OVERVIEWS OF RECENT RESEARCH ON ENERGETIC MATERIALS

Robert W Shaw Thomas B Brill Donald L Thompson Editors

.--

<*.

OVERVIEWS OF RECENT RESEARCH O N ENERGETIC MATERIALS A d v a n c e d S«rles In Physical Chemistry

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Advanced Series in Physical Chemistry

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OVERVIEWS OF RECENT RESEARCH O N ENERGETIC MATERIALS

Advanced Series in Physical Chemistry Editor-in-Charge Cheuk-Yiu Ng, Department of Chemistry, University of California at Davis, USA Associate

Editors

Hai-Lung Dai, Department of Chemistry, University of Pennsylvania, USA James M. Farrar, Department of Chemistry, University of Rochester, USA Kopin Liu, Institute of Atomic and Molecular Sciences, Taiwan David R. Yarkony, Department of Chemistry, Johns Hopkins University, USA James J. Valentini, Department of Chemistry, Columbia University, USA

Published Vol. 4:

Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping eds. H.-L. Dai and R. W. Field

Vol. 5:

Laser Spectroscopy and Photochemistry on Metal Surfaces eds. H.-L Dai and W. Ho

Vol. 6:

The Chemical Dynamics and Kinetics of Small Radicals eds. K. Liu and A. Wagner

Vol. 7:

Recent Developments in Theoretical Studies of Proteins ed. R. Elber

Vol. 8:

Charge Sensitivity Approach to Electronic Structure and Chemical Reactivity R. F. Nolewajski and J. Korchowiec

Vol. 9:

Vibration-Rotational Spectroscopy and Molecular Dynamics ed. D. Papousek

Vol. 10: Photoionization and Photodetachment ed. C.-Y. Ng Vol. 11: Chemical Dynamics in Extreme Environments ed. R. A. Dressier Vol. 12: Chemical Applications of Synchrotron Radiation ed. T.-K. Sham Vol. 13: Progress in Experimental and Theoretical Studies of Clusters eds. T. Kondow and F. Mafune Vol. 14: Modern Trends in Chemical Reaction Dynamics: Experiment and Theory (Parts I & II) eds. X. Yang and K. Liu Vol. 15: Conical Intersections: Electronic Structure, Dynamics and Spectroscopy eds. W. Domcke, D. R. Yarkony and H. Koppel

Advanced Series in Physical Chemistry

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OVERVIEWS OF RECENT RESEARCH O N ENERGETIC MATERIALS

Editors

Robert W Shaw Army Research Office, USA

Thomas B Brill University of Delaware, USA

Donald L Thompson University of Missouri, USA

\[p World Scientific NEW JERSEY

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British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

OVERVIEWS OF RECENT RESEARCH ON ENERGETIC MATERIALS Copyright © 2005 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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"... Which, into hollow engines, long and round, Thick rammed, at the other bore with touch of fire Dilated and infuriate, shall send forth From far, with thundering noise, among our foes Such implements of mischief, as shall dash To pieces, and o 'erwhelm whatever stands Adverse . . . " Paradise Lost

ADVANCED SERIES IN PHYSICAL CHEMISTRY

INTRODUCTION

Many of us who are involved in teaching a special-topic graduate course may have the experience that it is difficult to find suitable references, especially reference materials put together in a suitable text format. Presently, several excellent book series exist and they have served the scientific community well in reviewing new developments in physical chemistry and chemical physics. However, these existing series publish mostly monographs consisting of review chapters of unrelated subjects. The modern development of theoretical and experimental research has become highly specialized. Even in a small subfield, experimental or theoretical, few reviewers are capable of giving an in-depth review with good balance in various new developments. A thorough and more useful review should consist of chapters written by specialists covering all aspects of the field. This book series is established with these needs in mind. That is, the goal of this series is to publish selected graduate texts and stand-alone review monographs with specific themes, focusing on modern topics and new developments in experimental and theoretical physical chemistry. In review chapters, the authors are encouraged to provide a section on future developments and needs. We hope that the texts and review monographs of this series will be more useful to new researchers about to enter the field. In order to serve a wider graduate student body, the publisher is committed to making available the monographs of the series in a paperbound version as well as the normal hardcover copy. Cheuk- Yiu Ng

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PREFACE: E N E R G E T I C MOLECULES, E N E R G E T I C MATERIALS Robert W. Shaw US Army Research Office 4300 South Miami Boulevard Box 12211, Research Triangle Park NC 27709-2211, USA

Few books present experimental and theoretical methods to characterize energetic materials combustion. Of these, this book by major contributors to the field, is unique: it summarizes much of the most important recent work, it discusses what we know with confidence and it suggests the principal areas that remain to be investigated. Most of the following chapters comprise summaries of work spanning decades with expert commentary found nowhere else. This book focuses on energetic materials, but it also guides us to modern methods for investigations of condensed and gas phase reactions in general. The energetic reactions that are the subject of this book are complex and difficult to study; nevertheless the work discussed here has provided substantial understanding of the behavior of materials now in use and predictive capability for development of new materials based on target properties. Ignition and combustion of energetic materials are complicated: they involve several phases, they are time dependent, and their reactions follow multiple, branching paths. More than half a century ago, Crawford, Rice and their co-workers1'2 studied burning nitrate ester propellants and, based partially on their visual observations of the distinctive flame structure (see Fig. 1), postulated a three-stage model still used today. In the first stage, first-order solid decomposition produces organic fragments. This process may occur only on the surface or extend back into the solid. Above this condensed/gas interface is a second, non-luminous (dark) region in which products from the first stage react. The third stage is a luminous flame ix

X

Preface

Fig. 1. The three stage energetic flame: the surface/gas interface, the dark zone, the luminous flame. The material, XM-39, is mostly RDX combined with esters (photo by and courtesy of John Vandcrhoff).

where subsequent reactions occur and most of the energy is released. But how does one make this picture quantitative? Twenty-five years ago, a small group met to discuss ignition and combustion of energetic materials guided by their belief that "molecular mechanisms" are important. Their report 3 bears re-reading today. To begin, they noted that "chemistry in any detailed way is left out of present descriptions." They sought to determine what experiments should be done and observed that "the problem is of such complexity that modeling is required to tie together the various pieces " Later they asked, "How much is known about solid decomposition . . . ?" and remarked that, "To date, there have been no successful quantitative measurements of species concentration profiles for the flame zone of burning solid propellants." Since they raised those important questions, the field has seen remarkable progress. By the late 1980s, even the end-users of energetic materials had become convinced that knowledge of detailed chemistry was important and that characterization of the combustion reactions by, for example, a single fitted Arrhenius expression may not be sufficient for design of reliable systems and. especially, for diagnosis of systems that have gone wrong. They were driven to this conclusion by concerns about safety — premature or delayed ignition leading to explosions.

Preface

XI

As questions were raised about the underlying phenomena in energetic combustion, significant developments in laser diagnostics, chemical kinetics modeling, and molecular structure and dynamics calculations suggested that the ignition and combustion of energetic materials might be susceptible to a focused and coordinated research assault. A study group 4 in 1991, restricting their attention to nitramines, reviewed progress and developed comprehensive recommendations for research on fundamental chemistry and physics, improved models, and sensitivity analysis to provide key reacting species and pathways. A general review5 of energetic materials combustion with focus on chemical mechanisms appeared around the same time. This book follows the point of view just described: combustion diagnostics, chemical kinetics modeling, and computational chemistry can provide quantitative predictions of energetic materials ignition and combustion. Granted, the experiments are difficult and the tools to measure and the models to simulate them are being used at the current limits of their development. The chapters you are about to read were written by pioneers in their areas of energetic materials study. They discuss what we know now and recommend for exploration the research problems that they deem most important. There is much in these chapters to guide the research worker. The first set of chapters (Brill through Anderson) takes us through a range of experimental methods. In nearly every chapter, the experiment is unique. Tom Brill provides a leadoff for the rest of the book and introduces our principal theme: the prediction of combustion and detonation properties from molecular and materials properties. Professor Brill emphasizes the complex and time-dependent nature of energetic materials reactions and discusses a range of experimental probes, always noting their drawbacks and warning us against facile interpretations of apparently correlated behavior. Richard Behrens discusses two decades of work to understand the low and medium temperature thermal decomposition of solid energetic materials. His unique apparatus measures the time-dependent evolution of gas phase products. Dr. Behrens has combined this chemical reaction information with studies of the physical changes in the sample from scanning electron microscopy and has developed a remarkably detailed model for thermal decomposition. His model, a tour de force, enables us to predict the aging behavior of energetic (and other) materials and contributes to

XII

Preface

our understanding of decomposition, combustion, and detonation at higher temperatures. Oleg Korobeinichev, Tim Parr and Donna Hanson-Parr probe energetic flames. Professor Korobeinichev uses microprobes or skimmed molecular beams and mass spectrometers. The high resolution and sensitivity of the mass spectrometer enable measurement of trace as well as major species. The walls of the probe, however, may collect reactive species and the probe and the skimmer may distort the flame. Nevertheless, models of flame distortion allow the data to be corrected and considerable information about species and temperature profiles has been collected. These profiles provide crucial tests for combustion models. Tim Parr and Donna Hanson-Parr use laser spectroscopies to map species concentrations and temperatures in flames. Again, these maps enable the development and testing of combustion models. Laser probes (if not too intense) barely perturb the flame and highly reactive species can be detected. The Parrs show that this technology is sufficiently developed that results on the same systems from different laboratories generally agree. The temperature profiles and distribution of many of the most important combustion products in flames are now well known. The (often ill-defined) region near the condensed/gas-phase interface is of great interest; but probing it remains a challenge. The Parrs recommend more work close to the surface. Unlike the stable species in flames, the many short-lived radicals that drive combustion chemistry are not well measured. And almost nothing is known about the large radical fragments that we expect to emerge from the condensed phase surface when the parent molecule decomposes. Paul Dagdigian identifies the intermediate species expected during early and late stages of combustion, discusses what is known about these species, and describes methods to detect them. Professor Dagdigian points out that detecting larger polyatomic fragments takes us closer to the early stages of decomposition — the stages about which we know least. Elliot Bernstein seeks to understand the electronic state dependence of energetic molecule decomposition. His experiment requires generation of gas phase samples (difficult for these low vapor pressure materials), preservation of the molecules in a collision-free environment, their excitation, and measurement of their decomposition products. Professor Bernstein explores the difference between energetic and other molecules, their decomposition pathways and kinetics, and argues that the dependence

Preface

xm

of decomposition on electronic state may be an important part of energetic material behavior. William Anderson and Arthur Fontijn have collaborated over the past decade to unravel the complex gas phase combustion mechanisms. Their chapter discusses chemistry in the different parts of the flame and the means of measuring the elementary reaction kinetics that enable them to infer that chemistry. Their chapter includes detailed discussion of the most important elementary reactions — those to which the model calculations are most sensitive. The next chapters (Thompson through Miller) discuss what we have learned from computations: reaction paths in the gas phase from molecular dynamics, reactions and energy transfer in the condensed phase, ignition and combustion models, and predictions of energetic performance. Donald Thompson discusses classical dynamics models for rates of energetic molecule reactions on quantum potential energy surfaces. This chapter is about the gas phase where most of the combustion energy is produced. Professor Thompson reviews and points out the limitations of the various classical approaches to rate calculations. He then goes on to discuss important experimental measurements of reaction paths and rates and the role of theory in their interpretation. Laurence Fried, M. Riad Manaa and James P. Lewis have been developing models for condensed-phase reactivity in energetic materials. In their chapter, they focus on two approaches to condensed-phase reactions: chemical equilibrium methods and atomistic modeling. The equilibrium methods are simpler, but require valid Equations of State which, in turn, require valid intermolecular force potentials. Atomistic modeling links reactivity more directly to molecular properties but, again, valid intermolecular force fields are required. Drs. Fried, Manaa, and Lewis also discuss force fields now being used. Dana Dlott discusses the transfer of mechanical energy into molecular energy and the relation between energetic materials properties and explosion sensitivity. Professor Dlott argues that the transfer of phonons into vibrations is directly related to chemical bonding in energetic materials and points to the need for lattice-dynamic calculations that go beyond classical mechanics. A new era in materials design is being enabled by advances, especially in treating condensed phases, in computational chemistry. Betsy Rice describes modern tools for design of energetic molecules to provide materials with targeted properties. Dr. Rice is now predicting densities

XIV

Preface

and crystal structures and plans to move on to mechanical properties, the prediction of sensitivity from molecular structure, and modeling of solubility. The community appears to be approaching a golden time in which we can design a molecule, model its reactive behavior in the gas phase, and predict its physical and chemical properties in condensed phases. Eun Kim and Vigor Yang describe their transient ignition and combustion model for nitramines. Their review of previous efforts pays tribute to the very important work by Carl Melius, twenty years ago, whose pioneering model of nitramine combustion gave the community confidence that, in spite of their complexity, propellant flames could be successfully modeled. The Melius model provided the basis for several, increasingly powerful, later models. Professor Yang and Dr. Kim describe their own multiphase combustion model. They use global decomposition reactions for the condensed phase and detailed chemical kinetics for the gas phase. Their model uses a two-phase fluid dynamic model to incorporate evaporation, formation of and reactions in bubbles, and interfacial transport of mass and energy. They write that the two-phase, near-surface region requires further treatment and that the model is hindered by the lack of reliable thermophysical properties. We have learned much about ignition and combustion of energetic materials, but a detailed model entirely grounded in experimental observations and ab initio calculations remains beyond us and may not be achieved in the foreseeable future. Nevertheless useful, even powerful, models have been developed, some marked by clever ways round our lack of knowledge. Martin Miller posits a pyrolysis law. This "semi-empirical finesse" (his words) evades the need for detailed knowledge of condensed phase reactions. The remarkable success of his model — agreement with measured burning rates and concentrations of combustion products in the flames — suggests its validity. Dr. Miller's chapter provides an authoritative account of the development of, and assumptions used in, his model. Dr. Miller has now moved on to other interests, but his chapter provides the foundation on which others may build. The last chapter, on synthesis by Jeffery Bottaro, stands alone. In a book about processes we include one chapter on properties of energetic materials: their synthesis and likely energetic materials of the future. Dr. Bottaro has been an important and innovative contributor to the synthesis of energetic

Preface

xv

materials, especially high nitrogen compounds, and he provides a succinct and informative description of important energetic molecules and their families. A lot of chemistry is in this chapter. Dr. Bottaro also discusses ideas for energetic molecules not yet synthesized. These chapters are markedly distinct from one another, but some themes recur. Experimentalists continue to be challenged to measure the earliest reactions. For those studying flames, this means measuring closer to the solid/gas phase interface — as far upstream as possible. The earliest reactions are most directly related to the parent molecules and likely to be most helpful in the inference of energetic materials reactions based on molecular properties. Our need for better intermolecular potentials recurs again and again in the chapters on modeling. About nitramines: you will find much mention of them in this book — a consequence of early planning by the research community. Nitramines are interesting chemically: they have C-H, C-N, N-N, and N - 0 bonds. Because they are symmetric, their reaction paths are likely easier to unravel than more complex and asymmetric molecules. And nitramines have enormous, current commercial importance. The tools employed on the nitramines, however, and the conclusions about their combustion behavior are also relevant to other energetic materials. Many tools, experimental and theoretical, have been brought to bear on this difficult problem — ignition and combustion of energetic materials. After reading this book, you will likely agree that the progress has been remarkable. Look back at the report of twenty-five years ago described in my third paragraph. Today detailed chemistry is present in our ignition and combustion models. Those models successfully represent exceptionally complex processes. We now have quantitative measurements of species concentration profiles for the flame zone of burning solid propellants and we know a lot about solid decomposition. The principal enabler of this progress has been our detailed understanding, based on measurements and models, of molecular properties and reactions. We owe that detailed understanding, in large part, to the authors of this book. Shelby Clanahan read these chapters and found and corrected many errors. She also rendered the chapters into a consistent format. We thank Shelby for her careful, tireless work. Ms. Ying Oi Chiew carefully edited and assembled the pieces of this book and guided it through production. We are much indebted to her. We also thank Richard Behrens for preparing a table that identifies important molecular structures. That table follows this introduction.

Preface

Structures of Energetic Molecule N02

rS CUM'

0 v

NO,

2

N02 H2N^Jx^NH2

,N0 N ^ N - N0 2 2

-X~N." ~ N 0

,-N

02N'

02N

CL-20

RDX N-NO a 0,N——'

02N.

02N

TNAZ

TATB NO

,N02

(

N0 2

y N0 2 NH2

2

) ^^ N0 2 HMX

0,N

N02

ONDNTA CH 3

H N-N' 0

2

N ^

N

^ O

0 2 N^J\^N0 2

N0 2 H3C

CH3

H

NTO

DMNA

TNT

N02 N02 H H-N-C-N-H NH

N02 0 HoC—C—CHp

"CH2p-N02 ri2C—C—CH2 02M-6 H2C

NQ - nitroguanidine

•

9

>=<

H2N

DADE (FOX-7)

N02

NG

N02 N02

'

9

N0 2

PETN H2N

H

N0 2

N

f T°

NH 4 N(N0 2 ) 2

H

N^N

r*NY° N^NH

ADN Oxy-s-triazine (OST)

HN-NH2HN03 H 2 N-N=C; HN-NH2

H

ON0 2

CH2ON02

TAGN NC - nitrocellulose courtesy of R. Behrens

Preface

xvii

References 1. B. L. Crawford, C. Huggett and J. J. McBrady, J. Phys. Colloid Chemistry 54, 854-862, 929-954 (1950). 2. O. K. Rice and R. Ginell, ibid, 885-917. 3. D. R. Crosley, R. A. Fifer and G. E. Keller, ARO Working Group Meeting on Ignition Processes, ARBRL-MR-03005 (1980, unpublished). 4. M. H. Alexander, P. J. Dagdigian, M. E. Jacox, C. E. Kolb, C. F. Melius, H. Rabitz, M. D. Smooke and W. Tsang, Prog. Energy Combust. Set. 17, 263-296 (1991). 5. G. F. Adams and R. W. Shaw, Ann. Rev. Phys. Chem. 43, 311-340 (1992).

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CONTENTS

Introduction

vii

Preface

ix

1.

2.

3.

4.

5.

6.

C o n n e c t i n g Molecular P r o p e r t i e s t o Decomposition, C o m b u s t i o n , a n d Explosion T r e n d s Thomas B. Brill T h e r m a l Decomposition Processes of Energetic M a t e r i a l s in t h e C o n d e n s e d P h a s e at Low a n d Moderate Temperatures Richard Behrens S t u d y of Energetic M a t e r i a l C o m b u s t i o n C h e m i s t r y by P r o b i n g Mass S p e c t r o m e t r y a n d Modeling of F l a m e s Oleg P. Korobeinichev

1

29

75

Optical Spectroscopic M e a s u r e m e n t s of Energetic Material Flame Structure Tim Parr and Donna Hanson-Parr

103

Transient G a s - P h a s e I n t e r m e d i a t e s in t h e Decomposition of E n e r g e t i c M a t e r i a l s Paul J. Dagdigian

129

Role of Excited Electronic S t a t e s in t h e Decomposition of Energetic M a t e r i a l s E. R. Bernstein

161

XX

7.

Contents

Gas-Phase Kinetics for Propellant Combustion Modeling: Requirements and Experiments William R. Anderson and Arthur Fontijn

8.

Gas-Phase Decomposition of Energetic Molecules Donald L. Thompson

9.

Modeling the Reactions of Energetic Materials in the Condensed Phase Laurence E. Pried, M. Riad Manaa and James P. Lewis

191

241

275

10.

Multi-Phonon Up-Pumping in Energetic Materials Dana D. Dlott

11.

Applications of Theoretical Chemistry in Assessing Energetic Materials for Performance or Sensitivity Betsy M. Rice

335

Combustion and Ignition of Nitramine Propellants: Aspects of Modeling, Simulation, and Analysis Eun S. Kim and Vigor Yang

369

Burning-Rate Models and Their Successors, A Personal Perspective Martin S. Miller

419

Ideas to Expand Thinking About N e w Energetic Materials Jeffery Bottaro

473

12.

13.

14.

Index

303

503

CHAPTER 1 C O N N E C T I N G MOLECULAR PROPERTIES TO D E C O M P O S I T I O N , C O M B U S T I O N , A N D EXPLOSION T R E N D S Thomas B. Brill Department of Chemistry and Biochemistry University of Delaware Newark, DE 19716, USA

Contents 1. Introduction 2. Diagnostic Approaches 3. Timescale, Temperature and Pressure 4. Decomposition Behavior and the Parent Compound 5. Combustion Behavior and the Parent Compound 6. Explosive Behavior and the Parent Material 7. Conclusions References

1 2 5 10 13 21 25 25

1. Introduction It is well known that very small differences in the molecular structure, composition, and/or properties of a material can have a large influence on the outcome of a practical event in fields such as pharmaceuticals, biomolecules and electronic materials. Energetic materials are no different in this sense except that the practical event is usually the decomposition, combustion or explosion behavior. Examples of this fact include reports that the presence of 0.01% of NO^ in the crystal lattice of ammonium perchlorate increases the burning rate by 50%,1'2 and conversion of mildly shock-sensitive 2,6-dinitrotoluene into potassium salt imparts extreme shock sensitivity.3 Investigations continue to be mounted in the hope of uncovering and predictably correlating relations between molecular properties (e.g. composition and patterns in structure, bonding, and dynamics) and macroscale 1

2

T. B. Brill

events (e.g. the burning rate and the sensitivity to initiation by shock and impact). In many cases this endeavor taxes logical interpretation at the fundamental level, not to mention the limits of diagnostic methods, theory, and modeling. Nevertheless, the field of explosives and propellants is instantly advanced when such connections are uncovered and found to be predictive. Spirited by this line of thought, many types of correlations between macro behavior and molecular properties of energetic compounds have appeared in the literature. In my judgment, however, while the existence of a correlation between various molecular properties may have a fundamental origin, the extension to macro events requires great care. 4 One problem is t h a t frequently a number of molecular properties can be found to correlate with a particular macro event, which makes it difficult to discern whether any or all of these properties form t h e basis of a controlling property and, thereby, can reliably predict macro behavior. Another problem is t h a t mesoscopic properties of the bulk material, such as the defect number, orientation of molecules with respect to the crystal faces, properties of the binder and so forth, can significantly affect explosive and combustion behavior. One may even legitimately question whether the existence of generally valid connections should even be expected between molecular properties and macro events given the large number of variables. W i t h the above pitfalls in mind, examples of successes and barriers to success in relating properties of a parent energetic material to decomposition, combustion and explosive properties are discussed in this chapter. Considerations about diagnostic methods, and decomposition, combustion and explosive properties are covered to the extent t h a t the contents of related chapters in this book are not duplicated. This discussion does not criticize past practice, but rather points out and builds on some of the considerations and factors t h a t we now know need to be incorporated for successful prediction of macro behavior from molecular properties.

2. D i a g n o s t i c A p p r o a c h e s At the molecular level the macroscale events of decomposition, combustion or explosion of an energetic solid are extremely complicated, time-dependent processes which take place rapidly in a spatially-tiny heterogeneous reaction layer. Equilibrium is not achieved as a result of the steep t e m p e r a t u r e gradient and, in some cases, the short timescale. Of course, it would be helpful t o have diagnostic methods t h a t simultaneously

Connecting Molecular Properties to Trends

3

measure rate and pathway of every species produced under these conditions. But. at the moment there is no universally suitable diagnostic method that is capable of providing these details at the level needed. Instead one must adapt several of the elegant molecular-level diagnostic techniques that provide incomplete "snapshots" of the actual event, or simulate part of the event experimentally so that optimized diagnostics can be employed to gain a more complete picture. As a beginning strategy, global behavior, such as impact sensitivity and burning rate characteristics, rests on a common platform as thermal events are driven mostly by the rate and magnitude of the temperature change. Techniques that can elucidate chemical details under conditions of controlled, rapid heating seem to offer the most potential for revealing the chemical features of these events. Ideally, the species are identified and their time dependence measured rapidly as close to the onset of the event as possible. Devices that enable both fast heating and near real-time detection of chemical species are the temperature-jump (T-jump), shown pictorially in Fig. 1, and confined rapid thermolysis (CRT) 6 methods combined with detection by Fourier transform infrared spectroscopy (FTIR). Each of these methods has strengths and weaknesses as simulations. For example, T-jump/FTIR enabled rapid, near real-time detection of the IR active species generated by controlled rapid heating of a thin film of the material, but the heating rate is limited by the transfer rate from the heater to the sample. CRT/FTIR improved on the uniformity of heat transfer, but

Actual Burning Surface

Decomposition

T-Jump Experiment

Products

Flame (decomposition products) Flame Front

'-Sample

(Area modeled by experiment)

20-50nm thick which models burning surface

Energetic Material

Fast Response A Z Power Source

f

• Platinum Filament Output Voltage Precisery Controlled

Fig. 1. A pictorial representation of the T - j u m p / F T I R spectroscopy method in which a thin film of material simulating the reaction layer of a burning surface is rapidly and controllably heated while measuring the gaseous products and the condensed phase thermochemistry.

4

T. B. Brill

sacrificed somewhat on the heating rate and time of detection of the species. The use of an imbedded fiber optic in the burning solid has been tried, but the number of species detected was small. 7 Several other methods of note include laser heating followed by cryo-trapping of products and detection by FTIR, 8 which enabled extremely rapid, but uncontrolled heating; laser heating to sustain combustion followed by mass spectral detection, 9 combustion while using a microprobe to "sniff" the gaseous products 10 (see the chapter by Korobeinichev); and the flyer plate method to mimic shock heating with TOF mass spectral detection. 11 Mass spectrometry has the advantage of detecting essentially all species, but with occasionally ambiguous identification because only the mass is available, whereas vibrational spectroscopy provides identification but may miss species having low concentration. Nevertheless, with great care and experience, much has been learned in recent years about decomposition, combustion and explosion chemistry by using these techniques. The picture is still not sufficiently complete to declare victory for any compound. An advantage of infrared detection is the fact that Fourier transformation enables absorbances of all IR-active species to be measured simultaneously with as fast as 20 ms time resolution. Zero-order (i.e. the use of a single frequency)12 or preferably first-order (multiple frequencies)13 identification and quantification can be applied. The first-order method (see Eq. (1)) involves matrix manipulation, where C(m x n) is the sought-after concentration matrix, K(n x p) represents a calibration matrix that must be developed for each species, and R(m x p) is the spectral matrix. R = CK.

(1)

In these matrices n is the number of components, m is the number of spectra, and p is the wave number. The concentrations of the species are obtained by minimizing the residual of R. Such a procedure enables both the identities and concentrations of the species to be extracted in a time series of spectra, even for "buried" species. The concentrations of the species based on the zero- and first-order calibration methods give similar results for compounds whose absorbances do not overlap. The only product that has so far proven difficult to quantify accurately is H2O. This is mainly because of the tendency of water to condense on the cell walls and to nucleate with the help of products such as H O . 1 4 T-jump/Raman spectroscopy enables closure on the atom mass balance to be achieved for most compounds once the IR and Raman data measured at the same conditions are combined.15 The Raman spectra provide

Connecting

Molecular Properties to Trends

5

quantitative N 2 , H 2 and 0 2 concentrations. The H 2 and 0 2 concentrations are particularly helpful for determining the amount of H 2 0 produced. That is, when the amounts of all products containing H and 0 are known and the amounts of H 2 and 0 2 are determined as well, then the H 2 0 concentration can be calculated and checked against the value obtained by the IR measurement. The Raman spectroscopy method is complicated by Mie scattering if smoke particles form during pyrolysis. The IR spectral method is affected in the same way, but because the source wavelength is longer, the size of the offending particles must be larger to scatter the radiation. Hence, IR spectra of smoky samples frequently have a negative-sloping baseline, whereas the Raman spectrum may not be attainable at all under the same conditions.

3. Timescale, Temperature and Pressure The timescale and the intrinsic variables temperature and pressure are important to consider when attempting to learn how a chemical property or the occurrence of reactions might affect the decomposition, combustion or explosion processes. This is particularly true if the event occurs at high temperature and pressure. Temperature and pressure are frequently opposed forces in condensed phase reactions. Higher temperature usually favors reactions whose products occupy greater volume (have greater entropy), whereas higher pressure usually favors reactions where the rate determining step has negative volume of activation and/or the products occupy less volume. The volume of activation of energetic materials is, however, not always negative. For example, it is positive for HMX, but negative for RDX 16 which can be rationalized on the basis of the differences in the intermolecular association in solid HMX and RDX. HMX is associated in the solid in three dimensions, whereas RDX crystallizes with the strongest association between pairs of molecules. Unless both the temperature and pressure are varied systematically, which is very difficult and almost never done, it is probably expecting too much to unravel the chemistry taking place at the extreme conditions of a shock wave. Experimentally parameterized modeling may present the best opportunity in this case. Heating to relatively low temperatures using rates of seconds to hours are characteristic of the conditions of slow cook-off. Slow decomposition results in many competing reaction channels where numerous products may form and accumulate. These products can participate as accelerants and give rise to additional reactions that are not expected of the native

6

T. B. Brill

material (see chapter by Behrens). Such products are sometimes referred to as catalysts, although they do not fit the formal definition of a catalyst. Moderate heating times of 20-1000 //s to temperatures approaching 1000°C are induced by mechanical impact. 17,18 The pressure rises from ambient to 7-15 kbar, but thermal processes still dominate. The reactions thereby induced can still be relatively large in number, but some of them may differ from those at lower heating rate conditions because higher activation energy channels can be accessed. This behavior is illustrated in Fig. 2 which shows an Arrhenius plot of two processes having different activation energies. Above the isokinetic temperature, the higher activation energy process occurs at a faster rate than the lower activation energy process. The use of a shock wave produces heating times of less than 1 [is to very high temperatures. 19 The pressure developed at the shock front reaches hundreds of kbars. Obviously it is very difficult to determine or even imagine the type of detailed chemistry that takes place under these conditions. Conventional chemical kinetics and reaction notions may need to be modified to account for the possible occurrence of electronic excitation and the plasma state. With the comments above in mind, two important energetic materials where the time factor or, correspondingly, the temperature factor, has been

1/T Fig. 2. The Arrhenius plot of two processes having different activation energies showing that the higher activation energy process can have the faster rate at higher temperature.

7

Connecting Molecular Properties to Trends

analyzed are TNT 2 0 and nitrocellulose.21 Both compounds have very complicated decomposition chemistry, and the dominating processes depend on the temperature and time of reaction. In the case of TNT it is helpful to consider the reaction temperature, T rxn , and the time to complete a process At, which can be obtained using a modified form of the Arrhenius Equation (2): £ a /[i?(lnA + lnAi)].

(2)

Figure 3 illustrates the time to the exothermic event in terms of temperature and the Arrhenius kinetics for three processes. These are the induction phase kinetics, the acceleratory phase kinetics, and the C-NO2 homolysis rate. In time-to-explosion tests, which apply to slow and fast cook-off, Fig. 3 shows that the time-to-explosion from hours to tens of milliseconds fits the experimentally-found temperature measurements using the acceleratory stage kinetics rather than the induction stage kinetics. 20 Acceleratory stage kinetics of TNT are associated with condensed phase decomposition reactions in which a variety of radical and non-radical products involving oxidation of the methyl group (e.g. 2,4-dinitroanthranil and 2,4,6-trinitrobenzaldehyde) build up and "catalyze" the decomposition of

• • 0 V > • A

1000-

800 -

*v*

o 600-

\ *

Acceleratory Induction Daconsetal. McGuireetal. Brill et al. Wenograd C-N02 homolysis

N$

400-

200Impact

Shock -

6

-

4

-

2

TTX 0

2

4

6

tog(time/s)

Fig. 3. A plot of the time-to-exotherm vs. temperature for TNT. The three lines represent the rates for the induction phase, the acceleratory (catalytic) phase, and C-NO2 homolysis.

8

T. B. Brill

the remaining TNT. As one approaches the timescale of heating by impact, which is less than one ms, the experimental time-to-exotherm measurements of Wenograd 17 indicate a departure from autocatalytic control in the direction of C-NO2 homolysis control. Hence, the rates of methyl group oxidation and C-NO2 homolysis become competitive. 20 As the timescale for shock initiation is approached, the rate of C-NO2 homolysis dominates. The kinetics for the induction phase do not seem to fit any data except possibly in the time range of milliseconds and shorter. The behavior is reminiscent of that in Fig. 1, where the lower activation energy processes of autocatalysis govern the lower temperature range, but gives way to the higher activation energy process at higher temperature. The differences in the apparent controlling reactions of TNT as a function of temperature make it clearly apparent why relating any of the molecular parameters of TNT to its explosive characteristics is so difficult. In the cook-off regime the parameters that control oxidation of the methyl group are important. In the impact sensitivity regime, oxidation of the methyl group and the reactions of the C-NO2 bond compete, which implies that there is no single dominating factor. In the shock regime the C-NO2 bond homolysis chemistry appears to dominate. To complicate matters further it is known that the tendency to cleave NO2 versus isomerize to C-ONO followed by loss of NO depends on the electron density in the ring. 22 Greater electron density favors the isomerization step with loss of NO, whereas lesser electron density favors the homolysis step with loss of NO2. Therefore, these two channels can be expected to compete as the decomposition process proceeds and the ring electron density changes. A similarly complicated situation exists with nitrocellulose where competing temperature-dependent processes occur over the 50-500°C range. 21 Below 100° C the processes of slow depolymerization, peroxide formation and acid hydrolysis all appear to occur, but with very different activation energies. At 100-200°C, a combination of first-order and autocatalytic kinetics appears to dominate. The first-order step, which may represent O-NO2 homolysis, is faster than the autocatalytic step, which has been proposed to involve acid hydrolysis by the H2O formed during decomposition. 21 In the 200-250° C range, it was proposed that first-order O-NO2 homolysis would dominate, 21 while above 250°C, which includes the combustion and explosion regime, Zenin23 proposed that the rate was zeroth-order and was controlled by the rate of oxidation of the hydrocarbon fragments by NO2. On the other hand, Merzhanov 24 claimed that the rate of O-NO2

9

Connecting Molecular Properties to Trends

homolysis continues to control the process. Neither interpretation takes into account the finite rate of desorption of the fragments of NC. We have shown that the rate of desorption of the fragments from many polymers mainly controls the degradation rate at combustion temperatures, 25 and may also contribute in NC at higher temperatures. Finally, a surprisingly universal correlation between the time and temperature of an event in HMX has been shown recently by Henson et al.26 Whether the event is slow cook-off at one extreme or shock initiation at the other extreme, the relation between time and temperature on the log-log scale yields a straight line, as shown in Fig. 4. Moreover, when properly treated, the rates of the (H)N0 2 + HCN decomposition channel and CH2O + N2O channel, which are discussed later in this chapter, give a time-temperature relation that coincides with this straight line. 26 The implication is that the controlling reaction in the exothermic event of

Temperature (C) 394 1 , , 1 1 1 1 1 1 1 1 1 Zinn and Rogers, 1962 Tarveretal. 1978 Tarveretal. 1978 McGuire et al. 1981 McGuireetal. 1981 Tarver et al. 1996

1727 1

•

102 "i

T A A V O

"b

+ Brill and Brush, 1991

104 i

0

103 -i

227

727

•

i

1

i

i

i

Js

A Lengelle et al. 1991

10"' "1

•

10'2 "I

O Von Holle and Tarver,

10'3 "I

•

Henson et al. 1998

-Arrhenius

io~ 4 -}

/si

Green and James, 196^ \l/

10-5 -1 10" 6 1 10"7 "! 10"8 "1 O

10-9-

1

'<& 'o |

0.5

1

1

1

1

|

1

1 1

i

1.0

1 ' ' 1.5

1

1 1 1 1 1

2.0

1000/T(K)

Fig. 4. A time-to-explosion plot for HMX covering slow cook-off to detonation (used with permission from B. F. Henson, Los Alamos National Laboratory).

T. B.

10

Brill

HMX over 20 orders of magnitude of time remain the same, e.g. probably the exothermic reaction of NO2 and CH2O. 27 Such behavior is in sharp contrast to TNT and nitrocellulose where different processes control the rate of decomposition as a function of time. 4. Decomposition Behavior and the Parent Compound The gaseous products resulting from fast decomposition as a function of temperature and pressure provide a historical record of the mechanism. To this end the gaseous products produced by thermolysis of closely-related sets of energetic materials have been identified and quantified. 12 ' 28 The motivation for conducting these studies was the hope that the types and quantities of the gaseous species could be correlated with differences in an important combustion property, such as the burning rate, or explosive properties, such as the sensitivity to initiation. Several correlations have been found between the type and quantity of gaseous products and the structure of the parent energetic molecule. For example, the tendency of nitramines to liberate NC>2(g) correlates with the N-N bond distance and NO2 asymmetric stretching frequency. As f as ym(N02) increases, the N-N bond lengthens and the tendency to liberate NC>2(g) is experimentally found to increase upon fast pyrolysis.29 The correlation is shown in Fig. 5, where the compound identities are given in the original reference. NO2 is 50-60% of the gaseous products from Cl-20 1640 TNTO»

1620 • CL-20

E u 1600

I 1580 -

• DNTO

Less N0 2

• DNFP • RDX

la

O 1560 o-HMX»

BCMN

DATH. HMX • DPT

E

AZTC More N0 2

• DNCP *BCEN

I 1520

• DMNA

1.33

1.34

1.35

1.36 1.37 1.38 1.39 N-N02 bond distance (Angstroms)

1.4

1.41

1.42

Fig. 5. T h e r e l a t i o n b e t w e e n t h e N - N O 2 b o n d d i s t a n c e a n d N O 2 a s y m m e t r i c s t r e t c h i n g f r e q u e n c y in n i t r a m i n e s s h o w i n g t h a t t h e a m o u n t of N O 2 (g) f o r m e d u p o n fast t h e r m o l y s i s is g r e a t e s t for t h e l o n g e s t b o n d s .

11

Connecting Molecular Properties to Trends

DMHDNA •

• MBNA trans-TNAD DNCP

• TNSU »cis-TNAD TNDBN

DMEDNA^

4

• HNDZ DNNC, ,R T*NAZ * 0

1

2

AnNP

D X

HMX

3

4

5

6

7

H(CH2)/N02 Fig. 6. The relation between the percentage of HONO in the gaseous products liberated on fast thermolysis and the ratio of easily-removed H atoms relative to the number of NO2 groups in the parent nitramine.

and TNTO. In another study we have shown that the quantity of HONO(g) released scales roughly with the number of easily-removed H atoms compared to the number of N 0 2 groups in the parent nitramine (see Fig. 6). 30 The H atoms from the CH 2 groups are more easily removed by /3-elimination than are H atoms of the CH 3 group. Nevertheless, the trend in Fig. 6 is also found when all of the H atoms of the parent molecule are counted. Again the compound identities are given in the original reference. N 0 2 and HONO are important products because of their action as oxidizing agents in the later exothermic reaction steps. The tendency of nitramines to produce C H 2 0 is related to the presence of a single CH 2 group straddled by > N N 0 2 groups in the parent molecule.12 The amount of HN0 3 (g) released from alkylammonium nitrate salts is related to the basicity of the alkylamine, i.e. the more basic the amine, the less H N 0 3 that is liberated. 12 The percentage of hydrocarbons in oxygen-deficient nitrate esters scales witti tae oxygen balance. 31 Likewise the C O / C 0 2 and NO/CO ratios, and the amount of H 2 0 released by nitrate esters correlate with the oxygen balance. 31 In addition to these structure-decomposition relations, the ratio of individual products as a function of temperature is frequently useful for learning about the branching ratios of decomposition pathways. For example, the amount of N 2 0 relative to N 0 2 liberated by HMX and RDX depends on the temperature. 32 This finding enabled the Arrhenius kinetics of the two

12

T. B. Brill

important global decomposition pathways (the N2O + CH2O channel and the (H)N02 + HCN channel) to be determined. 27 In the azide-containing polymer GAP, the ratio of NH3 to HCN enabled the two main pathways of decomposition of the nitrene formed upon decomposition of an alkylazide to be extracted. 33 HCN is favored at higher temperatures because the route to its formation is more direct and thus faster than that to NH3, where multiple H transfer steps are required. Aside from mechanisms and species of decomposition, the decomposition rates of the bulk material and reaction rates of the most important species are needed for most modeling applications. Almost all of these measurements have been obtained at low heating rates. The most common methods of measurement include the rate of increase of the gas pressure (manometry), heat release (DSC and DTA), weight loss (TGA), and absorbance intensity by IR spectroscopy. It has been shown for HMX and RDX that quite large differences exist in the Arrhenius parameters, but the rates are approximately isokinetically related. 34 That is, when plotted against one another the Ea and In A values fall roughly on a straight line (see Fig. 7). Thus, most of the measurements are probably valid for the particular conditions used in their

60-

50-

40-

• • A

20-

Solid phase Melt phase Gas phase Regression

10-

o-l

10

.

1

20

•

1

30

'

1

'

40 Ea, kcal/mol

1

50

'

1

60

'

1

70

Fig. 7. The kinetic compensation effect of the Arrhenius parameters reported for the decomposition of HMX.

Connecting Molecular Properties to Trends

13

measurement, but it is dangerous to extrapolate any to higher temperature ranges, such as occur in combustion or explosion. Nevertheless, such extrapolations have been defended and sometimes loosely fit the combustion and explosion data. 35 ' 36 In part this correlation works because the uncertainty in the variables is rather large. It is noteworthy, as shown in Fig. 7, that the Arrhenius parameters for HMX do not cluster together in groups representing decomposition in the solid, liquid and gas phases. There is no strong support for a "cage effect" in the condensed phase when all of the available kinetic data is considered.

5. Combustion Behavior and the Parent Compound Burning rates can be measured in a variety of ways including photographically as a billet or strand of material regresses in a constant pressure bomb, and ultrasonically as the pressure is changed. The surface temperature at a given pressure is most commonly measured with an imbedded microthermocouple. The surface is judged to have been reached when a slight "knick" in the slope occurs in the temperature profile. Unfortunately, quite a large variation is found whenever a compilation of surface temperatures is made for a given compound. This fact alone raises issues with both the experimental simulation and modeling of the chemistry of the combustion process. Moreover, the faster one heats and the more violent the event, the more difficult it becomes to determine the controlling processes. One might therefore expect to have greater hope for relating combustion properties to chemical reactions of the parent material than developing these relations for the initiation and explosion properties. This is because combustion, although complex, occurs with reasonably well-defined conditions of timescale, temperature and pressure for which chemical kinetics and transport can be tractably measured or calculated. Such is not the case for the explosion/detonation event. During the combustion of a solid, a complex surface reaction zone develops in which the solid degrades by liquefaction, evaporation or sublimation, and/or decomposition. Whether all of the processes occur and what the relative role of each is depends on the material and the pressure. If evaporation or sublimation dominates, as it does with organic liquids and solids with substantial vapor pressure, then the combustion process can be expected to occur primarily in the gaseous phase. In such cases there may be a good opportunity to relate molecular properties to the combustion behavior. Caution is advised however since the nature of the surrounding atmosphere can affect the decomposition products of compounds having

14

T. B. Brill

significant vapor pressure. 37 If, on the other hand, significant decomposition takes place in the heterogeneous surface layer, as is frequently the case with solids having high melting points and low vapor pressures, then condensed phase reactions complicate the problem. The combustion behavior will more than likely be controlled both by the decomposition pathway in the condensed phase and by the exothermic reactions of the gaseous decomposition products near the surface. Because of the processes mentioned above, the description and even the definition of the surface reaction zone depends on the material and the pressure. Regardless of the details, there is ample time and space for chemistry to occur. For example, a reaction zone of 5 micron thickness corresponds to 5000 unit cells assuming a unit cell dimension of 10 A. The reacting front traverses 5 microns in 5 x 1 0 - 4 s assuming a burning rate of 1 cm/s. The highest probability of finding relations between a molecular property and the combustion characteristics lies in the study of both decomposition and combustion of closely-related sets of pure compounds. At the time when most of the structure-decomposition work described in Sec. 4 was conducted, the burning rate trends of the same compounds were generally not available. After 1993, however, the FLAME database of Fogelzang et al.38 became known and available outside of Russia. Examination of this database, while rich with exciting and important burning rate data, revealed that it did not contain information on many of the compounds for which the products of fast thermal decomposition had been determined. Thus, elucidation of the possible connections between the burning rate and chemistry could not be made directly for most of the compounds. An exception is the 5-aminotetrazole (5-ATZ) salts of HC1, HBr, and HI. 39 These salts are particularly well suited for identifying chemical pathways that control their burning rates. This is because the exothermic chemistry of the tetrazole ring occurs in the condensed phase early in the combustion process and is very likely the dominating factor in the burning rate. Hence, flash pyrolysis by the use of T-jump/FTIR spectroscopy has a higher probability of success for identifying the molecular property or properties of the parent tetrazole salt that are responsible for the burning rate differences. Figure 8 shows the burning rate data from the FLAME database and reveals that all of the 5-ATZ salts burn faster than pure 5-ATZ, despite the volumetric dilution of the energy by the halide ion. Sinditskii et al.4,0 noted that the burning rates correlated linearly with the pK a values of the

Connecting Molecular Properties to Trends

15

10 • • v A

5-ATZ [5-ATZH]l [5-ATZH]Br [5-ATZH]CI

0.1

0.1

1

10

100

Log P, MPa

Fig. 8.

The burning rates of 5-ATZ and its hydrohalide salts as a function of pressure.

acids HX (HI < HBr < HCl) and proposed that protonation destabilizes the tetrazole ring and enhances its decomposition rate. Neutral 5-ATZ was found by T-jump/FTIR spectroscopy to liberate HN 3 preferentially,41 whereas cationic 5-ATZH+ preferentially liberated N 2 . A molecular basis for this finding was revealed by a semi-empirical molecular orbital calculation. Shown below are the bond distances in angstroms calculated for the two forms of 5-ATZ.

1.344 •IN

423

-NH, N - ^ 1.327 5-ATZH+

//1.389 N

5-ATZ

The N a -N b distance in 5-ATZH+ is shorter, whereas the N b -N c and N a -N d distances are longer compared to 5-ATZ. This pattern favors the loss of N 2 from the 5-ATZH+ ring. On the other hand, N c -C is longer in 5-ATZ, which favors the opening of the tetrazole ring at this site leading to the liberation of HN 3 . The 5-ATZH+ ring is indeed less stable than that of 5-ATZ40 also on the basis of the fact that the sum of the ring bond distances is greater (6.80 versus 6.76 A, respectively).

16

T. B. Brill

The trend of the heat released by the 5-ATZ and 5-ATZH+ decomposition channels can be obtained from the heats of formation of the reaction components. 39 The 5-ATZ channel is expected to be less exothermic than the 5-ATZH+ channel because the heat of formation of HN3 is positive, while that of N2 is neutral. The trends in the relative roles of the low and high temperature decomposition channels (5-ATZ and 5-ATZH+, respectively) of the [5-ATZHJX salts compared to 5-ATZ help to explain the differences in the burning rates of these compounds as a function of pressure shown in Fig. 8. The IR spectra reveal 39 that a significant part of the decomposition process of the Cl~ salt involves the formation of HC1 and neutral 5-ATZ. Hence the decomposition reactions of neutral 5-ATZ make an important contribution to the burning rate of [5-ATZHJC1 and cause the burning rate to resemble most closely that of neutral 5-ATZ. The I - salt on the other hand exhibits no evidence of the 5-ATZ-decomposition channel in the gaseous products and therefore decomposes predominantly by the more exothermic 5-ATZH+ pathway (see Eqs. (3) and (4)). The reaction shown in Eq. (4) is a multistep process for which only the reactants and products are shown. H

HIM, *-

N2

+

/C

NH 2

(3)

NH+IHN, 2

)c

NH 2

•

NH4I + HI + HCN + NH2CN + N 2

(4)

NH+I" [5-ATZH]I has the highest burning rate of the three salts and least resembles the rate of 5-ATZ. The burning rates of the CI" and Br" salts are intermediate. The burning rate of 5-ATZ is lowest and is entirely controlled by the 5-ATZ channel (Eq. (5)). If it is assumed that the difference in the burning rates is a simple function of the balance between the 5-ATZ and 5-ATZH+ channels, then the percentages of each channel can be obtained from the ratios of the burning rates at a given temperature. Figure 9 was constructed for this purpose. The 1.1 MPa data in Fig. 8 was used because this pressure most closely resembles the pressure used

17

Connecting Molecular Properties to Trends

100

80 CD

c c ra .c O N

,

- 20

•

en •

L

Burns - 40 > —

60 --

faster 40 -

Burns slower

•*\ \^^

20 0 5-ATZ

+

- 60

i

[5-ATZH]CI

» -—80

O

3-

a>

CD

^

100

i

[5-ATZH]l

[5-ATZH]Br

Fig. 9. The percentage of the two main decomposition channels of 5-ATZ and its hydrohalide salts.

in the pyrolysis study. Of course these ratios could also be plotted versus the pK a values of HX. The observation of Sinditskii et al.40 that the burning rates correlate with the pK a of HX is thus placed on the footing of several specific chemical reactions. Reactions shown in Eqs. (6) and (7) may become important under some conditions and are well known to occur during pyrolysis.42

HN 3 + NH2CN

2NH2CN

(NH2)2CNCN

(NH2)2CNCN + NH2CN

(5)

(6)

(7)

NH 2

18

T. B. Brill

An additional feature of Fig. 8 is the different pressure dependencies of the burning rates of the four compounds. The 5-ATZ channel for the salts begins with the dissociative-evaporation as shown in Eq. (8): [5-ATZH]X - • 5-ATZ + HX

(8)

Because the contribution of this step is observed experimentally to decrease in the order 5-ATZ > [5-ATZH]Cl > [5-ATZH]Br > [5-ATZH]I, the relative pressure dependence of the burning rate is expected to decrease in the same order. This result is seen in Fig. 8 and is consistent with the fact that an evaporation-like process is expected to be suppressed as the pressure is increased. The electronic influence of a substituent on the tetrazole ring is reflected in systematic changes in burning rates. 43 Figure 10 shows that the electron density in the tetrazole ring, as mediated by the substituent X on the carbon atom in 5-X-tetrazole compounds, roughly correlates with the burning rate at constant pressure. The highest burning rates occur with the most strongly electron-withdrawing substituents. This series of tetrazoles has not been analyzed by T-jump/FTIR spectroscopy, but the trend in Fig. 10 is

N=NR NN

°2*

• N02

• Tz

• CI • Br

• CN

• H • NHTz

• OH • NH 2 -0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Hammett sigma The burning rates of 5-substituted tetrazoles as a function of the ring electron density (Hammett scale).

Connecting Molecular Properties to Trends

19

consistent with the interpretation given above for the hydrohalide salts of 5-ATZ in that the highest burning rate results when the tetrazole ring has the lowest 7r-electron density. The position of the substituent on the ring has been shown to affect the burning rate of azidonitrobenzene compounds. 44 Substitution in the m and p positions produces the same burning rate, but that is faster than substitution in the o position. The apparent explanation is the formation of the more stable benzofuroxan molecule by loss of N 2 from the o-azidonitrobenzene, shown in Reaction (9). This reaction does not take place when the substituents are in the m and p positions.

N2

N02

Nk

/ N ^o

Finally, it has been found that most metal salts of energetic molecules burn faster than the parent molecule despite the dilution of the energy by the mass of the metal ion. 45 The implication is that the metal ion participates as a catalyst in the decomposition/combustion process. The discussion above illustrates that it is possible to learn a great deal about the parent molecular properties and/or chemistry that dominate in determining the burning rate of a material. The examples were, however, carefully chosen to be those in which the process is largely controlled by early-stage, exothermic, condensed-phase chemistry, and the controlling decomposition channels are relatively few in number. Finding controlling factors in HMX and other nitramines requires a somewhat different line of thinking. It appears that the gaseous decomposition products of HMX mainly control the burning rate and surface temperature. HMX decomposes via a complex scheme of reactions that remain to this day a subject of debate. For example, using simultaneous thermal decomposition and molecular beam mass spectrometry, Behrens defined pathways of slow decomposition (see the chapter by Behrens). The role of reversible and recombination reactions in the condensed phase has recently been stressed 46 and is a likely source of many products. This is how the "cage effect" might be manifested in mechanistic data. Some of the pathways in Behrens' findings also appear to occur during fast decomposition and combustion. For example, the formation of the mono nitroso derivative

20

T. B. Brill

of RDX (MRDX) is detected in slow decomposition, flash decomposition, and burned propellants that had been rapidly quenched. 47 The amount of MRDX differs, but it is found in every case. Amides are present in both slow and fast heating. Despite these products, the two main global channels that dominate for practical modeling purposes during combustion appear to be the exothermic N2O + C H 2 0 pathway and the endothermic (H)N0 2 + HCN pathway. 32 However, these two pathways occur in parallel and are essentially thermally balanced. Therefore, they are not likely to control the burning rate. Instead, the early strongly exothermic reactions are the most important for this purpose. One of the most important early exothermic processes is the reaction of the fuel (CH2O) from one channel and the oxidizer (NO2) from the other channel as shown in Eq. (10). In fact, a reaction with about the same stoichiometry (in terms of NO, CO, CH2O and N0 2 ) 5CH 2 0 + 7N0 2 -f 7NO + 3CO + 2C0 2 + 5H 2 0

(10)

has been found to occur at the exothermic stage in the flash decomposition of HMX. 32 ' 48 It is also provocative to note that the temperature at which the reactants for this highly exothermic reaction are in their proper stoichiometry for Eq. (10) corresponds to several surface temperature measurements of burning HMX. Could it be that the surface temperature, and correspondingly the burning rate, of HMX settles in at the temperature at which the stoichiometry of this early stage and strongly exothermic reaction is optimized to provide the maximum amount of heat in the reaction zone of the burning surface? Ignition delay in HMX probably results primarily from the need to build the concentrations of NO2 and CH2O before the exothermic Reaction (10) has a major effect. All of the examples above deal with combustion of pure materials. Of course, most energetic materials used in practice are formulated with a binder and other materials to modify the ballistics (e.g. metals, metal oxides) and improve the aging and mechanical properties (e.g. stabilizers and plasticizers). A logical question is whether these additional components can have an overriding influence on the combustion behavior compared to the pure energetic material. Sometimes they do as is evident by the influence of the agent used to cross-link the binder of an AP composite propellant. 49 We have suggested that the influence of the cross-linking agent is related to its volatility from the matrix as the propellant heats toward combustion. 50

Connecting Molecular Properties to Trends

21

6. Explosive Behavior and the Parent Material The impact and the shock sensitivity of a material can be experimentally evaluated in several ways, the most common of which are the drop hammer test and the gap test, respectively. In the impact test, a weight having a standard mass and contact area is dropped on the anvil on which a measured amount of sample has been spread. This is done repetitively from different heights and the height at which the sample is judged to have exploded 50% of the time is considered to be the drop height impact sensitivity. It is well known that the drop hammer test is crude and is subject to much uncertainty. The results differ from machine to machine. Shock sensitivity is frequently measured by sending a shock wave through a buffer plate to the explosive of interest. The pressure at which an explosion is initiated 50% of the time for a given density of material is the shock sensitivity. If one assumes a shock velocity of 6000 m/s, then 6 unit cells each having a dimension of 10 A are traversed in I ps. This is space and time enough for reactions to occur assuming that reactions on the ps timescale are important. Owing to the high and changing density and temperature in the shock front, the reactions are very difficult to decipher. Progress has recently been made by simulation of HMX at these conditions, which seems to offer the best opportunity for understanding at this time. 51 Because of the extreme conditions of shock and impact initiation, specifying molecular properties that control explosive behavior has also been a dicey activity attracting considerable thought. An inescapable and widely known fact is that nascent and dynamically-formed defects in a solid energetic material are the sites where the explosive reaction is initiated. Initiation does not originate in the defect-free region. Consequently, the possible relations between impact/shock sensitivity and fundamental molecular, crystal, and bulk properties of an explosive should always be considered in the context of how the behavior of molecules at the defect differ from those in the perfect solid. For example, the orientation of molecules relative to the direction of the shock wave has a significant effect on the shock sensitivity. This has been shown by Dick and co-workers in the case of PETN, 52 ~ 54 where initiation by impact is related to the energy localization and dissipation that takes place during plastic deformation and the shearing along certain axes. Shock sensitivity depends on the crystal orientation; that is, those directions in which shear bands do not easily occur experience the greatest local heating. A fundamental question arises as to how mechanical energy becomes coupled to the molecule in a way that starts a chemical reaction. If thermal

22

T. B. Brill

equilibrium is maintained during a mechanical impact, then the sensitivity of a material should directly correlate with its decomposition temperature, which it does not. In fact, direct coupling of mechanical energy into vibrational motions is too slow to cause deviations from thermal equilibrium. 55 A coupling mechanism must exist that allows deviations to occur from thermal equilibrium. A concrete discussion of how shock-generated mechanical energy becomes converted at the molecular level into dissociation reactions has been presented by Dlott and Fayer. 56 They proposed that "up-pumping" of selected vibrational modes occurs to a different degree at the defect site than in the perfect crystal lattice. In particular, hot spots form at the defect sites because the anharmonic coupling between phonons and the low frequency "doorway" modes is greater at defects compared to the ordered crystal sites. Consequently, the molecules at the defect heat faster and to a higher temperature than do the molecules uniformly distributed in the crystal. Following this line of thinking, Fried and Ruggiero 57 considered the coupling between phonons and internal vibrational modes from the point of view of the density of states of the phonon modes. They found that a correlation existed between the rates of energy transfer from the phonon modes to the fundamental modes that probably initiate the reaction. Figure 11

? ! &

-ou

gamma-HMX

*

-50 • RDX

cha

s. c

PETN

• beta-HMX

-40-

>. ?

• TNT

u c 9>

2 -30o

fc c ra

E -20c o E

-10 -

ial

£a.

• NQ • TATB

s c

n0.05

0.1

1

i

1

1

0.15

0.2

0.25

0.3

0.35

1/(N m)

Fig. 11. The energy transfer rate from the phonon density of states compared to the impact sensitivity of primary and secondary explosives.

23

Connecting Molecular Properties to Trends

shows this correlation for several important energetic materials that have significantly different impact sensitivity. McNesby and Coffey55 approached impact sensitivity from a similar point of view of rapid deposition of energy from a mechanical event into the phonon modes in such a way that causes non-equilibrium distribution of energy to occur in the internal vibrational modes. Thus impact sensitivity should be determined by how fast energy is transferred from the phonon system to the vibrational modes. As is shown in Fig. 12, they found that the impact sensitivity approximately correlated with the initial change in the phonon manifold of the molecule following shear dislocation. The mechanisms discussed above associate quantum mechanically-based properties of molecules with the macro events of impact and shock sensitivity. I think of these as primary correlations. In addition to these primary correlations, there are a myriad of crystal and molecular properties that sometimes tightly and sometimes loosely intertwine with the phonon and vibrational states of a complex molecule and thereby may also correlate with impact and shock sensitivity. I think of these as secondary correlations. An illustration of the confusion about whether and how various crystal and molecular properties exercise primary or secondary control over the

Pbstyphnate* • gamma-HMX

• RDX • beta-HMX picric acid • styphnic acid

•

• TATB 0

5

10

15

20

25

30

Energy Transfer Rate at 425 cm -1 Fig. 12. The initial energy change in the phonon manifold of several explosives as a function of the impact sensitivity.

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explosive characteristics is illustrated by the aminotrinitrobenzene series, TNB, MATB, DATB, and TATB.

At least seventeen bulk, crystal and molecular properties of these compounds are known to correlate with their impact and shock sensitivity.4 These include the bond distances, charge distribution, degree of hydrogen bonding, electron promotion energy, density, heat of explosion, oxygen balance, melting point, molecular weight, and so on. The existence of so many positive correlations of sometimes unrelated properties cast doubt on whether any (or all) of them contribute fundamentally to the impact and shock sensitivity. For example, the observation that the amount of hydrogen bonding in these compounds is responsible for the trend in sensitivity to shock is frequently heard. The thought is that hydrogen bonds can act as "shock absorbers" to help minimize the concentration of vibrational energy in the molecule. While this may be true because of the influence of hydrogen bonding in the phonon mode structure, the existence of hydrogen bonding alone does not desensitize a material. For example, the extent of hydrogen bonding is very similar in nitroguanidine and trinitroethylnitroguanidine, yet the latter is much more sensitive to impact. 58 The reason is that the added, highly energetic trinitromethyl group sensitizes the molecule regardless of whether hydrogen bonding exists or not. The observation that the oxygen balance of nitroaromatic compounds correlates roughly with their impact sensitivity is evidence that the exothermicity of the secondary reactions following the initial steps is a factor in the operator's interpretation of the response to the hammer. 18 Indeed the types and quantities of products from the aminonitroaromatic series reflect an energy difference that follows the same trend in impact sensitivity.4 As a consequence, oxygen balance, which manifests itself in the impact sensitivity through the degree of exothermicity of the secondary reactions, is as legitimate a parameter as any of the seventeen to correlate with explosive properties of the aminotrinitrobenzene series above (or any other series for that matter). If one dares to make such correlations, then it is wise to

Connecting Molecular Properties to Trends

25

choose closely-related compounds. In the case of oxygen balance for example, many explosives are available t h a t do not possess any oxygen yet display the full range of sensitivities. Taken at face value the predictive value of the secondary correlations is doubtful in most cases.

7.

Conclusions

Relating parent molecular properties of an energetic material to decomposition, combustion, and explosion characteristics requires considerable care. There is no question t h a t correlations can be found and t h a t some may be meaningful, but the prima facie existence of a correlation is not necessarily meaningful. Correlations among various molecular properties have the most significance because they may have a q u a n t u m mechanical basis for the connection. Correlations among molecular and crystal properties require greater care to interpret properly, because there may or may not be a chemical or physical basis by which they can be connected. Correlations between molecular properties and macroscale bulk behavior are riskiest of all because the myriad of processes taking place may defeat most of the simple fundamental connections with the parent molecule. This rather pessimistic assessment of molecular correlations with macro events should be taken as a cautionary note as opposed to a call to avoid these types of studies altogether. For example, the connections made between shock and impact initiation and the phonon mode structure appear t o be a step in the right direction. Progress in this area will be an important component for designing b o t h conventional and new generations of energetic materials.

References 1. E. E. Hackman, III and H. C. Beachell, AIAA J. 6, 561 (1968). 2. A. K. Galwey, P. J. Herley and M. A. Mohamed, Thermochim. Acta. 132, 205 (1988). 3. M. L. Batz, P. M. Garland, R. C. Reiter, M. D. Sandborn and C. D. Stevenson, J. Org. Chem. 62, 2045 (1997). 4. T. B. Brill and K. J. James, J. Phys. Chem. 97, 8752 (1993). 5. T. B. Brill, P. J. Brush, K. J. James, J. E. Shepherd and K. J. Pfeiffer, Appl. Spectrosc. 46, 900 (1992). 6. E. S. Kim and S. T. Thynell, CPIA Publ. 685, 145 (1998). 7. J. Wormhoudt, P. L. Kebabian and C. E. Kolb, Combust. Flame 111, 73 (1997). 8. T. R. Botcher and C. A. Wight, J. Phys. Chem. 97, 9149 (1993).

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9. C. J. Tang, Y. J. Lee, G. Kudva and T. A. Litzinger, Combust. Flame 117, 170 (1999). 10. O. P. Korobeinichev, Combust. Explos. Shock Waves 23, 565 (1988). 11. A. C. Aiken, B. A. Jones, C. A. Arrington, Jr., S. J. Buelow and J. E. Anderson, Abstracts of Papers (CHED 904), 223rd ACS National Meeting, Orlando, FL, 7-11 April, 2002. 12. T. B. Brill, Prog. Energy Combust. Sci. 18, 91 (1992). 13. H. Arisawa and T. B. Brill, Combust. Flame 109, 87 (1997). 14. T. B. Brill and B. T. Budenz, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 3. 15. B. D. Roos and T. B. Brill, Appl. Spectrosc. 54, 1019 (2000). 16. G. J. Piermarini, S. Block and P. J. Miller, in Chemistry and Physics of Energetic Materials, ed. S. Bulusu, NATO ASI 309 (Kluwer, Dordrecht, The Netherlands), p. 391. 17. J. Wenograd, Trans. Farad. Soc. 57, 1612 (1961). 18. M. J. Kamlet and H. G. Adolph, Prop. Explos. 4, 30 (1979). 19. G. I. Kanel, Fiz. Goreniya Vzryza 14, 113 (1978). 20. T. B. Brill and K. J. James, J. Phys. Chem. 97, 8759 (1993). 21. T. B. Brill and P. E. Gongwer, Prop. Explos. Pyrotech. 22, 38 (1997). 22. T. B. Brill, K. J. James, R. Chawla, A. Shukla and J. H. Futrell, J. Phys. Org. Chem. 12, 819 (1999). 23. A. A. Zenin, in Nonsteady Burning and Combustion Stability of Solid Propellants, Progress in Astronautics and Aeronautics, Vol. 143, eds. L. DeLuca, E. W. Price and M. Summerfield (AIAA, Reston, VA, 1992), p. 197. 24. A. G. Merzhanov, Combust. Flame 11, 201 (1967). 25. T. B. Brill, H. Arisawa and P. E. Gongwer, in Challenges in Propellants and Combustion, ed. K. K. Kuo (Begell House, Inc. New York, 1997), p. 3. 26. B. F. Henson, B. W. Asay, L. B. Smilowitz and P. M. Dickson, in AIP Conference Proceedings 620, Shock Compression of Condensed Matter, Pt. 2 (2002), p. 1069. 27. T. B. Brill, J. Propuls. Power 11, 740 (1995). 28. T. B. Brill, in Chemistry and Physics of Energetic Materials, ed. S. N. Bulusu, NATO-ASI Vol. 309 (Kluwer Publ. Amsterdam, 1990), p. 277. 29. T. B. Brill and Y. Oyumi, J. Phys. Chem. 90, 2697 (1986). 30. T. B. Brill and Y. Oyumi, J. Phys. Chem. 90, 6848 (1986). 31. B. D. Roos and T. B. Brill, Combust. Flame 128, 181 (2002). 32. T. B. Brill and P. J. Brush, Phil. Trans. Roy. Soc. (London) 339, 377 (1992). 33. H. Arisawa and T. B. Brill, Combust. Flame 112, 533 (1998). 34. T. B. Brill, P. E. Gongwer and G. K. Williams, J. Phys. Chem. 98, 12242 (1994). 35. S. Zeman, Thermochim. Acta. 49, 219 (1981). 36. G. Lengelle, J. Duterque and J. F. Trubert, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 287.

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37. R. I. Hiyoshi and T. B. Brill, Prop. Explos. Pyrotech. 27, 23 (2002). 38. A. E. Fogelzang, V. P. Sinditski, V. V. Serushkin, V. Y. Egorshev, Y. K. Shchipin and V. A. Tropynin, in 24th Int. Ann. Conf. ICT, Karlsruhe, Germany, 29 June-3 July 1993, paper 59-1. 39. T. B. Brill and H. Ramanathan, Combust. Flame 122, 165 (2000). 40. V. P. Sinditskii, A. E. Fogelzang, A. E. Levshenkov, A. I. Egorshev, V. Y. Korlesov and V. V. Serushkin, in Proc. 21st Int. Pyrotech. Seminar, Moscow, 1995, p. 162. 41. A. Gao, Y. Oyumi and T. B. Brill, Combust. Flame 83, 345 (1991). 42. C. E. Stoner, Jr. and T. B. Brill, Combust. Flame 83, 301 (1991). 43. V. P. Sinditskii, A. E. Fogelzang, A. I. Egorshev, V. V. Serushkin and V. Y. Kolesov, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 99. 44. A. E. Fogelzang, A. I. Egorshev, V. P. Sinditskii and M. D. Dutov, Bet. Shock Waves 26, 69 (1990). 45. A. E. Fogelzang, V. P. Sinditskii, A. I. Egorshev and V. V. Serushkin, in Decomposition, Combustion and Detonation of Energetic Materials, Proc. Mat. Res. Soc, Vol. 418, eds. T. B. Brill, T. P. Russell, W. C. Tao and R. B. Wardle, 1996, p. 151. 46. C. F. Melius and M. C. Piqueras, in Proc. 29th Int. Symp. Combust. (2002). 47. P. E. Gongwer and T. B. Brill, Combust. Flame 115, 417 (1998). 48. T. B. Brill, P. J. Brush, D. G. Patil and J. K. Chen, in 24th Int. Symp. Combust. (The Combustion Institute, Pittsburgh, PA, 1992), p. 1907. 49. R. R. Miller, R. L. Stacer and B. B. Goshgarian, in 19th JANNAF Combustion Meeting, Vol. II, CPIA Publ. 366 (1982), p. 67. 50. J. K. Chen and T. B. Brill, Combust. Flame 87, 217 (1991). 51. M. R. Manaa, L. F. Fried, C. F. Melius, M. Elstner and T. Frauenheim, J. Phys. Chem. A106, 9024 (2002). 52. J. J. Dick, Appl. Phys. Lett. 44, 859 (1984). 53. C. S. Yoo, N. C. Holmes, P. C. Souers, C. J. Wu, F. H. Ree and J. J. Dick, J. Appl. Phys. 88, 70 (2000). 54. Z. A. Dreger, Y. A. Gruzdkov, Y. M. Gupta and J. J. Dick, J. Phys. Chem. B106, 247 (2002). 55. K. L. McNesby and C. S. Coffey, J. Phys. Chem. B101, 3097 (1997). 56. D. D. Dlott and M. D. Fayer, J. Chem. Phys. 92, 3798 (1990). 57. L. E. Fried and A. J. Ruggiero, J. Phys. Chem. 98, 9786 (1994). 58. Y. Oyumi, A. L. Rheingold and T. B. Brill, Prop. Explos. Pyrotech. 12, 1 (1987).

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CHAPTER 2 T H E R M A L D E C O M P O S I T I O N PROCESSES OF E N E R G E T I C MATERIALS IN T H E C O N D E N S E D P H A S E AT LOW A N D M O D E R A T E T E M P E R A T U R E S Richard Behrens Sandia National Laboratories Combustion Research Facility Livermore, CA 94551-0969, USA

Contents 1. Introduction 1.1. Scientific Issue: Understanding Processes Far from Equilibrium 2. Reactive Processes: Experimental Methods 2.1. Experimental Challenges 2.2. Experimental Requirements 2.2.1. Experimental Design Principles 2.2.2. Analysis of Data from High-Level Information Content Experiments 2.3. New Mass Spectrometry-Based Experimental Protocol 2.3.1. Qualitative Models Require Both Chemical and Spatial Information 2.3.2. Development of Mathematical Models 2.4. Comparison of Conventional Thermal Decomposition Experiments 2.4.1. Global Measurements 2.4.2. Product Identification Measurements 3. Condensed-Phase Reactive Processes 3.1. Evidence for Complex Processes 3.2. HMX Decomposition Processes 3.2.1. General Nature of Condensed-Phase Reactions in Energetic Materials 3.2.2. Decomposition of Composite Materials 3.3. Characterization of Decomposition Processes: RDX and HMX Case 3.3.1. Development of a Conceptual Framework to Represent and Analyze Decomposition Processes 29

30 31 35 35 36 36 37 38 38 42 43 44 44 46 46 48 50 53 53 53

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3.3.2.

Reaction Pathways: Solid-Phase Reactions, Nonlinear Processes, Feedback Loops and Autocatalysis 3.3.3. Emergent Phenomena 3.4. Effects of Experimental Conditions on Observed Decomposition Processes 3.4.1. Reaction-Coordinate Vectors 3.4.2. Environmental Conditions Determine Location of Reaction-Coordinate Vector 3.4.3. Conditions Probed by Various Experiments 4. Reaction Kinetics 4.1. Extracting Reaction Kinetics from Condensed-Phase Experiments 4.1.1. Simple Kinetics — Direct Inversion from Experiment 4.1.2. Kinetics of Complex Reaction Networks 5. Conclusions and Future Research Acknowledgments References

54 59 60 60 60 62 64 65 65 65 67 70 70

1. I n t r o d u c t i o n T h e processes t h a t control the thermal decomposition of energetic materials in the condensed phase at low and moderate temperatures present a challenge to the chemical kineticist in the 21st century. Meeting this challenge will provide new means t o develop improved propellants and explosives and to assess the safety and aging characteristics of existing ones. Currently, there is great interest in developing less sensitive munitions and extending the shelf life of existing ones. T h e development of new insensitive munitions will require understanding how reactive processes t h a t occur at t e m p e r a t u r e s associated with fires or other abnormal environments will alter the characteristics of the energetic ingredients and lead to violent reactions. 1 ' 2 A more fundamental understanding of the underlying reactive processes, which occur in these environments, can guide the development of new compounds, or the development of new formulations, t h a t will mitigate t h e violence of t h e reactions and lead t o less sensitive munitions. T h e underlying reactive processes are also related to safety, aging, and performance in propulsion and explosive applications. Slow reactions related to aging behavior clearly involve spatiotemporal controlled reactions. They are also influenced by interfacial reactions with other ingredients. Safety issues related t o slow and fast cook-off behavior are influenced by changes in the chemical, physical and morphological properties of the material. Finally, performance issues related to the combustion process t h a t occurs on the surface of a burning propellant are dependent on condensedphase reactive processes. To develop the understanding required to address

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these issues demands a more fundamental understanding of the processes that occur in the condensed phase, at low and moderate temperatures, than is currently available.

1.1. Scientific Issue: Understanding from Equilibrium

Processes

Far

As the temperature at which reactions occur in energetic materials are lowered from those that are associated with combustion (600-3000° C), new types of processes start to play a more dominant role in controlling their decomposition. As the temperature decreases, the rates of reaction of individual molecules decrease and transport processes become more important. In the temperature range from room temperature up to approximately 400° C, most energetic materials are present as solids or liquids so that reactions in the liquid and solid phases can play the major role in the decomposition processes. This transition in the types of physical and chemical processes that control the decomposition of energetic materials creates reaction systems that are difficult to characterize. At lower temperatures the focus for examining the reactions shifts from the molecular spatial scale to larger spatial scales associated with thermal and mass transport processes that give rise to nonhomogeneities in the system. In the liquid phase, localized reactions may form in the vicinity of bubbles and gaseous products may diffuse into the surrounding liquid, creating gradients of the gaseous products in the liquid phase. In the solid phase, reactions may occur preferentially on the surface of particles or complex processes may occur within the solid phase via nucleation and growth processes. In addition, lower temperatures allow reactions to occur that create compounds that may have higher molecular weights and be more complex than the energetic materials themselves. Growth of these more complex compounds in the reaction environment opens new "catalytic-like" reaction pathways, where the secondary and tertiary structure of the complex compounds may play a role in controlling the reactive process. This type of process is analogous to the catalytic behavior of enzymes in living systems. Each new type of process that may occur during the decomposition of energetic materials in the condensed phase at low and moderate temperatures is irreversible and may occur far from equilibrium conditions. Thus, to understand the decomposition of energetic materials under these lower temperature conditions, one must work within the framework of the physics

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of nonequilibrium processes, which uses concepts such as self-organization and dissipative structures. Reactive systems that evolve under conditions far from equilibrium are characterized by processes that become unstable at some distance from equilibrium and bifurcate along multiple reaction pathways. When systems pass this bifurcation point, a set of new phenomena arises in which nonequilibrium spatial structures, chemical waves, or oscillating chemical reactions are observed. These spatiotemporal organizations are known as dissipative structures. The conditions that are usually necessary for this type of behavior and the creation of dissipative structures are: (1) reactions that occur far from equilibrium, and (2) catalytic-like reactions. Many experiments that have examined the decomposition of energetic materials in the condensed phase involve reactive processes that meet the criteria required for the creation of dissipative structures. In some cases, direct visual evidence of the evolution of the spatial structures is observed as will be described below. The complex nature of the reactive processes that control the thermal decomposition of energetic materials in the condensed phase at low and moderate temperatures present a great challenge to the chemical kineticist. The conventional methods available to the kineticist focus on characterizing reactions at the molecular level. While this is an important component of understanding the thermal decomposition process in the condensed phase, it does not address many of the issues associated with the irreversible processes that control their decomposition behavior. Given the complex nature of these reactive processes, how can a better understanding and characterization of these processes be achieved? This is the main question addressed in this chapter. To address this question, an analogy to the development and use of elementary reactions for characterizing gas-phase reactions may be posed, and then the ability to develop a similar understanding for condensedphase reactions examined. Elementary reactions 3 are fundamental to our ability to characterize and predict the behavior of complex physicochemical processes, such as gas-phase combustion. Can the concept of elementary reactions also be applied to the characterization of complex processes in the condensed phase? If so, how? A range of different types of reactions can control the decomposition process in the condensed phase. What are the reactions? How do the types of reactions change with increasing temperature and pressure ? At low temperatures, reactions may occur at interfacial boundaries, reaction rates may be

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limited by transport processes, nucleation and growth processes may play a role, or enzymatic reactions may be involved.4 For reactions at higher temperatures, the materials are heated more rapidly, thus, transport processes and the development of spatiotemporal features are less important, and reactions at the molecular level become dominant. In this realm, unimolecular decomposition and elementary bimolecular reactions control the reactive processes. Roles of different types of physical and chemical processes will change with experimental conditions (temperature and pressure). How does the transition from low-temperature spatiotemporal controlled reactions to hightemperature molecularly focused reactions occur? How rapid and how distinct is the transition? Reactions that are initiated by thermal heating, and occur in the solid and liquid phase, are likely to be controlled by more complex spatiotemporal processes. For this reason, compounds with lower rates of vaporization are more likely to remain in the condensed phase and react. Thus, condensed-phase processes may be relevant up to ~100°C above the melting point of a material, which would correspond to a temperature range from 200 to 400°C for energetic materials. There is a wide range of different types of processes that must be considered in condensed-phase reactions. The processes include the following: (1) (2) (3) (4) (5)

phase transitions: solid-solid, solid-liquid; reactions on the surface of particles; nucleation and growth of reaction regions (bubbles) within the solid; creation of other condensed-phase products within the sample; reactions between the reactant and its gas and condensed-phase reaction products; (6) creation of new morphological structures within the sample that can form new reaction zones with localized temperature and pressure environments; (7) reactions at surfaces and interfacial boundaries. The challenge is to unravel and understand these underlying processes. The scientific community has generally avoided this challenging problem. The main difficulty stems from the inability to divide the system (i.e., decomposition of the material in the condensed phase) into its individual components for independent examination. This standard "divide and examine" methodology has been used extensively to understand reactions in the gas phase, but it is difficult, perhaps impossible, to apply to organic materials in the condensed phase. For

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example, one could consider examining the decomposition of an energetic compound, say RDX, in the gas phase. 5 Done properly, this provides basic information on the elementary unimolecular decomposition of RDX. Unfortunately, this provides only one of several possible rate-limiting reaction pathways that may occur in the condensed phase. For example, a more rapid reaction may involve the interaction between RDX and one or more of its gas-phase or condensed-phase reaction products. Thus, the RDX unimolecular decomposition kinetics, while a useful piece of basic information, may not play a significant role in the rate-limiting processes that control its decomposition in the condensed phase. Therefore, we are left with the problem of how to extract information from a set of different processes that occur simultaneously during the course of an experiment. Given the complex and irreversible nature of reactions that occur in energetic materials in the condensed phase, and the limited experimental methods available to probe these reactions, a new conceptual framework is required to understand and communicate the ideas that are needed to address these issues. This framework must provide the basis for examining and understanding reactive processes in the condensed phase, in a way that is similar to the framework used to examine complex reaction processes in the gas phase. It must incorporate features that (1) allow discovery of underlying reactive processes, (2) relate underlying features to material properties, (3) assess the competition between underlying processes as a function of experimental conditions, and (4) provide a basis for mathematical characterization of the underlying processes. With these features, the conceptual framework will provide a basis for creating new knowledge of the underlying processes that occur in energetic materials in the condensed phase and building a roadmap, based upon this knowledge, that can be used to examine each of these underlying processes in more detail. This chapter focuses on the development and application of an experimental protocol to understand and characterize the reactive processes that occur in the condensed phase of energetic materials and how this work has lead to the development of a new conceptual framework to examine and communicate the details of these processes. It presents an outline of the type of information that is required, a discussion of experimental methods for obtaining the information, an overview of new numerical simulation methods for extracting reaction mechanisms and chemical kinetics from the data, an illustration of these methods with recent results on the

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decomposition of RDX and HMX, and a discussion of future directions for research on the thermal decomposition of energetic materials in the condensed phase. 2. Reactive Processes: Experimental Methods To obtain a better understanding of the reactive processes of energetic materials in the condensed phase, we have developed a new experimental protocol. This section describes the development of the experimental protocol and compares it with more standard measurement methods, which have been used in the past to examine the decomposition of energetic materials. First the experimental challenges are described. Next the experimental requirements needed to address these challenges are outlined. This is followed by a brief description of the experimental protocol. Finally, the protocol is compared to other methods. 2.1. Experimental

Challenges

Four general features of thermal decomposition reactions of energetic materials in the condensed phase pose significant experimental challenges: (1) A wide range of reactive processes controls the thermal decomposition of energetic materials. (2) Chemical, physical and morphological (spatial) features can play significant roles in controlling the decomposition process. The experimental method must be capable of capturing the nature and roles of these spatiotemporal processes. (3) The different reactive processes are often nonlinearly coupled. The experimental methods must enable us to characterize these nonlinearities. (4) The state of the sample is a function of the extent of decomposition. Consequently, the state of the reaction conditions changes continuously during the course of an experiment making steady-state experiments infeasible. This behavior makes it difficult, if not impossible, to isolate specific individual reactions to study in an independent manner. Hence, traditional chemical kinetics methods, which isolate and control the concentration of specific reactants and measure their rates of reaction, have limited applicability. These four general features of condensed-phase energetic material reactions are characteristic of nonequilibrium processes, which involve

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self-organization and the development of dissipative structures, 6 and require new methods to understand and characterize the underlying reactions. 2.2. Experimental

Requirements

Given the general features of the thermal decomposition process, guidelines for developing the experimental methods can be denned as follows: (1) Assume it is not feasible to isolate reactive processes to study them individually. Furthermore, assume that the development of dissipative structures are important and develop as a result of interactions between reactive components of the entire system. (2) Focus on identifying and characterizing underlying physicochemical processes. Experiments must identify and characterize the underlying physicochemical processes that control the decomposition. (3) Develop experiments that provide a high level of information content. The overall approach must use experiments that provide a high level of information on the underlying reactive processes over a wide range of controllable conditions. 2.2.1. Experimental Design Principles Several general principles are used to guide the development of new instrumental methods that will provide the high information content needed to study the reactions of energetic materials in the condensed phase. These principles may be summarized as follows: (1) Maximize simultaneous measurements. Design new experimental methods using the general principle that the greatest amount of information will be obtained by measuring as many different properties of a sample as possible, with the widest range of measurement methods, at the same time. This allows direct comparison of different types of information. Otherwise the data represents reactions collected under different reaction conditions and makes interpretation of the results more difficult. (2) Collect chemical information as a function of spatial location. Chemical reactions in the solid or liquid phase can occur in localized regions or at interfacial boundaries associated with the development of dissipative structures. Thus, their reaction rates are often controlled by both the rate of chemical reaction and the transport of reactants and products in the localized region. Development of instruments to provide detailed molecular information, as a function of spatial location in a

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material, will provide insight into how chemical reactions are coupled with transport processes in these materials. For example, a microscope that provides molecular information as a function of location, in a manner analogous to reflected light for optical images or secondary electrons for SEM images.

