 ) Intercalated Graphite Composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Superlubricity of C60 (C70 ) Intercalated Graphite Composite . . 10.5 Origin of Superlubricity of Fullerene Intercalated Graphite Composite 10.5.1 Elastic Property of New Composite . . . . . . . . . . . . . . . . 10.5.2 Internal Sliding of New Composite . . . . . . . . . . . . . . . . 10.5.3 Guideline for Designing Ultralow Friction System . . . . . . . . 10.5.4 Intercalated Fullerenes Can Control Ultralow Friction . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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161 161 161 162 162 164 165 165 166 168
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168 171 172 172 173 175 176 177
11 Superlubricity of Ag Nanometer-Thick Layers under Macroscopic Sliding System in UHV Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Goto and F. Honda 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Film-Thickness Effect on the Lubricity of Ag Film . . . . . . . . . . . . . 11.4 Determination of the Shear Plane in Superlubricity of Ag Film . . . . . . . 11.5 Morphological Effect on Superlubricity . . . . . . . . . . . . . . . . . . . 11.6 Effect of Crystal Orientation on Superlubricity . . . . . . . . . . . . . . . 11.7 Origin of Ag Film Superlubricity . . . . . . . . . . . . . . . . . . . . . . . 11.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
179 179 179 180 182 186 188 192 195 197 198
12 Superlubricity between Graphite Surfaces . . . . . . . . . . . . . . . . . . M. Dienwiebel and J.W.M. Frenken 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Incommensurability-Induced Transition to Frictionless Sliding . . . . . . 12.3 Atomic-Scale Observation of Superlubricity between Graphite Surfaces . 12.4 Towards Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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13 Superlubricity of Molybdenum Disulfide . . . . . . . . . . . . . . . . . . . J.M. Martin 13.1 Low, Ultralow and Superlow Friction . . . . . . . . . . . . . . . . . . . . 13.2 Characterization of Sputter-Deposited MoS2 Coatings . . . . . . . . . . 13.3 Experimental Details for UHV Tribometry and MoS2 Film Deposition . 13.4 Ultralow and Superlow Friction of MoS2 Coatings . . . . . . . . . . . . 13.5 HRTEM Investigation of MoS2 Wear Debris . . . . . . . . . . . . . . . . 13.6 Possible Explanation for Superlubricity of MoS2 . . . . . . . . . . . . . 13.7 Ultralow Friction by MoS2 Single Sheets. Towards Superlubricity under Boundary Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.8 Ultralow Friction by MoS2 Nanoparticles . . . . . . . . . . . . . . . . . 13.8.1 Nanotribology on MoS2 Crystals . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Superlubricity of Tungsten Disulfide Coatings in Ultra High Vacuum . L. Joly-Pottuz and M. Iwaki 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 WS2 Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3 IF-WS2 coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Superlubricity by H2 S Gas Lubrication of Mo . . . . . . . I.L. Singer and T. Le Mogne Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . 15.2.1 Friction and Surface Analysis Apparatus . . . . . 15.2.2 Sample Preparation and Friction Test Procedures 15.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3.1 Friction Coefficient vs. Gas Pressure . . . . . . . 15.3.2 Friction Coefficient vs. Speed . . . . . . . . . . . 15.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 15.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . 16 Superlubricity in Diamondlike Carbon Films A. Erdemir and O.L. Eryilmaz 16.1 Introduction . . . . . . . . . . . . . . . . . 16.2 Superlubricity in Crystalline Solids . . . . 16.2.1 Lamellar Solids . . . . . . . . . . . 16.2.2 Other Solids . . . . . . . . . . . . .
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16.3 Superlubricity in Amorphous Carbons . . . . . . . . . . 16.3.1 Diamondlike Carbon Films . . . . . . . . . . . . 16.3.2 Synthesis and Main Characteristics of DLC Films 16.3.3 Classification . . . . . . . . . . . . . . . . . . . . 16.3.4 Lubrication Mechanisms . . . . . . . . . . . . . . 16.3.5 Origin of Superlubricity in DLC Films . . . . . . 16.4 Summary and Future Direction . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .
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257 258 258 259 259 262 268 269 269
17 Superlow Friction of a-C:H Films: Tribochemical and Rheological Effects . J. Fontaine and C. Donnet 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.2 The Wide Friction Range of DLC Films . . . . . . . . . . . . . . . . . . . 17.2.1 General Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.2.2 Experimental Evidence of Superlow Friction . . . . . . . . . . . . . 17.3 Conditions for a-C:H Films to Achieve Superlow Friction . . . . . . . . . 17.3.1 General Requirements to Achieve Superlow Friction with DLC Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.3.2 Influence of Hydrogen Content in the Film: Low Interacting Surfaces 17.3.3 Influence of the Mechanical Behavior of the Film: Compliant Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17.4 Achievement and Preservation of Superlow Friction with a-C:H Films . . 17.4.1 How to Achieve Superlow Friction: Tribofilm Build-Up Controlled by Surface Chemistry of the Counterface . . . . . . . . . . . . . . . 17.4.2 How to Preserve Superlow Friction: Tribo-reactivity of the Contact Controlled by Gaseous Environment . . . . . . . . . . . . . . . . . 17.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
273 273 273 274 274 275 277
18 Suppression of Moisture Sensitivity of Friction in Carbon-Based Coatings . C. Freyman, B. Zhao and Y.-W. Chung 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.3 Surface Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.3.1 Compositional Analysis . . . . . . . . . . . . . . . . . . . . . . . . 18.3.2 Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.4 Tribological Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.5 Water–Film Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.6 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.6.1 Hardness and Elastic Modulus . . . . . . . . . . . . . . . . . . . . . 18.6.2 Film Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
295 295 295 297 298 298 301 302 304 306 306 307 309 309
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19 Application of Carbon Based Nano-Materials to Aeronautics and Space Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K.W. Street, Jr., K. Miyoshi and R.L. Vander Wal 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . 19.2.3 Analytic Techniques and Post Mortem Analysis . . . . . . . . . 19.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.3.1 Nano-onion Investigations . . . . . . . . . . . . . . . . . . . . . 19.3.2 Multi-walled Nanotube Investigations . . . . . . . . . . . . . . 19.3.3 Single-walled and Surface Fluorinated Nanotube Investigations 19.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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311 311 311 312 312 315 316 317 317 322 332 338 338
20 Superlubricity of CNx-coatings in Nitrogen Gas Atmosphere . . . . . . . . K. Kato and K. Adachi 20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2 Fundamental Properties of CNx-coatings . . . . . . . . . . . . . . . . . . . 20.2.1 Coating Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.2.2 Hardness and Microstructure . . . . . . . . . . . . . . . . . . . . . 20.3 Superlubricity of CNx-coating on Si-wafer sliding against Si3 N4 ball . . . 20.3.1 Friction on CNx-coatings in Vacuum After Short Time Exposure to Air, O2 or N2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.3.2 Friction on CNx-coatings in Gases of 7.4 × 104 Pa . . . . . . . . . 20.4 Superlubricity of CNx-coating on Si3 N4 Disk Sliding against Si3 N4 Ball or CNx-coating on Si3 N4 Ball . . . . . . . . . . . . . . . . . . . . . . . . . 20.5 Mechanisms of Low Friction and Low Wear of CNx-coatings . . . . . . . 20.5.1 The Effect of Humidity in N2 on Friction . . . . . . . . . . . . . . . 20.5.2 The Effect of O2 in N2 on Friction . . . . . . . . . . . . . . . . . . 20.5.3 The Effect of Surface Roughness on Friction . . . . . . . . . . . . . 20.5.4 Tribolayers of Superlubricity . . . . . . . . . . . . . . . . . . . . . 20.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
341 341 341 341 341 343 345
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365 365 365 368 368 374 378 378 384 391 392
21 Achieving Ultralow Friction by Aqueous, Brush-Assisted Lubrication S. Lee and N.D. Spencer 21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Macroscopic Scale Contacts . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Rigid Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Soft Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Micro/Nanoscopic Scale Studies . . . . . . . . . . . . . . . . . . . . 21.3.1 General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . 21.3.2 Water-soluble Polymer Brushes . . . . . . . . . . . . . . . . . 21.4 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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22 Friction Control at the Molecular Level: From Superlubricity to Stick-Slip D. Mazuyer, A. Tonck and J. Cayer-Barrioz 22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2.1 The Molecular Tribometer . . . . . . . . . . . . . . . . . . . . . . . 22.2.2 The Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2.3 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . 22.2.4 Properties of the Confined Layer under Loading . . . . . . . . . . . 22.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3.1 Squeeze Behavior of the Adsorbed Layer of the Friction Modifiers . 22.3.2 Frictional Properties of the Adsorbed Layers of Friction Modifiers . 22.3.3 Physical Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
397 397 397 402 402 403 405 406 409 409 411 422 424
23 Super Low Traction under EHD & Mixed Lubrication Regimes . . . . . . P. Vergne 23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.1.1 Superlubricity, Near Frictionless Sliding and Super Low Traction 23.1.2 Chapter Objectives and Summary . . . . . . . . . . . . . . . . . . 23.2 Traction versus Super Low Traction . . . . . . . . . . . . . . . . . . . . 23.2.1 Generalities on EHD Traction . . . . . . . . . . . . . . . . . . . . 23.2.2 Super Low Traction and Experimental Issues . . . . . . . . . . . 23.3 Experimental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.4 Lubricated Super Low Traction . . . . . . . . . . . . . . . . . . . . . . . 23.4.1 Newtonian Isothermal Piezoviscous Behavior . . . . . . . . . . . 23.4.2 Shear Thinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.4.3 Thin Film EHD Conditions . . . . . . . . . . . . . . . . . . . . . 23.5 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Annex: Main Properties of the Lubricants . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
427 427 427 427 428 428 428 430 431 432 432 435 436 440 442 442 442
24 Superlubricity of In Situ Generated Protective Layer on Worn Metal Surfaces in Presence of Mg6 Si4 O10 (OH)8 . . . . . . . . . . . . . . . . . . . J. Yuansheng and L. Shenghua 24.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.2 Tribochemical Principles of In Situ Reconditioning of Rubbing Metal Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.2.1 Tribological Process . . . . . . . . . . . . . . . . . . . . . . . . . 24.2.2 Tribochemical Reactions . . . . . . . . . . . . . . . . . . . . . . . 24.3 Superlubricity of Protective Layer Generated by ART Mechanochemical Reconditioner Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.3.1 Protective Layer Generated in Railway Locomotive Trials . . . . 24.3.2 Observation of the Protective Layer on Cylinder Bore . . . . . . 24.3.3 Nano-hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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24.3.4 Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . 24.3.5 Coefficient of Friction . . . . . . . . . . . . . . . . . . . . . . . . 24.3.6 Protective Layer Generated in Laboratory Conditions . . . . . . . 24.4 Possible Sources of Superlubricity of In Situ Generated Protective Layer on Worn Metal Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.4.1 Phase Structure of the Protective Layer . . . . . . . . . . . . . . . 24.4.2 Raman Spectrometry Analysis . . . . . . . . . . . . . . . . . . . . 24.4.3 Possible Sources of Superlubricity . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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461 462 466 466 467 467
25 Superlubricity of Diamond/Glycerol Technology Applied to Automotive Gasoline Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.I. De Barros Bouchet and M. Kano 25.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.2.1 DLC Materials Preparation . . . . . . . . . . . . . . . . . . . . . . 25.2.2 Tribological Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.2.3 Engine Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.2.4 Nanoscratch Measurement . . . . . . . . . . . . . . . . . . . . . . . 25.2.5 Mechanical Measurements . . . . . . . . . . . . . . . . . . . . . . . 25.2.6 Surface Analyses Techniques . . . . . . . . . . . . . . . . . . . . . 25.2.7 Microstructural Analysis Technique . . . . . . . . . . . . . . . . . . 25.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.3.1 DLC Materials Characterizations . . . . . . . . . . . . . . . . . . . 25.3.2 Steel/DLC Tribological Systems Lubricated by Glycerol Mono-Oleate (GMO) . . . . . . . . . . . . . . . . . . . . . . . . . . 25.3.3 DLC/DLC Tribological Systems Lubricated by Glycerol and GMO 25.3.4 Superlubricity Mechanism as Studied by Surface Analyses . . . . . 25.3.5 Engine Test Results and Application . . . . . . . . . . . . . . . . . 25.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
471 471 471 472 472 472 474 475 475 475 476 477 477 481 484 485 489 491 491 492 493
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Foreword “From Hard to Soft” David Tabor (and the British school around him) constructed our basic view of solid friction, induced by mesoscopic asperities. We often avoid solid friction by fluid intercalation: oils, water, lubricants . . . But some exotic situations still emerge. Among them, the extremely weak friction found with certain hard contacts: diamondlike films, and also incommensurate contacts between layered crystals (graphite, MoS2 , . . . ). These contacts can display a form of “superglide” “superlubricity” or “superlubrication”. They constitute the central subject of the present book. On superlubricity between two ideal graphite crystals, Friedel and the present author have recently presented a simple synthesis, using our classical knowledge on grain boundaries [1]. Two regimes are expected, depending on the missetting angle θ between the crystals: (a) Strong coupling, when θ ≤ U1 /UL where U1 /UL is the ratio of interplane/inplane interactions. Here, as shown long ago by F.C. Frank [2], we expect two ladders of screw dislocation on the interface, with a repeat distance d = aθ −1 (where a is a mesh size). The two crystals are then strongly locked: there is no superglide. (b) The other (more interesting) regime corresponds to θ > U1 /UL . Here, the Frank dislocations are too diffuse to show up, and we expect a very weak friction, analyzed by Sokoloff and others. The moving potential of (say) the top part creates phonons in the bottom part. One phonon processes are not allowed by energy and momentum conservation. Two phonon processes (Raman) are allowed, but are very weak. This discussion is helpful, although slightly incomplete, because it ignores the collective modes at the interface. On the whole, the incommensurate graphite/graphite contacts provide us with some beautiful physics, and this is well shown in the present book. But most experiments are performed with a small plaque torn out from a macroscopic crystal. When the linear size of this plaque becomes as small as the ladder periodicity d, we again enter into a very different domain. It may be that the low mutual friction between diamondlike films is related to the same concepts. Here we deal with a mosaic of small compact facets. Presumably most of the facets have θ > U1 /UL and are thus good candidates for superlubricity. But we should know more about the contact lines between adjacent mosaic units (a) when moving, they might generate a one phonon friction; (b) if the size L of the units is comparable to d, we enter in a different domain. Another gold mine of friction research is based on soft systems. The central example is the vertebrate joint with its amazing properties of low friction and resistance to squeezing. These systems are also discussed deeply in this book. The two interacting surfaces inside our hip, or knee, are based on fibrous films (hyaluronans, proteoglycans) separated by a synovial fluid of similar composition. This fluid in itself is not an exceptional lubricant xv
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(as shown by in vitro experiments). The low friction is not due to the fluid, but rather to polymer brushes on the fibrous film surface. They can be linear chains or statistically branched objects: in the real joint, the polymers are branched. Two geometrical parameters are important: – the average size R of a single molecule in water, – the average distance D between neighboring grafts. When D > R we talk of a “mushroom” regime. When D < R we have a true brush. The most useful, and realistic systems are at the cross over point (D ∼ R). Friction between synthetic brushes has been studied by a number of authors, and is reviewed recently by J. Klein [3]. From a global point of view, the quality of a brush/brush contact is essentially defined by 3 parameters: (a) the lubricant thickness λ, defined in terms of a shear stress σ and a slippage velocity V : λ = ηV /σ , where η is the velocity of water (in the narrow gap between the brushes, solute macromolecules cannot enter). We expect λ ∼ R ∼ D at the mushroom/brush cross over point; (b) the squeeze pressure ps above which the load flattens out the brush. A scaling discussion on forces confirms that ps is higher for branched objects (at the same overall molecular weight/graft); (c) the critical shear stress for tear out σt (above which the grafts are torn out). We also expect σt to be increased by branching. The conclusion (for future biomimetic systems) is relatively clear: (a) we should use branched chains; (b) they should not be too large (because ps and σt then become small); (c) at the other end, if R is too small, λ is small and the friction is too large. There is an optimum in between. Of course, this discussion is primitive. J. Klein introduces two other physicochemical factors which help to reduce the friction: (i) Hyaluronans and proteoglycans are negatively charged polyelectrolytes: this implies that the two partner brushes repel each other. (This is not a huge effect however, because, in hysiological conditions, we deal with water + salt: there is some screening.) (ii) The counterions carry an important hydration shell, which acts as a lubricant. On the whole, this preface presents a very crude view of friction processes for hard incommensurate solid contacts, and for soft polymer brushes. The contents of the present book will allow our reader to go much farther. But the present comments and rules of the thumb may provide a helpful introduction. P.-G. de Gennes Institut Curie, 26, rue d’Ulm 75005 Paris, France
REFERENCES [1] Similar ideas were produced much earlier by Lançon, F., Penisson, J.M., Dahmen, U. Europhys. Lett. 49 (2000), 603. [2] Frank, F.C. J. Cryst. Growth 51 (1981), 367. [3] Klein, J., Raviv, U., Perkin, S., Kampf, N., Chai, L., Giasson, S. J. Phys.: Con. Matter 16 (2004), S5437.
Introduction Among all physical phenomena, friction perhaps poses one of the greatest challenges to the scientific and industrial communities and has a direct linkage to energy efficiency and environmental cleanliness of all moving mechanical systems. In everyday life, we rarely think about friction or appreciate its importance, but there is no doubt that it is a major cause of lost energy, and as well as hazardous emissions to our environment. Hence, the prospect of further reducing friction in engineering systems has real-life implications From www.angstrom.uu.se/tribomaterials/. for not only preserving our limited energy resources, but also saving our planet from hazardous emissions for generations to come. Considering that in most industrialized nations, the annual cost of friction- and wear-related energy and material losses is estimated to be 5 to 7% of their gross national products, the further reduction (or even elimination) of friction in all kinds of moving mechanical systems would be extremely beneficial to the economical well-being of all nations. In short, reducing friction further is extremely important for conserving not only our ever-diminishing energy resources but also the environment and ultimately money. Recent advances in the computational, analytical, and experimental capabilities of modern tribology and related research fields have paved the way for a better understanding and hence control of friction across the force, length, and time scales. In particular, dedicated fundamental friction studies at the subnanometer scale using a wide range of advanced computational and experimental tools (i.e., ab initio and molecular dynamic simulations, atomic and friction force microscopy, scanning tunneling microscopy, surface force apparatus, and quartz crystal microbalance, etc.) have enabled scientists to not only more accurately predict/simulate, but also to identify, the specific types of materials and test conditions that can lead to near-zero friction or superlubricity in a number of nano-to-macro scale sliding systems. In particular, supercomputers with huge memory and processing capabilities now enable simulation and real-time visualization of atomic-scale friction and allow predictions of those conditions that can lead to superlubricity. The word “superlubricity” was first used by Motohisa Hirano to describe a theoretical sliding regime in which friction or resistance to sliding completely vanishes (see his chapter in this book). In this regime, the extent of physical and/or chemical interactions is extremely small or essentially absent, and hence the surfaces can slide over one another without causing much friction. Historically, the earliest studies on superlubricity started in mid-1980s, but the real progress occurred during the 1990s. In particular, theoretical studxvii
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ies by Professors Jeffrey Sokoloff and Motohisa Hirano predicted the existence of such superlubricious states between weakly interacting, atomically smooth surfaces (see their chapters in this book). Their studies have provided significant fundamental insight into the atomic-scale origins of friction in general and superlubricity in particular. Other researchers who entered the field later also confirmed that such a state of near-zero-friction may indeed exist between sliding surfaces of a number of solid materials that are brought into intimate contact in an incommensurate or ideally misaligned/misfit fashion. By bringing such surfaces from a commensurate to an incommensurate state, these researchers were able to observe a clear transition from a pure stick-slip (indicative of high friction) to smooth sliding (indicative of no friction). Due to the strict structural requirements (i.e., optimal imcommensurability and/or misalignment) for superlubricity, some scientists who worked in this field during the early 2000s often preferred to use the term “structural lubricity” rather than “superlubricity,” mainly because “superlubricity” seemed related to such well-known physical phenomena as superconductivity, superfluidity, etc. Because superlubricious situations were predicted and observed only in ultrahigh vacuum in the 1990s, there was a tendency to see an analogy with superconductivity, in which electrical resistance vanishes at very low temperatures. However, the term superlubricity is quite appropriate from a tribological standpoint in the sense that the prefix “super” means “extreme;” hence, superlubricity means extreme lubricity but in no way suggests “zero” friction. Also, we are presently unable to measure friction coefficients at values below 10−4 . In the case of superconductivity, electric resistance completely vanishes or it is “zero” so that the use of the term “super” may not be totally appropriate here, either. Overall, a better terminology or description is needed to dispel the controversy over the real meaning of the prefix “super” that is often used in so many other physical phenomena to mean something that is extraordinary or unusual. The main objective of this book is to bring together leading researchers who work in superlubricity and other related fields and to provide a concise state-of-the-art overview of the recent developments and discoveries. Because this field has become rather large, complex, and multidisciplinary in nature, the chapters in this book may not sufficiently cover everything that relates to superlubricity; however, the editors have done their best to bring out some of the most important developments in superlubricity during the last two decades in a coherent manner. Within the book’s 25 chapters, readers will find a wealth of information ranging from theoretical and practical aspects of friction in general to superlubricity in particular. Each chapter is written by a group of leading experts who are well-known for their invaluable contributions to the field. The book starts with a section covering the theoretical aspects of superlubricity. This is followed by other sections that deal with the observation and/or measurement of superlubricity in real systems ranging from nano-to-macro scales under dry-sliding, vacuum, or oil-lubricated conditions. Specifically, Chapters 1–7 are devoted to the theoretical aspects of superlubricity, while Chapters 8–11 provide fundamental insight into superlubricity of various sliding systems at the nanoscale. Chapters 12 to 15 cover the superlubricity of lamellar solids over a broad range of scales, and Chapters 16 to 20 discuss the superlubricity of carbon-based thin coatings at macro scales. Chapters 21–25 highlight the superlubricity of sliding surfaces under elastohydrodynamic and boundary lubricated sliding regimes.
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Readers will appreciate that recent advances in superlubricity research have indeed been phenomenal. However, they will also realize that there remain several key challenges for future scientists and engineers to overcome. In the very broad field of tribology, there are numerous test and environmental conditions, surface parameters, and material combinations that can affect friction and wear in so many ways. Early tribology pioneers and other dedicated researchers have made great strides despite the field’s very intricate and multifaceted nature. As we move forward in the 21st century with great hopes and expectations, we must work harder to develop novel surfaces, together with novel design concepts that can further reduce or even eliminate friction and hence save our environment and limited energy resources for future generations. Specifically, we need to engineer innovative ways to build new solid structures or systems that can provide universally achievable superlow friction across the physical scales. We should also increase our theoretical modeling capabilities so they can guide us in the right direction for the development of novel materials and/or sliding conditions that can lead to superlow friction and wear. Most of the tools (analytical, computational, and experimental) needed for the successful realization of this goal are now available, and the development of new and more robust tools is currently underway. Overall, the greatest challenge for the future seems to be the integration of the vast tribological knowledge bases accumulated over the years into the realization of smart tribosystems that generate little or no friction. From the very beginning, mankind has been on the move and in search of new ways and means to achieve easier and faster mobility. There should be no doubt that this trend will continue at a much accelerated pace during the 21st century, and we hope that this will result in the development of truly frictionless systems. The editors are truly indebted to the authors of each chapter in this book. Without their enthusiasm and eagerness, we could not have put this book together. They thank Prof. Pierre-Gilles de Gennes (Nobel Prize Laureate in Physics, 1991) for writing a very insightful and thought-provoking foreword. The editors also acknowledge the support of their institutions (Argonne National Laboratory—USA and Ecole Centrale de Lyon—France) and funding agencies (the United States Department of Energy, Office of Energy Efficiency and Renewable Energy, Freedom Car and Vehicle Technologies Program; and Centre National de la Recherche Scientifique de France CNRS). Also, Dr. Osman Eryilmaz of Argonne is gratefully acknowledged for his help in formatting some of the chapters. Last but not least, the editors thank their families for their support and understanding during the preparation of this book.
Ali Erdemir Argonne National Laboratory Energy Systems Division Argonne, IL, USA
Jean-Michel Martin University Institute of France, Paris Ecole Centrale de Lyon, LTDS Ecully, France
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Contributors Koshi Adachi
Tohoku University, Sendai 980-8579, Japan
Yehuda Braiman
Center for Engineering Science, Advanced Research Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
Carlos E. Campañá
Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
Juliette Cayer-Barrioz
Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes UMR 5513 CNRS/ECL/ENISE, F-69134 Ecully Cedex, France
Ginger M. Chateauneuf
Chemistry Department, US Naval Academy, Annapolis, MD 21402, USA
Yip-Wah Chung
Northwestern University, Evanston, IL 60208, USA
S. Ciraci
Department of Physics, Bilkent University, Ankara 06800, Turkey
S. Dag
Center of Nanophase Materials Science (CNMS) and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
Maria Isabel De Barros Bouchet
Laboratory of Tribology and System Dynamics, UMR CNRS 5513, Ecole Centrale de Lyon, 69134 Ecully Cedex, France
Martin Dienwiebel
Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The Netherlands and IAVF Antriebstechnik AG, 76187 Karlsruhe, Germany
Christophe Donnet
University Institute of France and Laboratoire Traitement du Signal et Instrumentation, UMR CNRS 5516, Université Jean Monnet, 42000 Saint-Etienne, France
Ali Erdemir
Energy Systems Division, Argonne National Laboratory, Argonne, IL 60439, USA
Osman L. Eryilmaz
Energy Systems Division, Argonne National Laboratory, Argonne, IL 60439, USA
Julien Fontaine
Laboratoire de Tribologie et Dynamique des Systèmes, UMR CNRS 5513, Ecole Centrale de Lyon, 69134 Ecully Cedex, France
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xxii
Contributors
Joost W.M. Frenken
Kamerlingh Onnes Laboratory, Leiden University, 2300 RA Leiden, The Netherlands
Christina Freyman
Northwestern University, Evanston, IL 60208, USA
Guangtu Gao
Chemistry Department, US Naval Academy, Annapolis, MD 21402, USA
Enrico Gnecco
NCCR Nanoscale Science, Department of Physics, University of Basel, CH-4056 Basel, Switzerland
Minoru Goto
Ube National College of Technology, Ube 755-8555, Japan
Steve Granick
Dept. of Material Science and Engineering, of Chemistry, and of Physics, Univ. of Illinois, Urbana, IL 61801, USA
O. Gulseren
Department of Physics, Bilkent University, Ankara 06800, Turkey
Judith A. Harrison
Chemistry Department, US Naval Academy, Annapolis, MD 21402, USA
Motohisa Hirano
Gifu University, 1-1, Yanagido, Gifu, 501-1193, Japan
Fumihiro Honda
Toyota Technological Institute, Nagoya 468-8511, Japan
Masanori Iwaki
Japan Aerospace Exploration Agency (JAXA), Tsukuba 305-8505, Japan
Sangmin Jeon
Department of Chemical Engineering, Pohang University of Science and Technology, Pohang, Korea
Lucile Joly-Pottuz
Ecole Centrale de Lyon, Ecully 69134, France
Makoto Kano
Nissan Research Center, to Kanagawa Industrial Technology Center, Kanagawa 243-0435, Japan
Koji Kato
Tohoku University, Sendai 980-8579, Japan
Seunghwan Lee
Laboratory for Surface Science and Technology, Department of Materials, CH-8093 Zurich, Switzerland
Thierry Le Mogne
Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes—UMR5513, F-69131 Ecully Cedex, France
Jean-Michel Martin
University Institute of France, Paris, France, and Ecole Centrale de Lyon, LTDS, 69134 Ecully, France
Denis Mazuyer
Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes UMR 5513 CNRS/ECL/ENISE, F-69134 Ecully Cedex, France
Contributors
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Ernst Meyer
NCCR Nanoscale Science, Department of Physics, University of Basel, CH-4056 Basel, Switzerland
Paul T. Mikulski
Physics Department, US Naval Academy, Annapolis, MD 21402, USA
Kouji Miura
Department of Physics, Aichi University of Education, Kariya 448-8542, Japan
Kazuhisa Miyoshi
NASA Glenn Research Center, Cleveland, OH 44135, USA
Martin H. Müser
Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
B.N.J. Persson
IFF, FZ-Jülich, 52425 Jülich, Germany
V.N. Samoilov
IFF, FZ-Jülich, 52425 Jülich, Germany and Physics Faculty, Moscow State University, 117234 Moscow, Russia
Naruo Sasaki
Department of Materials and Life Science, Faculty of Science and Technology, Seikei University, Tokyo 180-8633, Japan
J. David Schall
Chemistry Department, US Naval Academy, Annapolis, MD 21402, USA
Li Shenghua
State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
Irwin L. Singer
Naval Research Lab, Washington, DC 20375, USA
Anisoara Socoliuc
NCCR Nanoscale Science, Department of Physics, University of Basel, CH-4056 Basel, Switzerland
Jeffrey B. Sokoloff
Physics Department, Northeastern University, Boston, MA 02115, USA
Nicholas D. Spencer
Laboratory for Surface Science and Technology, Department of Materials, CH-8093 Zurich, Switzerland
Kenneth W. Street, Jr.
NASA Glenn Research Center, Cleveland, OH 44135, USA
U. Tartaglino
IFF, FZ-Jülich, 52425 Jülich, Germany and Democritos National Simulation Center, 34014 Trieste, Italy
Thomas Thundat
Center for Engineering Science, Advanced Research Life Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
André Tonck
Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes UMR 5513 CNRS/ECL/ENISE, F-69134 Ecully Cedex, France
xxiv
Contributors
Randy L. Vander Wal
The Universities Space Research Association (USRA), c/o NASA Glenn Research Center, Cleveland, OH 44135, USA
Philippe Vergne
Laboratoire de Mécanique des Contacts et des Solides— LaMCoS, UMR CNRS/INSA de Lyon n◦ 5514, 69100 Villeurbanne, France
C. Yang
IFF, FZ-Jülich, 52425 Jülich, Germany
T. Yildirim
NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Jin Yuansheng
State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China
Bo Zhao
Northwestern University, Evanston, IL 60208, USA
Yingxi Zhu
Dept. of Chemical and Biomolecular Engineering, Univ. of Notre Dame, Notre Dame, IN 46556, USA
–1– Superlubricity for Incommensurate Crystalline and Disordered Interfaces Jeffrey B. Sokoloff Physics Department, Northeastern University, Boston, MA 02115, USA
1.1 SUPERLUBRICITY FOR INCOMMENSURATE INTERFACES A few years ago, Hirano and Shinjo suggested that two crystalline surfaces whose periods are incommensurate with each other might be able to slide with respect to each other with negligible friction [1]. They named this phenomenon superlubricity. In fact, even when two crystalline surfaces of identical periodicity are placed in contact with each other, they will almost always be rotated with respect to each other by an arbitrary angle. Consequently, they will almost always be incommensurate. The reason that an incommensurate interface can exhibit low friction is that the two surfaces have no energetically preferred position with respect to each other, and hence they can be slid relative to each other with no cost in energy. What I have just said is of course obviously true, provided that the two surfaces are infinite in extent, are perfectly rigid and interact with simple potentials, such as the Lennard-Jones potential, for example. One would suspect that under similar conditions, two disordered surfaces (e.g., two glassy or amorphous solids, as opposed to the crystalline solids discussed earlier) should also exhibit no friction under the above conditions, since they also have no preferred position relative to each other. From what has been said to this point, it would appear that superlubricity should almost always occur. Since it does not, the reason must be that this phenomenon must break down once the surfaces are not perfectly stiff, infinite in extent and interact only with simple potential functions. Then, in order to explain the nonzero friction between two solid surfaces that is usually observed, we must understand how superlubricity breaks down when the above conditions are not satisfied. We hope that by doing so, we will also find a way to predict the conditions under which some vestiges of superlubricity might survive and serve as a possible mechanism for lubrication. These are the issues that I will attempt to address in this chapter. The first question that I will discuss is whether superlubricity goes away if the surfaces are not perfectly stiff. This problem was first considered by Aubry [2] for a simple one-dimensional model, which consists of an infinitely long chain of atoms connected by springs of lattice spacing b, to represent one solid, interacting with an infinitely long perSuperlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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J.B. Sokoloff
fectly stiff sinusoidal potential of spacing a, to represent the second solid. The chain and sinusoidal potential are incommensurate by definition if the ratio b/a is an irrational number, such as π , (2)1/2 , etc. In fact, Aubry proved that as long as the sinusoidal potential is below a critical strength, the chain-sinusoidal potential system has a continuously degenerate ground state, meaning that one can slide the chain by an infinitesimal distance with no cost in energy. This implies that there is no static or kinetic friction, at least in the very slow sliding speed limit (i.e., no “dry friction”) for a range of potential strengths, and hence superlubricity does not disappear as soon as the solids are no longer perfectly stiff. In order to understand how this occurs, Sacco and Sokoloff [3] numerically solved the equations for the equilibrium configuration for a finite chain of atoms in a sinusoidal potential, using both periodic and free end boundary conditions. For periodic boundary conditions, the sinusoidal potential and the chain are assumed to form a ring. Then if L is the circumference of the ring, L = Na = Mb, where N and M are integers, which implies that b/a = N/M, a rational number. Thus, this model only approximates an incommensurate system in the large N and M limit. We will focus in this discussion on the periodic boundary condition version of this model, since it is easier to follow, but the result does not depend on boundary conditions [3]. Allowed equilibrium configurations of the chain of atoms exist with the chain shifted by small amounts relative to the sinusoidal potential. They alternate in energy between two values. As the values of the integers N and M are increased (i.e., we approach the incommensurate limit), the difference between these energies decreases as the ratio of the potential strength to the product of the spring constant of the springs connecting to atoms in the chain and the square of a chain lattice constant raised to the power N [3]. Thus, for relatively small sinusoidal potential strengths, the ground state of the chain becomes translationally invariant. The physical reason for why this occurs is illustrated in Figure 1.1 (Figure 3 of [3]). As can be seen from the figure, for each configuration of the chain, one atom is near a minimum of the sinusoidal potential (e.g., in the plot at the top of Figure 1.1, it is the atom at the far left). Let us arbitrarily call this the origin of the chain. For each successive configuration of the chain, corresponding to sliding the
Figure 1.1 This is Figure 3 of [3], which shows the equilibrium positions in the sinusoidal potential of the atoms in the chain of atoms in the Frenkel–Kontorova model for successive amounts of sliding of the center of mass of the chain. This figure is reprinted with permission from J.E. Sacco and J.B. Sokoloff, Free sliding in solids with two incommensurate periodicities, Phys. Rev. B 18 (1978), 6549. Copyright 1978 by the American Physical Society.
Superlubricity for Incommensurate Crystalline and Disordered Interfaces
3
chain by a small amount to the right, a different atom somewhere else in the chain lies close to a potential minimum. If we translate the origin of the chain to this new point, the atomic configuration of the chain will be almost identical to what it was previously. This explains why the ground state energy of the chain becomes translationally invariant in the incommensurate limit for a chain which is incommensurate with the sinusoidal potential, even when the chain is not perfectly rigid. When the potential is larger than the product of the spring force constant and the square of the chain lattice constant, this simple picture breaks down. This is the origin of superlubricity for crystalline surfaces. A similar result has been found for two-dimensional atomic surfaces in contact using simulations [4–6].
1.2
SUPERLUBRICITY FOR DISORDERED INTERFACES
It was shown in [7] that two three-dimensional solids in contact at a disordered interface also exhibit superlubricity. By a disordered interface, I mean that the surfaces of the two solids in contact need not be completely amorphous; they only need to be not periodic. Intuitively, one would expect that there should be no static friction for such an interface, just as is the case for an incommensurate interface, because there is clearly no preferred position of the two solids relative to each other. The difference between disordered and incommensurate interfaces, is that static friction is only zero in the case of disordered interfaces if the solids in contact at the interface are thick (i.e., three-dimensional), whereas for incommensurate solids, the static friction is zero for thin (i.e., two-dimensional) solids as well [7]. For two thin solids in contact at a disordered interface, there is static friction which is inversely proportional to a length known as the Larkin length. For weakly interacting surfaces, the Larkin length is long, whereas for strongly interacting surfaces it is short. In contrast, for three-dimensional solids in contact at a two-dimensional interface, the Larkin length is infinite, i.e., comparable to the surface dimensions for weakly interacting surfaces and small relatively small for strongly interacting surfaces [7]. To see this let us consider a simpler model, which should be sufficient to capture the basic physics of this problem, namely we will consider a three-dimensional elastic solid in contact with a stiff two-dimensional disordered interface. The energy of this model can be written as E=
∂uα 2 ∂uα 2 d3 r K + K′ + V r + u(r) δ(z) , ∂xβ ∂xα solid α
(1)
α,β
where α and β run over the components x, y and z, uα (r) denotes the αth component of the displacement field at the point r in the elastic medium, K and K ′ are the elastic moduli (i.e., the Lame coefficients) and V (r) denotes the substrate potential per unit area. We look for an approximate solution of the form uα = uα (x/L, y/L, z/L′ ), where u varies by an amount of the order of the range of a potential well of the substrate potential when x and y vary over a distance of L or z varies over a distance of order L′ . These are the Larkin lengths along and perpendicular to the surface. We substitute this expression for uα in Equation (1), and approximate the integral of the first two terms in the integrand of Equation (1) over a single Larkin domain, by the product of the average over a Larkin
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domain of first two terms in the integrand of Equation (1) and the volume of a Larkin domain, L2 L′ , and then multiply by the number of domains, A/L2 , where A is the area of the interface. Minimizing with respect to L′ , we obtain L′ = L(Γ ′ /Γ )1/2 ,
(2)
where Γ =K
α,β=x,y
(∂uα /∂xβ′ )2
+ K′
(∂uα /∂xα′ )2
α=x,y
and
Γ ′ = K (∂uz /∂z′ )2 + K ′ (∂uα /∂z′ )2 , α
where (x ′ , y ′ , z′ ) = (x/L, y/L, z/L′ ) and · · · signifies an average over a Larkin domain. Since the derivatives of u are all of the order of atomic distances, L′ ≈ L. Assuming that V (r) is completely random and u(r) varies by a negligible amount as r runs over a domain of volume L2 L′ , the integral of V (r) over this domain is of order V0 c1/2 L/a, where V0 is the root-mean-square (rms) value of the potential of interaction between a surface atom and the substrate and c is the fraction of the surface atoms which are in contact with the substrate. In arriving at this result we assumed that the variation of u(r) when r varies over a distance small compared to L, is negligibly small compared to the length scales on the substrate. Consider two surfaces in contact which are disordered so that those atoms which are in contact are randomly distributed over the interface. Let us also assume that the atoms in contact at the interface interact only with hard core interactions. This could occur either because the surface atoms are chemically inert and there is negligible adhesion, or because the surfaces are being pushed together with a sufficient load so that the hard core interactions dominate. Let P denote the load or normal force per unit interface area, a, the mean atomic spacing and c, the fraction of the surface atoms of one surface that are in contact with the second surface. Then, each of the atoms in contact must contribute on the average to the normal force a of order P a 2 /c. Since the force due to the hard core interaction between a pair of atoms acts along the line joining the atoms, for most relative positions of the atoms, it has a component along the interface, as illustrated in Figure 1.2. In the strong pinning regime, each surface atom will sink into an interface potential minimum at the expense of the elastic forces holding it in place. Such a minimum will generally occur at an interstitial region on the second surface. If we now attempt to slide the surfaces relative to each other, each of the atoms in contact with the second surface will now, as it gets pulled out of its potential minimum, exert a component of its hard core interaction with the second surface parallel to the interface directed so as to oppose the attempted sliding motion. This is identified with the static friction. Since each of these atoms must also provide a component P a 2 /c normal to the interface on the average, it is clear the static friction is proportional to the load. This is the case because the contribution to the load and the static friction for each pair of atom in contact is provided by the same hard core force acting between the atoms. The proportionality constant μs is identified with the
Superlubricity for Incommensurate Crystalline and Disordered Interfaces
5
Figure 1.2 This figure illustrates how the hard core interaction between a pair of atoms, one belonging to each of the surfaces in contact, can both support the load and give rise to static friction between the surfaces. Since the force F between the pair of atoms can have both a component normal to the interface, Fz , which contributes to the normal force supporting the load, and a component along the interface Fx the mean value of the magnitude of Fx must be proportional to the mean value of Fz .
coefficient of static friction which is not too much smaller than 1. This accounts for Amonton’s law without the need to assume that the friction is proportional to an ill-defined area of real contact. In the weak pinning limit, the component along the interface of the hard core force is random, and hence, for an infinite interface area and hence an infinite number of interface atoms, the components along the interface of the hard core forces cancel, resulting in effectively no static friction in the thermodynamic or macroscopic solid limit. Hence, since the magnitude of the static friction per surface atom is P a 2 /c and V (r) varies on a length scale a, V0 ≈ P a 3 /c. Then substituting this in the expression for the mean value of V (r) under Equation (2) and L′ from Equation (2) in Equation (1), we obtain E = 2(Γ Γ ′ )1/2 − P a 2 /c1/2 A/L
(3)
for the energy, which is minimized for infinite L if 2(Γ Γ ′ )1/2 > P a 2 /c1/2 and for L = 0 (which in practice means that L is as small as the smallest length scale in the problem rather than zero) if P a 2 /c1/2 > 2(Γ Γ ′ )1/2 ≈ K. Thus, it is clear that as c decreases, the interface can switch from weak pinning (if it was already in the weak pinning regime) to strong pinning. In the latter regime, by the arguments given in the last paragraph, the surfaces will be pinned together, i.e., there will be static friction. Because the interface area between two asperities in contact is only of micron size, there will be a transition from low to high, rather than from zero to nonzero static friction (as would occur for an infinite interface). This problem can also be considered using perturbation theory in the weak pinning limit [8]. To do this, following [8], one calculates u(r) which results from the random forces found from V (r) and from it calculates |u(R) − u(0)|2 using the standard expression for the elasticity Green’s function [9]. Here, · · · signifies an average over the random substrate forces. R is considered to be equal to the Larkin length when this quantity is comparable to the square of the range of a substrate potential well, as this represents the distance over which the surface of the solid can be considered as rigid from the point of view of the random substrate potential. Following arguments similar to those in [8], we find a Larkin length that is an exponential function of the ratio of Young’s modulus divided
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by V0 , which can easily be quite large compared to any reasonable size solid interface when this ratio is reasonably large, as it is in the weak pinning regime. Thus, even though the variational method that I used above gives an infinite Larkin length in the weak pinning limit, whereas the perturbation theory method of [8] gives a finite Larkin length, since the Larkin length found in [8] is extremely large (i.e., an exponential function of a fairly large number) in the weak pinning limit, the two methods can be considered to give qualitatively the same result.
1.3 FRICTION RESULTING FROM MULTISCALE ROUGHNESS On the basis of the above arguments, it appears that solid surfaces should almost never exhibit friction. Of course, no surfaces are perfectly smooth, and in fact, there can be roughness on several length scales. Let us assume then that there are n orders of length scales, which we represent as follows: We divide the surface into Mn asperities, a fraction cn of which are in contact with the second surface. In the discussion in this paragraph, the asperities are treated as rigid “hills” on the surface. Effects of distortion of the asperities will be treated later. At each pair of asperities in “contact” the contact is likely to only occur at selected isolated regions, which we may refer to as n − 1 order asperities. The interface between a pair of n − 1 order asperities can be divided up into n − 2 order asperities as well. The surfaces can never be truly self-affine, however, because when we reach atomic dimensions at n = 0 order, this sub-division into smaller and smaller length scales terminates. In more detail, we divide an N -atom surface (N is of the order of the nominal area of the surface divided by a 2 , where a is the mean interatomic spacing) into Mn asperities of which a fraction cn are in contact with the second surface, which for purposes of obtaining a qualitative understanding of the problem can be replaced by a flat substrate, as described above. We then divide the areas of contact of each of these contacting asperities into Mn−1 asperities, of which a fraction cn−1 are in contact. We then divide the area of contact between two contacting asperities into Mn−2 asperities, a fraction cn−2 of which are in contact, etc., until we have done n sub-levels of this sub-division. The area of contact of a zeroth level (i.e., smallest) asperity will contain of the order of N0 = N/(M0 M1 . . . Mn ) atoms, a fraction ca of which are in contact. It is these atoms at the zeroth (i.e., the final) order of asperities which support the load. If the nth order set of asperities are in the weak pinning regime, the static friction acting on it is reduced by a factor (cn Mn )1/2 , because by the above arguments, the static friction forces from these asperities act incoherently, and if the atoms at the interfaces of zerothorder asperities in contact are in the weak pinning regime, the static friction is reduced from the strong pinning regime value (i.e., μs not too much smaller than 1) by a factor (ca N0 )1/2 . This mechanism is proposed as a possible way to explain why coatings of stiff materials are good lubricants [10]. The arguments in the above paragraphs are only correct if each asperity is completely rigid, as we have assumed that the elastic forces which oppose displacements of the points of contact with the substrate resulting from the forces that the substrate exerts on them are due to the bulk solid. Since each asperity has some height, however, it can distort so as
Superlubricity for Incommensurate Crystalline and Disordered Interfaces
7
to move its interface with the substrate closer to its potential minimum, even without distorting the bulk solid. Thus, whereas a particular substrate with completely rigid asperities might be in the weak pinning regime, if the asperities are able to distort by a sufficient amount, it might be in the strong pinning regime. This may explain why it is that although the estimates given earlier in this section indicate that most solids should be in the weak pinning regime, this is not consistent with the magnitudes of the friction coefficients that are observed for most solids. Let us now consider the distortions of the asperities that occur in response to the substrate potential [11]. What we will do now is to assume that there exists a bunch of smallest asperities (which will be considered the lowest or zeroth level) which are in contact with the substrate. There are several groups of these that are assumed to be attached to a bunch of larger next or first-order asperities. Groups of these first-order asperities are then attached to larger asperities called second-order asperities. This hierarchy continues until we reach an “asperity” of width equal to that of the whole interface. This hierarchy of asperities is illustrated schematically in Figure 1.3. Consider the zeroth, the lowest, order (i.e., the smallest) asperity. Let it have a height of order L′0 and a width of order L0 . To find its distortion resulting from the sum of the substrate potential energies of all of the atoms of the asperity which are in contact with the substrate, we must minimize the sum of its elastic and substrate potential energies. The substrate potential energy is given by V0 (L0 /a)f0 ( x0 /a), where V0 is the substrate potential strength felt by the asperity as it distorts while all higher level asperities remain in an arbitrary rigid configuration and f0 ( x0 /a) is a function of order unity which gives the variation of the substrate potential with x0 , the amount that the zeroth-order asperity distorts under the influence of the substrate potential, for fixed, undistorted asperities of higher order (i.e., larger size in the present context). (Clearly, each of the zeroth-order asperities has a different function; f0 denotes a generic function describing the interface
Figure 1.3 This is a schematic illustration of the asperity hierarchy on the top surface sliding on a flat substrate (i.e., the bottom block). (Real asperities have arbitrary shapes, as opposed to the square shapes shown in this schematic representation.) Each asperity of a given order has a number of (smaller) asperities of one order lower on its surface. In turn, each of these lower-order asperities has a number of (smaller) asperities of one order lower. This continues until we reach the zeroth-order asperity, whose surface consists of atoms, although only three orders of asperities are illustrated here.
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potential energy for a typical zeroth-order asperity.) Each function clearly must possess multiple minima. We are assuming here that the surface of the asperity in contact with the substrate is in the weak pinning limit. The factor (L0 /a), which is of the order of the square root of the number of atoms in this surface expresses this fact. If the surface of the asperity in contact with the substrate is in the strong pinning limit instead, this factor will be replaced by (L0 /a)2 , the number of atoms at the interface. (The scaling arguments used here for describing the asperities, assumes that we are considering the interface for a fixed load, and hence fixed area of contact for each asperity.) Treating this asperity as an elastic three-dimensional solid in contact with the substrate we find from the discussion earlier in this chapter that the interface between the substrate and this asperity is in the weak pinning limit if P0 < ca 1/2 K, where P0 is the mean load per unit interface area supported by this asperity and ca is the fraction of the surface atoms of this asperity that are in contact with the substrate. Assume that a fraction c0 of the zeroth-order asperities have atoms belonging to them in contact with the substrate. Let c1 represent the fraction of next order (first-order) asperities whose zeroth-order asperities are in contact with the substrate, c2 , the fraction of second-order asperities whose first-order asperities have their zeroth-order asperities in contact with the substrate, etc., up to nth order. Then P0 = P /(c0 c1 c2 . . . cn ), where P is the load per unit apparent area of the surface of the whole solid. Then, we conclude that the criterion for the atoms at the interface between the zeroth-order asperity and the substrate to be in the weak pinning regime is that P < (ca 1/2 c0 c1 c2 . . . cn )K. We see from this inequality that the more fractal the surface is, the more difficult it is for the zeroth-order asperity to be in the weak pinning regime. The cost in elastic energy due to the shear distortion of the asperity can be determined by the following scaling argument: The elastic energy density for shear distortion of the asperity is proportional to (∂ux /∂z)2 where ux represents the local displacement due to the distortion, the x-direction is along the interface and the z-direction is normal to it. The ux must scale with x0 and the dependence of ux on z has a length scale L′0 . Thus the elastic strain energy of the asperity is of the order of (1/2)L20 L′0 K( x0 /L′0 )2 , where K is the shear elastic constant and ( x0 /L′0 ) is the average shear strain and L0 is the mean width of the asperity. Minimizing the sum of these expressions for elastic and substrate potential energy, we obtain x0 /a ≈ V0 /Ka 3 (L′0 /L0 )f0′ ( x0 /a).
(4)
Since f0′ , the derivative of f0 with respect to its argument, it is of order one, from the definition of f0 . Let us follow a line of reasoning like that of [12] a modified version of which is given in Appendix B of [11]. For (V0 /Ka 3 )(L′0 /L0 ) below a certain value of order one, for small V0 /Ka 3 , Equation (4) can have only one solution for x0 . The reason for this is illustrated in Figure 1.4. Under such circumstances the average kinetic friction, in the limit as the sliding velocity approaches zero, is zero. For a surface with an infinite number of asperities, distributed uniformly in space, it was shown in [12] that the static friction is zero as well. A modified version of this argument, which points out that for a surface with a finite number of asperities the static friction is nonzero, but smaller by a factor of a/L0 compared to what it would be if the contributions of the asperities to static friction acted coherently is provided in Appendix B of [11]. If this asperity is in the strong pinning limit
Superlubricity for Incommensurate Crystalline and Disordered Interfaces
9
Figure 1.4 This figure illustrates the solution of Equations (4), (5), and (6) for x0 , x1 and xn , respectively. The function f ′ (x) is a schematic illustration of the functions f0′ , f1′ and fn′ , and x denotes x0 , x1 or xn , respectively. Lines A and B represent the line y = (Ka 3 /V0 )(Ln /L′n )x, for (Ka 3 /V0 )(Ln /L′n ) < 1 and (Ka 3 /V0 )(Ln /L′n ) > 1, respectively. For the situation illustrated by line A, there are multiple solutions (i.e., multistability), while for the situation illustrated by line B, there is only one solution (i.e., there is mono-stability).
instead, we replace the factor of (L0 /a) by (L0 /a)2 to account for this and as a result, the factor (L′0 /L0 ) gets replaced by (L′0 /a), which could would easily make the asperity satisfy the criterion for multistability, and consequently, the friction from these asperities will no longer be reduced by the factor a/L0 . For a load per unit area P , assumed to be primarily due to hard core interactions, we may assume V0 ≈ P a 3 /c, where c is the fraction of the surface atoms which are in contact with the substrate. By the above arguments, c = ca c0 c1 c2 . . . cn . Then, we see that the criterion for the zeroth-order asperity to be multistable is P > ca c0 c1 c2 . . . cn K. If the criterion for weak pinning for the zeroth-order asperity surface is not satisfied, the criterion for monostability of this asperity gets changed from the above inequality to (V0 /Ka 3 )(L′0 /a) < 1, which is more difficult to satisfy since L′0 /a can be considerably greater than 1. At the next level, we have an asperity surface in contact with the substrate which consists of a collection of the lowest level (i.e., the smallest) asperities discussed in the previous paragraph. Assuming this asperity to be in the weak pinning regime, the potential of interaction with the substrate, which is the sum of all of the interactions of the substrate with the lowest-order asperities, which cover a first-order asperity, is of order V0 (L0 /a)(L1 /L0 )f1 ( x1 /a). Here L1 represents the width of this order asperity, x1 represents a displacement of the lower surface of this level asperity for fixed (i.e., undistorted) configurations of all higher-order asperities, and f1 denotes one of the functions which describes the interface potential energy of one of the first-order asperities. It has at least one minimum and runs over a range of magnitude one as its argument runs over a range of order one. The elastic energy is of the order of (1/2)L′1 L21 K( x1 /L′1 )2 , by the argument given above Equation (1), where L′1 is the height of the body of the first-order asperity, which is assumed to be much larger than L′0 . Minimizing the sum of these two energies, we obtain x1 /a ≈ V0 /Ka 3 (L′1 /L1 )f1′ ( x1 /a).
(5)
Again, we conclude, based on the arguments presented in [12], that the static friction is reduced by a factor of L0 /L1 below what it would be if the contributions to the static
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friction from each of the mini-asperities at this level acted coherently. If the zeroth-order asperities attached to this first-order asperity are in the strong pinning regime, the factor of L1 /L0 in the equation for the interaction of this asperity with the substrate is replaced by (L1 /L0 )2 , and hence, the right-hand side of Equation (2) has the factor L′1 /L1 replaced by L′1 /L0 , which can make the solutions to this equation for x1 multistable. Continuing this procedure, we find that the displacement of the nth level mini-asperity is found by solving xn /a ≈ V0 /Ka 3 (L′n /Ln )fn′ ( xn /a),
(6)
where Ln and L′n are the width and height of the body of the nth level asperity. If (V0 /Ka 3 ) > 1, and L′n /Ln ≈ 1 for all n, asperities of all orders will be multistable, implying the occurrence of large static friction. Substituting for V0 using V0 ≈ P a 3 /c, we find that this condition is equivalent to P > cK. If the condition given earlier for strong 1/2 1/2 pinning at the zeroth-order asperity interface, namely P > ca c0 c1 . . . cn K = (c/ca )K is satisfied, the condition for multistability on all levels, P > cK is certainly satisfied. Although plastic deformation for a bulk solid occurs when P exceeds the hardness of the material, which is generally much less than Young’s modulus, such small values of the hardness result from the presence of dislocations in the material. In the case of the very small length scale asperities considered here, however, the asperity does not have enough volume to accommodate a dislocation. Therefore, plastic deformation at this level should occur when the forces at the atomic level exceed the maximum interatomic force. This translates into the requirement that P /c exceed a quantity comparable to Young’s modulus. Since Young’s modulus is generally significantly larger than the shear modulus K, it should be quite possible for P /c to exceed K (the above criterion for multistability) while still being less than Young’s modulus. Let us now make numerical estimates of whether the lowest-order asperity is likely to be monostable, implying low static friction. To do this, we will apply the present model to a single micron-scale asperity in contact with the substrate. Typical values of K are of the order of 1011 N/m2 . In [13], P at the micron scale asperity level was estimated from the Greenwood–Williamson model [14] to be about 109 N/m2 which is also the maximum value of the load per unit contact area in the Greenwood–Williamson model [14], and hence V0 /Ka 3 ≈ 0.01/c, since V0 ≈ P a 3 /c. (Figure 3 in [14] is actually not correct. The mean pressure per asperity as a function of load should actually be zero at zero load and saturate at a maximum value as the load increases.) Thus from Equation (1), if (L′0 /L0 ) is of order 1, the zeroth-order asperity will be monostable if c = ca c0 c1 . . . cn > 0.01. If this condition is not satisfied, the interface will be multistable, and hence, it will exhibit relatively high friction. This makes it likely that all order asperities and hence the interface will be monostable as well, resulting in very low friction. It should be pointed out here that the mechanism for weak pinning discussed here is different from the mechanism discussed in [7] and earlier in this chapter in that it does not result from interactions between asperities (i.e., the collective pinning mechanism). It produces the same result as we found earlier assuming stiff asperities, however, namely that the friction between two asperities at a given length scale is reduced by a factor of the square root of the number of asperities
Superlubricity for Incommensurate Crystalline and Disordered Interfaces
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at the next lower length scale order present on its surface. This means that the friction coefficient is reduced from the strong pinning value (which is not much less than one) by a factor of nn′ =0 (Ln′ −1 /Ln′ ) where L−1 = a and the product includes only values of n′ corresponding to orders of asperities which are monostable. When the zeroth-order asperity interface is monostable, we saw that all higher-order asperities will be monostable as well. In this case the above product reduces to a/Ln for the factor by which the friction coefficient is reduced below one. As Ln in our numerical example is approximately 1 µm, this leads to a reduction factor of the order of 10−4 . We saw that the condition for the interface to be monostable, and hence exhibit ultra-low friction is that the ratio P /c be less than K. The quantity c, as it was defined earlier, can be thought of approximately as the ratio of the area of contact to the apparent area of the interface (although, as pointed out earlier, this is not precise). Since all calculations of this quantity for rough interfaces [14,15] give a constant value of this ratio, at least for small values of P , whether the surface is in the strong or weak pinning regime in the small P limit, it will remain in that regime as P increases, implying that the criterion for weak pinning depends only on the value of K and the degree of roughness of the surface as evidenced by the value of c. Since for larger values (for which c ≈ 0.05) c was found in the finite elements calculation of [15] to be a sub-linear function of P , it is possible that the interface will switch from weak to strong pinning for sufficiently large P . The results presented here only require that the restoring forces for horizontal distortions of the asperities be elastic. Therefore, they might not be invalidated even if compressions of the asperities normal to the interface, resulting from the load, are plastic [14,15]. At the numerical values of P for which we estimate that we will be in the low friction regime, however, the assumption of a purely elastic solid is quite likely to be valid. The discussion given above predicts that a material with sufficient large shear modulus should have very low friction. This may be a possible explanation for the well known fact that coating a surface with a material which has a high elastic constant and is chemically inert, such as saturated diamond (whose shear modulus is at least a factor of 6 larger than that of other solids [16]) or amorphous carbon, can significantly reduce friction [10]. Tartaglino, Samoilov and Persson [17] have recently used a multiscale molecular dynamics simulation method [18] to show that relatively small amplitude multiscale roughness can eliminate superlubricity for a disordered interface. Although a detailed numerical comparison with the scaling treatment discussed here [7,11] has not as yet been made, the two methods seem to yield qualitatively similar results.
1.4 SUPERLUBRICITY RESULTING FROM POLYMER BRUSHES Another way to achieve extremely low friction is to coat the surfaces of two solids sliding in contact with each other with polymer brushes. A polymer brush consists of a fairly concentrated coating of polymer chains, each one of which has one of its two ends tightly bound to the surface. They serve as an extremely effective lubricant, producing friction coefficients as low as 0.001 or less [19,20]! Polymer brushes are a promising way to reduce friction to extremely low values. In order to function as a lubricant, they must be immersed in a good solvent. The presence of a solvent causes the polymer brush to extend,
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allowing it to support load and produce osmotic pressure which also partially supports the load. The polymer brush lubrication mechanism is a good candidate for the well known extremely efficient lubrication of human and animal joints [19,20]. This mechanism can also provide extremely effective lubrication in many other applications. At first thought, one might say that the existence of such low friction for polymer brush coated surfaces is a trivial result because they are soaked with solvent, and hence one would expect the solvent to provide hydrodynamic lubrication. Indeed, it is well known that it is possible to design specially shaped surfaces, known as hydrodynamic bearings which guarantee that the sliding surfaces will be supported by a liquid lubricant present at the interface [21]. For the slow speed sliding limit, however, there will not be significant hydrodynamic pressure to support the load. In this situation a viscous fluid will in general not be able to prevent two surfaces from touching because there is nothing to keep most of the fluid from getting squeezed out from between the surfaces. For most liquid lubricants, it is the thin quasi-solid coating [22] which remains at the interface which is responsible for the boundary lubrication. The resulting lubrication mechanism is not hydrodynamic, but rather must come about from other mechanisms [7]. Polymer brushes provide a way to hold the fluid in place between the surfaces, so that it can support the load. For example, if there exists a solute which is constrained to remain in the region between the surfaces, the fluid would be drawn in to dilute the solute, resulting in osmotic pressure, which might be able to support the load. The monomers belonging to the polymers attached to the two surfaces could play the role of such a solute. The monomers are constrained to remain between the surfaces because they are held together to form a polymer. If it were determined that the osmotic pressure due to the low monomer density in the interface region is able to support the load, the friction would be extremely low viscous friction, i.e., friction which approaches zero as the sliding velocity approaches zero, as opposed to the usual sliding friction between two solids, which approaches a nonzero value in the zero sliding velocity limit. Furthermore, because of the low polymer density in such an interface region, there would be little wear resulting from polymers getting detached from the surfaces as a result of polymers belonging to one brush getting entangled in the second brush and then being pulled out. Some experimental results on polymer brushes [23] do, however, show static friction. It is also likely that there will be nonzero kinetic friction as well in the limit as the sliding velocity approaches zero, as occurs for the usual friction between solid surfaces (i.e., Amonton’s law friction). Therefore, it is important to study theoretically how the interactions of two polymer brushes in contact can lead to the observed magnitude and time dependence of static and nearly velocity independent kinetic friction in the slow speed sliding limit. One important question that must be answered is whether it is possible to have true static friction for polymer brush lubricated surfaces, or whether it is only possible to have a highly viscous sliding motion, which over short times appears to be static friction. This question was addressed in a recent publication [24]. This treatment of the problem, which is based on the study of microscopic physical mechanisms, combines the mean field methods of Witten et al. [25], the Flory treatment of entanglement of polymers [26], the penetration of polymers from one brush into the second brush, and a Tomlinson-like model [12] to entangled polymers to obtain the observed static and slow speed kinetic friction. Whereas reptation [26] (snake-like diffusion of a polymer among other polymers
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among which it is entangled) may account for creep of the surfaces due to the polymers from the brushes becoming disentangled in time, the friction observed even at relatively slow sliding speeds cannot be accounted for by this mechanism because reptation is too slow. In [21], the creep rate for the polymer brush coated surfaces was found to be about a mm/h. The maximum load per unit contact area that a polymer brush lubricant can support before losing its low friction properties (because it becomes glass-like), is approximately one mega-Pascal. The combination of the roughness of the surfaces and the fact that the elastic constants for most solids are fairly large (around 1011 N/m2 ), however, result in the load being supported by a very small area of contact for most solid surfaces, resulting in each asperity supporting a mean load per unit asperity contact area of about 1 GPa [14]. For lubrication of human and animal joints by a polymer brush mechanism, the polymers are attached to cartilage, which is a relatively soft material [19,20,27], compared to most solids. Young’s modulus for cartilage is of the order of only 105 N/m2 . As a consequence, the load per unit contact area that must be supported is likely to be in the order of a mega-Pascal (MPa), making the polymer brush lubrication mechanism an attractive hypothesis for very effective lubrication in this system, as well as in other applications, as long as it is possible to first coat the surfaces that we wish to lubricate with an elastically soft material, to which the polymers are then attached. Since many polymers, are charged, it will be necessary to consider polyelectrolyte brushes, whose equilibrium properties have been studied using mean field theory by Zhulina et al. [28], Misra [29] and Miklavic [30]. Polyelectrolyte polymer brushes should be even more effective lubricants than neutral polymer brushes discussed above because the electric charge will support part of the load and there will be additional osmotic pressure produced by the counter ions always present in polyelectrolyte solutions to support the load. Milner et al. [31], proposed a simple way to solve the mean field theory for polymers attached at one end to a surface. In this treatment, the minimization of the free energy of the polymer brush requires that the location of the nth monomer on the ith polymer, ri (n) satisfies the equation d2 ri (n)/dn2 = ∇ wφ(ri (n) ,
(7)
where φ(r) is the monomer density and w is the strength of the monomer–monomer repulsion. This can be thought of as an “equation of motion” for the monomers, in which the index n labeling the monomers plays the role of time. It is formally analogous to Newton’s second law for motion of a particle in a potential equal to −wφ(ri (n)). Existence of a solution of the mean field equations of motion requires that φ(r) be a parabolic function of z [31]. In [20] Equation (7) was solved for forms of φ(r) which correspond to two polymer brushes in contact and two polymer brushes almost in contact. Specifically, in both cases, Equation (7) was solved for a polymer that extends out of the (parabolic [31]) monomer density profile of the polymer brush to which it belongs (by virtue of the fact that it is attached to the surface to which the polymers belonging to that brush are attached). For the case in which the two polymer brushes are actually in contact, this polymer will be entangled in the brush to which it does not belong (i.e., the polymer brush whose polymers are attached to the other surface). In both cases, the mean number of monomers of the polymer under consideration which extend out of its brush can be found by calculating from
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this solution to Equation (7) the cost in free energy to pull this polymer out of the brush. When the polymer brushes are in contact, any polymer that extends into the brush to which it does not belong forms “blobs” that fit in the spaces in mesh of that brush [26]. When one attempts to slide the surfaces relative to each other, these blobs must be pulled out of the brush in which they have gotten entangled. The force needed to do this was calculated in [24] and found to be consistent with the static friction measured in [23]. An argument based on the Tomlinson model [12] was then used, to find the kinetic friction in the limit of zero sliding velocity (which is likely not much different than the static friction) due to entanglement of the polymers. Reference [24] also discusses the possibility that the monomer density profile of the two brushes might not need to be in contact to support the load, leading to extremely low friction. The load would then be completely supported by the osmotic pressure in an interface region between the two brushes (i.e., the bulk regions of the two polymer brushes are not in contact) due to the fact that polymers from the two brushes occasionally fluctuate into the interface region. In such a case, there would be no static friction, and the kinetic friction would be relatively small viscous friction, which approaches zero as the sliding velocity approaches zero. The amount of load that can be supported by the osmotic pressure is estimated and found to be about 104 Pa.
1.5
CONCLUSIONS
In this chapter, the concept of superlubricity for interfaces between both incommensurate crystalline and disordered solid surfaces was discussed. Some of the differences in behavior of these two examples of superlubricity were discussed. A possible explanation for why superlubricity is not generally observed, based on multiscale surface roughness was given. It was suggested that the occurrence of superlubricity for stiff surfaces may provide an explanation for why hard carbon films are such good lubricants. Polymer brush lubrication was shown to be another mechanism for obtaining extremely low friction. It was argued that what the polymer brush might accomplish is to keep the lubricating liquid in place between the surfaces being lubricated, so that it is able to support the load while allowing the shear to take place within the fluid. This results in very low viscous friction.
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Hirano, M., Shinjo, K. Phys. Rev. B 41 (1990), 11837; Shinjo, K., Hirano, M. Surf. Sci. 283 (1993), 473. Aubry, S. In: Bishop, A.R., Schneider, T. (Eds.), Solitons and Condensed Matter. Springer, 1978, p. 264. Sacco, J.E., Sokoloff, J.B. Phys. Rev. B 18 (1978), 6549. Muser, M.H., Robbins, M.O. Phys. Rev. B 61 (2000), 2335. He, G., Muser, M.H., Robbins, M.O. Science 284 (1999), 1650. Lancon, F. Europhys. Lett. 57 (2002), 74. Sokoloff, J.B. Phys. Rev. E 71 (2005), 056107. Persson, B.N.J., Tosatti, E. Solid State Comm. 109 (1999), 739; In: Persson, B.N.J., Tosatti, E. (Eds.), Physics of Sliding Friction. Kluwer Academic Publishers, Boston, 1995, p. 179; Popov, V.L. Phys. Rev. Lett. 83 (1999), 1632. [9] Landau, L.D., Lifshitz, E.M. Theory of Elasticity, second edition. Pergamon Press, New York, 1970.
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[10] Heimberg, J.A., Wahl, K.J., Singer, I.L., Erdemir, A. Appl. Phys. Lett. 78 (2001), 2449–2451; Gao, G.T., Mikulski, P.T., Harrison, J.A. J. Am. Chem. Soc. 124 (2002), 7202–7209; Gao, G.T., Mikulski, P.T., Chateauneuf, G.M., Harrison, J.A. J. Phys. Chem. B 107 (2003), 11082–11090; Rha, J.J., Kwon, S.C., Cho, J.R., Kim, S., Saka, N. Proc. Wear 2005 Conference. [11] Sokoloff, J.B. Phys. Rev. E 73 (2006), 016104. [12] Caroli, C., Nozieres, Ph. European Phys. J. B 4 (1998), 233; Caroli, C., Nozieres, Ph. Physics of Sliding Friction, Persson, B.N.J., Tosatti, E. (Eds.). NATO ASI Series E: Applied Sciences, Vol. 311, Kluwer Academic Publishers, Dordrecht, 1996; M. Brillouin, Notice sur les Travaux Scientifiques. Gautier-Villars, Paris, 1909; Tomlinson, G.A. Phil. Mag. 7 (1929), 905. [13] Volmer, A., Natterman, T. Z. Phys. B 104 (1997), 363; Sokoloff, J.B. Static friction between elastic solids due to random asperities. Phys. Rev Lett. 86 (2001), 3312; Sokoloff, J.B. Explaining the virtual universal occurrence of static friction. Phys. Rev. B 65 (2002), 115415. [14] Greenwood, J.A., Williamson, J.B.P. Proc. Roy. Soc. London, Ser. A 295 (1996), 300; Mc Cool, J.I. Wear 107 (1986), 37060. [15] Hyun, S., Pei, L., Molinari, J.F., Robbins, M.O. Phys. Rev. E 70 (2004), 026117; Robbins, M.O. Invited talk at the March 2005 American Physical Society Meeting. [16] Kittell, C. Introduction to Solid State Physics, second edition. John Wiley and Sons, New York, 1956, p. 93. [17] Tartaglino, U., Samiolov, V.N., Persson, B.N.J. J. Phys.: Condensed Matter 18 (2006), 4143–4160. [18] Yang, C., Tartaglino, U., Persson, B.N.J. European Phys. J. E 19 (2006), 47–58. [19] Klein, J. Ann. Rev. Mat. Sci. 26 (1996), 581–612; Proceedings of the Institute of Mechanical Engineers, Part J. Journal of Engineering Tribology, Special Issue on Biolubrication 220 (2006), 691–710. [20] Yan, X., Perry, S.S., Spencer, N.D., Pasche, S., DePaul, S.M., Textor, M., Lim, M.S. Langmuir 20 (2004), 423–428; Lee, S., Muller, M., Ratoi-Salagean, M., Voros, J., Pasche, S., De Paul, S.M., Spikes, H.A., Textor, M., Spencer, N.D. Tribology Lett. 15 (2003), 231–239; Muller, M., Lee, S., Spikes, H.A., Spencer, N.D. Tribology Lett. 15 (2003), 395–405. [21] Dowson, D., Wright, V., Longfield, M.D. Biomedical Engineering 4 (1969), 160. [22] Chan, D.Y.C., Horn, R.G. J. Chem. Phys. 83 (1985), 5311; Israelachvili, J.N. J. Colloid Interface Sci. 110 (1986), 263; Reiter, G., Demirel, A.L., Granick, S. Science 263 (1994), 1741; Israelachvili, J.N. Intermolecular and Surface Forces, second edition. Academic Press, 1992; Bhushan, B., Israelachvili, J.N., Landman, U. Nature (London) 374 (1995), 607; Granick, S. Science 253 (1991), 1374. [23] Tadmor, R., Janik, J., Klein, J., Fetters, L.J. Phys. Rev. Lett. 91 (2003), 115503. [24] Sokoloff, J.B. Phys. Rev. E, submitted for publication. This reference is paper no. cond-mat/0602320 on the arxiv preprint server as well as at http://www.physics.neu.edu/Department/Vtwo/faculty/sokoloff.htm. [25] Witten, T.A., Leibler, L., Pincus, P.A. Macromolecules 23 (1990), 824–829. [26] de Gennes, P.-G. Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca, 1979. [27] Lambert, R.K., Baile, E.M., Moreno, R., Bert, J., Pare, P.D. J. Appl. Physiol. 70 (1991), 1152–1159. [28] Zulina, E.B., Borisov, O.V., Birshtein, T.M. J. Phys. II France 2 (1992), 63–74. [29] Misra, S., Varanasi, S., Varanasi, P.P. Macromolecules 22 (1989), 4173–4179. [30] Miklavic, S.J., Marcelja, S. J. Phys. Chem. 92 (1988), 6718–6722. [31] Milner, S.T., Witten, T.A., Cates, M.E. Macromolecules 21 (1988), 2610–2619.
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–2– Superlubricity of Clean Surfaces Motohisa Hirano Gifu University, 1-1, Yanagido, Gifu, 501-1193, Japan
2.1 INTRODUCTION When two solid bodies contact each other and one body begins to slide against the other, a frictional phenomenon appears. The friction force is the drag against sliding, appearing along the contacting surfaces. According to whether or not two bodies move relatively, the friction forces are classified into the static and the dynamic ones. They have the different physical origins [1]. Two pictures (or models) have been advocated for the origin of the friction forces [1–3]. The first is called the surface roughness model. The contacting solid surfaces are so rough that surface asperities are mechanically locked against the gravitational force. It is necessary to apply an external force to slide one body against the other. This mechanical-locking mechanism was conjectured especially by the earlier workers such as da Vinci, Amonton, and Coulomb, and concerns with the origin of the static frictional force [4,5]. The weakest point of the surface roughness model is that basically it fails to explain an energy dissipation for the origin of the dynamic friction force since the gravitational force is an energy-conserving force. Another is due to the adhesive force between constituent atoms. The importance of the adhesive force has been first recognized by Desaguliers [6]. The adhesive force, however, is clearly different from the friction force along the contacting interface. How do the friction forces relate to the adhesive force? From an atomistic point of view, Tomlinson has described a mechanism of the energy dissipation for the origin of the dynamic frictional force, based on the adhesion model [7]. He assumed the non-adiabatic (or abrupt) change of the positions of atoms during sliding, which subsequently transforms the elastic energy into the vibrational energy. His picture involves the irreversible physical process, i.e., the energy dissipation in its natural form. Tomlinson proposed the possible mechanism for the origin of the friction forces, but did not inquire of whether or not his mechanism occurs in the realistic frictional systems [7]. The state in which friction between two sliding solids is zero and the solids slide without resistance to motion is called “superlubricity”. While such absence of friction runs counter to common sense, superlubricity does appear in realistic systems where metallic bonding, Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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for example, operates. The state of zero friction is closely related to the state in which friction appears, and the existence of superlubricity has been predicted by defining the state in which friction appears. The question as to why friction appears, that is, the problem of finding the origins of friction, has been considered for a long time [1]. Friction, however, is influenced by many factors (such as plastic deformation, fractures, electromagnetic fields, chemical reactions, and ambient humidity) in a complicated manner, and it has been difficult to define these factors to examine the mechanisms that give rise to friction. In most experiments, the interpretation of experimental results has consequently been confined to phenomenology [3]. It is, therefore, important that the mechanisms of friction should be investigated at the atomic level and that the atomistic origins of friction should be clarified. New experimental techniques are making it possible to investigate friction on a clean surface at atomic-level resolutions [8]. From an atomistic point of view, the frictional systems of the idealized solid surfaces, which are assumed to be clean and flat, have been studied [9]. The system consists of many atoms interacting with each other by the Morse [10] or the Johnson potential [11], which is expected to simulate the realistic interaction potentials. The criterion for Tomlinson’s mechanism to occur has been obtained [9]. From studying the various systems, it has been concluded that Tomlinson’s mechanism is unlikely to occur in the realistic frictional systems [9]. This conclusion leads to finding superlubricity: a state of vanishing friction. Superlubricity was thus discovered from this research into the origins of friction [9,12]. This chapter describes the atomistics of friction explaining the atomistic origin of the friction forces and discusses the mechanisms of superlubricity based on a model from atomistic theory. The first condition for superlubricity to appear is the adiabatic motion of atoms. If this condition is satisfied, friction will always be zero at the limit, where sliding speed of the solid is zero, being independent of the time scale of observation. Superlubricity, i.e., a state of vanishing friction, is discussed and it is emphasized that the high dimensionality of friction model is essential for the appearance of superlubricity. The second condition is energy recurrence phenomena [13]. If this condition is satisfied, recurrence phenomena occur through the dynamics of atomic motion and the friction force observed in the time scale of recurrence is zero.
2.2
PRELIMINARIES: TOMLINSON’S PICTURE
Tomlinson proposed an atomistic picture for the origin of the frictional forces. Let us describe an essence of his idea. Suppose the friction system consisting of four atoms numbered by 1, and 1′ , 2′ , and 3′ as seen in Figure 2.1. All atoms are assumed to interact with each other. The atom 1 forms a part of the upper body, which interact with the other atoms of the upper body (not illustrated in Figure 2.1), and the atoms 1′ , 2′ , and 3′ form the lower body. We shall concentrate on the behavior of the atom 1 when the upper body slowly slides against the lower. When the atom 1 is on the atom 2′ , the atom 1 feels the attraction from the atom 2′ , as seen in Figure 2.1(a). During sliding, the atom 1 moves towards the right direction. When the sliding displacement is small, this is a process of storing the elastic energy, as seen in Figure 2.1(b). When the atom 1 goes beyond the certain distance, the
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Figure 2.1 The friction system consisting of four atoms numbered by 1, and 1′ , 2′ , and 3′ . All atoms are assumed to interact with each other. The atom 1 non-adiabatically (abruptly) changes its position during sliding. The non-adiabaticity leads to transforming the elastic energy into the vibrational or kinetic energy of the atom 1. The vibrational energy of the atom 1 may be considered to dissipate into the vibrational energies of other atoms, i.e., into the thermal energy. This picture involves the irreversible physical process, i.e., the energy dissipation in its natural form.
attraction from the atom 3′ overwhelms that from the atom 2′ . The atom 1 prefers the position on the atom 3′ . Then, he assumes that the atom 1 non-adiabatically (abruptly) changes its position. The non-adiabaticity leads to transforming the elastic energy into the vibrational or kinetic energy of the atom 1, as seen in Figure 2.1(c). The vibrational energy of the atom 1 may be considered to dissipate into the vibrational energies of other atoms, i.e., into the thermal energy. This picture involves the irreversible physical process, the energy dissipation in its natural form. If the atom 1 is assumed only to change its position slowly, the atom 1 may not take an excess kinetic energy, which is concluded from the adiabatic theorem [14]. Here, we shall list some timescales relevant to the frictional systems. The sliding velocity may be 10−3 to 100 meter per second. The frequency of the atomic motion is about 1014 times per second. The upper body may slide about 10−17 to 10−14 meters per a frequency of atom, which is very small compared with the atomic interdistance of an order of 10−10 meters. The change of the potential which the atom feels during the frequency time of the atomic motion is very small; the parameter characterizing its change, ( T /v) × dv/dT , becomes 10−7 to 10−4 . This consideration implies that the atom 1 can adiabatically follow the change of the potentials yielded by sliding if the atom 1 does not change its position abruptly. As pointed out by Tomlinson [7], the assumption of the slow movement of the atom 1 fails to explain the energy dissipation in the dynamic process of friction. To clarify his idea, we shall describe this process by using a simplified model [15,16]. The atom 1 interacts with the other atoms of the upper body whose coordinate is symbolically expressed by Q. The atom 1 also interacts with the atoms of the lower body, which is assumed to be rigid. We shall concentrate on the equilibrium position of the atom 1 during sliding. The equilibrium position of the atom 1 can be determined by minimizing the interaction potential energy v(Q, r) = v1 (Q − r) + v2 (r),
(1)
where r is the position of the atom 1, v1 (Q − r) describes the interaction between the coordinate Q and the atom 1, and v2 (r) the interaction between the atom and the lower
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M. Hirano
Figure 2.2 The explanation of Tomlinson’s mechanism by using the potential surface. The shape of the potential surface v(Q, r) depends on Q. The equilibrium position of the atom 2 is indicated by a circle, and another possible equilibrium position by the dotted circles. The left and the right local minima correspond to the equilibrium position on the atom 2′ and that on the atom 3′ , respectively. In the processes from (a) to (d), r(Q)continuously varies withQ. At the process in (d), r(Q) sites on the saddle point of the potential surface. When one proceeds further, r(Q) changes discontinuously from the left minimum to the right one as shown in (d) and (e). Then, the potential-energy difference E between two local minima transforms into the kinetic energy of the atom through the non-adiabatic change of the position of the atom 2. The kinetic energy may be consumed into exciting the vibrations of the surrounding atoms, i.e., into the thermal energy. The ingredient of this process is an appearance of the discontinuity in the equilibrium positions of atoms.
body. Q stands for the displacement coordinate of the sliding upper body against the lower one. The equilibrium position of atom is determined as a function of Q. Tomlinson’s picture may be described by using the potential surface as follows. The shape of the potential surface v(Q, r) depends on Q. Under the appropriate conditions, the potential surface takes the various shapes as Q varies, as shown in Figure 2.2. The equilibrium position of the atom 1 is indicated by a circle, and another possible equilibrium position by the dotted circle. The left and the right local minima, correspond to the equilibrium positions on the atom 2′ and 3′ , respectively. In the processes from Figure 2.2(a) to (d), r(Q) continuously varies with Q. At the process in Figure 2.2(d), r(Q) sites on the saddle point of the potential surface. When one proceeds further, r(Q) changes discontinuously from the left minimum to the right one, as shown in Figure 2.2(d) and (e). Then, the potential energy difference E between two local minima transforms into the kinetic energy of the atom by non-adiabatically changing the position of the atom 1. The kinetic
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energy further may be consumed into exciting the vibrations of the surrounding atoms, i.e. into the thermal energy. The ingredient of this process is an appearance of the discontinuity in the equilibrium positions of atoms. The same mechanism has been described by the other workers [15,16]. Tomlinson proposed the possible mechanism of the origin of the frictional forces, but did not inquire of whether or not his mechanism occurs in the realistic frictional systems. The criterion for the occurrence of his mechanism has been obtained, and it has been concluded that Tomlinson’s mechanism is unlikely to occur in realistic systems [9].
2.3 THE CRITERION FOR THE OCCURRENCE OF TOMLINSON’S MECHANISM The adiabatic potential of the frictional system is defined by the total energy when two contacting solid bodies slide against each other. This assumes that the upper body slides against a fixed lower body. It is also assumed that the upper body has N u atoms and the lower body N l atoms, and that the constituent atoms belonging to both bodies interact with y each other. The position coordinates of the atoms are denoted by ri = (rix , ri , riz ) where i = 1, 2, . . . , (N u + N l ). The adiabatic potential is obtained by u
V (Q) =
l
N N i
j
u
u
,N 1 N Vaa |ri − rj | . Vab |ri − rj | + 2
(2)
i,j
Q stands for the displacement vector of the upper body against the lower body. An ri coordinate set satisfies the relationship l
u
Q=
N
ri /N
i
u
and 0 =
N
ri /N l .
(3)
i
Thus, the adiabatic potential spans a 3(N u + N l − 1)-dimensional potential surface. Since that Vab (0) = 0 and Vaa (0) = 0. Here, the summation of j in the first term of the right-hand side is expressed by l
l
V (r) =
N j
Vab |r − rj | .
(4)
V l (r)is the interaction energy that the atoms of the upper body receive from the atoms of the lower body. The terms Vbb (|ri − rj |) is dropped, since it has no Q-dependence. V l (r) has a periodicity characterized by the primitive vectors of the top layer of the lower body. The occurrence of the nonadiabatic (discontinuous) motion of atoms, i.e., Tomlinson’s mechanism means that the atom can not take the arbitrary equilibrium position. This is
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M. Hirano
equivalent to a condition that the second derivatives of V (Q, r) with respect to r becomes be negative at the position where d2 V l (r)/dr 2 takes the largest negative value. The criterion for the occurrence of Tomlinson’s mechanism is given by [9], d2 V (Q, rmax ) d2 V u (Q − rmax ) d2 V l (rmax ) = + < 0 for a certain Q, 2 2 2 drmax drmax drmax
(5)
where V l (r) is interaction from the atoms of the lower body. V u (r) is interaction from the atoms of the 2nd, 3rd, . . . layers of the upper body. rmax stands for the position defining the largest negative value of d2 V l (r)/dr 2 , and Q stands for the displacement coordinate of the sliding upper body against the lower one. Here it is important to note that there occurs the case where Tomlinson’s mechanism does not occur. For example, we shall consider the case in which it is assumed that V u (Q − r) = k(Q − r − l)2 /2, where k is the elastic constant and l is the average mean distance between Q and r, and that V l (r) = f sin r, where f is the adhesive force and sin r represents atomic displacement whose amplitude is normalized to be unity. When substituting these interaction potentials into Equation (5), the relation k < f is obtained. For k = 1 and f < 1, Tomlinson’s mechanism does not occur. This result suggests that Tomlinson’s mechanism is likely to occur only when the interaction or adhesion between two bodies, being specified by f , becomes strong. This suggestion generally holds valid since the equilibrium positions of atoms of the upper body are slightly disturbed by the lower body for the weak case of adhesion. The equilibrium position r(Q) corresponds to the minimum point of the potential surface V (Q, r) for the given Q. Let us define an ensemble of r(Q) when Q takes various values, which is called a domain D. The problem of whether or not the Tomlinson mechanism occurs can be understood from the topological property of the domain D. When V l (r) has a periodicity of the crystalline structure, it is enough to examine the unit domain in the region 0 < r(Q) < l (l: the crystal periodicity length). The whole domain can be obtained by tiling this unit domain repeatedly. The domains are shown in Figure 2.3, according to whether or not Tomlinson’s mechanism occurs. The V l (r) is shown by a solid line, the domain for the non-occurrence of Tomlinson’s mechanism by the connected bold solid line, and that for the occurrence of Tomlinson’s mechanism by the disconnected bold lines. In moving relatively, the atom can slide by continuously changing its equilibrium position, shown by the connected bold lines. On the other hand, the atom can slide only by changing its equilibrium position discontinuously between two disconnected unit domains, shown by the disconnected bold lines. Thus, the occurrence (or non-occurrence) of Tomlinson’s mechanism is studied by examining whether the unit domains are disconnected or connected, i.e., the topological property of the tiled unit domains. This argument can be extended to the realistic frictional systems where the contacting interface is not one-dimensional but two-dimensional. The domains, where the atom can take its equilibrium position, are shown in Figure 2.4 when the adhesion increases between the upper and the lower bodies. Figure 2.4 corresponds to the case where the contacting surface of the lower body has the oblique-square crystalline symmetry. The point different from the one-dimensional case is that the path where the atom can slide by continuously changing its equilibrium position depends on the direction of sliding displacement coordinate Q. For example, let us consider four cases,
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Figure 2.3 Topological property of the whole domain obtained by tiling the unit domain repeatedly. Domains are shown according to whether or not Tomlinson’s mechanism occurs. v2 (r) is shown by a solid line, the domain for the non-occurrence of Tomlinson’s mechanism by the connected bold solid line, and that for the occurrence of Tomlinson’s mechanism by the disconnected bold lines. In moving relatively, the atom can slide by continuously changing its equilibrium position. On the other hand, the atom can slide only by changing its equilibrium position discontinuously between two disconnected domains. The occurrence (or non-occurrence) of Tomlinson’s mechanism is studied by examining the topological property of the tiled unit domains.
as shown in Figure 2.4(a)–(d). The atom can slide towards arbitrary direction by continuously changing its equilibrium position for the case shown in Figure 2.4(a) and (b). In the case shown in Figure 2.4(c), the atom can slide continuously in the x-direction, but can slide in the y-direction only by discontinuous transformation. The atom can slide only by discontinuously changing its equilibrium position in any direction for the case shown in Figure 2.4(d). As seen above, the frictional property depends on the topological property, i.e., the disconnectedness or connectedness of the domains where the atom can take the equilibrium position. The three-dimensional frictional system [9] consisting of many interacting atoms is written by Nu Nu 1 u l V ri (Q) − rj (Q) + V ri (Q) , V Q, ri (Q) = 2 i
(6)
j ( =i)
where Q is the vector specifying the center of mass of the upper solid body, and is given by u
Q=
N
ri /N u .
(7)
i
Here, ri (Q) describes the equilibrium position coordinate of the ith atom of the upper solid surface, and N u is the total number of atoms of the upper solid surfaces. It has been examined whether the domain is connected or disconnected at the critical points, the centers of the ridges lines connecting between two adjacent atoms of the lower solid surface, which are indicated by the arrows in Figure 2.4(a) [4]. The criterion is given as a condition that the potential energy is a concave function in a direction perpendicular to the ridge lines. Denoting this direction s = (sx , sy ), the corresponding criterion is Vc,c ≡ Vx,x sx2 + 2Vx,y sx sy + Vy,y sy2 < 0,
(8)
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M. Hirano
Figure 2.4 Topological property of the whole domain, where the atom can take its equilibrium position, similar to that in Figure 2.4. Figures show the cases where the contacting surface of the lower body has the oblique-square crystalline symmetry. The point different from the one-dimensional case is that the sliding path where the atom can slide by continuously changing its equilibrium position depends on the direction of sliding displacement vector Q. The atom can slide towards arbitrary direction by continuously transforming its equilibrium position for the case shown in Figure 2.10(a)–(b). In the case shown in Figure 2.10(c), the atom can slide continuously in the x-direction, but can slide in the y-direction by discontinuous transformation. The atom can slide only by discontinuously changing its equilibrium position in any direction for the case shown in Figure 2.10(d).
where Vα,β is defined by u
Vα,β ≡
N j
u l Vα,β s − rj (Q) + Vα,β (s).
(9)
u (s − r (Q)) and V l (s)(α, β = x, y) are the second derivatives of V u (s − r ) and Vα,β j j α,β V l (s) with respect to the α and β components, respectively. The criterion for Tomlinson’s mechanism states that nonadiabatic motion occurs when second-order derivative Vα,β , in a direction perpendicular to a V l (r) ridge line, is negative. The occurrence of Tomlinson’s mechanism can, therefore, be decided by judging whether or not Vα,β in Equation (8) is negative at the critical atom position. It has been examined whether or not the nonadiabatic motion occurs in realistic systems by applying Equation (8) to various systems of cubic metals in which Morse potentials are operated [9]. It has been found that Vc,c are all positive for all the metals that were examined. This shows that nonadiabatic motion of each atom does not occur, i.e., Tomlinson’s mechanism does not occur in cubic metals.
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2.4 ATOMISTIC ORIGIN OF FRICTION 2.4.1
Frictional Model
The atoms slide by changing their equilibrium positions continuously, and so the energy dissipation does not occur due to Tomlinson’s mechanism. How can the problem of the energy dissipation, i.e., the origin of the dynamic friction force as well as the origin of the static friction force be considered? Here, the new picture for the origin of the friction forces is described. The following frictional system will be considered to be given by N N N |pi |2 1 + v1 (ri − rj ) + v2 (ri ) , H {pi }, {ri } = 2 2
(10)
j ( =i)
i
i
which is obtained by adding the kinetic energy term of each atom to the model given in Equation (6). The first, the second, and the third term of the right-hand side stand for the rj ) between the atoms of kinetic energy of the ith atom, the mutual interactions v1 (ri − the upper solid body, and the adhesion energy given by v2 (r) ≡ j vα (r − rj )(vα (r − rj ): the interaction energy from the j th atom of the lower body), respectively. In the frictional process, it is convenient to distinguish the translational degree of freedom, i.e., the center of mass of the upper body from the other degrees of freedom concernN u u u u ing with the internal relative motions. The notations (P = N i ri /N ) i pi /N , Q = u and (pi = pi − P, ri = ri − Q) (i = 1, 2, . . . , 3(N − 1)) are introduced, where P and Q are, respectively, the momentum and the coordinate of the center of mass, specifying the translational motion, and pi and ri are, respectively, the momentum and the position coordinate of the ith atom, specifying the internal relative motions. By using these notations, the frictional system in Equation (10) can be rewritten by |P|2 + v2 (¯ri + Q) + H0 {p¯ i }, {¯ri } , H {p¯ i }, {¯ri }; P, Q = N 2
(11)
i
−1 N −1 N |p¯ i |2 1 H0 {p¯ i }, {¯ri } = + v1 (¯ri − r¯ j ). 2 2 i
(12)
i =j
H0 ({p¯ i }, {¯ri }) involves only the internal degrees of freedom of the upper body, and the translational motion (P, Q) is connected with the internal motions (p¯ i , r¯ i ) by the second term, i.e., the adhesion term in the right-hand side. The motion of equation for the center of mass of the upper body is given from Equation (11): dP = F {¯ri }; Q , dt
dQ = P, dt
(13) (14)
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M. Hirano
where F({¯ri }; Q) is a force acting on the center of mass of the upper body, and is defined by 1 ∂v2 (¯ri (t) + Q) F {¯ri }; Q = − u . N ∂Q
(15)
i
2.4.2
Static Friction
For the sake of simplicity, a picture for the one-dimensional frictional systems, shown in Figure 2.5, is described. The upper body is simply expressed by the linear chain where the atoms interact with each other. Each atom of the upper body feels the interaction of attraction from the lower body, which is represented by the potential curve. Here, imagine we apply an external force to push the linear chain in a right direction. Each atom rises the mountain part of the interaction potential. During sliding, the interdistances between two adjacent atoms change. The drag can be obtained by calculating the total potential energy for each Q, and by taking its first derivative with respect to Q. Alternatively, the drag against the applied force is the sum of the forces along the chain which each atom feels from the lower body. The drag from each atom can become positive or negative. Then we have the static friction force, Fs (Q) = −
∂v2 (¯ri (Q) + Q) i
∂Q
(16)
or by using Equation (15) = −N u F r¯ i (Q) , Q .
(17)
The positive part of this Fs (Q) gives the static friction force. The static friction force stems from the cooperative behavior of atoms as shown in Figure 2.5. This picture, i.e., atomistic locking, is simple and resembles the mechanical-locking mechanism in the surface roughness model shown in Figure 2.6, if one takes the following two correspondences: (i) the roughness → the non-flatter potential v2 (r) which the upper solid surface feels from the lower body, and (ii) the gravitational force → the adhesive force. The origin of the static friction force is ascribed to the atomistic surface-roughness, but not to the defects, dislocations and other imperfections.
Figure 2.5 Mechanism for the origin of the static frictional force, shown for the one-dimensional frictional systems. The upper body is simply expressed by the linear chain where each atom interacts with each other. Each atom of the upper body feels the interaction of attraction from the lower body, which is represented by the potential curve. When we apply an external force to push the linear chain in the right direction, each atom rises the mountain part of the interaction potential coherently or cooperatively. The drag against the applied force is the sum of the forces along the chain which each atom feels from the lower body.
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Figure 2.6 Surface roughness model. The contacting solid surfaces are so rough that surface asperities are mechanically locked against the gravitational force. It is necessary to apply an external force to slide one body against the other. This mechanical-locking mechanism concerns with the origin of the static frictional force. The weakest point of the surface roughness model is that basically it fails to explain an energy dissipation, i.e., the origin of the dynamic frictional force since the gravitational force is an energy-conserving force.
2.4.3
Dynamic Friction: Energy Dissipation
The origin of the dynamic friction force has been studied [12]. How can the energy dissipation be explained? In Tomlinson’s mechanism, the atoms near the sliding surface move independently and each atom repeats the non-adiabatic process of dissipating the elastic energy into the vibrational or kinetic energy of the atoms. Imagine the upper body is pushed to slide against the lower body at a constant velocity, namely with P(0) = constant and p¯ i = 0 initially. If this translational momentum P(t) subsequently decreases during sliding, the force is applied to push the upper body, keeping a sliding velocity constant. This applied force corresponds to the dynamic friction force. Thus, the origin of the dynamic friction force is reformulated as the problem of how the translational kinetic energy for the center of mass decreases. The energy dissipation rate R(t) at time t is given as the reduction rate of the translational kinetic energy, R(t) = −N u
d|P(t)|2 = −N u P(t) ∗ F {ri }, Q , dt
(18)
or by using Equation (15) R(t) = P(t) ∗
∂v2 (¯ri + Q) ∂Q
i
,
(19)
where a symbol ∗ stands for the inner product between two vectors. The dynamic friction force Fd (t) can be obtained from the relation R(t) = P(t) ∗ Fd (t). From Equation (19), we have Fd (t) = −
∂v2 (¯ri + Q) i
∂Q
,
(20)
as is equal to the N u times of the force acting on the center of mass, as seen from Equation (15).
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M. Hirano
If v2 (¯ri + Q) has a Q-dependence, namely, F({ri }, Q) = 0, the translational kinetic energy can be transformed into the kinetic energies of the internal relative motions. If the transformed energy does not turn again to the translational kinetic energy, this energy transfer occurs irreversibly. In order to examine the possibility of this irreversibility to occur, we shall compare the available phase space volumes. The phase-space volume concerning with the translational motion is estimated to have an order of N u |P|2 /2 since the translational kinetic energy, being less than or equal to N u |P|2 /2 is available. On the other hand, there are many combinations of how this kinetic energy N u |P|2 /2 may be distributed on many degrees of freedom for the internal relative motions. The number of combinations increases with an exponential order of the total number of the internal degrees of freedom. So the available phase-space volume of the internal relative motions may be estimated to u have an order of eγ (N −1) where the value of γ (> 0) depends on details of the model with internal variables, for an example, γ = 3 ln(|P|2 /2v) when H0 in Equation (11) is described as an ensemble of many independent harmonic oscillators with frequency v. From this study, the phase-space volume for the translational motion becomes negligibly small for a large N u , compared with that for the internal motions. Thus, the energy-transfer from the translational motion to the internal motion occurs irreversibly, and so it is concluded that the energy is dissipated from the translational motion to the internal motions. The frictional system is the dynamic one conserving the total energy. The irreversible energy dissipation indicates that the internal relative motions are excited, and hence the adiabaticity does not hold true for the internal relative motions. However, in order that the present idea is adequate, the system, described by H0 ({p¯ i }, {¯ri }), must work as a host system absorbing energy. In other words, the dynamic system in Equation (11) has the ergodic property. If the system energy is sufficiently low, one participates finding energy surface which is filled by the non-ergodic torus with the Kolmogorov–Arnold–Moser (KAM) stability [17]. As the energy increases, the system recovers the ergodic property. The number of empirical computer studies supports this picture. When the energy surface is filled by the KAM torus, the system is well known [13,18] to show the recurrence phenomenon where the energy repeats decreasing and increasing, and hence the energy does not diffuse. The number of studies has been made [19,20] to find the border, the critical energy, where the system becomes from non-ergodic to ergodic. The present simulations show that, for the frictional systems of the current interest, the energy seems to be distributed over the entire degrees of freedoms even for the case of the weak adhesion. The Frenkel– Kontorova frictional system [21], where the potential terms in Equation (10) is replaced by the pure Frenkel–Kontorova model has been studied [15,16,22]. The magnitude k of the spring describing the interaction between the atoms of the upper body and the magnitude f describing the adhesion are taken equal to 1 and 0.1, respectively. The momentum P(t) as a function of Q(t), started from the initial P(0), is shown in Figure 2.7(a). The momentum p¯ i (t) as a function of the coordinate r¯ i (t) is shown in Figure 2.7(b). Figure 2.7(b) implies that the system is ergodic, and so the host system works as an energy absorber, as seen Figure 2.7(a). The above mechanism can be applied to the one-dimensional frictional system, which was described previously. For any given Q, the total interaction energy where the atoms are assumed to have their equilibrium positions is shown in Figure 2.8. Suppose that the external force is applied to slowly slide the upper solid surface, keeping the lower body
Superlubricity of Clean Surfaces
(a)
29
(b)
Figure 2.7 Translational momentum P (t) as a function of Q(t) in (a) and the internal momentum p¯ i (t) as a function of r¯i (t) in (b) for the Frenkel–Kontorova frictional system. The dots stand for their values at every 1000 unit time intervals. The magnitude of k of the spring describing the interaction between the upper body and the magnitude f describing the adhesion are taken equal to 1 and 0.1, respectively. (b) implies that the system is ergodic, and so the host system works as an energy absorber, as seen from (a).
Figure 2.8 Mechanism for the origin of the dynamic frictional force, shown for the one-dimensional frictional system. For any given Q, the total interaction energy where the atoms are assumed to have their equilibrium positions for each Q is shown. Imagine we push the upper body to slide against the lower body. Q, the coordinate of the center of mass, begins to arise a mountain of the potential, and reach on top of the mountain. When Q moves in a right direction further, the system lowers the potential energy, and so gains the kinetic energy. This is a process of increasing the kinetic energy of the translational motion. The available phase-space volume of the internal motions becomes much larger than that of the translational motion. The energy transfer from the translational motion to the internal motion occurs irreversibly. So, the excess kinetic energy may be dissipated into the other internal motions in the body due to the mechanism.
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M. Hirano
fixed. Q, the coordinate for the center of mass, begins to arise a mountain of the potential, and reach on top of the mountain, When Q moves in the right direction further, the system lowers the potential energy, and so gains the kinetic energy. This is a process of increasing the kinetic energy of the translational motion. This excess kinetic energy may be dissipated into the internal relative motions due to the mechanism described above.
2.5 2.5.1
SUPERLUBRICITY
Superlubricity and Adiabatic Motion of Atoms
In Tomlinson’s mechanism, the atoms change their equilibrium positions non-adiabatically, which leads to the energy transfer of the elastic energy into the kinetic energy of the atoms. Tomlinson’s mechanism explains the energy dissipation. However, it has been shown that Tomlinson’s mechanism is unlikely to occur in the realistic frictional systems. The present picture for the origin of the dynamic friction force can explain the irreversible energytransfer of the translational kinetic energy into the internal kinetic energies, i.e., the thermal energy. This mechanism, however, works only when v2 (¯ri + Q) has a Q dependence. On the other hand, if v2 (¯ri +Q) has no Q-dependence during sliding, the energy-dissipation R(t) does not occur from Equation (19). Then, the translational kinetic energy is a constant for motion, and the frictional system is in a state of superlubricity. The superlubricity can appear when the sum of the forces of each atom vanishes. It has been proved that the superlubric state occurs when the atoms have their equilibrium positions for each Q and, at the same time, the frictional system satisfies some conditions [9]. The condition is satisfied when two solid surfaces are incommensurate. The superlubricity has been theoretically discussed by McClelland [15] and Sokoloff [16] for the weak adhesion. The result in Section 2.3 implies that this state appears for a wider class of the (strong or weak) adhesion including the metallic bond and the Van der Waals interaction. It was argued that the system of incommensurately contacting surfaces has zero dynamic threshold for sliding when two contacting surfaces form a perfect periodic lattice [16,20]. The state of superlubricity is not associated with the energy dissipation. Thus, the concept of superlubricity contradicts with Tomlinson’s mechanism. The problems will be interesting of how the superlubricity is influenced by the dynamic effect [22] when two bodies moves relatively so fast that r¯ i may not be in the equilibrium position r¯ i (Q) and by the existence of the surface roughness and the imperfections such as the defects and the dislocations. It has been considered that the superlubricity may be stable, as is different from the one-dimensional case of the charge density wave (CDW) pinned easily by the defects. Why is it that individual atoms do not move in a non-adiabatic manner in realistic systems? The answer lies in the degree of freedom of atomic motion. In the past theories, friction was investigated essentially on the basis of one-dimensional models, as shown in Figure 2.9(a) [15,16]. In such a one-dimensional system, the degree of freedom in the motion of an atom is low. This means that if unstable areas (the white parts in Figure 2.9(a) in which atoms cannot stably exist) appear, an atom will undergo non-adiabatic motion as it passes through those areas. Such an unstable area, which corresponds to the area
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(a)
(b)
(c)
Figure 2.9 Motion of atoms at a contact surface. The white parts represent unstable areas in which atoms cannot stably exist and the shaded parts to stable areas in which they can stably exist. (a) One-dimensional system; (b) and (c) two- and three-dimensional systems.
in the above chalk example where the chalk does not stick, appears as a result of strong interaction between solids, the existence of impurities, lattice defects, etc. In two- and three-dimensional systems, however, the degree of freedom in the motion of an atom is high. As a result, even if unstable areas appear, an atom can pass through the stable areas by moving around the unstable areas, as shown in Figure 2.9(b). (The white parts in Figure 2.9(b) correspond to an atom’s unstable areas and the shaded parts to an atom’s stable areas.) Simulations as well show that atoms perform non-adiabatic motion if unstable areas appear in a one-dimensional system but that they perform smooth adiabatic motion in twoand three-dimensional systems even if unstable areas appear [12]. The latter case makes it easy for superlubricity to appear [9]. Even if unstable areas should appear between lattices due to impurities and defects in two- and three-dimensional systems, non-adiabatic motion would not appear for the same reason given above (Figure 2.9(b)). In this case, while superlubricity would be stable for a certain concentration of impurities and defects, it is thought that exceeding a certain value will result in the appearance of friction with friction forces increasing monotonically as that concentration increases. Incidentally, unstable areas will grow if the interaction between solids is made strong in two- and three-dimensional systems, and non-adiabatic motion will occur if stable areas become cut off by unstable areas at some time (Figure 2.9(c)). This occurrence of nonadiabatic motion results in a friction transition in which friction changes from zero to a finite value [9]. 2.5.2
Friction Diagram
The one-dimensional friction system, given by N N pi2 1 f + (ri+1 − ri − ℓ)2 + sin(2πri ) , H {pi }, {ri } = 2 2 2π i
i
(21)
32
Figure 2.10
M. Hirano
Friction diagram for the one dimensional Frenkel–Kontorova model with kinetic energy terms.
where f stands for the magnitude of the adhesive force, is studied. This is one-dimensional Frenkel–Kontorova model [21] with kinetic energy terms. ℓ is the mean distance between two adjacent atoms. The periodicity length of the sinusoidal potential in Equation (21) is taken as a unit. The Frenkel–Kontorova model has been studied by many workers. It is known that this model shows nonadiabatic motion of atoms, as mentioned in Section 2.2, near at f ≃ 0.14, which is often called the Aubry transition [23]. The dynamics in friction has been studied by adding the kinetic energy terms to the model. To examine the friction properties including superlubricity, the dynamics has been studied after the upper solid surface at the ground state is pushed with initial sliding velocity P (0) (p¯ i (0) = 0 for any i), that is, the Hamiltonian dynamics conserving the energy. The dynamics is studied by examining quantities such as P (t), Q(t), r¯i (t), p¯ i (t) and the sliding distance ls (t) defined as the distance over which the upper solid surface slides during time t. These quantities are obtained by solving Equation (44). ℓ is assumed to be equal √ to the golden mean number ( 5 + 1)/2. Two regimes appear in the diagram shown in Figure 2.10; In the superlubricity regime, the superlubric state appears, i.e., two contacting solid surfaces slide without any resistance. The recurrence phenomenon occurs persistently; this regime repeats increasing and decreasing the translational kinetic energy with time. The friction force Fd (t) averaged over the recurrence time exactly vanishes. The sliding distance ls (t) increases linearly with time: ls (t) = c[P (0)]t. c[P (0)] is a averaged velocity satisfying c[P (0)] ≥ P (0), and depends on P (0). On the other hand, in the friction regime, the energy dissipation occurs; the translational kinetic energy is transferred into the kinetic energy of the internal motions. The upper surface slides but finally ceases to slide: ls (t) < ∞ for sufficiently large t. The friction occurs in this regime. As P (0) becomes smaller, the sliding distance decreases for the region f ≥ 0.14. The point at f = 0.14 and P (0) = 0 is the Aubry transition point: in the regime f > 0.14, the atoms change their equilibrium positions discontinuously. In the regime f < 0.14 and P (0) = 0, the atoms can slide by changing their equilibrium positions continuously, and the system can slide without any resistance. Nevertheless, the friction regime spreads over the region 0.0 < f < 0.14 with finite P (0). This is different from the result for the pure Frenkel– Kontorova model without any kinetic energy terms, and is due to a dynamic effect of the system. In particular, the distance, ls (∞), over which the upper solid surface runs till it
Superlubricity of Clean Surfaces
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ceases to slide is ls (∞) ≃ 1 as the parameters f (>0.14) and P (0) approach near the horizontal axis, while ls (t) tends to stretch with time t as one approaches the border line separating the friction regime from the superlubricity regime. In the friction regime, the temporal behavior of the friction force Fd (t) depends on P (0) and f in a complex manner. As the parameter f means the magnitude of the adhesive force between the upper and the lower solid surfaces, f < fwa , say fwa ≃ 0.1, corresponds to the weak adhesion. (Note that the strength of interaction between atoms of the upper solid surface is set equal to unity.) The diagram in Figure 2.10 shows that the superlubric state appears only for two cases of the weak adhesion and of the high sliding velocity. The property that the superlubricity appears only for the weak adhesion is peculiar for the one-dimensional system. 2.5.3
Superlubricity and High Dimensionality
In the superlubricity regime, two contacting solid surfaces can slide with no resistance. A general consideration of Equations (18)–(20) concludes that the superlubric state ap pears when the system satisfies either of two following conditions: (I) v2 (¯ri (t) + Q(t)) in Equation (19), hereafter denoted by v(Q(t)), has no Q dependence, and (II) the persistent recurrence phenomenon occurs. The second condition may be a special case of (I) if v(Q(t)) is regarded as the quantity averaged over the recurrence time. Then, there arises a problem of how to construct the friction systems showing the superlubricity. One among them, for examples, is to prepare the friction system consisting of two clean flat solid surfaces, as studied in previous sections. The condition (I) has been discussed as the condition for the phason mode to exist, and can be replaced by another two conditions: (I-1) the quasi-static sliding: the sliding velocity is so slow that the atoms follow their equilibrium positions adiabatically and (I-2) two solid surfaces contact incommensurately [8]. The nonadiabatic motion of atoms do not occur if these are both satisfied. On the other hand, the condition (II) is first pointed out here, which is a result of the dynamic effect of the system. An importance of high dimensionality in the friction system has been emphasized, which makes the superlubricity appear much easily. The term ‘dimensionality’ means the number of the spatial directions towards which the atoms can move or relax during sliding. The importance of high dimensionality is demonstrated by using two-dimensional Frenkel– Kontorova model analogous to that in Equation (21), given by N 1 x2 y2 pi,i + pi,i H {pi,j }{ri,j } = 2 i
+
N 2 y 2 1 x y x ri+1,j − ri,j − ℓ + rj,i+1 − rj,i − ℓ 2 i,j
x f y cos π ri,j (cos θ + sin θ ) + ri,j (cos θ − sin θ ) π x y × cos π ri,j (cos θ − sin θ ) + ri,j (− cos θ − sin θ ) , (22)
+
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where atoms arrange on the square-lattice points specified by two index numbers i and j . The position and momentum of the (i, j )th atom are, respectively, denoted by y x , r y ) and p x ri,j = (ri,j i,j = (pi,j , pi,j ). θ is a lattice misfit angle between the upper and i,j lower solid surfaces with square-lattice symmetry. The upper solid surface is pushed with initial sliding velocity P (0) = 0.02 along the x direction, or equivalently, along the θ direction against the lower surface. The dynamic property for the case θ = 0◦ or 90◦ becomes identical to that of the one-dimensional Frenkel–Kontorova model, as easily seen from Equation (22). The case θ = 45◦ gives the largest critical value fc (≃0.25), which is about 4 times of fc (≃0.06) of the one-dimensional case, which is seen from the diagram in Figure 2.10. For the parameter f < fc , the superlubric state appears. Why does the critical value fc arise for the two-dimensional Frenkel–Kontorova model? This is explained as follows; Suppose two-dimensional friction system where the lower solid surface is assumed to have a square-lattice symmetry, as shown in Figure 2.9(b). The region where each atom of the upper solid surface can move without occurring the nonadiabatic motion is shown by shaded part, while the region where the nonadiabatic motion occurs by empty part. Two dimensions allow the atoms to move by changing its position flexibly in the shaded region. Therefore, the atom can slide avoiding the region where the nonadiabatic motion occurs, as shown by the thin arrow. The appearance of nonadiabatic region does not mean that the superlubric state breaks down. This should be compared with the case of one-dimensional systems. When the dimensionality arises further, the atoms can move more flexibly. For the three-dimensional friction systems, it as shown that the critical value fc becomes much larger than that calculated for the realistic systems: the superlubric state appear for any combinations of metals with clean and flat surfaces. (The metals were simulated by using the Morse type potentials determined empirically.) The possibility for the superlubric state to appear has been discussed by other workers [15,16]. They was based on the result for the case of the one-dimensional systems with P (0) = 0, and concluded that it appears only for the case of the weak adhesion. The above analysis shows that the superlubricity is a general phenomenon, and appears for a wide class of the (strong or weak) adhesion including the metallic bonding and the Van der Waals interaction [9]. High dimensionality is a key to understand the physics of superlubricity. 2.5.4
Energy Recurrence Phenomena
If kinetic energy is given to a solid so that it is made to slide at a finite speed, it will come to a stop in a short time. In this case, the energy of translational motion dissipates due to friction. This energy dissipation does not originate from the non-adiabatic motion of atoms as concluded above. A new energy-dissipation mechanism, however, has been described [12]. In this mechanism, the energy of a solid’s translational motion is irreversibly transferred to energy of the internal motion of solids. This irreversibility occurs because the degree of freedom of translational motion is proportional to system size while the degree of freedom of internal motion is proportional to a power of system size. The degree of freedom of internal motion can therefore be dramatically larger [12]. In contrast to this irreversible energy transfer, superlubricity appears if the translational motion of a solid is independent of the internal motion of solids and the kinetic energy of translation does not dissipate constantly. The condition for the state of no energy dissipation to occur is
Superlubricity of Clean Surfaces
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existence of an energy recurrence phenomenon. If this phenomenon exists, the energy of a solid’s translational motion will increase and decrease repeatedly according to a certain recurrence time period. This corresponds to the repetition of positive and negative values of friction force in a recurrence cycle. Accordingly, if friction forces are averaged out on a time scale corresponding to the recurrence time period, average friction force will be zero. On the other hand, if the recurrence time period is much longer than the time scale of friction observation, friction will appear. This recurrence phenomenon depends on system size and energy. As a special case, we can consider a closed system consisting of a solid having a small number of atoms. In this system, the energy of the translational motion of solids will, at some point, be transferred to the energy of internal motion in the solid. Since the size of the system is small, however, this energy of internal motion will be returned to translational motion in a relatively short recurrence time. In a finite system, the recurrence phenomenon will likewise occur but the length of the recurrence time period will increase with increase in system size. In an infinite system, though, the recurrence time period becomes infinitely large and the recurrence phenomenon does not occur. If the energy of the system is sufficiently low, however, the phase space of the system will satisfy a non-ergodic orbit and the energy given to the system will exhibit the recurrence phenomenon without spreading throughout the entire system. In a friction system having finite friction forces, the energy of translational motion is irreversibly transferred to the energy of the solid’s internal motion giving rise to energy dissipation. In superlubricity, on the other hand, the recurrence phenomenon means that energy is not being continuously dissipated. Recurrence phenomena of this sort will now be investigated using the two-dimensional dynamic Frenkel–Kontorova model given by Equation (22). In this model, atoms are arranged on a tetragonal lattice. These atoms not only interact with each other, but also interact with the other solid (in the pair of solids making contact) through a sinusoidal potential function. Denoting each atom by the letters i and j , the position and momentum of atom (i, j ) are expressed as qi,j and pi,j . In Equation (1), θ is the lattice misfit angle between the solids. The momentum of all atoms is given only at first and the manner in which momentum of the center-of-gravity position varies with Q was investigated for various misfit angles θ (Figure 2.11) [24]. The interaction k1 between the solids was 0.1 and the momentum given to each atom was 0.02. Now, for small θ in which the orientations of the lattices at the contacting surfaces approach a match, the momentum of Q tends to decrease. In this case, the energy of the solid’s translational motion is irreversibly transfers to the energy of the solid’s internal motion and energy dissipates. Conversely, for larger θ in which the orientations of the lattices at the contacting surfaces do not match up, the momentum of Q does not tend to decrease, and at θ = 45 degree, the momentum of Q increases and decreases in a repetitive manner signaling the appearance of the recurrence phenomenon. In this case, the energy of the solid’s translational motion is independent of the solid’s internal motion and the energy of translational motion does not continuously dissipate. The states of atomic motion (momentum and position coordinates of each atom) for the cases of dissipation and no dissipation are instructive (Figure 2.12). For the case of energy dissipation, the atoms move in an ergodic manner so that the energy of translational motion is distributed among the many degrees of freedom of internal motion. For the case of superlubricity, however, the energy is distributed to only a few degrees of freedom.
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Figure 2.11
Momentum of a solid versus center-of-gravity position.
Figure 2.12 State of atoms’ momentum in phase space. (◦) represents state in which energy dissipates and friction appears for θ = 15 degree. (•) represents state of superlubricity in which energy does not dissipate continuously as a result of recurrence phenomena for θ = 45 degree.
2.6 SUMMARY In this chapter, we have shown that superlubricity appears in realistic systems where metallic bonding and the like operate. The conditions for the appearance of superlubricity are the adiabatic motion of atoms and energy recurrence phenomena. Two types of superlubricity can appear corresponding to each of these conditions. Because atoms move adiabatically in a realistic system, bringing two surfaces into contact so that the orientations of their lattices
Superlubricity of Clean Surfaces
37
do not match will produce a situation in which the forces acting one each atom cancel each other out. As a result, superlubricity is independent of the time scale of observation and is always zero. In a finite system, moreover, the energy recurrence phenomenon appears through the dynamics of atomic motion, and friction observed on a time scale equivalent to recurrence time is again zero. The concept of superlubricity was born out of research for the origins of friction. Investigation into the mechanism for generating friction forces has revealed the case in which friction appears and the case in which friction is zero. The problem of whether this state of vanishing friction is realistic or not is closely related to the problem of energy dissipation in friction. Specifically, superlubricity in which friction is zero is realistic if the conventional mechanism of dissipation is rejected. At the same time, a new dissipation mechanism has been proposed to replace the conventional one, and a picture of static and kinetic friction that describes the origins of friction has been drawn. The idea of superlubricity, moreover, should lead to new points of view in areas like friction control and friction in living organisms. The concept of superlubricity, i.e., the phenomenon of zero friction, thus emerged from research on friction at the atomic level [9,12,15,16,24–26]. The atomistic model of friction allows for the appearance of finite friction and zero friction depending on the commensurability of contacting surfaces [24]. It is well known that phenomena dependent on commensurability can occur in systems having two periodicities such as charge-density waves, ion conduction, epitaxial crystal growth, and adatom layers. The idea behind the commensurability of contacting surfaces has stimulated the theoretical and experimental research of atomic-scale friction, i.e., Nanotribology [25].
REFERENCES [1] For a review involving history in the field of friction see, e.g., Sota, N. Masatsu no Hanashi. Iwanami Syoten, Tokoyo, 1971 (in Japanese). [2] Bowden, F.P., Tabor, D. Friction and Lubrication of Solids, vol. II. Clarendon Press, Oxford, 1964. [3] Tabor, D. Proc. Roy. Soc. London A 251 (1959), 1266. [4] Dowson, D. History of Tribology. Longm C.A. [5] Coulomb, C.A. Mémories de Mathematique et de Physics de l’Acaddemie Royale (1785), 161. An, London, 1979. [6] Desaguliers, J.T. Phil. Trans. Roy. Soc. London 33 (1725), 345. [7] Tomlinson, G.A. Phil. Mag. 7 (1929), 905. [8] Mate, C.M., McClelland, G.M., Erlandsson, R., Chiang, S. Phys. Rev. Lett. 59 (1987), 1942. [9] Hirano, M., Shinjo, K. Phys. Rev. B 41 (1990), 11837. [10] Girifalco, L.A., Wezer, V.G. Phys. Rev. 114 (1959), 687. [11] Johnson, R.A. Phys. Rev. 134 (1964), 1329. [12] Shinjo, K., Hirano, M. Surf. Sci. 283 (1993), 473. [13] Fermi, E., Pasta, J., Ulam, S. Collected Papers of E. Fermi, vol. II. Univ. of Chicago Press, 1965. [14] Goldstein, H. Classical Mechanics, second edition. Addison-Wesley, Reading, MA, 1980. [15] McClelland, G.M. Adhesion and friction. In: Grunze, M., Kreuzer, H.J. (Eds.), Springer Series in Surface Science, vol. 17. Springer-Verlag, Berlin, 1990, p. 1. [16] Sokoloff, J.B. Surf. Sci. 144 (1984), 267. [17] See, e.g., Arnold, V.I., Avez, A. Probiernes ergodiques de la mecatiique classique. Gauthier-Villar, Paris, 1967.
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[18] Tuck, J.L. Adv. Math. 5 (1973), 11. [19] Benettin, G. In: Ciccotti, G., Hoover, W. (Eds.), Proc. Inter. School Phys. Enrico Fermi Course XCVII. 1988, p. 15. [20] Sokoloff, J.B. Phys. Rev. B 31 (1935), 2270. [21] Frenkel, Y.I., Kontorova, T. Zh. Eksp. Teor. Fiz. 8 (1938), 1340. [22] Sokoloff, J.B. Phys. Rev. B 42 (1990), 760. [23] Aubry, S. J. Phys. (Paris) 44 (1983), 147. [24] Hirano, M. Wear 254 (2003), 932. [25] Krim, J. Surf. Sci. 500 (2002), 741. [26] Matsukawa, H., Fukuyama, H. Phys. Rev. B 49 (1994), 17286.
