Fundamentals of Pressure Sensitivity

FUNDAMENTALS OF PRESSURE SENSITIVITY

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Handbook of Pressure-Sensitive Adhesives and Products Fundamentals of Pressure Sensitivity Technology of Pressure-Sensitive Adhesives and Products Applications of Pressure-Sensitive Products

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HANDBOOK OF

PRESSURE-SENSITIVE ADHESIVES AND PRODUCTS

FUNDAMENTALS OF PRESSURE SENSITIVITY

EDITED

BY

ISTVÁN BENEDEK MIKHAIL M. FELDSTEIN

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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4200-5937-3 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data Fundamentals of pressure sensitivity / editors, Istvan Benedek and Mikhail M. Feldstein. p. cm. Includes bibliographical references and index. ISBN 978-1-4200-5937-3 (alk. paper) 1. Pressure-sensitive adhesives. I. Benedek, Istvan, 1941- II. Feldstein, Mikhail M. III. Title. TP971.F86 2009 668’.3--dc22

2008012198

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Contents Preface ................................................................................................ vii Editors ...................................................................................................xi Contributors ...................................................................................... xiii

1

Surface Phenomena on a Solid–Liquid Interface and Rheology of Pressure Sensitivity Oksana A. Soboleva, Alexander V. Semakov, Sergey V. Antonov, and Valery G. Kulichikhin .......................... 1-1

2

Diffusion and Adhesion Costantino Creton and Régis Schach ......................................... 2-1

3

Transition Zones in Adhesive Joints Anatoly E. Chalykh and Anna A. Shcherbina ........................... 3-1

4

Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives in the Course of Bonding and Debonding Processes Christophe Derail and Gérard Marin ........................................ 4-1

5

Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives Eng-Pi Chang ............................................................................ 5-1

6

Probe Tack Costantino Creton and Kenneth R. Shull .................................. 6-1

7

Peel Resistance Hyun-Joong Kim, Dong-Hyuk Lim, and Young-Jun Park ...........7-1

v

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8

Shear Resistance Sergey V. Antonov and Valery G. Kulichikhin ........................... 8-1

9

Durability of Viscoelastic Adhesive Joints Sergey V. Kotomin ..................................................................... 9-1

10

Molecular Nature of Pressure-Sensitive Adhesion Mikhail M. Feldstein ............................................................... 10-1

11

Significance of Relaxation for Adhesion of PressureSensitive Adhesives Mikhail M. Feldstein, Mikhail B. Novikov, and Costantino Creton ....................................................................11-1

Appendix: Abbreviations and Acronyms ......................................... A-1 Index ................................................................................................... I-1

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Preface In recent years, pressure-sensitive products (PSPs) have reached a maturity that warrants a detailed and critical examination of their science and technology. Based on our experience in both scientific activity and industrial areas, as well as on the special knowledge of outstanding scientists and technologist as contributors, we have addressed all aspects of pressure-sensitive adhesives (PSAs) in the form of a handbook. The huge volume of data accumulated in this field over the past decade presents a delicate problem due to the gap between the fundamentals of pressure-sensitive materials and their practice. The application of PSAs requires a thorough knowledge of basic rheological and viscoelastic phenomena. Adhesive and polymer scientists, however, are not often employed as industrial managers or machine operators. Therefore, a need exists to investigate and summarize the most important features of PSA technology and explain the phenomena scientifically. This book covers the fields of manufacturing, conversion, application and end uses of PSAs using a classic approach to compile a treatise based on the work of various experts, theoreticians, chemists and engineers. The volume and diversification of the data, as well as the boundary between theory and application, imposed the need to impart our treatise in three books. The destination of this handbook is twofold. On one hand, it is addressed to scientists focusing on the fundamental processes underlying the complex phenomenon of pressure-sensitive adhesion; on the other hand, it is intended for industrial researchers who are involved in the practical application of these fundamentals for the development of various products and specialists working in various end-use domains of PSPs. Fundamentals of Pressure Sensitivity contains a detailed characterization of the processes occurring in PSA materials at all stages of the life of an adhesive joint: its formation under compressive force, under service as the bonding force is removed, and under adhesive bond fracture when the major type of deformation is extension. Technology of Pressure-Sensitive Adhesives and Products describes particular features of different classes of PSAs, such as rubber–resin-based adhesives, acrylics, and silicones, and presents a discussion of the synthesis of pressure-sensitive raw materials, their formulation, and the manufacture of PSAs and PSPs. Applications of Pressure-Sensitive Products describes the main classes and representatives of PSPs, their competitors, end use, application domains, application technology, and tests. vii

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The domain of pressure-sensitive materials includes several fields that would be sufficiently autonomous, complex, and large (e.g., bonding–debonding mechanisms, manufacture, equipment, quality assurance) to be described in separate books. Our goal to create a short vade mecum was made significantly easier because of our previous work in this field, which covered almost all aspects of pressure sensitivity and allowed for their detailed discussion. Separate works have discussed special aspects of this waste domain, such as Pressure-Sensitive Adhesives Technology (I. Benedek, Marcel Dekker, New York, 1997) and Pressure-Sensitive Adhesives and Applications (I. Benedek, Marcel Dekker, New York, 2004), which focused mainly on pressuresensitive labels; Development and Manufacture of Pressure-Sensitive Products (I. Benedek, Marcel Dekker, 1999), which describes the whole domain of self-adhesive products, with or without adhesive; and Pressure-Sensitive Formulation (I. Benedek, VSP, Utrecht, the Netherlands, 2000), which gives a detailed discussion of a special, prac tical segment of pressure-sensitive technology. Advances in PSA materials imposed the need for reediting of these books in cooperation with C. Creton and M.M. Feldstein, allowing a more detailed discussion of the scientific aspects, in Development in Pressure-Sensitive Products (Ed. Benedek, Taylor & Francis, Boca Raton, Florida, 2006), Pressure-Sensitive Design, Theoretical Aspects (Ed. Benedek, VSP, 2006), and Pressure-Sensitive Adhesives and Applications (Ed. Benedek, VSP, 2006). Because these books contained a detailed description of various pressure-sensitive science- and technology-related problems, it was possible to edit our handbook as a lexically constructed work, focused on key problems, which avoids undesired redundancy of aspects described previously in a detailed manner. In Chapter 1 of this book, “Surface Phenomena on a Solid–Liquid Interface and Rheology of Pressure Sensitivity,” rheological characterization of processes occurring in adhesive materials under application of bonding pressure (wetting and spreading flow) is studied as a function of the viscosity of test liquids and viscoelastic properties of a substrate. The rheological response of the PSA material to the application of bonding pressure has been proposed to be characterized in terms of dimensionless parameters, for example, the ratio of the time of adhesive joint formation under bonding pressure to the intrinsic relaxation (or retardation) time. Data are also presented that illustrate the effect of bonding pressure on the change of apparent viscosity and shear rate of a PSA material with time of adhesive bond formation. Chapter 2 of this book, “Diff usion and Adhesion,” is a contemporary, critical reexamination of the diff usion theory of adhesion, in correlation with pressure-sensitive adhesion. When two polymers are not identical and therefore fully miscible, but are partially miscible, they can interpenetrate by a small distance controlled by the thermodynamics of their interaction. In this case, the adhesion energy between the polymer layers depends strongly on the degree of interpenetration at the interface. In Chapter 3 of this book, “Transition Zones in Adhesive Joints,” the structure– morphological classification of transition zones in adhesive joints is presented. The interphase boundary between an adhesive and a substrate is a constituent part of such transition zones. The relationship between the structure and the morphology of the transition zones, with phase diagrams of the adhesive–substrate systems and interdiffusion coefficients, is described. Numerous examples of the structure of

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ix

transition zones are presented, including amorphous–crystalline and liquid–crystalline equilibriums. Chapter 4 of this book, “Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives in the Course of Bonding and Debonding Processes,” focuses on the effect of viscoelastic properties of PSAs оn their adhesive properties—measured using peeling or probe tack experiments. As demonstrated in Chapter 4, the viscoelastic properties govern, to a large extent, adhesive behavior. Chapter 5 of this book, “Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives,” describes the correlation of the viscoelastic properties of PSAs with industrystandard performance such as peel resistance, tack, and shear resistance. Using a fourquadrant viscoelastic window concept, the possibility of characterizing and aiding in the development of different types of PSAs is further demonstrated. Chapter 6 of the book, “Probe Tack,” is a very illustrative and informative test for adhesion. Structure transformations (cavitation and fibrillation) of adhesive material under a detaching force are discussed. The practical aspects of tack as a common test method for characterization of PSAs and PSPs, as well as its influence on the converting and end-use properties, are also discussed in the other two books. Chapter 7 of this book, “Peel Resistance,” focuses on the measurement of peel resistance as one of the most important characteristics in the evaluation of PSA performance because various factors such as properties of backing materials, surface of the adherend, peeling speed, and test temperature affect peel strength. Much information is provided not only by failure mode detection, but also by drawing up the master curves for peel resistance. The practical aspects of peel resistance as a common test method for the characterization of PSAs and its influence on the converting and end-use properties are discussed in the other two books. Chapter 8 of this book, “Shear Resistance,” describes shear resistance as an important factor affecting the performance of PSAs. The main parameters influencing shear resistance and the correlation among shear resistance, peel resistance, and tack are discussed. The practical aspects of shear resistance as a common test method for the characterization of PSAs and PSPs, as well as its influence on the converting and end-use properties, are also discussed in the other two books. Chapter 9 of this book, “Durability of Viscoelastic Adhesive Joints,” discusses the durability of PSA joints under constant detaching stress for a range of PSAs spanning different classes that have been analyzed using a squeezing–flow technique. The approach to the prediction of adhesive joint durability, one of most important characteristics of PSA performance, is proposed. The role of durability in practice is also discussed in detail in Applications of Pressure-Sensitive Products. Chapter 10 of this book, “Molecular Nature of Pressure-Sensitive Adhesion,” is based on the analysis of peel force in relation to the work of viscoelastic deformation of adhesive fi lm up to break under uniaxial drawing; a simple equation has been derived that represents peel adhesion as a function of the self-diff usion coefficient, relaxation time, and cohesive strength of the adhesive polymer. Chapter 11 of this book, “Significance of Relaxation for Adhesion of Pressure-Sensitive Adhesives,” examines the phenomenon of pressure-sensitive adhesion that is treated as a three-stage process, involving adhesive joint formation under compressive force,

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Preface

followed by relaxation of the adhesive material as the bonding force is removed, and then debonding as a detaching stress is applied. The mechanisms of PSA deformation at each of these stages are different, and the contribution of PSA relaxation to adhesion is also different. The strength of the adhesive joint requires the contribution of slow relaxation processes, which imply the specific importance of both longer relaxation time and large-scale structural rearrangements in the PSA material for proper adhesion. We suggest that our readers use the list of abbreviations and acronyms in the end of this book to facilitate the comprehension of various symbols, whenever they are not sufficiently clear. The role of this book is to provide comprehensive and convenient upto-date information for users in both industry and academia. We were pleased to see the participation of scientists and industrial experts, working in very different areas of the field, on this book. We thank our contributors for their efforts.

The Editors

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Editors István Benedek is an industrial consultant based in Wuppertal, Germany. After exploring his initial interest in macromolecular science, he transferred to the plastics processing and adhesive converting industry as research and development manager, where he has worked for three decades. He is the author, coauthor, or editor of several books on polymers, including Pressure-Sensitive Adhesives Technology (Dekker, New York, 1996), Development and Manufacture of Pressure-Sensitive Products (Dekker, New York, 1999), Pressure-Sensitive Formulation (VSP, Utrecht, the Netherlands, 2000), Pressure-Sensitive Adhesives and Applications (Dekker, New York, 2004), Development in Pressure-Sensitive Products (CRC, Boca Raton, FL, 2006), Pressure-Sensitive Design, Theoretical Aspects (VSP, Leiden, the Netherlands, 2006), and Pressure-Sensitive Design and Formulation, Applications (VSP, Leiden, the Netherlands, 2006), as well as more than 100 scientific research and technical reports, patents, and international conference papers on polymers, plastics, paper/fi lm converting, and web finishing. He is a member of the Editorial Advisory Board of the Journal of Adhesion Science and Technology. Dr. Benedek received his PhD (1972) in polymer chemistry and engineering technology from Polytechnic University of Temeswar. Mikhail M. Feldstein, one of the world’s leading experts in the development of new polymeric composites with tailored performance properties that span pressure-sensitive adhesives and other materials designed for medical and pharmaceutical applications, was born in 1946 in Moscow. In 1969 he graduated with honors from M.V. Lomonosov Moscow State University, Faculty of Chemistry, and in 1972 he earned his PhD in polymer science from the same university for the investigation of polyelectrolyte complexes with ionic surfactants and lipids. His early research interests were associated with the mechanisms of the formation and molecular structure of interpolymer complexes. Since 1972 he has worked in the industry of polymers for medical usage as a developer of hydrophilic pressure-sensitive adhesives for skin application in transdermal therapeutic systems and wound dressings. He received international recognition comparatively late: his earliest contacts with colleagues beyond the borders of former Soviet Union date to 1994 only. In 1999, a famous scientist and vice president of the Russian Academy of Sciences, academician Nicolai A. Platė, invited him to join A.V. Topchiev Institute xi

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Editors

of Petrochemical Synthesis of the Russian Academy of Sciences, one of the most wellknown academic institutes in polymer science. Later that year, Feldstein established long-term and large-scale research cooperation with a leading pharmaceutical company, Corium International, Inc. (CA). In 2005, Feldstein earned his DrSc in polymer science from the A.V. Topchiev Institute of the Russian Academy of Sciences. Since the second half of the 1990s, Feldstein has focused on the molecular origins of pressure-sensitive adhesion and the interrelationship between adhesion and other properties of polymer blends. Based on gained insight into the phenomenon of adhesion at a molecular level, he has developed the first-ever technology for obtaining numerous novel pressure-sensitive adhesives of controlled hydrophilicity and performance properties by the simple mixing of nonadhesive polymer components in certain ratios. Feldstein is the author of nearly 200 research papers, 7 book chapters, and 25 patents. He is a member of Adhesion Society and Controlled Release Society. Feldstein is also an associate editor of the Journal of Adhesion.

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Contributors Sergey V. Antonov

Sergey V. Kotomin

A.V. Topchiev Institute of Petrochemical Synthesis Russian Academy of Sciences Moscow, Russia

A.V. Topchiev Institute of Petrochemical Synthesis Russian Academy of Sciences Moscow, Russia

Anatoly E. Chalykh

Valery G. Kulichikhin

A.N. Frumkin Institute of Physical Chemistry and Electrochemistry Russian Academy of Sciences Moscow, Russia

A.V. Topchiev Institute of Petrochemical Synthesis Russian Academy of Sciences Moscow, Russia

Eng-Pi Chang

Dong-Hyuk Lim

Avery Dennison Research Center Pasadena, California

Laboratory of Adhesion & Bio-Composites Seoul National University Seoul, South Korea

Costantino Creton Laboratory of Physical Chemistry and Midfielders Dispersed Unit Joint Paris, France

Christophe Derail IPREM Institute Université de Pau et des Pays de l’Adour Pau, France

Mikhail M. Feldstein A.V. Topchiev Institute of Petrochemical Synthesis Russian Academy of Sciences Moscow, Russia

Hyun-Joong Kim Laboratory of Adhesion & Bio-Composites Seoul National University Seoul, South Korea

Gérard Marin IPREM Institute Université de Pau et des Pays de l’Adour Pau, France

Mikhail B. Novikov A.V. Topchiev Institute of Petrochemical Synthesis Russian Academy of Sciences Moscow, Russia

Young-Jun Park Laboratory of Adhesion & Bio-Composites Seoul National University Seoul, South Korea

Régis Schach Centre Technique de Ladoux Michelin, France

xiii

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Contributors

Alexander V. Semakov

Kenneth R. Shull

A.V. Topchiev Institute of Petrochemical Synthesis Russian Academy of Sciences Moscow, Russia

Northwestern University Evanston, Illinois

Anna A. Shcherbina A.N. Frumkin Institute of Physical Chemistry and Electrochemistry Russian Academy of Sciences Moscow, Russia

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Oksana A. Soboleva Chemistry Department M.V. Lomonosov Moscow State University Moscow, Russia

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1 Surface Phenomena on a Solid–Liquid Interface and Rheology of Pressure Sensitivity Oksana A. Soboleva M.V. Lomonosov Moscow State University

Alexander V. Semakov Sergey V. Antonov Valery G. Kulichikhin A.V. Topchiev Institute of Petrochemical Synthesis

1.1

1.1 Introduction .............................................................1-1 1.2 Surface Phenomena on a Solid–Liquid Interface ....................................................................1-2 Wetting of Solids by Low-Molecular-Weight Liquids • Wetting of Solids by Polymer Liquids • Wetting of Solids by Multicomponent Liquids • Wetting of Deformable Substrates (Gels)

1.3 Rheology of Pressure Sensitivity .........................1-18 Dimensionless Criteria of Pressure-Sensitive Adhesive Performance • Rheological Properties of Pressure-Sensitive Adhesives under Bonding Pressure

References ........................................................................1-22

Introduction

In accordance with the definition given by the Pressure Sensitive Tape Council, “pressure sensitive” is a “term commonly used to designate a distinct category of adhesive tapes and adhesives which in dry form (solvent/water free) are aggressively and permanently tacky at room temperature and that firmly adhere to a variety of dissimilar surfaces upon mere contact without the need of more than finger or hand pressure” [1]. This definition contains some uncertainties regarding the conditions of formation of the adhesive joint, namely, the exact pressure and duration of its action. It is clear, however, that

1-1

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Fundamentals of Pressure Sensitivity

because pressure-sensitive adhesives (PSAs) are viscoelastic in nature, these parameters are crucial for their application. The role of rheological characteristics for PSA performance was realized long ago. The main criterion of pressure sensitivity (Dahlquist’s) operates with the rheological parameter (absolute values of elasticity modulus). Attempts have been made [2] to replace this empirical, yet simple and quite reliable criterion with one based on relaxation characteristics. Performance properties of PSAs, especially those related to cohesive strength (e.g., shear resistance), also depend on their rheological behavior. The rheological behavior of adhesive formulations is important for the successful manufacturing of pressuresensitive products. To understand how PSAs work, it is necessary to understand not only the properties of the individual components of the adhesive formulation and those of the formulation as a whole, but also the processes that take place upon contact of the PSAs with different types of substrates. The substrates can be solid or viscoelastic. Good interfacial interaction with a substrate is essential for PSA performance. Such interaction is caused by forces of different natures (van der Waals, H-bonding, acid–base, and donor–acceptor interactions) [3–5]. At the macro level, this interaction between PSA and substrate results in a wetting– spreading process. Wetting of the substrate by the adhesive is crucial to establish good contact between them. Wetting is also important in the coating procedure. In this chapter we will first consider the fundamentals of the wetting–spreading process for simple models (e.g., wetting–spreading of Newtonian liquids on a solid surface). Wetting by polymeric liquids has specific features connected with their high viscosity and elasticity. The viscosity of PSAs upon application is very high. For this reason, spreading (i.e., increase of the wetted surface) proceeds as flow that is governed by the rheological properties. It can be assumed that the rheological characteristics of liquids in thin layers upon wetting should differ from values measured in macroscale by means of conventional rheometers, although the extent of this difference is unknown. To enable the spreading of PSAs onto a substrate’s surface, it is necessary to apply external pressure for a definite time depending on the PSA’s viscosity and elasticity. Spreading of multiphase liquids and influence of surfactants will be also discussed in this chapter. Another point of interest to be considered in this chapter is wetting of the deformable substrates, which is important in some specific applications of PSAs. Finally, we will discuss new rheological approaches highlighting the nature of pressure sensitivity.

1.2 1.2.1

Surface Phenomena on a Solid–Liquid Interface Wetting of Solids by Low-Molecular-Weight Liquids

Let us start with the wetting–spreading processes for low-viscosity Newtonian liquids and absolutely rigid supports, such as metallic surfaces. According to the modern concept [6], spreading of a liquid droplet on a solid surface proceeds through the formation of a primary (or precursor) film. The thickness of this film for different systems is in the range of 0.01–10 μm. The existence of the primary fi lm

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1-3

Surface Phenomena on a Solid–Liquid Interface

has been confirmed by various methods (measurement of electric resistance, ellipsometry, optical and electron microscopy, etc.). Several different mechanisms of precursor film formation have been discussed: surface diffusion, evaporation of a liquid with subsequent condensation on a solid surface, and emission of jets due to the difference in capillary pressure inside the drop and in the vicinity of the three-phase (solid–liquid–air) line. As a rule, in the majority of experiments the secondary spreading (i.e., spreading of a liquid on a surface covered with the precursor fi lm) was studied. Experiments confirmed that the thickness, structure, and composition of the precursor fi lm strongly affected the rate of drop spreading. Kinetic equations of secondary spreading are usually deduced from hydrodynamic models, according to which the spreading rate is limited by the delivery of the liquid to the three-phase line. The initial stage of the spreading process is controlled by the inertial forces in the drop volume [7]. The spreading rate at the end of the inertial stage vin, vin


dr dt

(1.1)

where r is the radius of the wetted surface and t is time, can be estimated from Bernoulli’s law, 1 2
vin

Pc 2

(1.2)

where ρ is the density of the wetting liquid and ΔPc is the difference between the values of capillary pressure inside the drop at the beginning and at the end of the inertial stage. If the drop upon spreading has the shape of a spherical segment, ΔPc can be calculated as  1 1 
Pc
2    Ri R* 

(1.3)

where σ is the surface tension of the liquid and R i and R* are the curvature radii of the drop surface at the beginning and at the end of the inertial stage of spreading, respectively. It is convenient to express the capillary pressure difference, ΔРс, as a function of the dynamic contact angle Θ. For a spherical segment of a constant volume, Ri  4   2 
sin  1 2 cos   2 2  R* 

1

3

(1.4)

Expression of the spreading rate in the inertial stage can be derived from a combination of Equations 1.2 through 1.4. 1 3  4   4  2   v
1   sin 1  2 cos   
Ri  2 2     

2 in

(1.5)

The inertial spreading regime is usually observed upon the contact of drops of lowviscosity liquids (hydrocarbons, water) with solid surfaces at ambient temperature.

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1-4

Fundamentals of Pressure Sensitivity 0.8

180 1

150

r (mm)

120 0.4

90 2

Θ (degree)

0.6

60 0.2 30 0 0.000

0.005

0.010

0.015

0.020

0.025

0 0.030

t (s )

FIGURE 1.1 Dependence of the radius of the wetted area (1) and contact angle (2) on time for water drop spreading on a steel surface.

At the initial stage of the spreading process, the surface of the drop is unstable and the drop height changes unpredictably, which is reflected by a “zigzag” dependence of the contact angle on spreading time. An example of such dependence is illustrated in Figure 1.1 for spreading of the water drop on a steel surface. The duration of the inertial stage is very short—about 10 −2 s; therefore, for its registration high-speed shooting [several thousands frames per second (fps)] is needed. At this stage the spreading rate does not depend on the viscosity of the spreading liquid. With the increased radius of the wetted area and reduction in the height of a drop, the role of viscous resistance in a volume of the drop increases. The inertial stage transforms into the viscous stage [7,8]. According to the hydrodynamic model, we can evaluate the kinetic features of viscous spreading, such as the change in radius of the wetted area r with time, by comparing the driving force of spreading, f d
2r (cos 0  cos )

(1.6)

where Θ 0 and Θ are the equilibrium and current values of the contact angle, respectively, with the force of viscous resistance, f
r 2 grad v

(1.7)

(v = dr/dt; η is viscosity). If the spreading drop has the shape of a spherical segment of height h, the whole volume is involved in the spreading process and gradv


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1 dr h dt

(1.8)

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1-5

Surface Phenomena on a Solid–Liquid Interface

If, otherwise, the drop spreads with a precursor fi lm, the main resistance is located in the layer with thickness δ. As the first approximation, this thickness can be accepted as constant and Equation 1.8 can be rewritten as gradv


1 dr  dt

(1.9)

These approaches led to the following expressions for r(t) dependence:  16V  r
A1t 0.25
   

0.25

t 0.25

(1.10)

for the first case (V is the volume of the drop) and 0. 5

 8  0.5 r
A2t 0.5
 t   

(1.11)

for the second. The kinetic relationships 1.10 and 1.11 have been verified in Refs 9–11 where spreading of mixtures of two miscible liquids was studied. The use of mixtures of low-viscosity and high-viscosity liquids allowed the viscosity of the spreading drop to vary over a wide range. Complete or partial wetting of the steel substrate was observed in the case of mineral (vaseline) oil solutions in dodecane (viscosity ranged from 1.5 to 150 mPa s, Θ0 = 0°) and glycerol in water (viscosity ranged from 1.0 to 386 mPa s, Θ 0 = 64°). For formulations with viscosity of η ≥ 100 mPa s, the shape of the drop during the process is close to a spherical segment and the propagation of the wetting front is described by a relationship similar to Equation 1.10. On the contrary, for low-viscosity mixtures of nonpolar liquids, the precursor fi lm is formed and the spreading kinetics is described by Equation 1.11. The regularities discussed above are generally applicable to the rather fast spreading inherent to low-molecular-weight liquids. However, PSAs are high-viscosity systems with an essential elastic response. Upon the spreading of liquids with very high viscosity, especially in the case of complete wetting, a very slow rate of wetted radius increase is observed. At this stage, the droplet can be considered as a flat fi lm. The dependence of the radius of the moistened area on time can be described as r ∼t

1

(1.12)

n

where n = 8–12. For polymer droplets n can be even higher [7,12,13]. The following expression of slow spreading was proposed in [11]. 0. 1

  r
A3t 0.1
  V 0.3t 0.1   

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(1.13)

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1-6

Fundamentals of Pressure Sensitivity

where κ is a correction factor, usually equal to ~10, that describes the increase of viscous friction in a layer with the shape of a spherical segment in comparison with a flat layer. The kinetic laws of the contact angle Θ changing can be deduced from the basic relaxation and rheological models of the spreading process [14]. Various versions of relaxation models are based on the assumption that the rate of wetting d cosΘ/dt is proportional to the deviation of the three-phase substrate/liquid/vapor line from the thermodynamic equilibrium conditions that correspond to the equilibrium contact angle, Θ 0. In accordance with this assumption, cos 0  cos  t
e  cos 0  cos i

(1.14)

where τ is the retardation time of the wetting process and Θi is the initial contact angle. Upon application of this model to experimental results, the dependence, Θ(t), should be linear if plotted in coordinates ln(cosΘ0 − cosΘ) − t. Such linear dependences were experimentally obtained for spreading of dodecane–vaseline oil and water–glycerol mixtures on steel plates. τ values were calculated from the slope of the experimental curves [10]. The Kelvin–Voight model, with parallel connection of viscous and elastic elements [15], can be used to calculate the retardation time of spreading. If such a system is loaded and deformed up to relative deformation εi, the kinetics of deformation after release of the load can be described by the equation   0 t
e  i   0

(1.15)

where ε0 is the residual equilibrium deformation and τ is the retardation time: 


 G

(1.16)

where G is the elastic modulus. Upon simulation of drop spreading by the Kelvin–Voight model, it can be assumed that the viscous (Newtonian) element is the liquid with viscosity η inside the droplet, and the elastic (Hooke) element represents the curved surface layer of the droplet with elasticity modulus G. Using some additional assumptions [14], the expression of retardation time can be written as 


 

(1.17)

where λ is a characteristic linear dimension that is close to the radius of droplet Ri for high-viscosity liquids. For low-viscosity liquids, the λ values are rather high (several

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1-7

Surface Phenomena on a Solid–Liquid Interface

centimeters), which requires additional modification of the spreading model. So, the rheological model of spontaneous spreading can describe the real process for highviscosity liquids only.

1.2.2

Wetting of Solids by Polymer Liquids

In our experiments we studied the kinetics of spreading r(t) and wetting Θ(t) of drops of oligomeric polyethylene glycol (PEG-400) and low-molecular-weight polyisoprene Isolene 40 (Elementis Specialities Inc., Hightstown, NJ-PI) on polyethylene terephthalate (PET) fi lm (Loparex 7300A, Loparex Inc, Willowbrook, IL). This fi lm has hydrophilic and hydrophobic (silicon coated) sides and was used as an example of conventional release liners. The relationships between the change in radius of the moistened area and contact angle with time are illustrated in Figures 1.2 and 1.3 for wetting of the release liner by the above-mentioned liquids within the first 20–30 s of spreading. The retardation times of contact angle evolution τ are summarized in Table 1.1. Because different sides of the tested release liner (untreated and siliconized) have different polarities (more hydrophilic and more hydrophobic, respectively), wetting of these surfaces depends on the liquid used. Microphotographs showing drops of different liquids on hydrophilic and hydrophobic sides of the release liner are presented in Figures 1.4 through 1.6. Water does not wet both surfaces (Figure 1.4): contact angle on a “hydrophilic” surface is 93.0 ± 2.9°; on a “hydrophobic” surface the contact angle is 105.2 ± 1.7°. 3.0 1

2.5 2

r/r0

2.0

1.5

1.0

0.5

0.0

0

10

20

30

t (s)

FIGURE 1.2 Spreading kinetics of PEG drops on the hydrophilic (1) and hydrophobic (2) surfaces of the release liner.

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1-8

Fundamentals of Pressure Sensitivity 0.0

ln(cosΘ0 − cosΘ)

−0.5 Hydrophilic surface Hydrophobic surface

−1.0 −1.5 −2.0 −2.5 0.0

0.5

(a)

1.0

1.5

2.0

60

80

t (s) 0.0

ln(cosΘ0 − cosΘ)

−0.5 −1.0 −1.5 −2.0 −2.5

0

20

(b)

40 t (s)

FIGURE 1.3 Evolution of contact angles upon spreading of PEG (a) and PI (b) drops on the surface of the PET release liner. TABLE 1.1 Contact Angle Retardation Times and Viscosities of the Spreading Liquids Calculated from Data on Spreading Kinetics Surface PET release liner, hydrophilic side PET release liner, hydrophilic side PET release liner, hydrophobic side

Liquid

τ (s)

η (Pa s)

PEG-400 PI PEG-400

0.83 59.2 0.61

26.6 1600 19.5

Drops of PEG and PI spread on both surfaces (Figures 1.5 and 1.6). Amphiphilic PEG easily wets both surfaces, whereas hydrophobic PI wets the hydrophobic surface much better. The contact angles reach equilibrium values after several hours for the hydrophilic surface and after more than 1 day for the hydrophobic surface (Figure 1.7).

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Surface Phenomena on a Solid–Liquid Interface

(a)

1-9

(b)

FIGURE 1.4 Water drops on the hydrophilic (a) and hydrophobic (b) surfaces of the release liner.

(a)

(b)

FIGURE 1.5 PEG-400 drops on hydrophilic (a) and hydrophobic (b) surfaces.

(a)

(b)

FIGURE 1.6 PI drops on hydrophilic (a) and hydrophobic (b) surfaces.

Using Equation 1.17, it is possible to estimate the viscosity, η, of the spreading liquid during the first stage of the spreading process. The calculated values are presented in Table 1.1. The values are quite reasonable, although they are essentially higher than the values measured by conventional rotational viscometry (~0.1 Pa s for PEG and ~30 Pa s for PI). This difference is understandable taking into account the adhesion contact of the PSA with a solid surface. Regarding the real multicomponent, multiphase adhesives, we

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1-10

Fundamentals of Pressure Sensitivity

80

Hydrophilic

60

Θ (degree)

Θ (degree)

80

PEG-400 40 PI

20 0

(a)

0

500

1000 t (min)

60

(b)

PEG-400

40

PI

20 0

1500

Hydrophobic

0

500

1000

1500

t (min)

FIGURE 1.7 Time dependences of PEG and PI contact angles on hydrophilic (a) and hydrophobic (b) surfaces of the release liner.

can expect much slower spreading, which is indeed observed upon PSAs application. Some insight into a possible role of individual PSA components in the wetting–spreading processes can be derived from the analysis of the model situation for multicomponent liquids.

1.2.3

Wetting of Solids by Multicomponent Liquids

Compared with individual liquids, wetting of solids by multicomponent mixtures is a complex process because wetting is accompanied by various processes, such as surface and bulk diff usion, adsorption of the components on different interfaces, mutual dissolution of solids and liquids, and possible evaporation of volatile components (VOCs). The rates of these processes usually differ for various components of a mixture, and frequently these processes control the movement of the three-phase line, predetermining the shape of the drop in the spreading process. Further, we will describe some examples concerning the spreading of mixtures of liquids, the influence of surfactants on spreading, and the role of mutual dissolution and deformability of a substrate in spreading kinetics. Surfactants are traditional components of many multiphase formulations that affect the dispersity, compatibility of components, and the stability of the system in general, as well as within wetting–spreading processes. 1.2.3.1 Spreading of Mixtures of Liquids One of the most important cases of spreading of mixtures of liquids is the case of liquids with different volatility and surface tension. Spreading of viscous hydrocarbons on high-energy surfaces in the presence of various additives was studied in Refs 16 and 17. The following effects were described: 1. Acceleration or deceleration of spreading 2. Reverse motion of liquid from the initially moistened area 3. Catastrophically fast spreading with a rate of two or three orders of magnitude faster compared with drops of individual liquid of similar viscosity The observed effects were explained in terms of the secondary flow caused by the local change in surface tension due to evaporation of one of the components of the mixed solution.

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Surface Phenomena on a Solid–Liquid Interface

1-11

This phenomenon is known as the Marangoni effect. Difference in composition inside the drop and in the precursor fi lm, due to more intense evaporation of one of the components from a thin layer, results in the occurrence of additional flow directed either from the drop to the fi lm (if the more volatile component has the lower surface tension value) or from the fi lm to the drop (the reverse situation). The two processes control the acceleration and deceleration of spreading, respectively. The influence of the Marangoni flow on spreading rate was investigated in detail, for example, in Refs 18 and 19. As an example, we can consider the spreading of vaseline oil–dodecane mixtures on a steel plate in the experiments mentioned previously. The instant shape of the drop was registered with a high-speed videocamera. It is possible to detect three stages in kinetic curves of spreading r(t) for drops of different composition, which are described by Equations 1.10, 1.11, and 1.13, respectively. The short-term initial stage proceeds with the maximum rate r = A1t 0.5. This stage was observed for mixtures with low viscosity (<30 mPa s). As follows from Equation 1.11, coefficient А1 should be proportional to (σ/η)0.5. This agrees with the experimental results: the dependence of А1 on (σ/η)0.5 is indeed close to linear and starts from zero time. The thickness of the primary or precursor film δ calculated from the slope of the straight line was estimated at ~20 μm. The mixtures spread more slowly than the individual liquids. This result was confirmed by comparing the spreading rate for pentadecane drops of the same σ/η ratio. The probable explanation of the effect is based on the assumption that the compositions inside the drop and in the precursor fi lm are different. We can expect enrichment of the fi lm by the more viscous component, presumably due to partial dodecane evaporation. The fast stage is followed by a slow stage, with kinetics described by Equations 1.10 and 1.13. These stages were observed for high-viscosity mixtures. The most pronounced difference in spreading kinetics for the mixtures compared with individual liquids was observed at these stages. According to Equations 1.10 and 1.13, the spreading rate should decrease monotonously with increased viscosity. The experimental data, however, contradict the expected regularities. Dodecane drops spread very rapidly. Small additives of vaseline oil (up to volume fraction 0.2) lead to approximately a twofold increase in viscosity, but the rate of spreading decreases to a much higher extent. Further, within a wide range of mixture compositions (for volume fractions of vaseline oil from 0.2 to 0.8), the spreading rate is approximately constant despite significant growth in viscosity. Upon spreading of mixed solutions, there exists no general dependence of the spreading rate on viscosity. For real multicomponent systems containing polymeric components we can expect much more pronounced deviations from the theoretical predictions. In this case, there is no evaporation of any VOC, but possible migration of low-viscosity components to the interface plays an essential role due to the difference in viscosity and surface energy. A similar situation was observed for the multicomponent, two-phase adhesives containing low-molecular-weight polyisobutylene (PIB) [20]. Because it is incompatible with other components of the PSA formulation, PIB forms a thin tacky fi lm at the interface, thus increasing the initial tack of the PSA to substrates. In addition, the viscoelastic nature of the polymers should be kept in mind: elastic forces slow down the spreading process.

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1-12

Fundamentals of Pressure Sensitivity

For precursor solutions with dissolved adhesive, the role of evaporation is significant upon fabrication of fi lm on release liner or backing surface. As mentioned previously, surfactants can play an important role in the development of multiphase formulations. To understand their effect on wetting–spreading processes, the consideration of model low-molecular-weight systems may be useful and important. 1.2.3.2

Spreading of Surfactant Solutions

Spreading of surfactant solutions on solid plates and capillary flow of surfactant solutions was discussed in many papers [21–27]. The main results obtained by various authors are close enough. Surfactants affect the surface tension (solution/air interface) and can be adsorbed on a solid surface. The adsorption of surfactants on various interfaces is a slow process and can exceed the characteristic time of wetting. As a result, upon fast moving of the wetting front (e.g., at the initial stage of drop spreading or at capillary rise and flow), the layer near the meniscus is depleted of surfactant and the spreading slows down. The adsorption of the surfactant on the interface increases the spreading rate, which approaches the equilibrium value. The experimental data revealed an interesting fact: at the movement of surfactant solutions under high pressure in capillaries, they can be considered as individual solvents noncontaining surfactants in a zone close to the meniscus [21]. By comparison of the spreading rates of the drops of water and aqueous solutions of anionic, cationic, and nonionic surfactants on glass plates, it was established for all liquids that the first, faster stage (with duration of ~1 s) of the spreading proceeds with approximately the same rate [22]. For some systems, the reverse flow was observed at the capillary rise of the surfactant solutions [23,24]: upon the fast initial capillary rising stage, the zone of the meniscus is depleted of surfactants and the driving force of flow that is proportional to the surface tension is high. Then, at the second stage, the surface tension decreases due to the adsorption of surfactants and, as a result, the capillary pressure becomes less than hydrostatic. Capillary raising will be then followed by lowering the solution level in the capillary. The rate of spontaneous spreading of aqueous solutions of surfactants is strongly affected by the orientation of surface-active ions (or molecules) within a precursor fi lm and along the adsorption layer at solid/aqueous interfaces. As experiments with wetting of glass by solutions of anionic, cationic, and nonionic surfactants have demonstrated, after the initial stage (identical to all liquids) spreading proceeds faster than for pure water. After this stage, the solutions of anionic surfactants continue to spread, but spreading of cationic and nonionic surfactant solutions stops as a result of surfactant adsorption on a glass surface, which leads to the hydrophobization of the surface. Upon spreading of the surfactant solutions, the character of the three-phase line movement changed as well. The stick–slip motion was reported for solutions of cationic surfactants on a glass surface [22,25]. For solutions of anionic surfactants, so-called dendritic spreading, with separation of jets orthogonal to the front of wetting, was observed. The autophobicity phenomenon (withdrawal of a liquid from the originally wetted area) was also observed upon the spreading of some surfactant solutions [7,28]. Initially, this phenomenon was revealed upon the spreading of liquids with molecules of amphiphilic structure on high-energy surfaces (e.g., upon spreading of 1- and 2-octanol on platinum,

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Surface Phenomena on a Solid–Liquid Interface

1-13

quartz, or sapphire). First, the liquid spreads due to the higher surface tension on a solid/ air interface compared with the sum of surface tensions at the liquid/air and liquid/solid interfaces. Then, an adsorption layer of surfactant molecules at a solid/liquid interface is formed, and conditions of wetting change. The liquid does not wet its own adsorption layer and the reverse movement of the wetting front is observed.

1.2.4 Wetting of Deformable Substrates (Gels) Wetting of deformable substrates is important in some specific applications of PSAs, for example, adhesives contacting biological tissues, such as skin or mucosa. Unfortunately, it is difficult to find a model material with properties similar to the skin or mucosa that can be considered a gel with a high water content. We tried to investigate wetting–spreading processes using aqueous gels of some polysaccharides that are “soft” materials, with a modulus of elasticity Е ~ 100 Pa. For such soft materials we can expect essential changes in substrate shape upon contact with a liquid drop. Let us assume that the pressure created by a drop onto the substrate surface is P
PC  PH

(1.18)

where Р Н is the hydrostatic pressure, РС is the capillary pressure, PC


2 R

(1.19)

where σ is the surface tension of the liquid and R is the radius of the curvature of the liquid surface. This pressure causes deformation of the substrate under the drop, with the formation of a dimple in the shape of a spherical segment. The depth of this dimple is proportional to the ratio P/E, which is very small. An appreciable deformation can therefore be observed only for soft materials with a low modulus of elasticity. The contact angle, measured as the slope of the drop’s surface relative to the horizontal plane of the substrate, decreases over the course of dimple deepening. Another type of deformation is the formation of a ridge near the three-phase contact line. As demonstrated by Bikerman [29] and later in a number of other papers [30–35], this deformation is caused by the vertical component of the surface tension (i.e., σ sin Θ). Although this deformation is typically small (<1 μm), for some systems (e.g., upon wetting of agar or gelatin gels) the height of the ridge can reach 0.1 mm. The value h can be calculated from the surface tension, contact angle, and elastic modulus of the substrate [36] (Figure 1.8). h


3sin E

(1.20)

Wetting of the agar gel by low-molecular-weight and polymeric liquids (water, PI, and PEG-400) is illustrated in Figures 1.9 through 1.15.

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1-14

h

Fundamentals of Pressure Sensitivity

2b

FIGURE 1.8 Gel deformation upon wetting in the vicinity of the three-phase line.

3 1

2 r (mm)

3

2

1

0 0.0

0.5

1.0

1.5

2.0

t (s)

FIGURE 1.9 Spreading of water (1) and PEG-400 (2, 3) drops on thin (1, 2) and thick (3) agar gel plates. Agar content is 0.3%.

FIGURE 1.10 PEG drop on agar gel. Agar content is 0.3%.

The initial stage of the wetting process was investigated using a digital camera (12 fps). The time dependence of the wetted area and the shape of the interface was calculated using a PC program for the analysis of video images. Static contact angles were measured using a horizontal microscope. Agar gels with a concentration of 0.1–0.5 wt % are hydrophilic and rather soft . Water drops coalesce upon these gels. The spreading rate of the water on the gel surface is high enough—more than 32 mm/s. PEG drops spread slower compared with water and form

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1-15

Surface Phenomena on a Solid–Liquid Interface 2.0

2

1

r (mm)

1.5

1.0

0.5

0.0

0

2

4

6

8

10

t (s)

FIGURE 1.11 is 1%.

Spreading of water drops on agar thin (1) and thick (2) gel plates. Agar content

FIGURE 1.12 Water drop on the surface of a thick agar gel plate. Agar content is 1%.

2.5

1

2.0

r (mm)

2 1.5 3 1.0

0.5

0.0

0

1

2

3

4

5

t (s)

FIGURE 1.13 Spreading of water (1), PEG-400 (2), and PI (3) drops on 1.5% agar gel.

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1-16

Fundamentals of Pressure Sensitivity

(a)

(b)

FIGURE 1.14

PEG (a) and PI (b) drops on the surface of agar gel. Agar content is 1.5%.

1.6

PEG-400

r (mm)

1.2

PI

0.8

0.4

0

0

10

20

30

40

50

t (min)

FIGURE 1.15 release liner.

Spreading kinetics of PEG and PI drops on the hydrophilic surface of the

nonzero contact angles (Figures 1.9 and 1.10). In all cases, the soft gel deforms under the drops, forming intrinsic dimples and ridges. The time dependence of the radius of the wetted area for the spreading of water drops on thick and thin plates of gels is presented in Figure 1.11. During contact with thick plates of gels, the volume of water drops decreases (by ~15%), whereas on the fi lm-like gels the volume of the drops remains constant (within 1 min after initial contact). The kinetics of water, PEG, and PI drops spreading on 1.5% thick gel plates is presented in Figure 1.13. The unstable spreading process observed for PI drops can be explained by the slow relaxation of the drop surface and by experimental difficulties connected with drop detachment from a pipette tip. Figure 1.14 represents the images of PEG and PI drops on the thick 1.5% gel (~10 min after moment of the initial contact). The wetting processes for PEG (or PI) drops on thick and thin gel plates are similar.

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1-17

Surface Phenomena on a Solid–Liquid Interface

At wetting of deformable substrates, a significant contact angle hysteresis, namely a difference between advancing and receding contact angles, was observed. The following equations were proposed for calculations of advancing, Θа, and receding, Θr,, contact angles [36], a
a 0 

6sin a bE

(1.21)

r
r 0 

6sin r bE

(1.22)

where Θa0 and Θr0 are the advancing and receding contact angles for the solid surface with negligible deformation (the true contact angles) and 2b is the width of the ridge (see Figure 1.8). As determined in Ref. 37, upon wetting of natural and butadiene rubber by water and ethylene glycol Θa − Θr = 50 ÷ 70°. For harder polyolefin surfaces [polyethylene(PE), polypropylene (PP), polystyrene (Pst) Θa − Θr = 10 ÷ 30°. The spreading of drops on gels surfaces requires additional energy to overcome a viscous dissipation of the substrate [32–40]. Spreading of the same liquids on rigid substrates therefore proceeds essentially faster than on the gel surface; see, for example, the spreading kinetics of water drops on steel (Figure 1.1) and agar gel (Figure 1.11) surfaces. A similar result was obtained in Ref. 38: the contact angle on a quartz surface reached its equilibrium value in 20 s, whereas on the soft epoxized natural rubber (Е = 1.1 MPa), it takes 1 h for the drop to reach the equilibrium state. The difference in spreading rate on soft and rigid surfaces is more pronounced for lowviscosity liquids than for high-viscosity liquids. Thus, as discussed previously, spreading water on a gel proceeds much more slowly than on a rigid surface. Figures 1.13 and 1.15 illustrate that PI and PEG-400 do not demonstrate a significant decrease in spreading rate on the gel surface. Data on PEG-400 spreading kinetics on gelatin and agar gels were used to estimate the contact angle retardation time and PEG-400 viscosity, utilizing a previously described approach—see Equations 1.14 and 1.17. The calculated values are presented in Table 1.2. The comparison of PEG-400 viscosity values in Tables 1.1 and 1.2 illustrates that spreading on a gelatin gel surface proceeds more slowly, with substantially higher apparent viscosity. Thus, spreading kinetics on deformable substrates (gels) is controlled not only by the viscosity of the spreading liquid, but also by the rheological properties of the gel. Wetting of the deformable substrates proceeds more slowly than that of substrates with a

TABLE 1.2 Contact Angle Retardation Times and Viscosity of PEG-400 Calculated from Data on Spreading Kinetics on Gel Surfaces

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Surface

τ (s)

η (Pa s)

Agar 1% gel Gelatin 10% gel

0.73 1.70

23.4 54.4

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1-18

Fundamentals of Pressure Sensitivity

high modulus of elasticity. The wetting process can be complicated by diff usion of a liquid into a gel (e.g., for a system water–agar gel), which also slows down spreading.

1.3 Rheology of Pressure Sensitivity 1.3.1

Dimensionless Criteria of Pressure-Sensitive Adhesive Performance

The defi nition of PSAs as a class of materials [1] is based on the assumption that their performance depends mainly on viscoelastic properties under pressure, which in turn lie within some range of values that can be determined experimentally. It is postulated, therefore, that there exist definite viscoelastic windows that are typical for such materials [41] (see also Chapter 5). Dahlquist’s criterion is based on this concept. In practice, this approach works fairly well. However, it cannot be regarded as truly criterial because it uses dimensional quantities, such as the elasticity modulus. In the strict sense, the criterial approach should use universal dimensionless variables that reflect cause–effect relations and are independent of the unit systems. Indeed, the term criterion relates to a standard that is used as a basis for qualitative and quantitative comparison of the behavior of various materials. The term “pressure-sensitive adhesive” itself presumes a defi nite pressure value necessary to form a strong adhesive joint. Upon converting to dimensionless variables, it would be logical to express pressure as a value relative to the elastic modulus. This is one possible approach to constructing the “dynamic” criterion of pressure sensitivity. The time criterion should be based on relationships between the time of formation of the adhesive joint and the intrinsic relaxation (or retardation) time of formulation for the PSA. The concept of durability of the adhesive joints (see also Chapter 9) is based on a thermofluctuation mechanism of adhesive bond failure under stressed conditions. It is a kinetic process that depends on bond dissociation energy and activation volume. The maximum relaxation time of the supramolecular structure can be considered as a characteristic time measure of the PSA’s adhesive failure. Chapter 11 demonstrates that it is the maximum relaxation time that governs the adhesive strength of various PSAs. It is therefore reasonable to express the contact time in values normalized by the maximum relaxation time of the tested material. External mechanical stresses decrease the value of the activation barrier; therefore, the durability of adhesive joints also depends on the applied stress. For dimensionless estimation of the role of external stresses, the external stresses can be related to adhesive strength. Thus, dimensionless time and stress characterizing formation and failure of the adhesive joint can be defined. In accordance with the principle of least action, an invariant product can be constructed that includes dimensionless force and time characteristics. Taking into account the dimension of action (work × time), “dimensionless action” is presented as a product of two normalized values: the work of fracture and durability of the adhesive joint. Normalized _ action


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Work Time  Elementary _ work Elementary _ time

(1.23)

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1-19

Surface Phenomena on a Solid–Liquid Interface

We assume that the extremums of this invariant product determine the range of PSA application. Let us explore the capabilities of the described approach for determining the influence of contact time on the durability of adhesive joints. A hydrophilic formulation based on poly(N-vinylpyrrolidone) (PVP) and PEG with a PVP/PEG ratio of 64/36 was chosen as the test system in our experiments. Th is ratio corresponds to the polycomplex formed by hydrogen bonding between the terminal hydroxyls of PEG and carbonyls of PVP [2,42]. Oligomeric PEG acts as a plasticizer (solvent) for PVP, enabling tackiness of the formulation. Formation of the PVP–PEG polycomplex strengthens the structure of the hydrophilic adhesive and improves its elasticity (recoverable strain) and cold flow behavior. It is logical to assume that the durability of the adhesives cross-linked by weak H-bonds is determined mainly by the kinetics of the H-bond dissociation, which leads to flow of the adhesive. To determine the intrinsic time characteristics of the formulation, creep and recovery were measured at room temperature (Figure 1.16). At the creep stage, the sample was squeezed from the gap between two parallel plates with constant load applied to the upper plate. Then the load was released and the thickness of the sample was partially recovered (recovery stage). The gap between the plates, h, as a function of time, t, is registered in this experiment. Because the rubbery state of the PVP–PEG formulation can be characterized by two processes (movement of polymer chain segments and relaxation of the H-bonds network), it is reasonable to describe the creep function as a sum of two exponents: h
h0  A1e 1  A2e t

t

(1.24)

2

where h0 is the initial gap, A1 and A2 are constants, and τ1 and τ2 are characteristic times. The obtained experimental data can be successfully described using Equation 1.24. The values of calculated characteristic times are as follows: τ1 = 8 s and τ2 = 327 s. 1.1 σ = 69 kPa

σ = 0 kPa 0.49

1.0

h/h0

0.9 0.8 0.7 0.6 0.5

Contact time 0

Recovery 500

1000

1500

t (s)

FIGURE 1.16 Creep and recovery of PVP/PEG PSA.

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1-20

Fundamentals of Pressure Sensitivity Increased contact time 12

3

4

5

6

7

89

600

h (µm)

400

Durability

200

0

0

50

100

150

Debonding time (s)

FIGURE 1.17 Deformation curves of adhesive joints formed by PVP/PEG formulation at different contact times under pressure: 5 (1), 10 (2), 20 (3), 50 (4), 100 (5), 300 (6), 600 (7), 1200 (8), and 3600 s (9).

It can be assumed that the shorter time (τ1) characterizes segment movement, whereas the longer time (τ2) should be related to the contribution of the H-bonds network. To measure the durability of the adhesive joints, a probe-tack-type setup with a quartz rod was used. The device allowed us to apply constant compressive or tensile force. The adhesive fi lm was reliably fi xed on the lower (steady) plate. Then the rod was pressed to the fi lm with a definite load for a specified time. Constant tensile force was applied to the rod until failure of the adhesive joint. The testing conditions were as follows: temperature: 23°C; pressing stress: 4 kPa; apparent tensile stress: 75 kPa. The contact time under pressure varied from 5 to 3600 s. As illustrated by the deformation curves (Figure 1.17), at contact times comparable with τ1, the failure of the adhesive joint proceeds via elastic mechanism without flowing of the adhesive. At longer contact times the flow of the adhesive with formation and breakage of fibrils is observed. Durability, which was determined as time to failure of the adhesive joint under standard detaching force, increases with contact time up to a virtually constant value. Therefore, it can be concluded that there exists a critical contact time after which durability is no longer sensible to this parameter. To describe this phenomenon, let us convert durability θ and dwell time td to dimensionless values normalized by the highest relaxation time, τ2 . These values are plotted in Figure 1.18, which demonstrates that for given experimental conditions the durability of the adhesive joints under fi xed detaching force reaches its maximum value at td ≥ 4τ2, that is, approximately 20 min. The maximum durability at said conditions is approximately 0.5τ2 . It can be concluded from the presented data that the least action principle sets restrictions on the time characteristics of formation and failure of adhesive joints: contact time and durability.

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1-21

Surface Phenomena on a Solid–Liquid Interface 0.5 0.4

θ/τ2

0.3 0.2 0.1 0.0

0

4

8

12

t d /τ2

FIGURE 1.18 Normalized durability of PVP/PEG formulation versus normalized contact time.

1.3.2

Rheological Properties of Pressure-Sensitive Adhesives under Bonding Pressure

The phenomenon of tackiness features a high shear flow of an adhesive material under a compressive force, thus forming the adhesive joint. The flow of the adhesive is needed in the fi rst several seconds to wet the surface of a substrate. Owing to the high viscosity of the PSA, proper wetting cannot be achieved in a reasonable time without compressive force. PSA behavior under compressive loading was studied in Ref. 42. The squeeze–flow technique was used to simulate the real situation of adhesive joint formation. This method involves squeezing a PSA fi lm between two parallel plates under a constant load. The kinetics of change in the gap between the plates is connected with the rheological properties of the adhesive and can therefore be used for their measurements (see also Chapters 8 and 9). At zero squeezing force, the shear stress and shear rate are also equal to zero. After application of a fi xed load the distance between the plates starts to decrease. The shear stress and shear rate grow almost instantaneously and then decrease with the decrease in the gap. Because shear stress decreases upon decrease of the sample’s thickness at constant applied force, the viscosity of the adhesive significantly increases over the course of the experiment. For formulations possessing yield stress, which is defined as a critical shear stress value below which the material does not flow, the residual gap corresponds to the yield stress value. Shear stress, shear rate, and apparent viscosity values of the PVP/PEG hydrogel roughly estimated from the kinetics of the gap change under constant compressive force are illustrated in Figure 1.19. It can be concluded from the data that the squeeze flow of the adhesive material has two stages: fast (within the first 3 min under 35 kPa pressure) and slow. The two stages correspond to two intrinsic times governing the flow process. Based on the shorter relaxation time, one could say that at least this much time is necessary for action of the

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1-22

Fundamentals of Pressure Sensitivity log τ (Pa) 8.0 4.44

log η log shear rate

log η (Pa.s)

7.5 7.0 log τ (Pa)

6.5

−2 4.40

−3 4.36

log shear rate (s−1)

6.0

4.32

5.5 0

200

400

600

800

−4 1000

Time (s)

FIGURE 1.19 Dynamics of the shear stress, shear rate, and apparent shear viscosity behavior for PVP–PEG (36%) adhesive hydrogels over the time of squeezing under a compressive force of 1 N. (Feldstein, M.M., Kulichikhin, V.G., Kotomin, S.V., Borodulina, T.A., Novikov, M.B., Roos, A., and Creton, C., J. Appl. Polym. Sci., 100, 522–537, 2006.)

compressive force at application, but to reach the maximum strength of adhesive contact we must use a contact time comparable with the highest relaxation time. The thickness of the PVP/PEG fi lm does not reach zero but tends toward a definite constant value that is determined, as noted above, by the yield stress of the system. The viscosity tends to infi nity upon approaching the yield stress value. The results presented in Figure 1.19 are of fundamental importance for the rheology of pressure-sensitivity because they demonstrate the change of shear stress, shear rate and PSA’s viscosity under compressive load imitating bonding pressure.

References 1. Pressure Sensitive Tape Council. Glossary. http://www.pstc.org/technical/glossary. php#glossary. 2. Feldstein M.M., Creton C. 2006. Pressure-sensitive adhesion as a material property and as a process. In Pressure-Sensitive Design, Theoretical Aspects. Volume 1, ed. I. Benedek, pp. 27–62. Leiden, VSP. 3. Good R.J., Chaundry M.K., van Oss C.J. 1991. Theory of adhesive forces across interfaces (2). Interfacial hydrogen bonds and acid/base phenomena as factors enhancing adhesion. In Fundamentals of Adhesion, ed. L.H. Lee. New York, Plenum Press. 4. Good R.J., Chaundry M.K., 1991. Theory of adhesive forces across interfaces (1). The Lifshitz – van der Waals forces of interactions and adhesion. In Fundamentals of Adhesion, ed. L.H. Lee. New York, Plenum Press. 5. Chaundry M.K. 1996. Interfacial interaction between low-energy substrates. Mater. Sci. Eng. R16:97–159.

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Surface Phenomena on a Solid–Liquid Interface

1-23

6. de Gennes P.G. 1985. Wetting: statics and dynamics. Rev. Mod. Phys. 57:863. 7. Summ B.D., Goryunov Yu.V. 1976. Fiziko-khimicheskie osnovy smachivaniya i rastekaniya (in Russian). Physical-Chemical Basis of Wetting and Spreading. Moscow, Khimia. 8. Eustathopoulos N., Nicholas M.G., Drevet B. 1999. Wettability at high temperatures. Amsterdam, Pergamon. 9. Soboleva O.A., Summ B.D., Raud E.A. 1989. Transition from inertial to viscous spreading of a drop. Colloid Journal. 51:1204–1207. 10. Soboleva O.A., Raud E.A., Summ B.D. 1992. Rastekanie smesey uglevodorodov po poverkhnosti stali (in Russian). Spreading of hydrocarbon mixtures on steel surface Vestnik MGU Ser 2 33:42–46. 11. Soboleva O.A., Raud E.A., Summ B.D. 1991. The initial stage of drops spreading on solid surface. Colloid Journal. 53:1106–1110. 12. Arslanov V.V., Ivanova T.I., Ogarev V.A. 1971. Kinetika rastekaniya polymerov na tverdykh poverkhnostykh (in Russian). Spreading kinetics of polymers on rigid surfaces. Dokl. Akad. Nauk SSSR. 198:1113–1116. 13. Vavkushevskii A.A., Arslanov V.V., Ogarev V.A. 1984. Rastekanie kapel’ polymerov po gladkim tverdym poverkhnostyam (in Russian). Spreading of a liquid droplet over a solid horizontal surface. Kolloid. Zh. 46:1076–1081. 14. Raud E.A., Summ B.D. 1984. Adgeziya rasplavov i paika materialov (in Russian) Adhesion of melts and soldering of materials. N12. p. 3. 15. Leaderman H. 1958. Viscoelasticity phenomena in amorphous high polymeric systems. In Rheology. Theory and Applications. Volume II, ed. F.R. Eirich, pp. 1–61, New York, Academic Press. 16. Cottington R.L., Murphy R.S., Singleterry C.R. 1964. Effect of polar-nonpolar additivities on oil spreading on solids, with application to nonspreading oil. In Contact Angle, Wettability and Adhesion. Adv. Chem. Ser. N43. pp. 341–354. 17. Bascom W.D., Cottington R.L., Singleterry C.R. 1964. Dynamic surface phenomena in spontaneous spreading of oil on solids. In Contact Angle, Wettability and Adhesion. Adv. Chem. Ser. N43. pp. 355–379. 18. Neogi P. 1985. Tears-of-wine and related phenomena. J. Colloid and Interface Sci. 105:94–101. 19. Pesach D., Marmur A. 1987. Marangoni effects in the spreading of liquid mixtures on solid. Langmuir. 3:519–524. 20. Kulichikhin V., Antonov S., Makarova V., Semakov A., Tereshin A., Singh P. 2006. Novel hydrocolloid formulations based on nanocomposites concept. In PressureSensitive Design, Theoretical Aspects. Volume 1, ed. I. Benedek, pp. 351–401. Leiden, VSP. 21. Zorin Z.M., Romanov V.P., Churaev N.V. 1979. Influence of surfactants on quartz wetting by electrolytes solutions. Colloid Journal. 45:1066–1073. 22. Princen H.V., Cazabat A.M., Cohen S.M.A., Heslot F., Nicolet S. 1988. Instabilities during wetting process. Wetting by tensioactive liquids. J. Colloid and Interface Sci. 126:84–92. 23. Zhmud B.V., Tiborg F., Hallstensson K. 2000. Dynamic of capillary rise. J. Colloid and Interface Sci. 228:263–269.

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1-24

Fundamentals of Pressure Sensitivity

24. Soboleva O.A., Summ B.D. 2001. Reverse flow of mixed surfactant solutions after their capillary rise. Colloid Journal. 63:769–773. 25. Frank B., Garoff S. 1995. Origins of the complex motion of advancing surfactant solutions. Langmuir. 11:87–92. 26. Kumar N., Varamasi K., Tilton R.D., Garoff S. 2003. Surfactant self-assembly ahead of the contact line on a hydrophobic surface and its implication for wetting. Langmuir. 19:5366–5373. 27. Afsar-Siddiqui A., Luckham P.F., Matar O.K. 2003. Unstable spreading of aqueous anionic surfactant solutions on liquid fi lms.1. Sparingly soluble surfactant. Langmuir. 19:696–702. 28. Zisman W.A. 1964. Relation of equilibrium contact angle to liquid and solid constitution. In Contact Angle, Wettability and Adhesion, Ј. Advances in Chemistry Series. Am. Chem. Soc. Washington. N43. pp. 1–50. 29. Bikerman J.J. 1950. Sliding of drops from surfaces of different roughness. J. Colloid Sci. 5:349–359. 30. Michaeles A.S., Dean S.W., Jr. 1962. Contact angle relationships on silica aquagel surfaces. J. Phys. Chem. 66:1790–1798. 31. Rusanov A.I. 1975. Theory of the wetting of elastically deformed bodies. Colloid Journal. 37:614–618. 32. Yuk S.H., Jhon M.S. 1986. Contact angle on deformable surface. J. Colloid Interface Sci. 110:252–257. 33. Shanahan M.E.R., Carre A. 1994. Anomalous spreading of liquid drops on an elastomeric surface. Langmuir. 10:1647–1649. 34. Carre A., Shanahan M.E.R. 1995. Direct evidence for viscosity-independent spreading on soft surface. Langmuir. 11:24–26. 35. Shanahan M.E.R., Carre A. 1995. Viscoelastic dissipation in wetting and adhesion phenomena. Langmuir. 11:1396–1402. 36. Extand C.W. 2006. Hysteresis in contact angle measurements. In Encyclopedia of Surface and Colloid Science. Volume 4, ed. P. Somasundaran, pp. 2876–2891. 37. Extand C.W., Kumagai Y. 1996. Contact angles and hysteresis on soft surfaces. J. Colloid Interface Sci. 184:191–200. 38. Carre A., Gastel J.-C., Shanahan M.E.R. 1996. Viscoelastic effects in the spreading of liquids. Nature. 379:432–434. 39. Long D., Ajdari A., Leibler L. 1996. Static and dynamic wetting properties of thin rubber fi lms. Langmuir. 12:5221–5230. 40. Chan L.W., Chow K.T., Heng P.W.S. 2006. Investigation of wetting behavior of nonaqueous ethylcellulose gel matrices using dynamic contact angle. Pharm. Res. 23:408–421. 41. Chang E.P. 1997. Viscoelastic properties of pressure-sensitive adhesives. J. Adhesion. 60:233–248. 42. Feldstein M.M., Kulichikhin V.G., Kotomin S.V., Borodulina T.A., Novikov M.B., Roos A., Creton C. 2006. Rheology of poly(N-vinyl pyrrolidone) – poly(ethylene glycol) adhesive blends under shear flow. J. Appl. Polym. Sci. 100:522–537.

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2 Diffusion and Adhesion 2.1 Introduction .............................................................2-1 2.2 Tack and Self-Diff usion ......................................... 2-2 Introduction and Experimental Details • Determination of Adhesion Energy from Probe Tack Tests

2.3 Tack at Interfaces between Immiscible Polymers..................................................................2-11

Costantino Creton Unit Joint CNRS-UPMC-ESPCI

Régis Schach Centre Technique de Ladoux

Introduction • Determination of the Interfacial Width by Neutron Reflectivity • Determination of the Adhesion Energy with Probe Tests

2.4 Discussion ...............................................................2-16 2.5 Conclusion ..............................................................2-19 References ....................................................................... 2-20

2.1 Introduction Unlike simple fluids, polymers have very slow dynamics so that even relatively far away from their glass transition temperature, highly entangled polymer melts can diff use distances of the order of the coil size in minutes or more. Th is was recognized some time ago1 and spurred the creation of the so-called interdiff usion theory of adhesion, which stated that the adhesion between two polymers put in contact in melt increased with the square root of the contact time. However, almost all the studies on that topic focused on a situation in which the interface is formed in the melt state, but its mechanical strength is tested after the system is cooled, in its glassy state.2–5 In many industrial processing applications such as coextrusion, molding, elastomer processing prior to vulcanization, or pressure-sensitive bonding by tack, both interface formation and some mechanical strength build-up must occur in the melt state.6–9 For pressure-sensitive adhesives (PSAs), the substrate surface is often rigid and impenetrable to polymer chains, but in certain cases the PSA can be bonded to an elastomer surface, where chain interpenetration is a possibility.

2-1

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2-2

Fundamentals of Pressure Sensitivity

Hamed and coworkers10–14 studied self-adhesion of elastomers using the classic peel test technique. This technique allows the measurement of adhesive properties, but only for long contact times. The technique is well adapted to filled elastomers, which have extremely long relaxation times, but would not be the technique of choice for unfi lled polymer melts due to its poorly defi ned geometry and difficulty in achieving short contact times of the order of seconds. To overcome that limitation, Gent and Kim15 developed another apparatus to study the tack at short contact times. They studied the tack of elastomers by measuring the impact and rebound velocity of a rigid pendulum with an uncross-linked rubber sample at its tip impacting another elastomer sample. With this experiment, very short contact times are accessible, but the contact time and the debonding velocity are not independent and the contact area is not exactly known. An alternative technique that combines the versatility of the peel test with the accessibility of short contact times in a well-defined geometry is the probe test commonly used in the PSA industry to evaluate the adhesive properties of sticky materials.16 As described in detail in Chapter 6, a flat steel probe approaches the adhesive layer (which has been deposited on a glass slide) at a constant velocity, applies a controlled compressive force during a set contact time, and is then removed at a constant debonding velocity while a chargecoupled device (CCD) camera allows observation of the debonding mechanism.17 With a few technical modifications, Schach and colleagues18,19 adapted this classic PSA technique to study the tack of uncross-linked elastomers. Two recent experimental studies focusing on the self-adhesion and adhesion of a series of model linear, high-molecular-weight polymers will be summarized in this chapter. Although these polymers are not, strictly speaking, PSAs, it is nevertheless instructive and relevant to examine their tack properties as an example of the effect of polymer chain interdiff usion on tack. This chapter will be divided into two parts: the first part will focus on tack and self-diff usion, that is, the gradual build-up of tack as chains mutually cross the interface and entangle on the opposite side.

2.2 Tack and Self-Diffusion 2.2.1

Introduction and Experimental Details

For the first study, three linear poly(styrene-r-butadiene) random copolymers with the same repeat unit composition (20% styrene; 42% 1,2; 19% cis1,4; and 19% trans 1,4) were used. Their molecular weights were 80,000, 160,000, and 240,000 g/mol and the Mw/Mn was lower than 1.1 (Table 2.1). The rheological properties of the materials in the linear regime were characterized with a parallel plate rheometer, whereas the adhesive properties were characterized with a custom-designed probe tack tester. From the frequency sweeps at different temperatures, master curves were constructed using the time–temperature superposition principle. The master curves obtained for the three styrene block copolymers (SBR) at a reference temperature of 20°C are illustrated in Figure 2.1 and are typical of wellentangled monodisperse linear polymers. Several molecular parameters of the polymers, and in particular their reptation time, which sets the self-diff usion rate of the polymer, were calculated based on these

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2-3

Diffusion and Adhesion TABLE 2.1 Molecular Weight and Polydispersity (Determined by size exclusion chromatography–Triple Detection) of the SBR Polymer

Mn Target (g/mol)

Experimental Mn (g/mol)

Polydispersity (Ip)

SBR80K SBR160K SBR240K

80,000 160,000 240,000

74,200 144,900 235,400

1.07 1.10 1.12

109 108

1000

SBR240K SBR160K SBR80K

G tan (δ)

100 107 10

105 1

104 103

tan (δ)

G ′ (Pa)

106

0.1

102 101

0.01 10−5

10−2

101

104

107

1010

1013

Frequency (rad /s)

FIGURE 2.1 Master curves of G′ and tan δ for the three SBR at a reference temperature of 20°C. (Schach, R. and Creton, R., J. Rheol., 52, 749, 2008. With permission.)

master curves. This is a critical parameter during the process of interface healing, as demonstrated in neutron reflectivity studies.20 The reptation times, as well as other important molecular or rheological parameters of the polymer, such as the viscosity at vanishing rate or the plateau modulus, are listed in Table 2.2. These master curves are essential for estimating the type of behavior expected from materials during a tack experiment. Using the fi lm thickness and the debonding velocity of the probe, an average initial normal strain rate for the test (dε/dt∼vd/h) can be estimated, which indicates whether the entangled polymer has a typical elastic solid behavior or a liquid-like behavior at the debonding velocity. Of course, this simple method only gives an approximate estimate of the range of strain rates seen by the polymer layer during the debonding process. In reality, the strain rate is highly inhomogeneous, both spatially and as a function of time. The probe test experiments were performed on a custom-designed apparatus based on an MTS (Materials Testing Systems, Minneapolis, USA) 810 hydraulic testing machine.17 The typical probe test for this elastomer–elastomer situation can be divided into three

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2-4

Fundamentals of Pressure Sensitivity

TABLE 2.2 Mechanical Properties of the Three SBR Determined Using the Master Curves at Tref = 20°C Polymer SBR80K SBR160K SBR240K

Molecular Weight (g/mol) 74,200 144,900 235,400

τd (s)

η0 (MPa s)

GN0 (MPa)

13 ± 2 140 ± 15 1170 ± 200

1 ± 0.1 11 ± 2 120 ± 20

0.715 ± 0.15 0.75 ± 0.1 0.73 ± 0.07

stages. In the first stage, a flat, stainless-steel probe with a silicon wafer coated with a ∼1-µm-thick elastomer layer glued on its end approaches a 200-µm-thick elastomer layer grafted on a microscope glass slide. When a contact force of 70 N is reached (corresponding to a nominal contact pressure of 1 MPa), the probe stops during a contact time varying from 1 to 1000 s. The probe is then removed during stage 3 at a constant debonding velocity varying from 1 to 100 µm/s. Probe tack results are typically presented as tensile stress–strain curves measured during debonding. The stress is a nominal stress obtained by normalizing the tensile force by the maximum area of contact obtained during the compression stage, and the strain is given by the displacement of the probe normalized by the initial thickness of the fi lm. The adhesion energy (J/m2) is then calculated by multiplying the area under the stress–strain curve (which is equal to the total dissipated energy per unit volume) by the total thickness of the sample. To obtain reliable results for polymer–polymer adhesion, the two polymer layers must be strongly attached to the underlying rigid substrates. Th is problem was overcome by using a reactive mercaptosilane layer on the rigid substrates, which could react with the polymer and form covalent bonds. A thick layer was used on the glass slide and a thin layer on the probe for two reasons. First, it was easier to prepare a thin layer by spin coating on a small surface of 1 cm2 because of edge effects. Second, the thin layer on the steel probe deforms very little and effectively acts as a boundary condition for the debonding and deformation of the thick layer. This becomes particularly important when different polymers are used for the thin layer.

2.2.2 Determination of Adhesion Energy from Probe Tack Tests The adhesion energy and the failure mechanisms of the interfaces depend strongly on the experimental parameters: contact time, probe velocity, and the material tested. Figure 2.2 illustrates the main types of experimental stress–strain curves observed with these materials within the accessible range of experimental parameters. Th ree main types of curves are observed: fi rst are very symmetric curves, with a sharp decrease in stress after a sharp maximum; second are curves with a low maximum stress, followed by a long stress plateau with a failure of the adhesive bond for high strains (squares); and fi nally are curves with a very high maximum stress and high maximum strain (circles). These types of stress–strain curves are characteristics of different failure mechanisms. As illustrated in Figure 2.1, depending on the molecular weight of the polymer there can be one or two types of material response depending on probe velocity: a high-velocity

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2-5

Diffusion and Adhesion

2.0 SBR240K, tc = 100 s, v = 100 µm/s SBR80K, tc = 100 s, v = 1 µm/s

Stress (MPa)

1.5

SBR240K, tc = 1 s, v = 100 µm/s

1.0

0.5

0.0 0

1

2 Strain

3

4

FIGURE 2.2 Different types of tack curves observed with three different sets of experimental conditions. (Schach, R. and Creton, R., J. Rheol., 52, 749, 2008. With permission.)

2

tc = 1 s tc = 10 s

Stress (MPa)

1 6

tc = 60 s

4

tc = 1000 s

2

0.1 6 4 2

0.01 0

1

2

3 Strain (ε)

4

5

6

FIGURE 2.3 Evolution of the tack curves with contact time in the high-velocity regime (V = 100 µm/s) for the SBR240K polymer. (Schach, R. and Creton, R., J. Rheol. 52, 749, 2008. With permission.)

regime, in which the polymer responds as a viscoelastic solid, and a low-velocity regime, in which the polymer behaves as a viscoelastic liquid. These distinctions lead to very different deformation patterns for the polymer during the failure process. Figure 2.3 illustrates the evolution with contact time of the tack curves for the SBR of molecular weight 240 kg/mol at a debonding velocity of 100 µm/s (viscoelastic solid

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2-6

Fundamentals of Pressure Sensitivity

1.0 tc = 50 s

0.8 Stress (MPa)

tc = 100 s tc = 140 s

0.6

0.4

0.2

0.0 0.0

0.5

1.0

1.5

2.0

2.5

Strain (ε)

FIGURE 2.4 Evolution of the tack curves with the contact time in the low-velocity regime; SBR80K. (Schach, R. and Creton, R., J. Rheol., 52, 749, 2008. With permission.)

regime). At short contact times, the work of adhesion is low, with a symmetric tack curve characterized by a maximum stress of 1 MPa and a failure strain of 0.8. As the contact time increases, the mutual diff usion process of the polymer at the interface proceeds, the interface is able to transfer higher stresses, and the observed peak stress and failure strain both increase as the adhesion energy significantly increases. Furthermore, the tack curves are not self-similar: at short contact times, the failure is very sharp, and as the contact time increases they become asymmetric, characteristic of the bulk deformation by cavitation of a thin, confined elastic fi lm.21 Thus, in the high-velocity regime, there is a transition from an interfacial failure at short contact times to a bulk failure at long contact times. Figure 2.4 illustrates the evolution of the tack curves in the low-velocity regime (molecular weight 80 kg/mol, vd = 1 µm/s). In this liquid-like regime, there is no effect of contact time on the adhesion properties: the debonding rate is so slow that the polymer chains had time to diff use to the point where the interface is indistinguishable from the bulk, even for relatively short contact times. These liquid-like tack curves are very similar to the tack results obtained by Poivet et al.22,23 on silicone oils. Figure 2.5 illustrates the evolution of the tack curves at long contact times (100 s for a molecular weight of 80 kg/mol, i.e., a reptation time of 15 s) with debonding velocity. At low debonding velocity, the tack curve is fluid-like (low maximum stress, followed by a stress plateau), and when the velocity increases, there is a transition from this fluid-like behavior to a solid-like behavior, as described for the high-velocity regime (asymmetric curves with very high maximum stress and maximum strain).

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2-7

Diffusion and Adhesion

1.2 v = 1 µm/s v = 5 µm/s v = 10 µm/s v = 30 µm/s v = 50 µm/s v = 100 µm/s

Stress (MPa)

1.0 0.8 0.6 0.4 0.2 0.0 0

1

2

3

4

Strain FIGURE 2.5 Evolution of the tack curves with the debonding velocity at long contact time (100 s) for the SBR80K polymer. (Schach, R. and Creton, R., J. Rheol., 52, 749, 2008. With permission.)

These first qualitative results can be summarized as follows:18 • At short contact times and high debonding rate, the failure mechanism is interfacial and can be described by the propagation of a crack at the interface between a rigid surface and a viscoelastic medium. • At long contact times and high debonding rates, failure occurs in the bulk of the fi lm by forced disentanglement, initiated by cavitation. This regime is indistinguishable from the fracture under tension of a thin confi ned layer of the same polymer. • At low debonding velocity, the layer fails by a fluid flow mechanism, fully described using fluid mechanics tools and equations. Figure 2.6 illustrates the variations in adhesion energy with time of contact for different debonding velocities for the three SBR tested. These curves are directly correlated with the transition between debonding mechanisms. Indeed, the variations of adhesion energy with contact time are very different depending on both the debonding rate and the molecular weight of the polymer, suggesting the existence of reduced parameters describing the observed failure mechanisms. In the high-velocity regime, Wadh increases until it reaches a maximum for contact times of the order of magnitude of the reptation time. The adhesion energy is clearly related to the degree of interdiff usion at the interface, and the saturation corresponds to a fully healed interface. Figure 2.7 illustrates the variation in adhesion energy for the three SBR at 100 µm/s. Figure 2.7 clearly demonstrates the trade-off between a good

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2-8

Fundamentals of Pressure Sensitivity 6 5 4

V = 100 µm/s V = 10 µm/s V = 1 µm/s

3

Wadh (MPa)

2

100 6 5 4 3 2

10 1

10

100

1000

tc (s)

(a) 6 5 4 3

Wadh (MPa)

2

100 6 5 4 3

V = 100 µm/s V = 10 µm/s V = 1 µm/s

2

10 1

(b)

10

6 5 4

tc (s)

100

1000

V = 100 µm/s V = 10 µm/s V = 1 µm/s

3

Wadh (MPa)

2

100 6 5 4 3 2

10 2

1

(c)

3 4 56

2

3 4 56

10

2

100

3 4 56

1000

tc (s)

FIGURE 2.6 Adhesion energy, Wadh, as a function of contact time for the autohesion of (a) SBR240K, (b) SBR160K, and (c) SBR80K for three probe-debonding velocities. (Schach, R. and Creton, R., J. Rheol., 52, 749, 2008. With permission.)

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2-9

Diffusion and Adhesion

1000 8

SBR80K SBR160K SBR240K

6 4

100

SBR240K SBR160K SBR80K

0.3

8

Stress (MPa)

Wadh (MPa)

2

6 4

2

0.2

0.1

0.0 0.0

10 1

10

0.5

1.0 Strain

100

1.5

2.0

1000

tc (s)

FIGURE 2.7 Adhesion energy as a function of contact time at high debonding velocity (Vd = 100 µm/s) for the three SBR. Comparison with the stress–strain curves of the three SBR in a tensile test at constant cross-head velocity. The correlation between equilibrium adhesion energy and elongational properties is evident. (Schach, R. and Creton, R., J. Rheol., 52, 749, 2008. With permission.)

adhesion at short contact times, requiring sufficiently short and mobile polymer chains, and a good adhesion at long contact times, requiring long polymer chains for cohesive strength when the interface is fully healed. For the reported system the intermediate molecular weight seems to strike the best compromise. In the low-velocity regime, Wadh is independent of contact time because the debonding is so slow that the interface is always fully healed (diff usion continues to occur during debonding). This is the case for the SBR80K at 1 and 10 µm/s and for the SBR160K at 1 µm/s. Figure 2.8 illustrates the variation of Wadh for these experimental systems. It is worthwhile to note that the adhesion energy of the SBR80K at 10 µm/s and that of the SBR160K at 1 µm/s is identical. For fluid systems,23 the relevant parameter controlling the behavior of the thin fi lm should be the product Vdη, which is identical for SBR80K at 10 µm/s and SBR160K at 1 µm/s. It is useful to define two reduced parameters to describe more generally the effect of polymer interdiff usion on tack between polymer melts: first, the ratio of the contact time to the reptation time (tc/τd), and second, the Deborah number, which is defined here as the product of the average initial strain rate of the probe test and the reptation time of the polymer, De


vd d h0

(2.1)

with vd the debonding velocity and h0 the initial thickness of the sample.

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2-10

Stress (MPa)

Fundamentals of Pressure Sensitivity

6 5 4 3

SBR80K: 10 µm/s SBR160K: 1 µm/s

1.2 0.8 0.4 0.0

Wadh (J/m2)

2

0.0

0.5

1.0 Strain

1.5

2.0

100 6 5 4 3

SBR160K, V = 1 µm/s SBR80K, V = 10 µm/s SBR80K, V = 1 µm/s

2

10 1

10

100

1000

tc (s)

FIGURE 2.8 Adhesion energy as a function of contact time in the low-velocity regime. Comparison of the tack curves obtained for the debonding of SBR80K at 10 µm/s and SBR160K at 1 µm/s. (Schach, R. and Creton, R., J. Rheol., 52, 749, 2008. With permission.)

Using a CCD camera to identify the failure mechanism for each set of material and experimental parameters, a mechanism map can be constructed and is illustrated in Figure 2.9 as a function of the two reduced parameters. For De > ∼3, failure is in the high-velocity regime, where the polymer behaves as a viscoelastic entangled solid. The transition between bulk failure and interfacial crack propagation depends also on the De: the higher De is, the higher the critical ratio, tc/τd, becomes. For De < ∼3, the polymer behaves as a viscoelastic fluid. In this low-De regime, tc/τd is no longer relevant to describe the interface, which is fully healed during the debonding. This study clearly demonstrates the significant effect of polymer interdiff usion on selftack. It is also clear that short mobile chains can diff use quickly but do not impart much strength to the interface, whereas long chains are slow to diff use but strengthen the interface much more significantly. Of course, these model studies were carried out on linear chains and PSAs are always partially cross-linked. However, mobile chains exist in PSA formulation and if there is some degree of miscibility, for example, between the PSA and a release liner, blocking problems can arise. Also, when PSA need to be bonded to elastomeric substrates, some small degree of miscibility may help to increase adhesion. The second conclusion that can be drawn from the study is that it is very difficult to clearly attribute a mechanical reinforcement to an interdiff usion effect if one has not checked the changes in macroscopic rheological response of the PSA. Highly viscoelastic materials such as polymer melts can deform very differently when strained at different rates.

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10 Bulk failure

Liquid-like failure

tc /
d

1

0.1

0.01

Interfacial crack propagation

0.001

0.1

1

10

100

1000

De

FIGURE 2.9 Failure mechanism map as a function of the reduced contact time and the Deborah number. ❍, Interfacial crack propagation; ❏, bulk failure; ∆, liquid-like failure. ●, liquid/ interfacial transition; ■, bulk/interfacial transition; ▲, bulk/liquid transition. (Schach, R., Tran, Y., Menelle, A., and Creton, C., Macromolecules, 40, 6325, 2007. With permission.)

2.3 Tack at Interfaces between Immiscible Polymers 2.3.1

Introduction

As discussed in the preceding conclusion, a practically important situation is that in which the two polymers are not identical and therefore fully miscible, but are partially miscible and can interpenetrate by a small distance controlled by thermodynamics. Th is situation is amenable to a better characterization of the interpenetration depth because the interfaces will be at thermodynamic equilibrium. We now summarize a recent study on the characterization of the interfacial width and the mechanical strength of a series of interfaces between two partially miscible polymer melts: one model polymer: cis-1,4-polybutadiene, and a series of polymers of similar molecular weight but different chemical structures. All polymers used in this study are linear and have glass transition temperatures well below room temperature. The different values of the Flory χ parameter for these polymer pairs result in different depths of interpenetration. Experimentally, the interfacial widths of the different polymer pairs were characterized by neutron reflectivity and their strength was evaluated with a tack test. 2.3.1.1 Polymer Interfaces The thermodynamics of polymer interfaces has been extensively studied, both theoretically and experimentally.24–28 If the two polymers on both sides of the interface have a

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nonzero χ parameter, the interfacial width will be fi nite and at thermodynamic equilibrium will be given by25 w
w ( N
∞)

1  1 1  1 2 ln 2    N A N B 

(2.2)

where w ( N
∞)


a c

(2.3)

and a is the segment length and c is a constant that has a value of 6 or 9, depending on whether the interface is in the weak or strong segregation limit. The width of the polymer–polymer interfaces is usually measured by neutron reflectivity, which is an ideal technique to measure interfacial widths27 ranging between 2 and 30 nm with a resolution of the order of magnitude of several angstroms. This technique is sensitive to gradients of the scattering length density, which depends directly on the composition of the layers. Owing to the big difference in scattering length densities between hydrogen and deuterium, it is possible to obtain very good contrast between two polymers using isotopic substitution of hydrogen by deuterium. 2.3.1.1.1

Materials

The study was carried out mainly with a linear polybutadiene (PB; M = 420 kg/mol, more than 80% 1,4) with a well-defined micro- and macrostructure (PB420K-H). The adhesion properties of several elastomers with this PB were then investigated: the same three linear SBR described in Figure 2.1, one linear SBR with another type of microstructure (36% styrene) and a molecular weight of 160 kg/mol, and three “industrial” rubbers with some degree of branching: an ethylene–propylene–diene copolymer (EPDM), a polyisobutylene (PIB), and a poly(dimethyl siloxane) (PDMS). The molecular characteristics of the polymers are shown in Table 2.3. For neutron reflectivity experiments, the interfacial width between each of these polymers and a deuterated PB with the same chemical structure as PB420K-H but with M = 120 kg/mol (PB120K-H) was measured. The relevant characteristics and nomenclature of the materials are summarized in Figure 2.3.

2.3.2

Determination of the Interfacial Width by Neutron Reflectivity

Figure 2.10 illustrates the volume fraction profi les of the deuterated polymer PB120K-D obtained from the best fit of the neutron reflectivity data.19 The captions indicate the various hydrogenated elastomer layers studied. Figure 2.10a illustrates the effect of changing the monomer composition, whereas Figure 2.10b illustrates the effect of changing the molecular weight at identical monomer composition. From these data

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Characterizations of the Polymers Used in the Study

PB420K-H PB120K-D SBR80K SBR160K SBR240K SBR 36% Sty EPDM PIB PDMS a b

Mn (g/mol)a

PDIa

% 1,2b

% Styreneb

420,000 130,300 83,000 139,800 213,100 153,100 115,200 172,000 1,000,000

1.1 1.09 1.03 1.08 1.13 1.09 3.18 2.39 —

<20 <20

— — 41 40 39 36 — — —

11 11 12 8 — — —

By triple detection SEC. By 1H nuclear magnetic resonance. 1.0

φPB120K-D

0.8

PDMS PIB EPDM SBR160K SBR 36% Sty

0.6

0.4

0.2

0.0 −200

−100

0 z (Å)

(a)

100

200

1.0

φPB120K-D

0.8

SBR160K SBR80K SBR240K

0.6

0.4

0.2

0.0 −150 (b)

−100

−50

0

50

100

150

z (Å)

FIGURE 2.10 Volume fraction of deuterated monomer as a function of distance along the interface for interfaces between a deuterated PB and various polymers: (a) various polymers with different monomer composition and (b) three SBR polymers with identical monomer composition but different molecular weights. (Schach, R., Tran, Y., Menelle, A., and Creton, C., Macromolecules, 40, 6325, 2007. With permission.)

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Fundamentals of Pressure Sensitivity TABLE 2.4 Interfacial Width, w, and Flory Parameter, χ, for Polymer–Polymer Interfaces

SBR 36% Sty SBR160K SBR240K SBR80K EPDM PIB PDMS Note:

w (Å)

Flory Parameter (χ)

204 ± 6 184 ± 10 165 ± 6 144 ± 10 82 ± 6 30 ± 7 16 ± 5

0.0023 ± 0.0006 0.0033 ± 0.0009 0.0033 ± 0.0009 0.0033 ± 0.0009 0.006 ± 0.002 0.04 ± 0.02 0.15 ± 0.05

The deuterated polymer is always PB120K-D.

characterizing the interfacial width, the interpenetration distance of the polymer chains can be calculated by subtracting the broadening due to capillary waves18,29 and the final results are summarized in Table 2.4. The expected variations of interfacial width with molecular weight are observed for the three SBR polymers with the same chemical structure (Figure 2.10b): the higher the molecular weight, the sharper the interface. Figure 2.4 summarizes the relevant characteristics of the interfaces studied here. The sharpest interface is the PDMS/PB interface, with an interpenetration width, w, of 16 Å and a very high Flory parameter value of 0.15. The PIB forms a wider interface with PB (with w = 30 Å), giving a monomer–monomer interaction parameter of 0.04. The order of magnitude of the EPDM interface (82 Å) is closer to the radius of gyration of the polymers (order of magnitude of 150 Å), with a χ of 0.006. SBR rubbers have the widest interfaces, with interpenetrations between 150 and 200 Å. The χ parameter for the three SBR 40% polymers with PB is 0.0033, two orders of magnitude less than the PDMS/PB. Finally, the SBR with a lower styrene content has the widest interface, with 204 Å, and a Flory parameter with PB of 0.0023. Th is result is consistent with the fact that the immiscibility between PB and SBR comes from the styrene part of the SBR.