2.2.2. Analysis of Data from High-Level Content Experiments

Information

The overall objectives of experimental work with energetic materials are: (1) to develop a qualitative understanding of the underlying reactive processes and (2) to create mathematical models of the reactive processes. To achieve these objectives requires the extensive development and use of numerical algorithms. High-level information content experiments provide large amounts of data that must be analyzed to glean relevant information on the underlying reactive processes. This requires both the application of transformation algorithms to convert raw data to the desired information format, and the use of analysis algorithms to extract the chemical, physical, and temporal information from the data. Developing mathematical models of the underlying reactive processes and comparing these models to data collected from the high information content experiments provide a test of the postulated reactive processes. The optimized models that characterize the underlying reactive processes provide a basis for development of models that can be used to characterize the response of materials in larger-scale systems. To summarize, the experiments must provide information that can track the chemical and physical state of the sample as a function of time. They must also provide information that can be used to identify and track the progress of the rate-controlling reactions in the decomposition process. The experiments should also provide information on the identities and amounts of condensed-phase products and morphological changes that occur in the sample during the course of an experiment. To extract an understanding of the underlying reactive processes and the associated reaction kinetics, a numerical simulation method must be used to analyze the data. The method must allow one to postulate various reaction schemes, numerically simulate the reaction rates for the postulated reaction scheme, and compare the numerical results with the data from the experiments. Feedback between experiments and numerical simulations provide guidance to selecting new experimental conditions.

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2.3. New Mass Spectrometry-Based

Experimental

Protocol

A mass spectrometry-based experimental protocol, developed in our laboratories, addresses the experimental requirements for examining the decomposition of energetic materials in the condensed phase. The protocol uses new instrumental methods and numerical algorithms for data analysis and simulation of physicochemical processes in the condensed phase. A schematic diagram outlining the experimental methods and numerical algorithms and the types of information obtained by each is shown in Fig. 1. As illustrated in the diagram, the overall goal is to develop a model of the thermal decomposition processes based on the underlying fundamental reactions and the associated reaction kinetics. 2.3.1. Qualitative Models Require Both Chemical and Spatial Information Understanding the underlying reactive processes requires identifying the compounds and determining how fast they are formed as a function of experimental conditions. For reactions in the condensed phase, the development of dissipative structures may play a significant role in determining the rates of reaction. Therefore, it is important to determine the spatial characteristics of these features and how they may change during the course of an experiment. This requires determining the morphological characteristics of the samples during the course of an experiment in addition to the time-dependent chemical information on the reactants and products. The simultaneous thermogravimetric modulated beam mass spectrometry instrument The simultaneous thermogravimetric modulated beam mass spectrometry (STMBMS) instrument provides the main source of information on the thermal decomposition processes. It was designed to conduct experiments that would provide information on both the identities and rates of formation of the compounds involved in the reactive processes that control the decomposition of energetic materials. The instrument and the obstacles presented by using mass spectrometry have been described in detail previously 7-9 ; the STMBMS enables: (1) identification of compounds in a mixture; (2) quantitative measurement of each of the identified compounds; (3) control of rate of vaporization of condensed-phase species;

Thermal Decomposition

Instruments & Algorithms STMBMS Thermal Decomposition Experiments

T

TASHOWData Analysis Algorithms

Ifo@to$s

I

x_i REMKIN Compilation & Analysis Algorithms

Processes of Energetic

Information Obtained

1. Raw Mass Spectra of Products vs. time. 2. TGA Data. 3. TOF Velocity Spectra.

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Instruments

High resolution FTICR Mass Spec

Ion formulas Molecular structure. 1. Identities of products 2. Rates of formation of products. 3. Pressure of gases in reaction cell. 4. Vapor pressure of condensed phase reactants and products. 5. All as a function of time. 1. Structural changes of sample. 2. Morphology of microscopic material features. 1. Identification of high MW products. 2. Reactions at interfaces. 3. Spatial maps of chemical compounds. 4. Chem analysis of microstructures.

1. Underlying fundamental reaction mechanisms. 2. Arrhenius parameters for fundamental reactions. 3. Rate of heat generation. 4. Quantitative assessment of damage

Optical & Scanning Electron Microscopy

J Surface Analysis Ion beam & laser microprobes.

fsfcrasfe^

Model of Thermal Decomposition Based on Underlying Fundamental Reactions and Associated Reaction Kinetics. Fig. 1. Experimental protocol used to study thermal decomposition processes of energetic materials in the condensed phase.

R.

•1(1

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(4) control of the pressure of gaseous compounds formed in the reactions and contained in the reaction environment; (5) collection data that provides simultaneous information on all compounds. The STMBMS instrument (Fig. 2) incorporates several features to provide the desired information. The decomposition experiment is conducted in a reaction cell that is fitted with well-characterized exit orifice that can be used to control the rate of flow of gases out of the reaction cell. Varying the size of the orifice allows the pressure of gases within the reaction cell to be controlled. The simultaneous measurement of the rate of force change (mass loss and thrust) and the mass spectra of the gases exiting the reaction cell provides the rates of formation of compounds formed during

it>S-*-",h"i' IH'llorts

Modulating Wheel

540 l/s Turbo

Reaction Cell

Microbalance

Fig. 2. Schematic of STMBMS instrument. An experiment is conducted with the STMBMS instrument by placing the sample in the reaction cell, closing the reaction cell with a cover containing an orifice of desired diameter, mounting the reaction cell in t h e instrument on top of t h e thermocouple probe t h a t is seated in a microbalance, and then evacuating the instrument. The data is collected by heating the sample and collecting data on the rate of force change due to gas exiting the cell with the microbalance and collecting the mass spectra of the mixture of gaseous compounds exiting the cell with a modulated beam quadrupole mass spectrometer. The pressure of the gaseous compounds in the reaction cell may range from 10~ 6 to 10 3 torr, depending on experimental conditions.

Thermal Decomposition

Processes of Energetic

Materials

41

thermal decomposition. The time-of-flight velocity spectra of the neutral gases that exit the reaction cell are used to determine whether ion signals measured with the quadrupole mass spectrometer are parent or daughter ions. Thus ion signals at a specific m/z value, measured with the mass spectrometer, can be associated with a compound that evolves from the reaction cell. Enhanced product identification and molecular structure determination Three methods are used to help identify the compounds that evolve from the reactive processes. Two of these provide additional information to assign formulas to the ions that make up the mass spectra of the evolving compounds. The third method sorts ion signals into groups of m/z values that are associated with each compound. In the first method, isotopically-labeled analogues of the energetic materials are synthesized (deuterium, 1 3 C, 15 N, and 1 8 0) and the corresponding isotopic shifts, recorded in the STMBMS experiments, are used to determine the formulas of the ions. In the second method, high resolution and high mass accuracy measurements are made using a Fourier Transform Ion Cyclotron Resonance (FTICR) mass spectrometer. These two methods provide the information needed to determine the formulas of the ions in the mass spectra. The FTICR mass spectrometer provides a more rapid means of determining the formulas, eliminating the need to synthesize isotopicallylabeled analogues. The third method employs a correlation analysis of the temporal dependence of the ion signals in the mass spectra to sort the ion signals into groups whose m/z values represent the mass spectra of the individual compounds that evolve from the reaction cell. Quantification of the data After the compounds are identified and ion signals from the mass spectra are assigned to represent each compound, the data are quantified using the TASHOW analysis algorithm. The ion signals, measured with the mass spectrometer, and the rate of force change, measured with the microbalance, are used to determine the sensitivity parameters that relate the measured ion signals to the number density of the corresponding compound in the reaction cell as a function of time. 7 ' 9 This analysis may be used to calculate rates of reaction, partial pressures, and other related properties. At this point in the analysis, the following information is available to construct a

42

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qualitative model of the decomposition process: (1) (2) (3) (4) (5)

identities of the compounds involved in the decomposition process; rates of formation of the compounds; pressure of gases in the reaction cell; vapor pressure of condensed-phase compounds; all data as a function of time.

Morphological features Morphological features of the condensed-phase samples: surface roughness, grain structure, and bubbles can play an important role in the decomposition process. Because these features cannot be examined in situ during the course of a decomposition experiment, the morphological characteristics are determined by stopping the reaction at various stages of the decomposition process and removing the sample for examination by optical microscopy and scanning-electron microscopy (SEM). Some energetic materials form products that are nonstoichiometric, polymeric-like and have a low volatility; these are called nonvolatile residue (NVR). In many cases the NVR reacts with the remaining reactant or other decomposition products. Optical and SEM examination has shown that these NVRs may be located on the surface of particles, in reactive regions within solid grains, or on the walls of the reaction cell. Knowing the geometrical characteristics of these morphological features is often important for understanding and modeling the reactive process. While optical and SEM pictures provide valuable information about the structures created during the decomposition process, they do not provide information about the chemical compounds that are involved in the reactions at these localized regions. To improve our understanding of the role that interactions between chemical reactions and morphological features play in the decomposition process, we must probe the nature of the chemical reactions that occur at the boundaries of these morphological features. We are developing surface analysis methods such as secondary ion mass spectrometry (SIMS) and laser desorption mass spectrometry (LDMS) to examine these features in energetic materials. 10 2.3.2. Development of Mathematical Models Once a qualitative understanding of the underlying processes that control the thermal decomposition of an energetic material is obtained, the next

Thermal Decomposition

Processes of Energetic

Materials

43

task is to formulate this understanding into a set of mathematical expressions to characterize the thermal decomposition process. This task requires using the qualitative model of the decomposition process to construct the set of differential equations that represents the reaction rates of the underlying reactive processes, then solving this set of differential equations, and finally, determining the values of the parameters for the reaction model by comparing the results of the calculations to experimental data. This method is basically a numerical simulation method in which a reaction scheme is postulated, a mathematical representation of the reaction scheme is constructed, a guess for the reaction parameters in the model is made, and the model is solved. The model simulates a decomposition experiment. The reaction scheme and its associated parameters are iterated to capture the various features of the reactions that appear in the data from the thermal decomposition experiments. Further details are provided below.

2.4. Comparison Experiments

of Conventional

Thermal

Decomposition

So far we have (1) summarized the scientific issues that must be addressed to understand the underlying reactive processes of energetic materials in the condensed phase, and (2) outlined the experimental challenges that must be addressed and described the development of one experimental protocol intended to meet these experimental challenges. Later in this chapter, it will be shown how this work has led to a new understanding of reactions in the condensed phase. While this experimental protocol provides new opportunities to understand the underlying reactive processes in energetic materials, it is relatively expensive and unique. The highly-specialized equipment is not as accessible as the other methods previously used to examine the thermal decomposition of energetic materials in the condensed phase. In this section we provide a brief summary of the other methods and assess their strengths and weaknesses in meeting the experimental challenges for studying the thermal decomposition of energetic materials. Thermal decomposition experiments have been used extensively to probe the reactions of energetic materials. In general the various experimental methods may be grouped according to the type of data provided. One group focuses on measuring the overall behavior of a sample by measuring a global property, such as heat flow or mass loss. The second group focuses on identifying the products formed during a decomposition experiment.

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2.4.1. Global Measurements Standard thermal analysis methods such as thermogravimetric analysis (TGA), differential thermal analysis (DTA) and differential scanning calorimetry (DSC) have been used extensively to characterize the thermal behavior of energetic materials in the condensed phase. n ~ 1 4 The DTA and DSC methods track the heat flow as a sample is heated and are useful for detecting phase changes and the onset of decomposition of an energetic material. TGA measures the mass of the sample as it is heated and reveals when reactions occur that release gaseous decomposition products and result in a loss of sample mass. Thermal analysis methods are excellent for characterizing the behavior of simple, well-defined processes such as phase transitions or simple chemical transformations. However, for complex processes, such as those that occur during the decomposition of energetic materials, thermal analysis methods do not provide sufficient information to unravel the underlying processes as discussed by Pinhiero et al. The global nature of the measurement (i.e., total heat flow or total mass loss) is determined by the summation of all the underlying processes at any particular time during an experiment, providing a limited amount of information on the underlying processes. The thermal behavior of propellants and explosives has also been characterized by time to explosion experiments. In these experiments, such as the one-dimensional time to explosion (ODTX) experiment, 15 a sample is heated using a predefined isothermal boundary condition, and the time until the sample explodes is recorded. This has provided useful information for handling explosives, but, due to the limited amount of information collected during an experiment, this method has been of limited value in determining the underlying reactive processes that occur during the thermal decomposition process.

2.4.2. Product Identification

Measurements

To complement the global experiments and provide insight into the reactive processes that occur during the decomposition of energetic materials, a number of different types of spectroscopic methods have been used over the years. Some methods, such as mass spectrometry, have identified a broad range of different compounds formed during the decomposition process; other methods, such as electron spin resonance, 16 ' 17 have identified a more limited range of species, such as radicals.

Thermal Decomposition

Processes of Energetic

Materials

45

Infrared spectroscopy (IR) and mass spectrometry (MS) have been used extensively to identify products formed during the decomposition of energetic materials. MS has been used to identify the gaseous products that evolve during the decomposition process, while IR has mostly been used to probe the products formed in the condensed phase. IR spectroscopy can be applied over a wide range of experimental conditions: high-pressure, 18 ' 19 in thin films,20'21 during combustion, 22 ~ 24 in shocked materials, 25 and at very low temperatures. 26 ' 27 Depending on the specific experiment, IR may provide information ranging from individual steps in a decomposition reaction, 28 to a more detailed set of reaction kinetics. 19 While this information is often useful, the extent of the data is somewhat limited, making it difficult to develop complete reaction schemes and the associated reaction kinetics from the data. For applications to experiments focused on understanding the underlying reactive processes in the condensed phase at low and moderate temperatures, IR lacks some of the molecular specificity provided by mass spectrometry-based methods. Mass spectrometry measurements were some of the first experiments to identify the products formed in the thermal decomposition of energetic materials. 29 " 31 Analyzing gaseous thermal decomposition products with mass spectrometry can be done by either admitting the gas mixture directly into the mass spectrometer or by first chromatographically separating the mixture before introducing the gas into the mass spectrometer. Both methods have limitations. If the mixture of the reactant and its decomposition products is admitted into the mass spectrometer, it is difficult to associate individual ions with the corresponding decomposition products. For example, it has been shown8 that using appearance potential measurements developed to examine hydrocarbons 32 is not adequate to distinguish ions that originate from products formed in the thermal decomposition of HMX from ions formed by the fragmentation of sublimed HMX in the mass spectrometer. HMX fragments into daughter ions using electron energies of 12.5eV (~3eV above its estimated appearance potential). 8 - 33 If the mixture is chromatographically separated prior to entering the mass spectrometer, it is difficult to obtain time-dependent information to characterize the behavior of the sample. The sensitivity of the mass spectrometer varies for different species, which also makes it difficult to obtain quantitative data. Finally, depending on the type of mass spectrometer used for the measurements, there can be uncertainty in the identification of ions because of uncertainties in the exact mass of the ion: N 2 0 = 44.0083 and

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C 0 2 = 43.9898 would both be measured as m/z = 44 with most types of mass spectrometers, making the two compounds indistinguishable. Mass spectrometry provides useful information for identifying products, but may not clearly identify the thermal decomposition products. 3. Condensed-Phase Reactive Processes 3.1. Evidence

for Complex

Processes

In examining the decomposition of energetic materials, one may ask, what evidence suggests that their decomposition is controlled by a complex set of coupled reactive processes. The answer may be found in the general features of experimental results from two sources: a historical examination of the results from a wide range of different experiments and the results from STMBMS experiments on a number of different compounds. During the 1980s, Schroeder undertook an extensive examination of the entire literature on the thermal decomposition of energetic nitramine compounds. 34 ^ 36 This review of the wide range of results from both nominally similar and different types of experiments revealed a high degree of variation in the results. For example, in some decomposition experiments with RDX and HMX the major products were C H 2 0 and N2O. In other types of experiments, HCN and NO2 were the major products. Similarly, an accelerating type of "autocatalytic" behavior was reported in some cases but not in others. To describe the reactive processes in these older experiments, a unimolecular decomposition framework was used, and the experimental observations were attributed to a particular bond-breaking sequence of the reactant. For example, in experiments in which HCN and NO2 were observed, it was argued that N-NO2 bond fission was the rate-limiting step; whereas in experiments in which CH2O and N2O was observed, it was argued that fission of a C-N bond in the ring of the molecule was the rate-limiting step. These arguments also assumed that once the first bond in the molecule ruptured, the remaining bonds would rearrange rapidly and lead to the final reaction products. Additionally, in many experiments the temperature dependence of the experimental observable (i.e., weight loss, heat generation) was determined and reported as an activation energy, assuming that an Arrhenius expression described the underlying reaction. Schroeder reported 36 that the activation energies from these experiments varied widely. This variation in activation energies is not surprising if the decomposition process is controlled by an underlying set of coupled nonlinear

Thermal Decomposition

Processes of Energetic

47

Materials

reactive processes. For these types of processes, even slight variations in experimental conditions (e.g., the extent of confinement of gaseous decomposition products with the sample) can lead to variations in the identities of the products, as well as how fast the products are formed. This complex behavior was examined in the early 1970s by Batten for the case of RDX decomposition, 37-41 in which it was found that the decomposition of RDX below its melting point was controlled by a complex autocatalytic-like process. The results showed that a nonvolatile residue is formed during the decomposition and the addition of gases such as C H 2 0 increase the reaction rate. Batten also demonstrated that the past decomposition history of the sample can affect the subsequent decomposition processes. Our STMBMS experiments performed on a range of different types of energetic materials provide more detailed evidence for the complex nature of the thermal decomposition process. The compounds that we have investigated using STMBMS are listed in Table 1. We have studied the nitramines, Table 1.

Compounds studied with STMBMS methods. C-Nitro, Azoles, and Others

Nitramines

NO,

N0 2 0,N.

r

-N-. 0 2 rT ^>k^ N0 2

"N^

M> 02N^

^N

^ N

X

N0 2

x

N0 2

H

CL-20

RDX

OoNk

NO,

24DNI TATB

OpNs

N

.NO, ^N'

I—N-N0 2

fJ02 0?N-

NO, 0 2 NK

^ ^

v

N02

OpN'

HMX

^

^Nv "NO,

TNAZ

NTO

K6

N0 2

-N-NO

NO

-Nk

qVW* NO, TNCHP

0,N"

.N^/Ns

N-N O.N—V./^O N I H

N0 2 "NO,

ONDNTA

NDNAZ

Ammonium perchlorate

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RDX and HMX, most extensively. The thermal decomposition of all these compounds exhibits two common features, which show that their thermal decomposition is controlled by a complex set of coupled reactions. First the temporal behaviors of the rate of evolution of the gaseous decomposition products are never what is expected for a simple first-order decomposition reaction, in which the rate of reaction falls as the sample is depleted. Indeed, for most of the compounds listed in Table 1, there is an induction period, characterized by low rates of evolution of gaseous products, followed by an accelerating rate of reaction. In addition, the identities of the products and their rates of evolution are very sensitive to the extent of confinement of gaseous decomposition products in the reaction environment; higher pressures typically increase the rate of reaction. Second, a nonvolatile residue is always created during the decomposition process. Its presence is usually associated with higher rates of reaction. These two general features clearly indicate that the thermal decomposition behavior of these materials in the condensed phase is controlled by a set of complex nonlinear reactive processes.

3.2. HMX Decomposition

Processes

The decomposition of HMX provides a good example of the types of processes that occur in the condensed phase. An illustration of the features that are observed using the experimental protocol, outlined above, is shown in Fig. 3. The temporal behavior of the rates of formation of two of the main decomposition products (CH2O and N2O) indicates a complex process and is completely different from the exponential decay that is expected for a simple first-order reaction. Their behavior is more indicative of a nucleation and growth reaction or what is commonly referred to as an "autocatalytic" reaction. The temporal behaviors of the rates of evolution of the products can be divided into three stages: an induction period, an acceleratory period, and a late stage (2000 to 3800 s, 3800 to 5800 s, and 5800 to 7000 s, respectively in Fig. 3). The identities of the products and the temporal behaviors of their rates of formation provide information that can be used to guide the development of models of the reactive processes that control decomposition. The SEM pictures in Fig. 3 illustrate how spatial features can play an important role in controlling the decomposition process. The micronsize shell-like structures formed during the decomposition of HMX in the solid phase are remnants from reactive regions that were formed during

Thermal Decomposition

Processes of Energetic Materials

49

Fig. 3. Illustration of the gas evolution rates and the morphological structures created during the thermal decomposition of an HMX particle. The graph shows the rate of evolution of two products formed during the decomposition of a single particle of HMX that was heated to and held at 235° C. To examine the morphological structures that are created during the decomposition, the reaction was stopped at the "sample point". To expose the morphological structures that grow within the particle, about half of the HMX remaining after decomposition was stopped is removed by sublimation. The particle was cut in half to expose the interior of the particle for SEM analysis. Pictures A through C show increasing magnifications of the particle interior. In picture B the material in the upper left portion of the picture is the HMX that remains in the particle (note the granular structure). The lower right portion shows the structures of nonvolatile residue that is formed via reactions within the HMX grains. Picture C shows that the NVR forms both strands and shell-like structures.

the decomposition process. Localized decomposition within these regions suggests that several types of spatially-dependent processes may play a role in the overall reactive process. The rate of transport of products within the condensed phases can play an important role in controlling the rates of reaction. For example, in the localized micron-size reaction regions in solid HMX, which appear to be bubbles contained within the solid HMX, the gaseous decomposition products from the bubble may diffuse into the surrounding lattice. As a result, this process may control the reaction rate by transforming crystalline HMX into a molten solution in which the HMX may react more rapidly.

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The SEM pictures of HMX also illustrate the role that interfacial boundaries may play in controlling the decomposition process. New surfaces are created at interfacial boundaries within the HMX particle. Initially, a grain structure is created within the particle (upper left of Picture B), which forms a new reaction environment on the surface of the grains. As the decomposition progresses, another type of reaction environment is created at the interfacial boundaries in the micron-size reaction regions, associated with the formation of bubbles within the grains. The formation of strands of NVR (Picture C) appears to be associated with reactions that occur at the grain boundaries, whereas the shell-like structures appear to be associated with the formation of bubbles within the grains. Both the development of the morphological features associated with the creation of interfacial boundaries and the transport of reactants and products in the vicinity of these boundaries illustrate the important role that spatial features can play in controlling the underlying nature of the reactive processes and the rates at which these processes occur. Isotopic scrambling experiments and deuterium kinetic isotope effects (DKIE) using isotopically-labeled analogues of HMX 42 and RDX 43 have provided further information on the sequence of bond-breaking steps that occur in the various reaction channels during the decomposition process. This provides further evidence of the complex nature of the decomposition process.

3.2.1. General Nature of Condensed-Phase Reactions in Energetic Materials The experimental protocol developed to investigate the decomposition of energetic materials in the condensed phase has been applied to examine a relatively wide range of different types of energetic compounds, which are listed in Table 1. Data with the level of detail shown above for HMX has been collected on most of these compounds. All of the compounds listed in Table 1 exhibit complex nonlinear reaction behavior. The degree of complexity varies from compound to compound. The most complex processes are observed in HMX 14 ' 42 ' 44 ' 45 and AP. 4 6 - 4 8 The decomposition of both materials involve tightly-coupled interactions between the chemical reactions and the spatial aspects of the morphological features created in the particles during the thermal decomposition process. The least complex processes are observed in the decomposition of K6 and TNCHP. 49 ' 50 The presence of the keto group in K6 appears to promote a more direct reaction to the gaseous decomposition products.

Thermal Decomposition

Processes of Energetic

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51

Decomposition of TNCHP has a number of similarities to the decomposition of RDX and HMX in terms of the chemical reactions involved, but is not complicated by morphological issues associated with the solid phase, since it melts at approximately 170°C and is relatively stable in the liquid phase. The complexity of the decomposition process for the other compounds falls somewhere in between these two groups. Types of processes that control decomposition in the condensed phase Examination of the data from experiments with the compounds listed in Table 1 show that a wide range of processes can be a factor in the decomposition process. The types of processes that may contribute to the overall decomposition behavior include the following: (1) Phase changes. Solid-solid, melting, and vaporization all may play a role in controlling the rate of decomposition. (2) First-order reactions. The direct reaction to the gaseous decomposition products can play a role, but it is unlikely to be the sole reaction pathway in the condensed phase. (3) Formation of solutions. Mixtures of the reactant with its decomposition products may occur in either the solid or liquid phase, creating solutions of the components. (4) Reactions of parent compounds with decomposition products. These appear to be the main rate-limiting reactions for decomposition in the condensed phase. (5) Secondary reactions of products. All of the decomposition processes involve secondary reactions of the products. For nitramines, the creation and decomposition of the mononitroso analogue of the reactant appears to play an important role in their decomposition. (6) Nucleation and growth of bubbles. For compounds that remain solid at higher temperatures, such as HMX, AP, and TATB, the nucleation and growth of reaction regions within the solid, which forms microscopic bubbles, can be very important in controlling the decomposition process. (7) Reactions on surfaces and interfacial boundaries. Several compounds that remain solid at relatively high temperatures (>170°C) react on the surface of the particles by nucleating and growing an NVR on the surface of the particles. This behavior has been observed for 24DNI 51 ' 52 and RDX. 53 ' 54

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(8) Formation and growth of new morphological structures. For compounds that remain solid at higher temperatures, such as HMX, AP, and TATB, the growth of new morphological features creates dissipative structures that play a role in controlling the rates of reaction. The relative importance of these different processes depends on the intrinsic properties of the energetic compound and raises an interesting question: How do the molecular structure, crystal structure, and morphological characteristics of these materials determine which types of reactive processes will play a role in the overall decomposition process? Spatial dimensions of reactivity Is it possible that the physicochemical properties of the material may determine spatial dimensions of reactivity? The development of spatiotemporal structures is associated with some of the underlying decomposition processes in an energetic material. The spatial structures may be characterized by cellular units: volumes of material in which a physicochemical reactive process occurs within the volume and is controlled by a combination of chemical reactions, transport of species within the volume, and the development and growth of interfacial boundaries. This concept is similar to a unit cell used to represent crystal structure or a grain structure in a metal, except that the volume contains a reactive system on a microscopic scale. This concept is also similar to nucleation and growth concepts used to describe solid-state reaction chemistry of inorganic compounds. 55 Using this concept of a reactive unit cell, it may be possible to characterize and categorize the underlying reactive processes in an energetic material with a set of reactive cellular units with several different discrete and representative dimensions. For example, for HMX there may be one cellular unit to represent the reactions in bubbles and another to represent reactions at grain boundaries, essentially forming a hierarchy of cellular subunits. Within this framework, a reactive unit cell may be defined as a volume of material that contains a reactive system with self-contained chemical, physical and morphological features. Thus, characterizing the reactions in a reactive unit cell can be used to describe the overall behavior of any size sample, assuming appropriate heat and mass transfer processes can be properly characterized.

Thermal Decomposition

Processes of Energetic

Materials

53

3.2.2. Decomposition of Composite Materials Up to this point, discussion has focused on reactive processes in energetic compounds, however, the same general ideas can be applied to the reactions of composite energetic materials such as propellants and explosives. In this case, the chemical nature of the reactants, the morphological structure of the material, and interfacial boundaries are determined by the material design and manufacturing processes. For example, a binder or plasticizer that may be included with the energetic compound will (1) create new boundaries between the binder and energetic compounds, and (2) create potential interactions between the plasticizer and its decomposition products with the energetic compound or the binder. Understanding these processes requires the same type of information that is required for the individual energetic compounds. Hence the framework developed to examine and characterize energetic compounds may be used to characterize more complex propellants and explosives, which are composite materials with a cellular structure. 3.3. Characterization of Decomposition and HMX Case

Processes:

RDX

3.3.1. Development of a Conceptual Framework to Represent and Analyze Decomposition Processes Characterization of the complex processes that control the thermal decomposition of energetic materials requires a framework on which to build and test new concepts. Historically, a basic concept has been used to represent, analyze, and understand the experimental observations from thermal decomposition experiments. This concept may be expressed as "the harder you drive something the more likely it will happen." This concept was formulated into a model to characterize chemical reactions by Arrhenius, 56 in which the amount of energy available drives a chemical reaction. We have established a new framework to integrate the data derived from high information content experiments with concepts derived from everyday, anecdotal, and scientific experience. The framework consists of a suite of concepts that are built on parallel representations of two types of natural phenomena. The resulting framework is designed to achieve two main objectives: (1) develop an understanding of the underlying processes; (2) form the basis for predicting the behavior of the decomposition processes over a range of physical conditions.

54

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The suite of concepts borrows from two widely-used models: Darwinian evolution of biological systems and physicochemical control of hightemperature combustion. While both models characterize complex reactive systems, they are quite different, focusing on substantially different phenomena, but providing complementary means to represent and analyze thermal decomposition processes. The Darwinian evolution model provides a means to represent sets of interacting processes, which are not necessarily elementary reactions, and analyze how these processes compete and spawn new processes over a range of controllable environmental conditions. In contrast, the high-temperature combustion model provides a framework to represent the physical processes and chemical reactivity at a more fundamental level, associated with elementary processes, and creates mathematical representations of the underlying behaviors. A conceptual framework being developed to represent, analyze, and understand the decomposition of energetic materials draws from general features of the models for both metabolic pathways and high-temperature combustion. The general Darwinian approach used to characterize metabolic pathways forms the basis for describing the general competitive nature of the reactions that occur in the condensed phase of energetic compounds at low and moderate temperatures. Once the general nature of the underlying reactive processes is determined, physical and mathematical features, similar to those used in the high-temperature combustion model, are applied to further test the original reaction concepts and to develop a deeper understanding of the reactions. Many details of this conceptual framework are still under development. However, in the course of its development, the underlying concepts have been used to represent and analyze the decomposition of four energetic compounds: 24DNI, NDNAZ, RDX, and HMX. The use of the conceptual framework is illustrated with a discussion of the decomposition of the cyclic nitramines: RDX and HMX.

3.3.2. Reaction Pathways: Solid-Phase Reactions, Nonlinear Processes, Feedback Loops and Autocatalysis The Darwinian model has been used to construct a qualitative depiction of the competing processes that control the thermal decomposition of RDX and HMX over a range of conditions. It is based on data collected using the mass spectrometric experimental protocol and is illustrated in Fig. 4. The

Thermal Decomposition

Solid HMX/RDX Pristine solid/crystal

,

Materials

55

Liq.

HMX/RDX 5

Processes of Energetic

r»~

'

OST/I1CN t

T

Solid

NO t

NO. i ll.O

T

T

Completely damaged'

I ! Minor Products

l

CHj Hfi' 0

"CHj Hfi' HjC, 0

(7/.0

~CHj H,C%

0

•*-

CH 2 0 + HjO * CO + NjO

N;N-C

Pressure Fig. 4. Reaction diagram showing the underlying reactive processes t h a t control t h e decomposition of HMX and RDX.

competing reaction pathways are gleaned from the analysis of extensive sets of experimental data on the decomposition of R.DX43,53'54-57-58 and HMX 42,44.45 i n t h e c o n ( i e n s e d phases. Typical data for HMX is shown in Fig. 3. The representation of the decomposition process for RDX/HMX, shown in Fig. 4, describes the general set of reactions and interconnections between the main reaction pathways. It also contains a set of pressure and temperature scales, whose purpose is described below. Illustrations of how the reactive processes were gleaned from the data have been described previously 53 for several of the pathways. The reactants are listed in the upper left corner. The products detected using the experimental protocol are listed in the two boxes. The species that are denoted as "Exit Products" are compounds that have been involved in the reactive processes within the reaction environment, but eventually leave the reaction environment and are detected without undergoing further reaction. Several of these products (i.e., H2O, CO, N2O) are considered nonreactive under the conditions of the experiment, whereas the others can

56

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continue to react. The amount of each reactive species observed depends on the competition between the various reaction pathways that dominate under different sets of reaction conditions. The species listed as "minor products" are also formed in reactive processes, but represent only a small fraction of the total amount of products formed during decomposition. While only minor species, these compounds provide valuable insight into the nature of the underlying processes, since their time-dependent rates of formation track the various underlying behaviors, such as the decomposition of the NVR. The reaction at the top of the diagram represents a relatively direct reaction pathway between the reactants and exit products. This reaction represents the elimination of HONO from the RDX or HMX to form oxy-s-triazine in the case of RDX, and the subsequent reaction of these products to HCN, NO, N 0 2 and H2O. This reaction is first order in the amount of reactant, and is the only pathway whose reaction rate is consistent with a unimolecular decomposition process. The bond-breaking sequence of this reaction has been determined via DKIE and isotopescrambling experiments. 43 The five circles shown in the reaction diagram represent the main nonlinear reactive processes that occur in RDX and HMX. These reactions are described as cycles, as is done for biochemical pathways, in order to track and illustrate how the different reaction pathways are interrelated. The arrows connecting the different reaction cycles show how various compounds move between the different reaction cycles. This movement of compounds between reaction cycles also illustrates the coupling and extent of nonlinearity that occurs during decomposition. The five reaction cycles can be divided into two groups with similar features. One group represents chemical reactions at the molecular level. The second group represents complex physicochemical processes involving multiple phases, reactions at interfacial boundaries, and emergent phenomena. The three reaction cycles representing the chemical reactions play a major role in the decomposition of RDX and HMX in the molten or liquid phase. The chemical reaction cycles include the NO Cycle, the Nitroso Cycle and the C H 2 0 / N 0 2 Cycle. The NO Cycle involves the reaction of NO with RDX or HMX to form the mononitroso analogue of these compounds. Isotope-scrambling experiments 43 have shown that this is the primary reaction leading to the formation of hexahydro-l-nitroso-3,5-dinitro-5-triazine (ONDNTA) from RDX in the liquid phase. NO can originate from several different sources.

Thermal Decomposition

Processes of Energetic

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For example, during the decomposition of RDX in the liquid phase, NO produced by the direct reaction (OST/HCN) provides the initial source of NO to form ONDNTA. Note that, as the DKIE lowers the rate of the direct reaction, the rates of the NO Cycle and Nitroso Cycle may also be reduced if the direct reaction is the primary source of NO. The Nitroso Cycle is more complex. The mononitroso analogues of RDX and HMX may be formed initially by reacting with NO. Once formed, the decomposition of the mononitroso analogue can itself be quite complex. Thermal decomposition studies of ONDNTA 59,6 ° have shown that N 2 0 , H2O, and CH2O are the major products formed during its decomposition. However, a large portion of each ONDNTA molecule is incorporated into the nonvolatile residue. Once the NVR is present, a new pathway leading to the formation of the mononitroso analogue is created. In this case, the isotope-scrambling experiments indicate that the reaction involves the removal of an oxygen atom from the NO2 group, rather than the replacement of the NO2 groups with NO, since there is no scrambling in the N-NO bond. The C H 2 0 / N 0 2 Cycle is a facile reaction that involves reactants formed from different reaction pathways and results in the generation of a substantial amount of heat (AH = —185 kJ/mol). This type of behavior shows how the extent of self-heating of the sample may be influenced by the relative rates of the different reaction cycles since separate reaction cycles produce the CH2O and NO2 reactants in this heat-generating cycle. The two remaining cycles represent complex physicochemical processes, play a major role in solid-phase decomposition, and are responsible for morphological damage created in the material that can lead to sensitized explosives and propellants. The NVR Cycle is characterized by the creation of an amorphous higher molecular weight material that has a low volatility. Infrared spectra and thermal decomposition of the NVR indicate it has amide and cyano groups. The NVR is formed during the decomposition of HMX, RDX, and ONDNTA. In each case, the same minor products, shown in the box, are either associated with its formation or decomposition. The location in the sample where the NVR is formed differs for ONDNTA, RDX, and HMX. ONDNTA becomes molten at relatively low temperatures (125-165°C, depending on experimental conditions), and the NVR is formed in the molten mass of the sample. In contrast, the NVR nucleates and grows on the surface of the RDX particles when the sample is maintained below the melting point of RDX (~170-190°C). In these experiments, it is clear that the rate-controlling reaction involves the

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interaction between the NVR and the RDX at the surface of the RDX particle. 58 Formation of the NVR during the decomposition of HMX occurs in micron-size reaction centers, which are distributed homogenously throughout an HMX particle (the strand and shell-like structures shown in Fig. 3). In HMX, formation of the NVR may involve the reaction of HCN with CH2O under high-pressure conditions, since both of these compounds are observed at lower rates when the sample remains solid compared to when the sample is allowed to liquefy. Given the range of physical conditions under which the NVR is formed in these three compounds, it is remarkable that the reaction products associated with its formation are the same in each case. This again emphasizes the nonlinear and cyclic nature of the processes involved in the formation and decomposition of the NVR. The Solid-phase Cycle is the most complex of the five cycles. The processes involved in the Solid-phase Cycle are quite different, depending on whether the reactant is RDX or HMX. In RDX, the surface of the particles appears to roughen and undergo a morphological change. This is accompanied by the formation of the "reddish" NVR on the surface of the particle. Once the NVR is formed on the surface of the RDX particle, the rate of reaction accelerates, leading to an increase in the amount of NVR and the continued acceleration of the reaction rate. In HMX, the solid-phase processes are more complex, creating a set of morphological features as illustrated in Fig. 5. HMX first undergoes the Grain Structure Strand location

Bubbles

Flake Fig. 5. Illustration of the morphological features created in an HMX particle during the thermal decomposition process.

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P —> 5 phase transition, which creates a granular structure within the particles. This is followed by the nucleation and growth of reaction centers within the grains of HMX. The gaseous products formed in the reaction centers create bubbles, which grow in size as the reaction progresses. The smallest dimension of the HMX grains limits their maximum size, since the gas is released from the bubbles as they intersect the grain boundaries. The high-pressure conditions within the bubbles appear to favor the formation of the NVR within the bubbles as the bubbles grow. The NVR remains behind as a remnant of the reactions that have occurred within the bubble. Once a substantial amount of decomposition has occurred (~30%), the particle becomes relatively porous, allowing HMX and its decomposition products to flow within the porous structure and interact with the sample surfaces during the later stages of the decomposition process, forming flakes of NVR in the intergranular regions. What is especially intriguing about the processes involved in the Solid-phase Cycle is that there is no a priori way to anticipate their emergence from the properties of either RDX or HMX.

3.3.3. Emergent

Phenomena

The concept of emergence has been developed to describe the behaviors of complex systems and may be defined as a set of interacting components whose collective behaviors cannot be predicted from the behavior of the individual parts. 61 In examining the decomposition behavior of energetic compounds, we are confronted with similar issues. For example, can the behaviors that emerge on a larger spatial scale during the decomposition process of HMX be predicted from its underlying physical and chemical properties? If so, how? At this point, we do not have the answers to these questions. However, further examination of these systems may provide new insights into how basic chemical reactions and physical phenomena may be coupled to create systems that exhibit new and independent behaviors. From the chemical point of view, energetic materials are comprised of carbon, hydrogen, nitrogen and oxygen. From the physical point of view, energetic compounds are relatively easy to characterize. Their molecular crystal structures are readily measured and known. Calculations on the energetics and dynamics of their reactions at the molecular level have been made, 62 " 64 and calculation of their interactions at larger spatial scales are now possible. 65 ' 66 Thus, the main question becomes how do we determine the rules that control the evolution of these systems in time?

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3.4. Effects of Experimental Conditions Decomposition Processes

on

Observed

The complex physicochemical thermal decomposition reaction network, described above for HMX and RDX, can be used to understand the rules that control the competition between the various reaction pathways. This, in turn, will provide insight into the apparent discrepancies observed in experiments conducted using different experimental techniques. The reaction network can be interpreted as a diagram that illustrates the set of possible reaction channels by which a sample of HMX or RDX may decompose during an experiment. The entire set of channels is active for any given decomposition experiment; however, what is observed for a particular experiment is simply the subset of reaction channels that successfully compete and dominate the reactive process under a given set of experimental conditions. The most successful pathways will consume the RDX/HMX the fastest.

3.4.1. Reaction-Coordinate

Vectors

To provide a framework to represent and discuss the details of the reactive process, we introduce the concept of a reaction-coordinate vector. The reaction-coordinate vector represents the progress of a reaction through a set of conditions defined by an experiment. Graphically, a vector joining two points on the reaction network represents the reaction-coordinate vector. Thus, the dominant rate-limiting steps encountered, and therefore measured, by an experiment conducted under a specific set of conditions, will correspond to the reaction cycles and coupling pathways directly intersected by the reaction-coordinate vector. Reaction cycles not intersected by the vector will play only a minor role under the given conditions; the extent of contribution decreases for reaction cycles that lie farther away from the vector. For example, the line between the solid-phase cycle and point 1 represents one such reaction-coordinate vector. 3.4.2. Environmental Conditions Determine Location of Reaction-Coordinate Vector Figure 4 shows the global thermal decomposition reaction network for HMX and RDX. Depicted, are the different reactive processes: NO, ONDNTA, C H 2 0 / N 0 2 , NVR, and the Solid-phase Cycles. The complex interaction pathways connecting these distinct reaction cycles are also shown. The extent to which each reaction cycle contributes to the overall decomposition

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process is dependent on several "environmental" factors. These factors include: (1) pressure of gas in contact with the RDX/HMX, which is represented by a vertical line and increases qualitatively as one moves to the left in the diagram; (2) temperature of the RDX/HMX, which is represented by the horizontal line and increases qualitatively as one moves up in the diagram; (3) heating rate of the RDX/HMX, which is depicted by the horizontal axis in the grid surrounding the Solid-phase Cycle, with heating rates increasing from left to right in the grid; and (4) initial state of the RDX/HMX, qualitatively depicted by the two horizontal lines (labeled "pristine solid/crystal" and "completely damaged") to the left of the solidphase cycle, with initial "damage" to the RDX/HMX sample increasing as one goes down between the lines. Qualitatively, a vector connecting the "starting point" of the RDX/ HMX sample with a point formed by the intersection of the relative pressure and temperature lines can be thought of as a reaction-coordinate vector. The starting point is a point within the grid located in the upper left region of the reaction network that represents the initial state of the sample, which is determined by the heating rate in an experiment. The heating rate controls the relative amount of initial "damage" created in the sample, with slower heating rates being associated with the creation of more damage. In this context, the reaction cycles and "coupling" pathways that are intersected by this reaction-coordinate vector are indicative of the dominant decomposition processes followed during a specific thermal decomposition event. This is not to say that any processes not intersected are inactive for this specific set of circumstances. Indeed, due to the coupling of the different reaction cycles, all processes must play some role. A correct interpretation of this vector is that it depicts the dominant processes during the thermal decomposition under this specific set of circumstances, and therefore, these processes will be the ones observed during an experiment that is conducted under these same conditions. With this interpretation of the decomposition process, the apparent discrepancies observed by previous experiments may be addressed. As mentioned above, different experimental investigations have shown different sets of products. Until now, this discrepancy was thought to indicate that different unimolecular decomposition mechanisms were at play under different thermal decomposition conditions. The decomposition diagram shows that each of these different experimental results (i.e. product distributions) is correct. One may use this framework based on different "simplified" (i.e. unimolecular) reaction mechanisms to interpret the results from

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experiments collected under different sets of conditions to account for the apparent discrepancy. The reaction network expresses the idea that a single complex reactive process, with interactions between the distinct reaction cycles, is responsible for the overall decomposition. The varied experimental conditions simply serve to "shift" the reaction coordinate vector to regions of the reaction mechanism where different reaction cycles dominate the reactive process and lead to different distributions of the observed products.

3.4.3. Conditions Probed by Various Experiments The three numbers in red circles (Fig. 4) depict the regions of the global thermal decomposition reactive process network probed by several different experimental techniques. The initial state of the sample is of significant importance when determining the dominant reaction pathway. The initial state of the RDX or HMX sample at the onset of decomposition in the STMBMS and other experiments can be mapped to a point within the region formed by the initial state and heating rate parameters. This region essentially encompasses the solid-phase reaction cycle and accounts for the possible states of RDX/HMX powders or single crystals used in various experiments (grid region). At the upper left of the region is pristine RDX/HMX solid or single crystals. Rapid heating moves the sample to the right through the upper portion of the grid, corresponding to an experiment in which there is minimal damage in the solid due to nucleation and growth in the Solid-phase Cycle. Continuing towards the right in the grid, liquid-phase RDX/HMX is formed in experiments that start with pristine, undamaged RDX/HMX and the sample is rapidly heated above its melting point, to again minimize the extent of "damage" due to the solid-phase reaction cycle. The bottom left is a "fully damaged" solid/single crystal, liquid-or meltphase RDX/HMX, (i.e. RDX/HMX where the solid-phase nucleation and growth process has fully developed and an NVR has been produced). The bottom right depicts solid/single crystal, liquid-or melt-phase RDX/HMX that has become fully "reactive" (i.e. the nucleation and growth process is fully developed, and the condensed-phase RDX/HMX is completely saturated with intermediate stage decomposition products). Within this region, the possible initial states of RDX/HMX used in the thermal decomposition studies can be "mapped".

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Region 1 in Fig. 4 is occupied by TGA/DSC and vacuum laser-pyrolysis experiments. In a typical TGA/DSC experiment, a fast heating rate is used to obtain temperatures above the melting point of RDX/HMX, thereby minimizing the amount of time spent in the solid-phase reaction cycle during the heat ramp and resulting in essentially pristine liquid-phase RDX/HMX as the isothermal temperature is reached. Decomposition then proceeds in parallel by unimolecular liquid- and gas-phase processes, typically accompanied by significant RDX/HMX sublimation. The lack of high gas-confinement near the condensed-phase surface minimizes the contributions of secondary reactions between the condensed- and gas-phase decomposition products in the TGA/DSC measurements. The vacuum laser-pyrolysis experiments 67 also generate rapid heating of the solid surface, again leading to essentially pristine liquid-phase RDX/HMX at the sample surface and consistent with the reactioncoordinate vector for Region 1. There is a significant contribution to the decomposition through the OST/HCN decomposition pathway and also contributions from the NO Cycle. Interactions between these two channels are controlled by the coupling pathways. Contributions to the overall decomposition process by reaction cycles and coupling pathways that are not directly intersected by the reaction-coordinate vector decrease the farther removed from the reaction-coordinate vector the individual process lies. The parameter space depicted by Region 1 in Fig. 4 does not include all variations of the space encountered by current ongoing TGA/DSC and laser-pyrolysis experiments; it simply maps the relative parameter space that is typical of the majority of work in these types of experiments. Region 2 (Fig. 4) is the relative parameter space occupied by flashheating mass spectrometry and FTIR experiments. 68 In these experiments, very fast heating rates are used to "flash" the solid sample to isothermal temperatures ranging from just below to significantly above the melting point of RDX/HMX. This flash heating produces a sample surface temperature that initially falls within the transition region between pristine solidphase and pristine liquid-phase RDX/HMX. This creates a surface that exists as a melt or "froth" prior to the onset of significant decomposition, with minimal "damage" created by the solid-phase reaction cycle before decomposition initiates. The visual indications of a residue in these experiments, along with measurements of a mononitroso derivative of RDX (ONDNTA) indicate that there is a contribution to these experiments from the ONDNTA and NVR

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reaction cycles. Thus, results from these experiments can be mapped to Region 2, with the dominant processes lying along the reaction-coordinate vector and minor processes falling farther away from the vector. A comparison of the reaction-coordinate vectors for Regions 1 and 2 shows that ONDNTA and solid-phase decomposition contribute to Region 2 processes, 41 while the first-order OST and NO channels contribute more to Region 1 processes. Region 3 depicted in Fig. 4 is the experimental parameter space filled by the slow-heating rate sealed bulb type experiments such as those by Batten 3 7 - 4 0 and Cosgrove and Owen. 69 ' 70 In these experiments, the slow heating allows the Solid-phase Cycle to contribute significantly to the decomposition. Thus, the NVR reaction cycle is the major contributor to the rate-limiting processes controlling the overall decomposition for the solid-phase experiments and plays a contributing role in the melt-phase experiments. Summarizing: one unified picture captures the overall decomposition process. This picture is a network of complex interactions amongst different reactive processes with multiple pathways coupling the individual processes. This network captures all of the seemingly contrary results obtained in many different investigations in one unified picture. The network also provides a framework where most experiments can be mapped to distinct regions within the network. Differences among experiments can be attributed to variations in the experimental parameters which shift the dominant, rate-limiting steps to different reaction paths within one overall reaction network. 4. Reaction Kinetics While the reaction network provides a qualitative picture of the decomposition process and illustrates how various reaction pathways may compete under different sets of conditions and lead to the emergence of different observed behaviors, it falls short of the ultimate goal: predicting the behaviors of propellants and explosives over a wide range of conditions. To achieve this goal requires applying the second aspect of our conceptual framework: physicochemical control of high-temperature combustion reactions. The various reactive pathways in the reaction network must be individually characterized and represented by a set of mathematical expressions in a manner analogous to the use of elementary reactions to characterize gasphase reactions in high-temperature combustion processes. This requires

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new numerical algorithms that can be used to characterize the reaction kinetics associated with reaction networks that characterize the decomposition of the different energetic compounds and various energetic materials. 4.1. Extracting Reaction Experiments

Kinetics

from

Condensed-Phase

4.1.1. Simple Kinetics — Direct Inversion from Experiment For simple reactive processes, the reaction kinetics can be determined directly from experiments by means of an Arrhenius-type analysis. Inversion of the data from the experiment provides the required reaction rate constant and its temperature dependence. If this type of analysis is applied to thermal decomposition results from experiments with energetic compounds, the rate constant will only represent the reaction rate along the reaction-coordinate vector that represents the conditions of the particular experiment in the overall reaction network. The obvious limitation of this approach is that each reaction-coordinate vector requires its own set of reaction rate parameters. 4.1.2. Kinetics of Complex Reaction Networks The development of mathematical models to represent combustion processes is a good example of how the kinetics of complex reaction networks has been developed. In this case the reaction kinetics have been determined by two different approaches. In the first approach, experiments are conducted to investigate and measure the rate of elementary reactions, thus providing pieces to be used in the overall reaction network. In the second approach, the distribution of reactants, intermediates, and final products are measured as a function of spatial location in a flame. Then the reaction rate parameters of the elementary reactions that represent the reaction network are optimized to match the details of the experimental measurements. The conceptual framework that has been developed to investigate reactions of energetic materials in the condensed phase incorporates an approach to characterize the reaction kinetics that is analogous to the one used to characterize reaction kinetics in flames. In this approach, the timedependent rates of formation of the reactants, intermediates, and products are measured using the experimental protocol. Next, reaction schemes are postulated, sets of differential equations representing the underlying processes constructed, solved, and compared to the experimental data (Fig. 6).

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Reaction Scheme Refinement Postulate or Refine Reaction Scheme

Set or modify Parameters

No

Kinetics Parameters Optimization Yes

Does Postulated Model Capture All Features in Data?

Compare reaction scheme to experiments covering range of experimental conditions and optimize parameters.

1

Assess reaction schemes strengths and weaknesses in capturing underlying reaction processes.

Construct and Solve Equations

i Compare to STMBMS Data

T

No

Yes

Add results to database and publish.

Comparison OK? Fig. 6. Algorithm used to create mathematical models to represent the reaction kinetics of thermal decomposition processes.

The analysis procedure is divided into two primary tasks. First the reaction scheme is postulated and refined and then the kinetics parameters are optimized. Sets of differential equations are constructed to characterize the various processes in the reaction network that represent the decomposition of an energetic compound, such as the one above for RDX and HMX. The procedure used to build the model starts with a small set of differential equations that represent specific aspects of the decomposition process. The parameters for these processes are optimized by minimizing the difference between the calculations and the corresponding experimental measurements. If the differential equation for a specific aspect of the reaction network captures the features observed in the experimental measurements, it is retained in the model. If not, it is discarded and another process is postulated and tested. Using this procedure, a model of the reaction network is built. Once the reaction scheme is developed to a point where it captures most, if not all, of the features observed in the data, it is then used to assess its ability to capture the features observed in experiments collected over a range of experimental conditions. When the model can capture the behavior over a range of experimental conditions, the parameters used in the model are then optimized to provide the kinetic parameters for the different pathways in the reaction network.

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The modeling aspects of the conceptual framework for investigating the thermal decomposition of energetic materials are still under development. A higher level programming language, Mathematica®, has been used to develop the analysis methods. Papers on the decomposition of 24DNI52 and NDNAZ, 71 illustrate how models of the reaction networks are developed for complex reactive processes in the condensed phase. A new reaction modeling and kinetics (REMKIN) compiler and analysis tool is currently under development. The design goal for REMKIN is to provide a set of numerical algorithms to facilitate the development of mathematical representations of the reaction networks that control the decomposition of energetic materials. With the completion of the REMKIN compiler and analysis tool, the conceptual framework for investigating the thermal decomposition of energetic materials will be complete and new advances in our understanding of reactive processes in energetic materials in the condensed phase at low and moderate temperatures will be possible.

5. Conclusions and Future Research Understanding the physicochemical processes that control the thermal decomposition of energetic materials in the condensed phase will help to characterize the safety and aging behavior of existing explosives and propellants. This understanding will also provide new insight for designing and developing new energetic compounds. Obtaining this understanding is a challenge due to the complex nature of the decomposition processes in these materials, which occur far from equilibrium conditions. The development of a new experimental protocol to examine the complex processes associated with the thermal decomposition of energetic materials in the condensed phase has been described. The fundamental concept of the new protocol is to maximize the extent of information obtained from the experiments so as to reveal the greatest insight into the underlying reactive processes. The protocol described in this chapter is primarily based on mass spectrometric methods. However, the general concepts of using multiple instrumental methods to make simultaneous measurements on a system, with the goal of obtaining the maximum amount of temporally correlated information, is a general principal that provides guidance for creating other types of experiments to probe reactive processes in the condensed phase.

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The new experimental protocol has been used to examine a range of different types of energetic materials and has revealed new insight into the underlying reactive processes. It has been found that the decomposition of most energetic compounds is controlled by a set of coupled nonlinear physical and chemical reactive processes. These features create complex reactive systems whose behavior is characterized by the emergence of dissipative structures that play a major role in controlling the overall decomposition. Several different types of spatiotemporal structures have been observed for different materials. For example, reactions on the surface of 24DNI and RDX particles control the decomposition of these compounds in the solid phase, whereas nucleation and growth of sub-micron size reaction regions within HMX particles control its decomposition in the solid phase. The experiments have also provided new insight into the multiple reaction pathways that compete to control the evolution of the decomposition process in time. This competition and interaction between the underlying processes has been illustrated with results from the decomposition of RDX and HMX. It has been shown how the effects of temperature and pressure of the contained gaseous decomposition products can alter the reaction pathways and lead to divergent results. It has also been shown which reaction pathways are likely to dominate the decomposition process using a variety of the more conventional thermal analysis methods. These methods typically provide insufficient information to identify and characterize the underlying processes. The complex reaction behavior poses a challenge to develop a new conceptual framework that can be used to represent, develop, and convey understanding of the underlying behavior of energetic materials. While this is a new challenge in the field of energetic materials, understanding similar types of processes have been of great interest in the more general scientific community. The entire set of behaviors observed in the decomposition of energetic materials in the condensed phase falls under the new science, born over the past several decades, of nonequilibrium processes. This new science uses concepts such as dissipative structures and self-organization and describes processes in terms of unidirectional time and irreversibility.6 This context has been used to characterize a range of different phenomena, including complex chemical systems, such as the well-known Belousov-Zhabotinski chemical oscillator reaction. Use of these concepts will most likely play an important role in the characterization of decomposition processes of energetic materials in the future.

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More recently, Wolfram has developed a description of complex processes in his book "A New Kind of Science".72 It uses cellular automata to explore the behavior of complex systems and categorizes the evolution of these systems using a set of rules to guide the evolutionary progress. Some rules lead to the rapid development of simple, repetitive and predictable structures; others evolve as complex unpredictable patterns. This behavior illustrates that, for some set of rules, one can develop mathematical representations that predict the future state of the system, but with other sets of rules this is not possible and the system is not computationally reducible. Thus, the only way to characterize the evolution of the computationally irreducible system is to let it evolve and examine its structure at the time of interest. These concepts developed by Wolfram72 for cellular automata may be applied to the characterization of the decomposition processes in energetic materials by allowing the physicochemical processes to represent the rules that guide the evolution of the system and using the corresponding set of differential equations to compute the evolution of the system. This is essentially the process that has been developed for the numerical simulation features of the experimental protocol described in this chapter. A set of chemical reactions and physical processes are postulated (the rules to control the process), the evolution of the system is computed, and the results are then compared to the experimental results to determine if the chemical reactions and physical processes (the rules) describe the observed results. From one point of view, the high-information content experiments developed in the experimental protocol can be considered an experimental implementation of the computational processes (rules), which guides the evolution of a system. Basically, a non-silicon analogue computer. One of the main challenges remaining from the scientific viewpoint is connecting the behavior of the nonequilibrium reactive processes to the chemical and physical properties of the compounds (i.e., chemical functionality, molecular and crystal structure, and constitutive properties). The ability to meet this challenge is in its infancy, for it requires first identifying the underlying reactive processes and then determining how these underlying processes are linked to the molecular, physical, and constitutive properties of the material. Currently, this is being approached by collecting data from high-information content experiments on a diverse set of different compounds and carefully examining the data to uncover correlations between decomposition behavior and the properties of the compounds. Until now, most experiments that have examined the underlying detail of reactions of energetic materials in the condensed phase at low and

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moderate t e m p e r a t u r e s have focused on individual pure compounds. However, development of new experimental methods now allow the interactions of ingredients t h a t make u p explosive and propellant formulations to be examined in more detail. This should provide a more fundamental understanding of how the ingredients interact and what effects these interactions have on the mesoscale mechanics and aging behavior of these materials.

Acknowledgments T h e development of the new experimental protocol and its applications to the examination of energetic materials is the result of contributions of many people at Sandia National Laboratories over the past twenty years. Contributors include: Mr. N. Toly, Mr. J. Collins, Mr. J. Damico, Mr. M. Mitchell, Mr. D. Puckett, Dr. T. Land, Dr. L. Minier, Dr. K. Anderson, Mr. R. Hannush, Ms. L. Johnston, Ms. J. Wood, Ms. S. Mack, Ms. D. Wiese-Smith, Ms. E. Cooper, and Dr. S. Maharrey. Many advances in our understanding were through discussions and collaborations with Dr. Surya Bulusu (U.S. Army, A R D E C ; deceased). T h e work has been supported over t h e years by U.S A r m y / D O E M e m o r a n d u m of Understanding (MOU), the Army Research Office, DoD Office of Munit i o n s / D O E MOU, and United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94-AL85000. T h e author thanks Dr. G. Anderson, Dr. W . Alzheimer, Mr. P. Gildea, Mr. Tom Hitchcock, Dr. S. Johnston, Dr. R. Carling, Dr. A. Ratzel, Dr. F . Tully, and Dr. D. Hardesty for support and encouragement for this work within Sandia. Finally, we t h a n k Dr. R. Shaw for his long-term support and encouragement in our efforts.

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34. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data Preliminary Comments on Autoacceleration and Autoinhibition in HMX and RDX Decomposition (US Army Ballistic Research Laboratory, 1984). 35. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Product Distributions from HMX and RDX Decomposition (US Army Ballistic Research Laboratory, 1985). 36. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Activation Energies and Frequency Factors for HMX and RDX Decomposition (US Army Ballistic Research Laboratory, 1985). 37. J. J. Batten and D. C. Murdie, Aust. J. Chem. 23, 737-747 (1970). 38. J. J. Batten and D. C. Murdie, Aust. J. Chem. 23, 749-755 (1970). 39. J. J. Batten, Aust. J. Chem. 24, 945-954 (1971). 40. J. J. Batten, Aust. J. Chem. 24, 2025-2029 (1971). 41. J. J. Batten, Aust. J. Chem. 25, 2337-2351 (1972). 42. R. Behrens and S. Bulusu, J. Phys. Chem. 95(15), 5838-5845 (1991). 43. R. Behrens and S. Bulusu, J. Phys. Chem. 96(22), 8891-8897 (1992). 44. R. Behrens, J. Phys. Chem. 94, 6706-6718 (1990). 45. R. Behrens, S. Mack and J. Wood, in JANNAF 17th Propulsion Systems Hazards Subcommittee Meeting, Vol. 1, CPIA Publication 681 (1998), pp. 21-44. 46. R. Behrens and L. Minier, in 33rd JANNAF Combustion Meeting, CPIA Publication 653 (1996), pp. 1-19. 47. L. Minier and R. Behrens, in JANNAF 17th Propulsion Systems Hazards Subcommittee Meeting, CPIA Publication 681 (1998). 48. A. I. Atwood, K. J. Kraeutle, T. P. Parr, D. M. Hanson-Parr, R. Behrens, L. Minier and A. Rutzel, in 49th JANNAF Propellant System Hazards Subcommittee Meeting, CPIA (1999). 49. R. Behrens and S. Bulusu, in 29th JANNAF Combustion Meeting, Vol. II, CPIA Publication 573 (1992), pp. 453-463. 50. R. Behrens and S. Bulusu, in Fall 1992 Meeting of the Materials Research Society, Vol. 296 (1992), pp. 13-24. 51. L. Minier, R. Behrens and S. Bulusu, in Decomposition, Combustion and Detonation Chemistry of Energetic Materials (Materials Research Society, Boston, MA, 1996). 52. R. Behrens, L. Minier and S. Bulusu, in 34th JANNAF Combustion Subcommittee Meeting, CPIA Publication 662 (1997), pp. 549-567. 53. R. Behrens and S. Maharrey, in Combustion of Energetic Materials, eds. K. K. Kuo and L. T. DeLuca (Begell House, New York, 2002), pp. 3-21. 54. S. Maharrey, D. Wiese-Smith and R. Behrens, in Proc. 38th JANNAF Combustion Meeting, Chemical Propulsion Information Agency, Destin, FL (2002), pp. 373-386. 55. M. E. Brown, D. Dollimore and A. K. Galwey, Reactions in the Solid State. Comprehensive Chemical Kinetics, Vol. 22, eds. C. H. Bamford and C. F. H. Tipper. (Elsevier Scientific Publishing, Amsterdam, 1980), p. 340. 56. S. Arrhenius, Z. Phys. Chem. 1, 110 (1887). 57. R. Behrens and S. Bulusu, J. Phys. Chem. 96(22), 8877-8891 (1992).

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58. S. Maharrey, R. Behrens and L. Johnston, in 19th PSHS Meeting, Chemical Propulsion Information Agency, Monterey, CA (2000), pp. 17-32. 59. R. Behrens and S. Bulusu, in Proc. Materials Research Society, Vol. 296 (1993), pp. 13-24. 60. R. Behrens and S. Bulusu, in Challenges in Propellants and Combustion 100 Years after Nobel, ed. K. K. Kuo (Begell House, Inc., New York, 1997), pp. 275-289. 61. J. Bickle, Minds Much. 11, 467-481 (2001). 62. C. C. Chambers and D. L. Thompson, J. Phys. Chem. 99(43), 15881-15889 (1995). 63. D. Chakraborty, R. P. Muller, S. Dasgupta and W. A. Goddard, J. Comput. Aided Mater. Des. 8, 2-3 (2002). 64. C. J. Wu and L. E. Fried, J. Phys. Chem. A13(101), 8675-8679 (1997). 65. D. C. Sorescu, B. M. Rice and D. L. Thompson, J. Phys. Chem. B103(32), 6783-6790 (1999). 66. D. Bedrov, C. Ayyagari, G. D. Smith, T. D. Sewell, R. Menikoff and J. M. Zaug, J. Comput. Aided Mater. Des. 8, 2-3 (2002). 67. T. R. Botcher and C. A. Wight, J. Phys. Chem. 98(21), 5441-5444 (1994). 68. P. E. Gongwer and T. B. Brill, Combust. Flame 115(3), 417-423 (1998). 69. J. D. Cosgrove and A. J. Owen, Combust. Flame 22, 13-18 (1974). 70. J. D. Cosgrove and A. J. Owen, Combust. Flame 22, 19-22 (1974). 71. K. Anderson, J. Homsy, R. Behrens and S. Bulusu, in 11th Int. Detonation Symp., Vol. 1 (1998), pp. 239-245. 72. S. Wolfram, A New Kind of Science, 1st edn. (Wolfram Media, Inc., 2002).

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CHAPTER 3 S T U D Y OF ENERGETIC MATERIAL C O M B U S T I O N CHEMISTRY BY PROBING MASS SPECTROMETRY A N D M O D E L I N G OF F L A M E S Oleg P. Korobeinichev Institute of Chemical Kinetics and Combustion Siberian Branch Russian Academy of Sciences 630090 Novosibirsk, Russia

Contents 1. Introduction 2. Experimental Techniques 2.1. Microprobe and Molecular Beam Mass Spectrometric Techniques 2.2. Coupled Mass Spectrometric and Laser Technique 2.3. Mass Spectrometric Technique for Studying the Kinetics and Mechanism of Thermal Decomposition of EMs and their Vapors 3. Validating the Method of Probing Flames with Narrow Combustion Zones 4. Flame Structure of AP and AP-Based Composite Propellants 5. RDX and HMX Flame Structure 6. Flame Structure of ADN and ADN-Based Propellants 7. Conclusions References

75 77 78 79 80 81 83 88 91 97 98

1. I n t r o d u c t i o n Progress in the understanding of energetic material (EM) combustion will arise from a clearer picture of the chemistry and physics t h a t take place in flames. We now recognize t h a t the combustion of E M s is a complex multistage process based on t h e chemical transformations in t h e condensed a n d gas phases. Much more detailed information about the combustion chemistry of E M s is required. It is important to understand the combustion chemistry because this is the type of information a propellant formulator or a chemist 75

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may use to tailor and/or improve the performance of the propellant. 1 The theories of Zel'dovich2 and others on combustion of gun powder and explosives have played an important role in the development of the combustion theory of EMs. But, due to their simplified assumptions about the EM combustion mechanism and kinetics of reactions, they could not obtain satisfactory agreement with experiments on burning rates and their dependence on pressure and initial temperatures. New developments in advanced numerical methods and experimental techniques have enabled progress in the understanding of EM combustion chemistry, kinetics and mechanisms of chemical reactions in flames, and the derived combustion models much better describe the characteristics of burning EMs and the structures of their flames. Studies of EM combustion have mostly investigated physical characteristics and neglected chemistry because of the experimental difficulties of studying chemical reactions in EM combustion waves. These difficulties are due to the high reaction rates (reaction times in condensed phases are of the order 10 _ 1 -10^ 5 s), the high temperatures (up to 3000K in the flame zone), the narrow spatial zones (of the order of 1 0 - 3 mm in the condensed phase and 10 _ 1 -1 mm in the gas phase), the high burning rates, and the short time available for experiment (0.1-10 s). The difficulties are increased by the presence of heterogeneity and multiple ingredients. Although studies of combustion have been intensively conducted for about 60 years, only during the last decade has appreciable progress been achieved. Our knowledge of the combustion chemistry of EMs comes mostly from flame structure studies. 3 These studies allow us to identify species in flames and to measure temperature and species concentration and their spatial distributions. 3 ~ 16 Analysis of the data on EM flame structures provides information on the composition of the condensed phase reaction products that are produced by EM thermal decomposition on the burning surface. These analyses, in turn, enable understanding of reactions in the condensed phase and their mechanisms. On the other hand, the chemical structure of the EM flame also provides information on the mechanisms and kinetics of gas-phase chemical reactions of further transformations of products emerging from the surface. These reactions are responsible for heat release in flames. The principal methods applied to the investigation of chemical and thermal flame structures of EMs are: (1) probing mass-spectrometry (PMS), 4 ^ 9 (2) spectroscopic methods 1,10 ~ 16 for absorption and emission, including planar laser induced fluorescence (PLIF), spontaneous Raman scattering (SRS), coherent anti-Stokes Raman spectroscopy (CARS), and (3) the micro thermocouple technique. 17 Systematic studies of EM flame structures

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77

using laser spectroscopic methods have been done mainly by Parr and Hanson-Parr 11,13 ' 14,16 and Vanderhoff et al.10'15 Spectroscopic methods are relatively non-intrusive; but there are many species in flames (very often the key species) which cannot be detected spectroscopically (see the chapter by Dagdigian). For example, the spectra of important species may be inaccessible because of wavelength or apparatus sensitivity limits. Until recently there were few studies of EM flame structure. The improvement of experimental techniques, however, along with the development of flame-structure modeling and the rise of interest in EM combustion chemistry, has significantly increased the number of studies and their results have been used to understand EM combustion chemistry, to create chemical kinetics mechanisms of reactions in EM flames, and to develop EM combustion models. This paper describes briefly the PMS method for EM flame structure studies and presents the results of the application of this method to EMs such as AP, RDX, HMX, ADN and some composite solid propellants (SP).

2. Experimental Techniques Probing mass spectrometry (PMS) is one of the most effective and universally used experimental techniques for studying EM flame structures. Heller and Gordon 18 performed some of the first studies using a capillary probe to sample a double-base propellant flame at 10-20 atm. The closest approach of the probe to the burning surface was 1 mm; the surface was held at a constant position using a gold wire or quartz fiber restraint upon the propellant strand, which was pushed from below by a compressed spring. We developed an improved method19™21 allowing the detection in situ of many species in the flame and the determination of their concentrations and their spatial distributions. In this improved method, a burning strand of EM moves with a velocity exceeding the burning rate toward a probe so that the probe continuously samples gaseous species from all the zones including those next to the burning surface. The probe ensures free gas-dynamic expansion of the sample accompanied by a rapid decrease in temperature and pressure and, hence, freezing of the mixture composition, which allows detection of atoms and free radicals. A skimmer placed after the probe cuts out the central part of a supersonic jet: free from possible heterogeneous and catalytic reactions on internal hot walls of the probe. The sample is then transported to the ion source of a time-of-flight (TOF) or quadruple mass spectrometer (again, the beam is not permitted to collide with the apparatus). Mass

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spectra of samples are recorded with simultaneous filming of the probe and the burning surface. We have described the electronic system for stabilization of the EM burning surface using microthermocouples. 20

2.1. Micro-probe and Molecular Beam Spectrometric Techniques

Mass

Two types of apparatus have been developed to study flame structure. The sample is transported to an ion source (1) as a molecular flow using a microprobe (MPT) with an inlet orifice of 10-20 micron, or (2) as a molecular beam (MBT) using a sonic probe with an inlet orifice of 20-200 micron. The microprobe has high spatial resolution and only slightly disturbs the flame, allowing the study of flames with a narrow combustion zone of 0.1mm or less. Radicals, however, may recombine and unstable species, including EM vapors, may decompose and react on the inner hot walls of the probe and deposit on the cold parts of the probe walls. So EM vapors, very important EM gasification products, may not be detected using this setup. Molecular beam mass spectrometric (MBMS) sampling 21 allows detection of radicals and other unstable species but disturbs the flame more strongly and therefore has reduced spatial resolution. We reported 19 the first use of MPT to study the solid propellant (SP) flame structure of ammonium perchlorate (AP) and polymethylmetacrylate. MPT was further applied to the study of EM flame structures with narrow combustion zones using AP and AP-based composite propellants. Figure 1 is a sketch of the MBMS system, 4 ~ 7 which has been used to examine the flame structures of AP, RDX, HMX, ADN, GAP and some composite SP. It includes a molecular beam sampling system, a time-of-flight mass spectrometer (type MSKh-4), a combustion chamber, a scanning system, a data acquisition system and an experiment controller based on CAM AC equipment and a computer. The sampling probe (item 3) is a 25-mm high cone with a 50-degree external angle, a 40-degree internal angle, and a 50-100 micron diameter orifice at the apex (at l a t m ) . The probe produces a molecular beam, which passes to an ion source (item 4). The ignition spiral (12) is automatically removed from the combustion zone after ignition. The EM flame is scanned using a control system and a stepper motor (13) to move the burning strand (14) at a speed of less than 20mm/s. A thermocouple (15) measures temperature profiles. To study the flame structure at high pressure by MBMS, we use a quartz probe with an inner angle of 40 degrees and an orifice of 50 microns at 3 atm, 20 microns at 6 atm and wall thickness near the probe tip of 25 microns. We

Energetic Material Combustion

Fig. 1.

Chemistry

MBMS system for studying the name structure of EMs with TOFMS.

visualize the combustion using a video camera (Panasonic NV-M3000EN). CAMAC equipment assisted the measurement of peak intensities of selected masses as a function of time. It is not always possible, however, to predict which peaks will be found in a mass spectrum. To reveal unpredictable peaks in the mass spectrum an oscilloscope (LeCroy 9310AL with a memory of 1 MB) was used. This allowed detection of singular mass spectra within short time intervals of 0.01 s. To stop data acquisition at the time of probe contact with the burning surface, a special device was designed and manufactured: an end switch of the stepper motor moving the sample to the probe was used as a sensor keeping a record of contact. Video recording of the ADN strand burning surface and probe was performed simultaneously with mass spectra recording. The synchronization of the two measurements was achieved by allowing the contacts of the stepper motor end switch to close at the moment of probe contact with the strand-burning surface. The latter was accompanied by light diode luminescence simultaneously with the stoppage of step frequency generator, which starts the oscilloscope. The light diode luminescence was recorded by video camera. 2.2. Coupled Mass Spectrometric

and Laser

Technique

The MPT technique was also developed by Litzinger et al.8,9'22'23 to study laser-supported combustion (LSC) using a triple quadruple mass spectrometer 15 and an ionization energy of 22 eV. Laser-supported

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combustion enables studies at lower pressures in which the chemical reaction zones in the EM flame are spread and the errors in flame concentration profiles measured by the probe are reduced. It is generally believed that the flame zone width should be greater than the probe tip dimensions. But, in LSC, one must ensure that the probe does not shield the burning surface from the laser, reducing the energy to the surface, and that the probe is not heated by the intercepted laser beam. This inadvertent heating may increase the rate of chemical reactions in the extracted sample. Laser irradiation is widely used for the study of EM ignition. A recent paper by Yang et al.24 is devoted to comprehensive analysis and modeling of laser-induced ignition of RDX. Generally, the only measured characteristics of laser-induced ignition are ignition delay and surface temperature of EM as a function of heat flow. Unfortunately there are no experimental data on the gasification products and species concentrations as functions of time. The available data 9 ' 22 have been obtained using MPT and do not contain information about EM vapors in the narrow (0.1mm) zone near the EM surface. This near-surface information is necessary for understanding the mechanism of EM ignition and its transition to combustion on a molecular level, and for development of comprehensive ignition and combustion models. We have described experiments for study of ignition and combustion of EMs supported by CO2 laser irradiation using MBMS. 25 The tip of the probe was 100-150 microns from the sample surface. This distance is close to the value of the sampling shift ZQ (see below). So the probe sampled the products evolving directly from the EM surface during its ignition and its combustion as a function of time. The beam of the laser made a small angle to the surface, excluding possible probe shielding of the EM surface from the laser beam. Positioning was controlled with the help of a video camera. The tip of the probe was heated to the temperature of the burning surface to prevent clogging of the sampling orifice by reaction products.

2.3. Mass Spectrometric Technique for Studying the Kinetics and Mechanism of Thermal Decomposition of EMs and their Vapors Probing mass spectrometry can also be successfully applied to the study of kinetics and mechanism of the thermal decomposition of an EM and its vapors. The thermal decomposition of EM is one of the most important stages of its combustion; hence knowledge of the kinetics and reaction mechanism of EM thermal decomposition under different conditions (including the temperature at the burning surface) is

Energetic Material Combustion

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81

necessary for development of EM combustion models. Such information can result from using Rapid-Scan FTIR spectroscopy, SMATCH/FTIR, and T-Jump/FTIR — all methods developed by Brill26 and by the method of differential mass-spectrometric thermal analysis (DMTA) developed in our laboratory. 27 These methods give information about the products of EM decomposition including EM vapors (e.g., the molecules HMX, RDX, etc.) as well as their rates of evolution. We have described the setup for mass spectrometric investigations (e.g., MBMS) of the kinetics of EM thermal decomposition under the non-isothermal conditions approximately similar to those present in the condensed phase in the vicinity of the EM burning surface.27 The EM sample was applied to a metal ribbon located in flow reactor near the tip of the probe and heated by electrical current at 100-1000 K/s. This technique also can be used for obtaining calibration coefficients for EM vapors.

3. Validating the Method of Probing Flames with Narrow Combustion Zones Quantitative results of the mass spectrometric probing technique for EM flame structure depend on the performance of the probe. Detailed studies 2 8 - 3 1 have been carried out to validate the probe method when the ratio of the flame zone width, L\>, to the probe tip outside diameter, d, is close to one. The studies were made for a preheated (T = 533 K) AP flame32 where the burning zone was about 0.1mm wide at 0.6 atm. Distortions caused by the probe can be divided into external and internal ones: the external ones being hydrodynamic and thermal. The probe acts as a sink for matter and heat, which causes distortions of temperature and species concentration profiles.33'34 Errors were determined 28 ' 29 ' 35 by measuring perturbations in the velocity field in one-dimensional gas flows using submicron particles and a pulsed laser. The flow starts deviating from onedimensional type at a distance depending on the sampling factor, which is defined by the equation a^ = AQ/-K(1^VQ. Here Q is the sink flow rate, d0 is the probe orifice diameter, and w0 is the flow velocity. The velocity fields and stream lines near the orifice of a probe have been calculated from Rosen's disk sink model. 33 This model can be used to evaluate measurement errors. Probe-error estimates have also been carried out for a real flame. A preheated AP flame with Lb ~ 0.1mm was used, but we were unable to find reliable data on the AP flame chemical structure. Model experiments were, therefore, performed with a methane-air flat flame with argon additive having a 0.5 mm burning zone width. A

82

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special quartz probe was used (subsequently referred to as a macroprobe) with an outside tip diameter equal to the flame zone width of 0.5 mm and with a probe orifice of do = 0.012 mm. This probe and flame were similar in such dimensionless parameters as do(ao)05 / L^, L^/d ss 1 and Red w 1 to those used in the case of the AP flame (Re d is the Reynolds number of the flow determined from the probe outside diameter). According to similarity theory, the equality of these numbers for the model flame and probe and the AP flame and real probe allows us to use the results from the former to study the latter. The following methods were applied to study the structure of the model flame: (1) microthermocouple technique (MT) using II-shaped platinum-platinum/rhodium thermocouples (wire diameter of 0.02 mm) for measuring temperature profile; (2) probe mass-spectrometry measuring methane concentration profiles by macroprobe and quartz microprobe with do = 0.06 mm, d = 0.12 mm; (3) Spontaneous Raman Scattering (SRS) spectroscopy for measuring methane and nitrogen concentration profiles. The comparison of the results of measuring methane concentration profiles in the model flame by probing methods and non-intrusive diagnostics showed that the error of the probe technique in finding concentrations at the burning surface was less than 10%. When the tip of the probe diameter was reduced 7 times, the change in concentration was about 15%. Concentration profiles of methane measured with a probe agree within 15% with the undisturbed profiles, if the first profile is shifted toward the burner by a value close to ZQ, the calculated shift of the sampling point with respect to the unperturbed flow. Calculations 35 based on simplified assumptions of the flame and flow perturbations (using Rosen's model 33 ) provided the following values: ZQ « OAdo(ao)0'5 and A « 0.3do(ao) 0 ' 5 , where A is a samplingzone width representing spatial-sampling resolution. At mass-spectrometric study of preheated AP flame structure do was 0.012 mm and «o = 75. After applying appropriate corrections for the sampling point on the concentration profiles (ZQ shift), the error in finding concentrations by the probe method was less than 15% of its maximal value. The sampling zone width was within ±15% of the AP flame zone width. This error is reasonably small for quantitative modeling of AP flame structure data. We note, however, that Smith 36 gives other formulas for the shift. In judging these experiments, one must be aware that the thermal disturbance of a flame by a probe strongly depends on the shape, wall thickness, and composition of the probe. Specification of these probe characteristics is frequently omitted in published work. Estimation of the thermal disturbances should be carried out by comparison of temperature

Energetic Material Combustion

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83

profiles in a flame measured by thermocouples located both close to the tip of a probe and far from it. If the difference in these profiles is small, the thermal disturbances of the flame by the probe is likely to be small. To reduce thermal disturbances, one should use probes made of quartz or alumina, with an angle of opening of a cone less than 30-40 degrees and with thin (about 100 microns) walls, especially near the tip of the probe. Making these probes is difficult. Large wall thickness may be the cause of significant disturbances reported in some work. 8,38 Composition distortions in MBMS sampling has also been considered and discussed by Knuth. 39 Validations of the MBMS method for determination of product composition of SP combustion at high temperatures and pressures (40atm) typical of combustion chambers of rocket motors have been reported in Refs. 40-42. Estimation of internal distortions of sample inside-probe and skimmer were performed by the numerical solution of the full set of unsteady Navier-Stokes equations for axially-symmetric flows of compressible gas. The combustion products of stoichiometric mixtures of ammonium dinitramide (ADN)-polycaprolactone (pPCLN) at 4MPa were chosen as the object of investigation. The gas dynamics and chemical kinetics were simulated to assess the correctness of sampling. We showed that, during the sampling from flames, the relative change in concentrations for most of the stable species does not exceed 3% and, for H 2 and O2, it does not exceed 12%. Results of experiment and calculation are in good agreement.

4. Flame Structure of A P and AP-Based Composite Propellants The homogeneous condensed mono-propellants: AP, RDX and ADN have been examined in detail. They have simple chemical structures, so they provide good models for studying combustion mechanisms. They are also the main components of commonly-used composite solid propellants so knowledge of their combustion mechanisms is essential to developing compositesolid propellant combustion models. An AP flame preheated to 533 K was studied at 0.6 and 1 atm using MPT 3 2 and MBMS. 21 Figure 2 presents the results of some peak intensity profile measurements obtained with MBMS probing of an AP flame preheated to 533 K at 1 atm. 21 These experiments showed detection of mass peaks for m/e equal to 83 and 100 — characteristic of perchloric acid. Thus, these experiments provided the experimental support of the hypothesis that perchloric acid is the main AP gasification product in the combustion wave and plays a key role in the AP combustion mechanism. This result laid the

84

O. P.

a

i 0.4-

r

n

°

Korobeinichev

H20

02

"°—cr5~~° o

P^T5~

1

HCI

NO 0.1

sv-

NH 0

ctior

102 a. 4-1 o

NO, —rlSn

0.2 1.1 o_

o

nfc —ss 4 - j n o_

r—

1.3

Cl2 CIOH N20

£ o r " £ A -i 2

Fig. 2.