–3– Theoretical Studies of Superlubricity Carlos E. Campañá and Martin H. Müser Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
3.1 INTRODUCTION Superlubricity refers to the occurrence of extremely small friction between two solids in mechanical contact. Its existence was predicted by Hirano and Shinjo in the early nineties [1,2]. They argued that lateral forces are likely to cancel systematically when two incommensurate crystals are brought into contact. They furthermore suggested that many solids may not be sufficiently compliant to suppress superlubricity via elastic deformations. Whenever their arguments hold, one may expect the possibility for superlubricity. Even though the suggestion of a super-low static friction contradicts our common sense, it does not necessarily contradict classical mechanics. If the two solids in contact have flat interfaces and wear and plastic deformation are not considered, then one may expect the same (free) energy at the beginning of a sliding process as at its end, because of translational symmetry. Consequently, no work would have to be done when taking the solids from their initial to their final configuration, implying the possibility of very low friction. Even, if the surfaces of the two solids are rough, there should be as many bumps (or atoms) in the substrate pushing the slider to the right as there are surface irregularities in the substrate pushing the slider to the left for each spatial direction within the contact plane. Hence, statistically speaking, there is the possibility of an almost perfect annihilation of lateral forces. Experimentally, there is growing evidence pointing to the existence of superlubricity [3–8]. Shortly after Hirano and Shinjo’s original work, a set of experiments suggested friction coefficients μ (the ratio of friction F over load L) below the experimental resolution of 10−4 [3]. This is three to four orders of magnitude less than usually observed. Recent studies performed on nanoscale objects also suggest that lateral forces may cancel systematically at the interface between two solids. One interesting aspect of these works is that it was possible to switch in a controlled fashion between a superlubric and a regular regime. In one case this was done by rotating a graphite flake with respect to a graphite surface, thereby changing the degree of incommensurability [7]. In a second case, the superlubric regime was achieved by varying the load of an atomic force microscope tip [8]. Besides, Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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an increasing number of recent analyses on superlubric, hydrogen-terminated diamond surfaces have been reported [5,6]. There are many processes that can destroy superlubricity, including plastic deformation, adsorbed layers, and cold welding [9–11]. However, in most cases, it is assumed that these friction mechanisms can be suppressed by preparing the samples and setting the laboratory conditions appropriately. This leaves the competition between elastic interactions and interfacial forces as the main opposing force to sliding. Two simple but very illustrative atomic models that show how this competition can induce solid friction at small velocities are the Prandtl–Tomlinson [12,13] and the Frenkel–Kontorova model [14]. These models, which will be introduced, further below, have been very popular because of the possibilities they offer to capture characteristic features of the frictional behavior of elastic solids. Although each one of the previous models is able to qualitatively reproduce some of the experimental findings, new and more sophisticated descriptions are needed to also make quantitative, material-specific predictions on tribological properties. Reviewing the main theoretical efforts towards achieving this goal is the purpose of this contribution. The remainder of this chapter is organized as follows: In Section 3.2, a general overview of the theoretical aspects of superlubricity is provided. The role that elastic instabilities and long-range elastic deformations play within different atomic models of rigid elastic solids in contact will be discussed. Also, some basic dimensional analysis will be used to study the scaling laws that friction forces follow as a function of the system’s dimensions. Section 3.3 reviews selected computer simulation studies shedding light on various processes that can occur in sliding interfaces. Having the possibility of varying at will the geometrical properties of the interfaces or their chemical composition and being able to observe the motion of individual atoms during sliding, makes computer simulations a powerful tool in creating qualitative understanding of tribological phenomena. Conclusions will be presented in Section 3.4.
3.2
THEORY
From every-day experience one knows that a finite force has to be overcome to start lateral motion of one solid relative to another. This threshold force Fs is known as the static friction force. Once the motion has been initiated a force equal to or greater than a second threshold value, the kinetic friction force Fk has to be applied. If the shear force falls below Fk , the interface appears to be pinned—at least on experimental time scales. Superlubricity refers to situations in which the kinetic friction force becomes very small. The reasons why one can find exceedingly small threshold forces and thus superlubricity, will be described in this section. Included is a description of processes that can break superlubricity with an emphasis on the competition between intra-bulk elasticity and lateral interfacial forces, whose microscopic origin may result, for example, from roughness. 3.2.1
Friction and Superlubricity
In one of his contributions Hirano discussed the mechanisms of superlubricity based on a model from atomistic theory [15]. A similar argument was suggested by Prandtl within the
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context of his work on friction many years earlier [12]. Hirano introduced two different conditions that a system must satisfy in order to be superlubric. The first condition is the adiabatic motion of the atoms. The second condition is energy recurrence phenomena. The first condition can be understood as the invariance of the total energy of the ground sate of the system with respect to translations of its center of mass. It is worth to mention that this requirement does not depend on the type of inter-atomic potentials or crystalline lattices but only on the atomic arrangement within the interfaces in contact. In the case of energy recurrence phenomena, the translational motion of the solid has to be independent of the motion of the internal degrees of freedom, i.e., the translational motion energy will fluctuate with a given recurrence period. We follow Prandtl’s argument, which required only adiabicity, or the absence of instabilities, see further below. A rigorous definition of superlubricity appears to be a difficult task. Even if there is some correlated motion of the atoms, no pair formation occurs as in the case of superfluids or superconductors. Also, the friction forces between two solids in sliding motion remain finite at finite velocities. Moreover, from the experimental point of view it will be unfeasible to test directly the adiabicity of atomic motion. For these reasons it is necessary to use an ad-hoc definition of superlubricity. A practical way of defining it is to require that the kinetic friction coefficient μk must be less than 10−3 while the local load on the contact should be in the order of 10% of the indentation hardness of the softer material. Another requirement would be that the sliding velocity has to be sufficiently high so that the system cannot relax stress through creep or thermal relaxation, but it may be small compared to the velocity of sound. It is important to keep in mind the different nature of kinetic and static friction. Kinetic friction is related to (molecular) hysteresis or non-adiabicity while static friction is due to energy barriers. Some model systems may have finite energy barriers and hence exhibit finite static friction, although hysteresis effects might be negligible, thus leading to an absence of kinetic friction. An impressive demonstration of such a system was given in a recent contribution of Socoliuc et al. [8]. Within their experiment, a transition from stickslip into continuous sliding motion of the tip of a friction force microscope was observed. The transition was achieved in a controlled fashion by changing the applied load on the tip. Even though at all times energy barriers existed, the hysteresis loop corresponding to the scanning forward–backward process disappeared for normal loads below a certain threshold and consequently the kinetic friction force vanished as well. Of course, the reason of such behavior is connected to the absence of mechanical instabilities. This will be explained in more detail in the next section. 3.2.2
Dry Friction on Idealized Zero Temperature Analytic Models
The way how the competition between elastic interactions and interfacial forces can induce large friction at small velocities is most easily demonstrated in the Prandtl–Tomlinson (PT) model [12,13]. It can be described as follows: A particle without internal degrees of freedom is pulled over a sinusoidal potential V (x) = V0 cos(2πx/a) with a spring of stiffness k. Here, V0 is the amplitude of the energy modulation due to the interaction with the substrate, a is the substrate’s lattice constant and the spring reflect the mean-field description of the coupling between an atom and its ideal lattice site. It is also assumed that there
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is a drag force linear in velocity. This non-conservative force describes the interactions between the particle and the substrate’s lattice vibrations, which are not explicitly included in the model. The equation of motion of the particle reads mx¨ + γ x˙ =
2πV0 sin(2π/a) − k x − xd (t) , a
(1)
where xd (t) is the position of the atom’s ideal lattice and γ is the damping coefficient. ′′ is smaller than k, there can If the maximum (negative) curvature of the potential Vmax only be one mechanically stable position for the particle at every instance of time. The equilibrium position moves at the macroscopic sliding velocity v0 and the particle will always be close to it so that the trajectory of the particle will be very smooth. This implies that a negligibly small amount of energy is dissipated into the damping term at small ′′ is violated, then there will be moments values of v0 . However, if the condition k > Vmax in time at which a local energy minimum suddenly disappears as the equilibrium position advances in sliding direction (such as shown in Figure 3.1). The particle then drops into the next available energy minimum thereby dissipating the energy difference E of its initial position and the new mechanical equilibrium site into the damping term. The same process and energy dissipation occur per slid distance a, which usually is the substrate’s lattice constant or an integer multiple thereof. This scenario renders the friction force to be approximately ( E/ a) over a large range in velocity. Velocities that are non-negligible compared to the speed of sound and velocities sufficiently small to allow for creep motion require additional considerations. Another simple model that also includes elasticity is the Frenkel–Kontorova (FK) model [14]. Its simplest form consists of a one-dimensional chain of atoms coupled by harmonic springs and interacting with a periodic potential as shown in Figure 3.2. Unlike the PT model, it allows for long-range elasticity. An important feature of this model is that in the limit of low-sliding velocities the average kinetic friction depends on the ratio Ω = a/b, while Fk is independent of a/b in the PT model. For any irrational value of Ω, a threshold spring constant kc is found. If the springs are stronger than kc static and kinetic friction vanish. For k < kc , several energy minima can coexist in a way similar to that shown in Figure 3.1. As a consequence, the static and kinetic friction become finite. Despite its simplicity, the FK model and its generalizations to higher dimensions are useful to describe various tribological phenomena conceptually and sometimes even quantitatively. In both models, elastic instabilities induce finite friction and thus prevent superlubricity. Similar arguments apply to higher-dimensional systems. Whenever there is mechanical multistability leading to the disappearance of mechanical stable sites under sliding, instabilities occur. They result in significant energy dissipation even at small sliding velocities. One may argue that such instabilities become unavoidable due to long-range elastic deformations in macroscopically large objects [16,17]. However, one has to keep in mind that the effective elastic interactions in three-dimensional solids are fairly strong. Simple scaling arguments suggest the possibility for superlubricity even if the contacts are rough and/or disordered [18]. Both, the PT and the FK model can be combined into a more sophisticated description that includes some new subtle features but maintains the main characteristics of the previous two approaches. Known as the Frenkel–Kontorova–Tomlinson (FKT) model [11], it is
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Figure 3.1 Schematic representation of an instability in the PT model. The time-dependent potential V (x) (dashed lines) is the superposition of a sinusoidal substrate potential, fixed in space, and a moving parabolic potential representing the elastic interaction between the atom and its unperturbed equilibrium position in the bulk. The full circles show mechanically (meta) stable positions. When the stable position suddenly disappears, the atom quickly advances to the next available energy minimum, e.g., when the particle position becomes unstable at x ≈ −1.7 it jumps to x ≈ 2.6 dissipating an amount of energy E = 16.6. Such a jump occur every time the solid moves by one lattice constant (in this case a = 2π ) resulting in an average kinetic friction force Fk = 16.6/2π = 2.65.
Figure 3.2 Schematic representation of the FK model. The substrate is a periodic potential and each atom is coupled to its neighbors through springs of stiffness k. The ratio of the lattice constants chain-substrate: Ω = a/b determines the degree of commensurability of the contact.
formed by a rigid substrate with its center of mass kept fixed and a free slider where each atom is coupled to its ideal lattice site and its two neighboring atoms. The effect of the competition between interfacial and intra-bulk interactions can be summarized as follows: commensurate solids, i.e., solids that share a common periodicity, have a friction coefficient that is independent of the area of contact, or, more generally speaking, independent of the number of atoms in direct contact with the substrate. If intra-bulk elasticity is sufficiently strong to prevent instabilities, symmetry plays an important role on how the friction coefficient depends on the area of contact or the number of particles N in contact. Incommensurate interfaces show a friction coefficient that vanishes linearly with the area of contact. Lastly, within disordered interfaces due to the
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random distribution of the lateral forces directions, the friction coefficient increases only with N −1/2 [10,11]. These claims will be further investigated in the next section. A more quantitative discussion of how the friction forces change as a function of the local arrangement of the atoms within the surfaces and the symmetry of the lattices will be given in the next section, which will also address the role of dimensionality. 3.2.3
Disorder, Symmetry and Dimensionality
The surfaces of most real solids are not perfectly crystalline but show certain degrees of disorder. Moreover, surface atoms are not coupled elastically to their lattice sites but interact non-linearly with the other atoms that form the solid. This affects the tribological properties of the materials sensitively. Under sliding, instabilities of surface atoms do not necessarily involve the sudden motion of single atoms but they may involve the collective motion of many of them. Whether such collective instabilities occur depends on whether or not the intra-bulk elastic interactions dominate the interfacial interactions on length scales larger than atomic scales [10,18]. Furthermore, the dimensionality of a system has a direct influence in the competition between the random substrate–slider interactions and the elastic coupling within the solid. If the elasticity dominates a superlubric state becomes possible. To get an order of magnitude estimation for the relevant variables at the atomic scale, it is reasonable to assume that the elastic coupling k(Latomic ) between adjacent atoms is in the order of the bulk modulus B, say 40 GPa for a soft solid, times a lattice spacing, say 2 Å. Thus, k(Latomic ) will be approximately 8 N/m which is a reasonable value for relatively soft solids. One can also estimate the maximum local curvature of the substrate potential ks . Solids that are tied together by physical bonds have bulk moduli in the order of 4 GPa and nearest neighbor separation are in the order of 3 Å, resulting in an estimate of ks = 1.2 N/m. Thus, at the atomic scale, k > ks , so that elastic instabilities cannot be expected to occur involving only the motion of individual atoms. Of course, the condition k > ks at the atomic scale is necessary but not sufficient for superlubricity. An important question to ask is how these interactions change if we change the length scale on which the system is described. For instance, if the interactions strengths are known on a linear scale of length L, what will their respective values be on a scale twice as large? In one-dimensional systems the spring constants become softer upon coarse-graining, just like the effective capacitance of capacitors connected in series. For instance, if we replace a linear chain of N beads with interatomic distance a by N/2 beads that are separated by 2a, then we need to reduce the stiffness of the coarse-grained springs by a factor of 2. A graphical representation of this analysis can be seen in Figure 3.3. In dimensions greater than one, springs are not only coupled in series but also in parallel. As is the case for capacitors, series coupling decreases the stiffness (capacitance), while parallel coupling increases the stiffness (capacitance). This implies that the stiffness will increase upon coarse graining in higher dimensions, while it decreases in one dimension. The dependence of the
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Figure 3.3 Schematic view of the interaction between chemically passivated LJ solids. Part (a) corresponds to a snapshot of the simulation. Part (b) represents the coupling of a surface atom to its neighbors and the substrate. The parabola indicates the curvature of the potential within the PT model. Part (c) describes the scaling procedure for a one-dimensional elastic chain.
spring stiffness as a function of the system’s dimensionality D and the length scale L on which the system is described can be summarized in the following equation:
k(L) =
L Latomic
D−2
k(Latomic ).
(2)
Scaling laws for the forces between substrate and slider are more difficult to establish. The scaling of these forces strongly depends on the dimensions of the interface Dint . In simple approaches, it is assumed that ks is proportional to the static friction force associated with a rigid domain of linear scale L. In a contact of solids with identical lattice constants, the curvature adds up always in phase, thus ks ∼ N , where N is the number of atoms in intimate mechanical contact. If a flat, but disordered solid is placed on a crystal, different curvatures add up in a random fashion, thus ks ∼ N 1/2 . (Contact between two disordered surfaces follows the same argument.) If the solids are incommensurate, then there will be a systematic annihilation of those curvatures, thus ks cannot grow systematically with N , i.e., ks ∼ N 0 . (The proportionality coefficient may be large for systems close to commensurability.) These arguments can be summarized in the following equation: ⎧ Dint ⎨L ks (L) ∝ L0 ⎩ LDint /2
commesurate, inconmesurate, disorder.
(3)
For a crystalline substrate, the net potential must be a Fourier sum with a leading order coefficient V0 cos(2πx/a + ϕ) or generalizations for higher dimensions. The maximum friction force 2πV0 /a and the maximum curvature (2π)2 V0 /a 2 thus follow the same scal-
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ing laws which are all embedded in V0 . As the area of contact A is proportional to N we may thus conclude ⎧ 0 ⎨A μs ∝ A−1 ⎩ A−1/2
commesurate, inconmesurate, disorder.
(4)
Whenever the ratio k(L)/ks (L) increases systematically with L, one should expect the intrabulk elasticity to dominate and thus expect to have the possibility of superlubricity. In real contacts, due to the roughness at many length scales, the distribution of the normal loads sometimes allow for large values of the local pressures which would increase the value of ks at the local contact regions. In those points it is reasonable to expect elastic instabilities and hence, the loss of superlubricity. However, these instabilities typically require pressures higher than the yield strength of the material. One may thus expect the asperities to yield rather than to deform elastically. 3.2.4
Thermal and Quantum Effects
Temperature certainly has an important effect on friction. It can be incorporated in the PT and the FK model by adding random forces to the equation of motion [19]. These thermal fluctuations usually help the particle to hop from one minimum to the next one, leading to corrections in Fk that are logarithmic, or approximately logarithmic, in velocity within the low-velocity regime, which can be rationalized within Eyring’s theory [20]. Similar corrections can be obtained for the static friction force as a function of the rate of loading. For very small barriers or sliding velocities/loading rates friction can disappear completely. However, practical applications are usually far away from such extreme conditions. In FK chains, point masses also have to overcome energy barriers, which, however happens in a collective fashion via the motion of so-called kinks [21]. Kinks are narrow regions where some atoms will sit close to or on the top of the potential energy. For weak elastic coupling, no particle will sit on top of an energy barrier at zero temperature. This is the reason for the existence of finite static and kinetic friction. At finite temperatures the probability of particles to sit on top of the barrier is not zero any longer. This enables kinks to creep and as a consequence static and kinetic friction vanish provided that the experimental time scales are sufficiently long. Besides trying to understand how thermal fluctuations affect friction, there have also been attempts to study the influence of the ionic quantum-mechanical zero-point vibrations. One study by Popov [22] investigated how quantum fluctuations modify the phononic drag forces between solids, which were sub-summarized in the drag coefficient γ introduced in Equation (1). Popov thus studied friction between incommensurate, weakly interacting solids, rather than friction due to elastic instabilities. It turned out that due to the quantum nature of phonons, the phononic drag forces would decrease with the fourth power of T upon cooling. Krajewski and Müser investigated whether quantum fluctuations automatically depin FK chains [23,24]. They found that this is not the case in contrast to thermal fluctuations. Specifically, for the quantum-mechanical version of the original FK
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model, they identified a critical mass for the FK atoms, below which the chain was depinned (small masses lead to large quantum fluctuations) and above which the chain was pinned, i.e., showed finite friction. For self-affine embedding potentials, no such critical masses exist. The FK chains remain pinned in the thermodynamic limit, no matter how small the atomic masses. It is important to note that in real systems, temperature-induced phenomena cannot only decrease friction, as argued in this section, but also enhance friction. Thermally-assisted plastic flow will increase the effective contact area, which increases the effective load and consequently the friction.
3.3 COMPUTER SIMULATIONS The analytical models discussed in the last section can generally not be used to make quantitative predictions for specific materials, because they elude chemical detail. In some cases, it is possible to parameterize the adjustable coefficients of the models in use such that they reflect the properties of real materials and interfaces. However, even these simplified mathematical representation of solids require the use of numerical methods, molecular dynamics (MD) being one of the most important techniques. In MD simulations atomic configurations are set up in a computer experiment, interactions between atoms are assumed (or calculated with quantum chemical first-principle techniques) and Newton’s equation of motion is solved for each individual atom. The boundary walls are typically coupled to a driving device and boundary conditions are chosen such that a tribological experiment is mimicked in the best possible way. Sliding produces heat, which then requires the use of (artificial) thermostats that remove the heat from a sliding contact. A large part of the literature is concerned with so-called generic models, where the interactions between atoms are only simple two-body potentials. Simulations of generic models can capture many tribological effects qualitatively or in some cases even semiquantitatively. Some of those models will be commented on in the next section. In the context of superlubricity, one important question to address is whether solids generically have the tendency to show finite static and kinetic friction when brought into contact or whether one should expect superlubricity only for very specific materials. 3.3.1
Rough Interfaces, Elastic Solids and Superlubricity
Even highly polished surfaces maintain roughness on many different length scales. The height profile h(x, y) of a surface is a fluctuating quantity. Its first moment corresponds to the average height. A function containing important information on the statistical properties of the profile is the height-difference correlation function C2 (r) defined as 2 C2 (r) = h(0, 0) − h(x, y) ,
(5)
where r is the magnitude of the vector r = (x, y). In many cases C2 (r) increases algebraically with r, i.e., over many orders of magnitude C2 (r) ∼ r 2H , where H is known as
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Figure 3.4 Illustration of the contact between an elastically-deformable solid and a rigid rough substrate. Only the bottom layer of the top solid is shown and explicitly simulated within GFMD. The direction normal to the interface is magnified approximately 20 times with respect to the directions that lie within the interface. The right half of the GFMD layer is represented in a more transparent fashion than its left half. From [31].
the Hurst roughness exponent [25]. Besides the complexity of roughness profiles, other difficulties arise in analytical approaches [16,26,27] to tackle the tribology of real solids. Even numerical approaches of interfaces between solids with realistic roughness on many length scales are still in their infancy [26–31]. These studies are mainly focused on the contact mechanics rather than on sliding. However, as outlined further below, knowing the contact mechanics may allow one to make predictions on the friction between the solids. Recent advances in the numerical treatment of realistic interfaces were made possible by new computational methods. Many of these methods are based on the idea that a system can be described on ever more coarse-grained meshes as one moves away from the contact region [27–30]. A different approach was taken by the current authors, who implemented a Green’s function-based molecular dynamics (GFMD) technique, in which only the outermost layer has to be simulated explicitly [31]. The elastic deformation within the bulk can be integrated out prior to the simulations and encrypted in the effective interaction between surface atoms. Thus, when simulating a flat semi-infinite solid that is placed on top of a rigid, rough substrate, only one layer of atoms needs to be simulated. This is illustrated in Figure 3.4, in which one can see the true microscopic points of contacts, which occupy only a small fraction of the full contact. Note that in these simulations, the macroscopic normal pressure was 10−3 times the Young modulus E of the elastically deformable solid, which would constitute a very large value for most technological applications. An important quantity in contact mechanics is the pressure distribution function P (p). In those regions, where the pressure p exceeds the yield strength of the material, the system will yield and show dissipation. Thus, when P (p) has a significant tail at large values of p, the system must be expected to deform plastically. Moreover, at large values of p, one may expect the onset of instabilities akin of the instabilities in the PT or the FK model. Figure 3.5 shows the pressure distribution calculated for a roughness profile from a highly polished steel surface. One can see that P (p) has essentially vanished at 0.1E. Thus, no instabilities should be expected that are pressure induced at the microscopic scale.
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Figure 3.5 Pressure distribution P (p) in the contact region between elastic bodies with realistic roughness. The solid line shows an exponentially decaying function. From [31].
Figure 3.6 Sliding velocity v as a function of the driving force F divided by the external load L for an elastic solid rubbed over a substrate. Experimental roughness profiles from highly-polished steel surfaces were used in the calculations. Two models are investigated: One which is based on the bare experimental data. The resulting curves are labeled as “without atomic roughness”. In the other model, roughness was artificially added at the atomic scale and labeled “with atomic roughness”. The slope of the dashed line reflects the velocity of a solid that experiences a lateral force F and the damping of the thermostat but no additional friction. In all cases, F is gradually increased.
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Even if the pressure distribution in a contact is known, frictional forces can only be ascertained via sliding. For the system, whose pressure distribution is shown in Figure 3.5, it turns out that kinetic friction vanishes and that static friction, if present at all, must be very small. This can be seen in Figure 3.6: Very small shear forces, i.e., 10−4 times the normal load, are sufficient to initiate sliding. In these simulations, neither adhesion nor adsorbed molecules were included. Thus, the analysis focuses entirely on the competition of intra-bulk elasticity and roughness-induced interfacial forces. The promising result is the absence of instabilities, which thus implies that even rough surfaces can be superlubric. In the calculations, the roughness profiles were taken from experimental data of polished steel surfaces. As the data did not include roughness on the atomic scale but only down to a wavelength of 1 nm, some simulations were run at which typical atomic scale roughness was added artificially. This atomic scale roughness apparently helps to pin the interface, or at least to enhance the dissipation, as evidenced by the much reduced sliding velocities computed at shear forces that were less than 10−4 times the load. It thus appears that the roughness of the very last layer may play a key role for superlubricity, as already pointed out by the Robbins group [29]. 3.3.2
Lennard-Jones Systems
In the previous section, we discussed studies in which the interactions between atoms within solids were predominantly modeled as being elastic. However, many processes, such as plastic deformation, formation of debris, and related phenomena cannot be captured by such simple approaches. A common approach to incorporate the atomistic nature of solids in computer simulations is the study of “Lennard Jonesium,” which is a (virtual) material in which atoms interact through the Lennard-Jones (LJ) potential V (r) = 4ε[(σ/r)12 − (σ/r)6 ], where σ and ε are the LJ length and LJ energy. Using simple two body potentials allows one to validate predictions made for the role that dimensionality, commensurability, surface roughness and other variables play on the tribological properties of a system. In the context of superlubricity, simulations based on potentials as generic as Lennard-Jones, allow one to assess potential limitations to ultra-low friction. Since the detailed molecular structure of the last layer appears to play a crucial role in tribological systems, crystalline materials are favorite targets for computer simulations. One important question to address is at what interfacial strength instabilities and thus solid friction becomes unavoidable. A characteristic example addressing this question investigated the interaction between two solids, each of which was a face-centered cubic solid with (111) surfaces [32]. Figure 3.7 shows a snapshot of the simulations, in which the two solids were brought out of registry by rotating them by 90◦ . An important assumption in the simulations was the absence of chemical reactions between the solids and the lack of contamination on the boundary surfaces. All interactions between identical atoms were normalized in a way that σ = ε = 1 and the LJ parameters for pairs of atoms located on opposed sides of the interface were chosen σi = σ and the strength of (dislike) atoms εi was varied. In order to obtain instantaneous instabilities the ratio εi /ε had to be approximately equal to eight. These instabilities, however, were not elastic in nature, but they involved large rearrangement of the atoms which could be
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Figure 3.7 (a) Low-load configuration of chemically-passivated solids with terraces. Both configurations are [111] surfaces of fcc LJ solids. (b) Snapshot of a configuration that result from configuration (a) after applying a high normal pressure. The friction coefficients remained below 10−2 for both systems.
interpreted as cold welding. If the simulations could be run for much longer times these instabilities could have been observed for any value of εi > ε, because mixing is thermodynamically favorable. As long as the pressure conditions are not extreme and plastic deformation is absent or relatively small, full-atoms simulations of curved tips show that many of the analytical arguments discussed before for flat contacts also apply to curved tips [33,34]. Friction appears to be largest for commensurate, intermediate for disordered and smallest for incommensurate contacts. A significant conclusion arising from those simulations is that large radii of curvature lead to a smaller ratio of lateral and normal pressure. This means that layered materials may be one possibility to achieve ultra-small friction. Despite all the insights from simulations of Lennard Jonesium, many tribological aspects cannot be captured within this model, for instance, whenever directed bonds are important. These play an obviously crucial role in molecular solids, layered materials and other chemically complex solids such as the low-friction Teflon. Also, metals are poorly described by LJ potentials, i.e., the well-known necking during contact formation between bare metals is a consequence of the particular many-body form of metals. Generally, metals have a larger propensity to annihilate free surface than Lennard Jonesium, which favors cold welding. Lennard Jonesium is unable to reproduce these effects and thus more realistic studies are required to predict friction (or the absence thereof) between these materials. 3.3.3
Adsorbed Layers, Confined Fluids and Boundary Lubrication
So far, contaminants, lubricants, or other “third bodies” have not yet been considered in this chapter. However, their presence at the interface has been shown to provide a simple and quite general explanation for the prevalence of static and kinetic friction between solid bodies [9,35–37]. Small hydrocarbon molecules are able to move relative freely along the interfaces thereby producing a local energy minimum. When the pressure increases, these adsorbed films solidify and thus lock the two contacting surfaces, even if their surface geometries do not match. Third bodies are frequently modeled within MD simulations as simple atoms or chains of atoms. Typically, monomers interact with wall atoms via LJ potentials. At large pressures, the repulsive interactions between the monomers and wall atoms dominate. The atoms behave then similar to hard disks or hard spheres. Depending on the radii of the atoms, the lubricant particles penetrate the wells between the wall atoms more or less deeply. In order to start sliding, monomers must overcome the barrier of the ramp defined by the closest surface. This geometric argument yields a static friction force Fs = μL where μ is
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the local slope of the ramp and explains in a semi-quantitative way why the shear stress often increases linearly with normal stress in single-asperity contacts. When the atomic diameters of lubricating or contaminating particles are large compared to the interatomic distances within the surfaces, one would expect small friction coefficients. This argument may explain why superlubricity can be observed experimentally even when no ultra-high vacuum is applied. Of course, one of the most important functions of lubricants is to keep surfaces from making intimate mechanical or chemical contact. Thus, it can reduce the friction by an order of magnitude, in particular in contacts between metals [38]. Interestingly, it has been observed that contacts can be essentially superlubric even under boundary lubricating conditions [39,40]. Zhu and Granick [39] found that the friction between two mica sheets separated by a confined alkane fluid can be exceptionally small, i.e., much smaller than one would expect from the geometric interlocking picture for adsorbed layers suggested in [9,35–37]. Inspired by molecular dynamics simulations that were based on realistic interatomic potentials, Jabbarzadeh et al. [40] proposed that the extremely low friction was due to layering in the confined film. They observed a mechanism similar to solid lubrication in which simple shear planes existed within the fluid—see also the next section. In this scenario, the detailed nature of the confined lubricant proved crucial for the observed superlubricity. More research has to be done. However, the present results are certainly encouraging. 3.3.4
Solid Lubricants and Layered Structures
Solid lubricants are technologically important because of their practical applications in circumstances where liquid lubricants malfunction. Space and ultra-high vacuum technologies are two examples. The most prominent examples of solid lubricants are graphite, WS2 , and MoS2 , which, like other layered materials, have strong chemical bonds within the plane and weak, mostly van-der Waals interactions between the planes [41]. The low-friction behavior of these materials is related to the low shear strength between neighboring layers. For this reason, one would expect that layered solids are natural candidates for superlubric materials. Experimental recent work on the tribological properties of MoS2 suggests a combination of some specific factors as the mechanisms responsible for its extremely good lubrication properties [42,43]. Maintenance of the lamellar structure, oxidation prevention, homogeneous transfer, films formation, and inter-crystallite slip have been considered responsible for its successful performance [44]. Another interesting aspect of many layered materials, in particular graphite and WS2 is their ability to form nanotubes. These nanotubes, unlike atomic force microscope tips whose structures have remained elusive, allow one to study friction in a single-asperity contact for well-defined geometries [45–47]. In many cases nanotubes are multiwalled and the friction forces between the inner and outer tube can be measured within experiments [48]. For incommensurate tubes, nonextensive shear stresses are found suggestive of the dominant roles of surface effects in those systems. In a large number of cases, computer simulations of double-walled nanotubes show extremely small friction forces. While trying to minimize the free energy of the system, in the absence of instabilities only very little amount of heat will be dissipated
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upon sliding. Surprisingly, also commensurate tubes can show small kinetic friction, at least in idealized computer simulations [49]. In the absence of any defects, the net damping calculated for commensurate and incommensurate nanotubes turned out to be of similar magnitude. Idealization of the nanotubes geometry in simulations has proven to be the main source of error when calculating the values of the friction forces [50]. However, one can obtain reasonable good agreement for kinetic friction if chemical details of the fractured end are incorporated into the simulations. Edge defects drive friction calculations to higher values especially when covalent bonds are established between inner and outer tube. In practice, an important disadvantage of layered materials is that the sheets are easily rubbed off. This process leads to the generation of debris and consequently friction increases. This effect may become particularly severe under the presence of chemical point defects. 3.3.5
Metallic Contacts
Metals are obviously not good candidates for superlubric materials, in particular due to their propensity to necking and cold welding. They are yet interesting to study, even in the context of superlubricity, for mainly two reasons: First, the term superlubricity was coined based on a theoretical study of copper interfaces [1] and second, limitations of superlubricity become probably more obvious for metals than for other materials. Under idealized conditions, i.e., absence of contact lines, perfect crystalline structures, etc., it can almost be seen as established that simple, incommensurate metals would be superlubric [15,32,51]. In real situations, however, atomic diffusion and interface reconstruction are certainly important processes at the contact regions between clean metals in ultrahigh vacuum, i.e., when two metallic surfaces are placed in contact, in the absence of contamination, metal atoms will diffuse to maximize the metal/metal and minimize the metal/vacuum surface energies. This welds the two surfaces together and thus leads to friction [38,52]. One can yet ask the question, how much friction one should expect in idealized situations. A particularly interesting study addressed the role of roughness in the very last layer. Qi et al. studied atomically smooth Ni(100)/Ni(1000) interfaces [53]. Their idealized geometries display the same superlubric behavior as expected in idealized copper interfaces. However, roughening the top layer with a mere 0.8 Å variation, changes the behavior completely, with friction coefficients increasing by several orders of magnitude. The calculated values for the surfaces with the 0.8 Å additional roughness match the available experimental data [54] extremely well. Simulations incorporating generic embedded atom models have also been used to compute the friction forces of metallic interfaces. Partial transformations of fcc structures under shear were observed creating transient, grained microstructures. Mixing of the material due to this grain formation was obtained triggering stick-slip motion at large length scales [55]. In another study by Zhang et al. [56], chemical passivated incommensurate Al2 O3 surfaces showed small but yet non-negligible friction at moderate normal loads, although no wear occurred. This behavior is in contrast to that of simple metals, where finite friction typically goes hand in hand with more dramatic structural rearrangements. It is tempting
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to speculate that the directed bonds in the Al2 O3 layers are responsible for wear-less instabilities to occur. Unfortunately, no analysis was made regarding the detailed atomic nature of the instabilities. 3.3.6
Carbon Films and Hydrogen-Terminated Surfaces
Hydrogen-terminated carbon films are probably the most promising candidates as superlubric materials for industrial applications [5,6,57]. Diamond-like carbon (DLC) and carbidederived carbon (CDC) based materials represent the most significant compounds included within this group. They show typical values for the friction coefficient in open air in the range 0.20–0.25. In dry nitrogen, the values may decrease up to 0.15 and using special hydrogenation techniques post-hydrogen-treated films exhibited friction coefficients as low as 0.003 [5]. The difference between the values in dry nitrogen atmosphere (under hydrogen treatment) and open air is commonly explained by the presence/absence of sigma-bonds. Hydrogen treatment effectively reduced or eliminated those bonds providing the small values registered on the experiments [6]. Molecular dynamics simulations of the impact behavior of many hydrocarbon species on DLC physical properties have been reported recently. In particular, the sticking and H-abstraction of those species relevant for the growth of the DLC films via the updated Brenner potential were considered [58,59]. Unfortunately, there have not yet been many simulations concerning friction studies on hydrogen-terminated surfaces. Interesting new results are expected in the near future, in particular from the Harrison group, which makes efficient use of force fields that allow the modeling of chemical reactions. So far, a large fraction of computational studies of chemically-passivated surfaces has been concerned with self-assembled monolayers (SAM) [60–62]. These physical entities are much softer than chemically bonded solids, and thus while being low in friction, they appear to be inappropriate candidates to provide super-low friction. The crucial role that surface orientation plays (commensurability issues) was also found in a second computational work on friction involving monolayers. For truly commensurate layers the (differential) kinetic friction coefficient (∂Fk /∂L) turned out much larger than in those cases where line defects significantly reduced commensurability [61]. The packing density of atoms within the layers and its influence on the local hardness, contributes also to the change in friction. Less densely packed and hence softer systems will become more easily unstable than dense, hard systems. For instance, friction between an amorphous carbon tip and an SAM decreased with increasing packing [62].
3.4
CONCLUSIONS
Analytical models and computer simulations clearly point to the possibility of identifying superlubricity for many pairs of materials. Chemical passivation and smoothness of the interfaces are some of the most important ingredients favoring superlubricity. Also, the absence/saturation of dangling bonds on the contact regions between solids as well as
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the property of some materials to form layered structures appear to be other necessary conditions to achieve ultra-low friction. Systems similar to diamond-like carbon, obtained using hydrogen treatment, are currently the best candidates to show superlubricity. They have very smooth and non-reactive interfaces. In theory, the dangling bonds in this type of systems could be terminated with atoms larger than hydrogen such as fluorine making the surfaces even smoother. However, it may be that fluorinated layers may rub off easily resulting in the formation of debris which could ultimately increase friction. As a last point, we would like to emphasize that superlubricity is not a well-defined term. Some commensurate systems where the static friction is high may not show any kinetic friction at all. To avoid confusion, the term structural lubricity had been suggested. Systems that show small static friction could be named to be structurally lubric (absence of geometric interlocking), while systems showing small kinetic friction (absence of instabilities) are superlubric. Using this terminology, structural lubricity would be a subset of superlubricity. For instance, the small friction between a graphite substrate and a missoriented graphite flake observed by Dienwiebel et al. [7] should be classified as structurally lubric, while Socoliuc et al.’s experiment [8] demonstrated superlubricity (absence of hysteresis) but not structural lubricity, because relatively large instantaneous lateral forces and thus interlocking or finite static friction were measured.
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–4– Ab-initio Atomic Scale Study of Nearly Frictionless Surfaces S. Ciraci1 , T. Yildirim2 , S. Dag3 and O. Gulseren1 1 Department of Physics, Bilkent University, Ankara 06800, Turkey 2 NIST Center for Neutron Research, National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA 3 Center of Nanophase Materials Science (CNMS) and Computer Science and
Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
4.1 INTRODUCTION The dry sliding friction [1–3] of two objects, which are in direct contact through their asperities, involves many interesting and complex phenomena induced by the long- and short-range forces [4,5], such as adhesion, wetting, atom-exchange, bond-breaking and bond-formation, elastic and plastic deformation. In general, phonons are generated and electron–hole pairs are created at the expense of damped mechanical energy. Even the photons can be emitted. The nonequilibrium phonon distribution generated locally is dissipated by phonon–phonon and electron–phonon coupling. Simulations of dry sliding friction between a metal asperity and an incommensurate metal surface have revealed unusual atomic processes [6]. For example, the lateral force exhibits a quasiperiodic variation with the displacement of an asperity; each period consists of two different stick-slip processes involving structural transitions. It has been also found that the perpendicular elastic deformation of the substrate that is induced by the sliding object is crucial in the energy damping in friction [7]. In certain condition, owing to the elastic deformation of the substrate the corrugation of the surface potential energy can be inverted under high loading forces. This situation gives rise to the occurrence of second state (or bistability) in the stick-slip motion and anisotropy in the hysteresis curve [7]. It is also very well-known that the stiffer the sliding surfaces, the smaller is the friction coefficient [7]. The dry sliding friction between atomically flat, commensurate or incommensurate sliding surfaces is perhaps the simplest but most fundamental type of friction in tribology. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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The relative motion of two commensurate surfaces can take place through repeating stickslip stages and hence helps us to visualize the energy damping under weak elastic deformation. However, the situation is rather complex if the sliding surfaces are incommensurate and undergo an elastic or plastic deformation involving the atom-exchange and wear. The atomic-scale analysis of the interaction between sliding surfaces is necessary to understand the nature of non-conservative lateral forces and various mechanisms of energy damping. In fact, studies based on the Tomlinson’s model [8] or calculations using Frenkel–Kontorova model [9] have revealed valuable information about atomic processes in friction. The invention of atomic force microscope [10] and the friction force microscope [11,12] has made an important impact on the science of friction and opened a new field called nanotribology. Nowadays, various atomic processes can be easily observed and lateral forces in the range of a fraction of nano Newton (1 nN = 10−9 N = 0.62415 eV/Å) can be measured with precision by using these microscopes. Meanwhile atomic scale simulations involving several atoms have been performed using realistic empirical potentials [13–18]. Moreover, ab-initio studies based on Density Functional Theory (DFT) [19] treating relatively smaller systems have provided accurate calculations of interaction forces between two surfaces [5,20] and also led to the development of new empirical potentials. Theoretical studies, on the other side, have started to investigate microscopic aspects of energy transfer and energy damping processes [21–24]. While friction invokes the lost of enormous resources, the lowering of the friction coefficient has been the principal goal in various fields of science and technology. Lubricants have been used to lower the friction coefficients and to eliminate the wear in machining and in the transportation industries. In the last decade, progress made in materials science and surface coating technologies has led to a steady lowering of the friction coefficient. Developing of nearly frictionless surfaces or coating materials has been an ultimate goal of tribology and surface physics. In this work we carry out an atomic scale study based on ab-initio (first-principles) calculations and reveal physical mechanisms underlying the superlow friction coefficient in dry sliding friction. To this end, we investigate dry sliding friction between the commensurate surfaces of a covalent crystal (namely friction between two diamond (001) surfaces) and an ionic crystal (namely friction between two BN (001) surface). We examine interaction between bare surfaces and explore the effect of hydrogenation. The organization of this chapter is as follows: We first present general theoretical arguments regarding to the nearly frictionless sliding friction and outline recent experimental progress made in the field. We review theoretical methods and present a short description for the atomistic model and essential features of our ab-initio calculations. Discussion of our results obtained from the ab-initio calculations on the sliding friction of two diamond (001) and two BN (001) surfaces constitute the prime part of this chapter.
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4.2 FRICTIONLESS SLIDING 4.2.1
General Theoretical Arguments
Absence of energy damping in mesoscopic objects has been pointed out earlier [25]. This question can be clarified by examining the energy damping agents involved in friction. These are long- and short-range interactions between two surfaces and various elementary excitations, such as phonon, electron–hole creation, charge density waves and photon emission. High energy excitations such as surface plasmons do not contribute to the energy damping process. Bond-breaking or rebonding, and atom exchange between surfaces and local surface reconstruction can damp mechanical energy and or mediate excitations. Normally acoustic phonons with small excitation energy can easily be excited and hence contribute to the energy damping process. Experiments performed using non-contact AFM [26] have shown that the tip vibrating over the sample gives rise to the energy dissipation even if its minimum spacing from the surface is farther than the range of short-range forces [27–30]. This argument eliminates the possibility that absolutely zero coefficient of kinetic friction, namely μk = 0 can ever occur. Apparently, superlubricity with μk = 0 (reminiscent of superconductivity or superfluidity) cannot be achieved in normal operation conditions, but very low (superlow) friction coefficient is a target one can achieve. The interaction energy, Ei (ρ, z) between two flat surfaces is a function of their spacing z and their relative lateral position ρ = x iˆ + y jˆ. Usually, the interaction energy is small and attractive (i.e. Ei < 0) for large z (z < 0), but decreases (becomes more attractive) as z decreases. It then starts to increase by passing through a minimum and eventually becomes repulsive (i.e. Ei > 0). The attractive interaction energy is specified as adhesion between two surfaces and involves the formation of bonds between surfaces which may give rise to high friction coefficient in the course of sliding motion. Under loading forces Ei can increase and change into repulsive range where elastic and at least local plastic deformations may occur. Substances (solid lubricants, inert gas atoms, etc.) are placed between surfaces to weaken Ei . In ultrahigh vacuum conditions, the friction coefficient as low as μ = 0.01 have been observed for MoS2 and diamond-like carbon (DLC) coatings [31–33]. Even if the lubrication of surfaces coated with such low friction coefficient materials appears to be desirable, the low friction coefficient can increase under different ambient and operation conditions. Coating of surfaces with special materials resulting in repulsive interaction for a wide range of spacing between sliding surfaces is required. Then the loading force will be balanced by the repulsive force derived from the interaction energy, Fz (ρ, z) = −∂Ei (ρ, z)/∂z and the atoms on one surface will be prevented from merging into other surface through a large spacing maintained between them. This way bond-breaking, rebonding and severe deformations will be eliminated. Flying of trains over the superconductive rails is reminiscent of the sliding of surfaces under a repulsive interaction between coated surfaces. In order to reduce the energy damping in the relative motion and hence to lower μk one has to also take the force constants determining the vibration frequencies of atoms into account. It is well-known that the stiffer the sliding surface the lower is the friction constant. Being the principal energy damping agents, the availability of phonons which can get excited by the any sudden release of elastic deformation is not favored. In this respect,
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coating materials made of short and stiff surface bonds are required in nearly frictionless sliding. 4.2.2
Recent Experimental Progress
In an effort to lower the friction coefficient, Erdemir et al. [34–36] reported superlow friction and wear between diamond-like carbon (DLC) coated surfaces using a hydrogen-rich plasma. They achieved kinetic friction coefficient μk as low as 0.001 and wear rates of 10−9 –10−10 mm3 /Nm in inert gas environment under 10 N load and 0.2–0.5 m/s sliding velocities. It has been shown that observed low magnitude and time-variation of μk have a close correlation with hydrogen content of the source gas. This work by Erdemir and his coworkers has been a breakthrough towards the achievement of superlow friction and long durability of moving parts in various mechanical applications ranging from the automotive industry to nanotechnology.
4.3
DESCRIPTION OF THEORETICAL MODEL
Normally, the structure of sliding surfaces contains several types of defects, such as asperities of different shapes and sizes, vacancies, impurities, domains, etc. A realistic simulation of dry sliding friction has to include all these defects. Hence the atomistic models of sample surfaces have to comprise a large number of atoms. In this respect, the classical molecular dynamics (CMD) method using empirical potentials to represent atomic scale interaction is convenient for the simulation of friction process. Recently, various processes have been simulated and new structures have been predicted by using empirical potentials developed for certain systems. Since numerical calculations using these empirical potentials are not time-consuming, large systems comprising several thousands of atoms have been treated. However, the main drawback of CMD simulations appears when a completely new system is treated. In particular, when the character of the surface atoms (such as their effective charge and bonds) deviate dramatically from those of bulk structure. Under these circumstances, whether the empirical potential parameterized using the bulk properties becomes questionable. On the other side, ab-initio calculations can provide reliable results for the optimized atomic structure, mechanical, electronic and magnetic properties and phonon density of states of a given system, if it involves small number (200–300) of atoms. Various mechanisms underlying the energy dissipation and estimations of friction coefficient with upper and lower limits can be revealed. In this respect, ab-initio methods are superior to classical methods if the system can be represented by 200–300 atoms. Besides, ab-initio methods are complementary to CMD in revealing the correct charge and bonding structure and hence in developing reliable empirical potentials. 4.3.1
Atomistic Models and Details for Ab-initio Calculations
In this study, sliding surfaces are represented by two infinite slabs made from the atomic layers of the coating materials. The atoms of slabs are treated in two different categories. In the first category, the atoms at the back surfaces of both slabs are kept fixed in their ideal
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configurations, xi , yi , zi . The layers of fixed atoms represent sample or coating layers away from the sliding surface. Normally, they are not affected from the friction process. By displacing all the fixed atoms of one slab relative to the fixed atoms of the other slab one can achieve a lateral displacement of two slabs and induce a loading force. The atoms at the surface region of the slabs facing each other are treated in the second category and are relaxed while the first category atoms are fixed at given xi , yi , zi positions. This way, relative sliding of two slabs including atomic displacements, elastic and plastic deformations, etc. are modeled from the first-principles. The atomic process and forces in sliding friction have been investigated by carrying out calculations from the first-principles within DFT, which were proven to yield accurate predictions for many metal and insulator surfaces. Here we present crucial parameters of first-principle calculations. The sliding friction is treated either by supercell method using periodic boundary conditions or by finite size surfaces using local basis set. In the supercell method, the wave functions are expressed in momentum space. The magnitude of the largest wave vector sets the cutoff energy and hence the number of plane waves used in the expansion. The ionic potentials are represented by ultrasoft pseudopotentials [37,38] and then the cutoff energy is taken 300 eV. The exchange correlation potential is represented by using Generalized Gradient Approximation [39]. The Brillouin zone corresponding to the supercell is sampled within the Monkhorst–Pack special k-point scheme [40]. Optimization of atomic positions is performed by conjugate gradient method. Lateral components Fx , Fy and perpendicular component Fz of the net force induced between two slabs are calculated. We did not included the long-range Van der Waals force since it is negligible as compared to the perpendicular force Fz induced under high loading force FN .
4.4
SUPERLOW FRICTION COEFFICIENT BETWEEN HYDROGENATED DIAMOND SURFACES
Hydrogenated DLC (H:DLC) coating by all means is a complex, amorphous structure showing various irregularities. The sliding surfaces cannot be commensurate and contain irregularly distributed asperities and perhaps voids. We believe that determination of the structure of DLC by itself is important and treated earlier [42]. However, even if the structure of H:DLC realized in superlow friction [34–36] and also physical and chemical processes taking place in the course of friction are stochastic in nature, the local bond orders and C–H bond topology are expected to be similar to various hydrogenated diamond surfaces. Therefore, the interaction between H:DLC surfaces and the nature of interaction between these surfaces can be understood by using two hydrogenated diamond surfaces. In this section we will present our study of superlow friction coefficient between two hydrogenated diamond (001)–(2 × 1) surfaces using first-principle plane wave method [41]. Clearly, our study does not promise a realistic simulation of the experiment resulted with superlow friction coefficient [34]. Our objective in this atomic scale study is to better understand the physical mechanisms involved in the superlow friction observed between hydrogenated DLC coated surfaces [34]. We hope that the ingredients of the superlow friction coefficient revealed from our study will be useful for developing new coating materials
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which are stable in the desired operating conditions. In particular, developing coating materials which can sustain to ambient conditions and oxidation is the objective our study. How simple our model can be, its two features are of particular importance. These are the full relaxation of surface atoms at any instant of sliding process, and accurate calculation of the variation of lateral force components under the constant loading force FN . Diamond (001)–(2 × 1) surfaces are represented by two slabs facing each other at a distance. Each slab consists of 6 layers of carbon atoms. Carbon atoms at the back surface of each slab are saturated by hydrogen atoms. The atomic structure of the one individual slab is first optimized and then the carbon atoms at the 6th layer (at the back surface of the slab) and saturating H atoms (i.e. those atoms in the first category) are kept at their equilibrium positions. We believe that such configuration mimics the semi-infinite slab (or thick coating). Figure 4.1(a) illustrates two diamond (001)–(2 × 1) slab with H saturated, fixed back sides. The other surfaces of slabs face each other and are free when the distance d between them is large. The structural parameters of the bare surface which reconstructs to form dimer bonds are successfully reproduced. The normal force Fz originate from the short-range interaction between the surfaces of the slab. To this end, we kept the distance D between the back surfaces of the slabs at the preset value and calculated the total energy of whole system, ET (D, ρ) and total force on one of the slabs. Here the total energy and total force are obtained after the optimization of positions of atoms in the second category. We note that since two slabs are pressed against each other by fixing D, the calculated forces on the atoms at the back side balance the external (loading) forces which maintain D at a preset value. Therefore, total calculated
Figure 4.1 (a) Two diamond (001)–(2 × 1) slabs used to model the sliding of two diamond (001) surfaces. Carbon atoms at the back sides of the slabs are saturated by H atoms. The positions of these carbon atoms and those of saturating H atoms are fixed at the configuration corresponding to that obtained from the optimization of individual (free) slabs. The distance between the back surfaces of slabs is D, and that between two sliding surfaces facing each other is d. The crystal directions are identified by Cartesian axes shown by inset. C and H atoms are shown by filled and empty spheres, respectively. (b) Calculated normal force Fz is generated when two diamond (001) slabs are pressed towards each other by decreasing D and hence d. do and d correspond to spacing between two sliding diamond (001)–(2 × 1) surfaces before and after relaxation. (Reproduced from [41].)
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vertical force on one of the slabs is equal to the vertical interaction force Fz . By definition the loading force FN = −Fz . The variation of Fz is plotted in Figure 4.1(b) with respect to the separation between slab surfaces before relaxation, do , as well as the actual separation, d after the relaxation. The interaction is weak and repulsive for d > 2.75 Å, but Fz becomes attractive as D decreases and then jumps to contact attaining the value approximately equal to −6 eV/Å. Strong bonds form between the sliding surfaces of two diamond (001)–(2 × 1) slabs near equilibrium separation corresponding to Fz ≃ 0. Once a normal force is applied to press the slabs against each other, atoms of different surfaces come close to each other at d ∼ 1.5 Å and subsequently Fz becomes repulsive. Under these circumstances, since the sliding motion can involve local deformations, bond-breaking and rebonding, the dynamical friction coefficient, μk as well as the wear rate are expected to be high. In fact, the dynamical friction coefficient has been measured to be equal to 0.65 for the sliding DLC-coated surfaces which are free of hydrogen. 4.4.1 Force Variations in the Sliding Friction of Two Hydrogenated Diamond Surfaces
First, we will examine the variations of normal force when the sliding diamond surfaces are hydrogenated. Dangling bonds of carbon atoms on two slab surfaces facing each other are saturated by H atoms to form a monohydride phase, i.e. H:diamond (001)–(2 × 1). Upon the saturation of the surface dangling bonds the dangling bond surface states disappear and a wide energy gap opens between the valence and conduction bands of the slab. The surface charge density differs dramatically from that of the clean diamond (001)–(2 × 1). In Figure 4.2 we show the atomic configuration of the H:diamond (001)–(2 × 1) surfaces. Moreover, Mulliken analysis indicates that 0.25 electrons are transferred from H atom to the C atom that is bound to it. This situations complies with the fact that the C atom is more electronegative than the H atom. As a result, the H atom is positively charged. The depletion of electrons on H atoms induces a repulsive interaction and hence a repulsive Fz even for d < 2.5 Å between H:diamond (001)–(2 × 1) surfaces. This is the most essential feature in obtaining superlow friction coefficient from H:DLC coated sliding surfaces. The variation of Fz with spacing d is shown in Figure 4.2. This repulsive force Fz keeps the sliding surfaces wide apart at a distance d and balances the loading force FN . As a result, sliding surfaces are prevented from being too close. This way, deformation of C–H bonds are suppressed to a great extend. It is interesting to note that like carbon silicon is also a Group IV element and has diamond structure. A strong attractive interaction is generated between clean Si (001) slabs. However, similar to diamond (001) slabs, the attractive interaction turns repulsive upon the hydrogenation of Si (001) surfaces and generates a strong repulsive normal force. It appears that H:Si (001)–(2 × 1) displays a feature similar to that of H:diamond (001)–(2 × 1). We next examine whether this feature, namely the repulsive normal force between surfaces can lead to superlow friction coefficient. 4.4.2
Sliding Friction of Hydrogenated Diamond (001) Slabs
Having examined the perpendicular variation of Fz , we now address following questions: (i) Does the repulsive interaction continue to keep surfaces wide apart, if one of the diamond slabs is laterally displaced relative to other one. (ii) What is the range of FN
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Figure 4.2 (a) Atomic configuration of two diamond (001)–(2×1) slabs with the dangling bonds on the surfaces facing each other are saturated by hydrogen atoms to form monohydride phase H:diamond (001)–(2 × 1). The spacing d between these surfaces, normal force Fz , loading force FN . (b) Variation of the calculated normal force Fz between the two surfaces of H:diamond (001)–(2 × 1) as a function of their actual, relaxed separation d. Fz is generated when two diamond (001) slabs are pressed towards each other by decreasing D. The inset shows the variation of the same force between hydrogenated Si (001)–(2 × 1) surfaces. Right: Directions of the loading force FN , Fz , lateral force components Fx,y , and lateral displacements, x and y. Lateral force component, which is in opposite direction of displacement is indicated by superscript “<”. (Reproduced from [41].)
where the repulsive interaction between surfaces persists without any serious deformation? (iii) Can one present an upper limit for the friction coefficient? To answer all these questions we carried out a series of first-principle calculations for the interaction energy Ei , normal force Fz , lateral force FL corresponding to different loading force (hence D) and displacements ( x, y) of the upper slab. In these calculations, all the atoms have been relaxed, except C and H atoms at the back side of both slabs. The latter atoms are kept fixed in their ideal configurations after their planes are displaced to different perpendicular and lateral positions by varying D and ( x, y) in sequential increments. We note that by keeping two back ends of slabs at a distance D but relaxing the rest of the atoms induces a loading force FN (D), which in turn is balanced by Fz . Fz itself is obtained from the sum
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Figure 4.3 (a) and (b) Variation of the calculated interaction energy Ei as a function of the perpendicular distance d calculated at the different lateral displacements x and y. (c) and (d) The same variation of the normal force Fz . Energy and force units correspond to per (2 × 1) unit cell. (Reproduced from [41].)
of the perpendicular component of calculated forces on the fixed atoms of one of the slabs. Namely Fz = i Fz,i , where i is the index of fixed atoms of one slab. The same sum on the other slab yields Fz with the same magnitude but in opposite direction. Similarly, the lateral forces along x (or y) axis are obtained from the sum Fx(y) = i Fi,x(y) . Performing ab-initio calculations of Ei , Fz , Fx,y as a function of d (or D) at different relative lateral positions, x and y a data base is created. In these calculations, the values of D have been varied in small steps to yield normal forces in an appropriate range of interest. Figure 4.3 presents calculated variations of Ei and Fz as a function of d for different lateral displacements, x and y, of the top slab. Here we note that the interaction energy Ei = ET − ET ,d=∞ , where ET ,d=∞ is the total energy corresponding to very large d (or twice the total energy of one slab in the absence of the other one). We note that the variation of Ei and Fz is not a smooth function owing to discrete changes of D and to the relaxation of the C–H bonds. Note that since Fz remains always repulsive and strong even at significantly large spacing, the sliding surfaces are kept apart even for large loading forces. As a result, C–H bonds of different surfaces neither merge nor interfere with each other. In the course of sliding C–H bonds experience neither significant deformation (i.e. bending, stretching or shrinking) nor wear through bonding–rebonding.
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If the sliding motion were adiabatic, no energy would be damped in sliding motion of two commensurate surfaces like we treat here. However, this is not the case; various sudden processes generate excitations and give rise to energy damping. Now we present a global approach to estimate an upper limit for μk using the variation of the lateral force from the present calculations. To this end we consider displacements along x- and y-axis and we construct lateral force variation under the given constant loading force using our data base, namely FL=x ( x, y = 0, FN ) and FL=y ( x = 0, y, FN ). Keeping the loading force FN constant is the most difficult part of our study and requires a large number of numerical calculations corresponding to different x, y and D. We considered the loading force FN = 1 and 1.2 eV/Å per cell, which are actually too high as compared to the loading force in the experiment [34] as well as in practical applications. In this respect, our estimation of μk is a stringent test. The variations of Fx and Fy are illustrated in Figure 4.4. For the reasons pointed out earlier the variation of lateral force is not smooth. Since lateral force is calculated using coarse displacement steps of D, the elastic deformation of slabs and C–H bonds induced by sliding are released suddenly. This gives rise to the stick-slip process as described by the Tomlinson’s model [8]. Of course, error bars involved in the calculation of forces. In particular, achieving the constraint of the constant loading force by limited number of data in the data base generated through ab-initio calculations can lead to hysteric variation of the lateral force. Now as an ad hoc approach to estimate μk in an energy damping medium, we assume that the work done by the lateral force FL (i.e. when it is parallel to the direction of motion as denoted by FL> ) is totally lost. Then the average friction force is calculated by F f = Fx< dx/R, R being the period of the motion. Using the data in Figure 4.4 we extract the average friction force, F f ∼ 0.05 eV/Å for FN = 1 eV/Å and F f ∼ 0.07 eV/Å for FN = 1.2 eV/Å. Then the kinetic friction coefficient 0.05 for both cases. A more realistic is calculated from μk = F f /FN to be approximately < > estimation could be obtained from F f = (Fx + Fx ) dx/R if lateral force variation were calculated precisely. Although our force variations in Figure 4.4 are too crude to obtain precise values, μk is calculated for the sake of comparison to be ∼0.01.
Figure 4.4 (a) Variation of the lateral force, FL=x [in eV/Å per (2 × 1) cell] as a function of the displacement x of the top slab relative to the bottom one. (b) Same as (a) for the displacement y. In the course of sliding the loading force FN is taken approximately constant. (Reproduced from [41].)
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Figure 4.5 Calculated atomic configurations showing the effect of the oxygen atom on the H:diamond (001)–(2 × 1) surface. (a)–(d) The oxygen atom is placed at different sites of the surface unit cell before the relaxation of the surface. (a′ )–(d′ ) Atomic structure and bonding after relaxation of the system. The adsorbed oxygen atom is negatively charged. (Reproduced from [41].)
It should be noted that in the sliding of commensurate surfaces the lateral forces acting on each atom or cell are added constructively to yield a high total lateral force. These lateral forces are, however, conservative and do not give rise to energy damping, if the sliding motion is adiabatic. In the case of incommensurate surfaces, the total lateral force is relatively lower owing to the cancellations. H:DLC coated surfaces can be viewed incommensurate except that the disorder gives rise to higher energy damping. Consequently, the above estimation of μk obtained from hydrogenated diamond surfaces with the assumption that all mechanical energy stored into elastic is damped, is an upper limit for H:DLC coated surfaces; but it is still too low. 4.4.3
Effect of Oxidation
That the superlow friction coefficient obtained from H:DLC coated surfaces cannot be sustainable in the ambient conditions is the most serious issue [34,35]. The oxygen atom is the potential candidate which destroys the superlow friction when H:DLC coating is exposed to the air. In what follows, we clarify the effect of oxygen on the hydrogenated DLC coating leading to superlow friction. To test the effect of oxygen, we placed O atoms at the proximity of different sites of the H:diamond (001)–(2 × 1) surface. Upon relaxation, the system attains the minimum energy configuration, whereby O atoms break the surface bonds to form new C–O–C, or C–O–H and C–O bonds and hence they become attached to the surface. Favorably, they attacked the C–H bonds to form C–O–H radicals. Charge
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transferred to O from H and C makes O atom negatively charged as shown in Figure 4.5. This way the interaction between two atoms in different surfaces can be attractive when they carry charge of different polarity. As a result, the steady and strong repulsive interaction between the H:diamond (001)–(2 × 1) surfaces gradually becomes weaker or turns attractive. Eventually, the superlow friction ends.
4.5 AB-INITIO STUDY OF ATOMIC-SCALE FRICTION BETWEEN CUBIC BN-SURFACES We believe that BN crystal is very hard and is expected to yield very low friction coefficient in the dry sliding [47]. In view of what we learned from hydrogenated diamond surfaces, we next investigate atomic-scale friction between two cubic BN-slabs as shown in Figure 4.6(a) using the computational approach discussed above. These two slab are placed in a supercell with lattice constant c = 24 Å. Each slab consists of 5 atomic (100) planes. Atoms of last two layers are fixed in their equilibrium bulk positions but otherwise relax all the atomic degrees of freedom using a temperature annealing minimization as a function of slab–slab distance, D and translation (along x-direction). In order to study the effect of the hydrogenation of the layers on the friction coefficient, we also consider two different hydrogen-saturated BN-surfaces as shown in Figure 4.6(b)–(c). For each system we have performed about 300 calculations, yielding almost thousand different configurations for the three systems shown in Figure 4.6.
Figure 4.6 Three different slab structures that we considered in this study. (a) BN layers, which forms N–N-dimer on the surface. (b) Single hydrogen-passivated BNH slab with bended NH-bonds. (c) Doubly passivated BNH2 slab. The distance between the fixed-B atoms on the top and bottom slabs is shown as “D”. The relevant bond-distances and atomic charges for these three structures are summarized in Table 4.1.
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Table 4.1. Chemical formula, bond distances (in Å), and Mulliken atomic charges (in electrons, e) for three systems shown in Figure 4.6. The lattice parameters of the supercell are 7.23 × 7.23 × 24 (Å) for all three systems. Below Qs and Qb indicates the atomic charges for atoms at the consecutive layers, respectively System
Formula
Bond distances (Å)
Charges (e)
BN
B48 N48
dNN = 1.42, dNB = 1.56
BNH
B48 N48 H16
dNH = 1.02, dHH = 2.56, dNN = 2.56
BNH2
B48 N48 H32
dHH = 1.43, 2.61, dNH = 1.02, 1.08, dNN = 2.56
Q1 (N) −1/3, Q2 (N) = −2/3, Q3 (N) = −2/3, Q1 (B) = 1/3, Q2 (B) = 2/3, Q3 (B) = 2/3 Q(H) = 0.38 Q1 (N) = −0.78, Q2 (N) = −0.63, Q3 (N) = −0.66 Q1 (B) = 0.71, Q2 (B) = 0.64, Q3 (B) = 0.35 Q(H) = 0.25, 0.39 Q1 (N) = −0.91, Q2 (N) = −0.65, Q3 (N) = −0.65 Q1 (B) = 0.66, Q2 (B) = 0.62, Q3 (B) = 0.29
We first studied the total energy as a function of slab–slab distance as shown in Figure 4.7. For BN-layer, when the slabs are far enough, the energy is nearly zero and then goes to a minimum and then increases, with a attractive energy of 0.6 eV (Figure 4.7(a)). The N atoms on the surface are negatively charged by Q = −0.33 electrons owing to the ionic nature of BN compound. The charge on the bulk N atoms are even larger. It is noticed that when two slabs is put close enough, the N atoms on different slabs are bonded to each other, resulting sudden decrease in the energy. However this adhesive behavior requires about 1 eV energy barrier. Figure 4.7(b) shows the effect of the single hydrogenated BN-layer on the binding energy of the slabs. The energy curve is very different than that of bare BN layer shown in Figure 4.6(a). It has almost no minimum and mainly repulsive. It should be noted that GGA underestimates some of the vdW attraction. In principle, the interaction between two slabs should become slightly attractive when the Van der Waals interaction were included. This suggests that single hydrogenation of N atoms on the surface is expected to reduce the friction significantly and yield superlow friction coefficient. During the structural optimization of the BNH-layers, we also found a second metastable minima where the H-atoms are attached to B atoms and aligned perpendicular to the surface. However the system lowers its energy by about 1.4 eV/bond when the NH-bonds are bent so that BN-bond is parallel to the BN bonds as in the bulk (Figure 4.6(b)). Finally Figure 4.7(c) shows what happens if we saturate the N atom on the surface with an additional hydrogen atom. The energy curve looks like the bare BN layer but slightly larger binding energy of 0.9 eV. Hence, saturating with more hydrogen atom does not automatically mean that we would minimize the attractive part of the potential and make it repulsive. We anticipate that the large binding energy for the BNH2 case is mainly due to large atomic charges and thus the Coulomb interaction between the two slabs. Finally, while we study the different (D or z and x) slab configurations for BNH2 , we observed that when the top slab moves along x-axis by about the half of the lattice constant at small slab–slab distances, two hydrogen atoms on the different slabs actually are bonded to each other forming a H2 molecule. The energy curve of the minimization as this process occurs is shown in Figure 4.8 along with the final system configuration where we have now one free H2 molecule. Hence for BNH2 surface, we expect reconstruction on the surface
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Figure 4.7 Energy curves as the slab–slab distance D is varied for (a) BN, (b) BNH, (c) BNH2 slabs, respectively. Note that for BNH system, the potential curve is very flat and mainly repulsive. For BNH2 –BNH2 we observed H2 formation from two hydrogen atoms of two slabs for D < 9.0 Å. This reconstruction of the slab surface is shown in Figure 4.8.
as the slabs move with respect to each other. When the slab–slab distance, D, is small enough, we also observe similar reconstructions even for bare BN-slabs as we discuss it briefly below.
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Figure 4.8 Energy curve during the structural minimization. When two slabs are close enough, the system lowers its energy by forming a free H2 molecule as the top slab moves along x-direction.
Figure 4.9 summarizes the energy and z-component of the total force (i.e. normal force) for the BN system for different values of slab–slab distance D as the top slab is translated along the x-axis. For most of the slab–slab distances (i.e. D = 10.6–11.0 Å), the energy first increases, reaching its maximum at half-way x-translation and then decreases back. When the top slab is translated by one-lattice vector, we recover the original structure back, indicating that we are at the elastic regime. However this is not the case for D = 10.4 Å or smaller slab-distances. Interestingly for D = 10.4 Å, the energy start to increase normally as the top-slab is being translated up to x/a = 0.5 (a is the lattice constant of the surface unit cell along x-direction) but then the energy curves does not go back to its original value; instead continue to increase. This behavior becomes clear when we inspect the optimized atomic positions as the slabs are being translated along x-axis. We find that at D = 10.4 Å, the slab–slab interaction causes the N–B bond on the surface to break, increasing it from 1.56 Å to 1.75 Å. This is shown in the inset to Figure 4.9. In fact, for slab–slab distances less than D = 10.4 Å, we also observed that the broken N-atom actually forms a new bond on the other N-atom of the other slab. Hence we expect to see adhesive behavior between two BN-slabs when they are put together close enough. We note that the optimum distance between two BN-slabs is about 10.8 Å (see Figure 4.6). Hence it is quite interesting that at D = 10.4Å (which is not too much different than 10.8 Å), there are already significant surface reconstructions. Figure 4.9(b) shows the normal forces acting on the BN slabs for different slab–slab distance. It shows an interesting variation; becomes almost flat with respect to slab translation at z = 10.7 Å. Since the Fz is almost constant at this particular z, it is very convenient to calculate the atomic-scale friction using this particular slab–slab distance. We will discuss this further later. Figure 4.10 summaries the energy and force curves for the BNH slab. The nature of BNH–BNH slab interaction is very different than BN-slabs. This is clear by comparing the
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Figure 4.9 Energy and normal forces Fz as the top slab is translated along x-direction with respect to bottom slab for different slab–slab distance D. For D = 10.4 Å, we observe significant surface reconstructions involving broken BN-bonds as depicted in inset to top panel.
curves shown in Figure 4.9 and Figure 4.10. We note that Fz force acting on the BNH layer does not become constant for any slab-distance that we studied (unlike the BN case). The energies shown in Figure 4.10(a) are much smaller indicating the weak slab–slab interactions. Below we will combine the data presented in Figure 4.10 to obtain roughly constant force loading and estimate the atomic friction force. As a last point, in Figure 4.11 we show some example plots of the forces on the slab as one of the slab is translated along x-direction for the three cases. We note that the resulting forces are oscillatory function of x-displacement for BN layer while it is very noisy for BNH2 layer. This is a nice demonstration of the effect of the surface structure on the energy and forces. In the case of BN layers, the surfaces are identical and in phase (or commensurate) with respect to each other. Therefore when one surface slides we see large variations in the energy and forces. However for the case of BNH2 system, the surface structure is quite complicated due to four H atoms and therefore two surfaces almost random (incommensurate) with respect to each other. Hence when we translate one slab, it
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Figure 4.10 (a) Energy and (b) normal forces Fz as the top BNH slab is translated along x-direction with respect to bottom slab for different slab–slab distance D.
does not change the energy or the forces with respect to each other. This confirms the fact that the friction coefficient is usually low between incommensurate surfaces. Finally we obtained an estimate for the friction coefficients using the forces shown in Figure 4.11. For the normal loading force, we integrate the Fz over the cell to obtain an average force. For the x- and y-components of the lateral force, if we integrate them over the cell, we always obtain very small number from 0.01 to 0.001 eV/Å, suggesting that the most of the relaxation process during the minimization is in the elastic range. If one assumes that the induced strain or energy is efficiently removed from the system by phonons, then we can estimate an upper limit for the friction. In compliance with the discussion in Section 4.4.2, for this purpose, we calculate the average value of the lateral force Fx which is in opposite direction of the displacement. The average values are given in Figure 4.11. We note that by hydrogenating the BN layers, we reduce the friction coefficient significantly (which is given by μk = Fx /Fz = 0.06). BNH2 layer has slightly lower friction coefficient (μk = 0.03) than BN layer even though the energy dependence of the slab–slab interactions are very different. In the case of BN, it’s mainly repulsive while in the case of BNH2 it has strong attractive component. However as we discussed above, the friction is
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Figure 4.11 Forces as the top slab is translated along x-direction with respect to bottom slab. The values of the absolute-averaged forces over the unit cell are also given. For Fx and Fy , the average forces are nearly zero (less than 0.01 eV/Å). The numbers are for the integration of the absolute forces for (a) BN, (b) BNH, (c) BNH2 slabs, respectively.
very low in BNH2 because the incommensurability of the surfaces due to complex atomic structure of the surface. The above atomic-scale study of dry sliding friction between bare and hydrogenated cubic BN (001) surfaces exhibit differences from that between two diamond (001)–(2 × 1) surfaces. While the interaction between bare BN (001) surfaces weakly attractive, it be-
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comes strongly repulsive upon H-saturation of each N atom. On the other hand, the dihydride formation on BN-layers by adsorbing two hydrogen atom to each N atom show strong attractive potential. However, the resulting forces and variation in the energy as the slabs are translated with respect to each other is still small. This is due to a different effect; namely the incommensurability of the surfaces with respect to each other. With two H atoms saturating N atoms, we obtain complicated surface structure and therefore as one slide moves with respect to other, nothing is really changed, resulting small forces and binding energy. Stated differently, even if |Fz | is large, lateral force components, Fx and Fy may become small due to cancellations. We also observed that under very large loading forces (with activation energy of several eV), it is possible to obtain surface reconstruction and even H2 formation by breaking the NH bonding.
4.6 CONCLUSIONS We presented a comparative study of the dry sliding friction between the atomically flat and commensurate surfaces of two different systems, namely between two diamond (001) and between two BN (001) surfaces. While the interaction between bare diamond (001)– (2 × 1) surfaces is strongly attractive until small spacing d ∼ 1.5 Å and forms strong chemical bonds between two surfaces. However, the interaction turns repulsive if two surfaces are pushed under high loading force. Upon hydrogenation, hydrogen atoms donate charge to the carbon atom and become positively charged. Then the interaction between surfaces carrying the same type charge becomes repulsive. This appears to be the most important ingredient of the superlow friction. The repulsive interaction persists at any relative position of the sliding surfaces and is strong even at large distance to prevent C–H bonds from merging. Strong and stiff C–H bonds and stiff diamond crystal by itself prevent excessive energy from dissipation. It is found that oxygenation of surfaces in the atmospheric conditions destroy the steady repulsive interaction. However the interaction between two bare reconstructed BN (001) surfaces are different from that of the diamond (001) surface due to ionic nature of the crystal. BN being an ionic crystal with electron transfer from B to N the bare surface is already negatively charged. Under these circumstances the strong chemical interaction is canceled by the repulsive Coulombic interaction resulting in a weak attractive interaction (or adhesive forces). As a result, the friction coefficient is already small in dry sliding friction two bare BN (001) surfaces. Upon saturation of each N atom by a single H-atom the weak attractive interaction is further reduced. This situation changes when single N atom is saturated by two H atoms, and the interaction becomes again attractive. The present analysis of dry sliding friction between bare and hydrogenated BN (001) surfaces indicate that this material is a potential candidate for superlow friction.
ACKNOWLEDGEMENTS This work was supported by Scientific and Technological Council of Turkey, TÜB˙ITAK under Grant No. TBAG-104T537. Authors acknowledge the useful assistance of Engin Durgun in preparation of the manuscript.
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–5– Molecular Dynamics Simulations of Tribology J. David Schall1 , Paul T. Mikulski2 , Ginger M. Chateauneuf1 , Guangtu Gao1 and Judith A. Harrison1 1 Chemistry Department, US Naval Academy, 572 Holloway Road, Annapolis,
MD 21402, USA 2 Physics Department, US Naval Academy, 572 Holloway Road, Annapolis,
MD 21402, USA
5.1 INTRODUCTION During the past two decades, there has been much research devoted to the study of atomicscale friction. Steady advances have been made experimentally through the use of devices such as the atomic force microscope (AFM), whereby a nano-scale tip (essentially a single asperity) mounted to a cantilever is dragged across a prepared sample. With knowledge of cantilever and tip properties, inferences can be made about friction and load from the deflections of the cantilever. Related technologies, such as the friction force microscope and surface-force apparatus, are also used to probe experimentally the tribology of many liquid and solid systems with nanometer, and sometimes atomic, resolution. Complementing experimental work, computational studies of atomic-scale tribological processes using molecular dynamics (MD) have provided much insight due to the direct information they can yield about individual atomic interactions. Even with the rapid growth of computational power, dealing effectively with time-scales and system sizes is still challenging. Model systems typically include thousands of atoms and system sizes in the range of tens of thousands of atoms confine typical dimensions of the simulated tip and sample to no more than tens of nanometers in any direction. Given that AFM tips used for investigating tribology can have radii of curvature of over one hundred nanometers, it is common to employ periodic boundary conditions in the plane of the sliding interface in MD simulations. Furthermore, with first principle or quantum mechanical ab initio calculations being limited to system sizes of hundreds of atoms, atomistic tribology simulations traditionally have been approached through the use of empirical classical models of atomic interactions. Such models are built by fitting functional forms for interatomic interactions to experimental data and the results of ab initio calculations. The functional forms may Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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range from simple mathematical approximations of atomic interactions to more complex models based on sound quantum–mechanic bonding principles. With regard to time-scales, adopted sliding speeds for simulations are usually much higher than what is utilized experimentally. Simulated times typically are of the order of a nanosecond at most for simulation with time-steps in the range of a fraction of a femtosecond. Fortunately, and perhaps somewhat surprisingly, simulation results have been shown to be insensitive to sliding speeds ranging over orders of magnitude for systems under significant loading [1]. Despite these challenges, MD provides a way of probing fundamental processes that is unsurpassed in terms of its level of detail and directness. Consequently, MD has proven to be an invaluable aid in the interpretation of atomic-scale experimental studies that are beset with their own distinct challenges. The following serves as a review of the use of MD in the study of tribology. Section 5.2 reviews the MD technique with some emphasis on issues that are of particular importance to using MD in the study of tribology. Section 5.3 reviews some of the reactive potentials that have been used heavily in the study of atomic-scale friction along with some historical perspective of their development and use. Finally, Section 5.4 concludes with some of the recent work by Harrison and coworkers on the tribology of amorphous carbon films and self assembled monolayers (SAMs).
5.2 MD SIMULATION METHODS 5.2.1
Outline of Method
In molecular dynamics simulations, atoms are treated as discrete particles whose trajectories are followed by numerically integrating classical equations of motion. After the geometry and boundary conditions of the system are specified and the initial position and velocity of each atom are given, numerical integration is carried out. Typical timesteps range between 0.1 to about 15 femtoseconds depending on the largest vibrational frequency of the model system. Instantaneous values of quantities such as energy, force, velocity, strain, and stress can be calculated at regular intervals and saved for post-simulation analysis. Two numerical integration schemes that are widely used in MD are the Gear predictor-corrector method [2] and the Verlet methods [3,4]. Doing work on a system through the application of external forces, as is done during sliding or indentation, can result in a rise in internal energy and temperature of the system. Therefore, methods of dissipating excess energy and maintaining a constant temperature must be employed in computer simulations. In the following, we briefly discuss three popular temperature regulation approaches. For details, the reader is referred to Allen and Tildesley [4]. A sophisticated approach to maintaining a given temperature is through Langevin dynamics, which was originally used in describing Brownian motion [5,6]. In this approach, additional terms corresponding to a friction force and a random force are added to the dynamic equation of motion of each atom, mv˙ = F − mξ v + R(t),
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where F is the force due to the interatomic potential, m is the atom’s mass, v is its velocity, ξ is a friction coefficient, and R(t) represents a random “white noise” force. For heat flux via nuclear (as opposed to electronic) degrees of freedom in solids, it has been shown that a reasonable approximation for the friction coefficient ξ is 6β/π , where β is the Debye frequency of the solid. The random force is sampled from a Gaussian distribution where the width, which is chosen to satisfy the fluctuation–dissipation theorem, is determined from the equation
R(0) · R(t) = 2mkT ξ δ(t),
where k is Boltzman’s constant, T is the temperature, and δ(t) is the Dirac delta function. The width of this distribution depends on the temperature and the friction coefficient. The temperature regulation approach developed by Berendsen et al. [7] employs a variable friction coefficient that depends on the ratio of desired temperature to the instantaneous temperature calculated from the current kinetic energy of the system. The resulting equation of motion is mv˙ = F + mξ
T0 − 1 v, T
where T0 is the desired temperature and T is the current temperature of the system. The advantages of this approach are its simplicity and efficiency; however, if the system is not pre-equilibrated to properly populate the vibrational modes, or if nonrandom external forces are applied to the system, it can be slow to properly equilibrate the system. A thermostat that rigorously corresponds to a canonical ensemble has been developed by Nosé [8]. In this approach, an extra degree of freedom, representing the heat bath, is included in the dynamic equations of motion. This extra degree of freedom, denoted by s, relates the velocity and the time derivative of position by v = s r˙ . The dynamic equations of the system then become, m¨r = s¨ =
2m˙s r˙ F , − s s2
s s˙ + nf kB (T − T0 ), s Qs
where nf is number of degree of freedom of the system, kB is Boltzmann’s constant, and Qs is the thermal inertia parameter, which can be adjusted to control the rate of temperature fluctuation. Too large a value for Qs results in slow energy flow between the system and reservoir. If Qs is too low, long-lived, weakly damped oscillations of the energy occur, resulting in poor equilibration. Nosé discusses the choice of Qs in more detail [8]. Though the total energy is not conserved because the system exchanges energy with the thermostat,
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the Hamiltonian of the bath plus the system can be derived and is conserved, providing an indicator for checking the program code. Pressure of the system can also be regulated allowing MD simulations to be used to study systems in a constant pressure environment. Andersen [9] originally developed a method for constant pressure MD simulation by making the volume V of the system a dynamical variable. Scaled particle coordinates rs and the coordinates divided by V 1/3 are used in the dynamic equations of motion, m¨rs =
F 2mV˙ r˙s , − 1/3 3V V
(P − P0 ) V¨ = , QV where P0 is the external pressure applied to the system, P is the internal pressure calculated through the Virial theorem. The dynamics of this system mimic the action of a piston on a real system. The constant Qv represents the piston’s mass and is empirically chosen to control the rate of volume fluctuation of the system. Anderson recommends that the time scale for box-volume fluctuations should be approximately the same as that for a sound wave to cross the simulation box. It has been shown that Andersen’s theory generates the isoenthalpic–isobaric ensemble of classical statistical mechanics [10–12]. Whereas Anderson’s method changes only the system size, Parrinello and Rahman [13] generalized Andersen’s method to also allow for changes in the shape of the simulation box. A changing shape allows for a constant external stress condition; the resulting system corresponds to an isoenthalpic–isostress ensemble of classical statistical mechanics. In Parrinello–Rahman theory, the simulation box is generalized to be a parallelepiped. If the simulation box is constructed from three vectors a, b, and c, a matrix formed by the three vectors can be defined as h = [a, b, c]; h is a dynamical variable describing the size and shape changes of the simulation box. This h matrix is also the transformation matrix between the scaled coordinates rs and the real non-scaled coordinates r, as r = hrs . The strain tensor with respect to a reference state h0 is ε=
1 −1 T −1 h0 Gh0 − δij , 2
where G = hT h, and T represents the matrix transpose. Generally, the reference state h0 is chosen to be the equilibrium average value of h in a system under zero tension. Dynamic equations for rs and h are given as ˙ rs , m¨rs = h−1 F − mG−1 G˙ (P − P0 ) −1 T h¨ = V h − hΓ, Qh
where V = |h| = a · b × c, is the volume of the system, P0 is the hydrostatic pressure, and Qh is an empirically chosen constant used to control the fluctuation rate of the h matrix.
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Like the Qv constant in Anderson’s pressure control method, Qh may be thought as a box ‘mass’. The external stress S is related to Γ via the following expression,
5.2.2
−1 T Γ = h−1 V0 . 0 (S − P0 ) h0
Simulation of Tribology
Shown in Figure 5.1 is a schematic diagram of a typical setup for a tribology simulation. Here a surface and opposing counterface are brought into contact by setting the displacement between the two regions to some constant value, through some sort of force-feedback that controls the applied normal force FN by varying the displacement, or by applying a constant pressure to generate a constant normal force. The bottom layer of the surface is held rigid to insure contact is maintained. Typically the surface structure varies according to some variable to be analyzed. This variable could be anything from chemical composition to microstructure to surface roughness. The counterface is typically, but not necessarily always, some well defined, well characterized microstructure. This allows for direct comparison of results between different sets of simulations. Alternatively the surface and counterface could be self-mated; that is, the surface and counterface are both the same. In both the surface and counterface, a region is thermostated using one of the thermostats described above. Not only is the choice of the thermostat important, but its location relative to the sliding interface also plays a critical role. If the thermostated region is too close to the interfacial region, it may interfere with the dynamics of the system and unduly influence the results of the simulation. If the thermostated region is too far away from the interface, it may not be effective in dissipating the thermal energy generated by the interface, which may lead to unrealistic effects, such as localized melting. The choice of the damping parameters or friction coefficients that determine the magnitude of the random forces applied to the atoms is also of some importance. The wrong choice of these parameters may either cause large random forces, which obscure sensitive fluctuations in the contact forces between atoms in the simulation, or the thermostat will not provide enough control over temperature. To further complicate matters, Robbins and Müser [14] have also shown that to some (possibly small) extent even the number of degrees of freedom (i.e. directionality) of the thermostat plays a role in the tribological response of the system. The type of
Figure 5.1
Schematic diagram of typical molecular dynamics simulation tribology experiment.
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material to be modeled may also play a role in the choice of thermostat. The thermostats described in Section 5.2.1 are only effective for controlling heat flux via nuclear phonon– phonon interactions. Such thermostats are effective for modeling many covalent materials such as silicon and diamond; however, in metals where the primary transfer of heat occurs through electron–electron interactions, properties such as thermal conductivity and diffusivity are grossly underestimated. Schall and Brenner [15] have proposed an ad hoc continuum-based thermostat that uses experimentally obtained values for thermal diffusivity to help address these and other issues. Padgett and coworkers [16] have successfully applied this thermostat to study the sliding of metal asperities subjected to resistive Joule heating. For a more detailed discussion of thermostats the reader is referred to a recent review article by Robbins and Müser [14]. After the surface and counterface are brought into contact, a rigid displacement of the top layer of the counterface is applied to initiate sliding. This can be accomplished in several ways. Most often the velocity of the upper layer is set to some constant value and this velocity is maintained throughout the duration of the simulation. Occasionally, a constant force is applied to the upper layer for some prescribed amount of time. This force is then removed and the dynamics of the system are monitored as the counterface slows down and energy is dissipated. It is important to remember that in atomic-level simulations, all the information for each atom in a simulation, from exact coordinates in space, to individual components of force, velocity, acceleration, etc., is available at every time step. This, of course, amounts to an enormous amount of information. The trick is to use insights and intuition to pare down this information into usable, useful data. In any case, several key things may be monitored as the simulation progresses. These may include: • Friction and normal forces (referred to in Figure 5.1 as FF and FN , respectively) between the surface and counterface or on individual atoms. • Displacement between surface and counterface (in constant-normal force simulations). • Structural changes in the free regions such as change in hybridization, dislocation nucleation, stacking fault formation, etc. • Chemical bond forming and breaking between atoms of the surface and counterface. Chemical bond forming and breaking is typically only found in a certain class of interatomic potentials known as reactive potentials. Such potentials will be discussed in detail in the following section.
5.3 5.3.1
REACTIVE POTENTIALS
Covalent Potentials
Atomistic simulation of a large number of atoms using molecular dynamics is a powerful tool for understanding the fundamental mechanisms of friction and tribology. The underpinning of such calculations is the assumed atomic interaction potential. The most desirable circumstance would be to take the atomic interactions directly from first-principles calculations; however, such calculations are orders of magnitude too slow for the shear number
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of energy evaluations required to study a system of reasonable size and practical interest. To obtain useful information in a reasonable amount of time, researchers have developed empirical and semiempirical approximations to the atomic potentials. There are two sides to creating an effective analytic potential. The first is the development of a relatively simple functional form that captures the essential essence of the underlying quantum mechanical bonding. The second is making the potential practical by including additional empirically derived functions and parameters. An effective analytic potential energy function should have the following features; flexibility, accuracy, transferability, and computational efficiency. The potential should be flexible enough to accommodate a wide range of fitting parameters. Data might include cohesive energy, elastic constants, lattice constants, and surface energies. The potential form should then accurately reproduce the fitting database. Ideally, the potential should also have some degree of transferability, having the ability to describe structures not included in the fitting database, at least in a qualitative sense. Finally, the resulting function should be relatively efficient computationally. The process of developing a potential, sometimes referred to as an art as well as a science, requires a combination of chemical insight, trial and error, and tenacity on the part of its developer [17]. Covalent materials such as silicon and carbon form strong, directional bonds. This poses a challenge for potential development for this important class of materials. Many standard potential functions such as the Lennard-Jones potential or embedded atom method do not include any bond directionality. The Stillinger and Weber potential for solid and liquid phases of silicon was one of the first attempts to use a classic potential to overcome this challenge [18]. Stillinger and Weber based their potential model on a many-body approach. In this many-body approach, the total energy is given as a linear superposition of terms representing different types of interatomic interactions: stretching, bending, rotation, torsion, etc. For the Stillinger–Weber potential, the total energy includes only two of these terms, a pair and triplet term based on the geometric factors of bond length and bond angle, respectively. The total potential energy is given by Etot =
1 1 2 . φij (Rij ) + g(Rij )g(Rik ) cos θj ik + 2 3 ij (i =j )
ij k
Here φij is a pair-term (bond stretching) representing electrostatic interactions between atoms i and j . The second summation, a three-body term, represents bond bending between atoms i, j , and k. The term g(R) is a decaying function with a cutoff between the first- and the second-neighbor shell, and θj ik is the bond angle described by two neighbors j and k of atom i. The inclusion of the triplet term allows the potential to achieve an acceptable description of short-range order and of atom-exchanging diffusive motion in the liquid phase. While this potential is reasonably accurate when used for modeling solid silicon in the diamond cubic phase, the potential is very biased towards the ideal tetrahedral bond angle through the explicit inclusion of a factor of (cos θj ik + 1/3) in the three-body term. The inclusion of this trigonometric factor discriminates in favor of pairs of bonds with the tetrahedral geometry, i.e. cos θj ik = −1/3, and limits the transferability of the potential. For instance, it cannot accurately predict the correct energies for various non-tetrahedrally
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bonded high-pressure phases of silicon, it does not correctly predict surface structures, and coordination in the liquid phase is too low. The family of potentials derived from the many-body approach described above for the Stillinger–Weber potential is often used in simulation of organic systems. These, so-called, force-field models are able to model structural and dynamical properties of very large molecules with a high degree of accuracy. However, it is important to note that, in general, force-field methods do not allow for bond-forming or breaking to occur during simulation. Connectivity must be determined a priori. Force-field models are common in the study of tribological systems. In one example, Landman and coworkers [19,20] have applied such models to the study of the structures, solvation forces, and shear of a molecular fluid confined between both smooth and rough interfaces. Thompson and Robbins [21], Sokol et al. [22], Bitsanis [23], and others [24,25] have demonstrated confined fluids form well defined ordered layers normal to the surface and that these layers may actually lock in place. In Landman and Gao’s model, a surface and opposing counterface were represented by an embedded atom method representation of gold (the embedded atom method is discussed briefly below). The molecular fluid was represented by a united-atom force-field representation of the alkane hexadecane (each CH2 group represented by a pseudo-atom) and the interactions between the alkane molecules and the gold atoms of the substrates were represented by a simple Lennard-Jones potential. Their simulations show that there is a remarkable sensitivity to the confining surface morphology. There is a significant reduction in the ordering of films confined between rough surfaces and a strong suppression of solvation forces and the development of liquid-like dynamic and response characteristics. When the rough-surface boundaries are put into motion, the molecular interfacial layer tends to stick to the substrate resulting in a shear stress inside the fluid layer, in contrast to the atomically flat crystalline boundaries where there is vanishingly small shear stress. This result suggests that morphological patterning of surfaces could provide ways for controlled modifications of frictional processes in thin-film lubricated nanotribological systems. For a more complete review of modeling confined lubricants see [26]. In another example, Irving and Brenner [27] have conducted a series of simulations of the diffusion of the mobile lubricant tricresylphosphate (TCP) on a bound self-assembled monolayer (SAM) comprised of octadecyltrichlorosilane (ODTS) using AMBER forcefields [28]. Such bound + mobile systems are of significant importance for protecting interfaces in silicon microelectromechanical systems. The chemically bound SAM protects the device during the early stages of the device lifetime while the mobile lubricant is present to replenish the lubricant coating as the SAM fails. In their study, Irving and Brenner created a SAM substrate by affixing head groups of the ODTS molecules to a hexagonal lattice. All hydrogen atoms were treated explicitly (in contrast to the unified-atom method employed by Landman and coworkers above). The TCP was found to diffuse sufficiently fast to recover damaged areas in most, if not all experimental time cycles. They found that the dynamics of the TCP change as the TCP transitions from the SAM surface to defected areas, at which point the TCP becomes localized and tries to embed into the SAM. From a practical stand point, they argue three advantages to the TCP + SAM combination; rapid diffusion on the SAM is good because TCP molecules can quickly get to defects, local-
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ization on the sides of the defects leads to preferential filling of the defects, and favorable TCP–TCP interactions can lead to the filling of larger defects. In 1987 Baskes proposed a modification to the already popular embedded atom method (EAM) [29,30]. In the original method, the energy of a cluster of atoms is given as
Etot =
1 F (ρh,i ), φij (Rij ) + 2 i,j (i =j )
i
where ρh,i is the spherically averaged electron density of atom i embedded in the host h electron density, Fi is the energy required to embed the atom into this density, and φij is a pair-potential term representing electrostatic interactions between atoms i and j separated by a distance Rij . Typically, the EAM method has been used to model metals, principally those with the face-centered cubic structure. Variants of the embedded atom method have been used successfully to study tribological properties of metal interfaces. Perhaps one of the most important insights gained from this type of interatomic potential has been the explanation of the jump-to-contact phenomenon observed in atomic-force and scanning-tunneling microscopy experiments. The jump-tocontact phenomenon was first reported in 1988 by Pethica and Sutton [31]. They observed that for a sufficiently small separation of a tip and a flat, ∼1–2 Å, the tip and substrate will jump together. In 1990, Landman et al. [32,33], using a series of molecular dynamics simulations of a nickel tip and gold substrate modeled using embedded atom potentials, showed that the experimentally observed hysteresis in the force versus tip-to-sample distance relationship was due to an inelastic deformation of the surface characterized by adhesion of the substrate atoms to the tip. At small sample-tip separations, this mechanical instability causes the jump-to-contact, which leads to adhesion-induced wetting of the tip by surface atoms. Baskes was somewhat surprised to find that the simple EAM model was also sufficient to describe covalent bonding in diamond-cubic materials [34]. With only bulk experimental properties for diamond-cubic silicon used for as fitting parameters, the EAM model gives semiquantitative agreement with structural energies and bond lengths of silicon calculated from local-density approximation calculations. However, there are two major problems. Both problems are related to the elastic shear constants. First, for the diamond-cubic structure, the spherically averaged EAM model gives C11 = C12 . This condition is strongly violated for silicon in the diamond-cubic structure. Second, the experimental Cauchy discrepancy C12 − C44 for diamond-cubic silicon is negative. In the EAM, the Cauchy discrepancy is proportional to the second derivative of the embedding function Fi , which is always positive. The problem lies in the directionality of the silicon bonding. Because the electron density is formulated as a spherical average, all directionality is lost. Recognizing this Baskes offered a modification to the EAM that includes more neighbors and an angular-dependent modification to the density term [35,36]. The inclusion of more neighbors allows the experimental values of C11 and C12 to be fit exactly. A modification to and
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the electron density is required to fit the C44 elastic constant, which corrects the Cauchy discrepancy. The modified density is given as ρh,i =
j =i
ρja (Rij ) +
aj1 ak1 cos θj ik − aj2 ak2 1 − 3 cos2 θj ik ρja (Rij )ρka (Rik ). j =i k =i
The first term is the usual linear superposition of atomic densities, whereas the double summation in the second term is an angular modification. A scaling factor of ρja (Rij )ρka (Rik ) is applied to the angular term such that it decreases in magnitude as either the bond lengths of the three atoms ij or ik increases. The 1 − 3 cos2 θj ik term is similar to the angular function found in the Stillinger–Weber potential in that it biases the potential towards the tetrahedral bond angle. However, the ai1 and ai2 constants give the potential far greater transferability by weighting the bias. Fitting C44 is accomplished by adjusting the constants ai1 and ai2 . The modified EAM could be used to simulate friction and wear properties in covalent materials and, in principle; it is possible to model chemical reactions at the interface using this potential with a proper parameterization. To the best of the authors’ knowledge, no such simulations have been conducted to date. This is in part due to the development of empirical reactive bond-order potentials based on the Abell–Tersoff formalism. 5.3.2
Development and Fitting of Bond-Order Potential
In 1985, Abell presented a very general description of bonding based on the observation of a universal relationship between binding energy and bond length [37]. This relationship placed the bonding in crystalline solids and molecules on the same footing. The only criterion for bonding preference is the optimization of the binding energy with respect to the local coordination. The local coordination is, in turn, the dominant topological variable in the determination of binding energy. Soon after Abell’s work was published, Tersoff developed a potential constructed to guarantee that this universal behavior was obtained [38–42]. The Tersoff potential was the first to attempt to incorporate the structural chemistry of covalently bonded systems. The general form of the potential is given as follows E=
i
Ei =
1 Vij , 2 i =j
Vij = fc VR (Rij ) − Bij VA (Rij ) ,
where E is the total energy of the system, Ei is the site energy for site i, Vij is the interaction energy between atoms i and j , and Rij is the distance between these atoms. The sum is over the j nearest neighbors of i: VR (R) and VA (R) are pair-additive repulsive and attractive interactions, respectively, and fc is a cut-off function to limit the range of the potential. For the Tersoff potential, the repulsive and attractive terms are represented by the Morse-type functions VR = A exp(−λ1 Rij ),
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VA = B exp(−λ2 Rij ), where A, B, λ1 , and λ2 are all positive constants with λ1 > λ2 . All deviations from the simple pair potential are ascribed to the dependence of the bond-order Bij on the local bonding environment or coordination. More specifically, the bonding strength for a bonded pair should be a monotonically decreasing function of the number of competing bonds, the strength of the competing bonds, and the cosines of the angles of the competing bonds. The crucial feature of the Tersoff potential is that it does not assume different forms for the angular functions for different hybridizations. In his work, Bij is given the following form −1/2n , Bij = 1 + β n ξijn ξij =
k =i,j
fc (rik )g(θj ik ) exp λ33 (rij − rik )3 ,
g(θ ) = 1 + c2 /d 2 − c2 / d 2 + (h − cos θ )2 ,
where θj ik is the bond angle between bonds i–j and i–k. The angular function g(θ ) is determined globally by a fit to structures with different coordination. This gives the function a high degree of transferability. Tersoff extended his original silicon potential to include germanium, carbon, and combinations thereof. In 1990, Brenner reported an empirical bond-order expression that described hydrocarbon molecules and solid-state carbon on equal terms [43]. Based on work by Tersoff and others, the form of this expression allows for bonds to form and break with changes in hybridization. This so-called reactive empirical bond-order potential (REBO) was originally developed to model chemical vapor deposition of diamond films, and the potention is widely used in simulating many other processes. The first-generation Brenner potential is very similar to the Tersoff potential. Pair repulsive and attractive terms are again represented by Morse-type potentials. The primary difference is in how the bond-order is handled for hydrocarbon molecules. The expression for the total bond-order is given as B¯ ij = where
Bij + Bj i conj + Fij Nit , Njt , Nij , 2
−δ E E Bij = 1 + Gi (θj ik )fc (rik )eα[(rij −Rij )−(rik −Rik )] + Hij NiH , NiC .
The quantities NiC and NjH are the number of carbon and hydrogen atoms bonded to atom i. conj
The total number of neighbors, Ni t of atom i is (NiC + NjH ), Nij depends on whether a bond between carbon atoms i and j is part of a conjugated system, G(θ ) is a function of the angle between bonds i–j and i–k and has the same form as the Tersoff potential. The two and three dimensional cubic-splines, Hij and Fij , have discrete nodal values that
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are fit to various hydrocarbon molecules. The resulting potential successfully describes the different bonding characteristics of hydrogen and carbon radicals and nonconjugated double and triple bonds (hydrogen is monovalent while carbon has valency up to four). Brenner’s original REBO has proven to be very popular. Its form was adopted by Murty and Atwater [44] to model Si–H systems and was then extended independently by Beardmore and R. Smith [45] and by Dyson and P.V. Smith [46–48] to include C–Si–H interactions. Parameterizations also exist for Si–F, Si–Cl [49], and C–Pt [50]. At the time that this publication was prepared, the original Brenner potential had over 1000 citation in literature. However, even at the time it was published, Brenner recognized it had four basic limitations: (1) The Morse-type form of the pair potential was not flexible enough to allow a parameter set that could fit both structural energies and force constants simultaneously. In his original work, Brenner provided two parameter sets, one that provided an excellent fit to bond energies and another to fit force constants. He left it up to the reader to decide which parameter set to use. (2) The individual 0 Kelvin elastic constants C11 , C12 , and C44 for diamond were not included in the fitting database. As a result, these elastic constants are not accurately reproduced by this potential. (3) The Morse-type form for both the attractive and repulsive pair-terms have finite values at zero separation. In highly energetic atomic collisions, it may be possible for an atom pass through another atom with out being repulsed. (4) The derivatives of the cut-off function fij (r) are not continuous and may lead to spurious minima in energies for certain structures, particularly amorphous carbon. Brenner and coworkers [51] presented a second generation of the REBO potential in 2002, to correct the short comings of the original potential. The revised potential contains improved analytic functions and an expanded fitting database. The second-generation REBO potential provides significantly better description of bond energies, lengths, and force constants, as well as elastic properties, interstitial defect energies, and surface energies for diamond. In this second-generation potential, the pair potentials have the forms V R (r) = f c (r)(1 + Q/r)Ae−αr and V A (r) = f c (r)
Bn e−βn r
n=1,3
for the repulsive and attractive pair-terms, respectively. The screened Coulomb function used for the repulsive pair interaction goes to infinity as interatomic distances approach zero, and the attractive term has sufficient flexibility to simultaneously fit the bond properties that could not be fit with the Morse-type terms used in the original Brenner potential. The bond-order Bij term is also significantly different from either the Tersoff or first-generation Brenner potential. Separate terms are included that depend on local coordination and bond angles, radical character and conjugation, and dihedral angle for C–C
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double bonds. For more details on the second generation REBO potential, the reader is invited to review ref. [51]. In addition to Brenner’s parameterizations for C–C and C–H, Sinnott and coworkers have extended the REBO potential to include C–O–H and C–F–H interactions [52]. The authors of this chapter are currently in the final stages of producing a C–Si–H potential [53]. In principle, the REBO formalism could be extended to a wide range of interatomic interactions. 5.3.3
Covalent + Intermolecular Forces (AIREBO)
The AIREBO potential extends the REBO potential through modifications that include intermolecular interactions between non-bonded atoms and torsional interactions associated with a connected sequence of three bonds. This extension makes the AIREBO potential a particularly attractive tool for studying interfacial/tribological systems. The discussion given in this section focuses on how intermolecular interactions are introduced without compromising the reactivity of the potential. For a discussion of how torsional interactions are modeled the reader is referred to the publication describing the AIREBO potential in detail [54]. Intermolecular interactions are modeled through a Lennard-Jones (LJ) potential, V LJ = 4ε
12 6 σ σ − . r r
Only four parameters are taken as independent: σCC , σHH , εCC , and εHH . The heterogeneous parameters are fixed by Lorentz–Berthelot combining rules, σCH = 1/2(σCC + σHH ) and εCH =
√ εCC εHH .
To merge this with a reactive potential, this LJ potential may be either completely or partially turned off in response to the chemical environment of the interacting pair. The key feature of the AIREBO potential is that it provides a means of smoothly interpolating between pure bonded and pure nonbonded interactions. This is accomplished through a set of three switching functions Sdistance , Sbond , and Sconnectivity . Each one of these switching functions may turn off the LJ interaction partially or entirely, E LJ = (1 − Sdistance Sbond )(1 − Sconnectivity )V LJ . For each of these switches, 1 is associated with turning off the LJ interaction completely, 0 is associated with a full LJ-interaction, and values in between are associated with a partial LJ-interaction. Sdistance is a distance-based switch that is 1 for distances below r LJmin , and 0 for distances above r LJmax . A cubic-spline interpolates for distances falling between the setpoints r LJmin
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and r LJmax to give a value for the switch between 0 and 1. The set-points are fixed by requiring that the LJ potential minimum remain unchanged and that no artificial repulsive barrier is present as the LJ potential is switched off. These constraints require that r LJmin = σij and r LJmax = 21/6 σij . The bond-order-based switch Sbond interpolates to give values between 0 and 1 in the region bmin < b∗ < bmax using a cubic spline, 0 for a bond-order below this range and 1 for a bond-order above this range. The bond-order b∗ is evaluated at r LJmin for pairs separated by intermolecular distances (distances larger than r LJmin ), and thus at these distances b∗ is a hypothetical bond-order that assesses the potential for these atoms to bond should they approach one another. In the calculation of b∗ , the distances of each atom in the pair to its neighbors remain unchanged. The distance-based switch Sconnectivity takes into account the set of all one-, two-, and three-bond sequences that connect the pair of atoms under consideration. For each atom pair in each sequence of bonds, a weight is calculated that is 1 for distances below r LJmin and 0 for distances above r LJmax . These set-points are the same as in Sdistance ; however, for compatibility with the original REBO potential, a shifted half-period cosine function is used to interpolate between r LJmin and r LJmax . A weight for a sequence of bonds is calculated as the product of the sequence’s individual bond weights. The Sconnectivity switch is taken to be the largest sequence-weight found in the total set of sequences. In the adopted form for E LJ , the switches Sdistance and Sbond appear together as a product while Sconnectivity appears on its own. Consequently, a full LJ-interaction will be included for atom pairs that are not (1, 2), (1, 3), or (1, 4) neighbors and are either beyond the cutoff distance r LJmax or have a bond-order below bmin .
5.4 RECENT MD WORK The following section is a summary of important results recently obtained by Harrison and coworkers. The group has three major research areas which all fall under the general category of solid-phase boundary lubrication: friction and properties of diamond and diamond composite films, friction and properties of diamond like carbon (DLC) and amorphous carbon (a-C) films, and finally, friction in self-assembled monolayers (SAMs) systems. These solid lubricants may ultimately prove to be useful in a number of applications, including space-based technologies, microelectromechanical systems (MEMS), and hard disk storage technologies [55,56]. For example, due to high surface-to-volume ratios and low restoring forces present in silicon based MEMS devices, unwanted adhesion (stiction) and friction can dominate their performance. Coatings such as SAMs, DLC, and a-C have all been proposed as strategies to combat these issues [57–59]. These systems are ideally suited for study with the reactive bond-order potentials described in Sections 5.3.2 and 5.3.3. The molecular dynamics simulations presented here have provided several very important insights into experimental results. 5.4.1
Tribochemistry at the Sliding Interface
Amorphous carbon films have a rich variety of structures depending upon how they are deposited [60]. Experimentally the ratio of sp3 (four-fold) to sp2 (three-fold) coordination
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and hydrogen content determine the kind of structures obtained. These can range from diamond-like (high sp3 -to-sp2 ratio) to graphitic (low sp3 -to-sp2 ratio) structures. These films exhibit a wide range of often contradictory tribological properties. For instance, the friction of most DLC films increases with time in inert environments. Yet some DLC films exhibit superlow friction, with friction coefficients less than 0.1 when tested under similar conditions [60–62]. It has been proposed that the random structure of DLC films leads to low lattice commensurability between surface and counterface at atomic scale contacts. In some systems, lattice commensurability has been shown to have a significant effect on the measured friction coefficient. For example, experiments of carbon nanotube rolling and sliding on graphite conducted by Falvo and Superfine [63,64] have shown that nanotubes have preferred orientations on graphite substrates in which the structure of the nanotube is in registry with the structure of the underlying substrate. Falvo and Superfine’s experiments also showed that nanotubes preferred to roll when in-registry and slide while outof-registry. Resisting forces measured while the nanotubes were sliding were significantly lower than those measured during rolling, a somewhat counter-intuitive result. Simulations of carbon nanotube/graphite interactions by Schall and Brenner [65] showed that the difference in observed friction arises from the corrugation of the potential energy surface that the nanotube ‘sees’ as it moves across the graphite. Carbon nanotubes are best envisioned as rolled up sheets of graphite. When in-registry, the lattices of the graphite and nanotube line up in such away that the potential energy surface has its deepest corrugation. For the nanotube to move, it must either climb out of this deep potential well or roll. When outof-registry, the potential corrugation is minimized and the nanotube easily slides along the substrate with very little resistance. This same effect has been used to explain the lubricating properties of graphite [66,67]. In early MD simulations of a-C films using Brenner’s second-generation REBO potential [51], it was determined that under significant load and shear, film coatings would undergo tribochemical reactions with a hydrogen-terminated counterface [68]. Film composition, (i.e. sp3 -to-sp2 ratio and hydrogen content) was also shown to play an important role in the tribo-“reactivity” of the film. Early work on hydrogen-free a-C films showed that tribochemical reactions occurring between films and the counterface give rise to large friction coefficients. The reactions were shown to be dependent on both the structure of the films and the degree of hydrogen-termination on the counterface. Films with similar sp3 -tosp2 hybridization ratios were loaded and sheared against a hydrogen-terminated diamond counterface. At average loads of 300 nN, the results were dramatic as bond rearrangements and adhesion between substrate and counterface occurred. At this load, hydrogen atoms are worn away from the counterface as sliding occurs, creating reaction sites with which unsaturated carbon in the amorphous films can react. This led to the hypothesis that the degree of hydrogen termination of diamond would affect the frictional response due to the greater number of potential reaction sites. Indeed, complete hydrogen saturation of the diamond surface resulted in a lower frictional response, compared to ninety and eighty percent passivation. In another study, three films were compared: a hydrogen-free film (P00), films containing 20% (P20), and 38% (P38) hydrogen. These films are illustrated in Figure 5.2. Table 5.1 gives a list of their compositions and properties. The films have relatively low sp3 -to-sp2 ratios but show no indication of graphite-like layering. The density of the films decreases
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Figure 5.2 Films P00 (top), P20 (middle) and P38 (bottom). Carbons colored in red (sp), yellow (sp2 ), and blue (sp3 ). Hydrogens colored in green.
with increasing hydrogen content. As illustrated in Figure 5.3, films with higher densities (lower hydrogen content) are less compliant than lower density (higher hydrogen content) films. To study the reactivity of the hydrogen containing films three different counterfaces were applied with load and shear. The plot in Figure 5.4 shows that when infinite and
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Film composition and properties Film
Total C
sp (%)
sp2 (%)
sp3 (%)
Total to H
H–H (%)
H–C (%)
%H in film
czz (GPa)
P00 P20 P38
3000 3000 3000
2.2 2.1 6.5
85.3 83.4 71.1
12.5 14.5 22.4
0 750 1810
0 5.6 9.5
0 94.4 90.5
0 20 38
358.7 295.4 193.0
Figure 5.3 Plot of load versus strain for the P00 (squares), P20 (circles) and P38 films (triangles).
curved diamond tips were applied no reactivity was detected. The hydrogen-free film experienced the lowest friction (likely because it is the most ordered film). However, when an amorphous carbon tip that possesses some degree of roughness was applied, thereby introducing potential reaction sites for unsaturated carbons in the films, the hydrogen-free tip was the most reactive. This is reasonable because this film contains the greatest percentage of sp2 hybridized carbon. The ramifications of these results are two-fold. First, while lattice incommensurability undoubtedly plays an important role in the low friction observed in some DLC films, surface passivation is also very important. As these simulations have shown, high friction in DLC films arises from chemical-bond formation between the surface and counterface due to a lack of passivation. The degree of surface passivation of a film may explain why similar experiments yield widely varying results with high friction in some films and superlow friction in others. Second, the presence of water and other contaminates may act to enhance surface passivation. This may explain discrepancies found in experiments studying the effect of relative humidity on friction in DLC films. Humidity has been shown to reduce friction in some films [69] and increase it in others [70].
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Figure 5.4 Friction force versus applied load for three different counterfaces.
5.4.2
Intrafilm Tribochemistry
The friction response of a typical DLC film is characterized by an initial run-in period with high friction, followed by an intermediate constant-friction regime. During longer experiments, a further reduction in friction is often observed [71,72]. There are several possible explanations for this behavior. One is that contact asperities wear down with the wear debris forming a transfer layer on the counterface. Another possibility is that thermal and strain effects transform the DLC to graphite. The tribochemical reactions observed between hydrogen-terminated diamond and amorphous carbon films, seen in our earlier work [68], prompted further studies of these systems [73]. A series of five simulation systems were generated (see Figure 5.5). Films I–III contained the same number of carbon atoms and differed in the only in their sp3 -to-sp2 ratios. Films IV and V, both containing carbon and hydrogen, differed only in their hydrogen content while maintaining similar carbon hybridization schemes. To explain the tribochemical and frictional responses of these films, an understanding of the hybridization in the films was essential (see Table 5.2 for details). The mechanical properties of the films were measured by compression with a diamond counterface. Examination of the approximate slopes of the load-displacement curves for each film revealed values for the elastic constants to be lower than those typically found experimentally [74,75] and in calculated studies by other groups [76]; however, the elastic modulus calculated for each film was reasonable. Surprisingly, Film III, having the lowest degree of sp3 hybridization, had
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Figure 5.5 Snapshots of amorphous carbon films I–V (numbered sequentially from top to bottom). Carbons colored in yellow (sp), red (sp2 ), and blue (sp3 ). Hydrogens colored in green.
a higher modulus than Films I and II. This was explained by the fact that the sp2 rings contained in the film were oriented perpendicular to the substrate, thereby utilizing the high in-plane modulus of graphite. The two hydrogen-containing films behaved similarly and generally had higher elastic moduli due to their sp3 -carbon network. Hydrogen-free Film III behaved similarly to Films I and II in regions of low load; however, at loads above 150 nN tribochemical reactions occurred. Above loads of 600 nN, the other four films began to undergo tribochemical reactions. These bond-breaking and bond-forming events can be seen both within the film (intrafilm), as well as between the film and counterface (interfilm). Throughout the sliding simulation the sp3 -to-sp2 ratio continued to change. For example, in Film II, while sliding at 545 nN load, the number of sp3 carbon atoms first increases as the sp2 carbon atoms decreases, then the trend reverses, and as sliding proceeds the ratio remains fairly constant. These results roughly support the argument that graphitization occurs during sliding of DLC. Without the ability to simulate longer experiments it
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Film
C
H
sp3 (%)
sp2 (%)
sp (%)
h0 (A)
I II III IV V
837 837 837 1115 1075
0 0 0 120 200
73.6 38.7 14.9 94.4 97.5
26.4 60.7 82.4 5.6 2.5
0.0 0.60 2.6 0.0 0.0
7.10 7.70 7.65 9.95 10.4
d (g/cm3 )
avg coord
czz (GPa) (% error)
2.98 2.75 2.77 2.86 2.66
3.71 3.33 3.09 3.92 3.97
144 ± 9.8 117 ± 11 267 ± 4.4 462 ± 4.2 449 ± 6.7
is difficult to say with any clarity whether or not this leads to the greatly reduced friction coefficient observed in experiments. 5.4.3
Self-assembled Monolayers
Self-assembly refers to the process by which organic chain molecules in solution spontaneously arrange themselves onto a substrate forming an organized film. Self-assembled monolayers are of great interest as coatings for MEMS not only because they easily form well-ordered, wear-resistant, single-molecule thickness coatings, but also because there is a great deal of flexibility in tailoring the structure of these monolayers by changing properties like chain length and composition of terminal chain groups. Computationally, a number of groups have investigated the tribological properties of SAMs using MD [77]. Below is a brief discussion of recent work by the Harrison and coworkers on the so-called “odd–even” effect referring to tribological differences between n-alkane SAMs that differ in length by a single –CH2 – unit. Using the AIREBO potential described in Section 5.3.3, a number of simulations were conducted using an amorphous hydrocarbon tip sliding over a monolayer composed of odd-length chains (–(CH2 )12 CH3 ) and a monolayer composed of even-length chains (–(CH2 )13 CH3 ). Loads from 20 to 320 nN, in 20 nN increments, were investigated with the height of the tip regulated during sliding to maintain a constant load. With a system size of 100 chains distributed over an area of approximately 50 Å by 44 Å, these loads correspond to pressures of 0.90–14.4 GPa. The lower range of these loads is routinely probed in AFM friction experiments [78]; the higher range is required to achieve increased cant in response to load under the application of periodic boundary conditions. Under almost all loads in the investigated range, the odd-chain monolayer exhibits higher friction compared to the even-chain monolayer. This trend is related to the structural differences in how the hydrogen atoms from terminal chain groups are presented to the sliding tip as can be seen in Figure 5.6. With the last C–C bond in odd chains being nearly vertical under very light loads, all three hydrogen atoms attached to the carbon atom typically reside close to the sliding interface; in contrast, for even chains one of the terminal hydrogen atoms is buried below its parent carbon atom. The methyl angle associated with the last C–C bond (the angle of this bond with respect to the surface normal) in odd chains can change readily under load resulting in the emergence of a bi-modal distribution of methyl angles as the load is
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Figure 5.6 Snapshot of the odd SAM (top) and even SAM (bottom) each under a load of 20 nN. C–C bonds are shown as sticks and hydrogen atoms are shown as spheres. Sliding is conducted along chain cant (from left to right in this figure).
increased. In contrast, even chains maintain the same relative conformational geometry at all loads with atoms of these monolayers exhibiting more “locked-in” structure. Analysis reveals that the terminal hydrogen atoms of the even monolayer supporting the largest fraction of the load are responsible for the smallest contribution to the friction, a feature not evident in the odd monolayer. This is a particularly clear example of how MD can provide insight that is unavailable to experiment: net forces between individual atoms of the SAM and the set of tip atoms can be directly analyzed (the net force on the tip would thus be the sum over these “contact forces” between individual SAM atoms and the tip). In contrast, an experimental AFM study has access only to the net-force on the cantilever.
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This “odd–even” effect has been investigated by a few experimental AFM groups with one group observing an “odd–even” difference [79] and another seeing no evidence for such an effect [80]. That such conflicting results are not uncommon attests to the difficulty of interpreting AFM experiments and also the challenges faced when trying to connect computational studies with experiment.
5.5 CONCLUSION The aim of this chapter has been to provide an overview of the molecular dynamics technique and reactive potentials with special regard to their use in investigating atomic-scale friction. The examples illustrated give a clear portrait of how simulations open a direct window into fundamental aspects of atomic-scale friction. These simulations aid in the interpretation of experimental data obtained from atomic-scale measuring devices such as the atomic force microscope and surface force apparatus. Molecular dynamics simulations give the unparalleled ability to provide quantitative information about the trajectories and forces associated with the individual atoms that make up the tip and sample in model systems. Coupled with the ever-growing power of computational hardware and the development of increasingly sophisticated and broad reaching interatomic interaction potentials, it is clear that computational molecular dynamics will continue to fill a key role well into the future, uncovering the mechanisms that govern atomic-scale frictional processes.
ACKNOWLEDGEMENTS G.T.G. acknowledges support from the Air Force Office of Scientific Research (AFOSR) as part of the Extreme Friction MURI (F1AT05301G004). J.D.S. acknowledges support from AFOSR (F1AT05301G001). J.A.H. and P.T.M. acknowledge support from the Office of Naval Research under contract N0001406WR20205.
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–6– What Causes Low Friction; What Causes High Friction Yingxi Zhu1 and Steve Granick2 1 Dept. of Chemical and Biomolecular Engineering, Univ. of Notre Dame, Notre Dame,
IN 46556, USA 2 Dept. of Material Science and Engineering, of Chemistry, and of Physics, Univ. of Illinois,
Urbana, IL 61801, USA
6.1 INTRODUCTION The design of tribological interfaces is often motivated by a quest to minimize friction and wear. Among the many strategic design principles that have been developed to this end, the simple idea of decoupling frictional force from normal load is especially attractive. Recent work from the authors’ laboratory demonstrates that under certain conditions, it is possible to reduce this coupling significantly with the result that the friction coefficient appears to be very low. However, the materials design requirements to achieve this end are rather stringent. Furthermore, modern methods enable one under some conditions to measure directly the structure and motions of lubricants during tribological sliding. This chapter presents an overview of recent work from the authors and their coworkers pertaining to the issue of how to decouple friction forces from normal forces. Two main issues are addressed: in the first instance the problem of superlubricity [1,2], in the second instance the problem of how to control the boundary condition for hydrodynamic flow when fluid moves past a solid surface [3]. Finally, the perspective of how to purposely reduce friction by achieving the ‘slip’ boundary is discussed.