2.3.3 Determination of the Adhesion Energy with Probe Tests From Section 2.1 it is clear that fracture mechanisms between two polymer melt layers in this geometry will vary for a range of interfacial widths and molecular weights of the linear polymers. In this study all mechanical tests were performed in a regime in which the deformed polymer is not flowing, that is, for average strain rates higher than the inverse of the terminal relaxation time of the polymer. In this case, two mechanisms of failure are observed: an interfacial crack propagation mechanism30,31 for weak interfaces and a bulk deformation32 of the layer(s) for strong interfaces. The adhesion energy for all the interfaces at thermodynamic equilibrium and the fracture energy of pure PB420K-H in contact with itself were measured with the probe tester apparatus described in the experimental section.17 To be certain that interfaces were at thermodynamic equilibrium, the same interface was tested with increasing contact

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4 2

1

PDMS PIB EPDM SBR160K SBR 36% Sty

8 6

σ (MPa)

4 2

0.1

8 6 4 2

0.01

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

ε

FIGURE 2.11 Stress–strain curves obtained with the probe test at room temperature and Vdeb = 100 µm/s for the interfaces between PB420K-H and polymers with different monomer compositions. (Schach, R., Tran, Y., Menelle, A., and Creton, C., Macromolecules, 40, 6325, 2007. With permission.)

times: at equilibrium the tack curves became independent of contact time. Equilibrium contact time values varied between 300 and 2000 s, depending on the polymer–polymer system. Figure 2.11 illustrates the nominal tensile stress–strain curves obtained for the adhesion measurement at thermodynamic equilibrium for a series of different interfaces. As discussed earlier, for a probe debonding velocity of 100 µm/s, the thick PB layer behaves like a viscoelastic solid and two types of debonding mechanisms can be observed: interfacial crack propagation (leading to a very sharp decrease in stress after the maximum) and bulk cavitation (which leads to a more progressive decrease in stress). The adhesion energy of PDMS on PB is very low, <1 J/m2. The PIB has a better adhesion (22 J/m2), but the fracture remains brittle and apparently completely interfacial, as determined by video observation, with very little bulk deformation of the PB layer (maximum strain of 0.2). The fracture of the EPDM/PB interface is less brittle and the PB layer is completely detached from the EPDM surface for a strain of ∼60%, with a beginning of bulk fracture and an adhesion energy of 77 J/m2. Finally, the four SBR/PB systems are characterized by a bulk fracture behavior: fracture occurred in the PB layer, not at the interface. The adhesion energy measured is very close to the fracture energy of the PB, 120 J/m2. Note that the high-molecular-weight SBR and the SBR 36% Sty curves demonstrate a pronounced tail in the deformation curve. Although it is tempting to attribute this difference to the interface, one should remember that it is the PB420K-H that deforms in these experiments. The difference is much more likely due to a slight difference in the temperature at which the test was carried out and should not be interpreted further.

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140

Cohesive fracture energy of PB420K-H

120

Wadh (J/m2)

100 80 60 40 20 0 0

50

100

150

200

250

w (Å)

FIGURE 2.12 Adhesion energy, Wadh, of interfaces between PB420K-H and different polymers as a function of the interpenetration width at the interface w. (Schach, R., Tran, Y., Menelle, A., and Creton, C., Macromolecules, 40, 6325, 2007. With permission.)

Although two different polymers were used for neutron reflectivity experiments and adhesion energy measurements, the chemical structure of the two PB was exactly the same, the only difference being the molecular weight. Knowing the molecular weights of all polymers and assuming that χ is independent of molecular weight, neutron reflectivity results on the PB120K-D can be used to calculate the theoretical interfacial width of the different polymers with the PB420K-H using Equation 2.2. The measured adhesion energy can then be represented as a function of the calculated interpenetration distance. This comparison is illustrated in Figure 2.12 and clearly demonstrates that the adhesion energy between the polymer layers depends strongly on the degree of interpenetration at the interface. Adhesion energy increases from a value of several joules per square meter for a very sharp interface (10 or 20 Å) to the PB fracture energy for interfaces larger than 150 Å. It is important to note for the significance of the comparison that all samples except PDMS were tested in these experiments at a strain rate, which corresponds to their rubbery plateau, as is the case for PB.

2.4 Discussion It is worthwhile to discuss these results more generally in light of the state-of-the-art techniques regarding adhesion at soft polymer–polymer interfaces. It has been known for quite some time that for fully miscible identical polymers, mutual interdiff usion at the interface would lead to higher mechanical strength.2–5,33–36

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However, the effect of forming entanglements by mutual interdiff usion on mechanical strength of the interface between polymers above their glass transition temperature had only been discussed theoretically, 33,37 but not studied experimentally to our knowledge and the required degree of interpenetration was not known. An analogous situation has been studied more extensively: the adhesion between an elastomer and a solid surface. In this case, one of the polymers is clearly above its glass transition temperature, and if the solid surface is also a polymer, it could be above or below its Tg. Classic studies38–41 for soft polymers on solid surfaces emphasized the role of surface energetics and noted the thermodynamic (reversible) work of adhesion as follows. Wrev
1  2  12

(2.4)

The measured work of adhesion could then be written as41 Gc
Wrev (1  (aTv))

(2.5)

where G c is the critical energy release rate and φ(aTv) is a multiplicative factor depending on the dissipative properties of the soft polymer. Th is classic result obtained for elastomers was later modified through the use of two important concepts: the role played by the interpenetration of polymer brushes and the possible existence of interfacial slippage. If the solid surface is functionalized with a layer of end-tethered chains that is fully miscible with the soft polymer, the extraction of the chain from the polymer during debonding contributes significantly both to the measured G c and to the dissipative component φ(aTv), which is, however, still represented as a multiplicative factor.42,43 Interfacial slippage is important because the surface acts as a boundary condition and if the surface is unable to sustain shear forces, the dissipative shear deformation in the polymer layer during debonding is greatly diminished, reducing the multiplicative factor φ(aTv) for the same values of Wrev and the same rheological properties of the polymer. The groups of Chaudhury and Leger, in particular, demonstrated that resistance to interfacial slippage could be more important than surface energetics and dominates the macroscopic adhesive behavior44–48 and, therefore, Gc. For very soft elastomers or polymer melts, however, the measurement of Gc as a purely interfacial property becomes difficult because failure does not occur by crack propagation, but by a much more complex deformation pattern involving fi ngering instabilities and the formation of fibrils49 that cannot be easily separated from the experimental geometry. In this regime, the best way to compare the adhesive strength of different interfaces is therefore to measure the total work of detachment in the same experimental geometry. This parameter is defined here as Wadh. Few studies of these very soft polymers exist and either focus on surface thermodynamics changes50,16 or report only qualitative results.51 In the recent study summarized here, the interpenetration of polymer chains at the interface acts by modifying the boundary condition at the interface: the deeper the interpenetration is, the higher the interfacial stresses that can be sustained by the interface.

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This result has some interesting implications. For high-molecular-weight polymers in the strong segregation limit, the interfacial width between two polymers, 1 and 2, varies as 1/γ12. From the results of Figure 2.12, one expects Gc to vary approximately as the inverse of the interfacial tension.29 This result is directly at odds with Equation 2.2. Because typically the surface tensions are much larger than the interfacial tension, Equation 2.2 would predict a high adhesion between two very immiscible but high-surface-tension polymeric fluids and, on the contrary, a low adhesion between two nearly miscible but low-surface-tension fluids. The point that interpenetration favors adhesion is not new. However, this study demonstrates that, for interfaces between immiscible polymers, it is best to think in terms of transition from a Wrev-dominated regime (for high values of χ) to a γ12 dominated regime (for low values of χ ). For the weaker interfaces failing by interfacial crack propagation, Wadh ∼ Gc, and fracture mechanics concepts can be used to illustrate this point more accurately. Webber and coworkers30 proposed a model to describe the failure of a joint between a confined elastic material and a rigid substrate in the case of an interfacial failure at relatively low strains. This model, well adapted to describe experimental adhesion measurements, gives a relationship between the critical energy release rate Gc (characteristic of the resistance to interfacial crack propagation) and the failure average strain ε* (easily measured on the tack curves),

G *
 c   Eh 

1/ 2

(2.6)

with E representing Young’s modulus of the material and h the thickness of the layer. It can be used here to estimate Gc for three of our samples, PDMS, PIB, and EPDM, which indicate an interfacial failure mechanism. Using Equation 2.4 and the fact that the interfacial tension, γ1,2, is directly related to the interface width, one obtains the following.

1,2
kT
a

kT
a2
6 6w

(2.7)

Wrev can be estimated by the neutron reflectivity measurement to calculate the interfacial tension of the polymer–polymer interfaces and data from the literature for the surface energy of the polymers. Figure 2.13 illustrates the calculated Gc value versus the thermodynamic work of adhesion Wrev . There is no obvious direct correlation between the thermodynamic work of adhesion and the measured Gc. A second point that is interesting to discuss is the extent of interpenetration necessary to obtain a high mechanical strength. The fracture toughness between glassy polymers increases with interpenetration until it reaches the bulk fracture energy for an interpenetration value, which varies with the experimental system from 0.5 to 1.5 times the average distance between entanglements, de, in the bulk polymers.36,52 Figure 2.12 demonstrates that, for polymer melts, the increase in adhesion energy with interpenetration figure is more progressive and the maximum adhesion energy is

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Diffusion and Adhesion

14 12

Gc (J/m2)

10 8 6 4 2 0 0

10

20

30

40

50

60

70

Wrev (mJ/m²)

FIGURE 2.13 Gc estimated from the probe test curves and Equation 2.6 versus Wrev. (Schach, R., Tran, Y., Menelle, A., and Creton, C., Macromolecules, 40, 6325, 2007. With permission.)

achieved for a deeper interpenetration than de: the order of magnitude of the entanglement spacing is 20 Å for PB and 30 Å for the other polymers and the maximum value is achieved for an interpenetration of 150 Å equivalent to four to five entanglement lengths and comparable to the radius of gyration of the polymers. These results are also consistent with the theoretically proposed argument 33,37 that, for polymer melts, the adhesion energy should reach its saturation value when the interpenetration distance becomes of the order of the radius of gyration of the polymers and the degree of entanglement at the interface is the same as that in the bulk. This prediction follows from the fact that the force to extract a polymer chain in the melt should increase continuously with molecular weight because entanglements play a lesser role in transferring stress than in the glassy state. For very high-molecular-weight polymers or temperatures close to Tg, chain fracture rather than chain extraction may occur and modify this result, defining then a critical interpenetration distance for optimum toughness that is lower than the radius of gyration of the chains. The situation would then become closer to that of polymer glasses.

2.5 Conclusion The tack of uncross-linked polymer melts depends strongly on the De, defined as the ratio of the average strain rate applied to the polymer over its terminal relaxation time. Failure mechanisms can vary from a viscoelastic fluid fracture mechanism, where fracture is initiated by cavitation of only one or two large cavities and can then be modeled with a fluid mechanics approach, to an elastic, rubber-like mechanism in which fracture is initiated by cavitation in an elastic medium (at a stress well correlated to the elastic

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Fundamentals of Pressure Sensitivity

modulus of the rubber) followed by melt fracture in the filaments formed during separation. The transition from one type of mechanism to the other is observed when De > ∼3. For the increased tack between identical uncross-linked polymers due to molecular interdiff usion, the following results can be emphasized. 1. If the polymer is a viscoelastic fluid, the strength of the interface does not play a very important role and the fracture energy is independent of contact time. 2. For De > 3, two situations arise: a. For contact times much shorter than the reptation time of the polymer, the interface is the weak point in the assembly and the failure mechanism is cavitation at the interface, followed by the propagation of these cavities as interfacial cracks. This mechanism can be well described by a viscoelastic fracture mechanism analogous to the failure of interfaces between cross-linked rubbers. b. For contact times of the order of the reptation time of the polymer, the chains have time to interdiff use and the interface chains by bulk fracture, giving a higher value of tack if the molecular weight of the polymer is higher. In regime 2, the key aspect to understanding polymer tack is the compromise between the mechanical strength of the interface (optimum for long, well-entangled chains) and the fast build-up of strength (optimum for short very mobile chains). The situation that is more relevant for PSA interfaces is that of partially miscible polymers. The degree of interpenetration no longer depends on interdiff usion times (for times longer than the reptation time), but is a thermodynamic property. For these interfaces, the most important factor controlling tack is the degree of interpenetration at the interface. This result can be connected with theories based on wetting, in which surface energies of the two polymers chiefly determine the work of adhesion. Whenever the Flory χ parameter between two polymers is below 0.05, the mechanical strength of the interface between the polymers in the molten state will roughly increase with χ−1/2 until the interpenetration width reaches a value of the order of the radius of gyration of the polymers. The second important result from the experimental study relates to the mechanical strength one can expect from entanglements in the melt. The level of interpenetration necessary to retrieve the bulk strength of the interface between two polymer melts is of the order of several entanglements, rather than one entanglement, as in polymer glasses. This result is not unexpected because chains can be extracted much more easily from polymers above their glass transition temperature than from glasses.

References 1. Voyutskii, S. S. and V. L. Vakula, The role of diff usion phenomena in polymer to polymer adhesion, J. Appl. Polym. Sci. 7: 475–491, 1963. 2. Jud, K., H. H. Kausch and J. G. Williams, Fracture mechanics studies of crack healing and welding of polymers, J. Mater. Sci. 16: 204210, 1981. 3. Prager, S. and M. Tirrell, The healing process at polymer-polymer interfaces, J. Chem. Phys. 75(10): 5194–5198, 1981.

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4. Kausch, H. H. and M. Tirrell, Polymer interdiff usion, Annu. Rev. Mater. Sci. 19: 341–377, 1989. 5. Wool, R. P., B. L. Yuan and O. J. McGarel, Welding of polymer interfaces, Polym. Eng. Sci. 29(19): 1340–1367, 1989. 6. Wool, R. P., Molecular aspects of tack, Rubber Chem. Technol. 57: 307–319, 1984. 7. Wool, R. P. (1991). Welding, tack, and green strength of polymers. L. H. Lee (eds). in: Fundamentals of Adhesion. Plenum Press. 8. Arzondo, L. M., N. Pino, J. M. Carella, J. M. Pastor, J. C. Merino, J. Póveda and C. Alonso, Sequential injection overmolding of an elastomeric ethylene-octene copolymer on a polypropylene homopolymer core, Polym. Eng. Sci. 44(11): 2110–2116, 2004. 9. Zhang, J. B., T. P. Lodge and C. W. Macosko, Interfacial slip reduces polymerpolymer adhesion during coextrusion, J. Rheol. 50(1): 41–57, 2006. 10. Hamed, G. R., Tack and green strength of elastomeric materials, Rubber Chem. Technol. 54: 576–595, 1981. 11. Hamed, G. R. and C. H. Shieh, Flow criterion for elastomer tack, Rubber Chem. Technol. 55(5): 1469–1481, 1982. 12. Hamed, G. R. and C. H. Shieh, Relationship between the cohesive strength and the tack of elastomers, J. Polym. Sci., Polym. Phys. Ed. 21: 1415–1425, 1983. 13. Hamed, G. R. and C. H. Shieh, Relationship between the cohesive strength and the tack of elastomers: part II, contact time effects, Rubber Chem. Technol. 58: 1038–1044, 1985. 14. Hamed, G. R. and C. H. Shieh, Relationship between the cohesive strength and tack of elastomers: part III, various elastomer types, Rubber Chem. Technol. 59(5): 883–895, 1986. 15. Gent, A. N. and H. J. Kim, Effect of contact time on tack, Rubber Chem. Technol. 63: 613–623, 1990. 16. Zosel, A., Adhesion and tack of polymers: influence of mechanical properties and surface tensions, Colloid Polym. Sci. 263: 541–553, 1985. 17. Lakrout, H., P. Sergot and C. Creton, Direct observation of cavitation and fibrillation in a probe tack experiment on model acrylic pressure-sensitive-adhesives, J. Adhesion 69(3/4): 307–359, 1999. 18. Schach, R. and C. Creton, Adhesion at interfaces between highly entangled polymer melts, J. Rheol. 52(3): 749–767, 2008. 19. Schach, R., Y. Tran, A. Menelle and C. Creton, Role of chain interpenetration in the adhesion between immiscible polymer melts, Macromolecules 40: 6325–6332, 2007. 20. Karim, A., G. P. Felcher and T. P. Russell, Interdiff usion of polymers at short times, Macromolecules 27: 6973–6979, 1994. 21. Gent, A. N., Elastic instabilities in rubber, Int. J. Non-Linear Mech. Special Issue in Honour of C.O. Horgan 40(2–3): 165–175, 2005. 22. Poivet, S., F. Nallet, C. Gay and P. Fabre, Cavitation-induced force transition in confined viscous liquids under traction, Europhysics Lett. 62(2): 244–250, 2003. 23. Poivet, S., F. Nallet, C. Gay, J. Teisseire and P. Fabre, Force response of a viscous liquid in a probe-tack geometry: fingering versus cavitation, Eur. Phys. J. E 15: 97–116, 2004.

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24. Helfand, E. and Y. Tagami, Theory of the interface between immiscible polymers II, J. Chemical Phys. 56(7): 3592–3601, 1971. 25. Broseta, D., G. H. Fredrickson, E. Helfand and L. Leibler, Molecular weight and polydispersity effects at polymer-polymer interfaces, Macromolecules 23: 132–139, 1990. 26. Guckenbiehl, B., M. Stamm and T. Springer, Interface properties of blends of incompatible polymers, Phys. B 198: 127–130, 1994. 27. Stamm, M. and D. W. Schubert, Interfaces between incompatible polymers, Annu. Rev. Mater. Sci. 25: 325–356, 1995. 28. Agrawal, G. and R. P. Wool et al., Interdiff usion of polymers across interfaces, J. Polym. Sci.: Part B: Polym. Phys. 34: 2919–2940, 1996. 29. Jones, R. A. L. and R. W. Richards, Polymers at Surfaces and Interfaces. Cambridge, Cambridge University Press, 1999. 30. Webber, R. E., K. R. Shull, A. Roos and C. Creton, Effects of geometric confinement on the adhesive debonding of soft elastic solids, Phys. Rev. E 68: 021805, 2003. 31. Josse, G., P. Sergot, M. Dorget and C. Creton, Measuring interfacial adhesion between a soft viscoelastic layer and a rigid surface using a probe method, J. Adhesion 80(1–2): 87–118, 2004. 32. Lakrout, H., C. Creton, D. Ahn and K. R. Shull, Influence of molecular features on the tackiness of acrylic polymer melts, Macromolecules 34: 7448–7458, 2001. 33. Wool, R. P., Polymer Interfaces. Munich, Hanser Verlag, 1995. 34. Schnell, R., M. Stamm and C. Creton, Direct correlation between interfacial width and adhesion in glassy polymers, Macromolecules 31: 2284–2292, 1998. 35. Schnell, R., M. Stamm and C. Creton, Mechanical properties of homopolymer interfaces: transition from simple pullout to crazing with increasing interfacial width, Macromolecules 32(10): 3420–3425, 1999. 36. Creton, C., E. J. Kramer, H. R. Brown and C. Y. Hui, Adhesion and fracture of interfaces between immiscible polymers: from the molecular to the continuum scale, Adv. Polym. Sci. 156: 53–136, 2002. 37. Aradian, A., E. Raphael and P. G. de Gennes, A scaling theory of the competition between interdiff usion and cross-linking at polymer interfaces, Macromolecules 35(10): 4036–4043, 2002. 38. Gent, A. N. and J. Schultz, Effect of wetting liquids on the strength of adhesion of viscoelastic materials, J. Adhesion 3: 281–294, 1972. 39. Andrews, E. H. and A. J. Kinloch, Mechanics of adhesive failure I, Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 332: 385–399, 1973. 40. Andrews, E. H. and A. J. Kinloch, Mechanics of adhesive failure II, Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 332: 401–414, 1973. 41. Maugis, D. and M. Barquins, Fracture mechanics and the adherence of viscoelastic bodies, J. Phys. D: Appl. Phys. 11: 1989–2023, 1978. 42. Creton, C., H. R. Brown and K. R. Shull, Molecular weight effects in chain pullout, Macromolecules 27: 3174–3183, 1994. 43. Deruelle, M., L. Léger and M. Tirrell, Adhesion at the solid-elastomer interface: influence of the interfacial chains, Macromolecules 28: 7419–7428, 1995.

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Diffusion and Adhesion

2-23

44. Zhang Newby, B.-M., M. K. Chaudhury and H. R. Brown, Macroscopic evidence of the effect of interfacial slippage on adhesion, Science 269: 1407–1409, 1995. 45. Zhang Newby, B.-M. and M. K. Chaudhury, Effect of interfacial slippage on viscoelastic adhesion, Langmuir 13(6): 1805–1809, 1997. 46. Chaudhury, M. and B.-M. Zhang Newby, Friction in adhesion, Langmuir 14: 4865–4872, 1998. 47. Amouroux, N., J. Petit and L. Léger, Role of interfacial resistance to shear stress and adhesive peel strength, Langmuir 17: 6510–6517, 2001. 48. Léger, L. and N. Amouroux, Modulation of adhesion at silicone elastomer-acrylic adhesive interface, J. Adhesion 81(10–11): 1075–1099, 2005. 49. Shull, K. R. and C. Creton, Deformation behavior of thin compliant layers under tensile loading conditions, J. Polym. Sci.: Part B: Polym. Phys. 42: 4023–4043, 2004. 50. Toyama, M., T. Ito, H. Nukatsuka and M. Ikeda, Studies of pressure-sensitive adhesive tapes: on the relationship between pressure-sensitive adhesion and surface energy of adherends, J. Appl. Polym. Sci. 17: 3495–3502, 1973. 51. Costa, A. C., A. Chiche, P. Vlcek, C. Creton and R. J. Composto, Adhesion promotion between a homopolymer probe and a glass substrate coated with a block copolymer monolayer, Polymer 45(13): 4445–4451, 2004. 52. Benkoski, J.-J., G. H. Frederickson and E. J. Kramer, Model for the fracture energy of glassy polymer-polymer interfaces, J. Polym. Sci.: Part B: Polym. Phys. 40(20): 2377–2386, 2002.

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3 Transition Zones in Adhesive Joints 3.1 Introduction .............................................................3-1 3.2 Classification of Adhesives and Transition Zones ............................................. 3-3

Anatoly E. Chalykh Anna A. Shcherbina A.N. Frumkin Institute of Physical Chemistry and Electrochemistry

Structure-Mechanical Transition Zones • Structure-Gradient Transition Zones • Concentration Gradient Transition Zones • Combined Transition Zones

3.3 Conclusions ........................................................... 3-29 References ....................................................................... 3-30

3.1 Introduction There exist only a few physicochemical phenomena that are as multiform as the phenomenon generally referred to as adhesion. Sufficiently strong and stable interfacial adhesive bonds between adhesive and substrate layers ensure successful adhesive performance of various composite materials, reinforced plastics, glues, and paint and varnish protective coatings, as well as polymer blends. Numerous fundamental and applied studies, as well as experimental and theoretical investigations, demonstrate that the differences in the strength of adhesive joints can be accounted for by the nature of contacting phases, the composition and the structure of the substrate and adhesive, the thickness of the adhesive layer, the contact area, and the roughness of substrate surface, as well as bonding and debonding conditions [1,2]. In his works [3,4], Deryaguin repeatedly emphasized the duality of the meaning of the term of adhesion. He wrote, “On the one hand, adhesion is generally understood as a process resulting in establishment of a bond between two bodies, and the bond failure requires application of external force. On the other hand, a debonding process is often considered, and the energy required to separate the contacting bodies is taken as a quantitative measure of the strength of adhesive interaction.” To eliminate this ambiguity, Deryaguin suggested the term sticking when referring to the “process of establishment and progressive development of interfacial intermolecular bond with time, whereas the term ‘adhesion’ should be used to designate the achieved 3-1

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3-2

Fundamentals of Pressure Sensitivity

strength of this bonding.” Therefore, according to Deryaguin, sticking refers to a process of adhesive bond formation, whereas adhesion is a quantitative measure of the result of this process. This viewpoint is generally accepted, with a slight refi nement—sticking is considered a process of contact formation between the adhesive and substrate, or in other words, the process of transition zone formation between the adhesive and substrate, whereas adhesion is the course of debonding of adhesive joints [5–8]. Adhesion theories are classified in compliance with these concepts. On the one hand there are theories that examine the mechanisms of contact formation between the adhesive and substrate phases; on the other hand there are theories describing the regularities of joint fracture mechanics [5]. At the Institute of Physical Chemistry, Russian Academy of Sciences, the fi rst direction of investigations is represented by the successful works of Deryaguin et al. [1], Arslanov and Ogarev [9], and Rudoi and Ogarev [10]; and the second direction is represented by the works of Zubov and Sukhareva [11], Deryaguin and Toporov [12]. When discussing the concepts mentioned above, Deryaguin pointed out the necessity of working out techniques allowing the study of the process of adhesive joint formation without fracture of adhesive joint. At the time when the monograph Adhesion of Solids [3] was published, Deryaguin referred to this task as an unresolved problem. However, in our opinion, even at that time, a range of single attempts was undertaken in the studies performed by Voyutskii et al. [13] and in certain works of Krotova and colleagues [3,14,15] to gain information on the structure and morphology of transition zones in polymer systems. Meanwhile, the majority of investigations were and are still aimed at the resolution of the inverse problem based on using the data from adhesive debonding to restore the structure of transition zone and to propose a mechanism of adhesive joint formation [16,17]. A transition zone arises spontaneously upon contact of an adhesive film with the surface of a substrate. In real adhesive joints the transition zone includes an interphase adhesive–substrate boundary, an area of interdiff usion, layers of adhesive and substrate phases with changed structure or composition, phase inhomogeneities, and nonuniformities in the relief of phase surfaces, impurities, defects, air bubbles, etc. The transition zone includes a weakened material layer with a mechanical strength that is lower than the cohesive strength of any of the contacting phases, defined by Bikerman [18] as the weak layer. Thus, in the electronic theory of adhesion, for example, the transition zone was considered a superposition of the adhesive–substrate interphase boundary and a double electrical layer [3]. In the adsorption theory of adhesion the interfacial zone was identified with “interphase boundary layers” [19,20]. In diff usion theory, for compatible adhesive–substrate systems the transition zone was treated as the zone of mutual diffusion of polymer segments, migrating through the interphase boundary [21,22], whereas in the case of incompatible polymer systems it was referred to as the zone of solubility of macromolecular segments belonging to the adhesive and substrate phases [23]. None of these studies presented direct experimental evidence in favor of one or another mechanism controlling the formation of transition zone, and many works contain no data on the nature and topography of interphase surface, crack localization, or type and mode of crack propagation.* * Stable brittle, unstable brittle, and stable plastic deformation [5].

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Transition Zones in Adhesive Joints

3-3

In summary, it can be claimed that the transition zone, formed as the result of substrate–adhesive interaction, is one of the key elements of the adhesive joint. It accounts for the state of the substrate surface, the phase state of the adhesive joint, and the ability of the components to interpenetrate each other and form chemical or intermolecular interfacial bonds, etc. It is within the transition zone that various defects are generated; its phase composition and supramolecular structure define the strength of adhesive bonds, the mechanism of adhesive material deformation under debonding stress, and the path of crack propagation.

3.2 Classification of Adhesives and Transition Zones Among the many currently suggested classifications of adhesives and adhesive joints, the predominant classifications are based on one of the following criteria: chemical structure of polymer, target use, procedure of joint formation, phase state, and structure of substrate [5,24,25]. In terms of the chemical nature of monomer units and molecular weight characteristics of the components, it is common practice to identify the adhesives based on monomers, oligomers, and polymers [26,27]. In Refs 26 and 28, the authors suggested classification of the same adhesives by another property, relating them either to thermoplastic or to thermosetting materials. Another classification is based on the methods used to build up adhesive joints [29–31]. The following adhesives are distinguished: cold curable and anaerobic; heat and radiation curable; solution and hot melt; and water borne. The classification of adhesives by nature of the bonded materials and the conditions of their service should be also recognized as widespread. For instance, specific adhesives are high-temperature proof, stable at low temperatures and high humidity, thermal shock resistant, or fire resistant [26] (see also Applications of Pressure-Sensitive Products, Chapter 4). At the same time, it is also possible to identify adhesives for metals, plastics, rubbers, textiles, cord fabric, leather, paper, and wood [5,32]. The same features form a basis for differentiating between, for example, engineering adhesives for the aerospace and automotive industry and adhesives for producing solar-battery cells, medical patches and dressings, etc. [26] (see also Applications of Pressure-Sensitive Products, Chapter 4). In recent years, a specific group of pressure-sensitive adhesives (PSAs) has been formed [27,33]. The group includes polymers that are generally in a viscoelastic state during application, as well as under performance conditions. The adhesives in the other groups are in a viscous-flow state over the course of adhesive joint formation. Later, they transform into crystalline, glassy, or high-elastic solid-like states, where they stay under operation conditions. Another distinguishing feature of PSAs is their ability to remain tacky even after debonding; therefore, they are sometimes referred to as ever-tacky adhesives (see also Applications of Pressure-Sensitive Products, Chapter 7). PSAs are traditionally designed using common polymers (elastomers and viscoelastomers), such as natural rubber (NR), butadiene–styrene, and butadiene–nitrile copolymers, polyisobutene, acrylics, and polymer and oligomer blends. Meanwhile, the effect of ever-tackiness is achieved by rational choice of polymer molecular weights and usage of special additives, such as adhesion promoters or tackifiers [26,29] (see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 7).

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3-4

Fundamentals of Pressure Sensitivity

However, none of the suggested classifications of adhesives takes into account the structure and phase nature of transition zones. This is understandable because the tasks of material science and engineering fi rst require determination of the type of adhesive that is defined by the nature of bonded or welded materials, as well as the conditions of adhesive joint formation and service. The tasks concerned with the identification of transition zone structure usually gain priority at the second stage of the research, when it becomes necessary to develop the design of the adhesion joint, forecast its behavior under various processing and operation conditions, and optimize a formulation. Attempts to classify transition zones of adhesive joints have been undertaken repeatedly. Lipatov [20] suggested the use of morphological characteristics of the adhesive– substrate interface as the key feature of faceted classification, with many objects divided into two major groups. The first group should include the systems with the transition zone represented by two layers, divided by a boundary surface, which differ by morphology from the polymer in the bulk and have uniform chemical composition. The second group should be formed of systems with a transition layer of nonuniform composition, represented by a spontaneously forming emulsion of one polymer within the other polymer. According to Lipatov [20], the mechanism of transition zone formation in the systems of first group should be defined as thermodynamic, whereas the mechanism in the second group is colloid chemical. Vakula and Pritykin [34] also discussed faceted classification of transition zones, but in doing so, they noted three independent features—composition diff usivity, conformational inhomogeneity, and layer-by-layer distribution of chain packing density. The authors of Ref. 35 took virtually the same point of view in discussing “structure heterogeneities at the melt–substrate interface that propagate to the depth exceeding 400 µm; the orienting impact of the substrate; increase in concentration of more stable conformer; redistribution of copolymer units and admixtures near the interphase boundary.” However, when describing a vast variety of adhesive systems and materials, the specified classification features are insufficient. Therefore, in Refs 36–38, a complicated faceted hierarchical classification was developed, in which parallel grouping of a vast array of objects into independent classes is supplemented by sequential division of materials into subordinate subclasses. The structural and morphological characteristics of transition zones represent the basic classification features of independent classes. Researchers suggested distinguishing the following types of systems: structure-mechanical, structure-gradient, concentration-gradient, and systems of complex or composite structure. Within each of these classes, one can make further divisions according to other criteria, such as the phase or physical state of adhesive joint elements, the number of components, topological and conformational parameters of macromolecular chains, the degree of nonequilibrium, types of defects and distribution across the transition zone, etc. This classification has two important properties. First, it takes into account the basic processes that occur during the formation of adhesive joints in many systems. Second, it presents information on specific features of the internal structure of the adhesion contact zone that are eventually responsible for the deformation and strength parameters of adhesive joints.

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3-5

Transition Zones in Adhesive Joints

~ ~ 5 nm

~ ~ 40 nm

~ ~ 5 nm

Substrate (a)

Substrate (c)

Adhesive Oxide layer

(b)

Substrate

(d)

Substrate

FIGURE 3.1 Schematic drawing of the oxide layer (a) at the surface of the aluminum alloy (substrate) and consecutive stages of adhesive joint formation (b, c), and breaking (d) during peeling.

3.2.1 Structure-Mechanical Transition Zones This class of transition zones is distinguished by a discrete porous structure of the substrate (or its element*). Geometric parameters of this porous structure, such as the size and shape of pores and the state of the interphase boundary with the environment, usually remain unchanged during observation (i.e., in the course of adhesion joint formation and its performance). The adhesive is an amorphous high-molecular-weight compound that is thermodynamically incompatible with the substrate (or its element). The adhesive changes its physical or rheologic state in the process of joint formation [26,27]. For example, in hotmelt adhesive joints, the viscous-flow state of the adhesive transforms into a high-elastic or glassy state; for PSAs, the viscous-flow state converts into a rubber-like state, etc. The pattern of substrate porous structure, depending on the substrate nature, the method of manufacturing, and the target use, may differ. Thus, the substrate can reveal either the system of blind pores located at its interface layer or the structure of interconnected pores with chaotic or regular packing. As an example, Figure 3.1 illustrates schematically the structure of oxide layers at the aluminum alloy interface, and Table 3.1 presents topographic parameters of the surface of copper foil substrates. The procedure for obtaining a porous structure of epoxy substrate by powder sintering with subsequent grinding is described in Ref. 39. Various methods of different efficiency have been developed for treating the substrate surface to obtain layers with target relief, grade of roughness, and porosity. The most wide-spread methods are grinding; blast cleaning and sandblasting; chemical etching; and thermal, plasma, and electrochemical deposition of metals [5,30,40]. Electron microscopy, electron microprobe x-ray analysis, x-ray photoelectron spectroscopy, and ion probes were used to demonstrate that each of the above-mentioned methods leads not only to the formation of specific microrelief (see Table 3.1), but also to the appearance of functional groups of various natures at the surface. These groups are frequently used to regulate adsorption interaction between the adhesive and substrate. * For example, macroscopic oxide layers, specially formed at substrate surface [36].

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Fundamentals of Pressure Sensitivity

TABLE 3.1 Energy of Fracture (G) of Adhesive Joints between Electrochemically Deposited Foil and Epoxy Laminate during Peeling Surface Topography of Copper Foil Relief

Schematic Profile

G (kJ/m2)

Flat copper surface

0.66

Same with dendrites 0.3 µm high

0.67

Same with dendrites 0.3 µm high + oxidation

0.77

Acute-angled pyramidal copper ridges 3 µm high

1.0

Obtuse-angled pyramidal copper ridges 2 µm high with dendrites 0.3 µm high

1.3

Same + oxidation

1.5

Acute-angled pyramidal copper ridges 3 µm high with dendrites 0.3 µm high + oxidation

2.4

Nickel foil with club-shape nodules along its interface

2.3

The basic mechanism of transition zone formation for this class of substrates involves rheological fi lling of the porous structure at the substrate surface using viscous-flow adhesive. The stages of this process are schematically illustrated in Figure 3.1. It was reported in Ref. 41 that effective concentration profi le over the section of transition zone can be experimentally obtained with electron microscopy using the “wide screen” technique at comparatively small magnification and large observation area. Contrary to the transition zones of diff usion-gradient type, in which each iso-concentration plane changes its space position, in the structure-mechanical transition zones a similar change can be observed at the front-face part of the concentration profi le only. The rest of the profi le remains invariable with time. This feature seems to play a major role in the identification of the mechanism of contact formation between conjugated phases rather than the growth kinetics of adhesive joint strength. It is conventional to assume that fi lling a porous structure with adhesive results in its “mechanical coupling, seizure with rough edges of substrate surface (Figure 3.1 and Table 3.1)” and “increase in surface area of interphase contact” [42]. According to the mechanical interlocking theory, these effects represent a major strength-controlling factor in the adhesive interaction between joint components. Within the framework of the Washborn approach, Equation 3.1 was proposed [42] to describe the kinetics of the

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3-7

Transition Zones in Adhesive Joints

change of contact area, S, during joint formation between the substrate and adhesive, S
 2d 2

Pt 

(3.1)

where η is adhesive viscosity, d is average pore diameter, t is time, and P is pressure. It was reported in Ref. 43 that the rate of wetting of the voids of substrate relief with diameter d can be expressed by an empirical exponential relationship, d
d (1  t  )2

(3.2)

where α and τ are numerical constants and d∝ is the pore size at t∝. It follows from these equations that the change in the strength of adhesive joint, A, is determined by the expressions A ≅  2d 2

Pt ∑ (Eini ) and A  A0 A  A
et  

(3.3)

where Ei is the adhesive bond energy and ni is the number of ith type links per unit area of interphase contact. Multiple studies demonstrate that Equations 3.3 present a satisfactory description of a large body of experimental data, involving both mechanical and chemical treatment of the substrate surface [5,42]. Equation 3.1 underlies the so-called rheological theory of adhesion, whereas Equations 3.3 represent the basis of a “rheoadsorption” theory of adhesion. The latter theory is capable of predicting trends in the behavior of adhesive strength under the change in both environmental conditions and the nature of interphase surfaces. Nevertheless, other points of view exist on the role of mechanical treatment of the substrate surface, grade of roughness, and interlocking in adhesive–substrate interactions. First, observed strengthening of the adhesive joint relates to the removal of weak surface layers, impurities, and defects [5,23]. Second, the grade of roughness manifests itself in the formation of a “microfibrillar” structure in the adhesive layer that results, in turn, in increased energy dissipation within the zone of plastic deformation during the fracture of this class of adhesive joints [44,45] (see also Applications of Pressure-Sensitive Products, Chapter 7). Finally, it is time to abandon predominant erroneous ideas of porosity as “the cause of infinitely high polymer adhesion towards porous substrates” [5]. This concept contradicts the results obtained in Ref. 33, which demonstrated that upon certain limiting depth of pore impregnation, or porosity exceeding some critical value, subsequent impregnation makes no sense, because with depths greater than the critical L cr value, cohesive failure (Аcoh) occurs in bulky polymers. Arslanov [36] offered a criterion allowing the definition of the relationship between the strength and the geometric parameters of this type of adhesive joints: Acoh Lcr  A R

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(3.4)

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3-8

Fundamentals of Pressure Sensitivity

where R is the pore radius and A is the shear strength of a system polymer–pore wall. As follows from Equation 3.4, at Аcoh ≅ А, a pillar of interlocked adhesive pulled out of the pore will have length of the order of the pore radius. The size of the structure– mechanical transition zone seems to be confi ned to the length indicated.

3.2.2

Structure-Gradient Transition Zones

The distinguishing feature of this class of adhesive joints is spontaneous formation of specific phase organization or supramolecular structure in adhesives (or in adhesives and substrates simultaneously), near the interphase boundary in thermodynamically incompatible systems. This structure differs from the structures in the bulk of coupled components. In addition, element and chemical composition of the components remains unchanged over the whole zone, with its gradient pattern caused only by the change in structure-morphological and conformational parameters of polymer components in adhesive joints. Examples illustrating the structure-gradient zones in adhesive joints with crystallizable, liquid crystalline (LC), and amorphous adhesives are presented in Figure 3.2. Near interfaces with high-energy substrates, crystallizable adhesives [polyolefins, polyamides, polyurethanes, polytetrafluoroethylenes (PTFEs), etc.] form extended transcrystalline (columnar) or lamellar layers, whereas their interior part in the bulk is spherulitic (Figure 3.2). The thickness of these zones often exceeds 10 µm and can be as large as ~100 µm, if formed under special conditions (e.g., between two substrates) [36,43]. Mechanical and sorption properties, permeability, and surface characteristics of these layers differ from those in the bulk.

120 µm

a

Crack

b

FIGURE 3.2 Optical microphotograph of the structure-gradient zone in the PE–aluminum system: (а) spherulites and (b) transcrystalline structure.

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3-9

Transition Zones in Adhesive Joints

TABLE 3.2 Crystallinity (φ), Surface Tension (γ), and Phase State of Epitaxial Layers of Crystalline Polymers Adhesive Polyethylene

Nylon-6,6 Poly(chlorotrifluoroethylene) Poly(tetrafluoroethyleneco-hexafluoropropylene) Isotactic PP Atactic PP

Substrate Nitrogen PTFE PET Nickel Titan Aluminum Glass Chrome Gold Gold Gold Copper Gold Gold

φ (%) 0 0 0 53.3 60.1 63.2 63.2 66.2 93.6 100 100

γ20 (mJ/m2)

Phase State

36.2 36.2 36.2 51.3 53.8 54.9 54.9 56.1 69.6 74.4 58.9

Spherulite Spherulite Spherulite Transcrystalline Transcrystalline Transcrystalline Transcrystalline Transcrystalline Transcrystalline Transcrystalline Transcrystalline

95

37.4

Transcrystalline

100 0

39.5 28.0

Transcrystalline Domains

Source: Wu, S. in Polymer Blends (Paul, D.R. and Newman, S., Eds.), Vol. 1, Academic Press, New York, 1978. With permission.

It was determined in Refs 43, 46, and 47 that the structure of transcrystalline layers was inhomogeneous. Epitaxial layers that are in direct contact with substrate surfaces have the most ordered structure (the highest crystallinity). As illustrated in Table 3.2, different surfaces can produce different crystallinity degrees. Thus, for low-energy surfaces [PTFE and polyethylene terephthalate (PET)] the crystallinity degree tends to zero, whereas for high-energy substrates (glass, metals) the crystallinity turns out to be very large for many polymers of different chemical composition. As the distance from the surface increases, the orthogonal orientation of lamellar layers and flat spherulites degenerates, their sizes decrease, and their structure transforms to spherulitic (Figure 3.2). There are two approaches to explaining the formation mechanism of transcrystalline and epitaxial layers. The first is based on information regarding the change in the conformational set of macromolecular chains in the adsorption monolayer, followed by the formation of specifically oriented crystallites → lamellas → flat spherulites that form the macroscopic structure-gradient transition zone [35]. The second approach implies that transcrystalline layers appear in cases when the substrate surface initiates the formation of a large number of nucleation centers close to each other, which results in the intergrowth of crystalline areas at right angles to the surface [43]. The efficiency of substrate surfaces is assessed, in the first case, in terms of their adsorption activity (member Σ(Eini) in Equation 3.3), whereas in the second case it is assessed in terms of its nucleating capability [47]. For example, a transcrystalline structure can be formed if the rate of heterogeneous nucleation is higher than the nucleating capability of the polymer itself. Otherwise, these spherulites are formed in subsurface layers. Fracture-mechanical studies present evidence that the failure of adhesive joints with transcrystalline transition layer occurs at a significant distance from the interface (see Figure 3.2). Crack propagation most often takes place in the interface region

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3-10

Fundamentals of Pressure Sensitivity

(a)

0

1 P/P 0 (%)

log P/P0

1.0

−1

0.6

2

3

(b)

0.2 60 52 ϕ (% vol.) −1

0

1

2

log t

FIGURE 3.3 (a) Kinetics of the changes in adhesion strength during the fracture of adhesion joint tetrafluoroethylene-hexafluoropropylene copolymer–copper at various annealing temperatures: 443 (1), 473 (2), and 503 K (3). (b) The copolymer crystallinity−strength relationship.

between the columnar and spherulitic structure of the adhesive. As reported in Refs 46 and 47, it is in this region that internal stresses reach their highest values. The position of this region depends on the adhesive joint history. Thus, as illustrated in Figure 3.3, thermal annealing of structure-gradient transition zones in the tetrafluoroethylene– hexafluoropropylene copolymer–copper system [48] leads, on one hand, to the growth of adhesive crystallinity due to the decrease in transcrystalline structure area and the shift of the disruption zone toward the interface. On the other hand, it leads to a drop in adhesive joint strength during peeling. From the thermodynamic point of view, these results mean that the structure-gradient transition zones are in a nonequilibrium state, which must be taken into account when estimating the service life for this type of adhesive joint. The process of secondary crystallization is likely to be responsible for gradual transformation of the transcrystalline structure into a spherulitic structure. Calculation of the kinetics of the changes in adhesion strength of these joints can be based on the calibration curve of peeling strength against crystallinity, as illustrated in Figure 3.3b. Similar structure-gradient transition zones are also formed if adhesives are in the liquid crystalline (Figure 3.4a) or amorphous state (Figure 3.4c). In these cases, one must speak of a different nature of structural unit that “imprints” information from a solid surface [36–38]. For amorphous polymers, such a structural unit is a domain, and for liquid crystals it is a one- or two-dimensional mesophase element. Heteroepitaxy can be observed in such systems as crystalline polymer–amorphous adhesives (Figure 3.4d) and amorphous polymer–liquid crystalline adhesives (Figure 3.4a). This is especially pronounced in the case of random and block copolymers. For example, Figure 3.4 illustrates the formation of geometrically different epitaxial structures in ethylene–propylene copolymers and ethylene–vinyl acetate (EVA) copolymers laminated with biaxially oriented polyethylene (PE) and polypropylene (PP) substrates. Each of these structure-gradient transition zones has its own specific features, which include zone width, degree of ordering, and behavior with the distance from the interface.

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3-11

Transition Zones in Adhesive Joints

Polysulphone

LC polyester 200 nm

(a) PE

PEU

500 nm

PP

(b)

PEU

Epoxy oligomer

500 nm

(c) EVA 20

PE 500 nm

(d)

FIGURE 3.4 Structure-gradient transition zones in systems: polysulphone–liquid crystalline polyester (a), PE–polyester urethane (PEU)–PP (b), PEU–epoxy oligomer (c), and PE−random copolymer of ethylene with vinyl acetate (d).

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3-12

Fundamentals of Pressure Sensitivity

3.2.3

Concentration Gradient Transition Zones

This class of transition zones is distinguished by thermodynamic compatibility of the substrate–adhesive system, in which a process of adhesive–substrate interdiff usion can occur. Under these conditions, the gradient pattern of the transition zone can be attributed mainly to the change in system composition. This type of transition zone is most often formed in polymer systems. As reported in Refs 48–50, upon coupling of two polymers, transition zones are spontaneously formed in their adhesive contact region. Within this region, the structure, composition, and properties continuously change in the direction from adhesive to substrate. The structure of gradient transition zones in binary polymer systems is determined by at least three parameters: first, the position of a figurative point in the temperature–concentration field of the system phase diagram; second, deviation of actual compositions of coexisting phases from the compositions of coexisting phases outlined by the equilibrium phase state diagram; and third, the value of the mutual diff usion coefficient, which defines the geometric size of transition zones. 3.2.3.1

Systems with Amorphous Phase Separation

The behavior of such systems is illustrated in Figure 3.5. If the adhesive joint components are thermodynamically incompatible, binodal curves are adjacent to the ordinate of state diagram, T <<Т3 (see Figure 3.5). The structure of the transition zone includes the interface and “structure perturbation” regions (i.e., epitaxial layers), within which macromolecules, adsorbed at the boundary, undergo structural and conformational transformations. As indicated in Refs 43 and 44, interface dimensions in these cases vary in a relatively wide range from 0.8 to 130 nm.

(a)

T

wi T1

UCST

B

A

Temperature

(b) w1′

w1″

T2

A

B

w1″

(c)

w1′ w1″

w1′

T3

A

w1″

B (d) w1′

A

wi Composition

B

−x

0

+x

Diffusion coordinate

FIGURE 3.5 Diagram of amorphous phase separation of the A–B binary system (a) and concentration profi les in transition zones of adhesive joints at bonding temperatures: Т1 (b), Т2 (c), and Т3 (d). А is the adhesive and В is the substrate.

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3-13

Transition Zones in Adhesive Joints

If conjugated phases are above the upper critical solution temperature (UCST; Т1 > UCST), as illustrated in Figure 3.5b, and observation time is restricted, then the transition zone of the adhesive joint coincides with the diff usion zone (DZ) of component mixing. For such DZ a continuous change with time of the extension and composition distribution is featured, with the changes controlled by the rate of translational diff usion of macromolecules. It was reported in Refs 48 and 51 that in the whole concentration range, structure organizations, formed within these DZs, are similar to the structure organizations of polymer solutions. If adhesive–substrate bonding occurs at Т2 < UCST (Figure 3.5c), then, depending on the observation time, or to be more exact, on the ratio of the observation time (t) to the time of diff usional relaxation t D (t D = L2/D, where L is the thickness of adhesive and D is the diff usion coefficient), the transition zone may have various patterns in terms of structure and concentration. If the interfacing phases have finite size and t >> t D, the system has achieved its equilibrium state and the interface separating the coexisting phases is part of the transition zone. If the interfacing phases are represented by semi-infinite samples and t << t D, the transition zone, as illustrated in Figures 3.5b and 3.5d, consists of at least four regions: two DZs corresponding to component solutions in each other, the interface, and the regions of epitaxial structures in the A and B phases. 3.2.3.2

Adhesive Joints with Crystalline Substrate

For systems featuring crystalline equilibrium, the concentration distribution is different. In this case (see Figure 3.6), upon the contact of adhesive joint components A and B at Т < Тm, that is, when a substrate is in the crystalline state, an area of spontaneous mixing is formed between the amorphous adhesive and the crystalline substrate, which

wi

(a)

T

Melt

A

B

T1

(b)

Temperature

Tm w1′

T2

w1″

A I

T3 Crystal

III

B I

wi Composition

B

−x

(c)

II

A III

A

B w1′

w1″

II

(d)

+x 0 Diffusion coordinate

FIGURE 3.6 Phase diagram of crystalline equilibrium in a binary system (a) and concentration profi les in transition gradient zones at temperatures T1 (b); Т2 (c), and Т3 (d). A is the amorphous adhesive and B is the crystalline substrate.

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3-14

Fundamentals of Pressure Sensitivity

includes the zone of crystalline polymer solubility in an amorphous polymer (I), the zone of amorphous polymer solubility in the amorphous phase of a crystalline polymer (II), and the interface (III). At temperatures higher than the melting point, Tm, the profi le of the concentration distribution corresponds to the above-described profi le for the systems with amorphous phase separation at T > UCST. For systems featuring liquid crystalline equilibrium, there are two types of structure organization to be expected for the transition zone. At temperatures higher than the isotropization point, the transition zone is identical to the mutual diff usion zone. At Тm < T < Тiso, the transition zone is represented by a superposition of three zones—the zone of LC polymer solubility in contacting amorphous component, the zone of solubility of this component in the LC phase, and the interface. 3.2.3.3

Systems Featuring Complex Amorphous–Crystalline Equilibrium

This type of transition zones is illustrated in Figure 3.7. The number of possible transient gradient structures in the area of conjugated phases is drastically increased. Th is is because, in addition to phase interface, which corresponds to amorphous phase separation, and interdiff usion zones located to the left and right of the binodal curve, the following elements appear: phase interface corresponding to crystalline equilibrium, diff usion zone of the components of the melt into the amorphous phase of a partially crystalline polymer, and the zone of crystalline phase dissolution. Interrelations between the position of all these interfaces, concentration jumps, and lengths of diff usion zones are governed by the relative positions of UCST and the melting point of the crystallizing component, as well as by the temperature dependence of the interdiff usion coefficients. (a)

T

T1

Melt w ′′′ w′

Tm

Temperature

w ′′

T2 Crystal

wi A

B (b)

A

wi′′′

wi′′

B (c)

wi′ A

wi Composition

B

−x

0

+x

Diffusion coordinate

FIGURE 3.7 Complex amorphous–crystalline equilibrium. Phase state diagram of a binary system (a) and concentration profi les in transition gradient zones at temperatures T1 (b), and Т2 (c).

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Transition Zones in Adhesive Joints

3-15

It is reported in Ref. 50 that the situation becomes more complicated if transition zone formation takes place at elevated temperatures, followed by a decrease in temperature, which is typical for many adhesive systems. Figure 3.5d demonstrates the change in estimated concentration profi le within DZ when going from Т1 to Т3. In compliance with the temperature coefficient of solubility, one should expect the formation of interphase boundary, narrowing of concentration profi le (so-called negative diff usion), secondary phase separation near interphase boundaries, and the appearance of local dispersed structures of the matrix-impurity type. Th is transition zone is schematically presented in Figure 3.5d. In transition zones with such a complicated structuremorphologic organization, the formation of a weak region, according to Bikerman [52], will be responsible for the locus of adhesive joint failure. As an example, Figure 3.8 presents the data on phase equilibrium, the structure of the concentration gradient transition zone, and the mode of peeling failure in adhesive joints in polyvinyl chloride (PVC)–random copolymers of EVA [53,54]. All PVC–EVA systems exhibit UCST. As the content of vinyl acetate monomers in the copolymer chains increases, the heterogeneity region becomes smaller and UCST decreases. Translation diff usion coefficients of EVA in the PVC phase and those of PVC in the EVA phase, depending on temperature and copolymer composition, vary in the range from 1 × 10−13 to 1 × 10−10 cm2/s (Figure 3.8b). The values of activation energies for diff usion are listed in Table 3.3. By its magnitude, ED tends to the value of activation energy for viscous flow of the material, within which a diff usion penetration of adhesive or substrate macromolecules occurs. Typical surface microphotographs of cross-sections of PVC–EVA adhesive joints and corresponding concentration distribution profi les within the transition zones are illustrated in Figure 3.9. As follows from the analysis of the surface image formed by secondary electrons before (Figure 3.9a) and after etching the surface in the plasma of high-frequency oxygen discharge (Figure 3.9b), the jumpwise change in composition corresponds to the position of interface between the components of the adhesive joint. The width of the interface in PVC−EVA systems, depending on the copolymer composition, varied from 10 nm for EVA 20−PVC to 20 nm for EVA 70−PVC, whereas the width of the concentration gradient profi le can be as large as several micrometers (EVA 20 contains 20% vinyl acetate (VA) units; EVA 70 contains 70% VA units). Generalizing these results, one can come to the following conclusions. First, similar to the above-described case of systems with amorphous phase separation (see Figure 3.5), concentration profiles in all studied systems consist of three parts: middle or central (I) and two outer regions (II and III) (Figure 3.10). Their key distinguishing feature lie in the fact that figurative points of the region I (i.e., isoconcentration planes) hold their positions unchanged, whereas figurative points of regions II and III continuously move along the axis of the diff usion coordinate (Figure 3.10) [55]. In full accordance with the concepts of phenomenologic diff usion theory, figurative points of regions II and III are displaced with time in the direction from the interface. As the diff usion process proceeds, the total width of the whole transition zone of component mixing continuously increases.

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3-16

Fundamentals of Pressure Sensitivity

220

T (°C)

180

140 1 2 3 100

60

0.2

0

0.4

0.6

0.8

1

w

(a)

PVC

EVA (1/T ) × 103 2.0

2.2

2.4

2.6

2.8

−9 2

1 −11

Tg PVC

In D (cm2/s)

−10

−12 −13 (b)

FIGURE 3.8 Phase state diagram of the PVC−EVA system (a) and the temperature relationship of partial interdiff usion coefficients (b). Designations: (а) 1, EVA 70; 2, EVA 30; 3, EVA 20. Numbers correspond to the percentage of VA monomer units in the EVA copolymer. (b) 1, PVC diff usion into EVA copolymer; 2, EVA copolymer diff usion into PVC. Arrows mark the positions of PVC glass temperature and the change in diff usion coefficients.

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3-17

Transition Zones in Adhesive Joints TABLE 3.3

Values of Activation Energy for Diffusion

System PVC−EVA 20 PVC−EVA 30 PVC−EVA 70

ED (kJ/mol PVC in EVA Copolymer)

ЕD (kJ/mol EVA Copolymer in PVC)

58.5 54.3 50.2

58.5 66.9 87.8

(a)

PVC

Interface

EVA 20

200 nm (b)

FIGURE 3.9 Cross-section surface microphotographs of the gradient zone in a PVC−EVA 20 adhesive joint (Тanneal = 433 K; tanneal = 60 min), obtained with secondary electrons before (a) and after etching the surface in oxygen discharge plasma (b).

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3-18

Fundamentals of Pressure Sensitivity ω Cl 1

PVC

BNR 40 0.5

−16 (a)

−8

0 x (µm)

8

16

z 2.5

II 0.5 −16

−8

−0.5

∼ω ′1 8

I

x (µm)

16

∼ω ′′1 III (b)

−2.5

FIGURE 3.10 Diff usion profi les in the PVC−BNR system in coordinates w − x (а) and z − x (b), plotted using KαCl. Annealing time is 25 min; annealing temperature is 433 K.

Second, the above-described phenomena are most clearly demonstrated if the concentration profi les are presented in the coordinates of Equation 3.5 [50], 1 w i
[1  erf ( z )] 2

(3.5)

which is commonly used to describe the evolution of the concentration diffusion profiles in two conjugated semi-infinite media. Here, wi is the concentration expressed in a weight or ___ volume fraction, erf(z) is the Gaussian integral, z = x/√Dt is the tabulated value of the integral, D is the diffusion coefficient, t is the time of contact, and x is the diffusion coordinate. After these transformations are performed, the concentration profiles of transition zones take the shape of three intersecting straight lines (Figures 3.10 and 3.11). The slope angle of the outer regions (II and III) of the concentration profi les changes with annealing time, indicating the penetration of macromolecular diff usion fluxes into individual phases.

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3-19

Transition Zones in Adhesive Joints ω Cl 1

PVC

EVA 30 0.5

−8

−16 (a)

0

16

8

x (µm) 2.4

II

z

1.2 ∼ω1′

−16

−8

I

8

x (µm)

16

∼ω1′′

−1.2 III (b)

−2.4

FIGURE 3.11 Diff usion profi les in the PVC−EVA 30 system in coordinates w−x (а) and z−x (b), plotted using KαCl. Annealing time is 60 min; annealing temperature is 433 K.

The slope and experimental points of the middle profi le region remain unchanged for a specified annealing temperature. Third, of principal importance is the repeatedly confirmed experimental fact that the coordinates of the points formed by intersections of straight lines II and III with interphase boundary stay constant over time, varying only with change in annealing temperature (Figure 3.11b). In addition, the change in temperatures of bonding and annealing might always result in the same values of wi′ and wi″ at the interface. This implies the reversibility of the process and equilibrium composition of the phases, which coexist at the interface in the course of the interdiff usion of adhesive and substrate components. Fourth, the described character of the composition evolution in diff usion zones of contacting PVC and copolymer phases is sufficiently general. Similar dependences have been described earlier in PVC−butadiene–nitrile rubber (BNR) (Figure 3.10), PVC−polymethyl methacrylate (PMMA), polychloroprene−BNR, and others [49,50].

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3-20

Fundamentals of Pressure Sensitivity

Each individual system displays its specific values of the compositions of coexisting phases, the rates of isoconcentration plane movement, the width of the interphase boundaries, and the entire transition zones. It is also of fundamental importance that the diffusion coefficients are invariable with diffusion time, contrary to the suggestion by Vasenin [21], according to whom the translation mobility of the macromolecules of the adhesive within the substrate phase should decrease with observation time (Figure 3.12). The constant slope of the curves in Figure 3.12 is a direct indication of the invariability of the diff usion coefficients with time. Thus, the PVC–EVA systems can be referred to as partially compatible systems with UCST. The phase structure that is formed within the zone of adhesive–substrate contact is quite complex. It includes the interface region, where a jumpwise concentration profi le is observed that describes the compositions of coexisting phases, and two diff usion zones, formed due to the solubility of adhesive and substrate phases in each other.

1

x (µm)

12

8

2

4

0

4

8 t (min1/2)

(a)

x (µm)

12 2 8

4

0 (b)

5

10 t

15

(min1/2)

FIGURE 3.12 Kinetics of the increase in transition zone width for the PVC–BNR 40 (a) and PVC– EVA 70 (b) systems at annealing temperature of 453 K (PVC–BNR 40) and 393 K (PVC–EVA 70). (1) Diff usion of BNR 40 macromolecules into the PVC phase and (2) diff usion of PVC macromolecules into the copolymer phase.

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3-21

Transition Zones in Adhesive Joints

3.2.3.4 Diffusion and Adhesive Behavior of Transition Zones Along with structure morphological studies, measurements of the strength of adhesive joints were performed for the same systems [54]. Figures 3.13 and 3.14 illustrate typical effects of dwell time and temperature on the peel strength of adhesive joints (see also 4

2000 Cohesive failure A (N/m)

1500

3

1000

2

Adhesive failure 1

500

200

100

300

400

t (min)

FIGURE 3.13 Effect of dwell time and temperature on 180° peel strength of a PVC−EVA 30 system. Contact pressure is 0.5 MPa; contact time is 20 min. After removal of bonding pressure, the sample is annealed at a fi xed temperature for a specified dwell time. Тtest = 295 K. The temperature of annealing is (1) 373, (2) 393, (3) 413, and (4) 433 K.

2000

1500 A (N/m)

Mixed failure

Adhesive failure

Adhesive failure

Cohesive failure

3 1000 2 4 500

1 5 6

0 0

20

40

60

80

100

VA content (% wt)

FIGURE 3.14 Dependence of 180° peel force versus the content of VA monomer units (% wt) for various bonding temperatures: (1) 373, (2) 393, and (3) 413 K. (4) EVA–steel coated with epoxy, (5) EVA−steel, and (6) EVA−glass. Тtest = 295 K.

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3-22

Fundamentals of Pressure Sensitivity

Applications of Pressure-Sensitive Products, Chapters 7 and 8). The peel strength reaches its limit at a specified value of dwell time. The dwell time required to establish the maximum strength of adhesive joints decreases with the rise in temperature. Thus, for 373 K it amounts to 350 min, whereas for 433 K it is 60 min. A similar relationship is valid for copolymers of various composition. For this group of adhesives, information on the relationship between adhesive properties and copolymer composition is of fundamental importance. The relevant data are generalized in Figure 3.14. As the percentage of VA units in the polymer backbone grows, the peel strength goes through a maximum for all adhesive joints obtained at various temperatures and with various substrates. The position of the maximum corresponds to copolymers containing 70–80% wt VA monomer units. All adhesive joints, especially those obtained at high temperatures, exhibit a similar change in the mechanism of debonding with increased content of VA units. In the vicinity of the maximum of adhesion, cohesive failure is always observed, whereas the copolymers overloaded with either ethylene or VA units demonstrate decreased adhesion with the adhesive mechanism of debonding (this phenomenon is used in the practice of EVA-based, hot-laminated, self-adhesive fi lms; see also Applications of PressureSensitive Products, Chapter 7). Information on the type of deformation and the mechanism of debonding is of great importance for the interpretation and comprehension of the phenomenon of pressuresensitive adhesion. The results of two groups of studies are presented below. The first group deals with the analysis of substrate and adhesive surfaces upon adhesive joint failure and the second group with in situ analysis of deformation zones of these joints during debonding (Figures 3.15 and 3.16). Cohesive failure (Figures 3.15a and 3.15b) is associated with significant residual adhesive material at the substrate surface. The morphology of adhesive residual upon debonding is indicative of a plastic deformation of adhesive copolymers under peel stress. Upon adhesive failure (Figure 3.15d), there are no traces of adhesive remaining at the substrate surface. In both cases there must exist interpenetration of adhesive and substrate materials within the transition zone, confirming the conclusions made in Chapter 2. As illustrated in Figure 3.16, large extension strain achieving 3000–4000% for EVA 70 and 500% for EVA 30 is observed in the course of the debonding process. Negligible plastic deformation is observed for EVA 14. The measurements of concentration gradients and determination of diff usion fluxes of adhesive joint components through the interface, identification of the locus of failure, and observation of the kinetics of peel strength growth suggest the following mechanism to explain how diff usion affects adhesion. Figures 3.17 and 3.18 demonstrate that adhesive strength relatively quickly achieves its limiting value, despite rather intense continuation of the interdiff usion processes in the system. The results of morphological studies demonstrate that adhesive joint failure is located in a specific area of the concentration gradient (Figure 3.18), the position of which is independent of the length of diff usion path of PVC macromolecules within the EVA phase. This finding allows us to conclude that kinetics of the growth of adhesive joint strength relates not only to the diffusion processes, but also to the processes of Bikerman’s weak zone formation. Numerous

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3-23

Transition Zones in Adhesive Joints

(a)

(b)

(c)

(d)

FIGURE 3.15 Microphotographs of the PVC surface upon peeling of PVC−EVA joints of various compositions: (a) EVA 70, (b) EVA 40, (c) EVA 30, and (d) EVA 14.

Adhesive EVA 70

Substrate PVC Stress direction

FIGURE 3.16 Optical microphotograph of the deformation of EVA 70 adhesive under peeling from the PVC substrate.

investigations performed by our group with similar systems allow us to make the following conclusion. Kinetics of the growth of adhesive joint strength is only informative for the mechanism of adhesive joint formation when the kinetics of weak zone formation is controlled by the interdiff usion process.

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3-24

Fundamentals of Pressure Sensitivity

A (N/m)

2500

1500

3

500

Q (% wt/min)

2

2 1

1

0

t 0

200 Time (min)

FIGURE 3.17 The correlation relationship between kinetics of the growth of adhesive joint strength (1) and kinetics of mass transfer of EVA 70 into PVC (2), and PVC into EVA 70 (3). The amounts of interpenetrated EVA adhesive and PVC substrate are measured using an x-ray microanalysis technique.

PVC

1 w Cl

0.5

−30

EVA

"Weak zone"

0

30 x (µm)

Crack

FIGURE 3.18 Concentration distribution profi le in the gradient zone of the EVA–PVC adhesive joint. An arrow marks the position of a “weak zone,” where crack propagation and debonding occur.

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Transition Zones in Adhesive Joints

3-25

3.2.4 Combined Transition Zones This kind of transition zone is typical for the majority of adhesive joints formed by multicomponent adhesives, which undergo various chemical, phase, and concentration transformations during the formation of adhesive joints. PSAs rarely exhibit phase transformations in the course of the bonding process, and chemical transformations are also uncharacteristic of this class of adhesives (with the exception of special applications; see Technology of Pressure-Sensitive Adhesives and Products, Chapter 8, and Applications of Pressure-Sensitive Products, Chapter 4). Nevertheless, for elaboration on the general concept of combined transition zones, it is reasonable to consider the adhesive joints formed by the adhesives of different classes. The formation of combined structure-mechanics/structure-gradient/concentrationgradient transition zones in the steel–polyolefi n system is described in Ref. 54. The concentration gradient component of the transition zone appears as a result of the thermo-oxidizing destruction reaction of the polyolefin melt catalyzed by the substrate surface. The authors of this investigation convincingly demonstrated that the contribution of this process defines both the high strength of the adhesive joint and its high stability in moistened environments. Whereas the first type of transition zone is responsible for the catalytic activity of substrate surface, the zone of the second type specifies the level of internal stresses within the adhesive. As demonstrated in Refs 39 and 41, adhesive systems formed by atactic PMMA and polyvinylidene fluoride (PVDF) include combined structure-gradient/concentrationgradient transition zones. Initially, the contact of PVDF melt with PMMA leads to the formation of a diff usion zone, in which later, after a decrease in temperature, PVDF crystallization occurs, accompanied by the generation of spherulitic and transcrystalline structures. The latter grows through the amorphous PMMA phase. A weak zone, which is responsible for the locus of failure in this joint, corresponds to the region of PVDF solutions in PMMA that reveals the low crystallinity and high plasticity. Interesting results were obtained for the PE–butyl rubber (BR) system [39]. Direct electron microscopy examination indicated that the adhesive contact at a temperature range from 433 to 473 K results in the formation of a transition zone of the structuregradient type. If adhesive joints are formed at temperatures above 473 K, the generated transition zone is extended and relates to a combined structure-gradient/concentrationgradient type. The structure-morphological organization of a transition zone provides the high strength of PE–BR adhesive joints, also realized in a number of fi lm materials, such as laminated plastics with PSAs as an intermediate layer. Let us examine more closely the formation of the adhesive joint in the system steel– phenol formaldehyde oligomer (PFO)–BNR [39,41]. In this joint, the oligomer acts as an adhesive, whereas steel and BNR are substrates. Hence, the design of this adhesive joint makes it possible to expect the formation of at least two transition zones upon bonding of the joint’s components: steel–PFO and PFO–BNR. The accepted technique of coupling elastomers with steel includes four stages [56,57]: (1) steel surface pretreatment, (2) coating with the layer of PFO solution of 40–50 µm in thickness, (3) drying and bonding (under compressive stress) with elastomer composition, and (4) thermal treatment of the obtained joint as a whole under thermal

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3-26

Fundamentals of Pressure Sensitivity

T (K)

T (K) 1

3 2

2 425

450 T∗

1

3

400

400 375

350

350 0

BNR 40 (a)

0.25

0.5 w

0.75

1

0

PFO

BNR 40 (b)

0.25

0.5 w

0.75

1 PFO

FIGURE 3.19 Phase state diagrams of PFO−BNR (a) and BNR 40–PFO (b) systems at various degrees of oligomer conversion (α) in the polymerization reaction. Designations: (а) 1, BNR 18; 2, BNR 26; and 3, BNR 40; (b) conversion degrees 0 (1), 40 (2), and 50% (3). T* is the vulcanization temperature. The numbers indicate the content of nitrile groups.

and time conditions, providing for adhesive setting and substrate vulcanization. In addition, mixtures of phenol–formaldehyde Novolac oligomers with BNR are characterized by phase state diagrams with UCST (Figure 3.19). The PFO–BNR 40 system is of particular interest because its critical temperature is below the curing temperature of the adhesive joint. Second, due to the fact that interdiff usion coefficients in these systems are ∼5 × 10 −7 cm 2/s at the temperatures of structure formation within BNR, it can be expected that mass exchange processes between the elements of adhesive joint will be rather fast, resulting in the production of a concentration gradient transition zone. In terms of geometric dimensions, a nitrile substrate represents an infi nite medium, whereas the adhesive is a finite-size body. Several types of transition region can be formed depending on adhesive joint contact time (Figure 3.20). At short contact times (t), when L > (Dt)1/2, a diff usion zone with phase interface is formed in the PFO layer. At longer observation times, when L << (Dt)1/2, the diff usion frontline reaches the PFO– steel boundary. Further, the elastomer concentration in the adhesive layer increases, implying PFO dissolution in the elastomer. In actual systems, the process of PFO–elastomer bonding is accompanied by the formation of three-dimensional networks within the adhesive and substrate phases. Preliminary experiments demonstrated (Figure 3.19b) that elastomer cross-linking and PFO curing lead to decreased mutual solubility [50]. Figure 3.19b demonstrates that, with the increase in oligomer molecular weight (conversion degree), the heterogeneous

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3-27

Transition Zones in Adhesive Joints

w1 L w1′′

Steel

2

BNR 40

PFO w1′

1 (a)

1

−2

w1

1

0

Interface

0

(b)

0

x

(c)

w1

0

x

0

x

w1

Steel

1

Steel (d)

w1

Steel

Steel

Interface

1

×10−2 (µm)

2

0

0

0 0

x

(e)

FIGURE 3.20 The concentration distribution in the adhesive joint region steel–PFO–BNR 40 (a) at T = 423 K; t = 5 (1) and 50 min (2); w′ and w″ are compositions of coexisting phases. The stages of adhesive joint formation include initial contact (b), saturation of the PFO layer with elastomer (c), establishing a limiting rubber solubility w″ in BNR (d) at the steel interface, and the formation of dilute PFO solutions in rubber (e).

region of the phase state diagram becomes more extended and UCST becomes higher. This means that the setting reaction results in phase segregation if it occurs in the diffusion zone in regions of component concentrations exceeding the limiting values of mutual solubility. In bulky elastomer, PFO phase segregates, whereas in bulky PFOdispersed BNR phase arises. The schematic drawing in Figure 3.21 illustrates the pattern of the relevant structure-morphological organization of the transition zone. Experimental studies of transition zones in these systems provide support for the described regularities in their structure formation. As follows from the data of local x-ray microprobe analysis, in the cross-linked elastomer layer the PFO phase exists and, alternatively, in cured PFO there are particles of the BNR dispersed phase. Fractographic studies of the failure of steel–PFO–elastomer adhesive joints demonstrated that the initial stages of transition zone formation can be associated with cohesive brittle failure involving the phase of phenol formaldehyde adhesive (region I in Figure 3.22). After long-time contact, the BNR elastomer diff usion frontline reaches the metal boundary. As a consequence, specific interaction at the PFO–steel interface is disrupted [39],

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3-28

Fundamentals of Pressure Sensitivity

1

Steel

PFO

BNR 40

0.5

−2

(a)

0

1

×10−2 (µm)

2 2

BNR Steel

PFO

(b)

Crack

−2

0

×10−2 (µm)

2

FIGURE 3.21 Schematic presentation of the transition zone in a steel–PFO–BNR 40 adhesive joint at the stage of bond formation (diff usion) (a) and after oligomer curing (b). 1, BNR dispersed phase in PFO, 2, PFO dispersed phase in cured BNR 40.

30

20 A (kN/m)

I

II

III

10

30

60 t (min)

FIGURE 3.22 The relationship between peel resistance and the contact time of joint formation (the rate of adhesive curing) in rubber–metal products. Locus of failure: I, within the PFO layer; II, within rubber; and III, along the interface with metal.

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3-29

Transition Zones in Adhesive Joints

Crack

Steel

PFO

BNR 40

(a) I (KαBr) 1

0.5

(b)

x (µm)

0 20

60

100

FIGURE 3.23 Crack propagation in a real rubber–metal adhesive joint (a) and the distribution elastomer (contrasted with Br), recorded on a Br L-line (b). The dotted line indicates the initial thickness of the adhesive layer. The arrow marks crack localization within the concentration profi le. In this region, the PFO phase strengthens the elastomer by a dispersing mechanism.

followed by adhesive peeling (region III in Figure 3.22). The highest value of the strength of the adhesive joint is achieved at intermediate times of adhesive contact when crack propagates in the elastomer phase (region II). Hence, the ratio of diff usion rate to the rate of structure transformations in adhesive and elastomer substrate acts as a factor that controls the structure and strength of the adhesive joint in the combined transition zone occurring in the steel–PFO–BNR adhesive joint. The best case occurs when the phenol formaldehyde oligomer has fully reacted with functional groups at the metal surface, the particles of the rubber elastomer phase have been formed in its bulk, and the particles of the cured oligomer are formed in the bulky elastomer. This makes it possible to realize extensive adsorption interaction between the components of the adhesive joint and provide plasticization of the glassy phase of the Novolac phenol formaldehyde polymer, accompanied by dispersion strengthening of the BNR phase (Figure 3.23).

3.3 Conclusions Classification of the transition zones in adhesive joints involving the adhesives of different types and phase state was presented. The fact that the kinetic curve of adhesive strength reaches a state of saturation (see Figure 3.17) does not imply the completion of

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mass transfer processes, as assumed in the diff usion theory of Voyutskii and Vasenin [16,21]. This is indicative of the formation and stabilization of a weak zone, which is responsible for adhesive joint failure under debonding stress. The concept of transition zones in full measure presented in this chapter can be used for the analysis and design of PSA joints using various substrates.

References 1. Deryaguin B.V., Churaev N.V., and Myller V.M. Surface Force. New York: Consultants Bureau, Plenum Publishing Corporation. 1987. 2. Mittal K.L. The role of the interface in adhesion phenomena. Polym. Eng. Sci. 17(7), 467–473, 1977. 3. Deryaguin B.V., Krotova N.A., and Smilga V.P. Adhesion of Solids. New York: Cons. Bur. 1978. 320p. 4. Deryaguin B.V. and Krotova N.A. Adhesion [in Russian]. Moscow: Izd. Akad. Nauk USSR. 1949. 244p. 5. Kinloch A.J. Adhesion and Adhesives Science and Technology. London: Chapman & Hall. 1987. 441p. 6. Adamson A. Physical Chemistry of Surfaces. New York: John Wiley. 1990. 770p. 7. Wake W.C. Adhesion and the Formulation of Adhesives. London: Applied Science Pub. 1982. p. 89. 8. Feldstein M.M. and Creton C. Pressure-sensitive adhesion as a material property and as a process, in: Pressure-Sensitive Design, Theoretical Aspects. vol. 1, I. Benedek (ed.) Leiden: VSP. 2006. Chap. 2. 9. Arslanov V.V. and Ogarev V.A. Adhesive joints of light metals with polymers. Prog. Org. Coatings 15(1), 1–31, 1987. 10. Rudoi V.M. and Ogarev V.A. Certain methods for investigation of surface layers of polymers, in: Modern Physical Methods for Investigation of Polymers [in Russian]. Moscow: Khimiya. 1982. 11. Zubov P.I. and Sukhareva L.A. Structure and Properties of Polymer Coatings [in Russian]. Moscow: Khimiya. 1982. 12. Deryaguin B.V. and Toporov Yu.P. Role of the electric double layer in adhesion. Russ. Chem. Bull. 31(8), 1544–1548, 1982. 13. Voyutskii S.S., Kamenskii A.N., and Fodiman N.M. Direct proofs of self- and mutual diff usion in the formation of adhesion bonds between polymers. Mech. Composite Mater. 2(3), 279–283, 1966. 14. Morozova L.P. and Krotova N.A. Dokl. Akad. Nauk. USSR 115. 747, 1957. 15. Krotova N.A. and Morozova L.P. Dokl. Akad. Nauk. USSR 127. 141, 1959. 16. Voyutskii S.S. Autohesion and Adhesion of High Polymers. New York: Wiley Interscience. 1963. 212p. 17. Boiko Yu.M. Self-adhesion of amorphous polymers and their miscible blends. Mech. Composite Mater. 36(1), 79–82, 2000. 18. Bikerman J.J. The Science of Adhesive Joints. 2nd ed. New York: Academic Press. 1968.

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19. Basin V.E. Adhesion Strength [in Russian]. Moscow: Khimiya. 1981. 208p. 20. Lipatov Yu.S. Interfacial Phenomena in Polymers [in Russian]. Kiev: Naukova Dumka. 1980. 260p. 21. Vasenin, R.M. Adhesion, Fundamentals and Practice. London: McLaren and Son. 1969. 22. Voyutskii S.S. and Vakula V.L. The role of diff usion phenomena in polymer-topolymer adhesion. J. Appl. Polym. Sci. 7(2), 475–491, 1963. 23. Kuleznev V.N. Polymer Blends [in Russian]. Moscow: Khimia. 1980. 303p. 24. Dillard D.A. and Pocius A.V. (eds.), Adhesion Science and Engineering: The Mechanics of Adhesion. vol. 1. Amsterdam: Elsevier. 2002. 25. Pocius A.V. Adhesion Science and Engineering: Surfaces, Chemistry and Applications. Vol. 2. Amsterdam: Elsevier. 2002. 26. Petrova A.P. in: Adhesive Materials Handbook. E.N. Kablov and S.V. Reznichenko (eds.) [in Russian] Moscow: K i R. 2002. 196p. 27. Satas D. (ed.), Handbook of Pressure Sensitive Adhesive Technology. 3rd ed. Warwick, RI: Satas & Associates. 1999. 1017p. 28. Kardashov D.A. Structural Adhesives [in Russian]. Moscow: Khimiya. 1980. 29. Adams R.D., Comyn J., and Wake W.C. Structural Adhesive Joints in Engineering. 2nd ed. London: Chapman & Hall. 1997. 359p. 30. Petrie E.M. Handbook of Adhesives and Sealants. New York: McGraw-Hill. 2000. 880p. 31. Pritykin L.M., Kardashov D.A., and Vakula V.L. Monomer Adhesives [in Russian]. Moscow: Khimiya. 1988. 172p. 32. Freidin A.S. Strength and Durability of Adhesive Joints [in Russian]. Moscow: Khimiya. 1971. 352p. 33. Benedek I. Pressure Sensitive Adhesives and Applications. New York: Marcel Dekker. 2004. 747p. 34. Vakula V.L. and Pritykin L.M. Polymer Adhesion: Basic Physico-Chemical Principles. New York: Ellis Horwood Ltd. 1991. 350p. 35. Povstugar V.I., Kodolov V.I., and Mikhalova S.S. Structure and Properties of the Surface of Polymer Materials [in Russian]. Moscow: Khimiya. 1988. 192p. 36. Arslanov V.V. Doctor of Science thesis: Physical chemistry of forming and debonding processes of composite transition zones in adhesive joints polymer−metal. 1989. 425p. 37. Chalykh A.E. in: Surface Phenomena in Polymers [in Russian]. Kiev: Naukova dumka. 1982. p. 123. 38. Arslanov V.V. and Chalykh A.E. Current status and future prospects of the theory of adhesive joints. Zashch. Met. 25(4), 547–554, 1989. 39. Rubtsov A.E. PhD thesis: Transition zones in polymer systems. 1992. 228p. 40. Pluedemann E.P. in: Industrial Adhesion Problems. D.M. Brewis and D. Briggs (eds.) Oxford: Orbital Press. 1985. p. 148. 41. Chalykh A.E., Aliev A.D., and Rubtsov A.E. Electron Probe Microanalysis in Polymer Investigation. Moscow: Nauka. 1990. 192p. 42. Gul V.E. and Kuleznev V.N. Structure and Mechanical Properties of Polymers [in Russian]. Moscow: Labirint. 1994. 367p.

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43. Wu S. Polymer Interface and Adhesion. New York: Marcel Dekker Inc. 1982. 630p. 44. Evans J.R. and Packham D.E. J. Adhesion 10(1), 39–47, 1979. 45. Pickham D.E. in: Developments in Adhesives: 2nd ed. A.J. Kinlock (ed.) London: Applied Sciences Pub. 1984. p. 315. 46. Schultz J. Effect of orientation and organization of polymers at interfaces on adhesive strength. J. Adhesion 37(1–3), 73−81, 1992. 47. Wu S. in: Polymer Blends. D.R. Paul, and S. Newman (eds.) Vol. 1, New York : Academic Press. 1978. 48. Chalykh A.E. and Raisin I.B. J. Polym. Sci. Ser. A. USSR 16(5), 1068, 1974. 49. Chalykh A.E. Diff usion in Polymeric Systems [in Russian]. Moscow: Khimiya. 1987. 312p. 50. Chalykh A.E., Gerasimov V.K., and Mikhailov Yu.M. Phase Diagrams of Polymer Systems. Moscow: Yanus-K. 1998. 216p. 51. Zagaytov, A.I., Chertkov V.G., and Chalykh A.E. Comparative study of kinetics of structure formation in binary polymer systems and inorganic glasses J. Mol. Liq. 93(1–3), 177–180, 2001. 52. Bikerman J.J. Physical Surfaces. New York: Academic Press. 1970. 476p. 53. Chalykh A.E. and Gerasimov V.K. Phase equilibria and phase structures of polymer blends. Russ. Chem. Rev. 73(1), 59–74, 2004. 54. Gorbunov A.D. Master of Science thesis: Effect of miscibility and diff usion on adhesion performance in PVC−EVA co-polymers systems. 2004. 144p. 55. Aliev A.D., Vokal M.A., Chalykh A.E., and Gerasimov V.K. Phase diagrams of ethylene-vinyl acetate copolymers. Polym. Sci. Ser. A 48(12), 1281–1286, 2006. 56. Kalnin’ M.M. Changes in the interface in the adhesive reaction of polyethylene with steel. Mech. Composite Mater. 26(5), 571–576, 1991. 57. Kalnin’ M.M. Adhesive Interaction of Polyolefins with Metal [in Russian]. Riga: Zinatne. 1990.

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4 Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives in the Course of Bonding and Debonding Processes 4.1 Introduction ............................................................ 4-1 4.2 Viscoelastic Properties of Pressure-Sensitive Adhesives and Adherence Performance ............. 4-3 Some Examples of the Relationship between Adherence and Viscoelastic Properties • Process and Material Properties

4.3 Some Models of Debonding: A Story about Cavitation ................................................... 4-15 4.4 Measurement of Viscoelastic Properties of Soft Polymers .....................................................4-17

Christophe Derail Gérard Marin Université de Pau et des Pays de l’Adour

4.1

Time Dependent Effects and Linear Viscoelasticity • Large Deformations and Nonlinear Aspects

4.5 Conclusions ........................................................... 4-23 Acknowledgments ......................................................... 4-24 References ....................................................................... 4-24

Introduction

The use of pressure-sensitive adhesives (PSAs) has been steadily increasing in a large domain of industrial applications within the past 30 years [1] (see also Applications of Pressure-Sensitive Products, Chapter 4). This evolution is particularly due to the steadily 4-1

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Fundamentals of Pressure Sensitivity

improving design of efficient and custom adhesive formulations resulting from a better knowledge of the relationship between the relevant adhesive properties (such as rheological or interface properties) and the composition of the adhesive (primary polymer components, resins, and additives; see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 8). At the stage of bond formation, soft (highly viscoelastic) adhesives mainly possess shear deformation, whereas upon debonding, tensile strains may be dominant, when the elongation of the adhesive layer along the direction of the applied detaching force may achieve levels from a few hundred to a few thousand percent. The viscoelastic behavior of the adhesive then plays a leading role during bonding and debonding stages. Recent experimental developments have focused on measuring the physical properties of the adhesive and the visualization of its detachment from the substrate [2,3], which helped to understand more precisely the individual and coupled effects of the main components of the adhesive. The use of model adhesives allows the defi nition of a predictive relationship with their linear viscoelastic properties using relevant models of molecular dynamics. This approach allows the rationalization of PSA formulation through the use of analytical models that take into account the individual and coupled effects of the various components (“virtual formulation”) [4,5]. Despite important breakthroughs in industrial applications, some fundamental points are not yet resolved. In the case of strong affinity between a PSA and its substrate, the rheological behavior of soft adhesives governs, to a large extent, its adherence performance. However, when the PSA presents a low affinity with the substrate, the rheological properties of the PSA are no longer the governing factor of the adherence properties [6]. What are the driving forces governing detachment? These are interesting new research areas for the adhesion science arena in which fundamental studies take place. Some important features are as follows: 1. In the case of large adhesive deformation, the rheological behavior in the nonlinear domain of viscoelasticity is a major factor governing the mode of detachment when cavitation takes place, creating a fibrillar structure in the bulk of the PSA [7]. Is it possible to measure, understand, and finally predict the rheological behavior in the nonlinear domain for adhesives? Some examples will be presented here, specifically in the field of PSAs. 2. The structure formation of surfaces may improve and help to control adhesion properties, sometimes by mimicking the natural stickiness of plants or animals. Structure formation of surfaces at the micro- or nanoscale level seems to be a promising research domain to understand and fine-tune adhesion phenomena in practical applications. This is what we may define as modulation of adhesion. The nano or micro structure formation may also be obtained by chemical modification [8]. In this chapter we will first describe the general features of the relationships between rheological and adherence properties and will explain how a better understanding of these features can be used to improve PSA formulations for a wide range of applications. We will demonstrate that tack measurements, particularly the visualization of the

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

4-3

debonding processes, provide important information on the mode of detachment and, hence, the type of adhesive deformation. Next, we present some examples of models of debonding, particularly dedicated to the phenomenon of cavitation. This is, in fact, a mix of complex physical phenomena and it is difficult to derive a comprehensive model that accounts for all parameters governing the detachment stage. Finally, we will present the principles of measurement of viscoelastic behavior in the linear and nonlinear domains that are relevant to adherence. We will demonstrate that it is possible to predict the rheological behavior of adhesive formulations from their composition, particularly in the linear domain; as a consequence, one may be able to use analytical approaches to formulate soft adhesives such as PSAs. The focus will be on block copolymer-based adhesives. In conclusion, we will indicate new promising trends demonstrating how the control of nonlinear rheological properties and surface modification can be used to improve adherence properties.

4.2

Viscoelastic Properties of Pressure-Sensitive Adhesives and Adherence Performance

Viscoelastic properties play a leading role in the adherence performance of soft (deformable) adhesives on high-energy (high adhesion) surfaces. It is important to defi ne what we mean by the terms adhesion and adherence. Adhesion is generally used to define the mechanisms that allow building of the interface (a reversible process in general), whereas adherence is used to define the energy required to break the assembly (including dissipative phenomena). Two fundamental functions are generally related to these terms. 1. The thermodynamic work of adhesion (W0), which is the energy required to separate reversibly the interface between two bodies in contact, from their equilibrium state to infinity [9]. 2. The fracture energy (G), which can be defined as the energy required to create a unit surface of fracture. The relationship between W0 and G is particularly complex for soft adhesives because of the energy dissipated irreversibly during the debonding stage. A general expression derived from Ref. 10 is often proposed to link W0 and G: G = W0[1 + Φ(V, T, …)]

(4.1)

where the function, Φ, is an amplifying factor that depends on the temperature, the rate of debonding, and more generally on all parameters that modify the viscoelastic properties of adhesives. G may be 100–10,000 times larger than W0 in the case of soft adhesives. In this chapter, we will distinguish between adhesion performance with respect to surface properties and adherence performance with respect to the energy (or force) necessary to break an assembly.