)) ^ a-o—o——o—' N2 I i—iH0 0.2 1.1 1.3 Distance from burner surface (mm)

Distance from burner surface (mm)

AP flame structure (points are for experiment and lines are for calculation).

foundation for modern models of the combustion of AP. Chlorine dioxide and fragmentary ions of perchloric acid contribute to mass peak 67. We estimate that, at L = 0 to 0.05 mm, the contribution of perchloric acid to the intensity of mass peak 67 is about 50%. This means that the concentration of chlorine dioxide and perchloric acid are approximately equal near the burning surface. Because of this near-equality, when analyzing MPT data, we assumed that half of the intensity of mass peak 67 came from chlorine dioxide in the flame and the other half from chlorine dioxide formed by heterogeneous catalytic decomposition of perchoric acid on the probe walls. Radicals, like HO2, also recombined on the probe walls. Other species concentrations were determined using the measured calibration coefficients of individual species and mass-peak intensities obtained using MPT to study AP flames at 0.6 atm and 533 K. The ratio between the intensity of the perchloric acid peaks with m/e 83 and those of chlorine dioxide with m/e 67 (the latter being obtained with regard to the fact that the peaks with m/e 83 from perchloric acid contributes to the peaks with m/e 67) is shown in Table 1. This ratio (the intensity of the perchloric acid peaks with m/e 83 is equal to those of chlorine dioxide with m/e 67) was used when correlating the data obtained in setup No. 1, under which conditions chloride dioxide resulting

Energetic Material Combustion

Chemistry

85

Table 1. Species mass peaks intensities (in relative units) at different L in AP flame (a setup with molecular-beam sampling). L (micron)

0 230 290 310 200

100 65 190 230 130

50 140 280 270 180

150 10 90 160 90

200 0 20 80 30

250 0 0 0 0

from heterogeneous catalytic decomposition of perchloric acid on the probe walls into CIO2 and HO2 contributes to a peak with m/e = 67. Using the results of measuring calibration coefficients by individual species and mass peak intensities of the species obtained in the experiments in setup No. 1 studying AP flame structure at 0.6 atm (533 K), species concentrations were found. Profiles of species concentrations and temperature versus the distance from the burner surface L are presented in Fig. 2. Concentration profiles in an AP flame show the following two-zone structure: in a narrow (~fl.lmm wide) zone, NH 3 , HCIO4 and C10 2 concentrations fall and N 0 2 concentrations rise, and in the next wide (~1.5mm wide) zone N 0 2 concentrations fall while NO and 0 2 concentrations rise. Figure 2 also represents modeling results for the same flame structure (lines) 43 ' 44 performed using a mechanism incorporating 80 reactions. The reduced mechanism is presented below. C10 3 = C10 + 0 2 ,

(1)

NH 3 + CI = NH 2 + HC1,

(11)

C10 2 + CI = 2C10,

(2)

OH + HNO = H 2 0 + NO,

(12)

2C10 = Cl2 + 0 2 ,

(3)

HC10 4 = 0 H + C10 3 ,

(13)

C10 + NO = Cl + N 0 2 ,

(4)

HCIO4 + HNO

CIO + NH 3 = NH 2 + C10H,

(5)

0 H + HC1 = H 2 0 + C1,

(6)

N 0 2 + N 0 2 = 0 2 + 2NO,

(15)

CI + 0 2 + M = C10 2 + M,

(7)

NH 3 + OH = NH 2 + H 2 0 ,

(16)

HNO + 0 2 = N 0 2 + OH,

(8)

HCIO4 + HNO

NH 2 + 0 2 = HNO + OH,

(9)

ClOH + OH = CIO + H 2 0 ,

(10)

= C10 3 + NO + H 2 0 ,

= C10 2 + N 0 2 + H 2 0 .

(14)

(17)

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O. P.

Korobeinichev

Satisfactory agreement between the calculation and experimental results provides evidence for the suggested mechanism. Subsequent work provides a revised mechanism. 45 The obtained results were used when developing an AP combustion model. 4 6 - 4 9 Lin et al. have investigated unimolecular decomposition of perchloric acid and the related OH + C10 3 reaction 50 as well as C10 x reactions and the reaction of OH with CIO by ab initio molecular orbital and variational transition state theory calculations. It allows us to refine chemical kinetics models of reactions in AP flames. The flame structure of composite propellants based on AP (particle size less than 50 micron) and HTPB was studied at subatmospheric pressures in setup No. 1 with MPT and modeling. 51-53 Eighteen stable species (HC1, H 2 0 , CO, NH 3 , C 0 2 , HCIO, NO, 0 2 , H 2 , N 0 2 , N 2 0 , N 2 , C 4 H 6 , C 2 H 2 , CIO2, Cl 2 , HCN, HCIO4) were detected in the flame zone. No mass peaks 83 and 100 were found but HCIO4 concentration was determined as it was for the AP flame. Profiles of species concentrations and temperature in flames of model composition HTPB/AP (16/84) at 0.08 atm are shown in Fig. 3.

Fig. 3.

A P / H T P B flame structure.

Energetic Material Combustion Chemistry

87

Kinetics model includes 58 reactions and 35 species. Satisfactory agreement between the experimental and calculated d a t a was achieved. T h e reactions of oxidation of ammonia and H T P B destruction products with perchloric acid decomposition products (CIO2, ClOH, CIO, etc.) are the main reactions in the flame of composite propellants based on A P and H T P B . T h e chemical transformations in the A P / H T P B flame is shown in Scheme 1. T h e d a t a analysis of flame structure of composite propellant based on A P and H T P B (especially rich formulations) at low pressure indicates t h a t oxidation of hydrocarbon binder destruction products occurs in the flame

C4H6

+ C 1

-

»-C 4 H 5 (l,3)

/-C 4 H 5 (1,3) + CIO C4H4

C2H2 + C2H3

^ - » - CH 2 CO

CHO + C H 2 0

CO + H 2 NH,

+ C1 NH 2 + HC1

+ o2

HNO + OH +H + OH

+ NO N2H +

HC10 4

+ HNO ^ + HCO

OH

CIO,

NO

cio + o 2 + CO CI

cio2

+ CO

•

cio + co + CO Cl-<-co2 Scheme 1.

88

O. P.

Korobeinichev

much faster than ammonia oxidation. The obtained data were used when developing a combustion model of AP composite propellants. 54 The flame structure of a sandwich system consisting of alternating laminas of AP and polymerized mixtures of fine-grained AP and polybutadiene binder ("base" lamina) was studied in Refs. 55-57. The profiles of concentrations for 17 stable species and of temperature for three cross-sections corresponding to the middle of the AP lamina, to the middle of the "base" lamina, and to the interface between the laminas have been determined. The hypothesis assuming the existence of three types of flames at the boundary of the AP particle and the binder in composite SP have been verified and confirmed experimentally. It was observed that the concentration gradient of fuel species at the burning surface of the AP is directed towards the burning surface. A modeling of the flame structure sandwich system has been carried out. The ignition of the pseudo-propellants AP/HTPB and AP/PMMA and its transition to the combustion under C0 2 -laser radiation was investigated at 0.1 MPa of argon using MBMS. 25 The initial distance between the orifice of the probe and the surface of the propellant was equal to 0.1-0.15 mm. The perchloric acid and ammonia, the key species of SP gasification during its ignition and combustion were detected. In addition, the dependencies of mass peak intensities of gasification products on time during and after propellant ignition were determined. The data on propellant gasification products during the ignition with simultaneous measurement of temperature of gas phase near the burning surface were obtained in some experiments.

5. R D X and H M X Flame Structure The results of studying the flame structure in the high temperature zone of the RDX flame at 0.5 atm 2 8 ' 5 8 using the MBMS technique are shown in Fig. 4. The burning surface was identified, with allowance for the sampling shift ZQ calculated from the above mentioned formula (a.§ = 70, d0 = 0.1mm). These results show that the key species in the RDX high temperature flame zone are NO and HCN. The main reaction in the high temperature zone of the RDX flame is the reaction HCN + NO and not C H 2 0 + NO2 as was previously postulated. 59 Figure 4 also shows calculated profiles of mole fraction from the results of Ermolin et al.58 The calculations are in satisfactory agreement with the experimental data. List of the

Energetic Material Combustion

T, K

a, 0.3-

HzO

1 0.2 -

TNT

KJ

T

~~

o

0.3 - -3000

fraction

<Xi

89

Chemistry

CO

0)

-fc 4>

§0.1-

J \HCN 4ooo\s\ ?

o 5 0.1-

HNCO^. J =^L_?NO

co2 £^N 2 0

2 Distance from burning surface (mm)

0

N0 2 1

1

2 1 Distance from burning surface (mm)

Fig. 4. Temperature and species mole fraction profiles in RDX flame at 0.5 atm (points are for experiment and solid line for modeling).

most important reactions in high temperature flame zone selected from the full mechanism is presented below. HCN + OH = CN + H 2 0 ,

(18)

C 0 2 + H = OH + CO,

(28)

CN + NO = CO + N2,

(19)

NH + OH == N + H 2 0 ,

(29)

HCN + OH = NH 2 + CO,

(20)

NH + H = N + H 2 ,

(30)

N 0 2 + H = NO + OH,

(21)

NH 2 + OH = H 2 0 + NH,

(31)

NO + N = N 2 + O,

(22)

OH + H2 = H 2 0 + H,

(32)

NO + H + M = HNO + M,

(23)

NH 2 + NO = N 2 H + OH,

(33)

2HNO = H 2 0 + N 2 0 ,

(24)

N 2 H + NO = HNO + N 2 ,

(34)

H 2 + O = OH + H,

(25)

OH + N 2 0 = N 2 + H 0 2 ,

(35)

C 0 2 + M = CO + O + M,

(26)

H 0 2 + NO = N 0 2 + OH,

(36)

H 2 0 + O = 20H,

(27)

NH + NO == N 2 + O + H.

(37)

Melius' mechanism 60 ' 61 provided better agreement with the experimental results as compared with that of Ermolin et al.58 Later Ermolin 62 refined the mechanism and obtained better agreement with experiment than in Ref. 58. The obtained data have also been used by other researchers 63-66 when developing and validating detailed RDX combustion mechanisms and models. The analysis of experimental data 28 and Melius' model 60,61 predict the existence of a narrow "cool" flame zone (less than 0.1mm at 0.5 atm), where RDX vapor decomposition takes place.

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The flame structure at RDX self-sustained combustion at 1 atm has been studied using planar laser induced fluorescence (PLIF) and UV/vis absorption spectroscopy.14 Profiles of NO, N 0 2 , OH, NH, CN concentrations and of temperature have been measured. Some later similar measurement and modeling have been done in Ref. 67 and compared with data of Ref. 14. Results 67 of modeling RDX self-sustained combustion are in a good agreement with modeling results of Lian and Yang. 63 Low temperature flame zones in RDX and HMX flames have been studied by different authors 14 ' 68 ' 69 mainly using thin thermocouples. Some of the investigators reported a plateau on the temperature profile near the burning surface of a temperature of ~1000K. This plateau would provide support for the hypothesis of a narrow zone in "cool" flames where RDX or HMX vapor decomposition takes place. Other researchers 69 ' 14 however did not confirm this fact. The study of a narrow zone (~0.1mm wide) in an RDX flame using MPT with a probe having an orifice of about 0.01 mm could lead to erroneous conclusions. This is due to the fact that in this case the RDX vapors would be hardly detectable through their possible heterogeneous catalytic decomposition at the microprobe walls (similarly to HCIO4 decomposition at microprobe walls in AP flame). Due to the difficulties in MBMS study of flame zones less than 0.1 mm wide, there is to date no direct experimental evidence of the existence of RDX vapor decomposition in RDX flames. Nevertheless, in combustion models the existence of such a zone is supposed. This problem is to be solved in the future. There is much that is common to HMX and RDX flame structures, but there are differences as well. As is apparent from profiles of mass peak intensities in an HMX flame at 1 atm, 6 ' 70 and sandwich systems based on HMX, 55 ' 56 two clearly defined subzones are seen in the high temperature zone of the HMX flame. CH 2 0 and N 2 0 decomposition takes place in the first one, while HCN oxidation with nitrogen oxide, as in the RDX flame, takes place in the second. It should be noted that NO2 and CH2O were also found in the RDX flame at 0.5 and 1 atm. However, mass peaks at intensities of 46 (N2O) and 29 (CH2O) were detected in those cases to a much lesser extent. These observations are also confirmed by results of spectroscopic study. 14 The results obtained for HMX flame structures were used when developing the HMX combustion model. 71 CO2 laser-assisted combustion of RDX and HMX at 1 atm and the structure of a flame were studied in Refs. 14, 16, 23, 38, and 72-75. As comparison of temperature profiles in flames at self-sustaining (flame 1) and laser-assisted (flame 2) combustion shows, they strongly differ. In flame 2

Energetic Material Combustion

Chemistry

91

there is a dark zone and two-stage form of temperature profile,1 which is not observed in flame l. 69 It is necessary however, to note the distinction in the form of the temperature profiles received in Refs. 14 and 23: there is no plateau on the temperature profile at a distance of 1-2 mm from a burning surface in Ref. 23, which was observed in Ref. 14. The basic chemical processes going on in a dark zone of width 0.5 mm, adjusting to a burning surface, are the reactions of HCN oxidation and NO2 decomposition with NO formation. In the second luminous zone there is a further HCN oxidation with NO with formation of N2 and CO. There are also contradictions in the CH2O concentration in Refs. 23, 38, and 72. The results of modeling the RDX flame structure at laser-assisted combustion 38,62,66 ' 75 do not correspond with the results of experiment. Similar situations can be seen in the case of HMX laser-assisted combustion. 73 There is not enough understanding in HMX laser-assisted combustion chemistry. One of the reasons for the contradictions in the received results of the study of RDX and HMX laser-assisted combustion is probably error connected with the use of a microprobe method, which results in strong thermal disturbance of a flame by a probe with thick walls, and catalytic decomposition of a sample on the internal walls of a hot probe. The differences in RDX and HMX flame structure in self-sustained and laser-assisted combustion support the suggestion that the chemical combustion mechanisms are different in these two processes. So it is not possible to apply the laser-assisted combustion model for the development of a combustion model for self-sustained combustion of EM.

6. Flame Structure of A D N and A D N - B a s e d Propellants ADN is a new energetic material which can be used as an oxidizer in solid rocket propellants. 76 It presents an alternative to ammonium perchlorate (AP), being an ecologically pure oxidizer in solid propellants. ADN is a simpler mono-propellant than AP and RDX, as defined both by the number of elements and by the possible intermediate and final combustion products. In the last few years several works devoted to the study of the ADN combustion mechanisms have been published. 22 ' 27 ' 77 ^ 84 To understand the mechanism of the primary stage of ADN decomposition, and to study the mechanism and kinetics of secondary reactions of ADN decomposition products, two-temperature flow reactors combined with MBMS 27,85 and MPT 8 6 were used. ADN was heated at low pressure (6-10 torr) in the first reactor at temperature 350-410 K. Then decomposition products entered and reacted in the second reactor

92

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Korobeinichev

at temperature 430-1170 K. Authors of Ref. 86 assumed that products of ADN decomposition in the first reactor are products of ADN dissociative sublimation: dinitraminic acid (DA) and ammonia. They measured and calculated concentrations of four species (NH3, N2O, fi20,N 2 ) in products of thermal decomposition DA + NH3 in the second reactor at 370-920 K using the suggested model, involving 152 reactions. They also developed a kinetic model for dinitraminic acid thermal decomposition at low pressure. Authors of Refs. 27 and 85, based on the detailed study of the mass spectrum of products of ADN decomposition in the first reactor as well as the mass spectra of DA and ammonia using MBMS, came to the conclusion that ADN evaporation takes place in the first reactor. ADN decomposition at 350-410 K in a How reactor at 6-10 torr showed that more than 90% of ADN deposited on the cold walls of the tube at the exit of the flow reactor. Temperature dependence of ADN vapor pressure lg P = 18.32 — 8.09 x 10 3 /T, P (torr), T (K) was determined. Sublimation (evaporation) heat is AHsuhi = 37 ± 3 kcal/mole corresponding to this dependency, which is close to the calculated results, 38 kcal/mole, obtained in Ref. 87. From theoretical study it was suggested that the next mechanism of ADN thermal decomposition is: AH = 38 kcal/mole ADNS

> HN 3 [HN(N0 2 ) 2 ]

AH = 12-14 kcal/mole > NH 3 + HN(N0 2 ) 2

The kinetics and mechanism of the secondary reactions of ADN vapor decomposition at 6 torr have been studied 85 using MBMS and modeling based on kinetic mechanism. 86 The additional experimental evidence of ADN evaporation has been obtained: NH3 concentration increased in the temperature range 430 to 530 K. The authors of paper 86 did not notice this fact because they did not take into account the contribution of the fragmentary ion of ADNV to the intensity of mass peaks 17 and 16. Also if ADN decomposition yielding DA and NH3 was the first stage of the process, the temperature dependence of DA + NH3 vapors would correspond to AiJ su bi = 25-26 kcal/mole but not to AHSU\,\ = 37 ± 3 kcal/mole. The rate constant of ADNV dissociation ADNV + M —»• NH3 + HN(NC>2)2 + M has been determined from experimental data k = 3 x 10 12 exp(—12000/RT), cm 3 mole - 1 s _ 1 . These conclusions are in good agreement with the data of Ref. 87. So the mechanism of ADN evaporation differs from that of other ammonium salts. In the case of ammonium perchlorate and ammonium nitrate, dissociative sublimation takes place, yielding ammonia and the corresponding acid. The obtained mass spectra

Energetic Material Combustion

Chemistry

93

of ADN vapor allowed us to identify it in the "cool" flame zone at 1 and 3 atm and to measure its concentration. The temperature distribution in the wave of ADN combustion has been measured using thin thermocouples in a wide pressure range which has revealed several burning zones. The composition of ADN combustion products has been determined by the authors of paper 79 at 0.26-0.78 atm. But the purity of ADN in this study 79 was very bad. ADN combustion mechanisms suggested in Refs. 27, 78, 79, 83 are different. Thus, it is suggested in Refs. 79 and 83 that ADN reactions in the condensed phase result in ammonium nitrate. The dissociation of ammonium nitrate yielding NH 3 and H N 0 3 controls the temperature of ADN burning surface and, therefore, the burning rate. Another mechanism has been discussed in Refs. 27 and 82. It is based on the results of studying the chemical structure of the ADN flame at 1-6 atm using an MBMS and the microthermocouple technique. 27 The flame structure was found to involve three zones. At 1-3 atm a luminous flame zone was not observed. The burning rate at 1-6 atm is controlled by reactions in the condensed phase. At 3 atm a "cool" flame zone adjacent to the burning surface was found. The width of this zone is about 1-1.5 mm. The following species have been identified in the "cool" flame zone: HNO3, N0 2 , N 2 0 , NH 3 , NO, N 2 , H 2 0 and ADN vapor. The ratio between the mass peak intensities in the mass spectra of samples taken from the zone close to the ADN burning surface at 3 atm and those of ADN decomposition products 27 ' 85 are in reasonable agreement. The analysis of the mass spectra of the samples taken from the zone near the ADN burning surface at 3 atm has shown that gaseous ADN and dinitraminic acid are the key reactants in the near-surface zone. The product composition near the ADN burning surface has been determined. Gaseous ADN and dinitraminic acid decomposition in the near-surface zone results in a temperature rise of about 150 K. The second high temperature zone was found to be 6-8 mm from the ADN burning surface at 6 atm (Fig. 5). The main reaction in this zone is ammonia oxidation by nitric acid, while the temperature rise is 500 K. The combustion temperature is 1400 K and the combustion products are H 2 0 , NO, N 2 0 , N 2 . The ADN flame structure studied at a pressure of 40 atm 80 revealed the presence of three zones of chemical transformations. The first, a low-temperature ~0.1mm wide zone associated with the rise in temperature from 640 to ^970 K which is similar to the ~ 1 mm wide zone obtained in ADN burning at 3-5 atm. The second is a 1 mm wide zone associated with the rise in temperature from 970 to ^1370 K which is similar to the ~ l l m m wide zone found in the burning of ADN at 5-6 atm. The third zone is at a distance of ~ 1 to

94

O. P.

4

Korobeinichev

8

Distance from burning surface (mm) F i g . 5.

S p e c i e s m o l e f r a c t i o n profiles in A D N flame a t 6 a t m , e x p e r i m e n t a l r e s u l t s .

T a b l e 2.

P r o d u c t c o m p o s i t i o n in A D N

flame.

P (atm)

L (mm)

NH 3

H20

N2

NO

N20

ADN V

HNO3

02

3 6 40

0.2 4.4 1.5

0.08 0.07 0

0.30 0.30 0.42

0.08 0.10 0.18

0.19 0.23 0.21

0.24 0.28 0.14

0.03 0 0

0.08 0.02 0

0 0 0.05

6 mm from the burning surface and is associated with N2O consumption. The temperature in it increases from 1370 to 1770 K. The width of the third zone depends on the ADN burning rate. ADN combustion product compositions at 3 and 6 atm at different distances (L) from the burning surface are shown in Table 2. The temperatures, product compositions measured at the distances L = 0.2, 4.4 and 1.5 mm at 3, 6 and 40 atm and product mass flows were used as boundary conditions in the modeling of the ADN flame using CHEMKIN Code 88 and based on the developed mechanism (98 reactions and 22 species). Part of these reactions and their rate constants have been calculated and suggested by Park et al.m The results of temperature and species concentration profile calculations 80,82,84 are in a good agreement with experimental data. The calculation has also shown the existence of a fourth zone at higher pressures, where nitric oxide decomposes to nitrogen and oxygen with a temperature rise to a value (^2100 K) close to the thermodynamic equilibrium temperature. The results of sensitivity analysis for most of the important reactions in all flame zones are presented in Table 3. ADN combustion chemistry is described in Scheme 2. The obtained data is applicable for developing an ADN combustion model.

Energetic Material Combustion Table 3.

The most important reactions in ADN flame.

Zone number 1

Chemistry

Reaction 73. NH 3 + OH = NH 2 + H 2 0 111. HN3O4 = HNNO2 + NO2 114. HNNO2 + NO2 = HNO + NO + N 0 2 134. HNNO2 + NO = HNNO + N 0 2 135. HNNO2 + NO = HONO + N 2 0 172. ADN V + M = NH 3 + HN3O4 + M

2

36. NO + OH(+M) = HONO(+M) 65. NH 2 + NO = NNH + OH 66. NH 2 + NO = N 2 + H 2 0 73. NH 3 + OH = NH 2 + H 2 0 94. HONO + OH = H 2 0 + NO2 101. N 2 0 + NO = NO2 + N 2 105. NO + NO = N 2 + O2

ADN.

- • ADN,,

-• HN(N02)2 + NH3

HN4NO3 + N 2 0 Products * N H 3 + HNO3 I zone (>3 atm):ADN v

Products

-* HN(N0 2 ) 2 + N H 3

I Products II zone (>6 atm): HNO3+NH3 III zone (>40 atm): N 2 0 IV zone (>40 atm): NO

• Products

• N 2 + V202 •

!/2N2 + V2O2

Scheme 2.

95

96

O. P.

Korobeinichev

The flame structure of the composite pseudo-propellants based on ADN and several binders, such as PCL, HTPB and glycidyl azide polymer (GAP), was studied using MBMS. 81,89 ^ 92 Combustion of stoichiometric compositions based on ADN and PCL has been studied in details. 89,91,92 The combustion of PCL/ADN (10,92/89,08) and HTPB/ADN (3/97) propellants at 1 atm is jet-like in nature. Video-recording demonstrated the presence of several brightly luminous jets of about 0.5-1 mm in diameter at the burning surface, disappearing at one site and appearing at another with a lifetime of 0.2 s. The spatial heterogeneity and non-stationary nature of the propellant combustion process is in agreement with mass spectrometric and temperature measurements. The videotape recording of ADN/PCL combustion showed that a dark zone exists near the burning surface. The width of the dark zone varies from ~ 1 mm (near the bottom of the torch) to 3-4 mm (in the region between torches). Thermocouple measurements revealed the existence of three zones in the flame (1) the narrow dark zone adjacent to the burning surface (width of the zone ~0.2-0.3 mm), where the temperature grew from ~600 to ~1150 K, (2) the dark zone (width of the zone is ~0.5 to ~3mm) where the temperature slightly increased from 1150 to 1450 K, (3) the luminous zone (torch), where the temperature increased to 2600 K at the distance of 4-8 mm. Compositions of the combustion products in the luminous and dark flame zones of propellant ADN/PCL (molecular weight PCL 1250) are presented in Table 4. The temperature of the combustion products in the luminous zone, which is equal to 2600 K, is slightly less than the calculated equilibrium temperature (2695 K), i.e. 100% completeness of combustion is not achieved. The presence of NO in combustion products confirms this conclusion. The element balance in the luminous

Table 4. Concentrations (in mole fractions) of species and temperature in flame of propellant A D N / P C L at 1 atm and of ADN at 6 atm.

Luminous zone (exp) Thermodynamic calc. Dark zone (exp)

T (K)

H20

N2

~2600

0.39

2695 0.40 ~1120

0.32

N20

NO

NH 3

0.32

0

0.10

0

0.34

0

0.01

0.11

0.20

0.20

HNO3

H2

CO

C02

02

0

0.03 0.02

0.12

0.02

0

0

0.03 0.05

0.09

0.03

0.04

0.01

0.01 0.02

0.08

0.01

Energetic Material Combustion

Chemistry

97

zone was in satisfactory agreement (±5%) with that in the propellant. The calculated deficiency of carbon in the combustion products determined in the dark zone is equal to ~50% of the initial amount. This fact indicates that identification of carbon-containing products in the dark zone was incomplete. Besides, peaks of the following unidentified masses in the mass spectrum of species near the burning surface of the propellant have been obtained: 55, 57, 60, 67, 69, 70, 71, 73, 79, 81, 95, 108, 115. It was assumed that masses from 55 to 115 are responsible for the decomposition of PCL. For propellant HTPB/ADN (3/97) at 6atm, video-recording near the burning surface revealed a dark zone of ~0.3mm, which was in agreement with the data obtained when studying the flame structure of ADN-based sandwiches.90 The dark zone width increases up to 1.5 mm as pressure is reduced to 1 atm. Thermocouple investigations have shown temperature fluctuations of about ±400 K at 1 atm in the flame zone within 1.5-4 mm from the burning surface. Along with the temperature fluctuations, variations in the intensities of mass peaks 17 (NH3), 28 (CO, N2), 30 (NO), 46 (HNO3, N 0 2 ) , 44 (C0 2 , N 2 0) take place. The values for mass peak relative intensities of combustion products near the burning surface of ADN/HTPB 97/3 propellant and pure ADN at 1 atm are close. Analyzing the data on mass peaks intensities in the mass spectra of samples near a burning surface of ADN and ADN/HTPB at 1 atm, one can suggest that pure ADN combustion products are mainly found in the dark zone of propellant combustion, and that luminous jets are formed in the gas phase when ADN decomposition products are mixed with HTPB decomposition products. One of the explanations for the presence of luminous jets with a mean size of ~0.5-l mm at the burning surface may be the agglomeration of small ADN and (or) binder particles into larger ones at the burning surface. The combustion product composition of composite propellant ADN/HTPB 97/3 at 1 atm approaches the product composition of pure ADN combustion at 6 atm, in the content of nitrogen-containing components. So ADNHTPB interaction in flame provides an increase in final temperature and ADN combustion completeness.

7. Conclusions By the example of the study of the flame structure of AP, RDX, HMX, ADN and some propellants, the probing mass-spectrometry procedure has been shown to be an indispensable method providing important information on

98

O. P. Korobeinichev

E M chemical combustion mechanisms. Although it is limited t o some extent by pressure, flame zone width and other considerations, the results obtained with its aid have successfully been used to understand the chemical reaction mechanisms of E M combustion and to develop combustion models. Further application of this method, as well as other spectroscopic and thermocouple methods, will allow a refined and widened understanding of E M combustion mechanisms.

References 1. T. Edwards, Solid Propellant Flame Spectroscopy, Air Force Astronautics Laboratory, AFAL-TR-88-076, Edwards AFB, CA (1988). 2. Y. B. Zel'dovich, J. Exp. Theoret. Phys. 12, 498 (1942), in Russian. 3. R. M. Fristrom, Flame Structure and Processes (Oxford University Press, New York, 1995). 4. O. P. Korobeinichev, Combust. Explos. Shock Waves 23, 565 (1988). 5. O. P. Korobeinichev, Pure Appl. Chem. 65, 269 (1993). 6. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky and A. A. Chernov, Combust. Sci. Technol. 113-114, 557 (1996). 7. 0 . P. Korobeinichev, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 335. 8. T. A. Litzinger, Y. J. Lee and C. J. Tang, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 355. 9. T. A. Litzinger, Y. J. Lee and C. J. Tang, in Proc. Workshop on the Application of Free-Jet, Molecular Beam, Mass Spectrometric Sampling, National Technical Information Service (NTIS), US, Department of Commerce, Springfield, VA, 1994, p. 128. 10. J. A. Vanderhoff, M. W. Teague and A. J. Kotlar, Absorption Spectroscopy Through the Dark Zone of Solid Propellant Flame, Ballistic Research Lab. Rept. BRL-TR-3334 (1992). 11. T. P. Parr and D. M. Hanson-Parr, in Non-Intrusive Combustion Diagnostics, eds. K. K. Kuo and T. P. Parr (Begell House Publishing, Inc., New York, 1994), p. 517. 12. J. H. Stufflebeam and A. C. Eckbreth, Combust. Sci. Technol. 66, 163 (1989). 13. T. P. Parr and D. M. Hanson-Parr, in 26th Symp. (Int.) Combustion (The Combustion Institute, Pittsburgh, PA, 1996), p. 1981. 14. T. P. Parr and D. M. Hanson-Parr, in Decomposition, Combustion and Detonation of Energetic Materials, Proc. Mat. Res. Soc, Vol. 418, eds. T. B. Brill, T. P. Russell, W. C. Tao and R. B. Wardle (1996), p. 207. 15. S. H. Modiano and J. A. Vanderhoff, in 26th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, PA, 1996), p. 2017.

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16. T. Parr and D. Hanson-Parr, in Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 381. 17. A. A. Zenin, Fiz. Goreniya Vzryza 2, 67 (1966), in Russian. 18. C. A. Heller and A. S. Gordon, J. Phys. Chern. 59, 773 (1955). 19. O. P. Korobeinichev and A. G. Tereshchenko, Doklady Akademii Nauk USSR 231, 1159 (1976), in Russian. 20. O. P. Korobeinichev, I. N. Skovorodin, E. L. Emel'anov, K. P. Kassheev, S. V. Polozov, A. G. Tereschenko, L. V. Kuibida and V. V. Ivanov, Byulleten' Izobreteney i otkrytiy 30 (1980), in Russian. 21. O. P. Korobeinichev and L. V. Kuibida, in Flames, Lasers and Reactive Systems, Progress in Astronautics and Aeronautics, Vol. 88, eds. J. R. Bowen, N. Manson, A. K. Oppenheim and R. I. Soloukuin (AIAA, New York, 1982), p. 197. 22. B. L. Fetherolf and T. A. Litzinger, in 29th JANNAF Combustion Meeting, Vol. 2, CPIA Publication 593, (1992), p. 329. 23. Y. J. Lee, C. J. Tang and T. A. Litzinger, Combust. Flame 117, 600 (1999). 24. Y.-C. Liau, E. S. Kim and V. Yang, Combust. Flame 126, 1680 (2001). 25. A. G. Tereshchenko, O. P. Korobeinichev, A. A. Paletsky and L. T. DeLuca, in Rocket Propulsion: Present and Future, ed. L. T. DeLuca (Grafiche GSS, Bergamo, Italy, 2003), paper 24. 26. T. B. Brill, Prog. Energy Combust. Sci. 18, 91 (1992). 27. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky and A. G. Shmakov, J. Propul. Power 14, 991 (1998). 28. O. P. Korobeinichev, L. V. Kuibida, V. N. Orlov, A. G. Tereshchenko, K. P. Kutsenogii, R. V. Mavliev, N. E. Ermolin, V. M. Fomin and I. D. Emel'yanov, in Mass-Spektrometriya i Khimia Kinetika, ed. V. Tal'rose (Nauka, Moscow, 1985), p. 73, in Russian. 29. O. P. Korobeinichev, A. G. Tereshchenko, I. D. Emel'yanov, L. V. Kuibida, V. N. Orlov, R. V. Mavliev, K. P. Kutsenogii, A. L. Rudnitskii, S. Yu. Fedorov, N. E. Ermolin and V. M. Fomin, Probe Mass-Spectrometry for Condensed System Flames Having Narrow Combustion Zones (Institute of Chemical Kinetics and Combustion, Novosibirsk, 1985), preprint No. 14, in Russian. 30. O. P. Korobeinichev, A. G. Tereshchenko, I. D. Emel'yanov, A. L. Rudnitskii, S. Yu. Fedorov, L. V. Kuibida, V. V. Lotov and V. N. Orlov, Combust. Explos. Shock Waves 21, 524 (1985). 31. I. D. Emel'yanov, O. P. Korobeinichev, A. G. Tereshchenko and L. V. Kuibida, Combust. Explos. Shock Waves 22, 168 (1986). 32. N. E. Ermolin, O. P. Korobeinichev, A. G. Tereshchenko and V. M. Fomin, Combust. Explos. Shock Waves 18, 36 (1982). 33. P. Rosen, Potential Flow of Fluid into a Sampling Probe, Applied Physics Laboratory, Johns Hopkins University, Rept. CF-2248 (1954). 34. V. V. Dubinin, B. Ya. Kolesnikov and G. I. Ksandopulo, Fizika Goreniya i Vzryva 13, 920 (1977). 35. K. P. Kutsenogii, O. P. .Korobeinichev, R. V. Mavliev and A. G. Tereshchenko, Dokl. Akad. Nauk SSSR 282, 1425 (1985), in Russian.

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36. O. Smith, in Flame Structure and Processes, ed. R. M. Fristrom (Oxford University Press, New York, 1995). 37. A. T. Hartlieb, B. Atakan and K. Kohse-Hoininghaus, Combust. Flame 121, 610 (2000). 38. T. A. Lintzinger, B. L. Fetherolf, Y. J. Lee and C-J. Tang, J. Propul. Power 11, 698 (1995). 39. E. L. Knuth, Combust. Flame 103, 171 (1995). 40. O. P. Korobeinichev, A. G. Tereshenko, P. A. Skovorodko, A. A. Paletsky and E. N. Volkov, in Proc. 18th ICDERS (2001), paper 82-1. 41. A. G. Tereshenko, O. P. Korobeinichev, P. A. Skovorodko, A. A. Paletsky and E. N. Volkov, Fiz. Goreniya Vzryza 38, 91 (2002), in Russian. 42. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereshenko and E. N. Volkov, J. Propul. Power 19, 203 (2002). 43. N. E. Ermolin, O. P. Korobeinichev, A. G. Tereshchenko and V. M. Fomin, Combust. Explos. Shock Waves 18, 180 (1982). 44. N. E. Ermolin, O. P. Korobeinichev, A. G. Tereshchenko and V. M. Fomin, Sovetski J. Khimicheskaya Phizika 1, 2872 (1984), in Russian. 45. N. E. Ermolin, Combust. Explos. Shock Waves 31, 58 (1995). 46. M. Tanaka and M. W. Beckstead, AIAA paper (1996) 96-2888. 47. M. W. Beckstead, J. E. Davidson and Q. Jing, in Challenges in Propellants and Combustion/100 Years after Nobel, ed. K. K. Kuo (Begell House Inc., New York-Wallingford, 1997). 48. H. K. Narahari, H. S. Mukunda and V. K. Jain, in 20th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, PA, 1984), p. 2073. 49. N. Ilincic, M. A. Tanoff, M. D. Smooke, R. A. Yetter, T. P. Parr and D. M. Hanson-Parr, in 34th JANNAF Combustion Meeting, Vol. II, CPIA Publication 662 (1997), p. 23. 50. R. S. Zhu and M. C. Lin, Phys. Chem. Comm. 25, 1 (2001). 51. O. P. Korobeinichev, N. E. Ermolin, A. A. Chernov and I. D. Emel'yanov, Fiz. Goreniya Vzryza 28, 53 (1992). 52. O. P. Korobeinichev, N. E. Ermolin, A. A. Chernov, I. D. Emel'yanov and T. V. Trofimycheva, Fiz. Goreniya Vzryza 26, 46 (1990). 53. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky, A. A. Chernov and N. E. Ermolin, Prep. Pap. Am. Chem. Soc., Div. Fuel Chem. 36, 1582 (1991). 54. M. B. Jeppson, M. W. Beckstead and Q. Jing, AIAA paper (1998) 98-0447. 55. O. P. Korobeinichev, A. G. Tereschenko, V. M. Shvartsberg, G. A. Makhov, A. A. Chernov and A. E. Zabolotnyi, in Flame Structure, Vol. 1, ed. O. P. Korobeinichev (Nauka, Sibirskoe otdelenie, Novosibirsk, USSR, 1991), p. 262. 56. O. P. Korobeinichev, A. G. Tereschenko, V. M. Shvartsberg, G. A. Makhov, A. A. Chernov, A. E. Zabolotnyi and I. D. Emel'yanov, Combust. Explos. Shock Waves 26, 173 (1990). 57. A. A. Chernov, V. M. Shvartsberg, N. E. Ermolin, O. P. Korobeinichev and V. M. Fomin, Prep. Pap. Am. Chem. Soc, Div. Fuel Chem. 39, 188 (1994). 58. N. E. Ermolin, O. P. Korobeinichev, L. V. Kuibida and V. M. Fomin, Combust. Explos. Shock Waves 24, 400 (1988).

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59. M. Ben-Reuven and L. H. Caveny, AIAA J. 19, 1276 (1981). 60. C. F. Melius, in 25th JANNAF Combustion Meeting, Vol. II, CPIA Publication 498 (1988), p. 155. 61. C. F. Melius, in Chemistry and Physics of Molecular Processes in Energetic Materials, ed. S. Bulusu (Boston, Kluver, 1990), p. 51. 62. N. E. Ermolin and V. E. Zarko, Fiz. Goreniya Vzryza 37, 3 (2001). 63. Y.-C. Lian and V. Yang, J. Propul. Power 11, 729 (1995). 64. R. A. Yetter, F. L. Dryer, M. T. Allen and J. L. Gatto, J. Propul. Power 11, 683 (1995). 65. J. J. Cor and J. J. Branch, J. Propul. Power 11, 704 (1995). 66. K. Prasad, R. A. Yetter and M. D. Smooke, AIAA paper (1996) 96-0880. 67. B. E. Homan, M. S. Miller and J. A Vanderhoff, Combust. Flame 120, 301 (2000). 68. T. Niioka, T. Mitani, H. Miyajima, N. Saito, T. Sohue, K. Ninomiyya and L. Aoki, The Fundamental Study of HMX Composite Propellant and its Practical Application, National Aerospace Laboratory Report, TR-875 (1985). 69. A. Zenin, J. Propul. Power 11, 752 (1995). 70. O. P. Korobeinichev, L. V. Kuibida and V. Jh. Madirbaev, Combust. Explos. Shock Waves 20, 282 (1984). 71. A. Bizot and M. W. Beckstead, in Flame Structure, Vol. 1, ed. O. P. Korobeinichev (Nauka, Novosibirsk, 1991), p. 230. 72. D. Hanson-Parr and T. Parr, in 25th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburg, PA, 1994), p. 1635. 73. C. J. Tang, Y. J. Lee, G. Kudva and T. A. Litzinger, Combust. Flame 117, 170 (1999). 74. T. P. Parr and D. M. Hanson-Parr, in 35th JANNAF Combustion Meeting, CPIA Publication 685 (1988), p. 87. 75. J. E. Davidson and M. W. Beckstead, in 26th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburg, PA, 1996), p. 1989. 76. Z. Pak, AIAA paper (1993) 93-1755. 77. B. L. Fetherolf and T. A. Litzinger, Combust. Flame 114, 515 (1998). 78. A. A. Zenin, V. M. Puchkov and S. V. Finjakov, AIAA paper (1998) 99-0595. 79. V. A. Strunin, A. P. D'Yakov and G. B. Manelis, Combust. Flame 117, 429 (1999). 80. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko and T. A. Bolshova, in Combustion of Energetic Materials, ed. K. K. Kuo (Begell House Inc., New York, Wallingford, 2001), p. 486. 81. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko, E. N. Volkov, J. M. Lyon, J. G. Carver and R. L. Stanley, in 32nd Int. Ann. Conf. ICT, Karlsruhe, Germany, 3-6 July, 2001, paper 123-1. 82. O. P. Korobeinichev, T. A. Bolshova and A. A. Paletsky, Combust. Flame 126,1516(2001). 83. A. E. Fogelzang, V. P. Sinditski, V. Y. Egorshev, A. I. Levshenkov, V. V. Serushkin and V. I. Kolesov, in 28th Int. Ann. Conf. ICT, Karlsruhe, Germany, 1997, paper 99-1.

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84. O. P. Korobeinichev, L. V. Kuibida, A. A. Paletsky and A. G. Shmakov, in Proc. 21st Int. Symp. on Space Technology and Sciences, Vol. 1 (Society for Aeronautical and Space Sciences, Tokyo, 1998), p. 87. 85. A. G. Shmakov, O. P. Korobeinichev and T. A. Bolshova, Combust. Explos. Shock Waves 38, 284 (2002). 86. J. Park, D. Chakraborty and M. C. Lin, in 27th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, PA, 1998), p. 2351. 87. A. M. Mebel, M. C. Lin, K. Morokuma and C. F. Melius, J. Phys. Chem. 99, 6842 (1995). 88. R. J. Kee, J. F. Grcar, M. D. Smooke and J. A. Miller, Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia Rept. SAND85-8240, Livermore, CA, 1989. 89. O. P. Korobeinichev and A. A. Paletsky, Combust. Flame 126, 151 (2001). 90. L. V. Kuibida, O. P. Korobeinichev, A. G. Shmakov, E. N. Volkov and A. A. Paletsky, Combust. Flame 126, 1655 (2001). 91. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko and E. N. Volkov, J. Propul. Power 19, 203 (2003). 92. O. P. Korobeinichev, A. A. Paletsky, A. G. Tereschenko and E. N. Volkov, in Proc. Combustion Institute, Vol. 29 (2002), p. 2955. 93. A. A. Zenin, Fiz. Goreniya Vzryza 2, 67 (1966), in Russian.

CHAPTER 4 OPTICAL S P E C T R O S C O P I C M E A S U R E M E N T S OF ENERGETIC MATERIAL FLAME STRUCTURE Tim Parr* and Donna Hanson-Parr Naval Air Warfare Center, Weapons Division Code 4T4320D China Lake, CA 93555-6106, USA * Timothy. ParrQnavy. mil 'Donna. Hanson-ParrQnavy. mil

Contents 1. Propellant Combustion Environment 1.1. Global Data 1.1.1. Burning Rates 1.1.2. Ignition Data 1.1.3. Radiative Response Function 1.2. Nature of Combustion Environment 1.2.1. Effect of Pressure on Flame Structure 1.2.2. Two-Stage Flames 2. Optical Spectroscopic Techniques Applied 2.1. Absorption and Emission Spectroscopy 2.2. Laser-Induced Fluorescence 2.3. Raman 2.4. CARS and DFWM 2.5. Uncertainties in Concentration and Temperature Measurements 3. Neat Nitramines 3.1. Deflagration 3.1.1. Laser-Supported Deflagration 3.1.2. Self-Deflagration 3.2. Ignition 4. Homogeneous Nitramine Propellants 5. Ammonium Perchlorate (AP) 5.1. One-Dimensional Counter Flow AP/Fuel Diffusion Flames 5.2. Two-Dimensional AP/Fuel Diffusion Flames 6. Summary References 103

104 104 104 105 106 106 107 107 108 108 110 110 111 112 113 113 114 117 118 119 120 120 122 123 126

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1. Propellant Combustion Environment Some important solid propellant performance properties, such as specific impulse and flame temperature, can be easily calculated thermodynamically. However, most properties critical to the design of rocket motors, such as burning rate, pressure exponent, temperature sensitivity, combustion instability response, and hazard response, are kinetically controlled and cannot be calculated using thermochemical codes. Some progress has been made recently in developing solid propellant combustion models based on detailed chemical kinetics. These codes offer hope of being able to a priori calculate the performance of a solid propellant even before it is formulated and mixed. With the addition of quantum mechanical calculations, these predictions of propellant performance could be undertaken even before new candidate energetic materials had been synthesized. If such tools were available, it would greatly reduce the cost of developing new solid propellants, as it would reduce the costly trial and error formulation, mixing, casting, and performance evaluation work. These tools must be validated, and since they provide detailed information on species concentrations, one good way to validate the models is to make spatially-resolved measurements of species concentrations in solid propellant flames. Optical diagnostics have proven to be useful in this task, especially when combined with complementary techniques such as mass spectrometry (see the chapter by Korobeinichev). 1.1. Global

Data

1.1.1. Burning Rates In the recent past, most models of propellant combustion were validated by comparison with measured burning (regression) rate as a function of pressure (P), and sometimes as a function of both P and initial temperature (To). Much regression data is available in the literature. For example, burning rate (r) data has been measured from To = — 100°C to +150°C, and P = latm-8000 PSIA for HMX, 1 and from T0 = -50°C to +150°C, P = 100-1500 PSIA for RDX. 1 The burning rates were found to have an essentially linear pressure dependence, r = A'Pn, over most of the pressure range. It is easy to fit a two-parameter result, even with simple global kinetic models like BDP (Beckstead-Derr-Price). 2 However, good quality fits to burning rate data can be obtained with wildly differing "global" kinetic parameters and, thus, these models do not uncover the real controlling

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kinetic mechanism. These simple models, therefore, cannot be used to predict ignition, combustion instability (CI), or be directly used for other families of propellants for which they were not directly parameterized via fitting to measured data. From the burning rate data sets, the temperature sensitivity (ap) can be calculated: dp = (d In (r)/<9T0)

at constant P

where To is the initial temperature of the sample. Being able to fit the temperature sensitivity is a more stringent test of a model for combustion. HMX at low P, high T0 shows a flattening out of the regression curve as P decreases, so that the simple equation for r is not valid at low pressures. Models often do not recover that behavior, so the T sensitivity for HMX at the lowest pressures is not accurately predicted. This low-pressure behavior may be indicative of condensed phase heat release. At high pressures, the heat input to the surface is provided mainly by the flame, whereas at low pressures, the flame standoff is much taller, and the heat provided by exothermic condensed phase reactions becomes more important. This reduces the pressure dependence and likely causes the lowering of the pressure exponent. 1.1.2. Ignition Data Other types of global data sets used to validate models are ignition results, presented as "first light" and "go/no-go" versus flux and pressure. 3 The energy sources used to ignite the samples included a high-power CO2 laser (infrared at 10.6/xm) and an arc-image (visible) lamp. "First light" is the time-resolved measurement, such as a photo-diode signal, of when visible light is first emitted from an igniting sample. Go/no-go is the minimum irradiation time beyond which the material continues to self-deflagrate. Go/no-go is really a de-radiative extinguishment issue, which was studied in some detail using optical spectroscopic methods, 4 ' 5 and discussed in Sec. 3.2. It was found that "first light" is not concurrent with the initial evolution of gases from the propellant (first gasification), but rather it signals the ignition of the gas phase secondary flame. First light occurs several milliseconds after first gasification for RDX at one atmosphere, and is a function of the energy flux level. A better choice of parameter for comparing a model to actual data would be to monitor the times to production of significant radicals (see Sec. 3.2). Formation of radicals signals the start

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of significant reactions, including chemiluminescent reactions that produce the light output. 1.1.3. Radiative Response Function Laser recoil data for HMX and RDX has been measured by several groups. 6 ~ 8 In these experiments, an energy source, like a high-power laser, is made to fluctuate about a mean power, and the thrust of the propellant sample is measured as a function of time. The resulting data yield the radiant heat flux response function, Rq, which can then be used to infer the pressure-coupled response (Rp) through models. Model validation can be accomplished by predicting i? q directly. Of course, using dynamic data to validate models requires dynamic models. The pressure-coupled response function is usually measured directly with a T-burner (a laboratory device used to evaluate a propellant's burning rate response to acoustic pressure oscillations occurring at the propellant surface), but it has also been obtained using a pressure-driven apparatus. 8 1.2. Nature

of Combustion

Environment

Solid propellant flames do not provide a benign environment in which to apply diagnostic techniques. There are four main challenges. First is length scale. Measurements and theory both indicate that at normal rocket motor pressures thermodynamic equilibrium is reached within a few microns of the surface of the propellant. Even at one atmosphere the flame standoff distance for many propellants is substantially less than a millimeter. Thus the entire kinetically important structure, in which species must be resolved as a function of distance, can occur inside less than 500 microns. The entire experiment fits inside the thickness of six pages of this text. The second challenge is the multiphase nature of many solid propellant flames. Most rocket propellants are fuel rich to produce lower molecular weight exhaust products and high exhaust velocity. This can lead to incomplete combustion of the carbon in the formulation, leading to soot. Even with relatively clean flames, such as with neat nitramines, the surface is often molten and gasifying so that tiny droplets of liquid are thrown into the gas phase. This has been experimentally verified using laser Mie scatter imaging. The third challenge is the complex nature of propellant chemistry. Energetic materials are often large complex organic compounds, usually

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containing nitrogen. Their possible gas phase decomposition products are often medium- to large-sized unstable molecules for which little spectroscopic information exists. Thus the spectroscopist is often faced with clear absorption or emission structures that cannot be assigned to known species. Many solid rocket propellants are based on a composite mixture of an oxidizer, such as ammonium perchlorate (AP), and polymeric binder fuels. In these propellants, complex three-dimensional diffusion flame structures between the oxidizer and binder decomposition products, are present on the length scales of the heterogeneous mixture and drive the combustion via heat feedback to the surface. That leads to the fourth challenge: resolving multidimensional structures. 1.2.1. Effect of Pressure on Flame Structure The flame standoff of a propellant is a function of pressure, and for HMX it was found to decrease approximately inversely with pressure. This is why propellants burn faster at higher pressures: the shorter flame standoff distance leads to higher heat flux into the solid. This trend becomes a diagnostic issue: at rocket motor pressures (around 68 atm), the HMX flame is 10-25 /im off the surface, and no current combustion diagnostic can resolve profiles inside so fine a spatial scale. The best that can currently be done are experiments over a range of low pressures where the kinetics are slower and the flame is stretched out. One then extrapolates to higher pressures. This approach is limited by three-body reactions and the pressure dependence of unimolecular kinetics that will not be validated by comparisons of low-pressure experiments with models. 1.2.2. Two-Stage Flames For some propellants, a two-stage flame is observed. Products coming off the surface of the propellant, such as NO2 and H 2 CO for nitramines, react rapidly in the primary flame zone, producing heat close to the propellant surface. Above the primary flame is the "dark zone", which contains the products from the primary flame. The molecular species in the dark zone are kinetically slow to react, creating an apparent standoff from the surface to a visible flame. Species such as NO and HCN are in the dark zones of HMX and RDX. This second stage flame is mostly oxidation of HCN by NO x . The visible flame is hot, its appearance starting just below where the flame temperature peaks, and is produced by the reaction of products

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in the dark zone. For HMX and RDX, the appearance of CN and NH radical flame emission marks the end of the dark zone. Heat feedback to the propellant surface from the secondary flame is vital in the combustion process. A two-stage flame was apparent during laser-supported combustion of RDX. 9 However, the two-stage structure collapsed and was unresolved for RDX self-deflagration,10 with a secondary flame standoff of about 0.5 mm at latm in air. The flame standoff for laser-supported combustion was dependent on the laser irradiance. Higher laser irradiance drives faster solid gasification which gives higher gas velocity and, with unchanged kinetics, stretches out the flame structure. HMX burns with a two-stage flame for both laser-supported and self-deflagration at low ambient pressure. 11 HMX self-deflagration in air at atmospheric pressure is not stable, and the secondary flame height was variable, ranging from about 4-7 mm. 5 ' 11 The flame height for HMX became more stable with the addition of CO2 laser irradiance to the surface. It seems apparent that HMX burning in air at one atmosphere is near the deflagration limit, with the heat feedback from the secondary flame barely adequate to sustain combustion. The standoff for RDX at one atmosphere is comparatively short with respect to that for HMX, and it has a stable flame. Two-stage flames present diagnostic difficulties. The second stage flame is much hotter than the primary flame, but it is much further from the surface. Heat feedback from the primary flame could be controlling, but it is substantially more difficult to resolve than the second stage. 2. Optical Spectroscopic Techniques Applied There are a number of books describing various optical spectroscopic techniques, 5,12,13 so only brief descriptions will be given here about the techniques that have been applied to propellant combustion. 2.1. Absorption

and Emission

Spectroscopy

Electronic emission and absorption spectra can be measured using a linear diode array detector or, more recently, an imaging spectrograph with a twodimensional CCD camera. Light is collected with a lens and focused onto the slits of the monochrometer so, with a 2D camera, the spectral characteristics are obtained as a function of a single spatial dimension (usually the height off the surface). Infrared vibrational spectroscopy has also been undertaken on propellant flames using FTIR spectrometers. 14

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For absorption spectroscopy, a light beam, focused at the center of the sample to avoid beam steering, is passed through the flame of a deflagrating sample and the transmitted light is measured spectrally using a spectrograph and intensified linear diode array detector or an imaging spectrograph and 2D CCD. The absorption spectrum is obtained by performing the ratio of the spectrum obtained with flame (I) to that without flame (Jo). Species concentration and temperature are then obtained by comparing data with calculated spectra, if the spectroscopy of the species is known. If the spectroscopy is not known, spectra from the literature are used for obtaining concentration only via comparisons with known concentrations. Spatial resolution for absorption measurements in our laboratory is typically fOO /im and can be as good as 50 /im, especially using the digitally imaging spectrograph. Species monitored with absorption include NO, OH, CN, NH, H 2 CO, HONO, N 0 2 , soot, and AlO. The absorption technique is line-of-sight, but quantitative. Absorption path information is obtained from the relevant planar laser-induced fluorescence (PLIF) results or from visible imaging with a camera. If there are variations in concentration and/or temperature over the absorption path length, the analysis becomes inaccurate. One procedure we have used involves assuming an axial spatial profile and a radial dependence of that profile, integrating along the various absorption path lengths and iteratively correcting the axial profile to match the measured absorption values at different axial positions. Time resolution can be a problem in this technique: it is not very good for measuring a transient event, such as ignition, because it takes a moderately long time to read out the pixels of the digital camera. Time evolution would have to be built up over multiple experiments with a moving gate time. The minimum exposure gate time would be controlled by signal to noise issues. NO, for example, absorbs in the deep UV where the light source does not have much spectral irradiance and the minimum gate time we can use is about 0.1s. For a steady state event such as deflagration, the signal to noise ratio is improved by holding the sample surface at a constant position and integrating over time. In our lab, this is done by confining the surface by a thin wire and spring loading the sample from below. Because this technique is line-of-sight, any gases outside the combustion zone in direct line from the light source to the detector are also sampled. Therefore, care must be taken that combustion gases do not re-circulate around the combusting sample.

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2.2. Laser-Induced

Hanson-Parr

Fluorescence

Laser-induced fluorescence is a technique whereby the molecule of interest is electronically excited by a laser beam tuned to the appropriate frequency, and the subsequent emission monitored spectroscopically. Planar laser-induced fluorescence, or PLIF, uses a sheet of laser light to excite the molecules within a plane. The emission is detected with a two-dimensional camera, using an interference filter to pass the desired fluorescence, but block Mie and Rayleigh scattering, occurring at the laser frequency. Thus two-dimensional species profiles can be measured. The laser used to excite PLIF in our laboratory is a Nd-YAG pumped tunable dye laser with nonlinear crystal mixing and doubling into the ultraviolet. The camera used to image PLIF is a gated image intensified chargecoupled device (CCD) with 752 x 480 pixels. The camera is gated on for about 80 ns only during and a bit after the diagnostic laser pulse; this discriminates against natural flame emission and monitors only the laserinduced fluorescence. Although fluorescent lifetimes can be relatively long, collisional quenching causes the LIF signal to decay very rapidly after the laser pulse is over. The thickness of the laser sheet is typically less than 150 /xm and the resolution of the two-dimensional (2D) camera system is from 4 to 9 microns (fj.m) per pixel. Such fine resolution is required for very short flames, such as for RDX. Species monitored with PLIF in our laboratory include: CN, NH, OH, NO, NO2, polyaromatic hydrocarbons (PAHs), and AlO. Other species monitored with PLIF but not reported here 5 ' 12 include H2CO, C2, and CH. Because of collisional quenching, the PLIF technique is not quantitative. However, the measured profiles are placed on an absolute scale by calibration with absorption spectroscopy. In addition, because PLIF is quantum state specific, separate levels can be pumped and the resulting signals used to obtain either rotational or vibrational temperature. This was accomplished for CN, NO, OH, and AlO. PLIF can easily detect species at the ppm level, and is excellent for applying to transient systems. Timing is critical, however, because the induced emission must be collected within nanoseconds of the exciting laser pulse. 2.3.

Raman

Spontaneous Raman is conceptually simple, but in practice difficult to implement. A full discussion of this technique can be found elsewhere. 13 ' 15 ' 16

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A laser beam is focused above the sample and the Raman signal detected at 90 degrees with a linear diode array camera attached to an imaging spectrograph. The signal level is directly proportional to the species concentration. Raman scattering cross-sections are very small, so great care must be taken to reduce as many sources of noise as possible. Majority species that have been quantified in propellant flames using this technique include: C 2 H 4 , CH 4 , C 2 H 2 , HCN, NO, H 2 CO,N 2 , CO, C 0 2 , H 2 0 , H 2 , N 2 0 , and 0 2 . The spatial resolution for Raman in our laboratory was about 100 lira. Temperature can be measured with this technique, either by using Stokes/Anti-Stokes ratios, or by summing all measured majority species densities and calculating temperature via the perfect gas law. An atom balance can partially verify results. Raman signals can have good SNR (signal to noise ratio) at low temperatures where the gas density is relatively high. At flame temperatures of over 2000 K, seen for propellants, the gas density is about 1/7-1/10 that at room temperature and, because of the Boltzmann population, the spectrum broadens out, distributing the signal over more elements and further reducing the SNR. Laser-induced breakdown is common in dirty (highly sooting) flames, making Raman impossible to implement. High emission from impurities common in propellants, like sodium, and from C 2 molecules also plague Raman measurements. Spatial resolution is defined by the smaller of the object projection of the spectrograph slits or the beam waist of the laser (these are usually matched at approximately 100 ^m). Spontaneous Raman has been successfully applied to propellants in our laboratory. 5 ' 15 ' 16 Only marginal success for pure HMX and RDX flames was achieved,16 due to the short flame height of the RDX flame, and the very high emission from Na. If it works, spontaneous Raman is a wonderful technique to see many species in the flame all at once, but, if it fails due to laser-induced breakdown or strong interference from atomic or molecular emissions, it is hard to salvage anything from the spectrum as meaningful data.

2.4. CARS

and

DFWM

Coherent anti-Stokes Raman (CARS) and degenerate four wave mixing (DFWM) are Raman-like techniques 13 which measure spectra similar to those seen for spontaneous Raman. The signal level, however, is a nonlinear function of the species concentration and analysis is complicated by the non-resonant background susceptibility. Although there have been attempts, we do not believe CARS or DFWM has been successfully applied to propellant flames.

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in Concentration

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and

Temperature

The greatest uncertainties in temperature data arise from measurements conducted in the region of the flame close to the sample surface, where there is a steep gradient. In thermocouple measurements it becomes difficult to differentiate condensed from gas phases in the temperature profile. In addition, the very steep thermal profile requires extremely thin thermocouples to prevent thermal lag. For PLIF temperature measurements based on population ratios, all experiments to date have been done with a single laser and camera. Because the laser cannot be tuned quickly during a single propellant burn, multiple experiments must be done to measure different quantum levels. We use video cameras to correlate surface location. In our propellant studies we normally use OH radicals for temperature measurements. Temperature is obtained from the slope of a Boltzmann-type plot. Due to the high laser power density, the molecular transitions are saturated and a plot of ln[ifl(l/sn + I/52)] versus Er/k will yield a straight line with a slope of — 1/T, where ifl is the measured signal laser-induced fluorescence intensity, g\ and g2 are the degeneracies of the lower and upper quantum levels of the transition, ET is the rotational energy in the ground electronic state, k is the Boltzmann constant, and T is the temperature in Kelvins. For the most part, correlation coefficients of the linear least squares fit of the line to obtain temperature were greater than 0.99, except near the surface, where there is little or no OH. A correlation coefficient of 0.99 yields about a +/—8% standard deviation in the slope, or +/—150K standard deviation in the temperature. The peak temperatures measured for RDX and HMX came very close to the adiabatic value proving the validity of the technique. The adiabatic value is the maximum flame temperature that can be achieved based on thermodynamics; heat losses in the system will necessarily cause the actual temperature to be less than this value. Laser-supported combustion could also enable the temperature to rise above the adiabatic value because heat is being added by the laser. One can also check temperature by comparing the OH radical PLIF-measured temperatures with that obtained from fitting absorption measurements from species such as NO or CN, by fitting the vibrational band structure. These appear to overlap well to within 100-200 K. To obtain concentrations from the absorption results, the temperature is usually taken from the PLIF and radiation-corrected thermocouple (where feasible) results and spectral simulations compared with the data.

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Sometimes, vibrational temperatures can be obtained from the absorption measurements (for example, for NO). The other sources of error in absorption measurements involve the path length and baseline noise. Absorption is essentially linear with path length, so a 10% error would yield a 10% error in concentration. The path length measurement is most uncertain near the secondary flame front, because of the 3D shape of the flame. Near the surface, where the path lengths are longer, a maximum of 5% error in path length would be typical. Baseline noise is worst for experiments for which little averaging is done and for which the concentration is small and/or the path length is short. Typical baseline noise has been about +/—5%. Therefore, an estimate of uncertainty in mole fractions would be typically 15% near the surface and 25% nearer to the secondary flame front. 3. N e a t N i t r a m i n e s Nitramines are energetic molecules that contain both fuel and oxidizer moieties and they burn by themselves without an outside oxidizer (i.e. neat). They have high energy, but only poor oxidizing abilities. The most-studied of the nitramines are HMX and RDX. Numerous research groups have worked together on understanding the combustion behavior of RDX, and detailed kinetic models have been written to compare with data obtained through experiments. Experimental data consists largely of the temperature and species profiles above the surface of deflagrating RDX, as well as burning rate and temperature sensitivity of burning rate as a function of pressure. Models have also been compared to time-resolved ignition and de-radiative extinguishment measurements. These data include the aforementioned go/no-go and first-light results as well as time-resolved species and temperature profiles. 3.1.

Deflagration

Our laboratory did measurements on RDX, 9 ' 10 HMX, 10 ' 11 XM39,10*16 and RDX-GAP 17 (glycidyl azide polymer) propellants under both lasersupported (all but RDX-GAP) and self-deflagration, from 1-25 atm (mostly latm). Laser-supported deflagration employs added energy at the sample surface from a CO2 laser. We used the techniques of PLIF, UV-vis absorption, and spontaneous Raman spectroscopy, obtaining species profiles for HCN, H 2 CO, N 0 2 , NO, HONO, N 2 0 , N 2 , C 0 2 , H 2 , CO, H 2 0 , OH, CN, NH, "RDX", and an unidentified "nitrosamine". We obtained temperature profiles from thermocouples, OH rotational temperature from

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PLIF experiments, and NO vibrational temperature from UV absorption experiments. Other laboratories that conducted flame experiments included Homan (ARL), 18 who used UV absorption to measure OH, CN, NH, and NO species profiles, and NO temperature for 1-2 atm self-deflagration of RDX. Litzinger (Penn State) did measurements on RDX, 19 HMX, 20 and RDX-GAP 21 propellants under laser-supported deflagration, obtaining species profiles for HCN, H 2 CO, N 0 2 , NO, N 2 0 , N 2 , C 0 2 , H 2 , CO, H 2 0 , using a microprobe triple quadrupole mass spectrometer. They also measured temperature profiles using thermocouples. It is important to compare results obtained by different research facilities in order to ascertain areas that need further study and to select those that agree well. The established experimental results can then be provided to modelers for validation of their codes. 3.1.1. Laser-Supported Deflagration Figure 1 shows species and temperature profiles measured in our lab for laser-supported deflagration of RDX. We measured a peak NO in the dark zone of 20 mole%, compared with 25 mole% measured by Litzinger under similar laser supported conditions. The NO profile shows a plateau in a dark zone. This dark zone was seen to be present for RDX only under laser-supported deflagration. As discussed below, under steady state RDX Laser Supported Deflagration

mm Above Surface Fig. 1. Selected species and temperature profiles for laser-supported deflagration of neat RDX.

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self-deflagration the secondary flame collapses towards the surface and the temperature profile becomes monotonically rising with no dark zone. HMX was found to have a dark zone even for self-deflagration at 1 atm. NO2 decays rapidly away from the surface of RDX and HMX. For RDX laser-supported deflagration, we measured a peak NO2 concentration of 18 mole%, whereas Litzinger (using mass spectroscopy) obtained about 17 mole%. For HMX, the peak N 0 2 was about 7 mole%, compared with about 13 mole%, in Litzinger's mass spectroscopic experiments. For RDX laser-supported deflagration, our laboratory and Litzinger's both observed low concentrations of H2CO: <3 mole%, versus about 1.5 mole%, respectively. There are considerably higher peak concentrations of H2CO for HMX, which decays rapidly away from the surface. We measured a peak of about 15 mole%, compared with 12 mole% for the mass spectral results from Litzinger's group. These data were made available to modelers. 22 ~ 26 The models had many areas of agreement with the data. For example, the Smooke, Prasad and Yetter model 22 ' 25 matched burning rate, pressure exponent, and temperature sensitivity (except at low P for HMX). The model recovered the two-stage flame for laser-assisted RDX; it predicted the collapse of the twostage flame for RDX self-deflagration; the temperature profiles matched well; the CN, NH, OH positions, widths, and peak concentration values matched; and the general behavior of the NO and NO2 profiles matched. This was the first time that an a priori model with detailed kinetics had been able to predict the ballistic properties of solid propellant combustion, as well as match the species and temperature profiles. The input from experimental measurements was vital in validating and developing this model. However, despite much back and forth interaction between modelers and experimentalists there still exist some significant discrepancies. The models predict high peak HONO concentrations (14 mole%) and low peak NO2 (about 4 mole%). The experiments are opposite: high NO2 and less than 0.3 mole% HONO (which can easily be measured by UV absorption). If the experimental data is to be believed, the model kinetics for conversion of HONO to NO2 are too slow. Indeed, subsequent ab initio calculations by Lin 27 indicated that two pathways for destruction of HONO that had not been considered in the original modeling22 were in fact substantially faster than the original reaction. However, the model rates are still not fast enough to convert HONO to NO2 close enough to the surface to explain the absence of HONO in our measurements and the high NO2.

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The model NO dark zone concentration (29 mole% in Ref. 20) was higher than either our or Litzinger's results (20 and 25 mole% respectively). Also, experimental results showed H 2 CO at less than 3 mole%, but the models all predict high H 2 CO (18 mole% in Ref. 22). H 2 CO decays rapidly near the surface, so perhaps the model H 2 CO decay rate is too slow. Alternately, the discrepancy could come from the definition of "surface". The surface, as seen experimentally for either laser-supported or self-deflagration at one atmosphere, is very uneven with a bubbly, frothing melt layer. Perhaps H 2 CO is consumed before the gases leave the frothy melt layer. This may also explain the HONO and N 0 2 discrepancies as HONO could be converted to N 0 2 within the froth zone. The models assume two major decomposition pathways for RDX (and HMX): one to produce HCN and HONO (which converts to NO + N0 2 ) and one to produce H 2 CO and N 2 0 . Currently the models must have some H 2 CO channel for exothermic reactions near the surface to drive the regression of the burning surface (the burn rate). In addition, Brill's FTIR results 28 show that the branching ratio between the HCN and H 2 CO channels is about 1 at the temperature measured for the surface of deflagrating RDX (about 605 K). Video movies taken during the experiments show bubbling on the surface and a liquid spray in the flame, possibly caused by bursting bubbles. We detected the spectrum of an assumed nitrosamine for RDX, especially at the surface, which is probably a condensed-phase product, formed in bubbles in the melt layer. During an experiment in this laboratory using a C 0 2 laser to heat RDX, but with insufficient irradiance for ignition, a huge bubble formed on the surface. When it finally popped, emitting the trapped decomposition gases, it was found that the level of formaldehyde inside the bubble was about 7.5 mole%. The nitrosamine was also observed inside of the bubble. Therefore, there is evidence of H 2 CO formation inside the bubbles. Exothermic reaction of H 2 CO within the bubbles might explain our inability to see it in the gas phase above the surface. Bubble formation is not just a low pressure effect: bubbles are present, especially for HMX, even at rocket motor pressures but are much smaller due to the thinner melt layer.29 Spectroscopic measurements of flame structure have been done in our laboratory at pressures up to 25atm. The CN flame height for lasersupported deflagration of HMX, for example, was seen to drop sharply with increasing pressure. At 1 atm it is 4.2 mm while at 12atm it was found to be only 0.13 mm. Extrapolation to realistic rocket motor pressures (about 60 atm) leads to flame standoff distances around 3.5 microns.

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It is not possible to make in situ measurements that resolve species and temperature profiles within that distance with any present diagnostic. Therefore, the models must be validated at lower pressures. However, that may mean that three-body reactions and the pressure dependencies of unimolecular kinetics cannot be validated through the flame structure measurements. 3.1.2. Self-Deflagration Without the added gasification rate caused by laser flux, the flame standoff distances decrease for nitramines. Figure 2 shows species and temperature profiles for self-deflagration of RDX at 0.92 atm. The dark zone disappears for RDX without added laser flux. The CN standoff for RDX self-deflagration at 0.92 atm was very short, in the order of about 0.5 mm. The CN peak occurs in the zone of maximum temperature rise just below thermodynamic equilibrium. The HMX CN flame standoff varied but the dark zone was still present. The flame appears to be unstable without laser support at atmospheric pressure. A reduced fuel spray was still observed for both HMX and RDX during self-deflagration, indicating that the added CO2 laser irradiance was not the sole contributor to spray formation. H2CO and NO2 were seen for HMX and both decay rapidly above the surface. For RDX, the NO2 decayed too rapidly from the surface to

£ a. a.

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Height (mm) Fig. 2. Selected species and temperature profiles for self-deflagration of neat RDX. Solid lines are model results from Ref. 23. The dashed line is experimentally-measured temperature. Symbol legend: o = OH (divided by 100), A = CN, O = NH, and • = NO (divided by 500).

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be resolved. The surface temperature, measured with thermocouples, was 660 K for HMX and 605 K for RDX. Our measurements of the self-deflagration temperature and species profiles of RDX at 0.92 atm can be compared with that of Homan et al.18 The NO shape is in reasonable agreement, but our peak NO concentrations of about 18 mole% is lower than Homan's measured value of 25 mole%. However, the temperature profiles agree well. The CN and NH peak positions agree well, but Homan's CN and NH concentrations were about 50% of ours, and their profiles were wider. Modelers have successfully predicted experimental results for nitramine self-deflagration22'23 even predicting the burning rate and pressure exponent up to 3400 PSIA for HMX self-deflagration.25 The discrepancies between modeling and experiment seen for laser-supported deflagration are not as extreme for RDX self-deflagration because H2CO,N02, and HONO decay rapidly near the surface and, with the compressed length scales seen in self-deflagration, they cannot be resolved.

3.2.

Ignition

Deflagration is a steady-state process. Ignition is a more difficult phenomenon to simulate because it requires a time-dependent model. Measurements in our laboratory 4 have shown several important stages during ignition. First the sample heats up, then decomposition starts and gases are emitted (first gasification), then those gases ignite a distance from the sample surface (first-light), and the flame "snaps" back towards the surface and adjusts to an equilibrium position as the solid establishes a steady-state temperature profile. Upon removal of the heating flux, the quasi steady state flame, positioned further from the surface than it would be without added laser flux, immediately attempts to move up towards the surface. As the gas phase flame temperature profile adjusts to the loss of added energy, the temperature profile in the condensed phase does too. At higher flux, and therefore, higher regression rate, the steady state thermal profile is shallow. At lower regression rates the thermal profile is deeper. Upon rapid removal of the laser flux the shallow heated zone may pyrolyze away before the selfdeflagration flame moves closer and re-establishes a deeper thermal profile. This process is called de-radiative extinguishment. The go/no-go locus is really a function of this extinguishment process. Models based on detailed kinetics are required to predict species concentration and temperature as a function of time in these kinetically-controlled processes.

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Data of this type has been measured by our laboratory 4 for RDX and HMX, and included time-resolved profiles of CN, NH, OH, and temperature during ignition and de-radiative extinguishment. The time-accurate Yang model 26 agreed reasonably well with these results. This model recovers the gas phase ignition away from the surface and the snap-back to short standoff distances; but there are minor discrepancies. The model does not predict the slow growth of the flame height after snap-back. Also there are minor quantitative differences: the flame height at ignition was measured to be approximately 3.5 mm while the model gave 5 mm and the time to ignition was measured to be 8.6 ms versus the model's 7 ms. Further, the model does not predict de-radiative extinguishment: removal of the laser flux just after ignition always leads to continued steady state deflagration in the model while the experiment shows extinguishment unless the laser flux is gradually reduced to zero. These discrepancies were attributed to heat loss effects in the experiments (the model is adiabatic). 26

4. Homogeneous Nitramine Propellants Building upon the success with neat nitramines, a composite propellant based on RDX with GAP as binder, was formulated for study. The plan was to keep the propellant homogeneous so that a ID model would be sufficient rather than a much more complex full 2D model. This propellant was chemically composite, but spatially homogeneous; i.e., the chemical complexity was increased, the dimensional complexity was not. RDX with GAP as a propellant was too smoky and fuel rich and substantial amounts of char were produced on the surface of the propellant during combustion, which would be nearly impossible to model. We added 1,2,4 butanetriol trinitrate (BTTN) as a plasticizer to improve combustion properties. Experimental studies done by our laboratory included PLIF, UV-vis absorption, spontaneous Raman spectroscopy, and thermocouple measurements. 17 Other experiments done on this propellant were micro probe mass spectroscopy,21 burning rate measurements as a function of pressure and initial temperature, and high heating rate pyrolysis studies using an FTIR. 30 The burning rate data was withheld from the modelers to provide a blind test of their models, to allow them a priori predictions of burning rate, pressure exponent, and temperature sensitivity. Modelers were given

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profile and flame structure data. Only self-deflagration was studied so that modelers would not have to include laser flux, which can make the flame three-dimensional. We also thought that the extra gasification rate of N2 from GAP should stretch out the flame structure by increasing flow velocity, and it was seen to do just that. Our laboratory provided 16 quantitative scalar profiles including: T, N 0 2 , NO, N 2 0 , H 2 C O , OH, CN, NH, HCN, H 2 ,N 2 ,H 2 0,C 2 H4, and C 2 H 2 . An atom balance analysis was performed to verify the experimental results and majority species were found to extrapolate to their proper adiabatic equilibrium concentrations. HCN, CO, and N 2 were found to be the major species near the surface, and CO, N 2 , and H 2 0 in the burnt gases. The surface temperature was determined to be 605 K, and a dark zone of about 1200 to 1300 K was observed in which the NO concentration was at its highest. NQg existed only very close to the surface. No formaldehyde was observed in the gas phase at measurable distances off the surface. Preliminary a priori modeling results are extremely promising, matching measured regression rates and pressure exponents within experimental error. 31 5. A m m o n i u m P e r c h l o r a t e ( A P ) AP is an oxidizer widely used in rocket motor propellant formulations. Even though AP has been in use for a long time, the combustion of AP-composite propellants is not all that well understood. Strong diffusion flames form between the decomposition products of AP and those of the binder. These oxidizer/fuel diffusion flames have been studied in our laboratory in both one-dimensional (ID) and two-dimensional (2D) configurations. 5.1. One-Dimensional Flames

Counter

Flow A P/Fuel

Diffusion

The counterflow, or opposing flow, configuration technique has the enormous advantages of creating a ID flame (thereby necessitating only a simplified ID model), and greatly stretching out the spatial scale, making diagnostics easier. We have studied a variety of AP/fuel systems 3 2 - 3 4 in collaboration with R. Yetter at Penn State and M. Smooke, at Yale, who have modeled these flames with very encouraging results. Although AP is a solid, a counterflow diffusion flame is still possible between a gas and the AP decomposition gases. Quantitative species and temperature profiles have been measured for a variety of fuels. For

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methane 32 and ethylene, 33 two strain rates were also studied, given by two separations, 10 and 5 mm, between the fuel exit and AP surface. Species measured with PLIF included CN, NH, NO, OH, and PAH. Laser-induced incandescence (LII) was used to measure soot volume fraction and diameter. The NO, OH, and CN measurements were made quantitative using absorption spectroscopy (NH concentrations were just below our detection limit). Temperature was measured using radiationcorrected thermocouples, OH rotational population distributions, NO vibrational population distributions, and spontaneous Raman spectroscopy. Raman spectroscopy was also used to measure major species concentrations including CH 4 , C 2 H 2 , C 2 H 4 , 0 2 , HC1, N 2 , H 2 0 , C 0 2 , H 2 , CO, and NO. Absorption spectroscopy was used to measure NO and N 0 2 species profiles. Emission spectroscopy was used to see NO*, CH*, OH*, NH*, CN*, and C 2 to correlate the observed stratified fiamelets seen with the species present. The burning rate of the AP was also measured as a function of flame strain rate. Selected species profiles for the AP/methane counter-flow diffusion flame are shown in Fig. 3. The immediate agreement between measurement and model was mostly good for the AP/methane case with a 5 mm separation between the AP surface and the fuel outlet, but there were discrepancies for the absolute values of NO and OH and for the shape of the NH profile. When the N H 2 + N 0 2 - • H 2 NO + NO reaction kinetic rate was modified in the model database, the

1

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Fig. 3. Selected species and temperature profiles for A P methane counter flow diffusion flame experiment done at a separation of 5 mm. Symbols are the data and lines are the modeling results of B e l 32. Symbol legend: X = HC1, • = H 2 0 , • = CH 4 , • = 0 2 , A = NO (times 1 ) , D § OH (tirfiES 25), O = CN (times 6000), and o = temperature (K).

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agreement improved markedly 32 : the computed profiles of NO, OH, and NH changed together to match the measurements. This change in kinetics was supported by recent data in the literature and by discussions with M. C. Lin of Emory University. Other fuels studied were ethylene, 33 a mixture of H 2 and CO, 34 and a mixture of N2,C 2 H 2 , and C 2 H 4 . 35 The H 2 /CO gas mixture was a surrogate, simulating the products of the semi-premixed fine AP crystals plus HTPB binder flame. C 2 H 2 and C 2 H 4 are likely intermediate products from hydroxyl-terminated polybutadiene (HTPB) decomposition. Again, the agreement between experiment and model was excellent for both of these fuels.33-34 The data was helpful in validating models of AP diffusion flames based on detailed kinetics. 5.2. Two-Dimensional

AP/Fuel

Diffusion 5

Flames

Our early studies of diffusion flames consisted of creating sandwiches of an oxidizer with the binder in the center, and then imaging a given species in the diffusion flame using PLIF. The thin oxidizer and binder slabs were mechanically squeezed together in a small vice. It was found that by far, AP had the strongest diffusion flames of all the "oxidizers" studied — stronger than HMX, RDX, hydrazinium nitroformate (N 2 H^C(N0 2 )3", or HNF), 1,3,3-trinitroazetidine (TNAZ), and ammonium dinitramide (ADN). Trying to model these types of diffusion flames is quite complex, so a somewhat simplified 2D experiment was designed.36 Holes were drilled through the centerline of AP pressed cylinders and CH4 gas flowed up through the hole. A C 0 2 laser was used to ignite the sample and the microstructure of these Burke-Schumann-like diffusion flames of co-flowing methane and ammonium perchlorate decomposition products were studied. The diffusion flames were imaged shortly after, but while the C 0 2 laser was irradiating the surface. Waiting too long to sample the flame led to crater formation in the surface, with the diffusion flame becoming inaccessible to the laser probe beam close to the surface. The flame length was quantified as a function of fuel exit diameter and found to follow diffusion flame theory. 2D species profiles of CN, NH, and OH were imaged at a spatial resolution of 8 microns using PLIF. 2D gas temperature profiles were obtained via OH rotational population distributions. The results have

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Fig. 4. Two-dimensional contours of OH radicals in co-flow methane AP (a) Experimental d a t a from OH PLIF. (b) Modeling result from Ref. 35.

flame,

been compared to a detailed kinetic-based 2D model, with good results."' Figure 4 shows the experimental OH 2D contour compared to the model results of Ref. 36.

6. S u m m a r y We have seen that, for the limited solid propellant ingredients or systems studied in multiple laboratories, agreement for the flame structure profiles is the norm rather than the exception. Agreement between model and experiment has also been shown to be relatively good for the flame structure away from the surface, i.e. the secondary flame. There still exist discrepancies in the zone near the surface. As mentioned, this might be due to errors

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in the kinetic rates for the conversion of HONO to NO and N 0 2 and for the consumption of H 2 CO, or, perhaps more likely, the problem stems from the uncertain definition of the surface. With many solid propellants, and especially with nitramines which have been most studied, the experimental surface is not a mathematical singularity as it is in most models. Instead, it is a distributed zone of mixed liquid and gas. Neither optical nor mass spectral diagnostics probe this region. In those experiments the "surface" starts at the point where the liquid completely disappears. But in reality, significant gas phase reactions could be occurring in the bubbles of the "foam" zone. These reactions might even be catalyzed by the immediate presence of high surface area of liquid. We think that more work needs to be done close to the surface. Higher resolution gas phase measurements of the primary stage flame directly above the surface would help elucidate reactions in the "foam" zone. In addition, despite the experimental difficulties, some way must be found to probe the "foam" zone and quantify these condensed-phase or mixed-phase reactions. We are exploring surface Raman spectroscopy. Figure 5 shows surface Raman spectra of neat energetic materials compared to a sample quenched from deflagration. Conventional wisdom suggests that there are no condensed-phase reaction products for AP, minimal products for RDX, and significant condensed-phase chemistry and associated products for HMX. At first glance, Fig. 5 shows this to be the case: the Raman spectra of neat and quenched AP are virtually identical, for RDX the spectra are nearly the same, while for HMX the spectra appear substantially different. Although it would appear from the Raman spectra that there is significant chemical change in the quenched HMX surface, most of the change in the spectra is actually due to a polymorph shift. The starting material is beta HMX while the quenched surface appears, in preliminary analysis, to be a mixture of beta and delta HMX. Further analysis is required to see if decomposition products are present as well. Despite the experimental difficulty, measurements in the melt layer and very near gas phase would help close the last remaining unknown gap in the understanding of the kinetics of solid propellant combustion and further the development of models to true a priori prediction tools for propellant ballistics.