6.2 SUPERLUBRICITY IN BOUNDARY LUBRICATION The physics of fluids moving past solid surfaces is fundamental in many science and engineering applications. If the solid surface is sufficiently rough, then the ‘no-slip’ boundary condition holds: fluid at the moving surface takes the same net velocity as that surface [4,5]. We are concerned here with the converse situation when surfaces are extremely smooth—a situation potentially relevant to boundary lubrication, to microfluidics and to Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Published by Elsevier B.V.
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nanofluidics. Common sense suggests that if a surface could be prepared so uniform that the fluid–surface potential of interaction were everywhere the same, this should be observable as very low friction when solids, separated by fluid, move past one another. This intuitive expectation [6] has been confirmed by numerous molecular dynamics (MD) simulations during the past 15 years [7–11]. Very low friction is also observed experimentally when solids slide on incommensurate solids [12,13] and, in atomic force microscopy (AFM) experiments, when fluid films of macroscopic thickness are squeezed between two surfaces whose separation is changed dynamically, even when the surfaces are wetted by the fluid [14,15]. Slip has also been inferred by other experimental methods [16,17]. Paradoxically, other experiments cast doubt on the generality of these conclusions. Experiments using the surface forces apparatus (SFA) report that when nonpolar fluids are confined between atomically-smooth mica sheets to a thickness of <5–10 molecular dimensions, the effective viscosity increases to the point that the frictional response turns solidlike [18–20]. It was at first supposed that the fluids might be commensurate with the mica surface lattice, thus pinning near-surface fluid molecules [9]. This possibility cannot be reconciled with the fact that confinement-induced solidification has been reported using a large family of confined fluids of different chemical structures and therefore different length scales. How to resolve the paradox? In this section, we present experiments showing that the condition of exceptionally low dissipation can be realized experimentally, using simple alkane fluids and very smooth surfaces. Inspiration for this work comes from the pioneering study of Frantz and Salmeron [21], who used mica sheets that were cleaved and mounted in the experimental apparatus using the standard protocol in this field of study [22] but then recleaved immediately before an experiment. They found that the adhesion was systematically larger by a factor of 50% than when using the standard [22] protocol. The Frantz–Salmeron method was followed in the present study. Muscovite mica (ASTM V-2 grade) was silvered on the back side and glued onto a cylindrical disk using the usual protocol for surface forces experiments, then adhesive tape was placed onto it and detached [21]. A drop of fluid was added rapidly. This produces freshly-cleaved mica and has the further advantage that exposure to ambient air is short, minimizing potential exposure to airborne contaminants. The surfaces were mounted in crossed cylinder geometry and oriented to be free of steps at their contact. Separation was subsequently calculated by optical interferometry. The reference “zero” thickness was the thickness of two sheets in adhesive contact in air. In the present experiments, the wavelengths of four adjacent interference fringes were analyzed to deduce the surface–surface separation. Experiments were performed at 25 ◦ C, with P2 O5 (a highly hygroscopic chemical) inside the sealed sample chamber. The sample of squalane (Fluka, purum grade >99%) were used after being dried over molecular sieves and filtered. The radius of curvature of the mica sheets was ≈2 cm, giving a slit-like geometry when the surface separation was molecularly-thin. This field of study has seen singular attention to comparing fluids of linear and branched alkanes. A survey of the literature shows no consensus. Figure 6.1 shows the force–distance profile for squalane, a branched alkane with a C24 backbone and 6 symmetrically-placed methyl groups.
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Force, normalized by mean radius of curvature of the mica cylinders, is plotted against surface separation. As the mica sheets were squeezed together, squalane drained smoothly until oscillatory forces of alternating attraction and repulsion were first detected at thickness ≈4 nm. This reflects the tendency of squalane to form layers parallel to the solids; application of pressure caused the fluid to drain in discrete steps corresponding to squeezing out of successive layers. The liquid could ultimately be squeezed to ≈ 0.9 nm, twice the thickness of the chain backbone. Recently, we repeated the original experiments with the following modifications: (a) the experiments were conducted independently by two fresh researchers uninvolved in the original publication; (b) the force changes were made using a piezoelectric actuator, not motor; (c) small changes of force were applied spaced in time by ≈30 sec for equilibration, the total time being 5–10 min depending on the experiment [2]. We found that these findings shown in Figure 6.1 were highly reproducible. These data resemble strikingly the molecular dynamics (MD) simulations of Gao, Luedtke and Landman [23] and also AFM experiments by Lim and O’Shea [24]. There is agreement even in the details—the magnitudes of the force maxima exceed the magnitudes of the force minima [23] and the magnitudes of the force maxima grow more strongly with decreasing separation the magnitudes of the force minima [23]. Prior experiments had reported that oscillatory forces with period of the chain width, characteristic of linear alkanes, disappear with the addition of a single methyl group [25] or the addition of numerous methyl groups, as for squalane [26,27]. Possible reasons for dependence of surface forces experiments on the method of surface preparation have been debated in the
Figure 6.1 Static force–distance profile of squalane at room temperature, 25 ◦ C; the confining mica surfaces were cleaved using the method of Frantz and Salmeron [21]. Static force, F , normalized by the mean radius of curvature, R (≈2 cm) of the crossed cylinders using the Derjaguin approximation in which F /R between curved surfaces is proportional to energy per unit area between parallel surfaces at the same closest separation [30], is plotted against surface separation, D. The circles show data measured without shear and the stars show that measurements were unaffected by concomitant oscillatory shear at 256 Hz with shear amplitude 0.5 nm. The triangles indicate outward jumps, which reflected instability when the gradient of attractive force exceeded the elastic force constant of the measuring device. The dashed lines (guides to the eye) represent regions inaccessible to measurement because the force gradient exceeds the apparatus spring constant. The inset shows the chemical structure of this fluid, squalane. Figure adapted from [1].
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literature without agreement [21,22,28,29] and we will not address them here. The main point is that, using the Frantz–Salmeron method to prepare mica [21], the inconsistency between simulation and experiment is now removed. We now consider the interplay between layering and friction, which is another problem that had seen no prior consensus in the literature. The same system (squalane, the model branched alkane) was considered. To apply shear, small-amplitude sinusoidal shear forces were applied to one piezoelectric bimorph, the resulting displacement was monitored by a second bimorph, and a lock-in amplifier decomposed the output into amplitude and phase. Linear viscoelastic response was confirmed [20]. The slowest, quasi-static quenches to a given thickness (compression at <10−2 nm sec−1 ) were produced by slow mechanical drifts in the apparatus. Figure 6.2 shows the frequency (ω) dependence of the linear viscoelastic dissipative and elastic shear moduli, G′′ (ω) and G′ (ω), for squalane nominally 2 layers thick (0.9 nm) produced in this quasistatic manner. One sees that G′′ (ω) ∼ ω; this signifies that these highly-confined films responded to shear deformation in the manner of a viscous fluid, with viscosity η ≈ 10 Pa sec. In other experiments (unpublished results), this pattern of viscous response was confirmed using ethylene glycol (a hydrogen-bonded fluid) and isododecane (a glass-former), so it appears to be general. This agrees with recent studies with a globular-shaped molecule, octamethylcyclotetra-siloxane, OMCTS [28,29] but contrasts with the confinement-induced solidification reported by other experiments [18–20,26,27]. A limitation of the recent experiments with OMCTS [28,29] was that the unusual cyclic structure of this fluid left uncertain the generality of those conclusions. The present experiments demonstrate this for the important class of alkane fluids, which possess the complexity of chain architecture characteristic of oils widely used in science and engineering.
Figure 6.2 Shear measurements of squalane, a model branched alkane, confined to thickness 0.9 nm between mica cleaved using the method of Frantz and Salmeron [21]. The effective viscous and elastic shear moduli, G′′ (ω) (circles) and G′ (ω) (squares), respectively, are plotted against radian frequency (ω) after quasi-static quench to thickness 0.9 nm without shear during the quench process (solid symbols) or with accompanying small-amplitude oscillatory shear at 256 Hz (open symbols). The pressure, normal force normalized by contact area of the flattened crossed cylinders, was 3 MPa. The shaded area shows the minimum resolvable numbers. The inset shows schematically this shear experiment. Figure adapted from [1].
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Other experiments with ethylene glycol and OMCTS confirmed the phenomenon of exceptionally low friction, also when the shear displacements were much larger than the film thickness. The conclusion therefore appears to be general. We hypothesized that fluidity observed here—which contrasts qualitatively with solidification reported in the literature [18–20]—resulted from low surface disorder using the Frantz–Salmeron [21] method of surface preparation. If so, it should be possible to produce disorder in the same chemical system by the converse strategy of introducing disorder in the fluid, simply by allowing less equilibration of that fluid. Exploring this idea, next we performed other experiments in which these same solid surfaces were brought together more quickly. It is striking that after these faster quenches, friction was observed starting at larger separation and was considerably enhanced. In Figure 6.3, the effective viscosity is plotted against film thickness for an experiment in which the compression rate was 500 times faster, 0.5–1 nm sec−1 (note that this was still sufficiently slow that hydrodynamic forces were too small to flatten the curved surfaces). In control experiments, we reproduced slow-quench findings after making fast-quench measurements, thus demonstrating that the surfaces were not damaged. Tentatively, we imagine that rapid quench nucleated less perfect layering of density waves parallel to the solid surfaces. Then friction resulted as multiple layers jammed against one another, as indicated also by a viscosity enhancement. Easy slip of layers past one another (produced by quasistatic formation of the confined layers) was impeded. Next, we turned to hydrodynamic flow. Physically, this signifies that the volume of fluid was altered by changing the surface separation dynamically, rather than keeping the surface separation constant but changing laterally the relative positions of the constraining
′ ≡ G′′ (ω)/ω, is plotted against film thickness for squalane (a model Figure 6.3 Effective dynamic viscosity, ηeff branched alkane), confined between mica sheets prepared using the method of Frantz and Salmeron [18]. The data contrast results obtained after rapid quench at shear frequency f = 1.3 Hz (open circles) and after quastistatic quench at f = 256 Hz (filled circles). The inset shows this same data on linear scales. Figure adapted from [1].
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surfaces, as in the experiments reported in Figures 6.2 and 6.3. Conditions were considered such that thickness of the fluid amounted to so many molecules that a continuum description should be expected to hold. Tetradecane and water were selected for study because simple Newtonian fluids were the focus of earlier pertinent data showing ‘no slip’ [5,30]. In this situation, ‘slip’—a limit to stress buildup when oils flow past solid surfaces—has been predicted from molecular dynamics simulations [8] concerning smooth surfaces and has been observed in AFM and other experiments [5,6,14–17].
6.3
CONTROLLING THE BOUNDARY CONDITION OF HYDRODYNAMIC FLOW
‘No slip at the wall’ has been a core concept in fluid mechanics. It stands at the bedrock of our understanding of the flow of simple low-viscosity fluids and comprises a springboard for much sophisticated calculation. While it is true that at some level of detail this continuum description must fail and demand description at the molecular level, it is tremendously successful as the basis for continuum-based calculations. As expressed in a prominent fluid dynamics in the textbook [31]: In other words there is no relative motion between the fluid and the solid. This fact may seem surprising but it is undoubtedly true. No matter how smooth the solid surface or how small the viscosity of the fluid, the particles immediately adjacent to the surface do not move relative to it. It is perhaps not without interest that Newton’s term for viscosity was ‘defectus lubricitatis’—‘lack of slipperiness’. Even for a fluid that does not ‘wet’ the surface this rule is not violated.
Is it necessarily so? These issues were controversial for centuries to those who developed the foundations of fluid mechanics [32,33]. The compelling rational arguments—for and against—were decided by the pragmatic observation that predictions agreed with experiments. The situation has changed but the enormous and enduring success of the no-slip assumption for modeling must be emphasized. It works beautifully provided that certain assumptions are met: a single-component fluid, a wetted surface, and low levels of shear stress. Then careful experiments imply that the fluid comes to rest within 1–2 molecular diameters of the surface [34–36]. But the necessary assumptions are more restrictive, and their applicability is more susceptible to intentional control, than is widely appreciated. Widely appreciated by practitioners, exceptions to the central dogma have made their way too little into the textbooks, but are documented abundantly in the engineering literature. In some situations, engineers work hard to prevent exceptions when they deal with suspensions in fluids—they routinely roughen the surfaces of their test instruments and verify that their measurements don’t depend on the sample thickness [37]. In other instances, engineers take advantage of it to reduce viscous drag—as in the flow of suspensions, foodstuffs and emulsions [38] or the addition of so-called ‘processing aids’ to facilitate the flow of plastics through molds [39]. These commonplace aspects of wall slip are not widely enough appreciated outside a small community of engineers. They are endemic when the fluid has more than one component and one of them has lower viscosity than others, as may happen when non-adsorbing polymers are dissolved in fluids of lower viscosity. Exceptions in cases of partial wetting—e.g., the flow of water past hydrophobic walls—have been reported from time to time for many years [32,33,40–42]. These reports
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appear never to have been widely considered to be trustworthy but the idea behind these observations was put recently on a firm quantitative basis (see below). Finally, there is the ‘weak link’ argument that whenever the rate of flow is sufficiently strong, something must break down. Let a fluid be sheared at some rate; some force will resist this. Let the shear rate be raised by a factor of (say) ten; the resisting force will rise by the same amount. This cannot continue without limit because if so, eventually the fluid would sustain forces larger than can be withstood by even the strongest material. Something must give, either at the wall (‘slip’) or within the fluid itself (this is called ‘shear banding’). This section will not further consider the literal exceptions to the no-slip boundary condition. In addition to the case of viscous polymers [43–45], these include gas flowing past solids whose spacing is less than a few mean free paths [46], superfluid helium [47], and contact lines when liquid droplets move on solids [48]. Recently much interest has also been given to slip in sheared films of molecularly-thin simple liquids, but those interesting anomalies disappear for films thicker than 5–10 molecular dimensions [49] and therefore are relevant mainly to friction. 6.3.1
The Mechanism that Controls Slip in Low-viscosity Fluids
Partial slip of so-called Newtonian fluids such as alkanes and water is predicted by an increasing number of computer simulations [50–55] and, in the laboratory when forces are measured, systematic deviations from the predictions based on no-slip are found [56–66]. Some sense of urgency comes from potential practical applications. Typical magnitudes of the slip length reported in the literature are submicron, so small that the practical consequence of slip would be minimal for flow in channels whose size is macroscopic. But if the channel size is very small, there are potential ramifications in microfluidics. The simulations must be believed because they are buttressed by direct measurements. In the past, all laboratory reports of slip were based on comparing mechanical measurements of force to fluid mechanics models and hence were indirect inferences. Recently, optical methods were introduced to measure fluid velocity directly. For example, Léger and coworkers photobleached tracer fluorescent dyes and from the time rate of fluorescence recovery, measured in attenuated total reflection in order to focus on the region within an optical wavelength of the surface, the velocity of flow near the surface was inferred [58]. They reported slip of hexadecane near an oleophobic surface provided that it was smooth, but not when it was rough. Tretheway and Meinhart used laser particle image velocimetry of tracer latex particles to infer the velocity of water flow in microchannels [66]. They reported slip when the surface was hydrophobic but stick when it was hydrophilic. Callahan and coworkers demonstrated the feasibility of using nuclear magnetic resonance (NMR) velocity imaging, though this method has been used to date only for multicomponent fluids [67]. An important hint about mechanism comes from the repeated observation that the amount of slip depends on the flow rate, in measurements using not only the surface forces apparatus (SFA) [60–63] but also atomic force microscopy (AFM) [59,64]. The main idea of all of these experiments is that two solids of mean radius of curvature R, at spacing D, experience a hydrodynamic force FH as they approach one another (or retreat from one another) in a liquid medium, thereby squeezing fluid out of (or into) the intervening gap.
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This force FH is proportional to rate at which spacing changes, dD/dt (t denotes time), is proportional to the viscosity, η (assumed to be constant), and is inversely proportional to D. The no-slip boundary condition combined with the Navier–Stokes equations gives to first order the following expression, known as the Reynolds equation: FH = f ∗
6πR 2 η dD · . D dt
(1)
The deviation of the dimensionless number f ∗ from unity quantifies the deviation from the classical no-slip prediction. The classical prediction is analogous when the surface spacing is vibrated. In that case a sinusoidal oscillatory drive generates an oscillatory hydrodynamic force whose peak we denote as FH,peak . The peak velocity of vibration is vpeak = d · ω where d is vibration amplitude and ω the radian frequency of vibration. Studies show that when the frequency and amplitude of oscillatory flow are varied, results depend on their product, vpeak and that deviations from Equation (1) depend on vpeak /D. This ratio, the flow rate, is the ratio suggested by the form of Equation (1). The formal idea of a ‘slip length’ is common. ‘Slip’ signifies that in the continuum model of flow, the fluid velocity at the surface is finite (the slip velocity, vs ) and increases linearly with distance normal it. The slip velocity is assumed to be proportional to the shear stress at the surface, σs : η · vs ≡ b · σs , where η is viscosity and b, the slip length, is the notional distance inside the surface at which the velocity equals zero, if the velocity profile is extrapolated inside the surface till it reaches zero. In much of the literature the slip length has been assumed to be a constant that characterizes the material response of a given fluid–surface pair, but evidence of additional dependence on velocity is discussed below. Without necessarily assigning physical meaning to this quantity, it can be used as an alternative expression of the same data. Mathematical manipulation [33] shows that f ∗ and slip length (b) are related as: D · f =2· 6b ∗
6.3.2
6b D ln 1 + −1 . 1+ 6b D
(2)
“Slip” at Partially-Wetted Surfaces with Roughness Varied
According to Equation (1), the ‘stick’ prediction (f ∗ = 1) corresponds to a horizontal line and one observes in Figure 6.4 that deviations from this prediction decreased systematically as surface roughness increased. In addition, deviations from the predictions of the no-slip boundary condition are alternatively often represented as the ‘slip length’ discussed above, the fictive distance inside the solid at which the no-slip flow boundary condition would hold; the equivalent representation of this data in terms of the slip length is included in Figure 6.4. While it was known previously that a very large amount of roughness is sufficient to generate ‘no-slip’ [68–70], an experimental study in which roughness was varied systematically [61] succeeded in quantifying how much actual roughness was needed in an actual system. The critical level of 6 nm considerably exceeded the size of the fluid molecules. As methods are known to achieve greater smoothness in MEMS devices, and potentially in microfluidic devices, this offers promise of having practical applications.
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Figure 6.4 Illustration that deviations from the traditional no-slip boundary condition depend systematically on surface roughness. Here the critical shear rate for onset of slip (left ordinate) and critical shear stress (right ordinate) are plotted semilogarithmically against rms surface roughness for flow of deionized water (solid symbols) and tetradecane (open symbols and semi-filled symbols as identified in [61]. The data in parentheses indicate the asymmetric situation—one surface was rough and the opposed surface was atomically smooth, as discussed in [61]. Maximum shear rate and shear stress on the crossed cylinders were calculated using known relations based on continuum hydrodynamics from [33]. Specifically R · vpeak (3) γ˙max = A · D D and
σpeak = 1.378ηR 1/2
vpeak . D 3/2
(4)
Figure adapted from [61].
The observation of rate-dependent slip suggests that fluid is pinned up to some critical shear stress, beyond which it slips. However, some laboratories report slip regardless of flow rate [56–58,65]. Perhaps, the essential difference is that the magnitude of shear stress is larger in the latter experiments. But in cases where slip is rate-dependent, this affords a potential strategy by which to effect purposeful mixing in a microfluidic device. The idea would be to simply make some patches on the surface hydrophobic and other patches hydrophilic, so that when flow was slow enough it would be smooth, but when it was fast enough, mixing would result from jerkiness at the hydrophobic patches. While it is true that slip at smooth surfaces is predicted based on computer simulations [50–55], the shear rate of molecular dynamics (MD) simulations so much exceeds shear rate in those laboratory experiments that the direct connection to experiment is not evident. To quantify the influence of surface roughness, Figure 6.5 considers the limit up to which predictions based on the classical no-slip boundary condition still described the data in Figure 6.4. Since the no-slip boundary condition still held, it was valid [61] to calculate the shear rate and shear stress by known equations. The data show that deviations from the no-slip prediction began at very low levels of hydrodynamic stress—on the order of only 1 to 10 Pa. Beyond this point, in some sense the moving fluid was depinned from the surface. ‘Slip’ need not necessarily be predicated on having surfaces coated with self-assembled monolayers to render them partially-wetted, though this was the case in most of the studies cited so far. The no-slip boundary condition switches to partial slip when the fluid contains a small amount of adsorbing surfactant [57,63].
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Figure 6.5 As a function of logarithmic flow rate, vpeak /D, f ∗ (top panel; f ∗ is defined in Equation (2) and the equivalent slip length (bottom panel), for deionized water (filled symbols) and tetradecane (open symbols) between surfaces of different levels of rms surface roughness, specifically: 6 nm (case a; squares), 3.5 nm (case b; circles), 2 nm (case c; down triangles), 1.2 nm (case f; hexagons), 0.6 nm (case e, upper triangles) and molecularly-smooth (case d; diamonds). The data, taken at different amplitudes in the range of 0.3∼1.5 nm and frequencies in the range 6.3∼250 rad sec−1 , are mostly not distinguished in order to avoid clutter. To illustrate the similarly successful collapse at these rough surfaces, data taken at the two frequencies 6.3 rad sec−1 (cross filled symbols) and 31 rad sec−1 (semi-filled symbols) for water are included explicitly. Figure adapted from [61].
6.3.3 “Slip” Can Be Modulated by Dissolved Gas—at Both Wetted and Partially-Wetted Surfaces
When experimental observations deviate from expectations based on the ‘stick’ boundary condition, there are at least two alternative scenarios of microscopic interpretation. One might argue that the fluid viscosity depends on distance from the wall, but for Newtonian fluids this would not be realistic. Why then do experimental data appear to undergo shear thinning with increasing values of the parameter vpeak /D, if it is unreasonable to suppose that the viscosity really diminished? Inspection shows that the data for smooth surfaces at high flow rates are consistent with a two-layer-fluid model in which a layer <1 nm thick, but with viscosity 10–20 times less than the bulk fluid, adjoins each solid surface [60]. A possible mechanism to explain its genesis was proposed by de Gennes (private communication), who conjectured that shear may induce nucleation of vapor bubbles; once the nucleation barrier is exceeded the bubbles grow to cover the surface, and flow of liquid is over this thin gas film rather the solid surface itself. Indeed, it is likely that incomplete air removal from the solid surfaces can profoundly influence findings in these situations where surface roughness is so low. It is identified by recent research as a likely source of the miss-named “long-range hydrophobic attraction” [71,72], gases also appear to influence the sedimentation rate of small particles in liquid [73].
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Accordingly, this laboratory has performed experiments in which the surface forces apparatus was used to measure hydrodynamic forces of Newtonian fluids that had been purged with various gases. Dissolved gas strongly influences hydrodynamic forces, in spite of the fact that gas solubility is low. Figure 6.6 (top panel) illustrates experiments in which a simple nonpolar fluid (tetradecane) was placed between a wetted mica surface on one side, and a partially-wetted methyl-terminated surface on the other, using methods described in detail elsewhere [61]. The surface–surface spacing of 10–100 nm substantially exceeded the size of the fluid molecules. The spacings were vibrated with small amplitude at these spacings where the fluid responded as a continuum, and the magnitude of hydrodynamic force was measured as a function of the ratio vpeak /D suggested by Equation (1). The experiments showed that whereas textbook behavior [32] was nearly followed when the tetradecane had been saturated with carbon dioxide gas, massive deviations from this prediction were found when the tetradecane was saturated with argon. This makes it seem likely that argon segregated to the solid walls, creating a low-viscosity Presumably, the amount of segregation is a materials property of the fluid, the chemical makeup of the surface, and the chemical identity of the dissolved gas. In this example, the fact that argon possesses low solubility in tetradecane may have made it more prone to segregate to the surfaces.
Figure 6.6 Illustration that the onset of ‘slip’ depends on dissolved gas, when simple Newtonian fluids flow past atomically-smooth surfaces, either wetted or partially-wetted. On log–log scales, the hydrodynamic force FH,peak is plotted against reduced flow rate, vpeak /D such that a straight line of slope unity would indicate ‘no-slip’ assumed by Equation (1). The vibration frequency is 9 Hz. Top panel: tetradecane flowing between the asymmetric case of a wetted mica surface on one side, a partially-wetted surface of methyl-terminated self-assembled monolayer on the other side, prepared as described elsewhere [61]. Filled symbols, tetradecane saturated with carbon dioxide; open symbols, tetradecane saturated with argon. Bottom panel: deionized water flowing between mica surfaces that are wetted by this fluid. The hatched region of the graph shows the range of irreproducible results obtained when the gas dissolved in the water was not controlled. Filled symbols, water saturated with carbon dioxide; open symbols, water saturated with argon. Figure adapted from [5].
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The influence of dissolved gas casts doubt on a traditional assumption of work in this field, which is that slip arises because fluid–fluid intermolecular interactions are stronger than those between fluid and surface, i.e. that the surface must be wetted only partially. Recent experiments show that dissolved gases can mediate apparent slip even for solid surfaces that are fully wetted by the flowing fluid. Figure 6.6 (bottom panel) summarizes experiments in which deionized water was placed between wetted surfaces of mica and the surface–surface spacing of 10–100 nm was vibrated with small amplitude in the manner described previously [60–63]. Hydrodynamic force is plotted against the ratio, vpeak /D. It is obvious that the prediction based on Equation (1), a straight line on the log–log plot with a slope of unity, was violated systematically when the hydrodynamic force reached a critical level. An intriguing point is that initial findings were found to be irreproducible (they varied within the range marked by the hatched lines in the graph) but became reproducible when the water was first deliberately saturated with gas. One observes that water saturated with argon appeared to ‘slip’ at a slightly higher level of shear stress than water saturated with carbon dioxide, and that in both cases the limiting hydrodynamic force was larger than when the nature of the dissolved gas was not controlled. This rich and complex sensitivity to detailed materials chemistry of the system disappears, unfortunately, when surfaces are so rough that the ‘stick’ boundary condition is produced trivially by the influence of surface roughness [61,68–70]. Therefore for scientific and practical reasons alike, these issues of flow past nearly-smooth surfaces comprise fertile ground for future work.
6.4
OUTLOOK—THE PURPOSEFUL REDUCTION IN FRICTION
Inspired by these ideas to design new engineering structures, one might strive to “grease” the flow of liquids past solid surfaces by altering the boundary condition. One strategy is to make the surfaces ultra-smooth [60,61]. Another (also mentioned already) is to add processing aids that segregate to the surface [39,57,63]. A third way is to purposefully use multicomponent fluids to generate concentration gradients and differential wetting to generate slip, as can occur even if there is no velocity gradient in the fluid [55]. These methods could potentially be used in nanomotors or nanopumps. Alternatively, one may seek to maximize contact with air, which is exceedingly solvophobic. Readers will have noticed that water ubiquitously beads up on the leaves of plants. Some plants can display a contact angle that approaches 180◦ , even though water at a smooth surface of the same chemical makeup displays a much lower contact angle. A beautiful recent series of experiments from the Kao Corporation in Japan provided insight into why [74]—the surfaces are rough on many length scales [75,76] and trap air beneath them. Readers will have noticed that if one tilts a leaf, a drop of water on it rolls smoothly, because it rides mainly on a cushion of air. It is the principle of an ingenious method introduced recently to lower the viscous drag when fluids [76] are caused to flow through pipes whose diameter is macroscopic. Of course, given a long enough period of time it is likely that the trapped gas would dissolve into the flowing fluid, but perhaps this effect could be enhanced by placing air nozzles along the walls of the tube and replenishing the trapped gas with a stream of inlet air.
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A final method by which flow of a Newtonian fluid past surfaces may be facilitated is to “ciliate” the surfaces by coating with chain molecules—polymers, proteins, or sugars. Recent experiments using a surface forces apparatus (SFA) suggest a similar (but less dramatic) rate-dependent slip in this case also [62]. This is possibly related to fluid flow in biological organs whose surfaces are also extensively ciliated, such as blood vessels and the kidney [78].
6.5 CONCLUDING REMARKS In summary, these experiments show that exceptionally low energy dissipation can be achieved by achieving the ‘slip’ boundary condition when the important class of alkane fluids moves past solids. These experiments concern not only shear flow, in which the volume was constant, but also hydrodynamic flow, in which the volume changed dynamically. It is gratifying to see this resolution of the persistent disagreements described in the introduction. However, the present mica sheets were surely not themselves perfectly orderly, as they had been exposed to ambient air and also possessed a random distribution of surface potassium ions after cleavage. An agenda for the future will be to understand the amount and type of disorder that a system can tolerate without pinning fluid to a solid surface resulting in high friction. The proof-of-concept presented here, that “superlubricity” [12,13] can exist in a realistic laboratory situation involving fluid lubrication, holds evident possibilities for nanofluidics, nanofabrication, and related applications where exceptionally low energy dissipation may be desired.
ACKNOWLEDGEMENTS Y.Z. gratefully acknowledges the financial support from the ACS Petroleum Research Fund and the University of Notre Dame (Faculty Research Program, Award #370857). S.G. appreciates financial support from the NSF (Surface Engineering Program) and also from the NSF (Polymers Program, Award DMR-0605947).
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–7– Frictional Dynamics at the Atomic Scale in Presence of Small Oscillations of the Sliding Surfaces Sangmin Jeon1 , Thomas Thundat2 and Yehuda Braiman3 1 Department of Chemical Engineering, Pohang University of Science and Technology,
Pohang, Korea 2 Center for Engineering Science, Advanced Research Life Sciences Division, Oak Ridge
National Laboratory, Oak Ridge, TN 37831 3 Center for Engineering Science, Advanced Research Computer Science and
Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
7.1 INTRODUCTION Friction between surfaces in contact is a longstanding and very important, yet unsolved, problem. Because of the complexity and multidisciplinary nature of the phenomenon, numerous factors play a key role in describing the relative sliding of adjacent surfaces; therefore, it is a multifaceted problem to address. In particular, the outstanding complexity significantly affects our ability to predict and control frictional sliding, properties that are highly desirable for a variety of technological applications including micro-electromechanical systems (MEMS), computer recording systems, and miniature motors and actuators. Friction can be affected by the application of small perturbations to accessible elements and parameters of the sliding system [1–8]. Implementation of a desirable level of control, though, requires a priori knowledge of the strength and timing of the perturbations. Such techniques are, in general terms, not developed yet. The effect of periodic surface oscillations on frictional dynamics was studied both experimentally and theoretically [1,2,9–11]. Ultrasonic vibrations were demonstrated to suppress friction in macroscopic as well as in microscopic sliding systems [12–16]. In a related problem, turbulent drag reduction by wall oscillations was demonstrated in the wind tunnel [17] and by numerical simulations of channel turbulent flow [18]. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Published by Elsevier B.V.
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Recently, Heuberger et al. [1] (experimental) and Gao et al. [2] (full-scale molecular dynamics computer simulation) showed that friction in thin-film boundary-lubricated junctions can be reduced by coupling small-amplitude (of the order of 1 Å) directional periodical mechanical oscillations of the confining boundaries to the molecular degree of freedom of the sheared interfacial lubricating fluid. Using a surface force apparatus modified to measure friction forces while simultaneously inducing normal (out-of-plane) vibrations between two boundary-lubricated sliding surfaces, load- and frequency-dependent transitions between “dynamical friction” states have been observed [1]. In particular, regimes of vanishingly small friction at interfacial oscillations were found. Methods to control friction in systems under shear that enable the elimination of chaotic stick-slip motion were proposed by Rozman et al. [3]. Significant changes in frictional responses were observed in the two-plate model [4] by modulating the normal response to lateral motion [5]. In addition, surface roughness and thermal noise are expected to play a significant role in deciding control strategies at the micro and the nano scales [6,7]. Friction response to surface oscillations may possess certain generic properties independent of the nature of a sliding system. Indeed, as different experimental systems are considered (each one poses variable degrees of experimental accessibility and controllability), understanding how oscillations affect friction poses a very challenging matter. In this chapter, we study the effect of surface oscillations on frictional properties of surfaces, using an atomic force microscope (AFM). Since the first measurement of friction with an AFM by Mate et al. [19], the AFM has been widely used to measure the frictional properties of materials on the nanometer scale [20,21]. Our experimental and numerical modeling results showed a significant (few orders of magnitude) reduction in the friction force as a result of surface oscillations. As in the surface force apparatus experiment [1], we observed very small values of the friction coefficient of the order of 0.01. Both periodic as well as random oscillations result in a significant decrease in friction coefficient.
7.2
EXPERIMENTAL
Mercaptopropionic acid was purchased from Aldrich and used without any further purification. It was selected as a boundary lubricant because of its simple structure and hydrophilicity. An atomically smooth mica surface was cleaved, and a 2.5-nm thickness of chromium and a 30-nm thickness of gold layers were sequentially deposited on it. A self-assembled monolayer of mercaptopropionic acid was formed on a fresh gold surface by dipping the gold-coated mica into a 1-mg/ml concentration of ethanol solution overnight. After being thoroughly rinsed with ethanol and completely dried with clean nitrogen, the substrate was immediately mounted on a piezoelectric actuator. The amplitude and frequency of vertical oscillation by the actuator were controlled with a digital function generator. We used an AFM (Multimode, Digital Instrument, Santa Barbara, CA) with a quadrant position-sensitive detector for friction measurement. A diode laser is focused on the end of the cantilever and aligned to reflect the laser beam to the center of the detector. Proportional and integral gains of a feedback loop were set to low values because high values can exert a large influence on the lateral force measurement. As the cantilever scans on the surface, the friction between the lever and the surface twists the cantilever, and the reflected laser beam
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moves out from the center position. The larger the friction value, the larger the difference between the trace and retrace appears. Scan speed and scan size were fixed at 1.97 Hz and 100 nm, respectively, throughout the measurements. 7.2.1
Results and Discussion
Figure 7.1 shows the friction loops at a fixed frequency of 10 KHz and various amplitudes of vertical oscillation against time. The upper and lower curves represent trace and retrace in standard AFM measurements, respectively. The bigger the difference is, the more pronounced the friction becomes. Although the accurate amplitude of the vertical vibration is not measured at this high frequency, its amplitude-to-voltage parameter is about 1 nm/V at low frequency, and the amplitude is linearly dependent on the applied voltage in the given frequency. The difference starts to decrease even at a low driving voltage of 0.1 V and reaches an almost negligible value at 1 V. Figure 7.2(a) demonstrated the friction coefficient dependence on the frequency and the amplitude of oscillations. To calculate friction coefficient μ, we used the following expression: μ = αF /L where F and L are a friction force and a normal load in voltage, respectively. Friction force F was calculated from the difference between trace and retrace (see Figure 7.1), and the normal load L was fixed at 2 V throughout the experiment. Since
Figure 7.1 Friction loops were measured with various amplitudes of vertical oscillation at a fixed frequency of 10 KHz. The difference between the trace (upper curve) and the retrace (lower curve) represents the friction force.
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Figure 7.2 (a) Friction coefficients are measured at various amplitudes and frequencies of vertical oscillation, 2: 1 Hz, ": 10 Hz, Q: 100 Hz, a: 1 KHz, F: 10 KHz, ◭: 20 KHz ◮: 50 KHz, ⋆: 100 KHz. (b) Friction coefficients at fixed driving amplitudes of 4 V are plotted against the logarithm of the driving frequency. Inset shows the same plot, but against the linear frequency. Reprinted with permission from Applied Physics Letters.
the spring constants of flexure and torsion are different, the ratio of the spring constants, α, should be considered. Here, α is assigned to be 30 based on the previous experiment using the same structure for the silicon cantilever [22]. At low value of the oscillation frequency (1 Hz), the friction is not much affected by the oscillation, regardless of the amplitude, because the vertical oscillation is much slower than the scanning speed of the cantilever. The friction force starts to decrease significantly for oscillation frequencies above 100 Hz, and the minimum value of the friction coefficient appears at the oscillation frequency of 10 KHz. At higher oscillation frequencies (above 10 KHz), the friction coefficient increases again. This tendency is more apparent in Figure 7.2(b), where the friction coefficient is plotted against the logarithm of the frequency at a fixed oscillation amplitude of 4 V. The inset in Figure 7.2(b) shows the same information as Figure 7.2(b) but frequencies are presented at the linear scale.
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Figure 7.3 The effect of the random oscillations amplitude on friction coefficient was measured by applying a random noise function to the piezoelectric actuator. As the oscillation amplitude increases, the friction coefficient decreases, approximately following the first-order exponential decay.
Figure 7.3 shows how the amplitude of random oscillation affects the friction coefficient on a bare gold surface. In our experiment, random noise from a function generator was applied to a piezoelectric actuator. A spectrum analyzer confirmed that the noise was truly random up to 100 KHz. As the amplitude of the vertical oscillation increases, the friction coefficient decreases, approximately following the first-order exponential decay which signifies that a single energy dissipation mechanism plays a role during the measurement. The decreasing tendency of the friction coefficient on bare gold is similar to that on mercaptopropionic acid, but the absolute friction coefficient on mercaptopropionic acid is smaller than that on bare gold because of the lubrication. Mechanical resonance of the instrument plays an important role in the measurement. To confirm whether the minimum friction coefficient is related to the mechanical resonance, the resonance response of the apparatus was measured. A lock-in amplifier (Stanford Research Systems, Sunnyvale, CA) was used to drive the piezoelectric actuator instead of the function generator, and it scanned from 1 to 100 KHz. Figure 7.4 shows that the resonance peak appears at 20.7 KHz; that is far higher than the frequency where the minimum friction was achieved. Moreover, the inset of Figure 7.4 shows that the amplitude is almost constant or decreases slightly up to 1 KHz; that implies that the friction decrease at this frequency range is not related to the resonance response of the system. The spikes at 60, 120, and 180 Hz come from electronic noise. We performed numerical simulations aimed to qualitatively describe the experimental findings. Our model imitates the AFM tip as a one-dimensional array of particles moving on a rigid substrate. Such an approach is a natural extension of single-particle model of the AFM tip [23,24]. The basic equations of motion for the driven dynamics of a one dimensional particle array of N identical particles moving on a surface are given by a set of coupled nonlinear equations of the form: mx¨n + Γ x˙n + ∂U/∂xn = F (xn+1 , xn ); (xn , xn−1 ) + K(vt − xcm ),
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Figure 7.4 Mechanical resonance response of the system has been measured using a lock-in amplifier and shows the resonance peak at 20.7 KHz. Inset magnifies the response below 1 KHz. Reprinted with permission from Applied Physics Letters 88 (2006), 214102.
n = 1, . . . , N,
(1)
where xn is the coordinate of the nth particle, xcm is the position of the center of mass, m is its mass, Γ is the linear friction coefficient representing the single particle energy exchange with the substrate, v is the external velocity. The particles in the array are subjected to a periodic potential, U (xn + a) = U (xn ), and interact with each other via a pair-wise force. The substrate potential is assumed to take a simple periodic form. System (1) provides a general framework of modeling friction although the amount of details and complexity varies in different studies. For this case, using the dimensionless phase variables zn = 2πxn /a, the equations of motion reduce to the following form: z¨n + γ z˙ n + sin(zn ) = α(vt − zcm ) + F (zn+1 , zn ); (zn , zn−1 ) .
(2)
Addition of normal oscillation introduces the following modification to the Equation (2): z¨n + γ z˙ n + 1 + A sin(ωt) sin(zn ) = α(vt − zcm ) + F (zn+1 , zn ); (zn , zn−1 ) .
(3)
For interaction potential we considered the Morse potential: F (zn+1 , zn ) =
κ exp −β(zn+1 − zn − p) − exp −2β(zn+1 − zn − p) . β
Here p is the misfit length, κ is the coupling constant, and β is the nonlinearity parameter. For small values of the parameter β, the interaction force becomes well familiar, linear
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Figure 7.5 Time-averaged friction force (numerical simulations) as a function of the oscillation amplitude for a given oscillation frequency (Equation (3)). The insert demonstrates the time-averaged friction force as a function of the oscillation frequency for a fixed oscillation amplitude. All the parameters are in dimensionless form. Reprinted with permission from Applied Physics Letters 88 (2006), 214102.
Frenkel–Kontorova interaction. We solved Equations (3) numerically for chain length of 16–256 particles and using periodic boundary conditions. Throughout the chapter, we used the following parameter values: γ = 0.05; α = 1.; κ = 1.; β = 0.2; p = 0.1111111; and v = 0.1. Initial conditions have been chosen randomly. We altered the values of the oscillation amplitude and frequency while the rest of the parameters were kept unchanged. Depending on parameters of the system (such as sliding velocity, oscillation amplitude and frequency), the friction force dependence on the oscillation parameters shows various trends. In this chapter, we only discuss how friction coefficient changes with the oscillation amplitude and frequency, keeping all the other parameter unchanged. An example of significant friction reduction by the oscillation is demonstrated in Figure 7.5 where we demonstrate the time-averaged friction force as a function of the oscillation amplitude for a given oscillation frequency. The insert demonstrates the time-averaged friction force as a function of the oscillation frequency for fixed oscillation amplitude. Both curves show significant reduction of friction and are qualitatively agree with the experimental results (Figure 7.2(a) and 2(b)). The friction force does not significantly depend on oscillations for small oscillation frequencies amplitudes and drops significantly when the amplitude of oscillations grows. For very large oscillation frequencies friction force increases and reaches approximately constant value that is independent on the oscillation frequency. As the frequency range for friction reduction is significant, we believe the observed reduction is not a resonant effect and manifests significant change in frictional dynamics due to oscillations.
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Different trends of frictional behavior may be observed for oscillation frequencies that are too close or much higher than the characteristic oscillation frequency defined by the AFM scanning velocity. Figure 7.6(a) demonstrates friction force dependence on the oscillation amplitude for oscillation frequency ω = 0.1. For the given values of the parameters and low oscillation frequency, friction force depends erratically on the oscillation frequency though both increase and decrease in friction force is not very large. Figure 7.6(b) demonstrates friction force dependence on the oscillation amplitude for high oscillation frequency ω = 10. Here, the general trend of the friction force is to decrease with the increase in the amplitude of the oscillation however, the friction force decrease is not very high. Figure 7.6(c) demonstrates friction force dependence on the oscillation amplitude for oscillation frequency ω = 5. The general trend of the friction force dependence in Figure 7.6(c) is very similar to the trend in Figure 7.5 however, the significant dropout in the frictional behavior occurs for higher oscillation amplitude (A = 2). To demonstrate some aspects of the oscillation response, we present (Figures 7.7) the power spectrum of friction force oscillations for three different types of frequency regimes. These spectra indicate profound changes in the dynamics of the array as the oscillation frequency was increased. In Figure 7.7(a) we show the power spectrum when the oscillations are absent (the pronounced peak in the power spectrum corresponds to the value of the sliding velocity, v = 0.1 in dimensionless units). Figure 7.7(b) illustrates the power spectrum for the case of ω = 1 and A = 1 and the major peak corresponds to the value of the external frequency. For these parameter values (Figure 7.7(b)) the value of the average friction force drops significantly. Figure 7.7(c) illustrates the power spectrum for the case of ω = 5 and A = 1. Even though the external frequency mode is presented in the spectrum (the peak at ω = 5), the most pronounced effect on the dynamics comes from the low frequency mode that corresponds to the sliding velocity (v = 0.1), and the effect of the oscillations on friction is minimal. As the average friction force for A = 1 is very small and the dynamics is dominated by the external drive (see Figure 7.7(b)), the friction force oscillates from the positive to the negative values with the main oscillation period given by the external excitation (this friction force behavior was verified through the time series). Consequently, friction force is negative for some portion of the time and acts as an additional driving force on the chain. For other cases (A = 0 and ω = 5, Figures 7.7(a) and 7.7(c)) the friction force is positive for the most of the time resulting in high average friction force. As the behavior of friction force in the presence of oscillations is very complex, additional studies needed to further understand and control frictional behavior by surface oscillations. We postulate the following atomistic mechanism of friction reduction by external vibration. The motion of the tip induces additional time scale to the system that we estimate in our experiment of the order of a kHz. As the scanning frequency is 1.97 Hz and the scan size is 100 nm, the velocity of the tip v0 is approximately 400 nm/sec. A characteristic length L of the inter-atomic distance is of the order of 0.2–0.3 nm, thus the characteristic frequency of the system in the lateral direction is f = v0 /L ≈ 1.4–2 kHz. Normal external vibrations introduce additional characteristic time scale to the system (also in the lateral direction) as the strength of the surface potential alternates with the external vibration. Interplay between these two characteristic frequencies is a very complex nonlinear phenomenon and may result in variety of responses of the friction force. However, when the oscillation amplitude is large enough (for an appropriate frequency range), the system will
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(a)
(b)
(c) Figure 7.6 Time-averaged friction force (numerical simulations) as a function of the oscillation amplitude for a given oscillation frequency (Equation (3)). (a) corresponds to ω = 0.1; (b) corresponds to ω = 10.; (c) corresponds to ω = 5.
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(a)
(b)
(c) Figure 7.7 Power spectra of the friction force for three different values of the oscillation frequencies. In (a) we demonstrate power spectrum when the oscillations are absent (the peak in the spectrum corresponds to the value of the sliding velocity, v = 0.1 in dimensionless units). (b) demonstrates the power spectrum for the case of ω = 1 and A = 1. (c) demonstrates the power spectrum for the case ω = 5 and A = 1. Reprinted with permission from Applied Physics Letters 88 (2006), 214102.
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follow the external excitation and the average friction force will decrease. The proposed mechanism is qualitatively described in the theoretical model. 7.2.2
Summary
In summary, a significant reduction in friction coefficient has been observed as a result of very small amplitude of surface oscillation in the KHz frequency range. Both periodic sinusoidal as well as random oscillations result in a significant decrease of friction coefficient, indicating the robustness of the effect. The significance of this result may be attributed to both fundamental and application aspects. Eliminating the need to select a proper range of oscillation frequencies (that may be very narrow) to achieve the desired effect significantly relaxes constraints on the implementation of such a method of friction control and indicates the robustness of the effect and the applicability to systems other than the AFM.
ACKNOWLEDGEMENTS We would like to thank Dr. Thomas M. Rosseel for his thoughtful comments about the manuscript. This research was supported by the U.S. Department of Energy (DOE) Division of Materials Sciences and Engineering, DOE Office of Biological and Environmental Research (OBER), and DOE-Environmental Science Management Program (EMSP). Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for DOE under contract DEAC05-00OR22725. Y.B. acknowledges the support of the DOE/BES Center for Excellence in Nanotribology.
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–8– Effect of Surface Roughness and Adsorbates on Superlubricity V.N. Samoilov1,2 , C. Yang1 , U. Tartaglino1,3 and B.N.J. Persson1 1 IFF, FZ-Jülich, 52425 Jülich, Germany 2 Physics Faculty, Moscow State University, 117234 Moscow, Russia 3 Democritos National Simulation Center, Via Beirut 2, 34014 Trieste, Italy
8.1 INTRODUCTION Friction between solid surfaces is a very important phenomenon for biology and technology [1] and it is very common in nature. Static friction always involves the coexistence of different metastable configurations at microscopic levels. When one surface slides on the other at low speed, first there is a loading phase during which the actual configuration stores elastic energy. Then, when the stored energy is large enough, an instability arises [2–4]: the system jumps abruptly to another configuration and releases elastic energy into irregular heat motion. The exact way of how the energy is dissipated does not influence the sliding friction force, provided that the dissipation is fast enough to happen before the next sliding event takes place. There are many possible origins of elastic instabilities, e.g., they may involve individual molecules or, more likely, groups of molecules or “patches” at the interface, which have been named stress domains [5–8]. As a result the overall motion may not exhibit any stick and slip behavior at macroscopic level, since the local rearrangements can occur at different times in an incoherent manner. Moreover, at least at zero temperature, the friction force does not vanish in the limit of sliding speed v → 0, but it tends to reach some finite value which depends on the average energy stored during the loading events. On the other hand, a system without instabilities cannot present a non-vanishing kinetic friction as v → 0: if for any sliding distance there exist only one stable configuration, the energy stored at the interface is a single-valued function of the relative sliding distance. Thus when sliding occurs slowly the process has to be reversible, i.e., with negligible friction. If the structure of the two contacting surfaces does not match, the formation of pinned states is hindered: when some groups of atoms are in registry with the other surface, occupying a local energy minimum, some other groups of atoms cannot adjust to the local Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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energy-minimum configuration without the deformation of the solids. In this case, there is a competition between two energies: the lateral corrugation of the interaction potential between the walls, and the elastic energy to deform the solid so that every surface patch adjusts into a local minimum. If the latter prevails, the system is pinned and static friction appears. Otherwise, if the solid is sufficiently stiff, local domains do not show any instability and can overcome reversibly the local barriers. The overall effect is a motion with no static friction, since when some domains move uphill some other regions move downhill, so that the total energy is constant. This absence of instabilities due to a mismatch of the two surfaces’ structures has been named superlubricity [9], although a more appropriate name would have been structural lubricity [10]. It is well known that elastically hard solids tend to exhibit smaller sliding friction than (elastically) soft materials [11]. One extreme example is diamond which under normal circumstances exhibits very low kinetic friction coefficient, of the order of 0.01, when diamond is sliding on diamond. This can be explained by the nearly absence of elastic instabilities because of the elastic hardness of the material. Recently, superlubricity has been observed during sliding of graphite on graphite: in the experiment described in [12] a tungsten tip with a graphite flake attached to it is slid on an atomically flat graphite surface. When the flake is in registry with the substrate stick-slip motion and large friction are observed. When the flake is rotated out of registry, the forces felt by the different atoms start to cancel each other out, causing the friction force to nearly vanish, and the contact to become superlubric. Graphite and many other layered materials are excellent dry lubricants. The most likely reason for this is that the solid walls of the sliding objects get coated by graphite flakes or layers with different orientation so a large fraction of the graphite–graphite contacts will be in the superlubric state. This will lead to a strong reduction in the average friction. However, the coated solid walls are unlikely to be perfectly flat and clean, and it is important to address how surface roughness and adsorbates may influence the superlubric state. Here we will show that even a relatively small surface roughness or low adsorbate coverage may kill the superlubric state.
8.2
MODEL
The results presented below have been obtained for an elastic flat block sliding on a rigid substrate. We considered both flat and rough substrates. The atoms in the bottom layer of the block form a simple square lattice with lattice constant a. The lateral dimensions Lx = Nx a and Ly = Ny a. For the block, Nx = Ny = 48. Periodic boundary conditions are applied in the xy plane. We have used a recently developed multiscale molecular dynamics model, where the block extends in the vertical z-direction a similar distance as along the x-direction [13] (see also [14]). The lateral size of the block is equal to that of the √ substrate, but for the latter we use a different lattice constant b ≈ a/φ, where φ = (1 + 5)/2 is the golden mean, in order to hinder the formation of commensurate structures at the interface. For the substrate, Nx = Ny = 78. The mass of a block atom is 197 a.m.u. and the lattice spacing of the block is a = 2.6 Å, so to get the same atomic mass and density of gold. The lattice spacing of
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the substrate is b = 1.6 Å. We consider solid blocks with different Young’s moduli from E = 0.2 GPa up to 1000 GPa. The Poisson ratio of the block is ν = 0.3. Many surfaces tend to be nearly self-affine fractal. A self-affine fractal surface has the property that if part of the surface is magnified, with a magnification which in general is appropriately different in the perpendicular direction to the surface as compared to the lateral directions, then the surface “looks the same”, i.e., the statistical properties of the surface are invariant under this scale transformation [13,15]. For a self-affine surface the power spectrum has the power-law behavior C(q) ∼ q −2(H +1) ,
(1)
where the Hurst exponent H is related to the fractal dimension Df of the surface via H = 3 − Df . Of course, for real surfaces this relation only holds in some finite wave vector regions q0 < q < q1 , and in a typical case C(q) has a roll-off wave vector q0 below which C(q) is approximately constant. In our calculations, we have used self-affine fractal surfaces generated as outlined in [15], with the fractal dimension Df = 2.2 and the roll-off wave vector q0 = 3qL , where qL = 2π/Lx . We have chosen q0 = 3qL rather than q0 = qL since the former value gives some self-averaging and less noisy numerical results. We also used q1 = 2π/b = 78q0 . The atoms at the interface between the block and the substrate interact with the LennardJones potential 6 r0 12 r0 − , (2) U (r) = 4ε r r where r is the distance between a pair of atoms. In the calculations presented below, we have used r0 = 3.28 Å and ε = 40 meV, which gives an interfacial binding energy (per unit area) γ ≈ 4ε/a 2 ≈ 24 meV/Å2 . As an illustration, in Figure 8.1, we show the contact between a flat elastic block (top) and a randomly rough rigid substrate (bottom). Only the interfacial block and substrate atoms are shown. Note the elastic deformation of the block, and that non-contact regions occur in the “deep” valleys of the substrate. In all results presented below the upper surface of the block moves with the velocity v = 0.1 m/s, and the (nominal) squeezing pressure p, if not stated otherwise, is one tenth of the elastic modulus E of the block, i.e., p = 0.1E. We did also some test calculations for v = 1 m/s (not shown) but found very similar results as for v = 0.1 m/s. In fact, neglecting heating effects, one does not expect any strong dependence of the friction force on the velocity, as long as it is much smaller than the sound velocity (typically 1000 m/s), and much higher than the velocities where thermally activated creep motion becomes important (usually a few µm/s). Furthermore, the sliding direction does not play a significant role since the commensurability ratio 8/13 is the same along the x and y directions. For the (randomly) rough surfaces we did some test calculations where we reversed the sliding direction and found that the friction force changed by at most 20%. This is a finite-size effect: for an infinite system sliding along the positive or negative x-axis cannot change the friction force.
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Figure 8.1 The contact between an elastic block with a flat surface and a rough rigid substrate. Only the interfacial layers of atoms are shown. The elastic modulus of the block is E = 100 GPa. The substrate is self-affine fractal with the root-mean-square roughness 3 Å, fractal dimension Df = 2.2. The applied pressure p = 10 GPa.
The reason for choosing p proportional to E is twofold. First, we consider solids with elastic modulus which varies over several orders of magnitude, and it is not possible to use a constant p as this would result in unphysical large variations in the elastic deformation of the block. Second, if two elastic solids are squeezed together with a given load, then as long as the area of real contact is small compared to the nominal contact area, the pressure in the contact areas will be proportional to the elastic modulus of the solids [16]. The system is kept at low temperature by a viscous friction (a Langevin thermostat at T = 0 K) applied only to the topmost layers of block atoms, which are far away from the interface. On the time-scale of our simulations we observed no significant variation in the frictional shear force which could be attributed to a (slow) heating up of the system.
8.3 NUMERICAL RESULTS We first consider the sliding of clean smooth and rough surfaces for elastic solids with different elastic modulus and surface roughness. We also study the influence of adsorbed molecules on sliding friction. We show that already a small surface roughness or less than a monolayer of adsorbed molecules may strongly increase the friction. 8.3.1
Clean Smooth and Rough Surfaces
Let us first assume that both the block and the substrate have atomically smooth surfaces. Figure 8.2 shows the shear stress as a function of the elastic modulus E of the block. Note the relatively abrupt decrease in the friction when the elastic modulus changes from E1 ≈ 0.7 GPa to E2 ≈ 2 GPa. For E > E2 practically no instabilities occur and the friction is extremely small, while for E < E1 relatively strong elastic instabilities occur at the sliding interface, and the friction is high. For E = 0.2 GPa the static friction μs > 2. This calculation illustrates that the transition from high friction to superlubricity can be very
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Figure 8.2 The shear stress at depinning (static friction) and during sliding (kinetic friction) as a function of the elastic modulus E of the block, for the flat substrate. In the calculation we have used the squeezing pressure p = 0.1E and the sliding velocity v = 0.1 m/s.
abrupt; in the present case an increase in the elastic modulus by only a factor of 3 (from 0.7 to 2.1 GPa) decreases the kinetic friction by a factor of ∼105 . We have studied the variation of the shear stress as a function of time when the elastic modulus of the block equals (a) E = 0.8 GPa and (b) E = 2 GPa. When the elastic modulus of the solid is above the superlubricity threshold as in case (b), no significant elastic instabilities occur; the stress is a periodic function of time, with the period corresponding to the displacement 0.2 Å. For softer solids, when strong elastic instabilities occur during sliding as in case (a), the shear stress is less regular (and the arrangement of the interfacial block atoms more disordered) than for the stiffer solid, and the (average) period is longer than 0.2 Å. The remarkable abruptness of the superlubricity transition is illustrated in Figure 8.3, which shows the average displacement of the interface block atoms (in the sliding direction) as a function of time, for the flat substrate. Note the onset of stick-slip as the elastic modulus of the block decreases from E = 1.3 GPa (upper curve) to 1 GPa (lower curve). The regular pattern with period 0.2 Å has a simple geometrical explanation related to the commensurability ratio 8/13 along the sliding direction: in the ground state each block’s atom has 8 allowed positions within the cell b of the substrate. Hence there are 8 equivalent configurations within a sliding distance b = 1.6 Å. Let us now consider the influence of surface roughness on the sliding dynamics. In Figure 8.4 we show the average shear stress for an elastic block sliding on a rough substrate, as a function of the elastic modulus E of the block. For the substrate with the largest roughness, no superlubricity state can be observed for any elastic modulus up to E = 1012 Pa. Our results are in agreement with the theoretical predictions of Sokoloff [17]: roughness on multiple length scales can induce a transition from a weak pinning regime to a strong pinning regime. The main difference between our model and the one of Sokoloff is that
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Figure 8.3 The average displacement of the interface block atoms (in the sliding direction) as a function of time, for the flat substrate. The elastic modulus of the block is E = 1, 1.1, 1.2 and 1.3 GPa. The transition from high friction (stick-slip) to superlubricity (steady sliding) is demonstrated clearly.
Figure 8.4 The shear stress for an elastic block sliding on rough substrates, as a function of the elastic modulus E of the block. The curves from top to bottom correspond to the root-mean-square roughness amplitudes of the fractal substrate 3, 1, 0.3, 0.1 Å and 0 (flat substrate).
the latter assumes purely repulsive interactions between the atoms, while here the attractive part of the Lennard-Jones potential gives rise to an adhesive pressure pad which will contribute to the effective load. Since in our case pad ≈ 10 GPa, the shear stress that we obtain is almost independent of the external load. We have also studied the shear stress as a function of time for different elastic moduli, see Figure 8.5. Note that in addition to major slip events, several small slip events occur in all cases. These events correspond to local slip at some asperity contact regions before the major slip involving the whole contact area. In all cases, the time dependence of the shear stress remains periodic with the period 2.6 Å, which corresponds to the lattice spacing of the block. At the current sliding speed v = 0.1 m/s the kinetic friction force is smaller
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Figure 8.5 The shear stress as a function of time for the rough substrate with the root-mean-square roughness amplitude 3 Å. The elastic modulus of the block is E = 100, 20 and 5 GPa.
for the stiffer solid even if the load is larger: although the maximum shear stress achieved before sliding is quite big in such case, the average shear stress is small and part of the elastic energy stored in the loading phase is not dissipated, but it is given back to the system. For the elastically softer blocks (E = 20 and 5 GPa), the stress-noise increases after each major slip event; this is caused by the elastic waves (heat motion) excited during the (major) rapid slip events and not completely adsorbed by the thermostat. In Figure 8.6, we show the effect of the substrate root-mean-square (rms) roughness amplitude on the shear stress as a function of time for the block with the elastic modulus E = 10 GPa. We varied the root-mean-square roughness amplitude from 3 to 0.1 Å. For the rms roughness amplitudes 0.3 and 0.1 Å the major slip is not as abrupt as for higher roughness amplitudes. In all cases, the time dependence of the shear stress remains periodic with the period 2.6 Å determined by the lattice spacing of the block. For the rms roughness 3 Å two small and a major slip events can be observed in each period, and the kinetic friction is high. For the case with the rms amplitudes 0.3 and 0.1 Å (almost) no elastic instability occurs, and the kinetic friction is very small. In Figure 8.7, we show the average displacement of the interface block atoms (in the sliding direction) as a function of time for the block with the elastic modulus E = 10 GPa, and for the rough substrate with various roughness amplitudes. The transition from high (stick-slip) friction for the most rough surface to very low friction (smooth sliding) for the surfaces with root-mean-square roughness 0.3 and 0.1 Å is clearly demonstrated. 8.3.2
Dependence of the Friction on the Load
We now study the dependence of the friction force on the load. We consider both flat surfaces and the case where the substrate is rough. For flat surfaces the frictional shear stress is independent of the squeezing pressure p as long as p is smaller than the adhesion pressure pad which is of the order of 1010 Pa. For rough surfaces the situation is more complex and the frictional shear stress will depend on the squeezing pressure p even for very small p unless at least one of the solids is so compliant that the attractive interaction becomes important for the contact mechanics.
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Figure 8.6 The shear stress as a function of time for the rough substrate with the root-mean-square roughness amplitudes 3, 1, 0.3 and 0.1 Å. The elastic modulus of the block is E = 10 GPa. The transition from high friction to superlubricity is demonstrated clearly.
Figure 8.7 The average displacement of the interface block atoms (in the sliding direction) as a function of time for the rough substrate with the root-mean-square roughness amplitudes 3, 1, 0.3 and 0.1 Å. The elastic modulus of the block is E = 10 GPa. The transition from high friction (stick-slip) to superlubricity (steady sliding) is clearly demonstrated.
Flat Surface During sliding, the atoms at the sliding interface will experience energetic barriers derived from both the attractive interaction between the atoms on the two opposing surfaces, and from the applied load. Thus, we may define an adhesion pressure pad , and as long as pad ≫ p, where p is the pressure in the contact area derived from the external load, the frictional shear stress will be nearly independent of the applied load. Let us first consider the limiting case where the elastic modulus of the block is extremely small. In this case, in the initial pinned state (before sliding) all the block atoms will occupy hollow sites on
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Figure 8.8 A block atom moving (or jumping) from the hollow site A over the bridge site B to the hollow site C. The maximum energy position along the trajectory is at site B.
the substrate, as indicated by atom A in Figure 8.8. During sliding along the x-direction, the atom A will move over the bridge position B and then “fall down” into the hollow position C (we assume overdamped motion). The minimum energy for this process is given by the barrier height δε ( the energy difference between the sites B and A) plus the work pa 2 δh against the external load, where a is the block lattice constant and δh the change in the height between sites B and A (which depends on p). Thus the frictional shear stress σf is determined by σf a 2 b = δε + pa 2 δh, or σf = δε/ ba 2 + pδh/b = (pad + p)δh/b,
where we have defined the adhesion pressure pad = δε/(a 2 δh). In our case δε ≈ 3 meV and δh ≈ 0.008 Å giving pad ≈ 1010 Pa. Thus, in the present case, only when the local pressure in the contact regions becomes of the order of ∼10 GPa, or more, it will start to influence the shear stress. This result is in accordance with our simulation results. Thus, for smooth surfaces, the shear stress acting on the block with the elastic modulus E = 0.5 GPa, squeezed against the substrate with the pressure p = 50 and 150 MPa, is identical (≈1 MPa) within the accuracy of the simulations. Rough Surface In the absence of adhesion, contact mechanics theories predict that the area of real contact A between two elastic solids with randomly rough (but nominally flat) surfaces is proportional to the squeezing force (or load) FN as long as A ≪ A0 (where A0 is the nominal contact area). The law A = αFN holds strictly only if the roughness occurs on many different length scales [18], but this is (almost) always the case for natural surfaces (e.g., a stone surface) or surfaces of engineering interest. For an infinite system (thermodynamic limit) not only A is proportional to FN , but the distribution of sizes of the contact regions, and the stress distribution in the area of real contact, is independent of the squeezing force if A ≪ A0 . The physical picture behind these results is that as the squeezing force increases, new contact regions are formed in such a way that the quantities referred to above
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remain unchanged. However, for any finite sized system this picture cannot hold exactly as it requires that some contact regions have infinite-size, which is possible only for an infinite sized system. When the attractive interaction cannot be neglected, the area of real contact is often assumed [19] to be of the form A ≈ α(FN + Fad ) where Fad represents an adhesive load, but this relation is only approximate [18,20]. If the friction force Ff is assumed to be proportional to the area of real contact, then one expects Ff = σc A ≈ σc α(FN + Fad ) so that the nominal frictional shear stress σf = Ff /A0 ≈ σc α(FN + Fad )/A0 = σc α(p + σa ),
(3)
where p = FN /A0 is the (nominal) squeezing pressure and where the so-called detachment stress [18,20] σa gives a contribution to the frictional stress from the attractive wall–wall interaction. From (3) it also follows that the friction coefficient μ = σc α(1 + σa /p) will diverge as the squeezing pressure p goes to zero. We have studied the dependence of the frictional shear stress on the squeezing pressure for the system studied above, for the block elasticities E = 10 GPa and E = 100 GPa, and for the rigid substrate with the rms roughness amplitude 3 Å. In Figure 8.9 we show (a) the (nominal) frictional shear stress and (b) the friction coefficient as a function of the squeezing pressure when E = 10 GPa. Note that, because of the attractive interaction, the
Figure 8.9 The shear stress at depinning (static friction) and during sliding (kinetic friction) (a) and the static and kinetic friction coefficients (b) as a function of the applied pressure, for an elastic block sliding on a rough substrate. For the substrate with the root-mean-square roughness amplitude 3 Å. The elastic modulus of the block is E = 10 GPa.
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frictional shear stress is constant for low squeezing pressures, while the friction coefficient diverges as p → 0. The adhesion contribution σc ασa to the frictional shear stress becomes important only when the elastic modulus of the block is small enough. The transition, with decreasing elastic modulus, from the case where the adhesion can be neglected to the case where it is important, is rather abrupt. To illustrate this we show in Figure 8.10 the interfacial atoms (the top atoms of the substrate and the bottom atoms of the block) for blocks with the elastic modulus E = 1000, 100, 10 and 5 GPa, and with the squeezing pressure p = 0.1E. In the absence of adhesion all the systems would exhibit virtually identical arrangement of atoms. Indeed the two stiffest solids exhibit very similar atom-arrangements, but there is a clear change when E decreases from 100 to 10 GPa; in the latter case the attractive interaction is able to pull the solids into intimate contact over most of the nominal contact area. Thus the bottom surface of the block is able to bend and fill out a substrate “cavity” with diameter D and height h if the gain in wall-wall binding energy, which is of the order of D 2 γ (where γ is the interfacial binding energy per unit surface area for flat surfaces), is equal to (or larger than) the elastic energy stored in the deformation field in the block, which is of the order of ED 3 (h/D)2 . This gives the “critical” elasticity Ec ≈ D γ / h2 . In the present case we have a distribution of roughness wavelength but we can obtain a rough estimate of Ec by taking h2 = h2 = 9 Å2 as the mean of the square of the roughness profile and D ≈ 100 Å as a typical roughness wavelength. Using γ ≈ 4ε/a 2 ≈ 24 meV/Å2 this gives Ec ≈ 40 GPa which is between 100 and 10 GPa. This change in the contact mechanics has a large influence on the sliding friction. Thus, as we now will show, for the block with elastic modulus E = 100 GPa there will be a negligible contribution to the friction from the attractive interaction and σa ≈ 0. Figure 8.11 shows the frictional shear stress for the same system as in Figure 8.9 except that the elastic modulus of the block is ten times higher. In this case the influence of the attractive interaction is negligible, and the frictional shear stress decreases continuously as the squeezing pressure decreases. However, the friction coefficient is not constant as expected from the arguments presented above related to the invariance of the pressure distribution and contact size distribution with the squeezing force. This fact must be related to the small size of the system used in our simulations. As the squeezing pressure increases the stress distribution at the interface and the average size of the contact regions will change in such a way that when p increases from p = 5 to 10 GPa there is a very rapid increase in asperity contact regions undergoing elastic instabilities during sliding. This can be directly demonstrated by comparing the time-variation of the shear stress for p = 5 and 10 GPa, see Figure 8.12. Note that at the higher pressure some slip events take place before the main slip event, i.e., new elastic instabilities appear and the frictional shear stress increases much faster than linear with the nominal squeezing pressure as p increases from 5 to 10 GPa. To illustrate the small influence of the adhesion on the contact mechanics for the block with the elastic modulus E = 100 GPa we show in Figure 8.13 the interfacial atoms for the squeezing pressures p = 10, 3, 1 GPa and 0. When p = 0 only the adhesion pressure is acting and the area of real contact almost vanishes.
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Figure 8.10 The contact between an elastic block with a flat surface and a rough rigid substrate. Only the interfacial layers of atoms are shown. The elastic modulus of the block is E = 1000, 100, 10 and 5 GPa (from top to bottom). The substrate is self-affine fractal with root-mean-square roughness 3 Å. The applied pressure p = 0.1E. Note the elastic deformation of the block, and that the real contact area is smaller than the nominal contact area for high values of the elastic modulus of the block.
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Figure 8.11 The shear stress during sliding (kinetic friction) (a) and the kinetic friction coefficient (b) as a function of the applied pressure, for an elastic block sliding on a rough substrate. For the substrate with the root-mean-square roughness amplitude 3 Å. The elastic modulus of the block is E = 100 GPa.
Figure 8.12 The shear stress as a function of time for the rough substrate with the root-mean-square roughness amplitude 3 Å. The elastic modulus of the block is E = 100 GPa and the applied pressure p = 5 and 10 GPa.
8.3.3
Role of Adsorbates
Extremely low sliding friction is possible only in the absence of elastic instabilities. As shown above, this is possible for stiff enough solids with incommensurate (or nearly incommensurate) surface structures. However, any types of imperfections may “lock” the surfaces together and introduce elastic instabilities during sliding. One type of “defect” discussed above is surface roughness. Another possibility is adsorbed molecules. Adsorbed molecules may arrange themselves at the interface between the two solids in such a way as to pin the solids together. A low concentration of (strongly bound) adsorbates is in
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Figure 8.13 The contact between an elastic block with a flat surface and a rough rigid substrate. Only the interfacial layers of atoms are shown. The elastic modulus of the block is E = 100 GPa. The substrate is self-affine fractal with root-mean-square roughness 3 Å. The applied pressure p = 10, 3, 1 GPa and 0 (from top to bottom). For the latter case only the adhesion pressure is acting. Note the elastic deformation of the block, and that the real contact area is smaller than the nominal contact area.
many ways similar to nanoscale roughness and it is clear that if the perfect system (flat surfaces without adsorbates) is in a superlubric state, one would expect a strong increase in the friction already at a low adsorbate coverage. We have performed an extensive set
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Figure 8.14 The kinetic friction coefficients for the elastic block (E = 100 GPa) sliding both on smooth and on rough substrates, as a function of liquid coverage (octane, C8 H18 ) θ confined between two walls [21]. The substrate has the root-mean-square (rms) roughness 3 Å and the fractal dimension Df = 2.2. The applied pressure p = 1 GPa.
of computer simulations to illustrate this effect both for atomically smooth surfaces and for rough surfaces. In Figure 8.14 we show the kinetic friction coefficients for the elastic block (E = 100 GPa) sliding both on smooth and on rough substrates, as a function of liquid (octane, C8 H18 ) coverage θ confined between two walls, for the applied pressure p = 0.01E [21]. Note that for flat surfaces, there is a very abrupt increase in the friction with increasing adsorbate coverage. In fact, the friction increases by a factor of ∼106 as the coverage increases from zero to 0.22 monolayer. For 0.22 < θ < 2 the friction is nearly constant. For the rough surface, the increase in the friction is much smaller. In this case the (small) increase in the friction results from octane molecules trapped in the asperity contact regions1 —this results in an effectively increased surface roughness and enhanced friction.
8.4
SUMMARY AND CONCLUSION
To summarize, we have studied the sliding of elastic solids in adhesive contact with flat and rough interfaces. We considered the dependence of the sliding friction on the elastic modulus of the solids. For elastically hard solids with planar surfaces with incommensurate surface structures we observe extremely low friction (superlubricity), which very abruptly increases as the elastic modulus decreases. Thus, at the superlubricity threshold, 1 In the simulations the C H bed-units interact with the solid wall atoms via the Lennard-Jones potential with 8 18 the well-depth parameter ε = 40 meV. This relatively strong interaction leads to lubricant molecules trapped in the asperity contact regions. Other studies (see [21]) with ε = 5 meV result in the squeeze-out of the lubricant from the asperity contact regions into the “valleys” or “cavities” of the substrate height profile. In this case, which we will report on elsewhere [21], we do not expect any adsorbate-induced increase in the friction.
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an increase in the elastic modulus by a factor of ∼3 resulted in the decrease in the frictional shear stress by a factor ∼105 . We have shown that even a relatively small surface roughness, or a low concentration of adsorbates, may completely kill the superlubricity.
ACKNOWLEDGEMENTS A part of the present work was carried out in frames of the ESF program “Nanotribology (NATRIBO)”. Two of the authors (U.T. and V.N.S.) acknowledge support from IFF, FZJülich, hospitality and help of the staff during their research visits.
REFERENCES [1] Persson, B.N.J. Sliding Friction: Physical Principles and Applications, second edition. Springer, Heidelberg, 2000. [2] Aubry, S. J. Phys. (Paris) 44 (1983), 147. [3] Persson, B.N.J., Tosatti, E. Solid State Commun. 109 (1999), 739. [4] Caroli, C., Nozières, P. In: Persson, B.N.J., Tosatti, E. (Eds.), Physics of Sliding Friction. Kluwer, Dordrecht, 1996. [5] Persson, B.N.J., Albohr, O., Mancosu, F., Peveri, V., Samoilov, V.N., Sivebaek, I.M. Wear 254 (2003), 835. [6] Persson, B.N.J. Phys. Rev. B 51 (1995), 13568. [7] Caroli, C., Nozières, P. Eur. Phys. J. B 4 (1998), 233. [8] Baumberger, T., Caroli, C. Adv. Phys. 55 (2006), 279. [9] Shinjo, K., Hirano, M. Surf. Sci. 283 (1993), 473. [10] Müser, M.H. Europhys. Lett. 66 (2004), 97. [11] Riedo, E., Brune, H. Appl. Phys. Lett. 83 (2003), 1986. [12] Dienwiebel, M., Verhoeven, G.S., Pradeep, N., Frenken, J.W.M., Heimberg, J.A., Zandbergen, H.W. Phys. Rev. Lett. 92 (2004), 126101. [13] Yang, C., Tartaglino, U., Persson, B.N.J. Eur. Phys. J. E 19 (2006), 47. [14] Hyun, S., Pei, L., Molinari, J.F., Robbins, M.O. Phys. Rev. E 70 (2004), 026117. [15] Persson, B.N.J., Albohr, O., Tartaglino, U., Volokitin, A.I., Tosatti, E. J. Phys.: Condens. Matter 17 (2005), R1. [16] Persson, B.N.J. J. Chem. Phys. 115 (2001), 3840. [17] Sokoloff, J.B. Phys. Rev. E 73 (2006), 016104. [18] Persson, B.N.J. Surf. Sci. Rep. 61 (2006), 201. [19] Derjaguin, B.V. Wear 128 (1988), 19; Tabor, D. In: Blakely, J.M. (Ed.), Surface Physics of Materials, vol. II. University Press, New York, 1975, p. 475. [20] Persson, B.N.J. Eur. Phys. J. E 8 (2002), 385. [21] Yang, C., Tartaglino, U., Persson, B.N.J. J. Phys.: Condens. Matter 18 (2006), 11521.
–9– Atomic-Scale Investigation of Superlubricity on Insulating Surfaces Enrico Gnecco, Anisoara Socoliuc and Ernst Meyer NCCR Nanoscale Science, Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
9.1 INTRODUCTION Controlling friction on the nanometer scale is one of nowadays’ greatest challenges for scientists and engineers. Since the first observation of atomic friction, reported by Mate et al. for a tungsten tip sliding on graphite [1], great progress has been made in our understanding of friction down to the atomic scale. An accurate description of the motion of a nanoasperity driven on a crystal lattice by a microcantilever was first given by Tomanek et al., who based their interpretation on the Prandtl–Tomlinson model [2]. The frictional force experienced by the tip is quantified by the torsion of the cantilever. The tip sticks to a given equilibrium position on the surface until the driving force becomes large enough to induce a jump into the next equilibrium position. The stick-slip motion reflects the atomic periodicity of the surface with a saw-tooth like modulation of friction. However, this scenario is observed only if a precise condition is verified. The elastic constant of the cantilever spring must be lower than the curvature of the surface potential. If this condition is not satisfied, the tip will move on the surface in a continuous way, and a ‘superlubric’ regime will be achieved. In 2004, superlubricity was observed by our group using a dedicated atomic force microscope (AFM) in ultra-high vacuum (UHV) on a NaCl surface [3]. In such case, the stick-slip motion disappeared if the normal load applied on the tip was reduced down to subnanonewton values. The effect was observed only with sharp silicon tips, whereas superlubricity could be hardly distinguished from noise when tips became blunt by usage. Almost at the same time, Dienwiebel et al. observed negligible friction driving a graphite flake out of registry on a graphite surface [4]. Even if this effect, which arises from the incommensurability of the surfaces in contact, was originally called ‘superlubricity’ by Hirano et al. [5], the term structural lubricity introduced by Müser et al. [6] looks more appropriate to define it. Friction is also reduced if the sliding velocity is very low (in the order of nm/s) [7]. This results from thermal activation of the slip process, which is enhanced at Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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low speeds (thermolubricity). More recently, we have also achieved negligible friction in a different dynamic way [8]. In this case, the contact between tip and surface is periodically excited in the normal direction, which led to a decrease of the energy barrier hindering the tip jumps, and consequently reduced the energy dissipation down to negligible values. Compared to the other methods, ‘dynamic superlubricity’ is not limited to exceptionally low loads or velocities, or to particular orientations of the surfaces in contact. Its applicability to technological devices like micro- and nano-electromechanical systems (MEMS and NEMS) is therefore quite promising. This chapter is organized in the following way. First we review the Tomlinson–Prandtl model in the one-dimensional case. A simple sinusoidal potential will be used, which allows to derive analytical expressions relating measurable quantities, like friction and contact stiffness, to fundamental quantities, like the interaction energy between the contacting surfaces. ‘Steady’ and ‘dynamic’ superlubricity will be naturally introduced in this context. The chapter will continue with a detailed overview of the experiments on alkali halide surfaces performed by our group, which revealed the occurrence of superlubricity in both cases.
9.2
THE TOMLINSON–PRANDTL MODEL
In this section, we address the ‘inverse problem’ of determining the tip–sample interaction from friction measurements. We consider only the one-dimensional case, where the tip slides across a periodic potential, driven by a spring representing the cantilever under torsion. The total potential Utot (x, t) ‘sensed’ by the tip apex is given by the sum of the periodic tip–surface interaction, and the elastic potential of the composite spring system formed by cantilever, tip and contact region. Assuming a sinusoidal shape for the first term of the sum, we can write Utot (x, t) = −U0 cos
2πx 1 + k(x − vt)2 , a 2
(1)
where U0 is the amplitude of the tip–surface interaction, a is the lattice constant of the surface lattice, k is the effective lateral spring constant of the system [9,10], and v is the sliding velocity of the cantilever. (The sign in front of U0 is introduced in order to have a minimum at x = 0 when t = 0.) In Figure 9.1, the total potential Utot (x, t) is represented at different time instants t. The values are typical of AFM experiments with silicon tips on alkali halide surfaces in UHV. The tip is localized in the first position x = xtip where the first derivative of Utot (x, t) with respect to x is zero: 2πxtip ∂Vtot 2πU0 = sin + k(xtip − vt) = 0. ∂x a a
(2)
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Figure 9.1 Potential describing the AFM tip (represented by the black circle) sliding over a periodic surface at t = 0 (thick line) and t = 0.5 s (thin line). The values U0 = 0.63 eV, k = 1 N/m, a = 0.5 nm, v = 1 nm/s have been used.
Expanding the sinusoidal term to the first order in Equation (2), we obtain the initial velocity of the tip, ! dxtip !! v , = vtip (0) = ! dt t→0 1 + η
(3)
where we have introduced the parameter
η=
4π 2 U0 . ka 2
(4)
With the values in Figure 9.1, the friction parameter η = 15.8 and the initial velocity vtip = 0.06 nm/s, i.e. much less than the velocity of the cantilever, v = 1 nm/s. Figure 9.2 shows a numerical solution of Equation (2), where xtip = xmin (t) is represented as a function of time t. The time dependence of the first local maximum of Utot (x, t), xmax (t), is also shown in the figure. The tip velocity does not change significantly as far as the first-order expansion we have used remains valid. At a certain point, however, the tip velocity increases sharply, and a critical value xc is reached, where xtip = xmax , the equilibrium is lost, and the tip suddenly jumps out of equilibrium. When xmin → xc the velocity of the tip tends to infinite [11].
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Figure 9.2 First minimum (thicker line) and maximum (thinner line) of the potential Utot (x, t) as a function of time.
The critical position xtip = xc is obtained from the condition that the second derivative of the total potential Utot (x, t) with respect to x is zero: ∂ 2 Vtot 4π 2 U0 2πx + k = 0, = cos 2 2 a ∂x a
(5)
which gives 1 a arccos − xc = . 2π η
(6)
The absolute value of the lateral force revealed by the AFM at the critical position, Fc , is obtained from Equations (2) and (5): Fc =
ka " 2 η −1 . 2π
(7)
Equations (6) and (7) show that the instability leading to the tip jump can be observed only if η > 1, i.e. if the contact is sufficiently soft and/or the tip–sample interaction is sufficiently strong. With the values in Figure 9.1, the critical tip position and the critical lateral force are xc = 0.13 nm and Fc = 1.25 nN. The critical instant tc at which the jump
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Figure 9.3 Time evolution of (a) the tip position xtip and (b) the lateral force |FL |.
occurs is simply given by Fc = k(xc − vtc ). With the values adopted in Figure 9.1, we obtain tc = 1.38 s, in agreement with the numerical solution in Figure 9.2. The lateral force |FL | = k(vt − xtip ) can also be analytically evaluated when t → 0. In such case, the tip velocity is given by (3), so that ! ! !FL (t)! =
η kvt. η+1
(8)
If the condition η ≫ 1 is satisfied the effective lateral spring constant k is approximately given by the ratio |FL (t)|/vt, which is directly accessible in the experiments. On the other side, if η → 1, the ratio |FL (t)|/vt tends to half the value of k. Incidentally, the absolute value of the lateral force reaches its maximum value Fmax slightly before xc , i.e. when xtip = a/4 [3]. In such position: Fmax =
2πU0 . a
(9)
If η ≫ 1, the previous expressions become quite simple: a xc = , 4
Fc = Fmax ,
tc =
2πU0 . kav
(10)
At any instant, the tip position and the lateral force can be only estimated numerically for a given tip–sample potential. Figure 9.3 shows the time dependence of both quantities for the sinusoidal potential that we have chosen. At the critical point, the derivative of the lateral force |FL | tends to −∞, due to the infinite tip velocity at this point. The lateral force |FL |, however, tends to the finite value (7). After the tip has jumped the cantilever starts to oscillate at its torsional resonance. If these oscillations would not be heavily damped, stick-slip motion would not occur and multiple jumps would appear [12]. Assuming high damping, the tip will quickly relax into the next equilibrium position xc′ . At this point, the lateral force is Fc′ = k(vtc − xc′ ). The values of xc′ and |Fc′ | can be estimated assuming that xc′ = a + δx, where δx ≪ a (this
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Figure 9.4 Friction loop observed on NaCl (from [13]). The non-uniform height distribution of the peaks is due to thermal activation, as explained in the cited reference.
assumption holds only if η ≫ 1). In such case, using expanding again the sinusoidal term in (2) to the first order, we get δx =
vtc − a , η+1
(11)
so that Fc′ = ηkδx. With the values in Figure 9.3: δx = 0.05 nm, xc′ = 0.55 nm, Fc′ = 0.83 nN. Thus, the friction force varies of the quantity | FL | = Fc′ − Fc = 0.42 nN, and an energy amount U = | FL |a = 3.36 eV is released into the sample as phonons. It is not difficult to describe the situation at the following instants. The lateral force |FL | increases again and new jumps of the tip occur whenever |FL | = Fc , as shown in Figure 9.3. What happens if the direction of the support is suddenly inverted? The lateral force |FL | decreases and, whenFL = 0, the situation is exactly the same we had at t = 0, except for the opposite direction. Drawing the lateral force FL as a function of the support position in a forward and backward scanning we get a so-called friction loop, resembling those observed in the experiments (Figure 9.4).
9.3
THE SUPERLUBRIC REGIME
The energy amount U released in each tip jump can be evaluated numerically as a function of the friction parameter η (Figure 9.5). If η < 1, i.e. when the contact is stiff or the tip–sample interaction is very weak, Equations (6) and (7) have no solutions. In such case, the instabilities are completely canceled, so that no abrupt release of energy occurs, and U = 0. In what follows, we will refer to this case as the superlubric regime. Figure 9.5 shows that the transition from stick-slip to superlubricity is smooth, i.e. the energy dissipation vanishes when η → 1 without abrupt variations. In this sense, we can say that the friction parameter η behaves like an order parameter in a second-order phase transition. The relation between U and η can be analytically evaluated only in the extreme cases η → 1 and η → ∞, where the dependencies U ∼ U0 (η − 1)2 and U ∼ U0 respectively hold [14].
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Figure 9.5 Energy dissipation per cycle as a function of the frictional parameter η. An effective stiffness of 1 N/m, similar with the value found in the experiment, and the lattice constant a = 0.5 nm were considered for the calculation of U .
In order to relate the energy dissipation to the normal force FN applied between tip and surface, one has to know the relation between the friction parameter η (or the energy amplitude U0 ) and FN . In our experiments on NaCl in vacuum, we found a linear relation [3]. The normal force FN required to reach superlubricity is always very low, often below the instrumental noise level. Even if superlubricity was observed in the ‘steady’ case, the applicability of these results is scarce. However, the restriction given by low normal loads can be easily overcome if the normal force FN is oscillated with time at a given frequency f . If the oscillation amplitude is small, this is equivalent to replace the constant U0 in (1) with U0 (1 + α cos 2πf t), where α < 1. Due to the fact that f ≫ v/a, the tip experiences the minimum corrugation U0 (1 − α) several times as the cantilever slowly crosses the distance which separates adjacent potential minima, and hence slides smoothly once
ηmin =
2π 2 U0 (1 − α) < 1. ka 2
(12)
In such way the parameter ηmin replaces η in the condition for the occurrence of superlubricity. This simple idea is confirmed by numerical calculations. As illustrated in Figure 9.6(a), the computed average frictional force FL decreases linearly with α and becomes negligible beyond a critical value αcr . As shown in Figure 9.6(b), curves obtained for different values of η essentially collapse on the “steady” curve when plotted versus ηmin . The curve α = αcr , where
αcr = 1 −
1 η
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Figure 9.6 (a) Numerical evaluation of the energy dissipation per cycle as a function of the parameter α. The four symbols correspond to η = 7, 5, 3 and 1 (top to bottom). (b) Numerical evaluation of the energy dissipation per cycle as a function of the parameter ηmin . The four symbols correspond to η = 7, 5, 3 and 1 (top to bottom). (c) Depending on the values of η and α(ηmin ), two sliding regimes are possible. The contact stiffness was considered to be 1 N/m, the lattice constant a = 0.5 nm, the modulation frequency 567 Hz.
divides the (η, α) plane in two regions (Figure 9.6(c)). Below the critical curve normal oscillations do not remove the instabilities leading to stick-slip and dissipation. In the upper region the oscillations prevent the tip slippage, and friction becomes negligible.
9.4
EXPERIMENTAL EVIDENCE OF SUPERLUBRICITY: QUASISTATIC CASE
Here, the first experimental observation of the transition from stick-slip to continuous sliding in atomic friction is described. The regime of ‘static superlubricity’ (η < 1), theoretically discussed in the last section, can be achieved experimentally, independent of the nature of the involved surface, if the parameters that determine the value of η can be correctly tuned. In the experiment η is reduced by decreasing the amplitude of the tip–sample interaction potential via a variation of the normal load. The measurements were realized with a home built friction force microscope operated at room temperature and under UHV conditions [15]. Silicon cantilevers with a spring constant of kN = 0.05 N/m for normal bending and kT = 29 N/m for torsion were used. The
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radius of curvature of the tip was nominally below 15 nm. The feedback loop controlling the tip–sample distance was operated very slowly, in order to avoid any influence of the feedback on the measurement of the lateral forces. The normal and lateral forces acting on the tip were calibrated according to the procedure given in [16]. The experiments were performed on NaCl single crystals previously cleaved in UHV and heated at 150 ◦ C to remove charges produced in the cleaving process. Figure 9.7 show the lateral force FL recorded with three different externally applied normal loads FN . The total normal force between tip and surface is the sum of the externally applied load and the attractive force between tip and sample. The latter has been determined to be 0.7 nN by measuring the force required to pull the tip out of contact. The scan
Figure 9.7 Measurements of the lateral force acting on the tip sliding forward and backward in (100) direction over the NaCl (001) surface. Cross-sections through a two-dimensional scan obtained for external loads (a) FN = 4.7 nN; (b) FN = 3.3 nN; (c) FN = −0.47 nN. Corresponding numerical evaluation of FL from the Tomlinson model for (b) η = 5, (d) η = 3, (f) η = 1. From [3].
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velocity was v = 3 nm/s. For FN = 4.7 nN the lateral force reveals two opposite sawtooth profiles when scanning forwards and backwards (Figure 9.7(a)). The sawtooth modulation has the periodicity of the crystal lattice along the (100) direction and is characteristic for the stick-slip process. The area enclosed in this hysteresis loop is the energy dissipated in one cycle. When the externally applied load is lowered to 3.3 nN the dissipated energy decreases, resulting in an overlap of the curves for the forward and the backward scan. In fact, the lateral force changes its sign in the slip event (Figure 9.7(c)). While the moving spring pulls on the contact before the slip, the contact pulls on the spring after it has slipped to the next atomic position and, thereby, has surpassed the moving support of the spring. A different picture is found when the load is further reduced. For normal loads below a certain threshold, the hysteresis loop and with it the dissipation disappears within the sensitivity of the experimental apparatus (Figure 9.7(e)). The sawtooth modulation of the lateral force is transformed into a continuous modulation of perfect match between forward and backward scan, still showing the atomic periodicity of the surface lattice. Next to the friction loops are the corresponding theoretical loops obtained for different values of the parameter η (Figure 9.7(b), (d), (f)). For η < 1 the movement is continuous and no dissipation occurs (Figure 9.7(f)), when η > 1 the stick-slip behavior is found (Figure 9.7(d), (b)). According to Equation (9), the corrugation of the sample felt by the tip is proportional to the maximum absolute value of the lateral force Fmax , which can be deduced from the curves in Figure 9.7(a), (c), (e). The load dependence of the potential amplitude U0 is shown in Figure 9.8(a). The corrugation of the surface potential U0 is linearly related to the maximum lateral force Fmax . The increase of the corrugation height of the potential with increasing normal load can be understood as an increase of the height between adjacent atomic positions when the contacting atoms are pressed closer towards the surface lattice. The dependence of the potential value between the tip and surface atoms on the tip position relative to the surface atoms was confirmed in previous studies [17,18]. Experimental determination of U0 were also done by Riedo et al. performing measurements on freshly cleaved and atomically smooth muscovite mica surface in controlled humidity
Figure 9.8 (a) The energy corrugation U0 as function of the normal load FN acting on the tip. U0 is evaluated accordingly to Equation (9) in the Tomlinson model; (b) effective lateral stiffness k of the contact as function of the normal load FN acting on the tip. k is evaluated accordingly to Equation (8) in the Tomlinson model.
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environment [19]. They found similar values for the surface corrugation and even a linear dependence on the external normal load. Figure 9.8(b) shows the load dependence of the lateral stiffness k, determined from the friction loops using Equation (8). The effective stiffness is of the order of 1 N/m, a range that has been found in most of atomic friction studies on different materials [13,20]. The little variation of the effective stiffness with normal load is not obvious. The reason for the constancy of the contact stiffness could be explained in a straightforward manner by assuming that the atomic structure of the contact does not change for normal loads in the nanonewton regime. In this case, the deformability of the structure at the tip apex and of the surface around the contact would not change significantly with load.
9.5
EXPERIMENTAL EVIDENCE OF SUPERLUBRICITY: DYNAMIC CASE
This technique is based on the modulation of the normal force acting between two contacting bodies at well-defined frequencies corresponding to normal resonances of the combined system. Here we show results obtained on NaCl and KBr single crystals cleaved along their (100) plane and heated in UHV for 30 minutes to 120 ◦ C to remove surface charges and contaminants. The thickness of both crystals was about 1 mm. The spring constants of the cantilever used on NaCl were kN = 0.12 N/m for bending and kT = 68 N/m for torsion, whereas kN = 0.03 N/m and kT = 18 N/m for the cantilever used on KBr. Figure 9.9 shows the effect of normal oscillations on atomic friction. When the oscillations are switched on, the characteristic saw-tooth shape of the lateral force vs. dis-
Figure 9.9 Frictional force detected by scanning forwards (continuous line) and backwards (dashed line) on the atomically flat KBr surface. An average normal load FN = 0.67 nN was kept constant by a feedback loop. A bias voltage with f = 41 kHz and amplitude of 5 V was applied and later removed when the cantilever was displaced 2 nm from its initial position.
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Figure 9.10 (a) Average value of the frictional force recorded while applying a modulated bias voltage with frequencies between 0 and 300 kHz. The inset (recorded with a lower sweeping rate) shows that friction falls below the sensitivity of our instrumentation at the resonance frequency fn1 = 40.8 kHz. (b) Thermal noise spectrum of the normal (continuous line) and torsional (dashed line) oscillations of a silicon cantilever in contact with a KBr surface. (c) Average friction force recorded with a lower sweeping rate shows that friction falls below the sensitivity of our instrumentation at the resonance frequency fn1 = 40.8 kHz.
tance curve disappears. The transition is fully reversible, as seen when the oscillations are switched off again on the backward scan. In the following we discuss how the frequency for obtaining the effect is chosen and how the normal load oscillation is applied to the contact. Mechanical resonances of the force sensor can be studied by a frequency analysis of the noise in the normal and lateral force signal. Figure 9.10(a) shows the resonance structure of eigenmodes of the force sensor. The measured resonance frequencies of the cantilever out of contact and in contact with the KBr surface in our measurements are in good agreement with the theoretical resonance frequencies of different vibration modes calculated for the free and pinned-configuration [21]. The resonant excitation of the cantilever in contact with the KBr surface is conveniently done by applying an ac bias voltage between the tip and the sample holder plate, UB . The crystal then acts as a dielectric spacer. Figure 9.10(b) shows the mean lateral force as a function of the applied frequency. Friction is strongly reduced when the frequency matches one of the bending resonance frequencies of the pinned lever or half those values. No similar effects were revealed when the torsional mode of the cantilever was excited. Because the thickness of the sample is much larger than the tip height, the capacitive interaction occurs mainly between the cantilever body and the sample holder. This interaction results
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Figure 9.11 Energy dissipated per cycle while scanning on NaCl(100) as a function of the voltage amplitude UB . The modulation frequency was 56.7 KHz. The average normal load FN = 2.73 nN was kept constant by a feedback loop.
in a capacitive force, FC , proportional to the square of the applied voltage. The attractive force FC oscillates with twice the excitation frequency f . Besides FC , any charge trapped at the tip or any charge layer at the surface results in a non-zero contact potential and in an additional force FQ , which oscillates at the actuation frequency f [22]. Thus, when one of the frequencies f or 2f matches a bending resonance of the pinned lever, the oscillation amplitude causes the normal force FN , and the energy corrugation U0 to vary between two extreme values. The quick variation of the electrostatic forces cannot be followed by the distance-controlling feedback, which keeps constant the mean value of the total normal force over several lattice constants. In the present case, the local interaction is described by a potential with the spatial periodicity of the surface lattice that changes with time as U (t) = U0 (1 + α cos 2πf t) (Section 9.3). A numerical evaluation of the energy dissipation per cycle, U , as a function of the parameter α was shown in Figure 9.6(a). U decreases linearly with α and becomes negligible beyond the critical value αcr . The four symbols correspond to η = 7, 5, 3 and 1 (top to bottom). The dependence U (α) calculated for η = 3 is similar to experimental results U (UB ) shown in Figure 9.11 for η = 3.1 measured from the friction loop in the absence of ac modulation.
9.6 CONCLUSIONS AND OUTLOOK In conclusion, we have introduced two simple methods to achieve superlubricity, and interpreted them on the theoretical basis of the Tomlinson model. Our results, obtained on alkali halide crystal surfaces, may not be easily applied to a general class of macroscopic bodies. It will usually be impossible to find one excitation frequency that is resonantly enhanced for a major part of the microscopic contacts between the surfaces. The situation is, however, totally different for micromechanical devices. These devices have an enormous
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surface-to-volume ratio and friction is a major problem in their application. On the other hand, contacting parts in MEMS often are small enough to constitute single asperity contacts, and their structure favors the development of distinct resonances. Consequently the method demonstrated here could find interesting and important applications in overcoming the problem of static friction in MEMS.
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
Mate, C., McClelland, G., Erlandsson, R., Chiang, S. Phys. Rev. Lett. 59 (1987), 1942. Tomanek, D., Zhong, D.W., Thomas, H. Europhys. Lett. 15 (1991), 887. Socoliuc, A., Bennewitz, R., Gnecco, E., Meyer, E. Phys. Rev. Lett. 92 (2004), 134301. Dienwiebel, M., Verhoeven, G., Pradeep, N., Frenken, J., Heimberg, J., Zandbergen, H. Phys. Rev. Lett. 92 (2004), 126101. Hirano, M., Shinjo, K., Kaneko, R., Murata, Y. Phys. Rev. Lett. 78 (1997), 1448. Müser, M. Europhys. Lett. 66 (2004), 97. Krylov, S.Yu., Jinesh, K.B., Valk, H., Dienwiebel, M., Frenken, J.W.M. Phys. Rev. E 71 (2005), R65101. Socoliuc, A., Gnecco, E., Maier, S., Pfeiffer, O., Baratoff, A., Bennewitz, R., Meyer, E. Science 313 (2006), 207. Carpick, R.W., Ogletree, D.F., Salmeron, M. Appl. Phys. Lett. 70 (1997), 1548. Lantz, M.A., O’Shea, S.J., Welland, M.E., Johnson, K.L. Phys. Rev. B 55 (1997), 10776. Gnecco, E., Bennewitz, R., Gyalog, T., Meyer, E. J. Phys.: Condens. Matter 13 (2001), R619. Johnson, K.L., Woodhouse, J. Trib. Lett. 5 (1998), 155. Gnecco, E., Bennewitz, R., Gyalog, T., Loppacher, Ch., Bammerlin, M., Meyer, E., Güntherodt, H.-J. Phys. Rev. Lett. 84 (2000), 1172. Baratoff, A. et al. Private communication. Howald, L., Meyer, E., Lüthi, R., Haefke, H., Overney, R., Rudin, H., Güntherodt, H.-J. Appl. Phys. Lett. 63 (1993), 117 Meyer, E., Hug, H., Bennewitz, R. Scanning Probe Microscopy. Springer-Verlag, Berlin, 2003. Fujisawa, S., Yokoyama, K., Sugawara, Y., Morita, S. Phys. Rev. B 58 (1998), 4909. Zhong, W., Tománek, D. Phys. Rev. Lett. 64 (1990), 3054. Riedo, E., Gnecco, E., Bennewitz, R., Meyer, E., Brune, H. Phys. Rev. Lett. 91 (2003), 084502. Bennewitz, R., Gyalog, T., Guggisberg, M., Bammerlin, M., Meyer, E., Guentherodt, H.-J. Phys. Rev. B 60 (1999), 11301. Rabe, U. et al. Rev. Sci. Instr. 67 (1996), 3281. Weaver, M.R., Abraham, D. J. Vac. Sci. Technol. B 9 (1991), 1559.
– 10 – Superlubricity of Fullerene Intercalated Graphite Composite Kouji Miura1 and Naruo Sasaki2 1 Department of Physics, Aichi University of Education, Hirosawa 1, Igaya-cho,
Kariya 448-8542, Japan 2 Department of Materials and Life Science, Faculty of Science and Technology,
Seikei University, Kichijoji Kitamachi 3-3-1, Musashino-shi, Tokyo 180-8633, Japan
10.1
INTRODUCTION
It is one of the ultimate goals of tribology researchers to realize an ideal friction-free machinery system with zero energy consumption. Since the proposal of the concept of an ideal frictionless sliding regime [1], fundamental studies on ultralow friction mechanism have been carried out to date based on mainly two different mechanisms: incommensurate contact [2–6] and weak interfacial interaction [7–9]. However, there have been few studies which aimed to use such a concept for practical lubrication engineering applications. Recently, we have shown that a C60 monolayer system confined by graphite walls exhibits ultralow dynamic friction [10,11]. Moreover, we showed that a C60 intercalated graphite film with the area of 2.3 × 2.3 mm2 prepared by chemical and thermal treatments exhibits an ultralow friction coefficient, i.e., μ < 0.001 which is smaller than μ = 0.002 for MoS2 [4] and comparable to μ = 0.001 for graphite [5]. It can be expected that the ultralow friction is induced by internal sliding of alternating close-packed C60 monolayers and graphite layers. Here several possible mechanisms to induce internal sliding, are proposed and discussed. Our results demonstrate that ultralow frictional properties can be controlled by the intercalated materials. C70 intercalated graphite does not exhibit as low an ultralow frictional feature as C60 intercalated graphite. The present study provides a novel lubrication system and an indication of what solid lubrication systems will be like in the future. First, we discuss the origin of utralow friction occurring at a graphite flake on graphite. Second, we explain ultralow friction occurring at graphite/C60 monolayer/graphite system and fullerene (C60 and C70 ) intercalated graphite composite. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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10.2 10.2.1
SLIDING OF GRAPHITE FLAKES
Sliding of Graphite Flakes over Graphite
Figure 10.1 shows images of three kinds of lateral forces (lateral force maps of lateral force acting between probe and surface at different position on the surface) at two different locations generated by sliding of a graphite flake [5] (in the case, a graphite flake of 1 mm2 some micrometers in thickness over graphite in the direction of scanning). The images show a scaly pattern (see Figure 10.1), and the observed periodic change of contrast indicates that the lateral force acting between the probe and graphite clearly varies [8]. The system includes two kinds of friction mechanisms: friction between the probe and graphite and friction between graphite flake and graphite. However, an image of lateral force acting between the probe and graphite is not shown in the figure. Consequently, obtained lateral force images show the lateral force acting between the probe and graphite is lager than the lateral force acting between a graphite substrate and a graphite flake. Thus, a graphite flake moves over a graphite substrate together with the probe during scanning. As Figure 10.1 indicates, images of lateral forces acting during the movement of graphite flake over graphite show diverse patterns. The images show patterns of a large period of transition in the direction from above to beneath. Three kinds of movement of the graphite flake are shown in the lower part of the figure (A to C).
Figure 10.1 Two kinds of lateral force maps of graphite, obtained by scanning the graphite flake along the x direction, where the arrows indicate the scanning direction. The three types (A–C) of movement of the graphite flake are shown in the lower part of the figure [5].
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Figure 10.2
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Experimental and simulated images for type A in Figure 10.1 [5].
Now, let us consider pattern A, which is most observable in the figure. We start by substituting the movement of a graphite flake over graphite into the movement of a single particle, which moves at a constant velocity under the following effective potential: 2π 2π 4π V = V0 2 cos x cos √ y + cos √ y , a a 3 a 3
(1)
where a = 0.284 nm. The effective potential is determined so that it would be minimal from the graphite lamination relation. In short, a = 0.284 nm is a distance of movement to the neighboring point of stability to maintain the AB layers of the graphite. Preliminary calculations show that experimental data are surprisingly reproducible, as it is evident from Figure 10.2. Similarly, other patterns show a movement providing the maintenance of the AB lamination relation of graphite as well (see Figure 10.1). When using 12 meV per about 1 carbon atom as the energy barrier between the AA lamination relation and the AB lamination relation [12], the energy barrier required for sliding is about 1 eV, therefore, the number of participating carbon atoms can be estimated to be more than 100 (the number of graphite unit lattices of some 10 atoms). Consequently, the true contact area between a graphite flake and graphite does not exceed just a part of the graphite flake.
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Lateral Force versus Load Acting between Graphite Surfaces
The behavior of the lateral force acting between a graphite flake and graphite [Figures 10.3(c) and (d)] versus load (normal force applied to the surface vertically by the probe) should be considered. The behavior in the case of the probe sliding over graphite [left-hand pictures (a) and (b)] is shown in Figure 10.3 for comparison. The case shown in Figure 10.3(c) is that when a graphite flake moves in parallel to the direction of scanning or to the direction of tension. In that case, the friction force is weak and proportional to the applied load, and the coefficient of friction equals 0.001. As a graphite flake moves along the [1230] direction of crystal, the foregoing coefficient can be defined as μ[1230] . However, in the case of 10.3(d) when the movement of a graphite flake is not parallel to the direction of tension (similar to A in Figure 10.1), the friction force satisfies the relation α + μFz Fn (α = 1.3 nN, μFz = 0.001, and Fn : load), the parameter α = 1.3 nN being larger than that in case (c) only. A difference observed between (a) and (c) or between (b) and (d) can be explained by a change of friction mechanism during a change from the contact with a single atom probe to the contact with a graphite flake probe (two-dimensional periodic surface). In the case when a graphite flake does not move in parallel to the direction of scanning, a difference between the probe and a graphite flake is observed, but in the case when it moves in parallel, a difference between them is not observed.
Figure 10.3 The mean friction force as a function of loading force for “atomic friction” [(a) “Atom-parallel” and (b) “Atom-zigzag” on the left-hand side] and for “flake friction” [(c) “Flake-parallel” and (d) “Flake-zigzag” on the right-hand side]. The lateral force maps and the tip movement corresponding to each are also presented [5].
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Results show that (1) friction force is minimal when a graphite flake moves in parallel to the direction of tension and (2) in the case when a graphite flake moves not in parallel to the direction of tension, it does not reach the point where the tensile force projection coincides with the force acting in the direction of movement toward the next point of stability. Consequently, the tensile force will increase with an increase of the angle of sliding. As a result, the direction [1230] in which arrays of atoms do not override each other between opposite sliding surfaces, establishes, and in that direction sliding occurs rather easily. In that case, an example of such easy sliding direction is the direction of sliding a MoS2 flake over MoS2 [13]. The common point in each of the foregoing cases is that there exists the direction in which arrays of atoms sliding between two opposite sliding surfaces do not override each other, which results in an easy sliding in the direction. From this point of view, it is interesting to note that a decrease of friction between sliding surfaces occurs.
10.3 10.3.1
SUPERLUBRICITY OF A GRAPHITE/C60 MONOLAYER FILM/GRAPHITE [10]
Structure of a Graphite/C60 Monolayer Film/Graphite System
The upper left-hand image in Figure 10.4 shows a topographic picture (image obtained on an AFM) of graphite (SA ), a C60 monolayer (SB ) on graphite, and a C60 bilayer (SC ) on graphite. When a graphite flake is placed as SA and SB and SC , we have graphite (D) on graphite, graphite (graphite/C60 monolayer/graphite:E) on a C60 monolayer-graphite, and graphite (graphite/C60 bilayer/graphite:F) on a C60 bilayer/graphite, respectively. An image of the lateral force for graphite (A) shows a notable load dependence at lower loads (normal force applied by the probe on the surface vertically). Along graphite crystallographic orientations [1230] and [1010], the probe shows the one-dimensional stick-slip motion and two-dimensional zigzag stick-slip motion [5,8]. Images of the lateral force generated in the case of the C60 monolayer (B) on a graphite and in the case of the C60 bilayer (C) on graphite indicate the one-dimensional stick-slip motion and two-dimensional zigzag stick-slip motion of the probe along scanning direction [110] and [112] in the (111) plane [14,15]. Now, as the contact between the probe and the C60 monolayer is unstable, it is more difficult to obtain clear images of the lateral force in the case of the C60 monolayer than in that of the C60 bilayer. As is evident from the B lateral force image, the C60 monolayer forms a dense structure on graphite (see Figure 10.4). It means that six-member rings of C60 molecules build up on graphite to maintain the AB lamination relation of graphite. Consequently, the position of a six-member ring is observable on the top of the C60 molecules. In the case of the D lateral force image, it becomes clear [5] that a graphite flake performs the zigzag movement over graphite to maintain the AB lamination relation of graphite, as it has been shown in the preceding section. Therefore, if graphite flakes pile up on the C60 monolayer as on the lamination relation of C60 molecules on graphite, the six-member ring network of the graphite flake uppermost layer is projected through the C60 monolayer. This coincides perfectly with the six-member ring network of the uppermost layer of a graphite substrate lying beneath.
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Figure 10.4 Topographs (atomic force microscope images) for graphite (area SA ), C60 monolayer on graphite (area SB ) and C60 bilayers on graphite (area SC ). Lateral force maps and tip movement for representative scan direction for graphite (A), C60 monolayer on graphite (B), C60 for graphite flake on graphite (D). Lateral force maps and tip movements for (B) an (C) are the same [10].
Consequently, a system consisting of a C60 monolayer squeezed by graphite from both sides is structured as a nanogear (AB lamination relation) by carbon six-member rings of the upper and lower C60 molecules. 10.3.2
Ultralow Lateral Movement of C60 Molecules
Figure 10.5 shows image of lateral force versus load for graphite/C60 monolayer/ graphite (E). Images of E show a change to a chain-type structure with load (see Figure 10.5). From the periodicity and contrast points of view, the images clearly differ from those of lateral force obtained from graphite (A) [5,8], C60 (111) surface (B and C) [14,15], and the graphite flake placed on graphite (D) [5]. As was discussed earlier, such systems involve two types of friction mechanisms: friction between the probe and graphite and friction of a C60 monolayer squeezed by graphite. However, images of lateral force obtained
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Figure 10.5 Lateral force maps versus loading force for graphite/C60 mono/graphite (E). Lateral force loops obtained from line profiles shown by the arrows a and b in the lateral force maps are also represented, where the solid and broken lines indicated one direction and in the opposite direction, respectively. Super cell structures of the lateral force maps are illustrated on the left-hand side. Mean frictional force versus loading force shown by the arrow a is shown on the bottom [10].
from graphite (A) are not given; therefore, obtained lateral force images show only a lateral force obtained from the C60 monolayer squeezed by graphite. The images show that the lateral force generated between the probe and graphite is larger than the lateral force generated in the case of the C60 monolayer squeezed by graphite (E). This indicated that a graphite flake moves over a graphite substrate together with the probe during scanning. Under a load of 9 nN, lateral force images show periods of 1 nm in the x-direction (scanning direction) and periods of 2.6 nm in the y-direction. It is suggested that the foregoing facts reflect the close-packed C60 molecular arrangement, but the reason behind the appearance of the structure with the additional periodicity of 2.6 nm in the y-direction has not been clarified yet at this stage. Therefore, notice that the lateral force established from the line profile shown in Figure 10.5 by an arrow a does not almost contain a hysteresis in a repeated lateral force. However, as the arrow b indicated the occurrence of two-dimensional zigzag movement of a graphite flake, the friction force has hysteresis, and dissipation does occur. As the lower part of Figure 10.5 shows, an increase of applied load leads to an expansion of a region of superlubricity and the almost zero mean friction force indicated by
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an arrow a. This is rather useful from a practical point of view because a region of superlubricity expands with an increase of applied load. In the present experiments, the maximal friction force is 1 nN and below. This compares with the force (0.4 nN) [15], which moves a single C60 molecule over graphite.
10.4 10.4.1
SUPERLUBRICITY OF C60 (C70 ) INTERCALATED GRAPHITE COMPOSITE Preparation and Structure of C60 (C70 ) Intercalated Graphite Composite
C60 (C70 ) intercalated graphite films were prepared as follows, as illustrated in Figure 10.6. Specifically, graphite (highly oriented pyrolytic graphite HOPG): for lateral force measurement and natural graphite powder for high-resolution transmission electron microscopy (HRTEM) were stirred for 16 hours in a reaction mixture of concentrated sulfuric acid and nitric acid (4:1, v/v). The acid-treated natural graphite was washed with water until neutralized and dried at 100 ◦ C to remove any remaining water. The dried graphite particles were heat-treated at 1050 ◦ C for 15 seconds to obtain exfoliated graphite particles, which were then immersed in 70% alcohol solution in an ultrasonic bath [16–18]. A C60 (C70 ) powder and the exfoliated graphite enclosed in a vacuum-sealed quartz tube were placed in a furnace at 600 ◦ C for 15 days [18]. The structure of the C60 (C70 ) intercalated graphite film was investigated using HRTEM (JEM-2000EX) for very thin sections of an intercalated graphite film prepared from natural graphite powder, which may not be representative of the entire sample. Thus, a structural model for the C60 (C70 ) intercalated graphite film is constructed only from HRTEM image. HRTEM images of the C60 intercalated graphite thin film (mean diameter: 500 µm) are shown in Figures 10.7(a) and 10.7(b), normal to the (0001) plane of graphite and parallel to the (0001) plane of graphite, respectively, where the indexes used are the same as those of graphite. These images show that the close-packed C60 monolayers of the nearest neighbor
Figure 10.6
Preparation of C60 (C70 ) intercalated graphite films.
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Figure 10.7 (a) and (b) High-resolution transmission electron microscopy (HRTEM) images of C60 intercalated graphite film, normal to (0001) plane of graphite and parallel to (0001) plane of graphite, respectively, where indexes of this film used are same as those of graphite. (c) Model for calculating equilibrium distance d with C60 molecule intercalated between graphenes. Normal load Fz and total energy U as functions of interlayer distance of graphenes d. For d ∼ = 1.3 nm, Fz = 0 (U takes a minimum value), which means that d ∼ = 1.3 nm is an equilibrium distance.
distance 1 nm between C60 molecules within the (0001) plane of graphite, are formed with a periodic spacing of 1.3 nm normal to the (0001) plane of graphite. Figure 10.7(c) shows a model for calculating the equilibrium distance d with one C60 molecule intercalated between graphenes. The normal load Fz and total energy U as functions of distance between graphenes d were calculated optimizing the structure of graphite/one C60 /graphite system, using the Tersoff potential [19] as a potential energy of chemical bonds within C60 molecules, and the Lennard-Jones potential [20] as an interaction potential energy between a C60 molecule and graphenes. For d ∼ = 1.3 nm, Fz = 0 (U takes a minimum value), which means that d ∼ = 1.3 nm is an equilibrium distance. Furthermore, HRTEM images of the C60 intercalated graphite film quite often have Moiré features, which exhibits that alternating C60 (C70 ) close-packed monolayers have orientations around c-axis of the graphite slightly different from each other. When the C60
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Figure 10.8 Lateral force maps and lateral force hysteresis loops as a function of displacement for a C60 intercalated graphite film obtained using a frictional force microscope, where the solid and dotted lines indicate one direction and its opposite, respectively. At a loading force of 100 nN, the lateral pattern with 1-nm-period spacing appears, which corresponds to the nearest neighbor spacing between C60 molecules within a clear C60 close-packed monolayer but not to that between the carbon atoms of the graphite.
close-packed monolayers distribute randomly around the c-axis of the film, ultralow friction is expected to be observed in all scan directions mentioned below. The essentially same mechanism—friction-induced reorientation of the (0001) basal planes of the MoS2 grains in the contact interface parallel to the sliding direction has been also pointed out by Martin et al. [4].
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Figure 10.9 Lateral force maps and lateral force hysteresis loops as a function of displacement for a C70 intercalated graphite film obtained using a frictional force microscope, where the solid and broken lines indicate one direction and its opposite, respectively. At all loading forces of from 0 to 100 nN, the lateral pattern with 0.7-nm-period spacing appears, which can be thought to correspond to the nearest neighbor spacing between C70 molecules within the C70 close-packed monolayer but not to that between the carbon atoms of the graphite. Here it should be noted that we do not correctly know a structure of a C70 monolayer on a graphite although we know a structure of a C70 bilayer on a graphite.
10.4.2
Superlubricity of C60 (C70 ) Intercalated Graphite Composite
The lateral force versus displacement hysteresis loops for the C60 intercalated graphite film (2.3 mm × 2.3 mm × 0.2 mm) using a frictional force microscope are shown in Figure 10.8. When the loading force is lower than 100 nN, the friction forces are not periodic and becomes smaller than 0.1 nN. Furthermore, the feature of ultralow friction force was
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observed in all scan directions, which is confirmed by rotating the scanner underneath the C60 intercalated graphite substrate. The relation between the mean lateral force FL and the load Fz exhibits friction coefficient μ < 0.001 which is smaller than μ < 0.002 for MoS2 observed by Martin et al. [4] and μ = 0.001 for graphite previously observed by our group [5]. However the loading force increases up to nearly 100 nN, which we call the critical loading force, the lateral pattern with 1-nm-period spacing appears, which corresponds to the nearest neighbor spacing between C60 molecules within a clear C60 close-packed monolayer but not to that between the carbon atoms of the graphite. The critical loading force ranges from 80 nN to 120 nN on the entire surface of a film. This result indicates that the motion of C60 molecules is inhibited by the squeezing action of graphite walls and/or by the formation of a chemical bond between a C60 molecule and a graphene [21]. This speculation indicates that an existence of fluid layers confined by solid surface would be important for lubrication. On the other hand, the C70 intercalated graphite film exhibits quite different behavior. The lateral force versus displacement hysteresis loops for the C70 intercalated graphite film (2.1 mm × 2.2 mm × 0.2 mm) using a frictional force microscope are shown in Figure 10.9. The lateral pattern with 0.7-nm-period spacing appears, which can be thought to correspond to the nearest neighbor spacing between C70 molecules within the C70 closepacked monolayer but not to that between the carbon atoms of the graphite at all loading forces of 0–100 nN, as illustrated in Figure 10.9. Interestingly, the periodic friction forces without any hysteresis is quite similar to those of the system of a C60 monolayer confined by graphite walls [10,11]. However, the friction coefficient μ < 0.001 is quite small and similar to that for C60 intercalated graphite film.
10.5
ORIGIN OF SUPERLUBRICITY OF FULLERENE INTERCALATED GRAPHITE COMPOSITE
10.5.1
Elastic Property of New Composite
The elastic property of the new composite, especially C60 intercalated graphite film, is qualitatively discussed by lateral spring model. If the C60 intercalated graphite film is assumed to be comprised of n + 1 parallel layers, which can be modeled by the series connection of the n lateral springs as illustrated in Figure 10.10, n is evaluated as n = 0.2 mm (sample thickness)/1.3 nm (interlayer distance) ∼ = 1.5 × 105 . Here the effective spring constant of each lateral spring, which corresponds to that of graphite/C60 /graphite layer is obtained as k ≈ 1 nN/1 nm = 1 N/m, since the lateral force curve for a graphite/C60 /graphite system measured by our group shows the sawtooth behavior with a magnitude on the order of 1 nN for a period of 1 nm [10]. Therefore, if it is assumed that the shear force is uniformly spread on the C60 intercalated graphite film, the effective spring constant of the series connection of the n lateral springs becomes keff ≈ 1/n N/m with n ∼ = 1.5 × 105 . Here the macroscopic scan length of 0.1 × n ∼ = 15 µm corresponds to the lateral force of 0.1 nN.
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However, we must be careful to conclude here only by this simple elastic model because it seems difficult to determine whether the scan process is within the elastic region or not, only from Figure 10.8, because of our limited noise level of 0.1 nN, even if the tip is moved far around 15 nm. Furthermore our preliminary simulations of the graphite/C60 /graphite system and the previous simulations by other groups [22,23] have shown that stick-slip sliding of the graphite sheet occurs even on an atomic scale, and that the periodic friction force of several piconewtons is obtained, that’s to say, the elastic region is less than 1 nm. Since this means 0.1 × n ∼ = 10, which is quite different from the = 1 nm, which leads to n ∼ 1.5 × 105 . This difference of n is due to the following possible reaabove evaluation n ∼ = sons that the shear force is not actually distributed uniformly due to the finite elastic contact radius between the tip and the surface, that only small parts of the gap between graphite sheets are packed by C60 molecules, and furthermore that the composite is comprised of nonuniform layered structure such as domains and island structures. These problems can be clarified by obtaining the lateral force curve with a scan length of nanometer to millimeter by friction force microscopy with an excellent noise level smaller than 0.1 nN, or by measuring the friction using larger tip with a curvature of radius of nanometer to millimeter. This kind of study is very important to clarify the mechanism of friction on the intermediate region between nm and mm, and the relation between the nanotribology and macrotribology, which can open a new research area of lubrication engineering. 10.5.2
Internal Sliding of New Composite
Since the lateral spring model (Figure 10.10) mentioned above can explain only the elastic region of our ultralow-friction system, more atomistic model which can describe nonelastic behavior such as the sliding process must be considered. Although the atomistic mechanisms of internal sliding have not been theoretically clarified yet, this effect can be speculatively considered as follows: Figures 10.7(a) and 10.7(b) indicate that the C60 (C70 ) intercalated graphite films consist of alternating close-packed C60 (C70 ) monolayers and graphite layers (graphenes), as illustrated in Figure 10.11, in which there are many possible
Figure 10.10 Lateral spring model of C60 intercalated graphite film comprised of n parallel layers, which is modeled by the series connection of the n lateral springs.