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Fundamentals of Pressure Sensitivity

General trends of the relationship between rheological behavior and adherence properties have been reported in a large number of cases. The pioneering vision of the diffusion and relaxation processes of flexible macromolecular chains of de Gennes [11] provided polymer scientists with effective and predictive models of the viscoelasticity of polymer melts. As a consequence, some authors proposed a kind of “predictive formulation” in the case of polymer-based soft adhesives by inverting molecular models of viscoelasticity [12,13]. In 1996, de Gennes proposed a simple theoretical picture to explain the strong adhesion properties of weakly cross-linked rubbers, known as the trumpet model [14]. Based on what Gent and Petrich describe as “the first transition,” this model qualitatively describes the transition between the cohesive fracture domain and the first interfacial fracture domain observed in peeling experiments of cross-linked butadiene–styrene rubbers adhering on a polyethylene terephthalate polyester fi lm [15]. Even if this model may seem crude in comparison with the complex behavior observed during the detachment stage, it describes the observed general features and indicates clearly that the rheological behavior may be dominant when fracture takes place. The trumpet model details the failure process for a soft model adhesive that presents a single relaxation time and two levels of storage modulus, as presented in Figure 4.1a. We do have the general features of this type of signature for lightly cross-linked elastomers typically used for soft adhesive applications. When failure takes place within this type of adhesive, the stresses relax along the crack that opens. De Gennes postulates that the form of the crack (the opening of the failure, U) depends on two main viscoelastic parameters of the adhesive: the relaxation time (τ) and the ratio between the two characteristic (hard/soft) storage moduli. This model demonstrates that the total length of the crack that totally relaxes the stresses may correspond to the thickness of the adhesive (W). This model refers to soft solid like adhesive with a single relaxation time. In that case the form of the crack looks like a trumpet as shown in Figure 4.1b.

4.2.1

Some Examples of the Relationship between Adherence and Viscoelastic Properties

As demonstrated in the next few examples, rheological properties govern, to a large extent, the physical properties of adhesives during the bonding and debonding stages. The link is particularly important in the case of PSAs. At various steps of the assembly process, the rheological behavior of the material plays a leading role. Typically, PSAs are used as thin films from 20 to 100 μm (see also Applications of Pressure-Sensitive Products, Chapters 1 and 4). They are processed and coated differently according to their composition [solvent based, water based, hot-melt PSAs (HMPSAs), etc.; see Ref. 16 for more details on the various families of PSAs and Technology of PressureSensitive Adhesives and Products, Chapter 10]. In the case of HMPSAs, high temperature and low pressure are used in the process, so one can define the relevant rheological parameters in the terminal region of relaxation to control the properties of the final film. In the case of solvent-based or water-based room-temperature liquid acrylic PSAs, a weak pressure must be applied during coating on the machine to help the adhesive cover the surface. In this case, compliance of the material is the relevant rheological parameter.

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

G (au)

G inf

G0

(a)

Time (au) Plastic

U

Hard

Flow

Static

U (w)

 O

V

o

X l1 V.τ V.τ.Ginf/G0

(b)

W

FIGURE 4.1 Crack shape during the detachment stage for a model soft adhesive. (a) Relaxation modulus versus time. (b) Opening of the crack. (From de Gennes, P.G., Langmuir, 12, 4497–4500, 1996.)

The viscoelastic properties are also responsible for the high energy losses during the debonding process. After we present some examples correlating the rheological properties with adherence performance, we will focus on rheological properties and identify the relevant rheological parameters in the bonding and debonding stages. 4.2.1.1 Correlation between the Various Peeling Domains and the Relevant Rheological Parameters: Some Examples in the Linear Viscoelastic Domain Figure 4.2 illustrates the complex adhesion/fracture behavior as a function of peeling rate in a typical floating roller test for a model formulation. Figure 4.2a demonstrates the evolution of the peeling force, F (corrected by a temperature factor Tref /T, with T the experimental temperature and Tref the reference temperature of the master curve to take into account the influence of temperature on force), as a function of peeling rate, V (corrected by a shift factor aT), using a floating roller test [17]. This peeling test is

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Flexible aluminum substrate

0 1

2

Cohesive failure

(c)

3

4

5

6

Length (au)

7

8

(d)

9

Glassy failure

Stick-slip failure

log (aT .V ) (mm/min−1)

Interfacial failure

Length (au)

FIGURE 4.2 (a) Peeling master curve (floating roller test, Tref = 20°C) for a model formulation based on a homopolymer (polybutadiene) and a tackifying resin. Peeling force is plotted (F) as a function of the logarithm of the reduced peeling rate (aT · V). The data were obtained at different temperatures (From Derail, C., Allal, A., Marin, G., and Tordjeman, P., J. Adhesion, 61, 123–157, 1997.) and shifted along the x-axis to build the master curve. In this example, the volume fraction of resin is equal to 70%. (b) Scheme of the floating roller test. (c) Force versus peeling length at constant rate in cohesive or interfacial domain. (d) Force versus peeling length at constant rate in the stick–slip domain.

(b)

Rigid aluminum substrate

F.Tref/T(N)

(a)

0

20

40

60

80

100

120

140

160

Force (au)

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Force (au)

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

particularly relevant for quantifying the adherence performance of adhesives in an experimental situation that approximates practical applications. The test consists of peeling a sample at constant rate with a 90° peeling angle using a thin fi lm of adhesive coated between two substrates, as illustrated in Figure 4.2b. The peeling rate strongly influences the adherence performance. It is important to recall that this master peeling curve was obtained by applying the time–temperature equivalence with a shift factor, aT , which is identical, within experimental uncertainties, to the shift factor obtained from rheological properties. The different failure domains from the cohesive zone (at low peeling rate) to glassy failure (at the highest peeling rates) are visible. For model adhesives with well-identified relaxation domains, each fracture domain is separated by a maximum of the peeling force. In each zone, we report the average force measured during the peeling test along about 20 cm of probe. That force is stable (see Figure 4.2c), except in the stick–slip domain where the force oscillates strongly (see Figure 4.2d). In this last case, the dotted lines in Figure 4.2.a correspond to the minimum force, Fmin, and the maximum force, Fmax, respectively, observed in the stick–slip detachment domain. Figure 4.3 illustrates the rheological behavior of the same formulation obtained by mechanical spectroscopy. Model formulations exhibit various relaxation domains that are well separated as a function of frequency; similarly, well-identified failure domains are clearly identified as a function of peeling rate on peeling curves, as previously described. The various rheological domains are linked to the adhesive performance, as depicted in the trumpet model for the fi rst transition (from cohesive failure to interfacial failure). In fact, it seems that this can be extended to other fracture transitions observed on a peeling master curve; this has been observed for different polymeric bases [4,6,18–22]. These qualitative relations may become analytical 8

log(G′, G ″) (Pa)

7 6 5 4 3 2 −3

−2

−1

0

1

2

3

4

5

log(a T. ω) (rad/s)

FIGURE 4.3 Rheological master curve [G′ (
) and G″ ()] as a function of circular frequency, Tref = 20°C) for a model formulation based on a homopolymer (polybutadiene) and a tackifying resin. (From Derail, C., Allal, A., Marin, G., and Tordjeman, P., J. Adhesion, 61, 123–157, 1997.) The volume fraction of resin is 70%.

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Fundamentals of Pressure Sensitivity

when the polymer is well defi ned. In that case, the maximum relaxation time, measured in the terminal domain of mechanical relaxation, is the relevant reduction parameter in the peel rate scale for peeling curves plotted in the cohesive failure zone [4] (see also Chapter 11). In the case of semicrystalline polymers for HM applications, the characteristic time of transition between a viscoelastic liquid behavior (amorphous) and a viscoelastic solid behavior (semicrystalline) by mechanical spectroscopy is of the same order of magnitude as the time necessary to observe the transition from cohesive to interfacial failure measured by a peel test at very low peel rate and room temperature [19]. A typical domain of application for which the rheological behavior of the adhesive is particularly relevant is the domain of medical applications (see also Applications of Pressure-Sensitive Products, Chapter 4). The deformation of the substrate (skin) is of the same order as the adhesive fi lm deformation during the debonding stage [23,24]. Finally, some authors have presented models that estimate the peeling force values from the rheological properties of the adhesive. The model proposed by Gent and Petrich [15] (see Equation 4.2, where F is the peel force, W is the thickness of the adhesive, σ is the tensile stress, and ε is the extensional deformation. F
W ⋅ ∫

 max

0

 ⋅ d

(4.2)

leads to a fracture criterion that is so large that this model cannot reasonably describe the physical fracture phenomenon. On the basis of the previous examples, one can conclude that rheological properties are relevant during the debonding stage, particularly for soft adhesives such as PSAs or HMPSAs. If the linear viscoelastic properties are directly related to the adherence properties in the case of soft adhesives, as presented above, the physics of the debonding process itself is not clearly understood. Other parameters must also be taken into account in relation to the adhesion processes at the interface/interphase itself. The previous cases dealt with strong adhesion (high-energy surfaces in general). When adhesion is poor, the relationships are more complex and the rheological properties of the bulk of the adhesive are not the relevant properties because of the competition between adhesion at the interface and rheological properties of the bulk, as well as the interphase [6] (“modulation of adhesion”). We may partly conclude that the linear viscoelastic parameters are relevant to formulate PSAs. Derail and colleagues [12,13] demonstrated that it is possible to design molecular structures to fit properties dedicated to a given application: adhesives based on triblock/diblock blends have been improved by designing tetrablockbased or star/diblock blend-based “calculated” formulations. Table 4.1 presents some adherence performances of various adhesives derived from this concept. When a similar rheological behavior is mimicked using molecular design, adherence performances are also similar. Some of these features were discussed in detail by Yarusso in Ref. 25.

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

4-9

TABLE 4.1 Comparison of Adherence Performances for PSA Blends Based on Different Types of Block Copolymers with Different Architectures SIS + SI

SISI

SI4 + SI

Peeling angle = 180° On glass at room temperature On glass at 3°C On polyethylene at room temperature On polyethylene at 3°C

36 24.5 24.5 23

N/25 mm 24 21 27 16.5

30 24.5 27 18.5

Loop tack On glass at room temperature On glass at 3°C On polyethylene at room temperature On polyethylene at 3°C

27 12 20.5 6

N 28.5 10 30.5 10

31.5 14 30 10

Basis of Formulation

Note: SIS + SI is a blend of a triblock copolymer and a diblock copolymer, SISI is a tetrablock copolymer, and SI4 + SI is a blend based on a radial copolymer and a diblock copolymer. All copolymers have been synthesized with the aim of obtaining a similar rheological behavior. The structural parameters of the copolymers were calculated from the model detailed in Derail, C., Cazenave, M.N., Gibert, F.X., Kappes, N., Lechat, J., and Marin, G., J. Adhesion, 80, 1131–1151, 2004.

4.2.1.2 Correlation between Rheological Properties in the Nonlinear Domain and Adherence Experiments Block copolymers are smart materials used as a polymer base for commercial HMPSAs (see also Technology of Pressure-Sensitive Adhesives and Products, Chapters 3 and 8). These polymers are also good candidates for fundamental studies on structure/property relationships because they are well-defi ned materials: anionic polymerization allows the synthesis of quasi-model copolymers with well-defined structures (chemical nature and length of the various sequences, branching topology with a low polydispersity index). These block copolymers must be formulated with adequate tackifying resins to exhibit high tack properties (see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 11). As demonstrated previously, various topologies of block copolymer can exhibit a similar rheological behavior in the linear domain [12]. However, Roos [26] demonstrated on similar samples that the nonlinear behavior obtained from tensile tests may be extremely different. Observation of the fibrillation process provides the experimental basis with which to answer questions about the effects of nonlinear viscoelastic properties of these materials on adherence and tack properties. The first observations of Kaelble during peeling tests [27], the investigations carried out by Zosel [28], the direct observations of Lakrout et al. [3] of the large deformation of viscoelastic adhesives, the observations of Poivet and co-workers [29] for liquids, and more recently the study of Yamaguchi et al. [30] reinforce the relevance of detailed studies at large deformation. Particularly, using a new visualization technique, the Doi team [30–32] performed in situ observations of the stereoscopic shape of cavities formed during the debonding stage in a probe–tack test. These authors determined that the cavity shape and the interfacial fracture behavior are strongly governed by the viscoelastic properties of the soft adhesives prepared with different amounts of cross-linker.

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Fundamentals of Pressure Sensitivity

Recently, Teisseire et al. [33,34] performed tack experiments on highly viscous silicone oils and describe the observed phenomena on the basis of Maxwell rheological behavior. They observed with these model fluids that, at high velocities, cracks appear before bubbles because of cavitation. An important conclusion of this work is that interfacial cracks can be observed even with liquid materials in a new regime where bubbles and cracks are observed simultaneously. According to these examples, it seems that all typologies of detachment have not been explored yet. An important conclusion is that the use of model materials helps to defi ne more specifically the various fracture modes as a function of the viscoelastic properties according to the time of deformation (i.e., the rate of detachment in the case of peeling or tack measurements). We will discuss further under modeling some of the examples presented above. 4.2.1.3

Quantitative Relationships

Zosel [35] drew a comparison between the stress–strain curves obtained for polymers with different average molecular weights between entanglements (Me). For Me values lower than 104 g/mol, one can observe fibrils during the debonding stage. At higher values of Me a homogeneous deformation is observed during the debonding stage. High values of Me can be obtained for acrylic systems (such as polybutyl acrylate [36]) or by adding compatible low-molecular-weight species (like compatible resins) to the polymer. Zosel [35] noted that when one refers to the Dahlquist criterion for obtaining pressure sensitivity (G′ ≤ 3 × 105 Pa), one can calculate an equivalent Me of 104 g/mol. This is indeed the value of Me at which Zosel observes the onset of fibrillation. Derail et al. [4] developed a model accounting for the rheological behavior of the adhesive during the debonding stage as well as the mechanical parameters in a floating roller test (geometry of the peeling system, radius of curvature of the substrate, etc.). The stress within the adhesive is calculated at high deformation using a nonlinear rheological integral constitutive equation. In this model, the fracture criterion proposed in the cohesive domain refers to maximum deformation. In the interfacial domain a critical energy criterion derived from the trumpet model is used. More recently, Lakrout et al. performed a study of nonlinear properties to describe tack results obtained on PSAs based on block copolymers. In particular, he studied the effect of the diblock copolymer content in a “full” formulation of PSA [7,26]. A PSA formulation based on block copolymers is basically composed of a blend of triblock and diblock copolymers with tackifying resins. Figure 4.4a illustrates the strain-hardening effect on the stress–strain curves measured with a probe–tack test. As explained in the last part of this chapter, one can clearly see an increase in stress at large strains (the plateau value increases), with high corresponding strain rates. Creton and co-workers noted that the value of the storage modulus G′ measured in the linear domain at an equivalent frequency is about the same regardless of the diblock content, whereas the behavior at high rates of strain is different. Creton et al. [7] propose to estimate the nonlinear elastic properties by a tensile test. In Figure 4.4b, for the same samples as Figure 4.4a one has reported the tensile stress–strain curves obtained at the highest rate from tack experiments. There is a large difference depending on the diblock content regarding probe–tack results.

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1.6

Stress (MPa)

1.4 1.2

Percent SI increases

1.0 0.8 0.6 0.4 0.2 0.0 0

5

10

15

Strain

(a)

Normal stress (MPa)

0.8 Percent SI increases 0.6 0.4 0.2 0.0 0 (b)

5

10

15

20

Deformation

FIGURE 4.4 (a) Stress–strain curves for different diblock content (0–54%) in SIS + SI blends and (b) tensile stress–strain curves on the same samples. (From Creton, C., Roos, A., and Chiche, A., in Adhesion: Current Research and Applications, W.G. Possart, Ed., Wiley-VCH, Weinheim, 2005.)

Creton et al. propose an analysis based on the comparison of the nominal stress obtained from tensile tests or probe–tack tests and conclude that the stress level obtained during the probe–tack test can be derived from uniaxial tensile data obtained at high strain rates. When parallel fibrils are formed during elongation of the adhesive, each fibril exhibits the same type of mechanical behavior observed in tensile testing. In this way, an estimate of the stress level is possible from tensile testing at high strains. A basic question remains, however: how does each fibril detach from the surface? The last point in Ref. 7 concerns the ability to form a fibrillar structure. Probe–tack tests have been performed on different surfaces (steel and ethylene–propylene copolymer, see Figure 4.5) with similar adhesives. Whatever the surface, stress increases rapidly. Cavities are nucleated in the two cases but, for the low-adhesion surface, cavities propagate as interfacial cracks coalesce and the stress drops rapidly to zero. For the high-adhesion surface, cavity walls are extended and foam is created with fibrils (Figure 4.6). The key parameter in this case, where there is a balance between interfacial propagation and bulk dissipation, is the ratio Gc/E, where Gc is the critical energy release rate and E is the elastic modulus. When Gc is lower (e.g., ethylene–propylene copolymer), interfacial crack propagation is easier. Marin and Derail [6] qualitatively observed the same behavior by peeling on different substrates. The ratio Gc/E seems to be a key parameter in controlling detachment.

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Fundamentals of Pressure Sensitivity

0.6 Detachment on steel

Stress (MPa)

0.5 0.4 0.3 0.2 Detachment on copolymer EP 0.1 0.0 0

2

4

6 Strain

8

10

12

FIGURE 4.5 Probe–tack data for a SIS + SI (19% SI) on steel and an EP copolymer. (From Creton, C., Roos, A., and Chiche, A., in Adhesion: Current Research and Applications, W.G. Possart, Ed., Wiley-VCH, Weinheim, 2005.)

FIGURE 4.6

Fibrils during a probe–tack test can be deformed with a very high extension.

However, the determination of Gc is rather complex and Gc can be identified as a first approximation with the thermodynamic work of adhesion [37].

4.2.2

Process and Material Properties

When an adhesive is deposited on a surface, the physical parameters relevant to the bonding stage are important to establish a good link between the surface and the

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

adhesive layer. For example, the time of contact or the force applied during the bonding stage can modify adherence properties [3,33]. The nature of the surface can be changed by making physical or chemical modifications. Lakrout et al. [3] demonstrated the strong coupling between surface properties (surface energy, roughness, etc.) and the bulk properties of the adhesive, the coupling governing the nature and location of the fracture (fibrillation, cavitation, etc.). In the particular case of HMPSAs, the deposition of the fi lm is performed at high temperature with a liquid-like adhesive. After this stage, the temperature of the fi lm of adhesive decreases and the variations in viscoelastic properties of the bulk adhesive during the process may be studied in laboratory experiments using thermomechanical analysis (see Figure 4.7). As thermomechanical analysis allows one to follow the evolution of the complex shear modulus as a function of temperature at a given heating or cooling rate and a given frequency. It is also possible to establish a relation between the temperature scale of thermomechanical curves and the time scale in a given process by knowing the evolution of temperature as a function of time within the adhesive during that process. According to the nature of the polymer, this variation may differ. The inset in Figure 4.7 presents the evolution of the temperature of an adhesive along the same process for two typical cases: a semicrystalline polymer and an amorphous polymer. Crystallization of the material modifies largely the time–temperature dependence by increasing the open time. For more details, please refer to Ref. 38. As illustrated in Figure 4.7, the adhesive becomes harder and increasingly elastic as the temperature decreases. Because adhesives are viscoelastic materials, one can observe various viscoelastic relaxation domains upon cooling. In the first stage (application of the adhesive), the relevant parameter (step 1 in Figure 4.7) is the viscosity at the application

3

G′

2

Temperature 3

2 1

Temperature

1

Semi crystalline

Amorphous

Setting time

Time

Open time

FIGURE 4.7 Deposition of the fi lm of adhesive for the HM case. Three relevant parameters exist for the bonding stage: (1) a viscosity level, (2) a modulus level (Dahlquist criteria), and (3) a compliance level. The inset graphs temperature versus time within the adhesive according to the type of adhesive.

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Fundamentals of Pressure Sensitivity

temperature. In the case of formulations based on homopolymers or random copolymers, that step of the process occurs above the melting or glass transition temperature, which can be adjusted by altering the composition of the formulation (molecular weights, copolymer structure, resin nature, and content, etc.; see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 11). For adhesives based on block copolymers, the process must take place above the order–disorder temperature [39]. The resin content and its nature, as well as the molecular weight of the elastomer part of the adhesive, allow the transition temperature to be adjusted, as well as the level of viscosity. The thermodynamic effect of tackifying resins allows adjustment of the glass transition temperature with respect to the domain (temperature) of use and process of the adhesive. One can then define an open time (top) for HM adhesives as the time during the process where the adhesive keeps its instantaneous stickiness. As a consequence, the contact between the two surfaces of an assembly must be performed within a time shorter than top. The open time can also be defined by thermomechanical analysis (see Figure 4.7) or mechanical spectroscopy using the Dahlquist criterion. In the first case (thermomechanical analysis), one must consider the value of temperature corresponding to a characteristic value of the storage modulus and translate this temperature value to a time value by taking into account the time–temperature correspondence, as explained above. In the second case, one may use the Dahlquist criterion [40] (i.e., a modulus value of about 105 Pa at a frequency of 1 Hz). Adding a resin to a polymer decreases its elasticity level by increasing the molecular weight between entanglements (topological effect), so the resin content may control the storage modulus level. PSAs present natural stickiness and the concept of open time is irrelevant. In this particular case, however, the elasticity of the adhesive fi lm plays an important role. In the process of making labels with HMPSAs, for example, there is a cutting stage in which the substrates and the thin fi lm of adhesives are cut together and relevant short-time elastic properties are necessary. In conclusion, the bonding stage in a practical situation is much more complex in comparison with a laboratory experiment because the temperature mapping within the adhesive, for example, is complex in a real adhesive processing situation. According to the discussion above, one could shift from one family of adhesives to another, taking as a reference an “ideal” rheological behavior defined for a given application. In Figure 4.8, we demonstrate that very similar viscoelastic properties (hence adherence properties) can be obtained with different types of polymers. 1. The first polymer (dots) exhibits a low secondary plateau in the terminal region (lowest frequencies). The level of the corresponding modulus, which lies below the Dahlquist criterion, is obtained by adjusting the morphology of block copolymers. This plateau defines a solid-like behavior that “eliminates” the flow domain observed at large times (low frequencies) for viscoelastic liquids. The glass transition temperature may be adjusted according to the temperature of use and type of application, using tackifying resins with relevant glass transition temperatures. This is the thermodynamic effect of adding resins, as opposed to the topologic effect on elasticity described above. With regard to processing, a low viscosity is obtained above the order–disorder temperature for copolymers.

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4-15

G ′ and G ″ (au)

Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

Frequency (au)

FIGURE 4.8 “Reference” rheological behavior [G′ (
) and G″ () at Tref = 20°C] for a PSA for a given family of applications. One distinguishes between the behavior of block copolymer formulations (secondary plateau for G′) and the behavior of an acrylic-based adhesive with a gel-like behavior in the terminal domain of relaxation (full lines).

2. The second polymer exhibits the typical signature of a critical gel in a wide frequency range. In the terminal relaxation domain, the elastic modulus varies slowly and its value is slightly higher than that of its viscous counterpart. The signature is typically obtained with acrylic emulsions for PSA applications.

4.3

Some Models of Debonding: A Story about Cavitation

The experimental results described and their analysis demonstrate that rheological behavior plays an important role in adhesive performance, especially for tack and peeling. Various authors proposed models for the debonding process based on probe–tack experiments in which it is possible to observe, in detail, the debonding stage (see also Chapter 6 and Applications of Pressure-Sensitive Products, Chapter 8). In this type of test (see Figure 4.9), a flat punch is indented onto a fi lm of a sticky adhesive on a rigid substrate (glass, metal, etc.). During the bonding stage, the normal force is controlled and kept constant during a given contact time (Figure 4.9a). Then, the flat punch pulls out at a constant rate. During this debonding stage, measurements of the force and displacement allow the derivation of a stress–strain curve. One can observe optically the mode of detachment from the substrate (Figure 4.9b). In this stage, according to the rheological behavior of the thin film of adhesive and the debonding rate, cavitation can be observed. Different experimental and theoretical studies of the growth kinetics of cavities have been recently presented in the literature, as discussed in this chapter.

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4-16

Force

Flat punch

0

Displacement

Fundamentals of Pressure Sensitivity

0 Adhesive film

Stress

(a)

(b)

Strain

FIGURE 4.9 (a) Probe–tack test and experimental parameters. (b) Different stages of the deformation on a typical stress–strain curve with pictures of the various detachment states of the adhesive.

Peeling experiments can provide important information in an experimental situation that is close to practical or industrial use. Although fibrillation has been widely studied in peeling experiments, this geometry is not the most relevant for fundamental studies exploring the debonding stage. In 1999, Gay and Leibler [41] identified an interest in viewing the thin fi lm of an adhesive upon debonding in a short review on tack. Hence, we will focus in this part on tack experiments, which recently yielded the most relevant information on the debonding stage. Using the probe–tack test, Lakrout et al. [3] studied the kinetics of the occurrence of cavities, which is an important phenomenon in understanding the origin of the debonding stage for soft adhesives. Dollhofer and co-workers [42] studied the effects of surface tension on the expansion of cavities. Assuming a spherical shape, they indicated a good agreement between the model and experimental results where rapid cavity growth is observed. In the same field, Chikina and Gay [43] proposed semiquantitative models to specify the exact role of cavitation, particularly the number of cavities, in the debonding process. More recently, Teisseire et al. [34], based on the observation of the debonding stage of viscous oils, described the kinetics in the debonding stage and they demonstrated to what extent interfacial fracture can be encountered with model viscoelastic liquids. A theoretical model is thus proposed and a representation of the different debonding regimes is proposed as a function of adimensional parameters.

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

4-17

Yamaguchi and Doi [44] proposed a block model which accounts for the main factors appearing during the debonding stage: viscoelasticity of the PSA, cavitation, and slippage at the surface. Although the authors make some simplifications, particularly for the cavity expansion (a spherical expansion is chosen in the model), the results of this model allow the reproduction of the stress–strain curve obtained with a probe–tack test. The model does not consider interfacial fracture, however, and the viscoelastic behavior of the adhesive seems oversimplified. Other models have been proposed in the literature. The two models described above demonstrate that the phenomena appearing during the debonding stage are quite complex. The viscoelastic behavior, in both the linear and the nonlinear regimes, is highly relevant. Therefore, we will focus on the measurement of viscoelastic properties of adhesives in the last part of this chapter.

4.4

Measurement of Viscoelastic Properties of Soft Polymers

As indicated in the previous paragraphs, different aspects of the viscoelastic behavior of polymers can be directly linked to the adhesive and process properties of PSAs.

4.4.1

Time Dependent Effects and Linear Viscoelasticity

One can define various rheological parameters of the adhesive relevant to specific processing or end-user (adhesion) properties (see also Chapter 7 and Applications of Pressure-Sensitive Products, Chapter 7). 4.4.1.1

The Complex Shear Modulus

In the case of soft adhesives, basic linear viscoelastic experiments are performed in the whole frequency domain. The evolution of the complex shear modulus as a function of circular frequency (G*(ω)) describes the rheological properties of the adhesive through its various relaxation processes. The real part of this complex function is the storage modulus (G′(ω)), which describes the level of “elasticity” of the system as a function of frequency (or time, through a Fourier transform). The imaginary part is the loss modulus (G″(ω)), which describes the variations of the “viscosity” of the system as a function of the frequency (or time) of solicitation of the material. The ratio between the dissipated energy and the stored energy gives the value of the loss angle, which is a relevant picture of the various relaxation processes in the frequency (or temperature) range. tan  = G″/G′

(4.3)

The complex shear modulus G*(ω) is measured using a rotational rheometer. The flow experienced by the material must be as close as possible to simple shear fl ow to generate well-defined experimental data in terms of material functions. Different flow geometries can be used, as summarized in Figure 4.10. In the case of soft adhesives, the most typical rotational geometries used are cone and plate, parallel plates, and rectangular torsion for hard materials (glassy domain).

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4-18

Fundamentals of Pressure Sensitivity

(a)

(b)

(c)

(d)

G ′ and G ′′ (au)

FIGURE 4.10 Measurement of viscoelastic properties with basic rotational geometries. (a) parallel plates, (b) cone and plate, (c) rectangular torsion, and (d) concentric cylinders (couette flow).

Frequency (au)

G′ and G ′′ (au)

(a)

(b)

Frequency (au)

FIGURE 4.11 Typical rheological behavior of a PSA. (a) Master curve at Tref = Tuse of a PSA (block copolymer + tackifying resins). (b) Master curve at Tref = Tprocess of the same adhesive.

The choice of the geometry depends on the behavior of the adhesive (from liquid-like to solid-like). Cone and plate or parallel plate geometries were used for the experimental data presented in this chapter. Figure 4.11 presents the typical rheological behavior of a PSA. A master curve is obtained at a reference temperature using time–temperature

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

4-19

equivalence. Figure 4.11a exhibits a solid-like behavior with a secondary elastic plateau due to either a nanostructure formation for block copolymers or crystallization in the case of semicrystalline polymers. As discussed previously, the level of the storage modulus is the key parameter for “instantaneous” adhesive properties. The secondary plateau at low frequencies insures a no-flow condition. Figure 4.11b exhibits a liquid-like behavior: this adhesive could flow at long times. The time for application of the adhesive would have to be smaller than the time to flow. The reptation concept introduced by de Gennes [11] and its subsequent improvements set up a general framework describing the linear viscoelastic behavior of polymers and, hence, the evolution of the complex shear modulus as a function of frequency for homopolymers. Benallal et al. [45], proposed an analytical approach to describe the relaxation function G(t) of linear homopolymers melts as a function of polymer structure. In this approach, G(t) can be considered the sum of different independent relaxation processes. G(t) = G rep(t) + GrA(t)

and

GrB(t) + GHF(t)

(4.4)

1. Grep(t) characterizes the low-frequency relaxation (longest times) and is linked to the terminal relaxation process, which is the signature of reptation (for free chains as homopolymers for example). The reptation time, τrep, is the relevant parameter in this domain. This domain is certainly the most important for the adhesive application. 2. GrA(t) and GrB(t) correspond to the Rouse relaxation processes, which characterize the relaxation of the entanglement network. 3. GHF(t) describes the α relaxation process, which is the mechanical image of the glass transition. For a more detailed model describing each relaxation domain, readers could refer to Refs 5, 45, and 46. This model can be modified and extended to the case of diblock and triblock copolymers, particularly by taking into account the effect of the nanostructure in the terminal zone of relaxation at the lowest frequencies as well as the specific relaxation of the elastomeric sequence of the diblock copolymers. In the case of diblock copolymers, the elastomer sequence is considered to relax like the branch of a star polymer [5]. As a consequence, by inverting these molecular models of viscoelasticity [10,12,46], it is possible to “design” new molecules to obtain tailored viscoelastic properties and improved adherence and process properties, as discussed previously (see Table 4.1). Figure 4.12 presents the rheological data obtained with three different types of block copolymer formulations designed (“calculated”) to achieve a similar rheological behavior: 1. Styrene–isoprene–styrene (SIS) + styrene–isoprene (SI), a traditional base for HMPSA 2. SISI, a tetrablock copolymer (without diblock added) in which the free isoprene sequences play the same role as the free isoprene sequence of the diblock copolymer added in (SIS + SI) blends 3. SI4 + SI, a star copolymer blended with a diblock copolymer (in the last case, the radial block copolymer improves the shear properties of the adhesive)

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Fundamentals of Pressure Sensitivity

+

=

+

+

=

G ′ for SIS + SI

G′ and G ′′ (au)

G ′′ for SIS + SI G′ for SI4 + SI G ′′ for SI4 + SI G ′ for SISI G ′′ for SISI

Frequency (au)

FIGURE 4.12 Molecular design. Structural parameters of new molecules or molecular topologies may be calculated to obtain an expected rheological behavior. Master curves have been vertically shifted. (From Derail, C., Cazenave, M.N., Gibert, F.X., Kappes, N., Lechat, J., and Marin, G., J. Adhesion, 80, 1131–1151, 2004.)

4.4.1.2

Zero-Shear Viscosity

As described previously, the adhesive must exhibit a liquid-like behavior in the application process. In the case of semicrystalline polymers [such as ethylene–vinyl acetate copolymers for HM applications], the process temperature must be above the melting temperature, whereas for adhesives based on block copolymers (e.g., SIS, SBS, SEBS, etc.) the corresponding temperature can be the order–disorder temperature. Figure 4.11b illustrates the rheological behavior at a reference temperature well above the temperature of use (typically the temperature of the process). The shape of the terminal region is different. The adhesive exhibits a liquid-like behavior, which can be characterized by its zero-shear viscosity and maximum relaxation time. These parameters are relevant to the process, as described previously. In the case of HM adhesives, concentric cylinders can be used to measure the low viscosities corresponding to the processing temperature. A constant strain rate (Sr) is applied, and the stress is measured (σ). The viscosity (η) is then calculated according to the following equation:  = /Sr

(4.5)

An important feature is the shear thinning (see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 8) or the shear thickening behavior of polymer-based

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

materials. The viscosity increases or decreases with the strain rate, so the strain rate of the viscosity measurement must be relevant to the process. 4.4.1.3

Compliance

The compliance of adhesives is certainly an important feature during the bonding stage in which the adhesive flows under low pressure (see also Applications of Pressure-Sensitive Products, Chapter 4). The compliance function, J(t), obtained from creep experiments, can be defined as follows: J(t) = (t)/0 = JG + t/0 + JR(t)

(4.6)

where JG is the instantaneous compliance that describes a purely elastic behavior; t/η 0 is a transient term that describes the partial flow of the material, and JR(t) is associated with the retardational creep behavior typical of a viscoelastic material. According to Equation 4.6, under low pressure (i.e., stress σ0), the PSA may be more or less deformed; depending on (i) the value of the newtonian viscosity (η 0) and (ii) the retardational compliance transient function, JR(t), the behavior upon bonding can be quite different. Figure 4.13 presents an example of the variation of the compliance function with the different terms described in Ref. 47. For more details on the viscoelastic behavior of polymers, one can refer to Ref. 48, and Ref. 49 contains more details regarding calculations for the various flow geometries.

1.E−2 J(t ) calculated

Compliance (Pa−1)

1.E−3

Retardation term Degenerated term J(t ) experimental

1.E−4

1.E−5

1.E−6 1.E−2

1.E −1

1.E 0 Time (s)

1.E +1

1.E+2

FIGURE 4.13 Transient creep function: the compliance is the sum of different terms as a function of time: t/η 0, viscous term; JR(t), retardational term.

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Fundamentals of Pressure Sensitivity

4.4.2

Large Deformations and Nonlinear Aspects

In 1947, Weissenberg [50] reported the “rod climbing” effect, a pioneering observation that opened the way to the study of the viscoelastic and nonlinear effects in a wide range of complex fluids such as polymeric materials. For adhesive applications, one of the most striking effects of nonlinear effects is the strain-hardening effect in elongational flow, as pointed out by Creton et al. [7]. At large strains, polymers in general and adhesives in particular may present strong strain-hardening effects that will govern adherence energy and kinetics in tack experiments. Experimental studies of the elongational viscosity of polymer melts demonstrate typical nonlinear effects such as shear thinning in shear flows and strain hardening in uniaxial elongational flow. One must use special elongational rheometers, such as the Meissner rheometer [51] order to obtain the relevant material functions. In this type of rheometer, a rectangular sample of polymer is elongated at constant strain rate and a temperature that corresponds to the flow domain (on the Meissner apparatus, the temperature ranges from 50 to 350°C and the strain rate from 10−3 to 1 s−1). Readers will find more details on this elongational rheometer in Refs 52–54. According to the nature and topology of polymers, one can observe different types of behavior. Homopolymers, even with broad molecular weight distribution, present a behavior, as illustrated in Figure 4.14. The transient curves follow basically the Trouton behavior, with the Trouton viscosity being three times the shear viscosity, up to the point at which the sample breaks. On the contrary, one can measure important strain-hardening effects in the case of long-chain branching and cross-linking (see Figure 4.15).

1.E+7

0.0506 s−1 0.1088 s−1

1.E+6

0.2782 s−1 0.9483 s−1

ηel (Pa s)

Linear viscoelasticity 1.E+5

1.E+4

1.E+3 1.E−2

1.E −1

1.E 0 Time (s)

1.E +1

1.E +2

FIGURE 4.14 Transient elongation viscosity at start-up of flow for a linear polymer (polypropylene, Mw = 370 kg/mol) at different strain rates. The solid line indicates the Trouton transient viscosity calculated from linear viscoelasticity.

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Role of Viscoelastic Behavior of Pressure-Sensitive Adhesives

1.E+8

4-23

0.01 s−1 0.0277 s−1 0.0941 s−1

ηel (Pa s)

0.2966 s−1 1.E+6 Linear viscoelasticity

1.E+4

1.E−3

1.E −1

1.E+1

1.E +3

Times (s)

FIGURE 4.15 Elongation viscosity versus time for long-chain branched (LCB) polyolefi ns at different strain rates. Strain hardening is a specific signature of LCB.

Figures 4.14 and 4.15 demonstrate that branched polymers (combs, trees, pom-pom structures, and random long-chain branched polymers) exhibit a strain hardening that can be controlled by the molecular weight and topology of the materials. In the case of adhesives, the behavior at high strain can be improved by the addition of triblock or star polymers, which govern strain-hardening effects. The description of this type of model is beyond the scope of this chapter, but for more information, one can fi nd examples of applications in Refs 55 and 56. Experiments on adhesives in elongational flow will certainly yield important information on the high viscoelastic losses one can obtain (and control) with these materials. More specifically, we believe that the control of the topology of polymers designed for adhesive applications may lead to breakthroughs in the control of adherence of PSAs and hot-melts, as polymer chain topology may lead to exotic shear and elongational properties in the bulk and in the interface/interphase. This feature, already used for improving the process and physical properties of thermoplastics, could lead to interesting applications in the case of adhesives.

4.5

Conclusions

This chapter focused on the effect of the viscoelastic properties of PSAs on their adherence properties, as measured using peeling or probe–tack experiments. The probe–tack test brings new insight to the physics of adherence with visualization of the detachment stage. One can identify, in particular, different stages such as cavitation, fibrillar extension, and interfacial cracking. The debonding stage is indeed quite complex and there is not yet a comprehensive understanding or model for all observations.

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4-24

Fundamentals of Pressure Sensitivity

Crude rheological models are often used to set up quantitative predictions, leading to unrealistic calculations. As indicated in this chapter, the viscoelastic properties govern, to a large extent, adherence behavior. The rheological behavior in the linear viscoelastic domain provides the main information and allows understanding and improvement of the main features in the formulation of adhesives. This may be directly applied in the case of practical/ industrial applications (formulation of adhesives, design of molecules, improvement of processes, etc.). Some authors recently indicated that nonlinear viscoelastic properties may be particularly relevant during the detachment stage, in which fibrils stretch out. Two points should be highlighted for better knowledge regarding the adherence of highly dissipative adhesives. 1. Correlation for the understanding of strain hardening in branched or structured polymers along elongation and tack experiments. Star polymers can improve performance. Could exotic topologies lead to a better control of adhesion/adherence? 2. Chemical or topological modification of surfaces allows the modulation of adhesion at the surface/interface/interphase. A large number of studies now deal with this aspect of adhesion. Some original ideas could come from examples derived from nature (gecko, mussel, fly, etc).

Acknowledgments The authors thank Costantino Creton from ESPCI for the data and figures on tack experiments. Frédéric Léonardi from IPREM-EPCP is also acknowledged for helpful discussions on the structure–property relationships and for the data and figures obtained using the Meissner rheometer.

References 1. Benedek, I., In Pressure Sensitive Design and Formulation, Application, I. Benedek, Ed. VSP, Leiden, 2006, pp. 1–23. 2. Creton, C., Fabre, P., In The Mechanics of Adhesion, D.A. Dillard and A.V. Pocius, Eds. Elsevier, Amsterdam, 2002, pp. 535–575. 3. Lakrout, H., Sergot, P., Creton, C., J. Adhesion, 69, 307–359, 1999. 4. Derail, C., Allal, A., Marin, G., Tordjeman, P., J. Adhesion, 61, 123–157, 1997. 5. Gibert, F.X., Marin, G., Derail, C., Allal, A., Lechat, J., J. Adhesion, 79, 825–852, 2003. 6. Marin, G., Derail, C., J. Adhesion, 82, 469–485, 2006. 7. Creton, C., Roos, A., Chiche, A., In Adhesion: Current Research and Applications, W.G. Possart, Ed. Wiley-VCH, Weinheim, 2005, pp. 337–363. 8. Lamblet, M., Ph.D. Thesis, Université de Paris VI, 2005. 9. Wu, S., In Polymer Interface and Adhesion, Marcel Dekker, Inc., New York, 1982. 10. Gent, A.N., Schultz, J., J. Adhesion, 3, 281–294, 1972.

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11. de Gennes, P.G., J. Chem. Soc., 55, 572–575, 1971. 12. Derail, C., Cazenave, M.N., Gibert, F.X., Kappes, N., Lechat, J., Marin, G., J. Adhesion, 80, 1131–1151, 2004. 13. Lechat, J., Myers, M., Cazenave, M.N., Derail, C., Kappes, N., Schroeyers, J., U.S. Patent, Exxon Mobil Chemical, WO 03/027182, 2003. 14. de Gennes, P.G., Langmuir, 12, 4497–4500, 1996. 15. Gent, A., Petrich, R.P., Proc. R. Soc. London, A310, 433–448, 1969. 16. Benedek, I., In Pressure Sensitive Design and Formulation, Application, I. Benedek, Ed. VSP, Leiden, 2006, pp. 291–365. 17. The floating Roller test: ASTM D 3167-76. 18. Derail, C., Allal, A., Marin, G., Tordjeman, Ph., J. Adhesion, 68, 203–228, 1998. 19. Gibert, F.X., Marin, G., Allal, A., Derail, C., J. Adhesion Sci. Technol., 13(9), 1029– 1044, 1999. 20. Gower, M.D., Shanks, R.A., Macromol. Chem. Phys., 205, 2139–2150, 2004. 21. Yarrusso, D.J., J. Adhesion, 670, 299–320, 1999. 22. Gower, M.D., Shanks, R.A., Macromol. Chem. Phys., 206, 1015–1027, 2005. 23. Renvoise, J., Burlot, D., Marin, G., Derail, C., J. Adhesion, 83, 403–416, 2007. 24. Chivers, R.A., Int. J. Adhesion Adhesives, 21, 381–388, 2001. 25. Yarrusso, D.J., In The Mechanics of Adhesion, D.A. Dillard and A.V. Pocius, Eds. Elsevier, Amsterdam, 2002, pp. 499–533. 26. Roos, A., Ph.D. Thesis, Université de Paris VI, 2004. 27. Kaelble, D.H., Trans. Soc. Rheo., 9, 135–163, 1965. 28. Zosel, A., Colloid Polym. Sci., 263, 541–543, 1985. 29. Poivet, S., Nallet, F., Gay, C., Fabre, P., Europhys. Lett., 62, 244–250, 2003. 30. Yamaguchi, T., Koike, K. Doi, M., Europhys. Lett., 77(64002), 1–5, 2007. 31. Yamaguchi, T., Morita, H., Doi, M., Eur. Phys. J. E, 20, 7–17, 2006. 32. Doi, M., Yamaguchi, T., J. NonNewtonian Fluid Mech., 145, 52–56, 2007. 33. Teisseire, J., Ph.D. Thesis, Université de Bordeaux I, 2006. 34. Teisseire, J., Nallet, F., Fabre, P., Gay, C., J. Adhesion, 83, 613–617, 2007. 35. Zosel, A., Int. J. Adhesion Adhesives, 18, 265–271, 1998. 36. Ahn, D., Shull, K.R., Langmuir, 14, 3637–3645, 1998. 37. Carelli, C., Deplace, F., Boissonnet, L., Creton, C., J. Adhesion, 83, 491–505, 2007. 38. Vandermaesen, Ph., Marin, G., Tordjeman, Ph., J. Adhesion, 43, 1–15, 1993. 39. For details on block copolymers see: Hadjichristidis, N., S. Pispas, G. Floudas, In Block copolymers: Synthetic Strategies, Physical Properties and Applications, John Wiley & Sons, Inc., Hoboken, NJ, 2003. 40. Patrick, R.L., In Treatise on Adhesion and Adhesives: Materials, Vol. 2, Marcel Dekker, New York, 1969. 41. Gay, C., Leibler, L., Phys. Rev. Lett., 82, 936–939, 1999. 42. Dollhofer, J., Chiche, A., Muralidharan, V., Creton, C., Hui, C.Y., Int. J. Solids Struct., 41, 6111–6127, 2004. 43. Chikina, I., Gay, C., Phys. Rev. Lett., 85, 4546–4549, 2000. 44. Yamaguchi, T., Doi, M., Eur. Phys. J. E., 21, 331–339, 2007. 45. Benallal, A., Marin, G., Montfort, J.P., Derail, C., Macromolecules, 26, 7229–7235, 1993.

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46. Derail, C., Marin, G., In Adhesion: Current Research and Applications, W.G. Possart, Ed. Wiley-VCH, Weinheim, 2005, pp. 229–248. 47. Léonardi, F., Ph.D. Thesis, Université de Pau et des Pays de l’Adour, 1999. 48. Ferry, J.D., Viscoelastic Properties of Polymer, 3rd edition, John Wiley & Sons, New York, 1980. 49. Marin, G., Oscillatory Rheometry, in Rheological Measurement, Chapman & Hall, London, 1998, Chap 1. 50. Weissenberg, K., Nature, 159, 310–311, 1947. 51. Meissner, J., Rheol. Acta, 10, 230–242, 1971. 52. Münstedt, H., J. Rheol., 23(4), 421–436, 1979. 53. Schulze, J.S., Lodge, T.P., Macosko, C.W., Rheol. Acta, 40, 457–466, 2001. 54. Schweizer, T., Rheol. Acta, 39, 428–443, 2000. 55. Sarrazin, J., Ph.D. Thesis, Université de Pau, 2004. 56. Bourrigaud, S., Ph.D. Thesis, Université de Pau, 2004.

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5 Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives 5.1 Introduction .............................................................5-1 5.2 Review of Previous Work ...................................... 5-3

Eng-Pi Chang Avery Dennison Research Center

Work of Dale et al. • Work of Tse • Work of Chu • Work of Chang • Work of Yang and Chang

5.3 General Conclusions ............................................ 5-20 References ....................................................................... 5-20

5.1 Introduction Pressure-sensitive adhesives (PSAs) are polymeric materials that can form a physical bond with another material upon brief contact and with light pressure. Examples of applications of PSAs include office, price marking, and electronic data processing labels, as well as office, packaging, diaper, auto/masking tapes, bandages, decals, etc. The general technical requirements for these types of materials are tack, peel resistance, and shear resistance. A wide range of PSA products have been designed based on the balance of these properties (see Applications of Pressure-Sensitive Products, Chapter 4). From a technical viewpoint, all PSA applications involve bond formation and debonding steps. Bond formation is the result of a polymeric material being able to flow and wet under light pressure and thereby is capable of establishing a contact area with a substrate. The debonding step involves deformation of the polymeric material under stress (typically extension), followed by separation from the substrate. Both the bonding and the debonding processes are related to the rheological properties of the PSA 5-1

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material, but at different rates. Bonding occurs typically in ∼1 s. Debonding, on the other hand, happens at a much higher rate, typically in the range of one-hundredth to one-thousandth of a second. Many investigators established that the adhesive performance of PSAs (e.g., peel resistance, tack, and shear resistance) depends strongly on the bulk viscoelastic properties of the adhesives [1–12]. The William Landel Ferry superposition procedure between rates and temperatures of the tests has been applied very successfully in adhesion tests, both in peel [2,3] and in other modes of debonding [4,7,8]. In addition, correlations between different peel-failure modes with different rheologic regions of PSAs have been established and reported by Aubrey and Sherriff [10]. By combining the small-strain (dynamic mechanical) and high-strain (stress–strain) measurements and correlating the mechanical properties with industry standard “application” properties (e.g., peel resistance and shear resistance), Dale and coworkers [13] determined that the majority of the performance range demonstrated by commercial PSAs is controlled by the bulk mechanical properties (tensile strength, storage modulus, and dissipation) of the adhesive polymers. In addition, room temperature performance properties correlated better with properties measured by dynamic mechanical analysis (DMA) at higher temperatures than those at room temperature, suggesting the trade-off of high strain and high temperature. Tse [14] identified the correspondence of adhesive performance frequencies with adhesive deformation frequencies on the rheological master curves. He proposed that the criteria for good PSAs are low plateau modulus (typically G′ measured at the bonding frequency satisfying the Dahlquist contact criterion) and high-energy dissipation at the corresponding debonding frequency. Chu [15], by comparing the dynamic mechanical properties of commonly employed elastomers and resins, together with their blends, demonstrated how they can be related to PSA industry standard test methods. Additionally, Chu was able to establish that the performance of commercial PSAs can be related to the glass transition temperature (Tg) and plateau modulus, as well as the frequency dependence of dynamic testing. Based on this principle, a viscoelastic window (VW) for good PSAs was proposed. More recently, VWs of different types of PSAs based on dynamic storage (G′) and loss (G″) moduli at bonding and debonding frequencies have also been proposed by Chang [16,17]. Other publications concerning the viscoelastic behavior of PSA material mostly involved the investigation of the effect of tackifiers on the viscoelastic behavior of base polymers, such as styrene–isoprene–styrene (SIS), styrene–butadiene–styrene (SBS) block copolymers [18–22], acrylic copolymers [23,24], natural rubber (NR), and styrene–butadiene rubber (SBR) [24–27]. Compatible tackifiers were very effective in decreasing the plateau modulus and increasing the Tg of the polymers. Tackifiers with poor compatibility normally result in less desirable PSA performance. Through the use of linear viscoelastic theory, one can correlate the PSA performance to fundamental polymer parameters such as molecular weight, entanglement molecular weight (Me), Tg, and cross-link density. The objective of this chapter is to review the correlation of the viscoelastic properties of PSAs with their adhesion performance to describe the role of viscoelastic properties and windows in the design of different PSAs.

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5.2 Review of Previous Work 5.2.1

Work of Dale et al.

Although the time scales of the dynamic mechanical experiments were not close to that of either peel test or shear test, Dale et al. [13,28] nevertheless presented useful correlations between the dynamic mechanical results and the standard peel test and shear test data. This work identified the superposition of high-temperature, small strain, dynamic mechanical measurements with room temperature, high-strain, peel, and shear measurements. Figures 5.1 and 5.2 illustrate, respectively, the excellent correlations between 20 min (dwell time) peel resistance versus log tan δ (dynamic mechanical loss factor) at 127°C and log shear failure time versus l27°C storage modulus. The adhesives used to generate the data in Figures 5.1 and 5.2 [29] are all solution acrylic pressure-sensitive formulations using a single-solution multipolymer, but they were formulated using varying amounts of a proprietary cross-linking system, ranging from zero to well in excess of the optimum. The test of peel resistance was carried out at a 180° angle at 12 in./min by PSTC Method 1 and shear test by PSTC-7 method, using a 1 kg weight hanging from a half-by-half inch joint [30]. Dale et al. also recognized the decisive dissipation in peel is at high strains (closer to the tensile tests) and cautioned the use of tan δ as a measure of energy dissipation because of its strain dependency [31,32]. The strain dependency of modulus and dissipation was recently emphasized by Creton and Deplace [33], who noted that for PSA debonding at high deformations, a large strain tensile test offers an alternative and complimentary methodology to linear viscoelastic correlations. 8

Peel strength (20 min) (ppli)

XLQ

6

4

r 2 > 0.9897 2

0 −0.6

−0.4

−0.2

0.0

0.2

0.4

Dissipation (log tan δ at 127°C)

FIGURE 5.1 Correlation of 20 min peel strength with log tan δ at 127°C. (From Dale, W.C., Paster, D.M., and Haynes, J.K., Mechanical Properties of Acrylic PSAs and Their Relationship to Industry Standard Testings, Taylor & Francis, London, 1989. With permission.)

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Fundamentals of Pressure Sensitivity

3

XLQ

Log shear (h) (kg)/psi at CTH

2

1 r 2 >0.87 0

−1

−2 3.2

3.4

3.6

3.8

4.0

4.2

4.4

Log storage modulus G ′ (Pa) at 127°C

FIGURE 5.2 Correlation of shear hang time with log-log storage modulus at 127°C. (From Dale, W.C., Paster, D.M., and Haynes, J.K., Mechanical Properties of Acrylic PSAs and Their Relationship to Industry Standard Testings, Taylor & Francis, London, 1989. With permission.)

The noteworthy features and contribution of Dale’s work are as follows: • Proposal of a concept of strain–temperature superposition to reconcile the small strain deformation in DMA with the large deformation tensile tests. • Demonstration that a main requirement of good PSA is to possess simultaneously both solid-like strength and liquid-like flow behavior. • Use of log tan δ (positive and negative, respectively) to delineate liquid-like and solid-like properties; cautioned regarding the use of the strain dependence of tan δ. • Emphasis of the importance of the differences in energy integral for adhesive failure (lower boundary stress) and cohesive failure in peel resistance test (i.e., utilizing the full stress–strain curve) adhesives. This identifies the possibility of achieving higher peel strength going from adhesive to cohesive failure (e.g., on substrates of increasingly greater surface energy). This also confirms that the surface adhesion serves primarily to prevent premature separation from the substrate [2,34,35], which results in a low peel resistance. • Confirmation of the major role that bulk viscoelastic properties play in PSA performance and demonstration of the usability of the tensile test and dynamic mechanical methods for correlations with standard peel and shear performance tests.

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5.2.2

5-5

Work of Tse

By combining the theoretical consideration of Kinloch and coworkers [36–38], the Dahlquist contact criterion, and the proposed bonding and debonding functions, Tse [14,39] presented the PSA performance as T = P0 BD

(5.1)

where T is the adhesion performance and P0 is an intrinsic interfacial failure energy (either the energy required to open up a unit area of PSA–substrate interface in the absence of viscoelastic energy loss or the thermodynamic work of adhesion, which is substrate dependent). B is the bonding function, assumed to be constant when the Dahlquist contact criterion is satisfied (i.e., the plateau modulus is lower than 3.3 × 105 Pa); D is the debonding function, which is the viscoelastic loss component. It is strongly dependent upon the characteristic debonding frequency (i.e., the separation speed of the PSA test). Although viscoelastic measurements involve low strains, whereas PSA adhesion tests involve high strains, Tse’s study confirms many earlier findings of good correlations of viscoelastic properties with PSA adhesion. The noteworthy features and contributions of this work are as follows: • The separation of the bonding and debonding steps in PSA adhesion. • The relationship between viscoelastic behavior at different frequencies and PSA. • Performance and the identification and location of the debonding frequencies for different adhesion tests on the rheological master curves. • The proposal of an end-block polystyrene domain transition temperature (Tdd), which is much lower than the end-block polystyrene domain disappearance (critical) temperature, Tc, proposed by Krause and Hashimoto [40] and the “monophasic” (when the morphology becomes single phase) temperature proposed by Widmaierer and Meyer [41]. The absence of correlation between shear adhesion failure temperature (SAFT) and Tdd suggests that the responsible mechanism for the lower SAFT observed in resin-rich systems is the lowering of the plateau modulus or narrowing of the plateau width. • The evidence for and against the existence of two phases, namely, polyisoprenerich and resin-rich in the mid-block rubber matrix. Such differences can most probably be reconciled by the different sensitivities and thermal histories of the different tests [e.g., differential scanning calorimetry (DSC) versus rheological measurements]. • The inference that resin restricts segmental motion of the rubber mid-block, resulting in a higher monomeric friction coefficient. • The identified criteria for good PSAs, namely, low plateau modulus to facilitate bonding and high energy dissipation at the PSA debonding frequencies and domain integrity. This is consistent with the proposed VWs by Chu [15] and Chang [16,17].

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5-6

5.2.3

Fundamentals of Pressure Sensitivity

Work of Chu

Extending earlier studies on the dynamic mechanical properties of rubber–resin mixtures, Chu [15,52], through his systematic studies, presented a coherent picture of how the interaction of rubber with resins affects the dynamic mechanical properties, which, in turn, affect PSA performance. Compared with previous publications, the noteworthy features and contribution of these papers are as follows: • The identification of the limitations and strengths/capabilities of different rheometrics fi xtures (torsional rectangular and different diameter parallel plates) for dynamic mechanical measurements of PSA materials. For individuals not too familiar with all the testing models, Chu highlighted the caution of instrument compliance at low temperatures or measuring glassy modulus, and he recommended different size parallel plates for different modulus range measurements. • The testing and characteristics of rubber–resin compatibility by the criteria of a pronounced shift in the tan δ peak maximum temperature, together with a decrease in the plateau modulus. • The confirmation that rubbers with a higher plateau modulus and Tg values are much more difficult to tackify than those with lower values. This criterion should compliment the matching of the solubility parameter between rubber and resin commonly used in the PSA industries. • The order of compatibility of different types of resins with different types of rubbers. This is particularly useful for formulation chemists who need guidance on the selection of compatible resins for these rubbers (such a “list” of compatibilities existed before DMA; suppliers published such lists, with compatibility being tested using other than DMA methods; see also Applications of PressureSensitive Products, Chapter 8). • The determination that good PSA systems (based on rubber tackified with an appropriate amount of compatible resins) have a depressed modulus at low frequencies (making bonding favorable) and an elevation in the high-frequency modulus (making debonding more favorable). This also demonstrates the importance of G′ω=100/G″ω=0.1 in achieving good PSA properties (Figure 5.3). • The proposal of room temperature modulus values at different frequencies for PSA systems (e.g., for tapes and labels; see Figure 5.4) and a VW for good PSAs for tapes based on modulus requirements (Figure 5.5). • The correlation of tack versus dynamic mechanical data; specifically G′ω=0.1 and ratio of G′ω=100/G′ω=0.1. This relationship indicates that low G′ω=0.1 and high G′ω=100/G′ω=0.1 ratio are desirable for high tack values. • The proposal of empirical windows for good PSA and good pressure-sensitive labels based on the loci of the room temperature plot of modulus and Tg values determined from the temperature at which tan δ is at the maximum (Figure 5.6).

5.2.4

Work of Chang −2

Using 10 and 102 rad/s as the bonding and debonding frequency, respectively, G′ and G″ values of different PSA samples at these two frequencies were measured, and their

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Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives

5-7

G′ (dyn/cm2) at 25°C

107

106

105 0.1 Bonding shear resistance

1.0 10 Frequency sweep data (ω, rad/s) tack

100 Debonding peel

FIGURE 5.3 Room temperature modulus requirement at various frequencies. Shaded area indicates the window with good PSA properties. (From Chu, S.G., Adhesive Bonding, Plenum Publishing, New York, 1991. With permission.)

107

25°C

145 Tape Label PSA

14.5

105

1.45

G′ (dyn/cm2)

Modulus (psi)

106

104 0.1

1.0

ω (rad/s)

10

104 100

FIGURE 5.4 Room temperature modulus values of label and PSA tape at various frequencies. (From Chu, S.G., Adhesive Bonding, Plenum Publishing, New York, 1991. With permission.)

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Fundamentals of Pressure Sensitivity

1010 ω = 10 rad/s

109

G′ (dyn/cm2)

108 107 106 105 104 103

Melt processing −10

25°C

80

120

150

Temperature (°C) Cold temperature performance

Room temperature performance (application temperature)

Storage (telescoping)

Good shear holding

FIGURE 5.5 Modulus (G′) requirements (windows) for good PSA tapes. (From Chu, S.G., Adhesive Bonding, Plenum Publishing, New York, 1991. With permission.)

VWs were constructed by plotting the four coordinates: (1) G′ at 10−2 rad/s, G″ at 10−2 rad/s; (2) G′ at 102 rad/s, G″ at 10−2 rad/s; (3) G′ at 10−2 rad/s, G″ at 102 rad/s; and (4) G″ at 102 rad/s, G″ at 10 2 rad/s on the log-log cross plot of G′ and G″. Chang [16,17] reported that for most PSAs, the range of G′ and G″ at room temperature within the selected frequencies fell between 103 and 106 Pa. In addition, there was a unique correlation between the adhesion performance of the PSAs and the location of their VWs. A four-quadrant concept was therefore adopted to categorize different types of PSAs. The location of different VWs is illustrated in Figure 5.7 [42], along with their corresponding operative viscoelastic regions. To illustrate the consistency of the VW concept for the different types of PSAs, several key materials in each group are listed below to ascertain their viscoelastic uniqueness. Quadrant 1 (top left-hand quadrant): high G′ and low G″. This quadrant corresponds to high modulus, low dissipation. The bonding and debonding frequencies, in this case, both occur at the plateau region of the rheological master curve. No PSA can be found in this quadrant because of the high bonding modulus (i.e., G′ at 10−2 rad/s) and highly elastic nature (lack of flow) of the material, making the bonding step unfavorable. Some elastomers and release coatings occupy this quadrant. Figure 5.8 illustrates the VWs of a polydimethyl siloxane (PDMS), PDMS + 40% control release agent (CRA, an additive to increase the release force, which is a tri- or tetrafunctional methylsilicate resin; see also Technology of Pressure-Sensitive Adhesives

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5-9

Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives

107

145

Vistanex Reichhold (TYLAX) Polysar Union chemical (AMSCO) Dow

SBR Latex

NR

208

SBR1011 L120 8226

G ′, 25°C (dyn/cm2)

3892

6130

30678

222 8244 106

Good PSA

444

14.5

8277 Good label

LM-MS

105 −60

Modulus (psi)

Hartex

1.45 −50

−40

−30

−20

−10

0

10

Tg (°C), tan δ maximum temperature

FIGURE 5.6 Viscoelastic properties of Piccotac HM2162L/Kraton 1107/oil blends and empirical windows required for various labels and PSA tapes. (From Chu, S.G., Adhesive Bonding, Plenum Publishing, New York, 1991. With permission.)

and Products, Chapters 6 and 10), and PDMS + 60% CRA. Because of the high bonding modulus (G′ at 10−2 rad/s) and low dissipation (G″), PDMS is not a PSA, but rather a release coating. However, with the incorporation of an increasing amount of CRA, the modulus is progressively reduced, accompanied by an increase in dissipation or flow. Such a progressive decrease in G′ and increase in G″ results in a progressive increase in the tackiness of the samples. Thus, PDMS, when modified with 60% CRA, is tacky. It can be anticipated that with further increase in CRA concentration, the VW of the resulting sample will move toward the central region, which, as described in a later section, is the location for general purpose PSAs. Quadrant 2 (top right-hand quadrant): high G′ and high G″. This quadrant corresponds to high modulus and high dissipation. The bonding frequency corresponds to

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Fundamentals of Pressure Sensitivity

106

Quadrant 2

Quadrant 1

Transition−plateu region High modulus High dissipation

Rubbery region High modulus Low dissipation 105 Transition−flow region Medium modulus Medium dissipation General purpose PSA

G ′ (Pa)

Release−Non PSA

104

Plateau−flow region Low modulus Low dissipation

Flow−flow Low modulus High dissipation

Removable PSA 103

High shear PSA

Cold temperature PSA Quadrant 4

Quadrant 3 103

104

105

106

G ′′ (Pa)

FIGURE 5.7 VWs of PSAs as related to different regions on the rheologic master curves. (From Chang, E.P., Viscoelastic Windows of PSAs, Taylor & Francis, London, 1991. With permission.)

106

G ′ (Pa)

105

104

103 103

104

105

106

G ′′ (Pa) Silicone coating

Silicone + 40% CRA

Silicone + 60% CRA

FIGURE 5.8 VWs of release coatings. (From Chang, E.P., Viscoelastic Windows of PSAs, Taylor & Francis, London, 1991. With permission.)

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5-11

106

G ′ (Pa)

105

104

103 103

104

105

106

G ′′ (Pa) HSPSA 1

HSPSA 2

HSPSA 3

FIGURE 5.9 VWs of high-shear PSAs. (From Chang, E.P., Viscoelastic Windows of PSAs, Taylor & Francis, London, 1991. With permission.)

the plateau region, whereas the debonding frequency corresponds to the glass transition region in the rheological master curves for high-shear PSAs. The high bonding modulus, compensated by the high dissipation or flow, makes the bonding marginally efficient. Shear is high because of the high G′ or cohesive strength of the material. Figure 5.9 illustrates the VWs of three high-shear PSAs: HSPSA 1, 2, and 3. All of the VWs occupy the top right-hand corner, which means that these adhesives have comparatively high modulus (G′) and high dissipation (G″) within the application rates (i.e., between 10 −2 and 102 s−1). In general, these adhesives have comparatively high Tg’s and are comparatively highly cross-linked to achieve the high shear performance. Quadrant 3 (bottom left-hand quadrant): low G′ and low G″. This quadrant corresponds to low modulus, low dissipation. The bonding frequency corresponds to the onset of the flow transition, whereas the debonding frequency corresponds to the plateau region in the rheological master curves for removable PSAs. Bonding is facilitated by the low modulus despite the low flow characteristics. Peel values are usually low because of the comparatively low debonding strength and low dissipation. Removable and medical-type PSAs fall within this quadrant. Figure 5.10 illustrates the corresponding VWs for removable adhesives RPSA 1, 2, and 3. The distinct characteristics of this type of adhesives are as follows: • Low bonding modulus so that the adhesive is very contact-efficient • Low dissipation, which implies more elasticity or better removability

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5-12

Fundamentals of Pressure Sensitivity

106

G ′ (Pa)

105

104

103 103

104

105

106

G ′′ (Pa) RPSA 1

RPSA 2

RPSA 3

FIGURE 5.10 VWs of removable PSAs. (From Chang, E.P., Viscoelastic Windows of PSAs, Taylor & Francis, London, 1991. With permission.)

Figure 5.11 illustrates the VWs of some of the removable PSAs used in medical applications (e.g., bandages). Comparing the VWs of these medical removables with those removables in Figure 5.10, one notes that they tend to occupy the lower (better conformability) and farther right (better flow) area of Quadrant 3. Some of the notable differences between the removable and the bandage adhesives are as follows: • The reference temperature for the medical adhesive is the body temperature, 37°C, rather than 23°C in the removable case. This makes the bonding modulus of the medical adhesives even lower (i.e., more conformable) than that of the removables because of the higher reference temperature. This is desirable for contact area considerations because of the rough, frequently varied, and contaminated nature of the skin. • The debonding moduli (top right-hand corner of the window) are usually higher than those of the removables. This, again, is necessary to prevent lift or detachment because of frequent flexing of the skin, especially on curved areas, such as knees and elbows. Quadrant 4 (bottom right-hand quadrant): low G′ and high G″. This quadrant corresponds to low modulus, high dissipation. The bonding frequency corresponds to the flow region, whereas the debonding frequency corresponds to the onset of the flow region in the rheological master curves for very quick or cold-stick PSAs. The low bonding modulus coupled with high flow makes bonding very efficient, thus permitting the material to stick even at low temperatures or very short contact time.

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Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives

5-13

106

G ′ (Pa)

105

104

103 103

104

105

106

G ′′ (Pa) MPSA 1

MPSA 2

MPSA 3

FIGURE 5.11 VWs of medical PSAs. (From Chang, E.P., Viscoelastic Windows of PSAs, Taylor & Francis, London, 1991. With permission.)

Three adhesives that have a significant portion of their VWs in the fourth quadrant should have low bonding modulus, G′, as well as good flow or highly dissipative nature, G″. So far, no good example of a PSA has been found with its VW located right in the fourth quadrant. Central area: medium G′ and medium G″. This central area corresponds to medium modulus, medium dissipation. The bonding frequency corresponds to the onset of the flow region, whereas the debonding frequency corresponds to the onset of the glass transition region in the rheological master curves (i.e., usually characterized by the absence of a distinct plateau region) of general purpose PSAs. Figure 5.12 illustrates the corresponding VWs for three general purpose acrylic PSAs, GPPSA l, 2, and 3. They all occupy the central region (overlapping part of the four quadrants), illustrating the general purpose nature of this type of PSAs. 5.2.4.1

Correlation and Prediction of Adhesive Performance with the Viscoelastic Window

Figure 5.13 illustrates the relative position of the VW with respect to the Dahlquist contact criterion line, as well as the diagonal line where G′ = G″ or tan δ = 1. 5.2.4.2 The Dahlquist Contact Criterion Line The Dahlquist line is an important reference line that indicates whether a material would be contact efficient (PSA) or deficient (non PSA). Except for the release coatings, all the different types of the adhesives shown in Figures 5.9 through 5.14 [43] have a bonding

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5-14

Fundamentals of Pressure Sensitivity

106

G ′ (Pa)

105

104

103 103

104

105

106

G ′′ (Pa) Emulsion acrylic

Office tape

Tackified acrylic

FIGURE 5.12 VWs of general purpose PSAs. (From Chang, E.P., Viscoelastic Windows of PSAs, Taylor & Francis, London, 1991. With permission.)

106 tan δ = 1

Dahlquist s criteria line

G′ (Pa)

105

104

103 103

G ′ (100) G ′′ (.01) Removability (elastic)

G ′ (100) G ′′ (100)

Flowability (viscous) G ′ (.01) G ′′ (.01)

G ′ (.01) G ′′ (100)

104

105

106

G ′′ (Pa)

FIGURE 5.13 Relationship of the VW with the Dahlquist contact criteria and tan δ. (From Chang, E.P., Viscoelastic Windows of PSAs, Taylor & Francis, London, 1991. With permission.)

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Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives

Storage modulus (G ′/Pa)

107

106

105 8400

= 21

MW

104

000

203

102 10−5 (a)

00

46

16

103

0

80

3 12

10−4 10−3 10−2 10−1 100 101 Frequency (ω/rad/s)

102

103

104

105

Loop tack (N/cm2)

8

6

4

2

0 (b)

0

2

4

6

8

1/G ′ × 105/Pa

FIGURE 5.14 (a) Storage modulus, G′, as a function of frequency. (b) Loop tack as a frequency of inverse of G′. Stainless-steel substrate (○) and polyethylene substrate (△) for a series of acrylic copolymer samples having the same composition (75 wt % 2-ethylhexyl acrylate, 23 wt % ethyl acrylate, 2 wt % acrylic acid) but different molecular weights. (From Yang, H.W.H. and Chang, E.P., The Role of Viscoelastic Properties in the Design of PSAs. Elsevier/Springer, New York, 1997. With permission.)

modulus (i.e., the base of the application window) much below the Dahlquist line (which means good conformability). In other words, by comparing the position of the base of the window with the Dahlquist line, we immediately know whether the material is a PSA. 5.2.4.3

The G′–G″ Cross-Over Line (tan δ = 1)

The diagonal tan δ = 1 line is another important line of demarcation because it separates regions in which the elastic or storage modulus (G′) is greater or smaller than the

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Fundamentals of Pressure Sensitivity

loss modulus, G″ (i.e., tan δ < 1 and tan δ > 1, respectively). The portion of the window to the left of the line (i.e., tan δ < 1) indicates the more elastic region. In other words, the closer the window is to the top left-hand corner of the G′–G″ plot, the more elastic (or better removeablity) the material characteristics. Conversely, the closer the window is to the lower right-hand corner of the plot, the more viscous (or cohesive failure prone) the material characteristics. Assuming that the adhesive is the only variable in the construction and that the surface effect is negligible, the following adhesion and convertibility performance can be correlated with the shape and location of the VW. 5.2.4.4 Shear Performance The shear performance can be correlated with the following features of the window. The base of the window (i.e., G′ at 0.01 rad/s) usually indicates the value of the plateau modulus (because the plateau modulus typically falls in the bonding frequency). In general, the higher the plateau modulus (provided the Dahlquist contact criteria are still satisfied), the better the shear. The high shear type of adhesive is a good manifestation of this correlation. In addition, if the base of the window (i.e., G′ at 10 −2 rad/s) is the same, or the more extended the plateau (i.e., the difference between G′ values at 0.01 and 100 rad/s is smaller), the better the shear. This is because a more extended or flatter rubbery plateau is indicative of either a higher degree of entanglement due to higher molecular weight or a higher chemical/physical cross-link density. Because the breadth of the plateau is inversely proportional to the height of the window, if the base of the window is the same, the shorter the window, the better the shear performance prediction. 5.2.4.5 Peel Performance Peel performance is dependent upon the efficiency of the bonding step, as well as the separation resistance in the debonding step. The bonding efficiency can be correlated with the plateau modulus at the bonding frequency (∼0.01 rad/s). In other words, the lower the G′ value at 0.01 rad/s (or the base of the window), the more favorable the bonding. The debonding strength comes from two contributing terms, the cohesive strength, which is indicated by the storage modulus, G′, and the energy of dissipation term, which is indicated by the loss modulus, G″. Both of these are measured at the debonding frequency (∼100 rad/s). Thus, the higher the debonding G′ and G″ values (i.e., more toward to the top right-hand corner), the higher the debonding strength. 5.2.4.6 Tack Performance The correlation of tack performance is similar to that of peel, except the bonding frequency for tack is about 1 rad/s, which means that the bonding efficiency relates approximately to the inverse of the half-height of the window. The debonding resistance can be related again to the height of the right-hand corner of the window. The usefulness of Chang’s VW concept is as follows: 1. It can be obtained by just making measurements at two frequencies (i.e., 10−2 and 102 rad/s at the specified temperature). Such simple and rapid measurements will immediately identify the nature and type of the adhesive.

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5-17

2. With the VW defined, qualitative information regarding adhesion performance and the mode of failure can be obtained as described. This is particularly useful for comparing, evaluating, and screening different adhesives because the shape and location of their VWs provide comparative qualitative performance information prior to measuring their peel, tack, and shear performances. The limitation of Chang’s VW method is that it only gives the G′ and G″ values at those two frequencies. There is no information for G′ and G″ at the in-between frequencies (e.g., 10−1, 100, and 101 rad/s) or other frequencies as in a master curve, which would be recommended for more quantitative information.

5.2.5 5.2.5.1

Work of Yang and Chang Bonding and G′

Yang and Chang [44] correlated bonding with G′ and debonding with G″ at their corresponding bonding and debonding frequencies. For a PSA material to form a physical bond, two requirements must be met: the bond formation must be thermodynamically favorable, and the contact area must be established upon light pressure within a reasonably short time. The first requirement is a thermodynamic process at the interface and can be expressed as an intrinsic surface energy, I. This energy is the result of thermodynamic interactions, such as dispersion forces and polar interactions. Maximum adhesion occurs when the adhesive and the substrate have similar surface tensions [45]. The second requirement, the bonding term, B, is a kinetic process and depends largely on how easily a PSA material can flow under pressure. If A0 is the total area available for the adhesive material to make a contact and A is the actual contact area established during time, t, then the bonding term, B, is proportional to the ratio A/A0, which is related to the creep compliance, J(t), given by the following equations, A/A0 = 1 − e−J(t) ∼= J(t)

(5.2)

J(t) = {1/G′(ω)} × {1/(1 + tan δ2(ω))} ∼= 1/G′(ω)

(5.3)

when tan δ << 1. In the above equations, G′ is the dynamic storage modulus measured at the bonding frequency, ω, and tan δ is the ratio G″/G′, where G″ is the dynamic loss modulus measured at the same frequency. In most cases, G″ is much less than G′ in the bonding region. Equations 5.2 and 5.3 reveal the kinetic aspect of the bonding process. Another important attribute of PSAs is the energy of separation (debonding). Debonding resistance is a measure of the energy dissipated upon deformation. The energy of deformation can be related to the dynamic loss modulus, G″, measured at the debonding frequency, through the following equation [46]: ∆E = πG″L2

(5.4)

where ∆E is the dissipation energy per cycle of the oscillatory shear deformation, and L is the applied strain amplitude of the deformation.

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Fundamentals of Pressure Sensitivity

By combining the effect of bond formation and separation, a simplified correlation for the PSA adhesive strength was proposed [24], P ∼ I × G″(ω1)/G′(ω2)

(5.5)

where G″ is measured at the peeling frequency, ω1, and G′ is measured at the bonding frequency, ω2. Equation 5.5 provides a basis for correlating PSA adhesive strength, measured by 180° peel or loop tack, with the linear viscoelastic properties of the adhesives. In a standard PSA peel test according to Ref. 30, the 180° peel is conducted at a rate of 30.48 cm/min with an adhesive layer thickness of 0.037 mm. The corresponding debonding frequency has been calculated to be 435 rad/s. However, the bonding is carried out at a much lower frequency, typically at ∼1 rad/s. To verify the validity of the above statements, a series of acrylic copolymers was synthesized [47] to test the validity of Equation 5.5. The first series of samples have the same composition and Tg but different molecular weights, as illustrated in Figure 5.14a. These samples have the same G″ at the debonding frequency region but a different G′ at the bonding (1 rad/s) region. The result of the adhesive strength test, as illustrated in Fig ure 5.14b, indicates that the loop tack is inversely proportional to G′. The slope of the straight line correlates with the intrinsic surface energy, as indicated in Equation 5.5. In Figure 5.14b, we see a steeper slope with a stainless-steel substrate than with a polyethylene substrate. This is evidently because of the higher intrinsic surface energy associated with the more polar stainless-steel substrate. Another set of acrylic copolymers with a wider range of compositions was also synthesized. In this case, G″ and G′ at the corresponding debonding and bonding frequencies were different. The test results indicate that 180° peel resistance is indeed proportional to G″/G′, as illustrated in Figure 5.15, again supporting the proposal stated in Equation 5.5. 2.0

Peel (lb/in.)

1.5

1.0

0.5

0 0

0.4

0.8

1.2

1.6

2

2.4

2.8

G′′(ω1)/G′(ω2)

FIGURE 5.15 180° peel strengths (PSTC-1 procedure 37 for a wide range of acrylic copolymers, G″ measured at debonding frequency of 435 rad/s, G′ measured at a bonding frequency of 1 rad/s). □, ethyl acrylate (EA)–ethylhexyl acrylate (EHA); +, methyl acrylate–EA–EHA; ●, methyl methacrylate–EHA; △, butyl acrylate; ○, EHA–EA–acrylic acid (various molecular weights). (From Yang, H.W.H. and Chang, E.P., The Role of Viscoelastic Properties in the Design of PSAs. Elsevier/ Springer, New York, 1997. With permission.)

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5-19

Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives

TABLE 5.1 Factors Affecting Dynamic Shear Storage Modulus, G′, and Dynamic Shear Loss Modulus, G″

Increase polymer molecular weight Increase polymer entanglement molecular weight Increase polymer glass transition temperature, Tg Add hydrocarbon resin or rosin Add plasticizer or oil Cross-link polymer chains

G′

G″

++ −− + −− −− ++

+ −− ++ ++ −− +

Note: G′ measured at 1 rad/s. G″ measured as 435 rad/s. ++ and −− refer to a significant increase or decrease. + and − refer to a minor increase or decrease.

5.2.5.2

Correlating PSA Performance to Fundamental Polymer Parameters

The simplified relationship expressed in Equation 5.5 can be used to design a wide range of PSA products. Through linear viscoelastic theory, G′ and G″ can be correlated with the basic polymer parameters such as molecular weight, molecular weight distribution, Tg, and Me. Table 5.1 lists some technical approaches to manipulate G″ and G′ in the desirable direction to meet the target peel resistance (or tack). Table 5.1 demonstrates that most approaches affect both G′ and G″ in the same direction. To significantly increase the adhesive strength, we must increase the debonding frequency, G″, but decrease the bonding frequency, G′. This can be accomplished by mixing a compatible resin into the polymer. Because tackifying resins normally have a higher Tg (typically 20–50°C) than the PSA polymers (typically −70 to –30°C), adding a compatible resin to the polymer will result in a higher Tg product. As a consequence, the G″ peak, which is associated with the Tg , will move to a lower frequency. This move will, therefore, result in a higher G″ at the debonding region. Another important effect of adding a compatible resin is to lower the modulus in the bonding region (see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 8). Because resins are low-molecular-weight materials, adding a compatible resin to the polymer matrix can be regarded as diluting a concentrated polymer solution with a solvent. The result is a decrease in the plateau modulus, Gn, according to the following equation [47]: Gn ∼= ρRT/Me(Vp)2

(5.6)

where Vp is the volume fraction of the polymer in the polymer–resin blend, Me is entanglement molecular weight of the polymer, ρ is the density of the blend, R is the gas constant, and T is the temperature in Kelvin. Hydrocarbon-based resins have been very effective in tackifying SIS and SBS block copolymers for hot-melt adhesives [14,15] (see also Technology of Pressure-Sensitive Adhesives and Products, Chapters 3 and 8). Waterbased hydrocarbon resins are also available to tackify acrylic, NR, and SBR latices [7]. The effects of resin and polymer compatibility on the viscoelastic behavior of the finished products and their PSA properties have also been investigated [7,13,21,48,49,51,52].

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Fundamentals of Pressure Sensitivity

Class and Chu [7–9] observed a pronounced shift in the tan δ peak (toward a higher temperature as a result of higher Tg), together with a decrease in the plateau modulus, when the resin and the rubber were compatible. As discussed earlier, the depression in the modulus at low frequencies facilitates the bonding process. The shift of the tan δ peak to a higher temperature also results in higher G″ in the debonding region, as indicated in Table 5.1. Another important parameter affecting G′ is the Me of the polymer. To have good bonding characteristics, we need polymers with low G′ at the bonding region. Low G′ normally associates with high Me. For acrylic polymers, Me increases with increasing monomer side chain length. Unfortunately, the Tg for these polymers also decreases with increasing side chain length. It is, therefore, necessary to employ some higher Tg comonomers, such as methyl methacrylate or methyl acrylate, to counterbalance the low Tg monomers such as butyl acrylate or 2-ethylhexyl acrylate. The entanglement molecular weight (Me) is closely related to the structure of polymer chain segments. A summary of Me values for various polymers can be found in a review by Fetters et al. [50]. The use of DMA to formulate and evaluate complex PSA systems is demonstrated by Chang and Holguin in Applications of Pressure-Sensitive Products, Chapter 3 (see also Applications of Pressure-Sensitive Products, Chapter 8).

5.3 General Conclusions This chapter emphasizes the two important steps of bonding and debonding in PSA adhesion. Both of these steps can be related to the viscoelastic properties and behavior of PSAs. Bonding, compared with debonding, is established at a relative long period of time or low frequency, ∼1 to 10−2/s. The efficacy of bonding is proportional to 1/G′ in this region. On the other hand, debonding occurs at a much shorter time or higher frequencies, ∼100 to 1000 s−1; the debonding resistance is proportional to G″ in this region. Through linear viscoelastic theory, G′ and G″ can be correlated with the fundamental polymer parameters such as molecular weight, molecular weight distribution, Tg, and Me. Through this polymer parameter/viscoelastic property relationship, we can then understand how polymer chain structure affects PSA performance. Various approaches can be employed to facilitate bonding and increase debonding resistance. Blending a compatible low-molecular-weight resin has been shown to be an effective way to lower the bonding storage modulus, G′, while increasing the debonding loss modulus, G″. A wide range of PSA products can hence be developed by applying G′ (bonding) and G″ (debonding) in a four-VW concept. The current understanding provides us with a scientific tool to create novel polymer structures for target PSA applications.

References 1. Dahlquist, C. A. (1966), Proc. Nottingham Conf. on Adhesion, Part I, Maclaren & Sons Ltd., London, Chap. 5, p. 134. 2. Kaelble, D. H. (1969), J. Adhesion, 1, 102. 3. Gent, A. N. and Petrich, R. P. (1969), Proc. Roy. Soc. (London), A, 310, 433.

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5-21

4. Chan, H. K. and Howard, G. J. (1978), J. Adhesion, 9, 279. 5. Kaelble, D. H. (1960), Trans. Soc. Rheol., 4, 43. 6. Kraus, G., Jones, F. B., Marrs, G. L., and Rollmann, K. W. et al. (1977), J. Adhesion, 8, 235. 7. Class, J. B. and Chu, S. G. (1985), J. Appl. Polym. Sci., 30, 805. 8. Class, J. B. and Chu, S. G. (1985), J. Appl. Polym. Sci., 30, 815. 9. Class, J. B. and Chu, S. G. (1985), J. Appl. Polym. Sci., 30, 825. 10. Aubrey, D. W. and Sherriff, M. (1980), J. Appl. Polym. Sci. Chem. Ed., 18, 2587. 11. Mocosko, C. W. (1977), Adhesive Age, September, 35. 12. Zosel, A. (1985), Colloid Polym. Sci., 263, 541. 13. Dale, W. C., Paster, D. M., and Haynes, J. K. (1989), J. Adhesion, 31, 1. 14. Tse, M. F. (1989), J. Adhesion Sci. Tech., 3, 551. 15. Chu, S. G. (1991), Adhesive Bonding, L. H. Lee (Ed.), Plenum Publishing Corp., New York, p. 97. 16. Chang, E. P. (1991), J. Adhesion, 34, 189. 17. Chang, E. P. (1997), J. Adhesion, 60, 232. 18. Tse, M. F. (1995), J. Adhesion, 48, 149. 19. Nakajima, N., Babrowlrz, R., and Harrell, L. R. (1992), J. Appl. Polym, Sci., 44, 1437. 20. Han, C. D., Kim, J., and Baek, O. M. (1989), J. Adhesion, 28, 201. 21. Tse, M. F. (1989), J. Adhes, Sci., Technol., 3, 551. 22. Kraus, G., Jones, L. B., Marrs, O. L., and Rollmann, K. W. (1977), J. Adhesion, 8, 235. 23. Kim, H.-J. and Mizumachi, H. (1995), J. Appl. Polym. Sci., 58, 1891. 24. Yang, H. W. H. (1995), J. Appl. Polym. Sci., 55, 645. 25. Class, J. B. and Chu, S. G. (1984), J. Appl. Polym. Sci., 29, 269. 26. Class, J. B. and Chu, S. G. (1985), J. Appl. Polym. Sci., 30, 605. 27. Sherriff, M., Knibbs, R. W., and Langley, P. G. (1973), J. Appl. Polym. Sci., 17, 3423. 28. Chang, E. P. and Chuang, H. K. (1991), Chemtracts-Macromol. Chem., 2, 7. 29. Dale, W. C., Paster, D. M., and Haynes, J. K. (1989), Mechanical Properties of Acrylic PSAs and Their Relationship to Industry Standard Testings, Taylor & Francis, London. 30. The Pressure Sensitive Tape Council (1976), Test Method for Pressure-sensitive Tapes (7th Edn.). 31. Andrew, E. H. (1985), J. Polym. Sci. Symp., 72, 285. 32. Andrew, E. H. (1974), J. Polym. Sci. Symp., 46, 1. 33. Creton, C. and Deplace, F. (2007), Proc. PSTC TECH 30 Global Conference VI, pp. 137–143. 34. Kaelble, D. H. (1971), Physical Chemistry of Adhesion, John Wiley & Sons, New York. 35. Petke, F. D. (1975), Adhesion Science and Technology, L. H. Lee (Ed.), Plenum Publishing Corp., New York, p. 177. 36. Gent, A. N. and Kinloch, A. J. (1973), J. Polym. Sci., Part A-2, 9, 659. 37. Andrew, E. H. and Kinloch, A. J. (1969), Proc. Roy. Soc. (London), Set. A. 332, 385. 38. Andrew, E. H. and Kinloch, A. J. (1969), Proc. Roy. Soc. (London), Set. A. 332, 401. 39. Chang, E. P. (1990), Chemtracts-Macromol. Chem., 1, 292. 40. Kraus, G. and Hashimoto, T. (1980), J. Appl. Polym. Sci. Phys. Ed., 27, 1745. 41. Widmaierer, J. M. and Meyerer, G. C. (1980), J. Polym. Sci. Phys. Ed., 18, 1237. 42. Chang, E. P. (1991), Viscoelastic Windows of PSAs, Taylor & Francis, London.

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43. Yang H. W. H. and Chang, E. P. (1997), The Role of Viscoelastic Properties in the Design of PSAs, Elsevier/Springer, New York. 44. Yang, H. W. H. and Chang, E-P. (1997), TRIP, 5, 380. 45. Toyama, M., Ito, T., and Moriguchi, H. (1970), J. Appl. Polym. Sci., 14, 2039. 46. Ward, I. M. (1983), Mechanical Properties of Solid Polymers (2nd Edn.), John Wiley & Sons, New York. 47. Yang, H. W. H. (1991), Proc. PSTC Annual Tech Seminars, p. 11. 48. Hayashi, S., Kim, H. J., and Mizumachi, H. (1970), J. Appl. Polym. Sci., 14, 2029. 49. Naruse, S., Kim, H. J., Tsukatami, T., Kajiyama, M., Takemura, A., and Mizumachi, H. (1994), J. Adhesion, 47, 165. 50. Fetters, L. J. et al. (1994), Macromolecules, 27, 4639. 51. Ferry, J. P. (1980), Viscoelastic Properties of Polymers, John Wiley & Sons, New York. 52. Chang, E. P. (1992), Chemtracts-Macromol. Chem., 3, 67.