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10000

500

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Wavenumber (cm-1) Fig. 5. Raman spectra from unreacted (solid) and quenched from combustion (dotted) surfaces of selected energetic materials, (a) AP, (b) RDX, (c) HMX.

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References 1. A. I. Atwood, T. L. Boggs, P. O. Curran, T. P. Parr, D. M. Hanson-Parr, C. F. Price and J. Wiknich, J. Propul. Power 15(6) 740-747 (1999). 2. M. W. Beckstead, R. L. Derr and C. F. Price, in 13th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, 1971), pp. 1047-1056. 3. A. I. Atwood, P. O. Curran, C. F. Price and J. Wiknich, in Proc. 32nd JANNAF Combustion Subcommittee and Propulsion Systems Hazards Subcommittee Meeting — Joint Sessions, Vol. I, CPIA Publication 638 (1995), pp. 149-159. 4. T. Parr and D. Hanson-Parr, in 27th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, 1998), pp. 2301-2308. 5. T. P. Parr and D. M. Hanson-Parr, in Solid Propellant Chemistry., Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. Brill and W.-Z. Ren (American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia, 2000). 6. J. C. Finlinson, T. P. Parr and D. M. Hanson-Parr, in 25th Symp. (Int.) on Combustion (The Combustion Institute, Pittsburgh, 1994), pp. 1645-1650. 7. M. Q. Brewster and T. B. Schroeder, Combust. Sci. Technol. 122(1-6), 363-382 (1997); P. S. Loner and M. Q. Brewster, in 27th Int. Symp. on Combustion (The Combustion Institute, Pittsburgh, 1998). 8. G. N. Kudva, in Mechanical Engineering, PhD Thesis, Pennsylvania State University, State College, PA (2001). 9. D. M. Hanson-Parr and T. P. Parr, in Proc. 31st JANNAF Combustion Meeting, Vol. II, CPIA Publication 620 (1994), pp. 407-423. 10. T. Parr and D. Hanson-Parr, in Proc. 32nd JANNAF Combustion Subcommittee Meeting, Vol. I, CPIA Publication 631 (1995), pp. 429-437. 11. T. P. Parr and D. Hanson-Parr, in Proc. 34th JANNAF Combustion Subcommittee Meeting, Vol. II, CPIA Publication 662 (1997), pp. 481-490. 12. T. Parr and D. Hanson-Parr, in Progress in Astronautics and Aeronautics, Vol. 143, eds. L. De Luca, E. Price and M. Summerfield (AIAA, Washington DC, 1992), pp. 261-324. 13. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, eds. A. K. Gupta and D. G. Lilley (Abacus Press, Cambridge, MA, 1988). 14. C. F. Mallery, Jr. and S. T. Thynell, in Proc. 34th JANNAF Combustion Subcommittee Meeting, Vol. II, CPIA Publication 662 (1997), pp. 389-406. 15. T. P. Parr, D. M. Hanson-Parr, M. Smooke and R. Yetter, in Proc. 35th JANNAF Combustion Subcommittee Meeting, Vol. I, CPIA Publication 680 (1998), pp. 671-685. 16. T. P. Parr and D. M. Hanson-Parr, in Proc. JANNAF Joint 35th Combustion Subcommittee Meeting and 7th Propulsion Systems Hazards Subcommittee Meeting, CPIA Publication 685 (1998), pp. 87-102. 17. T. P. Parr and D. M Hanson-Parr, Combust. Flame 127(1/2), 1895-1905 (2001). 18. B. E. Homan, M. S. Miller and J. A. Vanderhoff, Combust. Flame 120(3), 301 (2000).

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19. Y. Lee, C.-J. Tang and T. A. Litzinger, Combust. Flame 117(3), 600 (1999). 20. C.-J. Tang, Y. J. Lee and T. A. Litzinger, Combust. Flame 117(1/2), 170 (1999). 21. H. L. Lee, G. Kudva and T. A. Litzinger, in Proc. 37th JANNAF Combustion Subcommittee Meeting, Vol. I, CPIA Publication 701 (2000), pp. 383-390. 22. K. Prasad, R. A. Yetter and M. D. Smooke, Combust. Sci. Technol. 127, 35-82 (1997). 23. Y.-C. Liau and V. Yang, J. Propul. Power 11(4), 729 (1995). 24. J. E. Davidson and M. W. Beckstead, J. Propul. Power 13, 375-383 (1997). 25. K. Prasad, R. A. Yetter and M. D. Smooke, Combust. Flame 115, 406-416 (1998). 26. Y. C. Liau, E. S. Kim and V. Yang, Combust. Flame 126(3), 1680-1698 (2001). 27. M. C. Lin et al., J. Phys. Chem. 101, 60-66 (1997). 28. T. B. Brill, J. Propul. Power 11, 740-751 (1995). 29. T. L. Boggs et al, in 13th AIAA Propulsion Conf. (1987) AIAA paper 87-859. 30. T. B. Brill and B. D. Roos, in Proc. 37th JANNAF Combustion Subcommittee Meeting, Vol. I, CPIA Publication 701 (2000), pp. 373-382. 31. M. W. Beckstead, personal communication (2003). 32. M. A. Tanoff, N. Ilincic, M. D. Smooke, R. A. Yetter, T. P. Parr and D. M. Hanson-Parr, 27th Symp. (Int.) on Combustion, Vol. II (The Combustion Institute, Pittsburgh, PA, 1998), pp. 2397-2404. 33. M. D. Smooke, R. A. Yetter, T. P. Parr, D. M. Hanson-Parr, M. A. Tanoff, M. B. Colket and R. J. Hall, in Proc. 28th Int. Symp. on Combustion, Vol. 28(2), University of Edinburgh Scotland, 30 July-4 August, 2000 (The Combustion Institute, Pittsburgh, Pennsylvania, (2000), pp. 2013-2020. 34. T. P. Parr, D. M. Hanson-Parr, M. D. Smooke and R. A. Yetter, in Proc. 29th Int. Symp. on Combustion, Vol. 29, Part II (The Combustion Institute, Pittsburgh, Pennsylvania, 2002), pp. 2881-2888. 35. T. P. Parr, D. M. Hanson-Parr, M. D. Smooke and R. A. Yetter, in Proc. 39th JANNAF Combustion Subcommittee Meeting, Colorado Springs, CO, Dec. 2003 (Chemical Propulsion Information Agency, Columbia, MD, 2004), to be published. 36. M. D. Smooke, R. A. Yetter, T. P. Parr and D. M. Hanson-Parr, in Proc. 28th Int. Symp. on Combustion, Vol. 28(1), University of Edinburgh, Scotland, 30 July-4 August, 2000 (The Combustion Institute, Pittsburgh, Pennsylvania, 2000), pp. 839-846.

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CHAPTER 5 TRANSIENT GAS-PHASE INTERMEDIATES IN THE D E C O M P O S I T I O N OF E N E R G E T I C MATERIALS Paul J. Dagdigian Department of Chemistry Johns Hopkins University Baltimore, MD 21218-2685, USA

Contents 1. Introduction 2. Expected Intermediates and their Role in Energetic Materials Combustion 2.1. Later Stages of Decomposition 2.2. Early Stages of Decomposition 3. Detection of Intermediates 3.1. Laser Fluorescence Excitation 3.2. Ionization Techniques 3.3. Absorption Methods 3.4. Other Techniques 3.5. Special Problems in Probing Combustion Environments 4. Current Status Report 4.1. Diatomic Species 4.1.1. Hydroxyl (OH) 4.1.2. Cyano (CN) 4.1.3. Imidogen (NH) 4.1.4. Methylidene (CH) 4.1.5. Nitric Oxide (NO) 4.2. Polyatomic Species 4.2.1. Isocyanato (NCO) 4.2.2. Nitrogen Dioxide ( N 0 2 ) 4.2.3. Amidogen (NH 2 ) 4.2.4. Nitrosyl Hydride (HNO) 4.2.5. Formyl (HCO) 4.2.6. Nitrogen Hydride (HN 2 ) 4.2.7. Nitroamidogen (HNNO) 129

130 130 131 131 133 133 135 136 139 139 139 140 140 140 141 142 142 143 143 144 144 145 146 147 147

130

4.2.8. Nitrous Acid (HONO) 4.2.9. Methylene Amidogen (H2CN) 4.2.10. Methyleneimine (H2CNH) 4.2.11. Nitrosomethyl (CH2NO) 4.2.12. HCN Dimers (C2H2N2) 4.2.13. Methylene Nitramine (H 2 CNN0 2 ) 4.2.14. Hydrogen Nitramide [HN(N02)2] 4.2.15. Other Polyatomic Species 5. Conclusion and Prospects for Future Work Acknowledgments References

148 148 150 152 152 153 153 154 154 155 155

1. Introduction It is well known that free radical intermediates are essential for combustion processes to occur. For example, the highly exothermic combustion reaction of a hydrocarbon fuel with oxygen can proceed only through an initiation process, e.g. heating or a spark, which generates a small concentration of free radicals. In a similar fashion, the decomposition of an energetic material is initiated by a bond-breaking event, which forms two radical species. The subsequent decomposition steps occur through radical attack of closedshell species, reaction (bimolecular or termolecular) with another radical, or unimolecular decomposition events. It is desirable to develop sensitive diagnostics for these intermediates, both for their in situ detection as well as to enable measurement of rate constants of elementary reactions as ingredients in a detailed reaction mechanism. In this chapter, we discuss what is known about various intermediates (mainly free radicals) in the decomposition of energetic materials. Also presented are brief descriptions of various, mainly laser-based techniques for the detection of these intermediates. 2. Expected Intermediates and their Role in Energetic Materials Combustion Many of the free radical intermediates encountered in the decomposition of energetic materials are also present in the combustion of many organic fuels. What distinguishes media containing decomposing or combusting energetic materials are the intermediates present in the early stages of decomposition. An individual molecule of an energetic material contains both oxidizing and reducing components. We can distinguish between the early and later stages of the decomposition of an energetic material. Since energetic materials

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are generally solids, or are formulated as solid-state mixtures with other components such as binders, the first stage in the decomposition will involve volatilization, reactions within the condensed phase, or reactions of the condensed phase with radicals coming back from the gas phase. Once in the gaseous phase, the decomposition products can be in two general stages, as described below.

2.1. Later Stages of

Decomposition

The chemistry in the so-called secondary flame zone of a decomposing energetic material is similar to that of flames encountered in the combustion of nitrogen-containing organic compounds. The free radical species present in the later stages of the decomposition of energetic materials are essentially the same as those in the combustion of common fuels such as hydrocarbons and nitrogen-containing molecules. What distinguishes the secondary flame of a given energetic material is the stoichiometry of the parent molecule, namely the [C, H, N, O] mole fractions. Most energetic materials are composed of these four elements. To understand in more detail the later stages of the decomposition of energetic materials, the chemistry of model flames, such as CH4/N2O, to mimic the decomposition of nitramines, has been investigated. The intermediates encountered in the secondary flame zone include diatomic radicals such as OH, CN, NH, and NO, and small polyatomic species as well as atoms. A progress report on the detection of the molecular species is presented in Sec. 4.

2.2. Early Stages of

Decomposition

Polyatomic intermediates of importance in the decomposition of energetic materials may be deduced either from a theoretical consideration of the reaction pathways likely to occur in the decomposition process, or from experimental studies, usually involving sensitive detection of intermediates in the controlled decomposition of the energetic material. We consider here, in particular, the decomposition of nitramines such as RDX, HMX, and ADN, since the decomposition of these compounds has been extensively studied both experimentally and theoretically. Consideration of the possible bond-breaking pathways can lead to a list of likely intermediates of importance in the decomposition of these energetic materials. 1 Similarly, theoretical methods have been employed to delineate the energy landscape

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of the likely reactions and to estimate the rates of reactions, as an alternative or supplement to experimental measurements of the rates. 2 ' 3 A number of theoretical studies have considered the initial bondbreaking steps in the decomposition of energetic materials. For nitramines, this most likely involves the breaking of an N-N bond, with release of NO2, or for cyclic RDX or HMX possibly ring opening or HONO elimination. 4-6 Other studies have concentrated on assembling a network of chemical reactions to model the decomposition chemistry after an assumed initial bondbreaking step. 2 ' 7 Studies at low pressures are somewhat mitigated by the fact that the decomposition pathways are probably different at low versus high pressures. 8 Alternatively, we can look to experimental studies to help identify the larger intermediates formed in the decomposition process.9 As described in detail in his chapter, Behrens has employed thermogravimetric analysis with modulated mass spectrometric detection and time-of-flight velocity analysis to identify molecular species from heated samples of energetic materials and to correlate their production with weight loss of the sample. A number of species were mass-spectrometrically identified and fit into overall schemes of decomposition. In addition to many stable small molecules, several interesting larger intermediates were observed, including NH2CHO, CH 2 NHCHO, oxy-s-triazine (OST), and l-nitroso-3, 5-dinitrohexahydro-striazine (ONDTA). 10 The latter can be obtained from RDX by loss of an oxygen atom from one of the nitro groups. Litzinger and co-workers 11 ' 12 have studied the flames of a number of propellants, including RDX and HMX, pure and in mixtures, in CO2 laser-assisted combustion at pressures ranging from 0.1 to 3 atm. Gaseous products were interrogated through a quartz microprobe and detected with a triple quadrupole mass spectrometer. Tandem mass spectrometry with collision-induced dissociation was employed to differentiate ions of the same mass. In addition to observing a number of stable products, they also observed several larger transient species of interest for the early stages of energetic materials decomposition. Methyleneimine (H2CNH) was identified for the first time as a minor RDX decomposition product. Higher molecular weight species detected included C2H2N2, C2H4N2, and C2H2N2O (no structures determined). Triazine was also identified as a decomposition product from both RDX and HMX. Photoionization at 118 nm in a time-of-flight mass spectrometer has also proven useful in investigating the laser-induced decomposition of energetic materials. Garland and Nelson13 have carried out such studies, for example

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on TNAZ. They found that two reactions appeared to be important in the initial decomposition, namely unimolecular nitro-nitroso rearrangement followed by loss of NO and a bimolecular reaction generating nitrosodinitroazetidine. The nitro-nitroso rearrangement could also play a role in the decomposition of other nitramines. This process is discussed by Bernstein in his chapter. An older experiment relevant to the identification of the initially-formed intermediates which has generated much interest is a molecular beam experiment by Lee and co-workers.14 Here, RDX under collision-free conditions was vibrationally excited by multiphoton absorption from a CO2 laser, and the fragments were detected by a mass spectrometer. They concluded that most of the dissociation proceeded by a simultaneous dissociation to yield three CH2NNO2 molecules, which then underwent further fragmentation. This work was surprising since this was the first experimental evidence for the major role of ring opening in the initial decomposition of RDX. It is possible that this pathway is unique to the extremely low pressure in the experiment. Chambers and Thompson 4 showed that the barrier for concerted dissociation must be less than 40 kcal/mole for consistency with the branching ratio observed by Zhao et al14 From studies such as those discussed above, we can generate a list of intermediates likely to be of importance in the decomposition of energetic materials. In Sec. 4, we provide a status report for diatomic and polyatomic intermediates on how these species can be sensitively detected and, in some cases, a discussion of what is known about their reactions. 3. Detection of Intermediates Laser-based diagnostic techniques have found great utility in the probing of flames and combustion environments. Kohse-Hoinghaus 15 has written an extensive review on laser techniques for the quantitative detection of intermediates in combustion processes. Short descriptions of several of the more useful diagnostic methods for the study of the intermediates in the decomposition of energetic materials are presented in the following subsections. 3.1. Laser Fluorescence

Excitation

This technique is one of the most extensively employed techniques in combustion diagnostics 15 and has been applied to studies of the decomposition of energetic materials. Two important attributes of laser fluorescence detection are a high sensitivity and very good spatial resolution. Compared with

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nonlinear laser detection techniques such as coherent anti-Stokes Raman spectroscopy (CARS) 16 and degenerate four-wave mixing (DFWM), 17 the optical setup for laser fluorescence detection is relatively simple; the fluorescence emission from a (small) observation volume is viewed at right angles to the exciting laser beam. This arrangement can be combined with an array detector and a planar laser beam to allow two-dimensional imaging. Laser fluorescence detection can also be employed for local temperature measurements, since the extent of the rotational structure of a band is strongly dependent upon the temperature. The photophysics of laser fluorescence detection can be viewed as a type of action spectroscopy, whereby electronic absorption is monitored by the resulting fluorescence of the excited levels populated by the laser excitation process, as indicated schematically in Fig. 1(a). This scheme allows for much greater sensitivity than the conventional method of monitoring absorption by a reduction in the transmitted probe intensity. Obviously, laser fluorescence detection is applicable only to molecules which have a bound electronic state with an appreciable (preferably 100%) fluorescence quantum yield. At the finite pressures in flames and in the vapors above decomposing energetic materials, the excited state can undergo collisional processes, such as electronic quenching and energy transfer. For quantitative measurements of concentrations, these competing depopulation processes must be taken into account. To correct for collisional effects, rate constants

(a) LIF

(b) REMPI (2 + 1)

(c)1-PI M + + e~

M* ^detect

M Fig. 1. Schematic energy-level diagrams illustrating various optical methods for detecting reactive intermediates: (a) laser fluorescence excitation, (b) resonance-enhanced multiphoton ionization (REMPI), (c) 1-photon ionization. The ionization continuum is indicated with a shaded area. Straight arrows denote coherent radiation, and wavy arrows mark spontaneous emission.

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for electronic quenching and, to a lesser extent, collisional rovibrational energy transfer have been measured for a variety of perturbers and at various temperatures, with particular emphasis on the important OH radical. Kohse-Hoinghaus 15 has comprehensively reviewed the data available as of 1994 and its application to concentration measurements of radicals in flames. Variants of laser fluorescence detection have been advocated to alleviate the need to correct for excited-state collisional effects. One such method is saturated laser-induced fluorescence.15 In this case, very high laser energy densities are employed to excite the radical and hence saturate the electronic transition. In this limit, the signal is no longer affected by variations in the laser power. A significant fraction of molecules in the lower level of the transition are pumped into the excited state, and the dominant loss mechanism from the excited state becomes stimulated emission, thus reducing the sensitivity to collisional effects. Quantitative measurements with saturated laser fluorescence require consideration of the spatial variation of laser energy density, collisional transitions to and from levels not connected with the probed transition, and possible excited-state chemistry, because of the large concentration of laser-excited molecules. Saturated fluorescence is usually modeled as a 2-level system; however, at the pressures in typical flames, collisional energy transfer in and out of these levels is important and must be taken into account. Overall, linear fluorescence, with consideration of the electronic quenching by the major species, is probably a better method than saturated fluorescence. This approach has been considered in detail for the collisional quenching of OH(.4 2 £+), CH(A 2 A), and NO(,4 2 £ + ) in low-pressure hydrocarbon flames.18 With the exception of CH, good agreement was found between measured excited-state decay lifetimes and computed values, obtained using a model for the flame chemistry and literature values of quenching rate constants. The discrepancies for CH suggest inadequate knowledge of the quenching rates for H2O and N 2 at high temperature.

3.2. Ionization

Techniques

Ionization techniques offer the potential of high sensitivity because of the high efficiency with which ions can be detected. The main drawback of these techniques is the need to operate at low pressures in the ionization region if mass selection is required. Electron-impact ionization mass spectrometry to study decomposing energetic materials in situ is discussed in detail in

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P. J. Dagdigiaii

the chapter by Korobeinichev. We confine ourselves here to a brief review of laser ionization methods. Resonance-enhanced multiphoton ionization (REMPI) 19 has found utility in the detection of intermediates in experiments in molecular beams and at low pressures, as well as in flames. A schematic energy level diagram of the most widely used variant of this method, (2 + 1) REMPI, is presented in Fig. 1(b). The sample is irradiated with the focused output of a tunable laser. When the wavelength of the laser is resonant with a 2-photon transition in a molecule, this species will be promoted to an excited electronic state. If the photon energy is sufficiently large, absorption of an additional photon will access the ionization continuum, thereby leading to the creation of molecular ions, which are either directly detected or are amplified on a particle detector. While non-resonant ionization is also possible, the efficiency of ionization will be strongly enhanced at the molecular 2-photon resonances. As an example of the use of REMPI to study the chemistry in a flame, Cool and co-workers20 employed a probe which could measure the instantaneous electron current to detect HCO radicals in a CH4/O2 flame. In many experiments, the resulting ions are injected into a time-of-flight mass spectrometer (TOFMS) to discriminate against background ions of other masses. The use of a TOFMS would necessitate strong differential pumping or an experiment carried out at low pressure, such as the experiments described by Bernstein in his chapter. In experiments where information on the molecular internal energy distribution, such as the temperature, is not required, direct 1-photon ionization may be useful. This technique, which is represented schematically in Fig. 1(c), has been employed in kinetics experiments, with differential pumping of the ionization region. For polyatomic intermediates of importance in the decomposition of energetic materials, ionization at 118 nm (frequency tripled radiation of the tripled 355 nm output of a Nd:YAG laser) can be useful. This detection method has been employed with time-of-flight mass spectrometric detection to observe products from the laser-induced decomposition of several explosives. 13 ' 21

3.3. Absorption

Methods

Direct absorption is perhaps the simplest optical technique to implement in the laboratory and from which to calculate species concentrations. The diminution of the probe light of a given wavelength transmitted through the sample may be related to the molecular number density N through

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137

Beer's law: I = I0 exp(-Naahsl),

(1)

where IQ and / are the light intensities at frequency v incident on and transmitted through the sample, respectively, erabs is the frequency-dependent absorption cross-section, and I is the path length through the sample. Vanderhoff and co-workers22 have employed triple-pass absorption with an incoherent light source and a spectrometer with an array detector to record absorption spectra of self-deflagrating RDX flames. Column densities, and hence concentration profiles, of OH, CN, NH, and NO radicals were determined as a function of height in the flame. These profiles could then be compared with profiles computed from kinetic models of the flame. Parr and Hanson-Parr 23 have employed single-pass direct absorption to obtain concentrations of NO, NO2, CN, NH, OH, and H2CO above the surface of self-deflagrating model propellant/binder composites. These measurements were combined with 2-dimensional planar laser fluorescence excitation and spontaneous Raman spectroscopy to map out species concentrations in the flame. Resonant optical cavities have been employed to carry out long-path absorption measurements with a tabletop apparatus. Intracavity laser absorption spectroscopy (ICLAS) offers significant advantages in sensitivity over traditional absorption measurements and can be carried out in a time-resolved manner so that kinetic studies of transient species are feasible.24 A new, sensitive, recently-developed25 absorption technique, cavity ringdown spectroscopy (CRDS), 26 ~ 28 is seeing increasing use for spectroscopic and kinetic studies of intermediates and is particularly applicable to polyatomic species, whose excited states usually do not fluoresce. Thus far, CRDS has not yet been used to probe the vapors above energetic materials but has been employed for fundamental studies of intermediates of importance in the decomposition of energetic materials, as illustrated below by our recent study of the H2CN radical. A schematic diagram of a CRDS apparatus is presented in Fig. 2. The probed volume is inside a resonant optical cavity bounded by two highreflectivity mirrors. Tunable, pulsed laser radiation is injected into the cavity through one of the mirrors. In the absence of absorbers or scatterers in the cavity, the light will be reflected between the two mirrors, and its intensity will decay because of losses due to the finite (less than unity) reflectivity of the mirrors and other factors such as diffraction. The lifetime

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P. J.

laser beam

_ .... mirror j

Dagdigian

ring-down cavity mirror m

.'1....A. i r^ , —-)

PMT

mode-matching optics (optional)

absorbing medium

computer

^

diffuser

oscilloscope

Fig. 2. Schematic diagram of a cavity ring-down apparatus. Typical parameters for the ring-down cavity are a length of 1 m and radii of curvature of the mirrors of 6 m. The diffuser is placed in front of the photomultiplier (PMT) so that the entire photocathode is illuminated. The digital oscilloscope is used to capture the P M T decay profile from each laser pulse; these waveforms are transferred to the computer for determination of the photon decay lifetime.

TQ of the light circulating within the empty cavity can be expressed as TO

L c(l - R)'

(2)

where L is the length of the resonant cavity, R is the reflectivity of the mirrors (assumed to be the same), and c is the speed of light. Setting L equal to 100 cm and R to 99.9%, we compute a photon decay lifetime To of 3.3/is, which corresponds to an effective path length of 1km. This is an extraordinary path length for a tabletop size apparatus. One challenge for using CRDS in the UV spectral region is that the available mirror reflectivities are lower than in the visible or near IR. The value of R taken above is within the capabilities of commercial optics manufacturers for the UV region. The insertion of an absorber into the resonant cavity will reduce the photon decay lifetime to L

z{{l - R) +

Na^l}

(3)

where I is the path length of the absorber and is usually less than L. The molecular number density (concentration) N can be computed from the

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139

two measured photon decay lifetimes: N=(J^1)(T-1-T-1).

(4)

One attractive feature of CRDS is that the concentration measurement depends on the precision of the lifetime measurements and is independent of the noise characteristics of the source. The application of CRDS for quantitative absorption measurements requires that the absorption features be broader than the cavity mode spacings and the laser frequency bandwidth. These conditions are certainly satisfied for non-fluorescing, polyatomic species. It is also necessary to take care that the transverse profile of the injected light be matched to the lowest transverse modes of the cavity, to avoid multi-exponential decays. 28 ' 29 3.4. Other

Techniques

As illustrated in other chapters of this book, Fourier-transform infrared spectroscopy (see the chapter by Brill) and electron-impact mass spectrometry (see the chapters by Behrens and Korobeinichev) can be employed for the detection of the products of the decomposition of energetic materials. In some cases, it has been possible to detect transient intermediates with these methods, as described in Sec. 2. 3.5. Special Problems Environments

in Probing

Combustion

In their chapter, Parr and Hanson-Parr discuss spectroscopic probing of the combustion of energetic materials under conditions approaching that in the field. Some of the techniques described above are much more amenable to use in laboratory kinetic studies of elementary reactions. For example, the CRDS method is quite susceptible to interference by small particles as they will contribute to cavity losses by Mie scattering. 4. Current Status Report In this section, we discuss the most common diatomic and polyatomic intermediates which are encountered in the decomposition of energetic materials. The spectroscopy of each species is briefly reviewed. In addition, measurements of rate constants for elementary reactions of these species are described for many of the intermediates. The polyatomic intermediates are mainly those encountered in the decomposition of nitramines, since this class of energetic materials has been most intensively studied.

140

4.1. Diatomic

P. J.

Dagdigian

Species

4.1.1. Hydroxyl (OH) The OH radical is a very important radical in combustion and in the decomposition of energetic materials and is present in flames in fairly large concentrations. It is most conveniently detected by laser fluorescence excitation in the A2Y>+-X2H band system, whose origin lies at 308 nm. OH radicals have been extensively studied in combustion media by laser fluorescence excitation. Because OH can be present in high concentrations in flames and in the decomposition of energetic materials, direct absorption techniques have also found utility. 22 It is expected that OH will be most important in the later stages of decomposition. The spectroscopic parameters for this band system, including radiative transition probabilities, 30 are well established. The A2T,+ excited state is subject to predissociation by coupling with several repulsive electronic states which correlate with the ground state O + H atomic asymptote. This leads to a reduction in the decay lifetimes of higher vibrational and rotational levels. There is good agreement between measured decay lifetimes and a comprehensive theoretical treatment of the excited-state predissociation. 31 The availability of rate constants for electronic quenching and collisional energy transfer are of great importance in converting the measured laser-induced fluorescence intensities to molecular concentrations. Because of the importance of OH in combustion and atmospheric chemistry, there has been a considerable effort in many laboratories to measure electronic quenching rate constants of various rovibrational levels of OH(A 2 S + ) by a variety of molecular perturbers and temperatures. 15 There is also considerable information on the rates of reactions involving OH radicals (see, for example, databases on combustion 32 and atmospheric chemistry 33 ).

4.1.2. Cyano (CN) This radical is an important intermediate in the decomposition of materials containing both carbon and nitrogen atoms. Thus, the CN radical plays an important role in the decomposition of energetic materials, since these species usually contain both types of atoms. The CN radical can be conveniently detected through two band systems, A 2 n - X 2 £ + and 5 2 S + - X 2 E + . The former appears through the red spectral region, and the latter in the near UV, with band origin at 388 nm. The spectroscopic parameters 34 ' 35 and radiative transition probabilities 36 for both the

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141

A-X and B-X band systems are well determined. The _B 2 £+-X 2 X] + band system is more convenient for spectroscopic detection of the radical since the oscillator strength of the transition is large and the excited state has a relatively short radiative lifetime (70 ns), while the lifetimes of the vibrational levels in the A state range from 4 to 9 /us.36 Collisional electronic quenching from and energy transfer within the CN(A 2 II) state has been extensively investigated, while corresponding data for the CN(£? 2 I! + ) state is sparse 3 7 - 3 9 The collisional broadening by argon of spectral lines within the B-X (0,0) band has been determined as a function of temperature. 40 The rates of many reactions of CN have been determined, in some cases over a wide temperature range, as for example the CN + O2 reaction. 41,42 Most studies have involved photolytic production of CN and time-resolved detection by laser fluorescence excitation in the B-X band system. In shock tube experiments, narrow-line laser absorption in the CN B-X band system has been employed for the measurement of CN reaction rate constants at high temperature. 43

4.1.3. Imidogen (NH) The NH radical plays a role in the combustion of nitrogen-containing compounds, and hence of energetic materials. This species is conveniently detected through its A3IL-X3'E~ band system, whose origin band is at 336 nm. The spectroscopic constants for this transition are well established. 44 As reviewed recently, the radiative lifetimes of NH(A 3 n) levels have been reported, 45 and radiative transition probabilities for transitions for specified vibrational bands are available.46 Like OH, the lifetimes of higher vibrational and rotational levels are reduced by predissociation, in this case by coupling with a repulsive 5 E ~ state. 47 Rate constants for electronic quenching of NH(A 3 n) have been determined for a number of collision partners as a function of temperature 48 and degree of rotational excitation. 49 Imidogen is an important free radical intermediate in the decomposition of nitramines and other energetic materials. This free radical can be formed in the reaction of H atoms with NCO, among other reactions. The reactions of NH with NO and with NO2 are of particular importance since these yield H atoms and OH, which are important propagators of the laterstage combustion chemistry. The NH + NO reaction has been investigated experimentally by a number of research groups 5 0 - 5 3 to determine the total rate constant as a function of temperature and the branching into several

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P. J. Dagdigian

possible channels: NH + NO - • H + N 2 0

(5a)

-> N 2 + OH

(5b)

->HNNO(+M).

(5c)

This reaction has been investigated with theoretical methods, most recently with variational RRKM theory 54 by Kristyan and Lin. 55 4.1.4. Methylidene (CH) This diatomic radical is included for completeness although it does not appear to play a significant role in the decomposition of energetic materials. However, it does appear in the combustion of organic fuels and in the formation of synthetic diamond. This species is of particular interest in NO x chemistry because of the importance of the CH + N 2 reaction in prompt NO formation. 56 The concentration of CH is usually quite low, because of its high reactivity. Nevertheless, it may be conveniently detected through the y l 2 A - X 2 n and B2T,~-X2H transitions, whose origin bands lie at 432 and 389 nm, respectively. The spectroscopic parameters for both transitions are well determined, 57 and radiative lifetimes and transition probabilities are also available.58 The higher rotational levels of the v = 0 and 1 vibrational levels of CH(£? 2 E~) are predissociated and do not fluoresce.59

4.1.5. Nitric Oxide (NO) The stable free radical NO can be conveniently detected through its A2^+-X2H electronic transition, whose origin band lies at 226 nm. The line positions and spectroscopic constants for this transition are well determined, 60 and radiative lifetimes and transition probabilities are also available.61 Collisional quenching rate constants are available for analysis of experiments utilizing laser fluorescence excitation detection. 62 ~ 64 Strategies for the detection of NO in high-pressure flames have also been considered in detail. 65 Nitric oxide can also be detected by infrared absorption, albeit with much lower sensitivity. Nitric oxide is a very characteristic species in the decomposition of nitramines and other energetic materials. It can be produced upon electronic excitation of the parent compounds, as well as by dissociation of nitroso compounds formed by nitro-nitroso rearrangement. The

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chemistry of the excited electronic states is discussed by Bernstein in this volume. More generally, nitric oxide is an important combustion-generated pollutant. 56 4.2. Polyatomic

Species

4.2.1. Isocyanato (NCO) The NCO radical is an important intermediate in the conversion of fuel nitrogen, including energetic materials, to nitrogen oxides during combustion or decomposition. 56 In particular, it is involved in the pathway for cleavage of CN bonds and subsequent formation of carbon oxides. The reactions of HCN with oxygen atoms and of the CN radical with O2 both yield NCO products, in both cases converting the strong C-N triple bond to the weaker and easily cleaved C-N bond in the NCO radical. The ground electronic state of the triatomic NCO radical is orbitally degenerate (X2U) and hence is subject to the Renner-Teller effect.66 This radical possesses an electronic transition, to the A2YJ+ state, 67 whose origin is at 439 nm and which is strong and convenient for sensitive detection of the radical by laser fluorescence excitation. The A2Y,+-X2H electronic transition shows some activity in the v\ and v% stretch vibrational modes, while bend-excited levels are conveniently detected through hot bands. 68 ' 69 The radiative lifetime of the excited A2T,+ state has been measured for a number of vibrational levels and has a value of ~ 300 ns for the zero-point level. The lifetimes of vibronic levels with > 3000 c m - 1 vibrational energy begin to drop because of an excited-state predissociation. 70 The NCO radical has been detected in flames by laser fluorescence excitation. CoUisional quenching rate constants, required for correction of collisional effects at finite temperatures, have been measured both within flames71 and at room temperature. 72 A number of kinetic studies of the rates of elementary reactions of NCO has been carried out. Laser fluorescence detection of NCO has been employed in the measurement of thermal reaction rate constants. Several exemplary studies are mentioned here. Brownsword et al.73 have employed laser fluorescence excitation in the A2T,+-X2H band system to study the reaction of NCO with N atoms at 298 K. Hershberger and co-workers74 have utilized infrared transient absorption spectroscopy of the CO and CO2 products to study the product branching to N 2 0 + CO versus CO2 + N2 in the NCO + NO reaction. Gao and Macdonald 75 determined the

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P. J. Dagdigian

room-temperature rate constant for the O + NCO reaction through timeresolved infrared absorption spectroscopy.

4.2.2. Nitrogen Dioxide (N0 2 ) This stable free radical is a primary end product in the decomposition of energetic materials containing nitro groups. As a stable product, it can be detected by a variety of methods, including conventional electron-impact mass spectrometry and infrared absorption, as described in the chapters by Korobeinichev and Brill, respectively. The electronic absorption spectrum of NO2 in the visible and near ultraviolet is extremely complex and covers a broad spectral region.76 The spectral complexity arises because of the interaction between the X2 A\ and A2B2 electronic states. There has been much progress, reviewed recently,77 in understanding the spectrum and the coupling between the two electronic states through analysis of the spectra of jet-cooled molecules. However, most of the high-resolution electronic absorption spectrum of NO2 remains unassigned. An additional factor limiting the use of laser fluorescence excitation for the detection of NO2 is the long excited-state radiative lifetimes (ranging from 40 to 200 fis).78 Nevertheless, electronic absorption spectroscopy has been used to detect NO2 above decomposing RDX. 79 CRDS has also shown utility for the sensitive detection of NO2, as illustrated by its detection in the exhaust of a diesel engine.80 An alternative approach, using infrared vibrational transitions, is an excellent detection method for NO2.

4.2.3. Amidogen (NH2) The NH2 radical is an important intermediate in the oxidation of fuel nitrogen and in the decomposition of energetic materials. The reactions of NH2 with NO and NO2 are key steps in the combustion of ADN, as well as in the thermal de-NO^ process. These reactions, which generate major chain reaction propagators H atoms and OH, are further discussed below. The ground X2B\ electronic state of NH2 possesses a bent geometry. This radical has an electronic transition, to the A2 A\ state, toward the red end of the visible spectral region. 81 The X2B\ and A2Ax electronic states become degenerate at linear geometries and form a Renner-Teller pair. There are perturbations between these two states which cause some irregularities in the electronic spectrum. The radiative lifetimes of N H 2 ( J 4 2 > 1 I ) excited levels range from 4 to 10 /is, depending on the vibrational level. 82 ' 83

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Intermediates

145

Rate constants for electronic quenching by various molecules have also been determined. 82 The A-X transition can be used to detect NH2 radicals sensitively by laser fluorescence excitation 84 and has been employed for the detection of the radical in flames.85 One drawback to the use of laser fluorescence excitation detection of NH2 is its relatively long radiative lifetime, which makes this detection scheme especially susceptible to collisional electronic quenching. Laser fluorescence detection has been employed to determine rate constants for reactions of NH2. 86 Amidogen may be conveniently prepared by 193 nm photolysis of ammonia, although account must be taken of NH formed in the secondary photolysis of NH2. As discussed above, knowledge about the reactions of NH2 is important in the detailed kinetic modeling of the decomposition of energetic materials. Several product channels have been considered for the reaction with NO: NH 2 + N O ^ N 2 + H 2 0

(6a)

-> HN 2 + OH

(6b)

- • H + N 2 + OH.

(6c)

To explain experimental observations in the thermal de-NO^ process, processes (6a) and (6b) have been proposed as the major pathways for the reaction. 56 The reaction rate constant and product branching ratios have been measured by several groups as a function of temperature. 87 ~ 91 In the most recent study, frequency modulation absorption was employed to detect NH 2 . 91

4.2.4. Nitrosyl Hydride (HNO) The HNO molecule plays an important role in the mechanism of formation of nitrogen oxide pollutants in combustion, 56 as well in the decomposition of energetic materials. HNO is a closed-shell molecule in its ground electronic state. It is nonetheless included among the transient intermediates discussed in this chapter because of the weak H-NO bond and consequent ease of dissociation. The HNO molecule has an electronic transition, AlA"-XlA'®2 toward the red end of the visible spectral region, and this transition has been used to detect this species by absorption, emission, and laser fluorescence excitation. The sensitivity of laser fluorescence excitation is somewhat low because of the relatively small oscillator strength of the transition, leading to a long excited-state radiative lifetime (ca. 30//s). 93

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Infrared chemiluminescence from vibrationally-excited HNO has also been observed from the NO + HCO reaction. 94 Absorption techniques have found utility for spectroscopic studies of HNO. Pearson et al.95 have employed CRDS of the A-X electronic transition for a comprehensive study of many bound and quasi-bound vibrational levels of the A1 A" state. Through linewidth measurements, they were able to deduce the mechanism of predissociation of the quasi-bound levels. Cheskis and co-workers96 have employed intracavity laser absorption spectroscopy to probe the concentration profiles of HNO in low-pressure hydrocarbon flames doped with nitrogen oxides. A significant complicating factor in laboratory studies, e.g. measurements of reaction rate constants, of this species arises from the relatively weak H-NO bond. Schemes which have been employed for the generation of this molecule include 3-body recombination of H atoms with NO, 95 hydrogen transfer from a molecule with a more weakly bound H atom e.g. HCO + NO -> HNO + CO, 94 and the photolysis of ammonia in the presence of oxygen.97 Thus, the HNO molecule is produced in the presence of other, possibly interfering species, most commonly NO. Measurements of room-temperature rate constants for three reactions involving HNO, namely HNO + O, HNO + 0 2 and HNO + HNO, have been reported. 97 ' 98 Intracavity laser absorption 97 and photoionization mass spectrometry 98 ' 99 were employed to follow the HNO concentration. Rate constants for several other reactions of HNO of relevance to the combustion of nitramines have been estimated through theoretical methods by Chakraborty and Lin.3

4.2.5. Formyl (HCO) The HCO radical is important in the combustion of hydrocarbons and also plays a significant role in the decomposition of energetic materials. Two electronic transitions have been employed in laser fluorescence studies of this radical, namely the A2A"-X2A' transition in the red portion of the visible spectrum and the B2A'-X2 A' transition in the UV. The former transition is not particularly suitable for sensitive laser fluorescence detection of HCO since the excited state is strongly predissociated, 100 and only K' = 0 bender levels have an appreciable fluorescence quantum yield. This transition has been employed with both intracavity laser absorption spectroscopy and CRDS to detect HCO produced in the photolysis of aldehydes. 24 ' 101 The B2A'-X2A' transition 102,103 is well suited for laser fluorescence detection of HCO. Excited-state decay lifetimes have been measured for a

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number of rovibrational levels, 104,105 and the excited state is subject to a Coriolis-induced predissociation, whose rate depends on the vibrational and rotational quantum numbers. Bimolecular quenching rate constants for a number of collisional partners are available for the ground vibrational level of the B2A' state. 106 REMPI has also found utility for the detection of the HCO radical. Cool and co-workers have characterized the REMPI spectrum for the transitions to both the B2A' state and the 3p 2 II Rydberg state. 107 They also showed that REMPI could be used to detect HCO in a methane/oxygen flame.20 The transition was detected by monitoring the laser-induced electron current. No mass selection was employed for detection within the flame. Rather, the HCO radical was identified from the characteristic transition wavelengths for the 2-photon electronic transition. There have been a number of reported measurements of rate constants for reactions of the HCO radical, focusing on the important HCO + O2 reaction. In most of these studies, the HCO concentration was monitored by a spectroscopic method, including diode laser infrared absorption 108 and pulsed 109 or cw 110 UV laser-induced fluorescence. Photoionization mass spectrometry has also been employed in the measurement of HCO reaction rate constants (see, for example, Ref. 111). Photolysis of acetaldehyde at 308 nm is a convenient means to generate HCO.

4.2.6. Nitrogen Hydride (HN2) This species has been proposed as an important intermediate (see Eq. 6(b)) in the thermal de-NO^ process 56 and has also been suggested as an intermediate in the decomposition of nitramines. However, this species is weakly bound and is predicted to have a very short lifetime due to unimolecular dissociation. The lifetimes for the ground vibrational levels of HN2 and DN 2 have been computed to equal 10~ 8 and 10~ 5 s, respectively.112

4.2.7. Nitroamidogen (HNNO) This species can be formed in the 3-body recombination of NH and NO and is an intermediate in the bimolecular reaction channels to form H + N 2 0 and N 2 + OH products. The 2A" state can be accessed from the reagents along a barrierless potential energy surface, while there are barriers to the formation of the more strongly bound trans and cis 2A' states. 113 Both these isomers of HNNO, isolated in a cryogenic matrix, have been observed by vibrational

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spectroscopy.114 The cis form was prepared from the trans form by photoisomerization. Detection in the gas phase has not been reported. 4.2.8. Nitrous Acid (HONO) On the basis of theoretical study of decomposition pathways of HMX and RDX, 2 ' 6 ' 115 nitrous acid is thought to be possibly formed in the initial step of the decomposition in the condensed phase or in subsequent steps. It is also one of the possible end products of the decomposition of energetic materials and has been observed by IR absorption above the surface of decomposing energetic materials. 116 Like HNO, HONO is a closed-shell molecule in its ground electronic state but is nonetheless included in this chapter because of the weak HO-NO bond and ease of dissociation. The HONO molecule has an electronic transition, A1A"-X1A', in the near UV spectral region. This transition does show resolved vibrational bands, but the excited state is predissociative, leading to OH + NO fragments. While an indirect scheme for HONO detection through this electronic transition, which involves monitoring the OH fragment by laser fluorescence excitation, has been employed to observe the formation of HONO in the UV photodissociation of 2-nitropropane, 117 the most promising method using the electronic transition is through an absorption technique. CRDS near 355 nm has recently been employed for the sensitive detection of HONO. 118 Because of difficulties in generating HONO cleanly, i.e. in the absence of NOz, there is a dearth of experimental measurements of rate constants for reactions of this species. A method to quantify HONO concentrations, through the slow HONO + HCl —> C1N0 + H 2 0 reaction, has recently been described. 119 Chakraborty and Lin 3 have estimated rate constants for a number of bimolecular reactions of HONO of relevance in the decomposition of energetic materials. 4.2.9. Methylene Amidogen (H2CN) The methylene amidogen radical is a pivotal radical in the dark zone and can be formed by the dissociation of methylene nitramine (H2CNNO2), the monomer of RDX and HMX. Marston and Stief120 reviewed the spectroscopic and kinetic data available on H2CN as of 1989. Electronimpact ionization through a sampling port in a flow tube has been employed by Stief and co-workers for the measurement of rate constants of some elementary bimolecular reactions involving H2CN. This method suffered from

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interference from vibrationally-excited N2, which has the same mass-tocharge ratio (m/e = 28) as H2CN, and the use of deuterated reagent to generate D2CN alleviated this background problem. Sensitive spectroscopic detection of H2CN for observation of this species either in decomposition processes or in kinetic studies has proven to be problematic. The vibrational frequencies have been determined for matrixisolated H 2 CN by Jacox. 121 Flash photolysis studies utilizing formaldoxime and formaldazine as precursors identified electronic absorptions in the region of 280 nm. 122 ' 123 However, the excited vibronic states of these transitions are predissociative, 124 ' 125 precluding the use of fluorescence excitation as a diagnostic for H2CN. In a coupled-cluster study by Brinkmann et al.,12e the ground X2B2 and low-lying A2Bi, B2A', and C2A1 electronic states were computationally characterized. Davis and co-workers125 observed the previously reported 123 transitions of H 2 CN near 280 nm in a molecular beam study through Rydberg atom detection of the H atomic fragment from predissociation of electronicallyexcited H2CN. Through measurement of the H-atom translational energy distribution, they found that the HCN co-fragment was formed with a wide distribution of internal energy. The measured H-atom recoil anisotropy was consistent with a vibronically-induced transition to the A2B\ state. This work showed that H2CN could be detected by laser-based techniques; however, this scheme is not amenable to kinetics studies. In our laboratory, we have employed CRDS as a sensitive absorptionbased detection method for spectroscopic and kinetic studies of H2CN. 127 The radical was prepared by 193 nm photolysis of formaldoxime (H 2 CNOH). This precursor is convenient because both photolytic fragments, H 2 CN and OH, can be spectroscopically observed in the same wavelength region: the former by the previously identified transitions near 280 nm and the latter through its A-X (1,0) band. Figure 3 presents the room-temperature absorption spectrum of H 2 CN as recorded in our laboratory by the CRDS technique. 127 Two broad features, with additional structure, can be seen. In contrast to the other polyatomic intermediates discussed above, it has not been possible to analyze the rotational structure of these features to make definitive assignments of the upper levels, even with the availability of quantum chemistry calculations for the excited electronic states. 126 In this regard, it would be interesting to obtain a jet-cooled spectrum of the radical. Room-temperature rate constants for several reactions of H2CN with atoms have been determined. Stief and co-workers reported rate constants

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0.008 CO

en Q.

0.006

i _

en a. O

0.004

(1 i _

o CO o to

0.002

278

280

282

284

286

288

laser wavelength (nm) Fig. 3. Room-temperature cavity ring-down absorption spectrum of the H2CN radical. The radical was prepared by 193 nm photolysis of formaldoxime (500mtorr), diluted in 5 torr argon. The spectrum was collected 30 /us after the photolysis laser pulse. The broad features are due to H2CN, and lines in the A—X (1,0) of the OH co-fragment of the photolysis are also observable. Lines in the Qi branch of this band are marked in the plot. Spectrum adapted from Nizamov and Dagdigian. 1 2 7

for the H + H 2 CN and N + H 2 CN reactions. 120 Our group measured the room-temperature H2CN self-recombination rate constant in 5 torr argon. 127 In addition, we also derived the rate constant for the important OH + H2CN reaction, as well as upper bounds to the room-temperature rate constants for reactions with a number of stable molecules (O2, C2H4, CO, CH4, H 2 ). Chakraborty and Lin 3 employed theoretical methods to estimate temperature- and pressure-dependent rate constants and product branching ratios for the reaction of H2CN with N 0 2 , N 2 0 , NO, and OH, as well as for the unimolecular decomposition of H2CN. 4.2.10. Methyleneimine (H 2 CNH) This transient species has been identified in the CO2 laser-assisted decomposition of RDX at pressures of 0.1 to 3 atm by Litzinger and co-workers.11 It is the simplest member of the imine family. These compounds are very reactive and normally decompose by polymerization, oxidation, or hydrolysis. The microwave spectrum of H 2 CNH has been reported, and a molecular structure for the ground electronic state derived. 128 Its infrared absorption spectrum has been investigated by both matrix isolation spectroscopy 129 and in the gas phase. All nine fundamental vibrational frequencies have

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been observed in high-resolution gas-phase experiments. ' In these studies, H 2 CNH was prepared by pyrolysis of methyl amine. In our laboratory, we have developed a spectroscopic probe for H2CNH based on an electronic transition. There has been some theoretical work to characterize the excited states of H2CNH. The ground electronic state has a planar equilibrium geometry. As in the isoelectronic ethylene molecule,132 the Si and T\ states are computed to have a nonplanar geometry, with a dihedral angle of 90° between the planes containing the CH2 and NCH moieties. 133 ' 134 The vertical excitation energies are thus greater than the excitation energies to the zero-point levels of the excited states, and it is expected that the lowest electronic transition would be spread over a broad wavelength range. The dependence of the electronic energies of the ground So and excited Si and T\ states of H2CNH upon the dihedral angle between the two halves of the molecule has been investigated computationally. 133 A conical intersection between Si and So is found near the geometry of the minimum energy of the Si state. This crossing will lead to internal conversion in the molecule, and there is enough energy in the So state to allow dissociation to yield H atom fragments. To this author's knowledge, there was no information on the electronic spectroscopy or chemical reactions of methyleneimine prior to our work. We have developed a spectroscopic probe using electronic absorption spectroscopy so that the reaction kinetics of H2CNH could be investigated. Photoelectron spectroscopic studies have shown that pyrolysis of methyl azide is a very convenient method to generate H2CNH. 135 This process occurs by loss of N 2 and a 1,2-hydrogen shift on the lowest singlet CH 3 N potential energy surface. We have employed this generation technique with CRDS to observe the Si <— So transition in H 2 CNH. Figure 4 shows the evolution of the cavity ring-down absorption spectrum of a flow of methyl azide diluted in argon as the temperature of a heated section upstream of the CRD cell is raised. Spectrum (a) is that of methyl azide, which is known 136 to have a weak absorbance maximum at 286 nm and a strong peak at 215 nm. As the temperature of the heater is raised, the absorbance at long wavelengths increases. There also appears to be an isobestic point near 236 nm. This suggests that methyl azide can be quantitatively converted to H 2 CNH. Similar spectra were recorded with the heated section at distances of 10 to 90 cm from the CRD cell. We assign the new absorption to H 2 CNH. The observed range of excitation energies is similar to that calculated 133,134 for the transition to the Si state of H 2 CNH.

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0.005 co in

0.004

CO Q.

0.003 c '•§. 0.002 ^ o •§ 0.001 H CD Q.

0 233

235

237

239

241

243

245

laser wavelength (nm) Fig. 4. Room-temperature cavity ring-down absorption spectrum of a flow of methyl azide diluted in argon (total pressure 0.6torr) which was passed through a section of quartz tubing located 90 cm from the cavity ring-down cell and heated to (a) room temperature, (b) 450°C, (c) 510°C, and (d) 780°C. Spectrum (a) represents the spectrum of methyl azide, while spectra (b), (c), and (d) show an increasing contribution due to absorption of the H2CNH pyrolysis product.

There does not appear to be any resolvable structure in this transition. A more complete description of our observations, including extension to longer wavelengths and deconvolution to extract the H2CNH absorption spectrum, is presented elsewhere.137 Photolysis of methyl azide should prove to be a convenient source of H2CNH for kinetic studies. 4.2.11. Nitrosomethyl (CH 2 NO) This species can be formed in the decompose to yield either HCN + has been observed in an Ar matrix pairs. 138 Detection in the gas phase

reaction of H 2 CN with N 2 0 and can OH or HCNO + H. 3 Nitrosomethyl through UV irradiation of ketene-NO has not been reported.

4.2.12. HCN Dimers (C 2 H 2 N 2 ) As examples of other polyatomic intermediates which may be important in the decomposition of nitramines, Litzinger and co-workers11'12 observed species of chemical formula C 2 H 2 N 2 , which represents a dimer of HCN. There are actually several isomers of this formula, which are of considerable interest of potential interstellar and prebiotic molecules.139 The most stable of these dimers is iminoacetonitrile (HN=CH-CN), which is a derivative of

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methyleneimine. The next most stable isomer is the (HCN) 2 van der Waals complex, followed by iV-cyanomethaneimine (H 2 C=N-CN), and finally two free HCN monomers. The infrared spectra of the E and Z forms of iminoacetonitrile (both in the gas phase and in a cryogenic matrix) and of JV-cyanomethaneimine (only in a matrix) have been reported. 139 ' 140 In addition, ionization potentials of these molecules are available from observation of their photoelectron

4.2.13. Methylene Nitramine (H 2 CNN0 2 ) This species is likely an important intermediate in the early stages of the decomposition of RDX and HMX. Lee and co-workers14 studied the infrared multiphoton dissociation of RDX in a molecular beam experiment. They interpreted their observations to indicate that two thirds of the molecules underwent a symmetric 3-body dissociation to yield H 2 CNN0 2 , which is the monomer of RDX (trimer) and HMX (tetramer), with the remainder of the dissociations proceeding by N-N bond breaking and loss of N 0 2 . The H 2 CNN0 2 fragment subsequently dissociated to yield the detected HCN, N 2 0 , H 2 CO, and HONO products. The observation of a 3-body dissociation of RDX is controversial 143 since this was unanticipated from previous studies of the decomposition of RDX and probably is a result of the collision-free environment of the experiment. It would be interesting to generate and probe directly methylene nitramine, as well as its nitroso isomer. The spectroscopy of these species is not known. Mowrey et al.liA have carried out a computational study of the decomposition of H 2 CNN0 2 , with particular consideration of the relative importance of HONO elimination versus N-N bond rupture. Harmonic vibrational frequencies for H 2 CNN0 2 were computed in this study. It would also be of interest to have available theoretical estimates of electronic excitation energies. Spectroscopic and kinetic studies of this species will require a suitable means for the generation of this intermediate. The thermal decomposition of H 2 CNN0 2 has been considered theoretically by several research groups, and dissociation rates and product branching ratios have been estimated (see Ref. 3 and references therein). 4.2.14. Hydrogen Nitramide [HN(N0 2 ) 2 ] This species is expected to be of importance in the decomposition of ADN. Chakraborty and Lin 3 have applied theoretical methods to calculate

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P. J. Dagdigian

potential energy profiles for the unimolecular decomposition of HN(N0 2 )2 and for several reactions of this intermediate. This information was then employed to estimate thermal rate constants for these processes.

4.2.15. Other Polyatomic Species Several other large intermediates have been detected mass spectrometrically in studies of the decomposition of energetic materials. These include OST and ONDTA discussed above, observed in the decomposition of RDX. A number of polyatomic species have also been observed in the laser-induced decomposition of other energetic materials, including HMX, 12 ' 145 TNAZ, 13 and NTO. 2 1 To this author's knowledge, no information on the spectroscopy of these larger species is presently available.

5. Conclusion and Prospects for Future Work It would be quite interesting and important in the unraveling of the mechanisms of decomposition to be able to detect larger polyatomic decomposition products since their observation would take us closer to the initial stage of decomposition. Spectroscopic and kinetic characterization of these larger fragments would allow us to construct an even more complete kinetic model for the decomposition of an energetic material. The task of observation of these larger species for the purpose of spectroscopic characterization and measurement of elementary reaction rate constants is, however, very challenging both because of the difficulty of devising suitable generation schemes for their production in controlled laboratory experiments and their detection. In this chapter, we have emphasized the spectroscopic detection of intermediates through the use of electronic transitions. As we consider larger polyatomic species, the use of electronic spectroscopy becomes more problematic. As illustrated by both H2CN and H 2 CNH, it is quite likely that the excited electronic states of larger polyatomic molecules will dissociate photochemically. This leads to broad, unstructured spectral transitions. These processes are considered by Bernstein in another chapter in this volume. Thus, it may be more fruitful to consider infrared vibrational transitions for the detection of the larger intermediates which occur in the earliest stages of decomposition. Progress along these lines could benefit from the further application of sensitive spectroscopic absorption methods, such as CRDS, to the infrared spectral region.

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While this chapter has focused on the spectroscopy and kinetics of transient intermediates in the decomposition of nitramines and other energetic materials, detection of fragments can also be a useful means of detecting the energetic material itself. There has been much interest in the detection of the NO fragment from the laser excitation-dissociation of T N T and other explosive materials. 1 4 6 ' 1 4 7 N o t e a d d e d i n proof: A recent theoretical investigation 1 4 8 of the electronic states of methylene amidogen has shed new light on the electronic assignment of the observed electronic transition in this radical. This study suggests t h a t the experimentally-observed spectrum is due to the dipole allowed B2At - X2B2, and not the dipole forbidden A2BX X2B2 transition.

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CHAPTER 6 ROLE OF EXCITED ELECTRONIC STATES IN T H E DECOMPOSITION OF ENERGETIC MATERIALS

E. R. Bernstein Department of Chemistry Colorado State University Fort Collins, CO 80523-1872, USA

Contents 1. Introduction 2. Experimental Procedures for Gas-Phase Unimolecular Dissociation, Collision-Free Studies of Energetic Materials 3. Collision-Free Studies of Energetic Materials 3.1. Generation of Gas Phase Samples 3.2. Molecular Beam and Supersonic Jet Techniques 3.3. Laser Access to the Molecules 3.4. Time Resolved Kinetics Studies 3.5. Special Considerations for Systems with N^Oj, Moieties (RDX, HMX,...) 4. Results and Discussion 5. Conclusions and Future Work Acknowledgments References

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170 170 170 172 172 173 175 176 186 187 187

1. I n t r o d u c t i o n Energetic materials are a fascinating topic of research. Such materials serve as their own oxidation/reduction system. Much of this fascination revolves around three important fundamental questions: (1) W h a t makes these particular systems so different from other, apparently similar, molecules? (2) W h a t is the sequential reaction chemistry (mechanism) of their decomposition and release of chemical energy? (3) W h a t is the kinetics of these decompositions? T h e very nature of energetic materials 161

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(rapid kinetics, transformation of chemical energy into mechanical energy, final generation of small stable gas phase molecules, highly reactive radical intermediates, and small barriers along the reaction pathways) renders the answers to these questions elusive. The motivations for the study of energetic materials have arisen at a number of different levels. First, the fundamental questions posed above are important features. We want to understand the physics and chemistry of the reactions and processes that govern the conversion of chemical energy (bond enthalpies and Gibbs free energy of formation of reactants and products) into mechanical energy (basically translational energy). All aspects of physical chemistry are involved in this quest: thermodynamic, statistical mechanics, quantum mechanics, and kinetics. By their very nature, these processes are fast (fs to ps) and, thus, their elucidation falls at the cutting edge of chemical physics technology. Second, the importance of energetic materials is in the application of their properties for storage and generation of energy as fuels and explosives. Two issues arise in this instance: macroscopic, in the sense that energetic materials need to be synthesized with the highest possible energy density (Joules/cm 3 ); and microscopic, in the sense that the products of energetic material decomposition (e.g., CO2, O2, N2, • • •) must have as little internal (vibrational and rotational) excitation as possible and as much kinetic or external energy as possible. Thus, synthesis and molecular reaction dynamics (pathways, intramolecular energy redistribution (IVR) between rovibronic degrees-of-freedom, vibrational predissociation (VP), spin states of product radicals, etc.) are central factors in the practical applications and usage of energetic materials. To make the best use of energetic materials, their chemistry and physics must be understood at a fundamental level. This review deals with aspects of the physical chemistry of energetic materials; in particular, the physical chemistry of the initial steps of their decomposition. The present chapter of this volume on recent research on energetic materials deals with initial steps in the decomposition of isolated, molecular, energetic materials from their electronic excited states. We particularly focus our discussion on nitramines. This program immediately raises a series of questions: "Why?" Below we address the motivations behind these interests and this focus. Why study nitramines? Nitramines are one of the most common classes of high-technology energetic materials: they are currently important as military explosives, propellants, and fuels. The general formula for a nitramines is R,R'N(N0 2 ): R and R' can be H, CH 2 , C H 3 , . . . .

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Nitramine is H 2 NN0 2 , dimethyl nitramine is (CH 3 )2NN0 2 , RDX is cyclic (CH 2 NN0 2 ) 3 , HMX is cyclic (CH 2 NN0 2 ) 4 , ammonium dinitrarnine (ADN) is NHjN(N0 2 ) 2 , 1,3,3-trinitroazetidine (TNAZ) is a cyclic dinitroalkyl nitramine [CH 2 C(N0 2 ) 2 CH 2 ]NN02, and more exotic species exist built on aza adamantanes and aza cubanes. 1 ^) The current high-yield military explosives are RDX and HMX formulations and rocket fuels can also be comprised of these materials. Thus, nitramines are an appropriate set of compounds for both fundamental and practical studies of simple energetic materials. Energetic materials, as fuels or explosives, are typically employed at high density because one wants the maximum energy/unit volume as a practical matter. Why, then, study energetic materials as isolated individual molecules? How is this construction relevant to the use of energetic materials? We can address these questions on two levels. First, even though energetic materials are almost always employed as high-density materials, in order to understand their initial decomposition steps and overall mechanism, one must separate and elucidate their intra- and intermolecular behavior and properties. Surely, the first step in their chemical-tomechanical energy transformation must involve the breaking of a molecular chemical bond. Even if the condensed, high density phase behavior and mechanism are different from the molecular one, knowing the molecular behavior and the initial bond rupture or weakening for the isolated molecule is an essential step for elucidation of the entire decomposition process. Thus, the physical chemistry reductionist approach of simplifying, as much as possible, the system to be elucidated, is an important one for such a complex set of events as an explosion. Second, many molecules and intermediate species may indeed decompose in the gas phase, on a timescale that insures isolation. Initiation of the decomposition reaction can occur by rapid heating, arcs, sparks, shocks or from a "primary" explosive that begins the process. All of these initiation methods can generate gas phase species whose molecular chemistry can play an important role in the overall mechanism and kinetics of the energetic material decomposition. Why study the decomposition of energetic materials from excited electronic states? Can simple compression or Shockwaves which, after all, can initiate an explosion, create excited electronic states in molecular crystals? The answer to this latter question is "yes". Place certain organic molecular crystals in a mortar, mechanically grind them with a pestle, and out comes light: the emission can be from O^'0, N ^ 0 , N^' 0 , O^' 0 , C 2 , the molecules comprising the crystals, radicals, The light is called

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triboluminescence, 1 ^) and even laser-induced shock waves external to the crystals can generate excited electronic states. Note that the ionization energy of N 2 itself is over 15.5 eV and this only generates N^(X)! How does this happen and from where does all the energy come? Recall that the electrical potential between crystal planes is ca. 108 V/cm and this can easily remove electrons from molecules in the crystals and especially at defect and inclusion sites. Electrons can be very reactive in initiating chemical decomposition. As will be discussed below, shock and compression waves can generate excited electronic states by excitonic and HOMO/LUMO gap molecular mechanisms. Core electron excitations have also been suggested as the initiating step in condensed-phase valence excitation. 2 Additionally, the initiating event in the decomposition of energetic materials can also be a light pulse from a laser. Thus, the study of the decomposition of energetics (RDX, HMX, etc.) from excited electronic states of isolated gas phase molecules is both relevant and important for their practical application, fundamental understanding, and their long-term improvement, evolution, and development. The "background" research in the area of energetic materials is difficult to separate from that which is presented in this overview in detail. This overview focuses on electronically excited, gas phase, and isolated species: this typically implies supersonic expansion cooling, laser excitation, and some form of fluorescence or mass detection of decomposition of products. The problems associated with such measurements are many, and one must be aware of these difficulties in order to obtain interpretable, reliable, and meaningful data. Here are just a few of them: (1) nitramines (e.g., RDX, HMX,...) are basically nitrogen oxides that absorb in the same regions as other NO x s, and thus, have very confusing laser absorption properties; (2) RN0 2 , NO2, N O , . . . , have many electronic states with intense adsorptions whose cross-sections increase at higher energies, especially for multiphoton adsorption; (3) one must separate processes such as RDX ^ N 0 2 ^ NO, RDX ^ NO, RDX ^ HONO EJ NO + OH, RDX ^ CH 2 NN0 2 ^ N 0 2 , RDX ^ CH 2 NN0 2 ^ HONO EJ NO + OH, RDX ^ CH 2 NN0 2 ^ N 2 0 2 ^ N 0 2 , RDX ^ CH 2 N N 0 2 j^» N 2 0 2 E> N O , . . . , to find "initial steps" in the RDX chain of decomposition events; (4) because of these various pathways and multiphoton processes, one often finds what one seeks (e.g., OH or N 0 2 or NO) as a function of laser wavelength, pulsewidth, and intensity; (5) the first step in the decomposition can be a species not sought (e.g., O); (6) intermolecular

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interactions can change the products, even the initial steps; (7) model systems and model potentials can often lead to difficulties because details do matter with so many potential pathways separated in energy by only 1-10 kcal/mol; and (8) many of the reaction paths that lead to products have activation energies and barriers that render the "obvious path" (e.g., breaking of the weakest bond) not the one taken in the molecular decomposition process. These difficulties, plus rapid processes and potentially dangerous experiments, make energetic material research both exciting and challenging. Early references to the importance of electronic excitation for the initial steps in the condensed phase detonation process can be found in the works of Williams, 2 ^ ~2(h) Dremin 2 ^ and S h a r m a . 2 ^ - 2 ^ The relation of shock and impact sensitivity to electronic excitation is correlated with the shake-up promotion energy observed for x-ray photoelectron spectra. These excitations arise for core ionization of an atom in the time frame of ca. 10 fs, which is argued to be smaller than the transit time for a detonation wave in a solid over the dimensions of a molecule (<~100 fs). The Coulomb attraction of the ionized core for the valence electrons is of the order of the perturbation caused by high pressure (ca. 1Mb) or shock. Thus, a correlation between electronic excitation and shock-induced behavior could be postulated. The materials most likely to detonate then are those that experience electronic excitation in response to compression and shock. Basically, the mechanism is suggested to be an electron transfer from the HOMO to the LUMO of an energetic molecule due to reduction of the HOMO/LUMO gap upon shock compression. Other processes in such circumstances have been discussed above. Stephenson and co-workers3 have obtained ps photolysis results for dimethylnitramine (DMNA, (CH 3 ) 2 NN0 2 ) at 266 nm and find N 0 2 and NQ 2 as products. Three electronic transitions overlap in this region. The N 0 2 (X) is detected by 30 ps excitation at 532 nm (but is only one photon absorbed?) and N 0 2 (A) is detected by emission. Some collisional processes are present for these studies, and the 266 nm energy/pulse falls between 50 and 200 /iiJ, while the 532 nm energy/pulse can be as high as 1 mJ. Possible multiphoton transitions and effects cannot be excluded from these results because saturation effects for transitions following the initial one are difficult to suppress. Earlier studies of photodissociation of nitro and nitramine compounds are referenced in this report. We will discuss the more recent studies of dissociation of energetic materials (specifically, RDX and HMX) in the main section of this review.

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In the last few years, experiments on energetic materials have begun to address excited electronic states of energetic materials, and some of these studies serve as background for the main body of results we wish to present in this overview with regard to RDX and HMX. In particular, two publications seem particularly relevant. Garland et aZ.4 study the laser-induced decomposition of NTO (3-nitro-l,2,4-triazol-5-one

N

J,I !1

NO,

)

in the solid state. This study uses 266 nm laser radiation to heat solid NTO and 118 nm radiation to ionize it and its products in the gas phase. Product translational energies and relative yields are obtained in the singlephoton (118 nm, 10.5 eV) ionization/time-of-flight mass spectrum analysis. Translational energy depends on vaporization laser fluence (J/cm 2 /pulse). Decomposition of NTO is shown to be statistical and unimolecular, and the temperature dependence of NTO product yield is used to suggest the initial decomposition channels. One of the more interesting results of these studies is that loss of an O atom (not C-N bond session) occurs to yield the nitroso-TO analog ( ] S ) . Additional channels seem to be loss of NO2 and a nitro/nitrite (NO2/ONO) rearrangement followed by loss of NO. We find this work very interesting and informative, and we should take three important lessons from it in retrospect: (1) laser ablation, even at 266 nm at which wavelength the energetic molecule of interest absorbs, generates the neutral molecule in the gas phase without fragmentation/decomposition almost exclusively; (2) the lowest energy bond in a molecule is not always the one that ruptures first or most readily in a fragmentation; and (3) the fragmentation path can involve many "non-obvious" steps, such as isomerization and rearrangement, before the fragmentation step, reflecting low barrier paths to decomposition. Even though this process probably involves a ground electronic state path, it still shows us the complexity of energetic material unimolecular initial fragmentation behavior. Hankin et al.5 again use 266 nm laser ablation to generate neutral, unfragmented energetic molecules: trinitrobenzene (TNB), trinitrotoluene (TNT), and trinitrophenol (TNP) in the gas phase, followed by 80 fs, 800 nm laser pulses for multiphoton ionization. This process generates both precursor molecular ions as well as fragmentation daughter species. With this very high-energy ionization due to multiphoton absorption at 800 nm (at least seven photons for ionization alone), many fragmentation paths are observed. A good deal of theoretical work has appeared recently on the decomposition of energetic materials forming excited electronic states with

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special attention given to the excitation mechanism.6 Point defects (lattice vacancies) in RDX are a focus of much of this effort as they are found to lower the HOMO/LUMO or band gap in this material by more than 1 eV. Compression induced effects on the electronic structure of RDX are also investigated and edge distortions are found to be very significant for moving excited electronic states into the band gap. The authors suggest that such electronic state perturbations give rise to conditions that favor initiation and decomposition of RDX by external pressure. Excited electronic states are conjectured to play an important role in the initiation process:7 they are easily generated, more reactive, and have faster kinetics. Electronic excitations can be induced by an impact wave propagating through a crystal of RDX. The electronic excitations and various lattice defects are coupled to reduce the optical gap between valence and conduction bands. Pressure induced by the impact wave front also reduces the band gap. This promotes HOMO/LUMO degeneracy allowing N-NO2 and other bond breaking and bond creating rearrangements to initiate the detonation. A combined theoretical and experimental study of the relevance of electronic excitation and Shockwave pressure for initiation of RDX is presented by Kunz et al.6^ These authors put an RDX crystal sample under 5 GPa of pressure and irradiate it with 532 nm laser light at 1-10 J/cm 2 fluence. Each event alone would not cause initiation and detonation, but together they do. The claim is that electronic states in the gap (the crystal is still clear and colorless) absorb one photon and/or multiphoton processes are now much more intense such that decomposition chemistry is favorable. Exciton/hole mechanisms have also been suggested 6 ^ for the electronic excitation involved in the initiation process. Another recent theoretical study 8 has considered the combined effect of pressure, defects, and electronic excitation to show that proton transfer can occur in molecular crystals. Excited electronic states can play an essential role in this phenomenon and electron transfer reactions can accompany the translocation of a proton both intra- and intermolecularly. Charge transfer or excimer formation can be an initial source of a multistep reaction pathway. Lewis9 has performed density functional theory calculations that suggest HONO can form intermolecularly in an HMX crystal, which would be the initial step in a decomposition reaction. While this work does not directly compute excited electronic state contributions to the proton or hydrogen atom transfer, such a mechanism would be enhanced for

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excited electronic states as discussed above for either proton-coupled electron transfer, hydrogen atom transfer, or electron transfer. The general distillation of these studies of energetic materials is that many different electronic and vibronic states can contribute to their practical behavior, and that isolated molecule studies cannot only lead to an elucidation of energetic material molecular behavior, but they may also be a real, practical interest for the early stages of initiation, decomposition, and reaction propagation. The above discussion should enable the interested reader to get into the accessible and recent literature, both theoretical and experimental, dealing with electronic excited state mechanisms for energy material decomposition. Moreover, these current studies give one references to the older important, but often more difficult to access, government and conference reports. But, before we go into our main theme dealing with new electronic excited state pathways for RDX and HMX initial decomposition reactions, two studies not directly related to excited electronic state behavior but still very instructive for their results and comparisons must be discussed. The studies of interest are by Haas et al.10 and Lee et al.11 Consider first the report by Haas et al. of the decomposition of RDX and HMX in the gas phase excited by an IR CO2 laser at ca. 10/Ltm. In separate experiments, RDX and HMX are seeded in a supersonic expansion into a vacuum. They are heated to 150 and 180°C, respectively, and seeded into a He flow. The laser output consists of a 100 ns "spike" followed by a 1.5/is tail. The primary decomposition product is suggested to be OH, which is detected and monitored by a Nd/YAG pumped dye laser photons at the appropriate wavelengths (A2Y>(v = 1) <— X2U(v = 0)), for the generation of laser-induced fluorescence (LIF). Of course, OH is found and is assumed to be the primary dissociation product from hot RDX and HMX in their electronic ground states. The five-membered ring RDX/HMX unimolecular intermediate is assumed to be the path for the formation of OH. Apparently, both the CO2 and the dye laser photons must be present to generate OH and detect it through LIF. The OH radicals could be formed also from HONO generation first, still with the above mechanism. A doubt about these results must be raised: the OH could be produced in a multiphoton IR plus UV photon(s) process that would generate OH from an excited electronic or even ion state of RDX and HMX. We mention this latter possibility because of the work of Lee et al.11 Lee and co-workers use photofragmentation translational spectroscopy to study the IR (10.6/xm) multiphoton decomposition of RDX and a number of other energetic and model

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materials (e.g., nitroalkanes, TNAZ). The results are very different than those of previous work: they are unique, surprising, and quite instructive. RDX is found to have two competing primary pathways for decomposition: triple concerted reaction yielding three methylene nitramine (CH2NNO2) fragments and elimination of NO2 with branching ratios of 2/3 and 1/3, respectively. Following the primary loss of NO2 for the latter path, the remaining fragment continues to decompose in competing secondary steps: loss of HONO and loss of a second NO2. The methylene nitramines produced in the concerted primary step then decompose in another two secondary steps to yield HCN and HONO in one path, and N2O and H2CO in another. For nitroalkanes using the same techniques, one finds that the initial step in the decomposition by IR multiphoton absorption is isomerization from, for example, CH 3 N0 2 to CH3ONO. 11 Then C H 3 0 and NO products are detected. For nitroethane and nitropropane, HONO is found to be a major product. The simple C-NO2 bond rupture pathway is also found to be a major one. The surprising result here is that other pathways are open beside the C-N bond rupture and that the nitro/nitrite isomerization is an important part of the unimolecular collision free dissociation reactions. For TNAZ at low IR laser fluence, the sole primary reaction channel is loss of NO2. At high fluence, a second NO2 is found as a product. n ( b ) After loss of two NO2 moieties, the remaining fragment decomposes to C3H4 (CH 2 =C=CH 2 ) and N 2 0 . This suggests that the two nitro groups of the primary and secondary steps are from the geminal dinitroalkyl group: HONO is not found; nitro/nitrite rearrangement followed by NO loss is not found; and no concerted ring scission, such as observed for RDX, is found. One concludes from these studies that the dissociation process for RNO2 molecules (CH 3 N0 2 , RDX, HMX, C 2 H 5 N0 2 , 2-N0 2 C 3 H 7 , etc.) is a collection of competing pathways, activation energies, transition states, and quite dependent on the potential energy surface (electronic state) upon which the dissociation occurs. Before one can fully appreciate the condensed-phase behavior of energetic materials, one must understand the molecular processes that occur as a function of electronic state because solid state behavior can readily generate different electronic states in the initiation process. In the next sections of this overview, we will present some results on dissociation of RDX, in gas phase and for collisionless conditions, from excited electronic states. Given the difficulties discussed above for achieving consistent results from what appear to be similar experiments, we will speculate on the reasons for these difficulties.

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2. Experimental Procedures for Gas-Phase Unimolecular Dissociation, Collision-Free Studies of Energetic Materials As indicated in the Introduction, energetic materials research is fraught with difficulties and pitfalls, and many of these arise even if one is aware of the potential issues. In this section, we will try to explain how unimolecular, collision-free, gas-phase, dissociation experiments can be accomplished on excited electronic state potential energy surfaces of energetic materials. Fundamentally, such studies are not different than similar ones on stable radicals or molecules, but low vapor pressure, nitramines (RN2O2), intense UV absorption, rapid kinetics, large molecules (rapid IVR), large densities of state, no well-resolved rovibronic structure, safety concerns, and others, make these systems difficult to understand and elucidate definitively. We will try here at least to enumerate the problems, if not solve them all. 3. Collision-Free Studies of Energetic Materials This section presents the various techniques that need to be employed to carry out excited electronic state studies of unimolecular energetic material behavior: (1) generation of gas phase samples; (2) molecular beam or supersonic jet techniques; (3) laser access to the molecules; (4) time-resolved kinetic studies; and (5) general problems of RNO x studies. 3.1. Generation

of Gas Phase

Samples

Most energetic materials are solids (TNT, RDX, HMX, TNAZ, TATB, etc.) and decompose upon heating. Thus, vaporizing them is not a completely clean or safe process. Lee et al.11 heated RDX to 134°C, while Haas et al.10 have heated it to 150-160°C. Others have even used higher temperatures to increase the vapor pressure over the solid. At least a few per cent of the RDX will generate NO2 at temperatures around 150 to 160°C,12 so if one looks for NO2 in a sample that has been heated to these temperatures, one surely finds it, especially using optical, laser techniques. This may not be such a problem for the technique employed by Lee et al. because these workers measure the angle and flight time (center-of-mass velocity) for the generated fragments in a time-of-flight mass spectrometer and can thus distinguish between different sources of the same species in the beam system. The thermal approach to generating vapor phase energetic materials can be employed for production of a static sample in a cell, an effusive beam of molecules exiting an oven into a vacuum system at lower pressure, and also

Role of Excited Electronic

States

171

a supersonic expansion of the energetic molecules contained in a He, N2, Ar, He/Ne, etc., flow. The second method employed for generation of gas phase energetic materials is laser ablation. Here, three methods have been employed. First, a pellet or crystal of the energetic material is generated and placed at the tip of a probe that is then irradiated with a pulsed laser. This laser can be at almost any wavelength, but typically, one of the Nd/YAG laser outputs is used (e.g., 1.06, 0.532, 0.355, or 0.266/im at ca. lOns/pulse at a 10Hz rate). The pellet typically sits in the flow path of gas either inside or just outside a pulsed, supersonic nozzle (10Hz), such that the vapor of the energetic material is entrained in the effusing gas from the nozzle. This expansion cools the energetic material to a translational temperature of Tt rans ~ 1K, a rotational temperature of T rot ~ 10 K, and a vibrational temperature of Tv;b ~ 25 K, as is quite typical for large organic molecules.13 This technique has been shown, even when a molecular resonance is used for the ablation process (e.g., RDX at 266nm), to generate unfragmented species. 4 ' 5 Second, the energetic material can be applied to generate a thin film. The pure energetic material film is best formed on a drum from a solution. For example, an acetone solution of RDX can be sprayed on a graphite drum that is turned by a small motor. The solution is safe to handle, and the acetone evaporates as the sample reaches the drum. 14 The drum with an RDX film is then placed in a pulsed supersonic nozzle, laser ablation system. The ablation laser pulse hits the drum, and it is heated locally and the sample vaporized. The drum is rotated and translated so that each ablation laser pulse accesses a new sample. This method, too, is shown to generate unfragmented vapor phase energetic molecules. Third, an energetic material in some inert matrix can be placed on a metal (or dielectric, as above) drum in a matrix assisted laser desorption ionization (MALDI) experiment. A typical matrix has been dihydroxybenzoic acid. 15 Both ions and neutrals are thereby generated by laser ablation of the matrix, but fragmentation is not typically observed. The matrix can be placed on the drum with the same spray technique discussed above for thin films of RDX. Currently, we use a variant of this matrix or MALDI method. 16 The matrix and RDX are sprayed from an acetone solution onto an aluminum drum that has been electrochemically oxidized (~50/im depth). The prepared surface has a high area and is microscopically rough. The matrix is the laser dye rhodamine 6G (R6G) and the ablation is at 532 nm which is strongly absorbed by the dye. Again, RDX (or other energetic material) is placed into a supersonically-expanded gas stream with no decomposition: even the matrix R6G is not completely fragmented in the ablation process as it is

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observed in the mass spectrum of the sample following laser ionization. An absorbing matrix (carbon, R6G) is an excellent way to ensure access to almost any sample in the gas phase that has "no" vapor pressure and is not absorbing at the ablation wavelength. 3.2. Molecular

Beam and Supersonic

Jet

Techniques

Molecular beam/supersonic jet/laser spectroscopy techniques 17 have been available since the mid 1970s for the study of cold isolated molecules, so a detailed discussion of them can be found in many review articles and monographs. We have referenced just a few of them here. Nonetheless, the importance of this approach to the field of energetic materials is less well described and worth emphasizing here. First, beams provide a collision-free (mean free path >1 km), high-density (10 10 to 1012 seeded molecules/cm 3 ), directed flow sample perfect for time-of-flight mass spectroscopy and laser access (laser-induced fluorescence (LIF) and resonance enhanced multiphoton ionization (REMPI)). The low temperatures reached in this environment enable high-resolution mass and rovibronic spectroscopy to be explored even for large molecules. Second, laser ablation of the sample is well coupled to beam techniques, especially pulsed beams. Thus, sample generation is pulsed, lasers are pulsed, the beam is pulsed, and TOFMS is pulsed: very little sample is used under these circumstances and safety issues are greatly reduced. Third, because the sample is moving in a given direction with a very small velocity spread (Ttrans ~ 1K) and good intensity, many sophisticated spectroscopic approaches are available for study of energetic materials. These can include translational spectroscopies, 11 imaging techniques, 18 multiresonance spectroscopies, and reaction studies. Fourth, intermolecular reactions, solvation behavior, and crystal properties can be explored using the approach through the generation of solute/solvent clusters, and multimers of the energetic species. As one can see, even from this rather abbreviated presentation, the beam/laser approach to energetic material research can be very useful and rich. 3.3. Laser Access to the

Molecules

The sample of interest, monomer, cluster, multimer, is in a vacuum system in a beam and, thus, many laser approaches can be employed in these studies: Doppler-free single and multiphoton spectroscopy, Fourier Transform techniques, four wave mixing and other nonlinear spectroscopies, multiresonance approaches, and many others. 19 Because this has not been

Role of Excited Electronic

States

173

a major activity for energetic materials, we only mention such approaches here to emphasize how many more techniques are available to aid in the elucidation of energetic material properties and behavior.