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Figure 10.11 Structural model of C60 intercalated graphite films consisting of alternating close-packed C60 monolayers and graphite layers with 1.3-nm-period spacing. The film has many sliding planes formed between each C60 monolayer and graphene indicated by arrows.
Figure 10.12 Change of lateral force map due to a difference of sliding positions. (a) If sliding occurs mainly between the tip and the top layer of the C60 (C70 ) intercalated graphite film, information of graphite is obtained. (b) If sliding occurs both at the top and inside the C60 (C70 ) intercalated graphite film, information of superposition of graphite and C60 (C70 ) close-packed structure would be obtained. (c) If sliding occurs mainly inside the C60 (C70 ) intercalated graphite film, information of a C60 (C70 ) close-packed structure would be obtained.
sliding planes, depicted by the arrows. Information of the occurrence of sliding inside of the films can be obtained from the lateral force maps of Figures 10.8 and 10.9. First, if sliding occurs mainly between the tip and the top layer of the C60 (C70 ) intercalated graphite film as shown in Figure 10.12(a), the lateral force map of a graphite surface would be obtained. Next, if sliding occurs both at the top and inside the C60 (C70 ) intercalated graphite film as shown in Figure 10.12(b), the quasi-periodic friction force map consisting of the periodicity of a graphite surface and that of a C60 (C70 ) close-packed structure would be obtained, which will be discussed in detail elsewhere. Finally, if sliding occurs mainly inside the C60 (C70 ) intercalated graphite film as shown in Figure 10.12(c), the lateral force map of a C60 (C70 ) close-packed structure would be obtained. Since the lateral force maps obtained in our experiments show the periodicity of close-packed monolayers, it can be indicated that sliding occurs mainly inside a film as shown in Figure 10.12(c). It can be expected that such an internal sliding induces ultralow friction similar to the graphite and MoS2 . However, the novelty or superiority of our developed C60 (C70 ) intercalated graphite film is the unique intercalated structure comprised of the plane (graphene)
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Figure 10.13 C60 intercalated graphite system and the graphite system. (a) In the C60 intercalated graphite system, the “point contacts” between C60 molecules and graphite sheets reduce the area of contact to the minimum, point contact. (b) In the graphite system, the “surface contacts” occur between graphite sheets, where the nearest carbon–carbon bonds, are densely distributed within the graphite sheet.
and balls (fullerenes), which allows internal sliding to occur much more easily than the graphite and MoS2 . 10.5.3
Guideline for Designing Ultralow Friction System
Our results demonstrate one of the guidelines of designing practical ultralow friction system—reducing the contact area between intercalated fullerene and graphite sheet to the point contact, induces quite smooth internal sliding of alternating close-packed fullerene monolayers and graphite layers with small friction coefficient. Details are explained in the following. In the C60 intercalated graphite system, the “point contacts” between C60 molecules and graphite sheets reduce the area of contact to the minimum as illustrated in Figure 10.13(a). This means that the number of the carbon–carbon bonds per unit area involved in the sliding process can be reduced to the minimum. On the other hand, in the graphite system, the “surface contacts” occur between graphite sheets, where the nearest carbon–carbon bonds, are densely distributed within the graphite sheet as illustrated in Figure 10.13(b). The number densities of carbon–carbon bonds per unit area within the unit √ cell of the C60 intercalated graphite and the graphite, nig and ng , can be written as nig = 4 3N/3a12 √ [nm−2 ] and ng = 4 3/a22 [nm−2 ], respectively. Here N denotes the number of the carbon– carbon bonds included in the unit cell of C60 intercalated graphite, and a1 and a2 denote the lengths of one side of the unit cells (Figures 10.13(a) and 10.13(b)). For the case of N = 1, which corresponds to the case of the frustrated AB stacking model proposed by Legoas et al. [22], nig /ng = N · (a2 /a1 )2 ∼ = 0.06 is obtained. Thus the energy required for stretching or breaking bonds to slide the graphite sheet for the C60 intercalated graphite films is only several percent of that for the graphite, per unit cell. We think that’s one of the main reasons that our newly developed C60 intercalated graphite exhibits much more excellent ultralow friction property than the graphite. Thus the important point of our system is that this point-contact type bonds between C60 and graphite are not only weak enough to move C60 molecules smoothly as molecular bearings, but also strong enough to hold the C60
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intercalated graphite structures firmly. Therefore C60 intercalated graphite structure can be considered as one of the best carbon composites to achieve ultralow friction. 10.5.4
Intercalated Fullerenes Can Control Ultralow Friction
Furthermore, the novelty of our system is that the ultralow frictional properties can be controlled by changing the intercalated fullerene species. The observation for the C60 intercalated graphite film using a frictional force microscope shows nonperiodic ultralow friction force smaller than 0.1 nN. However, the observation for the C70 intercalated graphite film shows periodic friction force on the order of 1.0 nN. The speculative interpretation of this difference of frictional features between C60 and C70 intercalated graphite films can be explained by the difference of symmetry of molecular structures as follows: Since the high-rotational symmetry of C60 molecules produces many equivalent symmetric potential barriers and minima corresponding to many degrees of freedom of possible motions. As the graphite sheet slides, several equivalent potential barriers easily vanish to allow C60 molecules to roll and/or fluctuate and to find a path for maintaining the total energy nearly constant. A recent theoretical simulations [22,23] have shown that the rollings and/or fluctuations of C60 molecules induce ultralow friction. Furthermore, at room temperature, there is possibility that, C60 monolayer fluidize by thermal fluctuation, which prevents the periodic solid structure of C60 monolayer from being observed for Fz < 100 nN. Eventually ultralow friction force within the order of magnitude of 0.1 nN is observed. On the other hand, since the C70 molecule has the structural symmetry lower than the C60 molecule, there appear inequivalent asymmetric potential barriers and minima, which prohibit C70 molecule from jumping the energy barrier freely in all directions to find the path to keep the total energy nearly constant. Thus the maximum static friction force of C70 molecule becomes a finite value although that of C60 molecule is reduced to that smaller than 0.1 nN. Thus novelty or superiority of our present work compared to the previous works on superlubricity is to demonstrate one of the guidelines of designing practical ultralow friction system, actually develop practical fullerene intercalated graphite lubricants according to this guideline, and control ultralow frictional properties of this system. On the other hand, the previous works on superlubricity have been fundamental since ideal zero-friction or superlubric mechanism was proposed [1], and have tried to observe ultralow friction which are very small but finite on well-known sample surfaces such as mica [2], Si [3], MoS2 [4], graphite [5,6] and NaCl [9]. Little previous works have paid attention to how to develop a new practical ultralow friction system useful in the lubrication engineering. From the standpoints of technology, our novel system is a startpoint for developing more practical and effective ultralow friction lubricant using intercalated graphite, which will contribute to the reduction of the energy loss and the increase of durability, and eventually the energy and environmental problems. On the other hand, from the standpoints of basic science, our system will contribute to clarify the mechanism of friction on the intermediate region between nm and mm, and the relation between the nanotribology and macrotribology, which opens a new research area of lubrication engineering.
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REFERENCES [1] McClelland, G. Friction at weakly interacting interfaces. In: Grunze, M., Kreuzer, H. (Eds.), Adhesion and Friction. Springer-Verlag, Berlin, 1989, pp. 1–16. [2] Hirano, M., Shinjo, K. Phys. Rev. Lett. 67 (1991), 2642. [3] Hirano, M., Shinjo, K., Kaneko, R., Murata, Y. Phys. Rev. Lett.78 (1997), 1448. [4] Martin, J.M., Donnet, C., Le Mogne, Th. Phys. Rev. B 48 (1993), 10583. [5] Miura, K., Sasaki, N., Kamiya, S. Phys. Rev. B 69 (2004), 075420. [6] Dienwiebel, M., Verhoeven, G.S., Pradeep, N., Frenken, J.W.M., Heimberg, J.A., Zandbergen, H.W. Phys. Rev. Lett. 92 (2004), 1261011. [7] Colchero, J., Marti, O., Mlynek, J. Friction on an atomic scale. In: Guntherot, H.-J. et al. (Eds.), Forces in Scanning Probe Methods. Kluwer Academic Publishers, Netherlands, 1995. [8] Sasaki, N., Kobayashi, K., Tsukada, M. Phys. Rev. B 54 (1996), 2138. [9] Socoliuc, A., Bennewitz, R., Gnecco, E., Meyer, E. Phys. Rev. Lett. 92 (2004), 134301. [10] Miura, K., Kamiya, S., Sasaki, N. Phys. Rev. Lett. 90 (2003), 055509. [11] Sasaki, N., Miura, K. Jpn. J. Appl. Phys. 43 (2004), 4486. [12] Chalier, J.-C., Gonza, X., Michenaud, J.-P. Europhys. Lett. 28 (1994), 403. [13] Miura, K., Kamiya, S. Europhys. Lett. 58 (2002), 603. [14] Okita, S., Ishikawa, M., Miura, K. Surf. Sci. 442 (1999), L959. [15] Okita, S., Miura, K. Nano Letters 1 (2001), 101. [16] Nakajima, T., Matsuo, Y. Carbon 32 (1994), 469. [17] Chen, G., Wu, D., Weng, W., Wu, C. Carbon 41 (2003), 579. [18] Gupta, V., Scarf, P., Rich, K., Romans, H., Müller, R. Solid State Commun. 131 (2004), 153. [19] Tersoff, J. Phys. Rev. Lett. 61 (1988), 2879. [20] Lu, J.P., Li, X.-P., Martin, R.M. Phys. Rev. Lett. 68 (1992), 1551. [21] Wanlin, G., Zhu, C.Z., Yu, T.X., Woo, C.H., Zhang, B., Dai, Y.T. Phys. Rev. Lett. 43 (2004), 245502. [22] Legoas, S.B., Giro, R., Galvao, D.S. Chem. Phys. Lett. 386 (2004), 425. [23] Kang, J., Hwang, H. Nanotechnology 15 (2004), 614.
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– 11 – Superlubricity of Ag Nanometer-Thick Layers under Macroscopic Sliding System in UHV Condition Minoru Goto1 and Fumihiro Honda2 1 Ube National College of Technology, 2-14-1, Tokiwadai, Ube 755-8555, Japan 2 Toyota Technological Institute, 2-12-1, Hisakata, Tempaku, Nagoya 468-8511, Japan
11.1
INTRODUCTION
Soft metallic solid lubricants have been widely used as a solid lubricant in vacuum environments. The lubricity of the films was considered in terms of the material properties of the bulk, which has low shear strength compared to other metals [1]. Bowden and Tabor [1] described the tribological properties of physical-vapor-deposited indium layers, and reported that the coefficient of friction depended on the film thickness and that the minimum coefficient of friction was obtained in the thickness range from 0.1–1.0 µm. Spalvins et al. [2] derived the same conclusion. The thickness dependency on the friction performance of soft metallic films is defined as the film thickness effect, and the thickness of the minimum friction coefficient is called the effective thickness. Halling [3] theoretically analyzed the film thickness effect on a lead lubricant layer as a function of the surface roughness and hardness ratio between film and substrate, and described in detail the film thickness effect. The effective thickness of solid lubricant film could be reduced to the nanometer range if the surface roughness of both the substrate and the counter surfaces were in the nanometer range. Under this condition, the lubricity of the solid lubricant would be controlled by its nano-properties, such as the morphology of the film and the mechanical properties, which are considered to be different from that in the micrometer range. Nowadays, the surface layers at atomic-level contact-areas have been extensively studied using atomic-force microscopy (AFM) or surface-force microscopy [4–7]. In these experiments, the friction force is principally determined by the atomic interaction force between the atoms on the surface and those on the probe, as has been theoretically discussed [6,7]. These studies were performed in an atomic-size area using a small atomic-size probe. However, studies of superlubricity on soft metallic lubricant layers, which applied to the macroscopic sliding system, have not yet been conducted [8]. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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The objectives of this chapter are to demonstrate that the superlubricity can be obtained even if the interaction force between sliding interfaces is a metallic bond force. We selected Ag as a lubricant to minimize the macroscopic friction forces between clean Si (111) surface and single crystal diamond. The Ag is known not to form silicide or carbide; therefore, the sliding interfaces were limited to the atomic layers of Ag under the conditions of either elastic deformation of substrate and slider or no Ag film degradation. Since the shear strength of thick layers of Ag contained the effect of the Ag bulk deformation (i.e., the effect of dislocation motion increases the shear strength of the layers), the nanometer-thick Ag layers were expected to reduce the friction coefficient. In this study, Ag films with a thickness of 0.1 to 170 nm were investigated.
11.2
EXPERIMENTAL DETAILS
A top view of the experimental apparatus used in this study is shown schematically in Figure 11.1. The apparatus consisted of four UHV chambers: a scanning tunneling microscopy (STM) chamber, a reflection high-energy electron diffraction (RHEED) chamber, an Auger electron spectroscopy (AES) chamber, and a frictional experiment chamber, connected in series. The base pressure of the STM, RHEED and AES chambers was less than 1 × 10−8 Pa, and that of the frictional experiment chamber was less than 4 × 10−8 Pa.
Figure 11.1
Schematic diagram of the experimental apparatus.
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The evacuating system of the apparatus was composed of turbomolecular, ion-sputter, and titanium sublimation pumps to avoid oil fume contamination on the sliding surfaces. Substrates of Si (111) were cut from an n-type wafer with a roughness of 0.68 nm rms, and the oxide layer on the Si (111) substrate was removed by iterated flashings under a vacuum lower than 1 × 10−7 Pa [9,10]. The Si (111) surface was defined as clean when a clear 7 × 7 RHEED pattern was obtained, as shown in Figure 11.2. The RHEED pattern of the 7 × 7 structure on a Si (111) surface is generally accepted as a clean surface in investigations of the surface structure of silicon at the atomic level using STM or AFM [11,12]. Silver films were deposited on the substrates using a water-cooled pyrolitic boron nitride (PBN) crucible (Knudsen-Cell) with temperature control, and were used in the frictional experiments without exposure to the atmosphere. The Ag film thickness was precisely regulated as the product of the deposition time multiplied by the deposition rate determined by electron-probe microanalysis (EPMA) and AES [13]. The crystallographical and morphological characterizations of the films were determined in-situ by RHEED and STM techniques. The chemical analysis of the substrate of the surface was also made in-situ by AES. The surface composition on the substrate during the sample preparation process is summarized in Figure 11.3. A clean Ag film on the oxide-free substrate was obtained as a result of this process. A ball-on-flat type of frictional tester was mounted in the vacuum chamber. The frictional experiments were carried out by reciprocally sliding a pin against a substrate rigidly fixed on a sample stage. The pin was driven by a stepping motor at constant speed of 0.05– 5.00 mm/s with the variation of less than 12%. The sensitivities of normal load and friction force measurements were 0.188 mN/mV and 0.175 mN/mV, respectively. The dynamic range for friction force measurement was 0.5–250 mN, and the lowest detectable limit was 0.5 mN. The noise levels of both the normal load and friction force measurements were less than 1 mV. The pin was made of single crystal diamond, and was polished convexly with a curvature radius of 3 mm and with 2.6 nm rms finish, which was fixed on top of the JIS SUS304 stainless steel holder. The diamond pin was cleaned with diluted nitric acid to eliminate heavy metallic contamination, and was rinsed several times in an ultrasonic cleaning vessel with both acetone and methanol before being mounted in the UHV chamber. The absorption
Figure 11.2 RHEED pattern of Si (111) 7 × 7 surface. Acc. Volt.: 15 kV, incident direction: {211}, glancing angle: 3.8◦ .
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Figure 11.3
Results of AES analysis on substrate during sample preparation processes.
Figure 11.4
Backscattering Laue spot of the diamond.
of water molecules and/or hydrocarbons of low molecular weight could not be avoided on the diamond surface, but these have no effect on the friction force compared with those on the Si surface [14,15]. The crystallographic orientation of the sliding surface of the diamond (111) was ascertained by a back-reflection Laue spot of X-ray diffraction, as shown in Figure 11.4. The sliding direction of the {211} axis of the diamond surface against the Si substrate was parallel to the {211} axis of the substrate within the accuracy of ±5◦ . The experimental process was carried out in an UHV environment, with removal of the surface oxide layer from the substrate, and thus, the influences of oxidation and any molecules of contaminants on both Ag film and Si surface were completely eliminated from the frictional experiments.
11.3
FILM-THICKNESS EFFECT ON THE LUBRICITY OF Ag FILM
In this section, the friction performances of epitaxial Ag films, which depend upon the film thickness, are presented in the ultrahigh vacuum condition. Some tribological findings
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were obtained under the conditions eliminating surface roughness of specimens and surface contamination of the substrate. A result of XPS revealed that the tribo-film was not formed on the counter surface during the low friction sliding in this system, which had a mechanism different from the MoS2 and diamond-like-carbon (DLC) case. Before discussing the tribological properties of Ag, we demonstrate the crystallography of the Ag films on the Si (111) 7 × 7 surface. RHEED patterns of Ag films of 0.4, 1.5, and 8.4 nm were shown in Figure 11.5. The incident direction of an electron beam in the left column of the figures ((a), (c), (d)) was parallel to the {110} direction of the substrate. The right column of the figures ((b), (d), (f)) was obtained at the incident direction of {211}. The 7 × 7 pattern of the Si (111) clean surface still remained on the Ag-deposited surface of 0.4 nm, which indicated that the Ag atoms adsorbed on Si (111) clean surface maintained 7 × 7 periodicity. As the deposition process progressed, the RHEED patterns changed to the patterns originating from epitaxial Ag film, a tendency similar to that reported by Gotoh
Figure 11.5 RHEED patterns of Ag films 0.4, 1.5 and 8.4 nm thick. The left column in the figure indicate (a) 0.4 nm-, (c) 1.5 nm- and (e) 8.4 nm-Ag at incident direction of {110}, and the right column indicate (b) 0.4 nm-, (d) 1.5 nm- and (f) 8.4 nm-Ag at incident direction of {211}. Accelerating voltage was 15 kV and glancing angle was less than 4◦ .
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et al. [16,17]. The crystallographic orientation of epitaxial Ag films was maintained up to a thickness of 170 nm. Figure 11.6 indicates the relationship between the average coefficient of friction and the Ag film thickness in the range up to 170 nm during 100 reciprocal sliding passes at a sliding speed of 0.1 mm/s. The average coefficient of friction was 0.01–0.03 in the nanometer-thick region, and the minimum friction coefficient was 0.007 at the film-thickness of 5 nm, which is the same order of superlubricity as MoS2 and DLC [18–20]. The friction coefficient increased in excess of 5.0 nm as the film thickness increased and became 0.06 at 170 nm. On the contrary, the coefficient of friction increased again as the thickness of the film decreased below 5.0 nm, and it reached 0.8 or higher in the case of the clean Si (111) surface. The minimum coefficient of friction became 0.007 at 5 nm, which was approximately one order smaller than that at 170 nm. The correlation between friction coefficient and film thickness is similar to the result of Arnell et al. [21], but our thickness range, in which the lowest coefficient of friction was obtained, was two orders thinner than the range in their results. In our case, the film penetration and/or degradation caused by protrusions on the contact surface, was limited to the sub-nanometer thickness region, since the substrate roughness was in the sub-nanometer range while that of the pin was in the nanometer range. Figure 11.7 shows the results of AES and EPMA analysis on worn surfaces. The Ag MNN intensities √ worn surfaces √ √ of the on films thicker than 0.4 nm was higher than that of the Si (111) 3 × 3-Ag ( 3-Ag) surface which was covered with exactly 1 atomic layer of Ag. This result indicates that Ag films with nanometric thicknesses were hardly worn out during the sliding cycles of 100. The EPMA analysis also shows that the film thicknesses on the worn surfaces were comparable to those on as-deposited films with the thicknesses ranging from 5 to 170 nm. These results, therefore, indicate that the sliding plane appeared on the film/pin interface and/or on the film itself, and that the solid lubricant layer in the nanometer-thick range was still effective as long as the surface roughness of both the substrate and the pin remained smaller than the film thickness. The results of XPS observation of the frictional surfaces of diamond slid against 0.3-nm Ag film are shown in Figure 11.8, together with the XPS results of 0.3-nm Ag film and Si clean surface. The Ag transfer to the diamond surface was not observed in the analyzed
Figure 11.6
Relation between average coefficient of friction and Ag film thickness.
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Figure 11.7
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Results of AES and EPMA analysis on worn surfaces.
Figure 11.8 XPS analysis of the frictional surfaces of (a) diamond, (b) 0.3-nm Ag film and (c) Si clean surface.
area of 30 µm in diameter, whereas 0.3-nm Ag film indicated strong Ag 3d3/2,5/2 peaks on the Ag-deposited Si surface, as shown in Figure 11.8. Donnet and coworkers [18–20] reported the superlubricity of both diamond-like carbon (DLC) and sputtered MoS2 layers, at 0.007 and 0.002, respectively. These low coefficients of friction were characterized by the nature of the interactions between shear planes. The initial high friction forces decreased with the increasing number of reciprocation cycles, which were attributed to the process of the formation of transferred film on the counter surface, the so-called tribofilm formation. For a layered compound such as MoS2 , shearing stress can be released by sliding the basal plane that is bonded by van der Waals force, whereas the interaction would change with the H composition in the case of DLC. As for the obtained results in this study, neither Ag transfer to the diamond surface nor the lost amount of Ag films on the worn surface was observed as far as our XPS and AES analysis revealed. The mechanism of the low friction sliding observed in this study is, therefore, different from the mechanism of tribofilm formation on the counter surface. The shear plane of Ag film in the nanometer-thick region is discussed in the next section.
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DETERMINATION OF THE SHEAR PLANE IN SUPERLUBRICITY OF Ag FILM
In this section, detailed investigations are presented to determine the slip plane, and the role of the nano-morphology for the superlubricity of the Ag layer. Ag film with nanometric thickness changes its morphology by heat treatment on Si (111) 7 × 7 surface. The RHEED pattern obtained from the Ag film at RT reflects a fiber texture structure (FB), in which the Si (111) 7 × 7 surface was covered with Ag fine crystals [16]. The crystallographic orientation was mainly epitaxial with respect to the Si surface. The RHEED pattern of the Ag film at RT showed streaks on the weak 7 × 7 spots, as seen in Figures 11.5(a) and 11.5(b). The origin of the streak from the as-deposited Ag film on the Si (111) surface at RT is the Ag fine crystals on the substrate. The RHEED pattern dramatically changed when the temperature exceeded 470 K. Figure 11.9 shows the RHEED patterns of 0.4-nm and 1.5-nm Ag film annealed at 700 K. The new spots between the 0th Laue zone (L0) and the 1st Laue zone (L1) appear in Figure 11.9(a). These new spots originated from the surface structure, because the spots moved rotationally with respect to the screen when the azimuthal rotation of the substrate was√changed. obtained from the surface of the film were understood √ The RHEED patterns √ √ as 3 × 3-R30◦ superstructure ( 3-Ag) [11]. The 3-Ag is known to be an exact 1 Ag atomic layer on the Si surface, with the Ag atom chemical bonded to the Si topmost atom, and excessive Ag atoms √ forming 3-dimensional islands [11]. On the other hand, both the diffraction spots of the 3-Ag structure and the weak diffraction streaks “c” from the Ag crystals were observed on the film, as shown in Figure 11.9(b). This indicates that the domain of the Ag islands had increased on 1.5 nm-annealed-Ag film. The SEM ex-situ images of these films that were annealed at 700 K for 2 minutes are shown in Figure 11.10. In the case of 0.4-nm-annealed Ag √ film, the Ag facets of excessive Ag (see Figure 11.10(a)) were sparsely located on the 3-Ag surface (Figure 11.10(b)). The SEM image of Figure √ 11.10(b) shows that nearly the entire area on the substrate at 470 K to 700 K was in the 3-Ag domain√ when viewed macroscopically. On the other hand, the population of the Ag crystals on the 3-Ag surface increased for the 1.5 nm-annealed-Ag film, compared with the 0.4-nm-annealed film (Figure 11.10(c)).
Figure 11.9
RHEED patterns of (a) 0.4 nm- and (b) 1.5 nm-Ag film.
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Figure 11.10
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SEM ex-situ images of annealed films (a) Ag facet, (b) 0.4-nm Ag and (c) 1.5-nm Ag film.
Figure 11.11
Results of friction experiments on 3 types of silver films.
Figure 11.11 shows the results of frictional experiments on 3 types of films: 0.4 nm-asdeposited-Ag film, 0.4 nm-annealed Ag film, and 1.5 nm-annealed-Ag film. By the change in film morphology, the coefficient of friction increased from 0.02 to 0.1 on 0.4 nm Ag film, whereas a one-order lower coefficient of friction of 0.01 was still obtained on 1.5 nmannealed Ag film. The friction increase of 0.4-nm Ag film by annealing is understood by changing the shear plane. The friction coefficient of 0.02 for the as-deposited film is caused by shearing of Ag fine crystals on the substrate, whereas that of 0.2 for√the annealed film √ is attributed to the high shear strength between diamond surface and 3 × 3 surfaces covered with exactly 1 atomic layer of Ag atoms. Also, the low friction coefficient of 0.01 for the 1.5-nm-annealed film showed that to obtain the mili-range friction coefficient, the interlayer shearing of Ag crystals is necessary. Figure 11.12 shows the distributions of both the Ag MNN and the Si LVV Auger electron intensity ratio of the inside and outside worn track on 1.5-nm-Ag-annealed film. The Ag MNN intensity ratio increased compared to the undisturbed surface. Because the mean free path of Ag MNN Auger electrons in bulk Ag is approximately 1 nm, the increase in Ag MNN on the worn surface indicates that the
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Figure 11.12 Ag MNN and Si LV distribution across the worn track on 1.5-nm-annealed Ag film. (a) SEM image of worn track, (b) distribution of Ag MNN and Si LV from A to B in the SEM image.
√ Ag crystals on 3-Ag surfaces were crushed and extended by the diamond slider, which was reflected by the increasing coverage by Ag atoms. The fact that the Si LVV intensity ratio decreased on the worn surface supports this explanation. These results clearly prove that the inter-layer shearing in the fine Ag crystals was needed when the low coefficient of friction of 0.01 was obtained, and that the interface shearing between the C atom and the Ag atom was not the cause of the superlubricity in this case. We thus conclude that the low coefficient of friction of as-deposited Ag films on the Si (111) 7 × 7 surface having a thickness in the nanometer range is due to the inter-layer shearing in the Ag crystals.
11.5
MORPHOLOGICAL EFFECT ON SUPERLUBRICITY
The slip plane of Ag layers under the superlubric state has been clarified in the previous section. Subsequently, the morphological effect varying with the growth process of the film is demonstrated in this section. Figure 11.13 shows the STM and the AFM images of the epitaxial Ag films. The thicknesses deposited on the Si (111) 7 × 7 surface at RT were 0.1, 0.4, 1.5, 3.0, 5.0, 20, 75, and 170 nm, respectively. An STM image of the clean surface of Si (111) 7 × 7 was also shown as a reference (Figure 11.13(a)). The Ag films started to grow from a percolated structure on the Si (111) 7 × 7 surface up to one atomic layer that corresponded to 0.1 nm in average, as shown in Figure 11.13(b) [22]. With increasing thickness, Ag atoms formed islands on the terrace of the substrate, which have approximately the same height and a flat-top shape on the percolated structure of one atomic layer, as shown in Figure 11.13(c) and (d). The film structure in these thickness ranges was termed an island structure. The
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Figure 11.13 Relationship between morphological pattern of Ag film and the film thickness: The STM image of (a) 40 × 40 nm2 area on the clean Si (111) 7 × 7 surface, (b) 200 × 200 nm2 area on 0.1 nm-Ag film, (c) 200 × 200 nm2 area on 0.4 nm-Ag film, (d) 1 × 1 µm2 area on 1.5 nm-Ag film and (e) 1 × 1 µm2 area on 3.0 nm-Ag film were shown in this figure, respectively. AFM images of (f) 5.0 nm-, (g) 20 nm-, (h) 75 nm- and (i) 170 nm-Ag films were also obtained from the area of 1 × 1 µm2 , respectively.
Ag islands gradually expanded and combined with each other as the thickness increased, and in due course the network structure of Ag was completely formed over the step-edge of the substrate up to the thickness of 3 nm (see Figures 11.13(e)–(f)). By additional Ag deposition, the morphology of the film changed to continuous rough film, as shown in Figures 11.13(g)–(i). The coefficient of friction became very low at an Ag film thickness of 5.0 nm with a network structure. Figure 11.14 shows a magnified image of the network-structure for a 200 × 200 nm2 area. The image indicates that Ag (111) sheets 0.236 nm thick overlapped the steps of the Si (111) surface at a height of 0.157 nm. The image clearly indicated
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Figure 11.14
Figure 11.15
Magnified image of the network-structure for a 200 × 200 nm2 area.
RHEED patterns of 5 nm-Ag film before ((a) and (b)) and after ((c) and (d)) sliding.
that many defects were involved in the network structure, which reduced its shear strength parallel to the pin sliding direction. Figure 11.15 shows the RHEED pattern of 5-nm Ag film, and Figures 11.15(a)–(b) and Figures 11.15(c)–(d) show before and after sliding, respectively. Figures 11.15(b) and (d) present magnified images of the 1st Laue-zone (indication of L1-Ag (111) in figures) in Figures 11.15(a) and (c), respectively. The Ag (111) spots on the 1st Laue-zone became long extended after the frictional experiment, as shown in Figures 11.15(c) and (d). The results indicate that the Ag (111) plane is rotated within the same plane by shear stress with respect to the Si (111) surface. The corresponding STM images are also shown in
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Figure 11.16 STM images of the morphological change of 5-nm Ag film by sliding. The network-structure (a) disappeared by sliding, and the lamellar structure appeared (see (b) and (c)). The step height of the fragment in (c) was 0.3 nm (see (d)).
Figure 11.16. The network structure disappeared by sliding (Figure 11.16(a) → 11.16(b)), and a lamellar structure appeared instead as shown in Figure 11.16(c). The step height of each fragment was approximately 0.3 nm (Figure 11.16(d)), which corresponds to a single atomic layer of Ag (111), and Figure 11.16(c) image also indicates that the sliding occurred in an interlayer of the Ag (111) plane. The coefficient of friction increased with the decreasing thickness of film thinner than 5 nm. Correspondingly, the morphology of the film gradually changed from a network structure to an island structure, and then to a percolated structure covered with 1 atomic layer of Ag on the Si (111) clean surface, as shown in Figure 11.13(b). Some asperities on the diamond surface would penetrate the film and contact the Si substrate directly, and the number of directly contacting asperities increases as the thickness decreases. The shear strength between the 1 atomic layer of Ag or Si (111) clean surface and diamond asperity is stronger than that of the Ag interlayer [23], as has been discussed in Section 11.4. Thus, the increase of the friction coefficient with the morphological change from the network structure to the percolated structure via island structure can be explained by the fact that the shearing area of Ag (111)/Ag (111) was relatively decreased. Contrarily, the direction of the shear strain in the film was not parallel to the slip plane of Ag crystallites in a film thicker than 20 nm. Figures 11.17(a) and (b) show AFM images of 57-nm Ag film before and after sliding, respectively. The film is classified as a continuous
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Figure 11.17
AFM images of 57-nm Ag film (a) before and (b) after sliding.
Figure 11.18
Rocking curves of Ag (111) peak-intensity.
rough structure in this study. The bumpy surface of the film became smooth after sliding by the diamond pin. In this case, the characteristic RHEED pattern, which is omitted here, was not changed by sliding, but the intensity peak of Ag (111) in X-ray diffraction of Cu Kα was broader, as shown in Figure 11.18. The Ag (111) peaks were obtained by omega-scanmode, in which the angle of “θ ” was scanned with a fixed detector position in the θ –2θ method, on both the as-deposited Ag film and the worn surface of the film after sliding ten times. The results indicate that dislocations were accumulated in the film by sliding, and thus the resistivity of the film against deformation would become greater than that of the network structure when the film morphology changes to continuous film.
11.6
EFFECT OF CRYSTAL ORIENTATION ON SUPERLUBRICITY
The morphological effect plays an important role in the superlubricity of Ag film on the nanometric scale. The sliding plane between Ag (111) lamellae is kept parallel to the pin sliding direction for the sake of nano-morphology, as shown above. It is, therefore, es-
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Figure 11.19
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SOR-XRD results epitaxial and polycrystalline Ag films.
sential that the Ag (111) planes in the shear region is parallel to the pin sliding direction for the superlubricity of Ag thin film. In this section, the effect of the crystallographical orientation on the lubricity of the √ film is clarified for the thickness on a nanometer scale. Silver film growing on the 3-Ag surface at a temperature lower than 303 K has a polycrystalline structure. Figure 11.19 shows the synchrotron-orbital-radiated-X-ray diffraction (SOR-XRD) result of both epitaxial and polycrystalline Ag film with a thickness of 5 nm. Only Ag (111) diffraction peaks are observed on Ag film deposited on a 7 × √7 surface, whereas an Ag (200) peak is additionally observed on film deposited on the 3-Ag surface. This result indicates that Ag √ film grows epitaxially on 7 × 7 surface, whereas the film becomes polycrystalline film on 3-Ag surface. Two types of Ag films (epitaxial and polycrystalline) can be prepared by choosing different surfaces. The friction coefficient of polycrystalline Ag film with a thickness of 5 nm was 0.07 at the beginning of the sliding, then it decreased to 0.02 as the sliding cycle proceeded, as shown in Figure 11.20. The friction coefficient at the starting point of sliding was 3.5 times larger than that at the sliding cycle of 100. The friction coefficient decreased mainly up to 20 cycles and did not decrease subsequently. The two-dimensional orientation of the film surface was observed by RHEED. As a result, no-diffraction spots were visible in the 1st Laue zone of Ag (111) on as-deposited surfaces, whereas the diffraction pattern of Ag (111) was observed on slid surfaces after 10 sliding cycles [24]. This result indicated that the crystal orientation of the film surface had been changed by the mechanical rubbing motion of the diamond pin, i.e., tribo-assisted reorientation occurred on the rubbed surface of 5-nm-polycrystalline Ag film. Figure 11.21 shows STM images of as-deposited and slid surfaces of the film. STM images were obtained on the same surface where RHEED observations were performed. The film morphology of polycrystalline film with a thickness of 5 nm has an irregular appearance, whereas the morphology changed to a lamellar structure after rubbing, similar to the slid surfaces of epitaxial films showing a friction coefficient of 0.007 (see Figure 11.16). This result indicated that the orientation of the topmost layers of the film changed parallel to the pin-sliding direction, and the result agrees well with that of RHEED observations. Figure 11.22 shows Ag (111) and Ag (200) intensities by SOR-XRD as a function of sliding cycles. The intensity of Ag (111) reflection and Ag (200) reflection relate to the
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Figure 11.20
Figure 11.21 1 × 1 µm2 .
Figure 11.22
Friction coefficient of polycrystalline Ag films.
STM images of as-deposited and slid surfaces of polycrystalline Ag film. Thickness: 5 nm, area:
SOR-XRD results of (a) Ag (111) and (b) Ag (200) intensities as a function of sliding cycles.
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Figure 11.23
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FWHM of Ag (111) as a function of sliding cycles.
total amounts of Ag (111) and Ag (100) crystallites. The intensity of the Ag (111) peak became stronger, whereas that of Ag (200) decreased as the sliding cycle proceeded. This means that the Ag (100) domains are gradually disappearing and that the Ag (111) domains cover the entire surface after 50 sliding cycles, i.e., all the crystallites in the film were transformed to Ag (111) domains by the mechanical rubbing motion while undergoing the mechanical shearing force. Figure 11.23 shows a rocking curve width of Ag (111) reflection. The full width at half maximum (FWHM) of Ag (111) also decreases with an increase in reciprocal sliding cycles. Since the FWHM is related to the size of the Ag (111) grain, it is concluded that the domain size of Ag (111) grains increased from 5 nm to 40 nm as reciprocal sliding cycles increased [25]. These mean that the friction coefficient of the film decrease proportional to the re-orientation process. In conclusion, the Ag (111) planes of the crystallites in the film gradually reoriented parallel to the sliding direction, i.e. the film in rubbed area was changed to epitaxial-like film. The correlation between friction performance and crystallographic orientation of 5-nm Ag layer clearly demonstrated that a highly-oriented slip plane of Ag (111) lamellae is necessary to obtain the superlubricity of Ag. The two-dimensionality of the sliding layer is necessary to orient the crystallographic slip plane parallel to the pin sliding direction.
11.7
ORIGIN OF Ag FILM SUPERLUBRICITY
Up to the previous sections, the superlubricity of epitaxial Ag film in the UHV condition has been described in detail. In this section, the origin of the superlubricity of 5-nmepitaxial-Ag film is discussed using the knowledge obtained above. The superlubricity of the film with network structure originates from the weak shear resistance between highly oriented Ag (111) lamellae parallel to the pin sliding direction. Schematic images of the shearing process in the network structure during sliding are shown in Figure 11.24. Figure 11.24(a) shows the cross section of the contact region. At the beginning of sliding, the shear stresses in the film become parallel to the sliding direction (Figure 11.24(b)). Subsequently, plastic deformation occurs (Figure 11.24(c)). During this time, interlayer shearing of Ag (111) lamellae becomes parallel to the sliding direction due to moderate defects in the network structure. Finally, a highly oriented lamellar structure is formed (Figure 11.24(d)). The network structure prevents dislocation pile-up in the Ag layer during
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Figure 11.24
Schematic images of the shearing process in the network structure during sliding.
Figure 11.25 Lamellar structures originated from (a) epitaxial and (b) polycrystalline Ag films (area: 200 × 200 nm2 ).
the deformation, and serves to generate atomically flat lamellae. As a result, macroscopic sliding progresses by integration of the interlayer sliding of each lamella without the effect of work hardening caused by dislocation pile-up in the deforming layers. Figure 11.25 show the lamellar structures originated from epitaxial and polycrystalline Ag films. The lamellar structure originating from the polycrystalline structure was slightly more uneven, compared to that from network structure. This roughening increases the coefficient of friction from 0.007 (epitaxial) to 0.027 (polycrystalline). Atomic flatness of the sliding plane is necessary to reduce shear strength, and the images clearly demonstrated that the atomic flatness of sliding lamellae yields an extremely low friction coefficient. The formation of flat lamellae is important to obtain the superlubric state using Ag thin film.
Superlubricity of Ag Nanometer-Thick Layers
Figure 11.26
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Recrystallization of Ag lamellae by oxidation of Si substrate.
The shear strength between the Ag (111) lamellae is considered to be small, though the interaction between them is a metallic bond force, which is considerably stronger than the Van der Waals force. Figure 11.26 shows recrystallization of Ag lamellae by oxidation of Si substrate. This result indicated that the interaction between Ag (111) lamellae is weak enough to change their form by the change in surface energies on the substrate. Therefore, the lamella structure under the superlubricity of Ag film is in the metastable state. In a case of the superlubricity of MoS2 in the UHV condition as reported by Martin et al. [20], the shear plane is between the c-plane of MoS2 , and the interaction is a weak Van der Waals interaction between S–S atoms. The presented results, however, show that a millirange friction is obtainable, even by strong interaction of the metallic bond between Ag (111) lamellae. Hirano and Shinjo [26] predicted theoretically that the superlubric state will appear even if the interaction between the sliding interfaces is strong enough for metallic bonding, if the criteria for atomic arrangement between the sliding planes are satisfied. In conclusion, the superlubricity of the Ag nano-layer is attributed to the weak shear resistance between highly-oriented Ag (111) lamellae on a nanometer scale parallel to the macro scale sliding interface. The superlubricity of epitaxial Ag layer of nanometric thickness gives another example of the superlubricity originating from a different kind of interaction than a weak Van der Waals force.
11.8
CONCLUSION
This section has described the characteristic features of the superlubricity by epitaxial Ag films on a Si (111) clean surface in an ultrahigh vacuum (UHV) environment. Since the roughness of the contact surface is nanometric in dimension, the critical thickness at which the minimum friction coefficient is obtained, becomes 1–10 nm, which is approximately two orders thinner than that reported in the literature. The minimum friction coefficient is 0.007 at the thickness of 5 nm in which the morphology shows a network structure. The mechanism of superlubricity by Ag film is different from the tribofilm formation theory which was elucidated for the superlubricity by MoS2 and DLC.
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The superlubricity of Ag film originated from the weak shear strength between highly oriented Ag (111) lamellae parallel to the sliding direction. Since the shear strength between C atoms and Ag atoms yields a much higher friction coefficient of 0.2 than the case of interlayer shearing between Ag (111) lamellae, the interfacial sliding between C atoms and Ag atoms is not the cause of the superlubricity. The network structure of 5-nm Ag film contains moderate defects within, which serves to form atomically flat lamellae during the superlubric state of Ag film. The frictional experiments of polycrystalline Ag films show that the effect of crystallographic orientation of Ag crystallites in the film is an important parameter to determine the friction coefficient of Ag film. The two-dimensionality is also an important factor to maintain Ag (111) lamella gliding during sliding. The superlubricity of Ag film with nanometric thickness is attributed to weak shear resistance between highly-oriented Ag (111) lamellae of nanometer scale maintained parallel to the macroscopic sliding interface during sliding.
REFERENCES [1] Bowden, F.P., Tabor, D. The Friction and Lubrication of Solids. Oxford University Press, London, 1964, pp. 115–116. [2] Spalvins, T., Buzek, B. Thin Solid Films 84 (1981), 267–272. [3] Halling, J. Surf. Tribol. Int. 12 (1979), 203–208. [4] Jiang, Z., Lu, C.J., Bogy, D.B., Miyamoto, T. Trans. ASME 117 (1995), 328–333. [5] Shen, W., Jiang, B., Gasworth, S.M., Mukamal, H. Tribol. Int. 34 (2001), 135–142. [6] Luthi, R., Meyer, E., Bammerlin, M., Howald, L., Haefke, H., Lehmann, T., Loppacher, C., Guntherodt, H.J., Gyalog, T., Thomas, H. J. Vac. Sci. Technol. B 14 (1996), 1280–1284. [7] Sasaki, N., Kobayashi, K., Tsukada, M. Phys. Rev. B 54 (1996), 2138–2149. [8] Goto, M., Honda, F. Wear 256 (2004), 1062–1071. [9] Loenen, E.J., van Demuth, J.E., Tromp, R.M., Hammers, R.J. Phys. Rev. Lett. 54 (1987), 373–376. [10] Kraft, J., Surnev, S.L., Netzer, F.P. Surf. Sci. 340 (1995), 36–48. [11] Hasegawa, S., Ino, S. Int. J. Modern Phys. B 7 (1993), 3817–3876. [12] Yokoyama, K., Ochi, T., Sugawara, Y., Morita, S. Phys. Rev. Lett. 83 (1999), 5023–5026. [13] Goto, M., Nakahara, T., Honda, F. IMechE Part J. 218 (2004), 279–291. [14] Miyoshi, K., Buckley, D.H. Appl. Surf. Sci. 6 (1980), 161–172. [15] Goto, M., Honda, F., Uemura, M. Wear 252 (2002), 777–786. [16] Gotoh, Y., Ino, S. Thin Solid Films 109 (1983), 255–261. [17] Gotoh, Y., Ino, S. Jpn. J. Appl. Phys. 17(1978), 2097–2109. [18] Donnet, C., Martin, J.M., Le Mogne, T., Belin, M. Proceedings of the International Tribology Conference, Yokohama, 1995, p. 1153. [19] Donet, C., Martin, J.M., Le Mogne, Th., Belin, M. Tribol. Int. 29 (1996), 123. [20] Martin, J.M., Donnet, C., Le Mogne, Th., Epicier, Th. Superlubricity of molybdenum disulphide. Phys. Rev. B 48 (1993), 10583–10586. [21] Arnell, R.D., Soliman, F.A. Thin Solid Films 53 (1978), 333–341. [22] Gavioli, L., Kimberlin, K.R., Tringides, M.C., Wnedelken, J.F., Zhang, Z. Phys. Rev. Lett. 82 (1999), 129– 132. [23] Goto, M., Nakata, R., Honda, F. Wear 256 (2004), 726–734. [24] Honda, F., Goto, M. Wear 259 (2005), 730–737. [25] Akimoto, K., Fukagawa, K., Goto, M., Honda, F. Thin Solid Films, in press. [26] Hirano, M., Shinjo, K. Phys. Rev. B 41 (1990), 11837–11851.
– 12 – Superlubricity between Graphite Surfaces Martin Dienwiebel1,2 and Joost W.M. Frenken1 1 Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 2504, 2300 RA Leiden,
The Netherlands 2 IAVF Antriebstechnik AG, Im Schlehert 32, 76187 Karlsruhe, Germany
12.1
INTRODUCTION
In technical tribosystems, a reduction of the overall friction losses by a few percent is generally appreciated as a major success. Superlubricity, as we will show in this chapter, can lead to a reduction of friction by one order of magnitude or more, which has been demonstrated under laboratory conditions (i.e. in tribometer or friction force microscopy experiments). For several applications, such as micro-electro-mechanical systems (MEMS), nano-electro-mechanical systems (NEMS) and hard disk coatings, it seems possible to exploit the effect in a microscale technical system. Within this book the word “superlubricity” is used for a variety of situations with extraordinarily low friction forces. Within this chapter we will adopt the more restricted, original definition of the term, referring to the extreme slipperiness that may result when two parallel crystal surfaces slide over each other in incommensurate contact [1]. In such a contact geometry, the lattice mismatch may prevent collective, atomic-scale stick-slip motion of the two surfaces, and thus the static and kinetic friction forces can be so small that they fall below the detection limit of any device presently available to measure frictional forces. In this chapter we present measurements that demonstrate the effect of (in)commensurability on friction between two nanoscopic graphite sheets. At first sight, the results agree well with predictions calculated using the Prandtl–Tomlinson model [2,3]. However, for a more complete understanding it is necessary to also take into account the effect of thermal excitations (‘thermolubricity’). We end this chapter with a brief discussion of technical applications of superlubricity, addressing potential problems and solutions. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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12.2
INCOMMENSURABILITY-INDUCED TRANSITION TO FRICTIONLESS SLIDING
In the framework of the Prandtl–Tomlinson model [2,3], friction between the tip of a Friction Force Microscope (FFM) and the surface is the result of many rapid atomic slips from one minimum of the potential energy landscape to the next. However, when the amplitude of the potential energy surface is below a certain threshold or if a very stiff FFM cantilever is used, the tip can slide continuously over the surface, without the typical slip events that are accompanied by energy dissipation. The transition from stick-slip motion with energy dissipation to smooth, frictionless sliding occurs when the so-called Tomlinson parameter γ ≡ 4π 2 V0 /ka 2 becomes lower than unity. Here, V0 denotes the amplitude of the potential energy variations (assumed sinusoidal), k the spring coefficient of the cantilever and a the lattice constant. It is obvious, that the amplitude of the potential energy surface V0 can be reduced when the distance between the two sliding surfaces is increased. In practice this means that the normal load needs to be reduced. This approach has been taken in a beautiful demonstration experiment by Socoliuc et al. [4], who showed the transition to frictionless sliding upon sufficient lowering of the normal load of an Si tip on an NaCl(100) surface in ultrahigh vacuum (UHV). Hirano et al. first proposed to reduce V0 by changing the commensurability of the contact between two crystalline surfaces [1]. In this way frictionless sliding should become possible for a larger range of contact pressures. The feasibility of this idea was illustrated in several computer simulations, e.g. by Sørensen et al. [5] who performed minimum-energy calculations (at T = 0 K) to compute the friction between a (111)-terminated copper asperity and a copper (111) surface. For an aligned contact regular stick-slip motion was observed with high friction, i.e. a high average lateral force, whereas the friction force vanished when the contact was twisted 16.1◦ out of registry. Also experiments have provided first signs of superlubricity. Using a UHV tribometer, Martin et al. found a remarkably low friction coefficient between clean MoS2 surfaces after a short sliding distance [6]. Debris collected after the experiment was shown to consist of MoS2 layers (flakes) that were all rotated with respect to each other. Martin and coworkers concluded that the low friction coefficient was due to the superlubricity caused by the incommensurability between the rotated flakes. In 1997 Hirano et al. [7] have published a scanning tunneling microscopy (STM) experiment and claimed the observation of superlubricity in UHV between a tungsten tip and a Si(001) surface. The bending of the STM tip was monitored optically and translated into a lateral force. When the crystallographic axes of the two surfaces were aligned into a commensurate contact, a bending of the tungsten wire was measured during scans of the tip over the surface, which was absent when the orientation was changed.
12.3
ATOMIC-SCALE OBSERVATION OF SUPERLUBRICITY BETWEEN GRAPHITE SURFACES
The measurements below were performed with a unique FFM that allows quantitative tracking of the forces on the scanning tip in three directions, with a high resolution in
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Figure 12.1 SEM image of the Tribolever™ [9]. Four glass-fiber interferometers (artist impression) are used to monitor the motion of the scanning tip, which is mounted in the central pyramid [8].
the lateral forces, down to 15 pN [8]. The microscope is using an unconventional friction force sensor, which we call Tribolever™ [9] (Figure 12.1). This silicon sensor combines low and symmetric spring constants of 5.75 N/m (in the present experiment) in the two lateral directions with a high stiffness of 26 N/m in the normal direction. The displacements of the Tribolever™ tip are monitored using four all-glass-fiber interferometers. The instrument can rotate the sample to change the relative orientation between the tip and sample lattices. With this instrument, friction force images were recorded as a function of the normal force on highly oriented pyrolytic graphite (HOPG) [10,11] using a chemically etched tungsten tip, which had been glued in the force sensor. While some of the measurements showed familiar stick-slip motion combined with detectable friction, many measurements did not exhibit any sign of stick-slip and, within the lateral force resolution, no friction force could be detected. These initial observations suggested that the seemingly erratic switching between high and ultra-low friction was governed by variations in commensurability between a small graphite flake, which had been accidentally picked up by the tip and different parts of the (polycrystalline) graphite substrate; high friction would then correspond to a fully commensurate contact and ultra-low friction to an incommensurate contact. In a consecutive experiment, we replaced the HOPG sample by a single crystal of graphite (grade ZYA), so that the relative orientation between tip and sample was always well defined. This high-quality sample was rotated in small steps with respect to the tungsten tip.
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Figure 12.2 Lateral force images (forward direction) and friction loops measured between a tungsten tip and a graphite substrate. The displayed signals correspond to the X-direction of the Tribolever sensor and rotation angles of the graphite sample of 60◦ (a,d), 72◦ (b,e) and 38◦ (c,f). The normal force between the tip and the substrate amounted to FN = 18 nN in (a,d and c,f) and FN = 30.1 nN in (b,e). The gray scales in the force images cover force ranges of (a) 590 pN, (b) 270 pN, and (c) 265 pN. The image size is 3 nm × 3 nm. After [11].
For each orientation, we measured the lateral forces in the sliding direction over a distance of 3 nm (approximate 12 lattice periods) parallel to the surface. The measurements were performed for a variety of sliding directions and at a range of constant normal forces, between +25 nN and pull-off (typically −22 nN). Over this normal force range, all measurements were completely reproducible and reversible, with no detectable damage to the surface or the tip. Figure 12.2(a) shows a gray-scale representation of the lateral forces in the sliding direction, recorded in a twodimensional friction scan at a normal force of 18 nN. The periodicity of the graphite substrate lattice can be recognized vaguely in the force variations. Figure 12.2(d) shows a typical force loop (one forward scan line taken from Figure 12.2(a) and the subsequent backward line) of the force parallel to the X-direction. The lateral force in Figure 12.2(d) displays clearly resolved atomic-scale stick-slip sliding. Every time that the force is sufficiently high, the tip slips over one lattice period of the graphite substrate. The area enclosed in the complete loop corresponds to the energy dissipated irreversibly during the loop and is equivalent to an average, dissipative friction force experienced by the tip of 203 ± 20 pN. Although the normal and lateral forces used here are relatively low, the qualitative features of Figures 12.2(a) and (d) are similar to those in many previously published FFM measurements on graphite. Figures 12.2(b) and (e) show FFM measurements under precisely the same conditions as those in Figures 12.2(a) and (d), but with the graphite substrate rotated 12◦ around the surface normal, i.e. around the tip axis. The rotation has caused the average friction force
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Figure 12.3 Average friction force between a tungsten tip and a graphite substrate, plotted versus rotation angle of the graphite sample. Two narrow peaks of high friction are observed at 0◦ and 61◦ , respectively. Between these peaks a wide angular range with ultra-low friction is found, close to the detection limit of the instrument. The curve through the data points shows results from a calculation according to a modified Prandtl–Tomlinson model for a rigid, symmetric, 96-atom graphite flake sliding over the graphite surface, performed by Verhoeven et al. [12]. After [11].
to reduce by more than one order of magnitude to 15.2 ± 15 pN. Note in Figures 12.2(b) and (e) that the ultra-low lateral force still displays regular variations with the periodicity of the graphite substrate. This variation was completely reversible and symmetric with respect to the initial orientation, as can be seen in Figures 12.2(c) and (f), where the sample was rotated in the opposite direction and the average friction force was again reduced to a nearzero value. Figure 12.3 displays the average friction forces measured over a 100◦ range of substrate rotation angles. We recognize two narrow angular regions with high friction, separated by a wide angular interval with nearly zero friction. The distance between the two friction peaks is 61◦ ± 2◦ , which corresponds well with the 60◦ rotation symmetry of individual atomic layers in the graphite lattice. In order to exclude instrumental artifacts, the friction values in Figure 12.2 were always measured for the same sliding direction with respect to the substrate, which was possible because of the equivalence of the Tribolever’s sensitivities in all lateral directions. The solid line in Figure 12.3 was calculated using a modified Prandtl– Tomlinson model [12]. In this calculation, the flake was modeled as a rigid, finite lattice, with the hexagonal symmetry of a single layer of graphite. The calculations confirmed our expectation that the width of the angular regions with high friction depend inversely proportionally on the contact diameter. The fit was obtained for a symmetric flake with a contact area of 96 carbon atoms, i.e. a flake with a diameter of approximately 10 atoms. Although the agreement between theory and experiment in Figure 12.3 is excellent, further analysis of the data and additional theory have shown that a very important role is played by thermal excitations. Even for γ > 1 the potential amplitude V0 can be small enough that the thermal energy can make the system jump to the next potential energy minimum well before it mechanically is forced to slip [13–17]. At very low V0 this effect can be so pronounced that the tip performs a stochastic type of motion with many forward
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and backward jumps, in which case the motion is better described as ‘driven diffusion’. We refer to this situation as ‘thermolubricity’ [16]. These thermal effects make the friction force significantly lower than in the absence of thermal fluctuations and may extend the regime of extreme slipperiness noticeably beyond γ = 1, i.e. to higher normal loads.
12.4
TOWARDS APPLICATIONS
The very low friction coefficients of solid lubricants such as graphite and MoS2 suggest that superlubricity is already at work in many technical applications. Imagine, for example, how graphite powder decorates two surfaces in sliding contact. The graphite flakes cover the two surfaces and their asperities. A small fraction of these flakes may form commensurate bridges between a few asperities, but the majority of flakes will be incommensurate with each other, which should make most asperities very slippery. Averaging over a large ensemble of microcontacts between the sliding bodies, we should expect a rather low (but non-zero) friction force. We speculate that also the extremely good lubricating properties of diamond-like carbon (DLC) coatings and related materials are due to superlubricity and thermolubricity, deriving from incommensurate contacts of graphite flakes. During the running-in phase, some of the DLC coating may be transformed into graphite. A small amount of graphitized material should be sufficient to decorate all asperities and thus dominate the shear response. The primary role of the DLC film would thus be to provide the material (carbon) and the conditions (e.g. through its hardness) necessary to produce small amounts of graphite. An essential element of this scenario is that it is self-terminating. The high friction forces at the beginning of running in provide the local pressures and temperatures that should be high enough to shear off carbon from the DLC film and graphitize it. Once it has been formed, the graphite dramatically reduces friction, so that the local shear stresses on the DLC film are too low to continue wearing off the film and graphitizing it. It has indeed been demonstrated that under sliding conditions, a graphitized tribolayer is formed on top of DLC coatings, which goes hand in hand with the decrease of the friction coefficient during run-in [18]. Several experimental observations indicate that there are mechanisms at play that reintroduce friction and counteract the occurrence of full superlubricity in a macroscopic contact. One example is the tribometer experiment by Hirano et al. [19] on friction between mica sheets. Although a significant orientation dependence was found of about a factor four, the minimum friction force, for incommensurate orientations, was still relatively high. It is very difficult to avoid plastic deformation and the generation of wear particles in contact of macroscopic size under macroscopic loading force. Yet, these processes are inevitably connected with the dissipation of energy. When they are introduced superlubricity will not survive. These plastic processes can be avoided or reduced in materials with a sufficiently high bulk hardness and by working at sufficiently low contact pressures. In this respect, silicon-based NEMS and MEMS are very promising candidate systems for the manifestation of superlubricity in an application because of the high hardness of silicon and the relatively modest loading forces between the sliding components that can be achieved, provided that adhesion forces between these components can be kept to a minimum.
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The first experimental manifestations of superlubricity have been found on layered solids: MoS2 , graphite and mica. As already mentioned, these materials are known as good solid lubricants. In the Scanning Probe Microscopy community these materials are also known for the fact that their atomic structure can be resolved in air, because they do not oxidize or contaminate easily. Very recently, Park and coworkers investigated the potential of Al–Ni–Co quasicrystals as a superlubric material [20]. This type of intermetallic material exhibits aperiodic atomic ordering in several crystallographic directions and periodic ordering in other directions. When scanning with the tip of an FFM along the aperiodic directions, one should expect to observe superlubricity. This was confirmed on a clean Al–Ni–Co crystal in UHV where a strong dependence of the friction as a function of the crystallographic direction was measured. When the crystal was oxidized in air, this dependence disappeared and the friction was high in all sliding directions. Although in the oxidized state the contact was incommensurate along all crystal directions, superlubricity was not seen. This must mean that an alternative energy dissipation channel must have been introduced or strongly increased by the oxidation of the surface. Elastic deformations inside the contact may cause the asperities to partially lock into a locally commensurate contact and the translation of the resulting deformation pattern might introduce yet another channel for energy dissipation. Ritter et al. [21] measured the energy dissipation necessary to move Sb nanoparticles on graphite and MoS2 surfaces. Small, amorphous Sb nanoparticles were found to slide with very low energy dissipation, although friction forces could still be resolved. Larger particles, consisting of several crystalline domains, caused much higher energy dissipation than the smaller, amorphous ones. TEM measurements suggested that such particles probably do not move as a single, rigid entity. We end this section by speculating that it should be possible to obtain a fully superlubric, macroscopic system. For this one would have to develop a scenario to avoid significant internal elastic response inside each microcontact. We expect that this should be possible by a suitable nanopatterning of the surfaces, such that the size of the contacts would be limited. The idea is that for sufficiently small (nano)contacts the elastic distortions within each contact add up to a maximum deformation of the contact as a whole of much less than one interatomic distance. This basically forces each contact to move as a single, rigid unit, i.e. with full superlubricity, and it thus avoids the elasticity-related locking-in mechanism that would otherwise reintroduce dissipation.
12.5
SUMMARY
In this chapter we have reviewed our atomic-scale measurements on the extreme lowering of friction in nanoscale graphite–graphite contacts due to the superlubricity (and thermolubricity) introduced by the incommensurability between misoriented graphite lattice planes. We further have discussed the role that these phenomena might be playing in existing, meso- and macroscale applications and problems that may stand in the way of further applications. Silicon-based mechanical components (MEMS, storage devices) fulfill several of the requirements necessary to construct a macroscopic superlubric system, such as high hardness and low contact pressures. Also the development of superlubric coatings or nanostructured surfaces that will slide over each other with ultra-low friction seems realistic.
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ACKNOWLEDGEMENTS The authors are grateful to a large number of people for their valuable contributions to the work reviewed in this chapter. In particular we mention J.A. Heimberg for the design and construction of the friction force microscope, K.B. Jinesh and N. Pradeep for performing part of the experiments and analysis, G.S. Verhoeven for numerical calculations of superlubricity. The work presented here is part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie (FOM)” and was made possible by financial support of the “Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)”.
REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
Hirano, M., Shinjo, K. Phys. Rev. B 41 (1990), 11837. Prandtl, L. Angew. Z. Math. Mech. 8 (1928), 85. Tomlinson, G.A. Phil. Mag. Sec. 7 7 (1929), 905. Socoliuc, A., Bennewitz, R., Gnecco, E., Meyer, E. Phys. Rev. Lett. 92 (2004), 134301. Sørensen, M.R., Jacobsen, K.W., Stoltze, P. Phys. Rev. B 53 (1996), 2101. Martin, J.M., Donnet, C., LeMogne, T., Epicier, T. Phys. Rev. B 48 (1993), 10583. Hirano, M., Shinjo, K., Kaneko, R., Murata, Y. Phys. Rev. Lett. 78 (1997), 1448. Dienwiebel, M. et al. Rev. Sci. Instrum. 76 (2005), 043704. Zijlstra, T. et al. Sensors and Actuators A 84 (2000), 18. Dienwiebel, M. et al. Phys. Rev. Lett. 92 (2004), 126101. Dienwiebel, M. et al. Surf. Sci. 576 (2005), 197. Verhoeven, G.S., Dienwiebel, M., Frenken, J.W.M. Phys. Rev. B 70 (2004), 165418. Gnecco, E. et al. Phys. Rev. Lett. 84 (2000), 1172. Sang, Y., Dubé, M., Grant, M. Phys. Rev. Lett. 87 (2001), 174301. Riedo, E. et al. Phys. Rev. Lett. 91 (2003), 084502. Krylov, S.Yu. et al. Phys. Rev. E 71 (2005), 065101. Jinesh, K.B., Frenken, J.W.M. To be published. Liu, Y., Erdemir, A., Meletis, E.I. Surf. Coat. Technol. 86–87 (1996), 564. Hirano, M. et al. Phys. Rev. Lett. 67 (1991), 2642. Park, J.-Y. et al. Science 309 (2005), 1354. Ritter, C., Heyde, M., Stegemann, B., Rademann, K. Phys. Rev. B 71 (2005), 085405.
– 13 – Superlubricity of Molybdenum Disulfide Jean-Michel Martin University Institute of France, Paris, France, and Ecole Centrale de Lyon, LTDS, 69134 Ecully, France
13.1
LOW, ULTRALOW AND SUPERLOW FRICTION
The Bowden and Tabor model of friction provides a good starting point for understanding how a thin interface film (or a so-called third body or tribofilm) can drastically reduce the friction coefficient [1]. The friction coefficient depends on the normal load W , the real contact area A and the shear strength S of the interfacial tribofilm (or film transfer) written as μ=S·
A . W
The shear strength S of solid at high pressure has been observed to have a pressure dependence, which can be approximated by S = S0 + αP .
(1)
According to the Hertzian contact theory (below the elastic limits), and in the sphere-onplane configuration, the friction coefficient μ depends on three variables in the equation of μ = S0 π(3R/4E)2/3 W −1/3 + α,
(2)
where E is the composite elastic modulus of the contacting materials and R is the radius of the sphere. This simplified model assumes that the real contact area corresponds to the Hertz zone, as calculated in Equation (2). This assumption is verified in the case of soft and very thin interface films leading to a good accommodation in the contact geometry. Friction measurements at different normal loads can be useful to determine S0 and α values for a given tribological system. However, Equation (2) indicates that the minimum value of friction coefficient is α and consequently that friction cannot vanish completely. In the case Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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of MoS2 coatings, friction experiments have been performed under different atmospheres, and α values as low as 0.001 have been calculated [3]. On the other hand, if the shear strength of the interface is very low, say 25 MPa, μ is calculated and predicted to be a few thousandths. By definition, it is proposed that the friction coefficient can be divided in three levels (i) low friction with μ < 0.1, (ii) ultralow friction where 0.01 < μ < 0.1 and (iii) superlow friction if μ < 0.01. It is to be noticed that measurements of superlow friction is very difficult and that most of mechanical devices measuring tangential force and normal load simultaneously, have a limited accuracy so that friction measurements under 0.001 has no practical meaning. So, in practical situations, superlow friction is generally found to lie in the range 0.001 < μ < 0.01. In the case of very thin interface films such as H-terminated surfaces on carbon materials, or very thin tribofilms whose thickness would be below 1 nm, it is not certain that Equations (1) and (2) are still valid, and the existence of a limiting value to the lowest friction attainable remains questionable.
13.2
CHARACTERIZATION OF SPUTTER-DEPOSITED MoS2 COATINGS
The chemical composition of MoS2 coatings can been investigated by X-ray Photoelectron and Auger Electron Spectroscopies (XPS/AES) [4], Raman spectroscopy and by Rutherford Backscattering Spectroscopy (RBS). X-ray Diffraction (XRD) and Selected Area Electron Diffraction (SAED) in the TEM can study the long-range crystal structure in MoS2 coatings [5]. High Resolution TEM (HR-TEM) and Extended X-ray Absorption Fine Structure (EXAFS) have been used to investigate the short-range order in the MoS2 crystallites of the coating [6]. HR-TEM studies show that most of MoS2 crystallites exhibit many imperfections including faults, kinks and curvature. The origin of MoS2 curved sheets (or stacks) is not known accurately. It could be attributed to defects preferentially located in one of the S plane of the S–Mo–S sandwich, causing bending by an asymmetric distribution of bonds around the metal atoms. Other crystal forms of MoS2 in coatings have been suggested in the literature, such as rhombohedral (r-MoS2 ) and turbostratic (t-MoS2 ) structures [8]. Takahashi [8] suggested that easy glide of MoS2 could be due to transformation between rhombohedral and h.c.p. MoS2 (due to S–S glide in mechanical operations). Turbostratic structure of MoS2 has also been envisaged in Ion Beam Assisted Deposited (IBAD) MoS2 films, with a structure similar to turbostratic graphite in carbon black. This lead to the socalled Random Layer Structures (RLS) [9]. The crystal structure of 2H–MoS2 is shown in Figure 13.1. Scanning Tunneling Microscopy (STM) and Atomic Force Microscopy (AFM) are valuable techniques to observe the surface crystal structure of MoS2 coatings. The characterization of such coatings is very important because it has been shown that chemical composition and crystalline MoS2 films structure are strongly correlated with their friction properties and wear resistance [7].
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Figure 13.1 Crystal structure of 2H–MoS2 . The distance between two adjacent S–Mo–S sandwiches is quite large providing weak van der Waals interaction forces between the sheets.
Figure 13.2 Evidence for (100) lattice contraction as measured by X-ray diffraction due to substitution of sulfur by oxygen in the 2H–MoS2 structure. Magnetron deposited MoS2 coating in UHV is approaching the molybdenite crystal parameters.
Most of vacuum-deposited MoS2 coatings contain significant amounts of oxygen (10– 20 atomic percent) incorporated in their structure, mainly because small amounts of water are present during the sputtering process. The oxygen incorporation affects the crystalline structure, the orientation and the film morphology. The effect of increasing the oxygen content in a sputter-deposited MoS2 film, as studied by XRD and EXAFS [4], is threefold: (i) an increase in the content of a MoS2−x Ox phase (iso-structural with MoS2 with oxygen substituted to sulphur), (ii) an increase of x in the MoS2−x Ox phase and (iii) a decrease of both long-range and short-range orders. If the oxygen content is above 10%, there is about 20 times more MoS2−x Ox phase than the MoS2 phase. A typical shift of the (100) peak is observed in XRD and is strongly correlated with the oxygen content in the film, as shown in Figure 13.2. This shift has been attributed to the (100) lattice contraction (reduced a0 lattice constant of about 5% for 15% oxygen
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incorporated). It is also correlated with a lattice expansion of the (002) basal planes in the c direction. For higher values of the oxygen content, molybdenum oxides (MoOy ) are formed. It has often been claimed that such an expansion in the basal plane distance may result in the lowering of the shear strength (or bonding) between the S–Mo–S sandwiches in the crystallites. The decreasing of the friction coefficient of MoS2 coatings in the ultralow regime has generally been attributed to the increase of x in the MoS2−x Ox phase (i.e. expansion of the basal plane distance). Many studies have been performed on the incorporation of metal in vacuum-deposited MoS2 coatings (Pb [10], Ni, Au, Sb, etc.). The characterization of these films generally shows that the metal-containing films still consist mostly of the two phases described above [11], but exhibit poor crystallinity. This is due to highly dispersed metal oxide species causing interruption of MoS2 crystallite formation during film growth. Interestingly, the decrease of x in the MoS2−x Ox phase could be explained by a “gettering” of oxygen by the metal (Ni for example) that preferentially oxidized during the co-deposition.
13.3
EXPERIMENTAL DETAILS FOR UHV TRIBOMETRY AND MoS2 FILM DEPOSITION
Pure molybdenite coatings have been tentatively deposited by high frequency magnetron sputtering in the ultrahigh vacuum tribometer. Details of this apparatus are shown in Figure 13.3. After deposition, the stoichiometry of the coating material was investigated by XPS, AES and RBS and results indicate that the oxygen content is below 1%. This shows the absence of the MoS2−x Ox phase in the coating, as previously described. Accordingly, the XRD (100) peak shifts slightly but approaches the data of pure molybdenite crystal (Figure 13.2). The texture of these MoS2 coatings has been studied by HR-TEM performed on cross-section thin foils. It is observed that during the first early growth, MoS2 sheets align parallel to the substrate. However, as the deposition proceeds, the MoS2 crystals and stacks become progressively aligned perpendicular to the surface. The HR-TEM micrograph and corresponding electron diffraction pattern in Figure 13.4 show evidence for the long-range order of the MoS2 crystallites that have grown perpendicularly to the substrate surface with no specific orientation in the azimuth direction. The chemical composition of the film has been investigated by XPS and RBS (see Figure 13.5 and 13.6) and data show that the film is approaching pure and stoichiometric MoS2 (molybdenite). This will be a very important fact for superlubric behavior.
13.4
ULTRALOW AND SUPERLOW FRICTION OF MoS2 COATINGS
Molybdenum disulfide (MoS2 ) has long been known as low friction material. Low, ultralow and super-low friction properties of MoS2 are shown in this section. Friction of vacuum-deposited MoS2 coatings has been extensively studied because of the practical interest of such coatings in space industry (see for example Fleischauer [12] and Roberts [13]). It quickly appeared that the crystallite orientation in the pristine films
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Figure 13.3 Ultrahigh vacuum analytical tribometer used for superlubricity experiments in 1992 [14]. The steel or silicon substrate is introduced in the UHV preparation chamber by the fast entry lock (9), cleaned with ion etching (10), then the pure MoS2 coating is deposited using the PVD source in UHV conditions (14). After deposition, the coated flat is transferred into the main UHV chamber. The pin-on-flat tribometer test (1, 2, 3) can be started. At the end of the friction test, the wear scars of both pin and flat can be analyzed by XPS (19, 17) and AES (16, 17).
Figure 13.4 HRTEM micrograph and electron diffraction of the magnetron sputter deposited pure MoS2 coating, showing crystal growth essentially perpendicular to the substrate [extinction of both (110) and (100) lines]. The film thickness is about 300 nm.
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Figure 13.5 AES (left) and XPS (right) surface analyses performed in situ after the magnetron sputter deposition. The absence of any carbon and oxygen has to be noticed. From XPS the stoichiometry S:Mo has been calculated and is equal to about 2 as in molybdenite.
Figure 13.6 RBS analyses performed after the magnetron sputter deposition. From RBS, the stoichiometry S:Mo has been calculated and is equal to 2 as in molybdenite. The chemical composition is homogeneously distributed through the whole coating thickness.
was a one of the key parameter in the tribological efficiency. Coatings with high basal plane intensity ratios in XRD had high durability (>100,000 cycles), while those with low basal plane ratios tended to have shorter lifetimes. However, no clear relation between
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durability and film thickness was identified. On the other hand, in such coatings, the grain size determined by XRD (from the width of the (002) characteristic peak) is generally below 10 nm. This small grain size is also related to the presence of oxidized species blocking the MoS2 crystal growth during the coating process. In these conditions, it needs a very short sliding distance to rotate the small crystallites in the coating and to align them in the sliding direction. This can explain why the transient period generally found to obtain the ultralow regime is very small. In the presence of humidity, there is an oxidation of the edge side of MoS2 crystallites into oxides and sulphates and the easy rotation of crystal maybe more difficult. Most of MoS2 coatings exhibit ultralow friction either in ultrahigh vacuum or in inert gas environment, like nitrogen for example. There was evidence for friction-induced orientation processes of MoS2 crystallites as observed by HRTEM and selected area electron diffraction. The anomalous low friction behavior of pure and stoichiometric MoS2 (molybdenite) coatings in ultrahigh vacuum conditions has been observed in 1992 in our research team at Lyon [14]. This amazing behavior was absolutely not predictable because there was a previous relationship found by Fleischauer [12] between friction decrease and the increase in oxygen content in MoS2−x Ox phase [21]. This was certainly a reason why no research was carried out on tribology of pure MoS2 coatings at this period. In our experiment on a high-frequency magnetron sputtering-deposited pure MoS2 film on silicon, we expected rather high friction from this relation. Surprisingly, the friction coefficient quickly fell down in the thousandth range after a few passages of steel pin (Figure 13.7). The friction level was at least ten times lower than that with conventional oxygen-containing coatings. Unfortunately, the tribometer was not able to measure accurately friction coefficient below 10−3 , due to instabilities in the mechanical devices of the equipment at hand. It was observed that the transient period in the friction decrease was necessary to build up a transfer MoS2 film on the steel counterface. So friction rapidly takes place between MoS2 materials on each counterface. We decided to observe in more details the passes of the pin on the flat during a single cycle.
Figure 13.7 Evolution of friction coefficient as a function of the number of cycles in the reciprocating pin-on-flat tribometer. The experiment was performed in a vacuum state of 10 nPa on a pure and stoichiometric MoS2 coating. After 10 cycles, the friction level is immeasurable.
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Figure 13.8 Evolution of friction during a single cycle in the reciprocating pin-on-flat tribometer. Detailed friction recordings of cycle 1 (top) and cycle 20 (bottom) from Figure 13.7. At cycle 20, the friction level is practically immeasurable.
Figure 13.9 Friction of pure MoS2 coatings in different environmental conditions. The lowest friction coefficient is measured in ultrahigh vacuum (10 nPa or 10−10 mbar). Molecular oxygen and water vapor are detrimental.
Figure 13.8 shows the friction recording for cycle 1 (top) and cycle 20 (bottom). This definitely shows that the friction level was not measurable at cycle 20 and that even negative values could be obtained (see Figure 13.7). To investigate the effect of the environment on the coating performance, we have compared the friction properties of pure MoS2 coating in UHV (10 nPa), in HV (typically 10 µPa) and in presence of pure nitrogen. Figure 13.9 shows that the ultrahigh vacuum
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is necessary to reach the superlow regime. Even nitrogen may contain some oxygenated impurities and this is sufficient to raise friction, although always in the superlow regime. In HV, friction drops up in the ultralow regime.
Figure 13.10
SEM micrograph of a MoS2 wear particle originating from superlubric test.
Figure 13.11 TEM micrograph and SA electron diffraction pattern of a detail of the particle of Figure 13.10. The (002) ring is absent from the pattern, indicating the orientation of basal plane of MoS2 nanocrystallites in the image plane (corresponding to sliding direction).
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Figure 13.12 HR-TEM micrograph of a detail of the particle of Figure 13.11 with corresponding optical diffractogram. The particle thickness is less than 5 nm and superimposed MoS2 individual sheets are observed with different rotational angles between them. The rotational angle is obtained from optical Fourier transform of selected areas from the TEM image. The magic angle for incommensurability is 30◦ in the case of hexagonal lattice structure, and is observed in area 2.
13.5
HRTEM INVESTIGATION OF MoS2 WEAR DEBRIS
The mechanism of superlubricity of MoS2 , which is thought to be essentially structural in nature, has been investigated in details by TEM carried out on selected wear particles collected at the end of the friction test. The particles stick easily on the holey carbon film deposited on a TEM conventional copper grid, as shown in the SEM picture of Figure 13.10. As can be seen, elongated and flat micron-size particles are generally observed, suggesting the orientation of the basal planes of crystallites in the sliding direction. A more detailed investigation in the High Resolution TEM effectively demonstrates this orientation mechanism, which is in fact well-known from the literature. Figure 13.11 shows the TEM image and the electron diffraction pattern of the same region. Compared to the structure of the pristine film (see Figure 13.4), the orientation mechanism is easy to observe. However, another interesting result arising from Figure 13.11 is the existence of continuous rings in the electron diffraction pattern. This shows that the film structure has a nanocrystalline structure with not specific orientation is the plane of the particle. Figure 13.12 shows a HR-TEM image of a detail of the MoS2 wear particle of Figure 13.11 (collected in the superlubric state). The image shows the existence of several
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Figure 13.13 AFM images performed inside the wear scar of the superlubric experiment of Figure 13.7. (a) Low magnifiacation image showing a mosaic of nanocrystals distributed at the top surface of the wear scar, (b) lattice features of the MoS2 basal plane are well recognized with the hexagonal pattern associated in the optical diffractogram. This is a strong confirmation of the basal plane orientation of the MoS2 crystallites in the sliding direction.
rotational angles of nanometer-scale crystallites although the thickness of the whole particles does not exceed 5 nm (in fact 5 visible curled single sheets are visible on the top-left of the image). After the test in UHV, the surface inside the wear track was investigated by AFM. Figure 13.13 shows that the typical hexagonal lattice of basal plane is clearly visible in the wear scar, particularly from the optical FT of the STM image. This is another confirmation of the superlubric amazing situation.
13.6
POSSIBLE EXPLANATION FOR SUPERLUBRICITY OF MoS2
To explain the new result, it was necessary to introduce another crystal orientation mechanism in the friction process: the friction-induced rotation of crystallites around the c-axis [15]. It was also necessary to relate the findings to a previous theoretical prediction of superlubric state such as the one made by Hirano [16]. We briefly describe afterwards the basic assumptions of superlubricity between crystals, recent evidence for this theory and then possible application to MoS2 . Shinjo [17] has shown that superlubricity is related to the atomistic origin of friction and that the phenomenon occurs when the sum of the force acting on each moving atom against the entire system vanishes. Frictionless sliding between two crystal atomic planes needs three conditions to be satisfied: (i) Weak interaction forces between interacting atoms, (ii) Atomically clean surfaces, (iii) Incommensurate atomic lattices between the two crystal planes. In 2002, Dienwiebel in his Ph.D. thesis (Atomic-scale friction and superlubricity, Leiden University, The Netherlands) has experimentally verified most of theoretical predictions
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made of Hirano and Tomlinson [18] many years ago. He used graphite as a model solid lubricant and a dedicated homemade UHV nanotribometer. In his experiment, Dienwiebel measured the force between two graphite flakes as a function of the misfit angle (see Chapter 12). Results clearly demonstrate the importance of frictional anisotropy in super-low friction behavior. Recently, Matsukawa et al. [19] published molecular dynamics calculations on atomic-scale friction between clean graphite surfaces. Superlubricity-like behavior is also expected in this case. However two conditions must be satisfied (i) dangling bonds on the edges of graphite flakes have to be filled and (ii) lattice constants of upper and lower graphite surfaces along the sliding direction must be irrational. An important point in Matsukawa’s calculations is that he obtained a relatively high friction coefficient when sliding a single carbon atom tip on the graphite substrate, which is much larger that those calculated with a flake simulation and that of experiments. This is explained on the basis of cancellation mechanism of the substrate potential due to the existence of two kinds of lattice sites in the flake. What concerns the 2H–MoS2 structure, condition (i) is well satisfied because weak van der Waals forces are known to exist between S–Mo–S sheets in the crystal structure. Condition (ii) requires an oxygen-free MoS2 surface that is essentially satisfied by using stoichiometric MoS2 in ultrahigh vacuum conditions. Actually, the oxygen-substituted S atoms into the basal plane produces atomic-scale defects because the Mo–O bond is significantly shorter that Mo–S bond [6]. The third condition (iii) can be satisfied in the case of frictional anisotropy. In the case of two 2H–MoS2 crystal sliding surfaces, incommensurability can be obtained by rotation of the two 2-D sulphur hexagonal lattices of the surfaces by a misfit angle of 30◦ . The atomic sites coincidence is minimized at this misfit angle as shown by simple interference images shown here in Figure 13.14. Now, the question is to know if crystallites are able to rotate freely in the contact area by a driving force in order to get this magic angle and consequently to minimize the friction force. Another explanation could be the existence of pile-up composed of many superimposed small crystallites in the transfer film formation. In this case, there are probably some couples of crystallites in the pile-up showing, by chance, some misfit angle between them. In this latter case, there is no need to introduce a new friction-induced MoS2 crystal rotation, in addition to the well-known friction-induced basal plane orientation of MoS2 crystallites. Sokoloff [20] calculated that the friction force (or dissipative stress) is a factor of 1013 smaller for the shearing of an incommensurate interface than that for a commensurate one. Therefore, friction should decrease drastically by several orders of magnitudes as soon as we approach the misfit angle. However, it is not necessary to have exactly the misfit angle (30◦ for h-MoS2 ) to reach a very low friction regime. Recently, Robbins pointed out that even a very small rotational angle is sufficient to drastically decrease the friction force. Fleischauer [21] gave a simple and elegant explanation of friction changes of pure MoS2 surfaces due to the effect of some oxygen substitution. He proposed the reason why the friction rises rapidly for small quantities of substituted oxygen (on the order of 1 atomic %) is that discontinuities in the otherwise smooth surface of sulphur atoms are created. These discontinuities cause energy barriers towards the easy “glide” of incommensurate surfaces. Fleischauer refers to this phenomenon as the “notch” model of friction for MoS2 films. Following this model, additional substitution of oxygen in the basal plane has the
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Figure 13.14 Simulations showing interferences between two single hexagonal lattices superimposed at different rotation angles. These interferences images are very similar to TEM images of MoS2 sheets superimposed in rotational disorder (see Figure 13.12).
effect of atomically smoothing the surface and modifying the lattice spacing, both factors tending to reduce the friction coefficient. When the harsh oxidizing material, i.e. atomic oxygen, is irradiated on MoS2 surface, an opposite result to the lowering of friction is obtained. The studies on atomic oxygen naturally were conducted for the purpose of space tribology, since atomic oxygen is the dominant species in low earth orbit [21]. An irradiation of atomic oxygen at a fluence of 6.7 × 1017 atoms/cm2 increased the friction coefficient of the single crystal MoS2 up to 0.06, while the one in UHV before exposure to atomic oxygen was well below 0.01.
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The XPS Mo3d spectra before and after the irradiation of atomic oxygen at 6.7 × 1017 atoms/cm2 showed that the extra peak at 235.8 eV indicates the formation of Mo(VI), since the chemical shift of +3.5 eV is an evidence of MoO3 formation [22].
13.7
ULTRALOW FRICTION BY MoS2 SINGLE SHEETS. TOWARDS SUPERLUBRICITY UNDER BOUNDARY LUBRICATION
Compared with Hydrodynamic (HD) and Elasto-Hydrodynamic (EHD) Lubrication regimes, Boundary Lubrication (BL) is mainly governed by tribochemical phenomena. Under boundary lubrication, friction coefficient is in the 0.1 range due to the action of organic polar compounds. Recently, Organic Molybdenum Compounds (OMCs) as frictionmodifying additives in base oils have allowed friction to decrease in the 0.01 range (ultralow regime). On the other hand, superlubricity (f < 0.01) of pure and stoichiometric MoS2 has been reached only in ultrahigh vacuum conditions. The mechanism of action of these additives is based on the formation of MoS2 single sheets, which are generated by frictioninduced degradation of molecules in the contact [25,26]. Basically, lubrication is found to be correlated with selective transfer mechanisms of individual sheets between the two friction counterfaces. Superlow friction (<0.01) under BL would certainly be attainable if carbon impurities could be completely eliminated from MoS2 sheets generated inside the contact. So far, friction below 0.01 under boundary lubrication has not yet been reported in the literature. In ultrahigh vacuum (P < 10−9 Pa), friction of pure and stoichiometric MoS2 is below 0.01 and becomes difficult to measure accurately. Unfortunately, any oxygen impurity in MoS2 crystal structure (as substituted atoms to sulphur atoms) keeps friction well above 0.01. Then, ultra-low friction of MoS2 is only achievable in vacuum and in inert gases (pure nitrogen or argon gas for example [27]) or in the absence of any water vapor and/or molecular oxygen gas. On the other hand, superlow friction is also hindered by the presence of oxygen and water vapor environment in the friction test due to similar processes. The reason why friction of MoS2 increases in the presence of humid air is not accurately known. It has been suggested that water molecules may be chemisorbed on edges of basal planes and preventing orientation and easy glide as molecular asperities. Recent research works have been focused on in-situ MoS2 formation by organic molybdenum compounds (OMCs) additives under boundary lubrication. Two additives have been particularly studied in the frame of fuel economy in engine oils: molybdenum dithiocarbamate (Modtc) [24,25] and molybdenum dithiophosphate (Modtp) [28]. These molecules contain S–Mo–S molecular units in their chemical formula. Recently, it has been found that tribochemical reactions produce surface films about 100 nm thick (so-called tribofilms) containing MoS2 single sheets either in a carbon-rich matrix (Modtc) or in a phosphate matrix (Modtp). Figure 13.15 displays HR-TEM images of isolated MoS2 sheets in the case of phosphate matrix (Modtp case [28]). HR-TEM image of individual sheets showing the crystal structure of h-MoS2 is also shown in the figure. As can be seen in the micrograph, curved MoS2 sheets seem very flexible and their length lies in the 1–10 nm range. It is noticed that the only sheets whose
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Figure 13.15 TEM image of MoDTP tribofilm showing the formation of many curved MoS2 single sheets. The HRTEM of a single sheet (top and left) confirms the typical MoS2 crystal structure.
Figure 13.16 UHV friction experiments on previously made MoDTP tribofilm: (a) under 10 Pa oxygen partial pressure (b) in UHV (10−9 Pa) and (c) in UHV but after removal of the oxide layer and carbon contaminant by sputter cleaning with argon ions. In the absence of carbon on the surface, friction drops to the millirange (superlow regime), giving evidence of intrinsic superlubric properties of such Modtp films.
c-axis are oriented nearly normal to electron beam are imaged by HR-TEM. In the presence of Modtp (or Modtc) in the lubricant, friction coefficient in the 0.01 range is generally achieved (ultralow friction) even with a few percent MoS2 content in the tribofilm material. UHV friction experiments on previously made MoDTP tribofilms show a superlubric behavior (Figure 13.16). Unfortunately, the superlubricity has not yet been attainable in the lubricated tests. The minimum friction coefficient is around 0.04.
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Figure 13.17 AES images performed on the pin wear scar after the test (b) of Figure 13.16. The presence of Mo/S transfer inside the contact zone is clearly associated with superlow friction.
The reason why MoS2 single sheets in phosphate matrix have better friction properties than pure MoS2 crystals is twofold (i) first, curved MoS2 sheets are highly dispersed, flexible and more layered than 3-D nano-crystals. Moreover, they can cover efficiently nano-asperities of metal surface by acid-base reaction between sulphide (soft base) and nascent metals (soft acids) [26] (ii) second, MoS2 sheets are protected from oxidation by the anti-oxidant phosphate matrix ensuring that pure MoS2 is continuously available for being transferred in the contacting zone. Tribometry in “vacuum” was used to model these tribochemical reactions experimentally and to study precisely the effect of contaminants (carbon and oxygen) on this new lubrication concept. Superlow friction capabilities of such tribofilms produced under boundary lubrication were demonstrated by in-vacuum tribometry on previously formed Modtp tribofilms [30]. Friction on Modtp tribofilms is very sensitive to oxygen environment and also to the presence of carbon on the friction counterface (typically a steel hemispherical pin). The friction-induced tribofilm on steel originated from a standard lubricated test with Modtp (friction coefficient 0.04). The Modtp tribofilm was tested in ultrahigh vacuum in different conditions [30]. Figure 13.16 shows a set of friction tests performed successively on a Modtp tribofilm (a) under 10 Pa oxygen partial pressure (b) in UHV (10−9 Pa) and (c) in UHV but after removal of the oxide layer and carbon contaminant by sputter cleaning with argon ions. As can be clearly seen, in the absence of carbon on the surface and after a short induction period, friction coefficient drops to the millirange (superlow regime), giving evidence of intrinsic properties of such Modtp films for superlubricity. Mechanism of MoS2 sheets transfer in the contact has been clearly evidenced by in-situ surface analyses by AES. At the end of the test, MoS2 transfer film on the pin wear scar has been imaged by scanning Auger Spectroscopy (SAM). SEM and SAM images of sulphur (SLMM ), carbon (CKLL ) and oxygen (OKLL ) were then obtained (see Figure 13.17). The data show that the presence of Mo/S transfer inside the contact zone is clearly associated with superlow friction. No oxygen is detected in the wear scar. The effect of carbon is very interesting and the super-low regime is only attainable when carbon has totally been eliminated from
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the contact zone. More work is necessary to study the bonding of carbon to MoS2 film. Depth profiling has shown that the film is pure MoS2 with the thickness of about 1 nm [30]. It is reminded that the MoS2 sheet thickness is about 0.7 nm. Thus, MoS2 -single sheet lubrication has been definitely evidenced. From our data, we anticipate that super-low friction is now predictable directly in a boundary-lubricated test. In this case, however, dissolved molecular oxygen or peroxides have to be eliminated from the liquid phase to prevent pure MoS2 sheets from being oxidized where they are in-situ formed. Carbon will be more difficult to avoid, but this may be done in the near future by selecting specific multifunction additives and base oils.
13.8
ULTRALOW FRICTION BY MoS2 NANOPARTICLES
Following carbon fullerenes (C60 ) and carbon nanotubes, hollow nested (or onion-like) nanoparticles made of metal dichalcogenides have been synthesized as a response of the size-decrease need and replacement of organic compounds, generally environmentsensitive. Basically, a metal-doped powder in nanometer-size is converted into an inorganic fullerene-like (IF) structure by reacting it with H2 S at high temperature and turbulent flow regime in a reactor. Tenne et al. [31] have successfully synthesized IF-MoS2 , IF-WS2 and more recently IF-NbS2 . It was shown that IF-MoS2 and IF-WS2 demonstrate excellent tribological properties as solid lubricants and additives in oil and greases and also various coatings [32]. A high resolution TEM picture of IF-MoS2 nanoparticles shows that the distance between two consecutive sheets (c/2 = 0.63 nm) is in good agreement with the 2H–MoS2 crystal structure. The low quantity of oxygen content of IF-MoS2 was evidenced by XPS and EELS in the TEM. This can be well explained by the absence of crystal edges in the onion-like structure of the nanoparticles. IF-MoS2 can provide ultralow friction when used as an additive to a synthetic base oil in boundary lubrication conditions [33]. The explanation of low friction of onion-like structure has first been attributed to a rolling mechanism, like in a nanometer-scale ball bearing. However, it has been shown by TEM that most of nanoparticles entering the contact area are flattened at the exit, suggesting that friction finally occurs between MoS2 nearly flat external planes. In some cases, tearing and unwrapping of fullerene generates some MoS2 singles sheets [34]. These single sheets are known to lubricate in the ultralow regime. What concerns superlubricity of IF-MoS2 is not clear at the moment. We did not observe superlow friction in our conditions, although the purity of the MoS2 material should allow superlubric state to be reached, according to Hirano’s model. However, Chhowalla observed a case of superlow friction with IF-MoS2 coatings [34]. 13.8.1
Nanotribology on MoS2 Crystals
The question of superlow friction of MoS2 in nanotribology is not yet elucidated. Observation of a superlubric state has already described by Hirano by sliding W(100) against Si(100) in a dedicated UHV/STM [35]. Dienwiebel, in his Ph.D. thesis, evidenced the superlubric state of graphite in UHV in a friction force microscope. What concerns MoS2 ,
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Miura [36] studied the friction between two MoS2 flakes. He found that the Amontons– Coulomb law was satisfied and that the friction coefficient between MoS2 surfaces along the [1010] direction of the MoS2 (0001) surface was superlow at 0.003.
REFERENCES [1] Bowden, F.P., Tabor, D. The Friction and Lubrication of Solids. Clarendon Press, Oxford, 1964. Part 1, pp. 110–121, Part 2, pp. 158–185. [2] Bridgeman, P.W. Proc. Am. Acad. Arts Sci. 71 (1936), 387–395. [3] Singer, I., Bolster, R.N., Wegang, J., Fayeulle, S., Stupp. Appl. Phys. Lett. 57 (1990), 995–999. [4] Lince, J.R., Frantz, P.F. Anisotropic oxidation of MoS2 crystallites studies by XPS. Tribol. Lett. 9(3–4) (2000), 211–218. [5] Hilton, M.R., Fleischauer, P.D. TEM lattice imaging of the nanostructure of early-growth sputter-deposited MoS2 solid lubricant films. J. Mater. Res. 5(2) (1990), 406–420. [6] Lince, J.R., Hilton, M.R., Bommannavar, A.S. EXAFS of sputter-deposited MoS2 films. Thin Solid Films 264 (1995), 120–134. [7] Donnet, C. Problem-solving methods in tribology with surface-specific techniques. In: Rivière, J.C., Myhra, S. (Eds.), Handbook of Surface and Interface Analysis. Marcel Dekker, Inc., 2000. [8] Takahashi, N., Shiojiri, M. Stacking faults in hexagonal and rhombohedral MoS2 crystals produced by mechanical operation in relation to lubrication. Wear 167, 163–171. [9] Dunn, R.N., Seitzman, L.E., Singer, I.L. MoS2 ion beam assisted deposition: 2H or random layer structure. J. Mater. Res. (1998). [10] Wahl, K.J., Seitzman, L.E., Bolster, R.N., Singer, I.L. Low-friction high-endurance, ion-beam-deposited Pb–Mo–S coatings. Surf. Coat. Technol. 73 (1995), 152–159. [11] Lince, J.R., Hilton, M.R. Metal incorporation in sputter-deposited MoS2 films studied by EXAFS. J. Mater. Res. 10(8) (1995), 2091–2105. [12] Hilton, M.R., Fleischauer, P.D. Surf. Coat. Technol. 54/55 (1992), 435–442. [13] Roberts, E.W., Price, W.B. Mater. Res. Soc. Symp. Proc. 140 (1989), 251. [14] Martin, J.M., Donnet, C., Le Mogne, T. Superlubricity of molybdenum disulphide. Phys. Rev. B 48(14) (1993), 10583–10586. [15] Martin, J.M., Pascal, H., Donnet, C., Le Mogne, T., Loubet, J.L. Superlubricity of MoS2 : Crystal orientation mechanisms. Surf. Coat. Technol. 68/69 (1994), 427–432. [16] Hirano, M., Shinjo, K. Origin of friction: Superlubricity. Jpn. J. Trib. 36(5) (1994), 497–508. [17] Shinjo, K., Hirano, M. Dynamics of friction: Superlubric state. Surf. Sci. 283 (1993), 473–478. [18] Tomlinson, G.A. Phil. Mag. S. 7 (1929), 905. [19] Matsushita, K., Matsukawa, H., Sasaki, N. Atomic-scale friction between clean graphite surfaces. (2003). [20] Sokoloff, J.B. Theory of energy dissipation in sliding crystal surfaces. Phys. Rev. B 42(1) (1990), 760–765. [21] Ohmae, N. Influence of atomic oxygen on space tribology in a low Earth orbit. Wear 168 (1993), 99–103. [22] Tagawa, M., Ikeda, J., Kinoshita, H., Umeno, M., Ohmae, N. Effect of atomic oxygen exposures on the tribological properties of molybdenum disulfide lubricants. In: Kleiman, J.I., Tennyson, R.C. (Eds.), Space Technology Proceedings, vol. 4. Kluwer Academic Publishers, Dordrecht, 2001, pp. 73–84. [23] Tagawa, M., Yokota, K., Ohmae, N., Kinoshita, H. Surface characterization and tribological properties of MoS2 in a hyperthermal atomic oxygen exposures. In: Proceedings of International Tribology Conference, Nagasaki, Japan, October–November, 2000, pp. 1467–1472. [24] Fleischauer, P.D., Lince, J.R. A comparison of oxidation and oxygen substitution in MoS2 solid film lubricants. Tribol. Int. 32(11) (1999), 627–636. [25] Grossiord, C., Varlot, K., Martin, J.M., Le Mogne, T., Esnouf, C., Inoue, K. MoS2 single sheet lubrication by molybdenum dithiocarbamate. Tribol. Int. 31(2) (1998), 737–743. [26] Grossiord, C., Martin, J.M., Le Mogne, T., Inoue, K. Friction-induced mechanisms of Modtp/Zndtp combination: New insights in MoS2 genesis. J. Vac. Sci. Technol. A 17(3) (1999), 884–890. [27] Donnet, C., Martin, J.M., Le Mogne, T., Belin, M. Superlow friction of MoS2 coatings in various environments. Tribol. Int. 29(2) (1996), 123–128.
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[28] Martin, J.M., Le Mogne, T., Grossiord, C., Palermo, T. Tribochemistry of ZnDTP and MoDTP chemisorbed films. Tribol. Lett. 2 (1996), 764–766. [29] Grossiord, C., Martin, J.M., Le Mogne, T., Palermo, T. In-situ formation of MoS2 and selective transfer mechanisms from MoDTP films. Surf. Coat. Technol. 108–109 (1998), 352–359. [30] Grossiord, C., Martin, J.M., Le Mogne, T., Palermo, T. UHV friction of tribofilms derived from metal dithiophosphates. Tribol. Lett. 6(3) (1999), 171–179. [31] Margulis, L., Salitra, G., Tenne, R. Nature 365 (1993), 123–134. [32] Rapoport, L., Feldman, Y., Homyonfer, M., Cohen, H., Sloan, J., Hutchinson, J.L., Tenne, R. Wear 225–229 (2002), 975–982. [33] Cizaire, L., Vacher, B., Le Mogne, T., Martin, J.M., Rapoport, L., Margolin, A., Tenne, R. Mechanisms of ultralow friction by hollow inorganic fullerene-like MoS2 nanoparticles. Surf. Coat. Technol. 160 (2002), 282–287. [34] Chhowalla, M., Amaratunga, G.A. Thin films of fullerene-like MoS2 nanoparticles with ultra-low friction and wear. Nature 407 (2000), 164–167. [35] Hirano, M., Shinjo, K., Kanako, R., Murata, Y. Observation of superlubricity by scanning tunneling microscopy. Phys. Rev. Lett. 78(8) (1997), 1448–1451. [36] Miura, K., Asai, H., Kamyia, S. Amontons–Coulomb law appearing at friction between MoS2 surfaces. Europhys. Lett. (2002).
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– 14 – Superlubricity of Tungsten Disulfide Coatings in Ultra High Vacuum Lucile Joly-Pottuz1 and Masanori Iwaki2 1 Ecole Centrale de Lyon, 36 avenue Guy de Collongue, Ecully 69134, France 2 Japan Aerospace Exploration Agency (JAXA), 2-1-1 Sengen, Tsukuba 305-8505, Japan
14.1
INTRODUCTION
Tungsten disulfide (WS2 ) is a solid lubricant with a lamellar structure similar to that of MoS2 . However, it has not been so widely studied according to the research literature. Since it possesses a crystal structure similar to that of MoS2 , it is expected to exhibit similar tribological properties including a state of near zero friction or superlubricity. Jamison compared the tribological properties of different metal dichalcogenides and concluded that metal dichalcogenides having the same structure as 2H–MoS2 possess good tribological properties [1]. He also correlated the tribological properties to the axial ratio c0 /na0 , which must exceed 1.87 in order to have a low friction coefficient. This ratio is equal to 1.95 for 2H–MoS2 and 1.96 for 2H–WS2 . In Figure 14.1, the metal elements surrounded by dashed lines form lamellar structures when bonded with sulfur or selenium, but only sulfides and selenides of molybdenum and tungsten have favorable tribological properties (elements surrounded by solid lines in Figure 14.1). By studying the electron distribution in these crystals, Jamison gave another explanation to the good tribological properties of MoS2 and WS2 [2]. In their structure, six nonbonding electrons fill a band and are confined in the structure. These electrons create a net positive charge on the surface layer, promoting easy shear through electrostatic repulsion. WS2 is thermally more stable and resistant to oxidation (about 50 to 100 ◦ C) than MoS2 [3]. The slow rate of oxidation of WS2 can be explained by the formation of tungsten trioxide (WO3 ), which is also known to provide a lower friction coefficient than molybdenum trioxide (MoO3 ). In a dry nitrogen environment, the steady-state friction coefficient of WS2 films grown by pulsed laser deposited on stainless steel against a steel counterface is about 0.04 [4]. A transfer film made of very thin WS2 sheets is observed on the pin side [5]. Analyzed by SEM, the sheets are thin enough (60 nm) to be transparent to the electron beam. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Published by Elsevier B.V.
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Figure 14.1 Portion of the periodic table of elements showing metals that form lamellar structures (dashed line). Mo, W and Nb form lamellar structures with good tribological properties (solid line) [1].
In this chapter, we investigated the tribological properties of WS2 coatings or IF-WS2 coatings in an ultrahigh vacuum and at different temperatures (−130 to 200 ◦ C). Friction experiments were performed in an analytical ultra high vacuum tribometer [6]. This tribometer consists of a linear reciprocating pin-on-flat configuration installed directly inside an ultra high vacuum chamber. The system is equipped with traditional surface analysis techniques, X-ray Photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES). The pins were made of AISI 52100 steel with a radius of curvature of 4 mm. We used a normal load of 3 N on the pin leading to a maximum Hertzian contact pressure of 470 MPa. A very low friction coefficient was obtained with both types of coatings, indicating the very interesting tribological properties of WS2 coatings.
14.2
WS2 COATINGS
The samples prepared for the experiments were deposited on Si (100) substrates by an RF sputter deposition process with a thickness of 500 nm. Pin-on-flat experiments were conducted under an ultra high vacuum environment (1 × 10−7 Pa) with various temperatures ranging from −130 to 200 ◦ C. Figure 14.2 illustrates the friction profiles of WS2 coatings under these conditions. At room temperature (30 ◦ C), the friction coefficient was about 0.02. The friction coefficient then decreased with decreasing temperature, reaching 0.005 at −130 ◦ C, which is in the superlow friction regime. In contrast, the friction coefficient increased with increasing temperature at temperatures greater than 30 ◦ C. Thus, a linear relationship between the friction coefficient and the temperature can be seen (Figure 14.3). The relationship between the friction coefficient and the temperature was discussed in the 1940s by Eyring [7] then later summarized by Overney et al. [8]. Eyring’s thermalactivation model of lubricated friction predicts a linear relationship of friction and temperature, and Briscoe has experimentally verified this model for solid lubrication [9]. Our results confirm this relationship. Auger analysis (Figure 14.4) demonstrates that less carbon and oxygen can be seen on the pin tested at −130 ◦ C compared to that at room temperature (30 ◦ C), when the amount of sulfur is comparable. This means that a relatively “pure” transfer film of WSx is formed on the counterpart pin at −130 ◦ C. This is attributed to the fact that the chemical reaction is inhibited at lower temperatures.
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Figure 14.2 Friction profile of WS2 coating at various temperatures.
Figure 14.3 Steady-state friction coefficient of the WS2 coatings as a function of temperature. Line fitting was made by excluding the irregular data at 100 ◦ C and by plotting the line so that the friction coefficient is 0 at 0 K.
A pure and stoichiometric MoS2 coating that contains below 1% oxygen can exhibit an extraordinarily low friction coefficient [10]. However, the WS2 coating prepared for our experiment was considered to have at least several percent oxygen. Therefore, this result indicates that even a disulphide film without special preparation can achieve a superlow friction at cryogenic temperatures.
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Figure 14.4 Auger spectra of tribofilm on the pin after friction test at (a) 30 ◦ C and (b) −130 ◦ C.
Figure 14.5 TEM image of inorganic fullerenes showing their hollow nested structure (courtesy of Dr. Fleischer, Nanomaterials, Ltd.).
14.3
IF -WS2 COATINGS
In an analogy to a carbon onion consisting of concentric multilayered graphitic sheets, fullerene-like nanoparticles of MoS2 and WS2 , called IF-MS2 (M = Mo, W), were synthesized [11–13]. Subsequently, a large-scale synthesis has been reported [14], and new kinds of IF-MS2 were synthesized [15,16]. These nanoparticles are of particular interest for tribological applications. Indeed, their spherical shape, without dangling bonds, confers them a chemical inertness (Figure 14.5), and their hollow structure gives them a high elasticity [17]. Inorganic fullerenes exhibited better tribological properties than the lamellar structure when they were used as additives to lubricating base oils under boundary lubrication [18,19] or mixed lubrication [20]. Another application of IF was obtained by impregnating them into powder materials [21]. The lubrication performance was found to be based on an
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Figure 14.6 Friction coefficient of IF-WS2 and IF-MoS2 dispersed at 1 wt% in a PAO base oil (v = 2.5 mm/s, P = 1.12 GPa, T = 20 ◦ C). Friction coefficients did not decrease below 0.04.
Figure 14.7 Friction coefficients of MoS2 sputtered films in 45% humidity, MoS2 sputtered films in dry nitrogen and IF-MoS2 films in 45% humidity. A very low friction coefficient was obtained with IF-MoS2 films [22].
exfoliation mechanism of the IF into MS2 single sheets. The sheets generated could then be in incommensurate conditions [19]. However, the friction coefficient never went below 0.01 under these conditions (Figure 14.6). Chhowalla et al. [22] studied thin films of IF-MoS2 deposited by high-pressure arc discharge and observed superlow friction (friction coefficient below 0.01) in a nitrogen atmosphere and under 45% humidity (Figure 14.7). These films had better tribological properties than MoS2 sputtered films tested in the same conditions or in dry nitrogen. They attributed this behavior to the presence of curved MoS2 sheets that prevented oxidation of the sheets.
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Figure 14.8 Friction coefficients obtained with IF-WS2 coatings at 25 ◦ C and −130 ◦ C. A very low friction coefficient (0.006) was obtained.
IF-WS2 coatings were deposited on AISI steel flats by a burnishing process to obtain a thickness of 200 nm. They were tested at 25 ◦ C and −130 ◦ C (Figure 14.8). A superlow friction coefficient of 0.006 was readily obtained after 45 cycles. At 25 ◦ C, the friction coefficient decreased to 0.006 at the beginning of the test and increased regularly until it reached a value of 0.02 after 500 cycles. At −130 ◦ C, the friction coefficient was not stable. High average values measured for friction coefficients are due to high values at the extremities of the wear track (Figure 14.9(a)). Figures 14.9(a) and 14.9(b) depict the direct recording of friction coefficients during one cycle (number 140) at −130 ◦ C and 25 ◦ C. Their comparison indicates that friction coefficients measured at these two temperatures are actually similar except at the end of the scars. The origin of these high values at the end of the scar is not easy to explain but could be attributed to difficulties of working in the same track while the temperature changes. An important point to be noticed is that no scar is observed optically on the flat after friction for these two tribological tests. This means that the increase in friction is not due to the wear of the coating. A transfer film could be observed on the hemispherical pin after the friction tests and was subjected to Raman analysis. This technique is a particularly powerful way to analyze WS2 and to distinguish the lamellar and IF structures (Figure 14.10). 2H–WS2 is crystallized in the D4 6h space group and has 18 modes of lattice vibrations, four of which are Raman active: E2 2g (27 cm−1 ), E1g (323.5 cm−1 ), E1 2g (356.5 cm−1 ) and A1g (420.9 cm−1 ) [23]. Several differences can be observed in the peak positions and intensities of the modes between the two spectra. Even if these differences are difficult to explain, the spectra can be considered as fingerprints for these two structures. A comparison of the spectrum obtained on the transfer film with the ones of pure 2H– WS2 and IF-WS2 reveals that it is composed of a mixture of 60% of 2H–WS2 and 40% of residual IF-WS2 (Figure 14.11). This is in good agreement with the lubrication mechanism of IF used as lubricant additives. IF-WS2 is exfoliated into small single sheets to form a tribofilm on the counterface. This exfoliation is caused by uniaxial pressure exerted over
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Figure 14.9 Friction coefficient measured at one cycle at −130 ◦ C (a) and 25 ◦ C (b). Friction coefficients measured were similar except at the end of the scar.
Figure 14.10 depicted.
Raman spectra of 2H–WS2 and IF-WS2 . Three characteristic Raman modes of 2H–WS2 are
the nanoparticles inside the contact and occurs even without shear [24]. Tribofilms formed during friction with IF-WS2 were studied using a surface force apparatus and atomic force microscopy (AFM) [25,26]. These analyses reveal that the surface is covered with very thin islands of WS2 well distributed on the surface. Only a few IF at the top of the coatings were exfoliated since we observed no wear scar at the end of the test. The thin tribofilm observed on the pin was sufficient to lead to a very low friction coefficient. Auger analyses confirmed the presence of a tribofilm made of WS2 on the pin after the friction test (Figure 14.12). A very small quantity of oxygen was detected, confirming the advantage of the nested structure that prevented the presence of
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Figure 14.11 Raman analysis of the tribofilm observed after friction test. This spectrum is compared to those of 2H–WS2 and IF-WS2 . A simulation demonstrated that the tribofilm is a mixture of 60% of 2H–WS2 and 40% IF-WS2 .
Figure 14.12
Auger analysis of tribofilm after friction test at 25 ◦ C (a) and −130 ◦ C (b).
oxygen. In the case of the friction test at −130 ◦ C, the presence of carbon can be explained by the condensation of residual hydrocarbons on the cold surface. Transmission electron microscopy of the wear particles collected on the pin after the friction test revealed the presence of layers under incommensurate conditions (Figure 14.13). This could explain the very low friction coefficient measured. The same kind of particles had been observed by Martin et al.1 in the case of the friction of the MoS2 coatings [10] and with IF-WS2 dispersed in the base oil [19]. 1 See Chapter 13.
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Figure 14.13 HRTEM image of wear particle showing two superimposed layers. The corresponding calculated diffractogram indicates an angle of 30 ◦ between the layers.
14.4
CONCLUSIONS
The WS2 coatings presented very interesting properties in an ultra high vacuum especially at lower temperatures. Thus, they can be envisaged as lubricants for space applications. These favorable results were due to the formation of WS2 sheets on the counterface. The deposition method and the purity of the coatings influenced their properties. The use of IF-WS2 was advantageous in having pure WS2 coatings due to the curvature of the sheets in fullerenes, which preserve from the presence of oxygen. Temperature also influences the tribological properties of the WS2 coatings, and the lower the temperature, the lower is the friction coefficient. The results for IF-WS2 obtained at −130 ◦ C can be considered equal to the results at 25 ◦ C since the friction was high only at the end of the scar and because there was no wear influence. Further studies are necessary to really understand the lubrication mechanism of these coatings, which present very good potential for space applications.
ACKNOWLEDGEMENTS The authors would like to thank Thierry Le Mogne (Ecole Centrale de Lyon) for his support in the surface analyses (XPS, AES) and helpful discussions, and Dr. Niles Fleischer (Nanomaterials, Ltd.) for having supplied the IF-WS2 coatings.
REFERENCES [1] Jamison, W.E., Cosgrove, S.L. ASLE Trans. 14 (1971), 62. [2] Jamison, W.E. ASLE Trans. 15 (1972), 296.
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[3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
Bhushan, B., Gupta, B.K. Handbook of Tribology. McGraw-Hill, New York, 1991. Prasad, S.V., Zabinski, J.S., Dyhouse, V.J. J. Mat. Sci. Lett. 11 (1992), 1282. Prasad, S.V., Zabinski, J.S. J. Mat. Sci. Lett. 12 (1993) 1413. Le-Mogne, T., Martin, J.M., Grossiord, C. In: Symposium Leeds-Lyon. Lyon, 1998. Glasstone, S., Laidler, K.J., Eyring, H. Theory of Rate Processes. McGraw-Hill, New York, 1941. Overney, R.M., Tyndall, G., Frommer, J. Nanotechnology Handbook, 2004, Chapter 29. Briscoe, B.J., Evans, D.C.B. Proc. Roy. Soc. A 380 (1982), 389. Martin, J.M., Donnet, C., Le-Mogne, T., Epicier, T. Phys. Rev. B 48 (1993), 10583. Tenne, R., Margulis, L., Genut, M., Hodes, G. Nature 360 (1995), 444. Feldman, Y., Frey, G.L., Homyonfer, M., Lyakhovitskaya, V., Margulis, L., Cohen, H., Hodes, G., Hutchison, J.L., Tenne, R. J. Am. Chem. Soc. 118 (1996), 5362. Tenne, R., Homyonfer, M., Feldman, Y. Chemistry of Materials 10 (1998), 3225. Feldman, Y., Zak, A., Popovitz-Biro, R., Tenne, R. Solid State Sci. 2 (2000), 663. Schuffenhauer, C., Popovitz-Biro, R., Tenne, R. J. Mat. Chem. 12 (2002), 1587. Schuffenhauer, C., Parkinson, B.A., Jin-Phillip, N.Y., Joly-Pottuz, L., Martin, J.M., Popovitz-Biro, R., Tenne, R. Small 1 (2005), 1100. Rapoport, L., Feldman, Y., Homyonfer, M., Cohen, H., Sloan, J., Hutchison, J.L., Tenne, R. Wear 225–229 (1999), 975. Cizaire, L., Vacher, B., Le-Mogne, T., Martin, J.M., Rapoport, L., Margolin, A., Tenne, R. Surf. Coat. Technol. 160 (2002), 282. Joly-Pottuz, L., Dassenoy, F., Belin, M., Vacher, B., Martin, J.M., Fleischer, N. Tribol. Lett. 18 (2005), 477. Rapoport, L., Fleischer, N., Tenne, R. Adv. Mat. 15 (2003), 651. Rapoport, L., Leshchinsky, V., Lvovsky, M., Lapsker, I., Volovik, Y., Feldman, Y., Popovitz-Biro, R., Tenne, R. Wear 255 (2003), 794. Chhowalla, M., Amaratunga, G.A.J. Nature 407 (2000), 164. Sourisseau, C., Cruege, F., Fouassier, M., Alba, M. Chem. Phys. 150 (1991), 281. Joly-Pottuz, L., Martin, J.M., Dassenoy, F., Belin, M., Montagnac, G., Reynard, B., Fleischer, N. J. Appl. Phys. 99 (2006), 023524. Golan, Y., Drummond, C., Israelachvili, J., Tenne, R. Wear 245 (2000), 190. Drummond, C., Alcantar, N., Israelachvili, J., Tenne, R., Golan, Y. Adv. Funct. Mat. 11 (2001), 348.
[13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
– 15 – Superlubricity by H2 S Gas Lubrication of Mo Irwin L. Singer1 and Thierry Le Mogne2 1 Naval Research Lab, Code 6176, Washington, DC 20375, USA 2 Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des
Systèmes—UMR5513, BP163, F-69131 Ecully Cedex, France
ABSTRACT Friction tests were performed in an ultra high vacuum chamber with SiC and Al2 O3 pins sliding against a Mo flat during exposure to H2 S gas at pressures between 1.3 × 10−4 and 1.3 Pa. Both pressure-dependent and speed dependent friction behaviors were studied. Wear tracks were analyzed in situ with Auger electron spectroscopy and ex situ with scanning electron microscopy and energy-dispersive X-ray analysis. The friction coefficient fell from 0.7 to 0.01 as the gas pressure rose to 1.3 Pa, then remained low when the gas was pumped out. In addition, friction spikes occurred when valves were opened or shut. Friction coefficients showed a dramatic drop—to values as low as 0.001—as the speed decreased to 0.2 mm/s. Auger analysis showed that a MoS2 -like tribochemical film formed on Mo and a film resembling graphite plus silicon sulfide formed on SiC. The lubrication afforded by the gases is discussed in terms of the tribochemical films formed, and competitive rate processes are suggested to explain both the pressure and speed dependent friction coefficients. A method for achieving superlow friction with gas lubrication is discussed.
15.1
INTRODUCTION
Surfaces in sliding contact require some form of lubrication to avoid wear and attain low friction. The lubricant can be a liquid, a soft solid or even a film no thicker than a monolayer [1–4]. In addition, for long life, the lubricant must be able to enter and remain in the sliding contact, or at least be replenished from an external supply or by some sort of internal reservoir [5,6]. Gas or vapor phase lubrication is a proven means of replenishing lubricant to the interface. It can sustain low friction and protect solid surfaces from wear in environments Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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where both solid and liquid lubrication is impractical. In adiabatic heat engines, tricresyl phosphate vapor has been used to lubricate steel [7,8] and hydrocarbon gases to lubricate ceramics [9] and steel [10]. Carbon is another material whose friction and wear behavior have benefited from vapor phase lubrication. H2 O and O2 have been used to lubricate graphite [11–13] and H2 to lubricate diamond-like carbon (DLC) [14]. Bowden and Tabor report studies of H2 S gas lubricating Mo, I2 gas lubricating Ti and Cl2 gas lubricating Cr [15,16]. More recent studies have shown effects of H2 S gas lubrication of SiC/Mo in ultrahigh vacuum [17,18] and Mo and W alloys in air [19]. Vapors can also interfere with ‘good’ lubrication. For example, H2 O and O2 vapors can increase the friction coefficient and wear of a hydrogenated DLC coating [20,21], often referred to as “nearly frictionless carbon” (NFC) [22]. Although called vapor phase lubrication, it is believed that the lubrication is afforded by solid “tribochemical” films formed when surfaces are rubbed against each other in the presence of the gases [9,17]. Previously we investigated vapor phase lubrication of a SiC pin sliding against a Mo flat in the presence of O2 , SO2 and H2 S gases at pressures from 4 to 40 Pa [17,18]. H2 S was the primary gas of interest because thermochemical calculations indicated that H2 S reacts with Mo to form the well-known, ultralow friction (0.01–0.04) solid lubricant MoS2 . SO2 and O2 were examined because they react to form MoO2 + MoS2 and MoO3 , respectively, phases that are expected to interfere with ultralow friction. Friction tests were performed in a multi-analytical UHV chamber, where the substrates could be cleaned and surface films characterized in situ before and after testing. Two distinct friction behaviors were observed and correlated to the formation of surface films and other third bodies. In O2 and SO2 , the friction coefficient was steady in a range of 0.1–0.2. In H2 S, the friction coefficient varied with gas pressure, dropping below 0.01 at the highest pressure (40 Pa). Table 15.1 summarizes the friction coefficients and third bodies found [17,18]. The purpose of this chapter is to establish conditions needed to achieve superlow friction with H2 S gas lubrication. Superlow1 friction refers to friction coefficients below 0.01, which is the friction condition required for superlubricity. In the Results section, we present further studies of the lubrication effects of H2 S gas. Part one presents the friction behavior Table 15.1. Friction coefficients and third body products of a SiC pin sliding on a Mo flat in three gases at 10 Pa (8 × 10−2 Torr) [17,18] Gas
H2 S SO2 O2
Third body products Friction
Mo
SiC
coefficient
Tribofilm
Transfer
Debris
Tribofilm
Transfer
Debris
<0.01 0.1–0.15 0.1
MoS2 MoOx /MoS2 MoOx
none none none
none Mo Mo
SiSy , C SiOz /SiSy , C SiOz
none MoOx /MoS2 MoOx
none Mo Mo
1 Until the late 1980s, friction coefficients in the range of 0.01 were ‘unexpected’ for all but liquid lubricated contacts. Indeed, the 1988 edition of The Guinness book of world records (Bantam, New York, 1988, p. 182) stated that PTFE has lowest friction coefficient on record, μ = 0.02.
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239
and surface films formed on SiC vs. Mo as the pressure is cycled from 1 × 10−6 Torr2 to 1 Torr then back. Part two examines the friction behavior as a function of sliding speeds (from 0.2–4 mm/s) of SiC vs. Mo, SiC vs. a MoS2 coating, and Al2 O3 vs. Mo. In the Discussion section, we interpret the friction behavior in terms of third bodies and speculate on the origins of the pressure and speed dependence.