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6 Probe Tack 6.1 Introduction ............................................................ 6-1 6.2 Theoretical Background ........................................ 6-2 Homogeneous Deformation • Cavitation • Fibril Formation and Growth

6.3 Experimental Aspects .......................................... 6-12 6.4 Analysis of Probe Tack Debonding Curves Obtained for Pressure-Sensitive Adhesives ...... 6-15

Costantino Creton Unit Joint CNRS-UPMC-ESPCI

Kenneth R. Shull Northwestern University

6.1

Cavitation in the Probe Geometry • Weak Adhesion: Interfacial Nucleation and Propagation • Strong Adhesion: Fibril Formation and Extension • Transition between the Two Regimes

6.5 Conclusion ............................................................. 6-23 References ....................................................................... 6-23

Introduction

Pressure-sensitive adhesive (PSA) properties are typically characterized by three types of standard tests, peel tests, shear tests, and tack tests (see also Applications of PressureSensitive Products, Chapter 8). The latter type of test is designed to probe the ability of the PSA to stick on a surface under a light applied pressure. The test is often carried out with a loop of tape (loop tack test; see also Applications of Pressure-Sensitive Products, Chapter 8) or by testing the rolling resistance of a steel ball on the adhesive1 (see also Applications of Pressure-Sensitive Products, Chapter 8). An alternative way to test the tackiness of a PSA is by applying a rigid steel punch under controlled conditions on the surface of the adhesive and subsequently removing it at constant velocity, as illustrated schematically in Figure 6.1. Although this type of test has never been really adopted as a standard industry test for tack, it has emerged in recent years as a very powerful and sensitive analytical tool to evaluate the adhesive properties of PSAs2–4 (see also Applications of Pressure-Sensitive Products, Chapter 8). This success is due, first of all, to the high sensitivity of the test to small changes in chemical structure of the adhesive or interfacial interactions and then to the development of a detailed understanding of the specific deformation mechanisms observed during 6-1

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6-2

Fundamentals of Pressure Sensitivity

Force

Debonding

Approach

Time

Contact

FIGURE 6.1 Schematic of a probe tack test as normally performed with a texture analyzer or analogous equipment. The compressive force is applied until a set force is reached and then the displacement is kept constant, allowing the force to relax. The probe is then removed from the adhesive fi lm at constant velocity.

the test.5–9 The deformation of a soft, confined polymer disk is very sensitive to the detailed rheological properties of the material, not only in the linear regime of small strains but also in the highly nonlinear regime of large strains. Furthermore, when the probe test is carried out with a relatively large compressive force, it does not really test tackiness, but rather adhesive properties as measured in a peel test with the added advantage of being able to vary contact time, contact pressure, and debonding rate independently. The purpose of this chapter is not to review all previous work in this area but, rather, in the first section, to review the basis for the interpretation of probe test stress–strain curves as they can be obtained experimentally with a probe tester and, in the second section, to present some examples of interpretation.

6.2

Theoretical Background

A typical probe test experiment involves the compression of an adhesive layer by a flat-end cylindrical probe, followed by separation of the probe from the surface by an applied tensile load, P, as illustrated in Figure 6.2. We have drawn the adhesive layer as a continuous thin layer so that the initial radius of contact, a0, is defined by the radius of the probe itself. This is the geometry that is typically used for the testing of PSA fi lms, which have a solid-like character.2,3 In these experiments the compressive stage is used to form the contact and does impart some strain history to a viscoelastic material, as discussed in Chapter 11. However, in this chapter we will focus on the debonding part of the curve and will analyze the traction part of the experiment as if there were no previous deformation history, as one would for fully elastic solids. We will therefore present a simplified description of the mechanics of deformation of the adhesive layer in the tensile part of probe test, as discussed in detail by Shull and Creton.4 The deformation of an adhesive layer under a tensile stress can be divided into four main stages, described in Figure 6.3: homogeneous deformation, cavitation at the

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6-3

Probe Tack

P

2a 0

h0

2a

FIGURE 6.2 Schematic of the contact between a flat cylindrical probe and a thin fi lm and definitions of the layer.

Stress σ = F A0 (MPa) Cavitation

0.8

σmax Cavity growth

0.6

Fibrillation

1mm 0.4

εmax W adh = h0

0.2

1mm

σ(ε)d ε

0

Homogeneous deformation

Detachment of fibrils

εmax

0 0

2

4

Strain ε =

6

8

10

h − h0 h0

FIGURE 6.3 Example of a stress–strain curve obtained with a probe tester equipped with a flat-end probe. The various stages of deformation of the layer are illustrated by images in low and high magnification of the deformed layer. The appearance and growth of cavities under tensile stress are apparent.

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Fundamentals of Pressure Sensitivity

interface between the probe and the adhesive, lateral expansion of the cavities, and, finally, growth of a fibrillar structure.6 The first two stages are nearly always observed, whereas the last two stages depend on the interplay between adhesive properties and deformability of the layer.

6.2.1

Homogeneous Deformation

The key geometric parameter is the confi nement ratio a/h, which describes the lateral confinement of the adhesive layer. Here, a and h are respective actual values of the contact radius and thickness, which are equal to a0 and h0 at the beginning of the experiment. For large values of a/h, where edge effects can be ignored and the pressure distribution under the probe is parabolic,10  r2  p (r )
zz (r )
p0  2 N  1 2   a 

(6.1)

where r is the radial distance from the axis of symmetry, p0 is the external pressure (typically equal to 1 atm), λ is the extension ratio, and σ N is the nominal tensile stress. ≡ h / h0

N ≡ P/a02

(6.2)

Two underlying assumptions are involved in the derivation of Equation 6.1. The first is that the layer is thin enough that the pressure is nearly uniform throughout the thickness of the layer. This assumption is valid whenever a/h is large, regardless of the mechanical properties of the layer itself. The second assumption underlying Equation 6.1 is that the shear stress increases linearly with the radius, that is, σrz(r) ∝ r. This assumption is valid provided that the material is incompressible and that a no-slip boundary condition is observed at the confining surfaces of the deformed material. This no-slip condition is nearly always met for liquids, but is not always met for materials with a more solid-like character, such as PSAs.11 For large values of a 0/h0 and for elastic layers, the nominal stress σ N is proportional to strain and for sufficiently small strains (λ close to 1) it can be written as N 3
(a0 / h0 )2  2

(6.3)

where µ is the shear modulus of the solid, and ε = λ − 1. Equation 6.3 typically overestimates the normalized stress for values of a0/h0 that are larger than ~10. In this regime three factors contribute to a decrease in the confi nement effect. 1. The finite compressibility of the elastomer can no longer be neglected.10,12 In some cases, the compressibility may be attributed to the presence of small voids that cause the material to behave as if it had an effective Poisson ratio that is somewhat lower than the true value for the bulk material.13 2. The no-slip boundary condition may no longer be valid at the edges of the contact because of the very high shear stresses.10,14

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Probe Tack

3. The material at the edge of the contact is deformed well into the nonlinear regime so that linear elastic theory is no longer appropriate to describe the elastic behavior.15 A combination of these three effects results experimentally in a measured value of σ N/Eε that is distinctly lower than what Equation 6.3 would predict.11,16 In addition, the pressure distribution across the probe is more uniform than the parabolic distribution given by Equation 6.1. The result is that in very liquid systems, where the pressure distribution remains parabolic, cavitation occurs preferentially under the probe center,17,18 where the highest hydrostatic tension is observed. In contrast to this situation, cavitation in solid materials is often observed to occur uniformly throughout the entire cross section defined by the probe.6,11,19

6.2.2 Cavitation Cavitation in highly deformable elastic materials is generally a heterogeneous process, corresponding to the expansion of an existing cavity. For a sufficiently low elastic modulus, cavity expansion is determined by the pressure needed to overcome the internal Laplace pressure. The cavity is assumed to have an initial radius of curvature R0 and to be fi lled with an ideal gas at a pressure of p0. The presence of gas in the initial defect corresponds to the entrapment of atmospheric gas from the external environment (where the pressure is equal to p0 initially), within regions with a characteristic size that is defined by the roughness of the probe.9,20 Mechanical equilibrium requires that the applied pressure (p) is equal to the sum of the Laplace pressure (−2γ/R0) and the internal pressure (p 0V0/V), p


2

p0  3 r r R0

(6.4)

where the extension ratio, λ r, is equal to Rc/R0. We have made the simplifying assumption that the shape of the bubbles does not change with volume, so that V ∝ λr3. The addition of elasticity complicates the problem, because one must take into account an appropriate energy balance that can be addressed analytically in some limiting cases. For a spherical void of initial radius R0 in an infinite, incompressible material, the strain state around the void is fully specified by λ r = R/R0. One must now account for an additional “elastic” inflation pressure, pel, that must be applied to maintain this elastic deformation of the material. For a spherical void in an isotropic medium, the inflation pressure becomes p


p0 2

  pel ( r ) 3 r r R0

(6.5)

The specific form of pel(λ r) depends on the constitutive model that is used to describe the strain energy density of the deformed material. The problem involves large strains, and linear elasticity is no longer sufficient. Models are needed that relate the overall strain energy to λ1, λ 2, and λ 3, the principal extension ratios characterizing the strain state of

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Fundamentals of Pressure Sensitivity

the material. The simplest constitutive model describing the elasticity of rubber at fi nite strains is the neo-Hookean material, for which the elastic strain energy density, Uel, can be written in the following form:

(

U el ∝ 12  22  32  3

)

(6.6)

In this case pel(λ r) has the following form:21 pel
Ef el ( r )

1 4 1 f el ( r )
 5   4  6 r r 

(6.7)

where E is Young’s modulus as obtained in a small-strain experiment, and incompressibility has been assumed (λ1λ 2λ 3 = 1). This specific form for fel(λ r) corresponds to the neo-Hookean model. Other forms of this function can be obtained for different constitutive equations, which typically contain additional material parameters apart from the small-strain elastic modulus. These additional parameters provide a better description of the behavior of real rubbers. For the current discussion, however, the neo-Hookean model adequately reproduces the main physical features of elastic cavitation. At this point it is useful to combine Equations 6.5 and 6.7 to obtain the following relationship between the pressure and the extension ratio of the void: p


p0 2

  Ef el ( r ) 3 r r R0

(6.8)

Elasticity enters the problem only through the elastic modulus in the third term on the right-hand side of Equation 6.8. The magnitude of this term relative to the other two terms therefore determines the extent to which elasticity affects the cavitation behavior.4,9 This relative balance can be quantified by a dimensionless ratio, γ/ER0, which defines the surface-controlled and elastic-controlled limits for the cavitation stress. The distinct features of these different regimes are discussed in the following sections. The quantity γ/ER0 is proportional to the ratio of the Laplace pressure to the elastic expansion pressure for a sample with a characteristic defect size of R0. In situations where γ/E is small in comparison to the initial defect size, R0, surface deformations can be ignored, and the response of the system is determined by bulk elasticity. For small values of γ/ER0, the cavitation stress is therefore dominated by the elastic expansion pressure. In this case, Equation 6.7 for a neo-Hookean material predicts that a preexisting cavity in an infinite elastic medium under a constant tensile stress will expand indefi nitely when the magnitude of the negative hydrostatic pressure approaches 5E/6. If the material becomes softer and the interface is prepared more carefully, the Laplace pressure term in Equation 6.8 may exceed the elastic expansion term. The effect of the surface energy can be illustrated in a qualitative sense by assuming that p0/E is small and combining Equations 6.7 and 6.822 12 ( / ER0 )  4 p 1 1 
5  4 r r  E 6

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(6.9)

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6-7

Probe Tack

We define the pressure as negative because these negative values correspond to the state of hydrostatic tension that is relevant to our experiments. For γ/ER0 → 0, the size of the initial void is predicted to increase continuously with increasing hydrostatic tension. For values of γ/ER0 larger than a critical value of 1/3, the situation is more complicated and the cavity should expand rapidly once the applied tensile pressure exceeds the Laplace pressure corresponding to the original defect of size R0.23 The final size of the cavities is typically comparable to the thickness of the elastic layer itself, because this thickness controls the length scale from which elastic energy is available to drive the cavity growth.24,25 Th is picture is qualitatively consistent with experimental results illustrated in Figure 6.4.9 Small cavities that were optically invisible at the beginning of the test expand more rapidly and at higher stress levels than larger cavities that were optically visible at the beginning of the test. Furthermore, for these soft rubbery PSAs, the pressure necessary to observe cavities can be as large as 10 times Young’s modulus (E), while remaining much larger than the atmospheric pressure, suggesting that the growth of defects is

140 Cavity radius (µm)

120 100 80 60

Cavity 1

40

Cavity 2

20 0 0

2

4

6

8

10

Time (s)

t=7s

t=0s

2 1 1 500 µm

FIGURE 6.4 Time dependence of cavity growth and the contact images at early and late stages of the cavity formation process. Cavity 1 initiates at the early stages of the deformation process from a visible defect, at a relatively low value of normal stress. Cavity 2 initiates from a very small defect at a large value of stress and expands very rapidly. (From Shull, K.R. and Creton, C., J. Polym. Sci. Part B: Polym. Phys. 42, 4023–4043, 2004. With permission.)

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Fundamentals of Pressure Sensitivity

mainly controlled by surface defects and not by elasticity.6,19,11 In this surface-controlled regime, the size of the initial defect plays a role in the determination of the cavitation stress.9,26 As a result, the reproducibility of the cavitation stress for sufficiently soft materials will depend crucially on the characteristic size of the defects, which is, in turn, controlled by the topography of the probe and the adhesive layer. This picture is admittedly simplistic. For very small defect sizes, Equation 6.8 predicts unrealistic values of the expansion pressure that are never observed experimentally. The main point of our discussion here is that for solids with a sufficiently low modulus, one must account for the energy required to deform the bulk of the material and to create new surfaces. A more detailed theoretical treatment is needed to develop a quantitative understanding of the situation in which bulk and surface deformations both play a role. Despite its importance in the general area of adhesion science, this issue has been largely overlooked, although some preliminary theoretical and experimental attempts to treat problems like this have recently been made.23,27 Furthermore, this picture of cavity expansion completely avoids the issue of rupture of chemical bonds. For cross-linked rubbers, cavitation in the bulk cannot occur without irreversible fracture of bonds.28,29 This problem is mostly avoided for PSAs because the expansion of the cavity occurs from interfacial defects and not in the bulk and probably does not involve much bond fracture due to the very low cross-linking density.

6.2.3 Fibril Formation and Growth The shape of the growing cavity and its interaction with the neighboring cavities is the most difficult aspect of the experiment to model and yet one of the most relevant for practical applications. Indeed, if the cavities initially form on defects, coalesce, and form a crack, the interfacial debonding of the layer will be rapid and the practical work of adhesion (given by the integral of the load–displacement relationship) will be low. On the other hand, if coalescence of neighboring cavities does not occur, the walls between cavities will be extended as polymer fibrils in the direction normal to the probe, and a very large work of adhesion can be achieved in cases when the work to extend the fibrils is dissipated irreversibly upon rapid detachment of the probe from the surface.30,31 To understand this transition it is more convenient to introduce some concepts of fracture mechanics following the treatment of Shull and Creton.4 In essence, the transition from interfacial crack propagation to fibrillation can be seen as a competition between a fracture problem at the interface and a cavitation problem.12 It is, therefore, essential at this stage to introduce an energy-based description of failure. Up to this point we have implicitly considered the growth of the cavity to occur reversibly in the bulk by elastic deformation. However, in reality, the cavity growth also occurs by growth of the radius of the debonded area in Figure 6.5 (Rd), in response to a crack-driving force, G. For cavitation that occurs in the bulk of a material, θ = 90° and the interface corresponds to a fracture plane within the bulk material. The general question of cavitation by fracture has been discussed by Williams and Schapery32 and Gent and Wang.28 Although details of their calculations differ, they both conclude that the energy release rate, G, diverges when the far-field hydrostatic tension pressure approaches 5E/6.4 The useful aspect of the fracture mechanics calculation is that it

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6-9

Probe Tack

2Rd θ

hc Rc

(a)

2Rp

2Rd

(b)

FIGURE 6.5 Schematic illustrations of various cavity geometries: (a) an interfacial cavity and (b) ellipsoidal interfacial cavity with θ < 90, illustrating the distinction between debonded radius, Rd, and the projected radius, Rp. (From Shull, K.R. and Creton, C., J. Polym. Sci. Part B: Polym. Phys. 42, 4023–4043, 2004. With permission.)

introduces in a rather natural way the familiar balance between released elastic energy (G) and critical energy release rate, Gc. If one applies Griffith’s criterion, the cavity will grow/expand when G > Gc. The overall picture can be summarized by considering the response of an initial penny-shape interfacial crack (hc/Rd << 1) to an increasing hydrostatic tension, pel. For pel/E << 1, we recover the crack-driving force from standard linear elasticity theory33 G


3Rd E  pel  2  E 

2

(6.10)

As pel/E increases, several things happen. The crack begins to inflate in the vertical direction, and the value of hc in Figure 6.5a increases. The energy release rate also increases in accordance with Equation 6.10, which remains valid for values of pel/E less than about 0.4. For pel/E ≈ 1, the defect becomes hemispherical (hc ≈ Rd) and the energy release rate increases nonlinearly to a much higher value that is determined by the large-strain response of the material.34 The specific value of pel/E corresponding to this nonlinear increase depends on the details of the strain energy function that is used to describe the material.34 The example in Figure 6.6 is for a neo-Hookean material. If this large increase in G corresponds to an increase from a value that is below Gc to a value that is above Gc, cavities will grow. The fact that this sudden increase in G can be relatively large leads to a criterion for cavitation that is coupled to the elastic modulus of the material and is relatively insensitive to the specific value of the interface toughness, Gc.30 In other words, one expects that, if Gc/ER0 > 1, an interfacial defect will grow in the bulk at a value of stress roughly independent of the nature of the interface.

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6-10

Fundamentals of Pressure Sensitivity

100

G /ER

10 1

0.1 0.01

0.001

0.1

1 −p /E

FIGURE 6.6 Energy release rate for an interfacial cavity of debonded radius R0 as a function of p/E. (From Shull, K.R. and Creton, C., J. Polym. Sci. Part B: Polym. Phys. 42, 4023–4043, 2004. With permission.)

The length scale defined by Gc/E plays an important role in determining the overall behavior of the system, even when fibrillation occurs. The materials parameters that determine Gc are complex and include the linear and nonlinear viscoelastic properties of the adhesive layer35,36 and the frictional properties of the probe/layer interface.37–39 Our purpose here is not to elucidate all of the factors that determine the value of Gc for a given system, but to describe in qualitative terms how the overall deformation of the adhesive layer proceeds for different values of Gc/E. 6.2.3.1 Small Gc/E Consider an initially flat defect (θ ≈ 180°) of radius Rd that exists at the interface between the probe and the adhesive layer (Figure 6.5a). If Gc/E < Rd , G will exceed Gc for values of the hydrostatic tension that are less than the modulus (see Equation 6.10), so that θ remains large. Hence, the condition pel/E ∼1 fi xes a transition between deformation by crack propagation (an increase in Rd while θ remains large) and deformation by expansion in the bulk (θ ≤ 90°). In essence, this means that if Gc/E is smaller than the defect size, the defect will propagate at the interface and will not expand into the bulk of the material, giving an overall work of adhesion that is comparable to Gc. If Gc takes a typical thermodynamic value of 50 mJ/m2 and the modulus is typical of a cross-linked rubber (1 MPa), any defect larger than 50 nm will propagate at the interface. This expectation is consistent with results obtained for the work of adhesion of cross-linked rubbers on solid surfaces. These materials display low peak stresses (well below the elastic modulus) and very low values for the overall work of adhesion when separated from solid surfaces at low rates. In this regime of low Gc/E, the energy of adhesion is controlled by Gc (which, in turn, depends on crack velocity and sample thickness) but is independent of the modulus. Schematic examples of stress–strain curves obtained in this Gc-controlled regime are illustrated in Figure 6.7.

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6-11

Probe Tack

σ

Low Gc /E

ε

FIGURE 6.7 Schematic tack curves for low values of Gc/E, where the stress remains below the cavitation stress.

σ

High Gc /E

ε

FIGURE 6.8 Schematic tack curves illustrating the case where the cavitation stress is exceeded. The arrows in each part of the figure denote increasing Gc/E.

6.2.3.2

Intermediate Gc/E

If G c/E exceeds the initial defect size, the defects are able to expand into the bulk (pel /E > 1), but adhesive failure occurs before extensive deformation of the material into fibrils is possible. This situation corresponds to the behavior of softer rubbers such as PSAs, where E is typically below 0.1 MPa, on silicone release coatings where Gc remains low, although perhaps not as low as the thermodynamic value.40 The peak stress measured in the probe test is indeed controlled by the elastic modulus, or by the external pressure if p0/E > 1, and values of the local contact angle approaching 90° are expected. Because Gc is relatively low, adhesive failure occurs before a fully developed fibrillar structure is able to form, and the overall adhesion energy is relatively low. Nevertheless, a certain degree of fibrillation may still occur, and the overall work of adhesion will be larger than Gc by an amount that depends on the elastic properties of the adhesive. Schematic examples of typical probe test curves obtained for increasing values of Gc/E in this regime are illustrated in Figure 6.8. It is in this regime that the coupling between interface and bulk is stronger.4,31

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Fundamentals of Pressure Sensitivity

6.2.3.3

Large Gc/E

For viscoelastic materials on a high-energy surface, Gc can become significantly higher and Gc/E may become comparable to the adhesive layer thickness. Lateral cavity expansion by motion of the contact line is hindered in this case, so that a fi nely dispersed foam is formed as the walls between cavities are extended vertically into fibrils.19,41,42 The resulting foam of closed cells is observed for all high-performance soft adhesives. If the fibrils are completely elastic, they will stretch according to a nonlinear elastic constitutive equation for rubber elasticity,43 and the stress–strain curves will look like the examples corresponding to the highest values of Gc/E in Figure 6.8. The large strains corresponding to the fibrillation regime (λ > ∼2) complicate the development of a detailed adhesive failure criterion in this regime. The overall behavior is still dominated by a competition between elastic extension and adhesive failure. The complexity arises in the determination of the actual value of G that is operative at the foot of a fibril.44 Qualitatively, one expects that G will be relatively low if the contact angle characterizing the shape of the foot is low (θ < 90°). This correspondence can be attributed to the fact that when θ is low, an incremental decrease in the actual area of contact does not appreciably increase the overall system compliance. As discussed above, this increase in compliance is the overall feature that drives the behavior of both solid and liquid systems.

6.3

Experimental Aspects

Probe tests have been carried out for several decades in the PSA industry and the first well-documented instrument to perform such tests was the Polyken probe tester.45 This instrument, which is still commercially available today, is based on an inverted geometry in which a probe lifts a PSA fi lm deposited on a substrate. The contact pressure is determined by the weight that is attached to the substrate. The probe then retracts at a fi xed velocity and the contact breaks when the PSA substrate is stopped by a fi xed support. This very simple design provides a single value, the maximum retraction force, which is commonly called probe tack. It is, however, poorly reproducible and whereas the probe and the adhesive fi lm self-align during the loading stage, they also will become poorly aligned during the pulloff. It was several decades later that probe tests were significantly improved by the prototype of Zosel at BASF.2 Zosel realized that much information could be obtained from the analysis of the entire force displacement curve, rather than simply from the peak force. His instrument used a very small cylindrical probe (2-mm diameter) and typically very short contact times and low pressures.5,46 Although the reproducibility of the experiment was much better, it still did not integrate a proper way to visualize the contact area and debonding process. This improvement came in the late 1990s with a design illustrated schematically in Figure 6.9, in which a mirror placed at 45° underneath the transparent sample holder allows real-time observation of the bonding and debonding stage. Furthermore, this instrument had a device to control the alignment between the probe and the adhesive fi lm, which greatly improved reproducibility of the force displacement curves. In fact, the most crucial point to obtain reproducible results is to ensure that the only

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CRC_59378_C006.indd 13 :

Contact) Probe

Mirror

Adhesive layer

Microscope slide

Extensometer

Microscope slide Adhesive layer

Mirror

Steel ball

Lower actuator

Spring

Upper actuator

FIGURE 6.9 Schematic of the experimental design and setup used for the probe tests. (From Creton, C., Roos, A., and Chiche, A., Adhesion: Current Research and Applications, W.G. Possart, Ed., Wiley-VCH, New York, 2005. With permission.)

(

Video

Force cell

Probe Tack 6-13

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6-14

Fundamentals of Pressure Sensitivity

deformable part in the measuring chain is the adhesive itself. Therefore, great care must be taken to have a very stiff fi xture and possibly also a very stiff load cell. It must be kept in mind, however, that it is impossible to completely avoid any deformation of the instrument during a test and this deformation must be corrected for the results to be true material properties.40 Although prototypes with very stiff loading fi xtures and load cells may be desirable in the academic lab, commercial instruments such as the texture analyzer are perfectly capable of providing reproducible and reliable data if the sample holder is designed carefully. It is, however, important to ensure that the compliance of the apparatus does not greatly exceed that of the fi lm one wishes to test. This may lead to large differences in the curves that are measured, as illustrated in Figure 6.10.47 It is fi nally useful to discuss briefly the effect of the shape of the probe itself. In 1997, Chuang at Avery advertised a probe test protocol using a spherical probe.48 The main advantage of the spherical probe is the reproducibility because alignment is no longer a problem.7,49,50 However, the detachment of a spherical probe for a fibrillating PSA more closely resembles a peel test than a parallel plates test and imposes a less homogeneous stress field once cavities are fully formed. On the other hand, for weak adhesive forces or interfacial fracture, the spherical geometry is better defi ned and the so-called JKR analysis of the contact problem provides more meaningful data. Several detailed analyses exist for the spherical probe geometry and have been discussed in detail in a recent review. 36

10

Force (N)

5

0

−5

Sample Motor

−10 −50

0 50 Displacement (µm)

100

150

FIGURE 6.10 Measured uncorrected force–displacement curve (dashed line) and corrected adhesive displacement (solid line). In this case, the deformation in the initial stage of the test (compression and tension) is mainly due to the apparatus and sample holder rather than to the adhesive layer itself. Only after the layer fails do the two curves join each other. (From Josse, G., De l’Adhérence à l’Anti-Adhérence à travers le Probe Tack, Paris, Université Paris VI, 2001. With permission.)

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Probe Tack

6-15

6.4 Analysis of Probe Tack Debonding Curves Obtained for Pressure-Sensitive Adhesives 6.4.1

Cavitation in the Probe Geometry

A distinctive feature of probe test curves is the presence of a relatively sharp maximum in the stress–strain curve. Th is maximum is invariably due to a failure of the adhesive layer by cavitation. Because the factor a/h is usually rather large, the adhesive layer is highly confi ned and the hydrostatic pressure that builds during loading leads to the nucleation and growth of cavities. These cavities will always grow to a size commensurate with the thickness of the layer. 24 Such an example is illustrated in Figure 6.11. Earlier results suggested that the cavitation process was only controlled by elasticity and the peak stress should therefore be proportional to the modulus.6 A later analysis carried out by Chiche et al.9,26 demonstrated that this is only true for adhesives forming large defects at the interface with the probe. An example of the same acrylic-based PSA material debonded from a series of surfaces of increasing mean square roughness is illustrated in Figure 6.12 and demonstrates that the peak stress due to cavitation is lower when the PSA is detached from a rougher surface. The same type of experiments performed on styrene–isoprene–styrene (SIS)-based adhesives demonstrated that the plateau stress after the initial peak is a much more reliable material property than the actual peak stress.15,16,42 Nevertheless, if the probe tests are performed on the same probe, the value of the peak stress is representative of the elasticity of the material. However the peak does not correspond to the appearance of all cavities simultaneously but rather to the point at which the compliance of the

FIGURE 6.11 Images of cavities obtained with SIS-based PSA but three different layer thicknesses. The size of the cavities clearly depends on the thickness of the layer that is being tested. (From Chiche, A., Décollement d’Adhésifs Souples: Cavitation et Fracture, Paris, Université Paris VII, 2003. With permission.)

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6-16

Fundamentals of Pressure Sensitivity

0.7

0.15 A C

0.6 B

D

E

0.10

Stress σ (MPa)

0.5 C 0.4

0.05 D

A

B

0.3 E 0.2

0.00

0.6

0.8

1.0

1.2

0.1

0.2

0.4

0.6 Strain ε

1.0

0.8

1.2

Average roughness, RA (nm)

150 8 6

100

4 50 2 0

0 A

B

C

D

Average surface wavelength, λ (µm)

0.0 0.0

E

Polished probe identity

FIGURE 6.12 Representative stress–strain curves of the debonding of a polyethylhexyl acrylate latex at the same debonding velocity of 30 µm/s on rough stainless-steel surfaces. Letters on the probe test curves correspond to the mean square roughnesses reported in the bottom part of the figure. (From Chiche, A., Pareige, P., and Creton, C., Comptes Rendus Acad. Sci. Paris Ser IV, 1: 1197–1204, 2000. With permission.)

layer starts to increase faster due to cavitation than the hardening of the material itself. The process of cavity growth is rather complex, as clearly demonstrated by some recent theoretical arguments and numerical simulations.51–53 Hence, a direct and quantitative interpretation of the peak stress as a cavitation stress should be avoided. Figure 6.13a illustrates the stress–strain curves of three probe tests performed on the same probe surface with three different materials with increasing elastic moduli. The difference in

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6-17

Probe Tack

1.4 1.2

2AA 4AA 8AA

Stress (MPa)

1.0 0.8 0.6 0.4 0.2 0.0 0

2

4

6

8

Strain

(a) 107

G (MPa)

106

2 AA 4 AA 8 AA

105

104

103 10−3 (b)

10−1

101 ω*a T

103

105

FIGURE 6.13 (a) Nominal stress as a function of strain for acrylics with variable acrylic acid content. The first digit corresponds to the acrylic acid content (wt %). Probe tests were performed at Vdeb = 100 µm/s and room temperature; (b) master curves of storage modulus G′ as a function of reduced shear rate for three different adhesives with increasing acrylic acid content. Reference temperature: 25°C. (From Lindner, A., Lestriez, B. et al., J. Adhesion 82(3), 267–310, 2006. With permission.)

peak height and plateau stress can be directly attributed to the differences in the moduli, as illustrated in Figure 6.13b. These results are in agreement with the theoretical arguments presented in Section 6.2. Examples of cavities shown in probe tests are given in Figure 6.14. One example (Figure 6.14, left) illustrates the dense population of cavities that is observed for a strong,

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Fundamentals of Pressure Sensitivity

FIGURE 6.14 Images of cavitation of three different PSAs on the same steel surface. An SISbased PSA forming very small cavities that do not grow beyond a size comparable with the thickness of the layer (left). An acrylic all-purpose PSA where substantial lateral propagation occurs (center). A sample of 100 kg/mol linear poly(n-butyl acrylate) as an example of cavitation in a liquid (right).

permanent PSA where the lateral growth of cavities is nearly precluded. When the resistance to interfacial crack propagation is lower, the cavities can grow significantly in the plane of the layer from their original size. An example if this is given next (Figure 6.14, center). Finally, for very soft adhesives that are liquid-like, the cavities tend to nucleate toward the center of the probe and assume irregular shapes that resemble Saff man–Taylor fi ngers observed in fluids (Figure 6.14, right).54,55 As discussed in Section 2.2, it is important to remember that the pressure inside the cavities is nearly zero until air can penetrate from the outside of the layer.11,56 Th is air penetration is accompanied by a drop in nominal stress corresponding roughly to 0.1 MPa. Th is drop is generally not visible for normal PSA (see Figures 6.3 and 6.13a) where detachment of the fibrils occurs before the air pressure can equilibrate, but it nevertheless contributes to the measured stress. For very liquid PSA, on the other hand, such as that shown on Figure 6.14 (right), the probe test curve can indicate a distinctive double plateau, which is characteristic of the breakup of cavity walls without actual detachment of the fibrils.18,57

6.4.2 Weak Adhesion: Interfacial Nucleation and Propagation When Gc/E is very low, debonding occurs by interfacial crack propagation rather than by cavitation and fibril formation. This is generally observed for very weak interfaces, such as those formed between a PSA and a release liner. An example of debonding curves for an acrylic PSA against three different silicone release liner-coated probes is illustrated in Figure 6.15. The probe is removed at the same velocity of 30 µm/s in all three cases. During the loading stage, the probe tester puts the layer under stress and, because the layer is mostly elastic, it stores this elastic energy, which is then released by the fast propagation of interfacial cracks.40 An example of this propagation process is illustrated in Figure 6.16.58

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6-19

Probe Tack 0.30 0.25

σ (MPa)

0.20 0.15 Increasing G c 0.10 0.05

0.00 0.0

0.2

0.4

0.6

0.8 ε

1.0

1.2

1.4

FIGURE 6.15 Probe test curves of a removable acrylic adhesive on different surfaces. The arrow indicates increasing Gc values for the surfaces. In all cases the propagation is mostly or completely interfacial, with little deformation of the layer and no clear fibrillar structure. The surfaces are three different release coatings and a steel surface (the most adhesive surface). (Data from Josse, G., Sergot, P., Dorget, M., and Creton, C., J. Adhesion, 80(1–2), 87–118, 2004 and Josse, G., De l’Adhérence à l’Anti-Adhérence à travers le Probe Tack, Paris, Université Paris VI, 2001.)

It is clear from Figure 6.15 that whereas the peak stress is at about the same level for the three surfaces, the decrease in stress after the peak is very different. This difference is due to the very different rates at which the crack propagates.40 In essence, the initiation occurs for the same level of stored elastic energy, but the rate at which this elastic energy can be released back to the system varies and depends on Gc. For very low values of Gc the release rate is very fast and the stress drops almost instantaneously to zero. This rate dependence of Gc is analogous to what is always observed in the field of adhesion of well-cross-linked rubbers, where there is a unique relationship between Gc and crack velocity. One can typically write35,59 n  v  Gc
G0  1      v *  

(6.11)

Any variation in Gc can come either from a change in G 0, the component due to interfacial interactions, or from the viscoelastic dissipation component, which is typically more dependent on the dissipative properties of the rubber.60,61 For adhesion of PSA on silicone release liners, the level of adhesion is so weak that changes in the dissipative properties of the PSA do not change Gc much, which is therefore dominated by the value of G0. That is why release liner manufacturers tend to think of adhesion as a phenomenon controlled by the interface.

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Fundamentals of Pressure Sensitivity

FIGURE 6.16 Images of the different stages of propagation of interfacial cracks at the interface between a PSA layer and a silicone-coated probe surface. Time proceeds from top left to bottom right. (From Léger, L. and Creton, C., Adhesion Mechanisms at Interfaces between Soft Polymers, Philosophical Transactions of the Royal Society of London Series a-Mathematical and Physical Sciences, 2008. With permission.)

6.4.3 Strong Adhesion: Fibril Formation and Extension The other well-characterized experimental situation is the case in which Gc/E is larger than the initial thickness of the adhesive layer. The interfacial propagation of the cavities cannot occur easily and the adhesive becomes a foam through the continuous nucleation of additional cavities.19 Once the foam is fi lling the surface of the probe and the walls between the cavities are of the order of half the initial thickness of the layer, the deformation of the layer occurs in the direction of traction and the test starts to be analogous to a tensile test. This analogy between the plateau stress of the probe test and the tensile test is particularly obvious when the adhesive is very elastic.42 This is the case for PSA based on block copolymers and an example of tensile curves and probe test curves

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6-21

Probe Tack 1.6 1.4

σ (MPa)

1.2 0% SI

1.0

19% SI

0.8

42% SI

0.6 0.4 54% SI

0.2 0.0 0

5

10

15

ε

(a) 0.8

0% SI

σnominal (MPa)

0.6 19% SI 42% SI 0.4 54% SI 0.2

0.0 0 (b)

5

10

15

20

λ

FIGURE 6.17 (a) Probe tests of the debonding of four PSAs based on SI block copolymers from a steel probe. (b) Tensile stress–strain curves of the same adhesives. The four adhesive contain the same amount of tackifying resin but variable diblock(SI)/triblock(SIS) ratios, as specified. (From Creton, C., Roos, A., and Chiche, A., Adhesion: Current Research and Applications, W.G. Possart, Ed., Wiley-VCH, New York, 2005. With permission.)

on steel for a series of PSAs made from SIS and styrene–isoprene (SI) block copolymers is illustrated in Figure 6.17. The tensile curves demonstrate a distinctive strain hardening that is quantitatively reproduced by the probe test curves. The shape of probe tack curve is typical of strong adhesion and, in this case, the probe test can be used as an approximate characterization of the tensile properties of the PSA. Obviously, in this case the work of adhesion that is measured is rather sensitive to the nonlinear elongational properties of the PSA and not very sensitive to the details of the

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Fundamentals of Pressure Sensitivity

adhesive interactions, as long as they are sufficient to cause the fibril formation and stop interfacial crack growth. Finally, the fibrillar structure will detach from the surface. The quantitative criterion for this process to occur remains relatively poorly understood, but qualitatively the detachment of the fibrils is controlled by the strain hardening of the polymer in the fibrils.44 The more pronounced the strain hardening, the less the fibrils can extend before detaching from the surface of the probe. This can be seen in Figure 6.17 through a comparison of the fibril extension at detachment with the tensile stress–strain curves.

6.4.4

Transition between the Two Regimes

Between these two extreme cases lies the situation in which Gc/E is larger then the typical interfacial defect size (i.e., 500 nm) and smaller than the thickness of the layer h0 (i.e., 100 µm). In this case, the cavities initially formed grow laterally and vertically simultaneously and there is a competition between the two mechanisms. In this regime the resistance to lateral crack propagation is controlled by the dissipative properties of the adhesive, whereas extension is dependent on the nonlinear elastic properties of the adhesive. In this regime the shape of the probe tack curve can depend markedly on the value of Gc/E, with an increasing adhesion energy and maximum fibril extension with increasing values of Gc/E. A typical example of the variation in the shape of the curve with increasing Gc/E is illustrated in Figure 6.18, which demonstrates the same four adhesives in Figure 6.17, but this time detached from an ethylene–propylene surface. A distinctive

0.6

σ (MPa)

0.5 0.4 0.3 0.2 0.1 0% SI

42% SI

19% SI

54% SI

0.0 0

2

4

6

8

10

ε

FIGURE 6.18 Probe tests of the debonding of four PSAs based on SI block copolymers from an ethylene–propylene surface. The four adhesives contain the same amount of tackifying resin but variable diblock(SI)/triblock(SIS) ratios, as specified. (From Creton, C., Roos, A., and Chiche, A., Adhesion: Current Research and Applications, W.G. Possart, Ed., Wiley-VCH, New York, 2005. With permission.)

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sign of a mixed failure mode (detachment and extension) is a plateau in stress that decreases with increasing ε. This is typically never observed in tensile tests for elastic materials and demonstrates unambiguously that the fibril-stretching process in this case is not analogous to a tensile test, where the material cannot escape the grips of the tensile tester and typically hardens. In this transition regime between strong and weak adhesion, PSAs are very sensitive to subtle changes in rheological properties. The value of Gc becomes very sensitive to the dissipative properties of the PSA. A recent study indicated that better adhesion can be obtained with a dissipative layer close to the surface, backed by a more elastic layer.31

6.5

Conclusion

If executed and analyzed carefully, the probe test can be a powerful analytical tool to help interpret standard adhesive property tests of PSAs because of its sensitivity to small changes in the molecular structure of the PSA. We have described theoretically the process of cavity nucleation and growth and the transition from interfacial crack propagation to fibril growth. Most information comes from the shape of the stress–strain curve obtained during the debonding stage at different strain rates. A single peak with a sharp drop in force after the peak is indicative of weak adhesion and interfacial crack propagation. As the level of adhesion increases, the stress decrease more progressively after the peak and forms a distinct shoulder, which then turns into a plateau in stress. If adhesion further increases, the plateau in stress will become a second peak at higher elongation, which immediately precedes fibril detachment. The transition from one mechanism to the other can be described by the elastic length Gc/E, which represents the ratio between the critical energy release rate for crack propagation and the elastic modulus. When Gc/E < R0, failure occurs by crack propagation only. At the other extreme, when Gc/E > h0, failure occurs by fibril formation and growth and the adhesion energy is essentially controlled by the nonlinear properties of the adhesive in tension. The transition from one mechanism to the other occurs progressively and in this regime adhesion energy is particularly sensitive to the value of Gc/E.

References 1. PSTC test methods for pressure sensitive adhesive tapes, Pressure Sensitive Tape Council. 2000. 2. Zosel, A., Adhesion and tack of polymers: influence of mechanical properties and surface tensions, Colloid Polym. Sci. 263: 541–553, 1985. 3. Zosel, A., Fracture energy and tack of pressure sensitive adhesives, Adv. Pressure Sensitive Adhesive Technol. 1: 92–127, 1992. 4. Shull, K. R. and C. Creton, Deformation behavior of thin compliant layers under tensile loading conditions, J. Polym. Sci.: Part B: Polym. Phys. 42: 4023–4043, 2004. 5. Zosel, A., Adhesive failure and deformation behaviour of polymers, J. Adhesion 30: 135–149, 1989.

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6. Lakrout, H., P. Sergot and C. Creton, Direct observation of cavitation and fibrillation in a probe tack experiment on model acrylic pressure-sensitive-adhesives, J. Adhesion 69(3/4): 307–359, 1999. 7. Crosby, A. J., K. R. Shull, H. Lakrout and C. Creton, Deformation modes of adhesively bonded elastic layers, J. Appl. Phys. 88(5): 2956–2966, 2000. 8. Webber, R. E., K. R. Shull, A. Roos and C. Creton, Effects of geometric confinement on the adhesive debonding of soft elastic solids, Phys. Rev. E 68: 021805, 2003. 9. Chiche, A., J. Dollhofer and C. Creton, Cavity growth in soft adhesives, Eur. Phys. J. E 17: 389–401, 2005. 10. Gent, A. N., Compression of rubber blocks, Rubber Chem. Technol. 67(3): 549–558, 1994. 11. Lindner, A. and B. Lestriez et al., Adhesive and rheological properties of lightly crosslinked model acrylic networks, J. Adhesion 82(3): 267–310, 2006. 12. Creton, C. and H. Lakrout, Micromechanics of flat probe adhesion tests of soft viscoelastic polymer fi lms, J. Polym. Sci.: Part B: Polym. Phys. 38: 965–979, 2000. 13. Kakavas, P. A. and P. J. Blatz, Effects of voids on the response of a rubber poker chip sample .3, J. Appl. Polym. Sci. 43(6): 1081–1086, 1991. 14. Laun, H. M., M. Rady and O. Hassager, Analytical solutions for squeeze flow with partial wall slip, J. Non-Newtonian Fluid Mech. 81: 1–15, 1999. 15. Roos, A., Sticky Block Copolymers: Structure, Rheological and Adhesive Properties. Paris, Université Paris VI, 2004. 16. Chiche, A., Décollement D’adhésifs Souples: Cavitation et Fracture. Paris, Université Paris VII, 2003. 17. Tirumkudulu, M., W. B. Russell and T. J. Huang, On the measurement of “tack” for adhesives, Phys. Fluids 15(6): 1588–1605, 2003. 18. Poivet, S., F. Nallet, C. Gay, J. Teisseire and P. Fabre, Force response of a viscous liquid in a probe-tack geometry: Fingering versus cavitation, Eur. Phys. J. E 15: 97–116, 2004. 19. Brown, K., J. C. Hooker and C. Creton, Micromechanisms of tack of soft adhesives based on styrenic block copolymers, Macromol. Mater. Eng. 287(3): 163–179, 2002. 20. Gay, C. and L. Leibler, Theory of tackiness, Phys. Rev. Lett. 82(5): 936–939, 1999. 21. Gent, A. N. and P. B. Lindley, Internal rupture of bonded rubber cylinders in tension, Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 249 A: 195–205, 1959. 22. Gent, A. N. and D. A. Tompkins, Surface energy effects for small holes or particles in elastomers, J. Polym. Sci., Part A-2 Polym. Phys. 7: 1483–1488, 1969. 23. Dollhofer, J., A. Chiche, V. Muralidharan, C. Creton and C. Y. Hui, Surface energy effects for cavity growth and nucleation in an incompressible neo-Hookean material—modeling and experiment, Int. J. Solids Struct. 41(22–23): 6111–6127, 2004. 24. Chikina, I. and C. Gay, Cavitation in adhesives, Phys. Rev. Lett. 85: 4546–4549, 2000. 25. Lin, Y. Y., C. Y. Hui and H. D. Conway, A detailed elastic analysis of the flat punch (tack) test for pressure sensitive adhesives, J. Polym. Sci.: Part B: Polym. Phys. 38(21): 2769–2784, 2000.

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26. Chiche, A., P. Pareige and C. Creton, Role of surface roughness in controlling the adhesion of a soft adhesive on a hard surface, Comptes Rendus Acad. Sci. Paris Ser. IV 1: 1197–1204, 2000. 27. Lau, A. W. C., M. Portigliatti, E. Raphaël and L. Léger, Spreading of latex particles on a substrate, Europhys. Lett. (5): 717, 2002. 28. Gent, A. N. and C. Wang, Fracture mechanics and cavitation in rubber-like solids, J. Mater. Sci. 26: 3392–3395, 1991. 29. Fond, C., Cavitation criterion for rubber materials: a review of void-growth models, J. Polym. Sci.: Part B: Polym. Phys. 39: 2081–2096, 2001. 30. Creton, C., J. C. Hooker and K. R. Shull, Bulk and interfacial contributions to the debonding mechanisms of soft adhesives: Extension to large strains, Langmuir 17(16): 4948–4954, 2001. 31. Carelli, C., F. Déplace, L. Boissonnet and C. Creton, Effect of a gradient in viscoelastic properties on the debonding mechanisms of soft adhesives, J. Adhesion 83(5): 491–505, 2007. 32. Williams, M. L. and R. A. Schapery, Spherical flaw instability in hydrostatic tension, Int. J. Fracture Mech. 1: 64–71, 1965. 33. Lawn, B., Fracture of Brittle Solids. Cambridge, Cambridge University Press. 1993. 34. Lin, Y. Y. and C. Y. Hui, Cavity growth from crack-like defects in soft materials, Int. J. Fracture 126(3): 205–221, 2004. 35. Maugis, D. and M. Barquins, Fracture mechanics and the adherence of viscoelastic bodies, J. Phys. D: Appl. Phys. 11: 1989–2023, 1978. 36. Shull, K. R., Contacts mechanics and the adhesion of soft solids, Mater. Sci. Eng. R, Report 36: 1–45, 2002. 37. Zhang Newby, B.-M., M. K. Chaudhury and H. R. Brown, Macroscopic evidence of the effect of interfacial slippage on adhesion, Science 269: 1407–1409, 1995. 38. Chaudhury, M. and B.-M. Zhang Newby, Friction in adhesion, Langmuir 14: 4865–4872, 1998. 39. Amouroux, N., J. Petit and L. Léger, Role of interfacial resistance to shear stress and adhesive peel strength, Langmuir 17: 6510–6517, 2001. 40. Josse, G., P. Sergot, M. Dorget and C. Creton, Measuring interfacial adhesion between a soft viscoelastic layer and a rigid surface using a probe method, J. Adhesion 80(1–2): 87–118, 2004. 41. Creton, C., Pressure-sensitive-adhesives: An introductory course, MRS Bull. 28(6): 434–439, 2003. 42. Creton, C., A. Roos and A. Chiche Effect of the diblock content on the adhesive and deformation properties of PSAs based on styrenic block copolymers. in: W. G. Possart (eds). Adhesion: Current Research and Applications. Wiley-VCH, 2005. 43. Roos, A. and C. Creton, Nonlinear elastic properties of elastomeric block copolymers, Macromolecules 38: 7807–7818, 2005. 44. Glassmaker, N. J., C. Y. Hui, T. Yamaguchi and C. Creton, Detachment of stretched viscoelastic fibrils, Eur. Phys. J. E 25: 253–266, 2008. 45. Hammond, F. H., Polyken probe tack tester, ASTM Spec. Technical Publ. 360: 123–134, 1964.

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46. Zosel, A., The effect of bond formation on the tack of polymers, J. Adhesion Sci. Technol. 11: 1447–1457, 1997. 47. Josse, G., De l’Adhérence à l’Anti-Adhérence à travers le Probe Tack. Paris, Université Paris VI, 2001. 48. Chuang, H. K., C. Chiu and R. Paniagua, Avery adhesive test yields more performance data than traditional probe, Adhes. Age (September): 18–23, 1997. 49. Crosby, A. J. and K. R. Shull, Adhesive failure analysis of pressure-sensitive adhesives, J. Polym. Sci.: Part B: Polym. Phys. 37: 3455–3472, 1999. 50. Crosby, A. J., K. R. Shull, Y. Y. Lin and C. Y. Hui, Rheological properties and adhesive failure of thin viscoelastic layers, J. Rheol. 46(1): 273–294, 2002. 51. Yamaguchi, T. and M. Doi, Debonding dynamics of pressure-sensitive adhesives: 3D block model, Eur. Phys. J. E 21(4): 331–339, 2006. 52. Yamaguchi, T., H. Morita and M. Doi, Modeling on debonding dynamics of pressure-sensitive-adhesives, Eur. Phys. J. E 20(1): 7–17, 2006. 53. Teisseire, J., F. Nallet, P. Fabre and C. Gay, Understanding cracking versus cavitation in pressure-sensitive adhesives: The role of kinetics, J. Adhesion 83(7): 613–677, 2007. 54. Saff man, P. G. and G. Taylor, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 245: 312–329, 1958. 55. Derks, D., A. Lindner, C. Creton and D. Bonn, Cohesive failure of thin layers of soft model adhesives under tension, J. Appl. Phys. 93(3): 1557–1566, 2003. 56. Poivet, S., F. Nallet, C. Gay and P. Fabre, Cavitation-induced force transition in confined viscous liquids under traction, Europhys. Lett. 62(2): 244–250, 2003. 57. Lakrout, H., C. Creton, D. Ahn and K. R. Shull, Influence of molecular features on the tackiness of acrylic polymer melts, Macromolecules 34: 7448–7458, 2001. 58. Léger, L. and C. Creton, Adhesion Mechanisms at Interfaces between Soft Polymers, Philosophical Transactions of the Royal Society of London Series a-Mathematical and Physical Sciences 366: 1425–1442, 2008. 59. Shull, K. R., D. Ahn, W. L. Chen, C. L. Mowery and A. J. Crosby, Axisymmetric adhesion tests of soft materials, Macromol. Chem. Phys. 199: 489–511, 1998. 60. Ahn, D. and K. R. Shull, Effects of methylation and neutralization of carboxylated poly(n-butyl acrylate)on the interfacial and bulk contributions to adhesion, Langmuir 14(13): 3637–3645, 1998. 61. Ahn, D. and K. R. Shull, Effects of substrate modification on the interfacial adhesion of acrylic elastomers, Langmuir 14: 3646–3654, 1998.

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7 Peel Resistance 7.1 Introduction .............................................................7-1 7.2 Basic Principles, Theory, and Analysis of Peel Resistance .....................................................7-2 7.3 Peel Resistance Test and Analysis .........................7-7 Test Methods of Peel Resistance • Master Curve and Time–Temperature Superposition • Failure Mode

7.4

Hyun-Joong Kim Dong-Hyuk Lim Young-Jun Park Seoul National University

7.1

Parameters of Peel Resistance ............................7-15 Bulk Properties and Peel Resistance of PressureSensitive Adhesives • Surface Properties of Substrate and Peel Resistance

7.5 Conclusion ..............................................................7-31 References ........................................................................7-32

Introduction

According to a common definition, pressure-sensitive adhesives (PSAs) can be adhered to various surfaces with light pressure within a few seconds. In certain cases, they also can be removed without leaving any residue or contaminating the substrate. Such behavior is due to their ambiguous, solid-like, as well as liquid-like behavior, that is, their viscoelasticity (see also Chapters 4 and 5). The former behavior (called cohesion) gives high strength in the debonding process, whereas the latter behavior (called adhesion) allows wetting of the surface during the bonding process. The adhesive performances of PSAs can be evaluated as tack, peel resistance, and cohesive strength, such as holding power and shear adhesion failure temperature (SAFT) (see also Applications of Pressure-Sensitive Products, Chapter 8). Among these performances, peel resistance is an especially important parameter for PSAs. Peel resistance is the force required to peel off a pressure-sensitive product (label, tape, etc.) from a substrate. According to ASTM D 907 [1], the peel resistance is the average load per unit width of bondline required to progressively separate a flexible member from a rigid member or another flexible member. Control of peel resistance in PSA products is very important for both manufacturers and customers. For instance, in the label industry, the value of peel resistance is one of 7-1

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7-2

Fundamentals of Pressure Sensitivity TABLE 7.1 Classification of Pressure-Sensitive Adhesives versus Peel Resistance and Removability PSA Grade

180° Peel Resistance (N/2.5 cm)

Excellent permanent Permanent Semiremovable Removable and repositionable Excellent removable

>14 10–14 6–8 2–4 <1

Source: Czech, Z., J. Appl. Polym. Sci., 97, 886–892, 2005. With permission.

the criteria used to classify applications. Labels are usually classified by peel resistance as permanent or removable (see also Applications of Pressure-Sensitive Products, Chapter 1). PSAs used for permanent labels possess high peel resistance. Such labels are definitively laminated on the substrate. On the other hand, PSAs for removable labels have low peel resistance, which allows their slight detachment from substrates. A common classification of PSAs according to the value of peel resistance is given in Table 7.1 [2]. (Such classification is realistic in connection with the bulk and surface strength of the carrier material only. For instance, a peel resistance value of 14 N/25 mm causes paper-tear; that is, for paper, such PSA can ensure an excellent permanent bond. However, this behavior depends on the paper strength as well. Removability is peel value dependent, but repositionability is peel build-up dependent. That means that peel values of 2–4 N/25 mm, as given in Table 7.1, can impart or not impart repositionability.) In this chapter, we will examine the research regarding peel resistance, both to defi ne it and to illustrate its importance. An understanding of the origin of peel resistance, the mechanics of peel resistance, and its theory is essential. Moreover, the failure mechanism must be also considered (see also Applications of Pressure-Sensitive Products, Chapter 8) Finally, correlation between the PSAs’ bulk/surface properties and peel resistance will be discussed. The bulk/surface properties and peel resistance of PSAs are affected by various factors, such as chemical structure, tackifier type and content, cross-linking density, and viscoelastic properties.

7.2

Basic Principles, Theory, and Analysis of Peel Resistance

Flow properties during the bonding process, the nature of the PSA, and test geometry influence peel resistance. The study of experimental and analytical examinations of peeling is very important for understanding the peeling mechanism. A theoretical analysis of peeling was developed by considering 90° peeling of a thin, flexible elastic strip bonded to a rigid substrate by an elastic layer of adhesive [3]. The bonded part of the strip was represented as an elastic beam on an elastic foundation and the flexible part as an elastic beam under large deflection. In considering other angles of peeling, Kaelble [4] introduced the idea of cleavage and shear modes of failure. A good relationship exists between theory and experiment in the variation of peel force with

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7-3

Peel Resistance

peel angle and peel rate. Kaelble [5] extended the elastic analysis to include viscoelastic peeling. Kaelble described his peel resistance theory in early papers in 1959 [4]. The descriptive assumptions for an idealized type of peel resistance (simple stripback) are listed as follows: 1. A steady-rate debonding proves 2. Properties of the flexible member a. Of slender rectangular cross-section b. Elastically deformed c. Bonded and unbonded portions of semi-infinite length 3. Properties of the forces a. Applied force—acts in tension along the central plane of flexible members b. Shearing forces—distributed over the bonded interface of the flexible member c. Cleavage forces—a highly localized parallel array, perpendicular to the bond plane d. All forces uniformly distributed across the bond width Under these assumptions, the deformation curve of the flexible member under tension was characterized using the infi nite analysis method. Figure 7.1 illustrates the peeling behavior for cellophane/rubber–resin-based adhesive tape detached from the cellophane surface at various peeling angles. If the summation of moments of tensional and compressional forces in the bond are independent of the peel angle and cleavage is the controlling failure mechanism, then peel strength should vary inversely as (1 − cosω). Figure 7.1 presents steady-state peel strength data as a function of peel angle [5]. At low stripping rates and accompanying lower stripping force, experimental data confirm the theoretical inverse P versus (1 − cosω) relationship over a wide range of angles. At higher

10

44.48 Rate (in./min) 20 2.0 0.2 0.02

22.24

2

8.90

1

4.45

0.5

2.22

0

40

80

120

160

200

Peel strength (N)

Peel strength (LB)

5

240

Peel angle (°)

FIGURE 7.1 Peel force (P) versus angle (w) for aluminum foil tape. Peeling rate: 0.02, 0.2, 2.0, and 20 (in./min). (From Kaelble, D.H., Trans. Soc. Rheol., 4, 45–73, 1960. With permission.)

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7-4

Fundamentals of Pressure Sensitivity

stripping rates, the deviation becomes more marked due to the dual effect of tensile and flexural strains upon Young’s modulus of the backing. At low rates of peeling, a significant fall-off of jog in value of the peel force was observed when the peeling angle was in the range of 20∼40°. Kaelble [5] suggested that cleavage stress and shear stress interacted in some way to cause the unusual fall-off in peel force. This phenomenon was explained by the fact that the jog was associated with a relatively rapid change in decohesion (fracture) mechanism, according to Williams and Kauzlarich [6]. When peeling a flexible tape from a solid surface, there can exist a transition from a mechanism of decohesion relying on cleavage to one with a much greater component of shear. This change in mechanism requires that the specific energy for decohesion is less than decohesion by cleavage. This switch in mechanism is apparent only at low peeling angles, typically <40°, when the component of the applied tape tension acting parallel to the adhesive interface reaches some critical value. This critical value of peel force is influenced by the residual stress generated within the tape by the process of attachment to the rigid substrate. Figure 7.2 illustrates the diagrammatic view of the separation zone during peeling [7]. Gent and Meinecke [8] demonstrated that the stiff ness of such flexible sandwiched blocks depends on a “shape factor,” S, which is defined as the ratio of area of one of the loaded faces of the material to the area of the stress-free block. In peeling, the adhesive in advance of the peel front is constrained and exhibits an enhanced stiff ness, which may well be drawn out into fibrils. Figure 7.3 presents the value of S by ratio of the area. Peel resistance does not measure the adhesion bond strength directly, but the sum of the energy required to break the bond and to deform the backing and adhesive, as demonstrated in the following equation [9]: Gc
G0 

(7.1)

b Backing

Unconstrained adhesive forming fibrils

ha

L Constrained adhesive Peel front

Substrate

FIGURE 7.2 Diagrammatic view of the zone of separation in peeling. (From Williams, J.A., and Kauzlarich, J.J., J. Adhesion Technol., 21(7), 515–529, 2007. With permission.)

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7-5

Peel Resistance

90° Peeling direction

Substrate: cataphoresis

Foam of strengthening

PSA

A

O

Start of removing

Bending zone

FIGURE 7.3 Schematic representation of the PSA peel test. (From Horgnies, M., DarqueCeretti, E., and Felder, E., Int. J. Adhesion Adhesives, 27, 661–668, 2007. With permission.)

where Gc is the adhesive fracture energy, G 0 is the energy required to propagate a crack, which is a direct measure of the bonding forces, and ψ is the energy dissipated viscoelastically within the adhesive and backing. The value of ψ is the major contributor to the value of Gc and it is highly dependent on the rate and temperature of testing. We can measure Gc, but we cannot measure G 0. We can only estimate its value, which is fairly modest compared with the measured peel force values. This indicates that ψ is indeed an important factor in peel measurements. However, ψ is a function of G 0. If G 0 = 0, ψ is also equal to zero. The facture energy dissipation during debonding in a peel test seems to be connected to the formation and growth of fibrils during bond separation. Fracture energy dissipation is observed for polymers with a molecular mass between entanglements of about 104 g/mol, whereas below this limit debonding occurs by homogeneous deformation. Figure 7.3 illustrates the schematic representation of the 90° peel test [10]. The bending line (located at point O) is characteristic of the propagation of the crack between the adhesive and substrate. The start of removing line (located at point A) corresponds to the specific zone where the PSA fibrils are beginning to elongate. The facture energy, G, can be acquired by adhesion force, P, peel angle θ, and the bandwidth using Equation 7.2. G


P (1 cos ) b

(7.2)

Deformation of the PSA and the real contact area during peeling can be investigated using a fast charge-coupled device (CCD) camera and optical microscopy. Figure 7.4 presents

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7-6

Fundamentals of Pressure Sensitivity

Fibrils of elastomer PSA "Be"

Fibrils of acrylic PSA "Ba"

15 mm

3 mm

Foam of strengthening

(a)

(b)

FIGURE 7.4 Fibril elongation of elastomer PSAs (a) and acrylic PSAs (b) observed using a fast CCD camera during the stationary regime of peeling. (From Horgnies, M., Darque-Ceretti, E., and Felder, E., Int. J. Adhesion Adhesives, 27, 661–668, 2007. With permission.) 30 Maximum length of the fibrils compared to the initial thickness of PSAs (2 mm)

Length of the fibrils (mm)

25 20 15 10 5 0 0

1

2

3

4

5

6

7

8

9

10

Distance from the beginning of the bending zone (cm)

FIGURE 7.5 Fibril length distribution compared with the initial thickness of PSAs and according to the distance from the beginning of the bending zone. (From Horgnies, M., Dargue-Ceretti, E., and Felder, E., Int. J. Adhesion. Adhesives 27, 661–668, 2007. With permission.)

pictures taken every 8 ms during the stationary regime of peeling (peel resistance is almost constant) [10]. Figure 7.4 highlights fibrils that appeared during the (a) peel test of elastomer and (b) acrylic PSAs. Figure 7.5 illustrates the fibril length distribution of the PSA according to the distance (see Figure 7.3). The profiles of adhesive deformation and measured forces were constant during the peel test. Horgnies et al. [10] developed an original peeling procedure that can detect the local fracture energy and investigated the relationship between PSA deformation and local fracture energy. The interface between

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7-7

Peel Resistance

the PSA and glass substrate was observed by optical microscopy to measure the contact area. The interface between the PSA and the glass substrate is composed of adhesive and gaseous bubbles that are induced from the noncontact area. The increase in fracture energy is in direct relation to the contact ratio between the PSA and substrate. A schematic diagram representing the side profi le of a PSA tape undergoing peel is illustrated in Figure 7.6 [11]. Below the view of the bond is a typical stress distribution profi le as recorded by the measuring instrument, a newly designed bond stress analyzer. The instrument is a true accessory to the Instron tester in that the force-sensing substrate uses an Instron load cell as the force transducer. The weighing system is also utilized to measure and recorded the bond forces. As indicated in Figure 7.6, the bond stress is highly localized at the boundary of the bond. Tensional stress, which characterizes the micromechanisms of unbonding, is observed in the adjacent boundary region. Maximum compressional stress and compressional zone length are produced due to leverage of the flexible member. A low tensional stress zone appears as one proceeds farther away from the boundary and then the normal stress effectively drops to zero. The stress distribution displayed in Figure 7.6 strongly indicates that an important step during the fracture process is microcavitation of the adhesive layer, which is similar to the cavitation observed in the course of the probe tack test (see Chapters 4 and 6). The stress profi le of Figure 7.6 indicates a very rapid change in bond stress in the region between σc and σ t. In this narrow zone of the bond, it is evident that small spherical cavities are formed within the adhesive phase of the bond. Williams and Kauzlarich [7] have recently employed the finite element method for the calculation of stress distribution in the adhesive layer along with the corresponding strain from 90° peel test results. Obtaining the stress–strain curves allows us to gain an insight into the viscoelastic behavior of PSAs during peeling. A fundamental method of defining bond strength is expressed in energy or work. The definition of peel work (W) by Kaelble [4,5] isolates two separate contributions, as follows, W
WT WD

(7.3)

where WT is the nonrecoverable work of translation and WD is the work of deformation. Kinloch et al. [12] recently modeled the work of peel and produced analytic relations for the adhesion energy release rate for elastically deformed flexible laminates. Kinloch et al. [12] concluded that the apparent energy release rate is very dependent on the peel angle and does not provide a significant material parameter for describing peel adhesion.

7.3 Peel Resistance Test and Analysis 7.3.1 Test Methods of Peel Resistance Material performance testing is generally oriented toward practical uses that pertain directly to the application of the technology. Early testing was carried out manually to bond the adhesive-coated product to the substrates of interest and to determine whether it has adequate adhesion for the particular application. To fully understand the potential

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7-8

Fundamentals of Pressure Sensitivity

Backing material Adhesive

Adherend

6 σt

5

Stress

3 2

Stress

Compression

σx (kg/cm2)

Tension

4

1 0 −1 −2 −3 −4 −5

σc

−6 −0.8 −0.6 −0.4 −0.2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Bond distance X (mm)

FIGURE 7.6 Schematic representation of the peel profi le and experimental boundary distribution of normal stress. (From Kaelble, D.H., Trans. Soc. Rheol., 9(2), 135–163, 1965. With permission.)

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Peel Resistance

of PSAs, tapes were peeled at temperatures above and below room temperature to determine the usability of a product at various temperatures. In other cases, PSA tapes were peeled and reapplied several times to determine the product’s release ability (see also Applications of Pressure-Sensitive Products, Chapter 8). The properties and performance of a PSA are affected by several factors, including [13] the following: 1. 2. 3. 4. 5. 6. 7.

Coating weight Adhesive composition Substrates to which it is applied Temperature Bonding pressure Residence time before breaking the bond Type and characteristics of the surface where the adhesive is applied

In addition, testing under standardized procedures and condition is important in quality control by the producer in selecting raw materials, in the evaluation of process variables to assure process consistency, and in the evaluation of the final product for performance consistency (see Applications of Pressure-Sensitive Products, Chapter 7). For the end-user, those quality controls are required to evaluate adhesives for particular applications and to select the proper adhesive (see Applications of Pressure-Sensitive Products, Chapter 4). The peel strength of PSAs can be tested by T-peel, drum peel, and 90° and 180° peel tests, as illustrated in Figure 7.7 [10] (see Applications of Pressure-Sensitive Products,

(a)

(b)

(c)

(d)

FIGURE 7.7 Various peel test methods: (a) 180° peel, (b) 90° peel, (c) drum peel (tape unwind), and (d) T-peel. (From Satas, D., Handbook of Pressure Sensitive Adhesive Technology and Applications, D. Satas, Ed., Satas & Associates, Warwick, RI, 2002. With permission.)

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Fundamentals of Pressure Sensitivity

Chapter 8). Many researchers test peel strength using 90° or 180° peel strength. The drum test measures the property of the unwinding process, which is an important property of tapes (see Applications of Pressure-Sensitive Products, Chapters 4 and 8). The T-peel test measures the force required to break the bond between two adhesive layers. This test is also used to measure the force needed to separate the tape from a flexible adherend (see Applications of Pressure-Sensitive Products, Chapter 8). Figure 7.8 illustrates tools for (a) 180° and (b) 90° peel tests (see Applications of Pressure-Sensitive Products, Chapter 8). Another representative method for 90° peel is the mandrel peel test [14]. This method involves peeling around a circular mandrel while applying an alignment load to the base of the laminate to ease abutment of the peel arm to the mandrel. There are two major categories in peel testing—dynamic and static. For the purposes of definition, dynamic peel is measured by a force applied at some given rate of peeling, and the unit is the force per unit area. Most of the standard peel testing methods fall into this category. In the case of static peel testing, the force is applied by a fi xed weight and the time to fail is recorded. ASTM D2860 and PSTC 14 fall into this latter category. Industry organizations (ASTM, TLMI, and PSTC and FINAT and AFERA in Europe) have devised standard test methods that cover peel testing. For convenience, they are listed for comparison in Table 7.2 [15] (see also Applications of Pressure-Sensitive Products, Chapter 8). The standard specimen for peel strength testing is a 1 in. wide strip of tape. The specimen is adhered to a clean stainless-steel panel without air bubbles and is pressed by a constant weight of roller. After sufficient bonding time, the peel specimen is loaded on the test machine. One side of the strip is placed in one side jaw, whereas the other side jaw fastens to the test panel [16,17].

P (a)

(b)

FIGURE 7.8 Tools for (a) 180° peel test and (b) 90° peel test. (From Kawashita, L.F., Moore, D.R., and Williams, J.G., J. Adhesion, 80, 147–167, 2004; ASTM D3330. With permission.)

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7-11

Peel Resistance TABLE 7.2

Comparison of Standard Peel Test Methods

Organization

Method

Peel Angle (°)

Test Speed

Bonding Time

Notes

ASTM ASTM ASTM ASTM TLMI PSTC PSTC PSTC PSTC FINAT FINAT AFERA

D903 D1000 D2860 D3330 L-IA 1 1 2 3 14 FTM 1 FTM 2 4001

180 180 90 180 180 180 90 180 90 180 90 180

12 in./min 12 in./min Static 12 in./min 12 in./min 12 in./min 12 in./min 12 in./min Static 300 mm/min 300 mm/min 300 mm/min

Open 20 min 3 min <1 min Open <1 min <1 min <1 min 3 min 20 min, 24 h 20 min, 24 h 10 min

P1 P6 P2 P3 P1 P3 P4 P5 P2 — — —

P1 ASTM D903 and TLMI L-IA 1 describe the method, but do not specify residence times prior to peeling. The TLMI method suggests residence times ranging from 30 min to 24 h. P2 These methods are similar and describe static peel test from a standard linerboard material. P3 These methods are virtually identical. P4 These methods are similar. P5 Peel test taking into consideration the needs for testing double-faced PSA product. P6 There are two procedures in this method. Method A uses flat stainless plates, whereas Method B uses stainless drums. Source: Urahama, Y., Tokunaga, Y., and Tanaka, Y., J. Adhesion Soc. Jpn., 23(5), 171–177, 1990. With permission.

Variances of the standard peel test methods, product-specific peel test methods, and other methods for tests of peel resistance as well the dependence of peel resistance on different experimental parameters are described by Benedek (see also Applications of Pressure-Sensitive Products, Chapter 8).

7.3.2

Master Curve and Time–Temperature Superposition

For polymers, the effect of varying the temperature or time is identical. A large amount of knowledge regarding the molecular basis for polymer properties came from the experimental and theoretical studies of time–temperature superposition [18]. Relaxation and creep occur by diff usive molecular motions, which become more rapid as the temperature increases. Temperature is a measure of molecular motion. At higher temperature, the molecules move faster. The William–Landel–Ferry equation (Equation 7.4) expresses a logarithmic relationship between time and temperature: log aT


C1(T Ts ) C2  T Ts

(7.4)

Here, T is the temperature when the experiment is done, Ts is the standard temperature, C1 and C2 are constants, and aT is a shift factor. In a somewhat better approximation, fi xed values of C1 = 8.86 and C2 = 101.6 were used in conjunction with

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7-12

Fundamentals of Pressure Sensitivity

a reference temperature, Ts, which was allowed to be an adjustable parameter, but generally fell about 50°C above the glass transition temperature, Tg, as follows: log aT


8.86(T Ts ) 101.6  T Ts

(7.5)

Alternatively, if the standard temperature is chosen to be Tg, then log aT


17.5(T Tg ) 51.6 T Tg

(7.6)

Peel strength

T6 T5 T4 T3 T2

Peel strength

The existence of such a useful universal equation for the shift factor formed the basis for many experiments and theories regarding the viscoelasticity of polymers. Based on these ideas, the time–temperature superposition principle states that for viscoelastic materials, time and temperature can be superimposed onto data at another temperature by shift ing the curves along the time axis. In other words, time–temperature superposition allows prediction of peeling energies: (1) at a lower rate by shift ing data at T > T0 to the left and (2) at high rates by shifting data at T < T0 to the right. The curve obtained after the shifts is called a master curve. However, the range of peel rates for which someone can perform experiments is limited, because extremely low or high peel rates are hard to maintain and difficult to measure. If we conduct a peel test for a small rate range and measure the strength over a wide range of measurable temperatures, we can obtain the family of curves shown in Figure 7.9. The temperatures are in the order of T1 > T2 > T3 > T4 > T5 > T6. Examination of these generic data demonstrates that shifting the curves for temperatures T1 through T5 to the left from the standard temperature, T6, by some amount will cause all of the curves to form a smooth curve. This is the case for most PSAs. The result is known as a master curve and the amount by which a segment is

T1

Rate Temperature

log Va T

FIGURE 7.9 The making of a master curve. (From Pocius, A.V., Adhesion and Adhesives Technology, A.V. Pocius, Ed., Hanser, Munich, 1997. With permission.)

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Peel Resistance

shifted is known as a shift factor. Thus, a master curve is a plot of the peel strength as a function of a reduced peel rate. The reduced variable is obtained by multiplying the peel rate by the shift factor. Thus, the set of curves illustrated in Figure 7.9a can be reduced to a single curve, illustrated in Figure 7.9 [18]. Although direct testing of peel energy may be limited to a relatively narrow range of test speeds, time–temperature superposition allows prediction of peeling energies. Therefore, we can overcome the limit of the peeling tester and predict the peel resistance in an extended test range. Derail et al. [19] demonstrated that the shift factors derived from peel adhesion master curve construction were equivalent to those derived via rheologic measurement (see Chapter 4). Peel master curves are therefore examples of rheologic master curves. Peeling behavior through the construction of peel master curves can reveal the influence of adhesive molecular features, including molecular weight and composition. Failure mode location in peeling tests depends only on the rheological properties of the PSA at the temperature considered. This is a very important statement for industrial application. The fact that fracture does not depend on the location of crack initiation means that within a controlled range of temperature and deformation rates, the user may trust the adhesive even when some defect initiates a crack in fracture mode, which is different from what is expected.

7.3.3 Failure Mode The failure mode is classified into several types including cohesive failure, adhesive (or interfacial) failure between the adhesive and the substrate, stick–slip failure, and glassy failure between the backing material and adhesive. It is expected that a normal PSA will fail interfacially when tested under standard peel test conditions. Adhesive failure occurs when the adhesive strips are cleanly removed from the adherend, leaving no visually noticeable residue (see Figure 7.10). Some adhesives may fail cohesively, leaving

B-C C

B

A Peel strength (N)

P Time

Viscous

A

Glassy

B B-C

C Log rate (m/s)

FIGURE 7.10 Failure modes as a function of peeling rate. (From Urahama, Y., Tokunaga, Y., and Tanaka, Y., J. Adhesion Soc. Jpn., 23(5), 171–177, 1990. With permission.)

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7-14

Fundamentals of Pressure Sensitivity

3.5

Peel strength (kg/in.)

3.0

2.5

2.0

1.5

1.0 0

1

2

3

4

5

6

7

Length of tape peeled (cm)

FIGURE 7.11 Peel strength–strain curve demonstrating stick–slip peeling. (From Aubrey, D.W., Welding, G.N., and Wong, T., J. Appl. Polym. Sci., 13, 2193–2207, 1969. With permission.)

adhesive residue on the test panel. If the adhesive is not fi rmly anchored to the backing material, it may transfer from the backing material to the test panel, leaving at least part of the backing bare. In the case of transfer tapes, such behavior is designed intentionally; otherwise, it denotes product failure (see Applications of Pressure-Sensitive Products, Chapter 4). The facture shapes of four failure modes in peeling experiments are illustrated in Figure 7.10. Urahama et al. [15] observed that at relatively low peeling speeds below 10 mm/min, the stringiness conformation of adhesives of the porous backing had a honeycomb structure, whereas that of the nonporous backing had a sawtooth-shape structure. In the region of intermediate pulling rate, the mode of failure is stick–slip, which is a regular, jerky peel in which the observed peel force oscillates between well-defi ned limits. An autographic recording obtained in this region is illustrated in Figure 7.11 [20]. In this region, the alternative failure between adhesive and glassy failure was observed. The alternations of force were in step with the alternations of failure mode and, furthermore, the rising and falling parts of the autographic trace corresponded with cohesive and adhesive separations, respectively. The steady rate of pulling is insufficient to sustain peeling with the fast mechanism, so the mechanism reverts to the slow mechanism. This completes the cycle of stick–slip oscillation. In the case of adhesive failure, a general judging standard is the existence of adhesive residue. As previously mentioned, the test method must be selected considering the application of the adhesive (see Applications of Pressure-Sensitive Products, Chapter 4). For example, a special PSA tape is used to fabricate semiconductor chips [21]. Ultraviolet (UV)-curable dicing tape used in the die-bond process for semiconductors must hold tightly upon mounting of a silicon wafer. During the pick-up process, the adhesion strength of the dicing tape must be reduced with no residue so that the diced chip

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Peel Resistance

can be picked up easily. In this case, human sight is not enough to determine adhesive failure mode with no residue. Additional instrumental analysis like optical microscopy, Fourier transform infrared spectroscopy, or X-ray photoelectron spectroscopy (XPS) may be carried out for an exact determination. Th is is why with the recent rapid development in integrated semiconductor technology, higher reliability is required for the manufacturing process of electronic devices.

7.4 Parameters of Peel Resistance Figure 7.12 presents a simple flow chart of tape processing and peeling tests. We can consider seven factors that can influence on the results of peel resistance by reviewing the tape preparation and test processes. These parameters are summarized in Table 7.3. If we want to acquire correct data influenced by one parameter, we must control the other variables. Table 7.3 will help to control the variables for accurate peeling tests. Detailed effects related to a few select parameters will be described later. PSA adhesion is determined by two factors: the energy of deformation of the viscoelastic adhesive until rupture or separation from the surface occurs and the surface need to be contacted to such a degree that molecular attraction forces come into action.

Preparation of PSA

Coating onto backing material

Cleaning substrate

Preparation of strip

Bonding and sample stabilization

Peeling

Data analysis

FIGURE 7.12

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The flow chart of sample preparation and peel testing.

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7-16 TABLE 7.3

Fundamentals of Pressure Sensitivity Parameters of Processing and Testing that Affect Peel Resistance

Stage of Processing and Testing Preparation of PSA

Coating onto carrier material

Preparation of sample Cleaning substrate

Bonding step and sample stabilization Peeling test

Parameters Affecting Peel Resistance Chemical composition and cross-linking nature and density Viscoelastic properties Miscibility between PSA and other formulation components Modulus of carrier material PSA thickness Thickness of backing material Surface properties of carrier material Sample width Surface properties of substrate (surface energy and roughness) Surface treatment Degree of pollution Bonding pressure Bonding time Peeling angle or geometry and peeling tool Peeling rate Temperature and humidity

7.4.1 Bulk Properties and Peel Resistance of Pressure-Sensitive Adhesives The basic materials of acrylic PSAs are acrylic esters that yield soft and tacky polymers with low Tg. Suitable monomers for PSAs are alkyl acrylate and methacrylate containing 4–17 carbon atoms [22], such as butyl acrylate, 2-ethylhexyl acrylate (2-EHA), and iso-octyl acrylate (an isomer of 2-EHA). Homopolymers of these polymers are soft and tacky materials that cannot be used for good PSAs. They are modified by copolymerization with a small portion of other functional comonomers that affect a wide range of properties and also provide cross-linking sites. The composition of generalized acrylic PSAs is as follows: Main monomer: 50–98% Modifying monomer: 10–40% Monomer with functional groups: 0.5–20% Monomers that yield a homopolymer with low Tg plasticize the adhesive, whereas modifying monomers that yield homopolymers with high Tg increases the adhesive stiff ness. Tg is a useful indicator in choosing a comonomer (see Technology of Pressure-Sensitive Adhesives and Products, Chapter 5, and Applications of Pressure-Sensitive Products, Chapter 7). PSA flexibility and tackiness increase with increasing side-chain length until a certain chain length is exceed and the chains start to form crystalline regions that cause stiffening of the polymer. In the case of long branched side chains, branching decreases the tendency to form crystalline regions. Therefore, branching makes the polymer softer. The comonomer distribution is important and can be affected by the order of monomer addition. Usually, PSAs based on pure acrylics can be regarded as completely random, with the same monomer distribution in every polymer chain.

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7-17

Peel Resistance

100 Peel strength Probe tack SAFT

80

1200 60

40

SAFT (°C)

Peel strength (g/25 mm) and probe tack (g)

1600

800 20

0

400 5

10

15

Acrylic acid contents (wt %)

FIGURE 7.13 Adhesion properties such as probe tack, peel strength, and SAFT with variation in AA content. (From Joo, H.S., Do, H.S., Park, Y.J., and Kim, H.-J., J. Adhesion Sci. Technol., 20(14), 1573–1594, 2007. With permission.)

Comonomers, such as methyl methacrylate and styrene, which increase the Tg of the adhesive, can be used in limited amounts to improve cohesive strength. Much research exists regarding the formulation of acrylates on the properties of PSAs [23–26]. Gower and Shanks [27–29] discussed the formulation for polymerization on adhesive performance and peel master curve. They explained the relationship between comonomers and PSA performance. Figure 7.13 illustrates the effect of chemical composition of PSAs on peel resistance [30]. PSAs with varying amounts of acrylic acid (AA) were investigated, and the expected effects of AA addition were good adhesion to substrates, enhancement of cohesion, and increased viscosity. The Tg of the PSAs increased with increasing AA concentration, because AA has the highest Tg among monomers such as 2-EHA, vinyl–acetate (VAc), and AA. Peel strength slightly increased as AA concentration increased, although PSAs with an AA content of 10 and 15 wt % demonstrated somewhat similar peel strengths. These results can be explained, because the increase in AA concentration affected the viscosity and cohesive strength of synthesized PSA through hydrogen bond formation. Therefore, the peel strength of PSAs increased with AA concentration. The relationship between peel resistance and pulling rate has been examined using a range of poly(butyl acrylate) homopolymer adhesives with different molecular weights [20]. Results are illustrated in Figure 7.14. In the slow peeling region, the peel resistance increases with molecular weight, as would be expected if viscous flow of the adhesive is the controlling factor. The rate at which the transition to stick–slip occurs increases with decreasing molecular weight, although with the two lowest molecular weight adhesives this transition did not occur, even at the highest cross-head speed obtainable. In the fast

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7-18

Fundamentals of Pressure Sensitivity

5

e

d

Force range at stick−slip peeling c

Peel strength (kg/25 mm)

4 Range of force maxima a 3

b

Range of force minima d

b a

2

e e a b

1

f 0 −1.5

−1.0

0.0 0.5 1.0 −0.5 Log rate of jaw separation (cm/min)

1.5

2.0

FIGURE 7.14 Effect of molecular weight of poly(n-butyl acrylate) on peel strength at various rates of jaw separation. (Molecular weight: a > b > c > d > e > f, ○, cohesive failure; ●, adhesive failure between adhesive and glass surface (substrate); □, adhesive failure between adhesive and backing; △, mixture of two types of adhesives.) (From Aubrey, D.W., Welding, G.N., and Wong, T., J. Appl. Polym. Sci., 13, 2193–2207, 1969.)

peeling region, the amount of data available is small but gives no indication of appreciable dependence of peel resistance on molecular weight. To study the relationship between cross-linking density and peel resistance, UVcross-linkable PSAs were synthesized using the solution polymerization method using 2-EHA, VAc, AA, 2-hydroxyethyl methacrylate, and 4-acryloyloxydiethoxy-4-chlorobenzophenone (P-36) as polymerizable photoinititators with double bonds. The effect of photoinitiator content on the PSAs is illustrated in Figure 7.15 [31]. As expected, the higher photoinitiator content in SH3P2 produced a decrease in peel resistance of 69.8% at a UV dose of 210 mJ/cm2, whereas SH3P05 demonstrated only a 9.1% reduction in peel resistance with the same dose. The peel resistance is also influenced by the Tg. If the Tg of the PSA is sufficiently low, the wettability will be high after application to the substrate and, as a result, the peel resistance will also increase. Czech [2] synthesized removable and repositionable water-borne acrylic PSAs. In this study, the effect of copolymerizable emulsifier and plasticizer was investigated. Figure 7.16 illustrates how the influence of vinyl-unsaturated emulsifiers on peel resistance on steel depends on the type of investigated internal emulsifiers and their concentration. The relatively low peel adhesion is observed for the vinyl-unsaturated emulsifier SPMK. The increased amount of SPMK above 5 wt % has very little influence on removability. One possibility of reducing peel resistance in the water-based PSAs lies in the variation of the plasticizer used. The plasticizer, such as di-n-butyl phthalate, diethylhexyl phthalate, and di-n-octyl phthalate, was used in an amount between 10 and 30 wt %. Its influence is illustrated in Figure 7.17.

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7-19

Peel Resistance

4000

Peel resistance (g/25 mm)

PI content (phr) 0.5 1.0

3000

2.0

2000

1000

0 0

500

1000

1500

2000

2500

UV dose (mJ/cm2)

FIGURE 7.15 Change in peel resistance of UV cross-linkable PSAs with varying UV dose (PI, photoinitiator) (*phr:part). (From Do, H.S., Park, Y.J., and Kim, H.-J., J. Adhesion. Sci. Technol., 20(13), 1529–1545, 2006. With permission.)

9

Peel adhesion (N/2.54 cm)

8 7

SEMNa

Semi removable

6 5

AMPSNa

4 3

SPIK

Removable

2 SPMK

1 0 0

1

2

3

4

5

6

7

8

Internal emulsifier concentration (wt %)

FIGURE 7.16 Influence of internal emulsifiers on peel adhesion on steel (SPMK, potassium salt of sulfopropyl methacrylate; SEMNa, sodium salt of sulfoethyl methacrylate; SPIK, bis(3-sulfopropyl)-itaconic acid ester dipotassium salt; AMPSNa, sodium salt of 2-acrylamido2-methylpropyl sulfonic acid). (From Czech, Z., J. Appl. Polym. Sci., 97, 886–892, 2005. With permission.)

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7-20

Fundamentals of Pressure Sensitivity

6

Peel adhesion (N/2.5 cm)

5

Di-n-butyl phthalate

Diethylhexyl phthalate 4

3

Removable

Di-n-octyl phthalate 2

1 10

20

30

Plasticizer concentration (wt %)

FIGURE 7.17 Influence of plasticizer concentration on peel adhesion. (From Czech, Z., J. Appl. Polym. Sci., 97, 886–892, 2005. With permission.)

One effective PSA bulk property control methods is the addition of the tackifier into the elastomer. Adhesion properties such as peel resistance and tack can be easily controlled by the addition of tackifier into a styrenic block copolymer. To investigate the effect of tackifiers on peel resistance, PSAs were blended with various tackifiers such as GA-100 (rosin ester), Hikorez A-1100S (aliphatic hydrocarbon), Regalite R-125 (hydrogenated aromatic hydrocarbon), Quintone U-185 (Modified C5), and Sukorez SU-100 (hydrogenated dicyclopentadiene). Figure 7.18 illustrates the peel resistance of the SIS/ tackifier blends as a function of tackifier contents [32]. The PSAs blended with Sukorez SU100, Hikorez A1100S, and Quintone U-185 exhibit maximum peel resistance at 60 wt % of tackifier content, whereas other PSAs with GA-100 and Regalite R-125 exhibit a peak at 40–50 wt % of tackifier content. The GA-100 and R-125 have a higher softening point and Tg than the other tackifiers. Thus, the maximum peel strength shifts with lower tackifier content, depending on the softening point. Similar behavior is illustrated in Figure 7.19. The hot-melt PSAs (HMPSAs) were prepared by SIS copolymer and tackifier with various Tg: SU-90 (Tg, 39.1°C), SU-110 (Tg, 64.3°C), SU-130 (Tg, 75.4°C). As noted, the peak location of peel resistance shifts to lower tackifier content with increasing tackifier Tg [33]. Considering the fact that the PSAs are a mixture of elastomeric polymers and lowmolecular-weight tackifier resins, it is important to investigate the degree of miscibility between the components, because the phase structures are governed by miscibility; that is, when the components are miscible with each other, the blends must be in a uniform one-phase structure, but when they are immiscible with each other, phase separation occurs. The physical properties and the practical performance of the PSA are dependent on the phase structure of the materials.

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Peel Resistance

15000

Peel strength (g/25 mm)

12500

10000

7500 5000

2500

0 40 (a)

50

60

70

Wt % of tackifier 15000

Peel strength (g/25 mm)

12500

10000

7500 5000

2500 0 40 (b)

50

60

70

Wt % of tackifier

FIGURE 7.18 Peel strength of SIS/tackifier blends on SUS substrate (peeling rate, 300 mm/min): (a) Kraton D1107 blends and (b) Vector 4111 blends (○, Hikorez A 1100S; △, Regalite R 125; ▽, Quintone U 185; ◇, Sukorez SU 100; □, GA-100). (From Kim, D.J., Kim, H.-J., and Yoon, G.H., Int. J. Adhesion Adhesives, 25, 288–295, 2005. With permission.)