3.4. Time Resolved

Kinetics

Studies

When thinking about the photodissociation of energetic materials, one must, of course, consider the time resolution of the system (laser plus detection). While energetic species are not the only ones that can undergo photodissociation, they do have rapid dissociation kinetics because of their chemical (R(NNC>2)n) and physical nature. The Heisenberg relation AEM ~ h/2 {h = h/2n = 1.055 x 1CT 34 J s = 5.27 x l O " 1 2 ^ - 1 s = 1.5 x 10 _ 1 Hz s) implies that a pulse of 5 ps duration cannot be sharper in energy than ~ 1 c m - 1 (at the Fourier Transform limit) and thus, a 5 ns pulse can have an ultimate width of no less than 10 _ 3 cm~ 1 , and a 5fs pulse can have an ultimate width of 10 3 cm - 1 . Typically, one is pleased if a laser system is operating near five times the "transform limit." This combination of time and energy resolution has three effects on potential kinetics issues (such as, what is the initial step in the dissociation of RDX at a particular energy or excited electronic state?): (1) if the dissociation is fast (say, 100 fs) and the excitation pulse from the laser is long lived (say, 10ns), then by the time the pulse is over, and measurements (TOFMS, LIF, stimulated emission, etc.) can begin, many photons may have been absorbed from the laser pulse by the parent molecule and/or the primary initial product, and secondary, tertiary, etc., products, so that one may have no idea how to answer the "initial step" question; (2) as one tries to address the rapid kinetics by shorter and shorter time laser pulse, the line-width of the pulse is increasing and different excited states and linear combinations of excited states can be accessed so one is not accessing the same process with a 10 fs pulse as one is accessing with a 106 fs pulse; and (3) shorter pulses in time also generate coherence effects, such that wavepackets are generated and coherent linear combination of rovibronic states can be created by the excitation pulse that have their own dynamics on the excited state potential surface — even two or more excited electronic states can be coherently excited and potential surface approximations are no longer useful in this instance. One must always keep in mind that the dissociation process is governed by a set of competing processes characterized by VP (in the RRKM limit), IVR (Fermi's Golden Rule), coherence, and electronic effects that control the overall appearance of the dissociation.

174

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RDX and HMX may be large enough molecules that the dynamics in the gas phase and the condensed phase (density of states) are similar if only intramolecular interactions are important, but this is certainly not yet proved. For a 50 fs pulse, IVR destroying all coherences in the system, and a 100 fs repulsive dissociation process, the kinetics of the initial step in the dissociation of RDX could be evaluated. An example of such an event might be as shown in Scheme 1.

I j / *~

—

N

^ '

+ hv

—+-

I |^NN

+ O

•-.

OR NO, O.N

^ ^

N0 2

OR >- 3CH 2 NN0 2 OR NO

o

+

rr

+

OH

OR

OR

r^i Scheme 1.

HONO

Role of Excited Electronic

States

175

Another possible problem for laser/molecular "kinetics" studies has to do with laser power and multiphoton processes. A 1 mJ laser pulse at 10~ 8 s is 10 5 W peak power, but a similar pulse energy at 1 0 - 1 4 s is 10 11 W peak power (same number of photons in a much shorter time). Nonlinear optical effects, multiphoton resonant and non-resonant absorption, stimulated processes, and saturation can be controlling issues in such instances, but keeping peak power the same (e.g., 105 W on the ns, ps, fs timescales) for all timescales may not be feasible for an acceptable signal-to-noise ratio detection limit. We will elaborate on this point for energetic materials that contain nitramine groups and for NO x .

3.5. Special Considerations for Systems Nx Oy Moieties (RDX, HMX,...)

with

All of the suggested cautions and problems discussed above for the measurement of photodissociation mechanisms for molecules are important concerns for energetic materials containing the N^Oy moiety. First, nitramine (-NNO2)-, nitro (-NO2)-, nitroso (-NO), nitrite (-ONO) groups are very labile and can rearrange (RNO2 —> RONO), as well as dissociate, as an initial step. Second, these species typically have a high density of electronic states with an unfortunate spacing such that multiphoton resonance absorption is both intense and saturated (hard to demonstrate by laser power dependence studies). Thus, even for the study of NO2 dissociation to NO + O, much controversy and conflicting results and interpretations can readily arise 20 because both NO and NO2 can absorb the same photons. As pointed out above, products such as HONO, NO2, NO, N2O2 can thereby be difficult to identify as the "initial step" in the dissociation of energetic materials (RN^Oy) from excited electronic states. An example of such problems could be the IR/LIF study to find OH from gas phase RDX, 10 while the IR-only study finds 3CH 2 N 2 02 species as the first product set from RDX dissociated on the ground electronic state surface under collisionfree conditions. The interpretation of symmetric CH2N2O2 decomposition seems hard to fault under these circumstances, but secondary pathways could possibly come from very rapid, further decomposition of CH2N2O2 through subsequent IR photon absorption. One clearly sees that such considerations are speculative and difficult to substantiate; nonetheless, one must eventually explain all data for such processes before one can claim a complete understanding of the initial steps in the decomposition of energetic materials from different electronic states.

176

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4. Results and Discussion We have been able to find in the literature (after a thorough, but not exhaustive search) two references that deal directly with photodecomposition of energetic materials. Reference 21 refers to some earlier work and historical development. Reference 16 is from our laboratory. These two studies have significant differences (excitation wavelength, sample introduction, sample temperature, etc.) and reach somewhat different conclusions. Nonetheless, they are instructive because they bring out some of the difficulties mentioned above that can plague laser studies of nitramine and nitro compounds. The goal of these studies is to find the decomposition pathways for energetic materials that are active in excited electronic states: which state, how many photons absorbed, laser pulse duration, detection methods, etc. all contribute to the actual attainment of this goal. The studies of Ref. 21 deal with the decomposition of cyclic nitramines: RDX, HMX, TNAZ, and DMNA (dimethylnitramine (CH 3 ) 2 NN0 2 ). RDX, HMX, and TNAZ are all military explosives. According to this source (at a military laboratory), no prior studies of dissociation or initiation on excited electronic states have been reported. We concur with this assessment based on our survey of the open journal literature, but rely on Ref. 21 for the more comprehensive statement. The basic conclusions of this study (Ref. 21) at 248 mm (KrF laser) for gas phase RDX, HMX, TNAZ, and DMNA are that electronically excited N 0 2 ( 2 B 2 ) is created by a single-photon process: the N 0 2 then emits in the visible (400-800 nm). The radiative lifetime of the 2 B 2 state of N 0 2 was found to be 26 ± 1 /is. The single-photon process is a result of primary, initial N-N bond scission in the electronically-excited nitramine species. Electronically-excited OH* (A 2 E) was also observed and thought to be generated by a two-photon mechanism: the OH* was suggested to arise from the formation of a vibronically-excited HONO. The HONO is presumably derived from a five-membered ring structure of the form [N-N-O-H-C]. We now explore these findings to learn how they are determined and what ambiguities, if any, might arise for them. The experiment was based on a 15 ns KrF laser at 248 nm for photodissociation of the gas phase energetic materials. The cell for measuring fluorescence from the decomposition products was placed in a 250° C oven. The cell was stainless steel with quartz windows. The parent energetic material was placed in a small reservoir. The energetic material flowed out of the reservoir into the cell and was pumped away; mostly new energetic material was presented to each laser pulse and products from the previous

Role of Excited Electronic

States

177

laser pulse were not present for the next one. From our experience, NO, NO2, HONO, and other species are very difficult to remove from a vacuum system because they adhere to most surfaces and may react there (e.g., N 0 2 -> NO + O, HONO -> HO + NO, etc.). The oven and entire cell system with sample were kept at a constant temperature (155°C for RDX, 210°C for HMX, 84° C for TNAZ, and 25° C for DMNA). The cell was pumped continuously and fluorescence was measured from excited state NO2 and OH photoelectrically. The 248 nm laser beam passed through the cell, excites and dissociated the energetic material, and NO2 and OH fluorescence were collected. The energy/pulse of the KrF excimer laser was not given explicitly, but can be calculated to be 20-60 mJ/pulse for a 7 mm diameter beam from a fluence of 50-150 mJ/cm 2 . Three potential problems arise from this experimental procedure: (1) at these given oven temperatures (155°C for RDX, 210°C for HMX, etc.), thermal decomposition of RDX could be as high as 4% 22 ; (2) while laser energy/pulse is not specified, it could be much too high for single-photon photodissociation to occur; and (3) dissociation from excited electronic states of energetic materials can be expected to be from repulsive electronic states and could be as fast as lOOfs or less, which would expose products to continued and further laser excitation and fragmentation for a 15 ns pulse duration. I do not suggest that these data are incorrect or misleading: we must, however, examine the approach and be certain that we measure what is intended. All energetic materials studied in this work (RDX, HMX, TNAZ, DMNA) and others (nitroalkanes and tetranitromethane) seem to give the same results. The NO2 emission appears to be single 248 nm photon generated, while the OH emission seems to be two-photon generated. Such behavior could mean: (1) RDX

u

HONO

(2) RDX

u

N02;

(3) N 0 2

U

u

OH* + NO;

NO*.; or

(4) strong multiphoton behavior with some saturation for absorption beyond the first photon for all species. While these questions do not imply that the reported studies are deficient, they do suggest that more work may be needed to reach a final conclusion about such processes. The second investigation of energetic materials decomposition from excited electron state surfaces16 has both similarities and differences with

E. R.

178

Bernstein

the study of Ref. 21. Both experiments are ns pulsed laser dissociations and do not directly probe early decomposition steps, because the laser pulse duration is roughly 104 times as long as the dissociation timescale, and these photons are present after the initial products are formed. On the other hand, for the results of Ref. 16, RDX is generated by laser ablation, which is known not to dissociate large molecules with weak bonds, cooled in a supersonic expansion, and the issue of laser intensity has been explored. Below we evaluate the work of Ref. 16, its consistency with Refs. 20 and 21, and some unpublished preliminary data that points to and suggests a possible pathway for the decomposition of energetic nitramines like RDX, HMX, TNAZ, and others. Because RDX is thermally unstable, Ref. 16 generated cold, isolated, collision-free RDX using laser ablation in a matrix. To be even more careful that the RDX did not dissociate during the vaporization process, it was isolated in a laser-absorbing matrix of laser dye (R6G). The energetic material and absorbing R6G were sprayed onto an aluminum drum, the surface of which was electrochemically oxidized to form a porous coating to hold the matrix and increase surface area. This coated drum was placed in a laser ablation supersonic nozzle assembly as described in Ref. 16 and pictured in Fig. 1. The ablation laser was a doubled Nd/YAG laser (532 mn al 1.0 us/pulse.

~0.5 mJ, 5 x 106 W/cm 2 at the drum/matrix surface). The important point is that the matrix and not the energetic material absorbed the 532 nm TOFMS

Ablation Nozzle Ablation Laser 532nm

(MCP)

•

1 1

1

N

Molecular Beam

\iu

Pulsed Valve Expansion Gas: He

^Ionization / Fragmentation Laser Fig. 1. Schematic diagram of the pulsed supersonic nozzle/laser a b l a t i o n / T O F M S / fragmentation/ionization system for the generation of energetic materials in the gas phase.

Role of Excited Electronic

States

179

radiation. This technique placed the molecule of interest into the vapor phase without fragmentation. 4,5 Some easily fragmented species, such as dopamine, epinephrine, peptides, etc., can be generated in the vapor phase in this manner. 23 Other researchers also attest to the success of this process, as discussed above. The ablated material entered a 2 mm x 6 cm channel, and was mixed with carrier gas (10% Ar/90% He at ~100psig) from the pulsed nozzle, and expanded into the vacuum chamber. The supersonic expcmsion cooled molecules to -^trans '"""'' 1K, T rot - 5 K, and T vib ~ 25 K. This enabled, to a fair approximation, knowledge of the state of the energetic molecules prior to electronic excitation. The collisionless molecular beam then entered a time-of-flight mass spectrometer where it intersected with photolysis/product detection/ionization lasers. For RDX studies, the same laser completed the photodissociation/product excitation/ionization process; the laser was a Nd/YAG pumped dye laser at ca. 226 nm. This laser was used to excite and ionize the NO A <- X transition for (0,0), (1,1), (0,1), (0,2), (1,3), and (0,3) rovibronic transitions. The energy of this laser was in the range 0.2 to 0.5mJ/pulse with an intensity of 1.3 - 2.1 x 10 8 W/cm 2 . After reading this far, one can, of course, immediately anticipate some potential experimental problems: (1) Is laser ablation of the RDX, even under these conditions, perfect? Is no NxOy generated? (2) How can one distinguish between NO, NO2, N2O2, N2O, as the "initial" fragment because one or more photons of 226 nm radiation can be absorbed by all N x O y species in addition to RDX and these small species can readily be fragmented by such absorption processes? (3) How can one know the "initial step" with a ~10ns pulsewidth for the photolysis/detection laser? As we discuss the data obtained from these experiments, we will try to address these issues, with varying degrees of success, and then finally plan further assaults on the decomposition kinetics and mechanisms of energetic materials. Before getting into the results of this supersonic molecular jet/laser ablation investigation of the initial steps of the decomposition of RDX from excited electronic states, we should emphasize that ablated molecules are cold as they exit the nozzle and enter the collisionless region of the beam. The point where the RDX and other molecules are accessed for excitation/dissociation/detection of products in the ionization region of the TOFMS is at very low density, ca. 108 RDX molecules/cm 3 and 1010 He atoms/cm 3 . Thus, the dissociation products do not cool because they do not collide with anything either prior to or subsequent to ionization for

180

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TOFMS detection. They, of course, can be subject to further fragmentation during and after their excitation/ionization process. One thus measures their nascent temperatures (Ttrans, TIot, Tvib) generated in the dissociation process (es) above, and one can use conservation of energy to find or estimate the excitation levels for all product degrees-of-freedom, at least in principle. Some spectacular and surprising results of these experiments are shown in Figs. 2 and 3. We see that the photofragmented NO from RDX has a

1-color MRES of NO from LD of RDX

(0-3) 2 38600

38800

38700

k,

3

sv

m

(0-2)

5

VIA* .

hisu

40400

40600

40500

L

1

•

42300

(o-i) 22 i

1

42400

i 42500

(0-0) 100 44100

1

1

44200

44300

44400

Wavenumber (cm"1) Fig. 2. NO spectra A (v' = 0) <— IX (v" = 0,1,2,3). Each transition and its relative intensity to the NO (0-0) transition are indicated in the figure. NO is generated from the photodissociation of RDX.

Role of Excited Electronic States

181

1-color MRES of NO from LD of RDX

^

44650

44700

44750

44800

'55 c CD C

-I—'

(1-3)

40950

41000

41050

41100

41150

Wavenumber (cm-1) Fig. 3. N O / R D X spectra of the (1-1) and (1-3) transitions. These spectra look very similar to the other transitions obtained from nascent NO derived from RDX photodissociation (see Fig. 2).

TIot ~ 20 K and a Tvib ~ 1800 K: very hot vibrations but very cold rotations. The vibrations are hot because v" = 0, 1, 2, 3 are populated in NO(X) but the rotational structure is narrow. How do other nitro-containing, nitramine, or NO^ compounds behave under similar circumstances? Studies of "similar" samples of NO, NO2, CH3NO2, C 6 H 5 N02, 1,4-C 6 H 4 (N0 2 )2, hexamethylenetetramine (HMT, C6H12N4), and tyramine were carried out: the last three compounds are

182

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1-color MRES of NO @ (0-1)


C6H5-N02

RDX/NO 1

42300

42500

42400 1

Wavenumber (cm ) Fig. 4. NO spectra of the (0-1) transition from various model samples (from the bottom to top): RDX, photolysis, N 0 2 , CH3NO3, C 6 H 5 N 0 2 , and 1,4-(N0 2 )2C 6 H 4 . Each molecule shows its own pattern of NO rotational transitions. This means that each molecule has its own unique pathway for NO generation.

solid and were accessed by laser ablation as described above. Figure 4 shows just how different the NO (0,1) transition appears for these test, model, or similar compounds. HMT and tyramine do not decompose but appear in the mass spectrum as parent ions with the correct arrival time. Now, how does one, or can one, prove the assertion that NO is the primary, initial fragment from RDX in its first excited electronic (singlet) state at 226 nm (44,200 c m - 1 , 5.5 eV) above the ground state? First, NO or NO2 does not come from the nozzle as part of the ablation process

Role of Excited Electronic

183

States

because the spectra are different in all three instances: the RDX/NO is rotationally colder than fragmented NO2/NO, rotationally hotter than NO gas from the nozzle, and vibrationally hotter than any NO x from the nozzle. Second, the RDX/NO signal arrives at the mass detector at the appropriate flight time from the nozzle: slower than HMT (a test molecule), faster than R6G, as predicted by expected velocity slip studies, and having the RDX distribution (arrival time and pulse width) in the pulsed beam rather than the NO gas distribution from the nozzle. Thus, the NO signal does indeed arise from the dissociation of RDX following 226 nm excitation to an excited electronic state. The NO signal does not come from NO2 subsequent dissociation at 226 nm. 21 Note that laser intensity does not affect the observed spectra of NO from RDX, so probably the dissociation occurs at 44,200 c m - 1 and not 88,400 c m - 1 or higher. These results are displayed in Figs. 5(a)-5(c). Results from one more experiment aid the discussion of the initial step in the dissociation of RDX (and HMX) from its first excited electronic state. We have studied the photodissociation of the model compound

NO distribution comparison 1.0

RDX/NO NO gas

•

0.6-^

•« C

0.4.

£

0.2 •

0.0-

-20

20

40

60

—r80

100

Molecular beam timing (us) Fig. 5(a). A comparison between the detected distributions of NO TOFMS intensity from two different sources: (1) gas phase NO expanded through a supersonic nozzle (triangles); and (2) gas phase NO derived from MALD-generated RDX fragmented at the TOFMS ion source region (squares).

E. R-

ISI

Bernstein

1-color MRES of NO @ (0-1)

N O gas

3 CO

in

c: d>

RDX/NO 42300

42500

42400 1

Wavenumber (cm ) Fig. 5(b). N O spectra of t h e (0-1) transition from N O fragmented from RDX photolysis (bottom) and from NO gas itself (top). NO spectrum from RDX fragmented NO displays a much colder rotational temperature than NO gas itself.

Velocity Slip Experiment HMT NO C. • A

HMT(146) RDX(222) / NO • R6G(479) / C3

I •A>V,

- . . - . - • - ¥ = ¥*=*=*£*=•=¥=! -10

0

10

20

30

Molecular beam timing (ps) Fig. 5(c). Velocity distribution differences among laser desorbed H M T , RDX. a n d R6G. Equimolar quantities of H M T and RDX samples are coated together with the matrix molecule, R6G. Signals from the parent molecule for HMT, NO for RDX, and C3 for R6G have been used to determine the velocity distribution data.

Role of Excited Electronic

States

185

N-nitropyrrolidine (C4H8N2O2) under exactly the same conditions as used for the RDX study. The surprising result is that (without laser ablation), the signal in the TOFMS is a single peak at amu 100 (N-nitroso-pyrrolidine, C4H8NNO). The N-nitropyrrolidine (amu 116) has lost an oxygen atom and formed the stable nitrosamine. We are now in the process of investigating this process for N-nitropiperidine (C5H10N2O2) and N,N'-dinitropiperazine (C 4 H 8 (N 2 02)2). Thus, this process, RNN0 2 ^ RNNO + O could also be a potential first step for the decomposition of other nitramines like RDX and HMX. The difference between the energetic species and the pyrrolidines, piperazines, and piperidines is the stability of the nitrosamine intermediate. We know that RDX yields NO for a 10 ns, 226 nm excitation that does not come from NO2. Is this the initial step? Almost surely, no. At 248 nm excitation, NO2 may be the primary product, but this issue is plagued by unanswered questions. I suggest the following set of mechanisms for the 226 nm process: (1) RDX + 226 nm

A+ C 3 H 6 (N 2 0 2 )2N» + N 0 2

(2a) RDX + 226nm

-> C 3 H 6 (N 2 02)2NO + O

(2b) C 3 H 6 (N 2 0 2 )2NO

-v C 3 H 6 (N 2 02)2 + NO - • • • •

(3a) RDX + 226nm

- • (cycIic)-C 3 H 5 (N 2 02)2NNOOH

(3b) (cyclic)-C 3 H 5 (N202)2NNOOH -> C 3 H 5 (N20 2 )2N + HONO (3c) HONO + (226 nm?)

^ HO + NO

(4a) RDX + 226 nm

- • 3CH 2 NN0 2

(4b) CH 2 NN0 2

-> HONO or NO (or N 0 2 ) . . .

(5) RDX + 226nm

-y C 3 H 6 (N 2 02)2NONO -> NO + • • •

The most likely mechanism based on the studies of Refs. 16, 21, and 20 seems to be number (2) above. We know number (1) is out (because of the spectroscopy for NO2/NO dissociation), number (3) is unlikely because HONO probably would not give the observed distribution of degrees-offreedom energy for NO, and number (4) requires that NO be generated directly from CH 2 NN0 2 . This latter pathway would not be consistent with the results of Ref. 11 assuming CH2N2O2 were not highly excited. Mechanism (5) appears to be possible, but at present not the most likely one. I emphasize that no initial step can be definitively identified from a 10 ns experiment because the initial process, whether loss of O or isomerization or symmetric fragmentation or HONO formation or something else,

186

E. R.

Bernstein

must take place in less than 1 ps. It appears that the difference between a stable nitramine (e.g., N-nitropyrrolidine, etc.) and an "energetic" one (e.g., RDX, HMX, DMN) is that the stable species has a stable nitroso intermediate.

5. Conclusions and Future Work Firm conclusions for the behavior of energetic materials are difficult to reach, especially for excited electronic state behavior at the chemical mechanism level. Difficulties include time resolution, sample handling, and laser/matter interactions (single- and/or multiphoton behavior). I hope that the following tentative conclusions will stand the test of time. First, matrix assisted laser desorption seems to work for many different delicate systems to generate non-volatile fragile molecules in the gas phase. Second, the molecules can be cooled and isolated in supersonic expansion for LIF, TOFMS, and other sophisticated gas phase dynamics experiments. Third, at 226 nm and 10 ns time resolution, NO is generated by RDX decomposition in a characteristic rotational, rovibrational and translational energy distribution. Fourth, the most likely guess at an overall mechanism for the dissociation at 226 nm is first loss of an O atom and then loss of NO. Such an NO could be rotationally cold and vibrational^ hot in agreement with experiment. Fifth, RDX seems to be different from non-energetic cyclic nitramines (N-nitropyrrolidine) as well as other model nitro-containing species with regard to its photodissociation behavior. Sixth, 248nm, high-intensity excitation at 155°C in a non-cooled, non-beam environment seems to generate NO2. Energetically, NO2 generation is possible and not inconsistent with other results, but a number of questions concerning these experiments should be addressed. Future experiments central to the understanding of energetic material behavior in excited electronic states include: (1) fs studies, with the knowledge that these short times can add additional complications to the results; (2) studies of more energetic materials: HMX, TNAZ, DMN, and others; (3) studies of non-energetic models such as N-nitropiperidine and various N,N'-dinitropiperazines (1,2; 1,3; 1,4); (4) multi-laser experiments such that photodissociation and product detection can occur at different wavelengths;

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(5) study of gas phase solvation clusters of energetic materials (e.g., RDX(H 2 0) x , RDX(C n H 2n +2)s, etc.; and (6) multimers of energetic materials (e.g., (RDX) n , (HMX) n , etc.) to model condensed phase and bimolecular behavior. Clearly, lots of work remains to be done to unravel the chemistry and physics of energetic materials. These last research recommendations bring us full circle to the introductory paragraph of this overview. There we posed three essential questions concerning energetic materials: how are they different from other molecules and what are their decomposition pathways and kinetics? We cannot answer all these questions at present, in part because of the experimental problems and interpretational difficulties discussed in this overview. Nonetheless, we now understand much about the decomposition of energetic molecules and we have ideas of how to uncover and measure the details of this process. Both molecular and condensed phase results are clearly important: we must understand the molecular behavior first, before we can develop a clear picture of condensed phase behavior. Decomposition as a function of electronic state is an essential component of the energetic material properties. We are on the verge of uncovering these details and mostly know how to proceed effectively and judiciously. Acknowledgments These studies were supported by the U.S. Army Research Office. I would particularly like to thank Ms. Margo Greenfield for her help with a literature search on energetic materials. Ms. Greenfield and Dr. Yuanqing Guo have carefully read drafts of this manuscript and have made many helpful suggestions about the presentation and form of the final product. Dr. Richard Beyer, ARL, also helped with a literature survey through the Army Research Laboratory library facilities: this effort helped us find the more difficult-to-access references. References 1. (a) G. A. Olah and D. R. Squire (eds.), Chemistry of Energetic Materials (Academic Press, New York City, 1991); (b) Y. Tsuoboi, T. Seto and N. Kitamura, J. Phys. Chem. B107, 7547 (2003) and references to older work therein. 2. (a) H. M. Windawi, S. P. Varma, C. B. Cooper and F. Williams, J. Appl. Phys. 47, 3418 (1976); (b) J. Schanda, B. Baron and F. Williams, Acta

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7.

E. R. Bernstein Technica Academiae Scientiarum Hungaricae 80, 185 (1975); (c) J. Schanda, B. Baron and F. Williams, J. Luminescence. 9, 338 (1974); (d) S. P. Varma, F. Williams and K. D. Moeller, J. Chem. Phys. 60, 4950 (1974); (e) S. P. Varma and F. Williams, J. Chem. Phys. 60, 4955 (1974); (f) S. P. Varma and F. Williams, J. Chem. Phys. 59, 912 (1973); (g) R. B. Hall and F. Williams, J. Chem. Phys. 58, 1036 (1973); (h) F. Williams, Adv. Chem. Phys. 21, 289 (1971); (i) A. N. Dremin, V. Yu. Klimenko, O. N. Davidoua and T. A. Zolodeva, in Proc. 9th Symp. on Detonation, Vol. I, 28 Aug-1 Sept. 1989, Portland, OR, p. 319; (j) J. Sharma, B. C. Beard and M. Chaykovsky, J. Phys. Chem. 95, 1209 (1991); (k) J. Sharma, J. W. Forbes, C. S. Coffey and T. P. Liddiard, J. Phys. Chem. 9 1 , 5139 (1987); (1) J. Sharma, APS Topical Meeting on Shocks in Energetic Materials (APS, Williamsburg, VA, June, 1991). J. C. Mialocq and J. C. Stephenson, Chem. Phys. Lett. 123, 350 (1986); Chem. Phys. 106, 281 (1986). N. L. Garland, D. H. Ladouceur and H. H. Nelson, J. Phys. Chem. A l O l , 8508 (1997). S. M. Hankin, Rapid Commun. Mass. Spectrom. 16, 111 (2002). (a) M. M. Kukija and A. B. Kunz, J. Appl. Phys. 87, 2215 (2000); (b) M. M. Kukija and A. B. Kunz, J. Phys. Chem. Solids 61, 35 (2000); (c) M. M. Kukija, E. V. Stefanovich and A. B. Kunz, J. Chem. Phys. 112, 3417 (2000); (d) M. M. Kukija, B. P. Adver, E. D. Aluker, V. I. Krasheninin, A. G. Krechetove and A. Y. Mitrofanov, J. Appl. Phys. 89, 4156 (2001); (e) M. M. Kukija and A. B. Kunz, J. Appl. Phys. 89, 4962 (2001); (f) A. B. Kunz and M. M. Kukija, Theor. Chem. Acta 384, 279 (2002); (g) M. M. Kukija, Appl. Phys. A76, 359 (2003); (h) D. Margetis, E. Kaxiras, M. Elstner, Th. Frauenheim and M. R. Manaa, J. Chem. Phys. 117, 788 (2002); (i) J. P. Lewis, Chem. Phys. Lett. 371, 588 (2003). (a) F. J. Owens and J. Sharma, J. Appl. Phys. 5 1 , 1494 (1979); (b) J. Sharma and B. C. Beard, Mater. Res. Soc. Symp. Proc. 296, 189 (1993); (c) T. R. Botcher, H. D. Landouceur and T. R. Russell, in Shock Compression of Condensed Matter — 1197, Proceedings of the APS Topical Group, eds. S. C. Schmidt, D. P. Dandekar, and J. W. Forbes (AIP, Woodbury, New York, 1998); (d) B. P. Aduev, E. D. Aluker, G. M. Belokurov and A. G. Krechetov, Chem. Phys. Rep. 16, 1479 (1997); (e) B. P. Aduev, E. D. Aluker and A. G. Krechetov, Chem. Phys. Rep. 17, 643 (1999); (f) J. J. Gilman, Philos. Mag. B 7 9 , 643 (1999); (g) C. J. Wu, L. H. Yang, L. E. Fried, J. Quenneville and T. J. Martinez, Phys. Rev. B67, 235101/1 (2003); (h) S. Roszak, R. H. Gee, K. Balasubramanian and L. E. Fried, Chem. Phys. Lett. 374, 286 (2003); (i) M. R. Manaa, L. E. Fried, C. F. Melius, M. Elstner and Th. Frauenheim, J. Phys. Chem. A106, 9024 (2002); (j) E. J. Reed, M. R. Manaa, J. D. Joannopoulos and L. E. Fried, in AIP Conference Proceedings, Part 1, 620 (2002), p. 385; (k) M. R. Manaa, R. H. Gee and L. E. Fried, J. Phys. Chem. A106, 8806 (2002); (1) L. E. Fried, M. R. Manaa, P. F. Pagoria and R. L. Simpson, Annu. Rev. Mater. Res. 31, 291 (2001); (m) M. R. Manaa and L. E. Fried, J. Phys. Chem. A105, 6765 (2001);

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(n) E. J. Reed, J. D. Joannaopoulos, and L. E. Fried, Phys. Rev. B62, 16500 (2000); (o) M. R. Manaa and L. E. Fried, J. Phys. Chem. A103, 9349 (1999); (p) M. R. Manaa and L. E. Fried, J. Phys. Chem. A102, 9884 (1998). D. Margetis, E. Kaxiras, M. Elstner, Th. Frauenheim and M. R. Manaa, J. Chem. Phys. 117, 788 (2002). J. P. Lewis, Chem. Phys. Lett. 371, 588 (2003). H. Zuckermann, G. D. Greenblatt and Y. Haas, J. Phys. Chem. 9 1 , 5159 (1987). (a) X. Zhao, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 88, 801 (1987); (b) D. S. Anex, J. C. Allman and Y. T. Lee, in Chemistry of Energetic Materials, eds. G. A. Olah and D. R. Squire (Academic Press, New York City, 1991); (c) A. M. Wodtke, E. J. Hintsa and Y. T. Lee, J. Phys. Chem. 90, 3549 (1986). M. Hiskey (LANL) and R. Behrens (SRI), personal communication. E. R. Bernstein, in Atomic and Molecular Clusters, ed. E. R. Bernstein (Elsevier, New York, 1990), p. 551. R. Cohen, B. Brauer, L. Grace and M. S. de Vries, J. Phys. Chem. A104, 6351 (2000). (a) A. Meffert and J. Grotemeyer, Ber. Bunsenges. Phys. Chem. 102, 459 (1998); (b) K. W. D. Ledingham and R. P. Singhal, Int. J. Mass Spectrom. Ion Processes 163, 149 (1997), and references therein; (c) R. J. Conzemius and J. M. Cepellen, Int. J. Mass Spectrom. Ion Proc. 34, 197 (1980) and references therein. H.-S. Im and E. R. Bernstein, J. Chem. Phys. 113, 7911 (2000). (a) T. Burgi, T. Droz and S. Leutwyler, Chem. Phys. Lett. 225, 351 (1994); (b) E. R. Bernstein, Annu. Rev. Phys. Chem. 46, 197 (1995); (c) E. R. Bernstein, in Chemical Reactions in Clusters, ed. E. R. Bernstein (Oxford, New York, 1996), p. 147; (d) R. Compargue, Atomic and Molecular Beams: The State of the AH 2000(Springer, Berlin, 2001); (e) G. Scoles, Atomic and Molecular Beam Methods, Vols. I, II (Oxford, New York City, 1988, 1992); (f) D. M. Lubman, Lasers and Mass Spectrometry(Oxiord, New York City, 1990). A. G. Suits and R. E. Continetti, Imaging in Chemical Dynamics, ACS Symposium Series 770 (ACS, Washington, DC, 2000). (a) H. L. Dai and R. W. Field, Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping (World Scientific, Singapore, 1995); (b) A. B. Meyers and T. R. Rizzo, Laser Techniques in Chemistry, XXIII of Techniques of Chemistry (Wiley, New York City, 1995); (c) G. Hall and B. J. Whitaker, J. Chem. Soc, Faraday Trans. 90, 1 (1994); (d) M. Motzkus, S. Pederson and A. H. Zewail, J. Phys. Chem. 100, 5620 (1996). H.-S. Im and E. R. Bernstein, J. Phys. Chem. A106, 7565 (2002). C. Capellos, in 12th Int. Detonation Symposium, eds. J. M. Short and J. L. Maienschein (OCNR, Arlington, CA, 2003), p. 813. R. Behrens (SRI) and M. Hisky (LANL), personal communication. H.-S. Im and E. R. Bernstein, unpublished results.

CHAPTER 7 G A S - P H A S E KINETICS FOR P R O P E L L A N T C O M B U S T I O N MODELING: REQUIREMENTS AND EXPERIMENTS William R. Anderson U.S. Army Research Laboratory Aberdeen Proving Ground, MD 21005-5069, USA

Arthur Fontijn High- Temperature Reaction-Kinetics Laboratory The Isermann Department of Chemical and Biological Engineering Rensselaer Polytechnic Institute Troy, New York 12180-3590, USA

Contents 1. Introduction 2. Propellant Models and their Gas-Phase Chemistry Inputs 2.1. Primary Features of Propellant Combustion and their Relation to the Gas-Phase Mechanism 2.2. Gas-Phase Chemistry Issues of Primary Significance 2.2.1. First-Stage Chemistry 2.2.2. Dark Zone Chemistry 3. Experimental Input Data 3.1. Elevated Temperature Techniques for Obtaining Kinetic Data on Individual Reactions 3.1.1. Thermostated Reactors 3.1.2. Shock Tubes. Comparison of Techniques 3.1.3. Reaction Mechanisms 3.2. Examples of Results with Significant Impact on the Models 3.2.1. 0 + N 2 0 3.2.2. H + N 2 0 3.2.3. H + NH 3 <-> NH 2 + H 2 3.2.4. H + N 0 2 , C H 3 N 0 2 191

192 195 196 200 200 210 218 218 218 221 222 223 223 224 225 226

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3.2.5. H + NO 3.2.6. N + CO2, N 2 0 , 0 2 3.2.7. NH + C 0 2 , H 2 0 3.2.8. NH 2 + NO 3.2.9. CN + OH 3.2.10. NCO + NO N 0 2 4. Conclusions Acknowledgment References

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1. Introduction One of the most important characteristics of a propellant is its onedimensional burning rate and the dependence thereof on pressure and unburnt propellant temperature. Burning rate is controlled by propellant formulation. During the last ~15 years, one-dimensional models of solid propellant combustion have shifted from those using one or a few global gas-phase reactions to those including all the species and reactions thought to be important to the gas-phase flame. This means tens of species with associated thermodynamics and hundreds of elementary chemical reactions with associated kinetics. The overall gas-phase reaction rate must be properly predicted to obtain the rate of heat transfer to the condensed phase material; this heat transfer controls the rate of conversion of condensed phase material to initial gas-phase intermediates. Accurate kinetics mechanisms, consisting of the many possible elementary steps that can occur across a range of temperatures, pressures, and mixture ratios pertinent to propellants, are necessary to achieve success in predicting burning rates for the large variety of chemical ingredients that can be used. a Here we review the current status of the relevant gas-phase chemistry with emphasis primarily on solid propellants used in gun and rocket applications and recommend how to further the ability to model their combustion.^ 1 During the mid to late 1980s it was first recognized, largely due to the modeling efforts of Hatch 2 and Melius,3 that it had become feasible a

T h e term "gas phase mechanism" includes not only the elementary reactions and their kinetics parameters, but also the thermodynamics of the species. The latter can be critically sensitive input parameters. Some crucially important data, in particular heats of formation of some key radicals and molecules and even of some important propellant ingredients, are not well known. b A t one point there is also a very brief discussion of liquid rocket fuels which could be fruitfully studied.

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to develop models of propellant combustion that include a detailed gasphase description of the chemical kinetics and transport properties of the flame gases. It was recognized that a large number of elementary reactions would have to be understood for proper modeling. The best way to determine kinetics parameters for an elementary reaction is by experimental study under conditions designed to carefully isolate the reaction, when possible. Section 3 of this chapter will focus on methods by which this may be done. However, it is not possible to do this for every reaction. Also, if one focuses only on individual reactions, one may overlook key reactions of such intricate systems. Not only are isolated reaction studies of interest, but also more complex systems of reactions pertaining to intermediates of propellant combustion. A number of investigators decided that a "hierarchical approach" to development of submodels was appropriate, both for the chemistry and the physics of propellant combustion. For the gas-phase chemistry, this meant stable, small molecule fuel/oxidizer pairs, whose mechanisms were subsets of propellant mechanisms, were selected for study and arranged from simplest to most complex. These molecules are intermediate species formed during the decomposition and combustion of key propellant ingredients. The hierarchical organization clarified why certain chemical systems are of interest. Further discussion of the hierarchical approach, concentrating mainly on nitramine gas-phase mechanisms, is found in Ref. 4. This chapter is confined to propellants consisting of C, H, N, and O. AP and metallized propellants are not discussed. We focus on nitrate ester and nitramine-based propellants. These ingredients produce copious amounts of NO2 and/or N 2 0 oxidizers at intermediate combustion stages. Therefore, the detailed gas-phase propellant mechanisms are similar to those for modeling NO^ emissions formation and abatement processes during combustion of other fuels. Pollutants such as NO^ are of growing import to the Army since increased concern is being placed on the environmental impact of its weapons systems, vehicles, and programs. We will briefly mention some techniques which have been used to study global kinetics along with a few references pertinent to propellant combustion: low pressure burner stabilized flame,5 thermally initiated shock tube, 6 high pressure turbulent flow reactor, 7 and static reactor 8 techniques. Typically, a mechanism of many elementary steps (commonly referred to as a "complex" or "detailed" mechanism) is used to model results. The best work uses sensitivity analysis to single out the key reactions controlling the

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observed global results. Frequently, a new key reaction may be postulated and fits to the data made to extract its rate coefficients. The assumed reaction, however, may be incorrect or errors may occur in ancillary input data. For this reason, it is always important to compare results from a variety of techniques; when they agree, this lends confidence. Global kinetics approaches not only lend a check that all important reactions are included, but often yield rate coefficients for key reactions that cannot be isolated experimentally. Theoretical chemistry (e.g. ab initio or density functional approaches for determination of potential energy surface features, coupled with transition state, QRRK, and RRKM theories for estimation of rate coefficients) has also played a major role in the development of gas-phase propellant mechanisms.0 These techniques have greatly improved during the last two decades and calculated thermodynamic and kinetic parameters can be close to the best experiments. Theory can help assign proper products for isolated reactions. Agreement of the rates of key elementary reactions lends confidence that experiments are being interpreted properly — especially helpful in global kinetics experiments where assumptions for the key reactions are often made. In many cases elementary reaction kinetics cannot be experimentally measured. For example, it is possible only in a few cases to create a sufficiently pure gas-phase sample of solid propellant ingredients or their major, large radical breakdown products at known concentration. Some theoretical studies which have produced estimates for the initial reactions in the mechanisms of the ingredients RDX and HMX are mentioned in Sec. 2. In Sec. 2, the primary features of solid propellant combustion are described and gas-phase chemistry issues pertinent to various combustion zones within typical propellant flames are discussed. Sensitive elementary reactions are highlighted and discussion of which are in most need of further work is given. Ingredients and burning rate modifiers of highest interest are also discussed along with the current availability of reaction mechanisms. In Sec. 3, experimental techniques to obtain data for individual reactions at temperatures pertinent to the models are discussed. Several examples where these techniques have been successfully applied to reactions of interest to propellant modeling are given.

c

Sometimes experimental input is needed to scale key theoretical parameters to achieve the best kinetic descriptions.

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2. Propellant Models and their Gas-Phase Chemistry Inputs Models of solid propellant combustion which include detailed gas-phase chemistry and transport properties first began to appear in about the mid-1980s. All have used a one-dimensional assumption and the phase boundaries are assumed to be sharp, flat surfaces. Until recently all such models considered three phases: solid, liquid, and gas, and assumed that one or a few global reactions, with associated kinetics parameters, occur within the liquid layer.d Unfortunately, it has proven impossible to be certain what reactions or other processes occur within the near-surface condensed-phase region, let alone the proper formulation of rates. This is because of nearly insurmountable experimental obstacles to probing the condensed phases6 due primarily to: (1) inability to extract quantitative data from condensedphase spectra; (2) micron thickness and roughness of the reaction zone; (3) large temperature gradients; (4) short burn times of the propellants; and regression of the surface in the laboratory reference frame; (5) no actual propellant burns in one-dimensional, steady-state fashion; (6) high pressure; and (7) reactions continuing during sampling. Three groups that developed 3-phase models for RDX combustion used the same rate coefficients for liquid RDX consumption but assumed different products. 3 ' 10 ' 11 Because the thermodynamics of the reactions chosen are quite different, the heat feedback to the condensed phases varies greatly among these models. There are also significant differences in the assumed physics (e.g. whether bubbles form). Because all the efforts have achieved excellent agreement with experimental burning rates, the modeling solutions are not, apparently, unique (see the chapter by Miller). The community has oft-times referred to such models as "first principles" approaches, but this term may cause misunderstanding about how uncertain the assumptions are. These difficulties have led to slow application of such models to new ingredients: three-phase modeling has been applied mostly to single ingredients and simple mixtures. A few years ago, Miller and Anderson of ARL presented a two-phase approach to prediction of propellant burning rate and gaseous flame structure. The phases were condensed (solid or liquid) and gas, and the model

d

More reactions could be included: the situation is not computationally limited. Thermogravimetric mass spectrometer experiments, like those of Behrens, 9 allow condensed-phase kinetics of energetic ingredients to be measured; but the temperature range is well below combustion. This method is mainly relevant to slow reactions important for shelf life, slow cookoff, and safety. e

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was applied to a few pure ingredients and simple binary mixtures. 1 2 More recently, they have successfully applied the approach to several fielded nitrate esters, 1 3 and nitramine/energetic binder type propellants. 1 4 T h e approach uses two main inputs (besides the gas-phase chemistry): (1) a semi-empirical pyrolysis "law" is assumed applicable t o a broad range of propellants within a given class; this law relates the burning rate to the surface temperature; and (2) the mixture of gaseous species evolved from the surface for each propellant ingredient. (Miller and Anderson refer to this mixture as the "surface products" — not to be confused with "equilibrium products" which are obtained in the burnt gas region.) T h e pyrolysis laws have been measured for several major propellant types, classified according to ingredients, by Zenin. 1 5 Qualitative guidance for the surface products to use for each ingredient comes from pyrolysis experiments and chemical intuition. Ultimately, Miller and Anderson had to rely on comparison with experimental burning rates to guide selection, which is basically a fitting procedure. Once the "best" set is found, this is fixed and used for the mixture of ingredients in actual propellants along with the pyrolysis law appropriate for the propellant type. In this way, the model can be used for propellant predictions. The approach has been used successfully for about ten actual fielded and developmental propellants, based on nitrate ester or nitramine energetic ingredients. Besides needing the gas-phase mechanism for either the two- or three-phase approach, the two-phase approach would benefit from more reliable information about the surface products evolved by the pure ingredients. We will return to this issue later in this section. More discussion of the two-phase model is given by Miller in this volume.

2 . 1 . Primary Relation

Features of Propellant Combustion to the Gas-Phase Mechanism

and

their

Features typically observed during combustion of a solid propellant are shown in Fig. 1. W h e n initial propellant t e m p e r a t u r e s are close to ambient, most solid propellants cannot undergo sustained, steady-state combustion at pressures below about 5-10 a t m . Pressures in guns range from about 100 to 5,000 atm; for missiles/rockets they range from 5 to 100 a t m . So "low pressures" for guns means below 500 a t m . T h e idealized combustion picture in Fig. 1 uses a cylindrical strand in a pressurized vessel. An inhibitor on the side a n d / o r flowing inert gas causes the propellant to b u r n at one end only. T h e schematic has been drawn with a "dark zone" (DZ) — a nonluminous gas-phase region observed between the condensed-phase surface

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Propellant Strand 3000 2000

!

1000

Distance Fig. 1. Idealized schematic of a burning solid propellant strand with a dark zone. In typical experiments, the strand is oriented vertically, but it is shown rotated 90° clockwise here to make the correlation to the temperature profile clear.

and the luminous flame (burnt gas region). The DZ consists of intermediate combustion species at intermediate temperature while the luminous flame consists of equilibrium products at the final temperature/ The burning rate is that at which the solid surface regresses as the combustion wave moves through the propellant (assuming steady combustion has been reached). Most gun propellants exhibit a DZ at low pressures. In Fig. 1 the temperature within the solid is ambient — typically about 293 K. At the propellant surface, heat transfer from the gas-phase to the condensed phase causes gasification to occur yielding the initial gas-phase intermediates. In a very narrow region near the surface, a rapid, exothermic, global reaction rapidly converts the initial gas-phase intermediates to DZ intermediates. Coupled with this reaction is a strong upward gradient in the temperature profile. The near-surface region is also often called the "first stage flame". At the end of the first-stage flame, the comparatively low reactivity of the major DZ intermediates causes their concentrations and the temperature profile to linger at plateau levels for a time, often referred to as the "DZ ignition delay". This chemical delay, coupled with convection, causes formation of

f

T h e trace species — e.g. radicals and atoms — will not be at equilibrium at the leading edge of the luminous flame, though the major species are. Thus, the temperature there may be ~100 K different from the adiabatic flame temperature, even in model calculations.

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the DZ. The global reaction slows due to the low reactivity of DZ intermediates as the concentrations of trace radicals and, perhaps, temperature slowly build. At some point the chemical rates rapidly increase, the conversion of DZ intermediates to (nearly) equilibrium products quickly occurs, and heat is released, driving the temperature upwards to nearly the adiabatic limit. The thin region at the end of the dark zone where this occurs is called the "second-stage" flame. At the end of the second-stage flame, the temperature is high enough that the gases typically become luminous; this luminous region is often called the "luminous flame". It appears likely that 1 6 , 1 7 the primary factor causing DZ formation is the chemical delay between formation of the slowly reacting intermediates and their sudden, rapid conversion to near-equilibrium products at the end of the DZ. The DZ ignition delay time and gas-phase convective rate are the major determining factors of the DZ length. The state-of-the-art model of Ref. 16 is in good agreement with the measured DZ structure of actual propellants. There is, however, only scant experimental evidence with which to compare, especially for nitramine propellants. As will be discussed in Sec. 2.2.2(a), more experiments are needed. For some propellants, no DZ is observed at any pressure. Rather, the luminous flame seats itself very close to the condensed-phase surface (not shown in Fig. 1). The corresponding temperature profile rises slowly just below the propellant surface, then smoothly in a narrow region just above the surface to nearly the adiabatic limit. The corresponding species profiles also exhibit no plateau regions. The entire flame is luminous except for the very thin, cool region near the surface. We will discuss our suspicions below as to why no DZ occurs, at least for some propellants. Most solid propellants of U.S. Army interest fall into two major types based upon the chemically-energetic ingredients they contain: nitrate esters (R-O-NO2) and nitramines (R1-, R2-N-N0 2 ). Some of the gas-phase species which occur along the major chemical pathways within the main regions of the flames are discussed here. Much of the gas-phase kinetics study in this field has been related to combustion of these species. Chemistry in the near-surface, first-stage flame is considered first. For both nitrate esters and nitramines, the most important small fuel molecule in this region is CH2O. For nitrate esters containing nitrocellulose (NC), pyrolysis experiments suggest that CHOCHO and HCOOH are also important, though these have not received much consideration except in very recent combustion models. For nitramine propellants HCN also plays a central role. The most important small oxidizer molecules are nitrogen oxides.

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For both nitrate esters and nitramines, NO2 plays a central role; HONO may also be present: as a direct product of the condensed-phase material, or along the gas-phase pathways from nitrogen oxides. For nitramines, N2O also plays a major role. In first-stage flames of most propellants nearly all the N 0 2 and HONO, and a small fraction of the N 2 0 , are converted to NO, the majority of the N2O is converted to N2, and most of the C-containing species except HCN are converted to CO and CO2, with concomitant heat release. Various studies conclude that, during combustion, all nitrate esters and nitramines have major chemical pathways through NO; HCN is also important for nitramines. NO and HCN survive the first-stage flame in most propellants because there are few species present in the mixtures that will react rapidly with them and the equilibrium products, N2, H2O, CO, and CO2, can only form slowly. This blocks the immediate full heat release of the gaseous mixture, resulting in an intermediate temperature region, the DZ (see the plateau in the temperature profile of Fig. 1). When no DZ is formed, it is probably not because little NO and/or HCN are formed in the first stage. Rather, for certain ingredients, it is likely that a species is formed in the surface region or first-stage flame that can cause rapid conversion of these intermediates to final products. Corresponding temperature profiles have sharp, smooth upward gradients and the final temperature is reached close to the surface (not shown). In some cases, this new species may be NHX [x = 0,1,2,3). NH 3 typically leads to N, NH, and/or NH2 formation. These three species react very rapidly with NO, even at low temperatures, quickly leading to formation of final product N 2 . Thus, no DZ is formed. M30 propellant is an example. It contains a large amount of nitroguanidine (NQ), a known NH 3 precursor. Propellants using ingredients which form HNCO and other intermediates might behave similarly. (See also the discussion of NH 3 and HNCO flame chemistry and their precursors, such as NQ, as burning rate modifiers in Sec. 2.2.1(c).) When a DZ forms, it contains only a few major species. 16 ' 17 For nitrate esters, there are six major species present: H 2 , H 2 0 , NO, N 2 , CO and C 0 2 ; traces of CH4, C 2 H 4 , and CH 2 0 may also be found. For nitramines, there are also large amounts of HCN, a few percent of N 2 0 , and (perhaps) NH 3 . Model calculations suggest that the trace species, especially N 2 0 and NH 3 , could play important roles. Typical temperatures in propellant DZs are about 1200-1600 K. Because of the difficulty of measurements in propellant flames, there is a high degree of uncertainty in the DZ mixture ratios and temperatures. This makes checks of DZ models difficult. Even for the best data sets, at least one of the majority species is

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missing. For example, some researchers used sample extraction into evacuated vessels, hence the H 2 0 concentration cannot be measured because of significant condensation on the walls and must be inferred by mass balance, relying on the assumption that it is the only significant missing species. The trace species concentrations have high uncertainties for all propellant types. Finally, for nitramine propellants, there are very few data sets for which the majority species concentrations are well established. The dearth of data for nitramines may be because their associated flames are less steady, more flickering, than the better behaved nitrate esters. (Even for the best case of a "steady-state" propellant flame exhibiting a DZ, the DZ is inherently easily perturbed because the second-stage flame is not stabilized against a solid surface. Thus, some nickering even in the most carefully arranged experiments is common, and most measurements of DZ length are an average.) Recent work shows that the DZ chemistry at low pressures is much more important to the burning rates at high pressures than had previously been appreciated (see the introduction of Sec. 2.2.2). The DZ and its associated chemistry, therefore, deserve renewed, vigorous attention. 2.2. Gas-Phase

Chemistry

2.2.1. First-Stage

Chemistry

Issues

of Primary

Significance

(a) Small molecule issues common to a wide variety of propellants Some of the sensitive reactions pertinent to the small fuel/oxidizer species chemistry in the first stage of propellants are presented in Table 1. Much of what is presented in Table 1 regarding reactions important for nitrate ester propellants comes from a recent modeling effort.13 See in particular the sensitivity tables in Ref. 13 which refer to M10, a propellant consisting primarily of highly-nitrated nitrocellulose. The model in that case has the propellant evolving large amounts of C H 2 0 and NO2, as well as HCO, CH 2 , and CO, into the first-stage flame zone. As discussed in the introduction to Sec. 2, the list of species evolved for a given ingredient in the Miller and Anderson model is highly empirical, obtained by choosing (based on decomposition experiments and intuition) a set of species emitted from the surface (the "surface product set"). Once product sets are found which properly predict the burning rates for pure ingredients, these sets are fixed and used to model propellants according to the ratios of the ingredients in the propellant mixture. The product sets, of course, determine which reactions drive the model results. Excellent results

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Table 1. Sensitive reactions for small molecules commonly observed in the first stage of solid propellant combustion chemistry. Comments

Reaction Type: RH + N 0 2 = R + HONO * 0 H 2 O + N 0 2 = HCO + HONO * CHOCHO + N 0 2 = products * HCOOH + N 0 2 = products * H 2 + N 0 2 = HONO + H

Type: Major first-stage species decomposition reactions * N 2 0 ( + M ) = N2 + O ( + M ) Extremely sensitive for propellant combustion. Well-established, except M-efficiencies for only a few species are measured. * N 0 2 (+ M) = NO + O ( + M) [as above] HONO (+ M) = OH + NO (+ M) Others (general) * HCO + NO2 = H + C 0 2 + NO * HCO + N 0 2 = CO + HONO C H 2 0 + (H, OH) = HCO + (H 2 H 2 0 ) H + N 0 2 = OH + NO See Sec. 3.2.4. H + NO (+ M) = HNO ( + M) See Sec. 3.2.5. H + HNO = H 2 + NO * HONO + OH = H 2 0 + N 0 2 C H 2 C O (+ M) = CH 2 + CO (+ M) * CH 2 + NO = H + HNCO Others (nitramine) * H 2 CN + (H, OH) = HCN + (H 2 , H 2 0 ) * H 2 CN + M = HCN + H + M H 2 CN + NO2 = products H 2 CN + N 2 0 = products HCO + NO = HNO + CO * HCN + O = NCO + H * HNC + OH = HNCO + H Highly sensitive for 1 atm RDX. * HNC + O = products HNCO + H = NH 2 + CO NCO + M = N + CO + M * NCO + OH = NO + CO + H * CN + OH = NCO + H NH 2 + NO = NNH + OH NH 2 + NO = N 2 + H 2 0 * NNH + O = NO + NH N + NO = N 2 + O N + H 2 = NH + H NH 2 + H = NH + H 2

Example of a reaction studied and settled by the TSiOx community. See Sec. 3.2.8. Highly sensitive for 1 a t m RDX. The N O x community is also interested.

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(Continued)

Reaction

Comments

* H + N2O = N2 + OH

Extremely sensitive for propellant combustion; see Sec 3.2.2 for remaining issues. Moderately sensitive for nitramines and all propellant dark zones.

* H + HNO = NH + OH NH + O = NO + H

' T h e s e reactions need further study. Currently many of these are included in propellant combustion models only via crudely estimated rate coefficients. Efforts on these are especially desirable.

were obtained by including HCO, CH 2 , and CH3 radicals for some nitrate ester ingredients. The radicals appearing in future surface product sets might change. However, because of the ubiquitous nature of CH2O in the first-stage chemistry, HCO is expected to remain in future models: HCO, for example, will result by H atom abstractions from CH2O by H, OH, and N 0 2 . Thus, the branching of the reaction of HCO + NO2 is likely to remain high on sensitivity lists. CH 2 and CH 3 are more likely to be removed and their reactions would decline in importance. (Evidence does suggest that traces of CH4 are present in nitrate ester DZs. More complete models include CH 4 and sensitivity to CH 3 reactions will remain if this is done; see Sec. 2.2.2(b).) Reactions of the form RH + N 0 2 = R + HONO, where R represents a free radical, are usually sensitive in first-stage propellant combustion, and in experiments involving pertinent R H / N 0 2 mixtures. This results from the high concentrations of fuels and N 0 2 , and the radical source nature of this type of reaction. A few reactions of this type are grouped at the top of Table 1. Modeling has shown that such reactions with RH equals CH 2 0 or H 2 are sensitive examples; we expect that similar CHOCHO and HCOOH reactions will be sensitive when these species are included in future nitrate ester modeling. It is difficult to predict what the products of their reactions with N 0 2 will be, especially for the latter because several of the bonds have similar energies. Small molecule reactions peculiarly sensitive for nitramine propellant modeling are shown in the last section of Table 1 which is heavily influenced by a sensitivity calculation for pure RDX at 1 atm. 18 Note that many of the reactions involve HCN and its subsequent chemistry is particularly important for nitramine combustion.

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A significant controversy concerns HCN chemistry. The Emory group 19 has suggested the important pathways are 8 :

HCN + M = HNC + M, HNC + O = NH + CO, HNC + OH = HNCO + H.

(1) (2) (3)

If this is correct, then the competition between HNCO + H = NH 2 + CO NH 2 + NO = NNH + OH or N 2 + H 2 0

(4) (5a,b)

and HNCO + OH = NCO + H 2 0 NCO + NO = N 2 0 -f CO or N 2 + C 0 2

(6) (7a,b)

can be very important in propellant combustion modeling; also note the possibly sensitive radical versus non-radical branching of reaction (5). Alternatively the Stanford group 20 has suggested, based on shock-tube experiments on HCN/HN03/Ar mixtures, that the sequence above may be unimportant and only HCN + OH = CN + H 2 0

(8)

need be considered. Were the Reaction (8) used, the reactions involving HNCO, NH 2 , and/or NCO might not matter. However, they would still matter to modeling of propellants with burning rate modifiers, as discussed in Sec. 2.2.1(c). (b) Major propellant ingredients In this section we present a listing of some major ingredients being used in propellants. By "major" ingredients we mean compounds at 5 weightpercent or more. Additives are also used in typical propellants at the percent level to enhance shelf life (stabilizers) or to suppress muzzle flash/blast (high overpressure and luminosity at gun exit due to re-ignition of rich s

I n Sec. 2, reaction equations contain the = symbol, indicating that the reaction can occur in both directions. This is common in modeling and modeling programs. By contrast, in Sec. 3 the —• symbol is used instead, indicating that only the reaction in the direction of the arrow is considered and the data given pertain to it; obtaining such data is the goal of elementary reaction kinetics studies.

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Major propellant ingredients and burn rate modifiers of interest.

Homogeneous propellant ingredients NC NG DEGDN

Heterogeneous ("filled") propellant ingredients NQ ADN RDX HMX CL20

Binders

Modifiers

"Inert" CAB Energetic GAP BAMO-AMMO BNMO-NMMO

urea NQ TAGN TAGAzT DINGU

exhaust gases as they mix with air). Propellant combustion modelers currently ignore additives. Solid propellants are called homogeneous or heterogeneous. Homogeneous propellants are fully mixed on a microscale; heterogeneous ones are not. Heterogeneous propellants contain energetic crystalline ingredient — finely powdered and the size of the particles is carefully controlled. The powder "fill" is mixed with a binder and the mixture formed into the desired shape. Homogeneous, heterogeneous, and binder ingredients are presented in the first three columns of Table 2. Homogeneous propellants are further classified as "single base" or "double base". Single base propellants are composed mainly of NC (nitrocellulose), an energetic polymer. Double base propellants are composed mainly of NC and NG (nitroglycerine). Some energetic fill ingredients of interest are listed in the second column of Table 2. Triple base propellants generally use NC and NG as the binder and NQ (nitroguanidine) as fill. The nitramines RDX, HMX, and CL20 have received much attention recently as fill materials in attempts to make so called "low-vulnerability" propellants (propellants with a high threshold for shock initiated detonation). Finally, ammonium dinitramide (ADN) has received attention recently for possible missile/rocket applications because propellants made from it yield relatively little smoke. Some typical binder materials are listed in the third column of Table 2. These are used for "filled" propellants. Binders are divided into "inert" and "energetic". An inert binder is composed of hydrocarbon polymer or is based on hydrocarbon-oxygen linkages (e.g., ether structures). An inert binder usually cannot burn without the presence of the oxidizing fill material. An example is CAB (cellulose acetate butyrate). Energetic binders are polymers based on hydrocarbon-oxygen structural features but also

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containing azide or nitrate moieties. These nitrogenous moieties increase the combustion energy. Most of the combustion models using detailed chemical mechanisms are for pure RDX and HMX. All these combustion models have relied heavily on the earliest detailed mechanism developed by Melius.3 He used rate coefficients for a few reactions based on theoretical (BAC-MP4) calculations of transition states and estimates for most of the reactions involving RDX or its larger fragments. In Yetter's later variations, much of the small molecule chemistry was revised.21 However, Yetter adopted most of the reactions of RDX and its large fragments from Melius' original mechanism. Combustion models of HMX thus far have simply used the RDX mechanism with kinetics for HMX and its large fragment reactions estimated based upon analogy with Melius' similar RDX reactions. Better theoretical calculations were highly desirable for the RDX and HMX chemistry. Potential energy surfaces (PES), and results of some dynamical studies have recently been provided by three groups. 22 ^ 24 The situation is much improved, although comparison of results from those groups suggests that there are some differences that could lead to different predictions regarding the reaction pathways. One of the three groups 22 has calculated kinetics parameters for both RDX and HMX and a second 23(c) for HMX (that is, they, performed TST and RRKM calculations based upon their PES) and provided detailed gas-phase mechanisms. These mechanisms have not yet been used in solid propellant combustion models. PES calculations and some gas-phase experiments on ADN have been performed by the Emory group yielding kinetics for the initial steps. 25 Their results were used to model the structure of an ADN gas-phase flame over the burning solid by taking the measured mass flux (inferred from the observed burning rate) and near-surface mixture (assumed to be the premixed reactants) as inputs. 26 The same kinetics were also used by that group in three-phase modeling 27 and by Miller and Anderson in their semi-empirical approach (unpublished). The earlier workers were unable to achieve agreement with experiment — computed burning rates were at least an order of magnitude too low.27 Miller and Anderson achieved agreement in preliminary results but had to assume that the surface product mixture evolved from ADN chang function of pressure (and, thus, surface temperature). Smooth burning rate versus pressure curves were observed for most other ingredients, which suggests that usually there is little change in decomposition mechanism with pressure; this in turn suggests that there is little change in surface products. The assumption

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that there is no change has worked well in all other cases Miller and Anderson have modeled. So our need to relax this assumption for ADN is unsettling. However, unlike most other ingredients, ADN exhibits a long plateau region and two sharp changes in gradient in its burning rate curve; thus, relaxation of the constant surface product set assumption may be correct for this special case. Further cross-checking of gas-phase flame structure is needed to determine efficacy of the semi-empirical modeling solutions. The Emory group has also done theoretical calculations on a model monomer for polymeric GAP energetic binder. 28 Further calculations on GAP and the related BAMO-AMMO and BNMO-NMMO energetic binders would be desirable. Theoretical calculations similar to those for RDX, HMX, and ADN have not been attempted for NQ or the nitramine CL20. Nor have they been attempted for any of the burning rate modifiers listed in the last column of Table 2, discussed in the next section. The community would greatly benefit from such work. Efforts would not only provide combustion modelers the necessary gas-phase mechanisms, but would probably also provide guidance regarding estimates about the condensed-phase breakdown. (c) Burning rate modifiers Burning rate modifiers replace a large fraction of the ingredients in a propellant to reduce or to increase the burning rate without adversely affecting energy content, shock sensitivity, etc. Successful use of modifiers is one of the most important topics in formulation science. A brief discussion of several possible modifiers of interest, and suggested reasons for their effects, are given below. To include modifiers in modeling, we must understand them as well as the major ingredients. Several burning rate modifiers are listed in the last column of Table 2. Two of these, TAGN and TAGAzT (also called TAGZT), contain significant numbers of NHX moieties in their structure; and they are known to produce copious NH 3 , amongst other species, upon pyrolysis. Miller and Anderson, in their earliest work with the new semi-empirical approach, modeled some simple binary mixtures of NG where small amounts of "dissolved" gas phase molecules such as H2, N2, CH 2 0, and NH3 were included. 12 We found that, whereas all the other species that we tried had only a modest effect on the NG burning rate, addition of a small amount of NH 3 produced a strong increase in the burning rate. We knew that NH2 and NH, the typical products of elementary reactions of NH3 in combustion, react much more

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rapidly with NO than the other species commonly occurring in nitrate ester combustion. We wondered whether this would lead more rapidly to the final product N2 and concomitant increased heat release near the propellant surface. The radical chain branching product channel of the NH2 + NO reaction (5a), that is NNH + OH, and consequent increase in the radical pool, is extremely important in this regard. Detailed analysis of the comparative model solutions (that is, NG with versus without NH 3 ) shows that this NHX chemistry, resulting in conversion of NO to N2, and the concomitant radical pool increase is, in fact, responsible for the predicted NH3 burning rate enhancement. Therefore, it is likely that the presence of the NHZ moieties in TAGN and TAGAzT is the primary reason for the increase in burning rates commonly obtained with these modifiers. NH3 plays a central role in "Thermal deNO^", 29 an industrial process whereby NO pollutant is removed from industrial furnace exhaust gases by mixing NH 3 into them under the proper conditions. The main reaction responsible is the fast reaction NH2 + NO (5a,b). This chemistry led Miller and Anderson to postulate its similar role in the propellant modifiers and to study the effects of the idealized "propellant" NG + NH3. There is a similar NO x removal process, RAPRENO x , in which HNCO is used. 30 For HNCO, under conditions in which H is the primary flame radical present, the most important reactions are HNCO+H = NH2 + CO (4), followed by NH 2 reacting with NO (5a,b). If this were the main pathway for HNCO removal, one would expect that an idealized HNCO "additive" would increase burning rate, similar to the effect of NH 3 . If the breakdown occurred mainly in the DZ, that pathway would be followed because our modeling concludes that in the DZ [H] » [OH]. H is normally the major flame radical under such rich conditions. However, near the propellant surface — the first-stage combustion region, where changes in heat release have their greatest effect on burning rate — there is almost always considerable NO2 and H + N 0 2 = OH + NO,

(9)

converting H to OH, is one of the fastest reactions known. Due to reaction (9), Miller and Anderson find that, near propellant surfaces, even though the overall mixture is usually quite rich,h [OH] is typically much larger than [H]. Under these conditions, the reaction HNCO + OH = NCO + H 2 0 (6) is the main removal pathway of HNCO. There is also h

T h e mixture is especially rich when one considers that the NO formed may not be very reactive, driving the effective equivalence ratio 3 1 quite high.

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a large concentration of NO present, so that the subsequent reaction of NCO with NO rapidly follows. NCO + NO yields N 2 0 + CO or N 2 + C 0 2 (7a,b), all of which are stable, non-radical products: this pathway results in radical loss and slows the global reaction. Anderson, therefore, suggested recently that the presence of HNCO near propellant surfaces might reduce propellant burning rates. 32 Preliminary modeling on NG/HNCO mixtures bears this out. 33 Curiously, this may happen even though the HNCO may reduce DZ length or eliminate the DZ altogether, because the HNCO chemistry converts NO to N 2 . Elimination of the DZ is desirable because it may reduce gun ignition delay (not to be confused with DZ ignition delay). 34 Because HNCO may reduce propellant burning rates, we seek modifiers that will produce it upon decomposition. Urea is known to break down to equal amounts of NH 3 and HNCO during combustion and is used in the NOj, removal process NO^OUT. 30 Indeed, this compound has been used as a "coolant" — a modifier thought to reduce burning rate by its thermochemistry. Now it appears this result may be due to kinetics. It is not clear, a priori, whether addition of NH3 together with HNCO would produce a burning rate increase, decrease, or no effect. Preliminary modeling of NG/NH3/HNCO mixtures suggests the effects of the HNCO overwhelm those of the NH3. 33 Thus, the strong burning rate decreases observed for urea, which probably produces equivalent amounts of both, are likely due to the chemical effects of HNCO on the radical pool. Other compounds suitable as propellant ingredients which may produce NH 3 or HNCO upon combustion are being sought. Nitroguanidine (NQ) is a candidate for NH3 production. Indeed, Oyumi et al. have shown NQ produces copious NH3 upon pyrolysis.35 Curiously, NQ can be used to reduce burning rate. Williams et al. suggested that, for NQ and a number of similar ingredients, this may be due to the formation of a residue inhibiting mass flux at the burning surface.36 Alternatively, the result may simply be due to the lower energy of NQ which may overwhelm its kinetic effects. If used in small amounts, NQ might, instead, increase burning rates. 12 The issue is further complicated by the production of HNCO during NQ pyrolysis.35 As noted above, even small concentrations of HNCO retardant may overwhelm the effects of the NH3. These ideas on the chemistry of NQ are supported by Miller and Anderson's modeling of M30, a propellant which contains considerable NQ. The model correctly predicts that no DZ is produced at any pressure. Detailed analysis confirms that this result is caused by the breakdown of the major ingredient NQ to NHX, amongst other species; and

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Reactions important for modeling NH3 and HNCO producing additives. Reaction

NH3 producing additives NHa;+H = NHa:_i+H2 NrLs + OH = N H . - i + H 2 0 NH X + NO = products HNCO producing additives HNCO + H = NH 2 + CO HNCO + OH = NCO + H 2 0 NCO + NO = N 2 0 + CO NCO + NO = C 0 2 + N 2

Comments

x = 0-3 x = 0-3 x = 0-2

Most likely pathway in first-stage flame. More detailed discussion in Sec. 3.2.8 for NH 2 . Most important HNCO path in dark zone. Most important HNCO path in first stage. Primary NCO removal in first stage. Branching ratio in need of study. See Sec. 3.2.10.

the NH^ causes rapid conversion of NO to N2, preventing DZ formation (to be published).1 Isocyanates (R-NCO) might produce HNCO during combustion and be useful burning rate reduction modifiers. Brill, however, has pointed out that, although such compounds are frequently used during binder curing processes, they are currently thought too toxic for propellant formulation. Brill also suggested that another compound, DINGU, which produces copious HNCO upon pyrolysis, might be acceptable. 38 The importance of NH3 and HNCO as intermediates produced during combustion of propellants with modifiers suggests further elementary reactions that are of concern in the first stage of combustion for those propellants. These are listed, with comments, in Table 3. (d) Some related areas for future development Some nitrogen-containing, liquid fuels are used with inhibited red fuming nitric acid as oxidizer. In the past, hydrazine and its alkylated derivatives have found use, but monomethylhydrazine (MMH) has received most attention. 39 An MMH mechanism has been developed by Catoire et al.40 All the reactions of MMH and of its larger fragments need further study. Many of the rate coefficients are estimated, and the pressure dependence of the 'Bright orange flame emission directly above the propellant was always observed by Miller upon combustion of M30 in his strand burner. 3 7 Hot NH 2 is a strong emitter of yellow-orange emission, and there is little Na in the formulation, another common yellow-orange emitter. Of course, the observation of excited state emission by a given species is only suggestive of the presence of the ground state species, and no spectra were taken; nevertheless, this observation supports NH 2 formation during M30 combustion.

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unimolecular reactions is unknown. An MMH mechanism is being used in a vortex rocket engine model. 41 Diamino and amine azide compounds are being studied as possible replacements for the hydrazine compounds. Experimentalists should be vigilant about the results of theoretical estimates for new intermediates produced by the preceding solid propellant ingredients and burning rate modifiers. The models use the assumption that H2CNNO2 and H 2 CN are key intermediates produced during combustion of RDX and HMX. Of these species, only H 2 CN has received experimental study. Lack of a simple source and diagnostic for H 2 CNN0 2 has deterred study. Even for H 2 CN few kinetic data are available. Formerly, mass spectroscopy has been the only readily applied detection method. Recently, however, Nizamov and Dagdigian 42 (see the chapter by Dagdigian) have used intracavity ring-down spectroscopy to study kinetics of a few reactions at room temperature. This diagnostic tool will enable more studies.

2.2.2. Dark Zone Chemistry Prior to Miller and Anderson's modeling of the burning rates of several nitrate ester propellants, 13 many thought that the chemistry controlling the DZ length was not likely to affect the computed burning rates. Careful analysis of the solutions in Ref. 13 shows that this notion is wrong. Because the final flame zone at low pressures is separated from the propellant surface by the DZ, the burning rates at those pressures are quite insensitive to the reactions controlling DZ length (below about 300 atm in Ref. 13). In spite of our expectations, we found that the burning rates at high pressure are very sensitive to those same reactions. As pressure increases, the DZ collapses and the equilibrium products are close to the propellant surface. Previously, modelers thought that some short plateau region would probably be present in the gas phase temperature profile, blocking heat released in the second-stage flame from reaching the surface. In fact the computed solutions above 300 atm exhibit no plateau region. From the species profiles we found that, although the conversion of N 0 2 and HONO to NO precedes that of NO to N 2 , the conversion of NO to N 2 begins fairly close to the surface; the structured portion of those species' flame profiles is quite narrow. The concept of heat transfer characteristic distance, i.e. distance for 1/e falloff in effectiveness of transfer, helps to characterize results. 13 Considerable NO to N 2 conversion occurs within the heat transfer characteristic distance of the surface at high pressure, but not at low pressure. The reactions responsible for the conversion at high pressure are the same as those

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responsible for controlling the DZ length at lower pressures. To summarize: though the burning rate results at low pressures are not sensitive to the DZ reactions, they become highly sensitive to them at high pressures. Because only scant test data are available, the DZ formation should be studied and the DZ model improved. To guide this effort, we are reviewing the model and comparing it to the few available appropriate propellant combustion studies. 16 (a) Simplified DZ model A simplified model for propellant DZs is used to test the relevant chemical submechanisms. The approach and chemistry are also discussed elsewhere. 16 ' 17 ' 43 Composition and conditions of the DZs of nitrate ester and nitramine propellants were discussed towards the end of Sec. 2.1. Measured conditions at the leading edge of the DZ (e.g., temperature, pressure and mixture ratio) are used as inputs to an adiabatic, time-dependent chemical kinetics-only model to calculate the chemical ignition delay time of the DZ mixture. We assume adiabatic, convective plug flow; diffusion and conduction are ignored because the major species concentrations and temperature are fairly constant across the length of the DZ. The computed ignition delay is compared to experimental results by converting the measured DZ length to an equivalent ignition delay time using the convective gas flow rate. The latter in turn is computed using an estimated average molecular weight of the gases, the measured pressure, DZ temperature, and solid propellant burning rate, and a continuity assumption between solid and gas phases. The current model agrees with the available experimental data, but there are few measurements on solid propellants that provide all the information necessary to test the DZ model: the mixture ratio and temperature measured at the leading edge of the DZ and the DZ length, the propellant density, and burning rate at the pressure of interest. Thus the model has not been well tested. Heller and Gordon 44 studied three NC/NG propellants. For one of these, all data needed to test the DZ model was provided except the H2O concentration; that quantity is derived by a mass conservation assumption. The needed physical data for several other nitrate ester propellants was provided in the work by Aoki and Kubota 45 ; but the DZ mixture composition was not measured. One of Aoki and Kubota's propellants was similar to the key one of Heller and Gordon. Comparison with other works suggests the DZ mixtures do not vary strongly amongst such similar nitrate ester propellants (see results of Refs. 13, 44, 46, 47 compared in Table 4 of Ref. 13a).

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Therefore, it is reasonable to use the Aoki and Kubota DZ physical data for that one, but with the Heller and Gordon initial DZ chemical composition, as a further test of our DZ mechanism. A pleasing aspect of each of these two data sets is that both provide a measure of DZ ignition delay (length) over a range of pressures from about 10-35 atm. Another very important point regarding the Heller and Gordon data is that equilibrium conditions for the final gas phase products may be calculated starting with either the initial solid propellant composition or the DZ mixture. The results should be equivalent. They thus provide an important validity check on the DZ condition measurements. The adiabatic flame temperatures and equilibrium concentrations obtained in the two ways are, reassuringly, consistent. For nitramine propellants, fewer well-defined test data are available. In prior works, 17-43(b) comparisons were made with data from Kubota 48 on his own formulations of experimental HMX-binder propellants. It now appears the DZ mixture ratio in those experiments was not extracted reliably from the results and the data may have to be discarded. The main problem is that H 2 0 could not be measured and no HCN was observed. The lack of HCN in the DZ should be viewed with suspicion because it is known to form in copious amounts during HMX pyrolysis49 at the surface temperatures observed in Ref. 48. HCN has been observed in combustion experiments on other HMX propellants (see the review in Ref. 17). HCN is relatively stable; gas-phase models of solid nitramine combustion indicate it would survive through the first stage into the DZ. Because Ref. 48 leaves two major species concentrations unknown, the extraction of the complete mixture ratio is impossible. We have found only one data set 50 that can be used for nitramine propellant for an RDX-GAP mixture at f atm. A 400 watt CO2 laser beam impinges on the surface to heat the solid to obtain sustained, steady-state combustion of the propellant at this low pressure. Unfortunately, it is quite uncertain how much laser energy is absorbed into the propellant; some may go into the gas phase and some may reflect off the surface. Due to this absorption, the energy in the DZ is larger than in an equal mass of the solid phase propellant. Thus a consistency check like that performed with the nitrate ester propellants is not possible. Equilibrium calculations do at least show that the computed flame temperature of the DZ mixture is much larger than for the solid propellant, as one would expect. The current DZ chemistry submechanism is in good agreement with available experimental results for both nitrate ester and nitramine propellant types. The check for nitrate ester propellant DZs is reassuring, but at

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least one more complete data set, similar to Heller and Gordon's, should be obtained. For nitramine DZ chemistry, the available tests are not sufficient. Further measurements relevant to DZs for this propellant type should be made over a range of pressures similar to that used for the nitrate esters. The measurements should be made without heating-assisted combustion, e.g. using a CO2 laser. It is important to ascertain how much HCN is present without the laser assist because pyrolysis studies indicate that the branching to HCN versus CH2O formation in the condensed phases is strongly affected by temperature. 49 The [HCN] in the DZ is as important to know as [NO], because the HCN reactivity is similarly low. Modeling indicates that HCN formed in the first stage also contributes to the DZ formation. The temperature at the leading edge of the DZ should be measured as precisely as possible because the modeling calculations are extremely sensitive to temperature. In addition to measurements on propellants, the kinetics of reacting idealized DZ mixtures should be studied. Measurements on actual propellants, e.g. in strand burners, provide key information regarding actual conditions (initial temperature and mixture ratio). However these are clearly not the most desirable experiments for kinetics mechanism tests because the exact initial conditions cannot be controlled, or known, nearly so accurately as in a kinetics apparatus. For example, there are fairly wide error limits on measured species concentrations and temperature from experiments on propellant DZs. Calculated DZ ignition delays are quite sensitive to some of these input DZ conditions, especially the N 2 0 concentration and temperature. Also mixture ratios in kinetics apparatus usually can be varied easily while changing the DZ conditions cannot be done in a straightforward, controllable manner. Varying gaseous mixture ratios would provide a measure of global mechanism reaction orders for the components of the DZ mixture. Kineticists have found for many other chemical systems that such data provide stringent tests of proposed mechanisms. Such experiments could, for example, help resolve the issue about HCN chemistry discussed in Sec. 2.2.1(a). Relevant measurements would be most easily obtained in shock-tube experiments, perhaps by obtaining mixture ignition delay times; though possibly other techniques might be used. Experimentalists interested in pursuing this idea should note that the reactant concentrations likely to be required are quite high. This point could bring safety and collider vibrational energy transfer issues into concern.

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(b) Sensitive reactions in DZ submechanisms A listing of reactions to which DZ calculations are known to be sensitive is presented in Table 4. Parts of Table 4 highlight reactions of particular importance to nitrate ester and nitramine propellants. Comments in the table identify reactions needing the most work because of high sensitivity and poorly characterized rate coefficients. The last four reactions in Table 4 are no longer included in our reaction mechanisms. If included in DZ models, the first three of these reactions became reversed and were highly sensitive, in the models, because they were incorrectly predicted to be important radical sources. These three reactions are discussed further in the next few paragraphs. The results highlight how modeling of global reactions can yield important mechanistic insights. The last reaction is not included in current models because its rate is uncertain, but it is likely to be negligible. Our early effort at DZ modeling 17 highlighted the possible significance of the first of these now-discarded reactions, N + C 0 2 = N O + CO.

(10)

The rate coefficient expression used was from Ref. 51, which had been commonly used in DZ and other combustion modeling. The reaction reverses in DZ modeling, producing radicals, because there is considerable NO and CO in DZ mixtures, but no other significant source of N atoms. Although early modeling yielded good agreement with experiment when this reaction was used and the reaction was highly sensitive, a critical literature review reported in Ref. 17 brought its importance into question. The reaction was tentatively removed in spite of adverse effects on agreement with experiment and revisions were made to the models. Later efforts, discussed in Sec. 3.2.6, have yielded strong evidence that the reaction is too slow to be important under any condition, so it has been permanently discarded. It was also checked against later static reactor experiments, see a few paragraphs below. Rohrig and Wagner 52 performed shock-tube experiments on the reactions of NH with H2, CO2, and H2O. This was the first indication that the latter two reactions occur; they suggested that these proceed as NH + C 0 2 = HNO + CO,

(11)

NH + H 2 0 = HNO + H 2 .

(12)

Recent thermostated reactor work by Fontijn et al.53 yielded NH + H 2 rate coefficients in accord with those of Rohrig and Wagner, indicating

Gas-Phase Kinetics for Propellant Combustion Table 4.

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Sensitive reactions controlling propellant dark zone structure. Comments

Reaction

Relevant to both nitrate ester and nitramine propellant DZs Extremely important for dark zones of nitrate ester * HNO + NO = N 2 0 + OH propellants. High T study needed; challenging. * HNO + HNO = N 2 0 + H 2 0 See comments in Table 1. * N 2 0 ( + M ) = N2 + 0 ( + M ) Entire T range needs study. Likely to require high * N 2 0 + NO = N 2 + N 0 2 [NO], therefore complex modeling, N 2 0 ( + M = NO) likely to interfere. (Efficiency for M = NO in N 2 0 ( + M ) is a likely, desirable by-product of such a study.) NH + NO = H + N 2 0 H + N 2 0 = N 2 + OH See Table 1 and Sec. 3.2.2. H + HNO = H 2 + NO H + HNO = NH + OH NH 2 + NO = NNH + OH See Sec. 3.2.8. NH 2 + NO = N 2 + H 2 0 See Sec. 3.2.8. Primarily relevant to nitrate-ester propellant DZs * HNO + N 0 2 = HONO + NO H + NO(+M) = HNO(+M) See Sec. 3.2.5. N 0 2 O M ) = NO + O ( + M ) H + NO2 = NO + OH See Sec. 3.2.4. 0 + N 2 0 = NO + NO Reversed under dark zone conditions, modest radical source. See Sec. 3.2.1. N + NO = N 2 + OH NO + H = OH + N : :

C H 3 + N O = H 2 CN + OH CH 3 + NO = HCN + H2O

Primarily relevant to nitramine CO + O (+ M) = CO2 (+ M) CO + N 0 2 = NO + C O a HCN + O = NH + CO * HNC + O = NH + CO * HNC + OH = HNCO + H HNCO + H = NH 2 + CO NCO + NO = N a O + CO * NCO + N 0 2 = products

This reaction pair is sensitive only if CH4 trace species is considered in the starting mixture (best models include it). propellant

DZs

See Sec. 3.2.10. See Sec. 3.2.10.