15.2 15.2.1
EXPERIMENTAL
Friction and Surface Analysis Apparatus
Wear tests and surface analysis were carried out in situ in a load-locked, multi-technique ultra high vacuum (UHV) chamber described in detail in previous papers [17,18,23]. Strain gauges allowed measurement of friction coefficients from 0.001 to 1.0. The tribometer consisted of a pin loaded against a flat; both pin and flat could be repositioned in situ to perform from 4 to 8 tests without removing either sample from the UHV chamber. The chamber could be backfilled with gas and its pressure regulated between 0.1 and 1000 Pa (7.5 × 10−4 to 7.5 Torr) by opening and closing vacuum valves (Viton O-rings) and using a capacitance manometer (MKS Baratron) in feedback with a mass flow controller. LabviewTM software was used to program the tribometer and collect normal load and friction force data. The program acquired 256 load and force points per cycle. The analysis program computed the average friction coefficient by averaging the friction force over the mid 80% of the track and dividing by the mean load. Surfaces were analyzed in situ by Auger electron spectroscopy (AES) using a Vacuum Generators hemispherical analyzer. AES was taken with a 5 keV electron beam whose submicrometer spot size was broadened to between 5 and 20 µm by rastering. Sputter cleaning was performed with 5 keV Ar ions. Wear features were examined ex situ by two techniques: Auger sputter depth profiling (a PHI 660 system) and scanning electron microscopy with energy dispersive X-ray analysis (SEM/EDX) using a Kevex thin-window detector. EDX spectra were acquired with both 5 and 20 keV electron beams; the lower energy decreased the depth probed by a factor of 10 by decreasing the electron beam penetration in Mo from 1.4 µm to 0.14 µm [24]. 15.2.2
Sample Preparation and Friction Test Procedures
A rod of α-SiC was ground on one end to form a hemispherical pin of radius 1.8 mm. The pin and a 1 mm thick polycrystalline Mo flat were polished with successively finer pastes containing 6 µm, 3 µm and 1 µm diamond. After solvent cleaning, the SiC and Mo tribocouple was inserted through a load-locked chamber into the UHV chamber. An Al2 O3 pin (radius = 1/16") was constructed by mounting a sapphire ball in a steel shaft. The counterfaces were first cleaned by radiative heating to 600–800 ◦ C then by Ar ion sputtering for 15–30 minutes. They were next analyzed by XPS and AES. After each round of gas exposure and friction testing, both counterfaces were recleaned by ion sputtering then reanalyzed. A fresh, unworn area of the pin and flat were aligned for each new test. 2 The pressure data are given in Torr (1 Torr = 133 Pa) because the measurements were made in Torr.
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A reference sample of MoS2 was prepared by ion beam assisted deposition (IBAD) onto a polished SiC substrate [25]. The IBAD coating was 150 nm thick. Friction tests were run at gas pressures between 1.3 × 10−4 and 1.3 Pa (1 × 10−6 to 1 Torr). Normal and tangential forces were recorded throughout the test. Test conditions were: stroke length = 3 mm, speeds from 0.2 to 4 mm/s and loads from 0.5 N to 2 N; at these loads, the initial mean contact pressure ranged from 0.7 to 1.2 GPa, below the hardness (2.9 GPa) of the softer Mo counterface. After a series of test, both counterfaces were analyzed by AES. Then clean, unworn areas of the pin and flat were aligned for the next test. Several friction tests were also performed under high vacuum conditions, 10−6 Pa, on unworn areas of the counterfaces that had been exposed to H2 S gas. All tribotest results presented here were confirmed by two or more duplicate tests.
15.3 RESULTS 15.3.1
Friction Coefficient vs. Gas Pressure
Initially, both pin and flat were exposed to H2 S at 6 × 10−7 Torr for several minutes, then the chamber was pumped to <1 × 10−8 Torr. Test #1 was done at a load = 0.5 N, speed = 0.5 mm/s on a track length = 3 mm. Under UHV conditions, the H2 S-exposed tribocouple showed high friction coefficient μ ≈ 1 in first and subsequent passes. A second series of friction tests was performed on the same flat with new tracks and new areas on the pin. Test conditions were similar to the first test, except the load was L = 0.8 N. Friction force was recorded as the pressure was first increased to 1 Torr then decreased to 10−6 Torr. Figure 15.1 summarizes the steady state friction coefficient values
Figure 15.1 Steady state friction coefficient vs. H2 S pressure. The test started at 1 × 10−5 Torr, increased to 1 Torr then decreased to 10−6 Torr.
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Figure 15.2 Friction coefficient vs. cycles as H2 S gas pressure increased. Note that the y axis scales of (a) and (b) differ.
vs. gas pressure for the series. The friction coefficient dropped nearly two orders of magnitude (from 0.7 to 0.01) as the pressure increased, but remained below 0.1 even after the return trip to 10−7 Torr. We note that the friction coefficient fell nearly linearly with the log of the pressure. As the arrows on the graph indicate, H2 S gas lubrication resulted in significant ‘friction hysteresis.’ Figures 15.2 and 15.3 show cycle-by-cycle friction coefficients for the round trip excursion. The test was begun by flowing H2 S into the chamber with the turbopump still on; the pressure rose to 1 × 10−5 Torr (see Figure 15.2(a)). The friction coefficient remained a steady, but high value, μ = 0.7. At cycle 22, the pump was shut off, at which time the pressure rose gradually to about 1 × 10−2 Torr. After a small ‘spike’ increase, the friction coefficient dropped quickly to about 0.25; then as the pressure rose to 1 × 10−1 Torr, the friction coefficient dropped further, to about 0.15. The test was continued on the same track at 1 × 10−1 Torr with the pump off and no gas flow (Figure 15.2(b)). At cycle 21 of
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Figure 15.3 Friction coefficient vs. cycles as H2 S gas pressure was decreased.
Figure 15.2(b), the gas valve was opened to raise the H2 S pressure to 3 × 10−1 Torr, then closed. The friction coefficient dropped immediately to 0.06. The reverse journey was begun at 3 × 10−1 Torr on new areas of the pin and flat. Friction coefficients were recorded as the chamber was evacuated, first by the roughing pump then later by the diffusion pump. By the end of the test, the pressure was maintained at 2 × 10−6 Torr by bleeding in H2 S gas and throttling the diffusion pump valve. As seen in Figure 15.3(a), the starting friction coefficient was 0.30, about four times the steady-state value at the same pressure, but dropped rapidly to 0.06, then gradually to about 0.01. As the H2 S was pumped out of the chamber, the friction coefficient gradually increased to about 0.1, punctuated by several ‘spikes,’ e.g., from 0.01 to 0.15 at cycle 44 and from 0.15 to 0.35 at cycle 61. Spikes occurred when valves were either opened or closed. As the pressure dropped, the friction coefficient rose to about 0.1 during the time the diffusion pump was operating at relatively high pressure >1×10−3 . Ultimately, however, the friction
Superlubricity by H2 S Gas Lubrication of Mo
243 Table 15.2.
Auger ratios from wear scars on Mo and SiC, and from reference compounds P (Torr)
3 × 10−1 3 × 10−1 2 × 10−6
Location
Inside track Outside track Inside track
Mo flat
SiC pin
S/Mo
C/Mo
C/Si
S/Si
Mo/Si
O/Si
9.6 6.3 7.4
0.7 0.6 0.3
– – 0.8
– – 1.4
– – <0.1
– – 0.5
9.0 – – –
– – – –
– – – 0.4
–
– – – -
– 2.9
Reference compounds MoS2 (IBAD) SiO2 SiS SiC
2.6 –
–
Reference data for SiO2 and SiS from Handbook of Auger Electron Spectroscopy, Eden Prairie, MN: Physical Electronics Publishing, 1995.
Figure 15.4
Ex situ Scanning Auger analysis on Mo rubbed by SiC in H2 S. After 11 minutes of sputtering.
coefficient leveled off at a steady state value of 0.02 at constant pressure of 2 × 10−6 Torr (Figure 15.3(b)). Although the friction coefficient rose (and fell) as the pressure decreased, it never reverted to the initial high friction value of μ = 0.7 at the same pressure. Clearly the friction coefficient was not determined uniquely by either gas reaction chemistry or gas pressure. After evacuating the chamber, Auger electron spectra were taken on selected areas of the Mo flat and the SiC pin. As seen in Table 15.2, the Mo flat had a large S/Mo ratio, both in and out of the friction tracks. The ratio inside the track, however, was greater than outside the track, even after the test ending at 2 × 10−6 Torr. Previous XPS analysis indicated that
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Figure 15.5 Friction coefficient vs. cycle at selected speeds from 0.2 to 1.0 mm/s. SiC vs. Mo in H2 S gas at 1 × 10−2 Torr and initial load = 0.7 N.
the film formed by reaction of H2 S with Mo was a Mo–S film, but it was too thin (0.3 nm) to be a complete MoS2 film [17]. Nonetheless, rubbing produced a thicker Mo–S film, and it remained thicker even as the gas pressure decreased. Based on the S/Mo ratio of the reference MoS2 coating, the tribochemical film could be MoS2 . Auger ratios from the SiC pin scar indicated significant S on the surface of the wear scar, but virtually no Mo. This has been verified in many other tracks as well. Moreover, the C/Si ratio was considerably higher than on the (sputter cleaned) SiC surface. In addition, the shape of the Auger C(KLL) line was more ‘graphitic’ than ‘carbidic,’ and the shape of the Si(LVV) line was different from that of SiC. These composition and lineshape changes were interpreted to mean that the rubbed SiC surface was converted to graphite and SiS, consistent with thermochemical calculations. These speculations and other chemical interpretations of the Auger spectra are discussed more fully in earlier papers [17,26]. Several months after the in situ test, ex situ Scanning Auger analysis was performed on the Mo wear tracks discussed above. Figure 15.4 shows an SEM image at one end of the wear track, where the pin stopped and reversed direction. The track leading up to this turnaround patch was both grooved and highly burnished areas. High friction values at the onset of sliding would have caused grooving, while the more gently low friction sliding (often for hundreds of cycles) would have produced the burnishing. Sputter depth profiles were taken on and outside the pad, in the areas indicated by the white rectangles. After less than 1 min of sputtering, the S/Mo ratio outside the track was one-tenth that inside the track (0.3 vs. 3); after 10 min of sputtering, the S/Mo ratio was about one, suggesting that the turnaround patch contained significantly more S than the reaction film. The SEM image in Figure 15.4, taken after 11 min of sputtering, shows both dark and light areas in the track; these were identified as Mo–S and Mo rich areas, respectively.
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Figure 15.6 Steady state friction coefficient vs. speed from 0.2 to 4.0 mm/s. SiC vs. Mo in H2 S gas at two pressures: 1 × 10−2 Torr 1 × 10−1 Torr. Data labels indicate the sequence of testing. Initial load = 0.7 N.
15.3.2
Friction Coefficient vs. Speed
Figure 15.5 shows the friction coefficient (note the logarithmic scale) vs. cycle for a series of speed-dependent tests, all on the same track, at H2 S gas pressure of 1 × 10−2 Torr and an initial load of 0.7 N. The first test showed run-in behavior, where the friction coefficient started at μ = 0.22, dropped into the superlow friction range, down to μ = 0.001, then rose to μ = 0.035. The test was stopped after 82 cycles, indicated by the vertical dashed line, and then continued at the same speed of 0.5 m/s from 83 to 91 cycles. The remaining tests, performed at speeds from 0.2 to 4 mm/s, show that the steady-state friction coefficient depended on speed. Three features are clear: First, the fresh pin and flat surface required a run-in period to reach a steady-state friction coefficient; secondly, friction coefficients fell with decreasing speed; and thirdly, at this pressure, the friction coefficient reached the superlow friction range (<0.01) at speeds below 0.5 mm/s. Figure 15.6 summarizes the steady-state friction coefficients vs. speed (from 0.2 to 4.0 mm/s) at pressures 1 × 10−2 Torr and 1 × 10−1 Torr. The same behavior—friction coefficient increased with increasing speed—was seen at both pressures, with higher friction coefficients at the lower gas pressure, consistent with the earlier set of data in Figure 15.1. At speeds less than 1.5 mm/s, the friction coefficient rose rapidly and linearly with speed, then leveled off at higher speeds; the linear portions generally had slopes (dμ/dv) around 0.6 s/mm. (The slight drop in friction coefficient at speeds above 2 mm/s was an artifact of the 80% averaging process; it captured some of the friction values decreasing toward zero at the turn around points.) Moreover, at 1 × 10−1 Torr, superlow friction coefficients were routinely achieved at speeds at and below 1 mm/s.
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Figure 15.7 Steady state friction coefficient vs. speed from 0.2 to 4.0 mm/s. SiC vs. MoS2 coated SiC in H2 S gas at 1 Torr and initial loads of 0.5 N and 2.0 N. Data labels indicate the sequence of testing.
Identical tests were also performed in H2 S gas with a SiC pin sliding against a thin (0.2 µm) IBAD MoS2 coating on polished SiC. Figure 15.7 summarizes the steady-state friction coefficients vs. speed (from 0.2 to 4.0 mm/s) at a gas pressure of 1 Torr at two loads, 0.5 N and 2 N. The H2 S lubrication of IBAD MoS2 did not result in superlow friction coefficients nor did it show the dramatic speed-dependence of the friction coefficient seen with SiC against Mo, although at the lower load, there was a slight increase in friction coefficient with speed. The only significant variation in friction coefficient was the drop with increasing load, a well-known behavior [27]. Auger SEM and EDX analysis of the flat and pin showed that the MoS2 coating remained intact in the track and an MoS2 film transferred to the pin, the established lubricating mode for an MoS2 coating [28,29]. Finally, speed-dependent tests were performed with an Al2 O3 pin sliding against Mo at pressures 1 × 10−1 Torr and 1 Torr. Figure 15.8 shows friction coefficient vs. speed curves. The data indicated by solid symbols were taken two years after the open symbol dataset. Again, the friction coefficient increased with sliding speed, from superlow friction values (<0.01) at speeds below about 1 mm/sec. As with the SiC pin, the friction coefficient rose linearly at lowest speeds and leveled off at higher speeds. Interestingly, the friction coefficient at higher speeds at both pressures was considerably less for the Al2 O3 pin than for the SiC pin (0.02 vs. 0.06). Figure 15.9 shows SEM images of the Al2 O3 pin and the Mo track. The ball scar was surrounded by debris, but, like the SiC pin, did not have a transfer film; the Mo track had scratches, but also was heavily burnished by the pin. In summary, H2 S lubrication of Mo sliding against both SiC and Al2 O3 pins resulted in speed-dependent friction coefficients. In both cases, superlow friction coefficients were
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247
Figure 15.8 Steady state friction coefficient vs. speed from 0.2 to 4.0 mm/s. Al2 O3 vs. Mo in H2 S gas at pressures from 1 × 10−1 to 1 Torr at loads indicated. Data labels indicate the sequence of testing.
Figure 15.9
SEM images of wear scars on Al2 O3 pin and Mo flat.
achieved at speeds <0.1 mm/s, and over this range, the friction coefficient vs. speed curve rose nearly linearly at about 0.6 mm−1 s. In contrast, SiC sliding against a MoS2 coating in H2 S gas had a higher friction coefficient (0.03 to 0.06) at all speeds and also produced a MoS2 transfer film typical of MoS2 lubrication.
15.4
DISCUSSION
Pressure- and speed-dependent studies have shown that H2 S gas lubrication produces vast changes in friction coefficients and friction behavior of SiC and Al2 O3 pins against Mo. Friction coefficients varied from about 1 in UHV [18] to superlow friction values (<0.01) at high gas pressure and low speeds. Pressures of the order of 1 Torr were required to achieve
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ultralow and superlow friction coefficients. Once achieved, however, the friction coefficient remained low even at gas pressures six orders of magnitude lower, what we called friction hysteresis. The low friction, however, was temporarily interrupted and the friction coefficient spiked to values >0.1 when vacuum valves were opened or closed. In the previous investigation [18], we found that the higher friction values (μ > 0.1) were associated with adhesive wear and the lower values (μ < 0.1) with interfacial sliding between tribochemical films on the counterfaces. Can these mechanisms account for the friction hysteresis, friction spikes and speed-dependent friction coefficients? Auger and SEM analysis provided further evidence that film formation can account for all three. Hysteresis began with the friction coefficient falling from 0.7 to 0.01, as seen in Figures 15.1–15.3. The slow drop in friction coefficient with pressure in Figure 15.1 makes clear that the low friction film didn’t form immediately, and the logarithmic decrease in friction coefficient with increasing pressure suggests that some competitive mechanism of film formation and removal occurred during film formation [10]. The wear scar on the softer Mo flat suggests that plowing by the pin damaged the Mo and, likely, disrupted tribofilm formation. Ultimately, the friction fell when the surfaces became covered with protective tribofilms that form when H2 S triboreacts with both SiC and Mo: a MoS2 -like layer on the Mo flat and perhaps graphite and/or SiS on the SiC pin. The persistence of low friction, even when the H2 S pressure fell to the 10−6 Torr range, can be attributed to retention of the film. This could be due to a very low wear rate of the film. Alternatively, the film could have been worn away but replenished by transfer of Mo–S-like film from the end patches, which can serve as a reservoir [5]. Film formation can also explain the spikes in the friction coefficient when valves were opened or closed. Both actions produced mechanical compression or expansion of elastomeric (in this case, Viton) O-rings. Elastomers trap gases in the groove seal and outgas volatile species when compressed or decompressed [30]. The species include absorbed water vapor and carbon dioxide and reaction products with H2 S such as SO2 . Elastomers can also outgas low-molecular-weight species of antioxidants, UV stabilizers and unreacted polymer residues. As demonstrated in Table 15.1 from the previous studies [17,18], oxidizing gases such as O2 and SO2 produced tribochemical oxide films that generated adhesive debris and raised the friction coefficient to values above 0.1. The spikes, therefore, represent chemical disruption of the ultralow-friction tribochemical film by oxidizing gas species. This could also explain why the majority of reports on the friction coefficient of Mo in H2 S gas have found μ ≥ 0.1 [15,19]. It is likely that any contaminant gas will prevent ultralow and superlow friction coefficients. Although the tribofilms formed on Mo in H2 S had the same composition as MoS2 , the tribological properties differed from that of a MoS2 coating in two ways: The latter lubricates by forming a MoS2 transfer film on the stationery pin, whereas the former didn’t generate a transfer film. Moreover, the friction coefficient of the MoS2 coatings in H2 S gas was fairly constant (0.04–0.06) and independent of speed, whereas the friction coefficient the of the SiC/Mo tribocouple showed dramatic speed dependence, with superlow friction coefficients at speeds <1 mm/s. Therefore, the superlow friction obtained by vaporlubrication must be attributed to properties of the tribochemical films and not simply to formation of a MoS2 layer.
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Speed-dependent friction behavior is not common in simple sliding systems. It has been observed in multiparticle contacts [31], with viscoelastic materials [32] and with monomolecular films [33,34]. With the latter two, speed-dependent friction is associated with dissipation processes as contacts are made and broken. Theoretical models of sliding contacts also make clear that weakly coupled systems should exhibit liquid-like (Newtonian) friction behavior, and speed-dependent friction coefficients are the norm [35–37]. However, it has not been shown conclusively that these theories apply to macroscopic sliding contacts. The speed-dependent friction behavior observed with H2 S has precedence in other vapor phase lubrication studies. Zaidi et al. [38] measured speed-dependent friction coefficients on graphite exposed to oxygen in the same pressure range as in our studies (1 × 10−1 to 10 Torr) but with friction coefficients 10 to 50 times higher than the present case. Sawyer and Blanchet observed speed dependent friction coefficients during vapor phase lubrication of M50 steel, in combined rolling and sliding contacts at 540 ◦ C using nitrogen atmospheres containing acetylene [10]. Heimberg et al. [20] reported similar speed-dependent friction curves on a hydrogenated DLC coating run in nominally dry N2 . In the latter study, water-vapor acted as a contaminant and raised the friction coefficient, whereas in the former cases and in the present study, the vapor is believed responsible for lowering the friction coefficient. In liquid lubrication, fatty acid layers on caste iron produced speed-dependent curves similar to ours in the same speed range [39]. But what caused the speed dependent friction in H2 S lubricated Mo? The Mo–S tribochemical film can account for the ultralow and superlow friction coefficients seen with both SiC and Al2 O3 pins. Just as the pressure dependence of the friction coefficient at increasing gas pressures (Figures 15.1 and 15.2) appears to be due to competition between film formation and film wear by rubbing, the speed-dependent friction coefficient can also be due to competitive rate processes. In both cases, the changes in friction coefficient can be explained as a ‘time’ effect. In the speed-dependent tests, the time between sequential contacts—or ‘wipes’—determines the competition between wear and forming/healing tribochemical films. The same time effect might also cause slow film formation at low gas pressures. We defer to another paper quantitative analysis of the data, which will be done using recent models for competition between wear and film formation [10,40– 42]. In summary, the experimental results suggest how superlow friction can be achieved with gas lubrication. First, the gas must form a tribochemical film that protects the two surfaces from adhering. With transfer processes eliminated, the friction coefficient can be in the superlow friction range. Secondly, the velocity accommodation mode must be mainly interfacial sliding, where plucking and plowing by third bodies will be minimal. A thermochemical criterion for determining low adhesion interactions has been described elsewhere [26]. Thirdly, the films must be able to ‘heal’ from occasional wear, so that the repair rate should be faster that the wear rate. Healing could be due solely to the vapors ‘repairing’ worn films faster than they wear away; or it could be due to replenishment from reservoirs of third body material recycled in the contact to the flat. Finally, the chamber must be free of oxidizing gases that can contaminate the low friction tribofilm and result in relatively high friction coefficients (>0.1).
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15.5
CONCLUSIONS
1. Superlow friction coefficients (down to μ = 0.001) were achieved by H2 S lubrication of SiC vs. Mo and Al2 O3 vs. Mo at gas pressure around 1 Torr and sliding speeds below 1 mm/s. 2. The friction hysteresis, friction spiking and speed-dependent friction coefficients were attributed to tribofilms formed by rubbing SiC or Al2 O3 against Mo in H2 S. Films on Mo had a S/Mo ratio consistent with MoS2 formation, but the friction coefficient and velocity accommodation mode suggested that the Mo–S tribofilm behaved differently than a MoS2 coating. 3. Contamination of the low friction tribofilm by oxidizing gases led to friction spikes above 0.1. 4. H2 S lubrication of both SiC vs. Mo and Al2 O3 vs. Mo produced a dramatic speeddependent friction coefficient, which appears due to a competition between wear and film formation.
ACKNOWLEDGEMENTS The authors are grateful to Prof. Jean-Michel Martin for sharing his apparatus at Ecole Centrale de Lyon and to our early collaborator in the project, Dr. Christophe Donnet. I.L.S. would like to thank the Office of Naval Research for funding the investigation and for the opportunity to take a sabbatical at Ecole Centrale de Lyon.
REFERENCES [1] Bowden, F.P., Tabor, D. The Friction and Lubrication of Solids. Clarendon Press, Oxford, Part 1, 1950 and Part 2, 1964. [2] Buckley, D.H. Surface Effects in Adhesion, Friction, Wear and Lubrication. Elsevier, Amsterdam, 1981. [3] Iliuc, I. Tribology of Thin Layers. Elsevier, Amsterdam, 1980. [4] Bhushan, B., Gupta, B.K. Handbook of Tribology. McGraw-Hill, New York, 1991, Chapters 5 and 13. [5] Wahl, K.J., Singer, I.L. Trib. Lett. 1 (1995), 59. [6] Wahl, K.J., Belin, M., Singer, I.L. Wear 214 (1998), 212. [7] Graham, E.E., Klaus, E.E. ASLE Trans. 29 (1986), 229. [8] Graham, E.E., Nesarikar, A., Forster, N., Givan, G. Lubr. Eng. 49 (1993), 713. [9] Lauer, J.L., Blanchet, T.A., Vlcek, B.L., Sargent, B. Surf. Coat. Technol. 62 (1993), 399; Lauer, J.L., Vlcek, B.L., Sargent, B. Wear 162 (1993), 498. [10] Sawyer, W.G., Blanchet, T.A. Trans. ASME 123 (2001), 527. [11] Rowe, C.N. ASLE Trans. 10 (1967), 10. [12] Lepage, J., Zaidi, H. In: Dowson, D., Taylor, C.M., Godet, M., Berthe, D. (Eds.), Interface Dynamics. Elsevier, Amsterdam, 1988, pp. 259–266. [13] Zaidi, H., Robert, F., Paulmier, D. Thin Solid Films 264 (1995), 46. [14] Donnet, C., Fontaine, J., Grill, A., Le Mogne, T. Trib. Lett. 9 (2000), 137. [15] Bowden, F.P., Tabor, D. The Friction and Lubrication of Solids, Part 2. Clarendon Press, Oxford, 1964, pp. 210. [16] Bowden, F.P., Rowe, G.W. The Engineer (Nov. 1957), 667. [17] Singer, I.L., Le Mogne, Th., Donnet, Ch., Martin, J.M. J. Vac. Sci. Technol. 14 (1996), 38.
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[18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]
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Singer, I.L., Le Mogne, Th., Donnet, Ch., Martin, J.M. Tribol. Trans. 39 (1996), 950. Sawyer, W.G., Blanchet, T.A. Wear 225–229 (1999), 581. Heimberg, J.A., Wahl, K.J., Singer, I.L., Erdemir, A. Appl. Phys. Lett. 78 (2001), 2449. Kim, H.I., Lince, J.R., Eryilmaz, O.L., Erdemir, A. Trib. Lett. 21 (2006), 53. Erdemir, A., Eryilmaz, O.L., Nilufer, I.B., Fenske, G.R. Surf. Coat. Technol. 133–134 (2000), 448. Martin, J.M., Le Mogne, T. Surf. Coat. Technol. 49 (1991), 427. Goldstein, J.I., Newbury, D.E., Echlin, P., Joy, D.C., Fiori, C., Lifshin, E. Scanning Electron Microscopy and X-ray Microanalysis. Plenum Press, New York, 1981, p. 72. Bolster, R.N., Singer, I.L., Wegand, J.C., Fayeulle, S., Gossett, C.R. Surf. Coat. Technol. 46 (1991), 207. Singer, I.L. Langmuir 12 (1996), 4486. Singer, I.L., Bolster, R.N., Wegand, J., Fayeulle, S., Stupp, B.C. Appl. Phys. Lett. 57 (1990), 995. Fayeulle, S., Ehni, P.D., Singer, I.L. Surf. Coat. Technol. 41 (1990), 93. Singer, I.L. In: Singer, I.L., Pollock, H.M. (Eds.), Fundamentals of Friction. Kluwer Academic Publishers, Dordrecht, 1992, pp. 237–261. O’Hanlon, J.F. A User’s Guide to Vacuum Technology, second edition. Wiley & Sons, New York, 1989. Sections 16.3 and 17.2.1. Dieterich, J.H. J. Geophys. Res. 84 (1979), 2169. Vorvolakos, K., Chaudhury, M.K. Langmuir 19 (2003), 6778. Briscoe, B.J. In: Singer, I.L., Pollock, H.M. (Eds.), Fundamentals of Friction. Kluwer Academic Publishers, Dordrecht, 1992, pp. 167–182. Yoshizawa, H., Chen, Y.-L., Israelachvili, J. J. Phys. Chem. 97 (1993), 4128. Glosli, J.N., McClelland, G.M. Phys. Rev. Lett. 70 (1993), 1960. Thompson, P.A., Grest, G.S., Robbins, M.O. Phys. Rev. Lett. 68 (1992), 3448. Persson, B.N.J. Sliding Friction. Springer-Verlag, Berlin, 1998, Chapter 8.3. Zaidi, H., Paulmier, D., Lepage, J. Appl. Surf. Sci. 44 (1990), 221. Dorinson, A. ASLE Trans. 13 (1970), 215. Blanchet, T.A., Sawyer, W.G. Wear 251 (2001), 1003. Sawyer, W.G., Dickrell, P.L. Wear 256 (2004), 73. Dickrell, P.L., Sawyer, W.G., Heimberg, J.A., Singer, I.L., Wahl, K.J., Erdemir, A. J. Tribol. 127 (2005), 82.
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– 16 – Superlubricity in Diamondlike Carbon Films Ali Erdemir and Osman L. Eryilmaz Energy Systems Division, Argonne National Laboratory, Argonne, IL 60439, USA
16.1
INTRODUCTION
The word “superlubricity” refers to a sliding regime in which friction or resistance to sliding between two contacting surfaces literally vanishes [1]. Friction is a common yet poorly understood physical phenomenon. In our daily life, it is a source of lost energy and a cause of harmful emissions to the environment. If we could consistently produce and use tribological surfaces that are super-lubricious, then we would save a huge amount of energy and at the same time reduce toxic emissions to the environment. Given that in highly industrialized nations of the world, the annual cost of energy losses due to friction is estimated to be as much as 5% of their gross national products [2], the beneficial financial ramification of attaining superlubricity or near-zero friction in these systems is enormous. Accordingly, the old age quest to further reduce or even eliminate friction has gained considerable momentum during the last two decades. With the advent of novel experimental tools such as atomic and friction force microscopy (AFM and FFM), scanning tunneling microscopy (STM), surface force apparatus (SFA), and quartz crystal microbalance (QCM), etc. combined with powerful computational methods such as ab-initio and molecular dynamics simulation, studying friction at very small length, force, and time scales has become much easier than before. As a result, significant progress has been made during the last two decades in both understanding and controlling friction in nano-to-macro scale tribosystems [3–11]. Although the main focus of this chapter is superlubricity of certain diamondlike carbon (DLC) films, we provide a brief overview of the superlubricity research on other materials first and then concentrate on the synthesis and superlubricity of DLC films. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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16.2
SUPERLUBRICITY IN CRYSTALLINE SOLIDS
Using advanced experimental and computational capabilities mentioned above, several scientists have confirmed that superlubric sliding regimes can be achieved between atomically smooth surfaces of a number of crystalline solids, provided that these surfaces are brought into contact in an incommensurate or ideally misaligned/misfit fashion [12–18]. It is believed that under such sliding conditions, the lattice mismatch is large enough to avoid atomic-scale stick-slip, which can otherwise cause high static and kinetic friction. Due to such structural requirements for superlubricity (i.e., optimal incommensurability and/or misalignment), some scientists who worked in this field during the early 2000s often preferred the term “structural lubricity” over “superlubricity”, mainly because the word “superlubricity” implicitly meant some well-established physical phenomenon like superconductivity, superfluidity, etc. [19]. Most of the theoretical studies on superlubricity are based on the Tomlinson and/or Frenkel–Kontorova models [20,21]. These studies have provided significant fundamental insight into the atomic-scale origins of friction, in general, and superlubricity, in particular. 16.2.1
Lamellar Solids
There exist numerous solid materials with lamellar or layered crystalline structures. Some of these can provide excellent lubricity (more so than most of the liquid lubricants) to sliding contact interfaces [22]. They are often referred to as “solid lubricants”. Well-known examples are graphite, hexagonal boron nitride, boric acid, and the large family of transition metal dichalcogenides: MX2 (where M is molybdenum, tungsten, or niobium, and X is sulfur, selenium, or tellurium). These solids primarily owe their excellent lubricity to a layered lattice structure in which the atoms lying on the same layer are closely packed and strongly bonded to each other, while the layers themselves are relatively far apart, and the forces that hold them together, e.g., van der Waals, are weak (see the layered lattice structure of boric acid in Figure 16.1). When present on a sliding surface, these layers can align themselves parallel to the direction of relative motion and slide over one another with relative ease and hence, provide low friction. Indeed, Figure 16.1 shows not only the layered lattice structure of boric acid but also the evidence for interlayer shear which occurred during a sliding test. While this mechanism may primarily be responsible for the generally low friction nature of this class of solids, a favorable layered crystalline structure in itself
Figure 16.1 Layered lattice structure of boric acid and the microscopic evidence for interlayer shear as observed on a surface lubricated by boric acid.
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Figure 16.2 Layered lattice structure of graphite and the illustration of commensurate and incommensurate states between the layers.
is not sufficient for effective lubrication. The presence or absence of certain gaseous molecular species in their surroundings is also needed for achieving easy shear in most solid lubricants [22]. For example, moisture or some other condensable vapors are needed for graphite and boric acid to lubricate. In contrast, MoS2 and other transition metal dichalcogenides work the best in vacuum or inert gases. It is generally agreed that there exist no solid materials that can provide very low friction regardless of the test environment and/or conditions. Some of the earliest friction studies at nano-scales were conducted on lamellar solids. For example, using an AFM, Mate et al. [23] reported friction coefficients as low as 0.005 on graphite back in 1987. In a recent study, Dienwiebel et al. [18,24] have achieved zero friction on graphite under conditions of complete incommensurability in an instrument (called Tribolever™) with pN sensitivity. Figure 16.2 illustrates commensurate vs. incommensurate contact regimes for such lamellar solids as graphite. Obviously, the commensurate sliding regime has too many direct registry states between carbon atoms of opposing graphitic layers, while the incommensurate case, has only a few, and hence the least possibility for atom-to-atom interactions. Miura et al. [17,25] demonstrated superlow friction for C60 intercalated graphite films in which alternating monolayers of C60 were introduced between the graphene sheets. In their case, the incommensurability was not a pre-condition for superlubricity. Instead, Miura et al. proposed that C60 was acting as nano-scale ball bearings between the graphene layers and hence providing superlow friction. Friction studies on nested shells of multiwalled carbon nanotubes (which are essentially made of rolled-up sheets of graphite) further confirmed the existence of frictional anisotropy in these materials, and by bringing inner and outer tubes out of registry, one could obtain smooth sliding or superlow friction [26,27]. In another well-known lamellar solid (mica), Hirano et al. [3] further demonstrated the existence of a very strong relationship between incommensurability and frictional anisotropy. Specifically, they reported reductions in frictional force by factors of up to four when mica sheets were increasingly rotated out of registry and finally brought into an incommensurate state. Studies by Martin et al. [6,12] have confirmed that superlubricity is not limited to graphite and/or its derivatives like carbon nanotubes. Specifically, they demonstrated that superlubricity may be achieved in other lamellar solids, such as MoS2 . In their experi-
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mental study in ultrahigh vacuum tribometer, these authors were able to achieve friction coefficients as low as 0.001 with atomically smooth ultra thin films of MoS2 whose sliding surfaces were brought into a complete incommensurate contact regime. In a related study, Singer et al. [28,29] were able to achieve ultra-low friction (i.e., below 0.01) on Mo substrates under partial pressures of H2 S gas in a vacuum tribometer. Surface analytical investigation of sliding Mo surfaces confirmed the formation of a very thin surface film consisting mainly of Mo and S. 16.2.2
Other Solids
Besides the lamellar solids discussed above, researchers have demonstrated superlubricity with atomically smooth surfaces of Si, NaCl, and a few other solids. One of the early pioneers of this field, Prof. Hirano and his group [13], have not only theoretically modeled the conditions for achieving superlubricity but also demonstrated it experimentally by using a tungsten tip and the (001) surface of a Si substrate. They have performed their experiments in a modified STM and at ultra-high vacuum. Dedicated fundamental studies by Socoliuc and his co-workers [16] have shown the feasibility of achieving superlubricity in specially prepared ionic crystals, such as NaCl. Specifically, they observed a unique transition from stick-slip to continuous sliding without much friction under some very-light loading conditions (i.e., less than a nano-Newton) in ultra-high vacuum. Studies by Goto and Honda [30] have demonstrated that superlubric behavior is not limited to lamellar and other inorganic solids. They have shown that such a state of nearzero friction may also exist between sliding interfaces that contain certain metals, such as silver. Specifically, by depositing very thin (i.e., 5 nm thick) Ag films on Si substrates and rubbing the composite against a single-crystal diamond counterface, they were able to achieve friction coefficients of less than 0.01 in ultra-high vacuum. Just like the inorganic solids mentioned earlier, they found that such superlubric behavior is closely associated with the structural orientation and can only be achieved on highly oriented Ag (111) shear planes that are parallel to the sliding direction of the counterface diamond pin. In short, the state of the art in achieving and understanding superlubricity has now reached a critical threshold where friction can be controlled at sub-atomic scales. For example, recently Socoliuc and his co-workers have devised a system in which superlubricity could be switched on and off on demand (just like a light bulb) by simply exciting/deexciting the mechanical resonance of the sliding system [8]. Furthermore, it has become possible to design novel materials and coating architectures that can meet the specific lubrication and durability needs of new and highly sophisticated meso/macro-scale tribosystems. In particular, systematic work on carbon-based materials and coatings has led to the development of a new breed of near-frictionless carbon films that can provide superlow friction and wear to sliding surfaces under macroscopic test conditions. In the following sections, we will summarize the recent developments in carbon films, in general, and near-frictionless carbon films, in particular. We will also discuss the design criteria for superlubricity and propose a mechanistic model for their superlubricious behavior.
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16.3
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SUPERLUBRICITY IN AMORPHOUS CARBONS
Carbon is one of the most abundant elements in our planet. It exists in more than 90% of all known substances and is one of the most important building blocks of all biological systems. Furthermore, carbon has the largest number of allotropes, including diamond, graphite, and white carbon (or ceraphite), as well as carbon nanotubes, buckyballs, and other forms of fullerenes. Besides these allotropes, there exist several more carbon-based non-crystalline materials, including carbon–carbon composites, carbon nano-fibers, bulk glassy carbons, and amorphous DLC films. Some of the well-known self-lubricating polymers like Teflon and polyethylene are also carbon-based and used extensively by industry to overcome stiction in cookware or to achieve low friction and wear on sliding surfaces of biomedical implants. Teflon is well-known for its non-stick, low-friction behavior, and depending on the test conditions, its friction coefficients may vary between 0.02 and 0.1 [22]. Many of other natural and man-made carbon-based materials are now available, and they exhibit some of the most interesting friction and wear properties among all other materials. Besides graphite (whose superlubricity is primarily associated with incommensurability), most of the other carbon forms mentioned above provide a high-degree of lubricity when rubbed against other materials [31]. In fact, some of these carbons are structurally amorphous; hence, they will always be in an incommensurate state when in contact. A few researchers have demonstrated that under the right sliding conditions, these amorphous carbon films can provide friction coefficients as low as 0.001 [7,32]. Figure 16.3 shows
Figure 16.3 Superlow friction behavior of a highly hydrogenated (≈40 at.% hydrogen) DLC film in dry nitrogen (test conditions: load, 10 N; speed, 0.3 m/s; temperature, 23 ◦ C; test pair, coated-sapphire ball with diameter of 6.35 mm and coated sapphire disk). Reused with permission from A. Erdemir, O.L. Eryilmaz, and G. Fenske, Journal of Vacuum Science and Technology A, 18 (2000), 1987; Copyright 2000, AVS the Science and Technology Society.
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the friction coefficient of a nearly frictionless carbon film that was developed at Argonne National Laboratory. As will be elaborated later, one common prerequisite in all of these carbon films providing superlow friction is that large amounts of hydrogen have to be either incorporated into their amorphous structures or supplied onto their sliding surfaces during tests. 16.3.1
Diamondlike Carbon Films
The synthesis of DLC films was first reported back in the early 1950s [33], but the real progress and more systematic studies started in the 1970s [34]. Over the years, these films have attracted huge scientific and commercial interest mainly because of their superlow friction and wear, high chemical inertness, excellent optical and dielectric properties, etc. Unlike synthetic diamond films, the production of DLC is rather easy and can be accomplished over a broad range of deposition conditions and temperatures [31]. In recent years, many researchers in the field have devised more exotic forms of DLC by incorporating certain elements (such as H, N, B, F, Ti, Cr, W, and S) into their amorphous microstructures [35–38]. Some of these films are extremely hard (as high as 90 GPa) and resilient, while others are rather soft but provide some of the lowest friction and wear coefficients. These films are now used in numerous industrial applications, ranging from razor blades to magnetic hard disks, and from critical engine parts to microelectromechanical systems. 16.3.2
Synthesis and Main Characteristics of DLC Films
All kinds of physical vapor deposition (PVD) and chemical vapor deposition (CVD) methods can be used to fabricate DLC films on a wide range of substrate materials including metals, ceramics, and certain polymers. Depending on the carbonaceous precursors used and the specific deposition conditions and/or methods employed, the type of bonds (i.e., sp1 , sp2 , sp3 ) that hold carbon atoms together in DLC films may vary a great deal and can affect their mechanical and tribological properties [39]. Among other parameters, the deposition temperature can strongly influence the nature of chemical bonding in these films. During deposition, gas pressure, bias voltage, and other parameters may also be adjusted to increase the fraction of one bonding type over another. If a hydrocarbon gas (such as methane or acetylene) is used as the source for carbon, the resultant DLC films may contain considerable amounts of hydrogen in their microstructures. During deposition, one can also incorporate more hydrogen into DLC films by using gas mixtures with hydrogento-carbon ratios that are higher than normal [40]. These highly hydrogenated DLC films (containing more than 40 at.% hydrogen) can be relatively soft but exhibit some of the lowest friction and wear coefficients (as will be discussed later). Hydrogen-free DLC films are derived from pure carbon materials (such as graphite, glassy carbon, or carbon–carbon composites) using cathodic arc-PVD, laser ablation (or pulse laser deposition), ion-beam assisted deposition, and magnetron sputtering. Over the years, taking advantage of the latest advances in deposition technologies (such as hybrid systems), researchers have devised more exotic forms of DLC films composed of unique nano-structures and/or -phases. These novel films possess much improved physical, mechanical, and tribological properties. By the incorporation of Si, Ti, and W into DLC
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films at some optimum levels, researchers were able to achieve much lower friction and wear under dry and lubricated sliding conditions [38,41]. Adding nitrogen into DLC films resulted in significant increases in hardness and hence much improved tribological performance in magnetic hard-disk applications. A superlow friction version of carbon nitride has recently been pioneered by Kato and his co-workers [42]. When tested in dry nitrogen or under nitrogen gas flow conditions, such films provided friction coefficients of less than 0.01. Apart from the incorporation of various elements into DLC films, researchers have also engineered a number of nano-layered and -composite DLC films in recent years. Such films either consist of (1) alternating nano-layers of amorphous carbon and various metallic and/or compound phases; or (2) an amorphous carbon network with some nano-scale crystalline phases homogeneously dispersed in their microstructure. Some of the most popular examples include nano-layered or -composite DLC films consisting of carbon and W or carbon and Cr [43,44]. Because of their nano-layered and/or -structured nature, these films are quite tough and resistant to microcrack initiation and growth during tribological testing. In summary, DLC films have gained considerable attention in recent years mainly because of their ease of production and very impressive tribological and other properties. With recent advances in deposition processes (i.e., hybrids), a new class of multi-functional nanocomposite DLC films is currently used in a wide range of tribological applications. In an attempt to further improve their performance, researchers have lately been creating special textures on the sliding surfaces of these DLC films. In particular, high-precision shallow dimples created on DLC surfaces by excimer or femtosecond lasers have been shown to improve their tribological properties rather substantially, especially under boundarylubricated sliding conditions [45]. 16.3.3
Classification
As mentioned above, DLC films are structurally amorphous. However, depending on the deposition methods and/or carbon sources used, the type of bonding between carbon atoms (i.e., single (sp3 ), double (sp2 ), or triple (sp1 ) bonds) and other elements may differ substantially. The fractions of sp2 and sp3 bonds are the largest, but some trace amounts of sp1 bonding may also be present [39]. Those DLC films with a high fraction of sp2 -bonded carbon atoms tend to be relatively soft and behave more like graphite during tribological tests, while films with a high fraction of sp3 -bonded carbons behave more diamondlike in some of their properties [46]. The DLC films derived from a hydrocarbon source (such as acetylene or methane) contain large amounts of hydrogen within their structures. Figure 16.4 shows the regions of various DLC films with respect to their sp2 vs. sp3 bonds and hydrogen content [39]. In addition to the phases shown in this figure, there exist several more DLCs consisting of different kinds of alloying elements, discrete compound phases in a nanocomposite, and superlattice or nano-layered coating architectures, as discussed earlier. 16.3.4
Lubrication Mechanisms
Most of the tribological studies on DLC films were carried out during the 1990s. These and a few earlier studies have confirmed that these films were in general lubricious and
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Figure 16.4 Ternary phase diagram for various carbon films with respect to their sp2 , sp3 , and hydrogen contents [39]. Reprinted from Mat. Sci. Eng., 37 (2002), J. Robertson, Diamond like amorphous carbon, 129; Copyright (2002), with permission from Elsevier.
resistant to wear and corrosion. Unlike graphite and diamond which exhibit low friction in humid air, some of the very first DLC films exhibited relatively high friction in humid test environments, but very impressive performance in inert or dry test media in which graphite and diamond give rather high friction [47]. This finding was in contrast to the frictional behavior of both graphite and diamond, which are lubricious in humid test environments, but exhibit relatively high friction and wear in inert gases or vacuum [48,49]. Numerous systematic tribological studies on DLC films have consistently demonstrated that the tribology of DLC films was indeed very sensitive to the chemistry of test environments. Friction values as low as 0.001 and as high as 0.7 have been reported for various DLC films in different test environments [7,50–52]. Similar disparity has been found for their wear performance as well. Such a large variation in friction and wear of DLC films appears to result from a complex combination of intrinsic (or film-specific) and extrinsic (or test-condition-specific) factors [53] as will be briefly discussed in the following paragraphs. Intrinsically, the friction and wear behavior of DLC films may depend strongly on the degree of sp2 vs. sp3 bonding as well as the relative amounts of hydrogen and/or other alloying elements in their structure or on the sliding surfaces. Extrinsically, the extent of chemical, physical, and mechanical interactions between DLC films and counterface materials can have dramatic effects. For example, physically rough DLC films may suffer high friction and wear losses while sliding against another rough counterface. The temperature and chemical nature of the test environment can also play a major role in their friction and wear. The contribution from each type of interaction to overall friction can vary a great deal and may depend strongly on the specific test conditions or parameters (load, speed, type of motion, distance, etc.) employed during the sliding tests. The presence or absence of a transfer film on the sliding surfaces of counterface materials and the physical and/or chemical nature of such films can also influence their friction and wear behaviors. Physically rough surfaces can certainly trigger high friction and severe wear losses in most sliding contacts, and diamond or DLC films are no exception [31]. Specifically, me-
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chanical interlocking between surface asperities can lead to high frictional losses (especially during the run-in or initial stages of sliding tests). Previous studies on diamond and DLC films have confirmed that the higher the surface roughness, the greater the friction and wear losses. So to achieve low or super-low friction in DLC films, one has to attain and maintain a smooth surface finish. Being structurally amorphous, most DLC films can closely mimic the original surface roughness of the substrate materials. Therefore, by depositing these films on highly polished surfaces (such as Si wafers), their surface finish can be extremely smooth. Besides the surface roughness, a high degree of chemical and/or adhesive interactions between sliding DLC surfaces may also adversely affect their frictional behavior. The major source of adhesive interactions in these and other carbon-based films (like diamond) is covalent bonding between unoccupied or dangling σ -bonds of surface carbon atoms [53,54]. This type of bonding can cause very strong adhesion and hence friction between sliding surfaces. Such a situation may exist between sliding surfaces of hydrogen-free DLC films, which contain a high number of sp3 -bonded carbon atoms in their structure. When tested in dry nitrogen or high vacuum, friction coefficients of 0.5 to 0.7 were obtained and largely attributed to the high levels of covalent σ -bond interactions between carbon atoms of the sliding surfaces. In addition to these very strong adhesive bonds, van der Waals forces, π –π ∗ interactions, capillary forces, and electrostatic attractions may also exist between sliding DLC surfaces and can further increase adhesion and, hence, friction. In particular, if a DLC film is more graphite-like or consists of a large fraction of sp2 bonded carbon atoms, then a high level of π –π ∗ interaction may exist between sliding DLC surfaces and control their friction. Just like graphite, the graphitic DLC films work quite well in moist environments but suffer high friction and wear in dry or inert gases. Under the influence of repeated sliding during tribological tests, the sliding surfaces of DLC films may interact with counterfaces and with the gaseous species (such as water molecules, oxygen, and hydrocarbons) in test chambers. Some of these species are highly polar, and they can easily form a physisorbed layer on the surface. Recent systematic studies by Heimberg et al. [55] and Dickrell et al. [56] have confirmed that the extent of such gas–surface interactions can play a major role in the frictional behavior of certain DLC films. From a series of model experiments in controlled test environments, these authors concluded that the longer the exposure time between subsequent sliding passes, the higher the friction of DLC films [55,56]. Among the gaseous species that may exist in test chambers, oxygen and water molecules were shown to have the strongest effects on the friction and wear behavior of DLC films. For example, in vacuum and inert gases, friction coefficients of less than 0.01 are feasible with highly hydrogenated DLC films [51,57,58]; however, when oxygen and/or moisture were introduced into the test chambers, their friction coefficients increased more than an order of magnitude. The tribochemistry of sliding DLC surfaces is rather complex and has been the focus of numerous studies in recent years. Despite being highly inert under static conditions, they become chemically active and begin to interact with the chemical species in their surroundings during sliding contact tests [32,58,59]. Generation of a tribo-plasma on or near the sliding contact surfaces is thought to further accelerate the rate of tribochemical interactions [60]. In this respect, the incorporation of certain alloying elements (such as Si, F, B, P, N, and various metals) into DLC films is thought to change the nature of the tribo-
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chemical interactions and hence influence their friction and wear behavior. For example, the incorporation of Si, Bi, Ti, F, and S into DLC films is found to make them less sensitive to moisture [38,61–63]. The presence or absence of third bodies or transfer layers on sliding surfaces of DLC films may also have a strong effect on their frictional behavior [64–70]. These layers mostly form on the sliding contact surfaces of uncoated counterface balls and/or pins rubbing against the DLC-coated disks. In particular, those counterface materials that are wellknown carbide formers (Ti, Fe, W, Si, etc.) tend to generate such layers much faster and with a much higher degree of coverage and bonding. These transfer layers often have disordered graphite-like structures [59,68–71]. If the tests are run in humid air, the debris particles may contain considerable amounts of oxygen. If the tests are run in vacuum or inert gases, the carbon-rich transfer films will have a similar structural chemistry to the film on the disk side. Overall, the counterface materials and the tribotest parameters, together with the test environment, play a crucial role in the kinetics of the formation and composition of the transfer layers, and thus, strongly influence the friction and wear behavior of DLC films. At elevated temperatures, most DLC films may gradually transform to an increasingly ordered or graphitic state [71–73]. Specifically, carbon and/or other atoms in their amorphous structure may begin to re-arrange themselves and assume thermodynamically more stable structural configurations, such as graphite; as a result, the friction and wear behavior of DLC films may also change during or after exposure to elevated temperatures. In the case of hydrogenated DLC films, some of the un-bonded hydrogen may diffuse out and leave a relatively porous structure behind. Since such a structure will be much softer, it can wear out quickly. Hydrogen-free or tetrahedral-amorphous carbon (ta-C) type films may have much higher endurance limits to elevated temperatures (up to 500 ◦ C), but their friction coefficients increase substantially, mainly because the extent of σ -bond interactions increases [53]. 16.3.5
Origin of Superlubricity in DLC Films
As is clear from the foregoing, the sliding friction and wear behavior of DLC films are strongly influenced by intrinsic and extrinsic factors. To achieve superlow friction in these films, one has to consider and control these factors very carefully. First and most important, the sliding surfaces must be extremely smooth so that the adverse effects of mechanical interlocking and/or asperity–asperity interactions are at a minimum or absent. Secondly, the sliding DLC surfaces must have a high degree of chemical inertness so that the extent of adhesive or chemical interactions is extremely low. Owing to an amorphous structure, the surfaces of DLC films can be extremely smooth, provided that they are deposited on atomically smooth or highly polished substrates. To achieve high chemical inertness on sliding DLC surfaces, one can either introduce large amounts of hydrogen into DLCs during deposition [7,74–79], or supply hydrogen gas into their sliding surfaces during tribological testing [32,80,81]. By doing this, one can effectively eliminate those dangling σ -bonds that otherwise cause high friction. Due to its very small size in its protonic state, hydrogen can easily enter into the amorphous structure of DLC films. Studies have shown that as much as 50 at.% hydrogen can be
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Figure 16.5 Friction coefficients of DLC films derived from various source gases in a plasma enhanced CVD system (test conditions: load, 10 N; speed, 0.5 m s−1 ; temperature, 22–23 ◦ C; test environment, dry N2 ).
introduced into DLC during deposition in PVD or CVD systems. A significant amount of hydrogen may enter into DLC if the carbon source is a hydrocarbon gas, like CH4 or C2 H2 . In fact, it is almost impossible to obtain hydrogen-free DLC if the carbon source is a hydrocarbon. If needed, more hydrogen may be introduced by adding additional hydrogen gas (up to 90 vol.%) into the deposition chamber [7,77–79]. The resultant films will be super-hydrogenated (containing more than 40 at.% hydrogen). As is clear from Figure 16.5, the presence or absence of hydrogen in DLC films plays an important role in their frictional behavior. Specifically, the higher the amount of hydrogen available during deposition, the lower the friction coefficients of the resultant films. Conversely, if a DLC film has little or no hydrogen within its structure (i.e., hydrogen-free or -poor DLC), it provides high friction in dry and inert test chambers or in high vacuum. For example, the average friction coefficient of a hydrogen free-DLC film is 0.7, while a highly hydrogenated DLC film exhibits an average friction coefficient of 0.006 [7,51,77–79]. Note that the friction coefficient of a DLC film derived from pure methane is about 0.035. All of these films were deposited on H13 steel substrates at room temperature, and they were about 1-µm thick. In recent years, a number of researchers have supplied hydrogen gas into the test chamber where hydrogen-poor or -free DLC films are being subjected to sliding tests [32,82]. The results of these studies (see Figures 16.6 and 16.7) have also shown that as long as the sliding contact interfaces of sliding DLC films are supplied with sufficient amounts of hydrogen, superlow friction coefficients can be attained. Based on the friction test results from hydrogen-rich vs. -poor DLC films, the following mechanistic explanation can be proposed for the very critical role of hydrogen in the fric-
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Figure 16.6 Effects of various source gases on friction coefficients of hydrogen-free DLC films. Hydrogen-containing test environment provides the lowest friction [82]. Reprinted from Surf. Sci., 600 (2006), Y. Qi, E. Konca, and A.T. Alpas, Atmospheric effects on the adhesion and friction between non-hydrogenated diamondlike carbon (DLC) coating and aluminum—A first principles investigation, 2955; Copyright (2006), with permission from Elsevier.
tional behavior of these films. As is well-documented, hydrogen bonds strongly to carbon and thus effectively passivates any free σ -bonds available within the bulk or on the surfaces. C–H bonding is covalent and stronger than a single C–C bond. Once bonded, it will be very difficult to remove hydrogen from carbon even at fairly high temperatures [83]. Such a strong bonding and passivation of dangling σ -bonds can reduce or even eliminate the extent of adhesive interactions across the sliding interfaces, resulting in low friction. When DLC films are synthesized in highly hydrogenated gas discharge plasmas, the amount of hydrogen within the growing films as well as on their surfaces increases substantially [84]. Within the plasma, hydrogen molecules are broken into ions, and as these ionized hydrogen atoms reach the surface, they can easily react with carbon to establish C–H bonding. Some hydrogen may remain as un-bonded interstitials, as shown by a recent computer simulation in Figure 16.8. The existence of large amounts of hydrogen within the DLC structure as well on its surface should effectively eliminate the possibility of any unoccupied σ -bonds remaining and potentially participating in adhesive interactions during sliding. Excess hydrogen within the films can always diffuse to sliding surfaces and hence replenish or replace those hydrogen atoms that may have been removed due to frictional heating and/or mechanical wear during sliding contact. During deposition of DLC in highly hydrogenated gas discharge plasmas, another very important event takes place. Specifically, hydrogen is known to effectively etch out sp2 bonded or graphitic carbon during deposition. This is one of the reasons for using almost 99 vol.% hydrogen during deposition of crystalline diamond films. The removal of such
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Figure 16.7 Effects of partial pressures of hydrogen and argon on friction behavior of DLC films: (a) in UHV, (b) 1 hPa partial pressure of hydrogen, (c) 10 hPa partial pressure of hydrogen, and (d) 10 hPa of argon. Low friction is attained when a sufficient amount of hydrogen is present in the vacuum chamber [32]. Reprinted from Surf. Coat. Technol., 146–147 (2001), J. Fontaine, C. Donnet, A. Grill, and T. LeMogne, Tribochemistry between hydrogen and diamond-like carbon films, 286; Copyright (2001) with permission from Elsevier.
Figure 16.8
A periodic cell of the optimized NFC film. Dark atoms are carbon, and light atoms are hydrogen.
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Figure 16.9 A mechanistic model for the superlow friction behavior of highly hydrogenated DLC films. Reprinted from Surf. Coat. Technol., A. Erdemir, The role of hydrogen in tribological properties of diamondlike carbon films, 292; Copyright (2001), with permission from Elsevier.
graphitic carbons from the structure eliminates the possibility of π –π ∗ interactions that are typical of sp2 -bonded graphitic clusters. In fact, in a highly hydrogenated gas discharge plasma, strong C–H bonding rather than C=C double bonding is favored. As mentioned earlier, the presence of large amounts of sp2 -bonded carbon atoms can give rise to strong π –π ∗ interactions and hence high friction. When DLC films are produced in a highly hydrogenated gas discharge plasma, some of the surface carbon atoms can potentially bond to two hydrogens. Such a situation can readily occur on the unreconstructed (100) surfaces of crystalline diamond films. Undoubtedly, such a unique situation (that can easily be created in a highly hydrogenated plasma) will lead to a significantly higher hydrogen density on DLC surfaces, and thus provide stronger shielding or passivation, which can translate into superlow friction. Figure 16.9 presents such a friction model [75]. The other weak forces (van der Waals, capillary, electrostatic, etc.) may also contribute to overall friction. The van der Waals forces are always present at the sliding interfaces, but because they are weak, their relative contribution to overall friction may be insignificant, especially if tests are run under very high contact pressures. It is well-known that their contributions to overall friction may be significant when and if the tests are run under ultra-light loads and/or in AFM machines. The contribution of capillary forces to friction may also be significant if the friction tests are run in moist environments. However, in a dry nitrogen environment, the influence of capillary forces on the sliding friction behavior of DLC films will be small. Electrostatic forces that build on sliding contact interfaces of dielectric solids can also influence the frictional behavior of such solids. In fact, the
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Figure 16.10 wear tracks.
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2D and 3D ToF-SIMS images of sliding DLC surfaces confirming the existence of C–H within
accumulation of positive and/or negative electrical charges on both sides of sliding faces can cause the development of repulsive forces. As illustrated in Figure 16.9, the free electrons of those hydrogen atoms on the surface are paired with the dangling σ -bonds of surface carbon atoms. As a result, the electrical charge density of hydrogen atoms is permanently shifted to the other side of the hydrogen nucleus and hence away from the surface. Such a situation will result in positively charged hydrogen protons being closer to the surface than the paired electron, which is tied to the dangling σ -bond of the surface carbon atoms. Therefore, the creation of such a dipole configuration at the sliding interface should give rise to repulsive rather than attractive forces between the hydrogen-terminated sliding surfaces of the DLC films [75,84]. In support of the proposed mechanism described above, Dag and Ciraci [82] and Qi et al. [85] have recently demonstrated the existence of such repulsive forces between H-terminated diamond (001) surfaces. Time-of-flight secondary ion mass spectroscopy (ToF-SIMS) has emerged as a very powerful and versatile technique to visualize the chemical nature of surfaces and extremely thin films. In particular, 2 and 3D mapping of such surfaces provides excellent mass and spatial resolutions for a wide variety of chemical species including hydrogen and carbon. So, there is no doubt that it is an excellent technique for examining the surface chemistry of DLC films. Figure 16.10 shows the 2D and 3D ToF-SIMS images of a wear track that was formed on a highly hydrogenated DLC film that consistently provided friction coefficients less than 0.01. As is clear, both maps reveal hydrocarbon fragments within the wear track, thus further confirming that the sliding contact interfaces of these films consist mainly of carbon and hydrogen, whereas the non-contact or out-of-wear track areas are covered by other chemical species. In short, hydrogen plays a critical role in the frictional behavior of most carbon films, in general, and DLC films, in particular. Superlow friction in DLC films is not limited to highly hydrogenated DLC surfaces. Studies by Masuda and Honda [86] have shown that hydrogen-terminated Si (111) surfaces
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can also attain superlow friction (i.e., 0.003) when rubbed against a diamond slider in ultra-high vacuum. Thermal desorption of hydrogen from the Si surface at 600 ◦ C caused more than two orders of magnitude increase in friction. Based on these studies, Masuda and Honda attributed superlow friction to a monolayer of hydrogen atoms terminating the dangling bonds of the Si (111) surface. Systematic lubrication studies by Kano et al. [87] have achieved extremely low friction coefficients on hydrogen-free DLC films after termination of their sliding surfaces by OH under lubricated sliding conditions. Specifically, they blended a poly-alpha olefin base oil with glycerol mono-oleate (GMO) and used it as a boundary lubricant for sliding surfaces of hydrogen-free DLC films. Surface analytical studies confirmed the presence of a layer of OH on the surface. Based on these findings, Kano et al. proposed that alcohol function groups of GMO and the surface carbon atoms of ta-C were mechanically and tribochemically activated to result in a strongly bonded OH layer on ta-C surfaces. Just like hydrogen termination, OH termination of the dangling σ -bonds appears to have resulted in such ultralow friction. In another related study, Kato and his coworkers [42] demonstrated the feasibility of achieving superlow friction on a specially prepared carbon nitride (CNx ) film. Specifically, they obtained such low friction coefficients by blowing nitrogen gas into the sliding interfaces of the Si3 N4 balls and CNx coatings [42]. In short, they concluded that the chemical nature of the sliding surfaces of DLC films is primarily responsible for their unique and diverse range of frictional behavior. By properly controlling the chemical nature of such surfaces either during deposition or during testing, one can achieve superlow friction and wear. In particular, the elimination of intrinsic and extrinsic sources of friction seems to be the key to superlow friction in these materials.
16.4
SUMMARY AND FUTURE DIRECTION
During the last two decades, significant advances have been made in the formulation and diverse applications of DLC coatings with very low friction. With recent advances in the field of deposition technologies, it is now possible to synthesize all kinds of such films, ranging from hydrogen-free to hydrogen-rich, that can meet the increasingly multi-functional needs of various industrial applications. They can also be doped or alloyed with all kinds of elements and produced in nano-composite and/or -structured fashion. Structurally, all DLC films are amorphous and mainly consist of sp2 - and sp3 -bonded carbon atoms. Tribologically, their friction and wear behavior are strongly influenced by a number of intrinsic and extrinsic factors. For example, intrinsically, the ratio of sp2 - to sp3 -bonded carbon atoms and the amount of alloying elements can influence their friction and wear behavior rather substantially. Some of the extrinsic factors that can affect their tribological behavior include test conditions and environments, as well the type of counterface materials that are being used during sliding tests. Based on the knowledge gained from the large body of research during the past two decades, it has now become possible to design novel DLC films that can provide extremely low friction. In particular, by controlling their surface and structural chemistry, we are able to achieve friction coefficients as low as 0.001 on highly hydrogenated DLC films and because of their amorphous structure, they do not require a
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special sliding orientation and/or incommensurability to provide such super-low friction coefficients. Mechanistically, their super-low friction behavior is related to a very passive surface that can create very little or no adhesive bonding or cause chemical interactions during sliding.
ACKNOWLEDGEMENTS This work is supported by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, under Contract W-31-109-Eng-38. The authors thank their students and collaborators who participated in the preparation, testing, and characterization of the DLC coatings discussed in this chapter.
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Erdemir, A. Mat. Res. Soc. Symp. Proc. 697 (2002), 391. Erdemir, A., Erylmaz, O.L., Nilufer, I.B., Fenske, G.R. Surf. Coat. Technol. 133–134 (2000), 448. Erdemir, A., Eryilmaz, O.L., Nilufer, I.B., Fenske, G.R. Diam. Rel. Mater. 9 (2000), 632. Donnet, C., Grill, A. Surf. Coat. Technol. 94–95 (1977), 456. Fontaine, J., Belin, M., Le Mogne, T., Grill, A. Tribol. Int. 37 (2004), 869. Qi, Y., Konca, E., Alpas, A.T. Surf. Sci. 600 (2006), 2955. Su, C., Lin, J.C. Surf. Sci. 406 (1998), 149. Erdemir, A. Tribol. Int. 37 (2004), 1005–1012. Dag, S., Ciraci, S. Phys. Rev. B 70 (2004), 241401. Masuda, H., Honda, F. IEEE Trans. Magnetics 39 (2003), 903. Kano, M., Yasuda, Y., Okamoto, Y., Mabuchi, Y., Hamada, T., Ueno, T., Ye, J., Konishi, S., Takeshima, S., Martin, J.M., Bouchet, M.I.D., Le Mogne, T. Tribol. Let. 18 (2005), 245.
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– 17 – Superlow Friction of a-C:H Films: Tribochemical and Rheological Effects Julien Fontaine1 and Christophe Donnet2 1 Laboratoire de Tribologie et Dynamique des Systèmes, UMR CNRS 5513, Ecole Centrale
de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France 2 University Institute of France and Laboratoire Traitement du Signal et Instrumentation,
UMR CNRS 5516, Université Jean Monnet, 18 rue Professeur Benoît Lauras, 42000 Saint-Etienne, France
17.1
INTRODUCTION
Diamondlike carbon coatings have been the subject of numerous intensive studies for the last two decades. The general term DLC describes hydrogenated and hydrogen-free metastable amorphous carbon materials, prepared by a wide variety of physical and chemical vapor deposition techniques. The films exhibit a wide range of structure, composition, and a range of attractive mechanical, optical, electrical and chemical properties. The film structure and properties are determined by the H content and the relative ratio of the two sp2 and sp3 carbon hybridizations, the sp1 carbon hybridization being negligible. Hydrogen in DLC is important for obtaining a wide optical band gap and a high electrical resistivity, removing midgap defect states, stabilizing the random network and preventing its collapse into a graphitic phase. A general review on DLC films has been published by Robertson in 2002 [1]. Much of the previous efforts has been invested in the characterization of the tribological behavior of DLC films, mainly because of the low friction behavior and high wear resistance of these materials. Thus, the tribology of DLC coatings has been discussed extensively in the literature, and has been summarized in various reviews [2–7]. Friction and wear of DLC coatings are strongly affected by the nature of the films, as controlled by the deposition process, and by the tribotesting conditions, including material parameters (nature of the substrate), mechanical parameters (contact pressure), kinematic parameters (nature of motion, speed), physical parameters (temperature during friction), and chemical parameters (nature of the environment). DLC films are rather unique and have much to offer for a wide range of tribological applications. Over the years, scientists have made great strides in understanding the growth Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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mechanisms, surface chemical/physical states, and tribological behaviors of DLC films. This understanding has been used to design and customize dedicated DLC coatings in various industrial fields, including mechanics, automotive industry, computer technology or biomaterials. These industrial successes have certainly encouraged the efforts of scientists to go further in the fundamental investigations of the friction and wear mechanisms of DLC films. Probably one of the most spectacular results published in the past years is related to the superlow friction and wear behaviors observed in particular testing conditions with hydrogenated diamond-like carbon films (a-C:H). The purpose of this chapter is to provide an overview of the superlow friction mechanism observed with some a-C:H films from various suppliers. Emphasis is placed on the current state of the art in our understanding of the superlow friction and wear mechanisms of these films as well as on the correlation with their structure and mechanical properties. Referring to the structural and fundamental tribological knowledge gained during the past decade, the chapter will emphasize the importance of surface mechanical, rheological and chemical effects on friction and wear of these materials and will identify some key requirements to achieve superlow friction and wear. The chapter is divided into three main parts. The first part is devoted to a brief review on the general tribological behavior of DLC, and provides evidence of superlow friction with a-C:H films. The second part deals with the conditions for an a-C:H film to achieve superlow friction, namely low interacting and compliant surface. Finally, the third part explains how is superlow friction achieved through tribofilm build-up, why it can be lost in some cases and how it is possible to preserve this exceptional tribological behavior.
17.2 17.2.1
THE WIDE FRICTION RANGE OF DLC FILMS
General Behavior
DLC films may exhibit many different tribological behaviors due to the great variety of their compositions and structures, as reported elsewhere [4–7]. Thanks to their exceptional combination of properties—hardness higher than steel with equivalent elastic modulus, relatively low roughness and low surface energy—they are usually efficient tribological coatings. However, friction coefficients are reported between less than 0.01 up to 1, depending both on testing conditions and film composition. Figure 17.1 provides an overview of the friction ranges observed with DLC films. In ambient air, friction coefficients range generally between 0.05 and 0.3, whereas in inert environment (ultra-high vacuum, dry nitrogen or dry argon), they can reach either ultra-low values (down to 0.01) or high values (more than 0.5). Furthermore, the composition of DLC films strongly affects their tribological dependence to environment. In ambient air, the friction coefficient increases with increasing relative humidity (RH) for hydrogenated amorphous carbon (a-C:H) [8,9], whereas it decreases with increasing RH for pure amorphous carbon (a-C or ta-C) [10]. It is well established that a carbon-rich transfer film is build up on many metallic or ceramic counterfaces when friction and wear are low [7]. In such a case friction occurs between two surfaces coated with amorphous carbon, which might nevertheless be different from the original film, justifying the terms “tribofilm” instead of “transfer film”.
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Figure 17.1 Dependence of the steady-state friction coefficient versus the atmosphere surrounding the contact during the friction process, for hydrogenated and un-hydrogenated DLC films.
Several authors have reported the friction-induced conversion of sp3 to sp2 sites [11] and even “graphitization” [12,13] of the amorphous structure, as observed on the wear debris by Electron Energy Loss Spectroscopy (EELS) and also on transfer layer by Raman Spectroscopy. These tribochemical phenomena are dependent on the nature of the environment surrounding the contact, mainly the pressure of oxygen and/or water vapor. In the case of a-C:H films, hydrogen may also be released from the film during friction [14]. All these friction-induced modifications of the amorphous network have a strong influence on the tribological behavior of the DLC material. 17.2.2
Experimental Evidence of Superlow Friction
The lowest friction coefficient values of carbon-based films have been observed for hydrogenated DLC films in inert environments. With values lower than 0.01, this vanishing of sliding resistance is often named “superlubricity” or “superlow friction”. These very low friction coefficient values are not achievable with any DLC film: according to the literature, only hydrogenated amorphous carbon (a-C:H) allow such friction reduction under vacuum or inert environment. Nevertheless, not all hydrogenated amorphous carbon films lead to superlow friction. When slid in high vacuum, the friction coefficient of these films stabilizes either at very low or very high values, as reported by many authors. Miyake et al. [15] showed indeed that DLC with high hydrogen content (not quantified) leads to friction coefficients near 0.01 in vacuum, whereas films with low hydrogen content reach values higher than 0.35. Zaidi et al. [16] and Le Huu et al. [17] observed that hydrogen is responsible for an ultra-low friction level, and acts as a lubricating source when present in the nearsurface region. In 1994, Donnet et al. [18] have recorded friction coefficients lower than 0.01 and down to 0.001 with a-C:H films deposited by IBM (Dr. Grill). The same authors have shown in 1997 the existence of a threshold in hydrogen content of DLC films be-
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Figure 17.2 Coefficient of friction versus number of sliding cycles (a) and tangential force versus time (b) for an a-C:H films with 42 at.% of hydrogen sliding in ultra-high vacuum (256 data points are recorded for each pass).
tween high (>0.5) and low (<0.02) friction coefficients in ultra-high vacuum (UHV) [19]. The role of deposition conditions on superlow friction of a-C:H coatings has been demonstrated by Erdemir et al. [20] who reported superlow friction coefficients measured on DLC films derived from super-hydrogenated source gases (i.e., 75–90% H2 and 10–25% CH4 or C2 H2 ). Before investigating the mechanisms responsible for superlow friction of DLC, it is paramount to demonstrate that superlow friction forces are effectively recorded during the test with some of these films. This has been observed many times in the UHV tribometer of Ecole Centrale de Lyon. It consists in a linear reciprocating pin-on-flat tribometer placed inside a surface analysis vacuum chamber equipped with X-ray Photoelectron Spectroscopy (XPS) and Auger Electron Spectroscopy (AES) [21]. The applied load on hemispherical pins (generally with 1.5 to 8 mm radius) can be adjusted from 0.5 to 5 N. For steel counterfaces, the corresponding range of theoretical Hertzian contact pressure is roughly 0.3 to 1.8 GPa. The sliding speed can vary from 0.01 mm/s up to 2 mm/s, over a track length ranging from 0.5 up to 5 mm. The vacuum level is usually about 10−7 Pa, but pure gases can be introduced in the chamber, up to about 103 Pa. Measuring superlow friction in UHV is a challenge. The calibration of the tangential force has to be accurately performed in UHV conditions using an electromagnetic device. The analog-digital converter allows a minimal recorded force of 5 × 10−4 N. The electronic plus mechanical noises do not exceed a few millinewtons. Consequently, the minimal average friction force, which is detectable with the equipment at hand, is about 2 × 10−3 N, corresponding to a friction coefficient of about 2 × 10−3 for a 1 N normal load. Figure 17.2(a) shows the typical evolution of the average friction coefficient, versus the number of sliding cycles, of a superlow friction DLC film tested in UHV conditions, with a normal load of 3 N, against an uncoated 8 mm radius hemispherical pin made of AISI 52100 bearing steel. The corresponding maximum theoretical Hertzian contact pressure is about 550 MPa. The sliding speed was 0.5 mm/s with reciprocating amplitude of 1.5 mm. The residual pressure in the chamber was lower than 5 × 10−7 Pa. Figure 17.2(b) shows a detail of the unprocessed friction tangential force recorded over one cycle (two alternate passes of the ball against the DLC related to cycle number 300), during the su-
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perlow friction regime. As can be observed, the friction force change in direction (256 recorded data points for one way pass on the track length) can hardly be detected during this cycle. The average tangential force during one pass is about 7 mN, corresponding to a friction coefficient of about 2.3 × 10−3 . However, due to mechanical and electronic noise, the standard deviation around this value is about 10 mN, higher than the mean value. This highlights the difficulty of measuring such extremely low coefficient of friction, especially inside a vacuum chamber. The question then arises to explain the mechanisms involved in such a spectacular friction reduction, and also in the ability to control this superlow friction regime over long periods.
17.3
17.3.1
CONDITIONS FOR a-C:H FILMS TO ACHIEVE SUPERLOW FRICTION
General Requirements to Achieve Superlow Friction with DLC Films
Table 17.1 summarizes the major key requirements which have to be fulfilled to observe friction in the millirange with DLC films. Each key requirement may be influenced by some key parameters. Each of them needs to be accurately controlled through various experimental setups dealing with film deposition, conditions during the friction test and the tribological process itself. Superlow friction can be observed if contacting surfaces interact weakly during the friction process. However this condition is also suggested with other materials in the case of ultralow friction (10−2 range). As a consequence, a lower decay in friction (i.e., to achieve the superlow friction regime (10−3 range)), may probably require additional conditions. In the case of DLC films, both weak van der Waals interactions between smooth contacting tribofilms, combined with viscoplastic properties of hydrogen rich DLC films, are probably Table 17.1. Key requirements and influencing parameters to achieve superlow friction with DLC films Key requirements for superlow friction with DLC
Influencing key parameters
Experimental set-up control
Tribofilm build-up
Surface chemistry of the counterface
Native oxide/metal on the steel counterface
Low interactive surfaces
Surface topography
Emission of wear debris
High hydrogen content
Deposition process
Flexibility of the hydrocarbon network Absence of chemically active gaseous contamination
Deposition process
High viscoplasticity of contacting surfaces
Partial pressure of O2 , H2 O gases during friction
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two key requirements to allow superlow interactions between flexible hydrocarbon chains, as highlighted in Sections 17.3.2 and 17.3.3. To achieve superlow friction from the running-in process, transfer film build-up is probably the first step in order to induce a transformation of the initial film and transfer film into contacting adaptive tribofilms. As depicted in Section 17.4.1, the surface chemistry of the counterface is paramount to achieve this step, typically by controlling the presence of native metal on a steel ball counterface. One of the major challenges of tribology is to maintain high wear resistance and low friction over long periods. In the case of DLC, superlow friction requires an inert atmosphere inhibiting any “burning” of the top surface tribomaterials, which may be responsible for friction increase. This will be detailed in Sections 17.4.2 through the interaction between the gaseous environment and the contacting surfaces. Long wear resistance at the superlow friction level, in various environmental conditions, remains a challenging subject with DLC films, both from a scientific and technological point of view. Let us now review these conditions on the basis of already published experiments with model DLC films. 17.3.2
Influence of Hydrogen Content in the Film: Low Interacting Surfaces
As mentioned in Section 17.2.2, hydrogen content appears as a key element for the achievement of superlow friction with DLC films. Table 17.2 presents the deposition parameters, the composition and the tribological behavior in UHV of three different a-C:H samples from the same d.c.-PECVD process (Plasma Enhanced Chemical Vapor Deposition). These films were deposited at IBM T.J. Watson Research Center, by the team of Dr A. Grill [22]. More details on these samples and their compositions can be found in references [19] and [23]. By increasing the deposition bias (applied to the substrates) and by decreasing the pressure, the energy of the impinging ions on the growing film is increased, according to Bubenzer et al. [24]. The nature of the precursor gas will besides affect this ion energy, since a more stable molecule will need more energy to be broken. Thus, our three model samples doubtlessly experienced different ion energies during deposition, with decreasing values from AC8 to AC5 and to CY5. These differences account for the increase in hydrogen content from 34 at.% up to 42 at.%, as well as the decrease in sp2 carbon content or the increase of the fraction of hydrogen bounded to carbon. Drastically different tribological behaviors are observed under UHV. The less hydrogenated film, AC8, can achieve low or even superlow friction coefficients, but only for few tens of cycles. Then, friction increases in few cycles to reach values above 0.3, and many grooves appear on the surface. Nevertheless, the a-C:H film remain on the wear track, as observed by AES and XPS [19,25], and the increase in friction cannot be attributed to its removal. On the opposite, the most hydrogenated film, CY5, reached low friction coefficients of about 0.03. However, as can be seen on the optical micrograph, some loose debris are found around the wear track, indicating that some plowing might occur on this softer film. In between these two samples, with intermediate hydrogen content, AC5 film reached superlow friction values, about 0.003, with much lower wear since the wear track is barely
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Table 17.2. Deposition conditions, compositions, and tribological behavior of three model a-C:H films. Tribological behavior was investigated under UHV, against a 440C steel pin with curvature radius of 1.5 mm under 1 N load, corresponding to a maximum theoretical Hertzian pressure of 1 GPa Sample Precursor Bias/Pressure
AC8 C2 H2 −800 V/100 m Torr
AC5 C2 H2 −500 V/300 m Torr
CY5 C6 H12 −500 V/300 m Torr
Hydrogen content C sp2 :C sp3 (NMR) Bonded H (FTIR) Bonded H (NMR)
34 at.% 70:30 57% 93%
40% 65:35 73% 98%
42% 56:44 100% 100%
Coefficient of friction under ultra-high vacuum
Wear track on DLC-coated float
visible with an optical microscope. Finally, with these a-C:H samples, a threshold is evidenced in hydrogen content between high and low stabilized coefficient of friction, located between 34 and 40 at.%. Hydrogen is hence paramount for the achievement of superlow friction, probably by promoting weaker interactions between the sliding surfaces. Le Huu et al. [17] proposed that electro-static repulsion between hydrogen atoms was promoting low friction of a-C:H films, but the strong differences of bonding energy between hydrogen terminated surfaces and sp2 carbon covered surfaces could also account for such threshold [25–27]. Indeed, carbon atoms in these a-C:H films are mainly sp2 hybridized, and involved in C=C covalent double bonds. These bonds involve a σ bond—where two electrons are shared through overlapping of sp orbitals, thus located between the atoms loci—and a π bond—where two other electrons are shared through overlapping of p orbitals, thus located above and below the axis between atoms loci. Therefore, if C=C bonds are located on both counterfaces, then the out-of-plane π orbitals might interact strongly with each other [28]. These interactions account for the high friction observed in UHV with un-intercalated graphite or highly oriented pyrolitic graphite [29,30]. On the other hand, interactions between hydrogen atoms bonded to carbon through Van der Waals forces are much lower [31], as can be seen on Table 17.3. Moreover, hydrogen atom being monovalent, the C–H bond is thus much more flexible, resulting in easier motion of hydrogen atoms or hydrocarbon terminating molecular chains on the surface.
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Schematic representation and energy of two kinds of interactions supposed to occur between carbonaceous structures. Schematic from [25] and numerical values from [28,30,31] Interaction
Van der Waals
π –π ∗
0.008 eV high
0.4–0.8 eV low
Schematic representation
Binding energy Flexibility
Nevertheless, some open questions remains, and these atomic-scale phenomena might not be sufficient to elucidate the friction mechanism of multi-asperity macro-scale contacts. In addition to the previous PECVD set of samples, two other sets of samples were studied. A commercial r.f. High Density Plasma (HDP) process was used with acetylene and acetylene/hydrogen precursors at different deposition bias. This process is similar to the one described in [32] and details on the samples can be found in [33]. Finally, a third set (labeled “HEF”) consisted in some industrial samples from a hybrid process combining magnetron sputtering for metallic under-layers together with d.c.-PECVD from acetylene for the DLC top-layer. Details on the process and samples can be found in [34]. All these samples were characterized on the UHV tribometer of Ecole Centrale de Lyon, against AISI 52100 bearing steel pins of 8 mm radius, under 3 N normal load, at reciprocating speed of 1 mm/s over a track length of 3 mm. Maximum theoretical Hertzian contact pressure was then about 470 MPa, corresponding to a contact diameter of about 100 µm. Figure 17.3 displays the steady-state coefficient of friction, reached after 500 cycles or less for high friction films (to avoid any damage to the sensors from high tangential forces) as a function of the hydrogen content of the films, measured by Elastic Recoil Detection Analysis (ERDA). Although a threshold in hydrogen between high and low friction is clearly evidenced for each of the 3 processes, it appears to strongly depend on the deposition process [35]. Indeed, the threshold is between 26 and 30 at.% for HDP process, between 34 and 40 at.% for PECVD process and around 46 at.% for HEF process. With “bulk” contents varying between 26 and 46 at.%, the studied coatings should then have very different surface coverage by hydrogen atoms. If this result does not invalidate the atomic-scale interactions proposed in the literature, it nevertheless shows that some other phenomena must be invocated to account for the superlow friction observed on DLC films with macroscopic multi-asperity contact.
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Figure 17.3 Steady-state coefficient of friction in UHV (at 500 cycles) as a function of hydrogen content for HDP, PECVD and HEF samples.
17.3.3
Influence of the Mechanical Behavior of the Film: Compliant Surfaces
The previous section confirms that a sufficient amount of hydrogen in the film is necessary to achieve superlow friction. Since hydrogen is a monovalent atom, increasing its content will necessarily reduce the proportion of C–C bonds, and thus decrease the crosslinking of the carbon network. We can thus assume that superlow friction is correlated with cross-linking in the DLC film, as suggested by theoretical models [36,37]. However, the amount of required hydrogen depends strongly on the deposition process. It has been indeed demonstrated that the structure of amorphous hydrogenated carbon is more complex, since a substantial amount of unbounded hydrogen [23] and of aromatic clusters [38] can be found in the films. Differences in deposition techniques, precursors, plasma conditions, will lead to different amounts of variations from the theoretical random covalent network model. Thus, the cross-linking of the films cannot be deduced from the hydrogen content alone, except maybe for comparison between samples obtained with the same process. Mechanical properties appear then as indirect means to evaluate this cross-linking. Thus, nanoindentation experiments have been performed on the previous set of samples, with two specific procedures [35]. First, instrumented indentation was performed in continuous stiffness mode, allowing the measurement of hardness and Young’s modulus as a function of depth. Second, to avoid time-dependent effects during loading, the strain rate was kept constant by applying the load exponentially vs. time, i.e. by keeping the ratio of loading rate over load constant. Figure 17.4(a) shows the evolution of hardness as a function of this strain rate for PECVD samples. Hardness is definitely not independent of strain rate for a-C:H films, and it follows a Norton–Hoff law: H = H0 · ε˙ x —hardness is proportional to the strain rate ε˙ at the power of x, where x is called the viscoplastic exponent. This is the slope of lines fitting the data on the log–log plot on Figure 17.3(a). For a purely plastic behavior, x equals 0, since hardness is not dependent on strain rate. For a Newtonian fluid behavior, exponent x would equal 1. Intermediate values describe a more or less viscoplastic behavior. In the case of our a-C:H films, they all exhibit some viscoplasticity, but signifi-
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Figure 17.4 Hardness as a function of strain rate for PECVD samples (a) and steady-state coefficient of friction under UHV vs. viscoplastic exponent for HDP and PECVD samples (b).
cant values are mainly achieved by films with higher hydrogen contents. The viscoplastic nature of these materials implies that it is able to relax, probably through free volumes inside a random covalent network. Increased hydrogen content as well as presence of free, unbounded hydrogen atoms should favor such free volumes. Figure 17.4(b) displays the steady-state coefficient of friction under UHV versus the viscoplastic exponent of the films. It clearly shows that DLC films with low viscoplastic exponent lead to high friction values under UHV, while films with significant viscoplastic exponent achieve superlow friction values. The film with the highest viscoplastic exponent, CY5, reached intermediate friction values, but it is also the softest film, which might lead to a plowing contribution to friction (see Section 17.3.2). Once again, a threshold separates films with high and low steady-state friction coefficients. However, it appears less dependent on deposition process. Moreover, it also seems consistent with doped-DLC, since a fluorinated DLC, with only 18 at.% of fluorine and 5 at.% hydrogen, with significant viscoplastic exponent (x = 0.06) but high hardness, achieved a superlow friction coefficient of about 0.005 [35]. Other evidence of the viscoplastic behavior—or relaxation abilities—of a-C:H films has been observed by performing nanoindentation experiments at very low load with the ‘3D2F’ surface force apparatus of Ecole Centrale de Lyon [39]. Figure 17.5 shows images of the same indent within minutes and 6 days after indentation test. Depth of the indents decreased from ∼23 m to 15 nm. It clearly shows that a significant recovery tooks place, which is not elastic in regard of the time scale. This study showed also that Poisson’s ratio of DLC should be quite low, below 0.2, meaning that these films are relatively compressible. Finally, superlow friction a-C:H films are harder than steel (H > 5 GPa) but more compliant (E < 100 GPa), with significant compressibility and relaxation abilities. An explanation of the role of mechanical properties on the achievement of superlow friction might thus come from strain tolerance: if some adhesive junctions are created and broken during friction, then the changes made to topography should be small, and the material should be able to “heal” its surface.
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Figure 17.5 Images of indent obtained on AC8 sample at 2 mN load (a) a few minutes and (b) 6 days after indentation test [39]. Images are 720 nm wide and each gray scale corresponds to 1 nm height.
17.4
ACHIEVEMENT AND PRESERVATION OF SUPERLOW FRICTION WITH a-C:H FILMS
17.4.1 How to Achieve Superlow Friction: Tribofilm Build-Up Controlled by Surface Chemistry of the Counterface
In the previous section, steady-state values of the coefficient of friction were reported. Indeed, before reaching superlow friction regime, a ‘running-in’ seems necessary, especially when the counterface is not coated. This running-in is attributed at least partially to the build-up of transfer film, which might be nevertheless quite different from the pristine a-C:H, as mentioned in Section 17.2.1. Since this transfer film generally has a different structure and composition, we prefer the term ‘tribofilm’, to take chemical changes into account. This section presents indications on the way the tribofilm builds up on a steel counterface, and on the role of surface oxides. These results are also presented in [40]. Figure 17.6 presents depth profiles performed in-situ by Auger Electron Spectroscopy on a tribofilm obtained on a 52100 bearing steel after 500 cycles of sliding in UHV against AC5 sample (see Table 17.2), on the UHV tribometer of Ecole Centrale de Lyon. A pin with 8 mm radius of curvature was used with a 3 N load, in order to have a large contact area (about 100 µm), and the coefficient of friction was in the millirange (∼0.003) at the end of the experiment. Spectra were recorded concomitantly inside and outside the wear scar, in order to use the native oxide layer as reference. Figure 17.6 clearly shows that a carbonaceous layer is formed inside the wear scar, since carbon proportion is much higher than with adventitious carbon outside the wear scar. Moreover, the oxide contribution is roughly divided by two beneath the surface inside the wear scar, indicating its partial removal during tribofilm growth. No clues on the process of this removal are however available, either abrasion or tribochemical wear being possibly involved. It has to be mentioned that spectra were recorded on quite large spots, of few tens of microns wide. Thus, the lower contribution of oxide layer could be either due to thinning of the whole oxide layer or to a complete removal of the oxide layer only at some localized spots. Anyway, oxide layer seems to be detrimental to the growth of the tribofilm on the steel surface.
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Figure 17.6 Evolution of the proportion of carbon, oxygen and iron peak heights in Auger Electron Spectroscopy as a function of etching time, (a) outside pin wear scar and (b) inside pin wear scar.
Figure 17.7 Tribological behavior of AC5 coated flat against three different steel pin surfaces under UHV: (a) coefficient of friction vs. number of cycles and (b) tangential force vs. motor position during first cycle.
To further elucidate the role of the oxide layer, friction experiments were performed with etched pins, thanks to the argon ion sputtering system used for depth profiling. Three surfaces of the pin were then compared as far as friction in UHV is concerned: • raw pin, with its oxide layers and adventitious carbon; • oxidized pin, after a short etching to remove adventitious carbon; • Etched pin, with no oxide layer and no adventitious carbon. Figure 17.7(a) displays the evolution of the friction coefficient for these three different in situ surface preparations. The duration of the running-in clearly decreases as the adventitious carbon and the oxide layers are removed, as summarized in Table 17.4. Moreover, the initial values of the coefficient of friction decrease from 0.22 for both raw and oxidized pins down to less than 0.05 for the etched pin. However, this decrease in sliding friction comes along with increased sticking before sliding. Figure 17.7(b) exhibits the evolution of the tangential force as a function of the motor displacement for the first cycle of each type of pin. All the curves show similar trends. First, a linear increase of tangential force, corresponds to elastic bending of the tri-
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Table 17.4. Running-in durations and coefficients of friction for experiments performed in ultra-high vacuum on sample AC5 for three different steel pin surface preparations Raw pin
Oxidized pin
Etched pin
Number of cycles to reach μ = 0.01 Coefficient of friction μ at 500 cycles
34 4.1 × 10−3
7 2.2 × 10−3
4 1.8 × 10−3
Coefficient of static friction μs (cycle #1) Coefficient of dynamic friction μd (cycle #1) Static to dynamic friction ratio (cycle #1)
0.29 0.22 1.3
0.40 0.22 1.8
0.56 0.045 12
bometer, due to its relatively low stiffness. Then, a maximum is reached, corresponding to a static friction. Finally, tangential force drops and stabilizes at an almost constant value. This corresponds to the real beginning of sliding, from which the dynamic friction coefficient can be inferred. The different values of static and dynamic friction coefficients as well as their ratios are gathered in Table 17.4. While dynamic friction decreases, as mentioned above, we can notice that static friction significantly increases. Removal of oxide layer seems then to favor strong sticking between counterfaces, but allow then very low coefficients of friction to be reached right away, indicating a much faster build-up of the tribofilm. The HSAB principle (Hard and Soft Acids and Bases), also referred to as “Chemical Hardness” principle, could account for this phenomenon. This concept introduced by Pearson [41] attempts to explain the chemical reactions between Lewis acids (electron acceptors) and bases (electron donors) by stating that “hard acids bind strongly to hard bases and soft acids bind strongly to soft bases”. Hard elements will be more likely involved in ionic bonding, while soft ones will rather participate in covalent or metallic bonding. With this classification, iron is a soft acid in its metallic form and a hard acid in the oxide form, while the hydrogenated amorphous carbon covalent network can be considered as a soft base. Thus, reactions of hydrogenated amorphous carbon should be less favorable with iron oxide than with iron as metal. By removing the oxide layers, either by etching or by sliding, reactions between carbon and iron are favored, leading to the build-up of a tribofilm. 17.4.2 How to Preserve Superlow Friction: Tribo-reactivity of the Contact Controlled by Gaseous Environment
As mentioned in Section 17.3.2, a-C:H films with lower hydrogen content finally leads to high stabilized coefficient of friction under UHV, like sample AC8 on Table 17.2. However, it is noteworthy that for some of these samples, superlow friction is achieved during few tens of cycles. This section will describe the phenomena leading to the loss of superlow friction, and show how it is possible, through tribochemistry with surrounding gases, to restore or maintain this outstanding tribological behavior. It will summarize results obtained in earlier studies [40,42].
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Figure 17.8 Optical micrographs of steel pin wear scars and a-C:H coated flat wear tracks after friction experiment on AC8 sample in ultra-high vacuum, stopped in superlow friction regime (above) or high friction regime (below).
17.4.2.1
Loss of Superlow Friction under Ultra-high Vacuum
As shown in Table 17.2, AC8 sample, with only 34 at.% of hydrogen, exhibits first a friction decrease down to the millirange, and keeps this superlubricity for few tens of cycles. A carbonaceous tribofilm is then formed on the steel counterface, just as AC5 sample (see Section 17.4.1), and un-measurable wear is observed on the coated flat, the track being only slightly visible thanks to a small change in contrast (Figure 17.8). However, a sudden increase in friction occurs after a while, and after few cycles, friction coefficients are higher than 0.3. Almost no tribofilm seems to remain inside the initial contact area of the pin. Instead, a dark gray to black material is accumulated in the sliding direction outside this initial contact area, giving the new apparent contact area an elongated shape. The a-C:H coated flat is heavily damaged, with many grooves over the entire length of the track, although the substrate is not reached, as mentioned in Section 17.3.2. Surprisingly, very little loose debris can be found around the contact, either on pin or flat. These observations give the impression that carbonaceous debris stick strongly to sliding surfaces, and that the groove might be due to adhesive effects rather than abrasive ones. To corroborate this idea, friction data were carefully studied. On the UHV tribometer of Ecole Centrale de Lyon, the values of the friction force are recorded by a data logging system. Because the motion is performed at a constant speed, it is possible to convert timeresolved measurements into spatially resolved ones. It is thus possible to present friction data in a two dimension diagram, one axis being devoted to cycle number, one axis being devoted to position along the wear track on the flat, and color or grayscale reflecting the coefficient of friction (or any recorded signal during sliding). These charts are called “tri-
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Figure 17.9 Triboscopic image of friction coefficient for a typical UHV friction experiment on AC8 sample (close-up of last 50 cycles).
boscopic images”. Figure 17.9 shows such image for AC8 sample, focusing on the drastic friction increase. This image gives us evidence that the friction increase is starting only at very localized spots, spreading progressively albeit quickly to the entire wear track, while major part of the track remains in superlow friction regime (note the logarithmic scale for the coefficient of friction). If the tribofilm was suddenly removed, or if abrasion started to occur, then the friction would be significantly affected for whole cycles, no matter the position along the wear track. This clearly shows that the friction increase is due to strong interactions occurring at localized areas of the a-C:H coated flat. These interactions are most likely adhesive phenomena, probably due to the concomitant preponderance of sp2 carbon on both sliding counterfaces, which have high binding energies (see Section 17.3.2 and Table 17.3). 17.4.2.2 Healing Effect of Hydrogen Ambient In order to preserve the superlubricity observed for a short time on AC8 sample, it would then be necessary to avoid these strong interactions between sp2 carbon atoms on the surface. Earlier studies have shown that hydrogen ambient could preserve the superlow friction regime [26,43]. It was more recently confirmed and deeper studied [40,42]. Figure 17.10 presents the evolution of the coefficient of friction of AC8 in different ambient, from UHV (∼10−7 Pa) up to 1000 Pa of hydrogen gas. For hydrogen pressures lower than 100 Pa, the tribological behavior is similar to the one observed under UHV, with a drastic friction increase after few tens of cycles in superlow friction. However, at higher hydrogen pressures, although a friction increase is still observed, it is only temporary, the maximum friction value and the duration of this transient higher friction decreasing both with increasing hydrogen pressure. Hydrogen thus seems to be able to “heal” or “protect” the superlubricity.
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Figure 17.10 Coefficient of friction vs. number of cycles for experiments on AC8 samples performed under various hydrogen gas pressures, from UHV up to 1000 Pa.
Figure 17.11 Optical micrographs of steel pin wear scars and a-C:H coated flat wear tracks after friction experiment on AC8 sample in hydrogen ambient, at 200 Pa (above) and 1000 Pa (below).
The wear scars on the steel pins and on the a-C:H coated flat after the experiments at 200 and 1000 Pa are displayed on Figure 17.11. At 200 Pa of hydrogen, a dark brown material has been accumulated at both sides of the contact area in the sliding direction, almost like under UHV (Figure 17.8), but some iridescent colors inside the contact area show that a new tribofilm has grown on the pin, although more disturbed than in superlow friction regime, and apparently containing compacted wear debris. On the flat, some grooves are observed, like under ultra-high vacuum, but only in some sections of the wear track. At 1000 Pa of hydrogen, the wear scar on the pin seems to be a mixture of the one in superlow friction regime and the one at 200 Pa: a thin smooth transfer film is present in some areas,
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Figure 17.12 Triboscopic images of friction coefficient with corresponding wear tracks on the flat for friction experiments on AC8 sample in hydrogen ambient: (a) at 200 Pa and (b) at 1000 Pa.
but there are some stripes of darker materials that extend outside the initial hertzian contact area. On the flat wear track, which is difficult to localize with an optical microscope, few light grooves are present, apparently corresponding to the stripes of the pin scar. Better understanding of the involved friction mechanisms arises once again from the triboscopic images provides. For experiment at the 200 Pa hydrogen pressure, we can observe the drastic increase in friction, starting at cycle 490 (Figure 17.12(a)). Like under UHV, high friction is appearing at localized spots, but they spread out only to a part of the track length. It is noteworthy that these high friction zones co-exist with millirange friction zones. Furthermore, there is a good correlation between these friction bumps and the corresponding post-experiment photograph of the wear track. Finally, friction vanishes again while the test is running between cycles 570 to 650, giving evidence of the beneficial effect of hydrogen gas in restoring the millirange friction behavior. Conversely, during the experiment under the highest hydrogen pressure, we do not observe such large deterioration of the superlubricity (Figure 17.12(b)). Only local increases of friction can be observed, extending only to a small part of the track length, with scattered positions. These results confirm the occurrence of adhesion between tribofilm on the pin and aC:H surface, however controlled by interactions with hydrogen. The tendency to break C–H bonds and to form more sp2 carbon is probably at the origin of the strong adhesion that occurs between sliding counterfaces. Nevertheless, this adhesion can be reduced by interactions with hydrogen gas, which apparently helps also in rebuilding a transfer film. Since it seems possible to break C–H bonds on the sliding surfaces, we can assume that H2 molecules can also be broken during friction, allowing reactions with sp2 carbon and thus
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Ratio of measured to natural abundance of deuterium on AC8 sample surface, before and after etching, after 1000 cycles of sliding under 1000 Pa of deuterium
Before etching After etching
Outside wear track
Inside wear track
13 1.5
240 15
production of new C–H bonds. To confirm this hypothesis, experiments were performed with AC8 sample in deuterium gas, at a pressure of 1000 Pa. Tribological behavior is similar to the one observed in the same pressure of hydrogen. Being isotopes, hydrogen and deuterium are chemically equivalent. Then, the wear track on the flat obtained after 1000 cycles has been analyzed by time-of-flight Secondary Ion Mass Spectroscopy (ToF-SIMS). The peak height of negative ions at a mass of 2 can be undoubtedly attributed to deuterium negatives ions, since the probability of obtaining H2 negative ions is extremely low. This peak height was then divided by the one for negative ions at a mass of 1, corresponding to hydrogen negative ions. This ratio is the abundance of deuterium on the surface, and can be compared to the natural abundance of deuterium (0.015%). Such measurements were performed inside and outside the wear track, before and after a very short and soft etching of the surface, whose purpose was to remove the few monolayers of physisorbed molecules. Table 17.5 gathers the different values obtained. Outside the wear track, deuterium can be found, but it is removed after short etching, suggesting a weak bonding to the surface. On the contrary, a great amount of deuterium is found inside the wear track, and etching did not remove it completely. Thus, deuterium has a tendency to physisorb on the a C:H surface, but it is strongly bonded to the surface inside the wear track. Finally, we can assume that the loss of superlow friction is due to adhesion occurring locally between the pin and the flat, probably due to surface modification of the flat and the tribofilm, with increasing sp2 carbon content and decreasing hydrogen content. This is leading to at least partial tribofilm removal and also to groove formation on the flat. However, surface interactions with hydrogen gas, induced by friction, allow to rebuild a tribofilm and to reduce the adhesive interactions between both counterfaces. 17.4.2.3
Beneficial and Detrimental Role of Oxygen Ambient
Surprisingly, such healing phenomenon can also be observed to a certain extent with oxygen ambient [40]. However, oxygen is a much more reactive molecule, and phenomena are observed at lower pressures. Figure 17.13 presents the evolution of the friction coefficient on AC8 sample under various pressures of oxygen gas. Even at 1 Pa, oxygen has a significant effect on the friction coefficient, since the minimum friction coefficient achieved is about 0.009 instead of less than 0.005 for all experiments performed under ultra-high vacuum. It is thus clear that oxygen has a detrimental effect on superlubricity of a-C:H films. Nevertheless, the drastic friction increase mentioned previously under UHV is also observed after about 200 cycles, meaning that adhesive phenomena are still controlling the general evolutions of the tribological behavior.
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Figure 17.13 Coefficient of friction vs. number of cycles for experiments on AC8 samples performed under various oxygen gas pressures, from 1 Pa up to 200 Pa.
Figure 17.14 Optical micrographs of steel pin wear scars and a-C:H coated flat wear tracks after friction experiment on AC8 sample under 200 Pa of oxygen.
At 10 Pa, superlow friction cannot be achieved, the friction coefficient remaining above 0.01. However, a transient friction increase is observed, as for intermediate pressures of hydrogen (200 Pa). This friction increase is indeed very similar to the one observed with hydrogen gas: it also starts at localized spots on the flat wear track, extending then to the entire wear track, and worn surfaces exhibit same aspect. Then, friction stabilizes at values between 0.01 and 0.02, lower than before the transient increase. Thus, oxygen probably also reacts with carbonaceous surfaces during sliding, allowing the tribofilm to “heal”. At 200 Pa of oxygen, the friction first decreases quickly, but then increases progressively, to reach values equivalent to the initial ones, above 0.2. No features could be found on triboscopic images, the evolution of friction being the same whatever the position on the track length. Despite the numerous cycles performed at relatively high friction, the wear track on the flat is barely visible, except very few debris gathered on both ends (Figure 17.14). On the pin wear scar, the tribofilm seems to be reduced to a corona, around the initial hertzian contact area, suggesting that the tribofilm might have been “burned” by oxygen. Tribochemistry with oxygen seems also able to control evolutions of the tribological behavior of a-C:H films. Small amounts of oxygen will be detrimental to the friction level, probably because of other kind of molecular interactions, like hydrogen bond between
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oxygen and hydrogen on each counterface. However, oxygen is also beneficial, in the sense that it reacts easily with carbon, and most probably preferentially with sp2 carbon. Such tribochemical reactions will hence avoid adhesive phenomena, and thus preserve a low friction and wear regime. Open questions however remains, since tribochemistry with hydrogen and oxygen does not affect only molecular interactions, but also structure and composition of the surface layers of both tribofilm and a-C:H coating. Mechanical properties might thus be affected as well, and play a significant role. Moreover, effect of mixtures of gases, or of other gases like water vapor or nitrogen, should be investigated, since combination of gases might allow to better control superlubricity of a-C:H films and avoid adhesive phenomena.
17.5
CONCLUSION
Superlubricity in solid state is a challenging subject from a fundamental point of view. As illustrated in the present book, it constitutes a crossroads between theoretical and experimental approaches in material science. Diamond-like carbon films are model films to observe superlubricity in macroscopic contacts. The present review shows that such drastic friction vanishing in a large, multi-asperity contact cannot be explained only by molecular interactions, but rather suggests that the control of surface chemistry and rheology, as well as chemical interactions at sliding DLC interfaces, is extremely important for the friction and wear behavior of these films. Specifically, by controlling or effectively eliminating the intrinsic and extrinsic sources of friction in DLC films, one should be able to achieve superlow friction coefficients. We have highlighted the difficulty of measuring such extremely low coefficients of friction, especially inside a vacuum chamber of a macroscopic tribometer. The tribofilm build-up followed by weak intermolecular interactions between flexible hydrocarbon chains are paramount factors to observe superlow friction. We have also discussed the various experimental factors influencing the previous key conditions to reach superlow friction, including the initial surface chemistry of contacting bodies, the composition and viscoplasticity of the DLC film together with the presence of a specific gas during the friction process. Some of these factors are also paramount to control the duration of the superlow friction level. But at the present stage of investigations, the combination of factors responsible for superlow friction are far from the usual conditions of most contacts in technology. Moreover most of these factors are spoiled during the friction process, which is not favorable to keep superlow friction over long periods. From a practical point of view, research on superlubricity may drive significant improvements in mechanical devices lubricated with solids. Indeed most of the commercial solid lubricants exhibit friction in the 0.1 range. Thus the research activities on superlow friction with DLC films motivates both theoretical and experimental investigations which contribute to promote a better understanding in lubrication mechanisms, with both positive impacts on the knowledge of DLC films and improvements in technological applications integrating DLC lubricated contacts, with the objective to reach friction behaviors in the 0.01 range or, why not in the future, near “zero”.
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REFERENCES [1] Robertson, J. Mat. Sci. Eng. R 37 (2002), 129. [2] Grill, A., Meyerson, B.S. Development and status of diamondlike carbon. In: Spear, K.E., Dismuke, J.P. (Eds.), Synthetic Diamond: Emerging CVD Science and Technology. John Wiley & Sons Inc., New York, 1994, pp. 91–141. [3] Donnet, C. Condensed Matter News 4(6) (1995), 9. [4] Grill, A. Surf. Coat. Technol. 94–95 (1997), 507. [5] Donnet, C. Surf. Coat. Technol. 100/101 (1998), 180. [6] Erdemir, A., Donnet, C. In: Bushan, B. (Ed.), Handbook of Modern Tribology, vol. 2. CRC Press LCC, Boca Raton, 2000, Ch. 24. [7] Erdemir, A., Donnet, C. In: Stachowiak, G. (Ed.), Wear—Materials, Mechanisms and Practice. Wiley, 2005, Ch. 9. [8] Enke, K. Thin Solid Films 80 (1981), 227. [9] Donnet, C., Le Mogne, T., Ponsonnet, L., Belin, M., Grill, A., Patel, V., Jahnes, C. Tribol. Lett. 4 (1998), 259. [10] Voevodin, A.A., Phelps, A.W., Zabinsky, J.S., Donley, M.S. Diam. Rel. Mater. 5 (1996), 1264. [11] Le Huu, T., Zaidi, H., Paulmier, D., Voumard, P. Thin Solid Films 290–291 (1996), 126. [12] Erdemir, A., Bindal, C., Pagan, J., Wilbur, P. Surf. Coat. Technol. 76–77 (1995), 559. [13] Liu, Y., Erdemir, A., Meletis, E. Surf. Coat. Technol. 86–87 (1996), 564. [14] Racine, B., Benlahsen, M., Zellama, K., Zarrabian, M., Villain, J.P., Turban, G., Grosman, A. Appl. Phys. Lett. 75(22) (1999), 3479. [15] Miyake, S., Takahashi, S., Watanabe, I., Yoshihara, H. ASLE Trans. 30(1) (1987), 21. [16] Zaidi, H., Le Huu, T., Paulmier, D. Diam. Rel. Mater. 3 (1994), 787. [17] Le Huu, T., Zaidi, H., Paulmier, D. Wear 181–183 (1995), 766. [18] Donnet, C., Belin, M., Augé, J.C., Martin, J.M., Grill, A., Patel, V. Surf. Coat. Technol. 68/69 (1994), 626. [19] Donnet, C., Grill, A. Surf. Coat. Technol. 94/95 (1997) 456. [20] Erdemir, A., Erylmaz, O.L., Fenske, G. J. Vac. Sci. Technol. A 18(4) (2000), 1987. [21] Le Mogne, T., Martin, J.M., Grossiord, C. In: Dowson, D. et al. (Eds.), Lubrication at the Frontier. Elsevier, Amsterdam, 1999, pp. 413–421. [22] Grill, A., Patel, V. Diamond Film Technol. 1 (1992), 219. [23] Donnet, C., Fontaine, J., Lefebvre, F., Grill, A., Patel, V., Jahnes, C. J. Appl. Phys. 85(6) (1999), 3264. [24] Bubenzer, A., Dischler, B., Brandt, G., Koidl, P. J. Appl. Phys. 54(8) (1983), 4590. [25] Donnet, C., Grill, A., Fontaine, J., Le Mogne, T., Lefebvre, F., Patel, V., Jahnes, C. In: Dowson, D. et al. (Eds.), Lubrication at the Frontier. Elsevier, Amsterdam, 1999, pp. 333–341. [26] Donnet, C., Fontaine, J., Grill, A., Le Mogne, T. Tribol. Lett. 9(3–4) (2000), 137. [27] Erdemir, A. Surf. Coat. Technol. 146–147 (2001), 292. [28] Dresselhouse, M.S., Dresselhouse, G. Adv. Phys., 30(2) (1981), 139. [29] Buckley, D.H. In: Surface Effects in Adhesion, Friction, Wear and Lubrication. Elsevier, New York, 1981, p. 574. [30] Gardos, M.N. In: New Directions in Tribology, Proceedings of the Plenary and Invited Papers from the First World Tribology Congress (London, Sept. 8–12, 1997). Mechanical Engineering Publications, London, 1997, pp. 229–250. [31] Gardos, M.N. In: Spear, K.E., Dismuke, J.P. (Eds.), Synthtic Diamond: Emerging CVD Science and Technology. John Wiley & Sons, New York, 1994, p. 419. [32] Tuszewski, M., Tobin, J.A. J. Vac. Sci. Tech. A 14 (1996), 1096. [33] Sanchez-Lopez, J.C., Donnet, C., Fontaine, J., Belin, M., Grill, A., Patel, V., Jahnes, C. Diam. Rel. Mater. 9 (2000), 638. [34] Donnet, C., Fontaine, J., Le Mogne, T., Belin, M., Héau, C., Terrat, J.P., Vaux, F., Pont, G. Surf. Coat. Technol. 120–121 (1999), 548. [35] Fontaine, J., Loubet, J.L., Le Mogne, T., Grill, A. Tribol. Lett. 17(4) (2004), 709. [36] Angus, J.C., Jansen, F. J. Vac. Sci. Tech. A 6(3) (1998), 1778. [37] Angus, J.C., Wang, Y. In: Clausing, R.E. et al. (Eds.), Diamond and Diamond-Like Films and Technology. Plenum Press, 1991, p. 173.
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Tamor, M.A., Vassel, W.C. J. Appl. Phys. 76 (1994), 3823. Bec, S., Tonck, A., Fontaine, J. Phil. Mag., in press. Fontaine, J., Le Mogne, T., Loubet, J.L., Belin, M. Thin Solid Films 482 (2005), 99. Pearson, R.G. Hard and Soft Acids and Bases. Dowden, Hutchinson & Ross Inc., Stroudsburg, PA, 1973. Fontaine, J., Belin, M., Le Mogne, T., Grill, A. Tribol. Int. 37 (2004), 869. Fontaine, J., Donnet, C., Grill, A., Le Mogne, T. Surf. Coat. Technol. 146–147 (2001), 286.
– 18 – Suppression of Moisture Sensitivity of Friction in Carbon-Based Coatings Christina Freyman, Bo Zhao and Yip-Wah Chung Northwestern University, 2220 N Campus Dr., Evanston, IL 60208, USA
18.1
INTRODUCTION
Carbon-based coatings can be tailored for specific applications through different synthesis methods and doping with various elements. Hard amorphous carbon films have been used to coat industrial tools for protection against wear and corrosion [1,2]. Nitrogen-doped films (CNx ) are widely used as protective overcoats for magnetic media. Highly hydrogenated amorphous carbon films (CHx ) display ultra-low friction coefficients (μ < 0.01) in dry nitrogen environments [3]. Film properties vary widely according to testing conditions, film structure, and film composition. Many deposition techniques are used to synthesize carbon films with different dopants. Highly hydrogenated amorphous carbon films have been synthesized by plasma-assisted chemical vapor deposition (CVD). CVD films with 75% H2 in the deposition atmosphere and tested in dry nitrogen have friction coefficients on the order of 0.001 as illustrated in Figure 18.1 [4]. The low friction behavior of highly hydrogenated carbon films is attributed to hydrogen termination of surface carbon bonds. At a self-mated interface, these hydrogen-passivated surfaces interact weakly with each other, resulting in weak adhesion and low shear strength [3,5–7]. Clean carbon surfaces sliding against each other have larger friction coefficients than hydrogenated carbon films due to stronger adhesive interactions [5,8]. The observed ultra-low friction behavior of hydrogenated carbon films does not occur in all testing environments. Friction increases markedly with the addition of oxygen and water vapor to the testing environment. Oxygen in the testing atmosphere has been observed to interact with both carbon and hydrogen atoms in the film to cause increased friction [9]. Increased friction has been attributed to tribochemical oxidation of the film by atomic oxygen [10,11]. Donnet et al. found that a small amount of water increased the steadystate friction coefficient from 0.01 in ultra-high vacuum to 0.15 in 4% relative humidity as shown in Figure 18.2 [12]. This humidity dependence has been attributed to viscous and capillary forces induced by adsorbed water [5]. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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Figure 18.1 Relationship between friction coefficients of self-mated hydrogenated amorphous carbon films and hydrogen-to-carbon ratios of various source gases from which the films were derived. The measurements were made in dry nitrogen [4].
Figure 18.2 Friction coefficients of hydrogenated carbon films versus the number of reciprocating sliding cycles at different humidity levels. The addition of a small amount of water vapor to the environment increased the steady-state friction coefficient from 0.01 in UHV to 0.15 in 4% relative humidity [12].
To achieve ultra-low friction, Erdemir et al. specified three conditions that must be satisfied: (i) both sides of the sliding interface must be coated with sufficiently hydrogenated carbon films; (ii) surfaces must be smooth to minimize asperity interactions; and (iii) the testing must be performed in dry environments. The last condition limits the application of these carbon films in practical ambients [13].
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Figure 18.3
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Friction coefficient as a function of water coverage on carbon films [14].
Tagawa et al. connected friction increase and surface water coverage for hydrogenated carbon films. When water coverage exceeded one monolayer, friction coefficients drastically increased as shown in Figure 18.3 [14]. At 60% relative humidity, the water coverage on hydrogenated carbon surfaces was measured at about 1.5 monolayers [15]. If the amount of water adsorbed on the film surface in a humid environment could be reduced, these results suggest that films may retain their low friction properties in ambient environments. Dopants that physically adsorb to block binding sites or alter surface electronic properties have been shown to reduce adsorption of certain species [16]. Hydrogenated carbon films could similarly be doped to prevent water adsorption. Different elements such as silicon, boron, gold, and fluorine have been incorporated into hydrogenated carbon films as an attempt to reduce the moisture sensitivity of their friction properties. Silicon and boron react with water vapor in humid environments to form a lubricious layer of silicon oxide or boric acid respectively [17–19]. The low shear strength of gold enables it to act as a solid lubricant [20]. Fluorine reduces the surface energy of the film and makes the surface more hydrophobic [21]. While each dopant results in some reduction in the moisture sensitivity of friction, these films do not retain ultra-low friction in humid environments. Water physisorbs onto the hydrogenated carbon film surface via a dipole/induced dipole interaction. In polymer studies, sulfur is often used to cross-link polymer chains (the process is known as vulcanization). Such cross-linking results in the formation of C–S–C bonds. We postulate that this symmetry may decrease the magnitude of the induced dipole moment and hence weaken the dipole/induced dipole bonding. In an effort to mitigate the moisture sensitivity and achieve ultra-low friction behavior in ambient environments, we have explored the friction behavior of hydrogenated carbon films doped with sulfur.
18.2
SYNTHESIS
A variety of deposition techniques are used for hydrogenated carbon film synthesis, each resulting in specific film properties. Chemical vapor deposition and physical vapor depo-
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sition produce amorphous carbon films. Hydrogen is incorporated from the deposition atmosphere [22,23]. Fontaine et al. observed that for ultra-low friction properties, films must be softer than 12 GPa and have at least 30 atomic percent hydrogen incorporation [24]. Sulfur-doped hydrogenated carbon films have been deposited using reactive magnetron sputtering, a common form of physical vapor deposition. Magnetron sputtering uses magnetic fields to intensify the plasma around a target. In the synthesis of sulfur-doped hydrogenated carbon films, a 99.9% pure 5-cm graphite target was used. The deposition atmosphere contained argon, hydrogen, and hydrogen sulfide. Energetic argon species sputter carbon atoms from the target, which then deposit onto a substrate in a line-of-sight geometry. During this process, hydrogen and sulfur are incorporated from the atmosphere into the growing film. The base pressure of the chamber was better than 6.6 × 10−6 Pa to minimize impurities. The target power was set at 100 W and was pulsed at 150 kHz (80% duty cycle), with the positive voltage set at 10% of the negative voltage. The ratio of hydrogen to argon in the deposition atmosphere remained constant at 15% hydrogen, balance argon, at a sputtering pressure of 0.8 Pa. Based on elastic recoil experiments using 2.2 MeV helium ions, 15% hydrogen in the deposition atmosphere results in 30 atomic percent hydrogen composition of the film [23]. Sulfur was introduced by replacing a portion of the argon with a 0.5% H2 S, balance argon mixture to achieve the desired ratios. Two types of substrates were used: low-resistivity silicon (100) wafers and 6.35-mm stainless steel ball bearings. To facilitate adhesion between the film and ball bearings, the bearings were first coated with 75 nm of silicon by magnetron sputtering. All substrates were ultrasonically cleaned in acetone and methanol prior to introduction into the deposition chamber. The substrates were then sputter-cleaned in 100 mT Ar at 500 V for 5 minutes. Biasing the substrate results in ion bombardment of the growing film, which results in denser films with fewer defects and smoother surfaces. Hydrogenated carbon films have low electrical conductivity, and sulfur incorporation reduces the conductivity further. Because of the low film conductivity, we applied high-frequency substrate bias during film growth to minimize charging and provide for ion bombardment.
18.3 18.3.1
SURFACE CHARACTERIZATION
Compositional Analysis
Auger spectroscopy was used to study sulfur incorporation into the film by detecting the energy of emitted Auger electrons at ∼150 eV [25]. Surface composition of sulfur-doped hydrogenated carbon films is constant during annealing at 300 ◦ C, as shown in Figure 18.4, suggesting the absence of surface segregation. The sulfur concentration is uniform throughout the depth of the film as shown in Figure 18.5. All Auger electron spectra were obtained using a double-pass cylindrical mirror analyzer (Staib Instruments) at a primary electron energy of 3 keV. The depth profiling was obtained by sputtering with 2 keV argon ions.
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Figure 18.4 Auger analysis of 5 a/o sulfur-doped hydrogenated carbon films. The bottom spectrum was taken after sputter-cleaning at room temperature, followed by a series of Auger spectra taken after the indicated time of annealing at 300 ◦ C. Annealing does not change the sulfur-to-carbon ratio. Y -axis units are arbitrary intensity units.
Figure 18.5 Sputter-depth profile of sulfur-to-carbon Auger intensity ratios, showing that sulfur is uniformly distributed through the top 4.4 nm of the film.
X-ray photoelectron spectroscopy (XPS) was used to study the chemical state of sulfur by detecting photoelectrons emitted from the sulfur 2p core-level. Figure 18.6 shows the sulfur 2p core-level peak position at 163.3 eV, which is less than the binding energy of
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Figure 18.6 Sulfur 2p core-level spectrum from a sulfur-doped hydrogenated carbon film. Y -axis units are arbitrary intensity units.
Figure 18.7 Transmission electron micrograph from a sulfur-doped hydrogenated carbon film.
elemental sulfur (164.05 eV) [26]. This indicates that the sulfur incorporated into the film is in a chemically bound state. Chemical concentrations were calculated from intensity ratios. Films synthesized with 0.35% of H2 S in 6 mTorr deposition gas resulted in 5–6 atomic percent of sulfur in the film. XPS was performed on an Omicron ESCA system. Transmission electron microscopy is an excellent tool for structure analysis in thin films. A 5-nm thick sulfur-doped hydrogenated carbon film was deposited on freshly cleaved NaCl blocks. Films were floated off the crystal and placed on a TEM grid. Figure 18.7 is a plan-view image of the film, indicating that the film is amorphous.
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18.3.2
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Surface Roughness
Surface roughness is an important parameter that affects the tribological behavior of surfaces, e.g., asperity interlocking or deformation can increase friction. Figure 18.8 plots the root-mean-square (RMS) roughness of these carbon films as measured by an atomic force microscope (AFM) versus sulfur content. Generally, surface roughness increases with sulfur content. Figure 18.9 is a plot of surface roughness versus substrate bias frequency, showing a minimum surface roughness at an optimum frequency. This result suggests that surface roughening is due to the decreasing film conductivity with sulfur doping. As the substrate bias frequency increases, the amount of charging on the surface decreases, thus allowing more efficient ion bombardment of the growing film, and hence a smoother surface. At higher frequencies, excess ion bombardment results in surface roughening due to resputtering or gas atom implantation.
Figure 18.8 RMS roughness as a function of sulfur incorporation.