In the acrylic PSA/tackifier system, Kim and Mizumachi [34] studied systemically the effect of miscibility on adhesion properties. The peel resistance of PSAs is low at a low separation rate, and it gradually increases and decreases again as the separation rate is increased. In the case of a miscible system, incorporation of a tackifier resin results in modification of the bulk properties of the blend; therefore, the peel resistance master curves shift along the rate-axis, whereas the tackifier content changes, as illustrated in Figure 7.20. On the other hand, in the case of a system where the components are

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Fundamentals of Pressure Sensitivity

15000

Peel strength (g)

Vector + SU-90 Vector + SU-110 Vector + SU-130 10000

5000

0 30

40

50

60

70

Tackifier content (wt %)

FIGURE 7.19 Peel strength of vector/tackifier as a function of tackifier content. (From Lim, D.H., Do, H.S., and Kim, H.-J., PSA J. Appl. Polym. Sci., 102, 2839–2846, 2006. With permission.)

3000

Peel strength (gf/cm)

Tackifier content (%)

2000

: : : : :

0 10 20 30 40

1000

0 10−5

10−3

10−1

101

Va T (cm/s)

FIGURE 7.20 Peel master curve dependence on peeling rate in miscible blends. (From Kim, H.J. and Mizumachi, H., Advances in Pressure Sensitive Adhesive Technology-3, D. Satas, Ed., Satas & Associates, Warwick, RI, 1998. With permission.)

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Peel Resistance

Tackifier content (%) 1500

:

0

: 10 : 20

Peel strength (gf/cm)

: 30 : 40 1000

500

0 10−4

10−2

100

102

VaT (cm/s)

FIGURE 7.21 Peel master curve dependence on peeling rate in immiscible blends. (From Kim, H.-J. and Mizumachi, H., Advances in Pressure Sensitive Adhesive Technology-3, D. Satas, Ed., Satas & Associates, Warwick, RI, 1998. With permission.)

not miscible, physical properties of the two phases are not modified, even if the blend ratio is varied, and the master curve does not shift along the rate-axis, as illustrated in Figure 7.21, because the peel resistance depends mainly upon the properties of the matrix phase. The peak height of the master curve in peel resistance decreases as the amount of the dispersed phase increases. Fujita et al. [35] investigated the effects of miscibility on the peel resistance of natural rubber-based PSAs. In the case of miscible PSAs, the peak position of the pulling rate-peel resistance curve shifted to a lower velocity as the tackifier content increased. Immiscible PSA blends had lower peel resistances than miscible blends and did not exhibit any apparent peak shifts. Viscoelastic properties play a vital role in the study of adhesion behavior, including the application of PSAs, diff usion through interfaces, and internal stress (see Chapter 4). Viscoelastic properties deal with the problem of the action of mechanical forces on the adhesion system, depending on the velocity and loading frequency. Figure 7.22 illustrates the viscoelastic spectrum of typical PSAs [36]. Peeling is a high-rate process and takes place at a speed between 100 and 1000 rad/s. Peel rate can

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Fundamentals of Pressure Sensitivity

8 Tack zone

Shear zone

Log G′, Log G′′ (Pa)

7

6

Peel zone

G′′

5

G′ 4 −3

−2

−1

0

1

2

3

4

Log frequency (rad/s)

FIGURE 7.22 Viscoelastic spectrum of a typical PSA (G′, storage modulus; G″, loss modulus). (From Satas, D., Handbook of Pressure Sensitive Adhesive Technology and Applications, D. Satas, Ed., Satas & Associates, Warwick, RI, 2002. With permission.)

cover both the plateau and the transition zones. If the rate of peel is not too fast, then entanglements will dominate and control the peel strength of PSAs. If peeling occurs at higher rates, then small molecular structures, such as tackifying resins and short chain pendant groups attached to the base elastomer, can contribute to the peel strength of the PSA. The characteristics in a master curve will be described in reference to the characteristics of natural rubber/tackifier blends, as illustrated in Figure 7.23 [37]. In the master curve, three regions of steady peeling and one region of oscillatory (stick–slip) peeling may be distinguished. At high temperatures or very low peel rates, the adhesive experiences predominantly viscous flow, which allows it to be drawn out into long fibrils in the region where the tape curls away from the substrate. These eventually fail in tension, leaving traces of the adhesive on both the tape and the rigid surface, which is known as cohesive failure (see Figure 7.10). At higher peel rate or less elevated temperatures, the adhesive becomes detached from one of the solid surfaces, usually remaining attached to the flexible tape, either before any fibrils have formed or at least before they are well developed. This is characteristic of an interfacial or adhesion failure (see Figure 7.10). Both of these detachment modes are stable and if the peeling rate is kept constant, the peel force will be also. At either high peel rates or low temperatures, the adhesive may undergo transformation into its glassy or brittle form, which now allows deadhesion to proceed by the advance of a crack. Th is may be either stable or unstable and may run either cohesively through the adhesive layer or along the adhesive/substrate interface.

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7-25

Peel Resistance

40

T (K) 312 304 296 276 268 258 246 240

Cohesive separation Adhesive separation

P (N)

30

20

B

258 246 240

BC

10 A

C 0 −8

−6

−4

−2

0

2

4

Log Ra ′T (m/s)

FIGURE 7.23 Master curve of peel force against pulling rate at 296 K for the system 6:4 NR: Piccolyte S115, showing superposition of experimental data (A, cohesive failure; B, adhesive failure between adhesive and glass (substrate); C, adhesive failure between adhesive and baking; B-C, stick–slip). (From Satas, D., Handbook of Pressure Sensitive Adhesive Technology and Applications, D. Satas, Ed., Satas & Associates, Warwick, RI, 2002. With permission.)

Figure 7.24 illustrates the rheologic behavior at different temperatures and the corresponding peeling curves [38]. The terminal domain of relaxation corresponds to an interfacial fracture with a crack localized between the adhesive and the rigid substrate (Figure 7.24a). In the intermediate domain (transition region), one can observe stick–slip behavior (Figure 7.24b). Finally, at very low temperatures, the crack is localized between the adhesive and the flexible substrate with a very low peel force (Figure 7.24c). One can conclude that the propagation of the crack, as well as the value of the peeling force, depends largely on the rheological behavior of the adhesive, which is linked to the temperature and the peeling rate. In the case of EVA-based PSAs, Gibert et al. [39] demonstrated that the cohesive-to-interfacial transition observed on a peeling curve appeared at the same time as the liquid-like to solid-like transition induced by crystallization of EVA (Figure 7.25) [39]. Figure 7.25 provides a schematic diagram of the relationship between viscoelastic and peel properties (see Chapter 4). The failure mode does not always follow the four main types: cohesive, adhesive, stick–slip, and glassy failure. The peeling behavior illustrated in Figure 7.26 demonstrates differences. Figure 7.26a exhibits all four fracture domains already described (cohesive, interfacial 1, stick–slip, and interfacial 2), whereas the interfacial 1 fracture domain has disappeared in Figure 7.26b. Cohesive fracture can be shifted directly to a stick–slip behavior as the peeling rate increases. Aubrey and Sherrif [37] derived the same conclusion with another formulation. The addition of resin to the polymer not only diminishes the width of the elastic plateau region but also decreases the plateau

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Fundamentals of Pressure Sensitivity

Log (G′ and G ′′/[Pa])

9

G′ G′′

8 7 6 5 4 3 2

−5 −4 −3 −2 −1 0

1 2 3 ω (rad/s)

(a)

4

5

6

7

8

(a[i]) T = 20°C

5

Log (G′ and G′′/[Pa])

Peel force (N)

8 7 6 5 4 3 2 1 0

2

6

4

8

G ′ T = 20°C G ′′

4

3

2 0

10

−1

0

Time (s)

(b)

1 Log (ω/[rad/s])

2

(b[i])

8

G ′ T = −15°C G′′

6

T = −30°C Log (G′ and G′′/[Pa])

7 Peel force (N)

9

6 5 4 3 2

5

4

1 0

3 0

3 Time (s)

2

1

4

5

0

1 Log (ω/[rad/s])

2

1

2

(c[i])

(c) T = −30°C

8 7 6 5 4 3 2 1 0

Log (G ′ and G′′/[Pa])

Peel force (N)

−1

6

9

8

7

6 0

2

6

4 Time (s)

8

10

G′ T = 20°C G ′′

−1

0

Log (ω/[rad/s])

FIGURE 7.24 G′, G″ versus frequency for SIS + SI blend and peeling curves measured on the tensile machine at various temperatures: (a) terminal domain (rubbery plateau); (a[i]) adhesive fracture; (b) transition region; (b[i]) stick–slip; (c) glassy domain; and (c[i]) glassy fracture. (From Marin, G. and Derail, C., J. Adhesion, 82, 469–485, 2006. With permission.)

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7-27

Peel Resistance

F

F

Crack Crack Peel force

F Crack

Shear modulus

Cohesive fracture

Interfacial fracture

Stickslip

Glassy fracture Peel rate G′ G ′′

Terminal zone

Rubbery state

Glass transition

Glassy state Frequency

FIGURE 7.25 Schematic diagram of the relationship between viscoelastic and peel properties. (From Gibert, F.X., Allal, A., Marin, G., and Derail, C., J. Adhesion Sci. Technol., 13(9), 1029–1044, 1999. With permission.)

modulus value. The gradual disappearance of the type 1 interfacial fracture is probably due to both effects. Changing the resin content not only changes the plateau modulus value and extent, but also changes the Tg, so all these combined effects do not lead to a simple relationship.

7.4.2

Surface Properties of Substrate and Peel Resistance

Good bonding between a substrate and an adhesive is attained when their cohesive energy density or solubility parameters (δ) are matched (see Chapter 10). Figure 7.27 [40] illustrates the effect of thermodynamic compatibility, which is molecular attraction between an elastomer and low molecules on peel strength. Systems with high peel strength and cohesive failure contain adhesives with δ values that are close to that of polyethylene terephthalate (PET) (δ = 10.3 {J/cm3}1/2). Adhesion is low when the δ value of the adhesive is too low or too high, but gradually increases as δ corresponding to that of PET is approached from either side. Hata et al. [41] investigated the influence of the critical surface tension of adherends on the rolling friction coefficient and peel strength of PSAs. In the velocity region where the interfacial failure occurs in the case of acrylic PSAs, the rolling friction coefficient and peel strength have a positive correlation with the critical surface tension of the

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Fundamentals of Pressure Sensitivity

Interfacial 1

160

Interfacial 2

140 Cohesive

Stick-slip

PF TO/ T (N)

120 100 80 60 40 20 0 0

1

2

3

(a)

4 5 6 log (a T·V) (mm/min)

7

8

9

60

PF TO/ T (N)

50 40 30 20 10 0 1 (b)

2

3

4

5

6

7

8

9

log (a T·V) (mm/min)

FIGURE 7.26 Peel force as a function of reduced peel rate: (a) PB:tackifier = 170:30; (b) PB: tackifier = 270:30. (From Aubrey, D.W. and Sherrif, M., J. Polym. Sci. Polym. Chem. Ed., 18, 2597– 2608, 1980. With permission.)

adherends, indicating that both the rate of the bonding process and the failure criterion concerning the interfacial failure are closely related to the critical surface tension of the adherend. Performance of the natural rubber-based PSA was more complicated than that of the acrylic PSA. Kim et al. [32] reported the peel strength of the SIS/tackifier blends at various peeling rates with many substrates having different surface tension values (Figure 7.28). Table 7.4 presents the surface tension of various substrates. High peel strength was

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7-29

Peel Resistance

PET = 10.3 = Cohesive failure

44.48

5

22.24

Peel strength (N/25 mm)

Peel strength (lb/in.)

10

0

0 8

9

10

11

12

13

Solubility parameter (δ) of adhesive

FIGURE 7.27 Relation of compatibility to adhesion for Mylar–adhesive–Mylar system. (From Iyengar, Y. and Ericson, D.E., J. Appl. Polym. Sci., 11, 2311–2324, 1967. With permission.)

observed for stainless steel (SUS 304) and glass, medium peel strength for Bakelite, polyvinyl chloride (PVC), and polypropylene (PP), and low peel strength for polyethylene (PE) and Teflon. A similar classification was obtained using surface tension as the distinguishing factor. Although PE exhibits a surface tension similar to that of mediumpeel substrates, it has low peel strength due to the different failure mode. Interfacial failure was observed for PE, whereas cohesive failure was observed for other medium-peel substrates. This may be due to differences in the characteristics of the substrates. In the peel tests performed using PP substrates, cohesive failure occurred at various test temperatures. However, in the peel test performed using the PE substrate, adhesive failure occurred for the Kraton D1107 blends, but stick–slip failure was observed for Vector 4111 blends. After aging at 100°C, cohesive failure occurred in all blends except for the Regalite R-125 blends because PSAs transfer to the substrates during the aging process. A typical stress–strain curve of the Kraton D1107/Sukorez SU-100 blends with the PE substrate is illustrated in Figure 7.29. In the Kraton D1107/Sukorez SU-100 (40/60) blend, a stick–slip type of stress–strain curve was observed (Figure 7.29a), whereas cohesive failure (Figure 7.29b) was observed in the Vector 4111/SU-100 (40/60) blend. Although the curves in Figure 7.29a correspond to stick–slip failure, the adhesive was stripped cleanly from the substrate, leaving no visually residue. Therefore, the surface was clear after the test because of the high cohesion of the SIS-based, HMPSAs with a high SIS content. Not only is the peel force decreased for a higher energy surface, but also the positions of the transitions from cohesive to adhesion and from adhesion to stick–slip failure are changed. That is, the activation of the stiffening behavior of a PSA depends on the substrate to which the adhesive is bonded. Marin and Derail [38] reported similar effects of substrate nature on peel strength and mechanisms of fracture (see Chapter 4).

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Fundamentals of Pressure Sensitivity

15000

Peel strength (g/25 mm)

12500 10000 7500 5000 2500 0 0

200

(a)

400

600

Rate (mm/min) 15000

Peel strength (g/25 mm)

12500 10000 7500 5000 2500 0 0

200

(b)

400

600

Rate (mm/min)

FIGURE 7.28 Peel strength of SIS/Hikorez A 1100s (40/60) blends as a function of peeling rate: (a) Kraton blends and (b) Vector blends (□, SUS; ○, PE; △, PP; ▽, PVC; ◇, Bakelite; ◁, Teflon; and ▷, glass). (From Kim, D.J., Kim, H.-J., and Yoon, G.H., Int. J. Adhesion Adhesives, 25, 288–295, 2005. With permission.) TABLE 7.4

Surface Tension of Various Substrates

Substrates a

Surface tension (γc) (mN/m)

SS

PE

PP

PVC

Bakelite

Teflon

Glass

b

31

33

37

31

18

73

—

Note: SS, stainless steel; PE, polyethylene; PP, polypropylene; PVC, polyvinylchloride. a b

Determined by contact angle measurement. Not available.

Source:

Czech, Z., J. Appl. Polym. Sci., 97, 886–892, 2005. With permission.

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Peel Resistance

Peel strength (g/25 mm)

6000

4000

2000

0 0

20

(a)

40

60

80

60

80

Distance (mm)

Peel strength (g/25 mm)

6000

4000

2000

0 0 (b)

20

40 Distance (mm)

FIGURE 7.29 Typical stress–strain curve of Kraton/tackifying resin blends on PE substrate: (a) Kraton D1107/SU-100 = 40/60; (b) Kraton D1107/SU-100 = 60/40. (From Kim, D.J., Kim, H.-J., and Yoon, G.H., Int. J. Adhesion Adhesives, 25, 288–295, 2005. With permission.)

7.5

Conclusion

In the evaluation of PSA performance, the measurement of peel resistance is one of the most important characteristics because various factors, such as properties of backing materials, surface of the adherend, peeling speed, and test temperature, affect the peel strength. Failure mode detection and drawing up the master curves for peel resistance

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Fundamentals of Pressure Sensitivity

provide a great deal of information. Therefore, to gain insight into the peeling mechanism it is helpful to design PSAs and evaluate their performance.

References 1. ASTM D 907. 2. Czech, Z., 2005. Synthesis of removable and repositionable water-borne pressuresensitive adhesive acrylics. J. Appl. Polym. Sci. 97:886–892. 3. Chen W. T. and T. F. Flavin, 1972. Mechanics of fi lm adhesion: Elastic and elastic– plastic behavior, IBM J. Res. Dev. 16(3):203–213. 4. Kaelble, D. H., 1959. Theory and analysis of peel adhesion: Mechanisms and mechanics, Trans. Soc. Rheol. 3:161–180. 5. Kaelble, D. H., 1960. Theory and analysis of peel adhesion: Bond stress and distributions, Trans. Soc. Rheol. 4:45–73. 6. Williams J. A. and J. J. Kauzlarich, 2004. Peeling shear and cleavage failure due to tape restrain, J. Adhesion, 80:433–358. 7. Williams J. A. and J. J. Kauzlarich, 2007. Application of the bulk properties of an acrylic pressure sensitive adhesive to peeling, J. Adhesion Technol. 21(7):515–529. 8. Gent A. N. and E. A. Meinecke, 1970. Compression, bending, and shear of bonded rubber blocks, Polym. Eng. Sci. 10(1):48–53. 9. Satas, D., 2002. Peel. In Handbook of Pressure Sensitive Adhesive Technology and Applications, ed. D. Satas, Satas & Associates, Warwick, RI, pp. 62–86. 10. Horgnies, M., E. Darque-Ceretti, and E. Felder, 2007. Relationship between the fracture energy and the mechanical behavior of pressure-sensitive adhesives, Int. J. Adhesion Adhesives 27:661–668. 11. Kaelble, D. H., 1965. Peel adhesion: Micro-fracture mechanics of interfacial unbonding of polymers, Trans. Soc. Rheol. 9(2):135–163. 12. Kinloch, A. J., C. C. Lau, and G. J. Williams, 1994. The peeling of flexible laminates. Int. J. Fracture 94:79–88. 13. Muny, R. P., 2002. Testing pressure sensitive adhesives. In Handbook of Pressure Sensitive Adhesive Technology and Applications, ed. D. Satas, Satas & Associates, Warwick, RÌ, pp. 139–152. 14. Kawashita, L. F., D. R. Moore, and J. G. Williams, 2004. The development of a mandrel peel test for the measurement of adhesive fracture toughness of epoxymetal laminates, J. Adhesion 80:147–167. 15. Urahama, Y., Y. Tokunaga, and Y. Tanaka, 1990. Morphology at peeling pressure sensitive adhesives (II), J. Adhesion Soc. Jpn. 23(5):171–177. 16. ASTM D3330. 17. PSTC-1. 18. Pocius, A. V., 1997. Basic physico/chemical properties of polymers. In Adhesion and Adhesives Technology, ed. A.V. Pocius, Hanser, Munich. 19. Derail, C., A. Allal, G. Marin, and Ph. Tordjeman, 1997. Relationship between viscoelastic and peeling properties of model adhesive. Part1. Cohesive fracture, J. Adhesion 61:123–157.

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20. Aubrey, D. W., G. N. Welding, and T. Wong, 1969. Failure mechanisms in peeling of pressure-sensitive adhesive tape, J. Appl. Polym. Sci. 13:2193–2207. 21. Do, H. S. and H.-J. Kim, 2006. UV-curable pressure-sensitive adhesives. In Pressure-Sensitive Design and Formulation, Application Volume 2, ed. I. Benedek, VSP, Leiden, Boston, pp. 251–290. 22. Auchter, G., O. Aydin, A. Zettl, and D. Satas, 2002. Acrylic adhesives. In Handbook of Pressure Sensitive Adhesive Technology and Applications, ed. D. Satas, Satas & Associates, Warwick, RI, pp. 445–514. 23. Mayer, A., T. Pith, G. Hu, and M. Lambla, 1995. Effect of the structure of latex particles on adhesion. Part II: Analogy between peel adhesion and rheological properties of acrylic copolymers, J. Polym. Sci. Part B: Polym. Phys. 33(12):1793–1801. 24. Mayer, A., T. Pith, G. Hu, and M. Lambla, 1995. Effect of the structure of latex particles on adhesion. Part I: Synthesis and characterization of structured latex particles of acrylic copolymers and their peel adhesion behavior, J. Polym. Sci. Part B: Polym. Phys. 33(12):1781–1791. 25. Shen, H., J. Zhang, S. Liu, G. Liu, L. Zhang, and X. Qu, 2008. Effect of the chain-transfer-agent content on the emulsion polymerization process and adhesive properties of poly(n-butyl acrylate-co-acrylic acid) latexes, J. Appl. Polym. Sci. 107(3):1793–1802. 26. Rana P. K. and P. K. Sahoo, Synthesis and pressure sensitive adhesive performance of poly (EHA-co-AA)/silicate nanocomposite used in transdermal drug delivery, J. Appl. Polym. Sci. 106(6):3915–3921. 27. Gower M. D. and R. A. Shanks, 2004. The effect of varied monomer composition on adhesive performance and peeling master curves for acrylic pressure-sensitive adhesives, J. Appl. Polym. Sci. 93(6):2909–2917. 28. Gower M. D. and R. A. Shanks, 2004. The effect of chain transfer agent level on adhesive performance and peel master-curves for acrylic pressure sensitive adhesives, Macromol. Chem. Phys. 205(16):2139–2150. 29. Gower M. D. and R. A. Shanks, 2006. Acrylic acid level and adhesive performance and peel master-curves of acrylic pressure-sensitive adhesives, J. Polym. Sci. Part B: Polym. Phys. 44(8):1237–1252. 30. Joo, H. S., H. S. Do, Y. J. Park, and H. –J. Kim, 2007. Adhesion performance of UV-cured semi-IPN structure acrylic pressure sensitive adhesives, J. Adhesion Sci. Technol. 20(14):1573–1594. 31. Do, H. S., Y. J. Park, and H.-J. Kim, 2006. Preparation and adhesion performance of UV-cross-linkable acrylic pressure sensitive adhesives, J. Adhesion Sci. Technol. 20(13):1529–1545. 32. Kim, D. J., H.-J. Kim, and G. H. Yoon, 2005. Effect of substrate and tackifier on peel strength of SIS (styrene-isoprene-styrene)-based HMPSAs, Int. J. Adhesion Adhesives 25:288–295. 33. Lim, D. H., H. S. Do, and H.-J. Kim, 2006. PSA performances and viscoelastic properties of SIS-based PSA blends with H-DCPD tackifier, J. Appl. Polym. Sci. 102:2839–2846. 34. Kim, H.-J. and H. Mizumachi, 1998. Miscibility of acrylic pressure sensitive adhesives. In Advances in Pressure Sensitive Adhesive Technology-3, ed. D. Satas, Satas & Associates, Warwick, RI, pp. 77–128.

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35. Fujita, M., M. Kajiyama, A. Takemura, H. Ono, H. Mizumachi, and S. Hayashi, 1998. Effect of miscibility on peel strength of natural-rubber-based pressuresensitive adhesives, J. Appl. Polym. Sci. 70:777–784. 36. Satas, D., 2002. Dynamic mechanical analysis and adhesive performance. In Handbook of Pressure Sensitive Adhesive Technology and Applications, ed. D. Satas, Satas & Associates, Warwick, RI, pp. 62–86. 37. Aubrey, D. W. and M. Sherrif, 1980. Peel adhesion and viscoelastic of rubber-resin blends, J. Polym. Sci.: Polym. Chem. Ed. 18:2597–2608. 38. Marin, G. and C. Derail, 2006. Rheology and adherence of pressure-sensitive adhesives, J. Adhesion 82:469–485. 39. Gibert, F. X., A. Allal, G. Marin, and C. Derail, 1999. Effect of the rheological properties of industrial hot-melt and pressure-sensitive adhesives on the peel behavior, J. Adhesion Sci. Technol. 13(9):1029–1044. 40. Iyengar, Y. and D. E. Ericson, 1967. Role of adhesive-substrate compatibility in adhesion, J. Appl. Polym. Sci. 11:2311–2324. 41. Hata, T., T. Tsukatani and H. Mizumachi, 1994. The influence of critical surface tension of adherends on the rolling friction coefficient and peel strength of pressure sensitive adhesives, J. Adhesion Soc. Jpn. 30(8):352–357.

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8 Shear Resistance 8.1 Introduction ............................................................ 8-1 8.2 Characterization of Shear Resistance .................. 8-2 8.3 Description of Processes in the Shear Test ...................................................... 8-4 8.4 Behavior of Pressure-Sensitive Adhesives under Compressive Load: The Cold Flow Problem........................................................... 8-9 8.5 Factors Influencing Shear Strength ....................8-11

Sergey V. Antonov Valery G. Kulichikhin A.V. Topchiev Institute of Petrochemical Synthesis

Assembly Time/Preparation Conditions • Load • Temperature • Molecular Weight and Structure • Chemical Composition • Influence of Additives and Miscibility • Method of Polymerization • Cross-Linking Density • Physical Cross-Linking

8.6 Improving the Shear Behavior of Pressure-Sensitive Adhesives ......................... 8-15 References ........................................................................8-16

8.1 Introduction From the rheological viewpoint, pressure-sensitive adhesives (PSAs) can be described in general as viscoelastic materials with a specific complex of rheological properties. Under shear load they demonstrate creep behavior that can lead to failure of the adhesive joint. Shear resistance characterizes a PSA’s ability to resist shearing forces. Shear resistance is also sometimes termed holding power [1] (see also Applications of PressureSensitive Products, Chapter 8). Shear resistance is one of the most significant characteristics of PSAs. The requirements for shear resistance come from the application of PSAs (see also Applications of PressureSensitive Products, Chapter 4). Shear resistance is very important, for example, for packaging tapes and labels, upholstery, films for floor advertising, automobile industry, etc. In some applications PSAs are exposed to shearing forces at elevated temperatures (see also Applications of Pressure-Sensitive Products, Chapter 4) for relatively short times, whereas in other applications the material must withstand shear load for longer periods of time

8-1

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Fundamentals of Pressure Sensitivity

at lower temperatures (see also Applications of PressureSensitive Products, Chapter 4); the actual conditions should A therefore always be kept in mind. Shear adhesion is also essential for the reliability of PSA tapes used for heat shrink attachment in air-cooled electronic assemblies [2]. For this application, estimation of creep behavior in a rather wide temperature range is necessary. Shear deformations may be developed under compressive load as well, which would lead to squeezing the adhesive and its radial flow. This process is often referred to as cold flow of the adhesive (see also Applications of PressureB Sensitive Products, Chapter 8). Understanding the nature of the shear adhesion of PSAs is crucial for controlling their creep behavior. Shear resistance is often regarded as a measure of the PSA’s cohesive strength [1], which seems to be an oversimplified point of view, taking into account their viscoelasticity and the dependence of their mechanical characteristics on time and temperature. Many efforts have been made to relate the shear resistance of PSAs to their structure and properties (chemical composition, visC cosity, storage and loss moduli, miscibility of the components in the formulation, degree of cross-linking, etc.) and develop a model based on these properties that is suitable for predictFIGURE 8.1 Schematic ing the durability of adhesive joints under shear stresses. representation of the static shear test. (A) steel plate, (B) These attempts are examined later in this chapter. Before discussing the impact of different parameters on adhesive tape, and (C) load. shear adhesion, it is reasonable to consider the experimental methods used for estimation of shear resistance (see also Applications of Pressure-Sensitive Products, Chapter 8).

8.2 Characterization of Shear Resistance The most common method of testing shear resistance of PSAs is the static shear test. The standardized methods of the static shear test are similar and are described by ASTM D3654 [3], PSTC-7 [4], FTM 8 [5], and AFERA-4012 [6]. A PSA tape of standard size is applied to the substrate and rolled with a standard weight roller (usually twice). After a specified dwell time necessary for formation of the adhesive joint and stress relaxation, the prepared specimen is fi xed vertically in the shear tester (see Figure 8.1) and the static shear force is loaded to the free end of the tape parallel to the bonding surface. Results are typically reported as holding time, that is, the time to failure of the adhesive joint (in other words, the durability of adhesive joint is measured). The testing conditions used in different standards were summarized in Refs 1 and 7. Typically testing should be accomplished at 23 ± 2°C, the roll weight is about 2 kg, the substrate is steel or aluminum, the sample size is 1 × 1 in., and the load weight is 500–1000 g. The results obtained by

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Shear Resistance

3

2

5

E

1

6

4

FIGURE 8.2 Schematic design of the apparatus for a modified static shear test. (1) steady steel plate, (2) movable plate or backing, (3) adhesive layer, (4) load, (5) block, and (6) temperature chamber.

different authors using the static shear method can hardly be directly compared due to the differences in testing parameters and thickness of the specimens. Although this method simulates the real behavior of PSA tapes under shear loads, it has a drawback of determining only the “end point” (holding time), thus providing very limited information on the mechanism and kinetics of failure. Several authors [8–11] used a modified version of this test based on a device that is more sophisticated from a rheological viewpoint, known as a shear plastometer. The schematic design of such a device is illustrated in Figure 8.2. The constant shear load is applied via a block to the sample (PSA tape with backing) adhered to the substrate. The backing is sometimes reinforced by a second steel plate [8] to prevent the sample from bending. The sample can be placed in a heated chamber, permitting measurements at different temperatures. This equipment allows the displacement of the one of plates to be registered as a function of time at constant load during the experiment with good resolution (i.e., it is a creep measurement as well). As mentioned previously, devices of this kind have often been used by rheologists for the study of creep behavior and are known as shear (parallel plate, sandwich type, etc.) plastometers [12,13] (see also Chapter 4). In fact, the shear test is a creep test carried to high deformation [14]. Later in this chapter we will discuss a rheological description of the creep test in the shear plastometer. Zosel [8] reports 20% standard deviation of the experimental results obtained for a large number of similar specimens tested on such a device, explained by deviations in sample preparation. Imprecision of the tape’s geometric parameters, especially thickness

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Fundamentals of Pressure Sensitivity

and incomplete stress relaxation, can be mentioned among the possible reasons for data scattering. The main drawback of the static shear method is that the experiments are quite timeconsuming. Therefore, a “dynamic” test has been proposed (see also Applications of PressureSensitive Products, Chapter 8). A sample similar to that used for the static test is deformed and separated from the substrate, not at constant load but at constant strain rate [8,15]. The experiment can be performed with a tensile tester. The cross-head speed depends on the intended application of the PSA. The maximum force determined during the experiment can be regarded as a measure of shear resistance. The stress–strain curves obtained using this method can provide useful information about the failure of the adhesive joint. In some applications (e.g., packaging, insulation, mounting, or splicing tapes) it is necessary to know the shear resistance at elevated temperatures and the maximum permissible temperature. In the shear adhesion failure temperature (SAFT) method [1,16,17] a sample similar to one described above is loaded with a static weight while the temperature is ramped at rate of 0.4 C/min until the specimen fails. The testing conditions are generally the same as in the static shear test (except for the temperature) and the experiment can be carried out in the same machine if it is equipped with a temperature-controlled chamber. In this method the temperature of the failure of the adhesive joint is considered as a characteristic of shear resistance (see also Applications of Pressure-Sensitive Products, Chapter 8). Reliability of the results obtained in different shear tests depends on many factors. The most common errors in measuring shear resistance include nonuniform thickness of the adhesive layer, the presence of nonrelaxed stresses, the substrate surface is not clean, and the direction of the applied force is not parallel to the interface. Careful inspection of the surface of the adhesive joint after separation to determine the failure mode (cohesive, adhesive, or mixed adhesive–cohesive) can provide valuable information that can be useful for improving performance of the tested PSA.

8.3 Description of Processes in the Shear Test To identify the factors that influence shear resistance and propose ways to improve it, it is necessary to clearly understand the processes that takes place during testing. Satas [18] described three types of adhesion joint failure depending on the proportion between holding power and adhesion. If the holding power is much higher than the adhesion, adhesion failure proceeds. On the other hand, if adhesion is much higher than the holding power, cohesive failure must occur. If adhesion and cohesion forces are comparable, then a “mixed” failure mode (partially cohesive, partially adhesive) is observed. Most of the following discussion regarding holding power and holding time is applicable to the situation of cohesive failure when rheological parameters predetermine the shear resistance of the PSAs. As discussed previously, shear plastometers that are very similar in design to shear testers have long been used by rheologists, although their application was restricted by the region of small deformations for several reasons that will be analyzed later. Let us consider the typical strain versus time curve obtained using this device (Figure 8.3). The first segment (OA) represents a fast and relatively small elastic response. The deformation in the next segment (AB) is a combination of elastic and plastic (flow) modes.

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Shear Resistance

F = const. (creep) C

F=0 (elastic recovery)

B D Strain

B′

Unrecoverable strain

E A

O Time

FIGURE 8.3 Typical plot of plate displacement versus time in a shear plastometer (small deformations).

In the steady region (segment BC in Figure 8.3), which is characterized by constant slope, the elastic deformation has already passed through its maximum value and further deformation of the sample is connected only with flow (plastic deformation). The rheological parameters in this stage can be calculated as follows. Shear stress is 


F A

(8.1)

where F is the force applied to the adhesive tape and A is the overlapping area. Shear rate is




 d

(8.2)

where v is the current linear speed of the adhesive tape and d is the thickness of the adhesive layer. The overlapping area decreases with time during the test in accordance with Equation 8.3,  l  A
A0  1    l0 

(8.3)

where ∆l is the shift of the adhesive tape from the initial position and l 0 is the initial length of the overlapping area. It is, therefore, clear that shear stress grows with time. Taking into account that 


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dl dt

(8.4)

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Fundamentals of Pressure Sensitivity

it is possible to solve this system and prolong the analysis to the end point when the adhesive tape slides off the substrate. Th is was done by Zosel [8], who tried to predict the holding time from the flow curves of the adhesives. Unfortunately, such a model assumes sliding off of the tape governed by the viscous flow of adhesive as the only mechanism of failure and completely neglects the elasticity of the adhesive. All these equations are valid only when there is no slippage between the tested material and the substrate. It is not surprising, therefore, that this model was able to predict the holding time more or less correctly only for rather low-viscosity non-cross-linked adhesives. By extrapolating the steady segment to the strain axis it is possible to separate elastic and plastic deformations: segment AB′ in Figure 8.3 represents the elastic portion of the total deformation developed in segment AB. If the load is released, then elastic recovery starts with a fast stage (segment CD), followed by slower recovery (DE). The plastic deformation cannot be recovered (unrecoverable strain). Of course, everything noted regarding plastic deformations is applicable only to noncross-linked polymers. All stages of the creep process in polymers can be qualitatively described using Burgers’s model [19,15], which consists of four elements, connected as illustrated in Figure 8.4, where springs elastic constants (moduli) are G 0 and G1 and dashpot viscosities are η 0 and η1. This model combines Maxwell (index 0) and Kelvin–Voigt fluids (index 1). The total stress in this model is equal to the stress of each element: 
0
1

(8.5)

η0

G1

η1

G0

FIGURE 8.4

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Burgers’s model.

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8-7

Shear Resistance

and the total deformation is the sum of these parts,


0  1

(8.6)

d d 0 d 1
 dt dt dt

(8.7)

and, consequently,




An expression for stress can be derived from Equations 8.5 through 8.7 as follows: 
G1 1  1

 1 d d

  1   dt  G0 dt 0 

(8.8)

Differential Equation 8.8 can be solved to yield the total deformation:

(t )


t   0 0     1  e 1   0 t G0 G1   0

(8.9)

In this equation λ1 is the retardation time. Let us analyze Equation 8.9. The first term represents an instantaneous elastic deformation. The second term reflects the slow growth of elastic deformation. At t → ∞ τ it becomes equal to ___0 -equilibrium rubbery deformation. The third term, which G1 describes the linear growth of strain over time, demonstrates pure viscous flow. It corresponds to the “steady” region of the creep curve. τ due to the reaction Release of the load leads to instant recovery of deformation by ___ G0 of the spring in the Maxwell element, followed by slower recovery, described by the following expression:

(t )


tt

0   1 t1  0 e 1 0 G1

(8.10)

In Equation 8.10, t > t1, and t1 is the moment of load release. The plastic deformation τ0 developed in the dumper of the Maxwell element during creep stage, __ η 0 t1, is unrecoverable. Although Burgers’s model describes qualitatively the whole creep–recovery cycle, several authors proposed some modifications of this model to enable better compliance with experimental results obtained in shear tests of PSAs. Geiss and Brockmann [15] investigated the creep behavior of SIS-based PSA in cycling creep–recovery tests. The slope of the strain curve increases from cycle to cycle as if the viscosity of the PSA is decreasing. To describe this feature, a time-dependent nonlinear factor was introduced to the reaction of the G1 spring. Kano et al. [10] added a combination of friction and damper elements to extend the application of the model to adhesive failure. The friction element simulates slippage between the adhesive tape and the substrate.

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Fundamentals of Pressure Sensitivity

Another rheological phenomenon can be very important in the shear resistance of PSAs. Highly structured liquids (e.g., liquids containing fi llers or those with a strong network of H-bonds) may possess the yield stress. It means that at stresses lower than the yield stress value they behave like a solid. Plastic or rubbery deformation of the sample can start only after the yield stress is exceeded. There has been much discussion about the real existence of yield stress [20,21], but, nevertheless, because this phenomenon is observed in the timescale of PSAs application, it can be utilized. We can imagine a PSA that could be adhered to a substrate under some pressure, causing shear stress greater than yield stress, but exploited at lower shear stresses and therefore having excellent shear resistance. An example of a system with yield stress in a creep test was demonstrated in Ref. 22. To estimate typical shear stress in the beginning of the static shear test, let the sample with size 1 × 1 in. (25.4 × 25.4 mm) be loaded with a weight of 1 kg. In accordance with Equation 8.1, τ ≈ 1.5 × 104 Pa, which is comparable with yield stress values observed for many structured systems [21]. As mentioned previously, shear plastometers are used for rheological measurements only at small shear strains. There are several reasons for this. The overlapping area diminishes with time, thus increasing the shear stress (Equations 8.1 and 8.3). Therefore, simple viscoelastic models derived for constant stress conditions become inapplicable for creep description. The shear stress field becomes nonuniform. For example, the material at the edge of the moving plate (point E in Figure 8.2) is exposed not only to shear stresses but also to elongation. Cross-linked materials with limited ability for deformation would lose contact with either of the plates at small strain. The large deformations are, however, inherent for real shear tests. Figure 8.5 illustrates the typical dependence of the displacement of the adhesive tape on time. The diminishing overlapping area noted above has several consequences. First, if the viscosity does not depend on shear stress (Newtonian liquid), this leads to acceleration of the plate movement (see Figure 8.5). For many polymers, however, viscosity decreases with increased shear stress (viscosity anomaly), which means, in this case, even more prominent acceleration. Moreover, as determined by Vinogradov et al. [23], high shear stresses can be easily reached for very viscous systems such as fi lled rubbers, even at small strains, which can induce the forced transition of the polymer melt to a rubbery state, resulting in the loss of adhesion to the substrate and transition to the adhesive mode of joint failure. The elasticity of the adhesive plays a very important role in this process. It can be concluded from information noted previously that the shear resistance of non-cross-linked adhesives, as long as they remain adherent to the substrate, depends mainly on their viscosity and elasticity and, consequently, on the factors influencing the rheological parameters of the adhesive. Elasticity becomes more important at the fi nal stages of the creep test. As for the cross-linked adhesives, their limited ability to deform in the shear field depends mainly on parameters of cross-linking (cross-linking density and their nature).

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8-9

Plate displacement

Shear Resistance

Time

tc

FIGURE 8.5 Typical plot of plate displacement versus time in a shear tester (large deformations). The rectangular area in the left lower corner represents the region of small deformations illustrated in Figure 8.3.

8.4 Behavior of Pressure-Sensitive Adhesives under Compressive Load: The Cold Flow Problem As mentioned previously, shear stresses and shear deformations can develop not only under pure shear conditions, but also under compressive load, forcing the adhesive to squeeze out from a gap between parallel surfaces. Resistance to shear under compressive loading is very important for several applications. For example, wound dressings and patches for transdermal drug delivery should withstand the weight of the patient without adhesive leakage [22] (see also Applications of Pressure-Sensitive Products, Chapter 5). Such leakage is often referred to as cold flow. In this section we will consider the rheology of squeezing between parallel plates. The specimen can be arranged in two ways [24]: The thickness of the specimen is considerably smaller than its diameter; it is larger than the plates and the area under compression is constant. The excessive amount of material can flow freely from the gap. The thickness of the specimen is considerably smaller than its diameter; it is smaller than the plates and the volume of the specimen under compression is constant.

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Fundamentals of Pressure Sensitivity

F

d

A

h

C

B

FIGURE 8.6

Scheme of a squeeze tester. (A) movable plate, (B) steady plate, and (C) specimen.

We can also consider the situation of a constant applied compressive force and constant squeezing rate. We will, however, limit our discussion in this section to the case of a constant area under compression and constant compressive force because this situation is closer to that observed in practice. Figure 8.6 illustrates the scheme of a squeeze tester. The upper (movable) plate has diameter d. The kinetics of plate movement and the factors influencing it will be the matters of interest. Several assumptions must be made to derive the corresponding equations. • • • •

The tested liquid is incompressible. The plate’s motion is very slow (elasticity is negligible). The material is in immediate contact with the plates. The distance between the plates is small (the velocity component in the perpendicular direction is negligible).

For a Newtonian liquid the kinetics of the distance change can be presented in the form of Stefan’s equation: 1 1 4Ft
 h2 h02 3R 4

(8.11)

In this equation, h is the current distance between plates, h 0 is the initial distance, F is the applied force, t is time, R is the radius of the smaller plate, and η is the viscosity of the tested liquid. As seen from Equation 8.11, a reduction in the distance between plates slows down in time but never stops completely. In fact, however, even for low-viscosity liquids complete squeezing is impossible due to capillary forces. For a power-law fluid that can be characterized by the expression 
k  n

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(8.12)

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8-11

Shear Resistance

(where k and n are constants), the change in distance between the plates in time is determined by Scott’s equation: 2kRn3  2n 1  (dh/dt )n   n3  n  h2n1 n

F


(8.13)

If n = 1 and k = η, Equation 8.13 becomes Equation 8.11. The field of shear stresses in this operating unit is nonuniform. Expressions of shear stress and shear rate at the rim of the smaller plate are as follows: n  3 hF  2 R3

(8.14)

2n 1 ( h )R  n h2

(8.15)

R


 R


where h˙ = dh∕dt. Unlike in the static shear test, squeezing at constant force proceeds with decreasing shear stress, and for systems with yield behavior even if the initial shear stress is greater than the yield stress, sooner or later (depending on viscosity) the shear stress will approach the yield stress value. Th is approaching is accompanied by further slowing of the plate’s movement and there is a definite minimum distance at every given value of the applied force that corresponds to shear stress equal to the yield stress. As mentioned previously, Equations 8.11 through 8.15 were derived by neglecting the elasticity of the tested liquid. Several attempts to take into account the elastic properties of the material resulted in very sophisticated models [25]. Laun [26], based on the results of squeezing polyethylene (PE) melts, proposed an empirical criterion to eliminate experimental points with significant elasticity: t   40

(8.16)

where t is the time since the beginning of the experiment. Releasing the applied force leads to partial recovery of the sample’s thickness due to its elasticity. Such squeeze–recoil tests were discussed in detail in Ref. 27. The degree of thickness recovery depends mainly on the elasticity of the fluid (molecular weight, physical or chemical cross-linking, H-bond network, etc.), whereas the degree of squeezing is governed by the viscosity of the liquid, its dependence on shear stress, and yield stress.

8.5

Factors Influencing Shear Strength

The main factors influencing the shear strength are discussed in the following sections.

8.5.1

Assembly Time/Preparation Conditions

Typically, shear resistance improves gradually with increasing assembly time [14]. It may be connected with both kinetics of the adhesive joint formation and stress relaxation.

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Fundamentals of Pressure Sensitivity

8.5.2 Load Kano et al. [10] demonstrated that the holding time decreases significantly with increased dead load in the static shear test for poly(butyl acrylate) and its blends with poly(vinylidene fluoride-co-hexafluoro acetone). Similar results were obtained by Geiss and Brockmann [15] for a styrene–isoprene–styrene (SIS)-based hot-melt adhesive and a commercial high-performance adhesive tape. If a material possesses yield stress and the applied load does not exceed its level, then the creep is very limited [22].

8.5.3

Temperature

Because an increase in temperature usually leads to a drop in viscosity, it is understandable that temperature reduces shear resistance and decreases drastically the time to failure [14,15]. Kim [28] investigated the temperature dependence of the holding power in adhesive joints of an SIS-based hot-melt adhesive with different substrates: stainless steel, glass, Bakelite, polyvinyl chloride, PE, polypropylene, and Teflon. The holding power decreases with temperature for all adhesive joints though the slope of this dependence and absolute values of the holding power were different for each adhesive–substrate pair.

8.5.4

Molecular Weight and Structure

As demonstrated by Tobing and Klein [29], the shear adhesion of gel-free acrylic PSAs increases with molecular weight (MW), presumably due to the increased number of entanglements per molecule and, consequently, the growth of viscosity. Polymers with large side groups, such as non-cross-linked acrylates, have a high molecular weight between entanglements and therefore are characterized by rather high creep and low holding power [30]. The shear resistance of polyisobutylene improves greatly with molecular weight, but is accompanied by a drop in peel strength and detaching force upon probe tack testing. These properties can be compromised by using a polymer with a broad molecular weight distribution [31]. On the other hand, the durability of the joints undergoing adhesive fracture should depend only slightly on MW (if the MW is high enough), because the number of molecular contacts between an adhesive and a substrate, which determines the strength in this case, does not depend on MW [23].

8.5.5

Chemical Composition

Several works were devoted to the relationship between combinations of acrylic monomers in corresponding PSAs and their shear resistance. Kim et al. [14] studied the effect of the ratio of butyl acrylate (BA)/acrylic acid (AA) groups on the shear resistance of BA/ AA copolymers (see also Chapter 7). Increased AA concentration leads to increased holding time. This effect becomes more prominent at AA content greater than 10%. The possible explanation consists of an interaction between AA groups that increases cohesive

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Shear Resistance

8-13

strength. A similar effect was also observed by Demarteau and Loutz [32]. Indeed, it is well known from polymer synthesis that AA is used as a comonomer to increase the cohesion of various acrylic formulations. Park et al. [33] investigated the change in holding power with composition in quaternary copolymers of 2-ethylhexyl acrylate (2-EHA), BA, ethyl acrylate (EA), and vinyl acetate (VA). Increased BA and 2-EHA content leads to a significant decrease in holding time, probably because of the higher flexibility and lower intermolecular interaction introduced by these monomer sequences. Tobing and Klein [29] measured the shear resistance of poly(BA-stat-AA) and poly(2-EHA-stat-AA) copolymers. In all cases, poly(BA-stat-AA) demonstrates higher holding power than (2-EHA-stat-AA), regardless of the method of polymerization. This effect was attributed to a higher number of entanglements in poly(BA-stat-AA) per unit weight or volume. Gower and Shanks [34], however, determined that in BA/2-EHA/methyl methacrylate (MMA)/AA copolymers the holding power increases with 2-EHA concentration. It should be noted that in this case the shear properties were compared not at equal gel content, and the result can be attributed to the increased gel content in formulations with 2-EHA.

8.5.6

Influence of Additives and Miscibility

The influence of different additives on shear strength and correlation of the shear strength with the miscibility of such blends have been studied by several authors [10,11,14,28,35]. Fujita et al. [11] studied the effects of miscible and immiscible tackifiers on the holding power of natural rubber. The holding time of miscible systems tends to decrease with tackifier content. This trend correlates with the changes in plateau modulus. PSA tapes containing 50% or more miscible tackifier started to slip away from the adherent. In the case of immiscible systems, however, the holding time changes unpredictably with cohesive failure. According to Ref. 28, both the holding power and SAFT of the SIS-based PSAs decreased with tackifier level. According to Ref. [14], a completely different behavior is valid for acrylic adhesives modified with miscible and immiscible tackifiers. In this case, the holding time tends to increase with tackifier content, although in the case of miscible tackifiers this trend is much more prominent. Similar results were obtained by Naruse et al. [35] for a BA/AA copolymer modified by different tackifiers. Kano et al. [10] improved the holding power of poly(butyl acrylate) by blending it with poly(vinylidene fluoride-co-hexafluoro acetone). The increased holding time correlates with the increased viscosity of such blends. Unfortunately, data on the miscibility and rheology of studied systems supplied by the authors are insufficient to come to a definite conclusion about the influence of miscibility on shear strength, although formulation practice usually shows a decisive decrease in cohesion-related adhesive properties, especially of the holding time by tackification with compatible resins; see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 8. Th is negative effect increases with tackifier level.

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Fundamentals of Pressure Sensitivity

8.5.7 Method of Polymerization Tobing and Klein [29] compared the shear resistance of PSAs based on poly(2-EHAstat-AA) obtained via polymerization in solution and in emulsion. In accordance with the industrial practice, solution-borne PSAs demonstrate much higher (one to two orders of magnitude) holding power than emulsion PSAs. It is believed that microgels that formed during emulsion polymerization and their morphology could be retained after fi lm formation. Such discrete morphology could give much lower shear strength than the continuous network morphology that formed from solution (see above). It should be noted that the polymerization technology can include pre- or postpolymerization tackification, which also leads to different adhesion and cohesion properties (see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 1).

8.5.8

Cross-Linking Density

The influence of ultraviolet (UV) dose and cross-linking density on the SAFT of acrylic copolymers of 2-EHA, VA, AA, and 2-hydroxyethyl methacrylate (2-HEMA) was investigated in Ref. [17]. Cross-linking of these copolymers by UV irradiation increased their SAFT from 30 to 150°C. Higher photoinitiator and 2-HEMA contents led to higher SAFT values at lower UV dose (see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 10). Acrylic polymers demonstrated a dramatic decrease in holding power as the gel content decreased [29,34].

8.5.9

Physical Cross-Linking

Hydrogen bonding, ionic bonding, or acid–base exchange (in the general case, donor– acceptor interaction) have an effect similar to the decrease in molecular weight between entanglements, thereby raising the holding power of the PSA. Physical cross-linking has the following advantages: • • • •

No need for curing equipment, curing agents, etc. Thickness of the adhesive does not restrict cross-linking efficiency Cross-linking can be thermally reversible. Tackifiers and other components can be added to adjust properties of the PSA without interfering with the cross-linking mechanism [36].

A complex of high-MW polyvinylpyrrolidone (PVP) and short-chain polyethylene glycol (PEG) can be regarded as an example of physical cross-linking [37]. Th is complex has a “carcass-like” structure, which is characterized by the interaction of functional groups of high-MW polymer (carbonyls of PVP) with complementary groups of low-MW polymer (terminal hydroxyls of PEG) (see also Chapter 10 and Technology of Pressure-Sensitive Adhesives and Products, Chapter 7). Another type of interpolymer complex is formed due to the interaction between complementary groups of two long macromolecules. This type of structure can be called ladder-like. Such a complex is formed as a result of the interaction between a polyacid and polybase. An acid–base interaction was observed for blends of the copolymer of

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Shear Resistance

8-15

dimethylaminoethyl methacrylate (DMAEMA) with MMA and butyl methacrylate (polybase) and the copolymer of methacrylic acid and EA (polyacid) [37]. Everaerts et al. [36] report a significant improvement in the holding power of the isooctyl acrylate (IOA)/AA copolymer by blending it with IOA/DMAEMA. The reason for the improved shear resistance is the intermolecular acid–base interaction between AA and DMAEMA groups and, consequently, an increase in cohesive strength.

8.6

Improving the Shear Behavior of Pressure-Sensitive Adhesives

Improving PSAs’ shear behavior means, first, an increase in their cohesive strength. Therefore, there is a permanent risk of sacrificing tack and peel. Thus, the problem consists of achieving a reasonable compromise between the properties. For cross-linking polymers, the improvement of shear resistance is connected with parameters of cross-linking: as already mentioned, a higher degree of physical and chemical cross-linking increases SAFT and holding time. The choice of monomers is very important for acrylics: monomers with shorter side chains enable higher cohesive strength. The most evident way of enhancing the cohesive strength of melting polymers is to increase their MW. This method increases the viscosity of the PSA and does improve shear resistance, but higher viscosity may make processing difficult. Broad MW distribution can contribute to preserving good peel and tack, while increasing shear resistance [31]. Reinforcement of PSAs with fillers is a valuable method to improve shear resistance, because it can increase both PSA viscosity at application and yield stress. Geiss and Brockmann [15] introduced glass beads to a SIS-based PSA. Samples loaded with the fi ller demonstrated lower creep and higher holding time compared with unfi lled PSAs. This is a typical method in industrial practice to formulate and manufacture carrierless tapes; see also Technology of Pressure-Sensitive Adhesives and Products, Chapter 8. The filler geometry is very important in such applications. Fillers with larger surface (fibers, flakes) are preferable to spherical particles due to higher reinforcing effect at equal loading. Kulichikhin et al. [22] successfully used clay nanoparticles to reinforce the mechanical strength and improve the creep behavior of SIS-based PSAs. An additional advantage of this approach consists of higher water uptake and the transportation of absorbed moisture from the skin (footcare products) to the depths of the adhesive dressing. Introducing fi llers into PSA while improving cohesive strength under application conditions does not necessarily result in increased viscosity at processing temperature and, consequently, complicated processing. Sometimes [38] orientation effects may lead to a drop in viscosity (fi ller geometry is decisive in such applications; therefore, fiber-like fi llers are commonly used in industrial practice). Physical cross-linking by involvement of the PSA components into intermolecular polycomplexes is a new and very attractive method of improving the cohesive strength of noncross-linked PSAs (see Technology of Pressure-Sensitive Adhesives and Products, Chapters 7 and 8). It can combine high shear resistance with hot-melt processibility, often without compromising other properties [36]. To use this method one should select

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Fundamentals of Pressure Sensitivity

a pair of polymers with complementary functional groups, so groups of one polymer can interact with the groups of the other. For instance, H-bonding can be realized in pairs: hydroxyl–hydroxyl, hydroxyl–carboxyl groups, etc. The interaction between a carboxylic acidic group and a basic amino group is an example of acid–base interaction [37]. Depending on cross-linker functionality [36], it is possible to obtain a thermosetting or thermoreversible complex: primary and secondary amines as cross-linkers yield a thermosetting PSA, whereas tertiary amines produce a thermoreversible network.

References 1. Lim, D.H., H.J. Kim. 2006. General performance of pressure-sensitive adhesives. In Pressure-Sensitive Design, Theoretical Aspects. Volume 1, ed. I. Benedek, Leiden– Boston, VSP, pp. 291–317. 2. Eveloy, V., P. Rodgers, M.G. Pecht. 2004. Reliability of pressure-sensitive adhesive tapes for heat sink attachment in air-cooled electronic assemblies. IEEE Trans. Device Mater. Reliability 4:650–657. 3. ASTM D3654/D3654M-06. Standard Test Methods for Shear Adhesion of PressureSensitive Tapes. 4. PSTC-7. Holding Power of Pressure-Sensitive Tape (revised ed.), 1985. 5. FINAT Test Method 8 (FTM8). 1985. Resistance to shear from a standard surface, 1985. 6. AFERA Test Method 4012. Measurement of shear adhesion, 1979. 7. Brockmann, W., P.L. Geiß. 1997. Creep Performance of Mounting Tapes Based on Hot Melt Pressure Sensitive Adhesives. Proc. 1997 TAPPI Hot Melt Symposium, TAPPI Press, Atlanta, pp. 153–158. 8. Zosel, A. 1994. Shear strength of pressure sensitive adhesives and its correlation to mechanical properties. J. Adhesion 44:1–16. 9. Miyagi, Z., K. Yamamoto. 1987. Viscoelastic analysis of shear adhesion test for pressure-sensitive adhesive tape. J. Adhesion 21:243–250. 10. Kano, Y., S. Akiyama, Z. Miyagi. 1998. Analysis of holding power in the blends of poly(butyl acrylate) with poly(vinylidene fluoride-co-hexfluoro acetone). J. Appl. Polym. Sci. 68:727–738. 11. Fujita, M., A. Takemura, H. Ono, M. Kajiyama, S. Hayashi, H. Mizumachi. 2000. Effects of miscibility and viscoelasticity on shear creep resistance of naturalrubber-based pressure sensitive adhesives. J. Appl. Polym. Sci. 75:1535–1545. 12. Malkin, A.Ya., A.A. Askadsky, V.V. Kovriga, A.E. Chalykh. 1983. Experimental Methods of Polymer Physics. Mir Publishers, Moscow. 13. Dealy, J.M. 1982. Rheometers for Molten Plastics. A Practical Guide to Testing and Property Measurement. Van Nostrand Reinhold Company. 14. Kim, H.-J., H. Mizumachi. 1995. Miscibility and shear creep resistance of acrylic pressure-sensitive adhesives: acrylic copolymer and tackifier resin systems. J. Appl. Polym. Sci. 58:1891–1899. 15. Geiss, P.L., W. Brockmann. 1997. Creep resistance of pressure sensitive mounting tapes. J. Adhesion 63:253–263.

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Shear Resistance

8-17

16. ASTM D4498-00. Standard Test Method for Heat-Fail Temperature in Shear of Hot Melt Adhesives. 17. Do, H.-S., Y.-J. Park, H.-J. Kim. 2006. Preparation and adhesion performance of UV-crosslinkable acrylic pressure sensitive adhesives. J. Adhesion Sci. Technol. 20:1529–1545. 18. Satas, D. 1989. Handbook of Pressure Sensitive Adhesive Technology. Van Nostrand Reinhold, New York. 19. Burgers, J.M. 1935. Mechanical considerations—model systems—phenomenological theories of relaxation and of viscosity. In: First Report on Viscosity and Plasticity, ed. J.M. Burgers, New York, Nordemann Publishing Company. 20. Schramm, G. 1994. A Practical Approach to Rheology and Rheometry. HAAKE GmbH, Karlsruhe, Germany. 21. Barnes, H.A. 1999. The yield stress–a review or ‘παντα ρει’–everything flows? J. Non-Newtonian Fluid Mech. 81:133–178. 22. Kulichikhin, V., S. Antonov, V. Makarova, A. Semakov, A. Tereshin, P. Singh. 2006. Novel hydrocolloid formulations based on nanocomposites concept. In PressureSensitive Design, Theoretical Aspects. Volume 1, ed. I. Benedek, Leiden–Boston, VSP, pp. 351–401. 23. Vinogradov, G.V., A.I. Elkin, S.E. Sosin. 1978. Fracture of uncured linear flexiblechain polymers of narrow molecular mass distribution in triaxial stress (behaviour of elastomers as adhesives). Polymer 19:1458–1464. 24. Oka, S. 1960. The principles of rheometry. In Rheology. Theory and Applications. Volume 3, ed. F.R. Eirich, Academic Press, New York, pp. 17–82. 25. Leider, P.J. 1974. Squeezing flow between parallel discs II. Ind. Eng. Chem. Fundam. 13:342–349. 26. Laun, H.M. 1992. Rheometers towards complex flows: squeeze flow technique. Macromol. Chem., Macromol. Symp. 56:55. 27. Feldstein, M.M., V.G. Kulichikhin, S.V. Kotomin, T.A. Borodulina, M.B. Novikov, A. Roos, C. Creton. 2006. Rheology of poly(N-vinyl pyrrolidone)-poly(ethylene glycol) adhesive blends under shear flow. J. Appl. Polym. Sci. 100:522–537. 28. Kim, D.-J. 1995. Ph. D. Thesis. Performance of SIS-based hot-melt pressure sensitive adhesives. Seoul National University. 29. Tobing, S.D., A. Klein. 2001. Molecular parameters and their relation to the adhesive performance of acrylic pressure-sensitive adhesives. J. Appl. Polym. Sci. 79:2230–2244. 30. Benedek, I. 2006. Principles of pressure-sensitive design and formulation. In Pressure-Sensitive Design, Theoretical Aspects. Volume 1, ed. I. Benedek, Leiden– Boston, VSP, pp. 131–289. 31. Krenceski, M.A., J.F. Johnson. 2004. Shear, tack and peel of polyisobutylene: effect of molecular weight and molecular weight distribution. Polym. Eng. Sci. 29:36–43. 32. Demarteau, W., J.M. Loutz. 1996. Rheology of acrylic dispersions for pressure sensitive adhesives. Progr. Organ. Coatings 27:33–44. 33. Park, W.-H., S.W. Kim, S.C. Shim, I.R. Jeon, K.H. Seo. 2003. Properties of pressure sensitive adhesive made of acrylic quaternary copolymers and their blends with vinyl chloride copolymers. Mat. Res. Innovat. 7:172–177.

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34. Gower, M.D., R.A. Shanks. 2004. The effect of varied monomer composition on adhesive performance and peeling master curves for acrylic pressure-sensitive adhesives. J. Appl. Polym. Sci. 93:2909–2917. 35. Naruse, S., H.-J. Kim, T. Tsukatani, M. Kajiyama, A. Takemura, H. Mizumachi. 1994. Miscibility and PSA performance of acrylic copolymer and tackifier resin systems. J. Adhesion 47:165–177. 36. Everaerts, A., K. Zieminski, L. Nguyen, J. Malmer. 2006. Cross-linking of hotmelt-processible acrylic pressure-sensitive adhesives using acid/base interaction. J. Adhesion 82:375–387. 37. Feldstein, M.M., G.W. Cleary, P. Singh. 2006. Pressure-sensitive adhesives of controlled water-absorbing capacity. In Pressure-Sensitive Design and Formulation, Application. Volume 2, ed. I. Benedek, Leiden–Boston, VSP, pp. 181–230. 38. Kulichikhin, V.G., L.A. Tsamalashvili, E.P. Plotnikova, A.A. Barannikov, M.L. Kerber, H. Fischer. 2003. Rheological properties of liquid precursors of polvnronvlene-clay nanocomnosites. Polym. Sci. (Russia). 45:564–572.

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9 Durability of Viscoelastic Adhesive Joints Sergey V. Kotomin A.V. Topchiev Institute of Petrochemical Synthesis

9.1

9.1 Introduction .............................................................9-1 9.2 Triaxial Stress Tests ................................................ 9-2 9.3 Durability and Adhesion ..................................... 9-13 9.4 Conclusions ............................................................9-17 References ........................................................................9-17

Introduction

Adhesive strength is one of the main characteristics of pressure-sensitive adhesives (PSAs), but how long the adhesive joint can provide contact to the substrate over time and under various external conditions (debonding force, temperature, and relative humidity) is also important. Several methods exist to test the adhesive strength of PSAs, including tack, peel, and shear tests (see Chapters 6 through 8 and Applications of Pressure-Sensitive Products, Chapter 8). These are carried out under standard conditions in accordance with ASTM D1876-01 (Method for Peel Resistance of Adhesives (T-Peel Test) and probe tack test (according to ASTM D2979-01) or using other methods. For long-term durability of PSAs, there is only one standard test—the method for determining the durability of adhesive joints stressed in shear loading (ASTM D2919-01 or PSTC-7). In most publications, discussions of durability properties include the analysis of behavior under various environmental conditions [1,2] (see also Applications of Pressure-Sensitive Products, Chapter 8) or fatigue tests in cyclic mode [3]. The static shear experiment is similar to a creep measurement with a constant shear stress [4–6] (see also Applications of Pressure-Sensitive Products, Chapter 8). In the shear resistance test the contact area is not constant; thus, at a constant load force the shear stress gradually increases in time and there is no control of thickness and deformation of the adhesive layer in the normal direction. These factors can cause large scatter and discrepancies in test results (see Chapter 8). Any slight inclination in the 9-1

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Fundamentals of Pressure Sensitivity

direction of the tear force vector would cause a normal force component, which may influence fracture development for PSAs. The adhesive elastic fi lm under extension in the normal direction is in a triaxial stress state (or under negative hydrostatic pressure) [7]. The phenomenon of internal rupture of tensioned cylindrical rubber samples starting with the formation of microcavities was described 50 years ago by Gent and Lindley [8]. Twenty years previously, Yerzley (1939) first described “yield-point” in the load–extension relation of similar test pieces and attributed it to internal rupture [9]. The recent works of Creton and colleagues [10–12] analyzed the mechanism of cavity formation during fracture of a PSA in a probe tack test. The works of Yamaguchi and co-workers [13,14] are examples of a model approach for the analysis of the cavitation process during the same test using some assumptions.

9.2

Triaxial Stress Tests

Although the durability of viscoelastic adhesive joints in the triaxial stress state definitely has practical importance, to the best of our knowledge only a few works directly focused on this matter [15–17]. First, one must note a fundamental work devoted to elastic adhesive durability performed by Vinogradov et al. 30 years ago [15]. The study of long-term durability of adhesive joints under the action of constant debonding force on polybutadiene (PB) as a PSA model materials yields fundamental information about the structure and properties of adhesives. A description of the experimental device used in this work is presented in Figure 9.1. A support, B (Swedish precision block), is installed in a thermocontrolled unit, A. The adhesive fi lms, C, are placed on the ring edge of a cylinder, D. The ring, D, is fi xed inside the duct, E, of the guiding block, F, and loaded in the axis direction. The material

∆

H

I G F E J D C B A

FIGURE 9.1

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Schematic design of Vinogradov’s adhesiometer.

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Durability of Viscoelastic Adhesive Joints

9-3

of the duct, E, is low-frictional polytetrafluoroethylene (PTFE). The cylindrical ring, D, is hinged, via a rigid tie, G, to the right arm of the balanced lever, H. Weights, I, are suspended from the left arm of the lever, H. A hydraulic damper, J, suppresses the elastic vibrations of the polymer adhesive. Contact between the adhesive and the solid surface was formed at a temperature of 60°C for 30 min under a pressure of 0.5 MPa. The long-term durability t* of the PSA joints in the case of elastic adhesives is related to the stress, σ, by following Bartenev’s equation (Equation 9.1; Ref. 15), t *
B()m

(9.1)

or by an extended equation including the influence of temperature and molecular weight, t *
B1()m exp

U  M kT

(9.2)

where U is the activation energy of the rupture process and B1, m, and α are the constants characterizing the material and type of fracture. The physical meaning of coefficients B, B1, and m is explained in Ref. 18; for epoxy resins at T > Tg constant m = U0/3kTg [19]. Values of the coefficient B and the exponent m according to Ref. 20 are very sensitive to fracture type and decrease by several orders of magnitude as the fracture type changes from cohesive to adhesive. Equation 9.1 noticeably differs from Zhurkov’s classic equation for the durability of solid materials [18], t *
0 exp

U 0   kT

(9.3)

where τ0 is the thermal oscillation time of atoms (for polymers τ0 ∼ 10−12 to 10−13 s); U0 is the activation energy of self-induced rupture of polymer chains at σ = 0. The difference between Equations 9.1 and 9.3 might be explained by the standpoint of fracture mechanisms for brittle solids and elastic materials. In the first case the standpoint is a surface crack propagation; in the second case it is an internal cavity nucleation inside the material. Figure 9.2 illustrates that the t* versus σ* curves for PB in contact with a steel substrate exhibit two regions of durability values with different magnitudes of the indicated constants. These regions represent the different modes of fracture of PB fi lms. In the region of lower values of B and –m (indicated by fi lled symbols in Figure 9.2), cohesive fracture was observed. For cohesive fracture, similar to uniaxial extension, the long time durability reduces with decreasing Mw of the adhesive. Miscellaneous cohesive–adhesive fracture was observed at higher stresses (see symbols ∆ and ◊ in Figure 9.2). In this case, only a few areas of the contact surfaces were covered with the polymer. At stresses above 0.9 MPa the fracture becomes adhesive for two specimens of PB in contact with steel, but tear-off occurs very fast and it is difficult to measure the time

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9-4

Fundamentals of Pressure Sensitivity

6 4

4 3 log t ∗ (C)

2 2 1

0

−2 −1.2

−0.8

−0.4

0.0

log σ∗ (MPa)

FIGURE 9.2 Durability t* versus stress σ for PB in contact with PTFE (curves 1 and 2) and steel (curves 3 and 4) at 20°C. For 1 and 2 the unfi lled symbols relate to adhesive failure; for 3 and 4, the black symbols denote cohesive fracture; whereas unfi lled symbols indicate a miscellaneous cohesive–adhesive type of fracture. Mw = 1.5 × 105 g/mol (1, 3) and 6.4 × 105 g/mol (2, 4).

TABLE 9.1 Experimental Parameters B and m in Equation 9.1 at Various Temperatures for PB in Contact with Steel and PTFE (stresses range between 5 × 10−2 and 1 MPa) Coefficient B and m at Different Fracture Modes Cohesive Temperature (°C)

B

Cohesive–Adhesive –m

B

–m

3.2 × 10−1 7.9 × 10−3 5.0 × 10−5 6.3 × 10−4

5.9 15.5 14.7 25.1

4.4 × 10−8

10.0

5 6 20 20* 35 50 60 80

4.0 × 102 5.0 × 101 1.6 × 102 1.0 × 102

4.3 4.0 4.3 4.1

4.0 × 101

4.1

Adhesive B

–m

1.6 × 10−2

3.69

7.2 × 10−11 2.0 × 10−9

11.7 10.2

Mw = 6.4 × 105, except *Mw = 1.5 × 105 g/mol.

to fracture (<0.l s) The effect of Mw on the long-term durability in the case of adhesive fracture has been studied for PB in contact with PTFE. The results of these studies are presented in Figure 9.2 (open symbols). The calculated values of the equation constants B and m are given in Table 9.1.

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9-5

Durability of Viscoelastic Adhesive Joints

The fracture mode was adhesive and the long-term durability in this case was, in fact, independent of the Mw of the adhesive. The influence of temperature on long-term durability for the joint of PB (Mw = 6.4 × l05) with PTFE is illustrated in Figure 9.3, and the calculated coefficients in Equation 9.2 are also listed in Table 9.1. At 5 and 20°C the fracture was adhesive over the entire range of stresses; at 60°C a transition from cohesive–adhesive to adhesive failure was observed. In Figure 9.3 the region of cohesive–adhesive fracture is indicated by fi lled symbols. The transition from one type of fracture to another is clearly seen on the change in the curve’s slope. As follows from the experimental data, three characteristic regions may be distinguished on the t* versus σ* curve, which correspond to the cohesive, miscellaneous cohesive–adhesive, and adhesive fractures. Upon the transition from cohesive to cohesive–adhesive fracture, a sharp change in the dependence of long-term durability on stress is observed, so that in the case of adhesive fracture the long-term durability drops drastically with increasing stress, as for a brittle fracture. In the case of cohesive–adhesive and adhesive fracture mechanisms, the t* versus σ* curves at various temperatures have a more complicated character than those obtained for cohesive fracture. Fracture of the polymeric layer between two solid surfaces and its separation from the solid surface depends largely, according to the literature [21], on the state of the adhesive, namely, whether it behaves as an elastic, a viscoelastic, or a plastic body. The dependence of long-term durability on the inverse absolute temperature under conditions of cohesive–adhesive fracture and adhesive fracture is illustrated in

3 4

2

3

log t ∗ (s)

1 2

1

0 −1 −1.5

−1.0

−0.5

0.0

log σ∗ (MPa)

FIGURE 9.3 Durability versus stress σ for PB (Mw = 6.4 × 105 g/mol) in contact with PTFE at different temperatures. The unfi lled labels denote adhesive failure; the fi lled labels represent cohesive–adhesive fracture at temperature (1) 5, (2) 20, and (3) 60°C.

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9-6

Fundamentals of Pressure Sensitivity

7 3

6 8 3

log t ∗ (s)

2

5

4 1 2 0 1 −1 3.2

T −1 × 10−3 (K −1)

3.6

FIGURE 9.4 Cohesive–adhesive fracture. The long-term durability t* versus inverse temperature, T –1, at stress values: (1) 0.8, (2) 0.75, (3) 0.71, (4) 0.67, (5) 0.63, (6) 0.595, (7) 0.56, and (8) 0.53 MPa.

4 8

log t ∗ (s)

7

2

6 5 4 3

2

2

log t ∗ a (s)

4

1 0

0 3.0

3.2

3.4 T −1 × 103 (K−1)

3.6

FIGURE 9.5 Adhesive failure. The long-term durability t* versus inverse temperature at different stresses (solid lines). σ: (1) 0.071, (2) 0.075, (3) 0.08, (4) 0.084, (5) 0.089, (6) 0.094, (7) 0.1, and (8) 0.106 MPa. The dashed line represents the master curve of log t*aσ versus (T –1 + a σ). PB (Mw = 6.4 × 105 g/mol) in contact with PTFE.

Figures 9.4 and 9.5. The relationship between log t* and T−1 is reduced to the specific stress along the abscissa and the ordinate. The master curve of (log t*)aσ, versus (T−1 + aσ) for adhesive fracture is represented by a dashed line in Figure 9.5 (the reduction was made to stress σ0 = 0.106 MPa).

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9-7

Durability of Viscoelastic Adhesive Joints

The dependence of long-term durability on stress and temperature is similar to that reported in the literature for cured rubbers [22]. This may be regarded as proof that, in this range of applied stresses, noncured polymers demonstrate a strain hardening effect and behave like cured elastomers. The study of samples with various molecular weight demonstrated that, just as in the case of uniaxial extension, the long-term durability of thin fi lms upon cohesive fracture relates to molecular mass using the equation t *
f ( M )

(9.4)

where α ranges from 3.2 to 3.3. The nature of the long-term durability dependence on stress, temperature, and MW demonstrates that the cohesive strength of elastomers under triaxial stress is determined by their relaxation characteristics and, in particular, by the initial viscosity. Considering that relaxation governs the cohesive fracture, it is possible to use the reduction in temperature–time relationships with the shift factor calculated by the William–Landel–Ferry equation, log aT


C1(T T0 ) C2  (T T0 )

(9.5)

The values of the constants, C1 = 1.26 and C2 = 31, were calculated assuming that the relationship log αT versus (T – T0) is linear, and a reduction was made to T = 20°C. Figure 9.6 illustrates the master curve representing the relation between log t*aTaM and log σ* for PB with Mw = 6.4 × 105 and 1.5 × 105 g/mol, reduced to 20°C and Mw = 6.4 × 105 g/mol.

log t ∗ a Ta M (s)

6

4

2 −1.0

−0.5 log σ∗ (MPa)

0.0

FIGURE 9.6 Master curve for the dependence of durability versus fracture stress (reduced to 20°C) for PB (Mw = 6.4 × 105 and 1.5 × 105 g/mol). The signs are the same as in Figures 9.4 and 9.5; (+) for PB (Mw = 1.5 × 105 g/mol).

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9-8

Fundamentals of Pressure Sensitivity

A comparison of the obtained results with the data in the literature [7,23,24] indicates that the long-time durability of thin fi lms in the triaxial stressed state is 1.0–1.5 decimal orders of magnitude higher and the fracture stresses are 2–3 times greater than the corresponding values obtained under conditions of uniaxial extension. In triaxial stress the fracture begins with the formation of microcavities in the bulk of the adhesive. There is some delay from the moment of loading to the formation of the first cavities. The fracture process gradually develops upon increasing the size and the number of cavities for a certain period of time. At the fast fi nal stage, crack forking is observed. It is important that at all stages of the fracture process removal of the load does not lead to the recovery of continuity (for several hours), which indicates unrecoverable plastic deformation. Thus, the results of experiments carried out under triaxial stress proved the validity of Equations 9.1 and 9.2 for elastomer PB and are comparable with the data obtained for the same samples under simple shear and uniaxial extension [20]. In Vinogradov’s work [15], the rupture time of different types of PB was studied without the analysis of fracture kinetics, and the adhesive contact had the shape of a narrow ring to provide a uniform normal stress distribution. It was of practical importance to check these results using a test cell with the geometry of probe tack tester, where the adhesive fi lm was placed between flat surfaces. Research [16,17,25] presents the results of the study of durability and fracture kinetics of PSAs composed of blends of poly(Nvinylpyrrolidone) (PVP) with poly(ethylene glycol) (PEG), along with an uncured polybutadiene (PB) also used in Vinogradov’s experiments. In this study a simple experimental procedure, the squeeze–recoil technique, was developed. This technique provides comprehensive characterization of the viscoelastic and adhesive properties of the material with a small sample in the course of a single test cycle [25]. For experiments, blends of PVP (Mw = 106 g/mol) with PEG (Mw = 400 g/mol) and monodisperse PB (Mw = 120,000 g/mol) were used. Previously it was demonstrated that viscosity and the long-term relaxation properties (recovery compliance) of the system PVP (64%) + PEG and that of PB were similar [26]. Adhesive PVP–PEG hydrogels were prepared and tested as described previously [27] and other details may be found in Technology of Pressure-Sensitive Adhesives and Products, Chapter 7. The polymer sample is placed between flat silica surfaces formed by a loading rod and a supporting plate of the measuring cell of the thermomechanical analyzer DTMD, made by a special design workshop (SKB UP) of the Russian Academy of Sciences. The schematic representation of the test cell is shown in Figure 9.7. Sample loading under this test is similar to the process of normal compression for PSAs. The polymer sample squeezed out between flat silica surfaces under constant load (Figure 9.8, stage I), leading to a decreased gap between the upper and lower plates of the tester that is equal to the adhesive fi lm thickness. A sample loading under this test is the same as normal compression for PSAs. More details about the squeeze flow of viscous fi lm under compression can be found in Chapter 8. Removing the load after the squeezing stage leads to a partial recovery (II), whereas the change of direction of the applied force produces a gradual separation of the plates and, consequently, an extension of the sample (III).

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9-9

Durability of Viscoelastic Adhesive Joints

F

2

1

3

FIGURE 9.7 The scheme of the squeeze–recoil test under normal force, F: (1) upper plate, (2) polymer sample, and (3) bottom plate. (Redrawn from Kotomin, S.V., Borodulina, T.A., Feldstein, M.M., and Kulichikhin, V.G., in Proceedings of the XIIIth International Congress on Rheology, Cambridge, U.K., 4, 44–46, 2000.)

1 I Squeezing

Gap (mm)

II Recovery

III Debonding

0.1

200

400

600

800

1000

1200

1400

1600

Time (s)

FIGURE 9.8 The stages of the squeeze–recoil test: (1) squeezing, (2) creep recovery, and (3) debonding for a PVP (64% wt)–PEG hydrogel. (Redrawn from Kotomin, S.V., Borodulina, T.A., Feldstein, M.M., and Kulichikhin, V.G., in Proceedings of the XIIIth International Congress on Rheology, Cambridge, U.K., 4, 44–46, 2000.)

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9-10

Fundamentals of Pressure Sensitivity

1

2

4

3

5

1.0

0.8 Gap (mm)

0.8 0.6

0.6

0.4

0.4

0.2

Transparency (a.u.)

6

0.2

10

100

1000

t (s)

FIGURE 9.9 Gap change (1-5) and light transmittance (6) versus time during plate separation for PB (2,3) and for the PVP–PEG blends (1,4,5,6) with PVP content (1) 34%; (4) 50%; and (5,6) 64%. The debonding force is (1,4) 0.3 N, (2) 0.5 N, and (3,6) 1 N at ambient temperature.

Using this test, the kinetics of plate separation under constant detaching force and the strength of the adhesive joint were studied in terms of long-time durability (the time to debonding). The nucleation of microcavities in the sample and further fibrillation were observed with a vertical optical microscope and were also monitored by laser light transmission through the transparent adhesive layer. The procedure of plate detachment under fi xed tensile load is very similar to the conventional probe tack test (see Chapter 6), but the distinctive feature of the procedure is that the debonding occurs under constant force, and the time required for the rupture of adhesive bond characterizes the durability of the joint. The peculiarities of loading and recovery stages in these experiments were discussed in Ref. 28. The kinetics of adhesive debonding are illustrated in Figure 9.9 for the PVP–PEG blends of different compositions. For these polymeric blends the debonding time differs by several orders of magnitude. The slower stage of the debonding process results in fibril nucleation, followed by the faster stage of fibril elongation and fracture of the adhesive film. The first (slower) stage involves an orientation of polymer chains under applied tensile stress and the second (much faster) stage includes the elongation flow of polymer chains inside the fibrils until their cohesive fracture occurs. As demonstrated by many authors, at the early stage the formation of microcavities is observed [7–14]. The moment of fibril formation corresponds to the border between the slower and the faster debonding stages. The onset of global fibrillation is visible in Figure 9.9 with an abrupt fall in optical clarity, measured by the intensity of the transmitted light through the sample in a tension direction. Changes in the structure of the adhesive fi lm prior to fibrillation have been recently discussed in detail by Creton et al. [10–12] in probe tack testing of other PSAs. These results are also in accordance with the peel test data obtained by Chalykh et al. [27] for the PVP–PEG PSAs. The PVP (64 wt %)–PEG H-bonded stoichiometric complex

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9-11

Durability of Viscoelastic Adhesive Joints

500

5000

4000

400

3000

300

2000

200

1000

100

Peel force (N/m)

Durability (s)

Peel force (N/m) Durability (s)

0

0 0.1

0.2

0.3 0.5 0.4 PEG weight fraction

0.6

0.7

FIGURE 9.10 Peel adherence and durability for PVP blends with PVP–PEG-400 adhesive. (Redrawn from Feldstein, M. and Creton, C. Pressure-Sensitive Adhesion as a Material Property and as a Process in Pressure-Sensitive Design, Theoretical Aspects, VSP, Leiden, 2006.)

demonstrates the best peel and probe tack adhesion and exhibits the longest durability of the adhesive joints (Figure 9.10) [29]. As Figure 9.10 illustrates, the composition relationship of the long-term durability of PVP–PEG blends follows the pattern shown by peel strength. On the microphotographs in Figures 9.11 and 9.12 one can see the fi nal stage of plate separation for PVP–PEG adhesive composition at the maximal gap between plates of 3 mm. Fibrillation development for the PVP–PEG PSA depends on viscosity. For the viscous PVP (64%)–PEG system the fibril structure retains up to the moment of debonding (Figure 9.11), but for the low-viscosity blend PVP (50%)–PEG, only a single pillar is observed (Figure 9.12). In the latter case, the pillar formation proceeds most likely through very fast merging of “liquid” fibrils at extension flow resembling neck formation. For both systems the rupture has miscellaneous adhesive–cohesive character. As demonstrated in Ref. 25, in contrast to PB, the PVP (64%)—PEG hydrogel is a viscoplastic liquid with a defi nite yield stress. Thus, its behavior upon stretching is strain hardening. Probably for this reason, no PB fibrillation was observed and neck formation took place only at the lowest stress. At higher stresses (>6.6 × 103 Pa) the plate separation led to compete PB fracture, which is in accordance with the results obtained by Vinogradov et al. [15]. The experimental data proved the validity of Equations 9.1 and 9.2 for the durability of the PB joint for and for the PSA PVP(64%)–PEG, as illustrated in Figure 9.13. The calculated values of the coefficients in Equation 9.1 and activation energy in Equation 9.2 at the indicated temperature and stresses values are presented in Table 9.2. As follows from these data, the activation energy of cohesive fracture for adhesive PVP–PEG hydrogel is much higher than that for PB.

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9-12

Fundamentals of Pressure Sensitivity

FIGURE 9.11 Fibrillization of PVP (64%)–PEG PSA under separation of tester plates.

FIGURE 9.12 Neck formation under plate separation for PVP (50%)–PEG adhesive.

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9-13

Durability of Viscoelastic Adhesive Joints log σ (Pa) 5.8

6.0

6.2

6.4

6.6

4

1/T

log t ∗ (s)

3

log σ 2

1

0 2.8

3.0

3.2

3.4

3.6

1000/T (K−1)

FIGURE 9.13 Durability of PVP–PEG adhesive joints versus debonding stress at fi xed temperature and versus inverse temperature at fi xed tensile stress. (Redrawn from Kotomin, S.V., Borodulina, T.A., Feldstein, M.M., and Kulichikhin, V.G., in Proceedings of the XIIIth International Congress on Rheology, Cambridge, U.K., 4, 44–46, 2000.) TABLE 9.2

Activation Energy for Fracture of PB and PVP–PEG Adhesives

Type of Adhesive PB PB PVP (64%)–PEG

Normal Stress (σ × 103 Pa) 6.6 13.2 33.0

Activation Energy of Fracture, U (kJ/mol K−1) 18.1 9.5 70.1

In the experiments using PVP–PEG hydrogel, a complete fracture of the adhesive joint was not observed, because the elongation of the adhesive during plate separation was limited by the maximum gap value of the instrument cell. The studied adhesives, PVP (67%)–PEG, PVP (50%)–PEG, and PB, may be defined consequently as the strain-hardening, strain-thinning viscoelastic materials and Newtonian liquid, according to the description of the behavior of other PSAs [10].

9.3 Durability and Adhesion In recent work [30] the durability of adhesive joints made from a range of commercially available PSAs was studied. Characterized adhesives are as follow: 1. Gelva 3011—water-based emulsion of cross-linked acrylate copolymer 2. Duro–Tack 87-900A—solution of un-cross-linked acrylic copolymer in EA

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Fundamentals of Pressure Sensitivity

3. PIB—blend of three polymers with different molecular weights (Oppanol B-100, Oppanol B-12, and Indopol H-1900, BASF; see Table 4.2 in Technology of PressureSensitive Adhesives and Products, Chapter 4). Adhesive fi lms were prepared by casting the solutions followed by drying. The durability of adhesive joints was studied using the setup illustrated in Figure 9.14. The set of weights renders the control of the compression or extension of the sample located between flat butt-end surfaces of two steel rods. Varying the weight allows to squeeze the adhesive fi lm between the rods and then to detach them. To compare durability for different PSAs, one must use similar test conditions, such as the load and time of loading. The higher the load, the thinner the adhesive layer and the higher the long-time durability. The dependence of durability on loading time at a pressure of 350 KPa is illustrated in Figure 9.15. Long-time durability for every type of PSA increases gradually and Adhesive film between rods

Weights

FIGURE 9.14 Setup for durability test.

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9-15

Durability of Viscoelastic Adhesive Joints

500 5

t d (s)

4

250

3 2 1

10

20

30

t l (min)

FIGURE 9.15 Detachment time, t*, vs loading time, t l, for PSAs: (1) acrylic Gelva 3011, (2) PIB, (3, 4) PB, and (5) acrylic DuroTak-87-900A at (1–3, 5) 350 KPa and (4) 490 KPa. (Redrawn from Sadykova, I., B.Sci. thesis: Long-time durability of acrylic PSAs, Moscow, State Academy of Fine Chemical Technology (MITHT), 2007.)

3.5 4 log t (s)

3.0 2 2.5

3

1

2.0 5.62

5.64 5.66 log σ (Pa)

5.68

FIGURE 9.16 Durability versus stress for (1) Gelva, (2) PB, (3) PIB, and (4) DuroTak PSAs.

reaches a certain limit with time. The loading time was 20 min at a normal stress value of 350 KPa and at the same (but negative) extension stress. The dependence of PSA durability on extension stress is illustrated in Figure 9.16 and Table 9.3. The calculated values of coefficients B and m are presented in Table 9.3, along with the data obtained for the PVP–PEG hydrogel, which were taken from Figure 9.11.

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9-16

Fundamentals of Pressure Sensitivity

TABLE 9.3 Parameters B and m in Equations 9.1 and 9.2 Calculated from Data Presented in Figure 9.16 along with the Values of Practical Work of Adhesion (W) Derived from the Probe Tack Test Temperature (°С)

Adhesive Gelva DUROTAK 87-900A PIB PB PVP (64%)–PEG

Film Thickness (mm)

−m

B

Maximum Stress (kPa)

Work of Adhesion, W (J/m2)

30

0.13

46.5

7.8

140

1330

26

0.09

68.3

11.5

1020

300

20 29 25

0.13 0.11 0.10

56.8 80.0 20.0

9.6 13.7 0.43

280 300 1200

240 7.5 100

Source: Feldstein, M., Creton, C. 2006. Pressure Sensitive Adhesion as a Material Property and as a Process in Pressure-Sensitive Design, Theoretical Aspects. VSP, Leiden, pp. 22–67 and Sadykova, I. 2007. B.Sci. thesis: Long-time durability of acrylic PSAs, Moscow, State Academy of Fine Chemical Technology (MITHT). 1.2 1.0 0.8 4 0.6

Stress (MPa)

0.8 4

0.4 3

0.2 0.0

1

2

0

0.4

5

10

15

20

3 2 1 0.0 0.01

0.1

1

10

Distance (mm)

FIGURE 9.17 Probe tack curves (time–semilog scale): (1) PB, (2) Gelva, (3) PIB, (4) DuroTak [30]. In the upper right corner of the image the same figure is presented in linear time scale. The bonding force is 10 KN, the contact time is 1 s, and the probe detachment rate is 0.1 mm/s.