Reactions discarded from recommended combustion mechanisms N + C 0 2 = NO + CO It is now established that this reaction does not occur with fast enough forward rate to any products to be of significance in combustion. See Sec. 3.2.6. NH + C 0 2 = HNO + CO This reaction occurs with a significant forward rate, but not to the products shown. See Sec. 3.2.7.

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(Continued) Comments

Reactions discarded from recommended combustion mechanisms (Continued) * NH + H2O = HNO + H2 This reaction occurs with a significant forward rate, but not to the products shown. See Sec. 3.2.7. * CO + N2O = CO2 + N2 The rate coefficient expression for this reaction is highly controversial. Our opinion is that it should be discarded from combustion mechanisms. ' T h e s e reactions need further study, currently many of these are included only via crudely-estimated rate coefficients. Efforts on these are especially desirable.

that the respective techniques give correct results. However, if the products shown for reactions (11) and (12) are included in nitrate ester DZ models, the global rates are over-predicted by several orders of magnitude. This results from H + NO (+ M) = HNO (+ M)

(13)

H + HNO = H 2 + NO

(14)

and

having, very roughly, equal forward and reverse rates in DZs. This creates significant traces of HNO. Because the DZ mixtures also contain much CO and H2, and there is no other significant source of NH, reactions (11) and (12) reversed, producing NH radicals, when included in early DZ models. They were predicted to be so fast that they overwhelmed other sources of radicals. The result was that the predicted chemical delay time in the DZ, and hence the DZ length, was much too short, indicating no DZ would exist. This result is strongly contrary to experiment, suggesting that reactions (11) and (12), with the products as shown, are incorrect, as further discussed in Sec. 3.2.7. Further insight into reactions (10)-(12) is available from modeling of the isothermal static reactor experiments of Diau et al.,8 who studied H2/NO and H2/CO/NO mixtures diluted in Ar at 900-1225 K. Three example runs for the latter mixtures are given in their Fig. 2. Our (WRA) modeling results are qualitatively similar for each. Results for their case B, run 8 are presented here, see the present Fig. 2; conditions are constant pressure 0.930atm, constant temperature 1000K, and initial mole fractions of H 2 , NO, CO of 0.0263, 0.0161, 0.0430, respectively. Excellent agreement of base

Gas-Phase Kinetics for Propellant Combustion

0.5

1.0 Time, 101 s

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217

1.5

Fig. 2. Comparison of experimental 8 and modeling results (this work) for a H 2 / C O / N O / A r mixture at 1000K. Note the different timescales in (a)-(d). (a) Experimental results (points) and modeling result using baseline mechanism (curve). (b) Modeling result when N + CO2 = NO + CO (10) is added to the baseline mechanism, using experimental forward k(T) from Ref. 51 and thermodynamics to compute the rate of the assumed reverse reaction. (c) Modeling result when NH + H 2 0 = HNO + H 2 (12) is added to the baseline mechanism, using experimental forward k(T) from Ref. 52 and thermodynamics to compute the rate of the assumed reverse reaction. (d) Modeling results when NH + CO2 = HNO + CO (11) is added to the baseline mechanism, using experimental forward k( T) from Ref. 52 and thermodynamics to compute the rate of the assumed reverse reaction.

mechanism predictions with experiment for [CO2] is achieved, see Fig. 2(a). However, when N + CO2 = NO + CO (10) is added, using k from Ref. 51, the predicted CO2 production rate becomes about two orders-of-magnitude too fast, see Fig. 2(b). If instead NH + H 2 0 = HNO + H 2 (12) is added, using k\2(T) from Rohrig and Wagner, 52 the predicted rate is about three orders too fast, see Fig. 2(c). Finally, if NH + C 0 2 = HNO + CO (11) is added instead, using fcn(T) from Rohrig and Wagner, the predicted rate is four orders too fast, see Fig. 2(d). The suspicions raised by the

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preceding observations on dark zone and static reactor modeling spurred the isolated reaction experiments and ab initio studies discussed in Sees. 3.2.6 and 3.2.7.

3. Experimental Input Data 3.1. Elevated Temperature Techniques for Obtaining Kinetic Data on Individual Reactions Accurate information on individual reactions, which together govern global propellant combustion processes, can best be obtained in isolation from competing reactions, when possible. Techniques for providing such environments have originally been developed for at, or near, room temperature studies. Till about 1970 little information was available on individual energetic materials (EM) combustion reactions at temperatures of interest. Since then apparatus has been developed that operates on the same principles as the room temperature methods, but different materials have allowed temperatures up to around 1800 K to be reached. Thermostated reactors, used with optical spectrometric monitoring for the determination of reactant concentrations, are particularly relevant for EM reactions (Sec. 3.1.1). Thus, information on the kinetics of many of the reactions of interest to modelers can now be obtained at or near the temperatures of interest. Most of the processes which can be isolated are between atoms, or other small transient species, and a second, molecular, reactant. The equipment to be discussed is particularly suited for observations on such reactions. However, reactions between transient species can, and have in some cases, also been studied. Simultaneously with these developments, shock-tube techniques, which were typically used for multi-reaction environments observations above about 2000 K, have undergone refinements to allow measurement on isolated reactions below that temperature. This approach is discussed in Sec. 3.1.2. These technique developments are not unique to EM combustion. Thus, e.g., fossil fuel combustion and related NO^ (NO, N0 2 ) pollution generation and abatement models also require input data on elementary reactions at realistic temperatures. These have been investigated in the same type of apparatus. 3.1.1. Thermostated Reactors Isolation of individual reactions is achieved in these reactors by introducing small concentrations of two reactants in a large excess of inert bath gas.

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Usually Ar or He are used for this purpose, while N2 can sometimes also be useful. Under these conditions, the pressure and temperature of the bath gas are essentially the pressure and temperature of the reaction, which thus can be varied independently of the reactant concentrations. Several versions of this type of apparatus exist. Of these, high-temperature photochemistry (HTP) reactors have been most frequently used for EM studies at temperatures of interest. In that type of reactor, atomic or other small transient species are generated from a parent compound, the photolyte, by means of a flash lamp or pulsed laser. 53-55 These species are used as the rate-limiting reactants. Their relative concentration as a function of reaction time gives the reaction rate at the particular concentration of the second reactant, i.e. of the reactant present-in-excess, and of the bath gas. Varying these latter two parameters then allows determination of the rate coefficients. Since the limiting reactant is present in small concentrations, so is the product concentration limited, which usually prevents interference from secondary reactions. The transient species concentration is monitored by fluorescence or, occasionally, light absorption. A schematic of an HTP reactor is shown in Fig. 3. A ceramic reaction tube, surrounded by SiC resistance heating elements and soft ceramic insulation, is contained in a vacuum chamber. The use of these materials has allowed the «1800K maximum temperatures to be reached. The reaction tube has four holes at right angles which face windows in the chamber. Two windows at opposite ends are used for the photolysis and diagnostic radiation beams. At a third hole, a photomultiphier tube (PMT) and associated electronics is used to measure the fluorescence intensity, which is proportional to the transient species concentration. The observed reaction zone is thus delineated by the intersection of the photolysis beam, the diagnostic radiation, and the field of view of the PMT. Consequently, the measurements are made in an essentially wall-less reaction zone. The diffusion times of the reactants to the walls are long compared to the times during which the reactions are observed. A movable water or air-cooled inlet tube is used to minimize the exposure time of the reactants to high temperatures. The bath gas, Ar or N2, flows in from the upstream (bottom) reactor plate. The flows are sufficiently slow that mixing of the reactant and bath gases is at least 99% complete before the photolysis pulse. Observed reaction times are in the order of 10~ 4 to 10 _ 1 s, short compared to the gas residence times, i.e. these are real-time observations. The photolysis radiation repetition rate is such as to allow essentially complete replacement of the gas mixtures between pulses.

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REACTION TUBE HEATING RODS

SHIELDED THERMOCOUPLE CW RESONANCE LAMP hv, H ( 2 P - 2 S )

NH3orCH4 + nd 2 REACTANT

MULTI-CHANNEL SCALER/COMPUTER

Fig. 3. Schematic of a high-temperature photochemistry reactor. The reactor is shown as configured for H-atom reaction measurements.

Flash lamps, emitting in the UV and vacuum UV (VUV) regions of the spectrum, have been used as photolysis sources. The flashes tend to interfere with diagnostic equipment; pulsed lasers are, therefore, preferred. The principal atomic reactants of interest in EM reaction models, O, H, and N, all have resonance lines in the VUV. Their concentrations are conveniently monitored by excitation of fluorescence resulting from cw microwave discharge flow lamp radiation. The PMT output is then fed to multi-channel sealer-based electronics to produce the fluorescence intensity versus time plots, which yield the reaction rates. Many flashes are needed for accurate data. For di-, or poly-atomic species detection, e.g. NH, NCO, lasers are often needed. Pulsed dye lasers have been employed for this purpose. As each pulse of these yields only one point for the intensity versus time plots, variable time delays are used in those experiments. Details of the operation of HTP reactors and the data analyses have been discussed in many original papers, e.g. Refs. 53-55. Other diagnostic techniques could in principle also be employed in HTP experiments

Gas-Phase Kinetics for Propellant Combustion

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and have sometimes been used in lower temperature apparatus. The major requirement is that the diagnostic equipment can be placed outside the vacuum housing and not be significantly interfered with by radiation from the hot reaction tube walls. Several laser-based techniques would be suitable. Some of these have been used in flame research and in practical devices, and hence can be compatible with high-temperature observations. 56 (See also the chapter by Dagdigian.) For atomic and diatomic reactants in HTP-type reactors, there would be little advantage in using more laborious diagnostics. However, those techniques could become essential when extending the research to larger reactant species and to quantitative product measurements. Several reactions have been studied in thermostated tubular electricaldischarge fast-flow reactors (EDFFR). There, reaction time is determined from the flow velocity and the distance traveled and a steady state is obtained at each cross-section of the reaction tube. Optical techniques have been used there as well, but, importantly for product analysis, mass spectrometry can readily be employed with such reactors. The latter allows determination of the masses of the reactants and the products in one experiment, as well as for investigation of reactions between transient species.57 However, in EDFFR reactors, the reactants come in contact with the heated walls, which in many cases leads to dissociation of reactants or products in the temperature regime of EM interest. Thus their use in EM-oriented research has been limited. For the study of metallic species, involved in e.g. metallized solid propellant combustion, a thermostated fast-flow reactor has been developed, which allows measurements over the same temperature range as the HTP reactors. 58 It has also been used for product identification by mass spectrometry. 59

3.1.2. Shock Tubes. Comparison of Techniques Shock tubes are the most appropriate tool for obtaining kinetic information at temperatures above about 2000 K. In shock tubes, similar spectrometric transient reactant species detection methods as above are often used. By additionally monitoring the concentrations of simple intermediate products, information on the reaction channels has sometimes been obtained and the observed rates can then be associated uniquely with a particular reaction. 60 ~ 62 Tn most shock-tube experiments, the transient reactant species are produced as a result of thermal dissociation. This typically leads to a multiple reaction situation, requiring complex modeling to extract

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kinetics results. However, in the temperature domain of interest, the shock waves can occasionally be used to heat gases to selected temperatures where only specific small transient species are produced. Reactions of these species are thus isolated. Similarly, a high-temperature undissociated gas mixture can be generated in which flash- or pulsed laser-photolysis then produces the desired transient reactants. In such photolysis shock tubes (PST) an environment is thus also created for the study of isolated elementary reactions. PST is typically suitable for the temperature range 700-2200 K. 6 3 - 6 5 This range partially overlaps that of the thermostated reactors. It is therefore interesting to compare HTP and PST. In HTP work, the reactant gases become premixed and reach operating temperature while flowing to the observed reaction zone. PST uses premixed gas and provides very rapid heating. This results in shorter required survival times of thermally unstable species than in HTP. Neither PST nor HTP can be used at temperatures where significant dissociation occurs within the required time range. The indicated maximum temperatures can, therefore, often not be employed. However, because of the shorter residence times, PST can always be used to reach higher temperatures than HTP. At those temperatures, direct PST measurements are clearly to be preferred over extrapolation of HTP results. However, a wider rate coefficient range has been covered by HTP, from « 1 0 - 1 0 (which corresponds to reaction upon every collision) to « 1 0 - 1 7 cm 3 molecule^ 1 s _ 1 , as compared to « 1 0 _ 1 0 to «10~ 1 4 cm 3 molecule" 1 s _ 1 for PST. HTP has also been used for termolecular reactions, which has apparently not been attempted by PST. The capability of HTP reactors to work down to about 300 K, and with modification below that temperature, can yield important mechanistic information. In practice, the two techniques well complement each other and agreement between results obtained from both reactor types has usually been good. 66 ' 67

3.1.3. Reaction Mechanisms Many of the elementary EM reactions studied thus far have been atom reactions for which there is often little doubt about the products. If there are potentially alternative channels, thermochemistry is often used to define the actual reaction paths. Variation of the pressure, which is approximately determined by the bath gas concentration, allows one to distinguish between ter- and bi-molecular reactions. In several cases, the importance of the

Gas-Phase Kinetics for Propellant Combustion

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bimolecular channels increases with temperature. For polyatomic reactants, product identification becomes more difficult. The same type of optical diagnostic techniques as used for the reactants can sometimes still be used to identify simple products. In some lower temperature experiments, even tri-atomic products have thus been monitored, and branching ratios have been determined. 68 ' 69 Some reactions lead to chemiluminescent products, which are thus readily identified.70 To obtain experimental evidence, over wide temperature ranges, that even identified product paths are unique is at best very time-consuming and often not possible. However, it is especially here that theoretical calculations, such as by ab initio and quantum-RRK methods, can be very helpful. Moreover, the modeling of global experiments can sometimes reveal that an expected intermediate product cannot have formed to a significant degree. Several examples in Sec. 3.2 illustrate the ways by which information from various sources can be combined to yield the desired product information. The theoretical methods can also reveal what the likely intermediates and transition states along the reaction paths are, as also illustrated in that section. A detailed discussion of that topic, i.e. of microscopic kinetics, is beyond the scope of the present chapter. 3.2. Examples of Results on the Models

with Significant

Impact

3.2.1. 0 + N 2 0 This reaction has two channels O + N 2 0 - • 2NO, 0 + N 2 O ^ N 2 + 02,

AF 2 ° 98 = - I S O k J m o r 1 1

AF0 9 8 = - 3 3 1 k J m o r .

(15a) (15b)

Till fairly recently the accepted wisdom was that, from at least 1200 to 3200 K, both reactions occur with essentially the same rate coefficients, i.e. the branching ratio is about 50%, independent of temperature. However, most studies were made above 1700 K and no direct measurements were available below that temperature. Extrapolation down to dark zone temperatures of the results of a 1992 shock-tube study of N 2 0 pyrolysis suggested that k15 = k15a + fc15b had to be revised upward for that regime for which also fc15b > fci5a.71 A kinetic modeling study further showed that some ancillary chemistry, upon which the earlier evaluations were based, was not in accord with subsequent information.72

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An HTP study of fcis around HOOK then showed these rate coefficients to be much larger than previously assumed, though a factor 4 lower than the long extrapolation of the 1992 shock study would suggest. 73 This result, combined with those high temperature data that survived a critical evaluation based on current knowledge, then led to 7 2 fc15a (1370-4080K) = 1.5 x 10" 1 0 exp(-13,930K/T) and k15h (1075-3340 K) = 6.1 x 10" 1 2 exp(-8,020K/T) cm 3 molecule" 1 s" 1 . This indicates that channel (15b) dominates below 1840 K and (15a) dominates above that temperature.

3.2.2. H + N 2 0 This reaction is one of the most sensitive in propellant combustion modeling. Its principal path is AiJ^g = - 2 6 1 k J m o r 1 .

H + N 2 O ^ N 2 + OH,

(16)

The HTP observations yielded74 k16 (750-1310 K) = 7.3 x lO" 1 0 exp(—9690K/T) cm 3 molecule -1 s _ 1 . These are shown in Fig. 4, where they are compared to the 720 to 1120 K EDFFR results from Albers et al.75 T,K „

1500

1000

700

500

400

2.0

2.5

10

V

(/> 3 O 0>

1I U0-13

10-14

o E CO

E °. 10-" J*

10-16

0.5

1.0

1.5 1

1000/T, K"

Fig. 4. Plot of the rate coefficients obtained for the reaction between H and N2O. (•) H T P ; (—) fit to H T P work; (—) results of Albers et al.,75 discharge/fast flow reactor.

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There is excellent agreement in that temperature range. The lower temperature data show considerable curvature, as confirmed in several subsequent studies. 76 ' 77 The interpretation of this curvature has led to much debate. Marshall et al74'76 made BAC-MP4 and transition state calculations and found that the following detailed mechanism agreed with the data H + N 2 0 -> HNNO - • NNOH -> N 2 + OH.

(16')

The curvature was attributed to tunneling through the barrier for the HNNO —> NNOH transition. However, quantum-RRK calculations by Dean and Bozzelli et al.7S'79 suggested instead that collision-induced stabilization of the HNNO intermediate is responsible. While Marshall et al. did not observe any pressure affect, Dean and Bozzelli expect that more extensive pressure-dependence measurements at the lower temperatures would show that stabilization occurs. Ab initio calculations by Diau and Lin have led to the conclusion that the adduct stabilization is more significant than tunneling, with the latter increasing in importance at lower pressures. 80 However, they 80 consider the tunneling to be predominantly through the barrier for the H-atom addition step in (16'). Direct experimental evidence for a pressure effect remains desirable, but will be very difficult to obtain in view of the small rate coefficient values at the lower temperatures. 3.2.3. H + NH 3 ^ NH 2 + H 2 The reaction H + NH 3 -> NH 2 + H 2 ,

AH2°98 = ^ k J m o P 1

(18)

has frequently been studied, because of its interest not only to EM but also to various other problems, such as NO^ pollution prevention. Good agreement has been obtained by various techniques, as well as by ab initio studies. The work has been thoroughly reviewed by Michael,81 who, with his co-workers, also covered the widest temperature range, by using a PST technique. 82 They measured fc17 (910-1780 K) = 3.0 x 10" 10 exp(-8067K/T) cm 3 molecule -1 s _ 1 . This result is essentially the same as obtained from an HTP 6 7 and an EDFFR 8 3 study for the lower part of this range. Extension of the data to 470 K leads to 6 7 , 8 1 kn (490-1780 K) = 9.0 x l O " 1 9 ( T / K ) 2 4 0 exp(-4991K/T) cm 3 molecule- 1 s" 1 . This expression is also well-matched by various theoretical approaches. 84,85 The nearly thermoneutral H + NH 3 reaction is further of interest in that it represents one of the relatively rare examples where a reaction and

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its reverse NH 2 + H 2 - • NH 3 + H,

AiJ2°98 = - 1 7 k J m o r 1

(-17)

could both be measured. This was achieved indirectly by Sutherland and Michael86 on the assumption, apparently valid for their mild NH3-photolysis conditions, that in their PST experiments the initial [NH2] and [H] are equal. No observation of NH 2 was required under those conditions. An equilibrium constant was obtained, which, combined with kn, led to k-n (900-1620 K) = 5.4 x 10" 1 1 exp(-6492K/T) cm 3 molecule" 1 s" 1 . At the lower end of this temperature range, these results agree with those from the direct EDFFR study of Hack et al.,83 where the NH 2 was produced from the NH 3 +F reaction and observed by LIF. A recent shock-tube study for the 1360-2130 K temperature domain also gave very good agreement. 87 In that work, the NH2 was produced by N2H4 dissociation and its concentration was monitored by a novel frequency modulation technique. Computational studies 84 ' 85 again well describe these results. 3.2.4. H + NO2, CH3NO2 The reaction H + N 0 2 -> OH + NO,

AH%98 = - 1 2 4 k J m o r 1

(9)

has recently been studied from 1100 to 1650 K in a shock tube. 88 There the chemical isolation was achieved by producing H atoms from the thermal dissociation of C2H5I, rather than by photolysis. In addition to monitoring [H], rate coefficients were also obtained from 1250 to 2000 K by monitoring of the OH product, combined with chemical simulation. This yielded statistically overlapping data, as had lower temperature studies. It can, therefore, be concluded 88 that kg (195-2000 K) = 1.5 x 10~ 10 cm 3 molecule" 1 s" 1 . Thus, (9) is a very fast reaction, the rate coefficients of which approach gas-kinetic collision values and show no observable (<0.4kJmol _ 1 ) activation energy. In other words, there is no electronic energy barrier. Theoretical work has further confirmed this conclusion.88 In propellant combustion, N 0 2 can also be bound to other fragments. To investigate how this may affect its reactivity, studies have been made of H + CH3NO2 - • products.

(18)

Because of the low thermal stability of this compound such work was done at lower temperatures. An EDFFR study 89 yielded fcig

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(360-570 K) = 7.8 x 10" 1 2 exp(-1878K/T) cm 3 molecule" 1 s" 1 . Thus, a much slower reaction than for free NO2 occurs which proceeds with a reasonably large activation energy. The absence of an unpaired electron, as in free NO2, thus considerably affects the reactivity. A room temperature study in a similar apparatus 90 showed that 30% of the reaction goes to OH + CH3NO, i.e. the equivalent of reaction (9), and the remainder to CH 3 + HONO. Both paths are exothermic. These authors suggest 90 that other bound-N02 combustion species could react similarly, e.g. the NH2NO radical could be produced from the H-atom reaction with NH 2 N0 2 , which is isoelectronic with CH 3 N0 2 . Presumably this idea can be extended to several larger propellant combustion intermediates for which no good production methods are available, so that their reactions could be studied. 3.2.5. H + NO The three-body recombination reaction H + NO + M - • HNO + M,

Atf£ 98 = -206 kJ m o h 1

(13)

is important for several reasons. It can become significantly reversed under propellant burning conditions. As it is followed by the rapid reaction H + HNO -> H 2 + NO (14), the NO can act as a catalytic H-atom sink and hence as a flame retardant. As mentioned in Sec. 2.2.2(b), these reactions have a significant effect on global kinetics in propellant dark zones. 16 ' 43 ( c ) Reaction (13) also plays a role in NOa, conversion to N 2 , i.e. it is part of a pollutant removal process. Till recently there was considerable uncertainty regarding the ki3{T) for M = N2, a representative third body for propellant and other combustion environments. A literature estimate gave a value around 1000 K considerably higher than fitting procedures of two multi-reaction systems experiments suggested. Subsequently, HTP measurements yielded k13 (295-905K) = 1.0 x 10" 3 3 ( T / K ) 0 2 0 6 exp(+780 K/T) cm 6 molecule -2 s - 1 , in good agreement with these 1000 K measurements. 54 In a recently up-dated on-line computer model for natural gas combustion, GRI-Mech 3.0, reaction (13) was evaluated by letting it float against reactions for which k(T) was considered more certain. 91 This resulted in k13{T) = 1.2xl0" 2 8 (T/K)" 1 ' 3 2 exp(-370K/T) which, from 500 to 1300K, falls within 10% of the above expression.

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3.2.6. N + C 0 2 , N 2 0 , 0 2 As discussed in Sec. 2.2.2(b), early models of the combustion of nitrate ester and nitramine propellants, especially those for dark zone structures, contained the spin-forbidden reaction N( 4 S) + G02(X1T1)

-y NO(X 2 n) + COpf 1 !!), AH$9& = -99.4 kJ m o P 1

(10)

with fcio(T) from Ref. 51. The reaction reversed under dark zone conditions, becoming a major radical source in the models. The reaction was viewed with suspicion after a literature review,17 and was tentatively removed from ARL models. The issue spurred later studies, discussed here. The reverse reaction is strongly endothermic. The reaction had not been studied experimentally in the reverse direction (—10). Indeed, it would be very difficult to do so at relevant temperatures. However, an HTP study has been made of the forward process. 92 No reaction could be observed, indicating fcio (285-1142 K) < 5 x 1 0 - 1 6 cm 3 molecule -1 s _ 1 , which proves that the corresponding fc_io values contribute negligibly. An ab initio study of reaction (10) showed that even on the lowest possible path a barrier of 2 5 0 k J m o l - 1 needs to be surmounted. 93 The reaction has, therefore, been permanently removed from ARL models. This also confirmed that the models had to be revised. The models do not contain a reaction between N and N2O. However, a possible interpretation of observations on shock-heated NO/N2/Ar mixtures was that a fast reaction between these species could occur. 94 While N( 4 S) + N 2 0 ( X 1 S ) - • N2(X1i:+)

+ NO(X 2 n), AH 9 9 8 = - 4 6 4 . 4 k J m o r 1

(19a)

is spin-forbidden and hence an unlikely candidate for a fast reaction, the reaction leading to excited quartet state NO N( 4 S) + N 2 0 ( X 1 S ) - • N 2 (X 1 S+) + NO(a 4 n), AH$gs = -10.96 kJmol" 1

(19b)

is spin-allowed and exothermic and could well be fast. However, in an HTP study from 960-1130 K, no evidence of a reaction could be found.95 This indicates the rate coefficients for either reaction path to be < 1 x 10~ 15 cm 3 molecule -1 s~4 and that there is no need for inclusion of the process in models. As no evidence was found for reactions (10) and (19), it was important to demonstrate that this was not due to experimental artifact. A study

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of a known efficient N-atom reaction was, therefore, made in the same apparatus. 92 For the reaction N( 4 S) + 0 2 ( X 3 E ) - • NO(X 2 n) + 0 ( 3 P ) , Aff2°98 = - l S S k J m o l " 1

(20)

important to NOK pollution models, k20 (400-1220 K) = 2.0 x KT 1 8 ( T / K ) 2 1 5 exp(-2557K/T) cm 3 molecule" 1 s" 1 was obtained. This result is in excellent agreement with EDFFR measurements covering the 280 to 910 K temperature range. 3.2.7. NH + C 0 2 , H 2 0 These reactions were thought to proceed as NH(A"3E) + C 0 2 ( X 1 S ) -> H N O p ^ A ) + C O ^ E ) , AH%98 = 33kJmol" 1 , 3

1

(11)

1

NH(X S) + H 2 0(X A 1 ) - • HNO(X A) + H a ^ E ) , AF2D98 = - 8 k J m o r 1 .

(12)

They have been studied by Rohrig and Wagner behind shock waves.52 NH in its ground electronic state (A^3E) was produced by the dissociation of HN3. They obtained kn (1200-1910K) = 1.7 x 10" 1 1 exp(-7220K/T) and k12 (1330-1910 K) = 3.3 x 10" 1 1 exp(-6970K/T) cm 3 molecule" 1 s" 1 . However, considerable doubt has arisen regarding these reactions. As discussed in Sec. 2.2.2(b), models for different combustion systems, including one for the thickness of dark zones of nitrate ester propellants, have been found to produce global reaction rates that are several orders of magnitude too fast compared to experiments if reactions (—11) and/or (—12) with fc_n(T) and fc_i2(T), determined from the above expressions and the thermochemistry, are used. It thus appeared that either the rate coefficients or the assumed product channels of reactions (11) and (12) are incorrect. Modelers have, therefore, not included these reactions (cf. Figs. 2(a), 2(c), 2(d)). To provide an independent test of these shock tube studies, HTP measurements were made of NH + H 2 —» NH 2 + H from 830-1430 K. NH(X 3 E) was produced by multiphoton photolysis of NH3. 53 The obtained rate coefficients are in near perfect agreement with the Rohrig and Wagner results from 1155 to 1685 K, made in their same study. 52 Thus, the problem with reactions (11) and (12) is unlikely to be with Rohrig and Wagner's rate coefficients. It appears instead to be with their suggested products. Their measurements should thus not be applied to reactions (—11) and (—12).

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Other potential combinations of two separated products are too endothermic to be compatible with the observed activation energies. Ab initio calculations of NH(X 3 E)+C0 2 (X 1 i;) were then made. 53 These showed that the barriers for HNO + CO formation are too large for these products to form with the measured activation energy. A role for an addition product thus appears to be indicated. However, while the calculations showed that such a product can form, all adducts found are of low stability and would be likely to undergo further reactions. In the case of the NH(X £) + H 2 0(X AX) reaction, no such calculations have yet been made. However, Rohrig and Wagner indicated that two adducts could form exothermically, H 3 NO and H 2 NOH. Both reactions (11) and (12), and their adduct products, need further study.

3.2.8. NH 2 + NO This reaction is of major importance for NO reduction to N 2 in the Thermal-DeNO x process. 29 This process works best in the 1100-1400 K temperature range. It also may pertain to propellant first stage chemistry, (see Sec. 2.2.1.(a)) and clearly is important for some propellant burning rate modifiers (see Sec. 2.2.1(c)). Because of its extreme importance to DeNO^, and its complexity, a relatively large number of studies in and near the temperature range of EM interest have been made of NH 2 + NO - • NNH + OH, NH 2 + NO -> N 2 + H 2 0 ,

Aif2°98 = 2 kJ mol - 1 ,

(5a) -1

AH%98 = - 5 2 4 k J m o i .

(5b)

Reaction (5a) is also often written as leading to N 2 + H + OH, since under most conditions the NNH dissociates rapidly to N 2 + H. Theoretical studies have shown the reactions to proceed sequentially through NH 2 NO and HNNOH intermediates. 79 ' 96 Both the rate coefficients and the branching ratios have been the subject of considerable problems, originating from an inadequate knowledge of secondary reactions in complex environments. 97 ' 98 There now are consistent results for the total rate coefficients determined by (i) Silver and K o l b " from 294 to 1220 K in an EDFFR, using LIF to monitor the NH 2 , (h) a modeling study of Miller and Glarborg 97 for the NO, N 0 2 , N 2 0 , and NH 3 profiles from atmospheric pressure N O / N H 3 / 0 2 / H 2 0 / N 2 mixtures in a quartz plug flow reactor, (iii) a theoretical study by Miller and Klippenstein, 96 (iv) the extrapolation of a 1716-2507 K, 1.3-1.8 bar

Gas-Phase Kinetics for Propellant Combustion

Modeling

231

shock-tube study by Hanson, Bowman as., 9 8 of CH 3 NH 2 /NO/Ar mixtures, where a cw frequency-modulated narrow line (here 597.4 nm) laser absorption technique 98,100 was used to monitor the NH 2 , j and (v) a similar study by Hanson c.s. 101 from 1262-1726 K, where C 6 H 5 CH 2 NH2 was used instead as the NH 2 precursor. By combining their results with low temperature studies the latter, most recent, work led to k5 (200-2500 K) = 1.1 x 1 0 - 8 ( T / K ) - 1 2 0 3 exp(106K/T) cm 3 molecule" 1 s^ 1 . The reaction thus has a negative temperature dependence, in accord with the formation of intermediates. The branching ratio a = k5&/(k5a + fc5b) has been determined largely by the same groups. The Stanford group obtained it from [NH2]-time profiles and extensive modeling. 101 ' 102 The result is in agreement with the theoretical 96 and modeling 97 studies by Miller et al, indicating an increase in a from about 0.1 at 300K to 0.7 at 2000K. Deppe et al.,62 in a shocktube study, observed the product H and OH concentrations directly by, respectively, atomic resonance absorption and narrow laser line absorption. Their measurement of 50% at 1500 K is in accord with the other studies; at 2800 K, a approaches 90%.

3.2.9. CN + OH Individual reactions of CN and OH radical species have been studied at temperatures up to 1500 K in HTP reactors. 103,104 Shock-tube studies have included the reaction between these radicals CN + OH -> NCO + H,

AiJ2°98 =

97kJmor1

(21a)

CN + OH ^ HCN + O,

Aff° 98 =

gOkJmol" 1

(21b)

CN + OH -> NH + CO,

Aff° 98 =

227kJmor1.

(21c)

In that work 105 HCN/HN0 3 /Ar mixtures were used. The first compound served as CN source, the second as OH source. Both were monitored by cw narrow laser line absorption. The measurements gave fc21 (1250-1860 K) = 6.6 x TO"11 cm 3 molecule 1 s 1 . Reaction (21a) is thought to dominate in this temperature range, with (21b) becoming of increasing importance at higher temperatures.

JThe frequency modulation led to an order of magnitude increase in sensitivity for NH 2 over their earlier cw narrow laser line absorption technique.

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3.2.10. NCO + NO, N 0 2 The reactions NCO + NO -> N 2 0 + CO, NCO + NO - • N 2 + C 0 2 ,

AiJ2°98 = -278 kJ m o h 1

(7a)

1

(7b)

Ai72°98 = - 6 4 3 k J m o r

were studied, by techniques similar to HTP, by Atakan and Wolfrum106 from 294-1260 K and by Becker et al.107 from 290-1098 K, respectively. A shock-tube study in the 2380 to 2660 K range used narrowline absorption to monitor the NCO reactions. 108 These data, combined with further low temperature studies, yield k7 (294-2660 K) = 2.3 x 1 0 - 6 ( T / K ) ^ 1 7 3 exp(-384K/T) cm 3 molecule -1 s" 1 , independent of pressure. This reaction thus has a strongly negative temperature dependence, related to the formation of an OCN-NO intermediate complex. It can decompose to N 2 0 + CO or via a cyclic OC(0)NN intermediate form N 2 + C 0 2 . 1 0 7 Both channels are significant over the temperature range investigated. No accurate branching ratio information appears to be available at temperatures of EM interest. However, Hershberger c.s.68 made a determination from 296-623 K. They found 44 ± 7% to follow Eq. (7a), and 56 ± 7% to lead to the channel (7b) products, independent of temperature. These authors used UV laser photolysis, combined with time-resolved, narrow-line, infrared diode laser absorption spectrometry of the reactants and products. Their narrow line technique has an advantage over LIF in that absolute product concentrations can be more readily obtained. The method becomes increasingly less sensitive with temperature, which has, thus far, precluded its use at higher temperatures for kinetic studies. If this problem could be overcome, possibly by use of multi-pass cells, their method could become a valuable addition to the existing techniques for branching ratio measurements. Another NCO reaction important for the reduction of a heteronuclear reactive N-compound directly or indirectly to N 2 is NCO + N 0 2 -» N 2 0 + C 0 2 ,

A# 2 ° 98 = - 4 6 7 k J m o r 1

(22)

where the product channel shown is thought to be dominant. The N 2 0 formed can be reduced to N 2 via the H + N 2 0 reaction, discussed in Sec. 3.2.2. Wooldridge et al. measured reaction (22) in a PST experiment near 1250 K, with cw narrow laser line absorption monitoring of the NCO. 65 Juang et al. measured it from 294 to 774 K using laser photolysis-LIF. 109 The two data sets can be combined 109 to yield fc22

Gas-Phase Kinetics for Propellant Combustion

Modeling

233

(294-1250K) = 6.4x KT 1 0 (T/K)-°- 6 4 6 exp(164K/T) cm 3 molecule" 1 s" 1 . The product channel given is thought 65 to be dominant, apparently based on the 298-500 K III laser diode study of Park and Hershberger, 69 which indicated a 92% contribution for it.

4. Conclusions Modeling using kinetics mechanisms composed of elementary gas-phase reactions has greatly improved the understanding of propellant combustion. We have described: (i) why studies to improve our understanding of propellant combustion, especially the gas-phase structure and mechanisms, are of interest; (ii) methods to study kinetics of the relevant elementary reactions in isolation, thus increasing realism of the mechanisms; (iii) the current status of understanding of all these issues; and (iv) directions for future research that are likely to be most fruitful. The advances in propellant combustion modeling and in understanding of the associated gas-phase mechanisms have been achieved by a number of factors: (a) the increased sophistication of both propellant and kinetics modeling techniques; (b) the ability to perform measurements on isolated reactions at combustion temperatures; and (c) the possibility to study reactions by powerful new theoretical chemistry techniques. These factors have also contributed to the progress of chemical kinetics itself, from rate coefficient information to increased insight into mechanisms as exemplified by several of the investigations discussed in Sec. 3.2. For some, perhaps most, ingredients, it is not certain what the initial large fragments are. The reactions producing large fragments likely occur in the condensed phase and/or near-surface gas-phase regions. Because their vapor pressures are not high, many ingredients likely decompose, rather than vaporize. Which initial gas species are formed is clearly a major concern — it defines what gas-phase reactions must be considered. Suitable techniques for condensed-phase kinetic studies at temperatures relevant to propellant combustion have yet to be developed (a problem not limited to propellant research). One promising new technique that has yet to be applied to solid ingredients at combustion conditions is molecular dynamics modeling. However, problems of properly describing the potentials and handling the sampling of the very large numbers of atoms involved must be solved (see the chapter by Rice). We have shown that a fair number of the gas-phase reactions of importance are now well characterized, but similarly detailed information is

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needed for many more reactions. Most of the reactions studied are bi-, or ter-molecular processes of small species. Such reactions lend themselves best t o the newly-developed experimental techniques. However, gas-phase kinetics of the decomposition of larger molecules, which can occur in bubbles in a surface melt layer or in the first stage flame, must also be known. And, as for the condensed phases, the large molecules involved must be identified (cf. Sec. 2.2.1(b)). Of the larger propellant components, few have sufficient vapor pressure and stability to survive into the first-stage flame. RDX is an exception. A molecular beam-infrared multiple photon dissociation study of its dissociation p a t h s 1 1 0 has been made, b u t no r a t e information is apparently available. Another possibility is NG. Kinetic experiments on these would be useful if sufficiently pure gas-phase samples at appropriate conditions can be prepared.

Acknowledgment A F t h a n k s A R O for support under grant DAAD19-03-1-0046.

References 1. An earlier review of propellant gas-phase chemistry focusing on the subset of reactions pertinent to dark zones may be found in: W. R. Anderson, in U.S. Army Workshop on Solid-Propellant Ignition and Combustion Modeling, eds. R. W. Shaw, D. M. Mann and M. S. Miller, U.S. Army Research Laboratory Technical Report, ARL-TR-1411, July 1997. 2. R. L. Hatch, in 23rd JANNAF Combustion Subcommittee Meeting, Vol. I, CPIA Pub. 457 (1986), p. 157. 3. C. F. Melius, in Chemistry and Physics of Energetic Materials, NATO ASI Series, Vol. 309, ed. S. Bulusu (Kluwer Academic Publishers, Norwell, MA, 1990), p. 51. 4. R. A. Yetter, F. L. Dryer, M. T. Allen and J. L. Gatto, J. Propul. Power 11, 683 (1995). 5. (a) R. C. Sausa, W. R. Anderson, D. C. Dayton, C. M. Faust and S. L. Howard, Combust. Flame 94, 407 (1993); (b) D. T. Venizelos and R. C. Sausa, Proc. Combust. Inst. 28, 2411 (2000). 6. M. Rohrig, E. L. Peterson, D. F. Davidson and R. K. Hanson, Int. J. Chem. Kinet. 28, 599 (1996). 7. M. A. Mueller, R. A. Yetter and F. L. Dryer, Int. J. Chem. Kinet. 3 1 , 705 (1999). 8. E. W. Diau, M. J. Halbgewachs, A. R. Smith and M. C. Lin, Int. J. Chem. Kinet. 27, 867 (1995). 9. R. Behrens, this volume.

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10. Y.-C. Liau and V. Yang, J. Propul. Power 11, 729 (1995). 11. J. E. Davidson and M. W. Beckstead, J. Propul. Power 13, 375 (1997). 12. M. S. Miller and W. R. Anderson, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (American Institute of Aeronautics and Astronautics, Reston, VA, 2000), Chap. 2.12. 13. (a) M. S. Miller and W. R. Anderson, J. Propul. Power 20, 440 (2004); (b) M. S. Miller and W. R. Anderson, CYCLOPS, a Breakthrough Code to Predict Solid-Propellant Burning Rates, U.S. Army Research Laboratory Technical Report, ARL-TR-2910, February 2003. 14. M. S. Miller and W. R. Anderson, Prediction of Advanced Nitramine Propellant Burning Rates with the CYCLOPS Code, U.S. Army Research Laboratory Memorandum Report, ARL-MR-552, March 2003. 15. (a) A. A. Zenin, J. Propul. Power 11, 752 (1995); (b) A. A. Zenin, Study of Combustion Mechanism of Nitramine-Polymer Mixtures, Final technical report to the European Research Office of the U.S. Army, London, England, contract no. N68171-97-M-5771, November 1998; (c) A. A. Zenin, Study of Combustion Mechanism of Nitramine-Polymer Mixtures, Final technical report to the European Research Office of the U.S. Army, London, England, contract no. N68171-99-M-6238, August 2000; (d) A. A. Zenin, Study of Combustion Mechanism of Nitramine-Polymer Mixtures, Final technical report to the European Research Office of the U.S. Army, London, England, contract no. N68171-01-M-5482, May 2002. 16. W. R. Anderson, N. E. Meagher and J. A. Vanderhoff, to be published. 17. J. A. Vanderhoff, W. R. Anderson and A. J. Kotlar, in 29th JANNAF Combustion Subcommittee Meeting, Vol. II, CPIA Pub. 593 (1992), p. 205. 18. W. R. Anderson (1998), unpublished results. 19. M. C. Lin, Y. He and C. F. Melius, Int. J. Chem. Kinet. 24, 1103 (1992). 20. S. T. Wooldridge, R. K. Hanson and C. T. Bowman, Int. J. Chem. Kinet. 27, 1075 (1995). 21. R. A. Yetter, unpublished; however, the mechanism may be obtained from Yetter or many of the currently active modelers in the field (e.g. W. R. Anderson, M. W. Beckstead, V. Yang, or Y.-C. Liau). Version 2 is also quoted in full in Y.-C. Liau, Numerical Analysis of RDX Monopropellant Combustion with Two-Phase Subsurface Reactions under Steady and Transient Conditions, Ph.D. Thesis, Pennsylvania State University, University Park, PA, 1997. 22. (a) D. Chakraborty, R. P. Muller, S. Dasgupta and W. A. Goddard, III, J. Phys. Chem. A104, 2261 (2000); (b) D. Chakraborty, R. P. Muller, S. Dasgupta and W. A. Goddard, III, J. Phys. Chem. A105, 1302 (2001). NOTE: The combined mechanism for RDX and HMX combustion may be obtained by contacting those authors. 23. (a) S. Zhang and T. N. Truong, J. Phys. Chem. A104, 7304 (2000); (b) S. Zhang and T. N. Truong, J. Phys. Chem. A105, 2427 (2001); (c) S. Zhang, H. N. Nguyen and T. N. Truong, J. Phys. Chem. A107, 2981 (2003).

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98. S. Song, R. K. Hanson, C. T. Bowman and D. M. Golden, Proc. Combust. Inst. 28, 2403 (2000). 99. J. A. Silver and C. E. Kolb, J. Phys. Chem. 86, 3240 (1982). 100. M. Votsmeier, S. Song, D. F. Davidson and R. K. Hanson, Int. J. Chem. Kinet. 31, 445 (1999). 101. S. Song, R. K. Hanson, C. T. Bowman, D. M. Golden, Int. J. Chem. Kinet. 33, 715 (2001). 102. M. Votsmeier, S. Song, R. K. Hanson and C. T. Bowman, J. Phys. Chem. A103, 1566 (1999). 103. R. J. Balla and K. H. Casleton, J. Phys. Chem. 95, 2344 (1991). 104. W. Felder and S. Madronich, Combust. Sci. Tech. 50, 135 (1986). 105. S. T. Wooldridge, R. K. Hanson and C. T. Bowman, Int. J. Chem. Kinet. 28, 245 (1996). 106. B. Atakan and J. Wolfrum, Chem. Phys. Lett. 178, 157 (1991). 107. K. M. Becker, R. Kurtenbach, F. Schmidt and P. Wiesen, Ber Bunsenges. Phys. Chem. 101, 128 (1997). 108. J. D. Mertens, A. J. Dean, R. K. Hanson and C. T. Bowman, Proc. Combust. Inst. 24, 701 (1992). 109. D. Y. Juang, J.-S. Lee and N. S. Wang, Int. J. Chem. Kinet. 27, 1111 (1995). 110. X. Zhao, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 88, 801 (1988).

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CHAPTER 8 G A S - P H A S E D E C O M P O S I T I O N OF ENERGETIC MOLECULES Donald L. Thompson Department of Chemistry University of Missouri-Columbia 601 South College Avenue Columbia, MO 65211, USA

Contents 1. Introduction 2. Theoretical Methods 2.1. Simulations and Rate Calculations 2.2. Potential Energy Surfaces 3. The Chemistry 3.1. Basic Reaction Pathways 3.2. Experiments 3.3. Nitromethane 3.4. Methyl Nitrite 3.5. Dimethylnitramine 3.6. TNAZ 3.7. RDX 4. Concluding Remarks References

241 244 244 249 252 252 253 254 259 261 264 265 269 271

1. I n t r o d u c t i o n Determining the rates and mechanisms of the chemical decomposition of energetic materials is extraordinarily difficult. T h e y rapidly react upon heating or shocking to produce radicals which are hard to detect and rapidly undergo subsequent reactions. Furthermore, most energetic materials begin to chemically decompose in condensed phases the liquid phase, or a less characterizable melt phase. In some cases chemical reactions accompany or immediately follow melting. W h e n reaction begins in the solid phase, it is 241

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at defect sites where hot spots can form, which likely involve liquid centers where reaction or gasification occurs. These complexities greatly frustrate experimental studies of the chemistry which is far from simple. Even the chemical decomposition reactions of isolated energetic molecules are quite complicated and difficult to study, and thus they are still far from being fully understood. Because many of the gaseous products and much of the energy are produced in gas-phase reactions it is critical that we understand them. This chapter describes our understanding of the gas-phase unimolecular decomposition of some important energetic molecules and the role that theory and computations have played in achieving it. The bedrock of any scientific field is a body of experimental data, but science progresses by a cooperative interplay of theory and experiment. Given the difficulties in experimental studies of the reaction kinetics of energetic molecules, theory must play a central role. Theory is, of course, hindered by the size and complexity of the molecules and must be used judiciously; nevertheless, it is an indispensable part of the effort to unravel the reaction mechanisms. The emphasis here, in large part due to the state of our knowledge, is on the initial steps of the decomposition of a few representative molecules. The efforts, creativity, and progress in experimental kinetics and dynamics have over the past several decades been directed at more accurate and refined measurements of isolated elementary chemical reactions and energy transfer processes, e.g., those associated with changes involving a single transition state or stabilization of an excited species. This concentrated focus gave impressive progress in refined temporal and energy measurements and control of elementary chemical processes. At the same time, little progress has been made in monitoring and probing complex chemical processes that unfold over relatively long times (>/^s) and involve branching sequences of reaction pathways with a corresponding series of wells and transition states. We still attempt to map out this sort of chemistry by patching together individual elementary steps. We often have very accurate information for some steps, but for others we can only speculate within the context of a postulated mechanism not always well founded or confirmable. This is the way that reaction mechanisms have been developed for the past century. We can use measured data along with theoretically-predicted information and chemical intuition in models to reproduce the observed results. Computer modeling is the only modern major advance in methods for formulating mechanisms for complex chemical reactions. An excellent example of what can be done with this approach is the modeling of the complex

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chemistry of flames where it has been used quite successfully (see Miller's chapter in this volume). However, in many cases modeling is not satisfactory because of the lack of accurate data for critical steps in the mechanism. A full understanding of the temporal evolution of the chemistry of the complete decomposition of an isolated molecule as large and complex as RDX is greatly hindered by the pivotal but transitory roles of radicals that must be inferred rather than observed and, although progress is being made as Dagdigian discusses in his review of radical reactions in this volume, what we know with certainty is dwarfed by what we do not know. Some very good state-of-the-art experiments have been done (although only relatively few, given the importance of the field) that provide important data for the decomposition reactions. Although valuable, and well executed and interpreted, the experiments provide much less than is needed confidently to postulate complete mechanisms for the sequential, branching chemical decomposition of these molecules. Most of the experiments rely upon some harsh excitation process (e.g., laser pumping, shock waves) to initiate decomposition that results in the small molecules and radicals that are detected much later. The complicated chemistry occurring between the start and the end of the decomposition must then be postulated by some sort of modeling which can lead to erroneous conclusions because there are so many undetermined parameters needed to describe the complicated chemistry. Nevertheless, the experiments have provided some specific, though in some cases controversial, information that provides a basis for postulating mechanisms for the initial steps in the decomposition reactions of such important energetic molecules. This chapter focuses on the rates and mechanisms for the initial unimolecular reactions of NM, DMNA, TNAZ, and RDX. The goal is to delineate what is known, how we learned it, and what is uncertain or simply unexplored about the reaction mechanisms for the decomposition of isolated energetic molecules. This chapter is best read within the context of the overall volume. For example, the work reviewed here overlaps with Rice's review of ab initio PES calculations, and is closely linked with the radical reactions discussed by Dagdigian, and the flame chemistry described by Miller. I will attempt to point out these links to help the reader gain an overall perspective. I hope that this review not only informs but also inspires more work. The chapter is a two-part review: Theory and Chemistry. In the next section I describe the current state of theoretical methods used to study the kinds of chemistry discussed in Sec. 3.

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2. Theoretical Methods 2.1. Simulations

and Rate

Calculations

The theoretical focus here is on rate calculations which rely predominantly upon classical mechanics, so I mention the strengths, limitations, and caveats that attend the approximations in the various classical approaches. I only briefly review these and provide references to more in-depth treatments of the methods for those who wish to understand the methods at a deeper level. We have previously reviewed practical methods for computing rates of processes based on the classical approximation. x~3 In the standard classical trajectory approach, initial conditions are selected from the appropriate probability density distributions and the time evolution of the system is followed by numerical integration of Hamilton's equations of motion with the forces given by an assumed potential energy surface (PES). The physically significant results are averages of ensembles of trajectories. The crucial issue is how well these averages correspond to reality. Classical trajectories have been used extensively over the past four decades to study reaction dynamics, but there are still some significant practical problems in their application even when the classical approximation is valid. These problems fall into two main categories: (1) the practical application of classical simulations to compute rates, and (2) the formulation of accurate global PESs. Classical simulations must be augmented with other methods to calculate rates when straightforward trajectory calculations are not feasible, which is often the case when the rates are extremely fast or extremely slow. First I discuss the problem of computing rates with methods based on the classical approximation. Classical trajectory calculations have played a central role in the evolution of our understanding of chemical reactions in the gas phase. This is mainly because they are the only practical approach available to us because quantum mechanical methods for treating rate processes are still limited to systems no larger than about a half dozen atoms. Although progress is being made in extending the methods to larger systems, it appears that we will need to continue to depend upon classical methods for the foreseeable future for molecules of the sizes of interest in energetic materials. We really have no alternative to classical methods and they have some important features that make them attractive for certain problems: they provide insight into reactions at the level of atomic motions, by allowing visualization that is not obtainable from quantum mechanical calculations.

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The classical approximation is not valid for all rate processes and chemical reactions. Obviously, the main approximation is the neglect of interference effects, which are most explicitly manifested by tunneling. However, tunneling is likely not important in most practical applications of energetic materials, although it could play a role in aging of materials. Interference effects are most important at low energies, for light atoms, and in lowdimensional systems and they can dominate processes occurring at energies near threshold or, more generally, processes with very low probabilities due to energy requirements rather than entropy factors. Thus classical mechanics can overestimate the probability of close passages over an energy barrier. Fortunately, quantum effects are most significant at the microscopic level and they tend to be averaged out at the macroscopic level. Because we are usually most interested in averaged properties (e.g., thermal rates) of many-dimensional systems at relatively high energies, the classical results are often accurate enough. However, in treating the dynamics of reactions of polyatomic molecules, aphysical behavior of zero-point energy (ZPE) can be a problem. The ZPE of a large molecule can be sufficient to cause reaction if it flows into the reaction coordinate modes. This is especially true for energetic materials because the molecules usually have relatively low dissociation energies and many degrees-of-freedom. Because the ZPE in a classical simulation can flow among the molecular modes without quantum mechanical constraints, it can contribute to reaction as it cannot in nature. This aphysical behavior is less important at high energies where the quantum-classical correspondence is generally valid. Classical dynamics simulations determine the atomic-level mechanism and fundamental dynamical behavior of reactions. Furthermore, they are often the only option for treating reactions with non-statistical dynamics. However, for most rate calculations one can use a statistical theory such as Ramsperger-Rice-Kassel-Marcus (RRKM) theory 4 or Variational Transition-State Theory (VTST). 5 A statistical rate theory is valid if energy flow to the reaction coordinate modes is faster than reaction. The statistical assumption can break down at high energies because the rate of reaction can be so fast that energy transfer cannot maintain a statistical distribution of energy. At energies near reaction threshold the reaction rates tend to be much slower than the energy transfer, thus the statistical approximation is usually valid. The rates at low energies can be so slow that following trajectories long enough to observe reactions is not practical, then one must turn to a statistical theory. Alternatively, classical trajectory calculations can be performed at higher energies and the results extrapolated

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to lower energies. Correctly extrapolating to lower energies may not be straightforward. As the energy approaches the reaction threshold, the probability of reaction decreases and one must use larger ensembles or longer simulation times (in the case of unimolecular processes) in a MD simulation to compute a good estimate of the rate. For simulations of unimolecular reactions and reactions in condensed phases, the practical limitation is the length of time that the numerical integration of the equations of motion is stable. This time is roughly determined by the highest frequency modes of the molecule which determine the integration step size that must be used. Trajectory integrations are usually accurate for times no longer than tens of picoseconds. Thus in practice MD simulations of unimolecular reactions are usually carried out at energies well above the reaction threshold so that a sufficient number of reactions are observed for statistically significant estimates of the rate. Often this means that the MD simulations are at such high energies that the reaction rate is faster than the intramolecular vibrational energy redistribution (IVR) rate. Thus the rate of reaction is controlled by the rate of energy flow into the reaction coordinate modes and the reaction dynamics are non-statistical. Clearly we must consider other methods if we are to cover the entire range of problems of interest in simulating the chemistry of energetic materials. At energies near the reaction threshold E* the statistical and dynamical rates are the same and usually obey the Ramsperger-Rice-Kassel (RRK) equation

* = «(l-f).

(1)

but as the energy increases they diverge, with the statistical rates larger than the dynamical rates. 6 We have demonstrated this behavior for several systems, including DMNA 7 and RDX. 8 Transition-state theories (including RRKM) give upper limits to the true rates. A transition-state theory rate is an upper limit because all trajectories that pass through the transition state are counted and thus there is an overestimation of the rate because, in nature, some of those trajectories recross the transition state and return to the reactant region rather than go on to products. Because MD calculations must be carried out at energies where a statistically significant number of events can be observed on the timescale for which the numerical integration is stable, the rates are often in the dynamical regime. The only sure way to determine if the dynamics are

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statistical or non-statistical is to compare the MD and transition-state theory rates for the same PES. Normally practical applications of transitionstate theories such as RRKM are based on harmonic motions, thus it is not clear whether differences in dynamical and statistical rates are due to non-statistical behavior or differences in the PES. Below we will describe a Monte Carlo statistical theory approach we have developed that can be used to compute statistical rates for the same PES as used in a classical trajectory calculation. We need a variety of methods to compute the rates and unravel the mechanisms for the decomposition of energetic materials. With the focus on unimolecular decomposition reactions, we have developed practical methods to treat rate processes for various conditions. 3 These methods include quasiclassical trajectory simulations (the basic method), Monte Carlo variational transition-state theory (MCVTST) for calculating statistical rates for realistic PESs, intramolecular dynamics diffusion theory (IDDT) for treating rate processes in the intrinsically non-RRKM regime, and semiclassical approaches for incorporating tunneling effects into MD and MCVTST calculations. The rate coefficient k for a chemical reaction can be written as the flux through a dividing surface S that separates the phase space T into reactant and product regions

*=W-

(2)

where F is the appropriate probability density function: a delta function for the microcanonical ensemble and the Boltzmann factor for the canonical ensemble. The integral in the numerator is over the region of the dividing surface, which rigorously is a hypersurface in phase space but which, in practice, is usually taken to be a function of a few critical coordinates in configuration space. The variable v± is the velocity perpendicular to S. The integral in the denominator is over all the reactant phase space V. However, this equation illustrates the modern ideas of classical theoretical treatments of rate processes. In practice, the problem comes down to how one solves the integrals and evaluates the flux from reactants to products. In principle, in a classical trajectory calculation of a reaction rate one would determine the time evolution of an ensemble by solving the Liouville equation; however, this is not possible and in practice we compute rate constants by Monte Carlo averaging ensembles of individual trajectories obtained by numerically integrating Hamilton's equations of motion. The

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methods for performing Monte Carlo classical trajectory calculations are now more or less standardized and we have previously described them in detail. 1 ~ 3 It is worthwhile, however, to mention some aspects of how they are applied. The initial conditions for classical trajectories are selected such that the simulated ensemble corresponds to the experimental conditions of interest. When state specificity or non-statistical behavior is important, e.g., at low energies or for non-statistical excitations, a quasiclassical approximation is used. Here the initial conditions are selected assuming a distribution of energy among quantum levels and the coordinates and momenta are assigned values according to the appropriate probability density functions. For statistical systems the initial conditions can be selected assuming a random distribution of energy for a continuum of classical states, i.e., for a classical microcanonical distribution. Once the initial conditions are set the time evolution of the system is determined by numerical integration of Hamilton's equations of motion for the assumed PES. Equation (2) is based on the assumption that the rate of reaction corresponds to the flux through a hypersurface in phase space that divides reactants and products. In classical trajectory calculations of rates this assumption is not needed because one can begin trajectories in the reactant phase space and propagate them into the product phase space. The averaging over the reactant phase space is usually done by selecting the initial conditions for the trajectories from the appropriate probability density distributions by Metropolis Monte Carlo sampling.9 This sampling procedure assumes that the reactants randomly occupy the classical phase space, that is, the dynamics of the reactants are ergodic. The reaction rate is determined from the outcomes of the deterministic classical trajectories that have ergodic initial conditions. Thus, the results include the effects of any dynamics in the phase space between the reactants and products, that is, for passage through the transition state region. The usual Metropolis sampling procedure neglects the ZPE of the reactants; however, a method to take it into account has been presented. 10 This entails a Markov walk in the reactant phase space that is begun at a convenient location such as the equilibrium geometry where the total energy is all kinetic. A warm-up sequence, usually tens of thousands of steps, is used to walk the system to some random point far from equilibrium. Then, as the walk is continued, phase space points along the sequences are used as initial conditions for trajectories, which are integrated to determine the fate of the system for that particular phase space point.

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The Metropolis Monte Carlo procedure provides an estimate of the classical phase space integrals in Eq. (2). Alternatively, in the quasiclassical approximation the integrand in Eq. (2) is based on quantum mechanical constraints and is assumed to be separable; that is, the averaging is over individual dynamical variables (e.g., vibrational and rotational modes in the case of molecules), for which values can be randomly selected by the Monte Carlo von Neuman rejection technique. 11 In the case of unimolecular reactions the microcanonical rate constant is calculated in a manner analogous to how it is determined experimentally: the first-order decay rate is given by the slope of plot of In N(t) as a function of t. The lifetimes are fitted to

where N(t) is the number of unreacted molecules at time t and N(t = 0) is the number of reactant molecules in the ensemble. This means that the trajectories must be integrated for times in the order of one lifetime, r ~ 1/fc. If the energy barrier to reaction is large it may be necessary to perform the simulations at relatively high energies so that a significant fraction of the ensemble decays.

2.2. Potential

Energy

Surfaces

Most of the MD simulations of unimolecular dissociation reactions of energetic molecules have been carried out by using approximate PESs constructed by using arbitrary analytical functions parameterized with empirical and quantum chemistry results. For the most part the general forms of the potentials are derived from standard anharmonic force fields with the changes in forces and energies corresponding to isomerization, bond breaking, and bond formation being built into the formulism with ad hoc switching functions.2 Switching functions are analytical expressions that can be used to fashion the shape of the potential along specified directions, e.g., the internal coordinates along the reaction path. This approach provides a facile way to introduce specific realistic features while providing the flexibility to accurately describe the reactant, products, and transitionstate properties. In many cases, these PESs are sufficiently accurate to realistically model the chemistry; however, developing them requires meticulous fitting of many parameters as one adjusts for specific features and the overall behavior of the surface.

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Serious drawbacks to this approach are the enormous labor required to adjust the functions and the inherent inflexibility of any analytical function. In fact, this is the case for any global formulism used to describe the full range of configurations available to a system at energies for which reaction can occur. The recent developments in quantum chemistry, especially in density functional theory (DFT) methods, have now made it feasible to compute energies and forces sufficiently fast that one can bypass fitting the energies with analytical functions and compute the forces on the fly while integrating the equations of motion. There is still a limit on the size of the system for which this is practical and still the need for scaling of the quantum chemistry energies and forces because direct dynamics simulations are not yet feasible with high-level ab initio methods. This new capability is being most usefully employed in statistical theory rate calculations. These qualifying statements about the utility of direct ab initio MD simulations pertain to the current status of computational chemistry, however, it is clear that eventually this will be the common approach. Thus, we need to focus on developing efficient methods for incorporating ab initio energies and forces into classical simulations. One always pushes the limits of a method and there will continue to be a need to introduce scaling of ab initio points because lower-level quantum chemistry calculations, that may not be chemically accurate, will allow studies of a wider range of systems. The fitting methods must be sufficiently flexible to give accurate fits, with or without scaling, of ab initio points to produce a global fit or provide local fitting within the context of a direct dynamics simulation. Local fitting with polynomials meets these criteria. We first proposed local fitting in the 1970s based on cubic splines12 which are efficient and accurate if a sufficiently dense grid of points is used. Although cubic splines have been used in a number of applications, they have been replaced by other similar methods that require fewer points. Chief among these is a method introduced in 1994 by Ischtwan and Collins13 based on interpolating moving least-squares (IMLS). 14 We have recently presented an improved IMLS fitting method. 15,16 This new IMLS fitting approach is accurate and easily applied and could provide a general method for both global fitting and fitting on-the-fly in direct dynamics simulations. In the latter case, one wants an efficient method for interpolating points in regions of configuration space previously visited by the trajectories and where points have been calculated and saved so that new ab initio points are calculated only where there is not a sufficiently dense grid to give an

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interpolated point of sufficient accuracy for the next integration step. The IMLS methods will facilitate the use of ab initio PESs in MD simulations for systems for which quantum chemistry is reliably accurate, thus generalizing simulation codes and eliminating the need for formulating classical PESs. This is, perhaps, the most important challenge in the development of predictive theoretical chemical dynamics methods, except for the development of practical rigorous quantum mechanical methods. We have developed automatic interpolation methods that are highly efficient and accurate for polyatomic molecules, and that can be eventually used in a blackbox configuration requiring limited theoretical expertise to generate ab initio-b&sed chemical dynamics simulations. Fits using different-degree IMLS identifies regions where additional data points are needed, so an algorithm is used automatically to determine how to improve the fit to a preset accuracy. This method achieves much higher quality fits with many fewer ab initio points than other methods. To date we have focused on unimolecular dissociation reactions in relatively simple, small 3-atom (N 2 H -» H + N 2 ) 1 5 and 4-atom molecules (HOOH - • 20H), 1 7 but the method is, in principle, applicable to systems of any size because it scales economically with the number of atoms. One approach was inspired by a dual-level method proposed by Nguyen et al.18 in which they fit low-level quantum chemistry results corrected by a few high-level points to obtain a scaled PES. Our method eliminates the need for the low-level quantum chemistry calculations by using an analytical function which we refer to as the zeroth-order PES VQ. The VQ is a rough approximation to the actual potential V. We then use an IMLS method to fit the difference A ^ = V — VQ, which is a relatively smooth function and requires relatively few points to achieve a good fit. Obviously, AV is smoothest if it matches geometries at the critical points of the actual potential, which is easily done because one can readily determine the critical points on the high-level ab initio potential using standard techniques available in many quantum chemistry codes. We have tested this method by fitting a global PES for H2O2, with particular focus on the bond-fission to give 20H and the internal hindered rotation. It can be used with any local polynomial fitting method (and we have tested it for the modified Shepard 13 and the second-degree IMLS (SD-IMLS) method we recently introduced 15 ). We find that employing the zeroth-order PES greatly reduces the root-mean-square errors of the global and reaction path fits by both the modified Shepard and the SD-IMLS methods. Since the latter does not require gradients, as does the former,

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it will be the preferred method in most applications, especially in direct dynamics simulations. 3. The Chemistry 3.1. Basic Reaction

Pathways

There are two broad classes of reactions that are responsible for the initial unimolecular decomposition of a polyatomic molecule: simple bond-fission and molecular elimination. A simple bond-fission reaction, which produces radicals, occurs along a reaction path with no exit barrier; i.e., there is an energy barrier to the reverse reaction and the potential along the reaction path has the shape of a Morse function. The reaction coordinate is mainly composed of the internuclear distance of the bond that breaks, although it may also involve some other coordinates to describe the structural differences of the product fragments in isolation and in the parent molecule. The reaction coordinate of a molecular elimination reaction is usually a linear combination of several internal coordinates. Concerted reactions often involve significant intramolecular rearrangement (e.g., atom transfer, isomerization) prior to or accompanying the arrival of the system at the transition state. Molecular elimination reactions frequently have multicenter transition states involving several atoms (often four or five) arranged in a ring structure. Thus, they involve significant electronic rearrangement with the breaking and formation of several bonds and significant repulsion between the molecular products in the exit channel. An energy barrier to the reformation of the parent molecule from the molecular products is common. Many polyatomic molecules undergo unimolecular decomposition by simple bond-fission and concerted molecular elimination reactions relatively close in energy. This is the case for many nitro and nitramine compounds. Usually it is clear which bond rupture is most likely, e.g., C-N in nitroalkanes and N-N in nitramines. One should, however, consider more than one possible molecular elimination reaction. Completing bond-fission and molecular elimination reactions that have similar energy requirements may also have significant pressure (or caging) effects due to qualitative differences in the potentials along the reaction paths. The reasons mentioned above (i.e., speeds of the reactions, detection difficulties, pressure effects) make discrimination among the possible reaction channels difficult. Quantum chemistry methods are usually not capable of the accuracy necessary to determine which path has the lowest barrier. This

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is illustrated by the continuing lack of agreement about the mechanisms for the gas-phase decomposition of several nitro and nitramine molecules, which we review later in this section.

3.2.

Experiments

We begin with a brief discussion of key experiments that have provided the basis for continuing efforts to unravel the decomposition mechanisms. It is important to understand what they do and do not provide. Observations of chemical reactions in molecular beams ensure collisionless conditions. In the case of unimolecular dissociation it is necessary to employ an alternative excitation process, e.g., laser excitation. Lee's group has studied a wide range of unimolecular reactions in molecular beams using infrared multiple-photon pumping to provide the excitation energy to the molecules.19 The drawback to this method is that the level of excitation is not directly determinable. The translational-energy probability distribution for each of the products was measured by time-of-flight mass spectroscopy. By assuming statistical reactions and the reaction energetics, the branching ratios of the decomposition reactions were determined and an estimate of the level of internal excitation of the reactant molecules was obtained. The statistical assumption should be valid for their conditions. Based on numerous studies using almost every available experimental and theoretical method, it is clear that exciting the vibrational motions of a polyatomic molecule by rapid laser pumping, overtone excitations, or other means rapidly produces a statistical distribution of internal energy. The intramolecular vibrational energy redistribution (IVR) is much faster than chemical reactions because of strong mode mixing (not chaos as often assumed) that sets in at quite low levels of excitation and increases as the excitation energy reaches levels at which unimolecular decomposition can 2D

occur. These IRMPD experiments have been enormously beneficial in illucidating certain (albeit, limited) aspects of unimolecular dissociation reaction mechanism, particularly those where there are competing decomposition pathways. These paths may be simple bond-fission or concerted reactions, either molecular elimination or rearrangement followed by a bond rupture — often the case for energetic molecules. While it is generally agreed that NO2 elimination by simple bond-fission is the dominant initial reaction in most nitro and nitramine compounds, in many cases there is evidence of a competitive concerted reaction such as HONO elimination,

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nitro-nitrite rearrangement followed by O-N bond rupture, or ring fission in cyclic molecules. Thus, there is the likelihood of changes in the relative importance of the reactions with changes in temperature, pressure, and physical phase. The IRMPD experiments probe the reactions only for specific conditions; other means of excitation may lead to different decomposition mechanisms. Shock-tube experiments provide data for high temperatures and for a wide range of pressure. Shock tubes have not been used to a large extent to study energetic molecules but are well suited for probing the chemistry for conditions (i.e., high temperatures and pressures) approaching those in practical applications. For example, shock tubes provide a means of studying the pyrolysis of compounds under controlled conditions, with greater control and detection than is possible in flames. Spectroscopic and other techniques can be used to monitor reactant and products in shock tubes, but on a relatively long time scale (~/xs). Interpretation of the data requires fitting to a complex kinetics model. These gas-phase experiments are far removed from those corresponding to practical conditions where a condensed-phase material is subjected to high heat or mechanical shocks leading to combustion or detonation. Similarly they probe conditions very different from some of the experimental techniques from which we have learned so much about the chemistry, experiments such as fast heating and slow heating which have been so deftly used by Brill and Behrens. However, although we know there are links among, and overlap of the observations from, these various methods, the links are not always obvious because we are working with only pieces of the puzzle.

3.3.

Nitromethane

From both the standpoint of theory and experiment, nitromethane is a good prototype for energetic molecules. It is a small molecule — an important consideration in theoretical studies; it also undergoes the reactions typically observed or proposed in mechanisms for larger nitro and nitramine compounds, and it has been studied extensively both experimentally and theoretically. Thus, we have a better understanding of nitromethane decomposition than for other energetic materials although there remain some critical points still unresolved (see Rice's chapter). In 1972 Glanzer and Troe 21 carried out a study of the gas-phase decomposition kinetics of nitromethane using shock heating over the range 900-1400 K. They monitored only the concentrations of CH 3 N0 2 and N 0 2 .

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They proposed the mechanism: CH3NO2 - • CH 3 + N 0 2 ,

(Rl)

CH 3 N0 2 + M -> CH 3 + N 0 2 + M,

(R2)

CH 3 + N 0 2 - • CH 3 0 + NO.

(R3)

In 1979 Perche et al.22 studied the pyrolysis of nitromethane in a bulb over the temperature range 676-771K. They identified the following secondary products: CO, NO, CH 4 , H 2 , C 2 H 6 , CH 3 OH, HCN, C 0 2 , CH 2 0, H 2 0 , and N 2 . They proposed a mechanism involving 28 reactions. Hsu and Lin 23 performed shock-tube studies of the pyrolysis of CH 3 N0 2 over the temperature and pressure ranges, respectively, 940-1520 K and 0.4-2 atm. They monitored only NO and CO. They proposed a mechanism involving 37 reactions. Their data, when combined with those of Kutschke and co-workers24 show a sharp upturn above 1000 K in the Arrhenius plot. Later experiments by Choudhury et al.25 also gave a curved Arrhenius plot, although the curvature was much smaller. Also, the measured rate was more than an order of magnitude smaller than that based on the Hsu and Lin mechanism. These studies provide the backdrop for the more recent work of Zhang and Bauer 26 who carried out shock-tube experiments of the decomposition CH 3 N0 2 over the temperature range 1000-1100 K. They proposed a mechanism of 99 reactions with 41 chemical species that also accounts for the data reported earlier by Hsu and Lin, 23 Glanzer and Troe, 21 and Perche et al.22 They found that the pyrolysis involves chain reactions and that about 40% of the CH 3 N0 2 decay is due to secondary reactions — preventing determination of the unimolecular decay rate of CH 3 N0 2 . Zhang and Bauer 26 suggested that measurements are needed for a wider temperature range in which more intermediates and products are monitored. We think that it is also important to study the lifetimes, decay channels, and bimolecular reactions of some key radicals (especially H, OH, CH 3 , and N 0 2 ) in the postulated mechanisms (see the chapter by Dagdigian). For example, we agree with Zhang and Bauer that "N0 2 is an important intermediate in the decomposition of nitro compounds. A clear understanding of its kinetics is crucial for elucidating the mechanism of the overall conversion."27 The importance of reactions of N 0 2 with other radicals is also illustrated by the analysis of nitromethane high-temperature decomposition data by Glarborg, Bendtsen, and Miller.28

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The initial decomposition reaction of nitromethane in the gas phase is controversial because of the interpretation of IRMPD experiments carried out in Lee's laboratory in the mid-1980s. Wodtke et al.29-30 studied nitromethane by infrared laser excitation in a molecular beam. They explained their data by two primary unimolecular dissociation reactions: reaction (Rl) and CH3NO2 - • CH3ONO* - • CH3O + NO.

(R4)

They concluded that the branching ratio for the isomerization bond-fission reaction (R4) to the simple bond-fission reaction (Rl) is 0.6 ± 0.2. This has not been supported by other experiments and most ab initio calculations predict that the simple bond-fission reaction has a somewhat lower energy barrier (see Rice's chapter for a thorough discussion of the ab initio studies). The differences in the energy requirements are in the range 2-6kcal/mol near the limits of accuracy of quantum chemistry. One ab initio calculation 31 predicts that the isomerization channel is slightly lower in energy. This difference agrees with that assumed by Wodtke et al.29 in their analysis of the IRMPD/molecular beam data in which they used the early semi-empirical results of Dewar et al.32 Subsequent ab initio calculations have all predicted the simple bondfission reaction to be lower in energy. Recent ab initio calculations by Hu et al.33 predict that simple bond-fission to give CH3 + NO2 is favored by 2-3kcal/mol over the isomerization pathways: CH3NO2 —> irans-CHsONO and CH3NO2 —> CTS-CH2N(0)OH. It has been followed up by another ab initio study by Nguyen et al.3i in which the emphasis was on determining both the energy barriers and the natures of the transition states, tight or loose, which could determine the relative importance of competing reaction pathways so close in energy. Based on results computed by using CCSD(T) and CASSCF in conjunction with DFT (B3LYP) Nguyen et al. concluded that the barrier for CH3NO2 -> CH 3 + N 0 2 is 60 ± 2kcal/mol and that for the isomerization reaction CH3NO2 —> CH3ONO is at least 6kcal/mol higher. These calculations predict a tight transition state for the isomerization reaction; the influence of this on the kinetics needs to be determined. To summarize: the energy barriers are sufficiently close that quantum chemistry has yet to convincingly settle the matter of the branching ratio for the nitromethane dissociation. The computed values of the energy barrier to the simple bond-fission reaction are consistently around 60 kcal/mol,

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so the discord centers on the energy barrier for concerted molecular elimination. Given the variation in the energies calculated with the high-level ab initio methods, the conclusion by Wodtke et al.29 that the branching ratio of the isomerization bond-fission (to CH3O + NO) to the simple bondfission (to CH3 + NO2) is about 0.6 might yet be confirmed by ab initio calculations. Also, because the energy barriers are comparable, the structures of the transition states may be most important in determining the relative importance of the two reaction channels. Given the established general reliability of the IRMPD/molecular beam method, we cannot, on the basis of the current ab initio results, dismiss the Wodtke et al.29 conclusion and it is worthwhile to continue looking for other explanations for why the nitro-nitrite isomerization channel has not been observed in other experiments. The experiments that have been reported are not definitive enough to decide the matter. All of them depend on analyses of data that do not have sufficient information to provide a definitive mechanism. Clearly, it would be useful to have experimental confirmation of the Wodtke et al. work, the sole experiment on the decomposition of isolated nitromethane molecules. The analysis by Wodtke et al.29 has been faulted because it was based on semi-empirical quantum chemistry, some of which have subsequently been shown to be inaccurate. For example, Nguyen et al.34i argue that this is why Wodtke et al.29 reached their conclusion. Glarborg et al.28 did a careful analysis of the existing shock-tube data for the dissociation of nitromethane. They discuss the limitations of these experiments for determining the decomposition mechanism. They point out that the experiments by Hsu and Lin 23 detected only secondary products and that Zhang and Bauer 26 did not observe the temporal evolution of the chemical species but only the composition of the products. This is a general problem in chemical kinetics — reaction mechanisms are still determined more or less in the same way as they were at the end of the nineteenth century: by postulating a series of reactions that lead to the observed final products. As for other energetic materials, following the initial decomposition steps of nitromethane there is a build up of radicals that strongly influence the subsequent chemistry. The interpretation of IRMPD/molecular beam data may also be liable to errors because the analysis depends on statistical rate theory (RRKM) to work backwards from the data collected down the beam after several sequential reactions have produced a number of product species. One way to address this would be to use molecular dynamics to simulate the entire

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sequential branching chemistry following the initial excitation of the reactant molecule. If (and this is a significant IF) accurate PESs for the complete dissociation were available, one could presumably compute the raw data measured in the IRMPD/molecular beam experiments. An initial effort along these lines using assumed forms for the PES has been made. Rice and Thompson 35 performed classical trajectory calculations to study the unimolecular dissociation mechanism for nitromethane and to interpret the IRMPD results. They constructed three PESs that differ in the energy barrier to the nitro-to-nitrite isomerization, but for which the C-N bond dissociation energy is the same (60 kcal/mol). The energy required for the simple C-N bond rupture channel is 59.5 kcal/mol which appears to be well established; the role, however, of the concerted reaction channel is not firmly established. Wodtke et al.29 predicted the energy barrier to isomerization CH 3 N0 2 -> [CH3ONO]* - • C H 3 0 + NO to be 55.5 kcal/mol, which is lower in energy than C-N bond-fission. To study the possible role of the CH3O + NO reaction channel, Rice and Thompson considered PESs with isomerization barriers of 216 kcal/mol (to essentially prevent the reaction), 55.1 kcal/mol (corresponding to the estimate of Wodtke et al.29), and 47.6kcal/mol (based on the MINDO/3 calculations reported by Dewar and Ritchie 36 ). The highest barrier (216 kcal/mol) that Rice and Thompson 35 considered was chosen to prevent dissociation via the isomerization/N-0 bondfission pathway, thus (predictably) most of the decay is by simple C-N bond-fission. Interestingly they found that a small percentage of reactions did result in CH3O + NO products formed by a mechanism in which there is near dissociation to CH3 + NO2 but then a recombination to form a [CH3ONO]* complex that subsequently undergoes O-N bond-fission. This does not account for the branching ratio determined by Wodtke et al.29 The other PESs, with more reasonable barriers to isomerization of 47.6 and 55.1 kcal/mol, allow decomposition by a similar mechanism; that is, simple C-N bond-fission to form CH 3 + N 0 2 , interrupted by recombination, which is then followed by dissociation. The dynamics calculations show that, for these model PESs, there are three main decomposition pathways: CH3NO2 - • [CH 3 N0 2 ]* - • CH 3 + N 0 2 ,

(R5)

CH 3 N0 2 -v [CH3ONO]* -> CH3O + NO,

(R6)

CH 3 N0 2 — [CH3ONO]* -> CH 3 + N 0 2 .

(R7)

The calculated branching ratio (CH3O + NO/CH3 + N 0 2 ) for the PES with the 47.6 kcal/mol barrier is in agreement with the experimental value and

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259

the ratio computed with the PES with the 55.1kcal/mol barrier is about an order of magnitude smaller. The computed average product translational energies (which are directly measurable in a beam experiment) for reaction (R6) are higher than for the other two channels. The product energies for reactions (R5) and (R7) are similar and thus probably not distinguishable experimentally. These classical trajectory studies, even on model PESs, can determine possible reaction pathways. They can be used to compute the raw experimental data (i.e., what is directly observed rather than information derived by analysis) and serve as a valuable tool in interpreting experiments. The Rice and Thompson 35 calculations suggest that there may be three decomposition pathways and that the experiment by Wodtke et al.29 would not have distinguished between reactions (R5) and (R7). However, if both occur it could affect the analysis of various experiments and, certainly, the conclusions about the transition state for the nitro-nitrite isomerization. High quality ab initio calculation could be critical in finally resolving the mechanism (i.e., transition states) for the initial steps in the decomposition of nitromethane. Also, it would be useful to revisit the problem with MD simulations in light of the new experimental and theoretical results that have appeared since the Rice and Thompson 35 work was done; for example, we can now develop a more accurate PES. 3.4. Methyl

Nitrite

Given the role of methyl nitrite in the chemistry of nitromethane, we review what is known about its decomposition. Also, many nitro and nitramine compounds can isomerize to the -ONO form. The pathway for the conversion of a nitro or nitramine compound to the nitrite form involves the rotation of the N 0 2 group to exchange the C-N or N-N bond, respectively, for a C - 0 or N - 0 bond. The simplest case is the conversion of nitromethane to methyl nitrite, CH3ONO —> CH3ONO, which we discussed above. The barrier to simple bond-fission to produce CH3O + NO is sufficiently low (^41kcal/mol) 3 7 that the isomerization is immediately followed by the decomposition. This was an observation of Wodtke et al.29 in their IRMPD molecular beam experiments on the decomposition of nitromethane. For the pyrolysis of methyl nitrite He et al.38 proposed a mechanism that consists of 16 reactions with the initial unimolecular steps being: CH3ONO -> CH3O + NO

(R8)

CH3ONO -y C H 2 0 + HNO.

(R9)

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Experiments 37 ' 38 show that the simple bond-fission reaction (R8) is at least an order of magnitude faster than the concerted molecular-elimination reaction (R9). The latter involves a four-center transition state, thus a small Arrhenius A factor. He et al.3S gives the values: A = 6.3 x 10 1 5 s^ 1 and E& = 41.2 kcal/mol for reaction (R8) and A = 4.0 x 1 0 1 3 s _ 1 and E.A = 38.5 kcal/mol for reaction (R9). These parameters were taken from the kinetic modeling of the shock-tube decomposition of nitromethane by Zhang and Bauer. 26 Vazquez and co-workers39 have carried out a series of theoretical studies of the unimolecular dissociation of methyl nitrite via simple bond-fission, reaction (R8), and concerted molecular-elimination, reaction (R9). They performed quantum chemistry calculations to determine the barriers for the two decomposition channels. They predicted the barrier to N - 0 bondfission reaction (R8) to be 39.29 kcal/mol and that for the formation of C H 2 0 and HNO by reaction (R9) to be 43.64 kcal/mol. The disagreement with experiment may again illustrate a case where competing reactions are sufficiently close in energy that predicting their relative importance may be beyond current theory. The rates calculated using an analytical PES based on these barriers and by direct dynamics are in accord with experiment because there is a significant entropy effect in the molecular elimination reaction, that is, the differences in the transition state structures leads to frequency factors to give rates in agreement with experiment. The first dynamics studies of methyl nitrite focused on the cis-trans isomerization as a model for a chemical reaction in which non-statistical effects were anticipated because of the low density of states and low energy barrier for the process. The initial investigations of this were the experimental studies by Bauer and co-workers,40 who studied the intramolecular conversion by using NMR spectroscopy. This, and the subsequent theoretical studies, addressed the fundamental problem of non-statistical behavior of a reaction under conditions where the rate of reaction is fast relative to the rate of intramolecular vibrational energy redistribution (IVR). Shock waves are inherently non-statistical and it is reasonable to assume they leave in their wake (at least for very short times) excited molecules with non-equilibrium distributions of internal energy, but it is not established that nonequilibrium processes occur. In any case, understanding the flow of energy among the phonon modes, within the molecular modes, and between the phonon and molecular modes in condensed phases is critical to an atomiclevel understanding of the response of energetic materials to perturbations such as mechanical shocking (for a discussion, see the chapter by Dlott).