Figure 18.9
RMS roughness as a function of substrate bias frequency.
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18.4
TRIBOLOGICAL TESTING
Measuring friction coefficients under 0.01 is quite difficult. Any system noise can overwhelm the true friction force signal. Leveling is critical for such measurements. The apparent friction coefficient of a body sliding on a tilted surface is equal to the tangent of the tilt angle of the surface. A tilt of 1 degree will result in an additional friction coefficient of 0.017. The stiffness and alignment of the sample holder is also important. Bending of the holder during testing can result in false friction force measurements. The sensitivity of the force transducer divided by the minimum normal load should be lower than the expected friction coefficient. Deformation of the film occurs during loading events. Excessive deformation may result in film cracking, which contributes to the friction coefficient. From the Hertz theory, the
Figure 18.10 Friction-versus-time plots for undoped and sulfur-doped films in different humidity environments. (a) Friction coefficient versus time for an undoped hydrogenated carbon film in dry air (relative humidity <1%). (b) Friction coefficient versus time for undoped and 5 a/o sulfur-doped hydrogenated carbon films at a relative humidity of 50%.
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deformation (δ) of a flat surface when loaded by an infinitely stiff sphere is given by:
δ=
9W 2 16RE ∗2
1/3
,
where W is the applied load, R is the radius of the ball, and E ∗ is the composite (effective) modulus. E ∗ is defined as: (1 − v12 ) (1 − v22 ) 1 = + , E∗ E1 E2 where v and E are the Poisson’s ratio (the ratio of transverse contraction strain to longitudinal extension strain) and the elastic modulus respectively for each surface [27]. Normal loads should be chosen such that the deformation is less than the film thickness. Friction coefficients reported here were measured with a CETR Tribometer in a ball-onrotating-flat configuration. The load was applied through a coated ball normal to a rotating coated flat. The instrument was enclosed in a glove box where the addition of dry or humid air produced the desired humidity. Films were deposited with substrate bias of −25 V at 20 kHz. As stated earlier, doped films contained 5–6 atomic percent sulfur and 30 atomic percent hydrogen. Figure 18.10(a) shows friction coefficients of undoped hydrogenated carbon film tested in dry air. Figure 18.10(b) shows the effect of sulfur doping on the friction coefficient in humid air. The transient friction behavior shown in Figure 18.10 has been attributed to the removal of adsorbed species and the formation of a smooth surface [24,28]. As summarized in Figure 18.11, the steady-state friction coefficient of undoped films increases rapidly with the addition of humidity. However, the steady-state friction coefficient of sulfur-doped films does not change noticeably with humidity.
Figure 18.11
Friction coefficient versus humidity for undoped and 5 atomic percent sulfur-doped films.
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18.5
WATER–FILM INTERACTIONS
Friction behavior of hydrogenated carbon films is related to water coverage on surfaces. Reducing the amount of water adsorbed onto a film surface can reduce friction in ambient humid environments. Direct measurement of the amount of water adsorbed on the surface can be done with a quartz crystal microbalance, which can detect nanograms per cm2 . This resolution allows for the measurement of partial monolayer coverage [29]. Shukla et al. observed saturation coverage of about 1.5 ML of water (<0.45 nm thick) on a hydrogenated carbon surface at 60% relative humidity by quartz crystal microbalance. They observed that film thickness did not affect water adsorption on hydrogenated carbon films [15]. Therefore, adsorption is not related to film porosity. This observation is consistent with an earlier study by Smallen et al. Using ellipsometry at 90% relative humidity, they measured ∼1.5 monolayers of water adsorbed on films synthesized with the highest hydrogen concentration in the sputter gas [30]. Maxtek, Inc. 5 MHz AT-cut quartz crystal sensors with Cr/Au electrodes were used in this study. They were coated with 20 nm of hydrogenated carbon films or 20 nm of sulfur-doped hydrogenated carbon films under the same deposition conditions described in Section 18.2 with a substrate bias of −50 V at 20 kHz. The microbalance was allowed to equilibrate after humidity changes before the mass was recorded. Figure 18.12 plots the recorded mass change as a function of humidity. At 90% relative humidity, the undoped film adsorbed a maximum of 47 ng cm−2 , corresponding to 1.5 ML of water, while the sulfur-doped film adsorbed a maximum of 18 ng cm−2 of water, corresponding to 0.56 ML
Figure 18.12 Weight gain due to water adsorption on undoped and sulfur-doped hydrogenated carbon films. The dashed line indicates the weight per cm2 of 1 monolayer of water. At 50% relative humidity, a 1.4-fold reduction in adsorption is observed; at 90%, 2.6-fold reduction factor is observed.
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of water. At 50% relative humidity, the sulfur-doped films adsorbed about 1.4 times less water. At 90% relative humidity, the sulfur-doped film adsorbed about 2.6 times less water, and the water coverage stayed below one monolayer. Coupled with the result of Tagawa et al. [14], this reduction in water adsorption may explain the reduced sensitivity of the friction coefficient toward humidity. Temperature-programmed desorption (TDS) can also be used to probe water–film interactions [25]. TDS was performed in an ultra-high vacuum chamber (base pressure 1.5–3 × 10−10 Torr). A sputter-cleaned sulfur-doped hydrogenated carbon film was cooled to 140 K via a copper cold finger in contact with a liquid nitrogen reservoir. The surface was then exposed to water vapor by a needle doser placed 1 cm from the sample. Gas exposures were expressed in Langmuir units where 1 Langmuir (L) = 1 × 10−6 Torr sec. The water pressure was maintained at 1 × 10−7 Torr for gas exposure. The amount of exposure time was varied to produce specific Langmuir units as shown in Figure 18.13. The temperature was then increased at 2 K per second by resistive heating, while a residual gas analyzer monitored the water desorption signal at m/e = 18. As shown in Figure 18.13, water desorption peaks at 172 K and 195 K were observed. From literature studies, the peak at 172 K is assigned to water desorption from the top layer of ice, i.e., this peak is associated with the strength of water–water bonding. The peak at 195 K is attributed to the desorption of the first water layer from the film surface, i.e., this peak is associated with water–film bonding. The existence of the 172 K peak even at the lowest water exposure indicates that water forms 3D islands on the film surface. By analyzing the desorption spectra, the activation energy for desorption can be calculated. Assuming that there is no activation barrier for adsorption, the heat of adsorption is equal to the activation energy for thermal desorption [25]. Assuming first-order desorption kinetics, one can show that the activation energy for thermal desorption, Edes , is given by: Edes Edes v , = exp − β RTm RTm2
Figure 18.13 Temperature-programmed desorption spectra for water desorption as a function of temperature for varying initial exposures at 140 K. Y -axis units are arbitrary intensity units.
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Figure 18.14 Temperature-programmed desorption spectra comparing water desorption as a function of temperature for undoped and sulfur-doped films.
where R is the gas constant (= 8.3 J/mole K), Tm is the temperature at which the desorption signal is a maximum, v is the frequency factor, and β is the heating rate in K/sec. Figure 18.14 compares the TDS data for films with and without sulfur doping. In experiments of water desorption from sulfur-doped hydrogenated carbon films, the peak desorption temperature corresponding to water-film bonding occurs at 195 K. Substituting Tm = 195 K and assuming v = 1013 /sec, one can show that the activation energy for thermal desorption of water from the sulfur-doped hydrogenated carbon surface is 50.4 kJ/mole. For the undoped film, the peak desorption temperature occurs at 206 K. Substituting Tm = 206 K and assuming v = 1013 /sec, we calculate the activation energy to be 53.2 kJ/mole. This indicates that a slightly weaker bond exists between the adsorbed water molecules and the sulfur-doped surface. A 2.8 kJ/mole reduction in desorption energy ( Edes ) due to sulfur doping corresponds with a decrease of average residence time for adsorbed water molecules equal to exp( Edes /RT ). This factor is equal to 3.1 at 300 K. A shorter residence time correlates with a lower equilibrium concentration of adsorbed water molecules on the sulfur-doped surface. This is consistent with observations from QCM experiments that the water coverage on sulfur-doped films at room temperature is reduced by a factor of 1.4 to 2.6 compared with that on undoped films.
18.6 18.6.1
MECHANICAL PROPERTIES
Hardness and Elastic Modulus
Nanindentation is used to measure hardness and elastic modulus of thin films. To prevent substrate influence on these measurements, the indentation depth must be small compared to the thickness of the film. A widely cited guideline is 10–15% of the film thickness [31].
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A Hysitron Inc. TriboScope Nanomechanical Test System was used to measure the hardness and elastic modulus of both sulfur-doped and undoped hydrogenated carbon films. It is a load-controlled depth sensing apparatus. A three-plate capacitive force/displacement transducer measures the indentation depth. The position of the diamond indenter relative to the sample surface is monitored as a function of applied load to obtain a loading and unloading curve. The supplied software uses the Oliver and Pharr method to analyze the unloading curve [32]. The slope of the elastic unloading curve (dP /dh) is used to calculate stiffness. Stiffness (S) is related to the effective elastic modulus by: √ dP 2 = S = √ Er A, dh π where Er is the effective modulus and A is the projected contact area under load. Er is defined as: (1 − v12 ) (1 − v22 ) 1 = + , Er E1 E2 where v and E are the Poission ratio and the elastic modulus for the film and indenter respectively. Hardness (H ) is calculated from the normal definition: H=
Pmax , A
where Pmax is the maximum load [31]. The nanoindenter was calibrated with a fused quartz standard supplied by the manufacturer. Figure 18.15 shows the hardness of hydrogenated carbon films as a function of the hydrogen sulfide concentration in 6 mTorr sputtering gas. Figure 18.16 shows the effect of sulfur doping on the elastic modulus. Both hardness and elastic modulus decrease with sulfur doping. Sulfur incorporation reduces the fraction of carbon–carbon 3-D network bonding, which weakens the structure. A decrease in the 3-D network bonding has been correlated with ultra-low friction [24]. 18.6.2
Film Stress
For practical applications, films should have low stress (<1–2 GPa) to minimize the likelihood of delamination. Film stress (σ ) can be determined by the wafer curvature method and is given by: 1 δ σ = Es ts2 , 3 (1 − vs )L2 tf where Es /(1 − vs ) is the biaxial modulus of the substrate, v is the Poisson ratio, tf is the film thickness, δ is the deflection of the substrate, ts is the substrate thickness, and L is the scan length as measured by a profilometer [33].
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Figure 18.15
The hardness of the films as a function of hydrogen sulfide concentration in the sputter gas.
Figure 18.16
The elastic modulus of the films as a function of H2 S concentration in the sputter gas.
Figure 18.17 shows that addition of sulfur reduces film stress. Experimentally, it has been found that a high fraction of sp3 3-D network bonding between carbon atoms is
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Figure 18.17 6 mT.
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Compressive film stress as a function of percent of H2 S of the total deposition atmosphere of
associated with high stress [34]. Sulfur doping reduces the fraction of sp3 3-D network bonding, resulting in lower film stress. The reduced stress in sulfur-doped films enables the deposition of thick (> one micron) films. Thick films allow one to sustain higher loads during sliding friction experiments.
18.7
CONCLUSION
Tailoring of hydrogenated carbon film properties to minimize environment effects on friction is accomplished by proper deposition techniques and choice of film composition. Magnetron sputter-deposition results in smooth surfaces and mid-range hardness. Sulfur doping of hydrogenated carbon films has been successful in mitigating the humidity effects on friction. The stabilization of low friction in humid air can be attributed to the reduction of water adsorption on the surface. This reduction is verified by results of quartz crystal microbalance and temperature-programmed desorption experiments. Even at 90% relative humidity, sulfur-doped films have less than one monolayer of water adsorbed on the surface. This reduction in water coverage is due to the decrease in residence time of water on the surface. Residence time is related to the strength of the bonding between water molecules and the sulfur-doped surface. These results indicate that sulfur doping results in weaker bonding between water and the film surface.
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Erdemir, A., Eryilmaz, O.L., Fenske, G. J. Vac. Sci. Technol. A 18 (2000), 1987–1992. Erdemir, A. Surf. Coat. Technol. 146 (2001), 292–297. Andersson, J., Erck, R.A., Erdemir, A. Surf. Coat. Technol. 163 (2003), 535–540. Erdemir, A., Eryilmaz, O.L., Nilufer, I.B., Fenske, G.R. Surf. Coat. Technol. 133 (2000), 448–454. Fontaine, J., Donnet, C., Grill, A., Le Mogne, T. Surf. Coat. Technol. 146–147 (2001), 286–291. Ronkainen, H., Varjus, S., Koskinen, J., Holmberg, K. Wear 249 (2001), 260–266. Fontaine, J., Le Mogne, T., Loubet, J.L., Belin, M. Thin Solid Films 482 (2005), 99–108. Li, H., Xu, T., Wang, C., Chen, J., Zhou, H., Liu, H. Appl. Surf. Sci. 249 (2005), 257. Paulmier, D., Zaidi, H., Nery, H., Huu, T.L., Mathia, T. Surf. Coat. Technol. 62 (1993), 570. Donnet, C., Le Mogne, T., Ponsonnet, L., Belin, M., Grill, A., Patel, V., Jahnes, C. Tribol. Lett. 4 (1998), 259–265. Erdemir, A. Trib. Int. 37 (2004), 1005–1012. Tagawa, M., Ikemura, M., Nakayama, Y., Ohmae, N. Tribol. Lett. 17 (2004), 575–580. Shukla, N., Svedberg, E., van de Veerdonk, R.J.M., Ma, X.D., Gui, J., Gellman, A.J. Tribol. Lett. 15 (2003), 9–14. Goodman, D.W., Kiskinova, M. Surf. Sci. 105 (1981), L265–L270. Erdemir, A. Diamond-like carbon films. In: Vizintin, J., Kalin, M., Dohda, K., Jahanmir, S. (Eds.), Tribology of Mechanical Systems; A Guide to Present and Future Technologies. ASME Press, New York, 2004, pp. 139–156. Oguri, K., Arai, T. J. Mater. Res. 7 (1992), 1313–1316. Yang, S.H., Kong, H., Lee, K.R., Park, S., Kim, D.E. Wear 252 (2002), 70–79. Yan, X.B., Xu, T., Chen, G., Wang, X.B., Liu, H.W., Yang, S.R. Appl. Phys. A-Mat. Sci. & Process. 81 (2005), 197–203. Gilmore, R., Hauert, R. Thin Solid Films 398 (2001), 199–204. Erdemir, A., Eryilmaz, O.L., Nilufer, I.B., Fenske, G.R. Diam. Rel. Mater. 9 (2000), 632–637. Zhang, S.L., Wagner, G., Medyanik, S.N., Liu, W.K., Yu, Y.H., Chung, Y.W. Surf. Coat. Technol. 177 (2004), 818–823. Fontaine, J., Loubet, J.L., Le Mogne, T., Grill, A. Tribol. Lett. 17 (2004), 709–714. Chung, Y.W. Practical Guide to Surface Science & Spectroscopy. Academic Press, New York, 2001. Moulder, J., Stickle, W., Sobol, P., Bomben, K. In: Chsatain, J., King, R. (Eds.), Handbook of X-ray Photoelectron Spectroscopy. Physical Electronics, Inc., Eden Prairie, 1995. Bhushan, B. Principles and Applications of Tribology. John Wiley & Sons, Inc., New York, 1999. Heimberg, J.A., Wahl, K.J., Singer, I.L., Erdemir, A. Appl. Phys. Lett. 78 (2001), 2449–2451. Lee, S., Staehle, R.W. Corrosion 52 (1996), 843–852. Smallen, M., Lee, J.K., Chao, A., Enguero, J. IEEE Trans. Magn. 30 (1994), 4137–4139. Pharr, G.M., Oliver, W.C. Mrs Bulletin 17 (1992), 28–33. Triboscope Users Manual. Hysitron Inc., Minneapolis, 2004. Ohring, M. The Materials Science of Thin Films. Academic, San Diego, 2001. Sattel, S., Robertson, J., Ehrhardt, H. J. Appl. Phys. 82 (1997), 4566–4576.
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– 19 – Application of Carbon Based Nano-Materials to Aeronautics and Space Lubrication Kenneth W. Street, Jr.1 , Kazuhisa Miyoshi1 and Randy L. Vander Wal2 1 NASA Glenn Research Center, 21000 Brookpark Road, Cleveland, OH 44135, USA 2 The Universities Space Research Association (USRA), c/o NASA Glenn Research
Center, 21000 Brookpark Road, Cleveland, OH 44135, USA
19.1
INTRODUCTION
There are several ways for carbon atoms to bond to form carbon derived materials. Diamond and graphite, the naturally occurring materials, have been mimicked in the laboratory with the development of diamond-like carbon (DLC) and graphite-like carbon (GLC) materials that have been shown to have tribological properties superior to the natural materials in many instances. Carbon also forms smaller, more discrete chemical systems, such as the fullerenes, carbon nanotubes (CNT), and carbon nano-onions (CNO). Many of these latter materials are still in the early stages of tribological investigation. We have found that nano lubricants such as single-walled nanotubes (SWNT), multi-walled nanotubes (MWNT), and graphitized analogues, fluorinated SWNTs, and nano-onions, have superior coefficient of friction (CoF) and endurance lives in ultrahigh vacuum—a space like environment. Potential space and aeronautic applications of nanolubricants include the development of microelectromechanical systems (MEMS), and micromachines. Nanolubricants can be applied to or grown on contacting surfaces in relative motion. Friction contributing to decreased performance, increased energy consumption, wear damage, added maintenance, shortened lives or catastrophic failure constitutes a reliability issue for all contacting interfaces in all mechanical systems. All nanocarbon materials have demonstrated the ability to dramatically reduce stiction (or adhesion) and friction between contacting surfaces under dry conditions, a major concern in the development of MEMS and micromachines. Consequently, interest in the research and commercialization of nanotube technology and related materials continues to grow. A recent search by Miyoshi and Street [1] shows the number of articles published on this topic to be growing rapidly each year. Key to the proper functioning of satellites, space vehicles and aircraft are the proper functioning of mechanical components. A large number of specialty oils and solid coatSuperlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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ings have been developed to serve the needs of the operating conditions and unique environments of the individual components. Solid lubrication technology has advanced rapidly in the past four decades to where it is extensively used where contamination by liquids is a problem and when liquid lubricants do not meet advanced requirements such as ultra high vacuum (in space), high temperatures, cryogenic temperatures, radiation, clean environments, or corrosive environments, and combinations thereof. Friction and wear are still a primary concern in a large number of current and future applications. Solid lubricants must possess both desirable coefficient of friction (0.001 to 0.3) and maintain durability in a variety of environments, such as high vacuum, water, air, both cryogenic and elevated temperature, or dust. The tribological properties of materials and material couples often vary considerably with the environment. Therefore, the successful use of solid lubricants requires an understanding of their properties and knowing how a solid lubricant will perform in a given application. Materials issues such as surface pretreatment, compatibility of counterpart components and lubricants, and debris generation must be taken into account when designing a lubricated device or moving mechanical assembly. Carbon-derived materials have outstanding lubrication properties and materials such as graphite have been used as lubricants for many decades. Other similar carbon-based materials are the newest durable lubricants. Carbon nano-particles and carbon films such as diamond and graphite-like carbons are presently being investigated for lubrication applications. However, carbon based nano-particles have some unique properties which make them candidates for testing. They appear to be heat resistant, radiation hard, durable and provide low CoF (0.01–0.10) with a number of tribocouples. These materials come in many forms. We have tested CNOs [2], SWNT, cut SWNT, fluorinated SWNT [3], MWNT, and graphitized MWNT [4], under sliding and/or rolling conditions. The nano-tubes have been grown in-situ for testing in a vertically aligned configuration for comparison with randomly scattered neat material coatings. Further, these materials have been tested neat as well as dispersed in oils. The nano-carbon particles are still in the early stages of development, and it will be some time before their practical tribological usage is realized.
19.2 19.2.1
19.2.1.1
EXPERIMENTAL
Instrumentation
Spiral Orbit Tribometer
A Spiral Orbit Tribometer (SOT) [5,6] simulates an angular contact bearing (Figure 19.1). A 12.7 mm (1/2 inch) ball was rolled between a fixed plate and a rotary plate, running at 210 rpm. The load, providing a mean Hertz stress of 1.5 GPa, was applied through the fixed plate. The combination of the high load, the moderate speed, and of the small amount of lubricant (approximately 50 µg) allowed the system to operate in the boundary lubrication regime. The ball was rolling and pivoting in a spiral and maintained in the orbit by the guide plate. The force the ball exerted on the guide plate was used to determine the friction coefficient. Evaluation of a suspension of nano-onions in Krytox was
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Figure 19.1
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The Spiral Orbit tribometer.
conducted at room temperature (∼23 ◦ C), and under ultrahigh vacuum (∼1 × 10−6 Pa) or in air. The relative humidity ranged between 50 and 60% for the air tests. As the lubricant was tribologically stressed, it was degraded and eventually consumed. Test conclusion was defined when a friction coefficient of 0.28 was attained. Normalized lubricant lifetime (or inversely, its degradation rate) was then defined as the number of orbits divided by the amount of lubricant in micrograms. All tests were performed at least in duplicate. All specimens were made of AISI 440C stainless steel. For tribological purposes, ball and plate surfaces were polished to a roughness, Ra , of 0.05 µm. The parts were first rubbed with an alumina slurry and rinsed under running deionized water. Then they were ultrasonically cleaned for ten minutes each first in a bath of hexane, followed by deionized water. All drying was done with filtered nitrogen. The procedure was completed by exposing the specimens to ultraviolet/ozone for 15 minutes. 19.2.1.2 Pin-on-Disk Tribometer The pin-on-disc (PoD) tribometer [7] used in the investigation was mounted in a vacuum chamber (Figure 19.2). Unidirectional sliding friction experiments were conducted with the aligned MWNT coatings and the dispersed MWNT (nongraphitized and graphitized) coatings at room temperature in air (relative humidity, ∼50 percent) and in ultrahigh vac-
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Figure 19.2
The Pin-on-disk tribometer.
uum (∼7 × 10−6 Pa). All experiments were conducted with 6-mm-diameter 440C stainless steel balls, and 6-mm-diameter alumina-yttria stabilized zirconia pins in sliding contact with the MWNT films deposited on quartz disk substrates. For SWNT and fluorine modified SWNT, 6-mm-diameter sapphire balls were run against films deposited on quartz. All experiments were conducted with a load of 1.4 N at 120 rpm using a 6 mm track diameter. The friction force was continuously monitored during the sliding friction experiments. The sliding wear life, endurance life, for the coatings was determined to be the number of passes at which the CoF rose to 0.15 in a given environment.
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19.2.2
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Sample Preparation
19.2.2.1 Spiral Orbit Tribometry Samples Samples of carbon precursor were heat-treated in a resistance heated furnace using a graphite crucible under a He atmosphere. The nano-onions were obtained by inductive heating at 3000 ◦ C for 1 h duration and were used without further treatment (e.g. purification). The nano-onions appeared to be stable in air. These materials were characterized by transmission electron microscopy, TEM [8], thermo gravimetric analysis (TGA), and infrared and Raman spectroscopic analysis [2]. A solution of CNO in Krytox 143AB oil, already used in space applications, was prepared. It consisted of 10.33 mg of oil and 5.16 ml of solvent. Therefore, when 25 µl of the dilute solution was applied with a micro syringe on the ball, 50 µg of oil was left after evaporation of the solvent. The CNO particles were added in such a quantity that roughly a 20% (by weight) suspension was created. A quick visual observation showed that the particles were agglomerated, so as to have a proper suspension, the dilute solution of oil, particles and solvent was agitated in an ultrasonic bath before use resulting in a completely black solution with dispersed particles. 19.2.2.2 Pin-on-Disk Tribometry Samples 19.2.2.2.1 Aligned MWNTs The aligned MWNTs were synthesized within a hightemperature tube furnace around 1073 K on catalyst-coated quartz substrates. Physical vapor deposition was used to coat all quartz substrates with a 5-nm thick iron bondcoat, which formed iron islands resembling droplets and served as catalyst particles on the quartz. The procedure for creating the aligned MWNTs directly upon the catalyst-coated quartz disks involved (1) initial heat up, (2) catalyst reduction, (3) further temperature elevation, and (4) synthesis using xylene as the carbon source, (5) followed by cooling under an inert environment. Specifically, iron coated specimens (5 nm thickness) are held at 973 K for 1 h within a flow of Ar:H2 (4:1), followed by ramping to 1123 K under argon. Then to synthesize the MWNTs, the xylene is introduced for 25 min through a pre-evaporator (0.4 ml min−1 feedrate) using a metering pump with a carrier flow of Ar:H2 of 5:1. 19.2.2.2.2 Dispersed MWNTs In the CVD process, 6.5 mol% of ferrocene is dissolved in xylene to obtain a feed solution with approximately 0.75 percent of iron to carbon which is fed continuously into a two-stage tubular reactor using a syringe pump. Ferrocene (sublimation temperature, ∼413 K) has been shown to be a good precursor for producing iron catalyst particles that can seed nanotube growth, and xylene was selected as the hydrocarbon source since it boils (∼413 K) below the decomposition temperature of ferrocene (∼463 K). The liquid feed is passed through a capillary tube and preheated to ∼448 K prior to its entry into the furnace. At this temperature, the liquid exiting the capillary is immediately volatilized and swept into the reaction zone of the furnace by a flow of argon with 10 percent hydrogen. Various parameters, such as the furnace temperature (923 to 1323 K), ferrocene–xylene ratio and feed rate, total reaction time, and sweep gas flow rate were adjusted to determine the optimal growth conditions for high-purity MWNTs. After the reaction, the preheater and the furnace were allowed to cool to room temperature in
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flowing argon. Carbon deposits were formed on the walls of the quartz furnace tube and on plain quartz substrates that were placed within the furnace to act as additional sites for nanotube growth. The nanotube material was scraped clean from the walls of the reactor tube and weighed. The reactor was operated modestly above atmospheric pressure to prevent any influx of oxygen. Graphitized MWNTs were obtained by heating collected MWNTs within a graphite tube furnace under inert atmosphere. Temperatures exceeded 1823 K for several hours, permitting melting, draining, and vaporization of residual Fe catalyst. A potential added benefit of the heating is that some additional graphitization occurs within the nanotubes. Defects may be annealed and lattice planes oriented more parallel to each other, as in graphite. Other details are proprietary. Since the MWNTs were agglomerated, in order to have a proper suspension, a dilute solution of MWNT particles and solvent was placed in an ultrasonic bath prior to deposition on a quartz disk surface. The dispersed MWNT coating films were prepared by deposition of the dilute MWNT suspension on quartz disks followed by evaporation of solvent under dry nitrogen flow. Coating films with four different relative thicknesses (0.63, 1.26, 1.89, and 2.52 µg mm−2 ) were fabricated. The most unambiguous measure of thickness is weight per unit area which we use to define the coating load. Bonding between a coating and the substrate is due to van der Waals’ forces. The nanotubes are mechanically tangled with each other. The standard thickness of 2.52 µg mm−2 was used in most experiments unless otherwise specified. 19.2.2.2.3 Dispersed SWNTs All SWNTs were prepared by the HiPCO process, and were purified prior to use by wet air oxidation and subsequent hydrochloric acid treatment followed by washing and vacuum drying to remove all nontubular forms of carbon and iron catalyst according to a documented detailed procedure [9]. The iron content in the purified SWNTs was found to be <1 wt.% according to thermo-gravimetric analysis. The fluoronanotubes of the C2 F and C5 F stoichiometry were prepared by direct fluorination of purified SWNTs under controlled, well-established conditions [10,13]. Hydrazine treatment of the C2 F sample was used to reduce the fluoronanotubes to approximately a C20 F composition [10,12]. Cut-SWNTs of 100–300 nm lengths were prepared by treatment of SWNTs in 2M HNO3 by 30 minutes sonication [12]. Pyrolysis of C5 F fluoronanotubes in argon produced shorter nanotubes, F-cut-SWNTs, of predominantly 20–80 nm length distribution [13]. The films were prepared by deposition of nanotube sample suspensions either in toluene (SWNTs, cut-SWNTs, and C20 F) or isopropanol (C2 F, C5 F, and F-cut-SWNTs) on the quartz disk followed by evaporation of solvent under dry nitrogen flow. Films of four different relative thicknesses (0.63, 1.26, 1.89, and 2.52 µg/mm2 ) were fabricated and tested. All tests were run in air environment (∼40% relative humidity) at room temperature (∼23 ◦ C). 19.2.3
Analytic Techniques and Post Mortem Analysis
For characterization of the CNO and SOT postwear analyses, all infrared spectra were collected with an FTIR spectrometer with the sample mounted in a 7.6 cm diameter gold coated integrating sphere [14]. A Raman microscope that uses a 25 mW Ar Ion laser
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operating at 514.5 nm was employed to collect Raman spectra. The microscope objective was typically 20× with occasional spectra taken at 10× or 50× having spot diameters of 14, 28 and 5 microns respectively. In postwear analyses of MWNT samples, high-resolution transmission electron microscopy (HRTEM) and scanning electron microscopy (SEM) were used to determine nanostructure, microstructure, morphology, and defects of materials; electron energy loss spectroscopy (EELS) and energy dispersive X-ray analysis (EDX) were used for elemental analyses and stoichiometry of materials; and vertical scanning interferometry was used to determine surface topography and roughness, film or layer thickness, and wear volume. For the postwear analysis of SWNT samples, transmission electron microscopy (TEM) was used to determine nanostructure, microstructure, morphology, and defects of materials.
19.3 19.3.1
RESULTS AND DISCUSSION
Nano-onion Investigations
19.3.1.1 Background and Objectives Soot, carbon material, represents one of the very first nanostructured materials, although it has rarely been considered as such. Careful examination of the internal structure of these carbon materials reveals that the nanostructure is highly variable and depends upon the starting material and processing conditions, which is also true of carbon black [15]. The significance with respect to oxidation of the internal structure of carbon is its effect upon reactivity. In general, more graphitic carbons are less reactive towards oxidation [16]. Graphitic carbon is characterized by layer planes with large in-plane dimensions [17]. The connection between layer plane dimensions and oxidation is due to the anisotropic reactivity of the graphitic segments comprising the carbon. Carbon atoms within basal plane sites, surrounded by other carbon atoms, exhibit a far lower oxidative reactivity than those located at the periphery of such segments, so-called edge sites [18]. Changes in the carbon nanostructure, resulting in increased graphitic layer plane length, are correlated with reactivity loss [19]. Layer plane segments can grow by bonding to adjacent graphene segments and by addition of amorphous carbon material within the soot particle from which they are produced [20]. Whether thermally or oxidatively induced, an increase in the dimensions of graphene segments corresponds to graphitization and a parallel decrease in reactivity. Upon heating spherically shaped carbon black of nanometer scale dimensions in the absence of oxidant, graphene sheets form and the initial soot particle templates the growth of a graphitic particle into what is best described as a “sphere” with many flat sides, i.e. polygonal in nature and having a hollow interior. Due to the absence of edge sites, these polygonal graphitic particles, or CNOs, are relatively stable toward oxidation [8]. High resolution TEM images of the nano-onions (Figure 19.3(a)), and carbon precursor (Figure 19.3(b)) indicate the significant change in structure of the material upon graphitization. In these images, the dark lines indicate the graphene sheets of carbon atoms and the white lines are the spacing between sheets. The annealing process allows ordering of the sheets and length extension of the flat crystalline regions resulting
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High-resolution transmission electron micrograph of (a) nano-onions and (b) carbon precursor.
in considerable basal plane sites of low reactivity toward oxidation. The polygonal connection of basal planes eliminates edge sites to further reduce reactivity. While we have not measured the size distribution of the graphitized materials, the primary particle size, initially around 30 nm in diameter, is conserved in the graphitization process. Raman spectroscopy has been frequently used in the characterization of graphite and graphitic materials. The spectra shown in Figure 19.4 have been normalized to account for differing acquisition conditions. Two spectral peaks characterize the first-order Raman spectra of carbon materials; (Figure 19.4(a)) a peak near 1580 cm−1 , the “G-band”, and a peak near 1360 cm−1 , the “D-band” [21]. The former corresponds to an in-plane stretching motion of the graphitic layer planes. The latter arises from a breakdown of the Raman selection rules attributed to the finite-sized regions of graphitic structure, hence its nomenclature as the “disorder activated” transition. The narrowing of the D and G peaks indicates increasing homogeneity of the sample as disordered carbon is reorganized into graphitic sheets. The spectra obtained from the nano-onions contained sharp D and G peaks with the G peak much more intense indicating a highly ordered material considerably different from the starting carbon precursor. In addition, the second-order region between 2520 and 3300 cm−1 contains a sharp, intense band at 2696 cm−1 for highly ordered graphitic materials, like the CNO. This band is virtually absent in the degradation products and the starting carbon precursor [22]. Graphite is used as a solid lubricant due to its stability at moderately high temperatures. However, the temperature at which the graphite rapidly oxidizes is strongly influenced by surface area [23]. With the size of particles typically employed in lubrication, a great amount of thermal stability is lost due to size reduction either during grinding for application or during lubrication of contacting parts. The TGA analyses of the nano-onions and carbon precursor in air both indicate high purity materials having normal TGA profiles (Figure 19.5). The points at which 5% of the materials are oxidized indicate the approximate temperature where rapid oxidation of these materials proceeds. For the carbon precursor, this temperature is 588 ◦ C and for the CNO 792 ◦ C, indicating the improved oxidation resistance of the graphitic nanostructured material. For this reason, we have undertaken
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Figure 19.4 Raman spectra of carbon materials. (a) Nascent nano-onions. (b) Postmortem spectrum from 440C stainless steel ball run in vacuum with Krytox 143AB/nano-onion mixture. (c) Postmortem spectrum from 440C stainless steel ball run in air with Krytox 143AB/nano-onion mixture.
Figure 19.5 Comparative thermo-gravimetric analysis of carbon precursor and nascent nano-onions.
a study of the lubricating ability of nano-structured graphitic particles such as CNO and CNT. 19.3.1.2 CNO Tribology The lubrication role of solid particles introduced in a fluid lubricant, i.e. in grease, depends on the size of the particles, on their amount, and on the geometry of the contact. The introduction of small particles is beneficial in boundary lubrication, but particles present in the lubricant have to be of small size so as to allow a good fluid circulation within the contact and to not “jam” it. The amount of particles is generally low, a few percent
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Figure 19.6 Coefficient of friction traces for tests run in vacuum (upper scale) and in air (lower scale) with Krytox 143AB with nano-onions.
Table 19.1. Coefficient of friction and normalized lifetimes for Krytox 143AB and Krytox 143AB with nano-onions in different environments Sample
Environment
Coefficient of friction
Krytox 143AB Krytox 143AB Krytox 143AB/CNO Krytox 143AB/CNO
Air Vacuum Air Vacuum
0.13 0.13 0.05 0.13
Lifetime 476 43 3830 55
in volume, and up to 10% for graphite [24]. Under severe conditions, these particles can produce a layer which helps to protect the surfaces [24,25]. Hence, the evaluation of the ability of graphitic CNOs to improve the lubricating lifetime of a space oil, Krytox 143AB, in conditions simulating bearing operation was undertaken. After SOT testing at room temperature the average normalized lifetime, the number of orbits performed before failure per microgram of lubricant employed, was calculated. Examples of friction traces and the lifetime obtained are given in Figure 19.6 and Table 19.1 respectively. The use of CNOs did not improve the lifetime, nor did it change the friction coefficient of the Krytox 143AB, a perfluorinated polyether (PFPE), oil run in vacuum. Results of testing in air are reported in Figure 19.6 and Table 19.1. A very low friction coefficient (0.04–0.05) was observed with a long lifetime in air. Furthermore, the failure was more “progressive” compared to the one observed in vacuum. In air however, a significant improvement in lifetime occurs (Figure 19.6, lower scale) attributed to the CNOs, which arises from their ability to serve as a back-up lubricant. The nano-onions from the suspension are forming a lubricant layer on the surfaces of the ball and disk, similar to
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Infrared spectra of the Krytox 143AB with nano-onions after the tests run in (a) air and (b) vacuum.
Teflon thickener in commercial PFPE based greases. The nano-onions can replace the degraded oil as a lubricant, forming a graphitic material. Postmortem analysis indicates that the CNOs are sacrificed to form an amorphous graphitic layer. This behavior is typical of graphite which lubricates better in humid air. Similar superior tribological properties of CNO films is reported for PoD experiments [26]. In those experiments, the CNOs formed by heat treatment of diamond were more spherical with shorter graphene lamella, and produced CoF of ∼0.05 for the tribocouple of steel on a silicon wafer. Raman analysis on the balls run in vacuum (Figure 19.4(b)) indicated the presence of a large quantity of graphitic material having well defined D and G peaks as well as multiple small peaks in the second order peak region. These spectra are not similar to the applied CNOs but are similar to conventionally degraded carbon based lubricants. It is thus concluded from the Raman analysis that the nano-onions degrade during tribological contact and that they are completely consumed at failure. It should be noted that the CNOs degrade to produce spectra similar to degraded PFPE lubricants so it is not possible to distinguish the source of the degraded material. The ball run in air (Figure 19.4(c)) had similar spectral features but at much lower concentrations. Infrared analysis was also performed postmortem on the balls (Figure 19.7). Balls run in either air or vacuum showed peaks in the 2960–2850 cm−1 range and a broad band in the 3360 cm−1 range. These bands correspond to hydrocarbon and oxygenated materials (possibly water) respectively. No further evidence of oxygenated functional groups was found in either spectrum. The ball run in vacuum (Figure 19.7(b)) revealed traces of the original Krytox 143AB having bands in the 1346–970 cm−1 region of the spectrum. This result is unexpected since all the lubricant is typically consumed during a SOT experiment. 19.3.1.3 Conclusions on CNO Tribology 1. The CNOs provide lubrication similar to graphite when tribologically tested in ambient air. 2. The CNOs degrade to a final material characteristic of the degradation of other carbonbased lubricants.
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3. The CNOs are stable in air to over 750 ◦ C with stability attributed to the lack of edge sites vulnerable to oxidation. 4. These nano-structured materials are of the correct particle size range to allow adequate circulation of lubricants but still provide back-up lubrication under extreme conditions. These results suggest that the CNOs could also be used as a solid additive to grease replacing Teflon or MoS2 in several commercially available lubricants for use in ambient air. 19.3.2
19.3.2.1
Multi-walled Nanotube Investigations
Background and Objectives
In 1991, CNTs—long, thin cylinders of carbon—were discovered by Iijima [27]. A CNT is often described as a honeycomb lattice rolled into a cylinder. CNTs consist of graphene cylinders closed at either end with caps containing pentagonal rings. They are actually part of the fullerene family: essentially buckyballs expanded from the center into cylinders. CNTs may be either single- or multi-walled. Both types possess remarkable physical, electronic, and thermal properties. For example, the Young’s modulus of single-walled CNTs lies close to 1 TPa, and the maximum tensile strength is close to 30 GPa [28], with values for multi-walled CNTs being somewhat less. The precise values depend upon the CNT diameter, length, chirality, and number of walls and defects. Their intriguing structures have sparked much excitement in recent years, and a large amount of research has been dedicated to understanding them. The CNTs are still in the early stages of development in the field of tribology, and it will be some time before practical tribological usage is realized. Tribology applications may emerge that can take full advantage of intrinsic structures and properties of carbon-based nanomaterials and films in such areas as solid films for dry lubrication, additives for liquid lubricants and greases, and composites for wear parts [1,2,29–31]. These films and materials may offer attractive new solutions to important lubrication problems as well as exciting challenges to the tribologist or product designer who seeks to exploit the performance and cost-effective potential of these materials. The primary objective of this section is to report our investigations on the steady-state CoF and endurance or wear life of MWNTs. Aligned MWNTs, dispersed nongraphitized MWNTs, and dispersed graphitized MWNTs were synthesized and coated on quartz disk substrates. To evaluate the friction behavior, unidirectional sliding friction experiments were conducted with 440C stainless steel balls and hemispherical alumina-yttria stabilized zirconia (Al-YSZ) pins in sliding contact with the MWNTs at room temperature in air and in ultrahigh vacuum. The main criterion for evaluating the solid-lubrication performance of materials was the CoF; it was determined that an effective solid lubricating material must generally have a CoF <0.15 in any given environment. Postwear analyses of wear surfaces, transfer films, wear debris, and microstructures were conducted. Finally, the lubrication mechanism of the nanostructured MWNTs is discussed. 19.3.2.2
Nano- and Microstructure of MWNT Solid Films
In Figure 19.8, a series of SEM images show MWNTs aligned perpendicularly to the substrate, densely grown as MWNT mats, “nanograss”, on quartz. The high density of growth
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Figure 19.8 Scanning electron micrographs of aligned multi-walled carbon nanotubes (MWNTs) grown on iron-coated quartz.
Figure 19.9 Scanning electron micrographs of dispersed multi-walled carbon nanotubes (MWNTs) deposited on quartz. (a) Nongraphitized. (b) Graphitized.
is the causative factor for the alignment. In contrast, Figure 19.9 presents SEM images of dispersed nongraphitized and graphitized MWNTs showing a tangle of long, thin cylinders (tubular, nanofiber-like particles). The directions of the cylinders are randomly oriented and are generally “parallel” to the surface of the substrate. Figures 19.10 and 19.11 show HRTEM images of the dispersed as-synthesized nongraphitized and graphitized MWNTs, respectively. These images are included here as a reference for post-wear analysis. As seen in Figure 19.10, the nongraphitized MWNTs possess different diameters yet invariably have the traditional inner channel, a characteristic of graphitic MWNTs. Some segmentation appears and is related to the uniformity of their growth process. The HRTEM image shows a wall structure with some breaks and discontinuities among the carbon lamellae. By comparison, in Figure 19.11 the HRTEM images of the graphitized MWNTs show the graphitic nature of a section of the sidewall. Segmentation is still observed in the MWNTs; however, some breaks and discontinuities among the carbon lamellae noticeable in the nongraphitized MWNTs are absent from the graphitized MWNTs. These graphi-
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Figure 19.10
Figure 19.11
High-resolution transmission electron micrograph of dispersed nongraphitized MWNTs.
High-resolution transmission electron micrograph of dispersed graphitized MWNTs.
tized MWNTs have been dispersed upon quartz, per the above procedure and their friction properties will be described later. 19.3.2.3
Tribology of MWNT
19.3.2.3.1 Aligned MWNTs Figure 19.12 presents friction traces obtained in humid air for an aligned MWNT-coated disk, an iron-coated quartz disk, and a bare quartz disk in sliding contact with a 440C stainless steel ball as a function of the number of passes. All the friction traces obtained with the three different disks fluctuated. The steady-state CoF for the aligned MWNT coating in contact with 440C stainless steel was between 0.025 and 0.060 which meet the friction criterion in humid air. The average CoF was 0.04, which is one-fourth to one-fifth of the averages for the bare quartz and the iron-coated quartz reference blanks. The wear life of this typical aligned MWNT coating was 172,500 passes.
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Figure 19.12 Coefficient of friction for aligned MWNT coating (MWNT/Fe/quartz), iron-coated quartz (Fe/quartz), and bare quartz in sliding contact with 440C stainless steel balls in air as a function of number of passes.
Figure 19.13 Coefficient of friction for (a) aligned MWNT coating (MWNT/Fe/quartz) and (b) bare quartz in sliding contact with Al-YSZ hemispherical pins in ultrahigh vacuum as function of number of passes.
In ultrahigh vacuum, the CoF for the aligned MWNT coating in contact with 440C stainless steel fluctuated between 0.19 and 0.48, while that for the bare quartz fluctuated between 0.40 and 0.59 and that for the iron-coated quartz fluctuated between 0.19 and 0.54. The material couple of the aligned MWNTs and 440C stainless steel did not meet the friction criterion in ultrahigh vacuum. Therefore, a different counterpart material was chosen to improve the friction behavior of the aligned MWNT coating in ultrahigh vacuum. Two-phase Al-YSZ ceramic [32] was selected: it is harder, but lighter, than the stainless steel and is more inert chemically. The PoD results are presented in Figure 19.13. In ultrahigh vacuum, the steady-state CoF for the aligned MWNT coating in contact with Al-YSZ was between 0.073 and 0.11, while that for the bare quartz fluctuated between 0.17 and 0.46 and that for the iron-coated quartz fluctuated between 0.18 and 0.53. The average CoF for the aligned MWNT coating in contact with Al-YSZ was 0.09, nearly one-third to one-fourth of those for the bare quartz and the iron-coated quartz. The material couple of the aligned MWNTs and Al-YSZ met
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Figure 19.14 Coefficient of friction traces for dispersed MWNT coatings (MWNT/quartz) in sliding contact with Al-YSZ hemispherical pins as a function of number of passes. (a) Nongraphitized MWNT coating in air. (b) Graphitized MWNT coating in ultrahigh vacuum.
the friction criterion in ultrahigh vacuum, although the wear life was only about 5,700 passes. 19.3.2.3.2 Dispersed MWNTs Figure 19.14 presents friction traces for the dispersed, nongraphitized MWNTs and the dispersed, graphitized MWNTs in sliding contact with Al-YSZ in humid air and in ultrahigh vacuum, respectively, as a function of the number of passes. Both friction traces fluctuated. In air, the average CoF for the dispersed, graphitized MWNT coating with a coating thickness of 2.52 µg mm−2 was 0.06. The wear life of this particular MWNT coating was greater than 3.5 million passes. In ultrahigh vacuum, the steady-state CoF for the dispersed, graphitized MWNT coating with a coating thickness of 2.52 µg mm−2 showed several phases of frictional evolution; the average CoF was 0.009 in the first phase, 0.027 in the second phase, 0.044 in the third phase, and 0.027 in the fourth phase over 1 million passes. The wear life of this particular MWNT coating was greater than 1 million passes. Figure 19.15 presents the steady-state coefficients of friction for the dispersed, nongraphitized MWNTs and the dispersed, graphitized MWNTs in sliding contact with AlYSZ obtained in humid air and in ultrahigh vacuum, respectively, as a function of coating thickness. Although the relationship between CoF and coating thickness was not quite consistent, an increase in coating thickness generally resulted in a decrease in CoF and an increase in wear life. All dispersed MWNT coatings of each thickness tested with Al-YSZ in either air or ultrahigh vacuum met the friction criterion. 19.3.2.3.3 Comparison of Aligned and Dispersed MWNTs The dispersed, graphitized MWNT coating (Figure 19.14(b)) exhibited better friction and wear life performance
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Figure 19.15 Coefficient of friction traces for dispersed MWNT coatings (MWNT/quartz) in sliding contact with Al-YSZ hemispherical pins as a function of coating thickness.
Figure 19.16 Scanning electron micrographs of aligned MWNT coating. (a) Wear surface of MWNT coating after contact with 440C stainless steel ball counterpart. (b) MWNT patches in wear scar on 440C stainless steel ball.
than those of the aligned MWNTs (Figure 19.13(a)) in ultrahigh vacuum. The CoF for the dispersed, graphitized MWNTs was one-tenth of that for the aligned MWNTs, while the wear life was at least 175 times greater. The dispersed MWNT coating is superior to the aligned MWNT coating. The results indicate that prearranged or prepatterned nanostructure, such as that of the aligned MWNT coating, is not necessary for MWNTs to provide a low CoF, that is, solid-film lubrication. 19.3.2.4 Wear Surfaces 19.3.2.4.1 Aligned MWNTs Figure 19.16 presents scanning electron micrographs for (a) a wear surface of the aligned MWNT coating, worn in air by a sliding 440C stainless steel ball, that reveals a smooth, burnished appearance and (b) a wear scar on the counterpart 440C stainless steel ball revealing a large amount of transferred MWNTs. The fine
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Figure 19.17 Postwear analysis high-resolution transmission electron micrographs of sample collected from wear track of aligned MWNT coating after sliding friction experiment of short duration.
tubular MWNT particles (Figure 19.8) were flattened and burnished in the sliding direction by sliding action, leaving the smooth, burnished appearance of smeared, agglomerated MWNT layers. The large transferred plate-like, smeared, agglomerated patches of MWNTs were mostly found at the edges of the wear scar. Although the wear scar contained such transferred MWNT patches, it revealed almost no wear of 440C stainless steel and quartz themselves even after 100,000 passes. Figures 19.17 to 19.19 present HRTEMs for a set of wear-debris samples collected from the wear track of an aligned MWNT coating batch. These samples represent increasing durations of sliding friction for the aligned MWNT coating. Many MWNTs were observed to be cut or broken in the sample with the shortest sliding duration (Fig. 19.17). The predominant fraction of such structures, particularly when compared to the nascent aligned MWNTs prior to sliding friction experiments, indicates their destruction during the sliding. As such, they represent nanolubricant degradation products. Notably the high resolution images show that while the tubular structure remains, the walls are highly fragmented
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Figure 19.18 Postwear analysis high-resolution transmission electron micrographs of sample collected from wear track of aligned MWNT coating after sliding friction experiment of intermediate duration.
Figure 19.19 Postwear analysis high-resolution transmission electron micrographs of sample collected from wear track of aligned MWNT coating after sliding friction experiment of long duration.
into many short graphene lamellas. This evolution, particularly in light of the high degree of graphitization of the nascent aligned MWNTs, suggests that the wear mechanism occurs via crushing of the tubes resulting in the extensive fragmentation of the walls. It is believed that this is a precursor stage to their complete disintegration. As shown in Figure 19.18, the sample representing an intermediate sliding duration exhibits similar characteristics, namely cut (or broken) MWNTs. The images reveal an amorphous carbon coating upon the exterior of the MWNTs. The origin may be the severe degradation of some portion of the aligned MWNTs. Notably the aligned MWNT containing the metal catalyst fragment retained its graphitic structure. This observation, in concert with the coating that underwent the shorter sliding duration, suggests that the degradation of the MWNTs occurs via crushing, where the graphitic walls become increasingly fragmented during the course of the experiment. The net result is eventual disintegration of
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Figure 19.20 Scanning electron micrographs of dispersed nongraphitized MWNT coating after contact with Al-YSZ pin counterpart in air. (a) Wear surface of MWNT coating. (b) MWNT patches in wear scar on Al-YSZ pin.
some MWNTs whose reformed, amorphous carbon coats the remaining intact MWNTs. Similar observations of cut MWNTs, intact tubes with highly fragmented walls, and tubes with an amorphous carbon coating were observed in the sample that underwent the longest sliding duration (Figure 19.19); it is noted that this structure is comparable to that of the as-synthesized nongraphitized dispersed MWNTs in Figure 19.10. The HRTEM images are consistent with an increase of duration of experimental sliding time in that they show an increasing amount of amorphous carbon, cut MWNTs, and MWNTs with fractured walls as generated by the increased sliding friction duration. The plastic deformation and cracks subdivide and fragment the multi-walled structure of MWNTs. The nature of the strain or structural surface damage of MWNTs varies with depth from the surface. The thickness of the deformed layer and degree of deformation in the multi-walls are functions of the duration of sliding friction. 19.3.2.4.2 Dispersed MWNTs Figure 19.20 presents SEM images for (a) a wear surface of the dispersed, nongraphitized MWNT coating, worn in air by a hemispherical Al-YSZ pin, that appears curled, with segments that are submicron to tens of microns long, with MWNT cylinders in the wear track on the quartz disk and (b) a wear scar on the counterpart Al-YSZ pin revealing large transferred MWNT patches. Although most fine MWNT cylinders were plowed out and piled at both sides of the wear track, a small amount of MWNTs were cut or broken by sliding action and remained in the wear track. The smeared, agglomerated MWNT layers seen in the wear track of the aligned MWNT coating (Figure 19.16(a)) are absent from the dispersed, nongraphitized MWNTs (Figure 19.20(a)). The transferred plate-like, smeared, agglomerated patches of MWNTs in Figure 19.16(a) were found in the wear scar and at the edges of the wear scar. Although the wear scars on the 440C stainless steel and Al-YSZ contained such transferred MWNT patches, both revealed almost no wear. Figure 19.21 presents SEM images for (a) a wear surface of the dispersed, graphitized MWNT coating, worn in ultrahigh vacuum by a hemispherical Al-YSZ pin, that shows agglomerated MWNT patches and particles in the wear track on the quartz disk and (b) a wear scar on the counterpart Al-YSZ pin revealing large transferred MWNT patches. The fine nongraphitized MWNT cylinders in the wear track obtained in air (Figure 19.20(a))
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Figure 19.21 Scanning electron micrographs of dispersed graphitized MWNT coating. (a) Wear surface of MWNT coating after contact with Al-YSZ pin counterpart in ultrahigh vacuum. (b) MWNT patches in wear scar on Al-YSZ pin.
are absent from the wear track of the dispersed, graphitized MWNTs (Figure 19.21(a)). The smeared, agglomerated patches of MWNTs transferred to the Al-YSZ were found in the wear scar and at the edges of the wear scar. Although the wear scar contained such transferred MWNT wear patches, it revealed almost no wear of Al-YSZ. Both the surfaces of the quartz disk and Al-YSZ pin were covered with agglomerated patches of MWNTs and were protected from wear because of no direct contact between these surfaces. 19.3.2.5 Solid Lubrication Mechanisms of MWNTs Examining the friction and wear behavior of the MWNTs provided detailed information about friction properties, deformation, wear debris, and transferred wear fragments of MWNTs during sliding. The presence of a thin transfer film provided a low CoF. The presence of the MWNT cylinders in the wear track, in which amorphous carbon layers were formed upon the exterior of the MWNTs during sliding, also contributed to the CoF. In general, the low CoF can be attributed to the combination of the transfer film and/or tubular MWNTs. Based on the experimental results, the following solid lubrication mechanisms can be postulated: Aligned MWNTs When an aligned-MWNT-coated quartz disk (MWNT/Fe/quartz) is brought into contact with a smooth rounded surface of 440C stainless steel or Al-YSZ ceramic, three factors contribute toward reducing the CoF: (1) Direct contact between the quartz or iron and the 440C stainless steel or Al-YSZ is avoided by agglomerated patches of MWNTs. (2) The shear strength and the surface energy of the interface [7,33] is minimized by agglomerated patches of MWNTs. (3) The real area of contact [7,33] is minimized because of the high elastic moduli of the MWNTs, Al-YSZ, and quartz. Dispersed MWNTs When a dispersed MWNT coating on quartz disk (MWNT/quartz) is brought into contact with a smooth, rounded surface of Al-YSZ ceramic, three factors are contributing toward reducing the CoF: (1) Friction resistance is minimized by the rolling motion of the cut or broken MWNTs and the short graphene lamellae in the wear track. (2) The real area of contact is minimized by the high elastic modulus of the MWNTs, Al-YSZ, and quartz. (3) The surface energy at the interface is minimized by the residual MWNTs.
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Conclusions on MWNT Tribology
To evaluate recently developed aligned MWNT coatings and dispersed MWNT coatings for solid-film lubrication applications, unidirectional sliding friction experiments were conducted with the MWNTs in sliding contact with hemispherical Al-YSZ ceramic pins and 440C stainless steel balls in air and in ultrahigh vacuum. The main criterion for evaluating the solid-film lubrication performance of the materials was the CoF, which had to be less than 0.15 in a given environment. The following conclusions were drawn: 1. MWNTs met the friction criterion and had superior friction properties and endurance lives in air or ultrahigh vacuum under dry conditions. The CoF of MWNTs is close to 0.05 and 0.009 in air and in ultrahigh vacuum, respectively. The wear life of MWNTs exceeds 1 million passes in air and in ultrahigh vacuum showing good durability. 2. Prearranged or prepatterned nanostructure, such as in the aligned MWNT coating, is not necessary for MWNTs to provide solid-film lubrication. The dispersed MWNT coating is superior to the aligned MWNT coating. 3. Three factors contribute toward reducing the CoF and providing a good, durable performance of the MWNT coating: (a) Friction resistance is minimized by the cut or broken MWNTs and the short graphene lamellae in the wear track. (b) The real area of contact is minimized by the high elastic modulus of the MWNTs, Al-YSZ, and quartz. (c) The surface energy at the interface is minimized by the residual MWNTs. 19.3.3
19.3.3.1
Single-walled and Surface Fluorinated Nanotube Investigations
Background and Objectives
The performance of solid lubricants largely depends upon the particle size and their shape at the nanoscale level [34–37]. Modeling and experimental studies suggest that the cagelike nanosize particles having either spherical or tubular morphology will provide great application advantages in the field of tribology [37]. Their seamless structure helps to inhibit the sticking and burnishing of the nanoparticles by the rubbing metal or other surfaces. These tubular particles may slide and roll in part during sliding contact, resulting in low friction and wear. The primary structures may also crack open during contact between the tribocouples leading to small graphitic low surface energy layers which behave similar to graphite. The spherical nanoparticles also can serve as effective spacers, prohibiting contact and wear of the metal surfaces under heavy loads where fluid lubricants are normally squeezed out. Other advantages include the superior oxidation and thermal stability of the tubular and spherical nanoparticles, prolonging their wear life. For example, as mentioned in Section 19.3.1.2, the 0.04–0.05 CoF obtained with the CNO/Krytox mixture in air was attributed to the CNO, which is well below the typical reported values for graphite of 0.13– 0.3 [38] or the Krytox oil. The discovery of synthetic methods to produce CNTs, structurally built of graphene cylinders, opened the research opportunities for a variety of applications, including lubricants. Surface modification of the CNTs as well as other carbon nanoparticles, CNOs [2] and nanodiamonds [39], through chemical treatment [12], e.g., fluorination [10,40], is expected to affect their friction and degradation behavior in lubricant applications. This expectation is supported by the experimental studies of graphite fluoride (CF)x powder films
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that demonstrate longer wear lives, low CoF and superior load-carrying capacities in comparison with graphite both in humid air and at elevated temperatures due to weakened interlamellar van der Waals’ forces [41,42]. The intent of this work is to examine the effect of surface modification of SWNTs on their tribological properties. Reported below is the evaluation data on CoF and wear life of neat lubricating films prepared from SWNT and fluorinated SWNT, “fluoronanotubes”, with variable Cn F (n = 2–20) stoichiometry. Samples of pristine and oxidative acid treated nanotubes, and the nanotubes which were short-cut by the fluorination-pyrolysis method [13] were also tested for comparison. 19.3.3.2 Nano- and Microstructure of SWNTs High resolution TEM images (Figure 19.22) show significantly different surface morphologies for all chemically treated nanotube samples in comparison with the pristine SWNTs. The SWNT form bundles of different diameter due to the random nature of the way they are collected and mounted. These bundles are held together by strong wall-to-wall van der Waals’ forces. Smooth sidewall surfaces of thick SWNT bundles (Figure 19.22(a)) generate slight protrusions as a result of oxidative acid (HNO3 ) treatment under mild conditions which creates minor defects on the sidewalls of nanotubes, cuts them into shorter lengths and opens their ends, as shown by the image of a cut-SWNT sample in Figure 19.22(b). Fluorination causes more dramatic changes in SWNT surface appearance by increasing both the size and number of protrusions on the sidewalls of nanotubes in C2 F and C5 F samples (Figure 22(c), (d)) that can be related to a great number of sp3 carbon–carbon bonds formed via the sidewall functionalization [12,40]. Significant reduction in bundle size is also noted for these fluoronanotubes. Treatment of the C2 F sample with hydrazine helps to remove fluorine without causing any significant destruction to the sidewalls of nanotubes in the resulting C20 F sample. The TEM image (Figure 19.22(e)) of this sample shows a largely restored smooth surface morphology, as in pristine SWNTs. In contrast with this sample, some surface areas of F-cut-SWNT (Figure 19.22(f)), are partially damaged and appear as split open tubes. This can be correlated with the persistent showing of the sidewall “defect” mode in the Raman spectra of nanotubes cut by fluorination [13]. The CoF determined for all tested neat nanotube samples at four relative disk coating thicknesses are summarized in Figure 19.23. These data show that almost all measured CoF lie well below the published range of values for graphite of 0.13–0.3 [38], the most commonly used solid lubricant in air environment, with the exception of only a very few values falling into a low vicinity of this range. This clearly indicates that all tested SWNT samples exhibit very good friction properties. However, for most samples tested the relationship between CoF and coating thicknesses was found to be inconsistent. Thus, in the case of pristine SWNTs a steady increase in coating thickness results in consistent lowering of the CoF, while similar increases in coating thickness for cut-SWNTs cause negligible effect, always yielding a CoF as low as 0.07–0.09. A steady decrease of friction coefficient is observed for fluoronanotubes C2 F and C20 F samples with increase in coating level from 0.63 to 1.89 µg/mm2 . At the highest coating level (2.52 µg/mm2 ) for C2 F and C20 F and at 1.89 µg/mm2 for F-cut-SWNTs, the friction coefficient again
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Figure 19.22 High-resolution transmission electron micrographs of SWNT samples studied. (a) Nascent SWNTs. (b) cut-SWNTs. (c) C2 F Stoichiometry. (d) C5 F Stoichiometry. (e) C20 F Stoichiometry. (f) F-cut-SWNTs.
increases. The C5 F samples demonstrate a very low friction (0.02–0.05) at 0.63, 1.26 and 2.52 µg/mm2 thicknesses, but show an elevated value (0.2) at 1.89 µg/mm2 . The observed
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Figure 19.23 Friction coefficients of SWNT samples determined at different relative coating thickness in contact with sapphire in air.
Figure 19.24
Lowest friction coefficients determined for SWNT samples in contact with sapphire in air.
discrepancy is likely related to the difficulty in applying a uniform coating of the nano materials onto the disk in some experiments. Nevertheless, the measured lowest CoF for SWNT samples in air (Figure 19.24) were found to either fall into the range known for the best lubricants, such as DLC (0.05–0.15) and Teflon (0.03–0.1), or even outperform the latter. For instance, F-cut-SWNTs and C5 F samples show very low values of 0.013 and 0.016, respectively, pristine SWNTs-0.011, while a C20 F sample yields an ultra-low friction coefficient of 0.002. It is likely that the lowest friction shown by these four SWNT samples in a humid air environment can be
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related both to the smooth (or relatively smooth) sidewall surface morphology and to the drastically increased surface area in the case of very short F-cut-SWNTs. It also appears that having a small amount of residual fluorine on the sidewall of the nanotube assists in obtaining an ultra-low friction, as observed for C20 F (0.002). Finally, as Figures 19.23 and 19.24 show, all materials tested exhibit CoF substantially lower than traditional carbon materials and generally better than DLC films. The SEM observations of the wear tracks indicated that although most nanotubes were generally plowed out and piled at both sides of the wear track, a small amount of tubular particles remained in the wear track. The measured relative order of CoF can be understood on the basis of material composition. By reference to bulk materials, fluorination can improve the lubricity of carbon materials. Yet fluorination can introduce “defects” within the SWNT sidewalls. These defects may result in premature degradation of the material (tubular structure) and corresponding loss of lubrication. Upon degradation, reactive edge sites will be created leading to binding between the lubricant and adjacent surfaces. Furthermore, sp3 hybridization of sidewall carbons will reduce the flexibility, modulus and tensile strength of the SWNT. Hence a lower degree of fluorination may provide a more resilient material, better able to resist buckling than a more highly fluorinated material. Notably this stands in contrast to bulk materials and arises from the nanosize scale of these lubricants. A second consideration is that fluorination will act to separate tubes within bundles. While some separation may be desirable, it is possible that individual SWNTs may not be best because surface roughness exceeds their diameter. Hence they cannot prevent contact between surface asperities like MWNT and CNO. Moreover, tubes within bundles permit the possibility of intertube sliding whereas single SWNTs necessarily slide between adjacent tribological surfaces. Under the conditions studied, the highest endurance or wear life was demonstrated by the pristine SWNT sample (Figure 19.25). This was followed by the C20 F and F-cut-SWNT materials. The other three nanotube samples show much lower wear lives as lubricants. These data show that the wear lifetimes exhibit a roughly inverse correlation with CoF: lower friction coefficient correlates with longer lubrication lifetime. Interestingly, the C20 F material shows a lifetime a bit lower than the pristine SWNTs. This can be understood on the basis of the fluorination introducing defects, namely sp3 hybridization sites within the SWNT sidewalls. These sites disrupt the integrity of the aromatic framework and create sites where buckling or other degradation can occur. The modest amount of F in the C20 F material results in its performance having somewhat less duration than the SWNT material. Notably, it has a longer wear life than any of the other fluorinated materials, all of which possess a higher F:C stoichiometry. Increasing F content necessarily introduces larger amounts of wall disruption, hastening degradation and shortening lubricant lifetime. While the F-cut-SWNT materials nominally have the same composition as the C5 F materials, their smaller length may aid lubrication. As they are produced by pyrolysis, the tube ends are expected to be closed by either bonding to adjacent carbon or the carbon atoms are terminated by –F or –H atoms. Notably, these groups are more thermodynamically stable than oxygen containing functional groups. For the cut SWNTs, the cutting action has been shown to introduce significant amounts of oxygen containing functional groups at the tube ends, terminating the carbon valencies. Apart from their reactivity, these groups can readily oxidize the SWNT ends during friction testing, thereby degrading the lubricant. Moreover,
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Figure 19.25
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Endurance (wear) life for SWNT lubricating coatings in contact with sapphire in air.
upon oxidation, radical sites will be created that will cause stiction with adjacent surfaces, thereby accounting for the relatively high friction coefficient. 19.3.3.3 Conclusions on SWNT Tribology Tribological studies of a series of SWNT samples in air revealed that the type of chemical treatment of nanotube surface has a significant effect on their lubrication properties. The CoF for fluoronanotubes, as well as pristine and chemically cut nanotubes, were found to reach values as low as 0.002–0.07, thus showing a promise for application of surface modified SWNTs as solid lubricants. Based on combined friction and wear life data, pristine SWNTs and C20 F samples show the best lubrication performance in air among all SWNT samples investigated thus far. We interpret the trend in SWNT materials as lubricants being partly related to the degree to which they can fill in pits and scratches, and between surface asperities, etc. between sliding surfaces. If this were the only mechanism, then all tubes would behave similarly; hence there are additional effects from the chemical nature of the surface modifications. A modest amount of fluorination can serve to break up SWNT bundles, without significant tube wall degradation, thereby creating a better lubricant. While cut SWNTs and F-cut-SWNTs should similarly have tube segments commensurate with surface roughness values, their production alters the graphitic quality of the SWNTs (on the tube ends), leading to a poorer lubricating ability. Magnifying this trend is the higher fluorination stoichiometry of the C2 F and C5 F materials. Though producing a nominally better lubricant by reference to bulk materials, their synthesis leads to substantial SWNT degradation (by
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introduction of sp3 hybridization, etc.). Consequently these highly fluorinated SWNTs can be less resilient towards deformation and more apt to rupture, producing dangling bonds and resulting stiction.
19.4
CONCLUDING REMARKS
While CNT and CNO have not enjoyed commercialization like other carbon materials such as DLC and GLC, the nanomaterials possess distinct advantages that will eventually lead to commercialization. A major problem in this field has been the expense of materials, driven by the manner of synthesis and requirements of further purification for the CNT. Development of inexpensive, commercially feasible, industrial scale production processes for CNO, on the other hand, are close to realization. A second problem for developing applications is the difference between nano materials obtained from different processes described by various researchers in the field, a problem which will be overcome by commercial production of these materials. In our efforts at Glenn Research Center, we have relied on numerous suppliers of MWNT and SWNT, and have developed the technology to produce large quantities of pure, high-quality CNO. As can be seen in this chapter, the conditions for successful deployment of these nano structured materials is highly dependent on the environment, the tribocouples involved and the nanomaterials employed. With proper choice of system, it is possible to obtain ultra low friction and long wear life. These materials would then appear to be reasonable choices to consider for replacing graphite, one of the most widely used solid lubricants.
REFERENCES [1] Miyoshi, K., Street, K.W., Jr. Novel carbons in tribology. Tribol. Int. 37 (2004), 865–868. [2] Street, K.W., Marchetti, M., Vander Wal, R.L., Tomasek, A.J. Evaluation of the tribological behavior of nano-onions in Krytox 143AB. Tribol. Lett. 16(1–2) (2004), 143–149. [3] Vander Wal, R.L., Miyoshi, K., Street, K.W., Tomasek, A.J., Peng, H., Liu, Y., Margrave, J.L., Khabashesku, V.N. Friction properties of surface-fluorinated carbon nanotubes. Wear 259 (2005), 738–743. [4] Miyoshi, K.W., Street, K.W., Jr., Vander Wal, R.L., Andrews, R., Sayir, A. Solid lubrication by multiwalled carbon nanotubes in air and in ultrahigh vacuum. Tribol. Lett. 19(3) (2005), 191–201. [5] Pepper, S.V., Kingsbury, E.P. Spiral orbit tribometry—Part I: Description of the tribometer. Tribol. Trans. 46(1) (2003), 57–64. [6] Pepper, S.V., Kingsbury, E.P. Spiral orbit tribometry—Part II: Evaluation of three liquid lubricants in vacuum. Tribol. Trans. 46(11) (2003), 65–69. [7] Miyoshi, K. Lubrication by diamond and diamondlike carbon coatings. J. Tribology 120 (1998), 379–384. [8] Vander Wal, R.L., Tomasek, A.J., Street, K.W., Thompson, W.K. Carbon nanostructure examined by lattice fringe analysis of high resolution transmission electron microscopy images. Appl. Spectr. 58(2) (2004), 230–237. [9] Chiang, I.W., Brinson, B.E., Huang, A.Y., Willis, P.A., Bronikowski, M.J., Margrave, J.L., Smalley, R.E., Hauge, R.H. Purification and characterization of single-wall carbon nanotubes (SWNTs) obtained from the gas-phase decomposition of CO (HiPco Process). J. Phys. Chem. B 105 (2001), 8297-8301. [10] Khabashesku, V.N., Billups, W.E., Margrave, J.L. Fluorination of single-wall carbon nanotubes and subsequent derivatization reactions. Acc. Chem. Res. 35 (2002), 1087–1095. [11] Gu, Z., Zhang, L., Margrave, J.L., Davydov, V.A., Rakhmanina, A.V., Agafonov, V., Khabashesku, V.N. Fluorination of pressure-polymerized C60 phases. Carbon 43 (2005), 2989–3001.
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[12] Khabashesku, V.N., Margrave, J.L. Chemistry of carbon nanotubes. In: Nalwa, H.S. (Ed.), Encyclopedia of Nanoscience and Nanotechnology, vol. 1. American Scientific Publishers, Stevenson Ranch, CA, 2004, pp. 849–861. [13] Gu, Z., Peng, H., Hauge, R.H., Smalley, R.E., Margrave, J.L. Cutting single-wall carbon nanotubes through fluorination. Nano Lett. 2 (2002), 1009–1013. [14] Street, Jr., K.W., Pepper, S.V., Wright, A., Grady, B. Determination of lubricants on ball bearings by FT-IR using an integrating sphere. NASA/TM—2006-214472, 2006. Available from http://gltrs.grc.nasa.gov. [15] Donnet, J.B., Bansal, R.C., Wang, M.-J. Carbon Black Science and Technology, second edition. Marcel Dekker, Inc., New York, 1993. [16] Thomas, J.M. In: Walker, Jr., P.L. (Ed.), The Chemistry and Physics of Carbon, vol. 1. Marcel Dekker, Inc., New York, 1965, Chapter 2. [17] Marsh, H. Introduction to Carbon Science. Butterworth, London, 1989, Chapter 4. [18] Rosner, D.E., Allendorf, H.D. Comparative studies of the attack of pyrolitic and isotropic graphite by atomic and molecular oxygen at high temperatures. AIAA J. 6 (1968), 650–654. [19] Davis, K.A., Hurt, R.H., Yang, N.Y., Headley, T.J. Evolution of char chemistry, crystallinity, and ultrafine structure during pulverized-coal combustion. Combust. and Flame 100 (1995), 31–40. [20] Vander Wal, R.L., Choi, M.Y. Pulsed laser heating of soot: Morphological changes. Carbon 37(2) (1999), 231–239. [21] Tuinstra E., Koenig, J. Raman spectrum of graphite. J. Chem. Phys. 53 (1970), 1126–1130. [22] Hiura, H., Ebbsen, T.W., Tanigaki, K., Takahashi, H. Raman studies of carbon nanotubes. Chem. Phys. Lett. 202(6) (1993), 509–512. [23] Braithwaite, E.R. Solid Lubricants and Surfaces. Pergamon Press, New York, 1964, Chapter 5. [24] Wan, G.T.Y., Spikes, H.A. The behavior of suspended solid particles in rolling and sliding elastohydrodynamic contacts. Tribol. Trans. 31(1) (1988), 12–21. [25] Wunsch, F. Synthetic fluid based lubricating greases. NLGI Spokesman 54(1) (1991), 12–22. [26] Hirata, A., Igarashi, M., Kaito, T. Study on solid lubricant properties of carbon onions produced by heat treatment of diamond clusters or particles. In: Miyoshi, K., Street, K.W. (Eds.), Novel Carbons in Tribology. Tribol. Int. 37(11–12) (2004), 899–905. [27] Iijima S. Helical microtubules of graphitic carbon. Nature 354(6348) (1991), 56–58. [28] Yu, M.-F., Files, B.S., Arepalli, S., Ruoff, R.S. Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties. Phys. Rev. Lett. 84 (2000), 5552–5555. [29] Hirata, A., Yoshioka, N. Sliding friction properties of carbon nanotube coatings deposited by microwave plasma chemical vapor deposition. In: Miyoshi, K., Street, K.W. (Eds.), Novel Carbons in Tribology. Tribol. Int. 37(11–12) (2004), 893–898. [30] Fernandez-Palacio, J., Arce-Garcia, I., Bull, S.J. Indentation response of fullerene-like CNx. In: Miyoshi, K., Street, K.W. (Eds.), Novel Carbons in Tribology. Tribol. Int. 37(11–12) (2004), 929–940. [31] JolyPottuz, L., Dassenov, F., Vacher, B., Martin, J.M., Mieno, T. Ultralow friction and wear behaviour of Ni/Y-based single wall carbon nanotubes. In: Miyoshi, K., Street, K.W. (Eds.), Novel Carbons in Tribology. Tribol. Int. 37(11–12) (2004), 1013–1018. [32] Miyoshi, K., Vander Wal, R.L., Tomasik, A.J., Sayir, A., Farmer, S.C. New effective material couple— oxide ceramic and carbon nanotube—developed for aerospace microsystem and micromachine technologies. NASA/TM—2004-212729, 2004. Available from http://gltrs.grc.nasa.gov. [33] Miyoshi, K. Solid Lubrication Fundamentals and Applications. Marcel Dekker, Inc., New York, 2001, pp. 94–144. [34] Glaeser, W.A. Characterization of Tribological Materials. Butterworth-Heinemann, Boston, 1993, p. 1. [35] Lansdown, A.R. Lubrication and Lubrication Selection. A Practical Guide, Edmunds, B.S. (Ed.). Mechanical Eng. Publ. Ltd., Suffolk, UK, 1996. [36] Summers-Smith, J.D. An Introductory Guide to Industrial Tribology. Mechanical Eng. Publ. Ltd., London, UK, 1994. [37] Tenne, R., Homyonfer, M., Feldman, Y. Nanoparticles of Layered Compounds with hollow cage structures (inorganic fullerene-like structures). Chem. Mater. 10 (1998), 3225–3238. [38] Pierson, H.O. Handbook of Carbon, Graphite, Diamond and Fullerenes. Properties, Processing and Applications. Noyes, New York, 1993, Chapter 3.
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[39] Dolmatov, V.Yu. Detonation synthesis of ultradispersed diamonds: Properties and applications. Russ. Chem. Revs. 70 (2001), 607–626. [40] Liu, Y., Gu, Z., Margrave, J.L., Khabashesku, V.N. Functionalization of nanoscale diamond powder: Fluoro-, alkyl-, amino-, and amino acid-nanodiamond derivatives. Chem. Mater. 16 (2004), 3924–3930. [41] Gisser, H., Petronio, M., Shapiro, A. Graphite fluoride as a solid lubricant. Lubr. Eng. 28 (1972), 161–164. [42] Kamarchik, P., Margrave, J.L. Poly (carbon monofluoride), a solid layered fluorocarbon. Acc. Chem. Res. 11 (1978), 296.
– 20 – Superlubricity of CNx-coatings in Nitrogen Gas Atmosphere Koji Kato and Koshi Adachi Tohoku University, Aramaki-aza-aoba, Sendai 980-8579, Japan
20.1
INTRODUCTION
The carbon nitride is supposed to have the hardness higher than that of diamond if it has the ideal atomic structure of β-C3 N4 [1,2]. However such an ideal structure with extreme hardness is hardly formed by the deposition of carbon in the presence of nitrogen. The carbon nitride introduced in this chapter is much more different from the ideal β-C3 N4 , and contains 12–13% nitrogen in an amorphous structure of carbon giving hardness values of about 30 GPa. Because of this reason, the carbon nitride coating of this chapter will be referred to as CNx-coating. These CNx-coatings exhibit friction coefficients below 0.01 when tested in a nitrogen gas atmosphere during sliding against itself [3], Si3 N4 [4,5], or steel [6] although these material combinations give friction coefficients higher than 0.1 in air. If the running-in process is taken place in oxygen for the initial sliding cycles, the following sliding in nitrogen gas gives the friction coefficient below 0.005 and the wear rate below 10−7 mm3 /Nm [3]. The observed low value of friction coefficient in the range of 0.005∼0.01 is believed to depend on the property of the tribologically generated product at the sliding interface in nitrogen gas atmosphere. Although the exact mechanism of the low friction is not yet understood, the various aspects of achieving low friction with CNx-coatings will be described in this chapter.
20.2 20.2.1
FUNDAMENTAL PROPERTIES OF CNx-COATINGS
Coating Method
CNx-coatings introduced in this chapter are produced on Si-wafers or Si3 N4 disks by having the deposition of carbon from a solid carbon target of 99.999% purity together with the mixing of nitrogen ions irradiated simultaneously from the ion beam gun. The carbon for Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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the coating on Si-wafer is sputtered from a carbon target by argon ion, and on Si3 N4 disk it is evaporated by heating with electron beam. The coating apparatus is schematically drawn in Figure 20.1 where the nitrogen ion gun for mixing, argon ion gun for sputtering, electron beam source for evaporation, and carbon target are shown together with rotary disk for the coating. The background and operating pressures in the vacuum chamber are lower than 2 × 10−4 Pa and 1.4 × 10−2 Pa, respectively. The acceleration voltage and the ion current of argon ions for sputtering is 1 keV and 100 mA, respectively. The deposition rate of carbon is monitored via calibrated quartz crystal oscillator and is varied in the range of 1∼50 nm/min. The energy and ion current density of assisted nitrogen ions were in the ranges of 0.5∼10 keV and in 10∼90 µA/cm2 , respectively. Substrates are sputter-cleaned
Figure 20.1 Coating apparatus with nitrogen ion gun for mixing, argon ion gun for sputtering, electron beam source for evaporation, carbon target, and rotary disk for the coating.
Figure 20.2 AFM image of CNx-coating formed on a Si-wafer by Ar ion sputtering of carbon target and IBMA of nitrogen, thickness: 100 nm, Rmax = 3.0 nm, Ra = 0.3 nm (a) and CNx-coating formed on a Si3 N4 disk by EB heating of carbon target and IBMA of nitrogen, thickness: 400 nm, Rmax = 880 nm, Ra = 50 nm (b).
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Figure 20.3 Typical surface roughness of CNx-coatings on Si-wafer (a) and Si3 N4 disk (b).
Figure 20.4 Hardness of CNx-coating of 100 nm thickness on Si-wafer measured by various indentation depths from 10 to 50 nm.
prior to deposition by 5 minutes bombardment with nitrogen ions of 1∼3 kV accelerate voltage and 100 µA/cm2 ion current density. 20.2.2
Hardness and Microstructure
The AFM images of CNx-coatings on Si-wafer and Si3 N4 disk are shown in Figures 20.2(a) and (b), and their typical surface profiles are shown in Figures 20.3(a) and (b). The big difference between coatings on Si-wafer and Si3 N4 disk is the surface roughness: Ra = 0.1∼0.3 nm and Rmax = 1∼3 nm at the coating of 100 nm thickness on Si-wafer, and Ra = 20∼80 nm and Rmax = 200∼800 nm at the coating of 400 nm thickness on Si3 N4
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Figure 20.5 FE-TEM image showing amorphous structure in cross section of CNx-coating on Si-wafer. Thickness: 100 nm.
Figure 20.6
Chemical composition of CNx-coating on Si-wafer analyzed by XPS.
disk. The hardness of coating on Si-wafer is about 30 GPa in the indentation depth from 10 to 50 nm as shown in Figure 20.4. The coating on Si3 N4 also showed the similar hardness value. Figure 20.5 shows the FE-TEM image of cross section of the coating on Si-wafer, where the micro structure of CNx-coating is confirmed as amorphous. Figure 20.6 shows the chemical composition of the coating on Si-wafer analyzed with the XPS, where the atomic concentration of nitrogen in the CNx-coating is observed as 12∼13%.
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20.3 20.3.1 or N2
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SUPERLUBRICITY OF CNx-COATING ON Si-WAFER SLIDING AGAINST Si3 N4 BALL Friction on CNx-coatings in Vacuum After Short Time Exposure to Air, O2
indexvacuum When the CNx-coating is rubbed against Si3 N4 ball with Ra = 2.0 nm, Rmax = 15.0 nm and the radius r = 4.0 mm under 100 mN load in the vacuum of 2 × 10−4 Pa immediately after coating without having the process of exposure of the coating surface to other gases, the friction coefficient fluctuates between 0.05 and 0.30 during running-in as shown in Figure 20.7. If the coating surface is once exposed to N2 , O2 and air of 7.4 × 104 Pa for 3 min, 3 min and 1 h respectively, the following sliding in vacuum of 2 × 10−4 Pa gives relatively lower values of friction coefficient as shown in Figure 20.7. It is obvious in the figure that 3 min exposure to O2 effectively stabilizes and reduces friction in vacuum but the exposure to N2 does not give a similarly strong effect. The 1 h exposure to air seems to give intermediate effect between those observed for O2 and N2 . 20.3.2
Friction on CNx-coatings in Gases of 7.4 × 104 Pa
When the CNx-coating is rubbed against Si3 N4 ball, the friction coefficient is quite different depending on the kind of surrounding gas. In Figure 20.8, friction is observed in each gas of 7.4 × 104 Pa after 1 h exposure of fresh coating surface to air of 35∼45 %(relative humidity, RH). Therefore, the initial surface condition of tested coatings in Figure 20.8 is similar to that used for air exposure in Figure 20.7, and the result for vacuum in Figure 20.8 is generated by the same process as that for air exposure in Figure 20.7. The friction coefficient in the former case is 0.04 and in the latter case 0.05, which confirms the similar effect of testing process on both cases. The coating of this kind of exposure experience to air before sliding gives the friction coefficient higher than 0.36 in O2 , lower than 0.01 in N2 and about 0.03 in CO2 at the
Figure 20.7 The friction behavior of CNx-coating in vacuum of 2 × 10−4 Pa just after its deposition, and after its exposure to N2 , O2 and air of 7.4 × 104 Pa for 3 min, 3 min and 1 h respectively.
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Figure 20.8(a) The effect of sliding cycles on friction coefficient at Si3 N4 ball/CNx on Si-wafer in air, O2 , CO2 and N2 of 7.4 × 104 Pa, and vacuum of 2 × 10−4 Pa.
Figure 20.8(b) The effect of surrounding gas or vacuum on friction coefficient at 240th cycle in (a). CNx-coating are exposed to air for 1 h after deposition before the test in each gas or vacuum.
steady state as shown in Figure 20.8(b). The friction coefficient of 0.16 observed in air of 7.4 × 104 Pa seems an intermediate value between those in O2 and N2 . By recognizing the big difference in values of friction coefficient depending on the exposure experience and the surrounding gas, the friction in N2 with the friction coefficient below 0.01 may be considered as the result of generating “some super lubrious materials” at the contact.
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Figures 20.9(a), (b) and (c) show the optical images of wear scars on Si3 N4 balls observed after 240 friction cycles in N2 , O2 and CO2 respectively with the same test results as shown in Figure 20.8. The three images clearly show that the ball tip has always some layer sticking on the surface.
Figure 20.9 Si-wafer.
The optical images of wear scars on Si3 N4 balls after sliding of 240 cycles against CNx on
Figure 20.10 The optical images of wear scars on Si3 N4 ball and CNx on Si-wafer after sliding of 240 cycles in vacuum of 2 × 10−4 Pa under 100 mN load and 4 rpm. (a) Wear scar of ball, (b) Wear particles on CNx along sliding contact, (c) Sliding surface of CNx after ultrasonic cleaning.
Figure 20.11 The effect of N2 pressure on friction coefficient of CNx at steady state. The value of friction coefficient of 0.152 at zero pressure of N2 is observed in vacuum of 3 × 10−5 Pa.
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Figure 20.12
The effect of ball material on friction coefficient against CNx in N2 of 7.4 × 104 Pa.
Figure 20.10(a) shows the similar image of wear scar observed on the ball tip after 240 friction cycles in air of 7.4 × 104 Pa and Figure 20.10(b) the image of wear scar on the coating where fine wear particles form two parallel lines along the both sides of sliding contact. Figure 20.10(c) shows the same part of contact on the coating on Si wafer after ultrasonic cleaning, where almost all particles are gone and no serious surface damage is observed on the coating. These observations in Figures 20.9 and 20.10 confirm that a small amount of wear particles are produced at the sliding interface and some of them form a layer by sticking on the contact area of the ball and others form parallel gatherings sticking weakly on the coating along the contact zone. Among such layers formed on balls during sliding in various surrounding gases, the one formed in N2 results in superlubricity with a friction coefficient of less than 0.01. The lubricity of the layer is very sensitive to the pressure of the surrounding N2 gas as shown in Figure 20.11, where friction coefficient drops linearly by increasing the pressure of N2 gas and goes below 0.01 at around 10−5 Pa. Figure 20.12 shows the effect of ball material on friction in N2 , where Si3 N4 ball gives the shortest running-in period to reach the steady low friction coefficient of about 0.02. Al2 O3 , SUJ2 and SiC give higher friction coefficients of 0.10, 0.10 and 0.15, respectively. This result confirms that the ball material is important for having lubricious layer in repeated sliding against CNx-coating in N2 .
20.4
SUPERLUBRICITY OF CNx-COATING ON Si3 N4 DISK SLIDING AGAINST Si3 N4 BALL OR CNx-COATING ON Si3 N4 BALL
Figure 20.13 shows the schematic drawing of the friction tester which has a tube of gas supply to the sliding interface in air. The CNx coated Si3 N4 disk slides against a ball at 250 rpm with the sliding velocity of 0.20∼0.27 m/s. Figure 20.14(a) shows the effect of
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sliding cycles on friction under 1 N load in air of 20∼40% (RH) for the contact material combinations of Si3 N4 ball/Si3 N4 disk, CNx on ball/Si3 N4 disk, Si3 N4 ball/CNx on disk and CNx on ball/CNx on disk. The friction coefficient at Si3 N4 ball/Si3 N4 disk is constantly high with the value of about 0.8, and it stays at 0.25∼0.40 in other three combinations. Figure 20.14(b) clearly shows the beneficial effect of N2 on reducing friction by supplying N2 gas stream to the inlet of contact with a flow rate of 2.1 cc/mm2 s (2.0 L/min) through the tube. In the case of Si3 N4 ball/CNx on disk, the friction coefficient at steady state is reduced from 0.24 to 0.10, and in the case of CNx on ball/CNx on disk from 0.25 to 0.07. Figure 20.15 confirms the most effective reduction of friction by N2 stream among the effects of streams of N2 , O2 , dry air and humid atmospheric air, where the steady state friction coefficients are observed as 0.07, 0.11, 0.16 and 0.25 in N2 , dry air, O2 and humid air respectively. The effect of N2 on reducing friction shown in Figure 20.14(b) is much more enhanced by supplying N2 to the sliding interface after a certain number of sliding cycles in air. It is shown in Figure 20.16 where N2 is supplied to the sliding interface after 1000 cycles of running-in in air and the quick reduction in friction is observed with both (a) Si3 N4 ball/CNx on disk and (b) CNx on ball/CNx on disk. This kind of running-in effect on friction in N2 stream is more strongly generated when the atmosphere for running-in is O2 for the first 50 cycles as shown in Figure 20.17(c). For comparison, Figure 20.17(a) describes the friction curve in the N2 stream supplied from the 1st friction cycle, and Figure 20.17(b) the friction curve with running-in in air for the first 100 cycles. The friction coefficients at the 10,000th cycle in steady state are observed in the figure as 0.07 in (a), 0.03 in (b) and 0.005 in (c), which shows the importance of running-in process for having a low and steady friction. The result of Figure 20.17(c) may mean that some super lubricious materials are produced at the sliding interface. The optical photos of Figure 20.18(a) show the images of wear scars generated on the ball in N2 stream at the 10th, 100th and 10,000th cycles, where the wear scar of about 100 µm diameter is already observed at the 10th friction cycle and the similar size of wear scar is still observed at the 100th cycle. It is grown up to about 500 µm diame-
Figure 20.13 Schematic image of friction tester with a tube of gas supply in air. Tube diameter = 4 mm, Gas flow rate = 2.1 cc/mm2 s (2 L/min), distance between ball center and tube end = 10 mm.
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Figure 20.14 The friction curves in 104 sliding cycles in air (a) and in the stream of N2 (b) for the sliding contacts of Si3 N4 /Si3 N4 , CNx/Si3 N4 , Si3 N4 /CNx and CNx/CNx.
ter at the 10,000th cycle. These three observations are made along the friction curve in Figure 20.17(a). Figure 20.18(b) shows the images of wear scars of similar size of about 100 µm diameter observed at the 10th, 100th and 10,000th friction cycles. These three ob-
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Figure 20.15 The effects of gases on friction at CNx on Si3 N4 ball/CNx on Si3 N4 disk in 104 sliding cycles. At the steady state, μ = 0.07 in N2 , μ = 0.11 in dry air, μ = 0.16 in O2 , μ = 0.25 in humid air.
servations are made along the friction curve in Figure 20.17(c) where O2 is supplied for the first 50 cycles and it is switched with N2 at the 50th cycle for the following up to 10,000 cycles. It is obvious that the size of wear scar is not changed from 100th to 10,000th cycle. Figure 20.19 summarizes the values of steady state friction coefficients and wear rates (specific wear amounts, mm3 /Nm) observed for the CNx-coated ball/CNx-coated disk in humid air, O2 stream, N2 stream, O2 stream for the first 50 cycles and N2 stream in the following cycles, and humid air for the first 100 cycles and N2 stream in the following cycles. The wear rate is measured from the ball surface. It is important to notice that the running-in in a proper atmosphere effectively reduces friction and wear in the following sliding in N2 stream.
20.5
MECHANISMS OF LOW FRICTION AND LOW WEAR OF CNx-COATINGS
There must be some differences in the properties of CNx-coating formed by sputtering of carbon target and deposition of carbon on smooth Si-water and that formed by heating of carbon target and deposition of carbon on rough Si3 N4 disk. Indeed the initial roughness of coating is much different on these two kinds of coatings as shown in Figures 20.3(a) and (b). Residual gases remaining in the vacuum chamber in Figure 20.7 and Figure 20.8 must be also different. In the case of a stream of gas supplied from a tube in Figure 20.13 unexpected gases must be involved from the surrounding air. Although many unknown factors can be thought in this way as influential to the above observed results, the strong effect of
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Figure 20.16 The quick reduction in friction coefficient by supplying N2 at the 1000th cycle after running-in in air. (a) Si3 N4 ball/CNx on Si3 N4 disk, (b) CNx on Si3 N4 ball/CNx on Si3 N4 disk.
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Figure 20.17 The reduction in friction coefficient by supplying N2 starting at the 1st cycle in air (a), 100th cycle after running-in in air (b) and 50th cycle after running-in in O2 stream in air (c) with CNx on Si3 N4 ball/CNx on Si3 N4 disk.
Figure 20.18 Optical images of wear scars on CNx-coated Si3 N4 ball rubbed against CNx on Si3 N4 disk. (a) Wear scars at 10th, 100th and 10,000th cycles in the N2 stream, (b) Wear scars at 10th and 100th cycles in the O2 stream and the one at 10,000th in the N2 stream started after 50th cycle in the O2 stream.
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Figure 20.19 The friction coefficients in steady-state and specific wear amounts observed with CNx on Si3 N4 ball/CNx on Si3 N4 disk under 1 N load at 0.21 m/s in air, in O2 stream, in N2 stream supplied at the 1st cycle in air, 50th cycles after running-in in O2 stream and 100th cycle after running-in in air.
Figure 20.20(a) The effect of relative humidity in N2 of 1.03 × 105 Pa on friction coefficient of Si3 N4 ball/CNx on Si3 N4 disk in 15000 sliding cycles.
N2 in reducing friction at CNx/CNx and Si3 N4 /CNx is clearly observed in general. Some strong influential factors involved in the mechanisms of low friction are discussed below.
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Figure 20.20(b) The effect of relative humidity in N2 of 1.03 × 105 Pa on friction coefficient of CNx on Si3 N4 ball/CNx on Si3 N4 disk in 15000 sliding cycles.
20.5.1
The Effect of Humidity in N2 on Friction
Figures 20.20(a) and (b) show the change of friction coefficient caused by the introduction of water vapor into the test chamber which is filled with N2 of 1.03 × 105 Pa [7]. The initial running-in for 100 cycles is carried in air before the replacement with N2 by expecting the same running-in effect observed in Figure 20.16. In both cases of contact of Si3 N4 ball/CNx on Si3 N4 disk and CNx on Si3 N4 ball/CNx on Si3 N4 disk in the figure, the friction coefficient increases as a quick response to the increase in relative humidity from 2 to 45%. A remarkable difference in their responses is the fluctuation of friction coefficient which is very large for Si3 N4 ball/CNx on Si3 N4 disk and very small for CNx on Si3 N4 ball/CNx on Si3 N4 disk. Figure 20.21 is described from Figures 20.20(a) and (b) for showing the effect of relative humidity on friction coefficient in N2 in a different way, where the linear relationship between the friction coefficient and the relative humidity is observed in 2–45% for CNx on Si3 N4 ball/CNx on Si3 N4 disk and similar linearity is observed in 2–40% for Si3 N4 ball/CNx on Si3 N4 disk. Below the relative humidity of about 4%, the friction coefficient is almost the same for both material combinations and the extrapolated value of friction coefficient at 0% is about 0.015 on the axis of friction coefficient. Therefore, the friction coefficient of 0.009 observed in Figure 20.8 must be a value which has well excluded residual water on the contact surfaces exposed to humid air before introducing N2 into the test chamber. Figure 20.22 describes the strong effect of residual water adsorbed in humid air of 90%(RH) on friction in the following sliding test in N2 stream surrounded by air of 20–30%(RH). It is shown there that the friction coefficient below 0.02 is attainable only when adsorbed residual water is well removed by heating at 200 ◦ C.
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Figure 20.21 The effects of relative humidity on friction coefficients at Si3 N4 ball/CNx on Si3 N4 disk and CNx on Si3 N4 ball/CNx on Si3 N4 disk under 400 mN load at 0.21 m/s in N2 .
Figure 20.22 The effect of water adsorbed in air of 90%RH on friction coefficient at CNx on Si3 N4 ball/CNx on Si3 N4 disk in the stream of N2 suurounded by air of 20∼30%(RH).
The steady state friction coefficient observed in Figure 20.14 and Figure 20.16 is mainly explained by considering a certain value of humidity of 0–10%(RH) introduced into the
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Figure 20.23 The humidity distribution around the sliding contact zone with N2 stream in air of 20%(RH). N2 flow rate = 2.1 cc/mm2 s, normal load = 400 mN, sliding speed = 0.21 m/s.
Figure 20.24 The effect of partial pressure of O2 or water vapor in N2 gas of 1.03 × 105 Pa on friction coefficient of CNx on Si3 N4 ball/CNx on Si3 N4 disk.
N2 stream from the surrounding humid air as shown in Figure 20.23 for the humidity distribution around the sliding contact zone with N2 stream in humid air of 18–20%(RH).
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The Effect of O2 in N2 on Friction
In the chamber filled with O2 , friction coefficient is increased up to 0.36 from 0.13 after 240 cycles at Si3 N4 ball/CNx on Si-water as shown in Figure 20.8(a). In the stream of O2 supplied to the contact interface at the inlet side in humid air, the steady state friction coefficient is 0.16 in Figure 20.15 and is higher than the value of 0.07 obtained similarly in N2 stream. These observations confirm that O2 does not reduce friction effectively like N2 . However, O2 is not effective like humidity in N2 to change friction in the range of concentration from zero to 12% (partial pressure of 0.2 × 105 Pa), which is shown in Figure 20.24 [7]. The big rise of friction coefficient caused by water vapor of the partial pressure of 0∼2 ×103 Pa is also shown in the figure to see the big difference of effectiveness between O2 oindexO2 and water vapor. O2 may be understood as harmless chemical in N2 for changing friction within the partial pressure of 0.2 × 105 Pa. The friction coefficient of 0.11 in Figure 20.15 observed in the stream of dry air must be generated, therefore, mainly by N2 in the dry air. 20.5.3
The Effect of Surface Roughness on Friction
High peaks of asperities cause high friction by the mechanism of mechanical interlocking. Low valleys of pits and pores work as reservoirs for free wear particles which cause abrasive or rolling action at the contact interface and increase or decrease friction. Isolated contacts of asperities reduce the chance of large scale stiction of contact surfaces by surface forces and meniscus force of adsorbed liquid film. The frictional change in the running-in process observed in Figure 20.7(a), Figure 20.8(a), Figure 20.12, Figure 20.14, Figure 20.15, Figure 20.16, Figure 20.17, and Figure 20.22 must be partly generated by the roughness change on friction surfaces caused by wear. Figure 20.25 shows the effect of initial surface roughness of CNx-coating on the friction coefficient in the running-in process with N2 stream at the inlet of contact in humid air [8]. The surface of the largest roughness (Rmax = 1.642 µm) takes the largest number of friction cycles (Nc = 4300 cycles) for reaching the steady state of friction coefficient μ = 0.030. The surface of the smallest roughness (Rmax = 0.499 µm) takes the smallest number of friction cycles (Nc = 200 cycle) for reaching the steady state of friction coefficient μ = 0.035. Although the mechanisms of rise and drop of friction coefficient observed in the runningin process in Figure 20.25 is not clear, it seems that the running-in period becomes shorter with smaller rise and drop of friction coefficient as the initial surface roughness becomes smaller. The running-in processes observed in Figure 20.8(a) and Figure 20.12 for N2 are understood by the small initial roughness (Rmax = ∼3 nm) of CNx-coating on Si-water, and those observed in Figure 20.14, Figure 20.15, Figure 20.16, Figure 20.17 and Figure 20.22 are understood by the large initial roughness of CNx-coating (Rmax = 0.88 µm) on Si3 N4 disk.
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Figure 20.25 The effect of initial surface roughness of CNx-coating on run-in friction of Si3 N4 ball/CNx on Si3 N4 disk in N2 stream. A: Rmax = 1.642 µm, Ra = 0.100 µm, B: Rmax = 0.673 µm, Ra = 0.043 µm, C: Rmax = 0.499 µm, Ra = 0.035 µm.
Figure 20.26 The relationship between the steady state friction coefficient and the steady state maximum roughness on wear scar of CNx on Si wafer in sliding against Si3 N4 ball in N2 . (T. Tokoroyama et al.)
The surface roughness on a wear scar in steady state is thus determined by wear depending on the initial surface roughnesses of the friction surfaces. Generally speaking, the initial high roughness generates high steady state roughness of wear scar and the high value of friction coefficient in steady state. Figure 20.26 by T. Tokoroyama et al. [9] shows the linear relationship between the friction coefficient and wear scar roughness of CNx-coating
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observed in N2 atmosphere. It is confirmed from the figure that steady state friction coefficient below 0.01 can be generated only when the wear scar is below 5 nm. It is shown by them at the same time that the resultant roughness on the wear scar controls the thickness of the tribolayer: the smaller roughness the thinner tribolayer in the similar range of nano meter. 20.5.4
Tribolayers of Superlubricity
It is well observed by F.B. Bowden and his co-workers [10] that diamond sliding against diamond gives friction coefficient larger than 0.8 in vacuum when surface contaminants are removed. Such a high friction coefficient is quickly reduced below 0.1 by exposing the contact surfaces to O2 or humid air, where humid air works better than O2 to reduce friction. The repeated sliding of diamond pin against DLC in air generates friction coefficient below 0.1 after about 100 friction cycles, and the low value of 0.02∼0.03 is observed when the initial combined average roughness of contact surfaces is below 10 nm [11]. In both cases of diamond/diamond and diamond/DLC, the microstructure of tribolayer which is expected to be formed on friction surfaces in air is unclear. It is assumed by D. Tabor and J.E. Field [12] as a compaction of wear debris, waxy deposit, hydrocarbons containing H, NH and OH, and its microstructure is assumed as amorphous with partial crystalline or graphitic. Its surface is supposed to have tightly bound CO and CH or CH2 . These observations and assumptions about low friction at diamond/diamond and diamond/DLC do not give any analogical solution to the observed results of friction and wear at Si3 N4 /CNx and CNx/CNx in N2 , if N2 is supposed to be inert and to give an atmosphere similar to vacuum.
Figure 20.27 The effects of N2 , air and vacuum on friction coefficient and wear rate in sliding of a diamond pin against DLC on disk. (Originally drawn with the data by K. Miyoshi et al.)
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Figure 20.28 The effects of dry N2 , ambient air, dry air and vacuum on friction coefficient at steel ball/CNx on Si wafer. (J.C. Sanchez-Lopez et al.)
Figure 20.29 The optical images of wear scars on the steel pins and CNx coatings after sliding tests in Figure 20.28. (J.C. Sanchez-Lopez et al.)
On the other hand, it is shown in Figure 20.27 by K. Miyoshi et al. [13] that diamond pin/DLC film gives much smaller friction coefficient of 0.015 and smaller specific wear amount of 10−7 mm3 /Nm in N2 than those in air. W. Zhang et al. got similar results with SiC pin/DLC on Si-wafer which showed the friction coefficients of 0.06 in N2 , 0.07 in dry air, 0.10 in O2 and 0.17 in vacuum [14]. Figure 20.28 confirms the effect of N2 in reducing friction for the contact between steel ball and CNx on Si-water [6]. In the figure,
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Figure 20.30 Si3 N4 disk.
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Raman spectrum on wear scar of CNx coated Si3 N4 ball after 104 sliding cycles against CNx on
friction coefficient drops from 0.10 to 0.01 after about 50 cycles in dry N2 although it stays at about 0.8 in UHV. The optical photos in Figure 20.29 [6] confirm that the low friction coefficient of 0.01 is generated by having a tribolayer sticking on the pin tip in dry N2 . The optical photos in Figure 20.9, Figure 20.10 and Figure 20.18 originally show various colors in the optical microscope such as red, green, blue, gray, brown and black, which means the tribolayer must be partly transparent. The analysis by Raman spectrum shown in Figure 20.30 tells a graphite-like structure is formed in the tribolayer [15]. This observation gives some explanation about the mechanism of superlubricity observed in this chapter if the graphitic structure of the tribolayer behaves similarly as graphite does in the experiment by H. Zhidi et al. where the friction coefficient are about 0.2 in O2 , 0.1 in water vapor and 0.02 in He or Ar at the sliding contact between steel pin and graphite plate [16]. The migration of He or Ar atoms into the lattice defects of graphite is supposed to cause the reduction of friction coefficient down to 0.02 in their study. This kind of model may give one type of explanation of the superlubricity observed in N2 atmosphere with CNx/CNx, Si3 N4 /CNx, Steel/CNx and diamond/DLC in this chapter. The model of termination of third-body molecules on diamond surface introduced by J. Harrison et al. [17,18] to explain the low friction and the model of hydrogen termination on DLC by A. Erdemir et al. [19,20] and J. Fontaine et al. [21] to explain the superlubricity of hydrogenated DLC in vacuum or nitrogen are another kinds which seem applicable to explain the superlubricity discussed in this chapter for CNx-coatings in N2 . Further observation and analysis of property and micro-chemical structure of the tribolayer are required for understanding the all behavior in friction and wear of those materials combinations.
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SUMMARY
It is experimentally confirmed by the authors [3–5,7,8,15] that the sliding of CNx-coating against itself or Si3 N4 in nitrogen gas atmosphere gives the friction coefficient in the range from 0.005 to 0.01 and the wear rate below 10−7 mm3 /Nm. The N2 -effect of reducing friction and wear is further enhanced by exposing the running-in process to O2 or humid air. The analysis of the tribolayer formed on the wear scar by Raman shows the existence of graphite-like structure. Therefore, the key of understanding the mechanism of low friction with CNx-coatings in nitrogen gas seems to exist in the interaction between the graphitelike structure of the tribolayer and the surrounding nitrogen. Finer chemical and structural analyses of the tribolayer formed in N2 and other gasses are required in this viewpoint. The property of superlubricity of tribolayers formed in N2 on wear scars in sliding will be better understood in this way and the base of N2 -lubrication will be established.
REFERENCES [1] Liu, A.Y., Cohen, M.L. Prediction of new low compressibility solid. Science 245 (1989), 841–842. [2] Liu, A.Y., Cohen, M.L. Structural properties and electronic structure of low compressibility materials: βSi3 N4 and hypothetical β-C3 N4 . Phys. Rev. B 41(15) (1990), 10727–10734. [3] Adachi, K., Wakabayashi, T., Kato, K. The effect of sliding history on the steady state friction coefficient between CNx coatings under N2 -gas lubrication. In: Dowson, D. et al. (Eds.), Proceedings of the 31th Leeds–Lyon Symposium on Tribology, 2004, Life Cycle Tribology. Elsevier Science B.V., 2005, pp. 673– 677. [4] Umehara, N., Kato, K., Sato, T. Tribological properties of carbon nitride coatings by ion beam assisted deposition. In: Proc. Inter. Conf. on Metallurgical Coatings and Thin Films, 1998, p. 151. [5] Kato, K., Umehara, N., Adachi, K. Friction, wear and N2 -lubrication of carbon nitride coatings: A review. Wear 254 (2003), 1062–1069. [6] Sanchez-Lopez, J.C., Belin, M., Donnet, C., Quiros, C., Elizalde, E. Friction mechanisms of amorphous carbon nitride films under variable environments: A triboscopic study. Surf. Coat. Technol. 160 (2002), 138–144. [7] Adachi, K., Sodeyama, N., Kato, K. Effect of humidity on friction of carbon nitride coatings under N2 gas lubrication. In: Proc. of WTC 2005, WTC 2005-64275. [8] Adachi, K., Tezuka, K., Kato, K. Effect of substrate on friction of carbon nitride coating under N2 gas lubrication. In: Synopses of the International Tribology Conference, Kobe, 2005, p. 34. [9] Tokoroyama, T., Umehara, N., Tomita, H., Takenoshita, Y. Effect of surface roughness and transfer layer of mating ceramic parts for ultra low friction phenomena in sliding between CNx and ceramics. Trans. Jpn Soc. Mech. Eng. C 69 (2003), 2824–2829. [10] Bowden, F.P., F.R.S., Young, J.E. Friction of diamond, graphite, and carbon and the influence of surface films. Proc. Roy. Soc. London A 208 (1951), 444–455. [11] Hayward, I.P. Friction and wear properties of diamonds and diamond coatings. Surf. Coat. Technol. 49 (1991), 554–559. [12] Tabor, D., Field, J.E. Friction of diamond. In: Field, J.E. (Ed.), Properties of Natural and Synthetic Diamond. Academic Press, London, 1992, pp. 547–570. [13] Miyoshi, K., Murakawa, M., Watanabe, S., Takeuchi, S., Miyake, S., Wu, R.L.C. CVD diamond, DLC, and c-BN coatings for solid film lubrication. Tribol. Lett. 5 (1998), 123–129. [14] Zhang, W., Tanaka, A., Wazumi, K., Koga, Y. Effect of environment on friction and wear properties of diamond-like carbon film. Thin Solid Films 413 (2002), 104–109.
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[15] Toyokawa, S., Kato, K., Adachi, K. Friction and wear property of carbon nitride film with N2 gas blow lubrication. In: Proceedings of the 38th Annual Meeting of Tohoku Branch of the Japan Society of Mechanical Engineers, 2003, pp. 54–55. [16] Zaidi, H., Robert, F., Paulmier, D. Influence of adsorbed gases on the surface energy of graphite: Consequences on the friction behaviour. Thin Solid Films 264 (1995), 46–51. [17] Harrison, J.A., White, C.T., Colton, R.J., Brenner, D.W. Molecular-dynamics simulations of atomic-scale friction of diamond surfaces. Phys. Rev. B 46 (1992), 9700–9708. [18] Perry, M.D., Harrison, J.A. Friction between diamond surfaces in the presence of small third-body molecules. J. Phys. Chem. B 101 (1997), 1364–1373. [19] Erdemir, A., Eryilmaz, O.L., Nilufer, I.B., Fenske, G.R. Synthesis of superlow-friction carbon films from highly hydrogenated methane plasmas. Surf. Coat. Technol. 133 (2000), 448–454. [20] Erdemir, A. The role of hydrogen in tribological properties of diamond-like carbon films. Surf. Coat. Technol. 146–147 (2001), 292–297. [21] Fontaine, J., Le Mogne, T., Loubet, J.L., Belin, M. Achieving superlow friction with hydrogenated amorphous carbon: Some key requirements. Thin Solid Films 482 (2005), 99–108.
– 21 – Achieving Ultralow Friction by Aqueous, Brush-Assisted Lubrication Seunghwan Lee and Nicholas D. Spencer Laboratory for Surface Science and Technology, Department of Materials, Wolfgang-Pauli-Str. 10, ETH Zurich, CH-8093 Zurich, Switzerland
21.1
INTRODUCTION
Nature is very effective at lubrication. When one considers the slipperiness of an eel, the low friction of human joints, the way in which a piece of toast slides down the esophagus, or the slimy trail of a slug, one can only marvel at the way in which such challenging lubrication problems have been so elegantly solved. In many of these cases, glycoproteins constitute the class of molecules that lie at the heart of the lubrication mechanism. Glycoproteins, such as mucin (Figure 21.1), consist of proteins—the principal building blocks of living tissue—that have been side-functionalized at many locations along the molecule with oligosaccharides (sugar chains). It is these glycoproteins, as well as the hierarchical bottle-brush-like structures that can be constructed from them, such as proteoglycans (Figure 21.2), that form the basic units responsible for lubrication in nature. A principal difference between man-made and natural lubricants is that while the former are generally based on oils, the latter are uniformly water-based. Man has generally avoided aqueous lubrication in all but a few special cases, mostly due to the disadvantageous properties of water under pressure: While oil increases its viscosity dramatically with pressure, which is essential for the functioning of the all-important elastohydrodynamic lubrication (EHL), pressurizing water hardly increases its viscosity at all, ruling out “conventional”1 EHL as a useful mechanism for aqueous systems. Instead, nature appears to rely on the use of brush-like systems, based on glycoproteins, for dealing with many of its tribological challenges. By coating them with glycoprotein brushes, sliding surfaces can be maintained in a separated state, as in boundary lubrication in manmade systems. Unlike boundary lubrication, however, the approach tends to yield an extremely low friction coefficient, more reminiscent of (elasto)hydrodynamic lubrication. This ubiquitous natural lubrication mechanism we have termed “brush-assisted lubrication” (BAL). 1 Piezoviscous-elastic EHL (see Section 21.2.1.2).
Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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Figure 21.1 A schematic illustration of mucins (from [1, Figure 1]).
Figure 21.2 Structural hierarchy of aggrecan in cartilage: (a) electron microscopy of aggrecan and the aggregates it forms with hyaluronan and link protein [2], (b) aggrecan core protein containing three globular domains (G1, G2, G3), keratan sulfate, and chondroitin sulfate region, (c) chemical structure of the disaccharide representing unit in chondroitin-4-sulfate glycosaminoglycan (from [2, Figure 1]).
Rapid progress in micro- or nanotribology over the last two decades [1–3] has now made it customary to divide the regimes of tribological phenomena according to contact scale,
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i.e. macro- vs. micro/nanotribology. The tribological properties in these two regimes differ not only due to issues of scale, but often also on quite a fundamental level. This is, however, partly because experimental assessment of the tribological properties in these two regimes is carried out under conditions that differ not in contact scale alone.2 The first issue is associated with the surface roughness of the tribological interface at each scale. In macrotribology, multi-asperity contact is generally unavoidable due to surface roughness, whereas in micro/nanotribology, single-asperity contact can be readily achieved in experimental studies. This difference leads to a difference in contact pressure as well as its distribution within the contact area. As is well known, local contact pressure at individual asperity contacts on the macroscale is significantly higher than apparent contact pressure and is extremely difficult to control. On the other hand, for a single-asperity contact in micro/nanoscale experiments, the apparent contact pressure is close to the real contact pressure, and is readily controlled by varying the applied load. Contact pressure is a critical parameter in determining the tribological properties of surface-grafted polymers in a liquid environment, since the conformation and the interacting forces of surface-grafted polymers change significantly depending upon the exerted contact pressure. The second issue is associated with the experimentally accessible range of sliding speeds in these two regimes. Sliding of the tribo-interface in macroscopic instruments, such as the pin-on-disk tribometer, is generally controlled by means of mechanical motors, and thus the experimentally accessible sliding speed lies in a much higher range, ∼10−4 to 100 m/s, than that of micro/nanoscopic instruments, e.g. the atomic force microscope (AFM) or the surface forces apparatus (SFA), ∼10−7 to 10−3 m/s, which are controlled by means of piezoelectric activators. For lubricated contacts, the sliding speed of the tribopair universally influences the entrainment speed of lubricant, which, in turn, influences the lubricating film thickness and consequent lubricating capabilities. For a tribosystem involving surface-grafted polymers, however, the sliding speed holds an additional significance in that the polymer segment mobility or relaxation time with respect to sliding speed often influences the relevant interfacial forces [6–8]. As discussed above, classification of the tribological phenomena according to contact scale provides an opportunity to look into several different aspects of the tribosystem involving surface-grafted polymers. We thus chose to constitute this chapter mainly according to contact scale, i.e. macro- vs. micro/nanoscale contacts. For macrotribological contacts, due to the highly complex nature of the tribointerface, theoretical models are difficult to formulate. However, simple experimental designs allow a wide range of materials to be investigated, and thus the macrotribology section (Section 21.2) will be subdivided according to the substrates (tribopairs) on which polymer brushes have been grafted: rigid materials (21.2.1) and soft materials (21.2.2). Rigid materials include thermoplastics (21.2.1.1) and metals and ceramics (21.2.1.2), and soft materials include elastomers (21.2.2.1) and hydrogels (21.2.2.2). For micro- or nanotribological contact, the need for highly smooth surfaces seriously limits the choice of materials to model surfaces, such as mica or highly polished silicon, as well as limiting the choice of polymers to be grafted onto the substrates. However, the relatively simple contact geometry allows the formulation of theoretical models with relative ease and in fact, numerous experimental studies, especially those by SFA, 2 For a sphere-on-plane contact, for instance, due to the difference in surface area/volume ratio, there still exist some fundamental differences in these two regimes, especially for adhesive contacts.
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have been directly compared with corresponding theoretical models. Since early studies of brush-assisted lubrication on the micro/nanoscale contacts and many important issues have been established by employing simple organic solvents and the polymers dissolved in those solvents, we will review the fundamental topics in organic solvents first (21.3.1), then extend our discussion to water-soluble polymers (21.3.2).
21.2 21.2.1
21.2.1.1
MACROSCOPIC SCALE CONTACTS
Rigid Materials
Thermoplastics
Early interest in thermoplastics for tribological applications originated from their distinct advantages over metallic materials when used as journal or ball bearings, including long life, low running costs, high corrosion resistance, and frequently observed low friction, even under unlubricated conditions [9,10]. Among these features, the high corrosion resistance is particularly relevant for the lubrication of thermoplastics by water. The efficacy of water as a lubricant for thermoplastics is partially dependent upon their surface properties; in general, the lubricity of water is greater for hygroscopic polymers, as typified by nylon 6 [9–11], which can be roughly assessed by measurement of water contact angles [9]. This tendency is enhanced when a polymer is slid against another polar surface, such as glass or clean metals [11], in water, due to increased likelihood of forming a water film at the interface [11]. In this context, surface grafting of ‘water soluble’ polymer brushes, which are known to impart hydrophilicity to the hydrophobic surfaces of thermoplastics, is also expected to enhance aqueous lubrication for these systems. One of the first tribological applications of this approach is to be found in the biomedical engineering area. The choice of water as a lubricant for biomedical applications is more a requirement than an option. In 1990 [12], Uyama and coworkers have shown that surface grafting of acrylic amide (AAm) and N,N-dimethyl acrylamide (DMAAm) onto polypropylene (PP), nylon 6, and ethylene-vinyl acetate copolymers (EVA), resulted in a remarkable improvement in aqueous lubricating properties. In that study, the substrates were first irradiated with UV light, and then placed in an aqueous solution containing monomers to promote polymerization. As shown in Figure 21.3, for instance, by grafting PAAm at 100 µg/cm2 onto PP, the coefficient of friction dropped from ∼0.25 to <0.01, accompanied by a reduction in water contact angle to ∼20◦ . Later, this approach was extended to other substrates, including plasticized poly(vinyl chloride) (PVC) [13], polyurethane [14,15], as well as other graft polymers, such as poly(N-isopropylacrylamide) (PNIPAAm) [15] with slight modification of experimental details [13–15]. An advanced study by these authors has shown that grafting of DMAAm onto EVA-based catheter tubes reduced the force needed to pull out from a PVC sheath to around 1/100th that of the unmodified tube [13]. In addition, the sliding of DMMAm-grafted plasticized PVC tube against a silicone sheet showed not only a reduction of the friction forces, but also a longer service time than that of conventional lidocaine-jelly-coated tubes [13]. The studies mentioned above [12–15] were inspired by specific attempts to modify the surface properties of tissue-contacting tubular devices, such as catheters, cannulae, endo-
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Figure 21.3 μ and contact angle (θ) values as a function of graft amount of the PAAm-grafted PP films (!) μ; (") θ (from [12, Figure 4]).
scopes, and cytoscopes. In principle, however, this methodology can be applied to any pair of sliding partners (substrate/coating) where polymer grafting is known to work [16–20], and thus holds significant potential as a lubrication approach. The only constraint in applying this method to aqueous lubrication is that the grafted polymer has to be water soluble. Some other candidates include poly(ethylene glycol) (PEG, also known as poly(ethylene oxide) (PEO)), poly(N-vinyl-2-pyrrolidone) (PNVP), poly(2-hydroxyethyl methacrylate) (PHEMA), poly(vinyl alcohol) (PVA), poly(methacrylate)-PEG, and poly(acrylic acid) (PAA) [16]. As briefly mentioned in the example above [12–15], in order to induce the surface grafting of polymers onto hydrophobic thermoplastics, which are usually inert, generation of active sites is generally a required initial step. Surface activation can be achieved not only by UV irradiation but also by other high-energy sources, such as corona discharge, ozone, plasma, γ -rays or even chemical oxidation [16–20]. As schematically shown in Figure 21.4(a), this approach has been known as the “grafting from” approach, to emphasize the fact that active sites are initially generated on the surface, followed by subsequent polymerization of monomers out from the surface. This approach is often cited in parallel with the “grafting to” approach, as shown Figure 21.4(b), where surface-grafting is achieved through the interaction between functional groups of an existing polymer chain and active sites on the surface. Generally, in the “grafting to” approach, polymer grafting is carried out in a liquid environment by immersing the substrates into polymer solutions, whereas in the “grafting from” approach, grafting can be performed either in solution or from the gas phase. Despite that the high costs involved in the “grafting from” approach and its inherent complexity, it has a distinctive advantage over the “grafting to” approach in that a high surface coverage of the grafted polymers can be readily achieved, usually ranging from a few tens to hundreds µg/cm2 . This value is 2 to 3 orders of magnitude higher than those obtained from the “grafting to” approach. This is mainly due to steric and/or electrostatic
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Figure 21.4 Schematic illustration of (a) “grafting from” and (b) “grafting to” approaches for the attachment of polymers to surfaces.
repulsion arising from the pre-adsorbed and incoming polymers, which imposes a barrier in the “grafting to” adsorption process, but is absent in “grafting from”. 21.2.1.2
Metals and Ceramics
Metals, metal oxides, and ceramics generally represent harder materials than thermoplastics, and the range of tribological applications is also considerably broader. Although some of these materials encounter aqueous environments in their tribological applications, such as in artificial articular joint implants [21–23], the specific motivation for using water as a lubricant is relatively weaker than in the case of flexible materials, such as thermoplastics. This is mainly due to the hard asperity contacts occurring between two rigid materials, especially in practical service conditions in machinery, leading to severe conditions that inhibit the formation of water-based lubricating films. Whether surface-grafted polymers on these materials can solve this problem, and how efficient this approach can be, is primarily dependent upon the load-carrying capacity of those films. Müller and coworkers have shown that poly(ethylene glycol) (PEG) grafted onto a polycationic backbone, poly(L-lysine) (PLL), thus generating PLL-g-PEG, can behave as an efficient boundary lubricant additive for a steel/glass tribopair in an aqueous environment. The molecular structure of PLL-g-PEG and its conformation at the liquid/solid interface is illustrated schematically in Figure 21.5. Since the amino groups at the end of lysine side-chains are positively charged in water (if pH ∼10), this copolymer is attracted by electrostatic interaction to negatively charged surfaces, including most oxides in an aqueous environment at near-neutral pH [24,25]. Water-soluble PEG side-chains are thus pushed out into the bulk water to form brush-like structures. A moderate reduction in the coefficient of friction, typically from 0.3 to 0.1, has been observed under sliding contact conditions [26,27]. A more enhanced lubricating effect was observed with rolling contacts. As shown in Figure 21.6, the film thickness at 10 N load, and speeds between 0.05
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Figure 21.5 (a) Molecular structure of PLL-g-PEG and (b) schematic illustration of PLL-g-PEG adsorbed onto oxide surfaces in aqueous solution (from [103, Figures 1 and 2]).
and 1 ms−1 , measured by means of ultra-thin-film interferometry [27], lies in the range ∼5 to 20 nm, respectively. This behavior is very significant, since water alone generally cannot form a lubricating film under these conditions (low-speed, high-pressure, rigid-onrigid contact), and leads to damage of the tribopair surfaces [28]. Parallel measurement of the rolling frictional properties, by means of a mini-traction machine (MTM) [29,30], has shown that the coefficient of friction reaches values as low as ∼0.0001, which is approximately two orders of magnitude lower than in the case of water alone. It is important to note that the adsorption of PLL-g-PEG onto oxide surfaces is achieved via the aforementioned “grafting to” approach. For the case of PLL-g-PEG, the surface coverage on oxide surfaces is normally not higher than 0.3 µg/cm2 [24,25], this value being significantly smaller than other surface-grafted polymers obtained from “grafting
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Figure 21.6 The influence of the molecular weight of PEG side chains on the coefficient of friction (squares: y-axis on the left-hand side) and lubricant film thickness (circles: y-axis on the right-hand side) was measured as a function of speed by means of MTM and ultra-thin-film interferometry. The test lubricants were aqueous buffer solutions containing either PLL(20)-g[3.4]-PEG(2) (black symbols) or PLL(20)-g[3.4]-PEG(5) (white symbols). The lines between data points serve as a guide for the eye (ball = stainless steel (19 mm in diameter), substrate = silica, buffer solution = 10 mM HEPES (pH 7.4), polymer concentration = 0.25 mg/ml, load = 10 N, T = 25 ◦ C) (from [27, Figure 4]).
from” approach, as mentioned in the previous section.3 PLL-g-PEG has a unique capability to “self-heal” in tribostressed areas, where polymer desorption has taken place, through its fast adsorption kinetics. Lee and coworkers have reported that the presence of the PLLg-PEG in bulk aqueous lubricants appears to prevent the degradation of lubricating performance under severe tribological contact conditions, e.g. a steel/glass tribopair [31]. As shown in Figure 21.7, the friction coefficient of a steel/glass tribopair with a monolayer coating of the copolymer, yet without polymer dissolved in the bulk lubricant, rapidly reached the values corresponding to sliding contact of a bare steel/glass tribopair, which suggests the removal of the film during tribological testing. Meanwhile, the same tribosystem with excess polymer dissolved in the bulk lubricant revealed consistently low μ values throughout the measurement. Since the viscosity of the lubricant remains unaltered by addition of the polymer at the levels used in these experiments, 0.25 mg/ml, this behavior is believed to have originated from the ‘self-healing’ effect of PLL-g-PEG. The tribostressinduced desorption and subsequent adsorption behavior of PLL-g-PEG on the tribopair has been investigated in a more vivid manner by fluorescent labeling of the polymers [31]. As shown in Figure 21.8(a), two batches of PLL-g-PEG polymer were labeled with different fluorescent chromophores on the tribopair (green, white in the figures) and in the bulk lubricant (red, gray in the figures). Fluorescence microscopy images obtained after a controlled number of passes in the pin-on-disk experiment, Figure 21.8(b), confirmed that the exchange of the pre-adsorbed polymer with polymer molecules dissolved in the lubricant 3 Note that most PLL-g-PEG systems investigated have involved relatively low-molecular-weight PEG chains, and so the moderate adsorbed mass belies the high grafting densities (in excess of 0.5 chains/nm2 ) that can be obtained, meaning that the PLL-g-PEG grafting approach yields something between “grafting to” and “grafting from” in the resulting chain densities obtained.