Table 9.3 also contains the results of the probe tack test derived from Figure 9.17 [29,30]. In Figure 9.17 the probe tack curves are presented as stress versus probe displacement, both in the linear and in the logarithmic scale, to discern the curves relating to the deformation of various adhesives. The constant rate of debonding was 0.1 mm/s. Table 9.3 indicates that the highest value of the practical work of debonding W is obtained for Gelva adhesive, but for the same PSA, as seen in Figure 9.16, the value of

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Durability of Viscoelastic Adhesive Joints

9-17

durability t*, as well as the apparent tensile stress, is the lowest. Th is contradiction can be understood if we take into consideration the low value of coefficient m, which provide for Gelva a good durability at higher stresses. The PVP–PEG PSAs have the lowest value of m, which means the best durability at high stresses. These results also mean that the relationship among the durability of various PSA may vary, depending on the value of apparent tensile stress.

9.4 Conclusions The dependence of long-term durability of thin viscoelastic polymer fi lms on temperature and stress is described by equations similar to those derived for cured rubbers, indicating the similarity between the effect of entanglement networks in noncured elastomers and that of a network of chemical bonds in vulcanized rubbers. The elasticity and the viscosity of the polymer play a decisive role in the fracture mechanism of thin adhesive fi lms. The study of adhesion characteristics of noncured polymers demonstrated that in the case of adhesive and miscellaneous cohesive–adhesive fractures, long-term durability is very sensitive to temperature. This feature is associated with the specific temperature dependence value of total deformation and its recoverable and plastic components for noncured polymers in the region of transition from the fluid to the rubber-like state. The behavior of viscoelastic adhesives drastically depends on the rate of deformation. In the case of constant stress, different types of fracture—cohesive, miscellaneous cohesive–adhesive, and adhesive—may be observed, depending on the stress value. The results of durability experiments carried out under triaxial stress proved the applicability of the simple phenomenological equations for the prediction of PSA behavior under various stresses and temperatures. Characteristic coefficients in Equation 9.1 for various PSAs can be determined both for adhesive fracture and for cohesive debonding. Using these coefficients, one can forecast the behavior and long-term durability of PSA at any stress and temperature. At the same time, the comparison of peel and probe tack adhesion with the value of long-term durability requires further study.

References 1. Kinloch A.J. 2002. The durability of adhesive joints. In Adhesion Science and Engineering, vol. 1. eds. D.A. Dillard, A.V. Pocius, Elsevier, Amsterdam, pp. 661–98. 2. Temiz, S., Ozel, A., Aydin, M.D. 2004. A study on durability of joints bonded with pressure-sensitive adhesives. J. Adhesion Sci. Technol. 10:1187–1198. 3. Sohn, S. 2003. A new method based on application of cyclic strain to evaluate the durability of pressure sensitive adhesives. J. Adhesion Sci. Technol. 17:1039–1053. 4. Lim, D.H., Kim, H.J. 2006. General performance of pressure-sensitive adhesives. In Pressure-Sensitive Design, Theoretical Aspects, ed. I. Benedek, Boston, VSP, Leiden, pp. 310–311. 5. PSTC-7. 6. ASTM-D3654/D 3654M-027.

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9-18

Fundamentals of Pressure Sensitivity

7. Lindsey, G.M. 1967. Triaxial fracture studies. J. Appl. Phys. 38:4843–4852. 8. Gent, A.N., Lindley, 1958. Internal rupture of bonded rubber cylinders in tension, Proc. R. Soc. London, Ser. A: Math. Phys. Sci., A 249:195–205. 9. Yerzley, F.L. 1939. Adhesion of neoprene to metal Ind. Eng. Chem. 31:950–956. 10. Creton, C., Lakrout, H. 2000. Micromechanics of flat probe adhesion tests of soft viscoelastic polymer fi lms, J. Polym. Sci.: Part B: Polym. Phys. 38:965–979. 11. Creton, C., Hooker, J.C., Shull, K.R. 2001. Bulk and interfacial contributions to the debonding mechanisms of soft adhesives: extension to large strains. Langmuir 17: 4948–4954. 12. Creton, C. 2005. Mécanismes de déformation, d’endommagement et de rupture de joints collés. Mécanique & Industries 6:37–43. 13. Yamaguchy, T., Doi, M. 2006. Debonding dynamics of pressure-sensitive adhesives: 3D block model. Eur. Phys. J. E 21:331–339. 14. Yamaguchi, T., Morita, H., Doi, M. 2006. Modeling on debonding dynamics of pressure-sensitive adhesives. Eur. Phys. J. E 20:7–17. 15. Vinogradov, V.G., Elkin, A.I., Sosin, S.E. 1978. Fracture of uncured linear flexible-chain polymers of narrow molecular mass distribution in triaxial stress (behavior of elastomers as adhesives). Polymer 19:1458–1464. 16. Kotomin, S.V., Borodulina, T.A., Feldstein, M.M., Kulichikhin, V.G. 2000. Durability and fracture of some viscoelastic adhesives. Proceed. XIIIth Intern. Congress on Rheology, Cambridge, UK, 4:44–46. 17. Kotomin, S.V., Borodulina, T.A., Feldstein, M.M., Kulichikhin, V.G. 2000. Durability and rheology of viscoelastic adhesives. Proceed. 23rd Annu. Meeting Adhesion Soc. pp. 413–415. Myrtle Beach, SC. 18. Vettegren, V.I., Kulik, V.B., Bronnikov, S.V. 2005. Temperature dependence of the tensile strength of polymers and metals at elevated temperatures Tech. Phys. Lett. 31:969–972. 19. Vettegren, V.I., Kulik, V.B., Bashkarev, A.Ya., Lebedev, A.A., Sytov, V.A. 2004. The temperature dependence of the strength of adhesion between steels and epoxyrubber glues and polyamides in a rubberlike state. Tech. Phys. Lett. 30:862–864. 20. Vinogradov, G.V., Malkin, A.Ya., Yanovsky, Yu.G., Borisenkova, E.K., Yarlykov, B.V., Berezhnaya, G.V. 1972. Viscoelastic properties of linear polymers in the fluid state and their transition to the high-elastic state. Polym. Sci., Polym. Phys. Ser. B 10:1061–1076. 21. Good, R.J. 1976. Definition of adhesion, J. Adhesion 8:1–9. 22. Bartenev, G.M. 1984. Strength and Mechanism of Polymers Fracture. Moscow, Khimia (in Russian). 23. Vinogradov, G.V. 1975. Viscoelasticity and fracture phenomenon in uniaxial extension of high-molecular linear polymers. Rheol. Acta 14:942–954. 24. Vinogradov, G.V., Malkin, A.Ya., Volosevitch, V.V., Shatalov, V.P., Yudin, V.P. 1975. Flow, high-elastic recoverable deformations and rupture of uncured high molecular weight linear polymers in uniaxial extension J. Polym. Sci. Polym. Phys. Ed. 13:1721–1735.

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Durability of Viscoelastic Adhesive Joints

9-19

25. Kotomin, S.V., Borodulina, T.A., Feldstein, M.M., Kulichikhin, V.G. 1999. Squeezerecoil analysis of adhesive hydrohels and elastomer. Polym. Mater. Sci. Eng. 81:425–428. 26. Feldstein, M.M., Lebedeva, T.L., Shandryuk, G.A., Igonin, V.E., Avdeev, N.N., Kulichikhin, V.G. 1999. Polym. Sci., Ser. A 41:867–882. 27. Chalykh, A.E., Chalykh, A.A., Feldstein, M.M. 1999. Effects of composition and hydration on adhesive properties of poly(N-vinyl pyrrolidone)—poly(ethylene glycol) hydrogels. Polym. Mater. Sci. Eng. 81:456–466. 28. Novikov, M.B., Borodulina, T.A., Kotomin, S.V., Kulichikhin, V.G., Feldstein, M.M. 2005. Relaxation properties of pressure-sensitive adhesives upon withdrawal of bonding pressure. J. Adhesion 81:77–107. 29. Feldstein, M., Creton, C. 2006. Pressure-Sensitive Adhesion as Material Property and as a Process, in Pressure-Sensitive Design, Theoretical Aspects. Ed. Benedek I., VSP, Leiden-Boston, pp. 22–67. 30. Sadykova, I. 2007. B.Sci. thesis: Long-time durability of acrylic PSAs, Moscow, State Academy of Fine Chemical Technology (MITHT).

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10 Molecular Nature of Pressure-Sensitive Adhesion 10.1 Toward a Universal Theory of PressureSensitive Adhesion .............................................. 10-2 10.2 Model System to Elicit Supramolecular Structures Responsible for PressureSensitive Adhesion .............................................. 10-4 10.3 Structure–Property Relationships for Model PVP–PEG Hydrophilic Pressure-Sensitive Adhesives ............................ 10-6 Deformation Mechanisms of Model PVP–PEG and Other Adhesives in the Course of Debonding • Tensile Properties of Model PVP–PEG Adhesive Blends • Relationship between Peel Adhesion and the Work of Viscoelastic Deformation up to the Break of the Adhesive Joint • Universal Character of the Viscoelasticity Theory of Pressure-Sensitive Adhesion

10.4 Factors Underlying Pressure-Sensitive Adhesion on a Molecular Scale ....................... 10-14 10.5 Why Do Pressure-Sensitive Adhesives Belong to the Class of Viscoelastic Materials? ............................................................ 10-15 10.6 Fundamental Quantities Outlining the Place of Pressure-Sensitive Adhesives among Other Viscoelastic Polymers .............. 10-16 Correlation of Adhesion with Free Volume • Diff usion Coefficients of Pressure-Sensitive Adhesives • Free Energy for Self-Diffusion and That for Debonding of PVP–PEG Model PressureSensitive Adhesives • Relaxation Times Featured for Pressure-Sensitive Adhesives • Glass Transition Temperatures Responsible for Pressure-Sensitive Adhesion • Correlation of Adhesion with Characteristics of Viscoelasticity • Inconsistency between Small and Large Strain

10-1

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10-2

Fundamentals of Pressure Sensitivity

Mikhail M. Feldstein A.V. Topchiev Institute of Petrochemical Synthesis

10.1

Behaviors: New Consideration of Dahlquist’s Criterion of Tack

10.7 Conclusions ......................................................... 10-37 References ..................................................................... 10-38

Toward a Universal Theory of Pressure-Sensitive Adhesion

For the rational design of new pressure-sensitive adhesives (PSAs), insight into the molecular structures of materials manifesting pressure-sensitive adhesion and the knowledge of quantitative structure–property relationship (QSPR) are keenly needed. The design of adhesives remains mostly empirical because the QSPR are not well known. PSAs exhibit different chemical compositions1,2 and, at first glance, this makes the problem of eliciting the specific features of their molecular structure that provide pressure-sensitive adhesion irresolvable. However, let us recall that PSAs have allied physical properties:3 specified values of glass transition temperatures (Tg),3,4 elasticity modulus (G′),5–7 loss tangent (tan δ),8 solubility parameters,9 and other physical properties. Because a material’s properties influence how its molecular structure functions, similarity in the properties of PSAs signifies closely related structures of PSA materials of various chemical compositions at a supramolecular level. The subject of this chapter is to move toward the emergence of a structure that makes materials tacky and provides the properties of typical PSAs. Adhesion is traditionally defined as the phenomenon in which surfaces of contacting materials are held together by interfacial forces.10 Adhesion may result from the attraction of electrical charges or from molecular forces due to the polarizability of molecules. Tack is the capability of a material to achieve a strong adhesive contact with the surface of a substrate under very light pressure (1–10 Pa) applied over a short time (a few seconds).1 Pressure-sensitive adhesion is a complex and multiform phenomenon that includes tack as a necessary component. However, high tack is a necessary but insufficient condition for pressure-sensitive adhesion.8,11,12 To obtain a high level of adherence, either a liquid-like fluidity or a low elastic modulus of the adhesive material is needed to establish proper contact at the molecular scale with the substrate under applied compressive force. In the stage where the adhesive contact is broken, the elasticity of the adhesive is also of particular importance. This is a characteristic feature of solid materials. A certain degree of elasticity is required to provide a high level of dissipated energy in the course of adhesive bond failure. This liquid–solid duality in the properties of PSAs is difficult to realize in practice when new PSAs are under development. In past years, diverse theories were proposed to explain the driving forces and mechanisms of adhesion. The best known of these theories are the mechanical interlocking, diff usion, adsorption, and electronic theories of adhesion, which were reviewed by Kinloch.13 The mechanical interlocking theory proposes that mechanical keying, or interlocking, of the adhesive into the irregularities at the substrate surface is the main source of intrinsic adhesion. However, the attainment of good adhesion between smooth surfaces exposes the mechanical interlocking theory as not generally widely applicable.

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Molecular Nature of Pressure-Sensitive Adhesion

10-3

The diff usion theory of adhesion, originally advocated by Vojutskii14–17 and further developed by Vasenin18–20 and Chalykh and colleagues, 21–23 states that the intrinsic adhesion of viscoelastic polymers is due to interdiff usion of polymer molecules across the interface. This requires that the macromolecules, or chain segments, possess sufficient mobility and are mutually soluble. The latter requirement may be restated by the condition that they possess similar solubility parameter values. However, when the solubility parameters of the materials are not similar or one polymer is highly cross-linked, crystalline, or below its glass transition temperature, then the interdiff usion is an unlikely mechanism of adhesion. Most recent advances in the diff usion theory of adhesion are reviewed in this book by Creton.24 Deryaguin’s electronic theory of adhesion25 treats the adhesive–substrate joint as a capacitor that is charged due to the contact of two different materials. Separation of the parts of the capacitor leads to a separation of charge and a potential difference, which increases until discharge occurs. Adhesion is presumed to be due to the existence of attractive forces across the electrical double layer. However, it is now established13 that for typical adhesive–substrate interfaces, generated the electrical double layer does not contribute significantly to intrinsic adhesion. Further, any electrical phenomena observed during the joint fracture process arise from the failure event, rather than from intrinsic interfacial forces. Nowadays, the adsorption theory has the widest applicability, whereas each of the other theories may be appropriate only in certain circumstances. The adsorption theory proposes that the materials adhere because of the interfacial interaction forces, which are established between the atoms and molecules in the surfaces of the adhesive and substrate.26 Although for most adhesive–substrate joints the main mechanism of adhesive bond formation is outlined by adsorption theory, this theory cannot be regarded as universal either, because the majority of PSAs adhere to substrates of different chemical nature. All these theories deal with various aspects involved in the attainment of intimate molecular contact at the adhesive–substrate interface. The attainment of such interfacial contact is invariably a necessary first stage in the formation of a strong and stable adhesive bond. The next stage is the generation of intrinsic adhesion forces across the interface, which hold the surfaces of the adhesive and substrate together. Both stages in combination represent the first stage of the complex phenomenon of adhesion, adhesive bond formation, or tack. The second and final stage of the adhesion phenomenon is adhesive joint fracture under applied detaching force that has recently been shown to represent a multistage process in itself.8 Much of the current confusion in the literature concerns the meaning of the term adhesion. According to classic definition noted previously, the phenomenon of adhesion relates rather to instantaneous adherence or tack, a process of adhesive bond formation. Adhesion, therefore, remains an illusive property, and it is suggested that tack is a measure of the capability of the adhesive to form a bond with the substrate.27 Information regarding the magnitude of the intrinsic adhesion forces due to adsorption, diff usion, mechanical interlocking, or electronic mechanisms and the resulting adhesive bond formation may be obtained indirectly, based on geometric factors and surface energy. Direct methods used to measure tack and adhesion (in the classic meaning of the term) rely mainly on measuring the energy required to break the adhesive bond. PSAs are

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10-4

Fundamentals of Pressure Sensitivity

viscoelastic materials that deform under attached debonding force, attaining large strain values. Thus, although the intrinsic adhesion forces affect the strength of the adhesive joint, their contribution is usually significantly obscured by the work of viscoelastic deformation of the adhesive material until the adhesive bond breaks. As demonstrated below, the contribution of viscoelastic deformation of the PSA in the course of debonding prevails against the strength of interfacial interaction forces. The importance of the rheological behavior of PSAs recently received wide recognition. The very name of the phenomenon of pressure-sensitive adhesion implies its rheological nature and the contribution of shear deformation under compressive load to the behavior of PSAs. Thus, although a viscoelasticity theory of pressure-sensitive adhesion seems to be more universal and provides the most productive approach to the comprehension of this phenomenon, it conflicts with the classic definition of adhesion.8

10.2

Model System to Elicit Supramolecular Structures Responsible for Pressure-Sensitive Adhesion

The development of PSAs encounters the problem of obtaining a material that is capable of providing high-strength adhesive joints with various substrates. For this reason, contrary to the classic definition of adhesion, we will always use the term adhesion to mean the actual work necessary to break an adhesive bond, including all dissipative mechanisms. Because adhesion is a macroscopic property that involves numerous processes at a molecular level, eliciting molecular structures underlying the adhesive behavior of materials represents a great challenge. Resolution of this problem is also complicated by the fact that existing PSAs, as a rule, are multicomponent systems, based on elastomers, that are widely varied in their chemical structures. For this reason, elaboration of a model PSA that is suitable for tracing the QSPR becomes a problem of paramount importance. High-molecular-weight, glassy poly(N-vinyl pyrrolidone) (PVP, Mw = 1,000,000; Mn = 360,000 g/mol) has been demonstrated to be easily soluble in low-molecular-weight, liquid poly(ethylene glycol) (PEG, Mw = 400 g/mol),28 yielding single-phase homogeneous blends.29,30 The miscibility of polymers is known to result most frequently from a specific favorable interaction between macromolecules in blends.31 However, as demonstrated by the structures illustrated in Figure 10.1, both PVP and PEG contain only electron-donating groups in monomer units of their backbones, but no complementary proton-donating groups. They are therefore expected to be immiscible. At ambient temperature, PVP is immiscible with high-molecular-weight fractions of PEG (Mw > 600 g/mol)32 and this behavior implies the contribution of proton-donating hydroxyl groups at the ends of PEG short chains to PVP–PEG compatibility.

HO CH2 CH2 O OH

CH2 CH N

n

m

O

FIGURE 10.1 Chemical structure of PVP (left) and PEG (right). m ≈ 10,000; n = 9–10.

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10-5

Molecular Nature of Pressure-Sensitive Adhesion

As demonstrated using Fourier transform infrared (FTIR) spectroscopy, 29,33 PVP’s solubility in liquid short-chain PEG is a result of hydrogen bonding between the terminal OH groups of PEG and the carbonyl C=O groups in PVP repeat units. A schematic view of the proposed structure of the PVP–PEG complex is illustrated in Figure 10.2. Because every PEG chain bears two reactive terminal OH-groups, PEG acts as an H-bonding reversible cross-linker of longer PVP macromolecules. In Figure 10.3, 180° peel adhesion (P) is plotted against the composition of PVP–PEG blends and the content of water absorbed as a vapor from the surrounding atmosphere.11,34

PVP

PEG

FIGURE 10.2 Simplified scheme of the proposed molecular structure of a PVP–PEG H-bonded complex.

Peel force (N/m)

400

300

200

100

2O

10 20 30 PEG c ontent

40 (%)

H

00

(%

)

60 50 40 30 20 10

50

60

0

FIGURE 10.3 Peel adhesion of PVP–PEG blends as a function of PEG concentration and content of absorbed water (percentage of water absorbed per 100% PVP + PEG).

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10-6

Fundamentals of Pressure Sensitivity

Although neither PVP nor PEG-overloaded blends demonstrate any pressure-sensitive adhesion, high adhesion appears in a very narrow range of PEG content (in the vicinity of 36 wt % PEG). Absorbed water affects adhesion in a complicated manner. Dry blends possess no appreciable adhesion. For blends containing less than 36% PEG, the water enhances adhesion, whereas the blends overloaded with PEG (45 wt % and higher) follow an inverse pattern and water sorption inhibits their adhesion. Both PEG and water are good plasticizers and solvents of glassy PVP. 35 They decrease the glass transition temperature of PVP (Tg = 175°C), although the plasticizing effect of PEG is much stronger. The blends containing less than 36% PEG have higher Tg and the plasticizing effect of water promotes adhesion. A PVP blend with 36% PEG is in the viscoelastic state at ambient temperature, and adhesion passes through a maximum at the 12% level of hydration. The blends containing 39% PEG and higher are too fluid-like; the higher the water sorption, the poorer the adhesion. Here, the water acts as a solvent that causes swelling of the PVP–PEG adhesive and dilutes the entanglement structure of the blend, hence obtaining a lower modulus. With the growth of the content of both plasticizers (PEG and water), the mode of adhesive joint failure changes from adhesive to cohesive. The maximum peel strength at 36% PEG corresponds to a transition point.11,34 The peel force behavior illustrated in Figure 10.3 makes the PVP–PEG system a very convenient model from which we are able to elicit the molecular structure responsible for pressure-sensitive adhesion. We have merely to compare the structures and properties of adhesive and nonadhesive PVP–PEG blends. The question, however, is pertinent: taking into account the rather atypical chemical composition of PVP–PEG blends, which has nothing to do with conventional PSAs, which are mainly formulated on the basis of hydrophobic rubbers, is the PVP–PEG system an adequate model? We believe that the common properties determined for the PVP–PEG complex and conventional adhesives might be of particular importance for their adhesive behavior. Consequently, to elucidate general criteria for pressure-sensitive adhesion we must compare the properties of PVP–PEG blends, which provide the best adhesion, with the properties of conventional PSAs and determine any similarities. If common features in the behavior of PVP–PEG and conventional PSAs are of particular importance for the comprehension of necessary conditions for pressure-sensitive adhesion, any distinctions might be due to the contribution of the network of hydrogen bonds, which is only typical for PVP–PEG adhesive hydrogels.

10.3 Structure–Property Relationships for Model PVP– PEG Hydrophilic Pressure-Sensitive Adhesives Both the structure and the properties of the model PVP–PEG adhesive system have received much study in relation to blend composition and the content of absorbed water. The interaction mechanism and the molecular structure have been investigated using FTIR spectroscopy, differential scanning calorimetry (DSC), wide angle x-ray scattering (WAXS), and water sorption techniques. 33,36–41 The stoichiometric

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Molecular Nature of Pressure-Sensitive Adhesion

10-7

composition of PVP–PEG H-bond network complex has been established. 36,39,40 The phase state of PVP–PEG blends has been considered with DSC in a series of research papers. 33,35,42–44 The free volume in PVP–PEG blends is evaluated using positron annihilation.45 Interdiff usion and PVP–PEG miscibility have been characterized with optical microinterference techniques, 30,32,46 whereas self-diff usion of polymer components and absorbed water has been studied using pulsed-field gradient (PFG) nuclear magnetic resonance (NMR).47,48 Rheological and mechanical properties are also described in detail.49–51 All structures and the properties have been related to adhesion and evaluated with peel 34 and probe tack 51,52 tests. The main results were reviewed. 8,11,29

10.3.1

Deformation Mechanisms of Model PVP–PEG and Other Adhesives in the Course of Debonding

In the course of adhesive bond failure under peel or probe tack tests, many PSAs undergo large tensile deformations and form separate fibrils53–58 that elongate up to a few hundred and even thousands of percentages compared with the thickness of the intact adhesive layer. Figure 10.4 illustrates how the debonding process looks in the plane of separation of conventional acrylic (probe tack test, top) and PVP–PEG (36 wt %) adhesive (peel test, bottom).8,11 As a result, the energy expended for the deformation and fibrillation of the adhesive fi lm constitutes by far the largest part of the total energy required for adhesive debonding. The fracture mechanics of adhesive debonding of PVP–PEG PSA in the course of peel testing (Figure 10.4, bottom) involves dramatic stretching and fibrillation of the adhesive layer. The length of the extended fibrils is 10–20 times greater than the thickness of the intact adhesive layer. The fibrils are located throughout the entire width of the adhesive fi lm at nearly equal intervals, implying that the mechanism of fibril nucleation is not random and that the adhesive material is spatially arranged into a three-dimensional network. The entire layer of the adhesive is thus subjected to elongational flow in fibrils, providing resistance to detaching stress and energy dissipation. The failure occurs in the region that is closer to the substrate surface than the backing fi lm. This means that the locus of failure is cohesive.34 The viscoelastic deformation of the adhesive in extension is a major energy-consuming mechanism for all PSAs, as well as adhesive fibrillation and cohesive mode of failure. More comprehensive data on the micromechanics of PSA cavitation and fibrillation can be obtained using the probe tack test data illustrated in Figure 10.5.51 Indeed, as Creton and Fabre demonstrated, 58 the parallel geometry of a flat-end probe is better adapted to examine the details of the debonding mechanisms of soft deformable PSAs than the geometry provided by peel testing. According to Creton and Fabre,58 the microscopic mechanisms involved in the detachment of PSA fi lm from a flat probe can be commonly divided into four parts: 1. Homogeneous deformation before σmax. 2. Cavitation around σmax. These cavities are seen in the microphotographs in Figure 10.5 as light spots.

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10-8

Fundamentals of Pressure Sensitivity

Backing film

Substrate

FIGURE 10.4 Microphotographs of the failure of an adhesive bond in the course of a probe tack (acrylic PSA, top)8 and a peel test (hydrophilic PVP–PEG adhesive, bottom).34 The intact adhesive layer of 0.25-mm thickness is seen in the bottom panel as a light band at the border between the backing film and the PE substrate. (From Feldstein, M.M. and Creton, C., Pressure-Sensitive Design, Theoretical Aspects, Vol. 1, I. Benedek, Ed., VSP, Leiden, 2006; Chalykh, A.A., Chalykh, A.E., Novikov, M.B., and Feldstein, M.M. J. Adhesion, 78(8), 667, 2002.)

3. Rapid lateral growth of the cavities during the steep decrease of nominal σ; then, if there is a plateau in the stress–strain curve, slow growth of these cavities in the direction parallel to the tensile direction; and fi nally 4. Elongation of the walls between cavities (fibrillation). These fibrils eventually either break cohesively or detach from the probe surface, causing complete debonding. As demonstrated by the data in Figure 10.5, the behavior of the PVP–PEG PSA model follows this general description fairly reasonably.51

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10-9

Molecular Nature of Pressure-Sensitive Adhesion

12 10

Force (N)

8 6 4 2 0 0

2

4

6

8

10

12

Strain

FIGURE 10.5 Direct observation of the debonding mechanisms and force-versus-strain curve in the course of probe tack test for a PVP blend with 36 wt % PEG at a debonding rate of 1 µm/s. Each image corresponds to a specific point in the stress–strain curve.. (From Roos, A., Creton, C., Novikov, M.B., and Feldstein, M.M., J. Polym. Sci. Polym. Phys., 40, 2395, 2002. With permission.)

10.3.2

Tensile Properties of Model PVP–PEG Adhesive Blends

Because the major mode of deformation of the adhesive under high-angle peeling is extension (Figure 10.4) and the contribution of shear is negligible,59 it is logical to consider the stress–strain curves under uniaxial extension up to fracture of the model PVP–PEG adhesive blends (Figure 10.6) to compare the behaviors of peel force and the work of deformation of PSA under its uniaxial drawing for PVP–PEG model adhesives. Figure 10.6 illustrates the effect of PEG content upon the stress–strain behavior to break the PVP–PEG blends.49 In general, the type of stress–strain curves obtained for the PVP–PEG adhesive blend in Figure 10.6 is typical of lightly cross-linked highmolecular-weight polymers.60 PEG is a good plasticizer for PVP and the addition of PEG results in increased elongation at break (ε b). With the increase in PEG concentration, the value of ε b increases linearly (Figure 10.7). For PVP blends containing <36% PEG, the ultimate tensile strength, σ b, is comparatively high and practically unaffected by PEG content. In contrast, at PEG concentrations >36% the σ b value declines rapidly with PEG amount (Figure 10.7). The transition from ductile to tight deformation type occurs in a fairly narrow range of PEG content, between 36 and 34% PEG (Figure 10.6). In adhesive behavior, this range of PEG concentration corresponds to the transition from the fibrillar type of adhesive joint failure (36% PEG and higher) to the brittle-like fracture without fibrillation of the adhesive. 34,51 The area under the

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10-10

Nominal stress (MPa)

Fundamentals of Pressure Sensitivity

1.0

31%

0.8

34%

0.6 36%

0.4

39%

0.2 41% 0.0 0

4

8

12

16

20

24

28

Tensile strain

FIGURE 10.6 Tensile stress–strain curves to break the PVP–PEG blends, containing 31, 34, 36, 39, and 41 wt % PEG-400 at 8–9% degree of hydration. The drawing rate is 20 mm/min. (From Novikov, M.B., Roos, A., Creton, C., and Feldstein, M.M., Polymer, 44(12), 3559, 2003. With permission.)

28

100 εb

24

εb, σb (MPa)

wb

16 12

60

σb

40

W b (MJ/m3)

80

20

8 20

4

0

0 30

32

34

36

38

40

42

PEG content (%)

FIGURE 10.7 The total work of viscoelatic deformation to break the PVP–PEG fi lm, Wb, the ultimate tensile strength, σ b, and the break elongation, ε b, as a function of PEG concentration in blends. The extension rate is 20 mm/min. (From Novikov, M.B., Roos, A., Creton, C., and Feldstein, M.M., Polymer, 44(12), 3559, 2003. With permission.)

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10-11

Molecular Nature of Pressure-Sensitive Adhesion

600 100 550

90 80

450

70

400

60

350

50

300

40

W (MJ/m3)

P (N/m)

500

30

250

20 200 10 30

32

34

36

38

40

42

PEG (%)

FIGURE 10.8 Effects of PVP–PEG composition on 180° peel force, P, and the work of viscoelastic deformation of the adhesive fi lm up to break, W, under uniaxial extension. The peel and drawing rates are 20 mm/min. (From Feldstein, M.M., Developments in Pressure-Sensitive Products, 2nd ed., I. Benedek, Ed., CRC-Taylor & Francis, Boca Raton, 2006.)

stress–strain curve that defines the value of the total work of viscoelastic deformation to break the PVP–PEG adhesive blends, Wb, correlates well with both peel34 and probe tack 51 adhesion and reveals a maximum at 36% PEG concentration for the blend demonstrating the best adhesion (Figure 10.8).

10.3.3 Relationship between Peel Adhesion and the Work of Viscoelastic Deformation up to the Break of the Adhesive Joint Taking into account the importance of tensile strain in adhesive bond failure of various PSAs (Figure 10.4), we now consider the relationship between peel adhesion and the work of viscoelastic deformation of model PVP–PEG adhesive blends of various compositions, which provide different levels of adhesion. This relationship is illustrated in Figure 10.8. An evident correlation between peel adhesion and the work of viscoelastic deformation of the adhesive, illustrated in Figure 10.8, signifies the controlling contribution of the process of viscoelastic deformation to adhesive performance. By replotting the values of peel force versus the work of deformation to break the PVP–PEG model PSAs, we obtain an insightful and illustrative relationship presented in Figure 10.9. Analysis of the relationship allows us to gain insight into the factors governing PSA behavior at the most fundamental, molecular level. First, the data in Figure 10.9 establish a demarcation line between the adhesive and nonadhesive PVP–PEG blends. Both PEG-overloaded (41% PEG) and underloaded (31% PEG) blends demonstrate the same, comparatively moderate adhesive capability,

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10-12

Fundamentals of Pressure Sensitivity

800 SIS

Peel force (N/m)

700 600 36%

500 400

39%

300

34% 41% PEG 31%

200 30

40

50

60

70

80

90

100

110

120

Work to break (MJ/m)

FIGURE 10.9 The contribution of the work of viscoelastic deformation of the PVP–PEG model adhesives and SIS-based PSA (Duro-Tak 34-4230, National Starch & Chemical Corp.) into their peel adhesion toward the PET substrate. The contents of PEG in the blends with PVP (in wt %) are indicated. (From Feldstein, M.M., Developments in Pressure-Sensitive Products, 2nd ed., I. Benedek, Ed., CRC-Taylor & Francis, Boca Raton, 2006.)

but only the latter blend belongs to the class of PSAs, whereas the former is, in essence, a tacky liquid. To be a PSA, a tacky material should dissipate an appreciable amount of energy in the course of debonding, and the value of the work of viscoelastic deformation to break the tacky fi lm under its uniaxial extension may be taken as a measure of the dissipated energy (60 MJ/m3 and higher). Second, the linear relationship between the peel force and the work of deformation in Figure 10.9 has, most likely, a general character, spanning not only hydrophilic PVP– PEG, but also hydrophobic rubber-based PSAs. Indeed, the values of peel adhesion and deformation work for traditional PSAs, based on a styrene–isoprene–styrene (SIS) triblock copolymer, are aligned with those for PVP–PEG adhesives. The linear relationship in Figure 10.9 can be described by Equation 10.1, b

P
kbl ∫   d

(10.1)

0

where b and l are the width and thickness of the adhesive fi lm, σ and ε are the tensile stress and relative elongation, εb is the maximum elongation of the film at the break, and k is a constant that takes into account the contributions of backing fi lm deformation and interaction between the adhesive and the substrate. If we compare the peel adhesion of various adhesives using the same backing fi lm and a standard high-energy substrate, we can accept k ≈ 1. Assuming further that the deformation of the adhesive fi lm in the

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Molecular Nature of Pressure-Sensitive Adhesion

10-13

course of both debonding and uniaxial drawing follows the linear elastic law, Equation 10.1 can be written as P


b  l  b2 E

(10.2)

where the σ b is the ultimate tensile strength and E is an approximate tensile modulus of the adhesive material. For a PSA, this is not a bad approximation because they usually soften and then harden at large strains. Equation 10.2 holds for PSAs in the linear elastic region of deformation, whereas for the PVP–PEG blend the deviation of the measured relationship from the law presented by Equation 10.2 was earlier shown to achieve 20%.34 Equation 10.2 is similar to the well-known Kaelble equation,60 P


b  l  f2 4E

(10.3)

where σf is a critical value of the ultimate stress upon fracture of PSA material under debonding from a substrate with a fixed rate. The implication of the similarity of Equations 10.2 and 10.3 is that the Kaelble equation, Equation 10.3, holds for any type of PSA, including the hydrophilic PVP–PEG. Thus, the rule described by Equations 10.2 and 10.3 is universal.

10.3.4

Universal Character of the Viscoelasticity Theory of Pressure-Sensitive Adhesion

Equation 10.2 can be easily modified to express peel adhesion, P, as an explicit function of the relaxation time, τ, and the self-diff usion coefficient, D, of a PSA polymer. Indeed, let us assume in the first approximation that a PSA represents a viscoelastic material that can be described with a Maxwell model characterized with a single apparent relaxation time, τ, and a microviscosity (or monomer–monomer friction coefficient of polymer chain), η. Taking into account that, according to the Maxwell model, E = 3η/τ, we obtain P
b  l

 2 b 3

(10.4)

The viscosity of the Maxwell model can then be substituted by the classic Einstein expression,61 


kT DaN

(10.5)

where N is a number of monomer units of size a in a segment of polymer chain and D is the self-diff usion coefficient of the polymer segment. The substitution of obtained values into the Equation 10.4 yields P
b  l 

aD 2  b 3kT

(10.6)

where a represents the size of the polymer chain segment, k is the Boltzmann constant, and T is temperature.

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10-14

Fundamentals of Pressure Sensitivity

Equation 10.6 is, of course, only qualitatively illustrative, because it makes many crude approximations, including ignoring the existence of the spectrum of relaxation times. It is inappropriate for quantitative calculations of peel force, because it includes immeasurable terms like a (the size of the diff using polymer segment). Nevertheless, it predicts qualitatively the significance of diff usion and relaxation processes (both of which require molecular mobility) for the adhesive behavior of polymers when their debonding is dominated by the formation of fibrils. Equation 10.6 was derived on the basis of the analysis of the deformation contribution to peel adhesion without resorting to the so-called diff usion theory of adhesion.14 Thereby, the rheological approach based on the analysis of viscoelastic deformation of the adhesive material under the debonding process, described here, has more universal character than others mechanisms of adhesion considered previously in this chapter.

10.4

Factors Underlying Pressure-Sensitive Adhesion on a Molecular Scale

According to Equation 10.6, pressure-sensitive adhesion requires a coupling of high molecular mobility, embedded by the high value of the self-diff usion coefficient of the adhesive polymer segment, D, with long-term relaxation processes outlined by large values of relaxation times, τ, and a high cohesive strength of the adhesive polymer, expressed in terms of the ultimate tensile stress upon break of the stretched adhesive under uniaxial drawing, σ b. High molecular mobility is a manifestation of large free volume. A fundamental quantity that underlies a high value of the self-diff usion coefficient at the molecular level is the fraction of free volume, fv ,62  B D
A  exp    fv 

(10.7)

where A and B are constants. A specific feature of all PSAs is that they should combine a high energy of cohesive interaction with a large free volume. Most commonly, the strong cohesive interaction between macromolecules causes a drastic decrease in free volume, which explains why pressure-sensitive adhesion is a comparatively rare phenomenon. In the model PVP–PEG system these apparently confl icting properties are nevertheless conciliated due to the location of reactive hydroxyl groups at the opposite ends of PEG chains of appreciable length and flexibility (see the scheme in Figure 10.2). In other PSAs of different chemical compositions, these confl icting properties may be conciliated in a variety of alternative ways. High cohesion energy may result from intermacromolecular cross-linking (both covalent and noncovalent and the entanglements of long chains), the addition of tackifiers with high Tg, or to the hydrophobic association of side groups of polymer chains. Large free volume is most frequently provided by the usage of elastomers with a low glass transition temperature, Tg.

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10-15

Molecular Nature of Pressure-Sensitive Adhesion

The glass transition temperature relates to the energy of cohesion and free volume by the equation63 Tg
0.445

z  D0 R

(10.8)

where z is the coordination number, a value that is inversely proportional to the free volume, and 〈D 0〉 is the total interaction energy of atoms forming a polymer segment. In acrylic PSAs containing neutralized carboxylic groups, the increase in free volume may result from electrostatic repulsion of the carboxylate anions. In un-cross-linked polyisobutene (PIB) PSA, cohesive strength is a consequence of the presence of a network of long-chain entanglements of high-molecular-weight fraction and is also due to the van der Waals interaction between nonpolar functional groups. In SIS-based triblock copolymers and other thermoplastic elastomers, cohesion is provided by the physical cross-links of high-Tg polystyrene blocks, whereas the free volume is provided by blocks of lower molecular weight polymers. The combination of high cohesion energy and large free volume, featured for all PSAs, is also embedded in such fundamental characteristics of adhesive materials as specific values of solubility parameters, δs, defined as the cohesive energy density or the ratio of the energy of cohesion to the total volume,  H v  RT  s
   Vm

1

2

(10.9)

where ∆Hv is the molar heat of vaporization, R is the gas constant, T is the temperature (K), and Vm is the molar volume. The heat of vaporization, ∆Hv, is the direct measure of cohesion energy because it is defi ned as the total amount of energy needed to overcome intermolecular attractive forces and transfer a molecule to the vapor phase, in which no intermolecular interaction occurs. The solubility parameter relates to the enthalpic component of the Flory interaction parameter χ between monomer units of two polymer chains i and j (or between a polymer and a solvent) by the equation ij


Vm (i   j)2 RT

(10.10)

The smaller the difference between the solubility parameters of an adhesive and a substrate, the greater the peel adhesion.9

10.5

Why Do Pressure-Sensitive Adhesives Belong to the Class of Viscoelastic Materials?

As Equation 10.6 predicts, high adhesion requires a high value of cohesive strength (σ b), high diff usion coefficient (D), and long relaxation time (τ). Although both the diff usion coefficient and the relaxation time are measures of molecular mobility, as illustrated in the scheme in Figure 10.10, they do vary in opposite directions under the transition

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10-16

Fundamentals of Pressure Sensitivity

Glasses

Viscoelastic materials

Liquids

τ D

σb

FIGURE 10.10 Directions of varying the values of relaxation time, τ, self-diff usion coefficient, D, and ultimate tensile strength, σ b, under the transition from glassy to liquid state.

from glassy polymer to viscous liquid, for example, with the increase of PEG plasticizer content in blends with PVP. Indeed, the longest relaxation times are featured for glasses (years and centuries), whereas low-molecular-weight liquids relax almost instantaneously. In contrast, the lowest diff usion coefficients are observed for glasses, whereas the highest diff usion coefficients are demonstrated in liquids and gases. According to Equation 10.6, maximum peel strength, P, relates to the maximum magnitude of the τD product. Evidently, this product achieves its maximum magnitude in a certain range of values of relaxation time and diff usion coefficient, which are intermediate between those inherent for liquids and glasses. The materials coupling the properties of the liquids and the solids are in a viscoelastic state, which is why all PSAs are viscoelastic materials.

10.6

Fundamental Quantities Outlining the Place of Pressure-Sensitive Adhesives among Other Viscoelastic Polymers

Equation 10.6 contains the product of the contribution of high cohesion energy and large free volume, whereas such fundamental characteristics of materials as the glass transition temperature (Equation 10.8), the solubility parameter (cohesive energy density, Equation 10.9), or the change in heat capacity at Tg(∆Cp) represent the ratios of cohesion energy and free-volume magnitudes. A question arises regarding what values of these fundamental quantities are typical for PSAs and how we can measure these two contributions separately. What magnitudes of diffusion coefficients (D), relaxation times (τ), and ultimate tensile strength under uniaxial drawing of adhesive films (σ b) are in favor of high adhesion? The following discussion is intended to provide fresh insight into these issues.

10.6.1

Correlation of Adhesion with Free Volume

The study of free volume in polymer systems is of great importance because the size and concentration of unoccupied spaces are thought to affect physical properties, such

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10-17

Molecular Nature of Pressure-Sensitive Adhesion

8.0

600

7.5

500

7.0

400

6.5

300

6.0

200

5.5

100

5.0

P (N/m)

f v (%)

as molecular transport, viscoelasticity of polymers, and mechanical, adhesion and other physicochemical properties of the polymers. As the free volume or volume fraction increases or the density of the polymer decreases, the viscoelasticity of the polymer increases. There must be a certain available free volume for a certain size molecule to diff use through. The transition from a glass to a rubber or solvent-swollen polymer can change the rate of diff usion by as much as 10 orders of magnitude, depending on the amount and the size of the penetrants. The free-volume concept was developed to describe the mobility of the polymer and the molecular transport occurrence when a molecule moves into holes with a size greater than some critical volume. The transport process has been described in terms of a redistribution of the local free volume arising from the cooperative motion of neighboring atoms. By the term free volume, we mean the microscopic free volume resulting from the thermal motion of the atoms and molecules that leads to the occurrence of fluctuations in molecular concentration on a nanoscopic scale. Direct experimental measurement of the fluctuational free volume in polymer composites requires the use of costly and not easily accessible techniques. Nevertheless, the free volume in model PVP–PEG blends has been measured using positron annihilation lifetime spectroscopy.45 Figure 10.11 illustrates a comparison of the behaviors of free volume and peel adhesion as functions of the composition of PVP–PEG blends. Fractional free volume ( fv) grows smoothly with PEG concentration in blends from a value of 5.15 vol % for glassy PVP containing 10 wt % absorbed water to 7.02% for a PVP blend with 43 wt % PEG-400. Values of fractional free volume between 6.0 and 8.0% are reported for all polymers in the viscoelastic state.64 The best adhesion is observed in PVP–PEG blends with a free volume fraction between 6.4 and 7.0 vol %. In this range, the average radius of nanoscopic holes has been demonstrated to increase from 2.95 ± 0.01 to 3.08 ± 0.01 Å, whereas their volume rises smoothly from 107.6 ± 0.96 to 122.26 ± 1.09 Å3.

0 0

10

20

30

40

50

PEG (wt %)

FIGURE 10.11 The fraction of free volume ( fv, %), and peel adhesion (P, N/m) of PVP blends with various amounts of PEG-400 at 100% relative humidity of the surrounding atmosphere.

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10-18

Fundamentals of Pressure Sensitivity

The PVP–PEG (36 wt %) blend demonstrating maximum peel adhesion is characterized by a free volume fraction of 6.6 vol %, a hole radius of 3.01 ± 0.01 Å, and a volume of 114.77 ± 1.09 Å3. Currently there is a lack of information regarding the free volume in PSAs of other chemical compositions, but taking into account that in the terms of free volume the PVP–PEG model PSA is a typical elastomer, we can assume that other PSAs possess similar free volumes.

10.6.2 Diffusion Coefficients of Pressure-Sensitive Adhesives The diff usion coefficients of various PSA polymers have been reported to be of the order of magnitude of 10−9 to 10−14 cm2/s (or 10−13 to 10−18 m2/s), which Vojutskii14 argues is completely adequate for the formation of an intrinsically strong interface between a PSA and a polymer substrate over a contact time of only a few seconds. As demonstrated in previous chapters of this book, 22,24 for proper characterization of the formation of an adhesive joint the PSA–substrate interdiff usion coefficient is mostly relevant. However, as Equation 10.6 demonstrates, the diff usivity of the adhesive polymer contributes to the amount of mechanical energy necessary to break the adhesive fi lm in the course of stretching that accompanies the process of adhesive bond fracture (see Figure 10.4). Sufficiently high molecular mobility, embedded in the magnitude of the diff usion coefficient, is needed to endow the adhesive material with high compliance and the capability to develop large tensile strain. As far as we know, the role of adhesive polymer diff usivity has not been discussed in adhesion science. The self-diff usion coefficients in model PVP–PEG adhesives have been evaluated with a PFG NMR method as functions of PEG and the absorbed water contents.47,48 In PFG NMR experiments, the incoherent intermediate structure function, Sinc(q, t), of the protons in a system, given by spin echo attenuation, is measured as a function of the generalized scattering vector, q = γδg (where γ is the gyromagnetic ratio of the proton, δ is a fi xed pulse width, and g is the magnitude of the field gradient pulses). The curves of spin echo attenuation are fitted by Equation 10.11, Sinc (q, t )
p1 exp(q 2tD1 )  p2 exp(q 2tD2 )

(10.11)

where p1 are the fractions (populations) of resonating species possessing the self-diff usion coefficient D1. For the PVP–PEG blend that contains 36 wt % PEG-400 and exhibits the best adhesion, only a single population of diffusing species (D = 2.3 10−13 m2/s) was observed 2 days after blend preparation. Within the following 32 days, the diff usion decay evolved into a biexponential behavior with a slower self-diff usion coefficient of 1.5 10 −13 m 2/s and p = 0.87.65 After this time, the diff usion properties of the system were unchanged. Such an aging process is typical for self-assembling supramolecular structures involving the hydrogen bonding and the stoichiometric complex formation.66 The established variation in molecular mobility has only a very slight effect on adhesion. The implication is that the best adhesion in the PVP–PEG system relates to the values of the self-diff usion coefficient ranging from 1.5 10−13 to 2.3 10−13 m2/s.

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10-19

Molecular Nature of Pressure-Sensitive Adhesion

To what component of the PVP–PEG blend may the established self-diff usion coefficient be attributed? The binary PVP–PEG blend contains three components: high-molecularweight PVP with an extremely low self-diff usion coefficient, a short-chain PEG with a comparatively high diff usion coefficient, and the product of their interaction—the stoichiometric H-bonded network PVP–PEG complex, whose formation underlies the occurrence of pressure-sensitive adhesion. The PVP–PEG blends may be also treated as concentrated solutions of glassy PVP in liquid PEG-400. Two populations of diff using molecules in the PVP–PEG system were detected. As the PEG concentration in blends decreases, tending to a stoichiometric complex composition ([PEG]:[PVP] = 0.15), the portion of slow-diff using protons, p, approaches unity (Figure 10.12). Such behavior demonstrates that the D value of the slow-diff using component characterizes the segmental mobility in the PVP–PEG complex. As [PEG]:[PVP] → 1, p → 0. Within this composition range, only the fast-diff using component (PEG) is observed. This area of the composition may be defined as a solution of the stoichiometric PVP–PEG complex in PEG. However, at [PEG]:PVP > 1, the fraction of slow-diff using component increases again. This effect may be treated as increasing involvement of PEG chains in the motion of PVP segments, whose self-diff usion coefficient increases in dilute solutions, approaching a value of D ≈ 10−12 m2/s. Figure 10.13 compares the peel adhesion (P) of the PVP–PEG model adhesives with their diff usion behavior expressed in terms of the self-diff usion coefficient of slowly diff using component, measured using PFG NMR techniques,47,48 and the partial diff usion coefficient of PEG-400 in blends with PVP (DPEG ). The latter has been evaluated

[PEG-400]/[PVP] 0.15

1.0

−11.2

0.9

−11.4

0.8 Dfast

log D (m2/s)

−11.6

0.7

−11.8

0.6 Dslow

−12.0

0.5

−12.2

P

−12.4

0.3

pslow

−12.6

0.2

−12.8

0.1

−13.0

0 30

40

50

60

70

80

90

100

PEG-400 (wt %)

FIGURE 10.12 The effect of PEG content (wt %) (bottom axis) in terms of the number of PEG molecules per one PVP repeating unit, [PEG-400]:[PVP], top axis, on the self-diff usion coefficient (D) and population (p) of the fast and slow diff using components at 20°C. The diff usion time is 103 ms. The composition in which the stoichiometric PVP–PEG complex is fully formed and that demonstrates best adhesion is denoted by the dashed line on the left.

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10-20

Fundamentals of Pressure Sensitivity

600

1E-11

550 DPEG

500

1E-12 D (m2/s)

Dslow

450 400 350

1E-13

P (N/m)

P

300 250 200

1E-14 20

30

40

50

60

70

80

90

100

PEG (%)

FIGURE 10.13 Partial diff usion coefficient (D PEG) of PEG-400 in blends with high-molecularweight PVP of different compositions, the self-diff usion coefficient of the slow diff using component, and peel adhesion (P) at room temperature.

from the values of the PVP–PEG interdiff usion coefficient (D v) with optical microinterferometry.30,32 DPEG relates to D v by the equation21 DPEG


Dv

PVP

(10.12)

where φPVP is the volume PVP fraction in the binary blend. As established, the values of DPEG exactly meet those of the self-diff usion coefficient of the fast-diff using component by PFG NMR (Figure 10.12). Thus, the fast-diff using component in PVP–PEG blends most likely represents the PEG that is uninvolved in the network complex with PVP. As follows from the data presented in Figure 10.13, the self-diff usion coefficient of PEG-400 within the H-bonded PVP–PEG network at 36% PEG concentration in the blend is DPEG = 1.3 10−13 m2/s. The independent data of the microinterferometry and PFG NMR are in good agreement and outline diff usivity of the model PVP–PEG adhesive that provides the best adhesion on the border between 10−12 and 10−13 m2/s. Such high self-diff usion coefficients are most likely due to low molecular weight and high flexibility of PEG short chains. Needless to say, such high diff usivity is also favorable for fast adhesive bond formation. Thus, the liquid-like diff usion mobility of PSAs is needed not only to provide deep penetration of the PSA polymer into a substrate under slight pressure, but also to develop large tensile strain of the adhesive layer under a detaching force. As Equation 10.6 predicts, high adhesion is associated with high diff usion coefficient values. As direct measurements of diff usivity in the PVP–PEG model PSA demonstrate, the PEG self-diff usion coefficient in this PSA relates to the border between elastomers and viscous liquids, ~10−13 m2/s.

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10-21

Molecular Nature of Pressure-Sensitive Adhesion

10.6.3

Free Energy for Self-Diffusion and That for Debonding of PVP–PEG Model Pressure-Sensitive Adhesives

Analysis of the values of self-diff usion coefficients, which are inherent in PSAs, provides only imperfect comprehension of the contribution of diff usion mobility to adhesion strength. Much like pressure-sensitive adhesion, the value of the diff usion coefficient is dictated by the ratio of cohesion energy to the free volume available for diff usion. Whereas the free volume facilitates the diff usion, the forces of intermolecular attraction decelerate it. For closer characterization of diff usive mobility underlying deformation of PSA material under the debonding process, the energetic component of the self-diff usion, the free activation energy for the diff usion, must be taken into consideration. The compositional profi le of PEG self-diff usion activation energy allows defi nition of the borders between the different stages of PVP dissolution in PEG (Figure 10.14). The fi rst stage of the dissolution process (under low PEG content) is PVP plasticization and the formation of a stoichiometric hydrogen-bonded complex, which results in a gradual reduction of the activation energy for PEG self-diff usion. The second stage of the dissolution process (at higher PEG concentrations) is defi ned as a gradual swelling of the H-bonded network in an excess of liquid PEG. Th is stage involves the emergence of mobile PEG in a blend, whose self-diff usion is hampered as indicated by the plateau on the plot of activation energy between 40 and 60% of PEG-400. At higher PEG contents the disentanglement of long PVP chains occurs, and blends containing more than 70% of PEG represent the PVP solution in PEG. Within these blends all the PEG macromolecules demonstrate the activation energy for self-diff usion inherent in the bulky PEG. As follows from Figure 10.14, the maximum adhesion appears as the blend composition (36 wt % PEG) coincides with the composition of the stoichiometric PVP–PEG complex. In this blend, the magnitude of the free energy for PEG self-diff usion is

400 Activation energy Peel force

70

350

60

300

50

250

40

200

30

150

20

100

10

50

0 0.2

0.4

0.6

0.8

Peel force (N/m)

Activation energy for self-diffusion (kJ/mol)

80

0 1.0

PEG weight fraction

FIGURE 10.14 Relationships between PEG content in the blends with PVP, free energy for selfdiff usion, and peel adhesion.

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10-22

Fundamentals of Pressure Sensitivity

55.3 kJ/mol. As the activation energy increases to 69.7 kJ/mol with the decrease in PEG concentration to 30 wt %, the locus of adhesive joint failure of the PVP–PEG PSA with PE substrate changes from miscellaneous (in the maximum of peel adhesion) to adhesive. In contrast, at higher PEG concentrations (40–60% PEG) the activation energy varies between 52.3 and 48.2 kJ/mol. For these blends the locus of failure is always cohesive. Because debonding occurs after a certain time under a fi xed tensile force, the time, t*, required to rupture the adhesive bond characterizes the durability of the joint. The durability of an adhesive joint is a fundamental quantity that characterizes pressure-sensitive adhesion, as described in Chapter 9.67 Temperature dependence of the logarithm of durability follows the Arrhenius relationship fairly reasonably, allowing evaluation of the activation energy for the fracture process of PVP–PEG adhesives under detaching stress. The latter value is plotted versus the composition of PVP–PEG adhesives in Figure 10.15, along with the durability of the adhesive joint and the activation energy for PEG self-diff usion, determined using the PFG NMR method.47,48 As the data in Figure 10.15 demonstrate, the activation energy for adhesive bond failure follows the pattern of the activation energy of the self-diff usion coefficient, climbing sharply with a decrease in PEG concentration below 36%, when maximum adhesion has been achieved. For a blend with maximum adhesion, the activation energy for adhesive debonding is 10–15 kJ/mol higher than the activation energy for self-diff usion. The translational mobility measured in terms of the self-diff usion coefficient takes an appreciable part of the activation energy for adhesive debonding in the blends, which exhibit a miscellaneous (adhesive–cohesive) mechanism of adhesive joint failure.34 For low PEG weight fractions, the activation energy of the debonding process reaches a value of 210 kJ/mol. Within this composition range the lack in 5000 Activation energy (kJ/mol)

200

4000

Adhesive durability 3000

150

2000 100 1000 50

Adhesive durability (s)

ED self-diffusion Ea adhesive debonding

0 0.2

0.4

0.6

0.8

1.0

PEG weight fraction

FIGURE 10.15 Relation of adhesive joint durability and activation energy for adhesive debonding and for PEG self-diff usion to the composition of PVP–PEG adhesive blends. (From Feldstein, M.M., Developments in Pressure-Sensitive Products, 2nd ed., I. Benedek, Ed., CRC-Taylor & Francis, Boca Raton, 2006.)

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Molecular Nature of Pressure-Sensitive Adhesion

10-23

molecular mobility makes a cohesive fracture of the joint impossible and the fracture proceeds mainly by an interfacial mechanism of crack propagation. If one examines the monomer unit level, the activation energy for self-diff usion, ED, should be a function of the product of the cohesive energy density (CED) and the volume of a mole of cylindrical cavities required for diff usion of a polymer chain segment of diameter d over a jump length λ, ED


d 2 CED
(1 f v )Ec 4

(10.13)

where Ec is the cohesive energy and fv is the fractional free volume in the polymer. Thus, a phenomenological analysis of the relationship between pressure-sensitive adhesion and the molecular mobility of the PSA, outlined by Equations 10.6 and 10.13, suggests that the two important parameters controlling pressure-sensitive-adhesion and diff usion are the energy of favorable intermolecular interactions (cohesion) and molecular free volume. The difference between adhesion and diff usion is rather quantitative: adhesion occurs only within a very narrow range of the ratio of cohesion energy to free volume, and in this case both the former and the latter magnitudes are to be high. In contrast, diff usion takes a place at any value of cohesion energy and free volume if only the gradient of concentration is available.

10.6.4 Relaxation Times Featured for Pressure-Sensitive Adhesives Diff usion and relaxation represent two sides of the same phenomenon—the molecular mobility of a material. High-diff usion coefficients (in liquids) are always associated with short relaxation times, whereas low-diff usion coefficients (in solids) relate to longer relaxation times (Figure 10.10). Relaxation is a material response to the perturbation of equilibrium structure caused by a temperature jump, magnetic impulse, or (as in the case of pressure-sensitive adhesion) the application of mechanical bonding or detaching stress. In the process of adhesive joint failure, relaxation is a driving force that is directed to the recovery of equilibrium material structure. In the process of relaxation, macromolecules or their segments change their positions, tending to initial, equilibrium structure. Diff usion is a process of spatial drift of molecules due to their kinetic motion. In this connection it is obvious that the relaxation process involves the diff usion as one of the main mechanisms, leading to the recovery of the equilibrium structure. Because pressure-sensitive adhesion is a material response to applied mechanical stress, the role of relaxation in providing both good adhesive contact and adhesive joint strength is quite significant. Paradoxically, the significance of the relaxation processes for pressure-sensitive adhesion remains poorly understood, although this investigation does not require sophisticated methods such as the techniques employed for the study of self-diff usion. To some extent, this can be explained by the abundance of information on the relaxation of elastomers, a family to which all PSAs belong, and recognition of the role of relaxation in well-known effects of bonding time and debonding

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10-24

Fundamentals of Pressure Sensitivity

velocity on the strength of adhesive joints.6 However, Equation 10.6 poses at least two new questions: 1. Are longer relaxation times of special significance for good adhesion? 2. What is the range of relaxation times that provides high adhesion strength of PSAs? Because the values of both the relaxation times and the moduli depend on the type of deformation of adhesive fi lm, which is different under compressive bonding force and at the stage of debonding, more extensive research is necessary before the significance of the relaxation processes for the adhesion can be properly established. For a detailed discussion of this problem, see Chapter 11.68

10.6.5

Glass Transition Temperatures Responsible for Pressure-Sensitive Adhesion

Equation 10.8 indicates63 the glass transition temperature is another fundamental quantity that can be employed to describe the balance of cohesion energy versus free volume in PSAs. As follows from the data listed in Table 10.1, typical PSAs possess glass transition temperatures (evaluated with DSC at a heating rate of 20°/min) ranging between −10 and −113°C.69 The maximum Tg values in this range have been found for acrylic PSAs (between −10.7 and −37.3°C), whereas the minimum Tg values were reported for silicone adhesives (−112.5°C). PIB adhesives occupy intermediate range (around−61°C). All the PSAs (except thermoplastic block copolymer elastomers) demonstrate a single glass transition temperature that certifies their homogeneity. Because the chemical composition of a model PVP–PEG adhesive has nothing to do with typical PSAs, the question now arises of whether the Tg values of PVP–PEG adhesive blends fall within the same range. TABLE 10.1 Glass Transition Temperatures and Relevant Values of Heat Capacity Jumps at the Glass Transition Featured for Typical Pressure-Sensitive Adhesives PSA Acrylic, DuroTak 387-22-87 Acrylic, DuroTak 87-900A Acrylic, DuroTak 180-129a Acrylic, DuroTak 180-129a 0-2 PIB Silicone, Bio-PSA Acrylic, Gelva 3011

CRC_59378_C010.indd 24

Heat Number

Тg (°С)

∆Ср ⋅ (J/g K)

1 2 1 2 1 2 1 2 1 2 1 2 1 2

−29.9 −30.8 −10.7 −16.4 −34.2 −37.3 −30.4 −31.8 −60.6 −60.6 −110.8 −112.5 −30.9 −32.5

0.27 0.22 0.22 0.35 0.17 0.22 0.36 0.23 0.28 0.31 0.16 0.21 0.35 0.30

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10-25

Molecular Nature of Pressure-Sensitive Adhesion

200

400 Upper Tg Lower Tg Tm Peel force

Tg,Tm (°C)

100

300

200

50 0

100

Peel force (N/m)

150

−50 0

−100 0

20

40

60

80

100

PEG (wt %)

FIGURE 10.16 Peel adhesion and phase state of PVP–PEG systems. Tg is the glass transition temperature and Tm is the melting temperature of PEG in blends with PVP. (From Feldstein, M.M., Developments in Pressure-Sensitive Products, 2nd ed., I. Benedek, Ed., CRC-Taylor & Francis, Boca Raton, 2006.)

Figure 10.16 compares adhesive behavior with the phase state of PVP–PEG blends.11 The PVP–PEG system is plausibly among the first and most illustrative examples of miscible single-phase polymer blends, which reveal two distinct relaxation transitions. These transitions are seen on DSC scans as the heat capacity jumps, resembling glass transitions, and the corresponding glass transition temperatures demonstrate coherent compositional behavior.40 The behavior of the upper Tg in PVP–PEG blends obeys the rule of homogeneous PVP–PEG mixing or glassy PVP dissolution in liquid PEG due to PEG chains H-bonding to PVP through one terminal group only.40 This un-cross-linked and labile PVP–PEG complex requires a small amount of heat for dissociation and is comparatively unstable. In contrast, lower Tg is due to the formation of a hydrogenbonded PVP–PEG network complex (gel), which behaves like a new chemical entity.38–40 In this stoichiometric complex, nearly 20% of PVP repeat units are cross-linked by PEG terminal OH-groups (via H-bonding). The lifetime of the cross-linked PVP–PEG complex is much longer due to multiple hydrogen bonds involved in its formation. Another example of a single-phase system with two Tg is partly denaturated proteins, where a lower Tg relates to glass transition and an upper Tg corresponds to the relaxation of denaturated protein.70 The data presented in Figure 10.16 demonstrate that the Tg values for adhesive PVP–PEG blends range between –55 and –71°C for blends containing 12 wt % of absorbed water.40 The effects of PEG and absorbed water contents on the Tg in adhesive PVP–PEG blends is illustrated in Figure 10.17. If the amount of absorbed water in the PVP–PEG adhesive is from 4 to 8 wt %, the Tg values have been found to vary from –45 to –52°C (Figure 10.17).35 Thus, the Tg values for the model PVP–PEG hydrophilic adhesives represent no exceptions to the rule that was established previously for typical, hydrophobic PSAs.

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10-26

Fundamentals of Pressure Sensitivity

PVP dry 150

Tg (°C)

100

PVP hydrated

50 0 −50 0 20

PEG

40 PE

G

60 (%

)

5

80 100

0

15 10 %)

( H 2O

FIGURE 10.17 The glass transition temperature of PVP–PEG adhesive blends as a function of PEG and water content. (From Feldstein, M.M., Kuptsov, S.A., Shandryuk, G.A., Platé, N.A., and Chalykh, A.E., Polymer, 41(14), 5349, 2000.)

10.6.6 Correlation of Adhesion with Characteristics of Viscoelasticity 10.6.6.1 Large Strain Behavior of Model PVP–PEG Adhesive In preceding sections of this chapter we established that pressure-sensitive adhesion results from a specific molecular structure that combines high cohesion energy with large free volume. Direct experimental evaluation of these fundamental quantities for the variety of PSAs is difficult to attain, and it would be highly desirably to find readily measurable quantities that characterize them indirectly. Furthermore, all the above-considered quantities, such as glass transition temperature, solubility parameter, and diffusion coefficient, relate to the ratio of cohesion energy to free volume. The question arises of how can we readily estimate the contributions of cohesion energy and free volume separately. The tensile test data allow us to estimate the cohesion in terms of the ultimate tensile stress at the break, σ b, which is a direct measure of the integral cohesive strength of stretched adhesive material. Tensile strain is large at the moment of adhesive bond fracture for various PSAs, as evident from Figure 10.4 for both probe tack and peel tests, and the advantage of the tensile test is that it provides a feasible tool to measure the viscoelastic properties of adhesives at large strains that approximate the PSA deformation in the course of debonding. Stress–strain curves for PVP–PEG adhesives containing different amounts of plasticizer, PEG-400, are presented in Figures 10.6 and 10.7. The free volume in the PVP–PEG blends has been measured with positron annihilation lifetime spectroscopy.45 Figure 10.18 compares the behaviors of free volume and maximum elongation at the break of adhesive film as functions of the composition of PVP–PEG blends.11 Plasticization of PVP with liquid PEG causes an increase in both

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10-27

Molecular Nature of Pressure-Sensitive Adhesion

30

30

35

40 7.0

25

εb

15 6.0

fv (%)

6.5

20

10 5.5 5 0 0

10

20 30 PEG in blend (%)

40

5.0 50

σb, σb / εb (10−1), σb εb (%)

FIGURE 10.18 Fractional free volume, fv, and maximum elongation of adhesive film at the break of uniaxially stretched material, εb, as functions of PVP–PEG composition. (From Feldstein, M.M., Developments in Pressure-Sensitive Products, 2nd ed., I. Benedek, Ed., CRC-Taylor & Francis, Boca Raton, 2006.)

9

σb

30

6

σb εb

20 εb εb 10

3 σb / εb 0 30

32

34

36

38

40

0 42

PEG (wt %)

FIGURE 10.19 Relationship of ultimate tensile stress (σ b) and maximum elongation at break (εb), their product, and the ratio to the content of PEG-400 in the blends with PVP. (From Feldstein, M.M., Developments in Pressure-Sensitive Products, 2nd ed., I. Benedek, Ed., CRC-Taylor & Francis, Boca Raton, 2006.)

fractional free volume and maximum elongation at break. Consequently, the εb value, which characterizes a process of elongational flow, can be taken as an indirect measurement of the free volume in PVP–PEG blends. With the rise in PEG concentration, the cohesive strength of PVP–PEG adhesives, embedded by the σ b quantity, grows until 36% PEG concentration is achieved and then decreases (Figure 10.19). This implies a twofold role of PEG in the blends. In PVPreached blends, where an H-bonded complex is forming, PEG acts simultaneously both

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10-28

Fundamentals of Pressure Sensitivity

as plasticizer, decreasing cohesive strength, and as cross-linker (enhancing cohesive strength). At PEG concentrations higher than 36%, when the PVP–PEG complex is fully formed, the former process dominates and the PEG acts as a plasticizer, decreasing cohesive strength and increasing free volume. As illustrated in Figure 10.19, the product σ b ⋅ εb, which approximates the work of viscoelastic deformation to break, passes through a maximum at 36% PEG content, in full accordance with the data in Figures 10.7 and 10.8 for the work of viscoelastic deformation of the adhesive fi lm up to break (W). The σ b ⋅ εb product is a measure of energy dissipated during the process of deformation of PSA material, and it is therefore not surprising that the maximum of the σ b ⋅ εb product corresponds to the blend with maximum adhesion. The σ b/ε b ratio can be interpreted physically as an average modulus of the adhesive at the moment of fracture. As the data in Figure 10.19 indicate, the maximum energy that must be expended to draw and break a unit volume of the PVP–PEG adhesive (~40–90 MJ/m3) corresponds to the apparent tensile modulus σ b/εb ≈ 2 – 9 × 105 Pa. Let us recall Dahlquist’s criterion of tack, defi ning the elasticity modulus of various PSAs in the order of 105 Pa.5 Although the chemical composition and structure of PVP–PEG blends are absolutely dissimilar compared with those for conventional PSAs, the behavior of PVP–PEG H-bonded network complex near the fracture of adhesive bond obeys Dahlquist’s criterion of tack. This allow us to appreciate the physical meaning of this phenomenological criterion. At the most fundamental, molecular level, Dahlquist’s criterion of tack specifies the ratio between cohesive interaction energy and free volume within PSA polymers. Thus, the analysis of tensile stress–strain curves provides further insight into the factors underlying viscoelastic behavior at a molecular level. 10.6.6.2 Effects of Debonding and Deformation Rates on Adhesion and Viscoelastic Properties It now remains to be elucidated whether tensile test results obtained for the model PVP– PEG adhesive are also typical for other, hydrophobic PSAs. In other words, by comparing the values of ultimate tensile strength (σ b) and maximum elongation at break (εb) for various PSAs, is it possible to make conclusions about the magnitudes of their cohesive strengths and the contents of free volume? Because the tensile stress–strain curves available in literature53,71 often relate to different drawing rates, and taking into account that the relaxation processes dramatically affect both adhesion and viscoelastic behavior, we should first consider the velocity dependence of the adhesion and uniaxial extension of the PVP–PEG model adhesive. The effects of debonding and deformation rates on the mechanism of adhesive joint failure and deformation provide one of the most illustrative examples of these structure–property relationships. As the results of probe tack testing in Figure 10.20 indicated, 51 for the blend containing 36% PEG, a clear transition between debonding without fibrils to debonding with extensive fibril formation occurs without any change in σmax with a rise in probe velocity. Th is result implies that an adhesive could be designed to have a high adhesion energy (defined by the area under the probe tack curve) at low debonding rates but a good release at high debonding rates. Adhesion tests

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10-29

Molecular Nature of Pressure-Sensitive Adhesion

2 1 6 4

80

20

σ (MPa)

10 2

5

2

1 µm/s

0.1 6 4 2 0.01 0

2

4

6

8

10

12

14



FIGURE 10.20 Typical stress–strain curves obtained in probe tests for different probe debonding velocities at a constant PEG content (36 wt % PEG). The maximum extension measured (the point where the force drops to zero) increases monotonously with decreasing debonding velocity. The velocities used are (from right to left) 1, 2, 5, 10, 20, and 80 µm/s. (From Roos, A., Creton, C., Novikov, M.B., and Feldstein, M.M., J. Polym. Sci., Polym. Phys., 40, 2395, 2002. With permission.)

performed with the probe method demonstrate an uncharacteristically high sensitivity to the velocity of removal of the probe, with a sharp transition from detachment by fibril formation at low probe velocity to brittle fracture at high probe velocity. This transition occurs in a very narrow velocity range, suggesting the existence of a well-defined relaxation time in the polymer network. This well-defined relaxation time may be related to the breakdown of the hydrogen-bonded network structure formed by the interaction between OH terminal groups of PEG with the carbonyl groups of the pyrrolidone repeat units (see scheme in Figure 10.2). The probe tack data in Figure 10.20 are in good agreement with tensile test results presented in Figure 10.21. As follows from Figure 10.21, a particular feature of the hydrogen bonded PVP–PEG network is the existence of a well-defined time for its structural rearrangement, which in turn depends upon the lifetime of H-bonds under applied mechanical stress. Under slow drawing rates, the PVP–PEG hydrogel behaves as a ductile, un-cross-linked elastomer, whereas at faster extension rates it deforms and breaks as a tight, cured rubber.49,60,72–76 The transition from the ductile to the tight stretching mode occurs in a narrow range of deformation rates (20–50 mm/min). In exactly the same manner, the type of extension changes from ductile to tight, with a very small decrease in the concentration of both plasticizers in blend–PEG (between 36 and 34%; see Figure 10.6) and water (between 6.5 and 3%).49 Taking into account the transient character and fast reformation of the H-bonded network, we believe that under slow extension the intermolecular H-bonds in PVP–PEG blends have time to rupture and reform anew at another place during deformation and do not contribute appreciably to the resistance to strain until the onset of a critical,

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10-30

Fundamentals of Pressure Sensitivity

1.6 100 mm/min

Nominal stress (MPa)

1.4 1.2 1.0 50 mm/min

0.8 0.6

20 mm/min 0.4 0.2

10 mm/min

0.0 0

5

10

15

20

25

Tensile strain

FIGURE 10.21 Stress–strain curves to break the PVP–PEG hydrogel, containing 36 wt % PEG400 and 8–9% water, at drawing rates ranging from 10 to 100 mm/min. (From Novikov, M.B., Roos, A., Creton, C., and Feldstein M.M., Polymer, 44(12), 3559, 2003. With permission.)

strain-hardening region, where the final rupture of H-bonded cross-links between the PVP chains occurs (Figure 10.21). In contrast, at higher extension rates the H-bonds have insufficient time for rearrangement at new places and behave like pseudo crosslinks, which must be ruptured to deform the polymer. The narrow transition from ductile to tight stretching with the rise of drawing rate in Figure 10.21 corresponds to a well-defined rate of rearrangement of the H-bonded network under drawing of the PVP–PEG adhesive. Assuming that breakup and reformation of hydrogen bonds forming a PVP–PEG network can occur below the critical deformation rate of 0.05 s–1, we can identify the characteristic time for this process to occur at about 20 s.51 The effects of deformation velocity on adhesion and large-strain viscoelastic behavior of the model PVP–PEG adhesive provide a highly illustrative example of how the relaxation processes control the performance properties of PSAs. 10.6.6.3 Comparison with Typical Hydrophobic Adhesives Figure 10.22 displays the peculiarities of the tensile stress–strain behavior of a PVP– PEG H-bonded network complex in comparison with that of two typical PSA polymers: highly tacky, un-cross-linked low-molecular-weight PIB and elastic SIS triblock copolymer, which is cross-linked physically through glassy polystyrene domains. The latter is fi lled with relevant tackifier to yield a blend coupling high tack at the stage of bonding under compressive force with perfect elasticity and adhesion in the course of debonding. Comparison of the data presented in Figures 10.21 and 10.22 clearly demonstrates the

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10-31

Molecular Nature of Pressure-Sensitive Adhesion

900 10 mm/min

Nominal tensile stress (kPa)

800

SIS 700 600 500 400 300 200 PVP−PEG 100 0

PIB 5

0

10

15

20

25

Tensile strain

Nominal tensile stress (kPa)

1400

100 mm/min

1200 1000 800

SIS

PVP−PEG

600 400 200 PIB 0

0

2

4

6

8

10

12

14

16

18

20

22

Tensile strain

FIGURE 10.22 Stress–strain curves to break the PVP–PEG (36%), PIB, and SIS block copolymer (Duro-Tak 34-4230) adhesives at extension rates of 10 and 100 mm/min.

fact that the 10-fold increase in drawing rate affects the ductile–tight behavior of the hydrogen bonded PVP–PEG adhesive to a much greater extent than in conventional hydrophobic adhesives. In other words, the ductile–tight transition in the SIS and PIBbased adhesives is much wider than that in PVP–PEG blends. Thus, the sharp transition between the ductile and tight deformation modes with the change of extension rate is featured only for the H-bonded PVP–PEG system and is atypical of SIS- and PIB-based adhesives. As follows from the comparison of tensile stress–strain curves presented in Figures 10.6 and Figures 10.21 through 10.23 and Table 10.2, according to their tensile behaviors

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10-32

Fundamentals of Pressure Sensitivity

20 18

10 mm/min PIB

16

σn (kPa)

14 12 10 8 6 Acrylic

4 2 0 0

10

20

30

40

50

60

70

ε

60

100 mm/min

50

σn (kPa)

40

Acrylic

30 20 10

PIB

0 0

10

20

30 ε

40

50

60

FIGURE 10.23 Stress–strain curves to break the PIB and acrylic (Duro-Tak 87-900A) adhesives at extension rates of 10 and 100 mm/min.

all PSAs can be classified into two main groups. The PSAs of the first group, exemplified by un-cross-linked PIB and acrylic adhesives, represent very soft, compliant materials with low tensile modulus (E, defined as the slope of initial part of the stress–strain curve), which deform like viscous liquids, demonstrating negligible or zero values of ultimate tensile strength (σ b), comparatively low work of viscoelastic deformation up to break (W), and extremely high values of maximum elongation at break (εb). In fact, such adhesives never break in the course of tensile test at the employed values of extension

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Molecular Nature of Pressure-Sensitive Adhesion TABLE 10.2 PSA PVP–PEG SIS PIB Acrylica PVP–PEG SIS PIB Acrylica a

Tensile Properties of Pressure-Sensitive Adhesives Extension Rate (mm/min) 10

100

E (MPa)

σb (MPa)

0.56 1.42 0.12 0.024 3.63 3.51 0.18 0.083

4.2 19.77 0.00006 10.4 28.57 0.063

σy (kPa) 37.9 21.4

84.1 143.4

εb

W (MJ/m3)

16 23 7.5 ∞ 8.6 20 15.8 ∞

17.9 114 0.14 24.6 156 0.88

Duro-Tak 87-900A.

velocities because the distance between tester cross-heads achieves its limit before the breakpoint. Therefore, the characteristic value of ultimate tensile stress, σ b, cannot serve as a measure of cohesive strength for these materials. Instead of σ b, the value of yield stress (the maximum on stress–strain curve), σy, can be used for comparative characterization of the cohesive strength of fluid adhesives (Figure 10.23). The strain-hardened PSAs of the second group, to which physically cross-linked SIS and PVP–PEG adhesives belong, deform like typical rubber-like networks,60,72–74 exhibiting much higher values of tensile modulus (E), work of extension up to break (W), and appreciable resistance to strain, expressed in terms of high tensile strength, σ b (see Table 10.2). Covalent cross-linking of fluid acrylic adhesives with Ti-chelate (namely with Ti-acetylacetonate) has been shown75 to change the type of tensile stress–strain curves to the deformation with pronounced strain hardening that is typical of the adhesives in the second group. In contrast to such quantities as glass transition temperature, the characteristic values of tensile test do not generate any universal range of magnitude for various PSAs. This implies that although the values of ultimate tensile stress and maximum elongation at break are, respectively, indirect characteristics of cohesive strength and free volume, this is true only for an individual PSA. The σ b and εb values cannot be utilized for comparison of cohesive strength and free volume of different PSAs that belong to different groups. The reasoning behind this conclusion is that most likely that the structures of the strain-hardened (cross-linked) and viscous adhesives at large tensile strain are too different to be characterized in terms of tensile test parameters.

10.6.7 Inconsistency between Small and Large Strain Behaviors: New Consideration of Dahlquist’s Criterion of Tack Whereas the preceding section dealt with tensile properties of PSAs at large strain, in this section we consider the viscoelastic behavior of PSAs in the linear elastic region of small deformations as measured with dynamic mechanical analysis (DMA). A considerable amount of research work has been performed on the correlation of dynamic mechanical properties with the accepted parameters of adhesive performance, tack, peel adhesion, and shear performance (reviewed by Satas77). Chu78 and Dale79 established a direct correlation of the dynamic mechanical properties of PSAs with peel adhesion.

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The storage modulus, G′, measures the elasticity of the adhesive. High G′ values are typical for hard polymers with great cohesion energy. The loss modulus, G″, is associated with energy dissipation during deformation. The factor underlying the G″ value at the molecular level is free volume. The greater the G″ value relative to G′, the more dissipative the adhesive. The G″/G′ ratio, defined as the loss tangent, tan δ, is the balance of viscous/ elastic behavior. tan δ = 1 is a limiting value. Above this value the adhesive is generally considered a viscoelastic fluid, whereas below this value, the adhesive can be considered a viscoelastic solid. Once tan δ > 1, the free volume dominates the cohesion energy. Conversely, if tan δ < 1, the contribution of cohesion energy overrides that of free volume. This suggests that all PSAs should possess the specific range of G′, G″, and tan δ values. The DMA technique allows us to estimate indirectly the ratio of cohesion energy to free volume in terms of tan δ values and provides indirect separate characteristics of the cohesion energy and free volume contributions in terms of G′ and G″, respectively. In this section we focus on outlining the range of G′, G″, and tan δ values, which are typical for both conventional hydrophobic and hydrophilic PVP–PEG model adhesives. Based on DMA data, one of the most important critera for a material to display PSA behavior is Dahlquist’s criterion of tack, which states that the elasticity modulus of a PSA should be below 105 Pa.5,6 Typically, at a deformation rate of 1 Hz and ambient temperature, the values of G′ for various PSAs fall in the range 0.01–0.1 MPa (Figure 10.24).80 Typical PSAs are used in a temperature range corresponding to the beginning of the high-temperature rubbery plateau or the end of the transition region (Figure 10.24). Typical values of tan δ for conventional PSAs range from 0.7 to 1.0, implying that either the contributions of free volume and cohesion energy are counterbalanced or the intermolecular cohesion slightly dominates. The temperatures relating to the loss tangent peak vary most frequently between −50 and +5°C.

9.5 tan δ

9.0

1.2

PSA

1.0

8.0 0.8

7.5 7.0

0.6

6.5

0.4

6.0

G ′′ 0.2

5.5 G′

5.0 4.5 −120

tan δ

log G′, log G′′ (Pa)

8.5

−80

−40

0

40

80

0.0 120

160

T (°C)

FIGURE 10.24 Idealized plot of the storage modulus, G′, loss modulus, G″, and tan δ for a typical PSA as a function of temperature.80 ωref = 1 Hz.

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Until recently, Dahlquist’s criterion of tack described fairly reasonably the interrelationship between the adhesive and rheological properties of all PSAs known to date. Recently a new class of PSAs has been obtained, exemplified by a part of triblock thermoplastic elastomers81 (Figure 10.25)82 and hydrophilic PVP–PEG model adhesive (Figure 10.26),8,11,29,49 the behavior of which sometimes disobeys appreciably Dahlquist’s criterion. G′

1E9

G ′′

1E7

1 tan δ

G ′, G ′′ (Pa)

1E8

10

1000000 100000 0.1 10000

tan δ

1000 −50

0

50

100

150

T (°C)

FIGURE 10.25 Temperature sweep curves of the storage modulus, G′, loss modulus, G″, and tan δ for a SIS-based hot-melt PSA (NSC 12602-60H1). (Courtesy of Dr. Y. Hu, National Starch and Chemical.) 9

2.0 G′

8

7

1.0 6

tan δ

log G′, log G ′′ (Pa)

1.5 G ′′

tan δ 5

0.5

4 0.0 −40

0

40

80

120

160

T (°C)

FIGURE 10.26 Temperature dependence of dynamic shear moduli G′, G″, and tan δ for PVP– PEG (36 wt %) PSA at a reference deformation frequency of 1 Hz.

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As illustrated by the curves in Figure 10.25, the values of G′ for SIS-based PSA lie in the range from 1.94 to 0.40 MPa with an increase in temperature from 15 to 40°C. SISbased PSA is used in a temperature range corresponding to the beginning of the hightemperature rubbery plateau and the end of the transition region (Figure 10.25). Only in this connection does its behavior not deviate too much from that of other PSAs. The values of tan δ for the SIS PSA range from 3.1 to 0.4 between 15 and 40°C. The temperature of loss tangent peak is 15°C, tan δ = 3.1. At ambient temperature (20°C), G′ = 0.96 MPa, G″ = 2.16 MPa, and tan δ = 2.2. At increased temperatures, the value of G′ for the PVP–PEG adhesive (Figure 10.26) decreases in the range from 2.95 (15°C) to 0.09 MPa (40°C). At 20°C, G′ = 1.23 MPa, a value clearly incompatible with Dahlquist’s criterion for tackiness, which specifies that an adhesive loses its tack if its elastic modulus at 1 Hz is higher than about 0.1 MPa. The PVP–PEG blend is tacky in a region corresponding to the center of the transition region, where the loss tangent peak occurs (25°C, tan δ = 1.6). The DMA data in Figures 10.25 and 10.26 were measured in the linear elastic regime, that is, at very small strains. Let us refer now back to large strain data for the PVP–PEG adhesive presented in Figure 10.19. The ratio of ultimate tensile stress to maximum elongation at break, σ b/ε b, can be interpreted physically as an average modulus of the adhesive at the moment of fracture under uniaxial extension.49 As the data in Figure 10.8 indicate, the maximum energy that must be expended to draw and break a unit volume of the PVP–PEG adhesive (~40 to 90 MJ/m3) corresponds to the apparent tensile modulus σ b/ε b ≈ 2 – 9 × 105 Pa. The latter values correspond exactly to those specified by Dahlquist’s criterion, taking into account that E = 3G. Thus, Dahlquist’s criterion holds for the PVP–PEG systems at large strains, rather than within the linear elastic region of deformation. In other words, the PVP–PEG blend is very stiff at small strains but undergoes a pronounced softening above 10–20% deformation, which puts it in the range to be a PSA. Similar yet less pronounced inconsistencies between small and large strain behaviors of PSAs are also observed for polymers with more complicated architectures and very pronounced elastic effects.83 For such polymers the elongational properties, involving the orientation of polymer chains, cannot be readily predicted from the linear elastic properties in shear. One such class of polymers is that of diblock and triblock copolymers of styrene and isoprene, which serve as base components of PSA formulations. As recently established by Roos and Creton,73 much like PVP–PEG adhesives, the blends of triblock and diblock copolymers of polystyrene (PS) and polyisoprene (PI) display marked nonlinear viscoelastic behavior and are much more dissipative at low strains than at high strains. Let us turn refer to Figures 10.22 and 10.23 and recall that, in terms of large strain behavior, the PVP–PEG and SIS adhesives form a separate group of PSAs, which elongate as lightly cross-linked rubbers with pronounced strain hardening, whereas other (un-cross-linked) PSAs (PIB, acrylic) deform as viscous fluids. The implication of these observations is that Dahlquist’s criterion of tack holds only for un-cross-linked adhesives with random structure. To become more universal, it must be now extended by taking into consideration the values of storage modulus obtained for cross-linked adhesives and supplemented by the inclusion of loss tangent magnitudes and peak temperatures.

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10.7 Conclusions In a manner quite similar to that of many other properties of materials, such as glass transition, solubility, or diff usion, pressure-sensitive adhesion results from the counteraction of molecular cohesion and free volume. The length scale where these two factors are important is different: a PSA requires a low density of strong bonds that are relatively far apart and a high density of weak bonds with a high molecular mobility. A large free volume, resulting in liquid-like fluidity, is necessary to facilitate the formation of good adhesive contact as compressive bonding force is applied and to develop large deformations of a PSA under detaching force. High cohesion energy of the PSA material is required to resist the fracture of adhesive bond and dissipate much mechanical energy in the course of debonding. Once the adhesive bond is properly formed, viscoelasticity theory describes the PSA behavior under detaching force fairly reasonably. This viscoelasticity theory claims that the strength of the adhesive joint is controlled by the amount of viscoelastic energy needed to stretch and break the adhesive fi lm cohesively. The viscoelasticity theory seems to be much more universal than other theories, such as mechanical interlocking, diff usion, electronic, and adsorption theories, and it involves the contributions of high cohesive strength, high diff usion coefficient, and long relaxation time. Because the cohesive strength, diff usion coefficient, and relaxation time vary in opposite directions under the transition from glassy materials to liquids, viscoelasticity theory requires that the values of cohesive strength, diff usion coefficient, and relaxation time should be in a specific and rather narrow range of magnitude to make the value of their product and, consequently, adhesion as high as possible. The specific value of the ratio between high cohesion energy and large free volume, featured for the PSAs of various chemical composition and structure, may be expressed in terms of the glass transition temperature, diff usion coefficient, relaxation time, elasticity modulus, and loss tangent. The glass transition temperatures of PSAs fall in the range between −10 and −115°C, the values of diff usion coefficients should be on the border between those typical of elastomers and viscous liquids, ~10−13 m2/s, and the appropriate values of the relaxation times are identified in the next chapter. According to their large strain behavior, all PSAs can be classified into two groups. The majority of PSAs belong to the group of low-modulus, soft polymer materials that flow upon attainment of yield stress in the course of uniaxial drawing. The second group of PSAs consists of comparatively high-modulus, cross-linked covalently (or noncovalently) and highly ordered polymer materials that exhibit a rubber-like type of deformation with pronounced strain hardening. Dahlquist’s criterion of tack, which states that the elasticity modulus of the PSA must be in the range 0.01–0.1 MPa, holds for adhesives in the first group, whereas the PSAs in the second group, such as thermoplastic elastomers and PVP–PEG hydrophilic PSA, based on the network of hydrogen bonds, demonstrate at 20°C the values of storage moduli in the range of 0.6–1.5 MPa, tan δ ≈ 1.2–2.2, and loss tangent peak temperatures around 20°C. The insight gained into the molecular structures responsible for the occurrence of pressure-sensitive adhesion opens the way to the molecular design of new PSAs with optimized performance properties by blending nonadhesive polymers. This approach is illustrated in Technology of Pressure-Sensitive Adhesives and Products, Chapter 7.