Gas-Phase Decomposition

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261

Comparisons of experimental rates with statistical theory predictions for methyl nitrite reported by Lazaar and Bauer 41 indicated that some of the vibrational phase space is only weakly coupled to the reaction coordinate. Preiskorn and Thompson, 42 using a PES based on ab initio calculations, 43 performed a classical trajectory study of the influence of the distribution of excitation energy on cis-trans isomerization. More recently, MartinezNunez and Vazquez 44 extended these studies using a PES based on higherlevel quantum chemistry calculations. These trajectory studies confirm the conclusions of Lazaar and Bauer that the reaction path is isolated from some of the molecular modes and provide a much more detailed picture of the intramolecular mode couplings and their influence on reaction. The isomerization rate is significantly increased when energy is initially placed in the CON bending, ONO bending, CO stretching, or NO stretching modes. Although these processes are not true chemical reactions, they do illustrate the importance of taking into account the possibility of non-statistical effects.

3.5.

Dimethylnitramine

Dimethylnitramine (DMNA) is the simplest experimentally-studied nitramine. It is often used as a prototype for the larger, more important nitramines because it undergoes the same sorts of reactions that have been postulated for RDX and HMX and it presents a much more tractable problem to theorists than do the larger compounds. Its decomposition has not proven easy to unravel because it presents the same basic problems in determining the dominant reaction path when two or more are close in energy and where variations in conditions can cause changes in the mechanism. Based on thermochemistry there are three possible initial unimolecular decomposition reactions for DMNA: (a) simple bond-fission: (CH 3 ) 2 N-N0 2 - (CH 3 ) 2 N + N 0 2 ,

(RIO)

(b) nitro-nitrite rearrangement followed by O-N bond-fission: (CH 3 ) 2 N-N0 2 - • (CH 3 ) 2 NO-NO - • (CH 3 ) 2 NO + NO, and

(Rll)

(c) HONO elimination via a 5-center transition state: (CH 3 ) 2 N-N0 2 -> CH 3 N=CH 2 + HONO.

(R12)

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Although there is still need for further experiments before final conclusions about a mechanism can be reached, it appears that reaction (RIO) is the first step in the thermal decomposition of DMNA. A wide range of values for the activation energy has been reported. However, it appears that the true value is probably in the range 43-46 kcal/mol and that the bond energy is 43.3 kcal/mol. 45 Lloyd et al.45 reported Ea = 45.5 kcal/mol based on thermal pyrolysis experiments. Experiments by Lazarou and Papagiannakopoulos 46 made measurements for IRMPD in a reaction cell that showed that the decomposition occurs via reaction (RIO), for which the enthalpy of reaction is 46.5 kcal/mol. Their analysis indicated that the average excitation energy of the molecules was 12 ± 3 kcal/mol above the dissociation limit. However, there is experimental evidence that other reactions may participate in the initial break up of DMNA. In a very early experimental study, Fluornoy 47 reported the results of static-bulb thermal pyrolysis experiments that showed that ~ 8 0 % is converted to dimethylnitrosamine, (CHs^NNO. This, of course, does not provide direct information about the initial reaction. McMillen and co-workers48 studied the decomposition of DMNA by using pulsed laser heating and determined the activation energy to be in the order of 30 kcal/mol which they attributed to reaction (Rll). Their thermal data, which are fitted by a rate constant expression with a low Arrhenius A factor, have a dependence that is too low to be explained by the simple bond rupture reaction (RIO). They concluded that the isomerization/bondfission reaction (Rll) is an important initial step in the decomposition at low (~500K) temperatures which is not in accord with Lloyd et al.45 No experimental data have indicated that HONO elimination, reaction (R12), is a competitive initial reaction in the decomposition of DMNA. Although it is frequently mentioned in discussions and even included analyses of the decomposition of nitramines such as RDX and HMX, there is no solid experimental evidence to establish that HONO elimination occurs in thermal decompositions of nitramines; however, it appears to be firmly established as an initial step in the decomposition of nitroalkanes, e.g., nitroethane and 2-nitropropane. 30 There have been estimates of ~ 38 kcal/mol as the lower bound for the activation energy for reaction (R12), 49 which would suggest that it would be competitive with reaction (RIO) unless the energy advantage is overridden by a small frequency factor. Johnson and Truong 50 have performed high-level quantum chemistry calculations for the reaction. Their calculations give 43.5 kcal/mol for the barrier to HONO elimination.

Gas-Phase Decomposition

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263

As this brief overview shows, our understanding of the thermal decomposition of DMNA is still rudimentary and further experiments are needed. In particular, experiments should be directed at determining the importance of reaction (Rll). This kind of reaction has been suggested for other nitro and nitramine decompositions, but without clear conclusions about its likely importance. The only exceptions, to our knowledge, are the IRMPD experiments of Wodtke et al.30 and the much earlier work by Spokes and Benson. 51 We also believe that additional experiments are needed before the HONO elimination channel can be accepted as an important initial reaction. (We discuss the evidence for it in RDX decomposition below, as does Rice in another chapter in this volume.) Zhang and Bauer 52 have presented a critical analysis of the decomposition mechanisms for several nitro and nitramine compounds including DMNA. Their conclusions, more substantially illustrated by results of a sensitivity analysis study than those given here, are essentially the same — more experiments are needed to resolve the mechanisms. The resolution of this problem will likely require a combination of experiments, theoretical calculations, and modeling. All of the experimental techniques probe the chemistry under poorly-defined conditions, late in the chemistry, and only for a very limited number of species. Quantum chemistry has reached the stage where we can compute energies for relatively large molecules, although for one as large as DMNA we are limited to only a few points on the PES. Nevertheless, electronic structure calculations can provide vital information about reaction pathways. But to fully link this information to experiments we must calculate rates for the experimental conditions. For experiments such as IRMPD, it may be necessary to compute the raw data such as product energy distributions. Classical trajectory simulations can be used to compute information for the individual elementary reaction steps. Then one can use this and other established information in modeling calculations to study the overall decomposition to again compute quantities directly comparable to measured basic quantities. Sumpter and Thompson 53 reported a classical trajectory study of DMNA in 1988. They included the HONO elimination channel with a barrier of 38 kcal/mol in an empirical PES for which the N-N bond energy was 46kcal/mol. They concluded that HONO elimination plays a very minor role in the thermal decomposition of DMNA. Theoretical and computational methods have improved significantly since these early calculations were done and now it would be feasible to perform a much more meaningful dynamics study of the system.

264

3.6.

D. L.

Thompson

TNAZ

Studies by Oyumi and Brill 5 4 - 5 6 of TNAZ decomposition using rapid heating of the solid show that NO2 is the initial and most abundant decomposition product and that the other products of the overall reaction include NO (second most abundant), HCN, H 2 CO, CO, C 0 2 , and HONO. 55 The implication is that one or both of the reactions shown in Fig. 1 initiates the decomposition. Anex et al.57 used IRMPD to study TNAZ in a molecular beam with product detection by time-of-flight quadrupole mass-spectrometry. They also found that the decomposition begins with the loss of NO2, although they could not determine the relative importance of reactions (R13) and (R14) or the details of the branching following the loss of N 0 2 . They proposed a mechanism of several steps beginning with N 0 2 elimination from the C- and N-sites on the ring. They found no evidence for HONO elimination or nitro-nitrite rearrangement. Zhang and Bauer 58 carried out single-pulse shock-tube experiments that show that the decomposition is first order. They determined the high-pressure unimolecular rate constant to be k^ = io 1 3 - 9 6 ± 0 - 3 6 _1 exp[(—39.45 ± 2.36)/RT], where k is in s and the activation energy is in kcal/mol. Infrared (IR) analysis of the reaction products showed that NO, N 0 2 , CO, C 0 2 , HCN, and H 2 CO are the major products, and HONO and H 3 C-C=CH are minor products; and tentative evidence for N 2 0 . A following experiment by Bauer and co-workers59 determined the primary products of a quenched reaction sample to be CO, HCN, H 2 CO, and NO. Thermodynamic calculations predict that the equilibrium mixture should primarily be composed of C 0 2 , N 2 , and H 2 . They concluded that the TNAZ

0,N

(R13)

r--No2

\

NO2

+ NOz

-NO, NO, 0,N

(R14) + N0 2 NQ2

Fig. 1.

Gas-Phase Decomposition

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265

decomposition is kinetically driven under these experimental conditions. Zhang and Bauer 58 proposed a mechanism of several steps beginning with NO2 elimination from the C- and N-sites on the ring, which differs in some details from that proposed by Anex et al.57 Because of its size, all of the quantum chemistry calculations for TNAZ have used DFT. 6 0 ~ 6 3 All predict the N-N bond energy, reaction (R13), to be lower than the C-N bond energy, reaction (R14) — but by only 2-3 kcal/mol. The most recently reported 63 predictions are 38 kcal/mol for reaction (R13) and 41 kcal/mol for reaction (R14). These values compare favorably with the experimental activation energy of 39.4 kcal/mol determined by Zhang and Bauer 58 for gas-phase TNAZ decomposition, but DFT may not be sufficiently accurate to distinguish between the two channels. Calculations have also been done for HONO elimination. The DFT results predict only 1 kcal/mol difference in the reactions occurring at the C-NO2 and the N - N 0 2 sites, i.e., 44 and 45kcal/mol, respectively. Highlevel ab initio calculations are needed to definitely determine the initial decomposition reaction.

3.7.

RDX

The initial steps in the decomposition of RDX are not clearly established although a lot of evidence suggests that simple N-N bond-fission plays a crucial role in the decomposition. Other unimolecular reactions may occur under certain conditions, but are likely inhibited by condensed-phase effects because they involve concerted molecular elimination with large volumes of activation. Apparently there are several possible first reactions with comparable energy barriers and which one actually occurs depends on the conditions (physical phase, heating rate, etc.). The results of a number of ab initio quantum chemistry calculations lead to different conclusions depending on the level of theory. The elucidation of the mechanisms for the initial stage of the chemical decomposition of RDX, as is the case for other cyclic nitramines, is frustrated by the complexity of the chemistry and its strong dependence on the experimental conditions; however, a great deal of progress has been made as illustrated by the reviews given in the chapters by Brill and by Behrens. The first experimental determination of the activation energy was done by Robertson 64 in 1949 for liquid RDX over the temperature range 213-299°C with the result Ea = 47.5kcal/mol. Analysis of the products showed N 2 0 , N 2 , NO, CO, C 0 2 , H 2 , H 2 0 , H 2 CO, and a solid residue.

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The basic conclusions of Robertson have withstood time and many subsequent experiments. Many others have since reported values for the activation energy close to the Robertson value, and the accepted value of Ea is 47 to 48kcal/mol. Excellent reviews were written by Schroeder 65 ' 66 in 1985; unfortunately these are not generally available. He compiled and critically evaluated all of the data, including much that are contained only in government laboratory reports. Although the details of the RDX decomposition mechanism are far from resolved, there is evidence that can be used to limit the number of initial reactions that have to be considered. Clearly, simple N-N bond-fission eliminating NO2 must be considered as a likely first step. Another initial reaction that remains an active candidate for the mechanism is the elimination of HONO following the transfer of a H-atom from carbon to oxygen. A single gas-phase experiment has been interpreted to predict that concerted ring fission (RDX —> 3H2C-N=N02) is an important route for the initial dissociation of RDX. No direct experimental studies to confirm this pathway have been carried out. There is good evidence concerning some of the early products of the decomposition regardless of the initial step. Clearly, methylenenitramine, H2C-N=N02, is likely produced if not in the first, then in a subsequent step, and it can dissociate to H 2 CN + N 0 2 , HCN + HONO, or N 2 0 + H 2 CO. Also, some experiments (see the chapter by Behrens) provide evidence that nitrosoamines are formed early in the decomposition, and then dissociate to yield radicals and smaller molecules. The end result of the chemistry is a set of relatively stable small gaseous molecules. The challenge is to understand how all of this occurs for various conditions. The most direct study of RDX molecular gas-phase decomposition is the IRMPD experiments of Zhao et al.67 Zhao et al. concluded that the initial decomposition involves two competing reactions: simple bond-fission eliminating NO2 and triple bond-fission giving 3CH 2 NN0 2 . They determined the branching ratio of ring fission to simple N-N bond-fission to be approximately two. The ring-fission reaction has not been definitely observed in other experiments. Nevertheless, given the reliability of this experimental approach, which has been widely applied, 68 it is not easy to dismiss the possibility that the ring-fission reaction occurs under collision-free gas-phase conditions. Recently, Long et al. 69 used thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) to study the thermal decomposition of RDX in open and closed (or pierced) containers. They determined the

Gas-Phase Decomposition

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267

activation energy as a function of the extent of decomposition. Evaporation, with Eg. ~ 23.9 kcal/mol, was prevalent in the open pan experiments. When RDX was heated in a closed container it decomposed in the liquid state with Ea ~ 47.8 kcal/mol, which corresponds to the generally-accepted values for simple N-N bond-fission. A gas-phase decomposition channel with E& ~ 33.5 kcal/mol was also observed. Long et al. suggested that this reaction might be concerted ring-fission to produce H 2 C=N-N02, as observed by Zhao et al.67 There is a decrease in the value of E& as the decomposition proceeds, which they interpreted to be due to competition between the simple N-N bond-fission reaction (liquid phase) and the concerted molecular elimination ring fission reaction (gas phase). Thompson and co-workers 70-73 developed empirical PESs to determine what the barrier height to the ring fission channel must be to account for the branching ratio measured by Zhao et al.67 They took the N-N bond dissociation energy to be 48 kcal/mol, and used a PES formulation that permitted variation of the barrier height for ring fission without significant changes in other features of the surface. They carried out a series of studies using this model to investigate the branching reactions. Their studies, which included classical trajectories, 70 ' 71 Monte Carlo variational transition-state theory (MCVTST), 72 and classical diffusion theory, 73 show that for this model the barrier to ring fission must be about 37 kcal/mol in order to obtain the experimentally-observed branching ratio of 2. Wight and Botcher 74 suggested that the ring fission reaction was not observed in other experiments because it has a large volume of activation and does not occur in condensed phases where the environment cages the fragments and causes recombination. Guo and Thompson 75 tested this idea by using the model PES in MD simulations of RDX decomposition in liquid xenon as a function of pressure. The results showed that pressure effects on ring fission are considerably greater than on simple bond rupture, which supports Wight and Botcher's suggestion. The extensive studies of condensed-phase decomposition of RDX for slow-heating conditions (see the chapter by Behrens) suggest that the initial reaction for those conditions is most likely HONO elimination. Much earlier, Zuckermann et al.76 had carried out experiments in which a pulsed C 0 2 laser was used to dissociate RDX and HMX in seeded supersonic nozzle beams and OH radicals detected by laser-induced fluorescence. Their results indicate that OH(X2IT) is produced in the primary unimolecular dissociation of these molecules. However, they could not determine the mechanism by which the OH is produced. They point out that OH may be formed

D. L.

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Thompson

either directly or by rapid dissociation of hot, nascent H O N O eliminated from RDX. Capellos et al.77 observed the formation of O H ( X 2 £ ) in experiments in which RDX was photolyzed at 2 4 8 n m and suggest t h a t the.initial photolysis leads t o elimination of vibrationally-hot H O N O , which absorbs a photon and dissociates to O H ( X 2 E ) and NO. Because the initial excitation is electronic, it is not clear how these results correlate with thermal excitation experiments or to shock-induced explosions. Presumably, the dissociation could occur after intersystem crossing to the ground state (see the chapter by Bernstein). Recently, Chakraborty et al.7S reported the results of ab initio D F T calculations t h a t predict t h a t RDX can decompose by elimination of 3HONO molecules plus 1,3,5-triazine at approximately 40kcal/mol. (For a more complete discussion of q u a n t u m chemistry predictions of decomposition pathways, see t h e chapter by Rice.) In 1990 Melius 7 9 proposed a detailed model for the decomposition of RDX based on B A C - M P 4 thermochemical calculations t h a t remains more or less intact in light of subsequent experiments and calculations. He predicted t h a t the decomposition channel initiated by NO2 elimination proceeds by t h e steps shown in Fig. 2. N 0 2 , H 2 C N , and 2 H 2 C = N - N 0 2 are formed and this mechanism is not consistent with the molecular beam experiments of Zhao et al.67 Recent ab initio results of C h a k r a b o r t y et al.7& predict 3 9 k c a l / m o l for Step 1 ( N - N bond-fission), which may be low (B3LYP D F T often underestimates barrier heights). However, Long et al.69 determined the value of the activation energy for N - N bond-fission in liquid

Stepl 49 kcal/mol

Step 4 2 kcal/mol

Step 2 28 kcal/mol

H2

N

O O

/ Step 3 16 kcal/mol Fig. 2.

Gas-Phase Decomposition

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RDX to be 47.8 kcal/mol. The Chakraborty et al.78 calculations predict that the ring opening, Step 2, requires 26.4 kcal/mol, again in accord with the earlier prediction by Melius.79 However, the ab initio results predict that the next step involves H-atom migration (8.7kcal/mol), followed by HCN elimination (which requires 16.2kcal/mol). 78 The Zhao et al67 experiments provide the only extensive study of the decomposition of RDX in the gas phase, but the conclusions continue to be questioned by many. There is no other experiment that leads to the conclusion that ring fission is a competitive initial step. The conditions studied in other experiments that have been reported to date differ too much to assign much significance to comparisons.

4. Concluding Remarks We have attempted to describe the current state of knowledge of the decomposition chemistry of nitromethane, methyl nitrite, DMNA, TNAZ, and RDX. These were selected to illustrate what is known about the decomposition mechanisms of energetic molecules in the gas phase. They are not only representative of energetic materials but are also probably the most studied. Our focus is on the initial decomposition reactions; however, we have also discussed the subsequent chemistry. As our discussion shows, the initial reactions are not firmly established in most cases and thus conclusions about the mechanisms for the complete decompositions are premature. The state of affairs we describe for these energetic molecules is representative of that of the broader field of reaction kinetics of large molecules — we are still in a primitive stage of not only understanding these complex reaction mechanisms but also in having the experimental and theoretical techniques to study them. We still do not know what reaction initiates the thermal decomposition of RDX and other important energetic compounds even though they have been known for over a century and in widespread use for more than half a century. For obvious reasons much of the experimental work has focused on the condensed-phase chemistry and considerable progress has been made in describing it (as several other chapters in this volume demonstrate). The gas-phase studies have provided activation energies that are sufficiently accurate to be of practical use in modeling, however, the specific reactions are not clearly established. This is in large part because, for most of these molecules, two or three reaction pathways are too close in energy for experiments to clearly distinguish which one is occurring, and which one actually

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occurs apparently depends on the specific conditions of the experiment. Also, complicating the analysis of an experiment is the prompt presence of radicals that result in chemistry that is very complex and very fast. Similar problems apply to many areas of chemistry besides energetic materials. In general, we do not yet have available the experimental or theoretical techniques that allows us to resolve the details of how a reactant or mixture of reactants undergo a series of branching reactions. The main focus, and thus the greatest progress, over the past half century has been on accurately determining the microscopic details of how elementary reactions occur. Experiment and theory have worked together to reach a point now where we can measure and compute highly-accurate minute properties of reactions involving small molecules. However, little effort has been devoted to developing techniques that would allow us to confidently postulate even the major pathways in the decomposition of a molecule as small as nitromethane. We still develop such mechanisms very much the same way Bodenstein did in the 1890s, although we now have computers and so can make fewer assumptions. For the chemistry discussed in this chapter, the experiments are modern only in the sense that they employ lasers, and in rare instances molecular beams, but otherwise they use traditional approaches such as bulbs, shock tubes, etc. In all cases, there is considerable modeling required to analyze the data. Thus, the emphasis has to be on obtaining more data, particularly the identification of transient species and their temporal appearance. Confirming the conclusions of some studies is needed, particularly in cases where conclusions must now be based on a single experiment. The main role that theorists can play at this point is to provide, based on high-level quantum chemistry calculations, energetics for species and transition states. The systems are sufficiently large that these are demanding problems, however, they are feasible (as illustrated by the discussions in the chapters by Rice and Fried et al.). By a synergistic process involving experiments (such as those described here and in the chapters by Dagdigian and Bernstein), theory can both guide and interpret the information needed to postulate mechanisms for the overall decomposition of energetic molecules in the gas phase. The quantum chemistry results can be used in MD and other methods for rate calculations to directly link theory to experiment, and to make predictions of data that are difficult or impossible to measure. In particular, the use of direct dynamics methods, although still in the developmental stage, will likely play a crucial role in developing a detailed understanding of the sequential, branching

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decomposition of energetic molecules. T h e realization of the methods to accurately predict rate processes in isolated molecules will lay the groundwork of improved methods for treating chemistry in condensed phases — the kinds of problems addressed by Rice in her chapter. Furthermore, the results directly feed into the modeling studies of the sort discussed by Miller in his chapter.

References 1. L. M. Raff and D. L. Thompson, in The Theory of Chemical Reaction Dynamics, Vol. 3, ed. M. Baer (CRC, Baca Raton, FL, 1985), p. 1. 2. T. D. Sewell and D. L. Thompson, Int. J. Mod. Phys. B l l , 1067 (1997). 3. D. L. Thompson, Int. Rev. Phys. Chem. 17, 547 (1998). 4. See, e.g., K. A. Holbrook, M. J. Pilling and S. H. Robinson, Unimolecular Reactions (Wiley, New York, 1996). 5. See, e.g., D. G. Truhlar, B. C. Garrett and S. J. Klippenstein, J. Phys. Chem. 100, 12771 (1996). 6. D. V. Shalashilin and D. L. Thompson, J. Chem. Phys. 105, 1833 (1995). 7. D. V. Shalashilin and D. L. Thompson, in Highly Excited States: Relaxation, Reactions, and Structures, eds. A. Mullins and G. C. Schatz (American Chemical Society, Washington, DC, 1997), p. 81. 8. (a) D. V. Shalashilin and D. L. Thompson, J. Phys. Chem. A 1 0 1 , 961 (1997); (b) Y. Guo, D. V. Shalashilin, J. A. Krouse and D. L. Thompson, J. Chem. Phys. 110, 5521 (1999). 9. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys. 2 1 , 1087 (1953). 10. For a comprehensive review, see: A. J. Marks, in Modern Methods for Multidimensional Dynamics Computations in Chemistry, ed. D. L. Thompson (World Scientific, Singapore, 1998), pp. 580-617. 11. See e.g., J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods (Chapman & Hall, London, 1964). 12. D. R. McLaughlin and D. L. Thompson, J. Chem. Phys. 59, 4393 (1973). 13. J. Ischtwan and M. A. Collins, J. Chem. Phys. 100, 8080 (1994). 14. For a review of this and related methods, see: G. C. Schatz, in Reaction and Molecular Dynamics, Lecture Notes in Chemistry, Vol. 14, eds. A. Lagana and A. Riganelli (Springer, Berlin, 2000), p. 15. 15. G. G. Maisuradze and D. L. Thompson, J. Phys. Chem. A107, 7118 (2003). 16. G. G. Maisuradze and D. L. Thompson, J. Chem. Phys. 119, 10002 (2003). 17. A. Kawano, Y. Guo, D. L. Thompson, A. F. Wagner and M. Minkoff, J. Chem. Phys., in press. 18. K. A. Nguyen, I. Rossi and D. G. Truhlar, J. Chem. Phys. 103, 5522 (1995). 19. For a review of this method and a discussion of some early studies, see: P. A. Schulz, Aa. S. Sudb0, D. J. Krajnovich, H. S. Kwok, Y. R. Shen and Y. T. Lee, Annu. Rev. Phys. Chem. 30, 379 (1979).

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20. (a) T. D. Sewell, D. L. Thompson and R. D. Levine, J. Phys. Chem. 96, 8006 (1992); (b) T. D. Sewell, C. C. Chambers, D. L. Thompson and R. D. Levine, Chem. Phys. Lett. 208, 125 (1993). 21. K. Glanzer and J. Troe, He.lv. Chim. Acta 55, 2884 (1972). 22. (a) A. Perche, J. C. Tricot and M. Lucquin, J. Chem. Res. Synop. 304 (1979); (b) ibid 3219 (1979); (c) A. Perche and M. Lucquin, J. Chem. Res. Miniprint 3257 (1979). 23. H. S. Hsu and M. C. Lin, J. Energet. Mat. 3, 95 (1985). 24. (a) A. Toby and K. O. Kutschke, Can. J. Chem. 37, 672 (1959); (b) A. R. Balke and K. O. Kutschke, Can. J. Chem. 37, 1462 (1959). 25. T. K. Choudhury, W. A. Sanders and M. C. Lin, J. Phys. Chem. 93, 5143 (1989). 26. Y.-X. Zhang and S. H. Bauer, J. Phys. Chem. B 1 0 1 , 8717 (1997). 27. Y.-X. Zhang and S. H. Bauer, J. Phys. Chem. A104, 1207 (2000). 28. P. Glarborg, A. B. Bendtsen and J. A. Miller, Int. J. Chem. Kinetics 3 1 , 591 (1999). 29. A. M. Wodtke, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 84, 1044 (1986). 30. A. M. Wodtke, E. J. Hintsa and Y. T. Lee, J. Phys. Chem. 90, 3549 (1986). 31. R. P. Saxon and M. Yoshimine, Can. J. Chem. 70, 572 (1992). 32. M. J. S. Dewar, J. P. Ritchie and J. Alster, J. Org. Chem. 50, 1031 (1985). 33. W.-F. Hu, T. J. He, D.-M. Chen and F.-C. Liu, J. Phys. Chem. A106, 7294 (2002). 34. M. T. Nguyen, H. T. Le, B. Hajgato, T. Veszpremi and M. C. Lin, J. Phys. Chem. A107, 4286 (2003). 35. B. M. Rice and D. L. Thompson, J. Chem. Phys. 93, 7986 (1990). 36. M. J. S. Dewar and J. P. Ritchie, J. Org. Chem. 50, 1031 (1985). 37. L. Batt, R. T. Milne and R. D. McCulloch, Int. J. Chem. Kinet. 9, 567 (1977). 38. Y. He, W. A. Sanders and M. C. Lin, J. Phys. Chem. 92, 5474 (1988). 39. (a) E. Martinez-Nunez and S. A. Vazquez, J. Chem. Phys. 109, 8907 (1998); (b) E. Martinez-Nunez and S. A. Vazquez, J. Am. Chem. Soc. 120, 7594 (1998); (c) E. Martinez-Nunez and S. A. Vazquez, J. Chem. Phys. I l l , 10501 (1999). 40. (a) S. H. Bauer and N. S. True, J. Phys. Chem. 84, 2507 (1980); (b) K. I. Lazaar and S. H. Bauer, J. Phys. Chem. 88, 3052 (1984); (c) S. H. Bauer and K. I. Lazaar, J. Chem. Phys. 79, 2808 (1983); (d) S. H. Bauer, Int. J. Chem. Kinet. 17, 367 (1985). 41. K. I. Lazaar and S. H. Bauer, J. Phys. Chem. 88, 3052 (1984). 42. A. Preiskorn and D. L. Thompson, J. Chem Phys. 91, 2299 (1989). 43. J. A. Darsey and D. L. Thompson, Chem. Phys. Lett. 145, 523 (1988). 44. E. Martinez-Nunez and S. A. Vazquez, J. Chem. Phys. 107, 5393 (1997). 45. S. A. Lloyd, M. E. Umstead and M. C. Lin, J. Energ. Mater. 3, 187 (1985). 46. Y. G. Lazarou and P. Papagiannakopoulos, J. Phys. Chem. 94, 7114 (1990). 47. J. M. Fluornoy, J. Chem. Phys. 36, 1106 (1962).

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48. (a) P. H. Stewart, J. B. Jeffries, J.-M. Zellweger, D. F. McMillen and D. M. Golden, J. Phys. Chem. 93, 3557 (1989); (b) S. E. Nigenda, D. F. McMillen and D. M. Golden, J. Phys. Chem. 93, 1124 (1993). 49. R. Shaw and F. E. Walker, J. Phys. Chem. 81, 2572 (1977). 50. M. A. Johnson and T. N. Truong, J. Phys. Chem. A103, 8840 (1999). 51. G. N. Spokes and S. W. Benson, J. Am. Chem. Soc. 89, 6030 (1967). 52. Y.-X. Zhang and S. H. Bauer, Int. J. Chem. Kinet. 31, 655 (1999). 53. B. G. Sumpter and D. L. Thompson, J. Chem. Phys. 88, 6889 (1988). 54. Y. Oyumi, T. B. Brill, A. L. Rheingold and T. M. Haller, J. Phys. Chem. 89, 4317 (1985). 55. Y. Oyumi and T. B. Brill, Combust. Flame 62, 225 (1985). 56. Y. Oyumi and T. B. Brill, Combust. Flame 68, 209 (1987). 57. D. S. Anex, J. C. Allman and Y. T. Lee, in Chemistry of Energetic Materials, eds. G. A. Olah and D. R. Squire (Academic Press, New York, 1991), pp. 27-54. 58. Y.-X. Zhang and S. H. Bauer, J. Phys. Chem. A102, 5846 (1998). 59. C.-L. Yu, Y.-X. Zhang and S. H. Bauer, J. Mol Struc. (Theochem) 432, 63 (1998). 60. P. Politzer and J. M. Seminario, Chem. Phys. Lett. 207, 27 (1993). 61. C. F. Wilcox, Y.-X. Zhang and S. H. Bauer, J. Mol. Struc. (Theochem) 528, 95 (2000); ibid. 538, 67 (2001). 62. C. A. Thompson, J. K. Rice, T. P. Russell, J. M. Seminario and P. Politzer, J. Phys. Chem. A101, 7742 (1997). 63. S. Alavi and D. L. Thompson, J. Chem. Phys. 119, 8297 (2003). 64. A. J. B. Robertson, Trans. Faraday Soc. 45, 85 (1949). 65. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Product Distributions from HMX and RDX Decomposition, Technical Report BRL-TR-2659 (US Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, 1985). 66. M. A. Schroeder, Critical Analysis of Nitramine Decomposition Data: Activation Energies and Frequency Factors for HMX and RDX Decomposition, Technical Report BRL-TR-2673 (US Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, 1985). 67. X. Zhao, E. J. Hintsa and Y. T. Lee, J. Chem. Phys. 88, 801 (1988). 68. P. A. Schulz, Aa. S. Sudb0, D. J. Krajinovich, H. S. Kwok, Y. T. Shen and Y. T. Lee, Annu. Rev. Phys. Chem. 31, 379-409 (1979). 69. G. T. Long, S. Vyazovkin, B. A. Brems and C. A. Wight, / . Phys. Chem. A104, 2570 (2000). 70. T. D. Sewell and D. L. Thompson, J. Phys. Chem. 95, 6228 (1991). 71. C. C. Chambers and D. L. Thompson, J. Phys. Chem. 99, 15881 (1995). 72. D. V. Shalashilin and D. L. Thompson, J. Phys. Chem. A101, 961 (1997). 73. Y. Guo, D. V. Shalashilin, J. A. Krouse and D. L. Thompson, J. Chem. Phys. 110, 5521 (1999). 74. C. A. Wight and T. R. Botcher, J. Am. Chem. Soc. 114, 8303 (1992). 75. Y. Guo and D. L. Thompson, J. Phys. Chem. B103, 10599 (1999).

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76. H. Zuckermann, G. D. Greenblatt and Y. Haas, J. Phys. Chem. 9 1 , 5159 (1987). 77. C. Capellos, P. Papaiannakopoulos and Y.-L. Liang, Chem. Phys. Lett. 174, 533 (1989). 78. D. Chakraborty, R. P. MuUer, S. Dasgupta and W. A. Goddard III, J. Phys. Chem. A104, 2261 (2000). 79. C. F. Melius in Chemistry and Physics of Energetic Materials, ed. S. N. Bulusu (Kluwer, Dordrecht, 1990), p. 21.

CHAPTER 9 MODELING THE REACTIONS OF ENERGETIC MATERIALS IN THE CONDENSED PHASE Laurence E. Fried and M. Riad Manaa Lawrence Livermore National Laboratory L-282, 7000 East Ave. Livermore, CA 94550, USA

James P. Lewis Department of Physics and Astronomy Brigham Young University N319 ESC, P.O. Box 24658 Provo, UT 84602-4658, USA

Contents 1. Introduction 2. Chemical Equilibrium 2.1. Thermodynamic Cycle Theory of Detonation 2.2. High Pressure Equations of State (EOS) 2.3. Example Applications 3. Atomistic Modeling of Condensed-Phase Reactions 3.1. Molecular-Dynamics with Bond-Order Potentials 3.2. Molecular-Dynamics with Quantum Mechanical Methods 3.3. Quantifying the Energetics of Reaction Pathways 3.4. Electronic Excitations in Shocked Explosives 4. Conclusions References

275 278 278 280 283 287 288 290 295 296 297 298

1. I n t r o d u c t i o n Energetic materials are unique for having a strong exothermic reactivity, which has made t h e m desirable for b o t h military and commercial applications. Energetic materials are commonly divided into high explosives, 275

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propellants, and pyrotechnics. We will focus on high-explosive (HE) materials here, although there is a great deal of commonality between the classes of energetic materials. Although the history of HE materials is long, their condensed-phase properties are poorly understood. Understanding the condensed-phase properties of HE materials is important for determining stability and performance. Information regarding HE material properties (for example, the physical, chemical, and mechanical behaviors of the constituents in plastic-bonded explosive, or PBX, formulations) is necessary for efficiently building the next generation of explosives as the quest for more powerful energetic materials (in terms of energy per volume) moves forward.1 In addition, understanding the reaction mechanisms has important ramifications in disposing of such materials safely and cheaply, as there exist vast stockpiles of HE materials with corresponding contamination of earth and groundwater at these sites. 2 In modeling HE materials there is a need to better understand the physical, chemical, and mechanical behaviors from fundamental theoretical principles. Among the quantities of interest in plastic-bonded explosives (PBXs), for example, are thermodynamic stabilities, reaction kinetics, equilibrium transport coefficients, mechanical moduli, and interfacial properties between HE materials and the polymeric binders. These properties are needed (as functions of stress state and temperature) for the development of improved micro-mechanical models, 3 which represent the composite at the level of grains and binder. 4 Improved micro-mechanical models are needed to describe the responses of PBXs to dynamic stress or thermal loading, thus yielding information for use in developing continuum models. Detailed descriptions of the chemical reaction mechanisms of condensed energetic materials at high densities and temperatures are essential for understanding events that occur at the reactive front under combustion or detonation conditions. Under shock conditions, for example, energetic materials undergo rapid heating to a few thousand degrees and are subjected to a compression of hundreds of kilobars,5 resulting in almost 30% volume reduction. Complex chemical reactions are thus initiated, in turn releasing large amounts of energy to sustain the detonation process. Clearly, understanding of the various chemical events at these extreme conditions is essential in order to build predictive material models. Scientific investigations into the reactive process have been undertaken

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over the past two decades. However, the sub-yus time scale of explosive reactions, in addition to the highly exothermic conditions of an explosion, make experimental investigation of the decomposition pathways difficult at best. More recently, new computational approaches to investigate condensedphase reactivity in energetic materials have been developed. Here we focus on two different approaches to condensed-phase reaction modeling: chemical equilibrium methods and atomistic modeling of condensedphase reactions. These are complementary approaches to understanding the chemical reactions of high explosives. Chemical equilibrium modeling uses a highly simplified thermodynamic picture of the reaction process, leading to a convenient and predictive model of detonation and other decomposition processes. Chemical equilibrium codes are often used in the design of new materials, both at the level of synthesis chemistry and formulation. Atomistic modeling is a rapidly emerging area. The doubling of computational power approximately every 18 months has made atomistic condensed-phase modeling more feasible. Atomistic calculations employ far fewer empirical parameters than chemical equilibrium calculations. Nevertheless, the atomistic modeling of chemical reactions requires an accurate global Born-Oppenheimer potential energy surface. Traditionally, such a surface is constructed by representing the potential energy surface with an analytical fit. This approach is only feasible for simple chemical reactions involving a small number of atoms. More recently, first principles molecular dynamics, where the electronic Schrodinger equation is solved numerically at each configuration in a molecular dynamics simulation, has become the method of choice for treating complicated chemical reactions. Recent developments, however, indicate that the use of transferable bond-order reactive empirical potentials may also be a viable option in studying condensedphase reactions. Please refer to the chapter by Rice for a more detailed discussion. Chemical reactions may also occur through diabatic processes involving several electronic states. The importance of such diabatic reactions on the overall chemistry of energetic materials is still a matter of debate. 6 ' 7 In addition to chemical equilibrium methods and atomistic modeling of reaction pathways on the ground electronic state, we also review recent work on the effect of high pressure and defects in modifying the excited electronic states of energetic materials.

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2. Chemical Equilibrium The energy content of a HE material often determines its practical utility. Accurate estimates of the energy content are essential in the design of new materials 1 and for understanding quantitative detonation tests. 8 The useful energy content is determined by the anticipated release mechanism. Since detonation events occur on a (is timeframe, chemical reactions significantly faster than this may be considered to be in an instantaneous chemical equilibrium. It is generally believed that reactions involving the production of small gaseous molecules (C0 2 , H 2 0 , etc.) are fast enough to be treated in chemical equilibrium for most energetic materials. This belief is based partly on success in modeling a wide range of materials with the assumption of chemical equilibrium. 9-12 Unfortunately, direct measurements of the chemical species in the detonation of a condensed are difficult to perform. Blais et al.13 have measured some of the species produced in detonating nitromethane (NM) using a special mass spectroscopic apparatus. These measurements pointed to the importance of condensation reactions in detonation. The authors estimate that the hydrodynamic reaction zone of detonating base-sensitized liquid nitromethane is 50 (i in thickness, with a reaction time of 7 ns. The hydrodynamic reaction zone dictates the point at which the material ceases to release enough energy to drive the detonation wave forward. Reactions may continue to proceed behind the reaction zone, but the timescales for such reactions are harder to estimate. Typical explosive experiments are performed on parts with dimensions in the order of 1-10 cm. In this case, hydrodynamic confinement is expected to last for roughly a (is, based on a high-pressure sound speed of several cm/(is. Thus, chemical equilibrium is expected to be a valid assumption for nitromethane, based on the timescale separation between the 7 ns reaction zone and the (is timescale of confinement. The formation of solids, such as carbon, or the combustion of metallic fuels, such as Al, is believed to yield significantly longer timescales of reaction. 14 In this case chemical equilibrium is a rough, although useful, approximation to the state of matter of a detonating material. 2.1. Thermodynamic

Cycle Theory of

Detonation

Thermodynamic cycles are a useful way to understand energy release mechanisms. Detonation can be thought of as a cycle that transforms the unreacted explosive into stable product molecules at the Chapman-Jouget (CJ) state 15 (see Fig. 1). This is simply described as the slowest steady-state

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ChapmanJouget

Energy

O Unreacted

"O

Combustion in air

Volume Fig. 1. A thermodynamic picture of detonation: the unreacted material is compressed by the shock front and reaches the Chapman-Jouget point. From there adiabatic expansion occurs, leading to a high volume state. Finally, detonation products may mix in air and combust.

shock state that conserves mass, momentum, and energy. Similarly, the deflagration of a propellant converts the unreacted material into product molecules at constant enthalpy and pressure. The nature of the CJ state and other special thermodynamic states important to energetic materials is determined by the equation of state of the stable detonation products. A purely thermodynamic treatment of detonation ignores the important question of reaction timescales. The finite timescale of reaction leads to strong deviations in detonation velocities from values based on the Chapman-Jouget theory. 16 The kinetics of even simple molecules under high-pressure conditions is not well understood. High-pressure experiments promise to provide insight into chemical reactivity under extreme conditions. For instance, chemical equilibrium analysis of shocked hydrocarbons predicts the formation of condensed carbon and molecular hydrogen. 17 Similar mechanisms are at play when detonating energetic materials from condensed carbon. 11 Diamond anvil cell experiments have been used to determine the equation of state of methanol under high pressures. 18 We can then use a thermodynamic model to estimate the amount of methanol formed under detonation conditions. 19 Despite the importance of chemical kinetic rates, chemical equilibrium is often nearly achieved when energetic materials react. As discussed above, this is a useful working approximation, although it has not been established through direct measurement. Chemical equilibrium can be rapidly reached

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at the high temperatures (up to 6000 K) produced by detonating energetic materials. 20 We begin our discussion by examining thermodynamic cycle theory as applied to high explosive detonation. This is a current research topic because high explosives produce detonation products at extreme pressures and temperatures: up to 40 GPa and 6000 K. These conditions make it extremely difficult to probe chemical speciation. Relatively little is known about the equations of state under these conditions. Nonetheless, shock experiments on a wide range of materials have generated sufficient information to allow reliable thermodynamic modeling to proceed. One of the attractive features of thermodynamic modeling is that it requires very little information regarding the unreacted energetic material. The elemental composition, density, and heat of formation of the material are the only information needed. Since elemental composition is known once the material is specified, only density and heat of formation need to be predicted. The C J detonation theory 15 implies that the performance of an explosive is determined by thermodynamic states, the CJ state, and the connected expansion adiabat as illustrated in Fig. 1. The adiabatic expansion of the detonation products releases energy in the form of PVwoik and heat. Subsequent turbulent mixing of the detonation products in air surrounding the energetic material leads to combustion processes that release more energy. Thermochemical codes use thermodynamics to calculate states illustrated in Fig. 1, and thus predict explosive performance. The allowed thermodynamic states behind a shock are intersections of the Rayleigh line (expressing conservation of mass and momentum) and the shock Hugoniot (expressing conservation of energy). The CJ theory assumes that a stable detonation occurs when the Rayleigh line is tangent to the shock Hugoniot, as shown in Fig. 2. This point of tangency can be determined, assuming that the equation of state P = P{V, E) of the products is known. The chemical composition of the products changes with the thermodynamic state, so thermochemical codes must simultaneously solve for state variables and chemical concentrations. This problem is relatively straightforward, given that the equations of state (EOS) of the fluid and solid products are known.

2.2. High Pressure

Equations

of State

(EOS)

One of the most difficult parts of this problem is accurately describing the EOS of the fluid components. Because of its simplicity, the

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281

Fully reacted Hugoniot

P Rayleigh^^^y line ^ \ ^giChapman-Jouget state

O Unreacted state •

V Fig. 2. Allowed thermodynamic stated in detonation are constrained to the shock Hugoniot. Steady-state shock waves follow the Rayleigh line.

Becker-Kistiakowski-Wilson (BKW) 21 EOS is used in many practical energetic material applications. There have been a number of different parameter sets proposed for the BKW EOS. 22 Kury and Souers8 have critically reviewed these by comparing their predictions to a database of detonation tests. They concluded that BKW EOS does not adequately model the detonation of a copper-lined cylindrical charge. The BKWC parameter set 23 partially overcomes this deficiency through multivariate parameterization techniques. However, the BKWC parameter set is not reliable when applied to explosives very high in hydrogen content. It has long been recognized that validity of the BKW EOS is questionable. 12 This is particularly important when designing new materials that may have unusual elemental compositions. Efforts to develop better EOS have largely been based on the concept of model potentials. With model potentials, molecules interact via idealized spherical pair potentials. Statistical mechanics is then employed to calculate the EOS of the interacting mixture of effective spherical particles. Most often, the exponential-6 (exp-6) potential is used for the pair interactions: V{r) = ^ — - [ 6 e x p ( a - ar/rm)

-

a{rm/rf].

Here, r is the distance between particles, r m is the minimum of the potential well, e is the well depth, and a is the softness of the potential well. The JCZ3 (Jacobs-Cowperthwaite-Zwisler) EOS was the first successful model based on a pair potential that was applied to detonation. 24 This EOS was based on fitting Monte Carlo simulation data to an analytic

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functional form. Ross, Ree, and others successfully applied a soft-sphere EOS based on perturbation theory to detonation and shock problems. 11 ' 25 ' 26 Computational cost is a significant difficulty with EOS based on fluid perturbation theory. Brown 27 developed an analytic representation of the EOS which uses Chebyshev polynomials. The accuracy of the above EOS has been recently evaluated by Char let et al.12; these authors concluded that Ross's approach is the most reliable. More recently, Fried and Howard 28 have used a combination of integral equation theory and Monte Carlo simulations to generate a highly accurate EOS for the exp-6 fluid. The exp-6 model is not well suited to molecules with large dipole moments. Ree 10 has used a temperature-dependent well depth e(T) in the exp-6 potential to model polar fluids and fluid phase separations. Fried and Howard have developed an effective cluster model for HF. 2 9 The effective cluster model is valid for temperatures lower than the variable well-depth model, but it employs two more adjustable parameters than does the latter. Jones et al.30 have applied thermodynamic perturbation theory to polar detonation-product molecules. However, more progress needs to be made in the treatment of polar detonation-product molecules. Efforts have been made to develop EOS for detonation products based on direct Monte Carlo simulations instead of analytical approaches. 31 This approach is promising given the recent increases in computational capabilities. One of the greatest advantages of direct simulation is the ability to go beyond van der Waals 1-fluid theory, which approximately maps the equation of state of a mixture onto that of a single component fluid.32 In most cases, interactions between unlike molecules are treated with Lorentz-Berthelot combination rules. 33 These rules specify the interactions between unlike molecules as arithmetic or geometric averages of single molecule pair-interactions. Non-additive pair interactions have been used for N2 and 02- 2 6 The resulting N2 model accurately matches double-shock data, but is not accurate at lower temperatures and densities. 28 A combination of experiments on mixtures and theoretical developments is needed to develop reliable unlike-pair interaction potentials. The exp-6 potential has also proved successful in modeling chemical equilibrium at the high pressures and temperatures characteristic of detonation. However, in order to calibrate the parameters for such models, it is necessary to have experimental data for product molecules and mixtures of molecular species at high temperature and pressure. Static compression and sound-speed measurements provide important data for these models.

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Exp-6 potential models can be validated through several independent means. Fried and Howard 29 ' 34 have considered the shock Hugoniots of liquids and solids in the "decomposition regime" where thermochemical equilibrium is established. As an example of a typical thermochemical implementation, we consider the Cheetah thermochemical code. 28 Cheetah is used to predict detonation performance for solid and liquid explosives. Cheetah solves thermodynamic equations between product species to find chemical equilibrium for a given pressure and temperature. From these properties and elementary detonation theory the detonation velocity and other performance indicators are computed. Thermodynamic equilibrium is found by balancing chemical potentials, where the chemical potentials of condensed species are functions of only pressure and temperature, while the potentials of gaseous species also depend on concentrations. In order to solve for the chemical potentials, it is necessary to know the pressure-volume relations for species that are important products in detonation. It is also necessary to know these relations at the high pressures and temperatures that typically characterize the CJ state. Thus, there is a need for improved high-pressure equations of state for fluids, particularly for molecular fluid mixtures. In addition to the intermolecular potential, there is an intramolecular portion of the Helmholtz free energy. Cheetah uses a polyatomic model including electronic, vibrational, and rotational states. Such a model can be conveniently expressed in terms of the heat of formation, standard entropy, and constant-pressure heat capacity of each species. 2.3. Example

Applications

High-pressure nuorocarbons provide a good example of the equation of state modeling based on simple exp-6 interactions. Fluorocarbons are challenging because of the highly polar and associated nature of HF as well as the scarcity of experimental data on the EOS. A reactive fluorocarbon model requires parameters for hydrocarbons, fluorocarbon, F 2 , and HF. Fried and Howard 29 determined hydrocarbon parameters with data from shock and static experiments. High-pressure EOS measurements have not been performed on F 2 . They used exp-6 parameters for F 2 as estimated by Zerilli and Jones. 35 Chemical equilibrium modeling predicts that PTFE decomposes into a fluid phase composed mostly of CF 4 , and carbon in the diamond phase. This is in agreement with shock recovery experiments. 36 This is supports the validity of chemical equilibrium modeling for shocked organic materials.

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The traditional exp-6 model has difficulty treating "associated" fluids with strong attractive intermolecular interactions, for example, highly polar molecules. HF is known to strongly associate, 37 in the gaseous, liquid, and fluid phases. Fried and Howard 29 have determined a simple HF association model that matches both high- and low-pressure data. The model treats the associated fluid as a set of clusters. The motivation for the cluster model is to determine the simplest possible model that will match both the lowpressure static compression of supercritical HF and the shock Hugoniot of polyvinylidene fluoride (PVF2). The Fried-Howard model succeeds in this regard, although the description of individual cluster species has not been validated against experiments, due to the difficulty in measuring speciation at extreme conditions. Fried and Howard found that it is possible to match the shock Hugoniot of PVF2 without the association model, but the static compression requires an explicit treatment of association through clustered species. We show the calculated isotherms of HF in Fig. 3; the calculated shock Hugoniot of PVF2 is shown in Fig. 4. The calculations predict that PVF2 dissociates to HF and carbon. The HF model works equally well in the pressure range 0.01 to 75 GPa.

40 35 30 "J? 25 CL

BT 20 15

10 5 2

4

6

8

10

12

14

V (cc/gm) Fig. 3. Measurements of the isotherms of HF at 543, 553, 563, and 573 K (points) compared to results for the Fried-Howard model (lines).

Modeling the Reactions of Energetic Materials in the Condensed Phase

285

80

70

^ 60 CO Q.

o ^50 40

30 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 V (cc/gm) Fig. 4. Measurements of the shock Hugoniot of PVF2 (error bars) compared to results for the Fried-Howard model (line).

We now consider how the EOS described above predicts the detonation behavior of condensed explosives. The overdriven shock Hugoniot of an explosive is an appropriate EOS test, since it accesses a wide range of high pressures. Overdriven states lie on the shock Hugoniot at pressures above the CJ point (see Fig. 2). The Hugoniot of PETN (penta-erythritol tetranitrate) is shown in Fig. 5. Fried and Howard 34 have calculated the Hugoniot with the exp-6 model and also with the JCZS 38 product library. Good agreement with experiment is found. Since the exp-6 model is not calibrated to condensed explosives, such agreement is a strong indication of the validity of the chemical equilibrium approximation to detonation. Despite the many successes in the thermochemical modeling of energetic materials, there are several significant limitations. One such limitation is that real systems do not always obtain chemical equilibrium during the relatively short (ns-jus) timescales of detonation. When this occurs, quantities such as the energy of detonation and the detonation velocity are commonly predicted to be higher than experiment by a thermochemical calculation. Partial-equilibrium calculations 14 can overcome this problem. In partialequilibrium modeling, the concentrations of certain detonation products or

286

L. E. Fried, M. R. Manaa & J. P. Lewis

140

'

'

'

'

1 '

'

'

'

1 '

'

'

' 1

-

120 •

\

\

100 -*

\

80

\ \

-

"A

-

\

-

Q.

o ST

60 40 20

.

0 0.2

.

.

.

i

.

0.3

.

.

.

i

.

.

.

.

:

i

0.4 0.5 V (cc/gm)

0.6

0.7

Fig. 5. The shock Hugoniot of P E T N as calculated with exp-6 (solid line) and the JCZS library (dotted line) versus experiment (error bars).

reactants are held at fixed values. This assumes a priori knowledge of the timescales of reaction and detonation. Since this information is not usually known, partial-equilibrium modeling is not fully predictive. Chemical kinetic modeling is another possible way to treat detonation. There are several well-developed chemical kinetic mechanisms for highlystudied materials such as RDX and HMX. 39,40 Unfortunately, detailed chemical kinetic mechanisms are not available for high-pressure conditions. Some workers have applied simplified chemical kinetics to detonation processes.16 The primary difficulty in high-pressure chemical kinetic models is a lack of experimental data on speciation. First principles simulations, discussed below, have the potential to provide chemical kinetic information on fast processes. This information could then conceivably be applied to longer timescales and lower temperatures using high-pressure chemical kinetics. Finally, there are several issues to be addressed in determining the EOS of detonation products. While convenient, the exp-6 model does not adequately treat electrostatic interactions. In a condensed phase, effects such as dielectric screening and charge-induced dipoles need to be considered.

Modeling the Reactions of Energetic Materials in the Condensed

Phase

287

Molecular shape is also neglected in exp-6 models. While the small size of most detonation product molecules limits the importance of molecular shape, lower temperature conditions could yield long-chain molecules, where molecular shape is more important. Also, ionization may become dominant at high temperatures or for systems with strong acids and bases. Equation of state information for molecular ions and a successful statistical mechanical treatment at high pressure do not yet exist.

3. Atomistic Modeling of Condensed-Phase Reactions Chemical equilibrium methods provide useful predictions of macroscopic detonation processes resultant product molecules. However, no details of the atomistic mechanisms in the detonation are revealed. We now discuss condensed-phase detonation simulations using atomistic modeling techniques. Such simulations are quite useful for understanding the condensedphase reaction mechanisms on the microscopic level. Numerous experimental studies have investigated the atomistic details of HE decomposition by examining the net products after thermal (lowpressure) decomposition (for example, see Ref. 41). More specifically for RDX and HMX, the rate-limiting reaction is most likely NO2 dissociation and a plethora of final products in the decomposition process have been isolated (see the chapters by Brill and Behrens for further discussion). Several theoretical studies have also been reported on the energetics of gasphase decomposition pathways for HE materials using a variety of methods. For example, we point to work on RDX and HMX where both quantum chemistry 42 ' 43 and classical simulations of unimolecular dissociation44 were used. The gas-phase results provide much insight into the reaction pathways for isolated HE molecules; however, the absence of the condensed-phase environment is believed to strongly affect reaction pathways. Some of the key questions related to condensed-phase decomposition are: (1) How do the temperature and pressure affect the reaction pathways? (2) Are there temperature or pressure-induced phase-transitions which play a role in the reaction pathways that may occur? (3) What happens to the reaction profiles in a shock-induced detonation? These questions can be answered with condensed-phase simulations, but would require large-scale reactive chemical systems (thousands of atoms). Here we present very recent results of condensed-phase atomistic simulations, which are pushing the envelope towards reaching the required simulation goal.

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3.1. Molecular-Dynamics

with Bond-Order

Potentials

A novel approach for investigating reactions in the condensed-phase is to take advantage of the computational efficiency of empirical force fields. Although traditional analytical force fields cannot model the required variety of chemical reactions, transferable force field terms dependent on the bond order can be included to model bond-breaking/making mechanisms. These bond-order terms describe the bond-breaking/making mechanisms needed for simulating reactions. The bond order defines the strength of the bond between two atoms where larger numbers imply stronger bonds; it is a measure of the net number of bonds between a specific pair of atoms in a molecule. Bond-order potentials have been proposed early in the history of atomistic modeling; several methods exist, and each has a different prescription for defining the bond order between reactants and products. 45 Bond-order potentials have been successfully applied to simplified models of shocked energetic materials. 46 Recently, Goddard et al.47 have developed a method (called ReaxFF) for hydrocarbons and energetic materials. In the ReaxFF method, the central-force formalism is used and nonbonded interactions and Coulomb forces are included to yield smooth bond dissociations. Local perturbations to geometries such as bond angles, and torsional angles, are also added to describe complex molecules more accurately. The bond-order term, BOj, between a pair of atoms is of the form BO;7- = exp KJ'-Z u

+ exp Plirl

~

• exp

The parameters, p, correspond to the bond-order curves associated with different types of orbitals for each atom type (see Fig. 6 for the C-C case). The method yields heats of formations within 1-2 kcal/mol of experimental values. In addition, the energetics of dissociations have the same qualitative features as those obtained from quantum chemistry calculations. Recent results for ReaxFF applied to RDX demonstrate the capabilities of the model. Strachan et al.48 applied it to the initial stages of a shock-induced detonation of RDX. Parameters were developed from 40 different reactions and 1600 different equilibrated molecules, which represent potential product molecules along the possible reaction pathways. Two two-dimensional periodic slabs (each slab having 32 RDX molecules forming a perfect crystal) were impacted into each other at velocities of 2, 4, 6, 8, and lOkm/s. The results of these shock-induced detonation simulations are quite interesting. First, the products yielded from the simulations (shown in

Modeling the Reactions of Energetic Materials in the Condensed Phase

289

ReaxFF C-C bond order vs distance -Bond order -Sigma bond - Pi bond • Double pi bond

1.5

2

2.5

C-C bond distance (A)

Fig. 6.

Interatomic distance dependence of the carbon—carbon bond order.

80 NO,

RDX shock v. = 8 km/s imp

60

o | 40

& ex OH

20

NO

H

2° com HCN(5), CN

O

MONO

n

HCO

HCNO

UJ.

10

15

20

25

30

35

40

ILL

45 •

50

mass (g/mol) Fig. 7. Mass spectrum corresponding to u i m p = 8 k m / s at time t = 4ps. Population as a function of mass for all the molecules found up to mass 50 g/mol (all species with population larger than 3 are labeled).

Fig. 7) are products that are observed experimentally under slow heating (cook-off) conditions. 49 Although the experimental conditions of slow heating differ from the detonation condition used in the simulations, it is probable that many of the products will be similar in type albeit not necessarily

290

L. E. Fried, M. R. Manaa & J. P. Lewis

similar in quantity. Second, the primary reactions leading to NO2, OH, NO, and N2 occur at very early stages of the simulations. Additionally, as the impact velocity increases, N2 and OH become the dominant product species at short times. Finally, the simulations show that although the barrier for the pathways leading to NO2 and HONO is essentially the same, NO2 is the main product for low shock-velocities ( < 6 k m / s ) , in agreement with experimental work by Owens and Sharma. 50

3.2. Molecular-Dynamics with Mechanical Methods

Quantum

Bond-order potentials are fast and appear to give correct qualitative results; however, there are difficulties in using them. First, many parameters must be used to correctly model the reaction pathway. Second, many quantum chemistry calculations of small systems must be done to fit these parameters. For systems like RDX and HMX, which are experimentally better characterized than most HE materials, bond-order potentials appear to work reasonably well.48 For less-known systems, for example TATB, bond-order potentials may be less accurate. In TATB, the molecular crystal is formed through hydrogen-bonding interactions and the bond-order potentials must be modified to take such weak interactions into account. Recently, quantum mechanical methods have been applied to systems with up to 1000 atoms. This is due not only to advances in computer technology, but also improvements in algorithms. A wide range of approximations can also be made to yield a variety of methods; each able to address a different range of questions based on the accuracy of the method chosen. We now discuss a range of quantum mechanical based methods used to answer specific questions regarding shock-induced detonation conditions. Atomistic simulations have recently been performed on condensedphase HMX (l,3,5,7-tetranitro-l,3,5,7-tetraazacyclooctane). This material is widely used as an ingredient in various explosives and propellants. A molecular solid at standard state, it has four known polymorphs. <5-HMX is believed to be the most highly reactive polymorph. In fact, /3-HMX often transforms into 5-HMX before reacting violently.51 In a recent study, Manaa et al.20 have conducted a quantum-based molecular dynamics simulation of the chemistry of HMX under extreme conditions, similar to those encountered at the CJ detonation state. They studied the reactivity of dense (1.9g/cm 3 ) fluid HMX at 3500 K for reaction times up

Modeling the Reactions of Energetic Materials in the Condensed

Phase

291

to 55 ps, using the self-consistent charge density-functional tight-binding (SCC-DFTB) method. Stable product molecules are formed very rapidly (in a less than one ps) in these simulations. Plots of chemical speciation, however, indicate a time greater than 100 ps is needed to reach chemical equilibrium. Reactions occur very rapidly in these simulations because the system is "pre-heated" to 3500 K. In a detonation, on the other hand, a temperature close to 3500 K would only be found after stable product molecules had been formed. The initial temperature of unreacted nitromethane after being shocked has been estimated to be 1800 K. 13 HMX likely has a similar initial temperature. Nonetheless, the simulations of Manaa et al. provide useful insight into the chemistry of dense, hot energetic materials. They are a useful complement to more traditional gas-phase calculations. There are numerous experimental characterizations at low temperatures (i.e. < 1000 K, well below detonation temperature) of the decomposition products of condensed-phase HMX. 41 ' 52 These studies tend to identify final gas products (such as H2O, N 2 , H 2 , CO, CO2, etc.) from the surface burn, and the authors aspire to establish a global decomposition mechanism. However, similar experimental observations at detonation conditions (temperatures 2000-5000 K, and pressure 10-30 GPa) have not been realized to date. Computer simulations provide the best access to the short timescale processes occurring in these regions of extreme conditions of pressure and temperature. 53 In particular, simulations employing many-body potentials, 46 ' 54 or tight-binding models have emerged as viable computational tools; the latter has been successfully demonstrated in the studies of shocked hydrocarbons. 55 Lewis et al.56 calculated four possible decomposition pathways of the a-HMX polymorph: N - N 0 2 bond dissociation, HONO elimination, C-N bond scission, and the concerted ring fission. Based on the energetics, the author determined that N - N 0 2 dissociation was the initial mechanism of decomposition in the gas phase, while they proposed HONO elimination and C-N bond scission to be favorable in the condensed phase. The more recent study of Chakraborty et al.40 using the density-functional theory (DFT) with. B3LYP Junctionals, reported detailed decomposition pathways of the /3-HMX, the stable polymorph at room temperature. It was concluded that consecutive HONO elimination (4HONO) and subsequent decomposition into HCN, OH and NO are energetically the most favorable pathways in the gas phase. The results also showed that the formation of C H 2 0 and N 2 0 could occur preferably from secondary decomposition of methylenenitramine.

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L. E. Fried, M. R. Manaa & J. P. Lewis

The computational approach employed by Manaa et al20 to simulate the condensed-phase chemical reactivity of HMX is based on implementing the SCC-DFTB scheme. 57 This is an extension of the standard tight-binding approach in the context of DFT that describes total energies, atomic forces, and charge transfer in a self-consistent manner. The initial condition of the simulation included six HMX molecules, corresponding to a single unit cell of the S phase, with a total of 168 atoms. The density was 1.9g/cm 3 and the temperature 3500 K in the simulations. These thermodynamic quantities place the simulation in the neighborhood of the CJ state of £-HMX (3800 K, 2.0 g/cm 3 ) as predicted through thermochemical calculations. The closest experimental condition corresponding to this simulation would be a sample of HMX, which is suddenly heated under constant volume conditions, such as in a diamond anvil cell. A molecular dynamics simulation was conducted at constant volume and constant temperature. Periodic boundary conditions, whereby a particle exiting the super cell on one side is reintroduced on the opposite side with the same velocity, were imposed. Under the simulation conditions the HMX was in a highly-reactive dense fluid. There are important differences between the dense fluid (supercritical) phase and the solid phase, which is stable at standard conditions. Namely, the dense fluid phase cannot accommodate long-lived voids, bubbles, or other static defects. On the contrary, numerous fluctuations in the local environment occur within a timescale of tens of femtoseconds (fs). The fast reactivity of the dense fluid phase and the short spatial coherence length make it well suited for molecular dynamics study with a finite system for a limited period of time. Under the simulation conditions chemical reactions occurred within 50 fs. Stable molecular species were formed in less than one ps. Figure 8 displays the product formation of H2O, N2, CO2, and CO. The concentration, C(i), is represented by the actual number of product molecules formed at time t. Each point on the graphs (open circles) represents an average over a 250 fs interval. The number of the molecules in the simulation was sufficient to capture clear trends in the chemical composition of the species studied. It is not surprising that the rate of H2O formation is much faster than that of N2. Fewer reaction steps are required to produce a triatomic species like water, while the formation of N2 involves a much more complicated mechanism. 39 Further, the formation of water starts around 0.5 ps and seems to have reached a steady state at 10 ps, with oscillatory behavior of decomposition and formation clearly visible. The formation of N 2 , on the other hand, starts around 1.5 ps and is still progressing

Modeling the Reactions

0

10

20

30

t(ps)

of Energetic Materials in the Condensed Phase

40

50

293

60

t(ps)

u

Fig. 8. Product particle-number formations as a function of time of H2O, N2, CO2, and CO.

(the slope of the graph is slightly positive) after 55 ps of simulation time, albeit at small variation. Due to the lack of high-pressure experimental reaction rate data for HMX and other explosives with which to compare, we produce in Fig. 9 a comparison of dominant species formation for decomposing HMX obtained from an entirely different theoretical approach. The concentration of species at chemical equilibrium can be estimated through thermodynamic calculations with the Cheetah thermochemical code. 28 ' 58 As shown in Fig. 9, the results of the MD simulation compare very well with the formation of H2O, N 2 , and HNCO predicted by the Cheetah code was predicted by the thermochemical calculations. The relative concentration of CO and CO2, however, is reversed, possibly due to the limited time

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L. E. Fried, M. R. Manaa & J. P. Lewis

Species Fig. 9. Comparison of relative composition of dominant species found in the MD simulation and in a thermodynamic calculation.

of the simulation. In addition, Cheetah predicts that carbon in the diamond phase is in equilibrium with the other species at a concentration of 4.9 mol/kg HMX. No condensed carbon was observed in the simulation. Several other products and intermediates with lower concentrations, common to the two methods, have also been identified. These include HCN, NH 3 , N 2 0 , CH3OH, and CH2O. It is hoped that a comparison between the two vastly different approaches can be established at much longer simulation times. In the future, the product-molecule set of the thermochemical code could be expanded with important species determined from ab initio-based simulations. It should also be noted that the accuracy of DFT calculations for chemistry under extreme conditions needs further experimental validation. One expects more CO2 than CO as final products as predicted by Cheetah (Fig. 9), since disproportionation of CO to condensed C + CO2 is energetically favorable. The results displayed in Fig. 8 show that at simulation time of 40 ps the system is still in the second stage of reaction chemistry. At this stage the CO concentration is rising and has not yet

Modeling the Reactions of Energetic Materials in the Condensed Phase

295

undergone the water gas shift reaction (CO + H 2 0 —> C 0 2 + H 2 ) conversion. Interestingly, this shift seems to occur at around 50 ps in the simulation, with CO2 molecules being formed while the CO concentration is correspondingly diminishing. Although the simulation sheds light on the chemistry of HMX under extreme conditions, there are methodological shortcomings that need to be overcome in the future. The demanding computational requirements of the present method limits its applicability to short times and high-temperature conditions. A second issue is that the SCC-DFTB method is not as accurate as high-level ab initio methods. Nonetheless, the present approach could still be considered as a promising direction for future research on the chemistry of energetic materials. 3.3. Quantifying

the Energetics

of Reaction

Pathways

In condensed-phase reactions of energetic materials, the initial problem is to identify particular reaction pathways. Once particular reactions pathways are known, the next step is to accurately quantify the energy profile of the decomposition mechanism. Semi-empirical quantum mechanical methods or empirical force fields yield free energy barriers that are accurate to within roughly 15 kcal/mol. This is sufficiently accurate for very high-temperature applications, as described above, but higher accuracy is needed to describe reaction rates at temperatures characteristic of slow thermal decomposition (600K). It is possible, in the case of isolated molecules, to investigate the importance of excited electronic states using sophisticated electron correlation techniques. 59 But such methods are not applicable to condensed-phase reactions, where often 100+ atoms are required to accurately model the environmental effects from the crystal surrounding the reaction of interest. DFT calculations with extended basis sets should be the method of choice, as such methods can accurately and efficiently model these relatively large condensed-phase simulations. 6,60 The prevalence of DFT for condensedphase simulations is based on the favorable N 3 scaling with the number of basis functions, and the ability to formulate efficient integral evaluation routines with plane-wave basis functions. One of the more prevalent products of HMX decomposition is HONO. Formation of HONO can likely occur by the unimolecular transfer of a hydrogen atom from a CH 2 group to an N 0 2 group. 61 However, the molecular packing in HMX would seem to suggest that hydrogen transfer could

296

L. E. Fried, M. R. Manaa & J. P. Lewis 150.0

§

100.0

W> 50.0

%-*

it B

w 0.0

Reaction Coordinate (Arbitrary Units) Fig. 10. Energy profiles of intermolecular hydrogen transfer along an arbitrary "path of least resistance" trajectory for the three pure polymorphic HMX phases (a, /3, and S).

occur between adjacent molecules; there is a very weak hydrogen-bondinglike interaction from the C-H of the CH2 group of one molecule to the O-atom of the NO2 group of its adjacent molecule. Lewis,62 using the ab initio tight-binding FIREBALL, 63 investigated the energetics of HONO formation in condensed-phase HMX, where intermolecular hydrogen transfer occurs. This work demonstrated that the energetics of the intermolecular hydrogen transfer (plotted in Fig. 10) follows the same trend as HMX shock sensitivity. It is well demonstrated that (5-HMX is more sensitive than /3-HMX and likely more sensitive than the transitional a-HMX. Lewis concludes that the energetic trend, and hence the sensitivity trend, is likely due to the densities; there is more empty volume for the reactions to proceed in <5-HMX (i.e., less intermolecular interactions due to crystal packing to hinder intermolecular hydrogen transfer). Furthermore, simulations by Lewis using umbrella sampling methodologies indicate that the free energy of the condensed-phase H-transfer reaction is ^ 5 kcal/mol higher than NO2 dissociation (the ratelimiting reaction). These results are comparable to gas-phase calculations for intramolecular HONO formation and NO2 dissociation.43 3.4. Electronic

Excitations

in Shocked

Explosives

All calculations discussed above assume that excited electronic states do not significantly contribute to the chemistry of detonating energetic materials.

Modeling the Reactions

of Energetic Materials in the Condensed Phase

297

In 1971, Williams 64 suggested that excited electronic states play a role in the initiation and propagation of detonation waves in explosives. Kuklja and Kunz 65 used quantum mechanical methods, in particular periodic HartreeFock calculations to investigate the electronic states in RDX with edge dislocation defects included in the simulation cell. It is proposed that such defects provide local sites for hot spots, which localize the energy of the impact wave and trigger chemical reactions. Kuklja and Kunz proposed that the edge dislocation defects in RDX introduce states in the gap, which produce electronic excitations or hot spots. The effect becomes more pronounced at higher pressures as the gap between the occupied and unoccupied states decreases, i.e., the excitations become more energetically favorable. Reed et al.6 considered band-gap lowering under uniaxial strain due to molecular defects and vacancies. They used a DFT molecular dynamics method with gradient-corrected exchange-correlation functionals (PW91 and PBE). Pseudopotentials were used with a plane-wave basis set. Simulations of all possible nearest-neighbor collisions at a shock front indicate that there is a band-gap lowering effect due to the molecular defects and vacancies. However, the band-gap is not lowered enough to produce a significant population of excited states in the crystal. Furthermore, dynamical effects are more significant than static effects, since relative molecular velocities in excess of 6 km/s are required to produce a significant thermal population of excited states. This work has helped to clarify the role of electronic excitations in shocked energetic materials. Excited electronic states are not accessible in perfect crystals under realistic pressures and temperatures, but may still be accessed through defects or other energy localization mechanisms. See the chapter by Bernstein for more discussion of the role of excited states in the gas phase.

4. Conclusions The ability to model chemical reactions in condensed-phase energetic materials is rapidly progressing. Chemical equilibrium modeling is a mature technique with some limitations. Progress in chemical equilibrium modeling continues, but is hampered by a lack of knowledge of condensed-phase speciation and equation of state. For instance, we still do not know the prevalence of ionic species under detonation conditions. A useful theory of the EOS of ionic and highly-polar molecular species needs to be developed.

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T h e role of unconventional molecular species in detonation needs to be investigated. Finally, the study of high-pressure chemical kinetics needs to develop further as a field. Atomistic modeling is much more computationally intensive t h a n chemical equilibrium or kinetic modeling, and is currently limited t o picosecond timescales. Nonetheless, this method promises t o yield the first reliable insights into the condensed-phase processes responsible for high explosive detonation. Further work is necessary to extend the timescales in atomistic simulations. T h e accuracy of D F T methods also needs to advance, either through improved functionals or higher-level approaches such as q u a n t u m Monte Carlo. Advanced empirical force fields may offer the ability to model the reactions of energetic materials for periods of many picoseconds. Recent work in implementing t h e r m o s t a t methods appropriate t o shocks 6 6 may promise to overcome timescale limitations in the non-equilibrium molecular dynamics method, and allow the reactions of energetic materials to be determined for u p to several nanoseconds.

References 1. L. E. Fried, M. R. Manaa, P. F. Pagoria and R. L. Simpson, Annu. Rev. Mater. Res. 3 1 , 291 (2001). 2. R. Bishop, D. Harradine, R. Flesner, S. Larsen and D. Bell, Ind. Eng. Chem. Res. 39, 1215 (2000); S. B. Hawthorne, A. J. M. Lagadec, D. Kalderis, A. V. Lilke and D. J. Miller, Environ. Sci. Technol. 34(15), 3224 (2000). 3. T. D. Sewell, R. Menikoff, D. Bedrov and G. D. Smith, J. Chem. Phys. 119 (14), 7417 (2003). 4. I. P. H. Do and D. J. Benson, Int. J. Plasticity 17(4), 641 (2001); M. R. Baer, Thermochim. Acta 384(1-2), 351 (2002). 5. Y. B. Zel'dovich and Y. P. Raiser, Physics of Shockwaves and High Temperature Hydrodynamics Phenomena (Academic Press, New York, 1966). 6. E. Reed, J. D. Joannopoulos and L. Fried, Phys. Rev. B62(24), 16500 (2000). 7. M. Kuklja, E. Stephanovich and A. B. Kunz, J. Phys. Chem. 112(7), 3417 (2000); M. M. Kuklja, Appl. Phys. A76, 359 (2003). 8. P. C. Souers and J. W. Kury, Propellants, Explosives, Pyrotechnics 18, 175 (1993). 9. M. Cowperthwaite and W. H. Zwisler, J. Phys. Chem. 86, 813 (1982); W. C. Davis and C. Fauquignon, J. De Physique IV5(C4), 3 (1995). 10. F. H. Ree, J. Chem. Phys. 84, 5845 (1986). 11. M. van Thiel and F. H. Ree, J. Appl. Phys. 62(5), 1761 (1987). 12. F. Charlet, M. L. Turkel, J. F. Danel and L. Kazandjian, J. Appl. Phys. 84(8), 4227 (1998). 13. N. C. Blais, R. Engelke and S. A. Sheffield, J. Phys. Chem. A101, 8285 (1997).

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14. M. Cowperthwaite, presented at the 10th International Detonation Symposium, Boston, Massachusetts, 1993 (unpublished). 15. W. Fickett and W. C. Davis, Detonation (University of California Press, Berkeley, 1979). 16. W. M. Howard, L. E. Fried and P. C. Souers, presented at the 11th International Symposium on Detonation, Snowmass, CO, 1998 (unpublished). 17. F. H. Ree, J. Chem. Phys. 70(2), 974 (1979). 18. J. M. Zaug, L. E. Fried, E. H. Abramson, D. W. Hansen, J. C. Crowhurst and W. M. Howard, High-Pressure Research 23(3), 229 (2003). 19. J. M. Zaug, E. H. Abramson, D. W. Hansen, L. E. Fried, W. M. Howard, G. S. Lee and P. F. Pagoria, presented at the 12th International Detonation Symposium, San Diego, CA, 2002 (unpublished). 20. M. R. Manaa, L. E. Fried, C. F. Melius, M. Elstner and T. Frauenheim, J. Phys. Chem. A106, 9024 (2002). 21. G. B. Kistiakowsky and E. B. Wilson, Report No. OSRD-69, 1941. 22. M. Finger, E. Lee, F. H. Helm, B. Hayes, H. Hornig, R. McGuire, M. Kahara and M. Guidry, presented at the 6th Symposium (International) on Detonation, Coronado, CA, 1976 (unpublished); C. L. Mader, Numerical Modeling of Detonations (University of California Press, Berkeley, CA, 1979); S. A. Gubin, V. V. Odintsov and V. I. Pepekin, Sov. J. Chem. Phys. 3(5), 1152 (1985); M. L. Hobbs and M. R. Baer, presented at the 10th International Detonation Symposium, Boston, MA, 1993 (unpublished). 23. L. E. Fried and P. C. Souers, Propellants, Explosives, Pyrotechnics 2 1 , 215 (1996). 24. M. Cowperthwaite and W. H. Zwisler, presented at the 6th Detonation Symposium, 1976 (unpublished). 25. M. Ross and F. H. Ree, J. Chem. Phys. 73(12), 6146 (1980); F. H. Ree, J. Chem. Phys. 81(3), 1251 (1984). 26. M. van Thiel and F. H. Ree, J. Chem. Phys. 104, 5019 (1996). 27. W. Byers Brown, J. Chem. Phys. 87, 566 (1987). 28. L. E. Fried and W. M. Howard, J. Chem. Phys. 109(17), 7338 (1998). 29. L. E. Fried and W. M. Howard, J. Chem. Phys. 110(24), 12023 (1999). 30. H. D. Jones, presented at the Shock Compression of Condensed Matter, 2001, Atlanta, Georgia, 2001 (unpublished). 31. M. S. Shaw, J. Chem. Phys. 94(11), 7550 (1991); J. K. Brennan and B. M. Rice, Phys. Rev. E66(2), 021105 (2002). 32. T. W. Leland, J. S. Rowlinson and G. A. Sather, Trans. Faraday Soc. 64, 1447 (1947). 33. T. M. Reed and K. E. Gubbins, Statistical Mechanics (McGraw-Hill, New York, 1973). 34. L. E. Fried, W. M. Howard and P. C. Souers, presented at the 12th Symposium (International) on Detonation, San Diego, CA, 2002 (unpublished). 35. F. J. Zerilli and H. D. Jones, presented at the High Pressure Science and Technology, New York, NY, 1993 (unpublished). 36. C. E. Morris, J. N. Fritz and R. G. McQueen, J. Chem. Phys. 80(10), 5203 (1984).

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37. M. L. Klein and I. R. McDonald, J. Chem. Phys. 7 1 , 298 (1979). 38. M. L. Hobbs, M. R. Baer and B. C. McGee, Propellants, Explosives, Pyrotechnics 24(5), 269 (1999). 39. C. F. Melius, in Chemistry and Physics of Energetic Materials, ed. D. N. Bulusu (Kluwer, Dordercht, 1990). 40. D. Chakraborty, R. P. Muller, S. Dasgupta and W. A. Goddard III, J. Phys. Chem. A105, 1302 (2001). 41. R. Behrens and S. Bulusu, J. Phys. Chem. 95, 5838 (1991). 42. C. Wu and L. Fried, J. Phys. Chem. A101(46), 8675 (1997); S. Zhang and T. Truong, J. Phys. Chem. A 1 0 5 ( l l ) , 2427 (2001); J. Lewis, K. Glaesemann, K. VanOpdorp and G. Voth, J. Phys. Chem. A104(48) 11384 (2000). 43. D. Chakraborty, R. Muller, S. Dasgupta and I. W. A. Goddard, J. Phys. Chem. A105(8), 1302 (2001). 44. T. Sewell and D. Thompson, J. Phys. Chem. 95(16), 6228 (1991); C. Chambers and D. Thompson, J. Phys. Chem. 99(43), 15881 (1995). 45. H. S. Johnston, Adv. Chem. Phys. 3, 131 (1960); H. S. Johnston and C. Parr, J. Am. Chem. Soc. 85, 2544 (1963); C. M. Landis, T. Cleveland and T. K. Firman, J. Am. Chem. Soc. 120, 2641 (1998). 46. C. T. White, D. H. Robertson, M. L. Elert and D. W. Brenner, in Microscopic Simulations of Complex Hydrodynamic Phenomena, eds. M. Mareschal and B. L. Holian (Plenum Press, New York, 1992), pp. I l l ; D. W. Brenner, D. H. Robertson, M. L. Elert and C. T. White, Phys. Rev. Lett. 70, 2174 (1993). 47. A. T. C. v. Duin, S. Dasgupta, F. Lorant and I. W. A. Goddard, J. Phys. Chem. 105, 9396 (2001). 48. A. Strachan, A. C. T. v. Duin, D. Chakraborty, S. Dasgupta and I. W. A. Goddard, Phys. Rev. Lett. 9 1 , 098301 (2003). 49. R. Behrens, J. Phys. Chem. 94, 6706 (1990); R. Behrens, J. Phys. Chem. 95, 5838 (1991). 50. F. J. Owens and J. Sharma, J. Appl. Phys. 5 1 , 1494 (1979). 51. A. G. Landers and T. B. Brill, J. Phys. Chem. 84, 3573 (1980). 52. B. Suryanarayana, R. J. Graybush and J. R. Autera, Chem. Ind. London 52, 2177 (1967); S. Bulusu, T. Axenrod and G. W. A. Milne, Org. Mass. Spectrom. 3, 13 (1970); M. Farber and R. D. Srivastava, presented at the 16th JANNA Combus. Meeting, 1979 (unpublished); C. V. Morgan and R. A. Bayer, Combust. Flame 36, 99 (1979); R. A. Fifer, in Progress in Astronautics and Aeronautics, Vol. 90, eds. K. K. Kuo and M. Summerfield (AIAA Inc., New York, 1984), pp. 177; R. Behrens, Int. J. Chem. Kinet. 22, 135 (1990); J. C. Oxley, A. B. Kooh, R. Szekers and W. Zhang, J. Phys. Chem. 98, 7004 (1994); T. Brill, P. Gongwer and G. Williams, J. Phys. Chem. 98(47), 12242 (1994); T. B. Brill, J. Propul. Power 11, 740 (1995); C.-J. Tang, Y. J. Lee, G. Kudva and T. A. Litzinger, Combust. Flame 117, 170 (1999). 53. P. Politzer and S. Boyd, Struct. Chem. 13, 105 (2002). 54. M. L. Elert, S. V. Zybin and C. T. White, J. Chem. Phys. 118, 9795 (2003).

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55. S. R. Bickham, J. D. Kress and L. A. Collins, J. Chem. Phys. 112, 9695 (2000); J. D. Kress, S. R. Bickham, L. A. Collins, B. L. Holian and S. Goedecker, Phys. Rev. Lett. 83, 3896 (1999). 56. J. Lewis, T. Sewell, R. Evans and G. Voth, J. Phys. Chem. B104(5), 1009 (2000). 57. M. Elstner, D. Pore'zag, G. Jungnickel, J. Eisner, M. Hauk, T. Frauenheim, S. Suhai and G. Seifert, Phys. Rev. B58, 7260 (1998). 58. L. E. Fried and W. M. Howard, Phys. Rev. B61(13), 8734 (2000). 59. M. R. Manna and L. Fried, J. Phys. Chem. A102(48), 9884 (1998); C. J. Wu, L. H. Yang, L. E. Fried, J. Quennevill and T. J. Martinez, Phys. Rev. B67(23), 235101 (2003). 60. C. J. Wu and L. E. Fried, J. Phys. Chem. A104, 6447 (2000). 61. B. Rice, G. Adams, M. Page and D. Thompson, J. Phys. Chem. 99(14), 5016 (1995). 62. J. Lewis, Chem. Phys. Lett. 371, 588 (2003). 63. S. D. Shellman, J. P. Lewis, K. R. Glaesemann, K. Sikorski and G. A. Voth, J. Comp. Phys. 188(1), 1 (2003). 64. F. Williams, Adv. Chem. Phys. 21, 289 (1971). 65. M. M. Kuklja and A. B. Kunz, J. Appl. Phys. 87, 2215 (2000). 66. E. J. Reed, J. D. Joannopoulos and L. E. Fried, Phys. Rev. Lett. 90(23), 235503 (2003); J. B. Maillet, M. Mareschal, L. Soulard, R. Ravelo, P. S. Lomdahl, T. C. Germann and B. L. Holian, Phys. Rev. E63(l), 016121 (2001).