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Figure 21.7 μ vs. number of revolutions for sliding contact of a steel/glass (pin/disk) tribopair, by means of pin-on-disk tribometry; (a) in HEPES buffer solution (!), in PLL-g-PEG solution (0.25 mg/ml in HEPES buffer solution) (1), and in HEPES buffer solution with PLL-g-PEG coating at surfaces (") (load: 2 N, sliding speed: 5 mm/s, radius of pin: 3 mm). Inset: expanded display of the data for the initial 6 revolutions (from [31]).
(a)
(b) Figure 21.8 (a) A schematic illustration of the pin-on-disk tribometer and the location of the two different fluorescence-labeled PLL-g-PEG copolymers (fluorescein isothiocyanate (FITC), a green dye, shown white pre-coating at both pin and disk, rhodamine B isothiocyanate (RBITC), a red dye, shown gray, in HEPES buffer). (b) Fluorescence microscopy image of the disk following pin-on-disk tribometry experiment. The number of revolutions was 9, 4, 2, and 1 (in the order of the experiment) in the tracks of radius 1.6, 2.0, 2.4, and 2.8 mm. The load and sliding speed were fixed at 2 N and 5 mm/s, respectively (adapted from [31]).
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Figure 21.9 μ vs. number of revolutions plots for sliding contact of a steel/glass (pin/disk) tribopair by means of pin-on-disk tribometry in HEPES buffer solution (!) and in HEPES buffer solution with Sil-PEG coating at surfaces (") (load: 2 N, sliding speed: 5 mm/s, radius of pin: 3 mm). Inset: enlarged display of the data for the initial 10 revolutions (from [31]).
does indeed occur, and that it accounts for the stable lubricating performance of aqueous PLL-g-PEG solution. In the absence of tribological stress, exchange does not detectably occur. A parallel study of silane-terminated PEG, attached onto the surface through covalent bonding, showed an interesting contrast in a pin-on-disk sliding experiment under pure water. As shown in Figure 21.9, the increase of μ is much slower than in the corresponding PLL-g-PEG case, probably because of the higher binding strength of the covalent bonds. However, μ eventually reached a level that also reflected the total removal of the film—this time in an irreversible way. Due to uncontrollable hydrolysis of silane units in an aqueous environment [32,33], addition of excess silane-PEG does not reproduce the ‘self-healing’ effect observed with the more weakly, but reversibly attached PLL-g-PEG. Earlier in this chapter, it was emphasized that the “grafting from” approach can yield several orders of magnitude higher surface coverage of grafted polymers than the “grafting to” approach. Since most “grafting from” procedures result in covalent bonding of grafted polymers to the surface [16–20], it is expected that a similar film failure observed in the silane-PEG case (Figure 21.9) will occur if typical “grafting from” polymers are exposed to extreme contact conditions. As exemplified by PLL-g-PEG, polymers adsorbing onto the surface from the lubricants via mechanisms with fast adsorption kinetics, such as electrostatic or hydrophobic interactions, can be a viable alternative to overcome such problems. 21.2.2
21.2.2.1
Soft Materials
Elastomers
In the context of aqueous lubrication, elastomers enjoy a special status, both in the fundamental and the practical sense. As briefly mentioned in the Introduction, the inability of water to increase its viscosity under pressure generally rules out the stable formation of lubricating films in conventional tribological contacts. However, when an elastomer is involved, either on one or both sides of the contact, this critical drawback of water as lubricant becomes of minor importance. Due to the highly compliant nature of elastomers,
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the pressure within the contact area can be maintained low, and thus liquids possessing low pressure-coefficients of viscosity, such as water, can also readily participate in the formation of a lubricating film. Even surface asperities are generally flattened out under moderate pressure. Once the lubricating film is generated, the low viscosity of water is rather advantageous since the hydrodynamic drag of the water film leads to a low value of the friction coefficient. The feasibility of water as a lubricant for elastomeric tribosystems has been empirically recognized since the 1960s, partly due to the importance of certain engineering applications such as windshield wipers, reciprocating and rotary lip seals, flexible-pad thrust bearings, soft-lined journal bearings, and tyres on wet roads [34–38]. A variety of elastomers, including polyisoprene [34–36], styrene-butadiene [37], polybutadiene [37], silicone [38], polyeurethane [38], ranging in elasticity modulus from 0.2 MPa [34–36] to 30 MPa [38], showed film thicknesses as high as 20 nm at a contact pressure of 0.01 MPa [35,36], or a coefficient of friction as low as 0.01 at the sliding speed of 0.1 m/s [35–38]. The theoretical models that account for these ‘unusual’ phenomena comprise part of elastohydrodynamic lubrication (EHL) theory. Dowson and Hamrock have demarcated four different EHL regimes depending on the relative role of elasticity of the tribopair and viscosity of the lubricant in the formation of the lubricating film [39,40]: isoviscous-rigid, piezoviscousrigid, isoviscous-elastic (soft EHL), and piezoviscous-elastic (hard EHL). Aqueous lubrication of elastomers typically belongs to the isoviscous-elastic regime, where the elastic deformation of the tribopair is a significant contributor to the thickness of the fluid film separating them, but the pressure within the contact is quite low and insufficient to cause an increase in viscosity. The minimum film thickness for this regime can be neatly expressed by the material and test parameters (elliptical parameter k = 1): ′
hmin ≈ 2.1 · R 0.77 · (η · us )0.66 · E −0.45 · W −0.21 , where hmin , R, η, us , E ′ , and W represent minimum film thickness, radius of sphere, viscosity of lubricant, sliding speed, effective elasticity modulus, and load, respectively. In spite of the feasibility of aqueous lubrication of elastomers, efforts to further improve the aqueous lubricating properties of elastomers have been relatively rare. A few exceptional examples include the addition of low-molecular-weight surfactants, e.g. sodium dodecyl sulfate (SDS) [34–36] also known as sodium lauryl sulfate (SLS) [38], to water, by which the formation of electrical double layers and consequent electrostatic repulsion is promoted between the tribopair [34–36]. It is only very recently that polymer brushes have been introduced as an additive to improve the aqueous lubricating properties of elastomers. Lee and Spencer have shown that, for instance, the aqueous lubrication properties of self-mated sliding of poly(dimethylsiloxane) (PDMS) is greatly improved by surfacegrafting with PEG-based copolymers, such as PLL-g-PEG [41] or poly(ethylene oxide)block-poly(propylene oxide)-block-poly(ethylene oxide) (PEO-b-PPO-b-PEO, also known as Pluronics® ) [41,42]. These studies were carried out in the context of highlighting the significance of surface-chemical properties of elastomers to enable the soft EHL mechanism; while the mechanical properties of PDMS (elasticity modulus, ca. 2 MPa) are sufficient to ensure soft EHL when lubricated by water, strong hydrophobic interactions between the sliding partners result in an extremely high coefficient of friction in the absence of surface
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Figure 21.10 μ vs. speed plots for the water-lubricated sliding of PDMS/PDMS contact in the absence of treatment, and hydrophilized by means of oxygen-plasma treatment, adsorption of PEO-b-PPO-b-PEO copolymer, and adsorption of PLL-g-PEG copolymer (load, w = 1 N) (from [41, Figure 8]).
modification, as shown in Figure 21.10. By rendering the PDMS surface hydrophilic, however, either by oxygen-plasma treatment (ox-PDMS) or oxygen-plasma treatment followed by surface-grafting with PEG (PEG-ox-PDMS), the coefficient of friction was observed to be significantly lower, ca. 0.03, in accordance with the soft-EHL model. It should be noted that while both ox-PDMS and PEG-ox-PDMS showed similar frictional properties in the high-speed regime, because soft EHL is sensitive to both mechanical properties and surface hydrophilicity, the transition to boundary lubrication in the low-speed regime is significantly retarded in the case of PEG-ox-PDMS. Details of the conformation of the surface-grafted PEG polymer chains during waterlubricated sliding between PDMS tribopairs, e.g. whether they are stretched or collapsed, still remain to be elucidated. At this point, it is to be emphasized that many watercompatible additives, not only surface-grafted polymer chains [41,42] but also surfactants [34–36,38] and even simple electrolytes [43], readily remain intact at elastomeric contacts, apparently due to the low contact pressure maintained within the contact area, and thus this approach holds significant potential to further tailor and improve the aqueous lubrication properties of elastomeric contacts. 21.2.2.2
Hydrogels
Hydrogels are polymer networks swollen with a large amount of water. The water content is generally higher than 50%, but the macroscopic physical properties are solid-like in that they have definite shapes and do not flow. A broad range in elasticity modulus is available for hydrogels, and those employed for tribological studies typically range from ca. 3 kPa to ca. 100 kPa, which is generally lower than values for the elastomers described in the previous section [34–38]. The motivation for tribological studies of hydrogels is closely associated with biological applications, such as the development of artificial cartilage for articular joints, and other bio-tissues [44–48]. Osada and coworkers have presented systematic studies of the friction and lubricating properties of hydrogels, varying parameters such as network structure (chemical or physical) [49–51], mechanical properties [52–54], substrates [55,56], charge properties [57–60], and environment [49–51,61]. In this section,
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we focus on the case where brush-like polymer chains are grafted on top of hydrogel surfaces. The polymer brushes to be discussed in this section are grafted onto the surfaces of hydrogels in a completely different way from those mentioned in the previous sections. Instead of bringing the polymer brushes from outside, Gong and coworkers have reported that the brush-like polymers can be generated during the gel-formation process [55]; when a hydrogel is synthesized on hydrophobic substrates, such as Teflon® or polystyrene, the gelation process (cross-linking) is significantly suppressed and the surface is terminated with branched dangling polymer chains, in contrast to the case when a hydrogel is synthesized on hydrophilic substrates. The impact of the polymer chains generated in this way on the lubricating properties of hydrogels is remarkable. As shown in Figure 21.11, the coefficient of friction of a poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPS)
Figure 21.11 Normal pressure dependence of (a) the frictional force and (b) the coefficient of friction of PAMPS gels slid against a glass plate in water at an angular velocity of 0.01 rad/s: (") prepared on glass, swelling degree, 21; (2) prepared on PS, swelling degree 27, and (1) containing linear polymer chains, swelling degree, 15 (from [55, Figure 1]).
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gel prepared on a polystyrene substrate was at least two orders of magnitude lower (as low as 10−4 ) than that prepared on a glass substrate in the low-pressure regime (Note that the surface in contact with the substrate is used for the measurement, after being detached). Similar behavior is observed with other hydrogels, including the sodium salt of styrene sulfate, acrylic acid, and acrylamide [62]. The enhanced lubricating properties of the brushterminated hydrogels are closely associated with the higher swelling degree and the lower compressive elasticity modulus of the surface than the bulk of the hydrogels [62]. These factors eventually contribute to enhanced hydrodynamic thickness of the solvent layer at the sliding interface [63].
21.3 21.3.1
MICRO/NANOSCOPIC SCALE STUDIES
General Aspects
Surface-attached polymers, either adsorbed or tethered, have received significant attention over recent decades, due to their direct relevance to many industrial applications, such as colloidal stabilization in inks, paints, and foods, and thus many fundamental studies on the micro/nanoscopic scale, especially by SFA, have been carried out on model systems [64–67]. It is generally established that the ‘steric’ stabilization introduces repulsive interactions between surfaces carrying polymer chains and thus reduces both adhesion and coagulation. Although the normal forces between two surfaces bearing polymer brushes in good solvents are fairly well understood, the shear and friction forces under shear motion have only recently begun to be explored. The tribological properties of surface-grafted polymer brushes on the micro/nanoscopic scale have initially been investigated by employing a non-aqueous solvent/polymer pair, such as polystyrene/toluene, by means of the surface forces apparatus (SFA) [6,7,69,70]. Although water-soluble polymers have recently received increasing attention [90,98–103], many fundamental properties had already been established by employing non-aqueous systems, and many of those principles are also applicable to aqueous systems. For this reason, we will initially review some fundamental issues identified during experiments with non-aqueous polymer/solvent systems. When simple liquids are compressed to a film thickness on the order of a few molecular layers, they generally undergo a liquid-to-solid transition owing to ordered layering of the fluid molecules parallel to the confining surfaces [68]. When these layers are sheared laterally, they exhibit a finite yield stress, often proceeding by stick-slip behavior [69,70]. Surface modification with end-grafted polymer brushes drastically changes these interfacial frictional properties. Pioneering research in this area was undertaken by Klein and coworkers [69,70]. As shown in Figure 21.12, the shear of two mica surfaces in toluene reveals solid-like stick-slip behavior and a coefficient of friction 0.6–0.7 at a separation of 14 ± 3 Å (corresponding to two monolayers of toluene molecules and an applied load of 19 ± 2 µN). Upon grafting the mica surface with polystyrene, the friction forces under a comparable load (20 µN) reduced to a level below the detection limit. Although the specific data shown in Figure 21.12 represent the case where the distance between the mica surfaces, D, is 37 nm, the noise-level friction forces were detected under even higher compression, down to D ≈ 20 nm (the applied load ≈100 µN). This behavior can be systematically presented
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Figure 21.12 The variation of the shear force Fshear with time between two mica sheets a distance D apart, compressed by a normal load Fnormal = 19.2 ± 2 µN, in response to an applied shear. The upper inset shows schematically the configuration of the surfaces mounted on crossed cylindrical lenses. The bending δx and δD of the two orthogonal springs K1 and K2 yields the respective forces Fshear and Fnormal . Lateral motion δx0 is applied to the top surface via the sectored piezocrystal P, whose bending configuration is indicated. The sliding velocities used in the present study were in the range vs ≡ d(x0 − x)/dt = 15–450 nms−1 . Curve a, sliding of bare mica surface in toluene. D = 14 ± 3 Å, corresponds to two monolayers of toluene between the surfaces. A clear stick-slip behavior is observed during sliding. The region where the surfaces stick and the shear force changes sign at t = 5–7 s indicates a reversal of the sliding direction. The sliding velocity vs = 45 nms−1 . Curve b, sliding of mica surfaces covered by a PS-X(1.4 × 105 ) brush, at D = 37 nm. On the scale of the main figure the shear forces are within the thickness of the line labeled b. The lower inset shows Fshear on an expanded scale: the shear force is less than the noise-limited resolution δFshear . There is no measurable change on reversing the sliding direction. The sliding velocity vs = 15 nms−1 (from [69, Figure 1]).
in conventional ‘friction-vs.-load’ or ‘friction-vs.-distance’ plots, but it is more instructive to understand the molecular conformation of the brush polymers during compression and lateral sliding by plotting the friction forces (and the load as well) as a function of the relative compression of the brushes. Figure 21.13 illustrates the change of both the normal load and friction forces as a function of inverse compression, β −1 = (D/2L) (L is uncompressed brush length). While the normal load increases monotonically with increasing compression from the onset of mutual interaction between the two surfaces bearing polystyrene, the lateral forces only reach the detection threshold from β −1 ≈ 0.2, which corresponds to a five-fold or greater compression of the polymer brush height. Another advantage of the force-vs.-compression plot is that it can be generalized to many polymers with different architectural details. For instance, Figure 21.13 shows that the onset of the rapid increase in the friction forces occurs at a compression ratio of β −1 ≈ 0.2 for all three different polystyrene brushes with varying molecular weights and inter-chain spacings. The coefficient of friction, μeff , at moderate compression regime, 0.2 < β −1 < 1, is estimated to remain below 0.0005 over the entire speed range employed, 15–450 nm/s. The drastic reduction of friction forces by end-grafted polymer brushes was attributed to the combined effect of increased load-carrying capacity of the polymer brushes and the fluidity of the interfacial layer; as the two brush layers come into overlap, they undergo a compressive distortion, and the mean segment concentration in the gap increases. As
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Figure 21.13 Normal and shear profiles for interaction between mica surfaces bearing PS-X(Mr ) brushes, plotted as (F s 3 /LR) versus D/2L, where s = sM is the mean spacing between chain anchoring points for the respective brushes, and L = LM are the respective brush heights. In the Alexander–de Gennes model, this reduction makes the Fnormal data independent of Mr . The Fshear (D) profiles have been similarly scaled for purpose for comparison. 2, ", Mr = 2.6 × 104 ; 1, !, Mr = 1.4 × 105 ; P, +, Mr = 3.75 × 105 . Results are shown from two or three experiments for each molecular weight; shear forces smaller than the resolution δFshear are not shown. The inset shows a typical Fshear (D) versus time plot for the highly-compressed (D < D0 ) region of the plot, for PS-X(3.75 × 105 ) brushes compressed to surface separation D = 190 Å (corresponding to D/2L = 0.083); sliding velocity 38 nms−1 ; the change in sign of Fshear at 38 and 76 s corresponds to a reversal of the sliding direction at these times (from [69, Figure 3]).
a result, the osmotic pressure due to the segmental interactions—arising from excluded volume effects in the good solvent—also increases. This supports the normal load compressing the two surfaces against each other. Meanwhile, the interpenetration between the opposing brush layers at low compression is weak, and the sheared interfacial region between them as they slide past each other remains quite fluid. These two properties can be quantitatively treated as discussed in the following sections. 21.3.1.1
Normal Forces-Osmotic Pressure
According to Alexander and de Gennes’ scaling theory [71,72], when two surfaces bearing polymer brushes approach each other, the normal interaction forces at moderate compression are expressed as follows. kB T f (D) ∼ = 3 s
2L0 D
9/4
D − 2L0
3/4 ,
(21.3.1)
where f (D) is normal force, kB is Boltzman constant, T is temperature, s is the spacing between adjacent polymer chains, L0 is the static polymer length under no compression, and D is the distance between two substrates (see Figure 21.14 for graphic illustration). The first term in square brackets of Equation (21.3.1) stems from the osmotic repulsion experienced by the brushes as they are compressed, and the second term stems from the reduction in free energy due to the compression of the overstretched chains. As is well known, Alexander–de Gennes scaling theory assumes a uniform stretching of the polymer chains
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and mean monomer concentration, which was later extended by Milner et al. in mean-field theory, to reflect the more realistic parabolic distribution of the chain ends [73,74]. Equation (21.3.1) is only strictly applicable to a polymer layer revealing ‘brush’ conformation. If the polymer density is insufficiently high to push neighboring polymers into the brush regime (i.e. leading to the ‘mushroom regime’) or adsorbed polymers display different behavior, one typically observes more adhesive interactions during the compression– decompression cycle, e.g. bridging and hysteresis, and eventually degraded lubrication behavior during shear motion [75,76]. As shown in Equation (21.3.1), for quantitative measurement of the normal forces between two surfaces bearing polymer brushes, it is critical to characterize the conformation of the polymer layer not only in its static state, but also during compression. In this sense, SFA is an ideal approach since it can provide ideally smooth surface contacts on a micro/nanoscopic scale, while allowing the measurement of the absolute distance between two surfaces with or without shear motion. 21.3.1.2 Interpenetration Zone: Hydrodynamic Shear As mentioned above, another significant contributing factor to the extremely low frictional characteristics of polymer-bearing surfaces is the fluidity of the interpenetration zone under compressed shear. While this interpenetration was simply treated to be negligible in the scaling theory, consideration of the parabolic distribution, i.e. mean-field theory, allowed the estimation of the size of the interpenetration zone (see Figure 21.14) in a more quantitative way by Klein and coworkers [7]. d ≈ sβ 1/3 = s(2L/D)1/3
[7],
(21.3.2)
where β −1 is the compression ratio defined in the previous section. As expected, the interpenetration zone, d, between two compressed brushes varies very weakly with brush
Figure 21.14 A schematic illustration of tethered polymer brushes in the Alexander–de Gennes model (L0 is the equilibrium brush height, s is the spacing between adjacent anchoring polymer chains).
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compression. This expression can be extended to further estimate the shear stress experienced by the chains as they are dragged through the overlap region, d. σs = 6π · ηeff · vs · β 7/4 /s
[7],
(21.3.3)
where ηeff is the effective viscosity of the penetration zone, and υs is the sliding velocity. Thus, the effective coefficient of friction may be expressed as (shear force required to slide the compressed brush/normal load required to compress the brush to separation D) = σs /F (D) = 6π · ηeff · vs · s 2 · β −1/2 /kB T [7], (21.3.4)
μeff =
where F (D) is the normal force shown in Equation (21.3.1). By putting the experimental conditions that have been employed for the data shown in Figures 21.12 and 21.13, Klein has shown the validity of Equation (21.3.3) for the shear forces between polymer brush layers under moderate compression [7]. 21.3.1.3
Load-carrying Capacity: Higher Compression
As discussed earlier in the macrotribology section, the lubrication behavior of surfacegrafted polymers under tribological stress varies significantly depending upon the applied pressure, which is determined by the interplay between the applied load, the surface roughness, and the compliance of the tribopairs. Given that the immeasurably small friction forces and remarkable lubricating properties of polymer brushes are achievable under moderate compression, in terms of lubrication engineering, it is of great interest to establish the pressure limit at which such behavior can be counted upon. Based upon the SFA experimental data available in the literature, the maximum pressure that can be sustained between polymer brushes revealing only ‘noise-level friction forces’ appears to lie between 0.01 to 1 MPa, depending on the detailed molecular architecture of the polymers [77]. These values could be comparable to the pressure exerted between some internal or external biological organs (e.g. eye lid/eye ball or between intestinal organs), but still are somewhat lower than that applied in mammalian articular joints (ca. 10 MPa) [78]. Under compression of the polymer brush films at higher pressures than ‘noise-level friction’ regime, the films seem to become initially ‘vitrified’, due to increased segment density in the interpenetration zone. For instance, the concentration of polymer at the compression ratio β −1 = 0.1 in Figure 21.13 is estimated to be ca. 45%, which is roughly one order of magnitude higher than that under zero compression, ca. 4.5% [69]. With any further increase of compression, the shear motion starts to reveal ‘static friction’ before the onset of sliding, and at even higher compression values the films are eventually detached from the surface [77]. The exact pressure where polymer film failure occurs, of course, is dependent upon the detailed architecture and conformation of the polymer [77]. 21.3.1.4
Shear-rate Dependence
As briefly discussed in the Introduction, the influence of shear rate on the conformation and the interfacial forces is a unique and specific issue related to polymer brush-bearing
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Figure 21.15 The variation of the increment of F⊥ /R in the normal force between mica surfaces a fixed distance D apart, bearing terminally anchored PS-X layers, as a function of their mean lateral velocity v. Curves A and B are for D = 94.5 ± 1 nm and D = 155.2 ± 1 nm, respectively (from [6, Figure 2(b)]).
surfaces under a solvent. While it is generally agreed that the polymer chains are stretched along the direction of flow under shear, i.e. the polymer chains are diagonally tilted in the direction of flow, its influence on the polymer chain length in the vertical direction and thus the interfacial forces is still an on-going debate [7,79–88]. One of the earliest experimental studies regarding this issue was carried out by Klein and coworkers [6]; if the surfaces were either weakly compressed or uncompressed but separated by a small gap, there was an extra normal force observed at high shear rate (up to a few 100 Hz), suggesting an increase in the brush height of an uncompressed layer as shown in Figure 21.15. The fact that the onset of the extra normal force is shear dependent suggests that it probably arises from an interplay between the chain relaxation rate and the applied shear rate. Many theoretical models have shown results that are consistent with this experimental observation [79–82]. The essence of these models is that under shear, the size of the blobs (see Figure 21.14), which represents the volume that is excluded or screened by polymer segments, decreases as a result of lateral stretching, thereby increasing the overall osmotic interaction within the brush, and hence the normal forces [7]. Conversely, molecular dynamics simulation studies have mostly predicted no significant change in the vertical chain length under flow past the brush [83–85]. Grest, for instance, argues that most theoretical models are based upon scaling theory, and are thus inadequate to describe the shear-rate dependence of brush height [86]. Recent neutron reflectivity measurements support this argument by detecting no significant change in brush height under shear flows as high as 1.3 ×105 Hz [87,88]. However, experimental discrepancies may arise from the different modes of shear: oscillatory-mode in the case of SFA, or steady-flow-mode passing through polymer brush in neutron reflectivity studies.
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In the work by Klein and coworkers [6], it is noted that the increase in normal force arising from shear motion reaches a maximum when the distance between the two surfaces, D, slightly exceeds 2L. With the onset of overlap between opposing brushes, it begins to decay and finally disappears at β −1 ≈ 0.4. A simple explanation was that the chain stretching is not feasible any more under high compression due to increased monomer concentration in the gap. In this regime, where the compression is sufficient and the friction forces are finite, shear thinning appears to be dominant at high shear rates. For instance, Schorr and coworkers have shown that shear thinning was observed between two polystyrene brush layers in toluene sheared under high compression (β −1 ≈ 0.22) and high speed (>ca. 200 nm/s); at lower compression values and/or shear rates, the interfacial layer remained Newtonian [89]. A similar transition was consistently observed between poly(ethylene glycol) (PEG) brushes by Raviv and coworkers [90]. The sub-linear dependence of shear force on shear rate, i.e. shear-thinning, was attributed to the reduction in mutual interaction and the interpenetration zone between two brushes at high shear rate, arising from the lateral tilting of the polymer brush in the flow direction, as previously mentioned [89]. 21.3.2
21.3.2.1
Water-soluble Polymer Brushes
Poly(ethylene Glycol(PEG)
Poly(ethylene glycol) (PEG) is the prime example of water-soluble polymers that has been investigated for its tribological properties with respect to brush-assisted lubrication on the micro/nanoscopic scale. While normal interactions between two surfaces modified with PEG, especially with those displaying adsorbed conformations, have been extensively investigated [91–93], there are only a few experimental tribological studies that involve tethered PEG polymers on the micro/nanoscopic scale [90,102,103]. As is well known, PEG (– CH2 CH2 O–) carries both hydrophobic (–CH2 CH2 –) and hydrophilic (–O–) moieties, and thus it dissolves in both water and many organic solvents. Its water solubility is unexpected, since the homologous polyethers possessing one less (polymethylene glycol, –CH2 O–) or one more methylene unit (polypropylene glycol, (–CH2 CH2 CH2 O–) are insoluble in water [94]. Its water solubility is thus believed to be structural, in the sense that it forms a complex with water molecules. Another reason why it has gained considerable attention is due to its resistance to nonspecific protein adsorption, when present as highly dense and extended brush layers. This property, whose mechanism is still not completely understood, is particularly useful in biosensor applications. Raviv and coworkers have generated PEG brushes (3,400 Da) by functionalizing one end of PEG with trimethylammonium (–N+ (CH3 )3 ), and thus attached it electrostatically onto a negatively charged mica surface for SFA studies [90]. According to the authors, the PEG layer in their system has surface density, Γ = 1.5 ± 0.5 mg/m2 , adjacent chain spacing, s = 2.0 ± 0.3 nm, and the static film thickness of L0 = 5.5 nm. In contrast to the polystyrene-in-toluene system [60,70], however, the shear force between the polymer layers appears to commence soon after the polymer chains start to overlap, i.e. at compression ratio, β −1 = (D/2L) ≈ 1 (Note that the ‘threshold’ compression ratio, β −1 for the polystyrene/toluene was below 0.2). The effective coefficient of friction, μeff = 0.03 ± 0.015 down to D ∼ 4 nm, was followed by a rapid increase by an order
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of magnitude at higher compression. While the lubricating properties of the PEG layer in water are still quite effective, they are relatively inferior to the polystyrene/toluene pair; this was attributed mainly to the density of PEG layer employed in this work being insufficiently high, as mentioned by the authors. The mean volume fraction, φ = 0.25, is also approximately 10 times higher than that of the polystyrene/toluene system at the comparable compression ratio and thus the effective viscosity of the interpenetration layer is concomitantly higher. Raviv and coworkers [90] highlighted the influence of salts on the interfacial forces at the PEG/mica interface. Although the PEG brush layer in salt-free aqueous solution revealed long-range repulsion forces (starting from ∼200 nm), this was largely a result of incomplete shielding of the negative charges of the mica substrate and consequent doublelayer repulsion. Several differences were observed by addition of 0.1 M NaCl into the aqueous solution. Firstly, the long-range electrostatic forces were replaced by short-range steric repulsion—the range that is dominated by steric repulsion was observed to be only slightly higher than 10 nm. This value is considerably smaller than those observed in the polystyrene/toluene system [69,70] even if the differences in molecular weight and static film thickness are taken into account. Secondly, a small, yet evident adhesion was observed during the compression–decompression cycle, which was absent in the PEG/salt-free aqueous solution or, indeed, in the polystyrene/toluene system [69,70]. These two observations again point to the relatively low surface coverage of PEG brushes. Thirdly, in spite of degraded repulsive interaction, its lubricating properties have improved in terms of lubricant stability during shear motion; the PEG layer in salt-free water showed some evidence of tribostress-induced desorption at the strongest compression, but such behavior disappeared in salt solution (0.1 M NaCl). The authors speculated that the higher stability of the polymer layer in the salt solution might be related to the formation of complexes between the Na+ and a few PEG chains, i.e. a gel-like network. However, the influence of salts on the lubricating properties of the PEG-brush layer requires more systematic investigations, since at even higher salt concentration, the solvent quality of aqueous solutions for PEG is reported to be generally degraded [95,96]. Lea and coworkers have shown that the forcedistance profile obtained by AFM between PEG layers (2000 Da) and a bare silicon nitride tip exhibited a gradual transition from a repulsive to an attractive interaction by increasing the MgSO4 concentration up to 1.0 M [97]. As shown in the preceding example, experimental assessment of the interfacial forces between two mica surfaces bearing PEG brush layers, focusing on the steric effect originating from the brush–brush interaction alone, is not straightforward, unless the coverage of the neutral PEG brush is adequate to completely shield the negative charges of the mica substrate. Even though addition of salt can shield double-layer interactions to a certain extent, it can also complicate the system by changing the solvent quality of water with respect to PEG or adsorption properties of polymers that are anchored by electrostatic forces. More diverse and improved approaches to immobilizing PEG brushes with high polymer chain coverage are required in the future.4 4 Drobek and coworkers have employed aforementioned PLL-g-PEG copolymer (Figure 21.5) to generate a PEG brush layer on mica [98–100]. This approach is also based upon electrostatic interactions between cationic anchoring units (–NH3 + ) and the negatively charged mica substrate, but may involve a higher film stability due
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Yan and coworkers [101] have characterized the tribological properties of PLL-g-PEG (Figure 21.5) in aqueous media in the context of extending macroscopic studies [26,27] to the nanoscopic regime. A silicon wafer and a borosilicate glass colloidal AFM tip have been employed as the tribopair. The influence of surface modification by PEG layers was investigated by obtaining friction-vs.-load plots under a fixed sliding speed. The lubricating properties of PEG layers manifested themselves as both a reduction in the slope of the friction-vs.-load plot, as well as a significant diminution of the adhesive forces observed during the decompression process. This implies that the lubrication mechanism of the PEG layer in this system is related both to a modification of the interfacial shear strength as well as to its having an influence on the adhesive properties. As with the macroscopic studies [26,27], the lubricating properties of PLL-g-PEG were improved by increasing the surface EG density. It is, however, to be noted that even the most effective PEG-layer coating, i.e. PLL(20)-g[3.5]-PEG(5)5 (with resulting PEG chain density of 0.27/nm2 ), showed a clear increase of friction forces from the onset of the sliding contact. This is mainly due to the high pressure exerted by AFM in comparison to that generally used in SFA, rather than the low polymer-brush density on the surface; a preliminary friction study by SFA involving the same PLL-g-PEG polymer revealed the existence of a load regime where no friction is detected, as seen for the polystyrene/toluene system (unpublished data, see footnote 3 for more information). Müller and coworkers have also reported AFM studies of the surface-grafted PEG layers, focusing on the influence of solvation on their frictional properties [102,103]. In these studies, the amount of solvent (mass and/or number of molecules per unit area) absorbed within the polymer brush has been estimated by the combined techniques of quartz crystal microbalance with dissipative monitoring (QCM-D) and optical approaches, e.g. optical waveguide lightmode spectroscopy (OWLS) [104,105] or ellipsometry. While the surfaceadsorbed mass, as measured by QCM-D, includes a contribution from solvent molecules that are bound or “hydrodynamically coupled” to the adsorbed film, optical techniques are sensitive only to the “dry” mass of the adsorbed species. Thus, when used together, these two methods allow the quantification of the amount of solvent absorbed within the polymer brush. For a given PEG layer (i.e. fixed “dry” mass) adsorbed from aqueous solution, the solvation amount was varied by replacing water with three different solvents with varying PEG solubility, i.e. methanol, ethanol, and isopropanol. The measured areal solvation amount, ψ (ng/cm2 ), was then correlated with the frictional properties measured by AFM [102,103]. As shown in Figure 21.16, the coefficient of friction, obtained from the slope of the friction-vs.-load plots, revealed an increasing trend with decreasing solvation. Since the PEG-brush density is invariant for all solvents, the solvation amounts directly reflect to multiple interactions provided by the many amino groups along a long PLL backbone. Since the molecular weights of PEG employed in this approach (2,000 Da and 5,000 Da) are somewhat different from that used by Raviv and coworkers [90], it is difficult to directly compare the results with each other. Nevertheless, according to the values reported in the literature [100], the static brush lengths, L0 , of both the PEG films, 9 nm and 17 nm for PEG 2,000 and PEG 5,000 Da, respectively, appear to be higher than that by Raviv and coworkers [90] and smaller adhesive forces were also observed. Aqueous lubrication studies with these polymers are currently in progress and preliminary results show the existence of a load regime where the friction forces remain below the detection limit, as observed in the polystyrene/toluene system [69,70]. 5 “PLL(20)-g[3.5]-PEG(5)” corresponds to molecular weights of PLL and PEG of 20 kDa and 5 kDa, respectively, and a graft ratio (= lysine-mer/PEG side chains) of 3.5.
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Figure 21.16 Coefficient of friction, μ, vs. solvation, ψ , for both asymmetric (open symbols) and symmetric (filled symbols) PLL(20)-g[3.5]-PEG(5) coated tribointerfaces (", water; Q, methanol; F, ethanol; 2, 2-propanol). Coefficients of friction were derived from a linear regression of the friction-load plots, and represent the mean values of three experiments (±, standard deviation) (from [102, Figure 6]).
the conformation of PEG polymer layer, i.e. from more extended brush (in aqueous solution) to an increasingly collapsed state, as the solvent quality decreases. Interestingly, a similar approach employing a series of binary mixtures of water and isopropanol revealed a highly nonlinear change in the areal solvation, Figure 21.17(a), as well as the coefficient of friction, Figure 21.17(b) [103]. This behavior is related to a preferential solvation of PEG brushes by the good solvent component (water) and resulting uneven partitioning of the mixed solvent within and outside the brush layers for a wide range of mixing ratios, 0 < φ < 0.85. 21.3.2.2 Polyelectrolytes Water is far more polar than most other organic solvents studied for brush-assisted lubrication [7,64–70], and presents a unique opportunity to observe the behavior of charged polymer chains, i.e. polyelectrolytes, which more closely resemble the charged sugar chains that are ubiquitous in natural lubrication mechanisms. Klein and coworkers have grafted poly(sodium sulfonate glycidyl methacrylate) (PSGMA) chains by means of diblock copolymerization with hydrophobic poly(methyl methacrylate) (PMMA), which are attracted onto hydrophobized mica (see Figure 21.18 for the molecular schematic of PMMA-b-PSGMA) [106,107]. Some structural features of the grafted polyelectrolyte film include the unperturbed length, L0 = 13 ± 2 nm, surface coverage, Γ = 3 ± 1 mg m−2 , and adjacent chain spacing, s = 4 ± 0.7 nm. As with previous studies involving neutral polymer brushes [69], noise-level friction forces were detected, this time down to D ≈ 11 nm, and the effective coefficient of friction and the corresponding pressure were μeff ≤ 0.0006 and ca. 0.3 MPa, respectively. The load-carrying capacity and lubricating properties of these polyelectrolyte brushes are compared with other grafted polymers, including (a) polystyrene in toluene (b) PEG in aqueous solution and an adsorbed polyelectrolyte (c) chitosan, in good solvent conditions. Since all these polymers possess different molecular architectures and conformations on mica surfaces, the volume fraction, φ, occupied by the compressed, sheared polymer was taken as the universal parameter for comparison. As shown in Figure 21.19, the grafted polyelectrolyte brushes reveal the maintenance of low frictional properties to a significantly higher volume fraction (≈1) compared to the other
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Figure 21.17 (a) Areal solvation, ψ , of surface-bound PLL-g-PEG as a function of the composition of the binary solvent mixture, φ (φ = 1, pure 2-propanol, φ = 0, pure aqueous HEPES buffer solution). (b) Coefficient of friction, μ, vs. the chemical composition of the binary solvent mixtures, φ (φ = 1, pure 2-propanol, φ = 0, pure aqueous HEPES buffer solution). Coefficients of friction were derived from a linear regression of the friction-load plots shown in Figure 21.4 (from [103, Figures 3 and 5]).
polymers. As with neutral polymer brushes in water or organic solvents, excluded volume effects arising from the mutually interacting brush chains’ configurational entropy initially account for the lubricating properties of the polyelectrolyte brushes. Due to the presence of the charge, however, the osmotic pressure is also augmented by a large component exerted by mobile counterions within the brush (ca. 0.3 M even for unperturbed brushes) and hence the reduced mutual interpenetration. As another contributing factor to the effective load-carrying capacity and lubricating properties of polyelectrolyte brushes, the authors proposed that each of the charged polyelectrolyte segments rubbing against each other within the sheared interpenetration zone is surrounded by a tenaciously bound hydration sheath, which is very fluid and serves as
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Figure 21.18
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The chemical structure of the PMMA-b-PSGMA copolymer (from [107, Figure 1]).
Figure 21.19 Variation of the effective coefficient of friction μeff with volume fraction φ of confined polymer for different polymer lubricants. Volume fractions are based on absolute adsorbance values determined for the respective polymers from in situ refractive index measurements. Diamonds and upright triangles are for neutral brushes in non-polar [69] and in aqueous [90] good solvents, respectively, with respective bands indicating the range of the scatter. Inverted triangles are for an adsorbed cationic polyelectrolyte, chitosan, in an aqueous solution at pH 3.5 [120]; the normal force profiles of this chitosan sample, M = 6 × 105 and degree of deacetylation 85% (Fluka), are very similar to those reported in [120] where a comparable chitosan samples was used in similar conditions. The adsorbance of the chitosan samples onto each mica surface is 1.2 mgm−2 , determined by in situ refractive index measurements. The data shown are from two independent experiments and different contact points within each experiment. The black symbols and corresponding gray band are from the study on the PMMA-b-PSGMA brushes. Shear velocities for all data are in the range of 250–500 nms−1 . The cartoons illustrate the different charged and uncharged lubricant configurations, with positive or negative charge signs indicating the counterions (from [106, Figure 3]).
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an efficient lubricating layer. This idea was based upon other work by the authors [108], showing that in water with a high salt concentration (ca. 0.1 M NaCl), the bound hydration layer (or hydrated Na+ ions condensed on the surface) between two mica surfaces renders the normal approach repulsive (sufficient to overcome the van der Waals attraction at all separations), and yet remains extremely fluid, down to D = 1.0 ± 3 nm. The μeff was measured to be ca. 0.0002 under ca. 0.4 MPa and a shear rate of ca. 300 s−1 . This behavior is in sharp contrast with that of the aforementioned simple organic solvents, which reveal a solid-like behavior under similarly confined conditions. In fact, the fluidity of the confined water layer, whose viscosity is of a similar magnitude to that of bulk water, is also observed in salt-free or low-concentration (to 10−3 M NaCl) salt water as well [109]. These water molecules are, however, easily squeezed out by the confinement of the two mica surfaces as they come into adhesive contact. The “charge-bound water molecules”, in contrast, seem to remain at the sliding interface. The maintenance of fluidity is thus attributed not to the hydrated ions themselves or their exchange, but the rapid exchange of water molecules at the outer surface of the hydration layer (at the rate of 109 s−1 for the bulk case, which is much faster than the shear rate, ca. 103 s−1 ). It is important to note that the fluidity of the confined water layer is not observed, with or without salts, unless the water is extremely clean, and in the presence of contamination, high effective viscosities are observed at values of D < 2–3 nm. The relevance of such a mechanism to biolubrication, however, should wait for more experimental verification, since the high ionic strength of biological systems (ca. 0.15 M) is expected to remove the advantages of the polyelectrolyte brushes, to some extent. 21.3.2.3
Natural Brush Polymers
Lastly, we want to briefly comment on studies involving natural, brush-forming polymers, such as glycoproteins, proteoglycans, or polysaccharides. These natural polymers are, of course, all water-soluble, yet distinguished from the synthetic polymers discussed in this chapter in that they are constructed from sugar units. Since poly- or oligosaccharides have long been believed to function as a critical component of biolubrication, there have been numerous efforts to investigate the lubricating properties of glycoproteins [110– 112], mucins [113,114], or even synovial fluid itself [115–117], by employing standard tribological instrumental approaches. Recent micro/nanotribological studies involving natural brush systems have made some significant steps forward, in that the polymers have been grafted onto surfaces in controlled ways, as opposed to simply being added to lubricant systems. For example, thiol-functionalized glycosaminoglycan (S-CS-GAG) has been self-assembled onto gold substrates [2], and hyaluronic acid attached onto bilayer membranes either through a biotin-streptavidin interaction or by covalent bonding [78,118,119]. Nevertheless, the surface-grafting of polysaccharides through only one end is not a trivial task due to the chemical activity of functional groups along the polysaccharide backbone, and many of the systems studied have not been in a brush-like structure but have rather displayed an adsorbed conformation [78,118,119]. The reported lubricating properties of, for instance, a hyaluronic acid film [78], which are not as impressive as under biological conditions, are thus partially related to the inappropriate conformation generated in those model systems. While the micro/nanoscale tribological investigation of natural polymers
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grafted onto surfaces is expected to provide unprecedented understanding of the fundamental aspects of biolubrication, development of appropriate model systems must proceed in parallel.
21.4
SUMMARY AND OUTLOOK
In this chapter, we have reviewed the studies of brush-assisted lubrication, mainly in aqueous environments, that have been carried out in the last two decades. We started the discussion from the application-oriented studies on macroscopic scale contacts, including thermoplastics, metals, oxides, elastomers, and hydrogels as tribopairs, and went on to discuss more fundamental studies on the micro- and nanoscopic contact scales by employing ideally smooth surfaces, such as mica and highly polished silicon surfaces. Fundamental studies by SFA showed that, under moderate compression, the shear between mica surfaces bearing polymer brushes in good solvent can reveal immeasurably low friction forces: the coefficient of friction as low as ca. 0.0005. In this regime, the normal pressure is balanced by the osmotic pressure originating from the polymer brush layer, while the interfacial layer remains fluid-like, due to the configurational-entropy-limited interpenetration between opposing polymer brushes. The contact pressures at which such ultra-low frictional properties may be observed can be as high as 1 MPa, depending on the types and conformation of the grafted polymers. At higher contact pressure, however, lubrication is achieved by different mechanisms, as confirmed by SFA, AFM, and many other conventional tribological tests; the lubricated sliding contacts reveal solid-like behavior in the sense that the friction forces show a finite increase with increasing load, grafted polymers eventually being detached from the surface under harsher tribological conditions. In the high-pressure regime, it is generally recognized that the entrainment or retention of lubricant (water) at the tribointerface is enhanced when the surfaces are grafted with polymer brushes, leading to effective boundary lubrication. Given that the detachment of the grafted polymer is essentially unavoidable at high contact pressures, it is advantageous to design the polymer grafting in such a way that detached polymers can be quickly replaced by molecules dissolved in the lubricant, thus healing the tribostressed area. As far as lubrication engineering is concerned, the most distinctive merit of brushassisted lubrication is that many liquids that have been conventionally considered to be inadequate as lubricants, such as water—the focus of this chapter—can be readily lubricated if the tribopairs are properly modified by brushes. This is because the efficacy of brush-assisted lubrication is primarily determined by the conformation of the polymers on the surface, which is, in turn, determined by the interplay between the polymer and the solvent (lubricant), rather than either component in isolation. In other words, the osmotic pressure arising from highly stretched polymer brushes in good solvents compensates to a large extent for any shortcomings of the liquids as load-carrying lubricants themselves. Water is a particularly attractive liquid in this sense, since it possesses many other favorable features as a lubricant, being economical, environmentally friendly, non-flammable, biocompatible, and a highly effective coolant. Many biolubrication systems employ brush-like polymers as a major component, as mentioned in our Introduction. We expect that further studies of brush-assisted lubrication will not only lead to novel, water-based lubricants and
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sliding surfaces in the future, but will also greatly raise the level of our understanding of natural lubrication mechanisms.
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– 22 – Friction Control at The Molecular Level: From Superlubricity to Stick-Slip Denis Mazuyer, André Tonck and Juliette Cayer-Barrioz Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systèmes UMR 5513 CNRS/ECL/ENISE, F-69134 Ecully Cedex, France
22.1
INTRODUCTION
Friction plays a crucial role in the operation and performance of many engineering systems. The control of their tribological behavior is important for mainly two reasons: From an energy point of view, reducing the dissipated powers increases the efficiency and performance of these systems. From a reliability point of view, avoiding surface damage (fatigue, fracture or seizure) increases their reliability and lifetime. Lubrication is one of the means of achieving these goals. When two rubbing surfaces are separated by a bulk layer of lubricating fluid such as oils in gears or in automotive engines, the lubricant facilitates the relative motion of the solids and reduces friction. Then, the shearing of the lubricant accommodates the sliding velocity and the frictional dissipation is mainly dependent on viscosity. Thus, in order to increase the lifetime of contacts, tribologists need to quantify the basic properties of the lubricant and the surfaces it is separating. Previously, the bulk properties of these materials (lubricant and solids) were fairly sufficient. In most of the lubrication processes (e.g., metalforming, valve train, bearings, etc.), this is no longer true and a more precise knowledge of mechanical properties of solids and lubricants is required on a scale which is small or comparable with the film thickness. Nowadays, this means a scale in the range of 10−9 to 10−7 m at which the surface phenomena and the interface confinement cannot be neglected anymore. In this regime, the interfacial behavior changes significantly: relaxation times become orders of magnitude higher than those of the bulk and the thin lubricant films may have solid-like properties [1]. This is why, the study of sliding friction to understand its genesis at the molecular scale has recently come into focus in tribology [2–4]. In spite of its great practical importance [5,6], the microscopic origin of sliding friction is not well understood [7–10]. Nevertheless, Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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its physics has benefited from significant progress from two different, but complementary, lines of research [11]. The first one is concerned with the low velocity (or quasi-static) multi-asperity contact between two macroscopic rough solid surfaces. Within this framework, the friction force is usually expressed, following Bowden and Tabor, as: T = σ s · Σr ,
(1)
where Σr is the real contact area and the stress σs defines an interfacial shear strength. In the case of solid friction, the contact consists of a set of welded junctions that form, at the asperity level, a continuous solid. Because of the small size of the micro-contacts, the deformation regime of the load-bearing asperities is mainly plastic and the contact pressure is bound by the hardness of the softer material. Thus, the multi-contact interfaces are a homogeneous pure plastic medium and the interfacial shear strength σs is, with respect to the plasticity criterion, the yield shear strength, k of the solids. Associated with the work of Greenwood [12], the resulting friction law is the first explanation of the Amontons– Coulomb’s proportionality between frictional and normal forces that accounts for material characteristics (elasticity, plasticity, adhesion) and the geometrical properties related to the surface roughness [1,6,13]. However, it is now firmly established that the frictional response of multi-contact interface at low velocities often deviates from the Amontons–Coulomb friction behavior, for various materials such as metals [6], elastomers [14], paper [15], rocks [16] and polymer glasses [11]. The static friction coefficient μs , ratio of tangential force on incipient sliding to normal load is found to increase with the contact duration ts prior to gross sliding. For example, when deformed close to the yield stress of the materials, the asperities plastically creep [17] and the real contact area Σr augments with time. The interface ages and becomes stronger and the static force is: Ts = σs · Σr (ts ).
(2)
The dynamic friction coefficient μd depends on both the sliding velocity V and the whole slip history [18]. When motion starts, micro-contacts are gradually destroyed and replaced by fresh ones after a memory length D0 that has been evidenced for the first time by Dieterich [19]. During a velocity jump from V1 to V2 , the interface needs to slide along a characteristic distance D0 to reach its final stationary state. As soon as the resting time is greater than D0 /V , the real contact area after a D0 slip is smaller than Σr (ts ). Thus the dynamic force is lower than the static one suggesting that when the interface slides, it rejuvenates and weakens [20]. One generally observes quasi-logarithmic decreasing μd (V ) and increasing μs (ts ) respectively [21]. Even if these variations are very weak (roughly few percents over each decade of velocity or time), they have huge consequences on the sliding stability of a rubbing contact and may produce stick-slip oscillations. Thanks to experiments with an interface of constant Σr between a rough PMMA surface and a smooth silanized glass surface (avoiding the effects induced by the asperities
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refreshments), Bureau et al. [20] recently accessed to the rheology of the nanometer-thick adhesive joints in which shearing localizes [11]. They showed that each of them could be considered as a confined 2D glassy medium or threshold fluid. Thus, the dynamic friction regime appears as the analogous of the plastic flow of a confined amorphous solid. The glassy state of the adhesive joint is obvious when the bulk solids are themselves amorphous but it should be so for ordered solids due to defects in the bulk or the frequent presence of adsorbates [22]. Moreover, the velocity-dependence of the interfacial shear strength σs [11] is consistent with this rheology. This assumption suggests that there is a rheological “aging/rejuvenation” due to the dynamics of individual asperities in addition to the geometric “aging/rejuvenation” related to collective phenomena in the population of micro-contacts. The knowledge of these “rheological” effects has sharply increased over the past 15 years with the extension of SFA towards shear solicitation. This is the basis of the second line of research initiated by Yoshizawa and Israelachvili [23], Georges et al. [24] that deals with single micro-contacts between smooth surfaces with a typical lateral extension in the range 1–10 µm, under a normal stress ranging from 10 to 100 MPa. This approach allows an accurate investigation of the rheology of individual asperities and the effects associated with the interfacial materials involved in boundary lubrication. In this regime, a thin film is confined between the surfaces and displays specific properties very different from the viscous behavior of the bulk. It is usually admitted that the change of the material properties under confinement can be attributed to a liquid/solid transition [25,26]. In some cases, layering occurs in the interfacial material and the situation is similar to a liquid–crystal transition [25,27–29]. Usually, the liquid/solid transition occurs without any ordering and belongs to a large class of structural transitions [28,30,31]. For some lubricants, either glassy or layering transition can be observed depending on temperature [30], dwell time, surface roughness [32] and commensurability of the surface and the film [29]. Generally, the solid-like ordering in the film leads to the development of a static yield stress and stick-slip instabilities. This self-sustained regime appears for different reasons. One of them is related to inertial effects of the system when the time of slip is close to the relaxation time, τmech (roughly the reciprocal of the eigen frequency) of the measuring apparatus [33]. However, it is difficult to increase the stiffness of most SFA beyond about 3500 N/m. Thus, because of this low finite stiffness, SFA studies often evidence instabilities up to a system-dependent critical velocity, Vc . Several experimental studies combined to numerical simulations suggest that the stick phase is associated with freezing (generally in an amorphous state) while the onset of slip is associated with a shear melting transition [25,26]. The resulting intermittent motion can be erratic, chaotic or highly periodic according to the operating conditions (pressure, velocity, temperature), but also to the nature of the surfaces (dry or covered with adsorbed molecules, grafted . . . ) and their characteristics (mechanical properties, rough or corrugated surfaces . . . ). The nature of the transition from unstable sliding to smooth friction also depends on the shape of the confined fluid molecules [33]. For short linear alkanes, the instabilities disappear abruptly leading in a discontinuous way to smooth sliding at a critical velocity that depends on load and temperature [23]. Beyond the critical velocity Vc , the interface has a fluid-like behavior and the friction is mainly viscous. With branched hydrocarbons, the transition is continuous from very regular to stable sliding. Between these two regimes, there is a velocity range within, which neither phase prevails [33,34].
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Even though in practice, the use of adequate lubricants may reduce or even vanish these instabilities, transient effects and stick-slip oscillations reveal the history dependence of the frictional signature. Therefore, their investigation provides richer data concerning the microscopic mechanisms responsible for the dissipation than stationary states. Indeed, if simple lubricants consisting of small molecules have fast relaxation processes, long memory effects have been observed for complex fluids [35,36]. In the case of polymer surfaces and self-assembled monolayers, nano-scale shear measurements also display long relaxation times and characteristic “memory distance” [37–39]. The measured times are much longer than τmech showing that the dynamics is directly related to the boundary layer. The glassy state of the confined interface and the existence of memory effects indicate that the tribological behavior of these molecular systems is very close to that observed, at a much more macroscopic scale with multi-contact interfaces or in seismic phenomena. This short overview shows that even though the nature of the stick-slip oscillations and the transition from stable to unstable sliding are very different according to the molecular organization under confinement, they have common characteristics: Their dynamics is determined by intrinsic properties of the boundary layers. Most of the experiments reported in the literature are carried out within over-damped conditions in which the response time of the mechanical system is much shorter than characteristic slip time of the film itself. Whatever is the shape of the fluid molecules (i.e., spherical, linear, branched, brush, etc.), their friction trace is governed by long memory distances. This first indicates the presence of slip domains or long-range cooperativity extended over lateral distances huge compared with molecular dimensions [34,35]. As the associated relaxation times are much retarded by the confinement, a detailed description of the sliding history is required to obtain a complete picture of the physical shear processes and to be able to predict how the system will accommodate a change of tribological conditions. These that link the microscopic and the macroscopic scales in friction processes are the basis of the so-called phenomenological “rate and state” models to describe the frictional response of dry/boundary lubricated single or multi-asperity contacts as initiated by Ruina for friction of rocks [40]. The rate variable refers to the instantaneous sliding velocity and the state variable is meant to capture all the history dependent effects. This approach assumes that the interfacial area is large enough to be self-averaging. Therefore the mean-field state variable is sufficient to model collective dependence of friction both on the internal degrees of freedom of the interfacial materials and on the dynamical variables characteristic from the shear motion. That is why by relating the state variable to the average lifetime of individual contacts, Ruina’s constitutive equations have been successfully applied to dry friction between solids with micron scale roughness [11,19,41,42]. Carlson and Batista [43] used this phenomenological approach to describe the temporal evolution of single contact in boundary lubrication by associating the state variable to the degree to which the lubricant is melted. Even if they are effective on capturing steady state and transient effects on a wide variety of materials, the friction laws that these mechanisms inspire are not based on the underlying microscopic physics of the interface. Indeed, either in dry friction or in boundary lubrication, the dissipative pinning/depinning of domains whose lateral dimension is between the size of a micro-contact and the molecular size govern the interfacial rheology and the frictional response of contacts. These elementary units are the
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analogous of the elementary volumes of plastic deformation or the “shear transformation zone” (STZ) [44] used to describe the plastic flow of amorphous materials. The latter are at the origin of the multi-stability of micro-contacts in dry friction considering that their stress response involves nanometer-thick amorphous adhesive joints in which shear is localized [11]. Within this framework, Persson [45] proposed a model inspired by the older spring-block theory of Burridge and Knopoff [46] to describe the shear of confined lubricants. As in the nano-block model used in [11] to schematize a single contact, the boundary layer is made of a set of pinned solid-like islands called blocks or domains immersed in a 2D confined fluid. Persson introduced thermal processes that activate nucleation, growth or death of these fluid and/or frozen domains during sliding and stopping [47]. By simulating these islands with coupled mechanical oscillators, the local liquid/solid transitions are correlated to the nature of sliding instabilities. Assuming a size distribution of the blocks, a broadband spectrum of relaxation times emerges that is often associated with chaotic instabilities as observed for branched molecules [33]. The transition between stick-slip/steady sliding and the transient response of the friction force in stop-start tests have also been successfully modeled by an intermediate statistical theory which generalizes the STZ theory where the effects of glassy relaxation are treated via the introduction of a state variable related to the internal free volume [48]. The comparison between experiments and theories clearly shows that the understanding of the tribological response of engineering-type contacts has to account for the coupling between the lifetime of the bearing asperities and the interfacial rheology which both contribute, through their own dynamics, to the level and the stability of the friction force. However, to be related to the friction coefficient, this rheology cannot only be restricted to average mechanical properties such as viscosity or elastic moduli but should include the heterogeneity of the interface induced by both shearing and confinement. Considering the interface materials as a set of statistically treated interacting mesoscopic domains seems to be a promising way of modeling the friction and controlling its level in boundary lubrication. To aim this, long-chain, oil-soluble surfactants are often added to liquid lubricants and form an important class of lubricant additives termed “organic friction modifiers”. The traditional view concerning the mechanism by which these compounds control friction, is that they form physically or chemically adsorbed monolayers on polar solid surfaces and that these monolayers reduce adhesion between contacting asperities and thus limit junction growth [5]. This concept has been supported by studies that have shown that both deposited [55] and self-assembled [56] monolayers on solid surfaces can, indeed, reduce friction. Nevertheless, even if this assumption seems acceptable, it is not sufficient to explain the microscopic physical processes that govern the level and the stability of the friction coefficient. In this chapter, we are dealing with the molecular mechanisms and the associated dynamics of friction between weakly adhering compressed brushes that are often used in . Although the asperity interactions in a rubbing contact produce very high local stresses and surface deformations, which may lead to chemical processes, we show that the monolayer shearing behavior in idealized smooth contacts can bring new insights into the friction control at macroscopic scale by playing with the shape and the organization of friction modifier molecules. The super-low friction that such layers promote under moderate pressure (<100 MPa) is a direct consequence of their intrinsic mechanical anisotropy. It appears that their frictional response at the molecular level is not associated with a local
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ordering as previously shown for liquids under confinement but strongly depends on the interdiffusion of dangling ends within the interpenetration zone in which the chains deposited on the two opposite surfaces entangle [49–51]. The friction velocity dependence has been analyzed with a general model based on the kinetics of formation and rupture of adhesive bonds inside the interpenetration zone with an additional non-Newtonian viscous term. This is an extension of the model used by Drummond et al. [52] to describe the “inverted” stick-slip reported for bulk surfactant aqueous solutions [53,54] where the unsteady regime is bounded by smooth sliding at lower and higher velocities with periods of super-low friction. This approach allows us to interpret the transient effects and the associated memory distances induced by velocity changes from the dynamics of shear activated pinned and free junctions and eventually to deduce the properties of the entanglement area between monolayers.
22.2 22.2.1
EXPERIMENTAL
The Molecular Tribometer
The molecular tribometer with which the nanotribological experiments have been performed is widely detailed in the literature [58]. The basic principle of the molecular tribometer is shown schematically in Figure 22.1. It is derived from a surface force apparatus in which a macroscopic spherical body can be moved towards and away from a plane using the expansion and the vibration of piezoelectric actuators along the three directions Ox, Oy (parallel to the plane surface) and Oz (normal to the plane surface). Three specifically designed capacitive transducers measure the relative displacements of the supports of the surfaces with a resolution better than 0.01 nm in each direction. Three closed feedback loops are used to control the high voltage amplifiers associated with the piezoelectric
Figure 22.1 Picture of the surface force apparatus used as a molecular tribometer.
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actuators. Double cantilever sensors measuring normal and tangential forces support the sample holder. Each of them is equipped with capacitive transducers with a high resolution in spite of their low compliance (up to 2.5 × 10−6 m/N). The latter measure the quasi-static normal and tangential forces (respectively Fz and Fx ) with a resolution up to 10−8 N. Two displacement closed feedback loops allow controlling the tangential displacements x and y while the operations in the normal direction z can be carried out either in displacement or normal force control. An oscillating normal (or tangential) motion can be superimposed on the linear normal (or tangential) displacement. The resulting dynamic displacements and forces are measured with double-phase lock-in amplifiers giving the normal and tangential mechanical transfer functions of the interface between the sphere and the plane. From these signals the elastic and viscous properties of the contact can be derived [51]. All the experiments presented in this work are made at room temperature (23 ◦ C). Before the droplet of lubricant is introduced in the contact, a preliminary approaching of the sphere towards the plane until few nanometers under nitrogen controlled atmosphere is performed to check the topography and the cleanliness of the substrate. 22.2.2
The Materials
22.2.2.1 Solid Surfaces The sphere and the plane consist of a fused silicate glass and of silicon wafer, respectively. Both are coated with metallic cobalt. The sphere is manufactured from a droplet of melted glass to have a perfect control of the radius over the whole surface of the probe. Over a scan length of 1 micrometer, the surface cumulative peak to valley roughness does not exceed 0.5 nm. In comparison with the thicknesses of the adsorbed layer, the solid surfaces can be considered as very smooth. The thickness of the cobalt coating deposited on both surfaces is about 50 nm. XPS analyzes confirmed the presence of a very thin oxide layer about 0.3 nm thick on each surface. Nevertheless, they are highly conductive and permit the measurement of the electrical capacitance of the contact that is used to establish the zero of the displacement scale according to the following procedure. When the surfaces are far from each other (distance longer than ten times the size of the adsorbed molecules), their elastic deformation can be neglected and the normal displacement Z, is the sphere/plane distance, D. As shown by the curve in Figure 22.2, the electrical capacitance of the contact C follows the relation: dD D dZ = = , dC(Z) dC(D) 2πεε0 R
(3)
where ε is the dielectric constant of the liquid, ε0 is the permittivity of vacuum and R is the sphere radius. The straight line that extrapolates the dZ/dC(Z) curve to short distance intercepts the displacement, Z axis at a point corresponding to the location where the metal surfaces should touch. This point that is never reached because of the confinement effect is referred to as the origin of the contact (Figure 22.2).
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Figure 22.2 Reciprocal of the derivative of the electrical capacitance of the contact during the loading of the sphere towards the plane with a solution of stearic acid in dodecane (0.1% w/w). The experimental points are consistent with the linear law of electrostatics. The intercept of the straight line with the normal displacement axis gives the origin of the contact. The permittivity of dodecane can be deduced from the slope of the curve.
Figure 22.3
22.2.2.2
Scheme and dimensions of the stearic acid molecule (a) and of the amine friction modifier (b).
Liquids
Two blends containing friction modifiers have been investigated. The first one is a 0.1% w/w solution of stearic acid in dodecane. It will be called BS in the remainder of the chapter. The stearic acid molecule is schematized on Figure 22.3(a). At room temperature, the bulk viscosity of the blend measured with AR 2000 rheometer from TA instrument is 1.6 mPa.s. The sphere used to characterize this liquid had a radius of 2.95 mm.
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Sphere radii, liquid temperatures and viscosities measured in this work. All the bulk viscosities have been measured with an AR 2000 rheometer from TA instruments Liquid
Content (% w/w)
Radius (mm)
Temperature (◦ C)
Bulk viscosity (mPa.s)
Stearic acid/dodecane Amine/PAO
0.1 0.5
2.950 2.355
22 23
1.6 17
The second friction modifier that has been studied is a N-alkyl dioleate diamine, that we will simply call “amine”. It contains one primary nitrogen atom and one secondary nitrogen atom. The molecule of amine is schematically depicted in Figure 22.3(b). The skeleton of amine molecule is mainly made of C–C bondings, which allows us to determine its dimension. Because of their sp3 hybridizing, all the carbon atoms are not in the same plane. If the location of two among three successive sp3 carbon belonging to the same chain is fixed, the third is necessarily on a cone whose generator is 0.1514 nm long and with a top angle of 141◦ 04′ . It can be deduced from these geometrical properties that the amine molecule is about 2.35 nm long. The molar mass of the amine molecule has been estimated to a value of 902 g mol−1 , from its chemical formula. Combined to its density, the value of the molar mass gives a molar volume of 1.722 × 10−27 m3 . The friction modifier is dilute with a synthetic base oil (PolyAlphaOlefin, PAO) giving a blend with a viscosity of 17 mPa.s at room temperature. This blend will be noted BA. Table 22.1 summarizes the experimental temperatures, bulk viscosities of the liquids and the radii of curvature of the spheres used. 22.2.3
Experimental Procedure
A couple of solid samples (sphere and plane) is prepared and cleaned for each test. It is mounted on the molecular tribometer. As soon as the sphere/plane distance D, reaches 10 µm, a droplet of the tested liquid is carefully deposited between the two surfaces. The actual experiments are started after an adsorption time of 12 hours at this distance. The sphere/plane separation is monitored with the contact capacitance. For BA lubricant, the voltage used to measure the latter is applied only at large distance in order to avoid an orientation of the polar compounds by the resulting electrical field. From an initial operating distance of 1 µm, quasi-static force is measured as a function of D by making inward and outward motions with a constant speed of 0.15 nm/s. The thicknesses and surface properties of the adsorbed layers can be precisely determined from the force-displacement curves obtained during the quasi-static squeeze of the interface. Then, the normal load is maintained constant and the frictional response of the layers is measured for various sliding distances and velocities (from 0.1 nm/s to 500 nm/s). The additional dynamic measurements in both normal and sliding directions (see Table 22.2) permit to link the evolution of the interface stiffness to the friction dissipation and velocity accommodation processes.
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Experimental conditions used for the characterization of the interface in the dynamic mode both in the normal and tangential directions during the squeeze and the nano-friction experiments Experimental conditions
Normal direction
Tangential direction
Sliding speed (nm/s) Vibration frequency Ω (Hz) Vibration amplitude d (nm)
0.01 37 0.1
From 0.05 to 15 220 (BS) and 70 (BA) 0.03
22.2.4
22.2.4.1
Properties of the Confined Layer under Loading
Contact Modeling
In the surface force apparatus designed for the nano-scale tribological experiments, the contact area is not directly measured. Thus, the contact dimensions that give the size of the mechanical probe should be estimated through an appropriate modeling of the contact mechanics. As far as the short sphere/plane distances are concerned, the confinement of the fluid molecules is responsible for the elastic deformation of the solids, δ. The Hertz theory can be used to estimate δ and the contact radius, a assuming that the confined interface behaves as a rigid wall. While the sphere and the plane are being brought towards each other, the relative displacement Z, is a rigid solid displacement. Thus, with this simple modeling, the sphere/plane distance D, can be deduced from: Z + δ = D.
(4)
If adhesion occurs, local interactions have to be taken into account in the modeling of the contact including a surface energy term. Thus, at short distance, whether the adhesion force is negligible or not, the contact pressure can be deduced within the framework of Hertz theory or JKR theory, respectively. When the two surfaces are far from each other (D > 100 nm), they can be considered as rigid solids and the contact pressure results from the Derjaguin’s approximation. The latter links the normal force FZ (D) between a sphere (radius, R) and a plane and the energy per unit surface, W (D) between two planes at the same distance D, as follows: FZ (D) = 2πR · W (D).
(5)
Therefore, at large distance when no elastic deformation appears, the mean contact pressure is the disjoining pressure and can be calculated from the relation: Π(D) = 22.2.4.2
1 dFZ (D) dW (D) = · . dD 2πR dD
(6)
Interface Characteristic Thicknesses
The force/displacement measurement in the quasi-static squeeze of the lubricant within the contact is used to evaluate the thickness of surface layers. The sphere/plane distance on the
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Figure 22.4 Evolution of the normal force in a quasi-static mode versus the sphere/plane distance for a solution of 0.1% w/w of stearic acid in dodecane. The repulsive part of the force reveals the existence of an elastic wall, 5.5 nm thick. This corresponds to the thickness of the confined stearic acid layers at a 100 µN normal load.
incipient repulsive force characterizes the first contact between the adsorbed molecules on both the sphere and the plane. This distance is considered as twice the thickness, L of the adsorbed layer on each solid. When the sphere/plane distance is reduced, the thickness of the adsorbed layer decreases from L to LC due to confinement effect. The interaction is similar to “hard sphere” repulsion and the layers behave as an elastic wall. Its thickness is referred to as LC . It depends on the normal force, FZ . In this work, LC is given for a normal load of 100 µN. These interface thicknesses are reported in Figure 22.4. In the dynamic mode, the mechanical impedance of the interface that is measured by superimposing an oscillatory motion of given amplitude and pulsation, ω is divided into two additive components. The first one is the conservative part coming from the in-phase response of the interface, which gives its elastic stiffness KZ (ω). Thus, the compressive elastic modulus of the interface, E can be deduced from the relation: KZ (ω) = 2Ea,
(7)
where a is the contact radius. The second one is the dissipative part coming from the out-of-phase response of the interface, which gives its viscous damping AZ (ω). It is noteworthy that these measurements can also be carried out simultaneously in the sliding direction, X either during squeeze or friction experiments.
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Figure 22.5 Scheme of the interface squeezed between the sphere and the plane in the surface force apparatus. During the loading, in the quasi-static mode, the adsorbed layers are gradually confined from the thickness, L to the thickness, LC . Under the dynamic mode, the adsorbed layers interact with the flow of the bulk fluid. The analysis of the hydrodynamics shows that the wall of no-slip is moved from a distance LH (hydrodynamic length) over the solid surfaces. LH is interpreted as the thickness of an immobile layer insensitive to the flow.
For large sphere/plane distances and with a homogeneous Newtonian liquid, the Stokes’ law describes the hydrodynamic flow and the associated damping function AZ is given by: AZ =
6πηR 2 , D
(8)
where D is the sphere/plane distance, η is the bulk viscosity of the liquid and R is the sphere radius. The presence of an adsorbed layer drifts the wall where the flow velocity is vanishing towards distance, LH over the solid surface (Figure 22.5). This defines an infinite viscosity layer within which the molecules are not perturbed by the flow. Thus, accounting for this new boundary condition, the damping function becomes: AZ =
6πηR 2 . D − 2LH
(9)
According to relation (9) the plot of 1/AZ as a function of the distance, D allows us to determine the bulk viscosity of the lubricant and the hydrodynamic length, LH (Figure 22.6). When lower than LC , LH results from the capability of the fluid to flow through the molecules that build-up structures more or less ordered by their interactions with the surfaces. This local organization slightly roughens the surface and the volume fraction of the adsorbed molecules can be deduced by an appropriate modeling of the hydrodynamic flow through the surface micro-geometry. Using a multilevel method [59] to numerically solve the Reynolds equation and to compute the viscous fluid damping as a function of the sphere/plane distance, it has been found that the ratio LH /LC was exactly equal to the surface coverage of molecules (or particles) whatever their shape and height [60]. Thus, in the case of brush-like layers, the ratio of LH to LC is related to the layer heterogeneity: if LH /LC is close to 1, the surfaces are covered
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Figure 22.6 Variations of the 1/(AZ ω) damping function for a 0.1% w/w solution of stearic acid in dodecane (R = 2.95 mm and ω = 232 rad/s). At large distance, the slope of the curve gives a viscosity of 1.6 mPa.s, which is consistent with the value of the bulk viscosity. The best fit of the curve for large distance intercepts the distance axis at 4.3 nm, which defines the hydrodynamic thickness.
Figure 22.7 Scheme of the organization of molecules in a brush-like layer. When the monolayer is complete (a), the hydrodynamic length, LH is equal to the thickness of the confined layer, LC (i.e., the thickness of the monolayer). When the monolayer is uncompleted (b), the solvent flows through the layer and LH is less than LC . In both situations, LH /LC gives the value of the surface coverage.
by a dense homogeneous monolayer while if LH /LC < 1, the monolayer is uncompleted (see Figure 22.7). The surface density of the layer before confinement is given by LH /L.
22.3 22.3.1
RESULTS AND DISCUSSION
Squeeze Behavior of the Adsorbed Layer of the Friction Modifiers
The evolutions of the static force according to the sphere/plane distance measured for the blends BS and BA are not hysteretic between the loading and the unloading curves (Figure 22.4 and Figure 22.8). This indicates that the interface made of the contacting monolayers is an elastic wall. Before the repulsive part of the curve, an attractive force is measured. In both liquids, it is well fitted by a Van der Waals’ law with a Hamaker constant of 1.5 × 10−19 J (non-retarded effects over a distance range from 5 nm to 20 nm).
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Figure 22.8 Evolution of the normal force during an inward and outward motion for the solution of amine friction modifier. There is no hysteresis between loading and unloading. As shown in the insert, the adhesion force is well fitted by a Van der Waals law consistent with a Hamaker constant of 1.5 × 10−19 J. The hydrodynamic and the confined layer thicknesses are very close to each other indicating a high surface coverage of the surfaces by the amine molecules.
Table 22.3. Thicknesses characteristic from the adsorbed layers formed with stearic acid and amine molecules after 12 hours adsorption time. The ratio of the hydrodynamic length to the thickness of the layer is a straight indication of the layer surface density Liquid
2LH (nm)
2L (nm)
2LC (nm, 102 µN)
LH /L
LH /LC
Stearic acid/dodecane Amine/PAO
4.30 4.25
6.8 6.30
5.50 4.50
0.63 0.67
0.78 0.94
Thus, this weak adhesion is taken into account in the contact model to determine the parameters of the elastic contact versus normal FZ , i.e. contact radius, mean contact pressure and elastic deformation of the solids. All the thicknesses that characterize the interface are summarized in Table 22.3. The distance of the onset of repulsion, 2L and the confinement distance, 2LC (measured at a normal load of 100 µN corresponding to a mean contact pressure of 10 MPa) divided by the thickness of the immobile layer, 2LH is equal to the surface density before and during confinement, respectively. From the values of Table 22.3, it can be deduced that: The hydrodynamic distance is close to the double of the length of the individual molecule in both cases. This suggests that the plane and the sphere surfaces are covered with
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a nearly complete and homogeneous monolayer of friction modifier. The low thickness of these layers combined with their low compliance validates the use of JKR theory to estimate the contact pressure. The confinement increases the surface density of the layer adsorbed from both liquids. Moreover, before and under confinement, the surface density of the amine layer is higher than that of the stearic acid layer. The softer increase in the static normal force when the sphere/plane distance is close to the thickness 2L shows that the stearic acid layer is thicker and displays a higher compressive compliance. This could be due to its lower surface coverage, at low loads. 22.3.2
Frictional Properties of the Adsorbed Layers of Friction Modifiers
22.3.2.1 Experimental Procedure and Theoretical Background The tribological behavior of the friction modifiers layers is characterized from two types of friction experiments: (i) The sphere moves towards the plane, the normal force FZ is maintained constant after the squeeze of the monolayers by using the feedback in the force mode and the sphere is then tangentially displaced. The friction force is measured as a function of sliding distance, at constant normal load. The effects of sliding velocity on the accommodation of adsorbed layers to the shearing solicitation are more particularly investigated. During the friction process, a sinusoidal motion is applied in the sliding direction in order to simultaneously measure the tangential mechanical impedance of the interface (Figure 22.9). As schematically shown in Figure 22.9, the evolution of the tangential force FX follows two periods: • A linear reversible period described by tangential stiffness KX . • A non-linear period where the tangential force is increasing until an equilibrium valueFXℓ . The length noted X ∗ that represents the threshold beyond which the interface is no longer elastically deformed and starts sliding with energy loss is defined as: X ∗ = FXℓ /KX .
(10)
(ii) In order to analyze the tribological properties of the molecular layers over the whole range of load, the sliding is applied while the sphere is being slowly displaced normal to the plane. Thus, the frictional force is continuously measured as a function of the normal force. The squeeze velocity is 0.02 nm/s whereas the sliding velocity is 0.1 nm/s for stearic acid and 0.6 nm/s for lubricant BA. In these operating conditions, the stationary friction regime is achieved, as shown in Figure 22.9. Therefore, the instantaneous tangential force is the same as the force that would be measured if the two surfaces were sliding at the same load maintained constant. Moreover, oscillatory motions are superimposed on the normal and tangential displacements to measure the visco-elastic properties of the sliding interface in both normal and tangential directions. In that purpose, appropriate amplitudes and frequencies are chosen to avoid micro-slip that
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Figure 22.9 Typical evolution of the frictional force versus the sliding distance during an experiment at constant normal load. After a linear phase characterized by the elastic stiffness KX , the tangential force Fx reaches a limited value FXℓ . The transition between these two periods occurs at sliding distance X∗ = FXℓ /KX . The vibration superimposed on the tangential motion results in little reversible cycles with a slope KX , leading to a continuous measurement of the tangential stiffness during the friction process.
could be induced by the tangential sinusoidal displacement. As a consequence, the amplitude of the tangential vibration must be less than critical distance X ∗ associated with the adsorbed layers (Figure 22.9). The experimental conditions that must also take into account the loss of resolution due to the non-linearity of the friction process are summarized in Table 22.2. As the amplitude X of the oscillatory tangential motion is sufficiently small to prevent additional slipping, the measured tangential force corresponds to the force T = KX · X that is required to elastically shear the interface of thickness, D along a sliding distance, X. Assuming that the interface is homogeneously sheared overall its thickness in its elastic domain, the associated mean shear stress, τ is given by the Hooke’s law: τ=
KX · X X T = =G· , S S D
(11)
where S is the contact area. As the mean contact pressure is P = FZ /S, Equation (11) leads to the mean shear modulus, G normalized by pressure, P : G P
=
KX · D . FZ
(12)
In this “landing” experiment, the tangential force FX , the tangential stiffness KX and distance D are simultaneously measured according to the normal load varying over three decades between 1 µN and 1000 µN (contact pressure from 3 MPa to 30 MPa). The level of the friction coefficient will be correlated to the value of ratio KZ /KX . 22.3.2.2
Sliding Velocity Accommodation
The frictional behavior of stearic acid monolayers has been tested at a constant normal load, Fz = 1000 µN (contact pressure of 30 MPa) and varying sliding speed, as shown in Figure 22.10.
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Figure 22.10 Effect of the sliding speed on the friction of stearic acid monolayers at constant normal load (FZ = 1000 µN). The interface accommodates the friction force by correlated variations in thickness and tangential stiffness by 20 to 40%. When the sliding is stopped, these phenomena are also observed and the friction force does not relax completely. This suggests the existence of a visco-elastic dissipation localized in a zone where the monolayers may interpenetrate.
For sliding velocities higher than 10 nm/s, the friction coefficient is 0.007. The evolution of the friction force is associated with variations of both the tangential stiffness and the mean thickness (deduced from the simultaneous variations of the contact electrical capacitance) of the interface. Thus, when the sliding speed is increased, a first transient augmentation in the tangential force (suggesting a small viscous contribution to friction) is observed. It is followed by a slow decrease in the tangential stiffness and force. Meanwhile, the film thickness slightly but quite noticeably increases. Therefore the friction force is accommodated by a change in thickness and stiffness of the interface. These effects are clearly shown when the sliding is suddenly stopped resulting in a relaxation experiment: the friction force steeply drops to a minimum non-zero value whilst the tangential stiffness KX increases by 40% over a longer period. However, the small change in film thickness (about 0.001 nm) cannot explain the important increase in stiffness measured during the friction test. This suggests that stiffness KX is not related to the elasticity of the whole interface but more likely to the behavior of an interpenetration zone (whose thickness is very small compared to the bi-layer thickness) between the monolayers. Inside this zone, the mobility of defects could lead to the sliding at low shear strength in a similar way as the dislocations motions in the plastic flow. The relaxation experiment presented in Figure 22.10 clearly shows the visco-elastic response of the zone where the shear plane is located. The same kind of experiment has been performed with lubricant BA. Figure 22.11 shows the evolution of the friction force versus sliding distance X and the kinetics of its variations when a sequence of increasing and decreasing sliding velocities is applied. During the whole test, the normal force is maintained constant at 10−3 N. The sliding speed is aug-
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mented or diminished in four successive stages: 0.1 nm/s, 0.6 nm/s, 3 nm/s and 12 nm/s. In that procedure, the tangential vibration is switched off. The main results obtained with lubricant BA are detailed as follows: (i) The amine layers exhibit an extremely low friction coefficient (only few thousandth) offering outstanding superlubricity properties in the studied range of sliding velocities. (ii) The molecular tribometer is able to measure accurately significant tangential forces for sliding speeds as less as 0.1 nm/s, which is sufficiently slow to suppose that the resulting friction force is comparable to a static friction coefficient. This point is confirmed by the occurrence of a sharp peak at the beginning of the sliding (see Figure 22.11). (iii) Lubricant BA has a liquid-like behavior since each increase (resp. decrease) in the sliding velocity produces an instantaneous and transient increment (resp. decrement) of the friction force. This interface accommodation of the interface to speed variations suggests that a viscous component contributes to the friction coefficient. After three successive increases in sliding speed, by a factor four, the increment of the stabilized force preceding the speed shift is 13%, 17% and 9%, respectively. As explained in the following part, the shear viscosity of the interface can be deduced by combining these experimental results with the estimation of the apparent contact area and of the thickness of the shear plane. (iv) A lower steady-state frictional force characterizes the friction regime that follows this transient response. To be achieved, the latter requires an adaptation of the interface to the change of the contact kinematics over a sliding distance of few ten nanometres. A slight increase/decrease in the interface thickness is associated to this accommodation. For lubricant BA, a 0.1 nm levitation occurs once the stationary period has been
Figure 22.11 Friction trace of an amine bi-layer induced by a series of increasing/decreasing sliding velocities. The interface accommodates these shear solicitations by an immediate transient viscous response followed by a slow relaxation of the friction force along a memory length of about 20 nm. Beyond this displacement, the interface forgets the history of previous sliding kinetics, which explains that these transient effects are completely reversible.
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reached at 10 nm/s leading to a kinetic friction coefficient that is three times lower than the static one. This thickness increase will be used as an order of magnitude of the thickness of the shear plane. At faster velocity, the reduction of the friction dissipation is no more significant and the friction stabilizes at 0.003, which is a usual value in hydrodynamic lubrication but not in boundary regime. As for the stearic acid monolayers, the frictional response of the amine bi-layer depends on the sliding speed and is accommodated by thickness variations of few tenths of nanometers. When the sliding speed is increased, the tangential force decreases (after a little transient viscous increase) while the thickness of the interface is increasing. These correlated evolutions of tangential force and thickness follow the same kinetics. They are all the more rapid as the sliding speed is fast suggesting that for both friction modifiers, these phenomena are governed by a relaxation length rather than by a relaxation time. This length D0 , (1.5 nm for the stearic acid and 20 nm for the amine) appears as a memory distance beyond which the interface has forgotten the history of the previous sliding kinematics. This explains why these transient effects are completely reversible. Indeed, the interface recovers its initial state after a succession of identical steps of increasing/decreasing sliding velocities. 22.3.2.3 Mechanical Anisotropy: Is it a Possible Cause for Superlubricity of the Friction Modifier Layers? During an experiment, the normal stiffness is generally less easily determined than the tangential because of the elastic contribution of the solids due to the hydrodynamic fluid squeeze while the tangential vibration detects the properties of the actual contact. Fortunately, the use of adapted frequencies and the low pressure of the viscous flow give results that are independent of the visco-elastic fluid/solid coupling. In Figure 22.12, normal stiffness KZ is plotted against tangential stiffness KX , for both amine and stearic acid layers. At low contact pressures, the contacting stearic acid and amine monolayers are characterized by ratios KX /KZ of 1/20 and of 1/300 respectively. For Hertzian contacts between two bulk solids, the KX /KZ ratio becomes: KX /KZ = 2(1 − ν)/(2 − ν),
(13)
where ν is the Poisson’s ratio of the film. KX /KZ varies between 2/3 and 1, for ν varying between 0 and 1/2. When an interface is considered as a thin isotropic layer that can be described by classical mechanics of continuous media, KX /KZ is given by: KX /KZ = 1/ 2(1 + ν) .
(14)
As ν is between 0 and 1/2 (for non-compressible materials), relation (14) shows that KX /KZ lies from 1/3 to 1/2. The experimental data obtained for the amine and stearic acid monolayers are outside these ranges which suggests that the brush layers build by the friction modifiers are nonisotropic materials. Moreover the ratios KX /KZ are very low which supports the hypothesis that the significant non-isotropic behavior of the brush structure is responsible for their
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Figure 22.12 Tangential stiffness of the interface Kx , as a function of its normal stiffness Kz , for two adsorbed layers of friction modifiers: amine (flexible brush layer) and stearic acid (rigid brush structure). The gray area corresponds to the theoretical domain obtained for a thin isotropic layer from contact mechanics with a Poisson’s ratio varying between 0 and ½. The experimental points are outside this domain, which suggests that the formed brush layers are non-isotropic. The deviation of the measurements from the dotted straight line for the stearic acid indicates the appearance of the elastic deformation of solids.
capability to reduce friction coefficient with high efficiency. This assumption is confirmed by the particular case of the amine whose ratio KX /KZ is lower than the one of the acid stearic layer by about one order of magnitude and that gives a twice-lower friction force in the same tribological conditions. On the other hand, high friction (about 0.25) is obtained for entangled layers of poly-isoprene that display a KX /KZ ratio in the range of 0.3, characteristic from a thin isotropic film [51]. Thus, there is a strong correlation between the ratio KX /KZ of confined adsorbed layers and their frictional response. At higher pressure, the response of the layers is strongly affected by the contribution of the elastic deformation of the solids and the stiffness KX and KZ cannot be considered as issued from the interface elasticity. 22.3.2.4
Friction and Elasticity of the Friction Modifier Layers: Pressure Effect
The elastic properties of the friction modifiers layers contribute to their frictional behavior and depend on their confinement state. Thus, it can be expected that the pressure-induced effects investigated with “landing” experiments affect the friction coefficient. Actually, the landing test is equivalent to a tribological experiment at constant sliding velocity with a load increased at constant speed. Then, this allows us to measure the continuous evolution of the tangential force FX according to the normal FZ , for a given sliding velocity. Figure 22.13 shows that the friction coefficient, deduced from the slope of the FX (FZ ) curve is independent of the load for both friction modifier layers and is equivalent to the value that would be obtained at the same sliding velocity but with a constant normal load. This confirms that this friction test detects the stationary friction and that the superimposed oscillatory motion does not perturb the frictional response of the confined interface.
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Figure 22.13 Evolution of the tangential force versus the normal load during a “landing” experiment for stearic acid and amine layer, for a sliding velocity of 0.05 nm/s. The linearity of the curve shows that the friction coefficient is independent of load in the range explored in the test.
Moreover, as from (10), the friction force, at the first order, can be simply expressed, as: FXℓ = KX · X ∗ = (KX · D) × (X ∗ /D).
(15)
Then, the friction coefficient μ as the ratio of tangential force FXℓ to normal force FZ , follows the relation: μ = FXℓ /FZ = (KX D/FZ ) × (X ∗ /D) = (G/P ) × (X ∗ /D).
(16)
The friction coefficient appears as resulting from a conservative component controlled by the shear elasticity of the adsorbed monolayers (G/P ) and from a dissipative component given by X ∗ /D. This parameter is comparable with the elastic yield shear strain of the contacting molecules before the first slip between adsorbed layers occurs. G/P and X ∗ /D are directly measured in a landing experiment without any a priori modeling of the contact. Their evolution is plotted versus contact pressure in Figure 22.14 for the two monolayers of friction modifiers (i.e. stearic acid and amine). The evolution of G as a function of the contact pressure is also represented in Figure 22.15. These curves first show that the elastic moduli of the adsorbed layers increase with the contact pressure. As soon as the contact is loaded, the compressive elastic modulus of the amine layer immediately reaches a high value of about 2 GPa while the shear elastic modulus normalized by the contact pressure remains extremely low (about 0.04) during the whole squeeze (Figure 22.15 and Figure 22.14). The amine layers are consolidated under pressure and G increases from 0.12 MPa to 1.2 MPa in the range of load scanned in this work. The stearic acid monolayers are stiffer since G/P decreases from 1 to 0.5 when the load increases. The shear elastic modulus G has then the same order of magnitude as the contact pressure and increases from 3 MPa until a stationary value of 15 MPa. The sliding distance threshold X ∗ is longer for amine molecule than for the stearic acid molecule: it is 0.72 nm for the amine
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Figure 22.14 Evolution of the normalized shear elasticity G/P and sliding threshold X∗ /D versus the contact pressure, for the two friction modifiers (stearic acid and amine). The low values of G/P combined with the critical slip distance explain the low level of friction coefficient obtained with these brush layers. The higher flexibility (higher X ∗ /D and lower G/P ) measured for the amine layer seems to be responsible for its superlubricity capability.
Figure 22.15 Evolution of the elastic properties of the adsorbed layers of amine and stearic acid molecules under confinement during a squeeze experiment. For both friction modifiers, the shear elastic modulus is much lower than the compressive elastic modulus. This suggests that the confined layers exhibit a significant non-isotropic mechanical behavior.
(resp. 0.4 nm for the stearic acid), which corresponds to a ratio X ∗ /D of 0.16 (resp. 0.07). These values put together and combined with the low KX /KZ ratios show the high intrinsic flexibility of the amine layer compared to that of the stearic acid monolayer. This high compliance that characterizes both friction modifiers may explain their superlubricity capability (friction coefficient less than 0.01) and even the lower friction coefficient promoted by the amine layer. It seems that the elastic behavior mainly influences the static friction coefficient. However, the structure and density of these self-assembled monolayers depend
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on the adsorption process and are not controlled as in the case of Langmuir–Blodgett layers. That is why G/P may slightly vary from one monolayer to another. 22.3.2.5 Viscous Dissipation in Friction Figure 22.10 and Figure 22.11 have revealed that the stationary friction is velocity dependent: an increase, V (resp. decrease) in sliding velocity is accommodated by a transient increase, FX (resp. decrease) in the friction force. This clear evidence of a viscous-like contribution to the frictional behavior can be used to estimate an effective viscosity of the interface, thanks to the following relation: ηp =
FX · d , V · S
(17)
where S is the mean contact area and d is the thickness involved in the viscous shearing. This latter cannot be easily determined because it depends on the properties of the flow in the interface during the sliding: • If the shearing concerns the whole interface, d should be the total thickness of the confined layers. • If the flow is not homogeneous, a localization of the shearing occurs and d should be the thickness of the shear plane. Nevertheless, the very low thickness variations (less than 0.1 nm, which is much lower than the thickness of the layers themselves) associated to friction accommodation processes suggest that the tangential damping ωAX results from the viscous response of the interpenetration zone between the layers. Thus, the slip is located through the thickness of this zone, which acts as a shear plane (see Figure 22.16(a)) whereas the elastic shearing of the interface concerns its whole thickness. In this zone, the end of the molecules can diffuse through each other as previously mentioned for hydrogenated DLC [62] films or for grafted polymer brushes [49,50]. The mutual interaction of end-tethered friction modifier chains in the sheared interpenetration zone may explain the viscous contribution to the frictional force and the relaxation effects that have been observed even for purely elastic layers such as amine and stearic acid confined films (see Figure 22.10 and Figure 22.11).
Figure 22.16 Schematic picture of the shear processes at the molecular level in a stationary friction regime (a) and of the possible collapse of the amine layer (b) after several sliding cycles.
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This assumption enlightens the origin of the low value of KX /KZ ratio measured for the friction modifier layers which is actually due to a heterogeneous flow induced by a localization of the shear deformation rather than to a real mechanical anisotropy or to the rubber-like behavior of the layers. Meanwhile, the global elasticity of the friction modifier layers ensures load bearing. Using relation (17) and assuming that d has an order of magnitude of 0.1 nm for the amine layer, the three speed increments of 0.5 nm/s, 2.4 nm/s and 9 nm/s (see Figure 22.11) induce shear viscosities of 8.103 Pa s, 103 Pa s and 102 Pa s, respectively, for a normal load of 1 mN (leading to a contact area of 36.3 µm2 ). This suggests that the interface has a shear-thinning behavior. At the same load, the sliding viscosity of the stearic acid bi-layer is 3.3 × 104 Pa s for a speed increment of 0.1 nm/s. Even if this viscosity is higher than that of the amine layer, the viscous contribution to friction is lower since the damping function, ωAX is only one tenth of the elastic tangential stiffness, KX . The contact pressure, which is in the range 10 to 50 MPa is not sufficient to explain such an increase in viscosity by a simple piezo-viscous effect. This viscous component can also be determined from the measurement of the damping ωAX with the small oscillatory motion superimposed during a squeeze test. Then, the shear viscosity becomes: ηp =
AX · d . S
(18)
Numerical application gives for the stearic acid monolayer a sliding viscosity of about 103 Pa s (106 times higher than the viscosity of the bulk solution), for a vibratory motion with an amplitude of 0.03 nm and frequency of 220 Hz (which corresponds to a speed of 13.2 nm/s). For the amine layer, the tangential damping ωAX measured for an amplitude of 0.03 nm and a frequency of 70 Hz (i.e. a mean sliding speed of 4.2 nm/s) is about 40% of the tangential stiffness leading to a more important viscous component in the friction force. Applied to a 0.1 nm thick shear plane, Equation (18) gives a viscosity of 22 Pa s. The orders of magnitude of the interface viscosity are consistent whether they are deduced from its friction/velocity signature or from the dissipative component of its dynamic response. Their comparison suggests that the hypothesis of a shear plane thickness independent of the sliding velocity is not relevant. Furthermore, the values of the interface viscosities show that the amine molecules form liquid-like layers while stearic acid molecules tend to form solid-like layers, which is consistent with the differences in their frictional properties. It is worth noting that this behavior can only be exhibited by transient variations of the tangential force that steep changes of speed induce. 22.3.2.6
Shear Resistance of the Amine Layers
The capability of the amine layers to withstand shearing is characterized with a peculiar experimental procedure, called “triboscopy” that has been already applied to thin solid films at macroscopic scale. The principle of this tribological experiment is described in the literature. The sphere is bearing a constant normal load and is tangentially displaced back and forth on a unique track. These alternative friction tests are carried out at 10−3 N with
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Figure 22.17 Evolution of the friction coefficient of the amine layer that undergoes a series of 256 shearing cycles under a 1 mN normal load, FZ . The amplitude of the reciprocating motion is 1.1 µm and sliding velocity is 500 nm/s. The friction coefficient does not stop increasing, the amine layer is unable to withstand severe shearing and loses its non-isotropic behavior.
an amplitude of 1 µm, which is much smaller than the contact radius. The sliding velocity is 500 nm/s, which is faster than for the previous experiments. The friction force, the tangential stiffness and the thickness of the interface are simultaneously and continuously measured during 256 cycles. The friction coefficient is shown in Figure 22.17 for each cycle as a function of the location of the sphere on the plane. After a transient peak that reveals the viscous response of the layer at the onset of sliding, the frictional force is slowly decreasing down to very low values because of the existence of a memory length which is required for the adaptation of the interface to shearing. During the first cycles, the resulting steady-state friction coefficient at this high velocity has the same order of magnitude as at 12 nm/s. This behavior is in total agreement with the friction kinetics observed at slower speed (see Figure 22.11). However, once the viscous effect has been completely accommodated, the friction coefficient remains in the range 3 × 10−3 –6 × 10−3 until the breakdown of the amine layer that occurs after only 22 cycles. This damaging has several consequences: • The friction coefficient does not cease increasing and can reach a value of 0.3 (hundred times higher than for one cycle). In some cases, stick-slip instabilities appear despite the high stiffness of the apparatus. • The thickness increases of more than 3 nanometers. • The interface loses its initial elastic non-isotropic behavior that was mainly responsible for its ability to reduce friction towards superlubricity. These observations suggest that the organized structure of the amine molecules inside the adsorbed layers has totally collapsed (Figure 22.16(b)). This result is consistent with the molecular structure of the amine: its chains are only linked by polar interactions that are not energetic enough to sustain the energy dissipated in repeated friction cycles.
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Physical Interpretation
The experimental results of this chapter combined to several works of the literature show that the friction dynamics of confined layer depends on their organisation at the molecular level. The latter is governed by the local interactions of the molecules with the surface but is modified by the sliding process. This results in various times and memory lengths that characterize the relaxation and the accommodation processes involved in the frictional response of the boundary layers. One of the most important difficulties is the proposal of a realistic physical modeling of the shearing of these confined interface formed with complex fluids. Because of the extremely long times and length scales involved, the moleculardynamics simulation cannot give all the answers to this problem. To achieve a satisfactory description of the phenomena, a different or complementary approach has to be taken. Persson [45] has proposed the use of a thermally activated two-dimensional model of pinned islands in the contact region to describe the behavior of confined lubricants under shear, with promising results. This theory uses a statistical treatment of the dynamics of the pinning/depinning sites that are responsible for the evolution of the friction coefficient. However, like the phenomenological “state-rate” approach, it does not account for kinetics of the pinning/depinning activation. Moreover, the major drawback of the existing models is the lack of a physical meaning for the variables used in the equations. It is usually unclear how to relate the parameters in the models with molecular properties or with the experimentally measurable quantities. This is why we used a general model based on the kinetics of formation and rupture of adhesive bonds between the two shearing surfaces with an additional viscous term to understand frictional behavior of the friction modifiers at the molecular level. This model derives from a theory of adhesive friction, originally developed for “elastomer” surfaces [47,63]. Drummond et al. [52] have successfully applied this model to predict new instabilities regimes (inverted stick-slip) and friction/velocity traces of wetted surfactant monolayers. The confined interface is treated as a visco-elastic medium with a shear elastic modulus, G and a sliding viscosity, η. At any time of shearing, the total contact area, A is assumed to consist of N independent bonds or adhesive nanodomains, called “junctions,” each of average area δA. During motion, the whole contact area A does not slide as a single unit: individual junctions are continually formed and broken incoherently. Each junction can be either in a bonded state or in a free state and their activation involves two characteristic times: (i) τ0 , the mean time to break a junction due to thermal fluctuations under zero shear force is given by: τ0 = τ ∗ exp(−U0 /kT ), where τ ∗ is an elementary time and U0 is the energy barrier that has to be overcome to break an adhesive junction. (ii) τ , the mean time to thermally activate or reactivate a junction. During sliding, the junctions are elastically stretched until a yield point beyond which they are totally depinned (Figure 22.18).
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Figure 22.18 Sketch of junction shearing in a bonded state during a friction test. (a) At rest, the domain is bonded through an interpenetration zone of thickness γ . At the onset of sliding (b), the junction is elastically stretched and the cooperative motions of the molecules in the entanglement zone results in a viscous contribution to friction. When the junction breaks (c), heat dissipation induced by the vibration of molecules is responsible for the friction dissipation.
This results in reducing the energy barrier to transit from the bonded state to the free state. According to Schallamach, the reduction is proportional to the elementary elastic force, Fel = GδA · V t/d applied on one junction of thickness, d after a sliding time, t. Thus, the energy barrier becomes: U = U0 − γ Fel , where γ is a constant length. In addition, a junction is assumed to be always depinned when stretched up to yield point reached at a critical deformation (Figure 22.18(b)), where tb is the lifetime of the junction. Thus, the average lifetime tb of an adhesive junction can be deduced from the calculation of its survival probability. Following this model, during the shearing, a junction detaches either spontaneously, by thermal excitation, or by the external shear force, and reforms further after various thermoelastic relaxation processes have occurred. This elastic-adhesive model is not sufficient to capture the friction regimes at high velocity. As a consequence, it is necessary to introduce an additional viscous contribution that arises from the free junctions [52]. Therefore, the friction force can be written as [64]: kT F = φN · α
1
eα
tb A du ln(u) exp − u + (1 − φ) ηV , u ατ0 d
(19)
where φ(V ) = tb /(tb + τ ) is the fraction of bonded junctions and α = γ δAGl ∗ /kT d. In Equation (19), the first term represents the elastic contribution and the second one corresponds to the viscous contribution. The sliding velocity dependence of the friction force (or the friction coefficient, at constant load) can be analyzed for the friction modifiers within the framework of this model. This allows us to give a physical meaning to the model parameters and relate them to the experimental data. The main features that are obtained from the comparison between the experimental investigation and the viscous-elastic-adhesive model are detailed as follows: • The model predicts that the friction force at low velocity is T (V → 0) = AGl ∗ /2D. By comparison with relation (16), we deduce X ∗ = l ∗ /2. Then, the threshold sliding distance, X ∗ measured by the ratio of the stabilized friction force to the tangential stiffness
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of the interface gives the critical deformation l ∗ at the yield point beyond which all the junctions are depinned. The superlubricity properties of the friction modifier layers are due to an important viscous component of the friction force in addition to the non-isotropic elastic behavior of the layers. This suggests that a low fraction of junctions in a bonded state is involved in the shearing motion and that the average lifetime of a bonded junction should be shorter than the time required to activate a free nanodomain. The analysis of relation (19) shows that the elastic component of the friction force eventually vanishes at high velocities. However, it has been experimentally observed that the friction remains at non-zero value independent of the velocity, for V > 10 nm/s. From Equation (19), it can be deduced that the friction force has mainly a viscous origin. Assuming that the interface viscosity reaches a Newtonian plateau at high velocity (as classically observed with shear thinning fluid), the friction-velocity non-dependence for V > 10 nm/s combined with relation (19) implies 1 − φ ∝ 1/V . This means that φ decreases when the sliding velocity increases. Consequently, the lifetime of a bonded junction is expected to be shorter when the sliding is fast. For sliding velocities varying from 10 to 100 nm/s, the friction force displayed by both friction modifiers is in the range of few µN under a 1 mN load [24] (see Figure 22.10 and Figure 22.11). Even though the measured viscosity of the confined layer is high (about 10 Pa s for that range of velocity), a viscous flow through the whole thickness of the interface (≈5 nm) is not sufficient to explain such high values of the shear force. Thus, the flow should be localized in a much thinner layer, such as the interpenetration zone and the viscous term becomes Aη(1 − φ)V /γ . In the elastic-adhesive model, γ δA appears as an activation volume. Since δA is the lateral extension of a junction, the length γ can be considered as the thickness of the interpenetration zone between two nano-domains. As γ directly controls the time to break a junction (an increase in γ leads to an increase in tb ), this interpretation is consistent with the small variations of the interface thickness involved in the accommodation of the friction force to variations of sliding velocity (Figure 22.10). Once the monolayers have slipped against each other over a sliding distance δA1/2 , the whole population of the junctions in the total contact area has been completely renewed. Similarly to what has been demonstrated for solid friction in multi-contact interface [15], δA1/2 defines a characteristic length of the sliding process that can be regarded as the memory length governing the friction dynamics as illustrated in Figure 22.10 and Figure 22.11. Therefore, the junctions of size δA could correspond to the elementary mesoscopic area around which local shear arrangements occur. Thus, the interpenetration zone behaves as a thin glassy interface whose deformation involves cooperative molecular motion, as modeled by STZ theory [48].
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[3] Persson, B.N.J., Tosatti, E. (Eds.) Physics of Sliding Friction. Kluwer Academic Publishers, Dordrecht, 1996. [4] Robbins, M.O., Müser, M.H. In: Bhushan, B. (Ed.), Handbook of Modern Tribology. CRC Press, 2000. [5] Bowden, F.P., Tabor, D. Friction and Lubrication of Solids, Part I. Clarendon Press, Oxford, 1964. [6] Rabinowicz, E. Friction and Wear of Materials. Wiley, New York, 1965. [7] Landman, U., Luedtke, W.D., Burnham, N.A., Colton, R.J. Science 248 (1990), 454. [8] Sokoloff, J.B. J. Appl. Phys. 72 (1992), 1262. [9] Shinjo, K., Hirano, M. Surf. Sci. 283 (1993), 473. [10] Matsukawa, H., Fukuyama, H. Phys. Rev. 49 (1994), 17286. [11] Baumberger, T., Berthoud, P. Phys. Rev. B 60 (1999), 3928. [12] Greenwood, J.A., Williamson, J.P.B. Proc. Roy. Soc. London A 295 (1966), 300. [13] Bowden, F.P., Tabor, D. Friction and Lubrication of Solids, Part II. Clarendon Press, Oxford, 1964. [14] Ronsin, O., Labastie-Coeyrehourcq, K. Proc. Roy. Soc. A 475 (2001), 1277. [15] Heslot, F., Baumberger, T., Perrin, B., Caroli, B., Caroli, C. Phys. Rev. E 49 (1994), 4973. [16] Scholtz, C.H. The Mechanics of Earthquakes and Faulting. Cambridge University Press, Cambridge, 1990, Chapter 2. [17] Tabor, D. The Hardness of Solids. Clarendon Press, Oxford, 1951. [18] Berthoud, P., Baumberger, T. Phys. Rev. B 59 (1999), 14313. [19] Dieterich, J. J. Geophys. Res. B 84 (1979), 2161. [20] Bureau, L., Baumberger, T., Caroli, C. Eur. Phys. J. 8 (2002), 331. [21] Bureau, L. Ph.D. Dissertation, University of Paris 7, 2002. [22] He, G., Robbins, M.O. Phys. Rev. B 64 (2001), 035413. [23] Yoshizawa, H., Israelachvili, J.N. J. Chem. Phys. 97 (1993), 11300. [24] Georges, J.-M., Tonck, A., Mazuyer, D. Wear 175 (1994), 59. [25] Gee, M.L., Mc Guiggan, P., Israelachvili, J.N., Homola, A.M. J. Chem. Phys. 93 (1990), 1895. [26] Thompson, P.A., Robbins, M.O. Phys. Rev. A 41 (1990), 6830. [27] Schoen, M., Rhykerd, C.L., Diesler, D.J., Cushman, J.H. Science 254 (1989), 1223. [28] Thompson, P.A., Grest, G.S., Robbins, M.O. Phys. Rev. Lett. 68 (1992), 3448. [29] Gao, J., Luedtke, W.D., Landman, U. Phys. Rev. Lett. 79 (1996), 705. [30] Gourdon, D., Israelachvili, J.N. Phys. Rev. E 68 (2003), 21602. [31] Demirel, A.L., Granick, S. Phys. Rev. Lett. 77 (1996), 2261. [32] Gao, J., Luedtke, W.D., Landman, U. Trib. Lett. 9 (2000), 3. [33] Drummond, C., Israelachvili, J.N. Phys. Rev. E 63 (2001), 41506. [34] Demirel, A.L., Granick, S. Phys. Rev. Lett. 77 (1996), 4330. [35] Drummond, C., Israelachvili, J.N. Macromolecules 33 (2000), 4910. [36] Dhinogwala, A., Cai, L., Granick, S. Langmuir 12 (1996), 4537. [37] Luengo, G., Heuberger, M., Israelachvili, J.N. J. Chem. Phys. 104 (2000), 7944. [38] Cayer-Barrioz, J., Mazuyer, D., Tonck, A., Kapsa, Ph., Chateauminois, A. Trib. Int. 39 (2006), 62. [39] Georges, J.-M., Tonck, A., Loubet, J.-L., Mazuyer, D., Georges, E., Sidoroff, F. J. Phys. 6 (1996), 57. [40] Ruina, A.L. J. Geophys. Res. B 88 (1983), 10359. [41] Rice, J.R., Ruina, A.L. J. Appl. Mech. 105 (1983), 343. [42] Baumberger, T., Caroli, C., Perrion, B., Ronsin, O. Phys. Rev. E 51 (1995), 4005. [43] Carlson, J.M., Batista, A.A. Phys. Rev. E 53 (1996), 4153. [44] Falk, M.L., Langer, J.S. Phys. Rev. E 57 (1998), 7192. [45] Persson, B.N.J. Phys. Rev. B 50 (1994), 4771. [46] Burridge, R., Knopoff, L. Bull. Seism. Soc. Am. 57 (1967), 341. [47] Persson, B.N.J. Phys. Rev. B 51 (1995), 13568. [48] Lemaître, A., Carlson, J. Phys. Rev. E 69 (2004), 61611. [49] Joanny, J.F. Langmuir 8 (1992), 989. [50] Tadmor, R., Janik, J., Klein, J., Fetters, L.J. Phys. Rev. Lett. 91 (2003), 115503. [51] Tonck, A., Mazuyer, D., Georges, J.-M. In: Dowson, D. et al. (Eds.), The Third Body Concept, Tribology Series, vol. 31. Elsevier Science, 1996. [52] Drummond, C., Israelachvili, J., Richetti, P. Phys. Rev. E 67 (2003), 066110.
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[60] [61] [62] [63] [64]
– 23 – Super Low Traction under EHD & Mixed Lubrication Regimes Philippe Vergne Laboratoire de Mécanique des Contacts et des Solides—LaMCoS, UMR CNRS—INSA-Lyon n◦ 5514, Bâtiment Jean d’Alembert, 20 avenue A. Einstein, 69100 Villeurbanne, France
23.1 23.1.1
INTRODUCTION
Superlubricity, Near Frictionless Sliding and Super Low Traction
After the pioneering experimental works on superlubricity by Martin et al. on MoS2 [1], Hirano et al. on tungsten and silicon [2] and the further confirmation by Dienwiebel et al. on graphite [3], many groups around the word investigated the occurrence of near frictionless sliding contacts. This large mobilization of tribologists, materials science specialists, and physicists has lead to emerging solutions involving new materials and coatings, the most promising ones being the carbon based materials like graphite, diamond, carbon composites or diamond-like-carbons. Some of them are currently used in practical applications. However the introduction of a fluid between two contacting surfaces remains the traditional and still the most efficient way to prevent contact failures when the operating conditions generate high contact pressures, large thermal dissipation or when the presence of worn films or particles is prohibited. In the field of lubrication, super low traction does not probably have the same significance as superlubricity of carbon based materials which gives friction coefficients lying within 5% (near atmospheric conditions) to almost 0.1% (under vacuum) whereas values encountered under classical “dry” conditions are almost always greater than 10–20%. The situation is different especially in EHL: the highest friction coefficients are close to 10% when traction fluids are involved, i.e. fluids that have especially designed to transmit the highest friction, and they vary within 3–6% for the rest of lubricants. The range of variation is consequently very narrow and these typical values are really low compared to those obtained in dry contacts: as a consequence the gain expected from a super low traction regime (defined in Section 23.2.2) in lubrication will be probably more limited, especially in the case of experiments conducted at the meso or macro scales. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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This weak perspective could be one explanation on the relatively low number of articles in recent literature dealing with lubricated superlubricity in the above conditions. Nevertheless there is still strong interest in this topic and more generally in the fundamental understanding of friction between lubricated surfaces. Dowson and Ehret [4] have recalled that typical EHD films were about one micron thick when the first solutions to the elastohydrodynamic problem were proposed. But this situation has changed with time and nowadays EHD films are of nanometer rather than micrometer proportions. This has been possible thanks to numerous contributions—both experimental and numerical—on film thickness build-up mechanisms published during the last 20 years that improved our knowledge on very thin EHL films, the influence of surface features, etc. Nevertheless, very few of these publications also deal with friction. A second interest concerns industrial applications that are developed with increasing demands for higher energy efficiency, durability, and environmental compatibility. Since friction is one of the main sources of lost energy in mechanical elements, it becomes a matter of urgency to propose innovative solutions to control and to optimize this parameter. An intermediate step would be a better understanding of the friction mechanisms under lubricated conditions and a significant improvement of friction prediction. 23.1.2
Chapter Objectives and Summary
In this chapter, we will report and discuss the experimental appearance of super low friction forces that occurred in EHL or in mixed lubricated applications, i.e. tribological situations far away from those prevailing during nano- or micro-tribotests or during lubricated wear experiments. It means that we simulated lubricated contacts as those existing in real life, involving engineering surfaces and materials, applying representative speeds and normal loads. This domain is also called conventional tribology. The title of this contribution mentions both elastohydrodynamic and mixed lubrication regimes. Compared to dry conditions, we specifically focused on the lubricant response according to two directions: – From the rheological point of view to ensure that its behavior could favor super low traction under full EHD separation. – Based on the classical Striebeck diagrams that normally present a minimum friction in the EHL regime, to analyze the transition region between EHL and mixed lubrication where lubricated superlubricity could occur.
23.2 23.2.1
TRACTION VERSUS SUPER LOW TRACTION
Generalities on EHD Traction
Friction or traction in highly loaded lubricated contacts results from complex and coupled phenomena that are not yet totally understood. Formally one would have to account for two distinct contributions: rolling friction that comes from the inlet pressure rise and shearing friction that results from a velocity difference of the contacting surfaces. However both numerical and experimental previous works [5,6] showed that the contribution of the former
Super Low Traction under EHD & Mixed Lubrication Regimes
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Figure 23.1 Low traction values given by linear paraffinic mineral base oil (LP) at 40 ◦ C.
term is generally negligible compared to the latter. Consequently we will consider in the following that traction only results from the lubricant strength to slip and/or spin motions occurring in the high pressure region of the conjunction. Slip, small film thickness, and high contact pressure contribute to generate very important shear rates and very high shear stresses, as viscosity strongly increases with pressure this effect being one of those that allow the elastohydrodynamic lubrication (EHL) mechanisms to take place. Rheological and thermal effects can occur simultaneously. Moreover some unusual contact features reported in the literature suggest the occurrence of interfacial or boundary effects [4]. Compared to solid or dry lubrication, friction coefficient under EHL regime varies over a quite reduced range, from few % (see Figure 23.1) to a maximum rising 10 to 12% in the typical case of traction fluids (Figure 23.2). The traction coefficient (= friction coefficient) is usually evaluated and plotted as a function of the slide to roll ratio (SRR, see Equation (1)) defined by the ratio of the sliding velocity that generates lubricant shearing (and hence friction) to the mean entrainment velocity that is an essential parameter in separation build-up. SRR = U/Ue ,
(1)
where U = U1 − U2 is the sliding velocity, and Ue = (U1 + U2 )/2 is the mean entrainment velocity. The question of rating “super low traction” compared to “common traction” is developed in the next section together with the main related experimental issues.
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Figure 23.2 Typical high friction results obtained with a traction fluid (Santotrac 50, 25 ◦ C).
23.2.2
Super Low Traction and Experimental Issues
Compared to the two typical cases plotted in Figures 23.1 and 23.2, super low traction characterizes not only situations where lower friction coefficients are encountered but also when different shapes of the traction curves are reported. A very steep friction increase from SRR = 0 is characteristic of lubricated contacts working under EHL conditions. Traction coefficients close to the maximum friction value are found for low slide to roll ratios, typically in the range 1 < SRR < 5%. However different behaviors can be found according to the operating conditions and the lubricant properties. Among them one can find the super low traction response that corresponds to lower friction values than those reported in Figures 23.1 and 23.2. It can occur whatever the lubrication regime is, neither EHL nor mixed and gives a progressive friction increase with SRR. This peculiar behavior will be described and discussed in a next section. Since under classical EHL conditions important friction values are obtained for even low SRR values, more attention has been paid in the past to control very accurately the velocities of the two specimens. This was also motivated by the existence of low SRR in ball bearings (typically few percents) that could generate much more traction variations than in the cases where SRR > 5%. However, in the super low traction regime, the experimentalist has to face another practical problem: the challenge is now to measure very low friction forces with adequate accuracy. This difficulty can be illustrated by the following practical example. For a given normal load—let’s say 25 N—it was classically relevant to assume a friction force sensitivity of at least ±0.2% of the normal load (in our example ±0.05 N). For the purpose of super low traction study, the requirement becomes more demanding and an acceptable sensitivity should be 5 or 10 times higher than the value presented in the above example. In the superlow traction regime, this leads to a sensitivity lying in the range ±0.01 to ±0.005 N, these
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values being considered as minimum ones. Facing this requirement, it becomes evident that numerous devices will be no longer adapted to study super low traction, as for instance conventional large twin disk machines or basic ball-on-disk set ups. This new demand has been already claimed by several authors in order to achieve significant breakthroughs in the understanding of superlubricity. Realistic devices have to be both well-controlled and relevant to operating machinery [7]. In their recommendations for future endeavors, Perry and Tysoe [8] mentioned that both nanoscale devices (like AFMs) and macro-tribometers need to be improved. They underlined the importance of technical points that are rarely discussed in papers: reproducibility, reliability, calibration, uncertainty analysis, sample and surface preparation, environmental control, etc. They also pleaded for the improvement of the capacities of tribometers by a more precise control of forces and speeds.