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48. Vartapetian R.Sh., Khozina E.V., Karger J., Geschke D., Rittig F., Feldstein M.M., and Chalykh A.E., Molecular dynamics in poly(N-vinyl pyrrolidone)– poly(ethylene glycol) blends by pulsed field gradient NMR method: effects of aging, hydration and PEG chain length, Macromol. Chem. Phys. 202(12), 2648, 2001. 49. Novikov M.B., Roos A., Creton C., and Feldstein M.M., Dynamic mechanical and tensile properties of poly(N-vinyl pyrrolidone)–poly(ethylene glycol) blends, Polymer 44(12), 3559, 2003. 50. Feldstein M.M., Kulichikhin V.G., Kotomin S.V., Borodulina T.A., Novikov M.B., Roos A., and Creton C., Rheology of poly(N-vinyl pyrrolidone)-poly(ethylene glycol) adhesive blends under shear flow, J. Appl. Polym. Sci. 100, 522, 2006. 51. Roos A., Creton C., Novikov M.B., and Feldstein M.M., Viscoelasticity and tack of poly(N-vinyl pyrrolidone)–poly(ethylene glycol) blends, J. Polym. Sci., Polym. Phys. 40, 2395, 2002. 52. Novikov M.B., Borodulina T.A., Kotomin S.V., Kulichikhin V.G., and Feldstein M.M., Relaxation properties of pressure-sensitive adhesives upon withdrawal of bonding pressure, J. Adhesion 81(1), 77, 2005. 53. Zosel A., Adhesive failure and deformation behaviour of polymers, J. Adhesion 30, 135, 1989. 54. Zosel A., The effect of fibrillation on the tack of pressure-sensitive adhesives, Int. J. Adhes. Adhesives 18, 265, 1998. 55. Christensen S. F., Everland H., Hassager O., and Almdal K., Int. J. Adhesion Adhesives 18, 131, 1998. 56. Chiche A., Zhang W. H., Stafford C. M., and Karim A., Meas. Sci. Technol. 16(1), 183, 2005. 57. Lakrout H., Sergot P., and Creton C., Direct observation of cavitation and fibrillation in a probe tack experiment on model acrylic pressure-sensitive adhesives, J. Adhesion 69, 307, 1999. 58. Creton C. and Fabre P., Tack, in: Dillard D.A. and Pocius A.V. (Eds.) Adhesion Science and Engineering, Vol. I: The Mechanics of Adhesion, Elsevier, Amsterdam, 2002, chap. 14. 59. Kaelble D.H., Theory and analysis of peel adhesion, in: Satas D. (Ed.) Handbook of Pressure-sensitive Adhesive Technology, 3rd ed., Satas & Associates, Warwick, RI, 1999, chap. 6. 60. Ward I.M., Mechanical Properties of Solid Polymers, Wiley Interscience, London, 1983, chap. 2. 61. De Gennes P.G., J. Chem. Phys. 55, 572, 1971. 62. Fujita H., Fortsch. Hochpolym. Forsch., Bd. 3, 1, 1969. 63. Askadskii A.A. and Matveev Yu.I., Chemical Structure and Physical Properties of Polymers, Chemistry, Moscow, 1983, pp. 24–48. 64. Dupasquier A. and Mills A.P., Jr. (Eds.) Positron Spectroscopy of Solids, IOS Press, Amsterdam, 1995.

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65. Feldstein M.M., Borodulina T.A., Vartapetian R.Sh., Kotomin S.V., Kulichikhin V.G., Geschke D., and Chalykh A.E., Correlations between activation energy for debonding and that for self-diff usion in pressure-sensitive adhesive hydrogels, Proceed. 24th Annual Meeting Adhesion Soc. Williamsburg, VA, 137, 2001. 66. Kabanov V.A. and Zezin A.B., Makromol. Chem. (Suppl. 6), 259, 1984. 67. Kotomin S.V., Durability of adhesive joints, in: Benedek I. and Feldstein M.M. (Eds.) Fundamentals of Pressure-Sensitive Adhesion, Taylor & Francis, Boca Raton, 2009, chap. 9. 68. Feldstein M.M., Significance of relaxation for adhesion, in: Benedek I. and Feldstein M.M. (Eds.) Fundamentals of Pressure-Sensitive Adhesion, Taylor & Francis, Boca Raton, 2008, chap. 11. 69. Shandryuk G.A., personal communication. 70. Bessmertnaya L.Ya., Goncharova A.I., Rumsh L.D., Grokhovskaya T.E., and Feldstein M.M., Thermostability and phase behaviour of enzymes in solid state and within polymer matrices, Proceed. Intern. Symp. Control. Release Bioactive Mater. 26, 383, 1999. 71. Ferguson J., Reilly B., and Granville N., Extensional and adhesion characteristics of a pressure-sensitive adhesive, Polymer 38(4), 795, 1997. 72. Meissner B., Tensile stress–strain behavior of rubberlike networks up to break. Theory and experimental comparison, Polymer 41, 7827, 2000. 73. Roos A. and Creton C., Effect of the presence of diblock copolymer on the non linear elastic and viscoelastic properties of elastomeric triblock copolymers, Macromolecules 38, 7807, 2005. 74. Creton C., Roos A., and Chiche A., Effect of the diblock content on the adhesive and deformation properties of PSAs based on styrenic block copolymers, in: Possart W.G. (Ed.) Adhesion: Current Research and Applications, Wiley-VCH: Weinheim, 2005, pp. 337–364. 75. Lindner A., Lestriez B., Mariot S., Creton C., Maevis T., Luhmann B., and Brummer R., Adhesive and rheological properties of lightly cross-linked model acrylic networks, J. Adhesion 82(3), 267, 2006. 76. Creton C., Block copolymers for adhesive applications, in: Matyjaszewski K., Gnanou Y., and Leibler, L. (Eds.) Structure-Property Correlation and Characterization Techniques, vol. 3, 1st ed., Wiley-VCH, Weinheim, 2007, pp. 1731–1752. 77. Satas D., Dynamic mechanical analysis and adhesive performance, in: Satas D. (Ed.) Handbook of Pressure-sensitive Adhesive Technology, 3rd ed., Satas & Associates, Warwick, RI, 1999, chap. 10. 78. Chu S.G., Viscoelastic properties of pressure-sensitive adhesives, in: Satas D. (Ed.) Handbook of Pressure Sensitive Adhesive Technology, 2nd ed., Van Nostrand Reinhold, New York, 1989, pp. 158–203. 79. Dale W.C., Paster M.D., and Haynes J.K., Mechanical property–performance relations of acrylic pressure-sensitive adhesives, in: Satas D. (Ed.) Advances in Pressure Sensitive Adhesive Technology, Satas & Associates, Warwick, RI, 1995, pp. 65–111.

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Molecular Nature of Pressure-Sensitive Adhesion

10-43

80. Benedek I., Pressure-Sensitive Adhesives and Applications, 2nd ed., Marcel Dekker, New York, 2004, p. 9. 81. Derail C. and Marin G., Rheology of hot-melt PSAs: Influence of polymer structure, in: Possart W. (Ed.) Adhesion–Current Research and Application, Wiley-VCH, Weinheim, 2005, chap. 16. 82. Courtesy of Dr. Y. Hu, National Starch and Chemical. Unpublished data. 83. Christensen S.F. and McKinley G.H., Int. J. Adhesion Adhesives 18, 333, 1998.

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11 Significance of Relaxation for Adhesion of Pressure-Sensitive Adhesives 11.1

Pressure-Sensitive Adhesion as a Multistage Process .......................................11-2 Introduction and Defi nitions: Time Dependence in Pressure-Sensitive Adhesion • Pressure-Sensitive Adhesion as a Three-Stage Process

11.2

Relaxation under Compressive Load during Adhesive Bond Formation ................... 11-6 Experimental Setup for the Relaxation and Tack Tests • Adhesion in the Absence of PressureSensitive Adhesive Relaxation • Relaxation and Adhesion of Typical Pressure-Sensitive Adhesives • Correlation among Contact Time, Relaxation Time, and Adhesion • Impact of the Relaxation of Entangled and Network Structures on Adhesion • Optimum Range of Longer Relaxation Times Providing Strong Adhesion • Deborah Numbers of PressureSensitive Adhesives • Relaxation and Adhesion of a Model Pressure-Sensitive Adhesive Based on Interpolymer Complex

11.3

Relaxation Properties of PressureSensitive Adhesives upon Withdrawal of Bonding Pressure ..........................................11-26 Approach • Applicability of Burger’s Model of Viscoelastic Body for Elastic Recovery of Pressure-Sensitive Adhesives • Squeeze–Recoil Behaviors of Pressure-Sensitive Adhesives • Retardation Times Featured for Hydrophilic PVP–PEG Adhesives • Retardation Times

11-1

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11-2

Fundamentals of Pressure Sensitivity in Hydrophobic Pressure-Sensitive Adhesives • Correlation between Retardation Times and Pressure-Sensitive Adhesion • Relaxation Criteria for Pressure-Sensitive Adhesion • Major Conclusions

11.4

Mikhail M. Feldstein Mikhail B. Novikov A.V. Topchiev Institute of Petrochemical Synthesis

Costantino Creton Unit Joint CNRS-UPMC-ESPCI

Relaxation Properties of PressureSensitive Adhesives in the Stage of Debonding .....................................................11-37 Three-Stage Mechanism of Debonding • Evolution of Pressure-Sensitive Adhesive Structure during the First Stage of the Debonding Process • Mechanisms of Adhesive Relaxation at the Second Stage of the Debonding Process • Comparison of Relaxation Processes in Linear Viscoelasticity and Large-Strain Elongational Geometries • Relaxation Properties of PVP–PEG Model Pressure-Sensitive Adhesives

11.5 General Conclusions .........................................11-57 References ......................................................................11-59

11.1 Pressure-Sensitive Adhesion as a Multistage Process 11.1.1

Introduction and Defi nitions: Time Dependence in Pressure-Sensitive Adhesion

The adhesive and mechanical (rheological) properties of viscoelastic polymer materials are time dependent.1 These properties come into play when the material is deformed in compression2 in the course of adhesive bond formation or when it is deformed during detachment. Both stages require an input of energy. Under an applied force, part of the energy input is irrecoverably dissipated through a mechanism of viscous flow, whereas another part is stored and can be released elastically upon removal of the bonding or detaching force. 3–5 The dissipation never takes place instantaneously.6 As a result, the response of an adhesive material lags behind the application of a deformation force. For this reason, adhesive properties are time dependent and this dependence cannot be ignored when dealing with such materials. Although the mechanical properties of pressure-sensitive adhesives (PSAs) are the subject of extensive study and have been reviewed in relevant books,7,8 as well as in earlier chapters of this book, the significance of relaxation properties for pressure-sensitive adhesion are still not adequately understood.9 Although, in principle, all mechanical and adhesion properties are time dependent, they can often be treated as if they had a purely elastic or a purely viscous nature. Whether they can or cannot depends on a characteristic ratio of times, called the Deborah number, nD


CRC_59378_C011.indd 2

mat exp

(11.1)

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Significance of Relaxation for Adhesion of PSA

11-3

which is the ratio of the time scale of the material rearrangements, τmat, to the time scale of experimental observation, τexp (see Ref. 10, p. 35). Even some apparent solids “flow” if they are observed long enough. The origin of the name is the line “The mountains flowed before the Lord,” in a song by prophetess Deborah recorded in the Bible (Judges 5:5). When the Deborah number approaches zero, the material may appear purely viscous to the observer and purely elastic when it approaches infi nity. Real materials fall in between and are viscoelastic. In particular, polymeric materials have Deborah numbers around unity and are the viscoelastic materials par excellence. In fact, methods for dealing with time dependence in mechanical properties have developed largely with the development of polymeric materials. Time-dependent mechanical properties are traditionally characterized in terms of so-called response times and almost always by a distribution of such times.1 If the material is strained to a fi xed value, which is then held constant, the corresponding stress relaxes and the response times are called relaxation times. On the other hand, if a stress is applied and kept fi xed, the strain is retarded and the response times are called retardation times. Because the context nearly always makes it clear which are under discussion, both relaxation and retardation times are customarily designated by the same symbol, τ. However, the relaxation and the retardation times are not identical. When ranking both sets in ascending or descending order, they alternate (i.e., the retardation times are intercalated between the relaxation times).10 Each response time is associated with a corresponding spectral strength that may be a modulus, Gi, or a compliance, Ji. The time dependence of a material is thus revealed in a finite, discrete set of response times and their associated spectral strengths. When a shear strain is fi xed and a stress relaxation occurs, this set is {Gi, τi},3,11 i
n

Gt
Geq  ∑ Gi exp(t/i )

(11.2)

i
1

where Geq is the equilibrium relaxation modulus, τi is the-relaxation time, and Gi is the relaxation modulus associated with τ. When a stress is removed and a strain recovery occurs, this set is {Ji, τi},3,11 i
n

J
J 0  ∑ J i (1 et / i )

(11.3)

i
1

where Ji is the compliance (Pa−1) in the i element of a structure and τi is the retardation time (s). As t → ∞, J0 → 0. The corresponding value of relaxation modulus can be evaluated with Equation 10.3 as the reciprocal of the compliance, Gi = 1/Ji. Most well-known examples of time dependence in pressure-sensitive adhesion are the effects of contact bonding time12–15 and debonding velocity16,17 on the strength of adhesive joints. The former effect is often explained by the molecular diff usion of the PSA into the substrate.18–20 However, as Equation 10.6 (Chapter 10) predicts, both diffusion and relaxation processes contribute to the work of viscoelastic deformation of the adhesive fi lm and failure of the adhesive bond that control peel adhesion.21 In the following discussion we focus on this contribution.

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11-4

Fundamentals of Pressure Sensitivity

The well-known Dahlquist’s criterion of adhesion specifies that the values of elasticity moduli of various PSAs should be in the range between 0.01 and 0.1 MPa.22 As demonstrated previously, 22,23 this criterion is incapable of predicting adhesive behavior from the linear elasticity data at small strains for the PSAs, which are either crosslinked (covalently or physically) or based on ordered supramolecular structures. One such PSA is a hydrogen-bonded stoichiometric network complex of high-molecularweight poly(N-vinyl pyrrolidone) (PVP) with a short-chain polyethylene glycol (PEG), which serves in our study as a model PSA.24,25 Another type of PSA departing from Dahlquist’s criterion (although to a less pronounced extent) are the adhesives based on diblock and triblock copolymers of styrene and isoprene, which are physically crosslinked by the glassy domains composed of polystyrene chains with a higher glass transition temperature (Tg; see Technology of Pressure-Sensitive Adhesives and Products, Chapter 3). For both such PSAs the large strain elongational properties, involving the orientation of polymer chains, cannot be readily predicted from the linear elastic properties in shear at small strains. As demonstrated in Chapter 10, 22 for these PSAs, it is the large strain modulus (the derivative of the stress–strain curve at strains above 100%) that is in agreement with Dahlquist’s criterion, rather than the linear elastic properties at small strains. The implication of this fact is that the supramolecular structure of PVP-PEG and styrene–isoprene–styrene (SIS) adhesives under an applied detaching stress undergoes transformation in such a way that the behavior typical of a PSA is a result of the large deformation behavior. This means that the interpretation of the phenomenon of pressure-sensitive adhesion solely as an equilibrium material property cannot always be adequate and, to gain further insight into this phenomenon, adhesion should be also treated as a process. Adhesion is traditionally defined as the phenomenon in which surfaces of contacting materials are held together by interfacial forces.26 In this chapter, the term phenomenon is treated as any event, series of experimental facts, or experience that is detectable by our senses and measuring instruments and that can be scientifically described. In turn, the term property means a characteristic quality regarded as being possessed by a material or a group of materials and that is common to all the members of this group. Process is defined as a continuing development involving many changes or transformations of the structure and properties of the material. Within this framework, the phenomenon is a conjunction of the property and the process. In other words, the term property can be defi ned as an equilibrium feature of the molecular structure independent of time. To reduce the concept of pressure-sensitive adhesion to such a defi nition would be a gross simplification, because adhesion is a phenomenon that is due to a nonequilibrium process. Th is phenomenon consists of a series of transformations of the structure of the adhesive material under an applied bonding and detaching stress, that is, it involves the process of evolution of material structure, geometry (e.g., cavitation and formation of fibrils), and properties. The order and arrangement in time of these transformations has great importance for the perception of the phenomenon as a whole. In the following section we present a rheological and structural description of all stages of the process of pressure-sensitive adhesion.

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11-5

Significance of Relaxation for Adhesion of PSA

11.1.2

Pressure-Sensitive Adhesion as a Three-Stage Process

The process of making and breaking a PSA bond can be divided into three stages: (I) adhesive bonding under a compressive force, (II) relaxation upon the removal of the bonding pressure, and (III) rupture of the adhesive bond under a tensile force. The squeeze–recoil test 27 provides a simple but adequate characterization of all three stages (Figure 11.1; see also Chapter 9 in this volume).28 During the first stage (I), the adhesive film is compressed between a fi xed bottom plate and an upper cylindrical rod of the Squeeze–recoil Tester under a fi xed squeezing force applied to the upper rod. The rod displacement (the gap between the plates, h(t)), is measured as a function of time. Under a compressive load, the material is squeezed from a gap between the upper and the lower plates (squeezing flow) and the deformation of the tested material is registered in terms of ∆h. Adhesive bonding under a compressive force (I) is followed by the removal of bonding pressure and the relaxation of the adhesive material (II), after which the application of the detaching stress brings the process to an end when the fracture of the adhesive joint occurs (III) at high elongations via adhesive or cohesive mechanisms. Because the three consecutive stages of adhesive bonding under applied pressure, material relaxation, and bond fracture under a tensile force form a unique continuous process, it is not surprising that the detailed conditions of every preceding stage can affect appreciably the mechanism of the debonding process and the value of the practical work of adhesion evaluated with a probe test. The strength of a PSA adhesive joint can be at least a function of both contact time and contact pressure.9,12–15 It is, therefore, important to discuss the mechanism by which the process of adhesive bond formation can contribute to the process of adhesive debonding. As Figure 11.1 clearly illustrates, pressure-sensitive adhesion is a permanent process including three indivisible consecutive stages. This implies that the second (relaxation)

I Compression (bonding)

II

F

h (mm)

1

III

F

F=0

0.1

Relaxation 0

250

500

750 1000 Time (s)

Debonding 1250

1500

1750

FIGURE 11.1 Typical protocol of squeeze–recoil testing of PVP–PEG (36%) adhesive fi lm. Compressive and debonding forces are 0.2 N. (From Feldstein, M.M., in Benedek, I. Ed., Developments In Pressure Sensitive Products, 2nd ed., Chap. 4, CRC-Taylor & Francis, Boca Raton, 2006.)

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11-6

Fundamentals of Pressure Sensitivity

and the third (debonding) stages cannot be studied separately if the adhesive joint in the course of the first stage is never formed. The PSA behavior at each subsequent stage is affected by the conditions of earlier stages, providing a “memory effect.” In other words, at each stage of the process the PSA “remembers” the way as an earlier stage has been performed. In fact, only the second stage, relaxation, does not always occur if compressive bonding load is immediately followed by application of a detaching force, avoiding the stage of PSA relaxation (II; Figure 11.1). As illustrated below, the third stage, adhesive debonding, is a multistage process itself, as evidenced by structural and geometric transformations of adhesive material in the course of a probe tack test. In the following discussion we describe the relaxation properties of PSAs at each subsequent stage of the process and compare them with adhesive behavior to identify the values of relaxation times and corresponding moduli that produce strong pressuresensitive adhesion.

11.2 Relaxation under Compressive Load during Adhesive Bond Formation 11.2.1 Experimental Setup for the Relaxation and Tack Tests To evaluate the relaxation properties of adhesives under bonding pressure and adhesion, the probe tack test is most appropriate. The probe tack test is intended to mimic, in a more reproducible and quantifiable way, the process of touching the adhesive fi lm surface with a finger and sensing the force and energy required to remove it 29 (see also Applications of Pressure-Sensitive Products, Chapter 8). The probe tack experiment can be performed in two different ways. First, when the compression force remains constant during contact time (Figure 11.2a), and second, when the deformation of the adhesive layer is kept constant during the contact time and the material is able to relax in the course of bond formation (Figure 11.2b). If the compressive stress remains constant during the contact time (Figure 11.2a), the stage of relaxation is missed. The sample comes into contact with the tester probe until the predetermined contact force (10 N, in our case) is attained. Then the motor maintains a constant contact force during the specified bond formation time, which in turn decreases the thickness of the adhesive. At the end of the contact time, the probe is then separated from the adhesive with a constant velocity and a tensile force is recorded as a function of time (displacement).13 When, on the other hand, the deformation of the adhesive layer is kept constant, the probe test, as well as the squeeze–recoil test presented in Figure 11.1, can be divided into three successive stages (Figure 11.2b). The first stage is compression, when the flat cylindrical probe approaches the adhesive layer with a constant velocity, penetrates 0.1 mm into its depth, and then stops. The averaged thickness of all tested samples was ∼0.5 mm; thus, the deformation of the adhesive layer never exceeded 20%. The second is the stage of relaxation, when the adhesive material under the probe relaxes during the predetermined contact time (we varied contact times from 1 to 1000 s). The third stage is debonding, when the probe is removed with a constant debonding rate of 0.1 mm/s. Nominal stress (σn) and strain (ε) curves are obtained using the values of the initial film thickness (h0) and the initial contact area (A): σ = F(t)/A and ε = (h(t) − h0)/h0.

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11-7

Significance of Relaxation for Adhesion of PSA

σ (MPa)

t (s)

Compression

Debonding

(a)

Debonding

Relaxation

Compression

σ (MPa)

t (s)

(b)

FIGURE 11.2 Nominal stress versus time (displacement) curves of a typical probe test. (a) The compressive stress remains constant during the contact time and (b) the strain of the adhesive layer is kept constant during the contact time and the adhesive is allowed to relax in the course of bond formation.

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11-8

Fundamentals of Pressure Sensitivity

Of course, the more a PSA is viscoelastic and the thicker the layer is, the more the details of the bonding stage will affect the debonding stage.

11.2.2

Adhesion in the Absence of Pressure-Sensitive Adhesive Relaxation

As illustrated in Figure 11.3, if the adhesive is not allowed to relax during or after the process of bond formation, the value of contact time has no effect on the mechanism of adhesive deformation in the course of the debonding process. The sole parameter that demonstrates smooth growth with contact time is the value of maximum stress, whereas the practical work of adhesion (the area under the stress–strain curve) tends to increase insignificantly with contact time. The most plausible explanation for the observed rise of peak stress is the improvement of probe contact with the adhesive layer. At the microscopic level this means that the average size of the contact defects (microbubbles) decreases with contact time.23 Another possible reason behind the increase of maximum debonding stress is that the initial thickness of adhesive fi lm decreases slightly with contact time.

11.2.3

Relaxation and Adhesion of Typical Pressure-Sensitive Adhesives

An alternative procedure for the probe tack test includes the relaxation of compressive stress during contact formation, while the probe position (and material deformation) remains fi xed with contact time (Figure 11.2b). This procedure has the advantage of keeping the layer thickness independent of contact time and therefore avoiding any

0.8

500 s

σ (MPa)

0.6

300 s 0.4 50 s 1s

0.2

0.0 0

2

ε

4

6

FIGURE 11.3 The effect of contact time on the curves of probe separation for the acrylic adhesive Gelva 3011. Bonding pressure is constant (0.8 MPa) and debonding velocity is 0.1 mm/s.

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11-9

Significance of Relaxation for Adhesion of PSA

dependence of the debonding process on the layer thickness itself.30 The relaxation curves for PIB (Oppanol B15), silicone (BIO-PSA® 7-4302), and SIS-based Duro-Tak® 34-4230 PSAs are illustrated in Figure 11.4.31 By fitting the exponential relaxation curves in Figure 11.4 with the sum of exponents (Equation 11.2), it has been established that three populations of relaxation times and corresponding moduli can approximate the curves of stress relaxation in Figure 11.4. Values are presented in Table 11.1. For all adhesives examined, the following ranges of relaxation times and moduli have been established: Geq = 0–0.6 MPa, G1 = 0.08–0.8 MPa, τ1 = 1–6 s, G 2 = 0.06–0.5 MPa, τ2 = 5–50 s, G3 = 0.02–0.2 MPa, τ3 = 30–800 s. Figures 11.5 through 11.8 illustrate the effects of contact bonding time on the tack behavior for a variety of PSAs.31 All employed adhesives can be classified into two 0.35 0.30 0.25

σ (MPa)

0.20 SIS

0.15 0.10 0.05

Silicone PIB

0.00 0

20

40

60

80

100 t (s)

120

140

160

180

200

FIGURE 11.4 Compressive stress relaxation curves for PIB (Oppanol B15), silicone (BIO-PSA 7-4302), and SIS-based (Duro-Tak 34-4230) adhesives. TABLE 11.1 Relaxation Times and Corresponding Moduli for Acrylic (Gelva 3011), PIB (Oppanol), Silicone (BIO-PSA 7-4302), and SIS-Based (Duro-Tak 34-4230) Adhesives Obtained by Fitting the Compressive Stress Relaxation Curves with Equation 11.2 Adhesive Type

Geq (MPa)

G1 (MPa)

τ1 (s)

G2 (MPa)

τ2 (s)

GB (MPa)

τ3 (s)

BIO-PSA 0.025 ± 0.0007 0.8 ± 0.02 3.3 ± 0.1 0.5 ± 0.02 21.4 ± 0.8 0.2 ± 0.005 150 ± 5.4 7-4302 Oppanol 0 0.57 ± 0.01 1.2 ± 0.03 0.4 ± 0.01 7.2 ± 0.2 0.07 ± 0.003 48 ± 1.8 B15 Oppanol 0 0.2 ± 0.01 1.8 ± 0.04 0.17 ± 0.01 5 ± 0.4 0.02 ± 0.005 35 ± 3.4 B12 Duro-Tak 0.6 ± 0.005 0.2 ± 0.006 5.3 ± 0.3 0.1 ± 0.004 44.5 ± 2.9 0.2 ± 0.004 770.7 ± 56.1 34-4230 Gelva 3011 0.035 ± 0.0006 0.08 ± 0.003 5.1 ± 0.3 0.06 ± 0.002 43.4 ± 3.04 0.05 ± 0.001 355.7 ± 20.3

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11-10

Fundamentals of Pressure Sensitivity

0.8 0.6

σ (MPa)

0.4 0.2 0.0 −0.2 −0.4 0

200

400 Time (s)

600

800

FIGURE 11.5 Effect of contact time on probe tack curves of the silicone adhesive BIO-PSA 7-4302. The initial bonding pressure is 0.8 MPa and the velocity of probe separation is 0.1 mm/s. 0.15 0.10

σ (MPa)

0.05 0.00 −0.05 −0.10 −0.15 0

50

100

150

200 250 Time (s)

300

350

400

200 250 Time (s)

300

350

400

0.3

σ (MPa)

0.2 0.1 0.0

−0.1 −0.2 −0.3

0

50

100

150

FIGURE 11.6 Kinetics of nominal compressive stress relaxation during adhesive bond formation, followed by the debonding process for PIB Oppanol B12 (top) and Oppanol B15 (bottom).

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11-11

Significance of Relaxation for Adhesion of PSA

0.3 0.2

σ (MPa)

0.1 0.0 −0.1 −0.2 −0.3 0

FIGURE 11.7

200

400

600 Time (s)

800

1000

1200

Probe tack curves of Duro-Tak 34-4230 obtained under different contact times. 0.12 0.08

Stress (MPa)

0.04 0.00 −0.04 −0.08 −0.12 0

FIGURE 11.8

200

400

600 Time (s)

800

1000

1200

Effect of contact time on probe tack of acrylic adhesive Gelva 3011.

groups: (1) fully relaxing PIB adhesives (Figure 11.6), such as Oppanol B15 and Oppanol B12 PSAs, described in Technology of Pressure-Sensitive Adhesives and Products, Chapter 4, and (2) adhesives that are able to store energy in the course of deformation and exhibit a residual (unrelaxed) stress during the contact time. SIS-based (Duro-Tak34-4230, Figure 11.7) and, to a somewhat lesser extent, the acrylic Gelva® 3011 PSA (Figure 11.8), belong to the second group. Silicone adhesive BIO-PSA 7-4302 (Figure 11.5) takes an intermediate position.

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11-12

Fundamentals of Pressure Sensitivity

As a rule, the appearance of the second maximum on probe tack curve results from a network structure of adhesive material. For instance, in the SIS-based Duro-Tak-344230 adhesive, the network structure is provided by the glassy domains of polystyrene blocks. Polymer networks frequently reveal an apparent yield stress that is defi ned as the minimum pressure at which the material flows extremely slowly under an applied stress.28 Such behaviors are typical for SIS-based Duro-Tak 34-4230 (Figure 11.7) and, to a less pronounced extent, for acrylic Gelva 3011 (Figure 11.8) adhesives. As follows from the data in Table 11.1, 31 the relaxation times of SIS DURO-Tak 34-4230 and acrylic Gelva 3011 PSAs are appreciably higher than those for PIB Oppanol B12, Oppanol B15, and silicone BIO-PSA 7-4302. Thus, the longer relaxation processes are mostly associated with the appearance of a pronounced plateau on the debonding curves (BIO-PSA 7-4302, Figure 11.5), or even a second maximum (SIS Duro-Tak 34-4230, Figure 11.7, and acrylic Gelva 3011 PSA, Figure 11.8). Fully relaxing, soft viscous adhesives such as Oppanol B12 or B15 have low relaxation times and a liquid-like debonding mechanism typical of fluid adhesives. The values of characteristic modulus associated with shortest relaxation times, G1, are generally higher than G 2 and G3. The equilibrium relaxation modulus, Geq, is a direct measure of the stored elastic energy in a polymeric material. Fluid polyisobutene (PIB) adhesives (Oppanol B12 and Oppanol B15) do not reveal any apparent yield stress and, consequently, no equilibrium modulus. The complex geometry of the probe tack test does not allow us to present a straightforward physical meaning of the two shorter relaxation time values, because in addition to the viscoelastic response of the adhesive material and small-scale recovery of the material structure, these values account for the formation of adhesive contact and instrument compliance. However, let us take into consideration that the longer relaxation time has been earlier demonstrated to contribute to high adhesive strength (see Equation 10.6 in Chapter 10).

11.2.4

Correlation among Contact Time, Relaxation Time, and Adhesion

As the data presented in Figures 11.5 through 11.8 illustrate, 31 the contact time does not affect appreciably the mechanism of the debonding process. The peak stress increases with increasing contact time during the fi rst 20 s and achieves its limiting value after 50 s for PIB and after 100 s for all other examined PSAs. The value of the practical work of adhesion, W, is demonstrated in Figures 11.9 through 11.11, along with the maximum debonding stress as a function of contact time. The work of debonding is an increasing function of contact (relaxation) time. The maximum practical work of adhesion is achieved if the adhesive material is allowed to relax for 200 s or longer. For fluid adhesives (PIB Oppanol B12 and B15) the time to achieve a steady-state regime of W values is shorter: 25 and 50 s, respectively. Th is indicates that for maximum adhesive strength the contact time of adhesives should be comparable with the longer relaxation time. Of course, many PSAs have very long relaxation times because they are very solidlike and the contact time dependence more reflects the annealing of surface defects

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11-13

Significance of Relaxation for Adhesion of PSA

1.0 700

W

W (J/m3)

σmax

600

0.6

550

σmax (MPa)

0.8

650

0.4 500 0.2

450 0

100

200 300 Time (s)

400

500

FIGURE 11.9 Debonding energy (W) and maximum stress values (σmax) versus the contact time for silicone adhesive BIO-PSA 7-4302.

120 Oppanol B12

W (J/m2)

100

Oppanol B15

80

60

40

20 0

50

100

150 Time (s)

200

250

300

FIGURE 11.10 Practical work of adhesion (W) versus the contact time for PIB Oppanol B12 and Oppanol B15 adhesives.

than a true relaxation of the material per se, although the relaxation process contributes to the driving force for such annealing. At best, this example is illustrative of the fact that, in general, it is not wise to ignore the effect of the bonding stage when analyzing the debonding stage. This is particularly true when the PSA is very fluid-like with an important viscous component.

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Fundamentals of Pressure Sensitivity

0.40 550 0.36

W

500 450

0.28

400

0.24

350 Peak 2

0.20 Peak 1

0.16

W (J/m2)

Stress (MPa)

0.32

300 250 200

0

200

400 600 Time (s)

800

1000

FIGURE 11.11 Effect of contact time on the work of debonding and the values of two stress peaks for SIS-based Duro-Tak 34-4230 PSA.

11.2.5

Impact of the Relaxation of Entangled and Network Structures on Adhesion

Although it is difficult to attribute unequivocally the shorter and intermediate values of the relaxation times to the relaxation of polymer segments and macromolecules due to the complex geometry of the probe tack test, the longer relaxation times of the order of 50 s and higher relate most likely to the effect of a complex polymer architecture, network structure, and the effect of polymer chain entanglements.32 Let us compare first the relaxation and debonding curves for two PIB adhesives of different molecular weights illustrated in Figure 11.10.31 Oppanol B12 is reported to have Mw = 51,000 g/mol and Oppanol B15 has Mw = 88,000 g/mol. The entanglement molecular weight of PIB is reported to be 8700 g/mol.33 As evident from Figure 11.10, for lower Mw PIB the practical work of adhesion, W, achieves its steady-state values of 100–110 J/m2 almost instantaneously, whereas for the higher Mw fraction this process takes appreciable time that is comparable with the value of longer relaxation time for this polymer (50 s). Fluid adhesives relax faster than the elastic adhesives; however, the observed difference in behavior of these two PIB adhesives is not only due to the difference in their MW. The aggressive tack of highly soft, low-MW PIB hastens the formation of good adhesive contact and less time is required to achieve the maximum value of the practical work of adhesion. The correlation between relaxation and adhesion is presented in Figures 11.12 through 11.14 for acrylic Gelva 3011, silicone BIO-PSA 7-4302 and for SIS-based physically cross-linked Duro-Tak 34-4230 adhesives. The former (Figure 11.13) represents the behavior of fluid, fully relaxing adhesives with very low values of equilibrium relaxation modulus, Geq, whereas the latter stores mechanical energy under bonding pressure, demonstrating a high value of equilibrium relaxation modulus (see Table 11.1) and appreciable unrelaxed residual stress (Figure 11.14). As demonstrated by the stress relaxation curves, the initial period of fast relaxation (20–35 s) is followed by an intermediate period and

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Significance of Relaxation for Adhesion of PSA

1000

0.15 W

0.14

900 800

0.12 700

Peak 2

0.11

600

Peak 1

0.10

W (J/m2)

Stress (MPa)

0.13

500

0.09

400

0.08 200

0

400 600 Time (s)

800

1000

FIGURE 11.12 The contact time dependence of the work of debonding and the values of two stress peaks on probe tack curve for acrylic Gelva 3011 adhesive.

0.25 W

0.05

600

Intermediate

0.10 Fast

σ (MPa)

0.15 Slow

W (J/m2)

700

0.20

500

0.00 0

200

400 600 Time (s)

800

1000

FIGURE 11.13 Effect of contact time on the practical work of adhesion compared with the bonding stress relaxation curve for silicone BIO-PSA 7-4302 adhesive.

the process of slow relaxation (since 125–150 s). Shorter relaxation times dominate within the period of fast relaxation, whereas the longer relaxation times govern the steady-state (equilibrium) adhesion of both types of PSAs. In both cases, achieving maximum adhesion falls the end of the intermediate relaxation period and the onset of slow relaxation. Thus, in full agreement with Equation 10.6 presented in the Chapter 10, high adhesion is associated with longer relaxation time. The relaxation mechanism provides the links between all the stages of the process of pressure-sensitive adhesion.

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Fundamentals of Pressure Sensitivity

600 W

400

Intermediate

0.15

0.10 0

W (J/m2)

500

Fast

σ (MPa)

0.20

300 Slow 200 200

400 600 Time (s)

800

1000

FIGURE 11.14 Comparison of the bonding stress relaxation curve with the change in the practical work of adhesion as a function of contact time for SIS-based Duro-Tak 34-4230 PSA.

11.2.6

Optimum Range of Longer Relaxation Times Providing Strong Adhesion

As demonstrated in Chapter 10,22 for high adhesion a compromise must be reached among the values of the cohesion energy, diff usion coefficient, and relaxation times of PSAs. Figure 11.15 establishes the correlation between the practical work of adhesion and the values of longer relaxation times measured for the examined adhesives. Adhesion appears only when the longer relaxation times exceed 50 s and increases, passing through a maximum (acrylic Gelva 3011 PSA) at τ3 = 330–380 s. A further increase in longer relaxation times results in a gradual decline in adhesion. Good adhesion is assured as long as the longer relaxation time varies in the range from 150 to 800 s.

11.2.7

Deborah Numbers of Pressure-Sensitive Adhesives

Standard viscoelastic polymers have well-defined relaxation times such as a reptation time, rouse time, or entanglement time. Such relaxation times do not depend on the observation time and the Deborah number (for a given material) can only be changed by changing the observation time or the temperature. On the other hand, PSAs have very complex relaxation spectra and the approximate results obtained from the fits of Equations 11.2 and 11.3 to experimental data depend markedly on the experimental window used. Figures 11.16 and 11.17 illustrate the effect of the observation window, tobs, on the values of the fitted value of the longer relaxation time, τ3, for SIS-based Duro-Tak 34-4230, acrylic Gelva 3011, silicone BIO-PSA 7-4302, and PIB Oppanol B12 and B15 adhesives. As illustrated by Figures 11.16 and 11.17, for all PSAs examined except the most fluid low-molecularweight PIB (Oppanol B12), the fitted longer relaxation time is an increasing linear function of the observation window, although the points for the smaller observation window

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Significance of Relaxation for Adhesion of PSA

900

900 τ

800

700

700

600

600 W

500

500

400

400

300

300

200

200

100

100

0

W (J/m2)

τ3 (s)

800

O B1 ppa 2 no

l

l O B1 ppa 5 no

B 7− IO43 PS 02 A ®

G 30 elv 11 a ®

D 34 uro − 4 -Ta 23 k ® 0

0

FIGURE 11.15 Longer relaxation times and practical work of adhesion for SIS-based Duro-Tak 34-4230, acrylic Gelva 3011, silicone BIO-PSA 7-4302, and two grades of PIB adhesives (Oppanol B12 and B15). Observation time is 1000 s.

800 700

SIS

600

τ3 (s)

500 Acrylic

400 300 200

Silicone

100 0 200

400

600 tobc (s)

800

1000

FIGURE 11.16 Effect of the observation window on the values of longer relaxation time, τ3, for SIS-based Duro-Tak 34-4230, acrylic Gelva 3011, and silicone BIO-PSA 7-4302 adhesives.

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Fundamentals of Pressure Sensitivity

60 55 50


3 (s)

45

Oppanol B15 nD = 0,06

40 35 30

Oppanol B12 25 20 15 100

150

200

250

300

t obs (s)

FIGURE 11.17 Effect of the observation window on the values of longer relaxation time, τ3, for PIB Oppanol B12 and B15 adhesives.

TABLE 11.2 Values of Deborah Numbers, nD, Determined for SIS-Based (Duro-Tak 34-4230), Acrylic (Gelva 3011), Silicone (BIO-PSA 7-4302), and PIB (Oppanol B15) Adhesives by Treating the Relationships between the Longer Relaxation Times and Observation Times PSA SIS (Duro-Tak 34-4230) Acrylic (Gelva 3011) Silicone (BIO-PSA 7-4302) PIB (Oppanol B15)

Deborah Number (nD)

R2

Notes

0.857 ± 0.090 0.989 ± 0.089 0.388 ± 0.061 0.155 ± 0.008 0.058 ± 0.027

0.9788 0.9921 0.9765 0.9952 0.8378

Complete data set Taking four last points only Taking four last points only Complete data set Complete data set

tend to deviate from the linear relationship for the most elastic, cross-linked SIS Duro-Tak 34-4230 and acrylic Gelva 3011 adhesives. Interestingly, however, the slopes of the linear parts of the curves presented in Figures 11.16 and 11.17 are constant and can be related to the Deborah number, nD, of the PSAs. The values of the Deborah numbers are listed in Table 11.2, along with parameters of linear regression, R2. All PSAs are viscoelastic materials that couple the properties of solids and liquids. Values of the Deborah number are informative regarding the liquid-like and solid-like contributions. As nD = 1, a material is 50% solid and 50% liquid. Th is is the case of physically cross-linked SIS-based adhesive characterized by the magnitude of the Deborah number that approaches unity (Table 11.2). For all other adhesives considered, the liquid-like viscous contribution dominates the solid-like elastic contribution. Whereas the elastic contribution is appreciable for the chemically cross-linked acrylic Gelva 3011

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Significance of Relaxation for Adhesion of PSA

11-19

adhesive (nD = 0.388), silicone BIO-PSA 7-4302 and PIB adhesives are typical viscous liquids. For most liquid-like, lower-MW PIB fractions (Oppanol B12), the fitting of stress relaxation curves with Equation 11.2 at observation times less than 200 s does not yield plausible values of relaxation times (Figure 11.17). Cross-linked adhesives (SISbased and acrylic), as well as silicone PSA, which exhibit the best adhesion, demonstrate Deborah numbers between 0.15 and 1. The values of the Deborah number described in this section are only approximate and are calculated with longer relaxation times. They are only used to give an idea of the type of behavior (liquid or solid) of the PSA examined. In reality, the spectrum of the relaxation times in the linear viscoelastic region is a well-defined material property that does not depend on observation time. However, such viscoelastic properties as moduli G′ and G″ depend on both the relaxation time and the observation time.

11.2.8

Relaxation and Adhesion of a Model Pressure-Sensitive Adhesive Based on Interpolymer Complex

11.2.8.1 Model Pressure-Sensitive Adhesive Employed To gain improved insight into the relaxation properties that are responsible for the high adhesion of PSAs, the quantitative structure–property relationship (QSPR) is useful. In turn, the QSPR investigation requires the development of a model adhesive. Variation of the model adhesive composition offers a convenient tool to manipulate simultaneously the structure, adhesion, and relaxation properties. To evaluate the molecular nature of relaxation mechanisms that govern the adhesive behavior of PSA materials, in the present work we studied the relaxation and adhesive performance of a polybase–polyacid intermolecular complex as a function of its composition. The polybase was a copolymer of dimethylaminoethyl methacrylate (DMAEMA) with alkyl methacrylate (AMA), whereas the polyacid was a copolymer of methacrylic acid (MAA) with ethylacrylate (EA). Triethylcitrate (TEC) served as a plasticizer for the poly(DMAEMA-co-AMA)– poly(MAA-co-EA) blends. We studied the blends with different plasticizer content (25–45 wt %). In this particular region of the plasticizer concentration, the complex demonstrates pressure-sensitive character of adhesion.34 The molecular structure, adhesion, and viscoelastic properties of the complex are described in Technology of PressureSensitive Adhesives and Products, Chapter 7.35 11.2.8.2 Adhesive Properties The adhesive properties of the interpolymer complex versus its plasticizer content were studied using the probe tack method. Figure 11.18 illustrates the effect of TEC content on the values of maximum stress and the practical work of adhesion (area under the probe tack curve) for the interpolymer complex.36 Whereas σmax is a decreasing function of the plasticizer content, the work of adhesion passes through a maximum at 35 wt % TEC. The adhesive behavior of the blend with 35 wt % TEC corroborates the fact that the pressure-sensitive type of adhesive behavior requires a specific balance between solidlike and liquid-like properties.

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Fundamentals of Pressure Sensitivity

44

0.45 0.40

40

W

σmax

32 0.30 28 0.25

W (J/m2)

σmax (MPa)

36 0.35

24

0.20

20 24

28

32 36 TEC (wt %)

40

44

FIGURE 11.18 Values of maximum stress and the practical work of adhesion versus plasticizer (TEC) concentration for a model PSA adhesive based on a polybase–polyacid complex. Contact time, 1 s. Debonding rate, 0.1 mm/s. (From Novikov M.B., Kiseleva T.I., Anosova J.V., Singh P., Cleary G.W., and Feldstein M.M., Proceed. 30th Annual Meeting Adhesion Soc. Tampa, FL, 2007.) 1.6 25% TEC 1.4 30% TEC

σ (MPa)

1.2 1.0 0.8 35% TEC 0.6

40% TEC

0.4

45% TEC

0.2 0

50

100 Time (s)

150

200

FIGURE 11.19 Relaxation curves obtained in the course of adhesive joint formation for the blends of an interpolymer complex with different amounts of plasticizer (TEC). Contact time, 200 s. (From Novikov M.B., Kiseleva T.I., Anosova J.V., Singh P., Cleary G.W., and Feldstein M.M., Proceed. 30th Annual Meeting Adhesion Soc. Tampa, FL, 2007.)

11.2.8.3 Relaxation Properties Relaxation curves obtained in the course of adhesive joint formation between an adhesive layer and a probe are illustrated in Figure 11.19. The results of fitting the curves in Figure 11.19 with Equation 11.2 are listed in Table 11.3. We realize that the time chosen for this adhesive contact time of 200 s is insufficient to precisely identify very long relaxation

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11-21

Significance of Relaxation for Adhesion of PSA TABLE 11.3 Relaxation Properties of a Model PSA Made Up of a Polybase–Polyacid Interpolymer Complex Containing Different Amounts of Plasticizer (TEC) % TEC 25 30 35 40 45

Geq (MPa)

G1 (MPa)

1.342 ± 0.004 1.238 ± 0.004 0.515 ± 0.003 0.354 ± 0.002 0.180 ± 0.004

0.051 ± 0.003 0.110 ± 0.004 0.135 ± 0.002 0.058 ± 0.003 0.252 ± 0.011

τ1 (s) 1.29 ± 0.13 2.84 ± 0.13 0.66 ± 0.02 0.67 ± 0.08 2.55 ± 0.22

G2 (MPa) 0.091 ± 0.002 0.186 ± 0.003 0.314 ± 0.006 0.376 ± 0.002 0.421 ± 0.009

τ2 (s) 12.54 ± 0.56 16.29 ± 0.57 20.83 ± 0.38 11.3 ± 0.15 16.18 ± 0.77

G3 (MPa) 0.164 ± 0.002 0.106 ± 0.002 0.415 ± 0.003 0.526 ± 0.001 0.377 ± 0.009

τ3 (s) 161.12 ± 8.35 145.8 ± 15.18 111.99 ± 3.14 105.27 ± 1.31 91.33 ± 4.64

Note: Observation time is 200 s.

160 140

Time (s)

120 100 80 60 40 20 0 25

FIGURE 11.20 mer complex.

30

35 TEC (wt %)

40

45

Relaxation times versus TEC concentration in a polyacid–polybase interpoly-

processes within the polymer system. However, using the exponential Equation 11.2 and the Kelvin–Voigt model, we are able to define the short and large-scale relaxation processes within this time region. As illustrated in Figure 11.19, there is a sharp transition in the relaxation behavior of the blends that contain 30 and 35 wt % TEC. Although the interpolymer complexes containing 25 and 30 wt % TEC demonstrate a highly pronounced residual stress on the relaxation curves, which is a characteristic feature of crosslinked and ordered structures, the relaxation curves of the blends with 35 wt % TEC and more demonstrate a gradual decrease in stress that is rather typical of viscous liquids. Adequate fitting of the relaxation curves in Figure 11.19 with Equation 11.2 is possible using a sum of three exponents. The effect of TEC concentration on relaxation times is illustrated in Figure 11.20. The longer relaxation time is a decreasing function of plasticizer content. Accordingly, the values of the equilibrium relaxation modulus reduce with the increase in TEC concentration (Table 11.3). Faster relaxation processes, τ1 and τ2, are unaffected by the concentration of the plasticizer (Figure 11.20) that controls the

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Fundamentals of Pressure Sensitivity

adhesive properties (compare with the data in Figure 11.18). Based on this observation, a logical deduction can be drawn that the large-scale relaxation processes, characterized by the value of the longer relaxation time, contributes more to PSA performance. 11.2.8.4

Effect of Contact Time on Adhesion

Figure 11.21 illustrates the effect of contact time on the typical curve of nominal compressive stress relaxation during adhesive bond formation, followed by the debonding process, for the model adhesive based on an interpolymer complex and plasticized with 35 wt % TEC. The variation in contact time does not change the mechanism of the debonding process. The curve presented in Figure 11.21 is typical and relates to the blend that exhibits the best adhesion (compare with Figure 11.18). Figures 11.22 and 11.23 demonstrate the effect of contact time on the value of the practical work of adhesion, W, and maximum stress. Both σmax and W achieve their limiting values at contact times of ∼50 s. This time corresponds to the beginning of the domination of slow relaxation processes (compare with Figure 11.19) and, as a consequence, to the onset of large-scale rearrangements within the structure of the adhesive polymer. However, this tendency is less pronounced for the blend that contains 45 wt % TEC (Figures 11.22 and 11.23). Indeed, this blend exhibits a liquid-like behavior that is characterized by a faster relaxation. The σmax values increase with increasing contact time, whereas the increase in plasticizer concentration in the interpolymer complex results in a decrease of maximum stress values (Figure 11.22). However, the values of σmax for the blend containing 35 wt % TEC for a contact time longer than ∼50 s are higher than for other blends. It is important

0.8

Stress (MPa)

0.4 0.0 −0.4 −0.8 −1.2 −1.6 0

50

100 Time (s)

150

200

FIGURE 11.21 Effect of contact time on the curves of bonding stress relaxation, followed by probe separation from adhesive fi lm surface under detaching force for the model PSA based on an interpolymer polybase–polyacid complex containing 35 wt % TEC.

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11-23

Significance of Relaxation for Adhesion of PSA

35%

25%

0.6

30% 0.5 σmax (MPa)

40% 0.4

45%

0.3

0.2 0

50

100 150 Contact time (s)

200

FIGURE 11.22 Effect of contact time on the maximum values of probe detaching stress, σmax, for a plasticized interpolymer polyacid–polybase complex. (From Novikov M.B., Kiseleva T.J., Anosova J.V., Singh P., Cleary G.W., and Feldstein M.M., Proceed. 30th Annual Meeting Adhesion Soc. Tampa, FL, 2007.)

100

35% 30%

W (J/m2)

80

25%

60

40%

45% 40

20 0

50

100 150 Contact time (s)

200

FIGURE 11.23 Effect of contact time on the practical work of adhesion (W) for the plasticized interpolymer complex. (From Novikov M.B., Kiseleva T.J., Anosova J.V., Singh P., Cleary G.W., and Feldstein M.M., Proceed. 30th Annual Meeting Adhesion Soc. Tampa, FL, 2007.)

to note that the dependence of adhesion parameters on contact time for the blend that contains 45 wt % TEC is less pronounced than that for blends with a lower plasticizer content. Indeed, the relaxation of the most fluid blend containing 45 wt % TEC occurs much faster than for other blends. The values of practical work of adhesion for the blend containing 45 wt % TEC are much lower than for the blends containing 30 or 35 wt % TEC (Figure 11.23). On the other hand, the interpolymer complexes with still lower

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11-24

Fundamentals of Pressure Sensitivity

160

100

W (J/m2)

80

120

60 80 Contact time 1 s

Relaxation time (s)

Contact time 200 s

40 40 20 25

30

35 TEC (wt %)

40

45

FIGURE 11.24 Effect of TEC content on the values of longer relaxation time, τ3, and practical work of adhesion, W, for the model PSA based on an interpolymer complex.

plasticizer contents demonstrate solid-like behavior, with a highly pronounced maximum on the debonding curve and a low value of maximum elongation. 11.2.8.5 Comparison of the Composition Dependence of Adhesion and Relaxation Time Figure 11.24 illustrates the general conclusion that can be derived from the analysis in this work. Large-scale relaxation processes within the polymer system, characterized by the values of the longer relaxation time, τ3, predominantly govern pressuresensitive adhesion performance. This result confirms the prediction of Equation 10.6 in Chapter 10, which states that longer relaxation times are of particular importance for high adhesion. The best adhesion is observed for interpolymer complex blends with longer relaxation times between 100 and 145 s. These values are appreciably longer than those obtained earlier for a range of commercial adhesives (Figure 11.25) that possess a somewhat higher adhesion at a comparable observation time of 200 s. 11.2.8.6 Main Conclusions Relaxation properties and adhesion of PSAs have been studied with the probe tack method under conditions corresponding to adhesive bond formation. Typical examples of various PSA classes were examined: adhesives based on the SIS block copolymer, PIB of two molecular weights, and acrylic and silicone PSAs. In addition, an interpolymer complex between a polybase and a polyacid has been employed as a model PSA to elicit the structure–property relationship. Under the conditions corresponding to the process of adhesive bond formation under compressive force, for which the mode of deformation is typically in shear, PSAs reveal three retardation times, which, in their magnitudes, are about 1 decade apart. Only the

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11-25

Significance of Relaxation for Adhesion of PSA

900

3

80

800

600 500

40

W

400

W (J/m2)

Relaxation times (s)

700 60

300 20

200 2

100

1

PI B

D Acr 87 uro ylic -9 -Ta 00 k A

A G cryl e 30 lva ic 11

SI

Si lic on e

0 S

0

FIGURE 11.25 Comparison of relaxation times at observation time of 200 s and practical work of adhesion for a series of commercial adhesives (SIS, silicone, cross-linked acrylic Gelva 3011, un-cross-linked acrylic Duro-Tak® 87-900A, and PIB).

longer retardation times (150–800 s) are significant for high adhesion of various PSAs and they relate mainly to the energy-dissipating processes and chain entanglements, which in turn are associated with translational movement (self-diff usion) of polymer segments and entire macromolecules in the course of large-scale structural rearrangements. The minimum values of longer relaxation times are typical of fluid adhesives. Whether chemically or physically cross-linked, network adhesives reveal much greater values of longer relaxation times. Compressive stress relaxation in the course of adhesive bonding defines the mechanism of adhesive joint failure during debonding under a tensile detaching force. The adhesives exhibiting complete stress relaxation debond mainly as fluids, with or without a pronounced plateau on the probe tack stress–strain curves. In contrast, network adhesives, such as SIS and covalently cross-linked acrylic PSAs, are capable of storing mechanical energy during the bonding stage. They demonstrated the occurrence of residual, unrelaxed stress and typically have two peaks on the debonding stress–strain curves. For all PSAs, the practical work of adhesion achieves its maximum value as the contact time becomes comparable with the longer relaxation time or, more precisely, as the mechanism of slow relaxation is rendered dominating. If the stress during adhesive bonding is not allowed to relax, the mechanism and the energy of debonding are independent of the contact time. However, if the bonding stress can relax, the contribution of the contact time to the work of adhesive debonding is appreciable. Correlation between the adhesion and relaxation time for all PSAs examined can be described fairly reasonably with Equation 10.6 of Chapter 10, which relates peel adhesion to the relaxation time and translational mobility of adhesive polymer.

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11-26

11.3

Fundamentals of Pressure Sensitivity

Relaxation Properties of Pressure-Sensitive Adhesives upon Withdrawal of Bonding Pressure

11.3.1 Approach In this section we consider the relaxation properties of PSAs in the second stage of the process of pressure-sensitive adhesion, defined in Figure 11.1 as relaxation (elastic recovery) upon withdrawal of compressive bonding stress. The squeeze–recoil technique has been used for this purpose and has been described in detail in a range of publications.27,28,37 As model PSAs, we employed a hydrophilic adhesive based on a hydrogenbonded complex of high-molecular-weight PVP with short-chain PEG, 22,24,25,35 as well as the hydrophobic PSAs prepared by blending SIS triblock copolymer, butyl rubber (BR), and PIB with relevant tackifiers and plasticizers. The compositions of hydrophobic adhesives are listed in Table 11.4.37 The retardation times and characteristic moduli of the tested adhesives were estimated by nonlinear fitting the experimental squeeze–recoil curves with Equation 11.3. For slow relaxation processes, the total measuring time of the sample thickness, h, was limited to 6000–7000 s. This total observation time corresponds to an average time of elastic recovery of 2000 s upon the withdrawal of the compressive force.

11.3.2

Applicability of Burger’s Model of Viscoelastic Body for Elastic Recovery of Pressure-Sensitive Adhesives

Burger’s model of viscoelastic liquids can be applied to describe the squeeze–recoil curves of some PSAs. Burger’s model represents the combination of springs and dashpots outlined by the Kelvin–Voigt model of a viscoelastic solid and the Maxwell model of a viscoelastic liquid, which are linked to each other in series.11 Figure 11.26 illustrates the squeeze–recoil profi le of the idealized viscoelastic liquid according to Burger’s model. When the material is subjected to a compressive stress, three different strain responses can be observed.11 1a. Instantaneous step of elastic response due to the Maxwell spring. 2a. Gradual strain development related to the Kelvin–Voigt element, which reaches its equilibrium value with time tending to infi nity. 3a. Purely viscous response of Burger’s model related to the Maxwell dashpot that occurs as the Kelvin–Voigt element has attained its equilibrium. The slope of the strain–time curve is then constant and is equal to the shear rate. TABLE 11.4 Sample SIS + I SIS + R SIS + R + I B + PIB

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Compositions of Hydrophobic Polymers Examined Composition SIS Vector 4111 (57% wt)/Isolene 400 (43% wt) SIS Vector 4111 (50% wt)/Regalite R9110 (50% wt) SIS Vector 4111 (36.4% wt)/Regalite R9110 (27.2% wt)/Isolene 400 (36.4% wt) BR 065 (60% wt)/PIB Vistanex LM-MH (40% wt)

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11-27

Significance of Relaxation for Adhesion of PSA

Viscous flow 1a Strain / deformation

3b 2b

2a

Elastic recovery

3a

1b

Creep phase

Recovery phase

t1

Time

FIGURE 11.26 Typical view of the squeeze–recoil profi le according to Burger’s model. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

SIS

0.00

−0.04 h − h0 /h0

PVP-PEG 36% −0.08

−0.12

−0.16

0

1000

2000

3000 4000 Time (s)

5000

6000

7000

FIGURE 11.27 Squeeze–recoil profi les for SIS and PVP blends with 36% PEG under stepwise increasing compressive force of 0.5, 1, 2, and 5 N, respectively. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

When the compressive stress is removed, Burger’s model recovers in a two-step manner: 1b. Strain reduces instantaneously by the elastic response. 2b–3b. Strain reaches a value that is equal to the permanent, nonrecoverable strain and represents the viscous flow of the Maxwell dashpot. Agreement between the behaviors of the idealized Burger model (Figure 11.26) and real adhesives is illustrated in Figure 11.27 and provides qualitative evidence that the examined adhesives behave like linear viscoelastic systems, at least for intermediate

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Fundamentals of Pressure Sensitivity

times, implying the applicability of the squeeze–recoil test for characterization of the relaxation properties of adhesives upon the removal of compressive force.

11.3.3 Squeeze–Recoil Behaviors of Pressure-Sensitive Adhesives Typical squeeze-flow displacement–time curves for the SIS triblock copolymer and for the PVP–PEG adhesive blend are illustrated in Figure 11.27. A remarkable qualitative agreement is observed between the squeeze–recoil behaviors of real materials and the ideal Burger model of a viscoelastic body illustrated in Figure 11.26. As a fixed compressive force is applied to the sample, the gap (h) between the upper and lower plates of the tester, equal to the sample thickness, decreases gradually (Figure 11.27). The higher the squeezing stress, the more deformed the SIS rubber and the PVP–PEG hydrogel. Under a comparable compressive force, the PVP–PEG adhesive is compressed to a greater extent than the SIS rubber, indicating that the PVP–PEG blend is softer. The deformation of the samples under squeeze flow is partly recoverable. As the compressive force is removed, the sample tends to return to its initial shape. The profi le of the squeeze–recoil is indicative of the elastic contribution and relaxation properties of material. As evident from the curves in Figure 11.27, the SIS rubber recovers its initial thickness better compared to the PVP–PEG adhesive model PSA. For the latter, the viscous dissipation of mechanical energy is much more pronounced. Figure 11.28 illustrates the effect of PEG concentration on the squeeze–recoil profi les of PVP–PEG blends under a stepwise increasing compressive force. The higher the

0.0 31% PEG 36% PEG

h − h0 /h0

−0.1

−0.2

39% PEG

−0.3

41% PEG

−0.4 0

1000

2000

3000

4000 5000 Time (s)

6000

7000

8000

FIGURE 11.28 Effect of PEG content on squeeze–recoil profi les of PVP–PEG blends under stepwise increasing compressive force of 0.5, 1, 2, and 5 N. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

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Significance of Relaxation for Adhesion of PSA

PEG content, the greater the contribution of plastic deformation. Th is then requires a longer time to recover the equilibrium thickness of the hydrogel upon removal of compressive stress, indicating that the retardation time increases with the rise in PEG concentration.37

11.3.4 Retardation Times Featured for Hydrophilic PVP–PEG Adhesives For evaluation of the relaxation properties of adhesives from the data in Figures 11.27 and 11.28, the values of relative displacement at a recovery step (h − h 0)/h 0, have been taken with a positive sign and plotted against time in Figures 11.29 and 11.30. The (h − h 0)/h 0 value divided by the removed stress yields the compliance, J. The points represent the measured values, whereas the lines are the results of the data fitted with Equation 11.3. As follows from Figures 11.29 and 11.30, Equation 11.3 provides a fairly reasonable fit with a regression coefficient that is always no less than 0.98. Adequate fitting is obtained taking into account two terms in Equation 11.3, whereas adding a third and fourth terms does not improve the fit and yields corresponding retardation times that fall within the range of deviations from the values found with Equation 11.3 in the two-term form. Using Equation 11.3 with a single retardation time does not, however, provide adequate fitting (relevant regression coefficients lie normally around 0.96).

0.08 0.07

5N

0.06 2N h − h0 /h0

0.05 0.04 1N

0.03 0.02 0.01 0.00 0

100

200

300

400

500

600

700

800

900

1000

Time (s)

FIGURE 11.29 Impact of compressive force on the kinetics of strain recovery upon the removal of compressive force for PVP–PEG (36 wt %) adhesive. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

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Fundamentals of Pressure Sensitivity

0.35 0.30 41% PEG 0.25 h − h0 /h0

39% PEG 0.20 0.15 0.10

36% PEG 34% PEG

0.05

31% PEG

0.00 0

500

1000

1500 2000 Time (s)

2500

3000

FIGURE 11.30 Effect of PEG concentration on the kinetics of strain recovery for PVP–PEG blends. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.) 100

6 5

80

60 τ1 (s)

G1 (MPa)

4 3 40 2 20

1

0

0 30

32

34 36 38 PEG content (%)

40

42

FIGURE 11.31 Shorter retardation time and corresponding modulus as a function of the concentration of plasticizer (PEG) in PVP–PEG adhesive blends. The data are averaged for two values of compressive force (1 and 2 N). (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

The coefficients of regression with Equation 11.3 (G1 and G2 moduli) for the squeeze– recoil profiles, illustrated in Figures 11.29 and 11.30, are illustrated in Figures 11.31 and 11.32 as the functions of PEG content in adhesive blends with PVP. Two reliably different retardation times are determined for the PVP–PEG adhesives, which differ

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11-31

5

600

4

500

3

400

2

300

1

200

τ2 (s)

G2 (MPa)

Significance of Relaxation for Adhesion of PSA

0

100 30

32

34 36 38 PEG content (%)

40

42

FIGURE 11.32 Longer retardation time and corresponding modulus plotted versus PEG concentration in PVP–PEG adhesive blends. The data are averaged for two values of compressive force (1 and 2 N). (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

in their magnitudes by about 1 decade: the shorter time, τ1, is in the range of 10–110 s and the longer time, τ2, is ∼120–950 s. Within the framework of Burger’s model of viscoelasticity, the shorter retardation or relaxation time is mainly associated with an elastic contribution of the spring element into strain recovery, whereas the longer time characterizes the behavior of a coupled dashpot and spring elements of the model and the rate of strain recovery during the dissipation of the initially applied energy. The mechanism of the latter process involves large-scale rearrangement of the structure of the polymeric material via long-range motion (diff usion) of polymer segments and entire macromolecules. This process takes normally a much longer time than the elastic recovery of polymer chain conformations. The longer process may also be associated with the entanglements between polymer chains. The shorter retardation time relates mainly to the restoration of the original conformation of polymer segments between entanglements. As demonstrated in Figures 11.31 and 11.32, with increasing PEG concentration in blends, the shorter retardation time is nearly constant, whereas the longer time increased gradually and the relevant values of corresponding moduli decreased gradually with PEG content. The increase in the longer retardation time as a function of PEG content is also easily observable in Figure 11.28 and reflects the slowing down of strain recovery upon the removal of compressive force. Under relatively moderate compressive forces the retardation times and corresponding moduli are practically independent of the applied compressive stress.37 However, at comparatively high shear stresses (compressive force of 5 N and higher) both the retardation times and the corresponding moduli tend to increase. The higher the stress, the larger the molecular rearrangements occurring in the strained material and the longer the time required for relaxation. The values of retardation times and moduli at relatively moderate compressive forces of 1 and 2 N can be considered material characteristics.

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Fundamentals of Pressure Sensitivity

5

G1, τ1

31

G2, τ1

31 34

4

31 34

G (MPa)

31

36

3

2

36

31

34 36 34

39

41

41

36 1

39

39

39 41 0 0

100

200

300

400

500

τ (s)

FIGURE 11.33 The relationship between retardation times and the corresponding moduli for PVP–PEG blends. The PEG contents (wt %) are indicated. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

As a rule, to demonstrate the effects of composition on the spectra of retardation times in the examined PSAs, we use the values of retardation times and associated modulus averaged for compressive forces of 1 and 2 N. The retardation times and corresponding moduli are not fully independent material characteristics, but are correlated to each other. As follows from the data in Figure 11.33, in the course of PVP plasticization with PEG, the higher values of the longer retardation time are usually associated with lower values of the corresponding modulus. On the other hand, the shorter retardation time is independent of G1 (Figure 11.31). The inverse proportionality between the retardation time and the corresponding modulus, which is the case for all polymer blends studied in this work, suggests the applicability of the Maxwell, Kelvin–Voigt, and Burger models of viscoelasticity (G = η/τ) to describe the behavior of the hydrophilic PVP–PEG and hydrophobic adhesives. Although the comparison of the idealized behavior of Burger’s model illustrated in Figure 11.26 with the squeeze–recovery profiles of real adhesives (Figure 11.27) characterizes qualitatively these adhesives as linear viscoelastic systems, the data in Figure 11.33 provide quantitative support in favor of this observation and imply that the values of retardation times and corresponding moduli evaluated in this work can be treated as true material constants.

11.3.5 Retardation Times in Hydrophobic Pressure-Sensitive Adhesives Many hydrophobic elastomers have been used to produce PSAs, but generally the elastomers must be blended with tackifiers and plasticizers to obtain optimized adhesion.

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Significance of Relaxation for Adhesion of PSA

In a PSA formulation of that type, the rubbery polymer provides the elastic component, whereas a low-molecular-weight tackifying resin and a plasticizer constitute the viscous components. Most parent elastomers per se do not have the proper rheology to be PSAs. Typically, the addition of a tackifier raises the glass transition temperature, Tg, lowers the plateau modulus by diluting the chain entanglements of the elastomer, and increases the ratio of viscous to elastic response of the elastomer/tackifier blend, improving both the bond-making and the bond-breaking processes. Plasticizers demonstrate similar effects on rheology, but cause reduction in Tg. It is, therefore, of particular interest to trace how the formulation process affects the relaxation properties of a composite PSA. In this work we use a SIS block copolymer and BR as base elastomers. A hydrocarbon resin (Regalite R9100, R) has been employed as a tackifier. R is a partially hydrogenated resin with a specific balance of aliphatic and aromatic groups. As a plasticizer for the SIS, a low-molecular-weight polyisoprene rubber, Isolene (I), has been used. The pressure-sensitive adhesion in BR is provided by mixing the BR with a low-molecularweight PIB (Vistanex). The compositions of the samples examined in this work are presented in Table 11.4. As evident from the data in Figures 11.34 and 11.35, mixing elastomers (SIS and BR) with plasticizers (I for SIS and low-molecular-weight PIB for BR) and tackifying resin (R) results in an appreciable increase in retardation times (Figure 11.34) and a corresponding decrease in the corresponding moduli (Figure 11.35). However, their effects on the values of the shorter retardation time are less marked compared with the dramatic changes in the longer retardation time. The joint effect of the plasticizer and tackifying resin on the retardation time and corresponding modulus of SIS are much more pronounced than the

P

Retardation times (s); P (N/m)

700 600 500 400 300 200 100

τ1

τ2

0 SIS

SIS+I

SIS+R SIS+I+R

DT

BR

BR+PIB

FIGURE 11.34 Effects of plasticizers [isolene (I) and low-molecular-weight PIB] and tackifier resin [regalite (R)] on retardation times and peel adhesion (P) of SIS and BR compared with DuroTak 34-4230 (DT), used in this work as a typical hydrophobic PSA. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

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Fundamentals of Pressure Sensitivity

G1 G2 (102 MPa); P (N/m)

700

P

600 500 400 300 200

G2 G1

100 0 SIS

SIS+I

SIS+R SIS+I+R

DT

BR

BR+PIB

FIGURE 11.35 The impact of plasticizers (I and low-molecular-weight PIB) and tackifier resin (R) upon the retardation moduli and peel adhesion (P) of SIS block copolymer and BR compared to Duro-Tak 34-4230 (DT), used in this work as a typical hydrophobic PSA. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

separate effects of the plasticizer–tackifier mixture (compare the SIS + I + R system with the SIS + I and the SIS + R blends in Figures 11.34 and 11.35).

11.3.6 Correlation between Retardation Times and Pressure-Sensitive Adhesion The phenomena of tack, peel, and shear have been reported to depend upon the relative participation of the two primary molecular mechanisms of deformation: viscous flow that proceeds by diff usion via free volume and the elastic distortion that stores free energy.38 These two mechanisms are characterized by different time scales. Whereas the process of viscous flow requires appreciable time, elastic flow dominates at shorter time scales. To appreciate the significance of the relaxation properties for the adhesive behavior of polymers we must compare the effects of composition on relaxation and pressure-sensitive adhesion. Figures 11.34 and 11.35 illustrate the correlation between adhesive and relaxation properties for SIS blends with a plasticizer (I) and a tackifier (R), as well as BR plasticized with low-molecular-weight PIB. Unblended SIS and BR reveal no or low adhesion. Mixing the SIS with a plasticizer provides initial tack but comparatively low adhesion, whereas a plasticizer (low-molecular-weight PIB) significantly improves both the tack and the adhesion of BR. In SIS blends with a tackifier the adhesion is much improved. High adhesion is also reported for the ternary SIS blends containing both tackifier R and plasticizer I. As a reference, for hydrophobic PSAs in this work we employ a SIS-based Duro-Tak 34-4230, which demonstrates 180o peel adhesion of 775 N/m. The relaxation properties of this reference sample, tested under comparable conditions, are characterized by τ1 = 17 s, G1 = 0.74 MPa, and τ2 = 356–400 s, G2 = 2.48 MPa (Figures 11.34 and 11.35).

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Significance of Relaxation for Adhesion of PSA

600 P

P (N/m) τ (s)

500 400 300

τ2

200 100

τ1

0 30

32

34

36 38 PEG content (%)

40

42

FIGURE 11.36 180o peel adhesion, P, and retardation times of PVP–PEG adhesives as a function of PEG concentration at 50% relative humidity of the surrounding atmosphere. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

Let us compare now the values reported for the hydrophobic adhesives with values featured for hydrophilic PVP–PEG PSAs. The PVP–PEG system provides an appropriate model to illustrate the effect of the molecular structures underlying pressure-sensitive adhesion, because its adhesive behavior can be related to the changes in structure, interaction mechanism, phase state, and other physical properties as the PEG content is varied. The effects of PEG concentration on adhesive and relaxation properties of PVP– PEG blends expressed in terms of 180° peel force, 39 retardation times, and corresponding moduli are presented in Figures 11.36 and 11.37. Whereas the shorter retardation time is nearly constant, the longer time is a monotonously increasing function of PEG content, and the corresponding moduli decrease with the increase in PEG concentration between 31 and 41% PEG, peel adhesion comes through a maximum at 36% PEG concentration in the blends. The maximum adhesion relates to the PEG concentration at which a stoichiometric PVP–PEG H-bonded complex is completely formed within the PVP–PEG blends.22,24,25,40 This complex demonstrates properties that are not typical of both parent polymers. As evident from the data in Figures 11.36 and 11.37, the maximum adhesion in PVP blends with 34–39% PEG is observed when the shorter and longer retardation times range within 10–65 and 120–450 s, respectively, whereas the values of the corresponding moduli vary between 0.5–2.6 and 0.8–3.8 MPa, respectively. The relaxation properties of the blend containing 36% PEG and providing the best adhesion are characterized by τ1 = 26–46 s, G1 = 1.3–2.17 MPa, and τ2 = 325–430 s, G 2 = 2.94–3.3 MPa. Within the PEG concentration region (31–34%), where debonding occurs through a predominantly adhesive type of bond failure, 38 the gain in adhesion is always associated with an appreciable rise in the value of the longer retardation time (Figure 11.36).

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Fundamentals of Pressure Sensitivity

8

600 G1 G2

500

P

400

4

300

2

Peel force (N/m)

G (MPa)

6

200 0 30

32

34

36 38 PEG content (%)

40

42

FIGURE 11.37 Effect of PEG concentration on 180o peel adhesion, P, and moduli corresponding to shorter (G1) and longer (G 2) retardation times for PVP–PEG adhesives at relative humidity of 50%. (From Novikov, M.B. et al. J. Adhesion, 81, 77–107, 2005.)

However, as the PEG concentration reaches 36% and higher, the type of debonding becomes miscellaneous (adhesive–cohesive) and this rule no longer holds. For these blends, the longer retardation time continues to increase more smoothly, whereas peel adhesion begins to decrease. In the same manner as that established above for hydrophobic blends based on SIS and BR (Figures 11.34 and 11.35), for hydrophilic adhesives greater adhesion is associated with the values of longer retardation time ranging from 325 to 445 s (Figures 11.36 and 11.37).

11.3.7

Relaxation Criteria for Pressure-Sensitive Adhesion

Summing up the data in Figures 11.34 through 11.37, we come to the relaxation criteria for pressure-sensitive adhesion, which can be stated in a preliminary form as follows:37 1. To be a PSA, polymer compositions preferably possess two retardation times of 10–70 and 300–660 s, respectively. 2. For proper adhesion, the relaxation modulus, G 2, relating to the longer retardation time, is preferably higher than the modulus, G1, corresponding to the shorter retardation times. Because the G 2 and G1 values are the measures of energy dissipated, respectively, for predominantly large-scale and small-scale viscoelastic mechanisms of squeeze–recoil, and because the amount of energy dissipated in the course of the debonding process is the measure of adhesion, this requirement illustrates the prevailing importance of the larger-scale mechanism (that requires appreciable molecular mobility) for pressure-sensitive adhesion. 3. Optimum adhesion is achieved as the absolute values of the G 2 and G1 moduli range between 2.5–3.3 and 0.70–2.20 MPa, respectively.

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Significance of Relaxation for Adhesion of PSA

11-37

It is evident that further work is needed to demonstrate whether the established values of retardation times and relevant moduli are also typical of the entire variety of PSAs currently available. Furthermore, more data should be obtained to trace quantitative correlations between the adhesion and relaxation characteristics within the window outlined by the above criteria. As follows from the data in Figures 11.34 and 11.35, the retardation times and G1 modulus for SIS + I adhesive fall within the relaxation criteria for PSAs, yet the SIS + I adhesive exhibits a relatively low peel force. Th is is most likely due to the fact that the modulus G 2 = 1.61 MPa for the SIS + I blend is below the lower limit outlined by the relaxation criterion (G 2 = 2.5 MPa). It implies also that there exist different combinations of retardation times and corresponding moduli that are either favorable or unfavorable for high adhesion.

11.3.8 Major Conclusions Under the conditions imitating the removal of compressive force upon adhesive bond formation, for which the mode of deformation is typically in shear, PSAs reveal two retardation times, which are about 1 decade apart in their magnitudes. The shorter retardation times (10–70 s) define the rate of release of stored energy due to the recovery of conformation of polymer chains. The longer retardation times (300–660 s) relate mainly to the energy-dissipating processes and chain entanglements, which are associated with translational movement (self-diff usion) of polymer segments and entire macromolecules in the course of larger-scale structural rearrangements. Both plasticizers and tackifying resins increase the values of retardation times; however, their effects on the longer retardation time are much more pronounced compared with the shorter time. Correlation between adhesion and the retardation time for both hydrophilic and conventional (hydrophobic) PSAs can be described fairly reasonably with Equation 10.6 in Chapter 10, 22 which relates peel adhesion to relaxation time and the translational mobility of the adhesive polymer.

11.4 Relaxation Properties of Pressure-Sensitive Adhesives in the Stage of Debonding 11.4.1 Three-Stage Mechanism of Debonding Debonding is the third and final stage of the process of adhesion (see Section 11.1.2) and, in turn, can be treated as a three-stage process. The peel test geometry does not provide any detailed insight into the mechanisms of debonding of the adhesive layer from the hard surface and, in particular, it is not able to separate the small strain deformation (in the linear regime) from the large strain deformation (in the nonlinear regime) taking place in the adhesive layer during the debonding process. The parallel geometry of flat-end probe tack tests is better adapted for studying the details of the debonding mechanisms of thin layers of soft deformable adhesives under tensile stress.14,17,41,42 In these tests, the adhesive layer is submitted to a uniform distribution of stress and deformation in a confined geometry, making it easier to break up the debonding process into elementary steps. According to a universally accepted description,17 the first stage

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11-38

Fundamentals of Pressure Sensitivity

Stress σ (MPa)

0.8

σmax

0.6 0.4

250 µm

σbf

0.2

Wadhesion ~ 100−400 J/m2

0.0 0

1

2 Strain ε

3

4

1 mm

FIGURE 11.38 Direct observation of the debonding mechanisms and stress versus strain curve in the course of probe tack test for SIS-based PSA and corresponding images illustrating transformations of the PSA structure in the plane normal to the adhesive layer at different stages of the debonding process. Debonding velocity 0.1 µm/s. T = 22°C, contact time 1 s. (From Creton, C. et al. in Adhesion: Current Research and Applications, Possart, W.G., Ed., Weinheim, Wiley-VCH, 2005. With permission.)

of the debonding process is a homogeneous small tensile deformation of the adhesive layer until the initiation of failure mechanism occurs through the formation of cavities or cracks at the interface or in the bulk of the adhesive. This stage corresponds to the increase in stress and the appearance of a peak on the probe tack curve (Figure 11.38).43 The second stage of debonding represents the formation of a foamed structure of cavities in the direction normal to the plane of the adhesive fi lm. As a result, the tensile stress decreases, leading to a gradual decline or the formation of a plateau on the probe tack curve. The occurrence of the plateau relates to the elongation of fibrils, which initially represent the walls between neighboring cavities. The third and final stage of debonding involves separation of the adhesive and probe surfaces, either by failure of the fibrils (cohesive failure) or by detachment of the foot of the fibrils from the surface of the substrate (probe). The general features of a stress–strain curve obtained in a probe test of a PSA are characterized typically by four parameters (Figure 11.38): (1) maximum stress, σmax; (2) stress corresponding to the beginning of the fibrillation process, σ bf; (3) maximum extension, εmax; and (4) work of separation, W, defined as the integral under the stress– strain curve multiplied by the initial thickness of the layer h0. Adhesive polymer relaxation is involved in all three stages of the debonding process. In the course of debonding, the elongation of the fibrils often achieves many hundreds and thousands of percents. For the characterization of polymer relaxation as a material property, only the linear elastic region of very small deformations is usually taken into consideration. However, let us recall that adhesion is a process rather than a material property (see Section 11.1.1) and that debonding occurs at very high tensile strains.

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Significance of Relaxation for Adhesion of PSA

11-39

Consequently, in the following discussion we must consider the relaxation of adhesive polymers at large tensile deformations in various stages of the debonding process. We first consider the transformation of the structure of adhesive material during the debonding process.

11.4.2

Evolution of Pressure-Sensitive Adhesive Structure during the First Stage of the Debonding Process

Because over the course of a probe tack test a shear deformation in the plane of the adhesive layer is coupled with tensile strain in the direction normal to the adhesive fi lm, it is difficult to interpret the corresponding relaxation processes in terms of relaxation moduli and times. Nevertheless, the probe tack test allows an illustrative visualization of the mechanisms of transformations of the PSA structure and geometry during a process of elastic recovery at different stages of the probe tack test. To interpret correctly the probe tack stress–strain curves as characteristics of the process of debonding, it is essential to identify the transformation of the microstructure occurring in the adhesive material over time. With this purpose, we give a qualitative description of the structural changes observed in the adhesive fi lm if probe detachment is stopped for a certain time during different stages of the debonding process. 1. In the course of the first stage of homogeneous deformation, stress increases linearly with deformation under a fi xed debonding rate (Vdeb) before the stress reaches its peak.44 2. In the course of the second stage, intensive cavitation is observed, resulting in decreased stress.16,17,43 Figure 11.39 illustrates the displacement of motors and a typical force curve as a function of time during a relaxation experiment carried out in a probe tack setup. The displacement of the motors driving the probe was stopped at a given moment during different stages of the debonding process. The system, under tensile stress, was then left to relax for a given time, tstop. During this time, relaxation of the force occurs. At the end of the stop the displacement of the probe was resumed until complete debonding of the adhesive occurred.44 The model adhesives used in this study consisted of a series of acrylic copolymers based on 2-ethylhexyl acrylate as a base monomer. As comonomers, they contained increasing amounts (2, 4, and 8 wt %) of acrylic acid (AA). Adhesives are referred to as 2AA, 4AA, and 8AA, respectively. The advantage of using polyacrylates is that the pure polymers exhibit PSA properties without any need for additional formulation ingredients such as tackifying resins. Figure 11.40 illustrates the nominal stress as a function of time for a nonstop test and for three relaxation tests on a steel probe. The relaxation tests were always performed during the increase in force at the beginning of the debonding process before catastrophic failure was observed. The stops from stop 1 to stop 3 were performed at increasing values of stress at the beginning of the relaxation. The level of tensile stress at which the test is stopped and the adhesive allowed to relax is referred to as σ 0. Because this early loading stage of the debonding process is essentially elastic at the

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11-40

Fundamentals of Pressure Sensitivity

Displacement (motors) Vdeb Vdeb

tstop Time

Force

Stop Time

FIGURE 11.39 Force and displacement of the motors for a relaxation test as a function of time. The motors are stopped at a given moment, and the adhesive is allowed to relax for a given time, tstop. (From Lindner, A., Maevis, T., Brummer, R., Lűhmann, B., and Creton, C., Langmuir 20, 9156, 2004. With permission.) 0.30 Without stop

Stress (MPa)

0.25 0.20 0.15

Stop 3

0.10

Stop 2 Stop 1

0.05 0.00 0

50

150

100

200

250

t (s)

FIGURE 11.40 Stress, σ, as a function of time for 2AA acrylic PSA. A test without stop and three tests with stops at different initial values of σ 0: Stop 1, σ0 = 0.08 MPa; Stop 2, σ 0 = 0.16 MPa; Stop 3, σ0 = 0.25 MPa. For all stops, tstop is 180 s. (From Lindner, A., Maevis, T., Brummer, R., Lűhmann, B., and Creton, C., Langmuir 20, 9156, 2004. With permission.)

deformation rates used here, increasing the initial values of σ 0 corresponds to an increase in the amount of elastic energy stored in the adhesive layer at the beginning of the stop. Figure 11.40 illustrates that significant stress relaxation is taking place during the stop.44

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11-41

Significance of Relaxation for Adhesion of PSA

Figure 11.41 (top) illustrates the stress relaxation of the 2AA adhesive on a high-energy steel probe for the three different stops. Figure 11.41 (bottom) demonstrates the same relaxation process for 2AA but on an apolar low-energy poly(ethylene-co-propylene) (EP) substrate. As evident from these data, relaxation of the tensile stress is strongly affected by the nature of the substrate. This implies that stress relaxation is not only a property of the adhesive material, but also the property of the adhesive–adherent pair. In other words, the boundary conditions at the probe–adhesive interface contribute greatly to the relaxation of stress in the course of the debonding process. As follows from Figure 11.41 (top), the decrease in stress slows down toward the end of the stop and finally reaches a nearly constant value, as occurs for viscoelastic materials

0.25

Stress (MPa)

0.20 0.15 Stop 3 0.10

Stop 2 Stop 1

0.05 0.00 0

50

100 t (s)

150

200

150

200

0.25

Stress (MPa)

0.20

0.15 Stop 3 0.10 Stop 1

Stop 2 0.05

0.00 0

50

100 t (s)

FIGURE 11.41 Stress relaxation during probe stops for 2AA acrylic adhesive on high-energy steel (top) and low-energy EP substrates (bottom). (From Lindner, A., Maevis, T., Brummer, R., Lűhmann, B., and Creton, C., Langmuir 20, 9156, 2004. With permission.)

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11-42

Fundamentals of Pressure Sensitivity

possessing a yield stress. When visualizing the debonding process, it is obvious that most of the cavity growth and cavitation takes place during the first 60 s. The further comprehension of structural evolution process is possible if the characteristic times of the structural evolution are taken into consideration. To describe precisely the deformation mechanism during the debonding process observed in the probe tack test, we must define the terms cavitation and propagation. Confined fi lms of PSA under a tensile stress develop cavities. These cavities appear where surface defects were initially present,44 and we can optically detect them when their size becomes of the order of a few micrometers. The cavities then grow rapidly to a size of the order of the thickness of the fi lm. At this stage of the debonding process, two different mechanisms can be observed on video images made in the course of deformation and relaxation: either the cavity stops growing and new cavities progressively nucleate, eventually fi lling the space previously occupied by the adhesive fi lm, or the cavity continues growing laterally in a disk-like shape until it comes in contact with an adjacent disk-like cavity.45,46 The process of nucleation of new cavities under constant stress is called cavitation, whereas the growth of existing cavities in the plane perpendicular to the tensile direction is referred to as propagation. Video captures taken during the force relaxation process (Figures 11.42 and 11.43) reveal whether cavitation or propagation takes place. These observations reveal whether the cavities eventually coalesce or whether individual cavities persist and form a foamlike structure when the adhesive layer is stretched further. This last question is of particular importance to the long-term durability of the adhesive bond, because a coalescence of individual cavities leads to rapid complete detachment of the adhesive. 1a

1b

2a

2b

FIGURE 11.42 Snapshots taken during the relaxation process for 2AA (left) and 8AA (right) on steel.44 The pictures at the top are always taken at the beginning of the stop (t = 0) and the pictures at the bottom are taken at the end of the stop (t = 180 s). (1a) A stop at a low initial stress level (σ0 = 0.08 MPa, σ0/σmax = 28%). (1b) A stop at higher initial stress (σ0 = 0.25 MPa, σ0/σmax = 85%) for 2AA. One observes little cavitation, but some growth of the existing cavities. (2a) A stop at a low initial stress level (σ0 = 0.14 MPa, σ 0/σmax = 25%). (2b) A stop at a higher initial stress for 8AA (σ0 = 0.45 MPa, σ0/σmax = 81%). In this case one observes the nucleation of new cavities. (From Lindner, A., Maevis, T., Brummer, R., Lűhmann, B., and Creton, C., Langmuir 20, 9156, 2004. With permission.)

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11-43

Significance of Relaxation for Adhesion of PSA

a

b

c

FIGURE 11.43 Snapshots taken during the relaxation process of 2AA acrylic adhesive on a lowenergy EP substrate. The images at the top are always taken at the beginning of the stop, whereas the images at the bottom are made at the end of the stop (t = 180 s for a and b, t = 15 s for c). (a) Stop at a low initial stress level (σ0 = 0.13 MPa, σ 0/σmax = 51%). (b) Stop at intermediate initial stress (σ0 = 0.15 MPa, σ 0/σmax = 59%). (c) Stop at high initial stress level (σ0 = 0.22 MPa, σ 0/σmax = 86%). On the low adherence surface, no cavitation but substantial growth is observed. (From Lindner, A., Maevis, T., Brummer, R., Lűhmann, B., and Creton, C., Langmuir 20, 9156, 2004. With permission.)

When the adhesives were bonded to a steel surface, both mechanisms of cavity nucleation and growth were observed, whereas on low-energy EP surfaces, only crack propagation occurred. This result demonstrates that unless the sensitivity of these specific mechanisms to the molecular structure of the adhesive is understood, there will be no hope for predicting the lifetime of the bond. Because cavitation and crack growth are processes that entail locally large strains of the adhesive, it is highly unlikely that linear viscoelastic properties alone will be able to predict the nucleation or growth of these cavities. The sharp difference in behavior between the two substrates highlights the importance of adhesive interactions. On steel, resistance to crack propagation is high, so the most important property, that the adhesive must have, is good resistance to the formation of cavities. On the contrary, on EP surfaces, resistance to cavitation is not very important because failure occurs by crack propagation. It is the balance between these two properties that must be optimized.