23.3
EXPERIMENTAL CONDITIONS
Compared to micro-scale or nano-scale investigations, we applied operating conditions closer to those found in real lubricated mechanisms like in rolling bearing elements or in automotive components: concentrated circular contacts, medium to high contact pressures, continuous motion of both specimens, variable slide to roll ratios, smooth surfaces, controlled lubricant feeding flow, etc. These operating conditions were fulfilled by using a ball-on-disk test rig, similar to those designed to measure film thickness in EHD contacts and already described elsewhere [9–11]. A polished one inch ball of AISI 52100 bearing steel is loaded against a flat disk and both specimen are driven independently to allow for any desired slide to roll ratio. The ball and disk velocities are controlled with high precision and the cumulated geometrical defects are adjusted to minimize any fluctuation within the contact. The bottom of the ball dips into the reservoir containing the lubricant, ensuring fully flooded conditions. The contact and the lubricant are thermally isolated from the outside and heated (or cooled) by an external thermal controlling system. A platinum resistance probe monitors the lubricant temperature in the test reservoir within ±0.1 ◦ C. Parts in contact with the lubricant are made from chemically inert alloys and any type of material likely to react with the fluid (rubber, elastomer) has been inhibited. The balls and the disks were carefully polished and cleaned following a three-solvent procedure to ensure minimum surface contamination. Traction forces and normal load were recorded via a multi-axis strain gauge sensor. It combines a broad range of measurable forces, appropriate sensitivities over the different directions and high stiffness. This facility is directly positioned between the main frame of the test ring and the vertical assembly that includes the brushless motor, couplings, the shaft and its bearings and finally the disk. This design provides several important advantages: – High linearity and sensibility due to a continuously applied prestressed state along the 3 directions. – Only static parts are involved, leading to high signal to noise ratio compared to measuring systems attached to moving elements. Several materials have been used for the disks: BK7 glass, pure synthetic sapphire and AISI 52100 bearing steel leading to composite RMS roughnesses of the undeformed sur-
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faces of respectively 4, 5 and 9 nm. High pressure rheology and/or film thickness measurements have been carried out on most fluids investigated in this chapter. These previous experiments provided appropriate data for the evaluation of the λ parameter as the lubrication regime will be an important factor in our analysis. λ is defined as follows: λ = hmin /σ,
(2)
where hmin is the minimum film thickness, σ the composite rms roughness of the contacting surfaces. Furthermore: λ>3 3>λ>2 2>λ>1 λ<1
gives full EHL separation, EHL regime but local contacts may occur, mixed lubrication regime, severe mixed lubrication regime.
23.4
LUBRICATED SUPER LOW TRACTION
This part reports and discusses experimental results where super low traction coefficients have been encountered. Several lubrication regimes (from EHL to mixed lubrication) and different types of lubricants will be considered. A table reported in annex summarizes the main rheological properties of these fluids together with their chemical composition and structure. In the two first subsections, super low traction will be investigated under thick EHL conditions. Two really different lubricants will be studied and we will show that superlubricity can easily be explained thanks to the rheological behavior of each fluid. The last subsection will concern mineral base oils, with and without additives. We will focus on the transition region between full EHL separation and mixed lubrication where film thickness becomes close to surface roughness. In this context special attention will be paid to the influence of the lubricants chemical structure. 23.4.1
Newtonian Isothermal Piezoviscous Behavior
In this first section, the objective is to show how very low traction can be achieved using a simple viscous fluid that obeys in the simplest manner to EHD contact conditions. With this in mind, we considered glycerol, a pure tri-alcohol characterized by its very compact molecular structure and low pressure viscosity coefficient. Results reported in Figures 23.3–23.6 were obtained from various operating conditions varying the entrainment speed and the normal load and by changing the disk material from glass to sapphire and then to steel. Newtonian isothermal piezoviscous estimations of the friction coefficient based on the mean contact pressure P0 (= PH · 2/3, PH being the Hertzian pressure) and Barus law are also plotted in these figures with dashed or full lines. Experimental results are represented by symbols only. The traction response of this fluid is really different from that of the two boundary cases showed in Section 23.2.1, especially for the results plotted in Figures 23.3–23.5. Firstly
Super Low Traction under EHD & Mixed Lubrication Regimes
Figure 23.3
433
Traction curves measured with glycerol at 40 ◦ C, steel–glass contact.
Figure 23.4 Traction curves measured with glycerol at 50 ◦ C, steel–sapphire contact.
friction coefficient never exceeds 1% over the classical EHL range (0 < SRR < 50%) whatever the experimental conditions were. Secondly a linearly increasing friction coefficient is measured when the slide to roll ratio is increased. Finally a fair agreement is found between experimental results and those obtained from our basic numerical model. However increasingly noticeable deviations appear when contact pressure and/or entrainment speed are increased, as it can be seen in Figure 23.4 (PH = 0.87 GPa, 0.08 m/s), in Figure 23.5 (PH = 0.95 GPa) and in most cases plotted in Figure 23.6.
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Figure 23.5
Traction curves measured with glycerol at 40 ◦ C and 0.075 m/s, steel–steel contact.
Figure 23.6 Traction curves measured with glycerol at 40 ◦ C and 0.38 m/s, steel–steel contact.
Film thickness measurements—not reported here—showed that under pure rolling conditions (from 5 mm/s to 5 m/s, steel–glass contact, 40 ◦ C) glycerol behaved like a Newtonian piezoviscous fluid, as expected considering its simple and compact molecular structure. Shear thinning as may occur with polymers cannot occur with this fluid, only inlet shear heating has induced a drop on film thickness above 0.8 m/s. These experiments also showed that high values of SRR had a weak influence on film thickness: thickness reduction of −7% at most for 0.38 m/s, SRR = 180% and 0.52 GPa. This further study confirmed the idea that the applied power input and more specifically the pressure are likely the main
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causes of the observed deviations. A Hertzian pressure of 0.95 GPa corresponds to a normal load that is 3 and 6 times the ones required to generate respectively 0.64 GPa and 0.52 GPa for a steel–steel contact. The term α · P0 is sometimes used in the EHL community to describe the lubricant response: with glycerol, the deviation from the Newtonian isothermal piezoviscous behavior occurs when α · P0 becomes greater than 3.1. Increasing the entrainment velocity also favors the deviation from Newtonian piezoviscous isothermal behavior. The transition occurs when SRR exceeds 60% at low speed (Figure 23.5) and above 15% at 0.38 m/s (Figure 23.6). It is thus possible to estimate the corresponding in-contact mean shear rate by calculating the ratio of the sliding velocity to the central film thickness. This leads to values of 4 × 10+5 and 2 × 10+5 s−1 at respectively 0.075 and 0.38 m/s; in rheological terms it means that the deviation from Newtonian isothermal behavior appears more rapidly when the entrainment velocity increases. However one has to keep in mind that under the operating conditions of Figures 23.5 and 23.6, glycerol also shows super low traction behavior. Measured friction coefficients remain lower than 1% when SRR varies from 0 to 50%. 23.4.2
Shear Thinning
Shear thinning is probably the simplest and most frequent rheological effect that can reduce both film thickness and friction in an EHD conjunction lubricated by a conventional fluid. Shear thinning here concerns a steady shear rate dependence of viscosity. However it has been frequently combined with other effects like thermal heating and/or nonlinear high shear stress behavior, leading to certain confusion between the actual mechanisms that might influence friction. Compared to the glycerol, results reported in this section were obtained with a very different fluid, in terms of molecular structure, rheological properties and tribological response. The main objective in studying this lubricant model was to demonstrate that shear thinning that affects both film thickness and traction can be described by a unique ordinary non Newtonian relationship of the power law type [12]. This was accomplished by accurate measurements in viscometers (carried out by S. Bair at Georgia Tech) of the shear response of a high molecular weight polyalphaolefin (HMW PAO) and in-contact accurate measurements (performed at INSA de Lyon) of film thickness and traction under conditions which accentuate the shear thinning effect. This fluid possesses a very low critical stress for shear thinning, high viscosity at ambient temperature and pressure viscosity coefficient close to those of commonly used formulated lubricants. Moreover it also showed super low traction behavior. In spite of these properties, experimental values of traction coefficient (black symbols in Figure 23.7) are unusually low and sometime (at low speed and low slide-to-roll ratio) near the threshold of resolution of the sensor. In Figure 23.7, the full line represents the Newtonian isothermal piezoviscous estimation of friction for the entrainment speed of 0.13 m/s. Friction coefficients predicted by a numerical model assuming that shear thinning follows Carreau equation are plotted with dashed lines. Carreau equation is written: (n−1)/2 η = μ 1 + (λ · γ˙ )2 ,
(3)
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Figure 23.7 Super low traction obtained with a HMW PAO (75 ◦ C, 0.53 GPa, steel–steel contact).
where γ˙ is the shear rate, η the generalized viscosity, μ the low shear viscosity, n the power law exponent, and λ a characteristic time. The Newtonian isothermal piezoviscous calculation greatly overestimates the actual traction behavior of this lubricant while the Carreau shear thinning model gives a good agreement with the measured data. We also showed [12] that central and minimum film thicknesses were insensitive to sliding and well described using the power-law relationship previously mentioned as Equation (3). The in-contact central film thickness and traction were thus entirely predictable from the rheological properties obtained from viscometers using simple calculations. This proved that shear thinning—occurring mainly in the contact inlet—was the dominant effect that affected the shearing response of this fluid, in the absence of measurable thermal heating. As a consequence, the very low traction coefficients reported in Figure 23.7 were attributed to this rheological behavior enhanced by the lubricant molecular nature. 23.4.3
Thin Film EHD Conditions
Results discussed so far were obtained under operating conditions that generated thick EHL films: in Figures 23.3–23.7, the values of the λ parameter defined in Equation (2) varied in the range 6–150. In this section, we focus now on mineral base oils submitted to thin film tribological experiments performed under operating conditions where λ was lower than 7, and in most cases even lower than 3. All the tests were conducted on steel–steel contacts. Several objectives were followed: to check if these fluids studied under these specific conditions could give super low traction and to pursue investigations on the role of the lubricants’ molecular structure on their frictional behavior.
Super Low Traction under EHD & Mixed Lubrication Regimes
Figure 23.8
437
Traction curves obtained with different mineral base oils at 0.95 GPa and 3 m/s.
Mineral base oils of different structures were studied under 3 operating conditions: high contact pressure and high entrainment speed (0.95 GPa, 3 m/s, 40 ◦ C, Figure 23.8), medium contact pressure but associated with lower entrainment speed at the same temperature (0.64 GPa, 1.8 m/s, 40 ◦ C, Figure 23.9) and finally same pressure and speed conditions as in the second case but at higher temperature (0.64 GPa, 1.8 m/s, 70 ◦ C, see results in Figure 23.10). These conditions lead to thinner and thinner film thicknesses and consequently they permit to increase the severity of the contact conditions. 23.4.3.1 Mineral Base Oils The nomenclature chosen for these fluids is detailed in annex: ARO, PN, ISO and LP present typical carbon chain length in the range C11 –C14 as MIN contains longer chains (C17 –C21 ). Except MIN and ISO, the lubricants exhibit similar rheological properties (see table in annex) leading to almost constant λ values for given operating conditions. As a consequence, the results reported in Figure 23.8 correspond to λ equals to 7 (full separation) for MIN, 2.1 for ISO and 2.9 for the others fluids. Apart from MIN that gives friction coefficients of 3% for SRR absolute values of 50%, ISO, PN and ARO fluids show moderate traction values and a progressive friction increase when SRR is increased. Base oil containing aromatic fractions (ARO) gave the lowest traction, then the mixture of paraffinic and naphtenic fractions (PN), the isoparaffinic base oil (ISO) and finally the more viscous fluid considered here (MIN). Even if data reported in Figure 23.8 show that both relatively low friction coefficients and smooth variations with SRR could be encountered, these preliminary results seem still far away from super low traction. The cases plotted in Figure 23.9 represent λ values of 5.4 for MIN and respectively 2.2 for PN and ARO: ISO traction results are not reported in this figure because this fluid (100% isoparaffinic) produced much higher traction coefficients
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Figure 23.9 Low traction behavior obtained with 3 mineral base oils under more severe conditions than in Figure 23.8.
(6 to 8%) than the other lubricants. This deviation is likely due to the inability of this base oil to maintain a low friction when operating conditions become more severe (λ = 1.7 → mixed regime). This has been confirmed by further experiments where friction coefficients higher than 10% were found applying the same speed and normal load but increasing the temperature and consequently decreasing λ. It should be noticed that under the operating conditions of Figure 23.9, the low traction behavior of PN and ARO follows an almost linear increase when increasing the absolute value of the slide to roll ratio. A similar response has been found for the MIN base oil at 70 ◦ C where a maximum friction lower than 1% has been measured at |SRR| = 50%, 0.64 GPa and 1.8 m/s. LP traction results (see Figure 23.1) have been obtained under the same operating conditions than those mentioned in Figures 23.8 and 23.9. By comparison with base oils studied before and in spite of its low molecular weight, viscosity and pressure viscosity coefficient, the traction response of this 100% linear paraffinic fluid follows the classical EHL shape. Contact pressure has a dominant influence: rheological investigation carried out on this linear hydrocarbon showed the appearance of phase changes at very low hydrostatic pressures. Under the contact dynamic conditions all occurs as if the fluid was frozen within the conjunction and gave an almost constant friction coefficient only dependent on the slide to roll ratio sign. Moreover this behavior is consistent with solidification theories and visco-plastic models described in EHL literature. It also should be noticed that friction slightly increases when the pressure and the entrainment speed are decreased. This variation denotes a change from full EHL separation (λ ≈ 3) to mixed lubrication regime (λ ≈ 2).
Super Low Traction under EHD & Mixed Lubrication Regimes
Figure 23.10
439
Comparison of traction coefficients obtained on base oils with and without lauric alcohol at 70 ◦ C.
These results showed that under mild contact pressures but under very thin film conditions (2 < λ < 3) super low traction can occur with simple mixtures of mineral fractions. This superlubricity regime should be considered as an optimum compromise that occurs over a quite narrow range of operating conditions. Further experiments run at higher temperature have confirmed that friction may significantly increase when λ is approaching 1, according the lubricants chemical structure. It is not possible to advance a physical explanation on the near frictionless behavior of the mixtures, probably a favorable compromise between the paraffinic parts chain length and the lubricity contribution of naphtenic and aromatic fractions. However it is easier to understand why pure linear paraffinic (pressure induced rheological effect) and isoparaffinic (low viscosity and piezoviscosity coefficient, lower coverage of rubbing surfaces) base oils are unable to produce such interesting friction properties. 23.4.3.2 Additive Influence Results presented in the previous section were mainly obtained when 2 < λ < 3, i.e. when local contacts between the specimen surfaces may occur that corresponds to the transition between full EHL separation and mixed lubrication. In this situation additives are usually introduced to extend the acceptable working range towards real mixed regime. Here we chose to add 8% w/w of lauric alcohol (noted LA in Figure 23.10), actually a mixture composed of almost 70% of dodecanol and 30% of tetradecanol. This additive is considered as a lubricity improver (= friction reducer) and is used especially in the field of metal forming. Results will be discussed according the chemical structure of the base oils. In presence of lauric alcohol, friction given by MIN is slightly lower than the one measured on the neat base oil whatever the operating conditions (see Figure 23.10, 70 ◦ C). The
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additive has in this peculiar case (full separation even at 70 ◦ C) a rheological effect in reducing a little the film thickness. At 70 ◦ C a super low traction regime is achieved in both cases, with and without lauric alcohol. Friction generated by ISO is considerably reduced when LA is added, however the traction coefficients remain higher than those found with the other lubricants and above the typical yield value that defines super low traction. Even if the additive seemed to have a negligible influence on ARO friction at 40 ◦ C, the results obtained at 70 ◦ C show a significant but however limited increase (from 1.7 to 2.7%). The presence of aromatic fractions in the base oil suggests that an induced antagonistic effect between lauric alcohol molecules and the aromatic chains is the cause of the friction increase. The tendency found with PN is totally opposed to the last one (ARO). Without additive we observe a friction increase when the temperature varies from 40 (Figure 23.9) to 70 ◦ C (Figure 23.10), due to transition from soft to more severe mixed regime (λ varies from 2.2 to 1.4). Traction drops when lauric alcohol is added. As for MIN + AL, one can consider that a super low traction regime is reached when PN + AL is used at this temperature. Lauric alcohol addition permits to reduce NP friction for the three imposed operating conditions, but in any case values representative of super low traction regime were measured. Under these thin film conditions, it has been shown that a super low traction regime may occur. The apparition of such lubrication regime depends on the lubricant structure and rheological properties. For different reasons pure isoparaffinic and pure linear paraffinic fractions gave relatively high traction coefficients whereas mixtures of paraffinic and naphtenic chains showed superlubricity, enhanced when fatty alcohols were added. Furthermore it should be underlined that operating conditions that permit to observe super low traction coefficients correspond to λ values lying in the range 1–3. This means that in some cases the classical Striebeck curve that usually presents a minimum friction value that coincide with EHL regime could be modified to take into account an almost frictionless behavior occurring at the transition between full film (EHL) and mixed lubrication regimes.
23.5
DISCUSSION AND CONCLUSION
When trying to understand in detail the tribological mechanisms and interactions occurring in real contacts it would be useful to conduct separate analyses on three different scales, the macro, micro and nano scale and to study separately the mechanical and the tribochemical changes taking place in the contact. However much of the current information is fragmented, with linkages between individual results need have yet to be established. In our case, results and subsequent analyses were based on macro scale tribological simulations. As an illustration, we showed how the rheological behavior can influence friction generated by the different fluids. Moreover, we may consider that the micro scale is of minor interest mainly because very smooth surfaces have been used. The nano scale analysis appears much more promising. The results from Krim [13] for instance, showed that liquid layers being more flexible and therefore slightly more commensurate with the
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surface, exhibited higher friction than their solid counterparts. However this finding has to be considered as a boundary case of our simulations for two reasons: it entailed liquid monolayers confined between extremely smooth and clean substrates made of high purity materials whereas our experiments involved at least several tens molecular layers sliding between bearing steel surfaces. With the objective to merge information gained on the nano scale with that observed at the macroscopic scale, nonequilibrium molecular dynamic (NEMD) simulations may appear relevant. Jabbarzadeh et al. [14] showed the correlation between the degree of branching of C30 alkane isomers and many important flow properties. They simulated Couette shear flow of thin (≈7 nm) films submitted to very high shear rates. However, in spite of a great interest in the knowledge of lubricants high shear rate behavior, they assumed constant thickness and ambient pressure conditions. Bair et al. [15] proposed an approach that combined high shear rate NEMD simulations and high pressure rheological experiments to calculate EHD traction forces based on a Carreau shear thinning relationship. The comparison between simulated and experimental traction was successful but validated for only squalane. More recently Jabbarzadeh et al. [16] found that dodecane could exhibit a very low friction state when confined between perfect surfaces. However it appears that a confusion between shearing and friction exists and somewhat limits the contribution of this approach and the nanorheology one to a better knowledge of mechanisms that occur in lubricated macro contacts. Another direction to make substantial progress in the understanding of friction and super low friction concerns the influence of the fluid structure. In [14], it is reported that linear alkanes should give lower friction (apparent viscosity), higher layering (and shear thinning) and lower slip than branched fluids of the same carbon chain length. Based on molecular interaction considerations and with the objective of molecular design of efficient traction fluids, some authors [17] showed that the lowest traction coefficients were obtained with fluids that could not interlock each other when they passed through the contact, like aromatic compounds. These tendencies qualitatively confirm some of our experimental results obtained on mineral base oils. However some weakness in the arguments (effect of contact pressure, real lubricant composition, engineering surfaces influence . . .) do not allow a formal link between nano and macro approaches. To conclude on super low traction, it is expected that this concept will generate a similar scientific passion in the tribology community than thin film lubrication did in the early 90’s. This desire is at first justified as friction reduction remains a major challenge to reduce energy losses, to improve durability of manufacturing goods and to meet constantly renewed environmental requirements. Another motivation for this lies in the fact that much more numerous applications will operate under conditions where lubricated superlubricity could occur. The use of low viscosity lubricants is one but an example: low viscosity could be induced by increasingly working temperatures (like in automotive engines) or an intrinsic property of the fluids like in applications where fuels have to lubricate mechanisms. Concerning bridging the gap between nano and macro scale analyses and the improvement of friction understanding, it is expected that these issues can also contribute to a more quantitative prediction of traction coefficients. Obviously super low traction is included in these perspectives which could lead to extremely efficient solutions like for instance the one recently described by Kano et al. [18].
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ACKNOWLEDGEMENTS The author would like to thank several colleagues who accepted to share experimental data (S. Bair, Georgia Tech, Atlanta, USA) or who contributed to measurements on mineral base oils (F. Wiltord, former Ph.D. student at LaMCoS) and on glycerol (K. Yagi, post-doctoral fellow at LaMCoS). Special acknowledgments to J.-M. Martin (LTDS, Ecole Centrale de Lyon, France) who inspired the study on fatty alcohols and to Guillermo Morales (SKF-ERC and visiting professor at LaMCoS) for his valuable comments on the manuscript.
ANNEX: MAIN PROPERTIES OF THE LUBRICANTS Name
Type
Content
Structure
Viscosity (Pa s)
α∗ (GPa−1 )
Santotrac 50
Traction fluid
Dicyclohexyl alkane + additives
C18 H34
Glycerol
Trialcohol
HMW PAO
Synthetic hydrocarbon Mineral base oil Mineral base oil
0.056 at 25 ◦ C [20] 0.293 at 40 ◦ C 1.42 at 75 ◦ C 0.0047 at 40 ◦ C
36 at 25 ◦ C [20] 5.4 at 40 ◦ C [20] 14.8 at 75 ◦ C 13.5 at 40 ◦ C
0.0015 at 40 ◦ C 0.0015 at 40 ◦ C 0.0011 at 40 ◦ C 0.0015 at 40 ◦ C
10.2 at 40 ◦ C 10.5 at 40 ◦ C 8.7 at 40 ◦ C 8.4 at 40 ◦ C
MIN ARO
PN ISO LP
Mineral base oil Mineral base oil Mineral base oil
C3 H 8 O 3 Polyalpha olefine paraffinic + naphtenic paraffinic + naphtenic + aromatic paraffinic + naphtenic 100% isoparaffinic 100% linear paraffinic
M≈30000 kg/kmole C17 –C21
C12 –C14 C12 –C13 C11 –C14 C13 –C14
Note that the pressure viscosity coefficient α ∗ is actually the reciprocal asymptotic isoviscous pressure defined by Blok [19]. This parameter permits to account the pressure viscosity coefficient variation with pressure. When introduced in the classical EHL relationships, it gives the best agreement with measured film thicknesses.
REFERENCES [1] [2] [3] [4]
Martin, J.-M., Donnet, C., Le Mogne, T., Epicier, T. Phys. Rev. B 48(14) (1993), 10583. Hirano, M., Shinjo, K., Kaneko, R., Murata, Y. Phys. Rev. Lett. 78(8) (1997), 1448. Dienwiebel, M. et al. Phys. Rev. Lett. 92(12) (2004), 126101. Dowson, D., Ehret, P. Proc. Inst. Mech. Engrs 213(Part J) (1999), 317.
Super Low Traction under EHD & Mixed Lubrication Regimes
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
443
Gohar, R. ASME J. Lubr. Tech. (1971), 371. Dalmaz, G. Thesis, INSA de Lyon I-DE-7907, 1979, 221 p. Krim, J. Am. J. Phys. 70(9) (2002), 890. Perry, S.S., Tysoe, W.T. Tribol. Lett. 19(3) (2005), 151. Molimard, J., Querry, M., Vergne, P. In: Dowson, D. et al. (Eds.), Proc. of the 25th Leeds–Lyon Symp. on Tribology, Lyon 08–11/09/1998, Elsevier, 1999, p. 717. Hartl, M. et al. STLE Tribol. Trans. 44(2) (2001), 270. Jubault, I., Mansot, J.-L., Vergne, P., Mazuyer, D. ASME J. Tribol. 124(1) (2002), 114. Bair, S., Vergne, P., Querry, M. Tribol. Lett. 18(5) (2005), 145. Krim, J. Surf. Sci. 500 (2002), 741. Jabbarzadeh, A., Atkinson, J.D., Tanner, R.I. Trib. Int. 35 (2002), 35. Bair, S., McCabe, C., Cummings, P.T. Tribol. Lett. 13(4) (2002), 251. Jabbarzadeh, A., Harrowell, P., Tanner, R.I. Phys. Rev. Lett. 94 (2005), 126103. Tsubouchi, T., Hata, H. Trib. Int. 28(5) (1995), 335. Kano, M. et al. Tribol. Lett. 18(2) (2005), 245. Blok, H. In: Proc. Int. Symp. on Lubrication and Wear, Houston, 1963. McCutchan Pub. Corp., Berkeley, p. 1. Bair, S. Personnal communication.
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– 24 – Superlubricity of In Situ Generated Protective Layer on Worn Metal Surfaces in Presence of Mg6 Si4 O10 (OH)8 Jin Yuansheng and Li Shenghua State Key Laboratory of Tribology, Bldg. 9003, Tsinghua University, Beijing 100084, China
24.1
INTRODUCTION
Concerted efforts to reduce friction and prevent wear can potentially save billions of dollars annually to our society via lubrication excellence and equipment reliability. Occasionally, entire mechanical systems (be they simple chains or complicated combustion or turbine engines) are scrapped whenever only one or two of the critical components or parts are worn even to the repairable extent. More extreme scenarios of tribologically-rooted breakdown or failure of common mechanical systems concern locomotive and aircraft turbine engines which will require totally disassembling of the engine mainly because a single component was damaged or failed due to wear. Briefly, the consequences of friction and wear are always very serious and if left unattended can have grave implications for national security and quality of life. So, it can come as no surprise that tribomaterials, materials designed for use in moving contacts (sliding, rolling, etc.), and surface engineering methods have for decades attracted the attention of numerous researchers. In this chapter, a superlubricity phenomenon occurring in the process of in situ tribochemical reconditioning of worn metal surfaces will be presented and the underlying mechanisms will be discussed. By introducing a specially formulated reconditioner package, a fine-milled multi-component mineral mixture consisting mainly of magnesium silicate hydroxide (Mg6 Si4 O10 (OH)8 ) and special catalysts into the lubricant fluids that are circulating through the oil delivery channels, a protective layer with smoother and harder surface could be generated on worn metal surfaces. The layer has been experimentally demonstrated to exhibit superlubricity behavior. In this chapter, after introduction of the theoretical background to this work, the superlubricity phenomena of an in situ generated protective layer on worn metal surfaces both in laboratory simulation tests and in some real-world industrial applications are described. Finally the phase structure and the possible source of superlubricity of the in situ generated protective layer on worn metal surfaces are discussed in detail. Superlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Elsevier B.V. All rights reserved.
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24.2 24.2.1
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TRIBOCHEMICAL PRINCIPLES OF IN SITU RECONDITIONING OF RUBBING METAL SURFACES Tribological Process
During frictional processes, generation and dissipation of mechanical energy make the tribopairs’ contact surfaces subjected to very high flash temperatures and high local stresses and strains. The atoms of the tribomaterials and the third body components on and in the vicinity of contact points become highly excited to trigger complex physical and chemical reactions [1]. Mechanochemistry is a field that deals with athermal or ultra-fast chemical reactions between solids or between solids and surrounding gaseous or liquid molecules under mechanical forces [2]. The subordinate subject, tribochemistry, is one specific domain of mechanochemistry that concerns with chemical reactions between tribomaterial surfaces and lubricant/additive molecules under shearing actions and thermal influences [3]. In general, mechanical forces produce strain fields in solids, which makes the atoms leave their equilibrium positions due to lattice vibration, alter bond lengths and angles of their atomic arrangements, and excite their electronic subsystems into excited states [2,4,6]. The metastable and excited atoms may relax via thermal energy or undergo further plastic deformation and re-arrangements which create more defects and disorder in the structure [2,4–7]. As a rule, the energy field incurred by the tribophysical effects, e.g., exo-electron emission (EEE), triboluminescence, triboplasma, crystal defect and vibration, etc., gives rise to specific tribochemical reactions among the basic three bodies constructing the tribosystem (the tribosurface materials of the first and second body, and the lubricant formulation of the third body) [8]. In some designated environments, the fourth body, the chemical species in the surrounding atmosphere, will become chemically involved in the tribochemical reactions. Thanks also to the energy influx, the in situ generated tribochemical reaction products go through physical changes and autogenously form specific crystallographic structures that render expected tribological effects [1]. The design of reactants’ chemistry in the tribochemical reactor (viz. the tribochemical system) and manipulation of tribochemical reactions therein are determinant intrinsic factors once extrinsic factors are designated, such as operating parameters (load, kinematics, temperature, and time), and interaction parameters (contact mode, lubrication regime, etc.) [9,10]. Supposedly, the interactions implicated by all of these physical and chemical inputs are anticipated to yield the third bodies with desired tribological performance or with tribometric excellence [11]. The third bodies interposed between the first and second body in wet lubricated tribosystems are generated by tribo-induced chemical reactions of varied natures and shaped by tribo-induced physical changes via different routes [1]. In general, the third bodies exhibiting beneficial tribological effects are comprised of mixtures of inorganic and organic species that may assume layered configurations, colloidal structures, or networks with basic units of micron or nano-sizes [12]. In the following, two specific examples of tribo-induced chemical reactions, i.e., tribocarbonization and tribooxidation, are introduced. As evidenced in the following context, these two tribo-induced chemical reactions, which are mainly of inorganic nature, hold for very unique and practical tribological significances.
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24.2.2
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Tribochemical Reactions
24.2.2.1 Tribocarbonization Basically there are five forms of carbon allotropes: 3-dimensional diamond (Csp3 ), 2-dimensional graphite (Csp2 ), 1-dimensional carbene (Csp1 ), 0-dimensional fullerene (Csp0 ), and transitional carbons (admixtures of Csp3 , Csp2 and Csp1 ). Some of the carbon allotropes, though introduced in different manners into the contact (in situ or off situ) or applied in different forms (i.e., colloidal dispersion in liquid base stocks, or deposited thin films on substrates), exhibit very interesting tribological behaviors. In addition to the historically recognized lubricious graphite, many other carbon family members have been investigated for tribological applications, such as fullerene particles [13], carbon nanotubes [14], diesel soot [16], ultradispersed diamond containing soot [17], ultra-fine particles of clustered diamond [18], pyrolytic carbons [19–22], meso-carbon microbeads (MCMB, a member of carbonaceous mesophase) [23]. These, together with the currently flourishing tribology-oriented research and development of undoped and doped DLC, hydrogenated DLC, and tetrahedral amorphous carbon (ta-C) [22,24,25], constitute a carbon material-specific sub-discipline of tribology or Carbon Tribology [11]. In the tribochemical systems that operate under boundary lubrication, there may exist tribo-catalytic carbonization and graphitization of solid carbonaceous species from the pyrolysis of either petroleum-derived or synthetic base stocks [11]. In situ generation of lubricious graphitic carbon films is attributed to the contributions of all units comprising the tribochemical systems: the base stock of appropriate aromaticity, the additives with proper functional atoms, and the tribosurfaces with certain catalytic elements [26]. In other words, tribocarbonization of lubrication effects relies on the chemical compatibility between tribomaterials and lubricants, and this compatibility forms the chemistry basis for the selection of functional chemical elements composed of the tribochemical systems. Functioning of tribocarbonization in wear damage control and restoration has been identified in the burgeoning metal conditioning technologies. One is the FENOM technology developed by LT company in Russia and the other is the ART technology (AutoReconditioning Technology) originated by State Key Laboratory of Tribology in Tsinghua University, China. In the action mechanisms claimed by both technologies, carbonization products and their transformed derivatives are important contributors to worn surface reconditioning. In the reconditioning layer formed by the ART technology, nano-sized Fe–C compound phase has been identified with ESCA chemical state analysis and TEM structural and phase analysis while in the FENOM technology, formation of diamond-like carbons has been suggested [27]. 24.2.2.2 Tribooxidation In recent years, attempts have been made to incorporate lubricious oxides and/or oxide forming elements into coating systems in order to achieve low friction and wear. It is welldocumented that certain oxides (such as Re2 O7 , B2 O3 , MoO3 , V2 O5 , etc.) can provide friction coefficients of 0.1–0.3 to sliding surfaces at elevated temperatures and thus they are often referred to as lubricious oxides in the tribology literature. Oxidation of metallic tribosurfaces by atmospheric oxygen in friction and wear, or by dissolved oxygen in fluid
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lubrication has been a well-recognized triboevent. Metal oxides oftentimes exhibit better friction reduction and wear protection than their parent metals depending on the ionic potential and electronegativity of the metal oxides that are formed [28,29]. It is a common practice to include in the polishing medium certain oxy-acid salts which are found to be capable of facilitating the smoothing process of materials, such as diamond. It is not known what part these oxy-acid salts play in diamond polishing but it may be that the grinding of these salts releases atomic oxygen in the same way as described for silica. This very reactive species could then oxidize the diamond surface producing CO2 . This amounts to a delicate method of chemical polishing in which the polishing agent (atomic oxygen) is produced in situ by the fracture of the oxy salt crystals in close vicinity to the surface to be polished [30]. 24.2.2.3
Tribochemical Reconditioning
Based on knowledge about tribochemical conversions, it is generally accepted that carbon alloying and cermetting of worn tribosurfaces occurring in the tribosystems can offer the dynamic in situ reconditioning of rubbing surfaces. In terms of mechanochemistry and tribochemistry, alloying and cermetting can be achieved with generation of the tribochemical third bodies (TTB) and the third-body transform structures (TTS). Thus chemistry (mechanochemistry, tribochemistry as well as thermochemistry) plays the critical role in reconditioning worn metal surfaces. Fundamentally, chemistry is the interaction of energy and matter. Under friction contact, there inherently occur mechanochemical activation and energy relaxation of rubbing surfaces and in-between chemical species, and triboemission processes (formation of fresh surfaces and high-energy particles). These processes supply the reconditioning chemistry with the necessary ‘energy’ condition. A mechanochemical or tribochemical design approach has been proposed by the authors when developing the ART technology to supply the reconditioning chemistry with the necessary ‘matter’ condition [31–33]. In light of the unique approach, the specific ‘matters’ for worn surface reconditioning include the following basic components: metallic source (from rubbing surfaces), carbon source (from basestock of carrier oil), reconditioners, as well as additives and catalysts. The reconditioner chemistry is the core of the ART technology. ART mechanochemical reconditioner package for generating in situ protective layer on worn metal surfaces is a fine-milled multi-component mixture of serpentine minerals with catalysts which facilitate the mechanochemical reactions, especially oil pyrolysis and carbonization. The main constituent in the reconditioner is magnesium silicate hydroxide of empirical formulae Mg6 (Si4 O10 )(OH)8 . Figure 24.1 shows scheme of SiO4 tetrahedral rings and the structural model of serpentine. As a phyllosilicate, basic structure of serpentine is based on interconnected six member rings of complex tetrahedron (SiO4 )4− ions that extend outward in infinite sheets. Three apical oxygen atoms from each tetrahedron are shared with other tetrahedrons. This leads to a basic structural unit of (Si2 O5 )2− . Serpentine contains hydroxyl ion, OH− located at the center of the six-member rings. Thus, the group becomes Si2 O5 (OH)3− . When Mg2+ cations are bonded to the SiO4 sheets, they share the apical oxygen atoms and the OH− anions which are also bonding to the Mg2+ cations in octahedron. This forms a layer of Mg2+ cations in octahedron with the O and OH anions of the tetrahedral layer. The sheets
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Figure 24.1 Scheme of SiO4 tetrahedral rings and structural model of serpentine (Lizardite). Sources: Goldberg and Romanosky, National Energy Technology Laboratory, Pittsburgh, PA, USA, Chen, Science Applications International Corporation, McLean, VA, USA, and Nelson, Tulane University, Louisiana, USA. Table 24.1. Main elemental compositions of reconditioner package Element
Content/ppm
Element
Content/ppm
Mg Si Fe Al Ni
626 1119 165 12.2 24.8
Ca Na Zn P
16.3 118 9.3 20.3
Figure 24.2 Ferrograph of reconditioner powders.
are connected to each other by layers of cations, which are weakly bonded and often have water molecules (hydrated). Serpentine as a phyllosilicate displays good basal cleavage, and oxygen releasing capability. Table 24.1 displays the main elemental compositions of the concentrated reconditioner liquid (5 mg powders per milliliter of base oil) analyzed with Atomic Emission Spectroscopy. From the optical image of the reconditioner powders in Figure 24.2, which is ob-
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tained with ferrography, the estimated size of bulk of the reconditioner powders is smaller than 2 µm.
24.3
24.3.1
SUPERLUBRICITY OF PROTECTIVE LAYER GENERATED BY ART MECHANOCHEMICAL RECONDITIONER PACKAGE Protective Layer Generated in Railway Locomotive Trials
In a representative field trial co-conducted with Beijing Diesel Locomotive Depot on two DF11-type internal combustion locomotives driven by a 16V280Z model diesel engine, DF11-0063 and DF11-0163, which had just gone through overhauling (after 300,000 km running), the ART mechanochemical reconditioner package was blended into the engine crankcase oil with China’s classification of TB/T-2933-1998, equivalent to LMOA (Locomotive Maintenance Officers Association) Generation III in USA. Engines were disassembled after an extended operation of 300,000 km. No wear was detected on all piston rings and cylinder bores, and the original dimensions of other tribological parts, like camshafts and connecting-rod bushes, were also maintained. Surface appearances of some critical component parts disassembled from the DF11-0063 locomotive engine were exemplarily exhibited in Figures 24.3 through 24.6.
Figure 24.3
Figure 24.4
Disassembled camshafts.
Disassembled piston and plain bearing.
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Figure 24.5
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Disassembled connecting-rod bush.
Figure 24.6 Disassembled cylinder bore.
24.3.2
Observation of the Protective Layer on Cylinder Bore
A segment of the No.15 real-world cylinder bore of the disassembled 16V280Z diesel engine on the DF11-0063 locomotive was cut off and prepared by common metallographic method for SEM observation of cross section of cylinder wall with a CSM-950 Scanning Electronic Microscope. Figures 24.7 and 24.8 display the observed SE and BSE images of the protective layer mechanochemically annexed onto the original cylinder substrate. In appearance, the protective layer can be roughly divided into a top layer and an underlayer or interlayer, and they assume different thicknesses and varied elemental compositions. The total thickness of the protective layer is about 8∼10 µm with the top layer being approximately half of the underlayer in thickness. The BSE image suggests that there exist more lighter elements in the top layer than in the underlayer, and the SE image indicates fine adhesion of the underlayer to the pearlite substrate. Figure 24.9 presents elemental compositional analysis of the protective layer. It is very clear that the main elemental components Fe, C and O in the layer observe consistent distributions, suggesting that these three elements co-exist in some kinds of chemical combinations. An interesting point is that Mg and Si, which are the two major elements in the ART mechanochemical reconditioner package, have not been detected in the protective layer.
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Figure 24.7 SE photo of protective layers.
Figure 24.8
BSE photo of protective layers.
Figure 24.9 SE photo (a) and EDX multi-element mapping (b, c and d) of protective layer (×10 k).
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Figure 24.10
Figure 24.11
24.3.3
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Loading and unloading curve.
AFM 3D images of indentations on layer (left) and substrate (right).
Nano-hardness
A CSEM nano-hardness indenter was employed to measure the nano-hardnesses and elastic modulus on the cross-section of the protective layer and the cylinder bore substrate. The attached Atomic Force Microscope (AFM) was used to record morphology of the indentation. Measurement was conducted at the maximum load of 20.00 mN, and loading and unloading speed of 40 mN/min, as shown in Figure 24.10. The AFM images of typical indentations on the layer and the substrate were shown in Figure 24.11. Table 24.2 lists nano-hardnesses on the Vickers scale of the protective layer and the substrate. It is seen that the nano-scale Vickers hardness of the protective layer amounts to Hv1119 in average, about twice as high as that of the cylinder bore substrate. It has been suggested that hardness and elasticity in combination can be more accurately correlated to tribological behaviors of tribosystems under investigation [34,35]. So, the ratio of Hardness and Young’s modulus, H /E, is an important derived parameter capable of characterizing coating materials for tribological purposes. The measured minimum nanohardness and maximum elastic modulus of the protective layer are, respectively, 12.72 GPa and 210 GPa, and therefore the H /E ratio of the protective layer is about 0.0606.
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1
2
3
4
5
6
Averages
Protective layer Substrate
1229 473
1038 566
1178 547
1023 541
1146 494
1100 523
1119 524
Figure 24.12
24.3.4
Surface morphology of protective layer.
Surface Roughness
From the recorded morphology of the protective layer formed on the inner-arc surface of the cylinder bore by a Talysurf-type Profilometer, as displayed in Figure 24.12, the surface roughness Ra was estimated to be 0.0694 µm, corresponding to ultra-smooth surfaces achieved with ultra super-grinding, super-polishing and mirror surface milling. 24.3.5
Coefficient of Friction
An Optimal SRV Friction and Wear Tester was employed to measure the coefficient of friction of the protective layer. For the purpose, the upper and the lower specimens were cut off directly from the real piston ring and cylinder bore of the disassembled 16V280Z diesel engine on the DF11-0063 locomotive respectively. Diameter of the outer circle and width of the Cr-plated piston ring specimen are respectively 280 mm and 6 mm, and an arcshaped segment of 7 mm in length was cut off as the upper specimen. The lower specimen was cut from the cylinder bore into a 24 column. The upper and lower specimens are in surface contact and apparent contact area is 42 mm2 . Assemblage of the above tribomate specimens for SRV tribotest and their contact geometry are shown in Figure 24.13. Experimental conditions were set as follows: Loads 20 N, 30 N, 40 N, 50 N and 60 N; stroke 0.3∼0.6 mm; frequency 50 Hz; maximum average pressure 1.43 N/mm2 , maximum sliding speed 0.1 m/sec, and dry sliding (No-oil lubrication). Table 24.3 indicates that the protective layer presents a stable and low coefficient of friction of 0.005, demonstrating the greatest potentiality of the ART mechanochemical reconditioner in maintaining superlubricity offered by the generated protective layer under dry sliding conditions.
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Figure 24.13
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Geometry, fixture and contact of upper and lower specimen in SRV tribotest.
Table 24.3. Coefficient of friction of the protective layer
24.3.6
Load/N
20
30
40
50
60
Average pressure/N/mm2 μ
0.48 0.005
0.71 0.005
0.95 0.005
1.19 0.005
1.43 0.005
Protective Layer Generated in Laboratory Conditions
In laboratory conditions a Falex tribotester was employed to in situ generate a protective layer on both the 45# steel and cast iron tribosurfaces under designed tribological conditions in presence of ART superfine powders which were finely dispersed in a carrier oil of mineral base. The morphology, mechanical performances and chemical states of the formed protective layer on 45# steel tribosurfaces were characterized, and the coefficient of friction of cast iron tribopair was measured under boundary lubrication. 24.3.6.1 Experimental Details The real test specimens for Falex-1506 tribotester are shown in Figure 24.14. The contact area of the upper and lower specimen is 506 mm2 . The test schedule included three experimental periods as displayed in Table 24.4. The test parameters were as follows: loads 1∼5 LB, lever ratio 10:1, average contact pressures 0.088∼0.439 N/mm2 , revolution 500∼3000 rpm; average sliding line speeds of contact surfaces 1.23∼7.35 m/s. The total test periods were 400 hours and 80 hours for 45# steel tribopair and cast iron tribopair respectively according to the test matrix listed in Table 24.4. The lubricant was a blend of API SD/CC SAE40 engine oil formulated with the ART reconditioner at concentration of 1.6 g/L.
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Figure 24.14
Upper (left) and lower (right) specimen of Falex-1506 tribotester. Table 24.4. Tribotest matrix for Falex test
500 rpm First period 1 LB 10 min 2 LB 10 min 3 LB 10 min 4 LB 10 min 5 LB 10 min Second period 5 LB 10 min Third period 5 LB 10 min
24.3.6.2
1000 rpm
1500 rpm
2000 rpm
2500 rpm
3000 rpm
10 min 10 min 10 min 10 min 10 min
10 min 10 min 10 min 10 min 10 min
10 min 10 min 10 min 10 min 10 min
10 min 10 min 10 min 10 min 10 min
10 min 10 min 10 min 10 min 250 min
10 min
10 min
10 min
10 min
420 min
10 min
10 min
10 min
10 min
420 min
Characterization of the Protective Layer on 45# Steel Tribosurfaces
Figure 24.15 displays the cross section SEM image of the protective layer generated on the lower specimen surface after Falex test for 400 hours. It is clearly seen that the protective layer is about 2 µm thick and assumes a compact structure without clearly distinguishable physical boundary with the substrate. Microhardness measurement of the original surface and reconditioned worn surface of 45# steel specimen was made with an LECO DM-400 micro-hardness tester under 100 gram load. A CSEM nano-hardness tester was also used to measure nano-hardness and elastic modulus on the cross section of the protective layer and substrate of the specimen under same conditions as in the above railway locomotive scenarios. Measurement results of microhardness are presented in Table 24.5. A substantial increase of microhardness of the 45# steel surfaces with the protective layer, more than twice as hard as the original surface, can be noted. The AFM images and depth curves of the representative nano-hardness indentations on the protective layer and the 45# substrate are shown in Figures 24.16 and 24.17. Table 24.6 lists the nano-hardness values on the Vickers scale of the protective layer and the substrate. It is obvious from Figures 24.16 and 24.17 that both the width and the depth of the typical indentation on the protective layer are only half of the corresponding values on the 45# steel
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Figure 24.15
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SEM graphs of lower specimen cross section. Table 24.5.
Surface micro-hardnesses of lower specimen in Falex test Measurement positions
1
2
3
4
5
6
7
8
Average
Hardness Hv100g
234 970
290 707
301 757
299 734
290 748
321 720
331 864
321 738
298 780
Pre-test Post-test
Figure 24.16
AFM image (a) and depth curve (b) of the protective layer.
substrate. From Table 24.6, the nano-scale Vickers hardness of the protective layer is about three times as high as that of the 45# steel substrate. It is also remarkable that the minimum nano-hardness and maximum elastic modulus of the protective layer are 13.32 GPa and 240 GPa respectively, and H /E is about 0.0555, demonstrating that the protective layer
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Figure 24.17
AFM image (a) and depth curve (b) of the 45# steel substrate. Table 24.6.
Nano-hardness of the protective layer and substrate of lower specimen Measurement positions
1
2
3
4
Average
Hardness Hv20mN
353.30 1177.06
321.20 1389.45
338.18 1383.45
387.44 1149.85
350.03 1274.95
Substrate Layer
formed by mechanochemical reconditioning in laboratory conditions assumes the same mechanical performances as that obtained in the railway trial conditions. The chemical state in the protective layer was identified on an X-Ray Photoelectron Energy Spectroscope using a monochromatized Al Kα-radiation (1486.6 eV) with FAT scan mode. The vacuum chamber pressure is 2.7 × 10−8 Pa. Sputtering depth profiles were obtained by 5 keV Ar+ ion beam of 1.3 µA. The binding energies of the peaks were referenced to C1s binding energy at 284.6 eV. Considering possible contaminations on the utmost surface of the protective layer, the XPS analysis was conducted on its subsurface which was obtained with Ar+ sputtering for 10 minutes (about 50 nm in depth). Figure 24.18 presents the survey XPS spectrum. An obvious fact is that there only exist three elements, i.e., Fe, C and O in the protective layer. It is predicted that Fe is almost completely from the 45# steel surface and wear debris, C is almost exclusively from the carrier oil, and O is from many different sources, such as active oxygen released from Mg6 Si4 O10 (OH)8 , the dissolved oxygen in the bulk phase of the carrier oil, and gaseous oxygen from the environment atmosphere. The other two facts worthy of special attention are respectively: (1) the major constituent elements of the Mg6 Si4 O10 (OH)8 , Mg and Si, were never detected in the protective layer; (2) the functional elements S, P and Zn from the antiwear additive ZDTP and Ca from the calcium sulfonate detergent in the fully formulated carrier oil were also never detected. These facts denote that presence of the reconditioner package in the carrier oil initiates preferential mechanochemical interactions
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Figure 24.18
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XPS survey spectrum of protective layer after 10 min Ar+ sputtering.
Figure 24.19
Fe2p fine spectrum in the layer after 10 min sputtering.
among themselves and/or with the rubbing 45# steel surfaces and debris, which finally give rise to the formation of the protective layer. At the same time, these interactions excludes the tribochemical involvement of the traditional but must-be formulated additives with the ferrous rubbing surfaces, which would otherwise be the prevailing interaction modes in such a tribosystem. Figures 24.19 through 24.21 present the fine XPS spectra of the detected three elements Fe, O and C. From Figure 24.19 it can be deduced that there exist three basic chemi-
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Figure 24.20
O1s fine spectrum in the layer after 10 min sputtering.
Figure 24.21
C1s fine spectrum in the layer after 10 min sputtering.
cal forms for element Fe: elemental iron, iron oxides and iron carbide. These iron compounds assume five chemical states: elemental Fe (706.3 eV), Fe2 O3 (710.4 eV), Fe3 O4 (709.0 eV), Fe3 C (707.9 eV) and alloy Fe (707.1 eV). Existence of Fe3 O4 and Fe2 O3 can be corroborated by the binding energy peaks of oxygen respectively at 529.9 eV and 530.4 eV in Figure 24.20. Due to various sources of oxygen, it also exist in other chemical forms, such as adsorbed CO2 (531.1 eV), adsorbed O2 (529.2 eV), adsorbed water (530.8 eV, –OH), and other oxidation intermediates of organics (532.5 eV for carbonyl species, such as aldehydes and acetones). As for carbon, its effective chemical states are Fe3 C (284.1 eV), carbonyl species (283.3 eV), alloy carbon (282.6 eV) and adsorbed contaminants (285.3 eV).
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Figure 24.22 SEM graphs of cross section of cast iron lower specimen (a) SEM graph without etching (b) SEM graph with etching.
To sum up, in terms of chemical composition, the protective layer generated on 45# steel surface is mainly made of iron oxides and iron carbides. The existing adsorbed oxygen- and carbon-containing species may act as the oxygen source and carbon source for generating and replenishing the iron oxides and iron carbides. 24.3.6.3 Coefficient of Friction of Cast Iron Tribopair under Boundary Lubrication Figure 24.22 displays SEM morphological texture of cross section of the cast iron lower specimen after 80 hours in the Falex test. In average, the protective layer is approximately 4 µm in thickness. From the high magnification SEM image, it is clearly seen that the layer assumes a compact structure with no clearly distinguishable physical boundaries with the substrate. In order to measure the coefficient of friction of the protective layer generated on cast iron tribosurfaces under boundary lubrication, all used lubricant with the reconditioner package was drained out from the oil cup after an 80-hour Falex test. Then, the Falex test was restarted under boundary lubrication in terms of the first period of the schedule listed in Table 24.4. The curve of coefficient of friction recorded in the first period is shown in Figure 24.23. It can be observed that the coefficient of friction is still below 0.005 after running-in in the first test period. This again demonstrates that the protective layer generated by the ART reconditioner is of superlubricity characteristics.
24.4 POSSIBLE SOURCES OF SUPERLUBRICITY OF IN SITU GENERATED PROTECTIVE LAYER ON WORN METAL SURFACES In comparison with traditional surface treatment technologies the mechanochemical reconditioning technology takes positive advantage of the energy release and materials chemistry existing in the damaged regions on tribosurfaces. Formulation chemistry of the
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Figure 24.23
Curve of coefficient of friction of cast iron pair in Falex test after oil drain-out.
mechanochemical reconditioning package plays the key role in forming the protective layers in time and effectively. It has been demonstrated that the mechanochemical reconditioner package containing mainly Mg6 (Si4 O10 )(OH)8 can effectively generate in situ a protective layer on worn Fe-base metal surfaces both in laboratory experimentations and in field trials on locomotive diesel engines, and the protective layer exhibits superlubricity behavior. This section attempts to explore the phase structure of the in situ generated protective layer on worn Fe-base metal surfaces and to correlate it with the observed superlubricity behavior. 24.4.1
Phase Structure of the Protective Layer [36]
For detecting the phase structure of the protective layer TEM and HRTEM analyses were respectively completed on a JEM-2000FX Model TEM and a JEOL JEM-2010F Model TEM. TEM samples were cut off from the No.15 cylinder bore of DF11-0063 locomotive diesel engine. The preparation procedure of TEM samples for surface region and adjacent region to substrate of the protective layer are shown in Figures 24.24 and 24.25 respectively. Figure 24.26 is TEM photograph and SAD (Selected Area Diffraction) pattern of the protective layer showing iron oxide nano-particles on Fe–C compound (Fe3 C) matrix. Figure 24.27 shows HRTEM image of grain boundary of Fe–C compound nanocrystal matrix in the protective layer (arrows). Figure 24.28 exhibits amorphous nano-grain (dark arrow) surrounded by nanocrystal grains in the matrix. In Figure 24.29 are SAD patterns of nanoparticles distributed on the matrix in the protective layer. Obviously, the nano-particles are Magnetite (Fe3 O4 ) and Iron oxyhydroxide (FeOOH). TEM analyses also indicate that there exists a certain orientation relation between Fe–C compound (Fe3 C ) matrix and iron oxide nano-particles, i.e., ¯ ) Fe3 C // ( 020 ) Fe3 O4 , [ 012 ] Fe3 C // [ 001 ] Fe3 O4 , ( 210 ( 011¯ ) Fe3 C // ( 200 ) Fe3 O4
Superlubricity of In Situ Generated Protective Layer
Figure 24.24
Figure 24.25
Figure 24.26
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TEM sample preparation for surface region.
TEM sample preparation for adjacent region to substrate.
TEM photograph and SAD pattern of protective layer.
Figures 24.30 and 24.31 are HRTEM images of plane spacing of Fe–C compound (Fe3 C) matrix and Fe3 O4 nano-particle in the protective layer respectively. The 113 plane spacing and 221 plane spacing of Fe–C compound (Fe3 C) matrix are 1.878 Å and 1.643 Å respectively. The 220 plane spacing of Fe3 O4 nano-particle is 2.96 Å. The data about plane spacings of both the matrix and nano-particles further validate the fact that nano-crystalline
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Figure 24.27
HRTEM image of grain boundary nanocrystal matrix.
Figure 24.28
Figure 24.29
HRTEM image of amorphous nano-grain.
SAD patterns of nano-particles in protective layer.
Superlubricity of In Situ Generated Protective Layer
Figure 24.30
HRTEM image of plane spacing of Fe–C compound (Fe3 C ) matrix.
Figure 24.31
Figure 24.32
HRTEM image of plane spacing Fe3 O4 nano-particle.
HRTEM image of perfect nano-crystalline system in protective layer.
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Figure 24.33
Raman spectrum on surface of the protective layer.
structure in the matrix of the protective layer is mainly Fe3 C, and the nano-particle crystalline structure involves Fe3 O4 . Figure 24.32 shows a perfect nano-crystalline system existing in the protective layer which consists of Fe–C compound (Fe3 C) matrix, as well as Fe3 O4 and FeOOH nano-particles. TEM and HRTEM analyses have indicated that the protective layer, both surface region and adjacent region to substrate, consists mainly of Fe–C compound (Fe3 C) nanocrystal matrix with crystalline anisotropy on which nano-particles of magnet iron oxide (Fe3 O4 ) and iron peroxide (FeOOH) are dispersed along the habit planes of nanocrystalline Fe3 C matrix. 24.4.2
Raman Spectrometry Analysis
A Model RM2000 Microscopic Confocal Raman Spectrometer was adopted to give a preliminary identification of existing amorphous nano-grains, as shown in Figure 24.28, in the protective layer. Figure 24.33 shows the Raman spectrum acquired on the surface of the protective layer generated on the inspected cylinder bore. The spectra data were gathered by continuous scanning mode. The existence of both the characteristic D-peak and G-peak of carbon with almost the same intensity suggests that the amorphous nano-grains shown in Figure 24.28 are probably of DLC structures. 24.4.3
Possible Sources of Superlubricity
In general, novel tribological behavior of the observed protective layer could be anticipated based on surface modification by generation of nanocrystalline surface layer. Among the many possible inherent structures and properties of the protective layer that effectively decrease friction and reduce wear, effects from mechanical and chemical factors may be the primary contributors to the observed superlubricity of the protective layer. Firstly, the protective layer In the present case consists of a peculiar nanocrystalline coating material with nano-scale grain sizes (less than 100 nm), and surface roughness (Ra at nanometer scale). The smoother surface of the protective layer has eliminated fric-
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tion inducing effects such as asperity interlocking, and thus produces an additional reduction of the coefficient of friction. Secondly, the superlubricity of the protective layer may come from its super hard surface and suitable H /E ratio. It is recognized that elasticity in combination with hardness can be more comprehensively and accurately correlated to tribological behavior of coating materials, and the H /E ratio is of particular significance in characterizing and optimizing tribological performances of nanocrystalline coatings. In the present case, the protective layers on both tribotest specimen surfaces and real engine cylinder bore surfaces assumes high “ceramic” hardness (H = 13.32 GPa or higher) and still retain the elastic properties of metals (E = 240 GPa or lower). Such a peculiarity of the protective layers presents their H /E values very similar to that of typical nanocrystalline ceramic coating materials (ca. 0.06). In other words, high surface hardness and appropriate H /E value of the protective layers cause very small elastic deformation within nanocrystalline surface region in the elastic microcontacts, thus effectively excluding friction and wear arisen from plastic ploughing and adhesion. It has been reported that extreme low friction could be achieved via tribochemical formation of both oxides and hydroxide. The concept of “lubricious oxides” was developed and useful solid lubrication technologies have been developed through exploratory researches of multifarious metal and non-metal oxides. It has been suggested that the friction reducing effects of hydroxides result from the weak hydrogen bonds among the OH-containing species. In the present case, Fe3 O4 nano-particles dispersed on Fe–C matrix act as lubricious oxides, and FeOOH nano-particles in the form of hydrates supply the weak hydrogen bonds between protective layers and on the counter surfaces. This is probably the third origin of superlubricity of the protective layer. Finally, superlubricity exhibited by the protective layer may probably arise from generation of some DLC structures within the layer, whose existence was evidenced by Raman spectra of the protective layer.
ACKNOWLEDGEMENTS The authors would like to express their sincere thankfulness to Dr. Yang He, Dr. Wang Feng, and Zhang Zhengye for their experimental contributions and valued discussions during the implementation of the research program on ART technology in State Key Laboratory of Tribology, Tsinghua University, Beijing, China.
REFERENCES [1] Li, S., Erdemir, A., Jin, Y. Mechanistic modeling of tribo-induced chemical reactions at engineered tribological surfaces. In: Proceedings of WTC2005, World Tribology Congress III, September 12–16, 2005, Washington, DC, USA, WTC2005-64086. [2] Gilman, J.J. Mechanisms of shear-induced solid-state reactions. Mat. Res. Soc. Symp. Proc. 453 (1997), 227–232. [3] Boldyrev, V.V., Tkacova, K. Mechanochemistry of solids: Past, present, and prospects. J. Mater. Synthesis Process. 8(3/4) (2000), 121–132.
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[4] Gilman, J.J. Mechanochemical mechanisms in stress corrosion. In: Jones, R.H. (Ed.), Chemistry and Electrochemistry of Stress Corrosion Cracking: A Symposium Honoring the Contributions of R.W. Staehle, TMS, 2001, pp. 3–25. [5] Tolo-Labbe, A. Characterization of chemical reactions from the profiles of energy, chemical potential, and hardness. J. Phys. Chem. A 103(22) (1999), 4398–4403. [6] Gutman, E.M. Mechanochemistry of Materials. Cambridge International Science Publishing, 1998, pp. 162–164. [7] Gilman, J.J. Chemical and physical “hardness”. Mat. Res. Innovat. 1 (1997), 71–76. [8] Heinicke, G. Tribochemistry. Akademie-Verlag, 1984. [9] Li, S., Martin, J.M., Jin, Y. Tribochemical design. In: Proceedings of WTC2005, World Tribology Congress III, September 12–16, 2005, Washington, DC, USA, WTC2005-64070. [10] Li, S., Kajdas, C., Jin, Y. Meta-analysis of lubrication chemistry with DFT-based concepts and Lewis theory of acid-base reaction chemistry. In: Proceedings of WTC2005, World Tribology Congress III, September 12–16, 2005, Washington, DC, USA, WTC2005-63217. [11] Li, S. Tribochemodesign study based on case analyses. Postdoctorate Research Report, Tsinghua University, Beijing, April 2000. [12] Li, S., Lun, Z., Yang, H., Jin, Y. Views of mineralogical and organics chemistry on origin and structure of tribochemical films. Lub. Eng. 21(4) (2005), 37–44. [13] Gupta, B.K., Bhushan, B. Fullerene particles as an aditive to liquid lubricants and greases for low friction and wear. Lub. Eng. 50(7) (1994), 524–528. [14] Chen, W.X., Tu, J.P., Wang, L.Y. et al. Tribological application of carbon nanotubes in a metal-based composite coating and composites. Carbon 41(2) (2003), 215–222. [15] Nozaki, K., Nakajima, K. Role of smoke from combustion of oil in tribological applications to ceramics. Wear 217 (1998), 73–80. [16] Gautman, M., Chitoor, K., Durali, M. et al. Effect of diesel soot contaminated oil on engine wear— investigation of novel oil formulations. Tribol. Int. 32 (1999), 687–699. [17] Xu, T., Zhao, J., Xu, K. et al. Study on the tribological properties of ultradispersed diamond containing soot as an oil additive. Tribol. Trans. 40 (1997), 178–182. [18] Quyang, Q., Okada, K. Nano-ball bearing effect of ultra-fine particles of cluster diamond. Appl. Surf. Sci. 78 (1994), 309–313. [19] Jin, Y., Zhou, C. The effectiveness of high temperature lubrication by in situ formation of graphite/MoS2 films. Wear 205 (1997), 77–87. [20] Lauer, J.L., Bruce, G. Catalytic generation of lubricants from carbonaceous gases on surfaces undergoing friction at high temperatures. Paper No.880019 in Recent Developments in the Adiabatic Engine, SAE Publication SP-738, vol. 2, 1998, pp. 51–60. [21] Bunting, B.G., Lauer, J.L. The lubrication of metals and ceramics by the catalytic formation of carbon films. SAE Paper 87002, SAE International Congress and Exposition, Proceeding of the Symposium on the Adiabatic Engine, vol. 2, Detroit, 1987, pp. 23–27. [22] Barnick, N.J., Blanchet, T.A. et al. High temperature lubrication of various ceramics and metal alloys vis directed hydrocarbon feed gases. Wear 214 (1998), 131–138. [23] Cui, X., Li, S., Jin, Y. et al. A study of tribological performance and tribo-induced graphitization of mesocarbon microbeads. Tribol. Lett. 14(2) (2003), 53–59. [24] Donnet, C. Recent progress on the tribology of doped diamond-like and carbon alloy coatings: A review. Surf. Coat. Technol. 100–101 (1998), 180–186. [25] Grill, A. Review of the tribology of diamond-like carbon. Wear 168 (1993), 143–153. [26] Li, S., Jin, Y. The elemental periodicity and tribochemodesign. Progress in Tribology 4(3–4) (1999), 52–72. [27] Balabanov, V.I., Beklemshev, V.I., Mahonin, N.I. Tribology for All. Moscow, 2002 (in Russian). [28] Erdemir, A. A crystal-chemical approach to lubrication by solid oxides. Tribol. Lett. 8 (2000), 97–102. [29] Erdemir, A., Li, S., Jin, Y. Relation of certain quantum chemical parameters to lubrication behaviors of solid oxides. Int. J. Mol. Sci. 6 (2005), 203–218. [30] Fox, F.G. Mechanically initiated chemical reactions in solids. J. Mater. Sci. 10 (1975), 340–360. [31] Wang, F. Study on mechanism of self-reconditioning of worn surface of metals. Postdoctorate Research Report, Tsinghua University, Beijing, April 2004.
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[32] Yang, H. The function mechanisms and application case of a reconditioner for worn metal including Mg6 Si4 O10 (OH)8 . Ph.D. Dissertation, Tsinghua University, April 2005. [33] Zhang, Z. The experimental study of auto-reconditioning technology for worn metals. Master Degree Thesis, Tsinghua University, June 2004. [34] Leyland, A., Matthews, A. On the significance of the H /E ratio in wear control: A nanocomposite coating approach to optimised tribological behaviour. Wear 246 (2000), 1–11. [35] Holmberg, K., Matthews, A. Tribology of engineered surfaces. In: Stachowiak, G. (Ed.), Wear—Materials, Mechanisms and Practice, 2004, submitted for publication. [36] Yuansheng, J., He, Y., Feng, W., Minfray, C., Li, S. Phase structure and lubricity of in-situ generated protective layer on worn metal surfaces in presence of Mg6 Si4 O10 (OH)8 . In: Proceedings of WTC2005, World Tribology Congress III, September 12–16, 2005, Washington, DC, USA, WTC2005-63927.
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– 25 – Superlubricity of Diamond/Glycerol Technology Applied to Automotive Gasoline Engines Maria Isabel De Barros Bouchet1 and Makoto Kano2 1 Laboratory of Tribology and System Dynamics, UMR CNRS 5513, Ecole Centrale de
Lyon, 36 Avenue Guy de Collongue, 69134 Ecully Cedex, France 2 Nissan Research Center, to Kanagawa Industrial Technology Center, 705-1,
Shimo-imaizumi, Ebina, Kanagawa 243-0435, Japan
25.1
INTRODUCTION
During the age of machinery proliferation, economic pressures required manufacturers to improve the useful life of their machines. This promoted the search for chemical agents, so-called additives, to increase the life of the lubricant, provide corrosion inhibition and wear resistance to the hardware. In addition, these efforts resulted in specialization that adapted a lubricant to the needs of the specific hardware in which the lubricant was used. One such adaptation is seen in lubrication of automotive engine. The oil additives were identified that solved a variety of engine problems like ability to keep particles such as soot dispersed, ability to prohibit acidic combustion products from plating out as varnish on engine surfaces and ability to minimize wear by laying down a chemical film on heavily loaded surfaces. In the new millennium, the long-term impact of these additives on the environment, the engine oil recyclability and the fuel economy are becoming issues of particular concern. Development of new lubricant additives to reduce the concentration (or eliminate) of poisonous elements like phosphorus and sulphur from oil and the development of new mechanical components for more efficient combustion engine (lightweight body structures, direct-injection systems for gasoline engines . . .) [1–3] will play an important role to respond to these current issues. However, the replacement of an antiwear additive such as zinc dialkyldithiophosphates (ZDDP) will present a real challenge in terms of cost and efficiency and the development of new mechanical components has several disadvantages such as expensiveness and design limitations. A potential solution receiving increasing attention to respond to the environmental and economical requirements is the use of low friction and wear resistant coatings on the meSuperlubricity Edited by A. Erdemir and J.-M. Martin © 2007 Published by Elsevier B.V.
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chanical components submitted to boundary lubrication conditions. A such solution implies modifications of the lubricant to ensure that coated components are adequately lubricated. Diamond-like carbon (DLC) coatings which have been extensively studied in the last decade may fulfill this role [4,5]. Depending on their properties which are in turn dependent on the deposition procedure, the DLC coatings present a wide range of tribological behavior as shown in the Chapter 16 and 17 of this book concerning the superlubricity of carbon-based materials. This chapter presents a unique tribological system that is able to produce no measurable wear of material combination and that reduces friction markedly in the ultralow and superlow regimes under boundary lubrication. The surface material is tetrahedral hydrogen-free amorphous Diamond-Like-Carbon (denoted as ta-C). Ultralow friction was obtained by sliding the ta-C/ta-C friction pair in the presence of Poly-Alpha Olefin base oil containing 1% by weight of friction modifier additive Glycerol Mono-Oleate (GMO) at 353 K. Superlubricity was obtained by sliding the ta-C/ta-C friction pair in the presence of pure glycerol as a lubricant at 353 K. It is planned to apply this advanced DLC coating technology to valve lifters lubricated with a newly formulated engine oil in actual mass-produced gasoline engines. A larger friction reduction compared with the conventional material combination is expected at an engine speed of 2000 rpm.
25.2 25.2.1
METHODS
DLC Materials Preparation
The tetrahedral hydrogen-free DLC coating (so-called ta-C) was applied to the polished carburized steel disc and the hardened steel pins to a thickness of 0.7 micron from a graphite target by arc-ion plating, a physical vapor deposition (PVD) process, and did not contain hydrogen [6]. The hydrogen-containing DLC coating (so-called a-C:H) was applied to the polished carburized steel disc and hardened steel pins to a 1.0 micron thickness by a plasma-assisted chemical vapor deposition (CVD) process from hydrocarbon gas and contained about 20 at.% of hydrogen [6]. The surface roughness of these two kinds of coatings was in the 20–40 nm range. 25.2.2
Tribological Tests
The pin-on-disc sliding tests were conducted in the following manner. The pins, measuring 5 mm in diameter and 5 mm in length, were made of hardened bearing steel (AISI 52100) and polished to a surface roughness of Ra 0.05 micron. The disc measured 35 mm in diameter and 2.5 mm in thickness and was made of carburized steel. The three pins were secured to prevent them from rotating and were pressed against the toric sliding surface of the rotating disc at a position that was 20 mm in diameter from the center of the disc. Contact at the sliding interfaces was in the shape of lines under high Hertzian pressure of 700 MPa due to a normal force of 500 N, as shown in Figure 25.1. Lubrication was
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Figure 25.1 Pin-on-disc test rig.
Figure 25.2
SRV sliding test rig.
provided by an oil bath heated to 353 K. The sliding speed was varied in a range of 0 to 1 m s−1 for the tribological experiments and the sliding time was 60 minutes. The SRV sliding tests were performed with a reciprocating needle-pin-on-flat-disc tribometer that was lubricated before the test by wetting it with several droplets (5 cc) of the test oil heated to 353 K. The pins, measuring 18 mm in diameter and 22 mm in length, were made of hardened steel and polished to a surface roughness of Ra 0.05 micron. The disc measured 24 mm in diameter and 7.9 mm in thickness and was made of carburized steel. The reciprocating pins were pressed against the stationary disc by a force of 400 N that generated 270 MPa of pressure as shown in Figure 25.2. The length of the track was 3.0 mm and the reciprocating time was 15 minutes at 50 Hz. For each kind of tribometer, the friction experiment was repeated a few times under the same conditions in order to check the reproducibility of the measurements. At the end of the tests, the flat samples were washed in n-heptane to eliminate all the residual oil, gel-like species and contaminants and permit accurate surface analyses.
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Figure 25.3
Figure 25.4
25.2.3
Valvetrain system.
Single cam and follower test rig.
Engine Tests
The valvetrain system is a significant source of mechanical friction loss in an automobile engine, especially at low speeds where fuel economy is most important. Friction at the sliding interfaces between the cam and follower (Figure 25.3) accounts for about 80% of all valvetrain system friction and 20% of the total engine friction. Therefore, the DLC coating for obtaining a superlow friction level was first applied to the engine cam follower lubricated with standard 5W-30 engine oil. A cam and follower pair was tested, with the test cam made of chilled cast iron fitted to a shaft driven by a variable speed DC motor while the follower was pressed against the cam by a load spring, as shown in Figure 25.4 which presents the single cam and follower test rig. Friction torque was measured with a torque sensor. Based on the results of these preliminary experiments, bench tests were then conducted with an actual engine to examine the effect of the DLC coating on reducing friction losses. The cylinder head was mounted on a test stand, and the camshaft made of chilled cast iron was driven directly by a drive motor via a torque meter, as shown in Figure 25.5 which presents the engine valvetrain motoring test.
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Figure 25.5 Engine valvetrain motoring test.
25.2.4
Nanoscratch Measurement
Nanoscratch measurements were obtained in a constant-force nanoscratching process using a conical diamond tip as a stylus for scratching. The nanoscratching process consisted of applying a constant normal force by pressing the diamond stylus on the sample surface and then displacing the stylus to induce a lateral scratch on the surface. By detecting the lateral force and normal displacement, the friction coefficient relative to the scratch depth was determined on the basis of the ratio of the lateral force to the normal force. 25.2.5
Mechanical Measurements
Several tests of indentation have been made on the ta-C and a-C:H coatings in order to measure their mechanical properties (hardness and Young’s modulus). Experiments were performed using a nano-indenter with a Berkovich indenter (three-sided pyramid, angle between arête: 115◦ 12′ ). Thus, the imposed deformation is about 7%. The system has load and displacement amplitudes of 500 mN and 100 µm respectively and load and displacement resolution of 10 mN and 0.5 nm respectively. Continuous stiffness measurement is used: that means that a small oscillation is superimposed to the large-scale DC loading. The excitation amplitude is continuously adjusted such that the corresponding displacement amplitude remains constant at 3 nm. The displacement and force amplitudes, as well as the phase angle between the two, are monitoring using a lock-in amplifier (frequency specific amplification). By observing the resultant displacement amplitude and the phase shift between the force and the displacement, we can thus infer the stiffness S at all displacements can be measured. Thus, the elastic modulus and the hardness as a continuous function of indenter displacement can be obtained. The frequency of the sinusoidal motion ranges from 5 × 10−3 to 60 Hz. In the experiments reported in this paper, a 32 Hz frequency is used. 25.2.6
Surface Analyses Techniques
Different surface analytical tools are coupled to obtain complementary information on the nature of the studied DLC coatings and on the chemical species of the tribofilms formed during the friction on the DLC surface.
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XANES spectra at the C K-edge were recorded in order to characterize the DLC materials. Details on physical aspects of XANES spectroscopy can be found elsewhere [7]. X-ray absorption spectra were obtained at CSRF (Canadian Synchrotron Radiation Facility) using the 1 GeV Aladdin storage ring, University of Wisconsin, Madison, USA. The Grasshopper soft X-ray beamline which covers the photon region of 40–1000 eV was used to record the C K-edge spectra with an energy resolution of 0.1 eV and an analyzed area of 5 × 1 mm2 . The assignment of the fine structure in XANES spectra was obtained by using the spectra of model compounds. The maximum sampling depth probed by XANES at C K-edge is about 10 nm. XANES measurement did not induce any significant irradiation damage to the specimen, and other analysis can be carried out on the same surface with good confidence. Auger Electron Spectroscopy (AES) data were obtained using a VG 220I apparatus. AES spectra were recorded with the 0.5 × 0.5 µm2 focused electron beam which permits a high spatial resolution. Special attention has been paid to the Auger C KLL line to obtain a good signal/noise ratio. Interestingly, the thickness probed in AES is about 5 nm with the exponential decay. Time-of-Flight Secondary Ion Mass Spectroscopy (ToF-SIMS) experiments were performed with a ToF-SIMS V apparatus from ION-TOF. For static SIMS analysis (SSIMS), Au+ pulsed ion beam of 25 keV energy was used for scanning an area of 100 × 100 µm2 on the surface. The diameter of the spot was smaller than 1 µm in order to obtain average information. In SSIMS, chemical information is coming from a depth of 0.1–1 nm below the surface. This is much more near-surface information than the ones obtained with XANES and AES techniques. For dynamique SIMS (DSIMS), depth profiles were obtained combining depth profiling with secondary ion analysis. Sputter erosion was achieved using O+ 2 ions low energy beam of 0.5 keV. Analysis of the crater center was performed using Ga+ ions high energy beam of 15 keV.
25.2.7
Microstructural Analysis Technique
Direct determination and imaging of physical properties of DLC coatings were obtained using energy-filtered transmission electron microscopy (EFTEM) combined with valence electron energy-loss spectroscopy (VEELS). This was carried out on a cross-section TEM specimen of a thin DLC film deposited on steel substrate produced by focused ion beam (FIB) processing. The microscope is a Zeiss CEM912 fitted with a built-in Omega filter which is linked to an image analysis system. The Zeiss CEM912 microscope fitted with a LaB6 cathode was operating at an accelerating voltage of 120 kV. EFTEM has been used to map the sp3 and sp2 phase composition based on plasmon ratio images. In addition, the hardness of the DLC coating was evaluated by applying the strong scaling relationship existing between the plasmon energy and hardness shown previously by James M. Howe et al. [8].
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25.3 25.3.1
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RESULTS AND DISCUSSION
DLC Materials Characterizations
We evaluated the friction properties under boundary lubrication conditions for more than 50 different kinds of DLC coating materials, including: hydrogen-containing DLC (a-c:H), metal-containing DLC (Me-C:H), and hydrogen-free DLC (a-C and ta-C). We found that the best performance is for hydrogen-free DLC (ta-C), which we focus on here. Surface characterizations are suitable for describing surface properties, such as adhesion, which are primordial in friction. XANES spectra performed on the ta-C and a-c:H coatings are shown in Figure 25.6. The comparison with the XANES spectra of diamond and graphite compounds, also reported on this figure, clearly showed that the a-C:H coating contains a strong amount of sp2 carbon in relation to the ta-C coating which is mostly composed of sp3 carbon. AES experimentations performed on the ta-C coating confirm this result. Indeed, its AES derivated spectrum shows a fine structure that is assigned to KVV transitions involving pπ electrons (Figure 25.7). The distance D between the maximum of the positive-going excursion and the minimum of the negative-going excursion in the derivative AES spectrum, which is characteristic of the different carbon atoms arrangement as shown previously by Mizokawa et al. [9,10], indicates a percentage of sp3 sites of about 70%. Besides the surface sensitive application of AES and XANES, other techniques available for gaining direct imaging and information about changes in the cross-section of the sample were carried out. The EFTEM image at 180 eV energy-loss with 7 eV slit width obtained on the FIB cross-section of the ta-C coated steel sample is presented in Figure 25.8. This loss energy permits to diminish the contrast of the image due to the difference between the iron and carbon atomic numbers. This leads to a best visualization of the 100C6 steel structure and chromium-based interlayer used here to improve the ta-C coating adhesion on
Figure 25.6 XANES spectra recorded on ta-C and a-C:H materials. XANES spectra of diamond and graphite materials are also reported on the figure for the comparison.
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Figure 25.7
Derivated dN/dE XAES spectrum of ta-C coating.
Figure 25.8 EFTEM image at 180 eV energy-loss with 7 eV slit width of a cross-sectioned ta-C coating deposited on a steel substrate.
the steel substrate. Notice the metal W layer located above the ta-C coating was necessary for applying the focused ion beam technique. Figure 25.9(a) compares the low-loss PEEL spectrum obtained on the ta-C coating to those of diamond, graphite and 10 nm thin amorphous carbon film used to cover copper grids for the TEM observations. The ta-C coating presents a unique plasmon peak with a value at Ep = 31.7 eV, in agreement with the sp3 -bonded carbon structure of diamond. Note the absence of π -bonding peak at ∼6 eV energy-loss in the ta-C material as compared to graphite. The constancy of the sp3 bonding in the cross-section was visualized
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Figure 25.9 (a) Low-loss EEL spectrum obtained from a cross-sectioned ta-C coating (diamond, graphite and amorphous carbon are also reported for the comparison), (b) EFTEM image at 6 eV energy-loss with 4 eV slit width and (c) EFTEM image at 30 eV energy-loss with 4 eV slit width.
using π and σ bond imaging by EFTEM. Figures 25.9(b) and 25.9(c) show respectively the EFTEM images performed at 6 eV and 30 eV energy-loss, ideal regions that map respectively only the sp2 -bonded carbon and the both sp3 /sp2 carbon hybridizations. In
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Figure 25.10 Overall material Hardness and Young modulus (E ′∗ ) versus indentation depth for (a) hydrogen-free DLC coating ta-C coating and (b) hydrogen-containing DLC coating a-c:H.
the 6 eV energy-loss image corresponding to π/π ∗ transition, the 1–2 nm thick brighter layer which is closer to the ta-C coating surface (near to the W layer) has more graphitelike character (sp2 ) while the bottom darker area has more diamond-like character (sp3 ) as confirmed by the 30 eV energy-loss image. This means there is a chemical heterogeneity of the ta-C coating towards the surface region coupled probably with a gradient of mechanical properties. Unfortunately, it is very difficult to determine this gradient of mechanical properties since it concerns an outermost layer of less than 2 nanometers in thick. Nevertheless, based on the strong scaling relationship existing between plasmon energy and hardness, it is possible to determine the hardness of the bulk ta-C material. Following James M. Howe et al. which have reported the correlation that exists between the plasmon energy and hardness for covalently bonded semiconductors, compounds and soot particles [8], our ta-C material has a hardness varying between 60 and 70 GPa. This result is consistent with the high values of hardness and Young modulus directly measured by nanoindentation. Figure 25.10 presents the overall material (coating + substrate) hardnesses and Young modulus E ′∗ of the ta-C and a-C:H samples. The values obtained for the ta-C coating by considering the curves for very weak indentation depths (<100 nm) are about 75 GPa in hardness and 650 GPa in Young modulus. For comparison, the hydrogen-containing DLC coating presents poorer mechanical properties (15 GPa in hardness and 150 GPa in Young modulus) than those of ta-C material confirming its weak sp3 hybridization. To fully characterize our ta-C material from the extreme surface towards the deeper layers, DSIMS profiling experiments were also performed. They showed no hydrogen in
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Figure 25.11 DSIMS profiles of H, C, Cr and Fe elements obtained on the ta-C coated steel substrate. A chromium-based interlayer is detected between the ta-C coating and the steel substrate.
the ta-C coating (Figure 25.11). The metallic chromium-based interlayer used to improve the adhesion of the coating to the steel substrate is clearly seen. No oxygen is detected in the interfacial region confirming the strong adherence of the ta-C coating on the steel substrate. To summarize, our material would be denoted as tetrahedral amorphous hydrogen-free carbon (or ta-C) in the C–H phase diagram terminology of Robertson [11], closed to the diamond material. However, the upper surface region (<5 nm) of the ta-C coating, which has a determinant role in the friction behavior, consists predominantly of graphite-like carbon (sp2 ). 25.3.2
Steel/DLC Tribological Systems Lubricated by Glycerol Mono-Oleate (GMO)
Because automotive engine oil contains many kinds of additives, it was difficult to identify the interactions between the friction modifiers and the ta-C coating. Many types of friction modifier additives were examined, including amine, amide and ester. We evaluated the effect of the Glycerol Mono-Oleate (GMO) friction modifier additive on the friction property of ta-C, when used with a poly-alpha-olefin (PAO) based oil. First, tribological tests were conducted using a pin-on-disc type machine consisting of three fixed pins sliding on a rotating disc. Different tests were performed with steel/steel, ta-C/steel and a-c:H/steel friction pairs and different lubricants: 5W-30 engine oil, PAO and PAO+GMO (1% by weight of GMO). Results are shown in Figure 25.12. When lubricated with typical API SG 5W-30 engine oil, friction of ta-C/steel combination was reduced to 0.08 compared to 0.125 for the steel/steel pair, that is a 40% reduction. Interestingly, friction of a-C:H/steel lubricated with engine oil showed a higher value of 0.105. As shown in Figure 25.12, when GMO is used as additive in PAO it was found the ta-C/steel friction pair gave an ultralow friction coefficient of 0.02 instead of 0.07 with pure PAO. On the contrary, a-C:H/steel and steel/steel pairs displayed a much higher friction coefficient of 0.09 and 0.1 in the same conditions. In previous studies, it was found that the lower is the hydrogen content of DLC, the lower
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Figure 25.12 Friction coefficients of steel counterpart on tested materials lubricated with different oils measured in pin-on-disc sliding tests and SRV sliding tests. The sliding speed was 0.03 m/s and the sliding time was 60 minutes for the pin-on-disc tribometer. The friction coefficient was measured at 60 minutes. Oil temperature was 80 ◦ C for both test machines. The pins and cylinders were made of hardened steel AISI 52100. SCM415 was carburized steel. ta-C material was applied by a PVD coating process and a-C:H material was applied by a CVD process. 5W-30 was API SG standard engine oil. PAO was a poly-alpha-olefin oil that had the same viscosity at 80 ◦ C as 5W-30 oil. PAO+GMO contained 1 mass% of glycerol mono-oleate.
Figure 25.13 Nanoscratch measurements obtained for three surface conditions in a constant-force nanoscratching process using a conical diamond tip as a stylus for scratching. One was a non-cleaned surface after the sliding test, a second was a supersonic cleaned surface using a hexane solvent and the third was a surface rewetted with PAO+GMO oil after hexane cleaning. The circles and squares were measured on the non-sliding and sliding areas, respectively.
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Figure 25.14 AFM image of island structured tribofilm obtained on ta-C surface after friction test lubricated with PAO+GMO.
is the friction coefficient of this combination [6]. Generally, a tribofilm is known to form on sliding steel surfaces as a result of complex tribochemical reactions, and shearing of the tribofilm often increases the friction level [12–14]. Therefore, it is thought that a lowshear-strength tribofilm resulting from reactions with the friction modifiers contained in the engine oil presumably formed on the hydrogen-free ta-C surface and is responsible for the substantially lower friction coefficient observed for this material in Figure 25.12. Although the uppermost sliding surface and the underlying area are thought to control macro-scale friction behavior, it is experimentally difficult to estimate shear strength and friction behavior as a function of depth on a nanometer scale [15–17]. Recently, however, we have developed a novel nanoscratch method to elucidate the macro-scale effect of reduced friction in relation to the nanoscale tribological properties [18]. In Figure 25.13, nanoscratch measurements reveal that the sliding area of the ta-C coated steel disc, exhibiting ultralow friction in standard pin-on-disc tests, displays also low shear strength and low friction coefficients at nanoscale. Figure 25.13 also shows the evolution of nanoscale friction coefficient as a function of scratch depth for inside and outside wear scar area and this for the three surface conditions. The first one was a non-cleaned surface after the sliding test, the second one was a cleaned surface subjected to supersonic cleaning in a hexane solvent and the third one was a hexane-cleaned surface rewetted with PAO+GMO oil. The sliding area displayed a lower friction coefficient than the non-sliding area and exhibited an obvious reduction particularly near the surface within a depth of less than 5 nm. Additionally, island structured tribofilm was observed on the sliding surface directly by Atomic Force Microscopy (AFM) while uniform smooth surface without tribofilm was observed on non-sliding area, as shown in Figure 25.14 [19]. These results suggest that a very thin tribofilm with low shear strength formed on the sliding surface of the ta-C disc lubricated with PAO+GMO lubricant. The tribofilm was the reason for the ultralow friction observed for this material combination in the sliding tests.
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Figure 25.15 Friction properties of the ta-C/steel pair lubricated with PAO+GMO as a function of the sliding speed compared with those of a needle bearing.
To confirm this ultralow friction property, the ta-C/steel friction pair lubricated with PAO+GMO was evaluated using another sliding test rig, the SRV test machine, which is commonly used to evaluate the boundary lubrication properties of engine oil. The ta-C/steel couple showed a friction coefficient of 0.04 compared with the value of 0.02 measured in the pin-on-disc test as shown by Figure 25.12. The reason for this discrepancy is that the SRV value was actually averaged with those measured during reciprocating motion, including the high values at the reciprocating points. Nevertheless, friction of ta-C/steel was much lower than the friction coefficient exhibited by the a-C:H/steel couple and the steel/steel one, both of which showing a higher friction level than the pin-on-disc-test results in Figure 25.12. So, ultralow friction property of the ta-C/steel couple lubricated with PAO+GMO was observed in the two different testing machines. As a final step, friction properties were evaluated in a pin-on-disc test as a function of the sliding speed for the ta-C/steel pair lubricated with PAO+GMO and compared with those of the a-C:H/steel pair. Moreover, the sliding friction data were compared with the results found for a needle bearing lubricated with 5W-30 engine oil. The results are shown in Figure 25.15. Data show that friction coefficients of the ta-C/steel pairs are much lower than those of the a-C:H/steel pairs. The most notable result here is that the ta-C/steel pair lubricated with PAO+GMO exhibited a superlow friction coefficient of 0.006 at sliding speeds over 0.1 m s−1 (100 rpm), which was comparable to the friction coefficient of the needle bearing (pure rolling). This superlow friction performance demonstrates for the first time that the rolling contact friction level of needle bearings can be obtained in sliding contact under a boundary lubrication condition. 25.3.3
DLC/DLC Tribological Systems Lubricated by Glycerol and GMO
Friction tests with the DLC films deposited on both the flat and the pin were also performed with the SRV machine in presence of PAO+GMO lubricant to clarify the ori-
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Figure 25.16 Friction coefficients obtained with steel/steel and DLC/DLC couples lubricated with PAO+GMO oil and pure glycerol in SRV tests.
gin for ultralow friction. Figure 25.16 shows the friction coefficients of different kinds of material combinations lubricated with PAO+GMO and pure glycerol. Amazing results were obtained for the ta-C/ta-C combination. The friction coefficients of the ta-C couples were substantially lower than for a-C:H/a-C:H and for the ta-C/steel combination (see Figure 25.12). These results suggest strongly that the ultra-low friction phenomenon involves the interaction between the ta-C coating and the ester-containing oil due to the formation of a very thin and low-shear-strength tribofilm on the ta-C sliding surface. In addition, these outstanding characteristics of vanishing friction and zero-wear behavior were obtained for the ta-C/ta-C combination lubricated with pure glycerol G at 80 ◦ C. As shown in Figure 25.16, the friction coefficient was below 0.01, but the exact value could not be measured with available the equipment at hand. Indeed, the wear scar is not visible by optical microscopy. This result suggests that the superlubricity is related to the alcohol chemical function (OH), which is common to both GMO and glycerol molecules. 25.3.4
Superlubricity Mechanism as Studied by Surface Analyses
To study the origin of the superlow friction observed for glycerol lubricated ta-C coatings in boundary lubrication, surface sensitive chemical and molecular analysis techniques XPS and ToF-SIMS were used to investigate the nature of the tribofilm generated at the sliding surfaces of ta-C couples. In order to understand the tribochemical reactions which lead to the tribofilm (wear track), we used pure 13 C glycerol (13 C G) and deuterated glycerol (2 H G containing) lubricants. For the 13 C glycerol, we substituted 13 C for all carbon atoms and in the case of deuterated glycerol only the hydrogen atom of hydroxyl group was substituted. The friction results obtained with these specific products on ta-C material are very similar to those obtained with standard glycerol. SSIMS spectra were recorded inside and outside the tribofilm area to clarify the material change on the ta-C surface after the superlow friction tests. The negative ion spectra recorded inside and outside the tribofilm formed on ta-C coating after the 13 C glycerol lubricated friction test are compared in Figure 25.17
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M.I. De Barros Bouchet and M. Kano
Figure 25.17 ToF-SIMS surface analyses. The negative ion spectrum of virgin ta-C surface is compared with spectra obtained inside the wear track and outside the wear track after the friction test lubricated with 13 C glycerol. Table 25.1. The relative intensities of the 13 C glycerol molecule (13 C3 H7 O3 –) and their characteristic ion fragments (13 C2 H3 O2 –, 13 CHO–, 13 CH2 –, 13 CH2 O–,) versus to the sum of the cluster ion Cn (with n ≥ 5) intensities. The relative intensity of the alcohol group (OH) is also reported OH
13 CH
2
13 CHO
13 CH O 2
13 C H O 2 3 2
13 C H O 3 7 3
Cn
n≥5
Virgin ta-C Inside tribofilm on ta-C Outside tribofilm on ta-C
883479 63579
NM 1055
NM 155
NM 118
NM 1488
NM 208
100% 100%
54534
609
103
69
987
107
100%
to the spectrum of the virgin ta-C surface. They clearly show the presence of the 13 C glycerol molecule (13 C3 H7 O3 –) and their characteristic ion fragments (13 C2 H3 O2 –, 13 CHO–, 13 CH –, 13 CH O–) on the ta-C surface after the friction experiment. No higher molecular 2 2 masses containing 13 C obtained by polymerization of glycerol were found; thus the hy-
Superlubricity of Diamond/Glycerol Technology
487
Figure 25.18 ToF-SIMS surface analyses. The negative ion spectrum of virgin ta-C surface is compared with spectra obtained inside the wear track and outside the wear track after the friction test lubricated with deuterated glycerol.
pothesis that superlow friction results are due to long chain molecules lubrication can be rejected in our case. Also, no new species created by the friction were detected inside the tribofilm in comparison with outside. Table 25.1 reports the relative intensities of the 13 C glycerol molecule (13 C3 H7 O3 –) and their characteristic ion fragments (13 C2 H3 O2 –, 13 CHO–, 13 CH2 –, 13 CH2 O–) versus to the sum of the cluster ion Cn (with n ≥ 5) intensities which are mostly characteristic of ta-C material. The relative intensities of the 13 C components were found nearly twice higher inside the wear scar than outside indicating the possible adsorption of glycerol fragments on ta-C surface. It is also reported in Table 25.1 the relative intensity of the alcohol group (OH). No significant increase was observed for OH group after the friction experiment in
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Figure 25.19 Structure of the DLC surface (from density is 3.18 g/cm3 DLC). sp3 (pink): from 68% (bulk) to 52.0% (surface), sp2 (blue): from 32% (bulk) to 36.7% (surface), sp1 (green): from 0% (bulk) to 10.9% and there are 2 atoms (0.4%) only have one bond (brown).
comparison with virgin ta-C surface probably due to a tribofilm screening effect and to the strong presence of this specie in the ambient air contamination. However, the superlow friction experiments performed with deuterated glycerol (2 H G) lubricant on ta-C coating showed a significant increase in 2 H and O2 H species inside the tribofilm in comparison with outside as shown by the negative ions spectra displayed on Figure 25.18. The ratio between these masses intensity, which are characteristic of deuterated glycerol, and the sum of the cluster ion Cn (with n ≥ 5) intensities was calculated. This ratio was found to be more than twice higher inside the tribofilm, suggesting an hydroxylation of the surface carbon atoms due to frictional processes which leads to a low energy hydrogen interactions between glycerol molecules and hydroxylated ta-C surface. These experimental results are consistent with the results of a study on first principles computer simulations using the ReaxFF reactive force field reported elsewhere [20]. These simulations find that the bulk structure of ta-C coating has 71.5% sp3 carbons (our Auger spectroscopy and XANES experiments suggest about 70%) joined together to form a percolating 3D arrangement to which sp2 and sp1 carbons attach in chains of length 1 to 3. They also show that the ta-C surface is much more rich in sp2 carbon than the bulk material, it has only 52% sp3 carbons (Figure 25.19). This high percent of reactive C at the surface when exposed to glycerol react readily to form a very smooth carbon surface containing OH-terminated groups (Figure 25.20). This agrees very well with the results of our SIMS experiments. The simulations suggest that the origin of the superlubricity arises from strong noncovalent interactions (hydrogen bonds) between the glycerol molecules and/or
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489
Figure 25.20 Structure of the glycerol lubricated ta-C after sliding for 20 ps at v = 100 m/s. sp3 C: pink; sp2 C: blue; sp1 C: green. O: red; H: gray. Indicate how many surface structures there are. This surface leads to μ = 0.03 at 0.6 GPa.
the OH terminated surfaces that causes one monolayer of the glycerol to stick near the surface for long periods during sliding. Thus all sliding motions are confined within between the attached lubricant glycerol molecules film. This result is also in very good agreement with our ToF-SIMS results. 25.3.5
Engine Test Results and Application
The measured results for the friction torque at the single cam/follower interface are shown in Figure 25.21 as a function of the cam/follower composite surface roughness after the test under the boundary lubrication condition with the standard gasoline engine oil. The results indicate that friction torque decreased as the composite surface roughness was reduced. The ta-C coating is below a line drawn in relation to the composite roughness. This result reaffirmed the finding of the preliminary pin-on-disc tests.
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M.I. De Barros Bouchet and M. Kano
Figure 25.21
Figure 25.22
Reduction in cam/follower friction torque.
Reduction in valvetrain friction torque.
Figure 25.22 shows the effect of various coatings on valve train friction torque as a function of engine speed measured by motoring test using the actual engine valvetrain. The ta-C coating reduced friction torque by 45% compared with the result for a conventional phosphate coating at an engine speed of 2000 rpm. A durability test was then conducted at an engine speed of 4000 rpm for about 300 h, and none of the cam/follower interfaces showed any adhesive or abrasive wear or noticeable peeling of the coating.
Superlubricity of Diamond/Glycerol Technology
491
Figure 25.23
ta-C coated valve lifter.
This advanced DLC coating technology will be applied shortly to valve lifters (Figure 25.23) lubricated with a newly formulated engine oil in actual mass-produced gasoline engines. A larger friction reduction of more than 45% is expected to be obtained at an engine speed of 2000 rpm.
25.4
CONCLUSION
Summarizing, superlubricity was obtained by sliding the ta-C/ta-C friction pair in the presence of pure glycerol as a lubricant at 353 K in boundary lubrication conditions. The mechanism of friction vanishing was studied experimentally by performing ToF-SIMS analyses inside and outside wear scar and by using deuterated glycerol and 13 C glycerol. Firstprinciples-based computer simulations using the ReaxFF reactive force field were also carried out to create an atomistic model of ta-C material. Computer simulations and SIMS experiments provide an atomic level explanation for the superlubricity in terms of the formation of a low friction tribofilm involving first hydroxylation of surface carbon atoms, preferentially the sp2 -hybridized carbon atoms, that occurs upon beginning of the sliding. Second, the attachment of glycerol molecules to OH groups by hydrogen bonds is certainly an additional benefit.
ACKNOWLEDGEMENTS The authors would like to acknowledge Professor William A. Goddard III and his research team from Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA, USA, for the permission to include results of computer simulation using the ReaxFF reactive force field technique.
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REFERENCES [1] Hoshi, M. Reducing friction losses in automobile engines. Tribol. Int. 17(4) (1984), 185. [2] Rosenberg, R.C. General friction considerations for engine design. SAE Paper 821576, 1982. [3] Katoh, A., Yasuda, Y. An analysis of friction techniques for the direct-acting valve train system of a newgeneration lightweight 3-liter V6 Nissan engine. SAE Paper 940992, 1994. [4] Miyake, S., Takahashi, S., Watanabe, I., Yoshihara, H. Friction and wear behavior of hard carbon films. ASLE Trans. 30(1) (1987), 121. [5] Miyake, S. Tribological improvement of carbon films due to other material additions. J. Tribol. 41 (1996), 754. [6] Yasuda, Y., Kano, M., Mabuchi, M., Abou, S. Research on diamond-like carbon coatings for low friction valve lifters. SAE Paper 2003-01-1101. [7] Zhanfeng, Y., Kasrai, M., Fuller, M., Michael Bancroft, G., Fyfe, K., Tan, K.H. Application of soft Xray absorption spectroscopy in chemical characterization of antiwear films generated by ZDDP. Wear 202 (1997), 172–201. [8] Howe, J.M., Oleshko, V.P. Application of valence electron energy-loss spectroscopy and plasmon energy mapping for determining material properties at the nanoscale. J. Electron Microscopy 53(4) (2004), 339– 351. [9] Mizokawa, Y., Miyasato, T., Nakamura, S., Geib, K.M., Wilmsen, C.W. Surf. Sci. 182 (1987), 431. [10] Galuska, A.A., Madden, H.H., Allred, R.E. Appl. Surf. Sci. 32 (1988), 253. [11] Robertson, J. In: Silva, S.R.P., Robertson, J., Milne, W., Amaratunga, G.A. (Eds.), Amorphous Carbon: State of the Art. Wold Scientific, Singapore, 1998, p. 32. [12] Chhowalla, M., Amaratunga, G.A.J. Thin films of fullerene-like MoS2 nanoparticles with ultra-low friction and wear. Nature 407 (2000), 164–167. [13] Heimberg, J.A., Wahl, K.J., Singer, I.L., Erdemir, A. Superlow friction behaviour of diamond-like carbon coatings: Time and speed effects. Appl. Phys. Lett. 78(17) (2001), 2449. [14] Fontaine, J., Donnet, C., Grill, A., Le Mogne, T. Tribochemistry between hydrogen and diamond-like carbon films. Surf. Coat. Technol. 146–147 (2001), 286. [15] Donnet, C., Fontaine, J., Grill, A., Le Mogne, T. Tribol. Lett. 9(3–4) (2000), 137. [16] Sasaki, N. et al. Phys. Rev. B 57 (1998), 3785. [17] Tripaldi, G., Vettor, A., Spikes, H. Friction behavior of ZDDP films in the mixed boundary/EHD regime. SAE Paper 962036 (1996), 73. [18] Ye, J., Kano, M., Yasuda, Y. Evaluation of nanoscale friction depth distribution in ZDDP and MoDTC tribochemical reacted films using a nanoscratch method. J. Trib. Lett. 16 (2004), 107. [19] Ye, J., Kano, M., Ueoka, K., Yasuda, Y., Okamoto, Y. Superlow friction property of DLC lubricated with ester containing oil—Part 2: Nanometer-scale morphological, structural and frictional properties. In: World Tribology Congress III Proceedings, WTC2005-63921. [20] Goddard III, W.A., Zhang, Q., Van Duin, A., Cagin, T., Martin, J.M., De Barros Bouchet, M.I., Le-Mogne, T., Kano, M., Yasuda, Y., Mabuchi, Y., Sagawa, T., Ye, J., Konishi, S. Superlubricity of diamond-like carbon in the presence of glycerol, submitted to Proc. Nat. Acad. Sci.
Subject Index ART superfine powders, 455 ART technology, 447, 448 asperity, 6–9, 11 atomic flatness, 196 atomic force microscopy, 147, 301, 367 atomic interaction force, 179 atomic scale, 119–129 atomic-scale experimental, 80 atomic-scale frictional processes, 100 atomic-scale observation of superlubricity between graphite surfaces, 200 atomically flat, 75 atomically flat lamellae, 196, 198 atomistic locking, 26 atomistic model, 37, 60 atomistic origin of friction, 25 atomistics of friction, 18 attractive, 267 Aubry, 1 Auger, 237, 239, 243, 244, 246, 248 Auger analysis, 234 Auger spectroscopy, 298 auto-reconditioning technology, 447
1st Laue-zone of Ag (111), 193 7 × 7 pattern, 183 7 × 7 structure, 181 7 × 7 surface, 193 π bond, 279 σ √ bond, 279 √3-Ag domain, 186 √3-Ag√surface,◦ 186–188, 193 √ √3 × √3-R30 superstructure ( 3-Ag), 186–188 3 × 3 surface, 187 AB lamination relation, 163, 166 ab-initio calculations, 60 a-C, 92 acrylamide, 378 acrylic acid, 378 additives effect of, 439, 440 adhesion, 289 adhesion pressure, 138 adiabaticity, 28 adsorbed layers, 51 adsorbed molecules, 143 advanced DLC coating technology to valve lifters, 472 AFM, 217, 386 Ag crystallites, 198 Ag film, 198 AIREBO, 91, 98 Al2 O3 , 239, 246, 247, 250 allotropes, 257 alloying and cermetting, 448 AMBER force, 86 Amonton’s law, 5, 12 amorphous, 1, 3 amorphous carbon films, 80, 92 annealed film, 187 annealed-Ag film, 186, 187 applied technology to automotive gasoline engine, 471 area of real contact, 139 areal solvation, 386 ART mechanochemical reconditioner, 454 ART mechanochemical reconditioner package, 448, 450, 451 ART reconditioner, 455, 461
back-reflection Laue spot, 182 ball-on-flat type of frictional tester, 181 bistability, 57 blobs, 14, 383 bond-order, 89, 90 bonding energy, 279 boundary lubrication, 51, 399–401 brush-assisted lubrication, 365 C60 bilayer, 165 C60 (C70 ) close-packed structure, 174 C60 close packed monolayer, 170 C60 close-packed structure, 161 C60 intercalated graphite, 255 C60 monolayer, 161, 165, 166 carbon, 257 carbon alloying and cermetting, 448 carbon nano-onions (CNO), 311 carbon nanotubes (CNT), 311 carbon nitride, 259, 341 carbon nitride coating, 341 carbonization, 447 cartilage, 13, 376 493
494
Cauchy discrepancy, 87 ceramics, 370 chemical and/or adhesive interactions, 261 chemical composition of MoS2 coatings, 208 chemical hardness, 285 chitosan, 389 chondroitin sulfate, 366 classification, 259 clean surface, 181, 183 clean surfaces, 17 close-packed C60 (C70 ) monolayer, 173 CNO, 315–319, 321, 332, 336, 338 CNT, 319, 322, 332, 338 CNx-coating, 341, 343–345, 348, 351, 358, 360, 362, 363 CO2 , 345, 347 commensurate, 72 commensurate surfaces, 75 commesurate interface, 45 compliant surfaces, 281 computer simulations, 47 confined fluids, 51, 104 confined interface, 400, 406, 416, 422 contact forces, 99 contaminants, 182 contamination, 181, 183 continuous film, 192 continuous rough film, 189 continuous rough structure, 192 covalent bonding, 261 critical thickness, 197 cross-linking, 281 crystallographic orientation, 186, 195 crystallographic slip plane, 195 crystallography of the Ag films, 183 defect, 190 deformation, 302 Density Functional Theory (DFT), 58 deuterium, 290 diamond, 11, 96, 132 diamond (111), 182 diamond pin, 181 diamond-cubic materials, 87 diamond-like carbon, 60 diamondlike carbon (DLC) films, 253, 258 dislocation pile-up, 195, 196 disordered, 4, 14 disordered interface, 3 DLC, 92, 96, 97, 204 DLC film, 93, 95, 96 DLC/DLC tribological systems lubricated by glycerol and GMO, 484 domain size of Ag (111) grain, 195
Subject Index
doped carbon films, 297 dry air, 349, 358, 361 dynamic friction, 27, 398, 399 dynamic superlubricity, 157 EAM, 87 EDX, 239, 246 effect of crystal orientation, 192–195 effect of crystallographic orientation, 198 effective thickness, 179 elastic constants, 90 elastic deformation, 180 elastic instabilities, 131 elastic modulus, 96 elasticity Green’s function, 5 elastohydrodynamic lubrication, 365, 375 elastohydrodynamic lubrication (EHL, EHD) generalities, 428–430 thin films in, 436–440 elastomers, 374 embedded atom method, 86 empirical approximation, 85 energy dissipation, 27 energy recurrence, 34 energy relaxation, 448 engine test results, 489 entangled, 13 entangled polymers, 12 epitaxial Ag film, 182, 183, 188–191 epitaxial film, 193 epitaxial-like film, 195 extremely low friction coefficient, 196 extremely smooth, 103 extrinsic (or test-condition-specific) factor, 260 eye lid, 382 fiber texture structure (FB), 186 film morphology, 179, 187, 192, 193 film stress, 309 film thickness effect, 179, 182–185 flat lamellae, 196 Flory treatment, 12 fluid mechanics, 108 fluorescence, 373 fluorinated SWNT, 311, 333, 338 fractal dimension, 133 Frantz–Salmeron method, 106, 107 Frenkel–Kontorova model, 2, 35, 42 friction, 295, 302 friction coefficient, 7, 238–240, 242, 245–250 friction force microscope, 200 friction hysteresis, 241, 248, 250 friction loop, 152
Subject Index
friction parameter, 149 frictional anisotropy, 218 frictional dynamics, 119–129 frictional experiments, 181, 187 frictional surface, 184 frictionless sliding, 59 fullerene (C60 and C70 ) intercalated graphite composite, 161, 171, 172 gas lubrication, 237, 238, 241, 247, 249 generate in situ a protective layer, 462 glassy, 1 glycoprotein brushes, 365 glycoproteins, 365, 390 glycosaminoglycan, 366, 390 grafting from, 369, 370, 374 grafting to, 369, 370, 374 graphene, 172, 173 graphite, 132, 255 graphite flake, 161, 162, 165, 201 graphite sheets, 199 graphite-like structure, 362, 363 graphitization, 275 graphitized MWNT, 312, 316, 322, 323, 326, 330 Greenwood–Williamson model, 10 H2 S, 238, 241, 242, 245–250 hierarchy, 7 high dimensionality, 33 high-resolution transmission electron microscopy (HRTEM), 168 highly hydrogenated DLC films, 258 highly oriented Ag (111) lamellae, 197, 198 highly oriented pyrolytic graphite (HOPG), 168 highly-oriented slip plane, 195 HOPG, 201 human and animal joints, 12, 13 human joints, 365 humid air, 349, 351, 355, 357, 358, 360, 363 humidity, 295 Hurst exponent, 133 hyaluronan, 366 hyaluronic acid, 390 hydrodynamic bearings, 12 hydrodynamic flow, 108, 115 hydrogels, 376, 377 hydrogen, 275, 278 hydrogen-free DLC films, 258 hydrogen-terminated, 267 hydrogen-terminated surfaces, 54 hydrogenated diamond, 61, 67 hydrogenated DLC, 362 hydrophilicity, 368 hydrophobic surfaces, 368
495
IF-WS2 coatings, 230 in situ analysis, 238, 244 in situ generate a protective layer, 455 in situ generated protective layer on worn Fe-base metal surfaces, 462 in situ generated protective layer on worn metal surfaces, 445, 461 in situ generated tribochemical reaction, 446 in situ protective layer on worn metal surfaces, 448 in situ reconditioning of rubbing metal surfaces, 446 in situ reconditioning of rubbing surfaces, 448 in situ tribochemical reconditioning of worn metal surfaces, 445 incommensurability, 74, 199, 218 incommensurability-induced transition to frictionless sliding, 200 incommensurate, 1, 2, 14, 30 incommensurate contact, 199 incommensurate interface, 3 incommensurate solids, 104 incommensurate surfaces, 73 inconmesurate interface, 45 inorganic fullerenes, 230 interaction energy, 59 interface potential energy, 8 interlayer shearing, 188, 195, 198 interlayer sliding, 196 internal sliding, 173, 174 intrinsic (or film-specific) factor, 260 irrational number, 2 island structure, 188, 191 isoenthalpic–isobaric ensemble, 82 kinetic friction, 12 lamella, 196 lamella structure, 197 lamellar solids, 254 lamellar structure, 191, 193, 195, 196 Langevin dynamics, 80 Larkin domain, 3 Larkin length, 3, 5 lateral force, 66, 162, 164 Lennard-Jones potential, 169 lidocaine-jelly, 368 liquid lubricant, 12 loading force, 66 low-viscosity fluids, 109 lubricant for biomedical applications, 368 lubricants, 14 lubrication, 13
496
lubrication mechanisms, 259 lubrication regimes definition, 432 discussion on, 438–440 lubricious oxides, 447, 467 macro scale sliding, 197 macroscopic friction force, 180 macroscopic sliding, 196 magnesium silicate hydroxide, 448 magnesium silicate hydroxide (Mg6 Si4 O10 (OH)8 ), 445 magnetron sputtering, 298 MD, 80, 82, 92, 93, 98, 99 mean-field theory, 381 mechanical energy, 67 mechanical interlocking, 358 mechanical rubbing motion, 193, 195 mechanism, 254 mechanochemical activation, 448 mechanochemical interactions, 458 mechanochemical reactions, 448 mechanochemical reconditioning, 458 mechanochemical reconditioning package, 462 mechanochemical reconditioning technology, 461 mechanochemistry, 446, 448 memory distance, 400, 402, 415 memory effects, 400 memory length, 398, 414, 421, 422, 424 MEMS, 92, 98, 110, 311 metallic bond force, 180, 197 metals, 370 metastable state, 197 method of Frantz and Salmeron, 106 Mg6 Si4 O10 (OH)8 , 445 Mg6 (Si4 O10 )(OH)8 , 448 Mg6 Si4 O10 (OH)8 , 458 Mg6 (Si4 O10 )(OH)8 , 462 microfluidic devices, 110 microfluidics, 109 milli-range friction, 197 minimum coefficient of friction, 179, 184 minimum friction coefficient, 184 mixed lubrication definition, 432 evidence of, 438–440 modified EAM, 88 Moiré features, 169 molecular dynamics (MD), 79, 80, 92, 100 molecular dynamics simulation, 383 molybdenum disulfide, 207 monomer, 12, 13 monostable, 11 morphological effect, 188–192
Subject Index
MoS2 , 161, 165, 170, 238, 239, 244, 246, 248, 255 MoS2 nanoparticles, 223 MoS2 single sheets, 220 MoS2 singles sheets, 223 mucin, 365 multi-walled nanotubes (MWNT), 311, 322 multiscale molecular dynamics, 132 multiscale roughness, 6 muscovite mica, 104 mushroom regime, 381 MWNT, 315, 317, 322, 324, 326, 327, 330–332, 336, 338 MWNT coatings, 313 N,N-dimethyl acrylamide, 368 N2 , 345–349, 351, 355, 360–363 N2 -lubrication, 363 N2 gas, 348, 349, 351, 355, 358, 360, 362, 363 N2 gas stream, 349 N2 stream, 349, 351, 355, 357, 358 nano-composite DLC films, 259 nano-crystalline structure, 466 nano-crystalline system, 465, 466 nano-grains, 466 nano-layered DLC films, 259 nano-morphology, 186, 192 nano-particle, 463–466 nano-particle crystalline structure, 466 nano-scale grain sizes, 466 nanocrystal matrix, 466 nanocrystalline, 466, 467 nanocrystalline ceramic coating, 467 nanocrystalline coating material, 466 nanocrystalline coatings, 467 nanocrystalline surface layer, 466 nanofluidics, 115 nanolubricants, 311 Nanotribology, 37 nearly frictionless carbon, 258 network structure, 189–192, 195, 196, 198 neutron reflectivity, 383 Newtonian fluids, 109, 112, 113, 115 nitrogen, 341, 362 nitrogen gas, 341, 363 no-slip boundary condition, 103, 109, 111 normal forces, 71 Norton–Hoff, 281 Nosé, 81 O2 , 238, 248, 345–347, 349, 351, 358, 361, 363 O2 gas, 358, 362 O2 stream, 351 octamethylcyclotetra-siloxane, OMCTS, 106
Subject Index
odd–even effect, 98, 100 oil pyrolysis and carbonization, 448 oligosaccharides, 365 OMCTS, 107 Organic Molybdenum Compounds (OMCs), 220 orientation of the topmost layer, 193 origins of friction, 37 osmotic pressure, 13 osmotic repulsion, 380 OWLS, 386 oxidation, 182, 183 oxide layer, 283, 284 oxygen, 290, 341 oxygenation, 75 parabolic, 13 Parrinello–Rahman theory, 82 partial pressure, 358 partially-wetted, 111, 113 partially-wetted surface, 112 PDMS, 376 PEG, 385 PEG-ox-PDMS, 376 PEO-b-PPO-b-PEO, 375 percolated structure, 191 perturbation theory, 5 phase space volume, 28 phase structure of the protective layer, 462 pin-on-disk tribometer, 313 PLL-g-PEG, 370–375, 386 Pluronics, 375 PoD, 325 point contact, 175 poly(2-hydroxyethyl methacrylate), 369 poly(acrylic acid), 369 polycrystalline Ag film, 193, 198 polycrystalline film, 193 polycrystalline structure, 193, 196 poly(dimethylsiloxane) (PDMS), 375 polyelectrolyte, 13 polyelectrolyte brushes, 388, 390 poly(ethylene glycol), 369, 370, 384 polymer brush, 11–14, 368, 379, 382 polymer chains, 11 poly(methacrylate)-PEG, 369 poly(methyl methacrylate) (PMMA), 387 poly(N-isopropylacrylamide), 368 poly(N-vinyl-2-pyrrolidone), 369 polysaccharides, 390 poly(sodium sulfonate glycidyl methacrylate), 387 polystyrene, 377–379, 384, 385 polystyrene/toluene, 378 poly(vinyl alcohol), 369 Prandtl–Tomlinson model, 41, 203
497
protective layer, 445, 450–456, 458, 461–467 proteoglycans, 365, 390 QCM-D, 386 quartz crystal microbalance, 304 quasicrystals, 205 Raman analysis, 232 re-orientation process, 195 reactive empirical bond-order potential (REBO), 89 REBO, 90–92 reconditioner, 448, 450 reconditioner package, 445, 458 reconditioning chemistry, 448 reconditioning layer, 447 reconditioning worn metal surfaces, 448 reconstructions, 72 recrystallization, 197 relative humidity, 274, 355 repulsive, 75, 267 repulsive interaction, 75 Reynolds equation, 110 rheological behavior lubricant properties, 442 Newtonian isothermal piezoviscous, 432–435 shear thinning Carreau equation, 435, 436 rigid materials, 368 role of hydrogen, 263 rough surfaces, 260 running-in, 341, 345, 348, 349, 351, 355, 358, 363 SAM, 86, 92, 98, 99 Sb nanoparticles, 205 scale effect discussion on, 428, 431, 440, 441 scaling theory, 380, 383 self-affine fractal surface, 133 self-assembled monolayers, 98 self-healing, 374 SEM, 244, 246, 248 semiempirical approximation, 85 serpentine, 448 shear plane of Ag film, 185–188 shear strength, 190, 196 Si wafer, 341–345, 348 Si-water, 351, 358, 361 Si3 N4 , 341–345, 347–349, 351, 354, 355, 358, 362, 363 SiC, 238–240, 243, 246–250 silicon (Si) (111) 7 × 7 surface, 188 silicon (Si) (111) surface, 181
498
silver (Ag) (100) domain, 195 silver (Ag) (111) domain, 195 silver (Ag) (111) lamellae, 192, 195, 197, 198 silver (Ag) (111) sheet, 189 silver (Ag) (111) spots on the 1st Laue-zone, 190 silver (Ag) crystal, 186 silver (Ag) facet, 186 silver (Ag) film, 180, 181, 183, 184, 187, 188, 190, 193 silver (Ag) fine crystal, 186 silver (Ag) island, 186 silver (Ag) layer, 180, 188, 195 silver (Ag) transfer, 184 single crystal diamond, 181 single-walled nanotubes (SWNT), 311 sliding friction, 57, 63, 397 sliding interfaces, 197 sliding lamellae, 196 sliding motion, 4, 67 sliding plane, 192, 196 sliding process, 62 sliding surfaces, 119–129 slip events, 136 slip plane, 186, 188 SO2 , 238, 248 sodium dodecyl sulfate, 375 soft materials, 374 soft metallic film, 179 soft metallic solid lubricant, 179 solid lubricant, 179, 254 solid lubricant film, 179 solvent, 11 solvent quality, 385, 387 SOT, 316, 320 space tribology, 219 specific wear amount, 351, 361 spiral orbit tribometer, 312 squalane, 106 static friction, 5, 26, 398, 414, 418 static superlubricity, 154 steel/DLC tribological systems lubricated by glycerol mono-oleate (GMO), 481 steel/glass tribopair, 372 stick-slip, 165, 398–402, 421, 422 stick-slip processes, 57 stiff materials, 6 Stillinger, 85 Stillinger–Weber potential, 85, 86 stoichiometric MoS2 (molybdenite), 213 strong chemical interaction, 75 strong pinning regime, 135 structural lubricity, 132, 147 sulfur additions, 298 super low traction
Subject Index
chapter on, 427 definition, 430 examples, 432–440 mechanisms of, 440, 441 superlow friction, 60, 61, 75, 237, 238, 245–247, 249 superlubric regime, 152 superlubric state, 188, 196, 198 superlubricity, 132 superlubricity between graphite surfaces, 199 superlubricity by Ag film, 197 superlubricity by epitaxial Ag film, 197 superlubricity in boundary lubrication, 103 superlubricity mechanism as studied by surface analyses, 485 superlubricity of Ag, 195 superlubricity of Ag film, 192, 197, 198 superlubricity of Ag layer, 186 superlubricity of Ag nanometer-thick layers, 179–198 superlubricity of diamond/glycerol technology, 471 superlubricity of epitaxial Ag film, 195 superlubricity of epitaxial Ag layer, 197 superlubricity on soft metallic lubricant layers, 179 surface contact, 175 surface contacts, 175 surface forces apparatus, 104, 115, 367 surface grafting, 368 surface oscillations, 119, 129 surface roughness, 301 surface-grafted polymers, 370 SWNT, 314, 316, 317, 333, 337, 338 synovial fluid, 390 Teflon, 377 temperature-programmed desorption, 305 Tersoff potential, 88, 169 the generated protective layer, 454 thermal effects shear heating, 434, 435 thermolubricity, 148, 199, 204 thermoplastics, 368 third body, 238, 249, 446 third-body transform structures (TTS), 448 ToF-SIMS, 267 Tomlinson, 12 Tomlinson model, 14, 41 Tomlinson–Prandtl model, 148 Tomlinson’s picture, 18 towards applications, 204 transfer film, 274
Subject Index
transfer layers, 262 tribo-assisted reorientation, 193 tribo-catalytic carbonization and graphitization, 447 tribo-film, 183 tribo-induced chemical reactions, 446 tribocarbonization, 446, 447 tribochemical, 97 tribochemical film, 237, 238, 244, 248, 249 tribochemical reactions, 446, 447 tribochemical reconditioning, 448 tribochemical third bodies (TTB), 448 tribochemistry, 96, 261, 446, 448 tribofilm, 274, 283, 286 tribofilm formation, 185, 197 tribolayer, 360, 362, 363 Tribolever, 201 tribology, 79, 80, 83 tribology simulation, 83 tribooxidation, 446, 447 tribophysical effects, 446 tungsten disulfide, 227 two-dimensional orientation, 193 two-dimensionality, 195, 198 UHV, 238, 239, 247 UHV tribometry, 210 ultra-high vacuum, 274 ultra-low friction, 161, 175, 208, 295
499
ultra-thin-film interferometry, 371 unbounded hydrogen, 281 vacuum, 342, 345, 351, 360–362 van der Waals forces, 218 van der Waals interactions, 277 vapor phase lubrication, 237, 249 velocity accommodation, 249, 250 velocity dependence, 249 viscoplastic exponent, 281, 282 viscoplastic properties, 277 viscoplasticity, 281 water adsorption, 304 water desorption, 305 weak hydrogen bonds, 467 weak pinning, 5 weak pinning regime, 135 wear particles, 348, 358 wear rate, 341, 351, 363 wear scar, 347–351, 359, 360, 363 Weber, 85 wetted surface, 108, 110, 112 work hardening, 196 worn surface reconditioning, 447, 448 WS2 coatings, 228 X-ray photoelectron spectroscopy, 299 XPS, 239, 243
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