11.4.3 Mechanisms of Adhesive Relaxation at the Second Stage of the Debonding Process The relaxation data described in the previous section relate to the probe tack test, which was stopped at the stage of homogeneous deformation of the adhesive before the peak

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Fundamentals of Pressure Sensitivity

stress, when a fibrillar foam-like structure is not yet formed. Here, we consider the results of a similar relaxation test performed by stopping the driving motor of the probe tack apparatus and monitoring the force relaxation under constant displacement conditions while the fibrillar foam is well formed, the peak stress is covered, and a strainhardening effect is observed, indicating the formation of strong fibrils (Figure 11.44).47 The adhesive used in this case is based on SIS triblock copolymer. As indicated by the data in Figures 11.44 and 11.45, stress does not relax to zero, as one would expect for a viscous liquid capable of flow, but to ∼70% of its initial value before remaining constant. A similar relaxation curve with appreciable residual unrelaxed stress was obtained for an SIS-based adhesive at the conditions imitating adhesive bond formation under bonding pressure (compare with Figures 11.4 and 11.7). This relaxation behavior is typical of viscoelastic adhesives possessing an apparent yield stress and clearly demonstrates that the fibrils are able to store elastic energy during their formation and stretching; only during detachment or fracture is this elastic energy released.47 The video images of the debonding process, illustrated in Figure 11.46, clearly indicate that the plateau stress for the SIS adhesive corresponds to the formation and elongation of the fibrillar foam.48 The images demonstrated that the average cell size and the amount of cavities are fairly independent of the relaxation time so that observed differences in measured stress cannot be due to a different microscopic structure of the foam. Comparatively negligible changes in the structure of SIS adhesive occur during the relaxation process, emphasizing the very elastic nature of the polymer in the fibrils. Such an elastic fibrillating behavior has also been reported in an even more pronounced way for soft physical gels, which are composed of block copolymers swollen in a preferential solvent for the midblock.44

1.0

σ (MPa)

0.8

0.6

0.4

0.2

0.0 0

50

100

150 Time (s)

200

250

300

FIGURE 11.44 Stress-versus-time curves for probe tack tests with intermediate stops at different levels of initial stress for SIS adhesive. The test is stopped for 120 s and then resumed. Note that the stress–strain curves are almost identical for all tests. (From Roos, A. and Creton, C., Macromol. Symp. 214, 147, 2004. With permission.)

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11-45

Significance of Relaxation for Adhesion of PSA

0.5

σN (MPa)

0.4

0.3

0.2

0.1

0.0 0

100

200

300

400

500

600

t − t stop (s)

FIGURE 11.45 Stress-versus-t − tstop curves obtained by stopping the driving motors in the fibrillation regime at three different stress levels for the SIS adhesive. The test was stopped here for 600 s. (From Roos, A. and Creton, C., Macromol. Symp. 214, 147, 2004. With permission.)

t = tstop

t = tstop + 120

FIGURE 11.46 Snapshots taken during the relaxation process for SIS adhesive. The left image was taken at the beginning of the stop, whereas the right image relates to the end of the stop. The horizontal full scale is 1.5 mm. (From Roos, A., Ph.D. Thesis, Universite Paris VI, Paris, 2004. With permission.)

11.4.4 Comparison of Relaxation Processes in Linear Viscoelasticity and Large-Strain Elongational Geometries Due to a complex mechanism of PSA deformation in the course of the probe tack test, it is pertinent to consider it under simpler conditions. Recently, relaxation tests for SIS triblock copolymer plasticized with diblock PS–PI copolymer were performed.49 Shear geometry was used to test the relaxation of physically cross-linked SIS-based systems in the linear regime and elongational geometry to test them in the nonlinear range. In shear, the deformation from 1 to 5% was applied to the sample and the relaxation

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Fundamentals of Pressure Sensitivity

modulus was measured as a function of time G(t) for 103–104 s. In elongation, the relaxation tests were performed at a deformation of 500%. It took 9 s for the cross-head to go to this elongation (Vt = 500 mm/min). Tests were performed at room temperature, and the relaxation of stress was measured as a function of time for 1000 s. The relaxation moduli normalized by the moduli at the beginning of the relaxation (G 0) are presented in Figure 11.47 for the four model resin blends.49 G 0 is independent of the PS–PI content, but always lower than G′. The material relaxes more when there is more diblock in the blend, namely, from 30 to 85% of the stress after an imposed deformation of 2%. In all cases, the relaxation seems to be over after 1000 s. Figure 11.48 illustrates the relaxation of stress normalized by the level of stress at the beginning of relaxation for both pure SIS blends and resin blends.49 Unlike in the linear regime, the levels of stress at the beginning of relaxation decrease with increasing diblock and resin contents. This is not surprising because in the tensile geometry the stretch to 500% deformation takes several seconds, and some relaxation can take place already in this loading stage. Similar to what is observed in the linear regime, the more diblock in the blend, the more rapid and pronounced the relaxation. However, the similarity ends here. After 1000 s, the material only relaxes 18–27% of the initial applied stress for pure polymer blends and 18–34% of the stress for adhesive formulations. In addition, in all cases the relaxation process is not over after 1000 s. These two experiments demonstrate that there is a remarkable difference in the kinetics of relaxation at small and large strains. When the sample is stretched to large strains, the relaxation of polymeric chains occurs in a strongly oriented network at a rate that probably depends mainly on the relaxation of the triblock chains bridging between PS domains. On the other hand, at small strains the network of polymer chains is not oriented to such an extent and most of the stress, and then the relaxation, occurs between entanglements in the polyisoprene domains, which relax faster than the central PI blocks of the triblocks.49 The SIS blends with a PS–PI diblock copolymer display marked 1 9 8 7 6

4

54→0

G(t)/G0

5

3

2

0.1 10−1

100

101

102

103

104

t (s)

FIGURE 11.47 Relaxation modulus in shear for SIS blends with 60 wt % resin after a deformation of 2%.49 The content of PS–PI diblock copolymer varies between 54 and 0 wt %. (From Roos, A. and Creton, C., Macromolecules, 38, 7807, 2005. With permission.)

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11-47

Significance of Relaxation for Adhesion of PSA

1.0

54→0

σN(t )/σ0

0.9

0.8

0.7

0.6 (a)

2

4

6 8

1

2

4

6

10

8

2

4

6

100

8

1000

t (s) 1.0

54→0

σN(t )/σ0

0.9

0.8

0.7

0.6 (b)

2

1

4

6 8

2

4

10

6

8

100

2

4

6

8

1000

t (s)

FIGURE 11.48 Relaxation of the stress in elongation after a deformation of 500% for (a) SIS blends without resin and (b) blends with 60% resin. The content of the PS–PI diblock copolymer varies between 54 and 0 wt %. (From Roos A. and Creton C., Macromolecules 38, 7807, 2005. With permission.)

nonlinear viscoelastic behavior and are much more dissipative at low and intermediate strains than at very high strains. This suggests that free diblock chains dangling from PS domains may have very long relaxation times, which dominate the viscoelastic behavior at low and intermediate strains, whereas at high strains the behavior is dominated by the bridging chains provided by the triblocks. The significance of the relaxation data presented in this section for pressure-sensitive adhesion emerges from the fact that the adhesion of SIS blends increases with increasing contents of resin and PS–PI diblock copolymer. As evident from Figures 11.47 and 11.48, both tackifying resin and PS–PI plasticizer accelerates the stress relaxation, both in the linear elastic deformation region and at large strains. For a more insightful analysis, the values of relaxation times and corresponding moduli are to be taken into consideration. With this purpose in mind, the relaxation properties of another physically cross-linked model PSA based PVP–PEG H-bonded complex have been studied.

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Fundamentals of Pressure Sensitivity

11.4.5 Relaxation Properties of PVP–PEG Model Pressure-Sensitive Adhesives 11.4.5.1

Relaxation Spectrum of PVP–PEG Adhesive in Linear Elastic Shear

The dynamic mechanical properties of the PVP–PEG adhesives in the linear viscoelastic regime were measured on a parallel plate rheometer.28 The amplitude of deformation was chosen to be in the linear region over the whole range of temperatures. For our PVP–PEG blends this zone corresponds to a deformation varying from 0.1 to 1%, depending on the temperature. The relaxation spectrum in Figure 11.49 illustrates three different groups of relaxation times that are typical for the rheological behavior of the PVP–PEG adhesive under shear stress: about 10−5, 1–50, and 1000–3000 s. These values are in fairly reasonable agreement with the results of the direct evaluation of the retardation times of PVP– PEG blends recently measured with a squeeze–recoil test under conditions imitating the removal of a compressive force in the course of adhesive bond formation, which are presented in Section 11.3. Two values of retardation times were established in this work: the shorter retardation time of 10–70 s and the longer time of 300–660 s. Whereas the relaxation time of ∼10−5 s most likely refers to the transition from a glassy solid to a viscoelastic state, both longer times are supposed to be associated with the rearrangement of the network of H-bonds. In full agreement with the prediction of Equation 10.6 in Chapter 10, the longer retardation time has the most significance for pressure-sensitive adhesion.22

8

7

log H (Pa)

6

5

4

3 −12

−10

−8

−6

−4

−2 0 log τ (s)

2

4

6

8

FIGURE 11.49 Relaxation spectrum featured for the PVP adhesive blend with 36% PEG at 20°C. (From Feldstein M.M. et al., J. Appl. Polym. Sci., 100, 522–537, 2006. With permission.)

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Significance of Relaxation for Adhesion of PSA

11.4.5.2

11-49

Tensile Stress Relaxation at High Elongations: The Statement of the Problem

As demonstrated in Section 10.3.3 of Chapter 10, peel adhesion of the PVP–PEG adhesive blends is controlled by the work of viscoelastic deformation and fracture of adhesive fi lms under large uniaxial extension.22 This renders the study of relaxation properties of this model PSA in the course of stretching reasonable. Large-strain relaxation in entangled polymers has been examined in some detail.50,51 For a large step in strain, the relaxation modulus has been established to depend on the magnitude of the initial step in strain. However, the maximum relaxation time has been proved to be independent of strain, even outside the range of linear elasticity. Tensile stress relaxation of PSAs at large strains raises some specific questions. Indeed, in the course of a typical relaxation test, a material should be instantaneously stretched to a predetermined deformation before the relaxation of the stress is recorded. Quantities evaluated using this methodology are generally regarded as characteristics of the material. In our approach we consider pressure-sensitive adhesion as a process rather than as a material property. We are mostly interested in the characterization of relaxation under the conditions that approximate closely the scenario of an adhesion test. In the course of such an adhesion test, the PSA is usually loaded initially with a finite strain rate, sometimes very small, and a partial relaxation occurs during this loading stage. Measured in such a manner values cannot be regarded as the properties of the material solely, but also as the characteristics of the process of testing. To avoid any confusion with true values of the relaxation times and moduli, in further discussion we refer to the evaluated properties of the relaxation process as the characteristic times of elastic recovery, τ, and the characteristic moduli, E. In the present study we attempt to answer some questions that usually do not arise during a more classic examination of relaxation: How is relaxation affected by the drawing rate in the course of loading? How does relaxation depend on the maximum elongation reached? Another distinctive feature of our approach is that relaxation is always seen within the context of adhesion. This is necessary to identify the values of relaxation times and corresponding moduli associated with high adhesion. The PVP–PEG adhesive represents a convenient model PSA because its adhesion may be easily manipulated by a change in composition. Short-chain PEG serves simultaneously in binary blends with PVP as a noncovalent cross-linker of longer PVP macromolecules and as a plasticizer, affecting the balance between the energy of intermolecular cohesion and the free volume.25,52 The blend containing 36 wt % PEG exhibits maximum adhesion, whereas in the blends underloaded with PEG the increase in cohesion strength dominates the increase in free volume. On the contrary, in PEG-overloaded blends the increase in free volume dominates the increase in cohesion, resulting in the fluidity of the adhesive blends. Such behavior is obvious from Figures 10.6 and 10.21 in Chapter 10, which illustrate the effects of PVP–PEG blend composition and drawing rate on tensile stress–strain curves of adhesive films up to break.22,25,52 As follows from Figures 10.6 and 10.21, a specific property of the PVP–PEG model PSA is the occurrence of a surprisingly sharp transition from the ductile type of deformation that is typical of uncross-linked rubbers to a more elastic type of extension with pronounced strain hardening featured for cross-linked elastomers. This transition is observed in a very narrow range of the decrease in PEG content (Figure 10.6, between 36 and 34 wt % PEG)

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Fundamentals of Pressure Sensitivity

and increase in extension velocity (Figure 10.21, between 20 and 50 mm/min). The narrow transition from ductile to tight stretching with the increased drawing rate in Figure 10.21 corresponds to a well-defined rate of rearrangement of the H-bonded network during the deformation of the PVP–PEG adhesive. Assuming that the cooperative breakup and reformation of hydrogen bonds forming this PVP–PEG network can only occur below the critical deformation rate of 0.05 s−1, we can identify the characteristic time for this process to occur at about 20 s.53 What is of particular importance for the following discussion is the equivalence between the effects of the increase in plasticizer (PEG) content and the decrease in stretching rate on the tensile and, consequently, relaxation properties. Figure 11.50 represents the effect of drawing rate on tensile stress relaxation curves for the most tacky PVP blend with 36 wt % PEG containing 8% of absorbed water at a fi xed elongation, ε = 3. The relaxation follows the exponential law described by Equation 11.2 and written as i
n

Et
Eeq  ∑ Ei exp(t /i )

(11.4)

i
1

where Ei are the tensile relaxation moduli. Similar to what is observed for SIS adhesives in the shear regime (Figures 11.4 and 11.47), the PVP–PEG relaxation in Figure 11.50 illustrates the occurrence of a residual unrelaxed stress, Eeq. The lower the drawing rate in the loading stage, the more rapid and pronounced the relaxation and the lower the equilibrium value of the corresponding modulus, Eeq. The curves relating to a comparatively fast relaxation process can be satisfactorily described by Equation 11.4 with two characteristic times of elastic recovery. This is the case for blends containing 41 wt % PEG at low (10 mm/min) loading rates. In contrast, the blends containing 36 wt % PEG and less, as well as the samples deformed with higher extension rates, have relaxation curves that can be

340 300

E (kPa)

260 220 100

180

50

140

20

100 60 20

10

0

200

400

600 800 Time (s)

1000

1200

FIGURE 11.50 Relaxation curves recorded for the PVP blend with 36 wt % of PEG-400 that is stretched to a deformation of 300% (ε = 3) with a rate ranging from 10 to 100 mm/min. The content of absorbed water in the blend is 8 wt %.

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Significance of Relaxation for Adhesion of PSA

adequately fitted with Equation 11.4, including three populations of characteristic recovery times, τ. For this reason, in the following discussion we consider the effects of relative elongation on relaxation, which have been measured for the elastic PVP blend with 36% PEG, in terms of two characteristic recovery times, whereas the effects of stretching velocity and PEG concentration are treated with three different populations of recovery times. 11.4.5.3

Effects of Relative Elongation and Extension Rate on Tensile Stress Relaxation

In this section we discuss the relaxation properties of PVP–PEG model PSA under experimental conditions corresponding to adhesion testing. Figures 11.51 through 11.53 illustrate the effects of tensile strain and strain rate on the relaxation of the PVP blend with 36 wt % PEG that exhibits maximum adhesion. 80 100 mm/min

70 60

τ1 (s)

50 40 30 20 10 mm/min 10 1.0

1.5

2.0

2.5

3.0

ε

3.5

4.0

550 500 100 mm/min 450

τ2 (s)

400 350 300 250 10 mm/min

200 150 1.0

1.5

2.0

2.5

ε

3.0

3.5

4.0

FIGURE 11.51 Effects of relative elongation and extension velocity on characteristic times of elastic recovery for the PVP–PEG (36 wt %) model PSA.

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11-52

Fundamentals of Pressure Sensitivity

160 140

100 mm/min

Eeq (kPa)

120 10 mm/min

100 80 60 40 20 0 1.0

1.5

2.0

2.5 ε

3.0

3.5

4.0

FIGURE 11.52 Impacts of relative elongation, ε, and drawing rate on the values of equilibrium characteristic recovery modulus, E eq, for the PVP–PEG (36%) model PSA.

By fitting the relaxation curves with Equation 11.4, one can extract two characteristic times of recovery, which increase linearly with increasing elongation (Figure 11.51). The increase in strain rate during loading makes this relationship more pronounced. At a comparatively low velocity of stretching (10 mm/min), the shorter characteristic time varies between 18 and 75 s, whereas the longer time ranges from 200 to 520 s. The 10-fold increase in strain rate results in an appreciable decrease and narrowing of the characteristic time ranges: τ1 = 7–15 and τ2 = 145–230 s. The values of characteristic equilibrium moduli are presented in Figure 11.52. At the low strain rate of 10 mm/min the Eeq is an increasing function of elongation. The most growth is observed in the range of elongations between ε = 1–2, wherein the Eeq increases from zero to an almost constant value. At high strain rate (100 mm/min) the equilibrium characteristic modulus tends to increase linearly with tensile strain. Within a strain range ε = 2–4, the values of the equilibrium characteristic moduli are almost identical and independent of strain rate (Figure 11.52). The E eq value characterizes the amount of mechanical energy stored by the adhesive material in the process of loading. At low tensile rates the material has enough time to relax and the amount of stored energy is negligible. This behavior is typical of viscous liquids and un-cross-linked linear polymers. In contrast, at strain rates of 100 mm/min the material behaves as a cross-linked elastomer, storing elastic energy in the course of stretching. The transition from the liquid-like to rubber-like behaviors occurs in very narrow range of tensile rates that is due to the well-defined relaxation time of the network of hydrogen bonds in the PVP–PEG complex.

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11-53

Significance of Relaxation for Adhesion of PSA

350 300

E1 (kPa)

250 200 100 mm/min 150 100 10 mm/min 50 0 (a)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

3.0

3.5

4.0

ε

280

240

E2 (kPa)

200

160 100 mm/min 120

80 10 mm/min 40

0 (b)

1.0

1.5

2.0

2.5 ε

FIGURE 11.53 Relation of the characteristic moduli of elastic recovery to the relative elongation and drawing velocity of an adhesive PVP blend with 36 wt % PEG.

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11-54

Fundamentals of Pressure Sensitivity

As follows from Figure 11.53, the characteristic moduli corresponding to both shorter and longer relaxation times tend to increase with the increase of relative elongation at high drawing velocity, whereas the moduli, corresponding to the slow extension, decrease. Figures 11.54 through 11.56 illustrate the effect of strain rate on the relaxation of a PVP–PEG PSA at a fixed relative elongation of 300% (ε = 3). The treatment of relaxation

500 τ3 400

300

200

100

τ1

τ2

0 0

20

40

60

80

100

Tensile rate (mm/min)

FIGURE 11.54 Effect of loading tensile rate on the values of characteristic recovery times of PVP–PEG PSA; ε = 3. 45

Eeq (kPa)

40 35 30 25 20 0

20

40 60 80 Tensile rate (mm /min)

100

FIGURE 11.55 Equilibrium characteristic recovery modulus as a function of the tensile rate in the course of loading of a PVP–PEG (36%) model PSA; ε = 3.

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11-55

Significance of Relaxation for Adhesion of PSA

140 E3

120

E (kPa)

100 E2

80 60

E1

40 20 0 0

20

40 60 80 Tensile rate (mm/min)

100

FIGURE 11.56 The effect of extension velocity on the characteristic moduli of elastic recovery of a PVP–PEG PSA; ε = 3.

curves was performed using Equation 11.4 with three populations of characteristic recovery times. In agreement with the data in Figures 11.51 through 11.53, the 10-fold increase in strain rate from 10 to 100 mm/min does not affect the values of shorter and intermediate characteristic times (Figure 11.54), whereas the longer recovery time tends to decrease with the increase in strain rate. The equilibrium characteristic recovery modulus increases at lower deformation rates, achieving its limiting value since the velocity of 50 mm/min (Figure 11.55). Characteristic recovery moduli corresponding to shorter and intermediate recovery times, E1 and E2 , are increasing functions of the tensile rate, whereas the value of E3 decreases with the increase in loading tensile velocity (Figure 11.56). The results presented above suggest that the conditions of adhesion testing, such as strain rate and strain amplitude, affect appreciably the relaxation properties of adhesive materials. The effect of maximum strain on relaxation is in synergy with the impact of strain rate. The relaxation behavior is controlled by two major factors: the longer characteristic time of elastic recovery and the value of the equilibrium characteristic recovery modulus. The former value increases with strain and decreases with increasing strain rate; the latter increases in both cases. 11.4.5.4 Impact of Plasticizer Concentration and Relation to Adhesion As Figure 11.57 illustrates, the longer characteristic recovery time decreases with increasing PEG content in the blends, whereas both shorter and intermediate recovery times are unaffected by PEG content. The equilibrium characteristic recovery modulus decreases with PEG concentration (Figure 11.58), as well as the moduli associated with

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11-56

Fundamentals of Pressure Sensitivity

300 τ3 250

τ (s)

200

150

100

τ2

50 τ1 0 32

36 PEG (wt %)

40

FIGURE 11.57 Characteristic recovery times plotted versus the composition of PVP–PEG PSA. The composition displaying maximum adhesion is marked by a dotted line. The extension rate is 100 mm/min; ε = 3.

80

Eeq (kPa)

60

40

20

0 30

32

34

36 PEG (wt %)

38

40

42

FIGURE 11.58 The effect of PEG content in blends with PVP on the value of the equilibrium characteristic recovery modulus. The dotted line designates the composition exhibiting maximum adhesion. The extension rate is 100 mm/min; ε = 3.

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11-57

Significance of Relaxation for Adhesion of PSA

50

E2

40

E (kPa)

30 E1 20

E3

10

0 30

32

34

36 PEG (wt %)

38

40

42

FIGURE 11.59 Values of the characteristic recovery modulus for PVP–PEG adhesives of various composition. The extension rate is 100 mm/min; ε = 3.

the corresponding characteristic times (Figure 11.59). This behavior implies that PEG is a good plasticizer of PVP. It is instructive to compare the effects of PEG concentration in PVP–PEG blends on relaxation properties, illustrated in Figures 11.57 through 11.59, and on the retardation time and relaxation modulus, presented in Figures 11.36 and 11.37. With the increase in PEG content, the relaxation and recovery moduli decline, but the longer retardation time increases in contrast to the behavior of the characteristic recovery time that is, in essence, the relaxation time. This distinction accounts for a fundamental difference between the relaxation and the retardation processes, defined by the Equations 11.2 and 11.4 on the one hand and Equation 11.3 on the other. All PVP–PEG blends considered in this section demonstrate some level of pressuresensitive adhesion. However, the PVP blend with 36% PEG exhibits the best adhesion. Its relaxation properties indicate which values of the characteristic recovery times and corresponding moduli are associated with a high level of pressure-sensitive adhesion.

11.5 General Conclusions Pressure-sensitive adhesion can be seen as a process of transformation of the structure and properties of the adhesive material under an applied mechanical strain history, including three indivisible consecutive stages: (1) adhesive bond formation under a bonding pressure, when the main type of deformation is in shear, (2) relaxation upon the withdrawal of compressive stress, and (3) debonding under a detaching tensile force.

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11-58

Fundamentals of Pressure Sensitivity

In turn, the third stage, adhesive debonding, is a multistage process itself, including the steps of homogeneous deformation under a tensile stress, followed by cavitation and fibrillation of the adhesive material. Relaxation mechanisms accompany all stages of the adhesion process and provide the links between the stages. In terms of relaxation properties, all PSAs can be classified into two groups: (1) fully relaxing (fluid) adhesives and (2) elastic adhesives that are able to store energy in the course of bond formation and exhibit residual (unrelaxed) stress during the contact time. In terms of molecular structure, the group of fluid adhesives includes un-crosslinked, entangled polymers with low glass transition temperatures, whereas the elastic PSAs are most often networks of polymers that are cross-linked covalently or physically. The elastic PSAs of the second group demonstrate a much slower relaxation than the fluid PSAs. The longer relaxation processes are mostly associated with the appearance of a pronounced plateau or even of a second maximum on the probe tack curves. The equilibrium relaxation modulus is a direct measurement of the stored elastic energy in a polymer material and relates to its yield stress. Fluid adhesives do not have a yield stress or, consequently, an equilibrium modulus. As the comparison of the relaxation and adhesive properties of various PSAs indicates, high adhesion is associated with longer relaxation times. This conclusion is in full agreement with Equation 10.6 in Chapter 10, which predicts improved adhesion with the increase in longer relaxation time of the adhesive material. In turn, the longer values of relaxation time are typical of large-scale entangled and network supramolecular structures. This implies that large-scale rearrangements of molecular structures in the course of relaxation govern a high level of pressure-sensitive adhesion. The relationship between peel adhesion and the molecular structure of the adhesive material, predicted by Equation 10.6 in Chapter 10, also suggests that the greater the size of the relaxing molecular structures in adhesive material, a, the higher the adhesion. As predicted using Equation 10.6 in Chapter 10, for high adhesion a compromise must be reached among the values of cohesion energy, diff usion coefficient, and relaxation time of PSAs. It is, therefore, not surprising that a direct correlation between the practical work of adhesion and the values of longer relaxation times has been established for the examined PSAs. Adhesion appears with the rise of longer relaxation times values above 50 s and increases, passing through a maximum at τ3 = 330–380 s. A further increase in the longer relaxation times results in a gradual decline in adhesion. Good adhesion occurs when the longer relaxation time varies in the range of 150 to 800 s. Relaxation properties of the PSAs depend on the observation window. If the observation time is long enough, a PSA seems to be more fluid than at shorter observation time. PSAs are viscoelastic materials that combine the properties of solids and liquids. Relative contributions of the viscous and elastic behaviors can be estimated in terms of the Deborah numbers that relate the time scale of structural rearrangement in the material to the time of experimental observation. Because the viscous and elastic contributions are perfectly counterbalanced, the Deborah number is unity. Very fluid, quickly relaxing materials possess values of Deborah number tending to zero. Useful PSAs have demonstrated Deborah numbers between 0.15 and 1 if the longer relaxation time is chosen as the characteristic relaxation time of the adhesive.

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Significance of Relaxation for Adhesion of PSA

11-59

The relaxation behavior during the stage of strain relaxation upon withdrawal of the bonding pressure has been characterized in terms of retardation times. Retardation times are not identical to relaxation times. Whereas the relaxation times increase with plasticization, the retardation times decline. Two populations of retardation times have been determined for PSAs: shorter retardation times of the order 10–70 s and longer retardation times in the range of 300–660 s. The longer retardation times relate mainly to the energy-dissipating processes, which, in turn, are associated with large-scale rearrangements of supramolecular structures involving polymer chain entanglements and translational movements of polymer segments and entire macromolecules through a self-diff usion mechanism. The observed correlation between high adhesion and the values of longer retardation times supports the validity of Equation 10.6 in Chapter 10. The large-scale rearrangements of the structure of adhesive materials during relaxation can be easily visible and characterized if the probe tack tester is stopped at different stages of the debonding process, when the main mode of PSA deformation is in tension. When a soft adhesive is kept under a tensile load during the debonding process, two important failure mechanisms are observed: nucleation of new cavities and the growth of existing cavities as cracks at the interface between the adhesive and the adherent. The plateau stress in probe tack curves corresponds to the formation and elongation of a fibrillar foam. The stop of the probe at this stage for elastic adhesives demonstrated that the size and number of cavities remain the same in the course of relaxation. To describe quantitatively PSA relaxation in the course of debonding, when large tensile strain dominates, the method of stretching adhesive fi lms is useful. The work of viscoelastic deformation up to fi lm fracture under uniaxial extension has been established to control peel adhesion. If the relaxation properties of PSAs under a large tensile strain are expressed in terms of characteristic times of elastic recovery and corresponding characteristic moduli, the effect of debonding conditions, such as loading rate and tensile strain amplitude, on relaxation becomes evident. The effect of maximum tensile strain on relaxation is in synergy with the effect of strain rate. The relaxation behavior at large strains is controlled by two major factors: the longer characteristic time of elastic recovery and the value of equilibrium characteristic recovery modulus. The former value increases with strain and decreases with strain rate; the latter increases in both cases. The data presented in this chapter demonstrate the significance for pressure-sensitive adhesion of relaxation properties typical of PSAs, as well as the development and transformations of these properties in the course of adhesion testing.

References 1. Tshoegl N.W., Time dependence in material properties: An Overview, Mechan. Time-Depend Mater., 1, 3, 1997. 2. Moonan W.K. and Tschoegl N.W., The effect of pressure on the mechanical properties of polymers. 4. Measurements in torsion, J. Polym. Sci., Polym. Phys. Ed., 23, 623, 1985. 3. Ferry J.D., Viscoelastic Properties of Polymers, 3rd ed., Wiley & Sons, New York, 1980.

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4. Aklonis J.J. and MacKnight W.J., Introduction to Polymer Viscoelasticity, 2nd ed., Wiley & Sons. New York, 1980. 5. Christensen R.M., Theory of Viscoelasticity, 2nd ed., Academic Press, New York, 1982. 6. Matsuoka S., Relaxation Phenomena in Polymers, Oxford University Press, New York and Carl Hauser Verlag, Munich, 1992. 7. Satas D. (ed.), Handbook of Pressure-Sensitive Adhesive Technology, 3rd ed., Satas & Associates, Warwick, RI, 1999. 8. Dillard D.A. and Pocius A.V. (eds.), The Mechanics of Adhesion, Elsevier Science, New York, 2002. 9. Zosel A., The effect of bond formation on tack of polymers, J. Adhesion Sci. Technol. 11, 1447, 1997. 10. Tschoegl N.W., The Phenomenological Theory of Linear Elastic Behavior, SpringerVerlag, Heidelberg, 1989, p. 126. 11. Schramm G., A Practical Approach to Rheology and Rheometry, Haake Rheometers, Karlsruhe, 1994, p. 104. 12. Zosel A., The effect of fibrillation on the tack of pressure-sensitive adhesives, Int. J. Adhesion Adhes. 18, 265, 1998. 13. Zosel A., Fracture energy and tack of pressure-sensitive adhesives, in: Satas D (ed.) Advances in Pressure Sensitive Adhesive Technology, vol. 1, Satas & Associates, Warwick, RI, 1992, chap. 4. 14. Zosel A., Adhesion and tack of polymers: Influence of mechanical properties and surface tension, Colloid Polym. Sci., 263, 541, 1985. 15. Pickering J.P., Van Der Meer D.W., and Vancso G.J., Effects of contact time, humidity, and suface roughness on the adhesion hysteresis of polydimethylsiloxane, J. Adhes. Sci. Technol., 15(12), 1429, 2004. 16. Lakrout H., Sergot P., and Creton C., Direct observation of cavitation and fibrillation in a probe tack experiment on model acrylic pressure-sensitive adhesives, J. Adhesion 69, 307, 1999. 17. Creton C. and Fabre P., Tack, in: Dillard D.A. and Pocius A.V. (eds.) Adhesion Science and Engineering, Vol I: The Mechanics of Adhesion, Elsevier, Amsterdam, 2002, chap. 14. 18. Creton C. and Leibler L., How does tack depend on time of contact and contact pressure, J. Polym. Sci.: Part B: Polym. Phys. 34, 545–554, 1996. 19. Creton C. and Schach, R., Diff usion and adhesion, in: Benedek I. and Feldstein M.M. (eds.) Fundamentals of Pressure Sensitivity, Taylor & Francis, Boca Raton, 2008, chap. 2. 20. Voyutskii S.S., Autohesion and Adhesion of High Polymers, Wiley Interscience, New York, 1963. 21. Dahlquist C.A., in: Patrick R.L. (ed.) Treatise on Adhesion and Adhesives, vol. 2, M. Dekker, New York, 1969, p. 219. 22. Feldstein M.M., Molecular nature of pressure-sensitive adhesion, in: Benedek I. and Feldstein M.M. (eds.) Fundamentals of Pressure-Sensitive Adhesion, Taylor & Francis, Boca Raton, 2008, chap. 10.

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23. Feldstein M.M. and Creton C., Pressure-sensitive adhesion as a material property and as a process, in: Benedek I. (ed.) Pressure-Sensitive Design, Theoretical Aspects, vol. 1, VSP, Leiden, Boston, 2006, chap. 2. 24. Feldstein M.M., Molecular fundamentals of pressure-sensitive adhesion, in: Benedek I. (ed.) Developments in Pressure-Sensitive Products, 2nd Edition, CRC-Taylor & Francis, Boca Raton, 2006, chap. 4. 25. Feldstein M.M., Adhesive hydrogels: structure, properties and application, Polym. Sci., Ser. A., 46(11), 1265, 2004. 26. Zisman W.A., Adhesion and bonding, in: Mark H.F., Gaylord N.G., and Bikales N.M. (eds.) Encyclopedia of Polymer Science and Technology, Interscience Publishers (J. Wiley & Sons), New York, 1964, pp. 445–477. 27. Kotomin S.V., Durability of adhesive joints, in: Benedek I. and Feldstein M.M. (eds.) Fundamentals of Pressure Sensitivity, Taylor & Francis, Boca Raton, 2009, chap. 9. 28. Feldstein M.M., Kulichikhin V.G., Kotomin S.V., Borodulina T.A., Novikov M.B., Roos A., and Creton C., Rheology of poly(N-vinyl pyrrolidone)-poly(ethylene glycol) adhesive blends under shear flow, J. Appl. Polym. Sci., 100, 522, 2006. 29. Satas D., Tack, in: Satas D. (ed.) Handbook of Pressure-Sensitive Adhesive Technology, 3rd ed., Satas & Associates, Warwick, RI, 1999, chap. 4. 30. Chiche, A., Dollhofer J., and Creton C., Cavity growth in soft adhesives, Eur. Phys. J. E, 17, 389–401, 2005. 31. Novikov M.B., Gdalin B.E., Anosova J.V., and Feldstein M.M., Stress relaxation during bond formation and adhesion of pressure sensitive adhesives, J. Adhesion 84, 164, 2008. 32. Bartenev G.M. and Barteneva A.G., Relaxation Properties of Polymers, Chemistry Publishers, Moscow, 1992, p. 384. 33. O’Connor A.E. and Willenbacher N., The effect of molecular weight and temperature on tack properties of model polyisobutylenes, Int. J. Adhes. Adhes., 24, 335, 2004. 34. Feldstein M.M., Cleary G.W., and Singh P., Pressure-sensitive adhesives of controlled water-absorbing capacity, in: Benedek I. (ed.) Pressure-Sensitive Design and Formulation, Application, vol. 2, VSP, Leiden, Boston, 2006, chap. 3. 35. Feldstein M.M., Cleary G.W., and Singh P., Hydrophilic adhesives, in: Benedek I. and Feldstein M.M. (eds.) Technology of Pressure-Sensitive Adhesives and Products, Taylor & Francis, Boca Raton, 2008, chap. 7. 36. Novikov M.B., Kiseleva T.I., Anosova J.V., Singh P., Cleary G.W., and Feldstein M.M., Contribution of relaxation processes into pressure-sensitive adhesion of interpolymer complexes, Proceed. 30th Annual Meeting Adhesion Soc., Tampa, Florida, USA, 54, 2007. 37. Novikov M.B., Borodulina T.A., Kotomin S.V., Kulichikhin V.G., and Feldstein M.M., Relaxation properties of pressure-sensitive adhesives upon withdrawal of bonding pressure, J. Adhesion, 81(1), 77, 2005. 38. Rohn Ch., Rheology of pressure-sensitive adhesives, in: Satas D. (ed.) Handbook of Pressure-Sensitive Adhesive Technology, 3rd ed., Satas & Associates, Warwick, RI, 1999, chap. 9.

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39. Chalykh A.A., Chalykh A.E., Novikov M.B., and Feldstein M.M., Pressuresensitive adhesion in the blends of poly(N-vinyl pyrrolidone) and poly(ethylene glycol) of disparate chain lengths, J. Adhesion, 78(8), 667, 2002. 40. Feldstein M.M., Roos A., Chevallier C., Creton C., and Dormidontova E.D., Relation of glass transition temperature to the hydrogen bonding degree and energy in poly(N-vinyl pyrrolidone) blends with hydroxil-containing plasticizers: 3. Analysis of two glass transition temperatures featured for PVP solutions in liquid poly(ethylene glycol), Polymer, 44(6), 1819, 2003. 41. Zosel A., Adhesive failure and deformation behaviour of polymers, J. Adhesion, 30, 135, 1989. 42. Shull K.R. and Creton C., Deformation behavior of thin, compliant layers under tensile loading conditions, J. Polym. Sci., Polym. Phys., 42, 4023, 2004. 43. Creton, C., Roos A., and Chiche A., Effect of the diblock content on the adhesive and deformation properties of PSAs based on styrenic block copolymers, in: Possart W.G. (ed.) Adhesion: Current Research and Applications, Weinheim, Wiley-VCH, 2005, 337p. 44. Lindner A., Maevis T., Brummer R., Lűhmann B., and Creton C., Sub-critical failure of soft acrylic adhesives under tensile stress, Langmuir 20, 9156, 2004. 45. Shull K.R., Flanigan C.M., and Crosby A., Fingering instabilities of confined elastic layers in tension, J. Phys. Rev. Lett., 84, 3057, 2000. 46. Creton C., Hooker J.C., and Shull K.R., Bulk and interfacial contributions to the debonding mechanisms of soft adhesives, Langmuir, 17, 4968, 2001. 47. Roos A. and Creton C., Linear viscoelasticity and nonlinear elasticity of block copolymer blends used as soft adhesives, Macromol. Symp., 214, 147, 2004. 48. Roos A., Ph.D. Thesis, Universitė Paris VI, Paris, 2004. 49. Roos, A. and Creton, C., Effect of the presence of diblock copolymer on the non linear elastic and viscoelastic properties of elastomeric triblock copolymers, Macromolecules, 38, 7807, 2005. 50. Osako K., in: Nagasawa M. (ed.) Molecular Conformation and Dynamics of Macromolecules in Condensed Systems, Elsevier, Amsterdam, 1988, p. 175. 51. Isono Y., and Nishitake T., Stress relaxation and change in entanglement structure of polyisobutylene in large shearing deformations, Polymer, 36(8), 1635, 1995. 52. Novikov M.B., Roos A., Creton C., and Feldstein M.M., Dynamic mechanical and tensile properties of poly(N-vinyl pyrrolidone)–poly(ethylene glycol) blends, Polymer, 44(12), 3559, 2003. 53. Roos A., Creton C., Novikov M.B., and Feldstein M.M., Viscoelasticity and tack of poly(N-vinyl pyrrolidone)–poly(ethylene glycol) blends, J. Polym. Sci., Polym. Phys., 40, 2395, 2002.

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Appendix: Abbreviations and Acronyms Generally Accepted Abbreviations and Symbols aT AA BA DMA DMAEMA DSC EA FTIR G′ G″ MAA MMA Mn MW, Mw NMR PB PDMS PE PEG PET PI PIB PMMA PP PSA

shift factor acrylic acid butyl acrylate dynamic mechanical analysis dimethylaminoethyl methacrylate differential scanning calorimetry ethyl acrylate fourier transform infrared (spectroscopy) dynamic shear storage modulus dynamic shear loss modulus methacrylic acid methyl methacrylate number average molecular weight molecular weight nuclear magnetic resonance polybutadiene poly(dimethyl siloxane) polyethylene poly(ethylene glycol) polyethylene terephthalate polyisoprene polyisobutylene poly(methyl methacrylate) polypropylene pressure-sensitive adhesive

A-1

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A-2

PSP PTFE PVC PVP SAFT SIS t T tan δ Tg VA

Chapter 1

δ ε ε0 εi ρ σ τ Θ Θ0 Θa Θi Θr E fd fη G h h0 P ∆Pc PC PH Pst r R*

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Appendix: Abbreviations and Acronyms

pressure-sensitive product poly(tetrafluoroethylene) polyvinyl chloride poly(N-vinyl pyrrolidone) shear adhesion failure temperature styrene–isoprene–styrene triblock copolymer time temperature loss factor G″/G′, loss angle tangent glass transition temperature vinyl acetate

Surface Phenomena on a Solid– Liquid Interface and Rheology of Pressure Sensitivity thickness of the layer of the liquid current deformation residual equilibrium deformation initial deformation density surface tension retardation time current contact angle equilibrium contact angle advancing contact angle initial contact angle receding contact angle Young modulus driving force of spreading force of viscous resistance elastic modulus current gap between plates at squeezing initial gap between plates at squeezing pressure capillary pressure difference at the beginning and at the end of inertial stage of spreading capillary pressure hydrostatic pressure polystyrene radius of the wetted surface curvature radius of drop surface at the end of the inertial stage of spreading

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Appendix: Abbreviations and Acronyms

Ri v V vin VOC

A-3

curvature radius of drop surface at the beginning of the inertial stage of spreading spreading rate volume of drop spreading rate at the inertial stage of spreading volatile components

Chapter 2 Diffusion and Adhesion χ ε η η0 γ1, γ2 γ12 φ φ(aTv) ρ σ τd a c De E EPDM Gc G N0 h0 Ip k N, NA, NB SBR SEC Sty tc Tref V vd w Wadh Wrev

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Flory interaction parameter strain viscosity zero-shear rate viscosity surface tension interfacial tension volume fraction dissipative factor in adhesion density stress terminal relaxation time of the polymer monomer segment length constant with value 6 or 9 Deborah number Young’s modulus ethylene–propylene diene rubber critical energy release rate plateau modulus initial thickness of the adhesive fi lm polydispersity index Boltzmann constant degree of polymerization of the polymer poly-styrene-r-butadiene of 80 kg/mole molecular weight size exclusion chromatography styrene contact time reference temperature probe debonding velocity probe debonding velocity interfacial width adhesion energy reversible work of adhesion

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A-4

Appendix: Abbreviations and Acronyms

Chapter 3 Transition Zones in Adhesive Joints α η µm τ A Аcoh d d∝ D ED Ei erf(z) L L cr ni P PEU PFO PVDF R S tD Тiso Tm UCST wi w′i wi″ x z

Chapter 4

ε η η0 ω Φ σ τ

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numerical constant viscosity microns numerical constant peel strength of adhesive joint cohesive strength average pore diameter pore diameter at t∝ diff usion coefficient activation energy of diff usion energy of an adhesive bond Gaussian integral thickness of adhesive layer impregnation depth number of ith type links per unit area of interphase contact pressure polyester urethane phenol formaldehyde oligomer polyvinylidene fluoride pore radius contact area time of diff usional relaxation isotropization point melting point upper critical solution temperature concentration expressed in weight or volume fraction concentration of ith component in the first phase concentration of ith component in the second phase diff usion coordinate tabulated value of Gaussian integral

Role of Viscoelastic Behavior of PressureSensitive Adhesives in the Course of Bonding and Debonding Processes extension dynamic viscosity newtonian viscosity circular frequency amplifying factor tensile stress relaxation time

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Appendix: Abbreviations and Acronyms

τrep E F Fmin and Fmax G G* Gc Grep(t), GrA(t), GrB(t), GHF(t) G(t) JG JR J(t) Me Sr top Tref U V W W0

Chapter 5 ω ρ A A0 ATPSA B CRA CTPSA D DE Gn GPPSA HSPSA L Me P0 rad/s RPSA Tc

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A-5

reptation time elastic modulus peeling force minimum and maximum forces in the stick-slip domain fracture energy complex shear modulus critical energy release rate the various relaxation domains of the relaxation function relaxation function instantaneous compliance retardational creep compliance creep (compliance) function molecular weight between entanglements strain rate open time reference temperature of the master curves opening of the crack peeling rate thickness of the adhesive thermodynamic work of adhesion

Viscoelastic Properties and Windows of Pressure-Sensitive Adhesives frequency in rad/s density of the blend actual area of contact total area available for contact all temperature pressure-sensitive adhesives bonding function control release additives cold temperature pressure-sensitive adhesives debonding function dissipation energy per cycle of deformation plateau modulus general purpose pressure-sensitive adhesives high shear pressure-sensitive adhesives applied strain amplitude molecular weight between entanglements intrinsic interfacial energy radians per second removable pressure-sensitive adhesives domain disappearance (critical) temperature

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A-6

Appendix: Abbreviations and Acronyms

Tdd Vp VW

domain transition temperature volume fraction of polymer in the polymer–resin blend viscoelastic window

Chapter 6 ε εmax γ λ λ1, λ 2, λ 3 λr µ σ σmax σN σzz θ a a0 E F fel(λr) g go gc h h0 JKR p p0 PEHA pel r R0 Rc Rd Rp SI Uel v v* V

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Probe Tack

strain maximum extension of the fibrils surface tension extension ratio extension ratio along the three principal directions extension ratio of the cavity shear modulus stress maximum stress during a tensile debonding test nominal tensile stress normal stress in the tensile (z) direction contact angle of the cavity with the surface diameter of the contact area diameter of the probe Young’s modulus load elastic strain energy density function for the growth of a cavity energy release rate limiting value of Gc at a vanishing crack velocity critical energy release rate thickness of the layer initial thickness of the layer Johnson-Kendall-Roberts pressure external pressure poly(2-ethylhexyl acrylate) elastic inflation pressure distance along the radial direction initial radius of the cavity radius of the cavity initial projected radius of the cavity on the probe surface projected radius of the cavity on the probe surface poly(styrene-b-isoprene) elastic strain energy density crack velocity critical value of crack velocity above which dissipative effects are important volume of the cavity

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Appendix: Abbreviations and Acronyms

V0 Vdeb Wadh

A-7

initial volume of the cavity debonding velocity of the probe adhesion energy

Chapter 7 Peel Resistance δ ψ θ AA C1 C2 2-EHA G G0 Gc 2-HEMA P P-36 S SBC Ts VAc W WD WT

solubility parameters viscoelastically dissipated energy peel angle acrylic acid constants constants 2-ethylhexyl acrylate fracture energy energy required to propagate a crack adhesive fracture energy 2-hydroxyethyl methacrylate adhesion force 4-acryloyloxydiethoxy-4-chlorobenzophenone shape factor styrenic block copolymer standard temperature vinyl acetate peel work work of deformation non-recoverable work of translation

Chapter 8 Shear Resistance η γ γ˙ γ˙R λ τ τR A 2-EHA F G h h0 IOA k

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viscosity deformation shear rate shear rate at the rim of the plate at squeezing retardation time shear stress shear stress at the rim of the plate at squeezing overlapping area in the shear test 2-ethylhexyl acrylate shearing force elastic modulus current gap between plates at squeezing initial gap between plates at squeezing isooctyl acrylate consistency coefficient in the power law

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A-8

Δl n R UV v

Appendix: Abbreviations and Acronyms

displacement of the adhesive tape in the shear test power law index plate radius at squeezing ultraviolet speed of the adhesive tape in the shear test

Chapter 9 Durability of Viscoelastic Adhesive Joints α σ τ0 B B1 k m t* U U0

power constant at molecular weight in extended Bartenev’s equation tensile stress thermal oscillation time of atoms for polymers constant in Bartenev’s equation constant in extended Bartenev’s equation Boltzmann constant power constant long-term durability activation energy of the rupture process activation energy of self-induced rupture of polymer chains at σ = 0

Chapter 10 χ δ δs ε εb η γ λ ω φ σ σb σf σmax σn σy τ a b CED ∆Cp

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Molecular Nature of PressureSensitive Adhesion

Flory interaction parameter fi xed pulse width in PFG NMR solubility parameter relative elongation maximum elongation of the fi lm at the break microviscosity (monomer-monomer friction coefficient of polymer chain) gyromagnetic ratio of proton jump length of a polymer segment deformation frequency volume fraction tensile stress ultimate tensile strength ultimate stress at fracture of PSA under debonding maximum debonding stress in probe tack test nominal stress yield stress (maximum on tensile stress-strain curve) relaxation time size of monomer units in polymer chain segment width of adhesive fi lm cohesive energy density change in heat capacity

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Appendix: Abbreviations and Acronyms

A-9

d diameter of cavities required for diff usion of a polymer chain segment D self-diff usion coefficient interaction energy of atoms forming a polymer segment Dv interdiff usion coefficient E elasticity tensile modulus Ec cohesive energy ED activation energy for self-diff usion F force fv free volume fraction g magnitude of field gradient pulses ∆Hv heat of vaporization k Boltzmann constant l thickness of adhesive fi lm N number of monomer units in a segment of polymer chain P 180° peel force, resistance, adhesion PALS positron annihilation lifetime spectroscopy PFG pulsed-field gradient pi populations of resonating species possessing specific diff usivity q generalized scattering vector QSPR quantitative structure–property relationship R gas constant Sinc(q, t) incoherent intermediate structure function t* durability of the joint Tm melting temperature Vm molar volume W practical work of adhesion (the area under probe tack curve) Wb work of viscoelastic deformation to break adhesive fi lm in tensile test WAXS wide angle x-ray scattering z coordination number

Chapter 11 ε η σ σ0 σmax σn τ τmat τexp A AMA

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Significance of Relaxation for Adhesion of Pressure-Sensitive Adhesives

relative elongation viscosity stress level of tensile stress at which the probe tack test is stopped maximum debonding stress in probe tack test nominal stress relaxation (retardation) time time scale of the material rearrangements time scale of experimental observation contact area alkyl methacrylate

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A-10

BR D E Eeq EP F G0 Geq h H I J nD P PFG PS QSPR R R2 t* TEC Tm Vdeb W

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Appendix: Abbreviations and Acronyms

butyl rubber self-diff usion coefficient elasticity tensile modulus equilibrium elasticity tensile modulus poly(ethylene–co–propylene) substrate force relaxation moduli normalized by the moduli at the beginning of the relaxation equilibrium relaxation shear modulus rod displacement (a gap between the upper and bottom plates of squeeze-recoil tester), adhesive fi lm thickness relaxation spectrum isolene, polyisoprene rubber compliance Deborah number 180° peel force, resistance, adhesion pulsed-field gradient polystyrene quantitative structure–property relationship regalite R9100 hydrocarbon resin regression parameter durability of adhesive joint triethylcitrate melting temperature debonding rate practical work of adhesion (the area under probe tack curve)

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Index A Acrylics acid content of, 6-17, 7-17 based polymers, 5-20 composition of, 7-16 emulsions of, 4-15 fibril elongation of, 7-6 to 7-7 removable, 6-19 water solubility of, 4-4 Additives, 8-13 Adherence, process of, 4-12 to 4-15 Adherents, crystalline, 3-13 to 3-14 deformable, wetting out of, 1-13 to 1-18 surface properties of, 7-27 to 7-31 Adhesion (See also Peel resistance; Viscoelastic materials) composition dependence of, 11-24 contact time for, 11-12 to 11-15, 11-22 to 11-24 defined, 4-3, 10-2, 11-4 durability of, 9-13 to 9-17 energy of, 2-4 to 2-11, 2-14 to 2-16, A-3, A-7 experiments, 4-9 to 4-10 free volume in, 10-16 to 10-18 open time for, 4-14 as peel resistance free volume in, 10-17 master curve for, 4-6 performance in, 5-16 phase state influence in, 10-25 plasticizer concentration, role of, in, 7-20 of PVP blends, 9-11

of PVP-PEG blends, 10-5 rate and failure modes in, 7-13 to 7-14 stick-slip, 7-14 viscoelastic deformation in, 10-11 to 10-13 performance , 4-3 to 4-15 process, 4-12 to 4-15, 10-5, 11-2 to 11-6, 11-26, 11-37 to 11-47, 11-49, 11-57 to 11-59 properties, 7-17, 11-19 to 11-20 relaxation time in, 11-12 to 11-14 scientific research for, 4-2 strength of, 3-9 to 3-10, 6-18 to 6-22 theories of, 3-7, 10-3 of typical pressure-sensitive adhesives, 11-8 to 11-12 weak, 6-18 to 6-20 Adhesive (See also Pressure-sensitive adhesives) bandage of, 5-12 classification of, 3-3 to 3-29 combined transition zones in, 3-25 to 3-29 concentration gradient transition zones, 3-12 to 3-24 amorphous phase separation systems in, 3-12 to 3-13 complex amorphous-crystalline equilibrium systems, 3-14 to 3-20 crystalline substrate for, 3-13 to 3-14 diff usion and adhesive behaviour in, 3-21 to 3-24 ever-tacky, 3-3 joints with crystalline surface, 3-13 to 3-14 overview of, 3-3 to 3-5

I-1

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I-2 Adhesive (Contd.) structure-gradient transition zones in, 3-8 to 3-11 structure-mechanical transition zones in, 3-5 to 3-8 debonding, cavitation in, 4-15 to 4-17, 6-3 to 6-8, 6-15 to 6-23, 10-7 to 10-9, 11-38 to 11-39, 11-42 to 11-43 contact time for, 11-14 curves of, 6-15 to 6-23 definition of, 5-1 deformation mechanisms of model PVP- PEG, 10-7 to 10-9 energy of, 11-13 free, for self-diff usion of, 10-21 to 10-23 mechanisms, 10-9, 11-38 model PVP-PEG in, 9-10, 10-28 to 10-30 probe tests for, 6-15 to 6-23 stages for, 11-37 to 11-57 stress-strain curves for, 6-16 to 6-17 velocity in, 11-3 drug delivery, 7-33, 8-9 failure definition of, 9-6 during probe tack, 10-8 mechanism of, 2-10 to 2-11 modes, 7-13 to 7-15, 7-25 properties interpolymer complex for, 11-19 to 11-20 performance and viscoelastic window, 5-13 viscoelastic polymer materials as, 11-2 Adsorption theory, 10-3 Aging process, 10-18 Aluminum foil tape, 7-3 to 7-4 oxide layer of, 3-5 Amorphous phase separation systems, 3-12 to 3-13 Analysis of peel resistance, 7-2 to 7-7 Annealing, 3-10, 3-18 to 3-21, 11-12 to 11-13 Aqueous dispersions, 1-12 to 1-13, 1-24 Assembly time, 8-11 B Bandage adhesives, 5-12 Bartenev’s equation, 9-3

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Index Bending zone, 7-5 to 7-6 Bernoulli’s law, 1-3 Block copolymers, 4-9 Bond, formation of, 5-1 strength of, 7-7 Bonding, and G′, 5-17 to 5-19 pressure withdrawal in, 11-26 to 11-37 Burger’s model, 8-7 to 8-8, 11-26 to 11-28 C Carrier materials, 7-2, 7-16 Carrierless tapes, 8-15 Cavitation, 6-5 to 6-18 in debonding, 4-15 to 4-17 definition of, 11-42 formation process of, 6-7 images of, 6-18 interfacial, 6-9 to 6-10 probe geometry for, 6-15 to 6-18 in SIS-based PSA, 6-15 stages of, 6-5 to 6-8 Chang`s approach, for, 5-6 to 5-20 bonding and G′, 5-17 to 5-19 Dahlquist Contact Criterion Line, 5-13 to 5-15 fundamental polymer parameters, 5-19 to 5-20 G′-G″ Cross-Over Line, 5-15 to 5-16 peel performance, 5-16 PSA performance, 5-19 to 5-20 shear performance, 5-16 tack performance, 5-16 to 5-17 Chemical structures, 8-12 to 8-13, 10-4 Chu`s approach, 5-6 Cohesion energy, contribution of, to adhesion, 10-11 to 10-14 Cohesion energy contribution of to adhesion, 10-11 to 10-14 in diff usion and adhesive behavior, 3-21 to 3-24 overview of, 3-12 Cohesive-adhesive fracture, 9-6 Cohesive failure, 3-22, 7-25 Cold flow problem, 8-9 to 8-11 Combined transition zones, 3-25 to 3-29 Complex amorphous-crystalline equilibrium systems, 3-14 to 3-20

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Index Complex shear modulus, in linear viscoelasticity , 4-17 to 4-20 Compliance in linear viscoelasticity, 4-21 Composition dependence of adhesion, 11-24 Compressive load relaxation, 11-6 to 11-25 Concentration gradient transition zones, 3-12 to 3-24 in amorphous phase separation systems, 3-12 to 3-13 in complex amorphous-crystalline equilibrium systems, 3-14 to 3-20 for crystalline substrate, 3-13 to 3-14 Confi nement efect, 6-4 to 6-5 Contact angle retardation times, 1-8 to 1-10, 1-17 Contact time, for adhesion, 11-12 to 11-15, 11-22 to 11-24 for debonding, 11-14 in probe tack curves, 11-10 Coupling elastomers, 3-25 Creep-recovery tests, 1-19, 8-7 Cross-linking density, 7-18, 8-14 physical, 8-14 to 8-15 polymers, 8-15 Crystalline substrate, 3-13 to 3-14 Crystallization, 3-9 to 3-11 Curl, ability to, 7-24 Curl, properties of, 7-24 D Dahlquist’s Contact Criterion Line, 5-13 to 5-15, 10-28, 10-33 to 10-36, 11-4 Dale`s approach, 5-3 to 5-4 Dale`s approach in, 5-2, 5-4 to 5-6 Dead load, 8-12 Debonding cavitation in, 4-15, 6-15 to 6-18 contact time in, 11-14 curves of, 6-15 to 6-23 with cavitation in probe geometry, 6-15 to 6-18 fibril formation and extension in, 6-20 to 6-22 interfacial nucleation and propagation in, 6-18 to 6-20 transitions in, 6-22 to 6-23

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I-3 definition, 5-1 deformation mechanisms of model PVPPEG, 10-7 to 10-9 energy, 11-13 free energy for self-diff usion, 10-21 to 10-23 mechanisms of, 10-9, 11-38 model PVP-PEG for, 9-10, 10-28 to 10-30 probe tests for, 6-15 to 6-23 stages of, 11-37 to 11-47 first, 11-39 to 11-43 linear viscoelasticity and large-strain elongational geometries in, 11-45 to 11-47 relaxation properties in, 11-37 to 11-57 second, 11-43 to 11-45 three-stage mechanism of debonding, 11-37 to 11-39 stress-strain curves of, 6-16 to 6-17 velocity, 11-3 Deborah number, 2-9 definition of, 2-9 origin of, 11-2 to 11-3 of pressure-sensitive adhesives, 11-16 to 11-19 Deformation curves of, 1-20 of model PVP-PEG, 10-7 to 10-9, 10-28 to 10-30 stages of, 6-2 to 6-12 in cavitation, 6-5 to 6-8 by fibril formation and growth, 6-8 to 6-12 homogeneous, 6-4 to 6-5 Dendritic spreading, 1-12 Detachment time, 9-15 Dicing tape, 7-14 Diferential scanning calorimetry (DSC) in test of molecular nature of pressuresensitive adhesion, 10-6 to 10-7 in test of phase state, 10-25 Diff usion, 2-16 to 2-19 activation energy values in, 3-17 and adhesion, 2-2, 3-21 to 3-24, 10-13 to 10-14 in adhesion energy from probe-tack of immiscible polymers, 2-11 to 2-16

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I-4

Index

Diffusion (Contd.) for adhesion energy from probe tests, 2-14 to 2-16 for adhesive behavior of transition zones, 3-21 to 3-24 coefficients of, 10-18 to 10-20 in cohesive failure, 3-22 definition of, 10-23 experimental details of, 2-2 to 2-11 interfacial width of from neutron in materials, 2-12 overview of, 2-11 to 2-12 partial, 10-20 PVC-BNR system profiles in, 3-18 PVC-EVA 30 system profiles in, 3-19 reflectivity, 2-12 to 2-14 as self-diffusion, 2-2 to 2-11 for tack properties tests of, 2-4 to 2-11 theory of, 10-3 through polymer interfaces, 2-11 to 2-12 DMA (See Dynamic mechanical analysis) Drug delivery adhesives, 7-33, 8-9 Drum peel, 7-9 to 7-11 DSC (See Diferential scanning calorimetry) Durability, of adhesion, 9-13, 10-22, 11-42 definition of, 1-20 of joint, 9-1 to 9-17 molecular weight for, 8-12 normalized, 1-21 overview of, 9-1 to 9-2 in PVP-PEG systems, 9-13 stress and, 9-4 to 9-5, 9-15 test of, 9-14 triaxial stress tests for, 9-2 to 9-13 Dynamic mechanical analysis, in formulation and evaluation of complex PSA systems, 5-20 Dynamic peel test, 7-10 Dynamic shear test, 8-4

Elongation effects, 11-51 to 11-55 relative, 11-51 to 11-55 tensile stress in, 10-27, 11-49 to 11-51 viscosity in, 4-22 to 4-23 Emulsifiers, 7-19 Energy of adhesion, 2-4 to 2-11, 2-14 to 2-16 of fracture, 3-6 release rate of, 6-10, A-6 Entangled structures, 11-14 to 11-16 Ethylene-vinyl acetate, 3-10, 4-20 Ever-tacky adhesives, 3-3

E

G

Elasticity, 6-5 to 6-6 Elastomers coupling of, 3-25 fibril elongation in, 7-6 to 7-7 thermoplastic, 10-15, 10-35 Electronic theory of adhesion, 10-3

G′-G″ Cross-Over Line, 5-15 to 5-16 Gaussian integral, 3-18, A-4 Gel, deformable, wetting of, 1-12 to 1-18 General purpose PSAs, 5-14, A-5 Glass transition temperature, 10-24 to 10-26

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F Failure, during probe tack, 6-2 to 6-23, 10-8 mechanism of, 2-10 to 2-11 modes of, 7-13 to 7-15, 7-25 Fibril, defi nition of, 4-12 elongation of, 7-6 to 7-7 formation of, definition of, 9-10 extension of, 6-20 to 6-23 growth of, 6-8 to 6-12 length distribution of, 7-6 to 7-7 in PVP fibrillation, 9-12 Flory`s interaction parameter, 2-11 to 2-14, 2-18, 2-20, 10-15 Flow, cold, 8-9 to 8-11 properties, 7-2 Foaming test of PSAs, 6-12, 6-20, 11-38 to 11-44 Fractional free volume, 10-27 Fracture energy in adherence performance, 4-3 Free energy for self-diff usion, 10-21 to 10-23 Free volume, correlation of with adhesion, 10-16 to 10-18 fractional, 10-27

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I-5

Index adjusting of, 4-14 Chang’s research on, 5-11, 5-13 Chu’s research on, 5-2 of tackifers, 11-33 H Haynes theory, 5-3 to 5-4 Heteroepitaxy, 3-10 HMPSAs (See Hot-melt pressure-sensitive adhesives) Holding time, 8-2 to 8-4, 8-13 Homogeneous deformation, 6-4 to 6-5 Hot-melt pressure-sensitive adhesives, 4-9, 4-13 to 4-14 Humidity, 7-16 Hydrophilic surfaces, PI drops as, 1-8 to 1-10 PVP-PEG adhesives as, 1-7 to 1-8, 11-29 to 11-32 spreading on, 1-13 to 1-18 time dependence of, 1-10 Hydrophobic surfaces, compared with model PVP-PEG, 10-30 to 10-33 PEG drops as, 1-7 to 1-8 PI drops as, 1-8 to 1-10 polymers as, 11-26 retardation times for, 11-32 to 11-34 time dependence in, 1-10 I Immiscible blends, 7-23 Interfacial cavity, energy release rate of, 6-10 propagation of, 6-20 schematic of, 6-9 Interfacial nucleation and propagation, 6-18 to 6-20, 6-22 to 6-23 Interfacial slippage, 2-17 Interfacial width, In neutron reflectivity, 2-12 to 2-14 Interpolymer complex model, 11-19 to 11-25 adhesive properties of, 11-19 to 11-20 composition dependence of, 11-24 effect of contact time in, 11-22 to 11-24 as model pressure-sensitive adhesive, 11-19

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J Joint, and adhesion, 9-13 to 9-17 durability of, 9-1 to 9-17, 10-22, 11-42 overview of, 9-1 to 9-2 triaxial stress tests for, 9-2 to 9-13 K Kelvin-Voight model, 1-6 to 1-7, 11-21 L Labels, 7-1 to 7-2 Ladder-like structure, 8-14 to 8-15 Large-strain relaxation, 11-49 Linear elastic shear, 11-48 Linear viscoelasticity, 4-17 to 4-21 complex shear modulus in, 4-17 to 4-20 compliance in, 4-21 domain of, 4-5 to 4-9 large-strain elongational geometries in, 11-45 to 11-47 zero-shear viscosity for, 4-20 to 4-21 Liquids, spreading mixtures, 1-10 to 1-12 wetting out of, on solids, of low-molecular-weight, 1-2 to 1-7 of multicomponent, Marangoni effect of, 1-10 to 1-11 by polymer, 1-7 to 1-10 spreading for mixtures of liquids, 1-10 to 1-12 spreading of surfactant solutions, 1-12 to 1-13 for surfactants, 1-10 Load, compressive, relaxation by, 11-6 to 11-25 definition of, 8-12 behaviour of PSA by, 8-9 to 8-11 Loop tack, 4-9, 5-18 M Mandrel peel test, 7-10 Marangoni effect, 1-10 to 1-11 Master curve, 7-11 to 7-13 Maxwell model, 10-13 Medical PSAs, 5-13 Migration, 1-11

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I-6 Mirror test, 6-12 to 6-13 Miscible blends, 7-22, 8-13 Molecular structure, in correlation of adhesion with free volume, 10-16 to 10-18 in Dahlquist’s Criterion of Tack, 10-33 to 10-36 in pressure-sensitive adhesion, 10-1 to 10-37 design of, 4-20 mobility of, 10-14 to 10-15 for other viscoelastic polymers, 10-16 to 10-36 influence of on tensile properties, 10-9 to 10-11 for PVP-PEG H-bonded complex, 10-5 for PVP-PEG hydrophilic PSAs, 10-6 to 10-14 role of in deformation mechanisms of, 10-7 to 10-9 in relationship between peel adhesion and viscoelastic deformation, 10-11 to 10-13 and glass transition temperatures, 10-24 to 10-26 relaxation times of, 10-23 to 10-24, 11-1 to 11-59 role of in diff usion coefficients for, 10-18 to 10-20 in self-diff usion, 10-21 to 10-23 as supramolecular structures, 10-4 to 10-6 underlying factors, 10-14 to 10-15 in universal theory of pressure-sensitive adhesion, 10-2 to 10-4 Multicomponent adhesives, 1-9 to 1-11, 3-25 to 3-29 N Neo-Hookean material, 6-6 Network structures, 11-14 to 11-16 Neutron reflectivity, 2-12 to 2-14 In 90° peel, 7-5 to 7-11 NMR (See Nuclear magnetic resonance) Nonlinear domain, 4-9 to 4-10 Nuclear magnetic resonance (NMR), 2-13, 10-7, A-1 O Open time, 4-14, A-5

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Index P Packaging products, 5-1, 8-1, 8-4 Paper, 7-2 Partial diff usion, 10-20 Paster, 5-3 to 5-4 Patch, skin, (See Transdermal drug delivery system) Peel adhesion, master curve of, 4-6 performance of, 5-16 phase state in, 10-25 plasticizer concentration, role of in, 7-20 of PVP blends, 9-11 of PVP-PEG blends, 10-5 rate and failure modes in, 7-13 to 7-14 role of free volume in, 10-17 stick-slip in, 7-14 viscoelastic deformation in, 10-11 to 10-13 Peel force of aluminum foil tape, 7-3 to 7-4 pulling rate in, 7-25 relation of to cohesion strength, diff usion and relaxation, 10-13 to 10-14 Peel properties, 7-27 Peel resistance, 7-1 to 7-32, 7-15 to 7-31 (See also Adhesion) basic principles of, definition of, 2-2 dependence of, on bulk properties, 16 to 7-27 cross-linking density, 7-18 descriptive assumptions on, 7-3 emulsifiers, 7-19 failure mode, 7-13 to 7-15 pulling rate, 7-17 to 7-18 retardation times, 11-35 to 11-36 surface properties of substrate, 7-27 to 7-31 flowchart for, 7-15 influence of, on removability, 7-2 of labels, 7-1 to 7-2 overview of, 7-1 to 7-2 parameters of, 7-15 to 7-31 of PVP-PEG composition, 10-11 relation of to, cohesion strength, 10-13 diff usion, 10-13 relaxation, 10-13 test,

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Index master curve and time-temperature superposition, 7-11 to 7-13 methods for, 7-9 to 7-11 90° peel, 7-5 to 7-11 180° peel, 7-2 to 7-11 theory of, 7-2 to 7-7 tools for, 7-10 of UV cross-linkable PSAs, 7-19 Peel strength, 3-21, 5-18 for blends of, SIS/tackifer, 7-21 Vector/tackifer, 7-22 PEG (See polyethylene glycol) Performance evaluation, in adhesion, 4-3 to 4-15 as peel, 5-16 of pressure-sensitive adhesives, criteria of, 1-18 to 1-21 factors affecting it, 7-9 fundamental polymer parameters for, 5-19 to 5-20 of shear, 5-16 of tack, 5-16 to 5-17 with viscoelastic window, 5-13 PIB (See Polyisobutylene) Plasticizer concentration effects of, 11-33 to 11-34 impact and relation of to adhesion, 11-55 to 11-57 in interpolymer complex, 11-20 to 11-21 on peel adhesion, 7-20 Plate, displacement of, 8-5, 8-9 separation of, 9-10, 9-12 Polydisperity, 2-2 to 2-3 Polyethylene glycol, chemical structure of, 10-4 (See also Model PVP-PEG) Polyisobutylene, cohesive strength of, 10-15 durability study for, 9-14 Polyken probe tester, 6-12 for adhesion energy, 2-4 to 2-11, 2-14 to 2-16 contact time for, 11-10 curves for, 6-19, 9-16, 11-7, 11-11 debonding for, 6-21 to 6-22 fibril formation for, 4-12 parameters of, 4-16 schematic of, 6-2 to 6-3, 6-13

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I-7 setup of, 11-6 to 11-8 stress-strain curve of, 11-38 stress-versus-time curves for, 11-44 to 11-45 theoretical background of, 6-2 to 6-12 use of, 2-2 Polymer, interfaces of, 2-11 to 2-12 Polymerization method, 8-14 Polypropylene, epitaxial structures of, 3-10 peel strength of, 7-29 to 7-30 Polysaccharides, 1-13 Polyvinyl chloride, 3-15, 7-29, A- 2 Polyvinyl pyrrolidone, A-2 (See also PVPPEG model) blends, chemical structure of, 10-4 durability of, 9-13 fibrillation in, 9-12 peel adherence in, 9-11 PP (See Polypropylene) Preparation conditions, 8-11 Pressure-sensitive adhesion, contribution of cohesion, diff usion and relaxation to, 10-8 to 10-15 criteria of performance for, 1-18 to 1-21 bonding pressure in, 1-21 to 1-22 definition of, 1-1 as multistage process, 11-2 to 11-6 with three-stages, 11-5 to 11-6 time dependence of, 11-2 to 11-4 relaxation criteria in, 11-36 to 11-37 retardation times in, 11-34 to 11-36 rheology of, 1-18 to 1-22 Pressure-sensitive adhesive, bandage of, 5-12 bonding pressure for, 1-21 to 1-22 bulk properties of, influence on peel resistance, 7-16 to 7-27 cohesive failure for, 2-22 compressive load behavior, 8-9 to 8-11 Deborah number of, 11-16 to 11-19 ever-tacky, 3-3 failure of, 7-13 to 7-14 for general purpose, 5-14, A-5 improving shear behaviour of, 8-15 to 8-16 joints with crystalline substrate, 3-13 to 3-14 layer deformation of, 6-2 to 6-4 medical, 5-13 model of, 11-19 molecular nature of, 10-1 to 10-37

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I-8 Pressure-sensitive adhesive (Contd.) overview of, 1-1 to 1-2 peel test schematic for, 7-5 performance criteria for, 1-18 to 1-21 factors affecting, 7-9 fundamental polymer parameters for, 5-19 to 5-20 relaxation for, 11-38 removable, 5-11 to 5-12, 6-19 rheological properties of, universal theories for, 10-2 to 10-4 with contributions of cohesion, diff usion and relaxation, 10-8 to 10-15 universal theory of, 10-2 to 10-4 viscoelastic window for, 5-13 Probe tack, 6-1 to 6-23 adhesive bond failure in, 10-8 confinement effect in, 6-4 to 6-5 debonding curves for, 6-15 to 6-23 cavitation in probe geometry for, 6-15 to 6-18 fibril formation and extension in, 6-20 to 6-22 interfacial nucleation and propagation for, 6-18 to 6-20 transitions in, 6-22 to 6-23 experiments for, 6-12 to 6-14 fibril in, definition of, 4-12 elongation of, 7-6 to 7-7 extension, 6-20 to 6-23 formation of, 9-10 growth of, 6-8 to 6-12 length distribution of, 7-6 to 7-7 Propagation, definition of, 11-42 interfacial cracks in, 6-20 PSA, performance of, and fundamental parameters of, 5-19 to 5-20 tack for immiscible, 2-11 to 2-16 PSAs (See Pressure-sensitive adhesives) PSA/tackifer system, 7-21 to 7-23 Pulling rate, for peel force, 7-25 for peel resistance, 7-17 to 7-18 PVC (See Polyvinyl chloride) PVP, fibrillation in, 9-12 overview of, 6-1 to 6-2

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Index PVP (See Polyvinyl pyrrolidone) PVP-PEG model, comparison of, with typical hydrophobic adhesives, 10-30 to 10-33 Dahlquist’s Criterion of Tack for, 10-33 to 10-36 debonding effects and deformation rates for, 10-28 to 10-30 deformation of, 10-7 to 10-9, 10-28 to 10-30 for hydrophilic pressure-sensitive adhesives, 10-6 to 10-14 free volume of, 10-21 to 10-23 deformation mechanisms of, 10-7 to 10-9 peel adhesion and viscoelastic deformation of, 10-11 to 10-13 tensile properties of, 10-9 to 10-11 viscoelasticity theory, use of, for, 10-13 to 10-14 large strain behaviour for, 10-26 to 10-28 elongation/extension rate on tensile stress relaxation of, 11-51 to 11-55 relaxation properties of, 11-48 to 11-57 linear elastic shear for, 11-48 plasticizer concentration and relation to adhesion of, 11-55 to 11-57 tensile stress relaxation of, 11-49 to 11-51 Q QSPR (See Quantitative structure-property Relationship) Quantitative relationships, 4-10 to 4-12 Quantitative structure-property relationship, 10-2, A-9 to A-10 R Relaxation, 11-1 to 11-59 in adhesion, 11-12 to 11-14 in adhesive bond formation, 11-6 to 11-25 approach to, 11-26 and bonding pressure withdrawal, 11-26 to 11-37 composition dependence of, 11-24 for compressive load, 11-6 to 11-25 contact time effect for, 11-16 to 11-19

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I-9

Index criteria for pressure-sensitive adhesion, 11-36 to 11-37 curves of, 11-20 Deborah number in, 11-16 to 11-19 of entangled and network structures, 11-14 to 11-16 influence of, on, adhesive properties, 11-19 to 11-20 for interpolymer complexes, 11-19 to 11-25 large-strain, 11-49 for model pressure-sensitive adhesive, 11-19 in multistage process of pressure-sensitive adhesion, 11-2 to 11-6 as three-stage process, 11-5 to 11-6 optimum range of times of, 11-16 in polymers, 11-38 of pressure-sensitive adhesives, 11-8 debonding stage of, first, 11-39 to 11-43 linear viscoelasticity and large-strain elongational geometries in, 11-45 to 11-47 second stage of debonding process, 11-43 to 11-45 three-stage mechanism of debonding, 11-37 to 11-39 process of, 11-42 to 11-43 in PVP-PEG model, 11-48 to 11-57 in tensile stress, 11-49 to 11-51 influence of, extension rate on, 11-51 to 11-55 linear elastic shear, 11-48 plasticizer concentration, 11-55 to 11-57 retardation times in, for hydrophilic PVP-PEG adhesives, 11-29 to 11-32 for hydrophobic PSAs, 11-32 to 11-34 and pressure-sensitive adhesion, 11-34 to 11-36 and squeeze-recoil behavior, 11-28 to 11-29 in SIS adhesive, 11-45 in tack tests, 11-6 to 11-8 times of, for acrylics, 11-9 Release force, 5-8 to 5-9 Release liners, 2-10, 6-18 to 6-19 Removability, 7-2 Removable acrylics, 6-19 Removable adhesives, 5-11 to 5-12, 6-19, A-5

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Repositionability, 7-2 Reptation concept, 4-19, A-5 Research on adhesion science, 4-2 Retardation times, for contact angle, 1-8 to 1-10, 1-17 correlation of with pressure-sensitive adhesion, 11-34 to 11-36 definition of, 11-3 for hydrophilic PVP-PEG adhesives, 11-29 to 11-32 for hydrophobic pressure-sensitive adhesives, 11-32 to 11-34 Rheoadsorption theory of adhesion, 3-7 Rheological properties, 11-2 and bonding pressure, 1-21 to 1-22 master curve for, 4-7 performance criteria for, 1-18 to 1-21 in pressure-sensitive adhesion, 1-18 to 1-22, 4-18 structure-mechanical transition zones as, 3-7 of viscoelastic polymers, 11-2 Rubber, 3-25 to 3-29 S SAFT (See Shear adhesion failure temperature) SBC (See Styrene block copolymer) Schematic tack curves, 6-11 Scott’s equation, 8-11 Secondary spreading, 1-3 Self-diff usion, free energy in, 10-21 to 10-23 influence of, on, tack, 2-2 to 2-11 of viscoelastic materials, 10-16 Shear, deformation in, 8-2 hang time in, 5-3 to 5-4 as holding time, 8-2 to 8-4 linear elastic, 11-48 performance, 5-16 plastometer for, 8-3, 8-5 rate of, 1-22, 8-5, A-7 resistance of, 8-1 to 8-16 characterization of, 8-2 to 8-4 cold flow problem in, 8-9 to 8-11 dynamic test for, 8-4 static test for, 8-2 to 8-4 strength, factors influencing it, 8-11 to 8-15

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I-10 Shear (Contd.) additives, 8-13 assembly time/preparation conditions, 8-11 chemical composition, 8-12 to 8-13 cross-linking density, 8-14 load, 8-12 method of polymerization, 8-14 miscibility, 8-13 molecular weight and structure, 8-12 physical cross-linking, 8-14 to 8-15 temperature, 8-12 improving of, for pressure-sensitive adhesives, 8-15 to 8-16 overview of, 8-1 to 8-2 stress, 1-22, 8-5, 8-8, A-7 test methods for, 8-4 to 8-9 viscosity, 1-22 Shear adhesion failure temperature, 5-5, 8-4, 8-13 to 8-15, A-2 SIS-based PSA, 6-15, 11-45, A-2 Solid-liquid interface surface phenomena, 1-2 to 1-18 Solids, wetting out, of, by low-molecular-weight liquids, 1-2 to 1-7 Marangoni effect in, 1-10 to 1-11 by multicomponent liquids, 1-10 by polymer liquids, 1-7 to 1-10 spreading mixtures of liquids in, 1-10 to 1-12 spreading surfactant solutions in, 1-12 to 1-13 with surfactants, 1-10 Solubility, parameter of, 10-15, 10-1 to 10-37 Solvent-based PSPs, 4-4 Spreading, dendritic, 1-12 on gels, 1-13 to 1-18 kinetics of PEG drops, 1-7 to 1-8 of mixtures of liquids, 1-10 to 1-12 secondary, 1-3 of surfactant solutions, 1-12 to 1-13 Squeeze-flow technique, 1-21 to 1-22 Squeeze-recoil, behaviors of, 11-28 to 11-29 profi les of, 11-27 to 11-28 test of, 9-9, 11-5 to 11-8 Squeeze tester schematic, 8-10 Standard types of test, 6-1 Static peel test, 7-10

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Index Static shear test, 8-2 to 8-4, 9-1 to 9-2 Steel, 3-25 to 3-29, 6-18 Stefan’s equation, 8-10 Sticking, 3-1 to 3-2 Stick-slip failure, 7-14, 7-25 Storage modulus and bonding, 5-17 to 5-19 Strength of adhesion, 10-1 to 10-37 Stress, normal, 7-8 to 7-9 role of, in, durability, 9-4 to 9-5, 9-15 Stress-strain curves, in adhesion energy determination, 2-15 in debonding, 6-16 to 6-17 for deformation, 4-16 diblock content, influence of, on, 4-10 to 4-11 parameters of, 11-38 for resin blends, 7-31 schematic of, 6-3 in viscoelasticity, 10-29 to 10-32 Stress-versus-time curves, 11-44 to 11-45 Structure-gradient transition zones, 3-8 to 3-11 Structure-mechanical transition zones, for adhesive classification, 3-5 to 3-8 in “rheoadsorption” theory of adhesion, 3-7 in rheological theory of adhesion, 3-7 Structure-property relationships, for model PVP-PEG hydrophilic PSAs, 10-6 to 10-14 deformation mechanisms of, 10-7 to 10-9 for peel adhesion and viscoelastic deformation, 10-11 to 10-13 for tensile properties, 10-9 to 10-11 in viscoelasticity theory of pressuresensitive adhesion, 10-13 to 10-14 Styrene block copolymers, 2-2, A-7 Substrates, crystalline, 3-13 to 3-14 deformable, wetting out of, 1-13 to 1-18 surface properties of, 7-27 to 7-31 Supramolecular structures, 10-4 to 10-6 Surface properties of substrate, influence of on, peel resistance, 7-27 to 7-31 Surface tension, 7-30, A-2, A-6 Surfactants definition, 1-10 spreading solutions of, 1-12 to 1-13

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Index T Tack, curves of, 2-4 to 2-7 between immiscible polymers, 2-11 to 2-16 performance of, 5-16 to 5-17 self-diff usion in, 2-2 to 2-11 test of, 11-6 to 11-8 Tackifers, 8-13 Tapes, 7-14, 8-15 TDS (See Transdermal drug delivery system) Temperature, dependence on, 10-35 of glass transition, adjusting of, 4-14 for tackifiers, 11-33 work of Chang, 5-1, 5-13 work of Chu, 5-2 for modulus requirements, 5-6 to 5-8 as shear strength factor, 8-12 sweep curves, 10-35 Tensile, properties, of model PVP-PEG adhesive blends, 10-9 to 10-11 of PSAs, 10-33 strength, 10-16 stress, in elongation, 10-27 in relaxation, 11-49 to 11-51 strain curves, 6-21, 10-10 Test, of, creep-recovery, 1-19, 8-7 durability, 9-14 dynamic peel, 7-10 dynamic shear, 8-4 failure mode, 7-13 to 7-15 foam, 6-12, 6-20, 11-38 to 11-44 mandrel peel, 7-10 90° peel, 7-5 to 7-11 180° peel, 7-9 to 7-11 peel resistance, 7-7 to 7-15 probe tack, 6-2, 11-6 to 11-8 squeeze-recoil, 9-9, 11-5 to 11-8 static peel, 7-10 static shear, 8-2 to 8-4, 9-1 to 9-2 T-peel, 7-10 Triaxial stress, 9-2 to 9-13 Termodynamic work of adhesion, 4-3, A-5 Termoplastic elastomers, 10-15, 10-35 Time parameter,

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I-11 as contact time, 11-12 to 11-15, 11-22 to 11-24 dependence on, 11-2 to 11-4 of cavity growth, 6-7 of complex shear modulus, 4-17 to 4-20 of compliance, 4-21 of Deborah number, 11-2 to 11-3 in linear viscoelasticity, 4-17 to 4-21 in reptation concept, 4-19 for zero-shear viscosity, 4-20 to 4-21 master curve of, 7-11 to 7-13 as open time, 4-14 as relaxation time, 11-12 to 11-14 for acrylics, 11-9 for adhesion strength, 11-16 to 11-18 correlation of with contact time and adhesion, 11-12 to 11-14 definition of, 11-3 for pressure-sensitive adhesives, 10-23 to 10-24 for viscoelastic materials, 10-16 as retardation time, for contact angle, 1-8 to 1-10, 1-17 correlation of with pressure-sensitive adhesion, 11-34 to 11-36 definition of, 11-3 for hydrophilic PVP-PEG adhesives, 11-29 to 11-32 for hydrophobic pressure-sensitive adhesives, 11-32 to 11-34 time-temperature superposition, 7-11 to 7-13 T-peel test, 7-9 to 7-11 Transdermal drug delivery system, 8-9 Transfer tapes, 7-14 Transient creep function, 4-21 Transition zones (See also Concentration gradient transition zones) adhesion theories for, 3-2 adhesives classification for, 3-3 to 3-29 combined, 3-25 to 3-29 structure-gradient related, 3-8 to 3-11 structure-mechanical, 3-5 to 3-8 definition of, 3-2 role of in diff usion and adhesive behavior, 3-21 to 3-24 overview, 3-1 to 3-3 Triaxial stress tests, 9-2 to 9-13 Trouton behavior, 4-22 Tse`s approach, 5-5

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I-12 U Ultraviolet light, cross-linkable PSAs, 7-19 induced curing, 7-14 Universal theory of pressure-sensitive adhesion, 10-2 to 10-4 V Vinogradov’s adhesiometer, 9-2 Viscoelastic materials (See also Linear viscoelasticity; Peel adhesion; Peel resistance) adherence performance of, 4-3 to 4-1 linear viscoelastic domain of, examples, 4-5 to 4-9 nonlinear domain of, adherence experiments in, 4-9 to 4-10 overview of, 4-3 to 4-4 process and material properties of, 4-12 to 4-15 quantitative relationships for, 4-10 to 4-12 relationships between, 4-4 to 4-12 behaviour of, 4-1 to 4-24 in cavitation, 4-15 to 4-17 overview of, 4-1 to 4-3 as soft polymers, 4-17 large deformations of and nonlinear aspects, 4-22 to 4-23 reptation concept of, 4-19 time dependent effects for and linear viscoelasticity of, 4-17 to 4-21 contact time for, 11-12 to 11-15, 11-22 to 11-24 Dahlquist contact criteria for, 5-14 to 5-15 debonding rates of, 10-28 to 10-30 definition of, 4-3, 10-2, 11-4 deformation of, 10-10 to 10-13, 10-28 to 10-30 durability of, 9-13 to 9-17 durability and adhesion for, 9-13 to 9-17 overview of, 9-1 to 9-2 triaxial stress tests for, 9-2 to 9-13 energy of, 2-4 to 2-11, 2-14 to 2-16 experiments with, 4-9 to 4-10 free volume for, 10-16 to 10-18 future research for, 5-20

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Index as hydrophobic adhesives, 10-30 to 10-33 joint durability for, 9-1 to 9-17 linear domain for, 4-5 to 4-9 measurement for, 4-18 model PVP-PEG adhesive based on, 10-26 to 10-28 nonlinear domain and adherence of, 4-9 to 4-10 quantitative relationships for, 4-10 to 4-12 typical hydrophobic adhesives of, 10-30 to 10-33 overview of, 4-3 to 4-4, 5-1 to 5-2 peel properties of, 7-27 performance of, 4-3 to 4-15, 5-13 polymers, as, 10-15 to 10-16 adhesive and rheologic properties of, 11-2 adhesion and free volume for, 10-16 to 10-18 Dahlquist’s Criterion of Tack for, 10-33 to 10-36 diff usion coefficients for, 10-18 to 10-20 examples of, 11-8 to 11-12 general purpose, 5-14, A-5 high shear, 5-11 medical, 5-13 glass transition temperatures for, 10-24 to 10-26 pressure-sensitive adhesives as, 10-16 to 10-36 relaxation times for, 10-23 to 10-24 self-diff usion for, 10-21 to 10-23 theoretical background of, 10-13 to 10-14 processing of, 4-12 to 4-15 quantitative relationships for, 4-10 to 4-12 relaxation time of, 11-12 to 11-14 release coatings for, 5-10 as removable adhesives, 5-11 to 5-12 research background for, 4-2, 5-3 to 5-20 Chang, 5-6, 5-17, 5-20 Chu, 5-6 Dale, 5-3 to 5-4 Hayne, 5-5 Paster, 5-5 Tse, 5-5 Yang, 5-17 to 5-20 soft polymers as, 4-17 to 4-23

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I-13

Index large deformations and nonlinear aspects of, 4-22 to 4-23 time-dependent effects and linear viscoelasticity of, 4-17 to 4-21 Trouton behaviour of, 4-22 spectrum of, 7-24 strength of, 3-9 to 3-10, 6-18 to 6-22 structural properties of, 7-17, 11-19 to 11-20 theoretical overview of, 3-7, 10-3, 10-13 to 10-14 weakness of, 6-18 to 6-20 Viscosity, by elongation, 4-22 to 4-23, A-3 to A-4, A-7, A-9 of, PEG-400, 1-17 of, spreading liquids, 1-8 to 1-10 Volume, free, correlation of, with adhesion, 10-16 to 10-18 fractional, 10-27 W Water-based/soluble PSPs, 4-4, 7-18 Weak adhesion, 6-18 to 6-20 Wettability, test of, 1-23 to 1-24, 7-18 Wetting,

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of, deformable substrates (gels), 1-13 to 1-18 of, solids, by low-molecular-weight liquids, 1-2 to 1-7 by multicomponent liquids spreading mixtures of liquids, role in, 1-10 to 1-12 by spreading surfactant solutions, 1-12 to 1-13 by polymer liquids, 1-7 to 1-10 William-Landel-Ferry equation, 7-11 to 7-12 Y Yang`s approach, for bonding and G′, 5-17 to 5-19 polymer parameters, 5-19 to 5-20 for PSA performance and fundamental Yield-point, 9-2 Yield stress, 10-33, 10-37, 11-12, 11-33, 11-42, 11-58 Z Zero-shear viscosity, 4-20 to 4-21 Zhurkov’s equation, 9-3

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