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C H A P T E R 10 MULTI-PHONON UP-PUMPING IN E N E R G E T I C MATERIALS Dana D. Dlott School of Chemical Sciences University of Illinois at Urbana- Champaign 600 S. Mathews Ave. Urbana, IL 61801, USA

Contents 1. Introduction 2. Theory of Up-Pumping 3. Up-Pumping in Experiments and Simulations 4. Up-Pumping in Low Velocity Impact Initiation 5. Up-Pumping in Shock Initiation and Detonation 6. Summary and Conclusions Acknowledgments References

303 305 314 320 323 326 329 329

1. Introduction Many useful energetic materials, PETN, TATB, TNT, RDX, HMX and Cl-20 to name a few,1 are molecular crystals. Molecular crystals are defined by two distinct types of interatomic forces.2'3 Covalent bonding between atoms comprising individual molecules is the stronger interaction. Stretching these covalent bonds gives rise to excitations termed intramolecular vibrations or simply vibrations.4 Non-covalent bonding between atoms of adjacent molecules is the weaker interaction. Stretching the intermolecular bonds gives rise to collective delocalized excitations termed phonons.4 When looking at mechanical perturbations such as low-velocity impact (LVI) or shock compression, these dual interactions naturally lead to processes with two distinctly identifiable steps, either energy transfer from vibrations to 303

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phonons termed vibrational relaxation (VR), or energy transfer from hot phonons to vibrations, termed multiphonon up-pumping.5~7 Initiation and detonation of energetic materials are difficult problems due to the broad range of timescales (picoseconds to microseconds or more) and length scales (nanometers to millimeters or more) and the intimate coupling between chemical reactivity and mechanics. Mechanical engineers and physicists often try to understand these problems in purely mechanical terms. In this view, detonation is a fluid mechanics problem 8 and chemistry is merely a simple source of heat and volume expansion. Chemists, on the other hand, often try to understand these problems in purely chemical terms. In this view, high explosives are merely a complicated problem in chemical kinetics. However, neither of these isolated approaches have led to unified models that would allow us to understand and predict from first principles the sensitivity and detonation properties of an energetic material, knowing only its composition. A robust model for these processes, soundly based from first principles, must necessarily combine three ingredients: continuum mechanics, chemistry and quantum mechanics. 7 The multiphonon up-pumping concept is a promising way of unifying these three crucial concepts. In this chapter, I will discuss two intriguing aspects that follow from the up-pumping concept. Since low-velocity impacts do not produce enough heat to ignite bulk energetic materials, 9 the sensitivity of these materials is critically dependent on mechanisms that cause energy to become localized in hot spots. 10 So one interesting aspect is whether up-pumping can lead to the localization of impact energy at shear bands, crack surfaces or defect sites. Perhaps the most interesting question regarding multiphonon uppumping is whether up-pumping can result in novel chemical processes that are not observed with ordinary heat. The most likely places to look for such effects are when up-pumping rates are very fast, delivering chemicallysignificant amounts of energies to individual molecules faster than 10 ps or so. Studies of energetic material thermochemistry 11 often see chemistries that are a sensitive function of heating rate dT/dt, where typical heating rates are 10° to 106 K/s, but that is not what I mean here. This kind of heating rate dependence comes from the fact that the overall chemistry involves a large number of sequential and parallel reaction steps. The initial step always involves breaking the weakest chemical bond, and this does not change with heating rate in the cited range. However, the rate of every step has a different temperature dependence, so changing the heating rate can

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significantly modify the overall chemistry. With up-pumping it is possible to have such immense heating rates, say 1014 K/s (e.g. 1000 K in 10 ps), that chemical reactions may no longer occur in thermal equilibrium, suggesting the possibility that the weakest bond rule might be disobeyed. One might conclude this would have a drastic effect on the overall chemistry, but in the hot simmering stew characteristic of energetic material chemistry, there might in fact be little effect on the overall chemistry of a different first step. What is clear is that the first step in energetic material initiation can have an enormous effect on the impact or shock sensitivity of the material. The organization of this chapter is as follows. First the basics of the theory of up-pumping are discussed. The theory will at times be illustrated by a specific example, phonon pumping of a NO2 group of a nitrocarbon molecule in order to break a N-NO2 bond. Next, the existing experimental data and computer simulation data will be summarized. Then the applications of the up-pumping concept in areas relevant to energetic materials, involving LVI and the effects of initiation and detonation shock waves, will be discussed. For readers with further interest in more technical details, additional information about fast processes in energetic materials can be found in my chapter 7 of Politzer's book, Energetic Materials: Initiation, Decomposition and Combustion. 2. Theory of Up-Pumping An isolated (nonlinear) molecule with N atoms has 3N degrees-of-freedom. Since this isolated molecule can translate in three dimensions and it can rotate about three different principle axes, there are a total of 3iV — 6 normal modes of vibration per molecule.4 In a crystal the translations and rotations become hindered oscillations, leading to 6 phonon branches per molecule in the unit cell. We write the Hamiltonian for mechanical excitations of a crystal of these molecules in the following way, H = Hvib + Hph + Hint

(la)

H = ffvib + -ffph + #ph-ph + -ffvib-vib + -Hph-vib-

(lb)

Now I will try to describe in words and pictures what these Hamiltonians mean. The terms "perhaps" and "typical" will appear repeatedly because I am trying to make qualified general statements about a wide variety of structures ranging from e.g. nitromethane (NM) to HMX to octanitrocubane. The first two terms in Eq. (la), H°ih and H°h, describe zero-order non-interacting states of the harmonic oscillator Hamiltonian, termed

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"phonons" and the "vibrations" . 4 The zero-order phonons involve collective (i.e. delocalized) hindered translation and hindered rotation (libration) of rigid molecules in a crystal. The zero-order vibration states involve periodic molecular deformations of individual molecules. The Hmt term results from anharmonic corrections to the potential energy surface, which gives rise to a variety of interactions among and within the zero-order states. Usually Hlnt is expressed as a series expansion in powers of the normal coordinates \|/i. 4 ' 5 The nth term in this expansion is,

y(n) = 1 y -

a"V(W) Mo

In Eq. (2), V({\|/}) represents the potential energy surface for a molecular crystal with a set of normal coordinates {^}, and the partial derivative is evaluated at the equilibrium position {\|/}o- In what follows, we will use a shorthand where q represents a phonon coordinate, Q represents a vibrational coordinate, anharmonic terms are abbreviated QQq, Qqqq, etc., and matrix elements of these terms are abbreviated (V C T ), etc. 12 ' 13 The leading terms in Eq. (2) are cubic anharmonic couplings (n = 3), which are dominant in lattice-dynamic expressions for thermal expansion and the Gruneisen coefficient.4 The Hamiltonian Equation (la) can be rediagonalized in what can be called a "quasiharmonic" picture, 4 to give a new set of zero-order states that can interact dynamically with each other. Confusingly, these anharmonic excitations represented by the new Hamiltonian Hvlb + Hpn will still be called phonons and vibrations, with the understanding that these are much better representations of the real phonons and vibrations than the eigenfunctions of the harmonic Hamiltonian H°ib + H®h. The new (or "real") phonons acquire a bit of vibration character. When molecules librate or translate, they deform a small amount. The new vibrations acquire a bit of phonon character. When a molecule vibrates, it shakes up the nearby molecules a small amount allowing vibrational energy to be (inefficiently) transferred from one molecule to its neighbors. Since the potential energy surface is anharmonic, very high levels of excitation can lead to dissociation. High levels of phonon excitation can break up the crystal lattice, leading to cracking or sublimation. High levels of vibrational excitation can cause covalent chemical bonds to break. Whether an excitation is viewed as localized or collective depends on the magnitude of the interaction between an excited molecule and its neighbors. Strictly speaking, derealization hinges on the ratio of this

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intermolecular interaction to the magnitudes of disorder-causing processes such as static structural inhomogeneity and thermal fluctuations. A dispersion curve is a function that relates energy and wavelength.4 The energy difference between the shortest wavelength, in which the characteristic motion alternates phase on every lattice site, and the longest wavelength where the characteristic motion is in phase over the entire crystal, is termed the bandwidth. If the bandwidth is close to zero, an excitation on one molecule has negligible effect on adjacent molecules and the excitation is localized. If the bandwidth is significant (relative to disorder-causing processes), then the motions of nearby molecules are strongly coupled and the excitation is collective or delocalized. Dispersion curves can be accurately measured using inelastic coherent neutron scattering. A less powerful but much more practical method is polarization-dependent vibrational (IR or Raman) spectroscopy. The frequency difference between differently polarized transitions of a particular vibration can be a crude but effective measure of the bandwidth. 4 Phonons, typically in the 0-200 c m - 1 range, have typical bandwidths of 50-100 c m - 1 , and these are clearly collective excitations. The higher frequency fundamental excitations such as C-H or N-H stretching, skeletal C-C stretching, NO2 symmetric and asymmetric stretching, NO2 stretching, C-H bending and so forth, typically in the range of 800-3500 cm" 1 , have typical bandwidths of 0-10 c m - 1 , and we view these vibrations as mostly localized on individual molecules. The range of perhaps 100-800 c m - 1 is a gray area that is important. 5 Some of these vibrations have strong interactions with neighboring molecules and correspondingly significant bandwidths (perhaps 20-100cm - 1 ). These cannot be considered as isolated vibrations because the intermolecular interactions are significant, and they cannot be considered as phonons because they involve large amplitude motions of the molecular skeleton. Some pertinent examples would include N 0 2 wagging and NO2 torsion, and twisting of an RDX 6-member ring. The lower frequency vibrations with significant bandwidths are termed doorway modes or doorway vibrations. The doorway vibrations are well-coupled both to the motions of nearby molecules and to the intramolecular vibrations, so they provide an efficient pathway for energy outside a molecule, in the form of phonons generated by impact, to move inside a molecule and excite its vibrations. 5 An energy level diagram depicting typical molecular crystal states is shown in Fig. 1(a). The lowest energy states are the phonon fundamentals, which run continuously from zero to a cut-off frequency 6 D , the Debye frequency, typically 100-200 c m - 1 . Also depicted in Fig. 1(a) is a continuum

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(a) vibrational fundamentals phonon I I overtones phonon fundamentals

c

0

chemically _ significant energy

I III

®D

energy (b)

a>

IVR region 1

(c)

(

c:

©D

Fig. 1. (a) Energy levels of a molecular solid. The phonon fundamental cut-off frequency or "Debye frequency" is denoted as B p , In the intramolecular vibrational redistribution (IVR) region, the density of vibrational combination and overtone states is large enough to facilitate fast energy transfer among vibrational levels. Usually the region of chemically-significant energies lies above the IVR threshold, (b) and (c) Two scenarios for phonon up-pumping that causes chemical bonds to break. In (b), a series of phonons successively pump energy up a vibrational ladder, starting with doorway vibrations (lowest energy vibrational fundamentals). When an energy above the IVR threshold is reached, the vibrational energy becomes statistically randomized among all modes. When chemically-significant energies are attained, the weakest chemical bond breaks. In (c), a highly excited coherent phonon state pumps energy directly into the chemical bond to which it is most strongly coupled, causing this bond — not necessarily the weakest bond — to break.

of states running to much higher energy (up to near the sublimation energy) representing phonon overtone and combination excitations. The lowest frequency vibrations are potential doorway modes. One way to identify a potential doorway vibration is to note the gap between the vibrational frequency and 6 D - For instance in NM, 14,15 6 D ~ 160cm - 1 and the lowest energy vibration is 480 c m - 1 . This sizeable gap indicates poor mixing between phonons and lower frequency vibrations, so NM translates or librates as an approximately rigid body. In naphthalene this gap is small.5 The top of the phonon band is ~ 1 4 0 c m _ 1 and the lowest frequency vibration, the butterfly ring deformation, is at 175 c m - 1 . Two other naphthalene vibrations, skeletal twisting modes at 212 cm""1 and 360 c m - 1 can be

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identified as likely doorway vibrations. With larger non-rigid molecules, one or more of the lowest frequency vibrations, typically torsions, nitro rocking or skeletal bending modes, actually lie below 0 D - In this case we say a doorway vibration is amalgamated in the phonon band. This means the non-rigid molecule cannot translate or librate without undergoing considerable deformation. In HMX for example, calculations indicate there are 10 low-frequency vibrations below 160cm - 1 . 1 6 The highest energies of the 3N — 6 vibrational fundamentals are C-H and N-H stretching modes in the 2800-3500 c m - 1 range. The mid-range vibrations, typically 800-1700 c m - 1 have the longest vibrational lifetimes and the slowest VR processes. 13 ' 17 There are a vast number of combination and overtones of the higher, mid-range and doorway vibrations, as shown in Fig. 1(a), whose state density increases approximately exponentially with increasing energy. After the rediagonalization to quasiharmonic states, the remaining (last three) terms in Eq. (lb) can be used to describe dynamical processes that result in energy transfer among phonons, among vibrations, or between vibrations and phonons. There is a sizeable literature that shows how these three terms can be used to describe a variety of relaxation processes, where non-equilibrium populations of vibrations or phonons created by sudden perturbations relax back to equilibrium. 4,18 The ffph-Ph term causes phonon-phonon scattering. For instance if an impact on a colder crystal creates a bunch of non-equilibrium phonons, ffph-Ph causes them to decay into an equilibrium phonon distribution creating a warmer crystal in thermal equilibrium. ffph-vib allows an excess of vibrational energy to decay into a bunch of phonons or an excess of phonons to pump energy into molecular vibrations. It is here that the doorway vibrations play a critical role. When a perturbation such as a shock shoves adjacent molecules together, the doorway vibrations are the first vibrations excited.5 The doorway vibrations act as a conduit for mechanical energy outside a molecule to flow into modes of primarily intramolecular character. When a particular bunch of vibrations is created, for instance by phonon up-pumping or as the result of vibrational excitations produced by an exothermic chemical reaction, i?vib-vib allows energy exchange among these states and with other unexcited vibrations. Since i?Vib-vib is typically the smallest of the interaction terms in Eq. (lb), the density of vibrational states has to be relatively large for vibration-vibration energy transfer to become efficient. It is known that excitations above the energy where the state density reaches 100-1000 states/cm - 1 , termed the intramolecular

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vibrational redistribution (IVR) threshold, can move rapidly among many nearly isoenergetic states. 19 Chemically-significant energies, i.e. energies large enough to have a reasonable chance of breaking a covalent chemical bond, lie in the region of efficient IVR for almost all molecules with at least three C, N or O atoms. 19 For this reason it is an extremely difficult challenge to prepare a molecule with a chemically-significant amount of energy that stays localized in a particular bond for even 50 fs. Relaxations are by nature incoherent processes. An incoherent process is one that randomly affects individual excitations differently. The rate expressions for relaxation processes are usually treated well by Golden Rule formalisms,4 where the rate constant is proportional to the square of a matrix element of the operator in Eq. (2) and a density of states. For instance at OK, an excited vibration with energy Ml could relax by spontaneous emission of a lower energy vibration fuo plus a phonon 7kJphThis process would be enabled by cubic anharmonic coupling, and the rate constant /CVR would be given by,4 kvR = 36TT2 V

(Vg>y6(il

-w-

Wph),

(3)

where {VQ I w ), henceforth just (V^3^}, is shorthand for the matrix element of the cubic anharmonic Hamiltonian, I/O)

1 d 3 V(Q) 3! OQndQ^dq^

QnQuqwplL-

(4)

Q=0

Calculations using Eq. (3) can be greatly simplified if we assume that all the matrix elements for certain processes are approximately equal to an average matrix element (V^ 3 )} a v g . 1 3 ' 2 0 ' 2 1 That is because the matrix elements are difficult to calculate and are very sensitive to minute details of the potential energy surface,22~25 whereas the density of states is easier to calculate and even easier to estimate based on neutron or vibrational spectroscopy measurements. In that case, for the Q, —> UJ + wph process,

k = ^(v*)ls

J2s(n-0,-^

=^ ^ ) 1 ^ .

(5)

In Eq. (5), the summation over S-functions gives the density of states PQ /h. This is the density of states per unit energy having one phonon and one vibration whose energies Too + fiwph sum up to hfl. The usual terminology for this quantity is "two-phonon" density of states although the same term can be used to mean one phonon and one vibration or two vibrations. Equation (5) can be generalized to describe other processes using

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different matrix elements and different densities of states. For example, two of the myriad VR pathways observed for excited vibrations of NM can be expressed as, 2 6 - 2 8 i/ s (N0 2 ) -> 4 ( N 0 2 ) + /o(N02) + 3 phonons, p(N0 2 ) —> 3 phonons. In the first process, the symmetric N 0 2 stretching vibration (1379 c m - 1 ) decays by producing one quantum of N 0 2 scissors (657 c m - 1 ) plus one quantum of N 0 2 rock (480 c m - 1 ) plus three phonons adding up to 242 c m - 1 . In the language of Eq. (5) this rate constant depends on a (V^) matrix element and a five-phonon density of states p*-5) (1379 cm" 1 ). Similarly, decay of the lowest energy vibration in NM, the N 0 2 rock, by generating three phonons, would depend on a (V^4') matrix element and a three-phonon density of states p^ (480 c m - 1 ) . In using Eq. (5), one useful refinement is to use not one but rather a small number of different average matrix elements to describe a few different processes. 13 ' 21,29 ' 30 This can be done using the following ansatz. All things being equal, (V) becomes smaller as the order n becomes larger. 31 Furthermore the matrix elements (V") are generally larger when they contain more phonon coordinates q and fewer vibration coordinates Q because phonons are generally more anharmonic than vibrations. 13 These effects are, in a very approximate sense, about equivalent, that is to say changing a q to a Q, which makes a matrix element smaller, has roughly the same effect as moving up one order by adding another q.21 Thus, we can make a table of approximate matrix element ordering as follows: QQQ < QQq < Qqq < qqq,

for (W3>)

QQQQ < QQQq < QQqq < Qqqq < qqqq < Qqq and so on. Having developed this background, let us now see what it tells us about a practical example. Breaking the N - N 0 2 bond is believed to be the first step in thermal initiation of RDX in the solid state. 32 ' 33 Although we should recognize that we cannot for certain say if this remains true with shockinduced chemistry, let us still consider the possibility of impact-generated phonons breaking a N - N 0 2 bond. Breaking this bond requires an energy34 of ~140kJ/mol or equivalently ~ l l , 7 0 0 c m _ 1 per molecule. We can imagine two quite different scenarios for phonon-induced bond cleavage. The "conventional" scenario sketched in Fig. 1(b) has the phonons up-pumping doorway vibrations including N 0 2 torsion and rock, which bleed energy into the other vibrational states until the molecule has taken

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up a chemically-significant amount of energy. Depending on conditions, this could take anywhere from l p s to 100ps (vide infra). Due to fast IVR, this energy is rapidly redistributed in a statistical manner among many almostdegenerate vibrational states until the weakest bond is broken. On the basis of Wight's thin-film pyrolysis experiments, 32 ' 33 for RDX this is presumably the N-NO2 bond. The N-NO2 bond is broken when enough energy happens to become concentrated in the N-NO2 stretch. The well-known theory for this redistribution process, termed RRKM theory, 35 posits a random walk among isoenergetic vibrational states until the first bond breaks. In order to have a statistically reasonable chance of getting a minimum of 11,700 c m - 1 into the right state, some extra energy is required. RRKM theory shows that with more extra energy available, the needed energy gets to the right place in less time, so the chemical reaction rate increases with increasing excess energy.35 An "unconventional" scenario is depicted in Fig. 1(c). Here a highenergy phonon excitation pumps a particular bond right to the dissociation limit. 36 For this type of mode-specific chemistry the first broken bond is not necessarily the weakest bond, rather it would more likely involve the motion that is most strongly coupled to the shock-generated phonons. This scenario could potentially produce bond breaking in impacts that is completely different from what is observed with slow heating, so do not be confused that in the present example we are comparing two different ways of breaking the same bond. This hypothetical and novel bond-breaking mechanism has been termed "shock-induced bond scission" or "shear-induced chemical decomposition". 37 ' 38 The N-NO2 stretch is probably not the motion most strongly coupled to the shock front. Dick's molecular mechanics models 38 suggest that the coupling between N-NO2 rocking and phonons (in PETN) ought to be much stronger than between N-NO2 stretching and phonons, so either the N-NO2 bond must be bent to the breaking point ("sheared off") or the rocking energy must flow preferentially into the stretching mode (which seems at least reasonable) to break this bond. Working against either of these scenarios is the IVR process, which drains energy out of these coordinates and into the rest of the molecule. Thus for this unconventional scenario to be possible, the rate of energy input to coordinates that can cause bond scission must significantly exceed the IVR rate. For more than twenty years, researchers have tried without much success to achieve selective bond scission using photons rather than phonons. 39_41 Short intense tunable IR laser pulses are used to selectively deposit energy into chosen coordinates, but in almost every case IVR causes the weakest bond to break,

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thwarting the desire to achieve bond-selective chemistry. 40 ' 41 A prominent exception involves experiments on gas-phase HOD, an isolated triatomic molecule with slow IVR, where Crim's group 42 has shown it is possible to choose to break either the O-H or O-D bond using properly selected combinations of IR and UV laser pulses. The inability of lasers to accomplish much bond-selective chemistry makes many of us familiar with the laser literature pessimistic that impact-generated phonons can break one of the stronger bonds via direct bond scission. The pessimist says that if it cannot be done with a laser, an exceedingly precise tool, it cannot be done with a shock front. The optimist counters that a planar shock front creates a vast number of phonons with a great deal of momentum and a reasonable degree of coherence, all impacting a molecule along a particular direction, and the pulse duration (the shock front risetime) could be exceedingly brief. This debate continues and its resolution should be eagerly awaited by the energetic materials community. Equations (3) and (5) above describe the decay of a higher frequency vibration Q, by spontaneous emission of a phonon wph and a lower energy vibration u>. In order to treat the problem of phonon up-pumping, we have to introduce the possibility of phonon absorption.4'18 How this is done depends on how we view the phonons created by impact. 7 Heating a sample generates incoherent phonons. Incoherent means the phases of all the phonon excitations are uncorrelated, which is the usual case. A coherent bunch of phonons is one with a well-defined and enduring phase relationship among all the phonons. 43 Phonons that are generated from a thin source layer, one that is thin relative to the phonon wavelength, will at least initially all have the same phase. Various scattering processes and phonon-phonon relaxation processes will ultimately lead to dephasing of a coherent phonon bunch. Lower frequency acoustic wavepackets (sound) can travel long distances without dephasing, but with higher phonon frequencies and high phonon densities dephasing might occur within just a few picoseconds.44 One might expect a very steep shock front just one molecule wide to generate a phonon packet with a high degree of initial coherence, since the phonon amplitudes must cancel just ahead of the front and add in phase just behind the front. Another possible coherent phonon generator involves a moving edge dislocation or dynamically forming crack surface where intense bursts of phonons can be generated from a very thin interfacial source layer. The equations for incoherent pumping are well known and they express various transition rates as functions of the phonon occupation numbers.

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For instance, the rate constant for a representative up-pumping process involving two-phonon pumping and cubic anharmonic coupling is, 5 ' 18 fc2ph^vib = ^ < v ( 3 > } y 2 ) ( t t ) K h ( T ,

v)

_

nvib(Tj v)])

(6)

where (V^) is a matrix element of the Qqq type, p(2\£l) is the two-phonon density of states at the doorway mode frequency f), and n p h(T, V) refers to the occupation number of phonons of frequency w = fi/2 at temperature T and specific volume V, nUJ(T,V) = {exp(fruj(V)/kBT) - l } " 1 . With incoherent up-pumping, the initial vibrational population grows linearly in time, and then levels off when phonon and vibration populations equilibrate. 5 The problem of coherent pumping of vibrations by phonons has not been worked out as well as the incoherent pumping problem. However, a similar problem, coherent pumping of vibrations by laser photons, has been studied a great deal using density matrix formalisms.45 Coherent pumping becomes efficient when the pumping rate is faster than processes46 that destroy molecular coherence such as vibrational dephasing. In coherent pumping, it is the vibrational amplitude that initially grows linearly with time. 45 The initial increase in vibrational population thus grows quadradically with time. Although Eq. (6) shows that incoherent pumping can at best result in saturation, that is equal populations in ground and excited states, coherent pumping can produce highly-inverted states where the excited-state population greatly exceeds the ground-state population. 45 Coherent pumping is an exceedingly fast and efficient way of creating high levels of vibrational excitation. Several problems need to be addressed to further develop this intriguing idea. 7 Although there is a formal similarity between photon and phonon pumping of vibrations, we should not unquestioningly adopt the wellknown photon equations because in the limit of large amplitudes phonons and photons behave quite differently. We also need a better idea of what kind of phonon wavepackets are generated by shock fronts and moving edge dislocations, what is their duration, intensity, spectrum and so forth. The direction light is propagating when it hits a molecule is not very important but the direction a molecule is hit by a shock front is very significant.

3. Up-Pumping in Experiments and Simulations Direct measurements of up-pumping have proven difficult because of the problem of generating short-duration bursts of phonons that are intense enough to cause vibrational excitation in the 200-4000 c m - 1 range. In

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addition, it has proven difficult to combine available techniques for highintensity phonon generation with time- and vibrational state-resolved probes. Three methods have been developed to initiate up-pumping. The Dlott group introduced "molecular heaters" which are large dye molecules embedded in a sample that can emit many phonons in a short time after optical pumping. 47 One dye, IR-165, was shown to emit tens of thousands of c m - 1 of phonon energy per molecule when pumped by near-IR picosecond pulses, to produce temperature jumps at rates up to 1012 K/s. However, this dye heater does not do a good job of mimicking an impact, and its absorption spectrum can hinder many spectroscopic probe measurements. The Fayer group 48 introduced an interesting technique where a tunable laser generates an excitation that is initially colder than its surroundings. Up-pumping then causes this excited state to heat up to the temperature of its surroundings. Shock compression seems to be the most desirable way of generating phonons for up-pumping, but achieving the combination of picosecond time resolution and state-resolved probing has proven difficult. In 1994, Chen, Tolbert, and Dlott 27 used the molecular heater method to study up-pumping in NM. Prior to that time, several theoretical works 36 ' 49,50 had calculated the NM up-pumping rate into the C-N stretching vibration, with the intent of causing the C-N bond to break. A variety of theoretical results were obtained for C-N up-pumping times, ranging from 100 ns to 1 ms. Some of these works 49 ' 50 suggested that the 1 /zs induction time in NM shock initiation was a result of 1 /us up-pumping, so in particular establishing the timescale of NM up-pumping by experiment seemed important. The IR-165 heaters generated enough phonons to ultimately raise the NM temperature by AT = 30 K. Since this heating was so rapid as to be isochoric, the pressure also rose by ^0.05 GPa. Vibrational energy was probed using incoherent anti-Stokes Raman scattering, which is likely the most precise method for detecting up-pumping. With an anti-Stokes probe, all Raman-active vibrational transitions can be monitored simultaneously, and the intensity of each transition is proportional to the product of the instantaneous population and a known Raman cross-section. 28 ' 51 However, the weak anti-Stokes signal requires extensive signal averaging, and it is easily overwhelmed by even the smallest background of light caused by high-intensity laser pumping needed to generate phonons. NM up-pumping of two doorway vibrations at 480 c m - 1 and 657 c m - 1 , that involve N 0 2 bending and rocking, along with the 918 c m - 1 C-N stretch were observed, as shown in Fig. 2. Doorway vibration pumping occurred within the apparatus time response <25ps, with C-N stretch pumping occurring about

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S- 40i

rt

(

Er

-400

,

,

-200

,

,

,

,

,

,

0 200 400 delay time (ps)

,

,

600

, —

800

Fig. 2. Experimental measurement of multiphonon up-pumping in NM, reproduced from Ref. 27. Phonons are generated using a picosecond pulse to excite a dye molecular heater. Anti-Stokes Raman spectroscopy is used to monitor population changes expressed as vibrational quasitemperatures, which are the equilibrium temperatures needed to obtain a particular level of excitation. The 657 c m - 1 doorway vibration is pumped faster than the instrument resolution of 25 ps. The 918 c m - 1 C—N stretch, which must be activated to break a C-N bond, is excited 30 ps later.

30 ps later. This experiment was the first to positively establish that polyatomic molecules are up-pumped on the picosecond timescale. Keep in mind that NM is a liquid and because of the gap between ©D and the doorway vibrations, NM might have especially slow up-pumping, so a similar study was conducted using a solid material, poly-methyl methacrylate (PMMA) doped with IR-165 dye. 52 ' 53 The large PMMA chains (MW > 105) have many low-frequency modes amalgamated with the phonons. Anti-Stokes Raman proved impossible in PMMA due to weak light emission from the polymer. Transient absorption spectroscopy of the IR-165 cooling showed a two-stage process interpreted as showing that PMMA heated up in two different stages. In the first <25 ps stage the dye excites PMMA phonons, and in the second 50-100 ps stage these phonons pump PMMA vibrations. In 1994, the Fayer group studied W(CO) 6 in CC14 solution. 48 A picosecond IR pulse at 1980 c m - 1 excited the T l u C = 0 stretching vibration. An anti-Stokes probe showed picosecond timescale scattering from 1980 c m - 1 to the Eg mode at 2012 cm^ 1 , but not to the Aig mode at 2116 c m - 1 . The dependence of the Raman lineshape on the IR laser pulse energy showed that significant populations could be pumped into high vibrational levels of C = 0 stretching. This work was further extended by the Heilweil group in 1995.54 They used an IR absorption probe to look at the population generated in v = 1, 2, 3 of the Ti u state and observed T i u to Eg energy transfer via up-pumping on the 10-20 ps time scale.

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In 1995, Lee and co-workers55 were the first to detect up-pumping behind a shock front. In order to obtain high time resolution, which in shock experiments is usually related to the shock front transit time across the sample, 56 ~ 58 Lee et al. used picosecond laser pulses to drive a 2GPa shock through a target just 300 nm thick at a velocity of 5 km/s (transit time ~60ps). The target consisted of PMMA containing Rhodamine 640 dye probes. Rhodamine is a polycyclic organic compound with a molecular weight of 591. A high concentration of dye (~10wgt.%) was needed to get a reasonable absorbance in such a thin layer. A picosecond white-light continuum was used to probe transients in the dye absorption spectrum. As the dye vibrational population rises, the red absorption edge of the dye becomes extended, due to absorption of progressively (vibrationally) hotter molecules. Red edge probing provides an overall measure of the molecular heating rate, but unlike Raman, it gives little detailed information about state-specific vibrational population distributions. Some results are shown in Fig. 3. Figure 3(a) shows that the dye absorption spectrum obtained with

wavelength (nm) Fig. 3. The solid curves are absorption spectra of Rhodamine dye in a 300 nm thick layer of PMMA, embedded in a shock target array (a) at ambient pressure and (b) at a static pressure of 2 GPa. The dotted curves in (b) represent picosecond time-resolved spectra with a laser-driven shock wave. The shock-induced absorption peak shift gives the shock pressure as 2 GPa. Fast transients along the dye red absorption edge are attributed to transient vibrational populations produced by <100ps up-pumping of dye molecules in shocked PMMA. Adapted from Ref. 55.

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the picosecond laser apparatus is identical to the spectrum obtained using a conventional absorbance spectrometer with the sample in a diamond anvil static high pressure cell. When the shock front arrives, the dye absorption maximum shows a sudden 250 cm" 1 redshift, which is identical to the redshift of a static spectrum obtained at 2 GPa. However, the red absorption edge of the shocked sample has some fast time-dependent features. The red edge absorption jumps up promptly when the shock front arrives (in <60ps, limited by the shock front transit time) and within ~100ps the absorption edge settles down, which was interpreted to indicate <100ps shock up-pumping of the dye probe molecules in shocked PMMA. Molecular simulations are among the better ways of obtaining a molecular-level picture of energetic material dynamics, but many problems can arise when classical simulations are used to investigate vibrational dynamics that are intrinsically quantum mechanical. The first simulations of detonations in molecular crystals 59 showed no up-pumping at all, which might have dismayed proponents of this concept. But in the simulations by White and co-workers, hypothetical molecules that were extremely reactive were needed to drive a detonation wave. The barrier height to reaction was 640 c m - 1 whereas the vibrational frequency was 1064 c m - 1 . 5 9 Thus these molecules described by a reactive empirical bond-order (REBO) potential have no bound vibrational excited states at all, and it is no surprise that they dissociate before phonons can pump much energy into vibrations. Since 1994, several simulations of larger molecules with potentials more representative of actual secondary explosives have shown clear evidence for up-pumping on the picosecond timescale. White and co-workers observed picosecond up-pumping of diatomic molecules by shock waves in a 3D simulation. 60 Belak's simulations of 10 GPa shocks in liquid butane showed a high initial level of phonon excitation, followed by up-pumping on the picosecond time scale. 61 Preliminary results for NM gave an uppumping time constant of about 10 ps. 61 Pried and Tarver 62 and their coworkers have observed shock-initiated up-pumping that occurs in about 10 ps in simulations of HMX and TATB. Kim et al.63 observed up-pumping of a 10 K naphthalene molecule in 300 K surroundings occurring in ~50ps. One always has to view these up-pumping simulations with a degree of concern because of the use of classical mechanics. Classical mechanics does a reasonable job of modeling vibrations where huj/k^T <1, but a poor job otherwise. Figure 4 illustrates this point using 200 cm" 1 to represent a doorway vibration and 1600 c m - 1 to represent an NO2 stretching vibration. For a classical oscillator, the energy E = ksT, but for a quantum

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800

600

f

400

s>

C 0)

200

0 0

200

400

600

800

1000

temperature (K) Fig. 4. Calculation of the temperature-dependent energy of molecular vibrations at 200 cm and 1600 c m - 1 . The solid curves represent the exact quantum mechanical result. Classical mechanics gives k-gT for both vibrations, which drastically underestimates the energy in the higher wavenumber vibration.

oscillator, E = hw{\/2 + [exp(huj/k-eT) - I]"" 1 }. Figure 4 shows that the classical approximation is excellent for the doorway mode but it underestimates the energy in the stretching mode at all temperatures, and it seriously underestimates the energy at lower temperatures, e.g. by a factor of two at 300 K. Another approach that does incorporate quantum mechanics was taken by Kim and Dlott. 30 These authors used a master equation formalism to calculate the state-specific vibrational populations in a naphthalene crystal when a large amount of energy corresponding to the temperature jump of a 4 GPa shock was suddenly added to the acoustic phonons. A master equation describes the flow of probability, rather than probability amplitudes, which is adequate for the incoherent pumping problem. The matrix of rate constants in the master equation were computed using actual quantum mechanical expressions such as Eq. (6) and its analogs for the fourth and higher-order processes. The density of states was determined using available neutron scattering data. 64 A few of the anharmonic matrix elements needed, of the forms qqq, qqQ and qQQ were experimentally determined using low temperature VR data, 21 and then other elements of the same form were in the spirit of Eq. (5) simply assumed to be equal to the average of the measured quantities. 13 These simulations showed the acoustic phonon excess being redistributed among all phonons within ~ l p s . The

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doorway vibrations heated up next. Vibrational energy ran up to higher frequencies, and ultimately all phonons and vibrations came to equilibrium within ~100ps.

4. Up-Pumping in Low Velocity Impact Initiation Energetic materials can be made to react explosively by relatively minor insults such as a falling hammer from a few feet. 1 ' 10 ' 65 ' 66 This LVI process can be unpredictable and is difficult to understand. LVI is often studied using a drop-hammer apparatus to determine a minimum height needed for a 50% chance of LVI of a particular energetic material (H50). The peak stress in a drop-hammer test is thought to be ~ 1 GPa lasting for ~250/zs. 66 Developing a deeper understanding of LVI is needed to prevent dangerous accidents among workers who handle energetic materials. In 1994, Fried and Ruggerio 67 investigated up-pumping in seven primary, secondary or insensitive explosives, using the simplified expression in Eq. (6) which gives the up-pumping rate in terms of an averaged anharmonic coupling and a multiphonon density of states. The density of states of each material was constructed using neutron scattering data obtained by Trevino. In order to compare energetic materials with entirely different crystal and molecular structures, the densities of states were normalized using a method developed by Dlott. 12 A great simplification was made by assuming that the average anharmonic coupling per molecule was identical for all seven explosive compounds, ranging from highly-sensitive lead styphnate to highly-insensitive TATB, which then allowed a comparison of the relative up-pumping rates as a function of doorway vibration frequency. The data showed a general trend suggesting that faster up-pumping was associated with more sensitive materials. A plot of the up-pumping rate for doorway vibrations near 425 c m - 1 versus drop-hammer sensitivity suggested an approximately linear relationship between high sensitivity to LVI and up-pumping rate. It was also suggested that this relationship might also apply to shock initiation, because some authors have suggested a close connection between LVI and shock sensitivity,66 which sounds reasonable even though the actual evidence for this connection is rather shaky. 68 In 1997, McNesby and Coffey9 performed a similar but even simpler analysis, where the relative up-pumping rates of seven secondary explosives were estimated by counting the number of doorway states determined from Raman spectra of the doorway region. Once again there was a general trend of higher drop-hammer sensitivity being associated with faster up-pumping.

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Quite recently, Ye et al., used lattice dynamic calculations of the density of states with even more secondary explosives and observed a similar correlation. 69 Although none of these associations or correlations meet even lower quality tests of statistical significance, and they are all based on the assumption of approximately equal anharmonic coupling in different explosives, these works do suggest a deeper look at ways that fast up-pumping might increase explosive sensitivity to LVI. We do not have a firm understanding of what happens during a drophammer test. McNesby and Coffey9 point out that a typical drop-hammer impact adds only enough energy to raise the equilibrium temperature of a bulk sample by a few tens of degrees. Clearly LVI involves localizing the drop-hammer energy in hot spots 10,65 or in shear bands. 70 ' 71 Although these localization processes have been discussed many times, little direct experimental observational evidence actually exists. Khasainov's 72 extensive review of hot spots states that only recently have hot spots been directly observed, and these are only larger (millimeter) hot spots. Fast IR imaging techniques seem like a natural method to study localized heating in LVI, but only a very few such measurements were made. Miller et al. in 1985 used 73 a high speed IR detector to observe localized heating in crystalline solids during LVI, and Woody and co-workers74'75 used a high-speed IR imaging array. Just recently, Proud et al.76 at the Cavendish laboratory have obtained beautiful high-speed photographs of shocked ammonium nitrate showing the appearance of hot spots and showing which hot spots lead to ignition and which die out. One very interesting suggestion to relate fast up-pumping to higher LVI sensitivity involves thermal conductivity. When surfaces are rubbing together, the peak temperature depends on the thermal conductivity. 65 Lower thermal conductivity results in higher surface temperatures, favoring ignition. In insulating solids phonons carry most of the heat, so up-pumping which converts mobile phonons into localized vibrations can reduce thermal conductivity. In the well-known theory of lattice thermal conductivity, thermal conductivity K is given by,44

^ j E ^ "

(7)

i

where the sum is over all phonon modes, and C, v and I are the phonon heat capacity, velocity and mean-free path. The mean-free path is determined by phonon-scattering processes. Usually in insulators, heat is carried mainly by acoustic phonons whose scattering is dominated by Umklapp scattering

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at defects and surfaces. Equation (7) is a linearized expression that ignores a variety of higher-order terms. Thus, if there exists a dense sea of phonons, especially phonons near the zone edge, the mean-free path in Eq. (7) can be decreased due to phonon-phonon interactions caused by anharmonic coupling. In other words there are higher-order corrections to Eq. (7), for instance where pairs of mobile phonons pump immobile doorway vibrations, that cause a decrease in the thermal conductivity proportional to the square or higher powers of the phonon concentration. In 1952, Bowden and Yoffe65 gave the following expression for the temperature rise at the interface between two rubbing solids,

^

"

4aJ k1+k2'

(8)

where fj, is the coefficient of friction, W the load between the surfaces, V the sliding velocity, a the radius of the region of contact, J the heat capacity, and k\ and k^ the two solids' thermal conductivities. Initiation occurs if AT reaches a critical thermal explosion temperature. Equation (8) has two terms, the first representing heat generation and the second heat dissipation. For steady-state rubbing, AT is inversely proportional to the thermal conductivity. With shock compression, moving edge dislocations or rapid crack-induced heating, the nonlinear terms in the phonon scattering will come into play. The temperature at rubbing surfaces could become catastrophically higher than predicted by Eq. (7) as the thermal conductivity dropped off when the phonon concentration became sufficiently large. The onset of this catastrophic behavior would occur at lower phonon concentrations when the anharmonic coupling is large and up-pumping is fast. Thus the sensitivity to LVI might increase in materials characterized by fast up-pumping. This connection between fast up-pumping and poor thermal conductivity was first (to my knowledge) suggested by Fried and Ruggerio. 67 Holmes, Francis, and Fayer 77 developed a crack propagation heating model for energetic material ignition that shows crack surface temperatures increasing as the up-pumping rate is increased. However, nobody has yet combined the nonlinear thermal conductivity model with a good model for the phonon generation. In the Fayer model, the phonon generation rate was chosen to give agreement with the possibly questionable estimates of temperatures at RDX crack surfaces. All the heat needed to create a given temperature was initially deposited only into the phonon modes. Using this method, the initial phonon quasitemperatures at crack surfaces of RDX were estimated to be as high as 4000 K, which causes

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quite a bit of up-pumping. A microscopic picture of the phonon generation process has been discussed by a few authors, and in the context of hot spot generation by Coffey, who calculated the velocity of moving edge dislocations in a crystalline solid as well as the rate of phonon generation. 70,71,78 Coffey points out that dislocation velocities can easily be several nm/ps ( l n m / p s = l k m / s ) . For typical 1 nm molecules the dislocation velocity is several molecular diameters per picosecond, and the generated phonon frequencies can easily reach several multiples of 10 12 /s, or equivalently 100-200 c m - 1 . This non-equilibrium population of predominantly higherfrequency phonons launched predominantly along a particular direction should be among the most efficient for exciting molecular vibrations via multiphonon up-pumping. Several estimates have been made of the density of phonons near a crack or moving edge dislocation, based on estimated parameters that are difficult to judge or confirm, so this seems to be an interesting area for further work.

5. Up-Pumping in Shock Initiation and Detonation A wide-range of shock strengths is seen in energetic material phenomena. Initiating a sensitive material might involve a 1 GPa shock with a bulk temperature rise AT of several tens of degrees, 9,66 whereas a detonation might involve a 40 GPa shock with AT of several thousands of degrees.1 Thus one needs to be careful of making blanket statements about up-pumping in shock fronts without reference to the shock strength. In this section I will distinguish with separate discussions, between moderate strength initiating shocks and higher strength detonation shocks, realizing there will not be a sharp division between the two. In the "conventional" scenario mentioned above where up-pumping heats vibrations slower than IVR so that equilibrium vibrational populations cause only the weakest bond to break, up-pumping seems not to be very interesting. The only effect of up-pumping is a picosecond delay between the passage of the shock front and the attainment of a final temperature prior to bond breaking. The truly novel and interesting features of up-pumping in shock waves must be found in more unconventional scenarios involving non-equilibrium phonon and vibrational populations, 5 ' 7 and what follows should be regarded as informed speculation. The most likely situations where novel processes will be found occur when a shock front is very steep, so that it creates a highly non-equilibrium population of phonons. A gradual shock front will merely heat the molecules slowly. There are then

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two scenarios where up-pumping creates novel effects. The first involves the spatial localization of energy in hot spots when up-pumping is slow compared to the shock front risetime, and the second involves new chemistries that might occur when up-pumping is much faster than IVR. This first scenario was proposed by Dlott and Fayer. 5,6 A steep shock front creates a dense sea of delocalized phonons. In a perfect crystal, there is merely a brief delay before molecular vibrations are pumped. During this brief delay in a real crystal, the highly non-equilibrium phonon population might encounter defect sites. Of particular interest are those defects where the anharmonic coupling is somewhat greater than the bulk. The delocalized phonons will rapidly and preferentially pump energy into the molecules near these defect sites, resulting in a spatial localization of the shock-generated energy. This localization at anharmonic defects is one way that up-pumping can produce hot spots 5 that enhance the likelihood of initiation at lower shock pressures. 65 In the second scenario, up-pumping is faster than IVR so that specific vibrations are preferentially pumped. This could result in unique chemistries associated with violating the weakest bond rule. This second scenario works with both coherent and incoherent up-pumping but seems more likely with coherent pumping, since, all things being equal, coherent pumping is faster and more likely to overcome IVR. Since characteristic times for up-pumping or IVR are 1-10 ps, it matters a great deal whether the shock front rise time is <10ps, versus say 100 ps or Ins or more. In continuum mechanics, a shock front of whatever strength is an infinitely steep discontinuity, but in the real world there are a variety of dissipative processes that broaden shock fronts.79 When a flat impactor perfectly strikes a flat sample with no tilt (which is what happens every time in computer simulations), the initial shock front risetime ought to be very steep, since the interaction between the projectile and sample turns on in just a few angstroms. Even if this perfect impact could be realized, the shock front will broaden as it propagates until it attains a steady-state profile that results from a competition between the steady drive of the impactor and the dissipation. 79 To discuss shock front risetimes we have to know something about dissipation. The system with minimal dissipation is a simple atomic liquid. Solids including molecular crystals and polymer binders evidence a variety of dissipation processes with plastic deformation and viscoelastic behavior often playing pivotal roles. In a simple atomic liquid, moderate or high strength shock fronts are expected to be a few atomic diameters (a few A) wide, although no one has ever observed this except in computer simulations of thin perfect samples.

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Some quite indirect measurements have been used to infer a risetime in water of lps. 8 0 ' 8 1 In a molecular liquid such as NM, up-pumping causes some of the shock energy to be absorbed and subsequently re-emitted by vibrations which are immobile. This energy exchange between shock fronts and vibrations is a dissipative process that converts some of the directed energy of the shock front into randomly directed phonons and heat, 82 so it should impart a steady-state structure to the shock front. Nobody quite knows how this would look, but since VR and up-pumping in NM near ambient conditions takes tens of ps, and both processes are arguably faster at higher pressures and temperatures, one might expect tens of ps structures in NM lower pressure shock fronts and ones of ps structures in NM higher pressure shock fronts, corresponding to shock front widths ranging from hundreds of nm to just a few nm. Simulations of shock propagation, where the shock front is initially just a few molecules thick and the risetime is <100fs, do not show any of these structures, I believe for two reasons. First, there is no quantum mechanics. Second, it is rare for a simulated shock front to run even one micron, so the shock does not develop a steady-state structure. To address these issues, one ought to use quantum mechanics to develop a microscopic model that can be put into fluid mechanics equations to generate a long-term steady-state shock profile. Solid deformation processes are usually described in the context of viscoplastic or viscoelastic models. When the solid's atoms are shoved together, any initial small displacement looks elastic, meaning the solid could spring back to its original shape, but then with larger displacements barriers are encountered and surmounted. In atomic and molecular solids, large amplitude displacements result in plastic deformation, so viscoplastic models are useful.83 In polymers and viscous or supercooled liquids, large amplitude displacements result in plastic deformation with a diffusive component, 84 ' 85 and viscoelastic models 86 are useful. These two-part processes give rise to a two-part shock front structure with an elastic precursor that continually spreads out due to acoustic dispersion plus a steeper trailing plastic wave. 79,83 Shock front broadening effects are minimized in very thin and uniform solid materials such as metal thin films. The fastest risetime actually observed in a solid involved femtosecond laser-driven shocks in ~ 1 fj,m thick Al. 87 ' 88 The risetime of a moderate strength shock generated with a 150 fs laser pulse was observed to be 5.3 ps. With a velocity of 5 nm/ps, the shock front was 265 A thick. The same shock pressure in a thick slab of Al gives a complicated elastic-plastic waveform lasting about 1/is.79'89'90 The plastic deformation part which is usually regarded

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to give the shock front risetime has a risetime of ~100 ns. A higher strength detonation shock front ought to be steeper. Computer simulations of detonations in thin samples show shock fronts with 100 fs risetimes that are just a few molecules thick. 59,91 Technical problems 92 have so far prevented the generation by femtosecond laser pulses of detonation-strength shocks in thin films. One might suppose such a shock might have a risetime <1.6ps, but we presently do not know how much less. In a real detonation of a practical explosive such as plastic-bonded explosives (PBX), the steepening due to the high shock pressure can be offset by material inhomogeneity. A PBX formulation consists of molecular crystal pieces embedded in a polymer binder having a different shock velocity.1 So far the fastest measurement of detonation shock fronts, 93 ' 94 by Sheffield, Bloomquist, and Tarver, 93 revealed risetimes <300ps in a TATB-based PBX called PBX-9502 and also in TNT, but again we do not know how much less. This uncertainty is significant, because as discussed above, incoherent up-pumping phenomena become more important with shock fronts below 100 ps and quite important below 10 ps, and coherent up-pumping is most likely significant only below a few ps.

6. Summary and Conclusions Phonon up-pumping phenomena are a direct consequence of the fundamental nature of chemical bonding in molecular materials, so there is little room to argue that up-pumping does not occur. However, there remains a great deal of room to argue the significance of up-pumping in energetic material initiation and a great deal of room to discuss precisely what unique effects might be caused by up-pumping. The somewhat arbitrary division of molecular crystal states into phonons, doorway vibrations and intramolecular vibrations 5 is a preconceived notion that naturally leads to a clear sequence of events where shock fronts or moving edge dislocations create phonons that pump doorway vibrations that pump vibrations. However, this division is hardly a law of nature, so one should expect a continuum of effects. When a real shock front excites a real crystal of flexible molecules, there must be some direct excitation of all vibrations, with doorway vibrations being those that are predominantly excited. A better route to understanding such processes in better detail would be one that has fewer preconceived notions such as a classical simulation of molecules in a shock front. However, lacking quantum mechanics this method is unsatisfactory due to its poor treatment of higher frequency vibrations. Detailed

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lattice-dynamic calculations using a quantum mechanical Hamiltonian or quantum mechanical simulations would surely reveal a range of interesting and more realistic behaviors in larger polyatomic molecules impacted by shock fronts propagating in various directions. Even this approach lacks one important feature, the need to consider the detailed structure of the shock front itself, so it appears that the best long-range approach should be to consider quantum mechanical simulations of vibrational up-pumping induced by the appropriate steady-state shock front structure determined by a continuum mechanics approach. Unique and novel phenomena that might be associated with phonon uppumping ought to take on the greatest importance when large numbers of phonons, corresponding to chemically significant energies on a per molecule basis, are rapidly generated with a well-defined phase relationship. All these signs point to strongly perturbed and very thin source layers such as steep shock fronts and moving edge dislocations. Here "rapidly" might be taken to mean at minimum <100ps, but perhaps better would be <10ps or even < l p s . I have divided the discussion of novel effects into three distinct but probably overlapping regimes relevant to energetic materials, namely detonation, shock initiation and low velocity initiation. In detonation waves, the shock pressure might be great enough to overcome most dissipative effects as well as the inhomogeneous structure of composite explosives, resulting in strong steep shock fronts that propagate coherently over large distances. We know as a result of direct measurement that <300ps detonation fronts can be generated even in lumpy PBX materials, but a direct measurement of the actual risetime has yet to be achieved. In initiation by weaker shock waves, steep shock fronts can be generated in highly homogeneous materials such as thin metal films or thin layers of liquids, but the possibility of very steep lower pressure shock fronts (say 1-5 GPa) in macroscopic slabs of inhomogeneous materials such as PBX seems remote. However, these shock fronts can cause crack formation or moving edge dislocations in individual grains or crystallites, so perhaps one should think of up-pumping phenomena in the shock initiation case as resulting from multiple staccato bursts of phonons behind the shock front. Each burst is generated by the shockinduced destruction of a single crystallite. In LVI, impact energy is stored in a crystal lattice until it is released in localized regions by abrupt mechanical failure. Even though the local pressures at cracks and dislocations are generally much weaker than in detonation fronts, up-pumping could still be extremely important, because the phonons are generated by thin interfacial layers perhaps just a few molecules thick.

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There are two interesting scenarios where up-pumping could have a significant effect on chemical reactivity other than a brief delay between phonon generation and chemical reaction. The first involves the nonlinear thermal conductivity catastrophe. At a crack surface or moving edge dislocation, when a small number of phonons are generated the lower frequency acoustic phonons dissipate ballistically and the higher frequency phonons migrate diffusively. The surface temperature is in part determined by the net thermal conductivity. Under increasingly extreme conditions, the phonons will interact via anharmonic coupling to produce immobile vibrations that reduce the thermal conductivity. The catastrophic nature results from the combination of more phonons and less thermal conductivity, so that at a presumably rather sharp threshold rate for phonon generation, the ignition temperature will abruptly be exceeded at the surface. The second involves non-equilibrium vibrational populations caused by ultrafast uppumping that is faster than IVR. The thermochemistry of energetic materials with slow heating has been rather well characterized. In unimolecular processes, it is always the weakest chemical bond that breaks first. Energetic material thermochemistry can be strongly affected by heating rate, but this is not a consequence of vibrational energy transfer dynamics or a violation of the weakest bond rule, but rather a result of the different temperature dependences of the myriad chemical reaction pathways. With ultrafast heating, entirely new chemistries might result. Two possibilities were suggested that involve breaking some bond other than the weakest, depending on whether phonon pumping was coherent or incoherent. Coherent phonon pumping of a single coordinate, such as a N-NO2 stretch, could, if fast enough, lead to shock-induced bond scission. In this case, which bond is broken is not so much a matter of bond strength but instead a matter of which bonds are most rapidly pumped by the shock front. Incoherent pumping faster than IVR is unlikely to break specific chemical bonds by direct scission, but it would produce a non-thermal vibrational population. If the coordinates associated with the weakest chemical bonds happened not to be well populated by up-pumping, before IVR is complete some stronger bonds might be broken instead. To complete this conclusion section, I again stress that a full theoretical understanding of these processes requires an approach that combines continuum mechanics and quantum mechanics. Taking a look at the state of the art of theory today, I have been impressed by two quite recent developments. Goddard's group at CalTech have run extremely detailed simulations of detonation in RDX. 91 Over the course of a few picoseconds, one

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can watch an incredibly steep shock front pass over a layer of molecules which disintegrate within ~ 1 ps. Subsequently some of the molecular fragments recombine to generate products, heat and kinetic energy. Ab initio quantum theory was used to derive the potential energy surface for these molecules, in order to provide confidence that the chemistry will be correct. However, the simulation itself is purely classical, so there are two key features missing. Although up-pumping is observed, the quantum mechanical effects in up-pumping are missing, and the shock front generated by a perfect impact a short time earlier is nowhere near its steady-state structure, whatever that may be. Fried's group at LLNL, 95 and an LLNL collaboration with Joannopoulos 96 ' 97 at Harvard and with Martinez 98 at Illinois, have used advanced quantum simulation techniques to look at NM, HMX and TATB chemistry. These simulations are done at high temperatures and pressures associated with the CJ states of detonations. 95 Lacking from this work is the possibility of any dynamical or material failure effects resulting from the time-dependent passage of a shock front. So although theoretical progress in this field has made impressive strides, the techniques that are presently available are not by my judgment yet quite able to critically evaluate the significance of up-pumping in energetic materials. Acknowledgments This material is based on work supported by Army Research Office contract DAAD19-00-1-0036 and Air Force Office of Scientific Research contract F49620-03-1-0032. The author wishes to thank Dr. Robert Shaw and Dr. Michael Berman for their continued support of this research. Additionally I would like to acknowledge Dr. Shaw for encouraging me to get these ideas down on paper and for innumerable conversations requiring me to find better ways of explaining up-pumping. This work has benefited in many ways by scientific collaborations with Prof. M. D. Fayer of Stanford University and Prof. A. Tokamkoff of MIT, and by many stimulating conversations with Prof. Goddard of CalTech and Dr. A. Strachan of LANL, and with Dr. L. Fried and Dr. C. Tarver of LLNL. References 1. J. Kohler and R. Meyer, Explosives, 4th edn. (VCH Publishers, New York, 1993). 2. A. I. Kitaigorodskii, Molecular Crystals and Molecules (Academic Press, New York, 1973).

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3. A. J. Pertsin and A. I. Kitaigorodsky, The Atom-Atom Potential Method: Applications to Organic Molecular Solids (Springer-Verlag, Berlin, 1987). 4. S. Califano, V. Schettino and N. Neto, Lattice Dynamics of Molecular Crystals (Springer-Verlag, Berlin, 1981). 5. D. D. Dlott and M. D. Fayer, J. Chem. Phys. 92, 3798 (1990). 6. A. Tokmakoff, M. D. Fayer and D. D. Dlott, J. Phys. Chem. 97(9), 1901 (1993). 7. D. D. Dlott, in Energetic Materials: Initiation, Decomposition and Combustion, Part 2, eds. P. Politzer and J. S. Murray (Elsevier, New York, 2003), p. 125. 8. C. L. Mader, Phys. Fluids. 8, 1811 (1965). 9. K. L. McNesby and C. S. Coffey, J. Phys. Chem. B 1 0 1 , 3097 (1997). 10. F. P. Bowden and A. D. Yoffe, Fast Reactions in Solids (Academic Press Inc., New York, 1958). 11. G. A. Olah and D. R. Squire (eds), Chemistry of Energetic Materials (Academic Press, San Diego, 1991). 12. D. D. Dlott, Annu. Rev. Phys. Chem. 37, 157 (1986). 13. D. D. Dlott, in Laser Spectroscopy of Solids II, ed. W. Yen (Springer-Verlag, Berlin, 1988), p. 167. 14. R. D. Bardo, in Proc. 9th Symposium on Detonation, Vol. I, ed. J. M. Short (1989), p. 235. 15. D. Cavagnat, J. Lascombe, J. C. Lassegues, A. J. Horsewill, A. Heidemann and J. B. Suck, J. Physique (Fr) 45, 97 (1984). 16. H. V. Brand, R. L. Rabie, D. J. Funk, I. Diaz-Acosta, P. Pulay and T. K. Lippert, J. Phys. Chem. B106, 10594 (2002). 17. A. Nitzan and J. Jortner, Molec. Phys. 25(3), 713 (1973). 18. V. M. Kenkre, A. Tokmakoff and M. D. Fayer, J. Chem. Phys. 101(12), 10618 (1994). 19. J. D. McDonald, Annu. Rev. Phys. Chem. 30, 29 (1979). 20. C. L. Schosser and D. D. Dlott, J. Chem. Phys. 80, 1394 (1984). 21. J. R. Hill, E. L. Chronister, T.-C. Chang, H. Kim, J. C. Postlewaite and D. D. Dlott, J. Chem. Phys. 88, 949 (1988). 22. R. Righini, Chem. Phys. 84, 97 (1984). 23. R. G.Delle Valle, P. F. Fracassi, R. Righini and S. Califano, Chem. Phys. 74, 179 (1983). 24. R. Righini, P. F. Fracassi and R. G. Delia Valle, Chem. Phys. Lett. 97, 308 (1983). 25. V. K. Jindal and D. D. Dlott, J. Appl. Phys. 83, 5203 (1998). 26. S. Chen, X. Hong, J. R. Hill and D. D. Dlott, J. Phys. Chem. 99, 4525 (1995). 27. S. Chen, W. A. Tolbert and D. D. Dlott, J. Phys. Chem. 98, 7759 (1994). 28. J. C. Deak, L. K. Iwaki and D. D. Dlott, J. Phys. Chem. A 1 0 3 , 971 (1999). 29. J. R. Hill and D. D. Dlott, J. Chem. Phys. 89, 842 (1988). 30. H. Kim and D. D. Dlott, J. Chem. Phys. 93, 1695 (1990). 31. A. Nitzan, S. Mukamel and J. Jortner, J. Chem. Phys. 63(1), 200 (1975). 32. T. Botcher and C. A. Wight, J. Phys. Chem. 97, 9149 (1993). 33. C. A. Wight and T. R. Botcher, J. Am. Chem. Soc. 114, 8303 (1992).

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C H A P T E R 11 A P P L I C A T I O N S OF T H E O R E T I C A L C H E M I S T R Y IN ASSESSING ENERGETIC MATERIALS FOR P E R F O R M A N C E OR SENSITIVITY Betsy M. Rice U. S. Army Research Laboratory Aberdeen Proving Ground, MD 21005-5069, USA

Contents 1. Introduction 2. Theoretical Chemistry Methods Used in Energetic Materials Research 3. Quantum Mechanical Calculations 3.1. Gas Phase 3.1.1. Molecular Properties 3.1.2. Thermochemistry 3.1.3. Reaction Mechanisms 3.1.4. Electrostatic Potentials 3.2. Condensed Phase 4. Classical Molecular Simulation 4.1. Condensed Phase Interaction Potentials 4.2. Results Using the Sorescu, Rice, Thompson Model of CHNO Explosives 4.2.1. Rigid Molecule Approximation 4.2.2. Flexible Model: Nitromethane 4.3. Results Using the Smith and Bharadwaj Model of HMX 4.4. Molecular Packing: Ab Initio Crystal Prediction 4.5. Crystal Growth 5. Concluding Remarks References

1.

335 336 339 339 339 341 343 346 350 352 353 354 354 355 357 359 362 363 363

Introduction

Ever-increasing advances in computational capabilities and methodologies are transforming atomic-level theoretical calculations into viable and 335

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important tools for use in an energetic materials development process. Of particular interest is the capability to rapidly characterize a notional material using theoretical chemistry in order to evaluate its potential performance or assess its vulnerability characteristics before investing in its synthesis. If the candidate shows promise, further and more costly investigation can be justified. Likewise, poor performers are readily eliminated from further consideration. However, such predictive capabilities based on accurate theoretical chemical methodologies are only now beginning to emerge. Until the 1990s, reliable theoretical calculations of energetic materials were limited by computational constraints. Up to that time, accurate quantum mechanical calculations could only treat small polyatomic molecules, whereas the majority of energetic materials of interest consist of large polyatomic organic molecules containing C, H, N, O, and sometimes F: species that require significant computational resources. Additionally, many interesting processes occurring in energetic materials are in the condensed phase, which poses an additional computational challenge. However, with the advent of density functional theory (DFT), 1 the availability and distribution of user-friendly theoretical chemistry software,2'3 and significant progress in developing highly-scalable computational platforms, impressive achievements have been realized in the realistic modeling of atomic level processes in energetic materials. This chapter provides a description of the types of theoretical calculations that have been applied in energetic materials research, gives a few notable examples, and presents needs and ideas for advancing the methodologies in applications to energetic materials.

2. Theoretical Chemistry Methods Used in Energetic Materials Research Various computational methods have been used to study the static and dynamic properties of energetic materials, with most based on classical and quantum mechanical theories. With the exception of quantum mechanical calculations of isolated molecules and mapping of reaction paths of energetic materials, most of the methods that will be presented in this chapter are applied to energetic materials in the condensed phase; other chapters in this volume will address gas-phase dynamical processes. The methods based on classical physics include molecular dynamics (MD), molecular modeling/molecular packing (MM/MP), and Monte Carlo (MC). All are limited by the classical approximation and an accurate

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description of the potential energy surface (PES) for the system. The PES is usually represented by a model interaction function, whose parameters are adjusted to reproduce experimental and theoretically-generated information about the system under study. If the function well represents important regions of the PES (i.e. those that influence stability and reaction) and the process being simulated is not influenced by quantum effects, then the classical methods often provide detailed information that might be difficult to obtain experimentally. The method of molecular dynamics is an extremely powerful and popular atomistic simulation method used to investigate time-dependent behavior. 4 ' 5 An MD simulation involves integrating equations of motion in time to generate atomic positions and velocities, thus providing a dynamic description of the system. Also, thermodynamic information can be obtained by averaging properties evaluated at each integration step over the duration of the simulation. MC is another atomistic simulation method 4,5 used in energetic materials research, mainly to calculate time-independent equilibrium properties of a system through statistical ensemble averaging rather than time averaging. In this method, properties are calculated at randomly selected points in the phase space of the system (weighted according to a specified probability distribution), and the results averaged over the number of points sampled. MC has a computational advantage over MD in that it does not use atomic forces but rather only the interaction potential. However, interesting dynamic behavior of energetic materials, such as energy transfer or reaction, cannot be investigated using the MC method. Variational Transition State Theory (VTST) is a statistical mechanically-based method used to evaluate reaction rates of unimolecular and bimolecular reactions, 6 and requires a description of the important regions of the PES of a system, such as the global and local minima, transition states, and reaction paths. Quantum mechanical tunneling can be treated using this method, and applications to energetic materials using VTST with quantum mechanical forces are given in this chapter. MM 7 is loosely defined here as an atomistic simulation method that investigates structural features and properties very near local minima on the PES, and include simple energy minimizations, MD and MC. MP calculations 8 fall under this category, and typically involve the minimization of crystalline lattice energies by varying crystallographic parameters. This is a particularly useful technique in the energetic materials community because it allows for a rapid assessment of the ability of an empirical potential energy function to predict a crystal structure. MP calculations are also used in ab initio crystal prediction, to be discussed later in this chapter.

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The methods based on quantum mechanics (QM) 9 all involve solving Schrodinger's equation for the system under study, and will be characterized hereafter as either "ab initio" or "semi-empirical" (SE) calculations. Calculations labeled as "ab initio" are non-empirical and indicate that all integrals are included in solving Schrodinger's equation for the system under study. SE calculations, on the other hand, neglect certain terms in Schrodinger's equation and replace them with parameters. 10 Until the early 1990s, the state-of-the-art ab initio methods were limited to the smallest molecular systems and simplest reactions due to the extensive computational requirements. Low-to-modest levels of theory or semi-empirical methods were reserved to treat larger systems and more complex reactions, such as those corresponding to energetic materials. Thus, until recently, energetic materials were relegated to theoretical treatments using extremely low levels of ab initio theory or semi-empirical treatments. Although the early attempts to apply theoretical methods to energetic materials were commendable, the approximations inherent in these methods did not allow for confidence in the accuracy of the results. Density functional theory (DFT), 1 whose origins can be traced to the solid state physics community, was embraced by the molecular chemical physics community in the early 1990s, and has proven to be an extremely powerful and reasonably accurate method to treat large polyatomic systems at a fraction of the computational cost of other ab initio methods. DFT calculations of isolated molecules or small clusters of molecules are routinely performed to calculate various properties and elementary reactions of energetic materials. Additionally, the number of static and dynamic DFT calculations of condensed-phase energetic materials is increasing, particularly since the advent of hybrid classical-quantum mechanical dynamics calculations such as "Direct Dynamics" 11 or "Car Parrinello MD". 12 These calculations, collectively referred to here as QM/MD, are similar to the classical molecular simulations described above, except the methods use quantum mechanical forces. The methods have been applied to both gas and condensed-phase processes in energetic materials. The method of "Direct Dynamics" is simply standard atomistic simulations (both classical MD and VTST) in which quantum mechanical forces are evaluated at each simulation step. In the case of MD, the quantum mechanical forces are used to integrate the equations of motion. In VTST, points along the reaction coordinate used in evaluating reaction rates are generated by quantum mechanical calculations. Car-Parrinello MD 12 is another methodology similar to the classical MD method, but it includes equations of motion that treat electrons explicitly.

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An empirical predictive methodology popular in pharmaceutical and biological research is quantitative structure property/activity relationships (QSPR/QSAR). 13 In the QSPR/QSAR method, models are developed that describe statistical correlations between molecular descriptors (such as structural features) and macroscopic behavior (i.e. physical or chemical properties or biological activity). QSPR/QSAR has received some attention in the energetic materials field, mainly in attempting to find correlations between molecular properties and impact sensitivities of energetic materials. Some of the most popular molecular descriptors for use in establishing the correlations are those that can be readily determined through QM calculations, such as bond dissociation energies and features of electrostatic potentials. All of these computational techniques have been extensively reviewed and described elsewhere and will not be presented in detail here. Rather, I will provide a general description of the methods and refer the reader to more complete technical descriptions. My purpose here is to point out successful applications of the various methods to energetic materials research. This chapter describes QM studies in energetic materials for both gas and condensed phases; but the discussions of molecular dynamics simulations of energetic materials will be limited to non-reactive processes in the condensed phase; reactive MD simulations of energetic materials in both gas and condensed phases are discussed by Thompson and Fried in this book. 3. Quantum Mechanical Calculations 3.1. Gas

Phase

3.1.1. Molecular Properties The most routine QM calculations (DFT with a 6-31G* basis set) predict the molecular structures of stable conformations of an energetic material and provide vibrational analyses of these local minima. Earliest applications of QM to predict these properties 14 ' 15 were used to assess the quality of the calculational method by comparing results with known experimental data where available, but QM calculations are now being used to predict properties and stabilities of notional materials. QM calculations are particularly useful for energetic materials characterization, because experimental structural and vibrational data are often so complex that their interpretation is necessarily ambiguous. The QM methods have now evolved to predicting accurate structural information for molecules with only modest computational resources. Therefore, QM structures and vibrational spectra

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are routinely being used to complement the experimental information, and allow for assignment of vibrational frequencies that are otherwise difficult to assign with certainty. One particularly useful example of how such calculations can resolve certain structural discrepancies is found in theoretical studies in which vibrational and electron diffraction spectra were simulated. Before 1991, the gas-phase structure of the explosive 1,3,5-trinitro-s-triazine (RDX) had not been resolved. RDX, a monocyclic nitramine, is a solid at room temperature (denoted a-RDX), and x-ray diffraction measurements of the crystal indicated that the ring atoms are arranged in the chair conformation, with one of the nitro groups in an equatorial position relative to the ring, and the remaining two nitro groups in axial positions relative to the ring. Unfortunately, the gas-phase structure and the structure of the molecule in the liquid and the unstable /3-solid phase were not directly resolved. Karpowicz and Brill, in a series of FTIR experiments, showed that the infrared spectra of RDX in the vapor, solution and /3-solid phases could be explained only by assuming a molecular structure of higher symmetry (C^) than that of the a-solid. 16 Structural details of a molecule with this symmetry could not be obtained from the experimental results. Further, Karpowicz and Brill suggested that the results could be due to a "conformationallyaveraged" structure with C3„ symmetry rather than a single structure, due to the possibility of a significant degree of flexibility of the nitro groups and the ring. In 1991, electron diffraction (GED) measurements of gas-phase RDX were performed, 17 providing additional data about the molecular structure of RDX in the gas phase. Unfortunately, unambiguous resolution of structural details from such measurements can be obtained only for small molecules, because larger molecules have many similar interatomic distances and bond angles which are not separately measurable by GED. Thus, for such cases (including RDX), interpretation of the experimental diffraction intensities is accomplished by constructing molecular models whose structural parameters are adjusted until the diffraction intensities are reproduced. This method does not ensure a unique solution. The structural model that best reproduced the measured diffraction intensities for RDX had 03^ symmetry, with the ring in the chair conformation and the nitro groups all axial relative to the ring. 17 Although earlier theoretical calculations using low levels of QM and SE theories had been performed for conformers of RDX, two subsequent studies were published that used a level of QM theory that is known to produce accurate results. 18 ' 19 In one of these, 19 second-order Moeller-Plesser (MP2) and non-local DFT geometry optimizations and normal mode analyses were

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conducted for three conformers of RDX, one of which was consistent with the a-crystal form and the remaining two having C3,, symmetry. Simulated infrared spectra for the three conformers were then generated using the QM calculations and compared with experimental spectra. The simulated spectra for the two structures with C3,, symmetry were quite different, with one in good agreement with the FTIR results for RDX in the vapor phase. Further, the structure of this conformer was in overall good agreement with the electron diffraction results, with the exception of two structural parameters. Thus, in order to investigate possible causes of discrepancies between the theoretical and experimental structures, a subsequent QM calculation was performed in which electron scattering intensities were simulated for six conformers of RDX for comparison with the experimental intensities. 20 The results show that alternative structures to that proposed from experiment can reproduce the measured intensities. Also, this study predicted the barriers to interconversion between the six conformers, in order to investigate the possibility of rapid interconversion of the molecule at the temperature of the experiments. Zero-point energy corrected barriers range from 1.5-5 kcal/mol, suggesting that the conditions of the experiment allow rapid interconversion of the molecule and results could reflect a dynamically conformationally-averaged structure, as suggested by Karpowicz and Brill. 16 RDX is not the only energetic material in which interpretation of GED spectra predicted a structure inconsistent with calculated (QM) predictions. Bharadwaj and Smith, 21 in generating points on the PES for dimethylnitramine (DMNA), found that the equilibrium ground state structure of DMNA has C s symmetry, whereas the structure resulting from interpretation of GED results had C2t, symmetry. Upon fitting a classical force field to the QM information, Bharadwaj and Smith performed MD simulations of an ensemble of gas phase DMNA molecules at T = 343 K, the temperature of the GED experiments. The radial distribution functions (RDF) resulting from these simulations were consistent with the experimental RDF, suggesting that the GED results cannot be assigned unambiguously to a single molecular structure. These two examples clearly illustrate the need for QM calculations to augment experimental findings.

3.1.2.

Thermochemistry

Important thermochemical properties of gas-phase energetic materials are easily and accurately predicted using QM theory. 22 The heat of formation in the gas phase can be readily determined using a variety of QM-based

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schemes. One of the most accurate, though computationally expensive, approaches is the Gaussian-x method (most recent being the Gaussian-3 23 level and variations thereof), in which enthalpies of formation are determined using rigorous molecular orbital predictions of total energies of the molecule and experimental enthalpies of formation of the constituent atomic species. While the degree of accuracy of this method is quite good for the wide variety of molecules to which it was applied, its computational demands are prohibitive for all but the simplest energetic materials. Other methods, similar in spirit to the Gaussian-a; methods but requiring far less computational resources, are the BAC-MP4 method 24 (which introduces an empirical bond-additivity correction into the calculations) or those using DFT 2 5 ' 2 6 ; however, these do not have as high a degree of accuracy as the Gaussian-a: methods. Reaction enthalpies of gas-phase reactions calculated using QM methods can also be used to determine the gas-phase heat of formation of either the reactant or product according to the following relation 22 : A

#Reaction = &H°f (Products) - AH°f (Reactants).

(1)

In this case, the gas-phase heat of formation of, for example, the reactants is obtained by using the QM-predicted reaction enthalpy and a reliable experimental value (if available) of the heat of formation of the products. Accuracy of the method increases if the number of electron pairs and chemical bond types are conserved in the reaction, because errors inherent in the calculation due to the approximate treatment of electron correlation cancel. This approach was recently applied to a series of nitroaromatic compounds to discriminate among conflicting experimental data. 27 Equation (1) also corresponds to the bond dissociation energy (BDE) for a species, if the reaction that is being evaluated is a simple bond scission.28 The BDE has been calculated in several studies of energetic materials in which attempts were made to establish correlations between the magnitude of the dissociation energy of the weakest bond and sensitivity of the material to impact. 29 ~ 36 This work has shown that such correlations are weak, although a strong correlation was found between sensitivities to impact and the ratio of the BDE to heat of reaction for a series of explosives.37 A very convenient procedure for evaluating gas-phase heats of formation that circumvents limitations of the previously described approaches is the method of atom equivalents. In this scheme, the gas-phase heat of formation is defined as

AHi = Ei-Y,nJej

(2)

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where Ei is the energy of molecule i, Sj (denoted as an "atom equivalent") is defined as Sj = (Ej — Xj), Ej is the energy of an atom j that is a component of molecule i, rij is the number of j atoms in molecule i, and Xj is the correction for atom j at the level of theory used, or, if desired, for temperature and zero-point energy. The atom equivalents are determined through least-squares fitting of Eq. (2) to experimental heats of formation and quantum mechanical energies for several representative molecules. This approach has been applied to molecules with functional groups common to energetic materials (e.g. NO2) in several studies in which the energies were evaluated using DFT. 3 8 ^ 4 2 Comparison of the gas-phase values with experiment for several of the studies show standard deviation of the predictions from experiment are of the order of 3 kcal/mol. 39 ^ 41

3.1.3. Reaction Mechanisms In addition to providing molecular properties and thermochemistry, quantum mechanical calculations also provide details about the reactions of energetic materials, such as activation barriers and mechanistic information that might be hard to observe experimentally. These reaction details allow the assessment of the chemical kinetic mechanisms that are often required to model energetic material processes at the meso- and macroscopic levels. When performing such modeling, one must propose a chemical kinetics mechanism. A chemical kinetics mechanism consists of a series of elementary reactions that lead to the final products. These products are often some of the few experimental observables because reactions of energetic materials are complex and it is difficult to determine rate information. Often different chemical reaction mechanisms can produce similar product sets. Therefore, construction of a reaction scheme may rely on scientific intuition and experience rather than on measurements from which direct extraction of all fundamental individual reaction steps can be taken. Rate constants for the individual steps may be assigned either from known values or reasonable approximations, and series of chemical kinetics modeling studies performed to determine consequences of different reaction sets and rates. In addition to the uncertainties introduced with the assumed reaction set, there is often uncertainty in rate information associated with the various elementary reactions. For example: in fitting the Arrhenius form to measured data, often the value of the frequency (or A) factor is assumed, and the activation energy is adjusted during the fitting procedure. An improper choice of frequency factor could result in a poor activation energy, affecting a key reaction in

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the assumed chemical kinetics scheme. The following theoretical study of the unimolecular decomposition of nitromethane demonstrates how QM calculations can be used to identify and assess the probability of different reaction mechanisms, and reduce the uncertainty in reaction schemes for energetic materials that might lead to extremely misleading results if used in combustion modeling. For such a simple system, a reasonable assumption is that the unimolecular decomposition of nitromethane proceeds through cleavage of the weakest bond in the molecule, the C-N bond. The BDE is estimated to be ~ 60 kcal/mol. 43 ' 44 However, an analysis of results from infrared multiphoton dissociation (IRMPD) experiments led to the proposal that decomposition via isomerization to methyl nitrite followed by scission of the nascent C - 0 bond was a viable and energetically-favored mechanism. 45 Detailed theoretical studies have since been performed to investigate the viability of this step as the low-energy pathway, 46 ' 47 including one in which an extensive mapping of possible unimolecular decomposition pathways were performed.46 This study considered several different decomposition paths, involving numerous reaction intermediates and transition states. Structures for all critical points were determined using DFT and the B3LYP density functional; energies were refined using the G2 MP2 level. The studies showed that simple C-N bond scission is energetically favored over the two-step isomerization pathway by 2-3 kcal/mol, in direct conflict with the experimental result. A subsequent QM study 47 using higher levels of ab initio theory was performed in an attempt to clear up the discrepancy between experiment and QM predictions but the discrepancy persisted. This latter study predicted a C-N BDE of 60 + 2 kcal/mol, in agreement with both experimental and other theoretical results, but a barrier to isomerization to form methyl nitrite that is ~ 6 kcal/mol higher than the C-N bond scission. The authors of this QM study 47 point out that the experimental barriers were obtained from an RRKM analysis in which SE results were used. Because SE is an approximate quantum mechanical treatment, and has failed in predicting molecular properties of some energetic molecules, 48 ' 49 it is possible that error was introduced into the RRKM analysis of the experimental data. This example provides a most compelling demonstration of how QM calculations can be used to assess proposed reaction schemes through accurately mapping out the reaction paths of individual steps. The complexity of the PES of nitromethane decomposition is not unique to that system; complexities of unimolecular decomposition of other

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energetic species are evident from DFT mappings of the unimolecular decomposition pathways of the secondary explosives RDX 50 and HMX (octahydro-l,3,5,7-tetranitro-l,3,5,7-tetrazocine). 51 In the HMX studies, 51 for example, three reaction paths were mapped out in which the initiation step was assumed to be that of (a) N-N bond scission; (b) concerted HONO elimination; and (c) decomposition resulting from formation of CH2O + N 2 0 through either oxygen migration or secondary decomposition of methylene nitramine. The calculations identified at least 15 reaction intermediates and 16 transition states among the various reaction paths. All this information about the reaction intermediates and transition states would be very difficult, if not impossible, to determine experimentally. The calculations clearly indicate that the most probable unimolecular decomposition pathways involve consecutive HONO eliminations, whereas earlier it was assumed that cleavage of the weak N-N bond was the initiating step in the unimolecular decomposition.24<52~54 The results indicate that, while the initial N-N scission is energetically favored, subsequent decomposition of the fragments is less favorable. This study also showed that the RDX and HMX decomposition reaction pathways are similar, leading the authors to propose a unified reaction mechanism consistent with the majority of mass fragments observed in thermal decomposition experiments. 55 Subsequent to this study, four additional reaction channels for the HMX decomposition process were identified in a direct dynamics study of the HMX decomposition pathway. 56 The analysis of rate constants determined in this kinetics study, which used transition state theory and statistical thermodynamics, led the authors to conclude that the dominant reaction mechanism begins with scission of the N-N bond followed by unzipping of the ring. The conflicting conclusions of the theoretical studies and the complexity of this PES invite further study of this important energetic material. These examples demonstrate the importance of using QM calculations in the construction and assessment of proposed chemical kinetics mechanisms and for analyzing experimental data. However, the multi-reference nature of many energetic materials and their reaction intermediates and products requires that in some cases, they be treated with higher levels of ab initio theory than the more modest levels such as unrestricted Moller-Plesset theory (UMP2) or DFT that work well for many non-energetic chemical systems. An example of this was shown in an ab initio study of the reaction HNO + NO to form the products N 2 0 + OH. 57 Kinetic modeling of the flame resulting from combustion of a nitramine-containing propellant identified this reaction as the most sensitive in affecting the ignition chemistry

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of the propellant. Therefore, there was a critical need to quantify the rate of this reaction in order to proceed with the modeling and interpretation of experimental data. However, Bunte et al.57 found that UMP2 was not sufficient to treat this open-shell doublet reaction, because of large spin contamination in the unrestricted Hartree-Fock zeroth-order wave functions. Bunte et al. showed that reaction paths generated by the UMP2 calculations for this reaction differed significantly in some details from those determined at more suitable levels of theory to treat systems such as these. Unfortunately, these higher levels (coupled-cluster theory and its subsets) have large computational requirements and such treatments are currently too expensive for most energetic materials. However, we foresee that in the future, improvements in computational architectures and algorithms will allow for QM treatments of energetic materials at these higher levels of theory. It is notable that since the Bunte et al. study, a comparative study of the decomposition of DMNA using B3LYP and QCISD (quadratic configuration interaction calculations including single and double substitutions) treatments showed that the density functional calculations were in good agreement with the more computationally-intensive QCISD values. 58 Thus, I recommend that further comparisons be performed for energetic materials to determine if density functional treatments are suitable for energetic materials. Until then, however, care should be taken when assessing results of modest calculational treatments of systems with multi-reference character.

3.1.4. Electrostatic Potentials QM calculations of isolated molecules can be used to generate molecular descriptors for use in the QSPR/QSAR approaches to predict properties and behavior of energetic materials on the macroscale. The methods described here are based on ideas proposed by Politzer and co-workers,59 who developed a general approach for predicting macroscopic properties of condensed-phase materials from electrostatic potentials (ESP) of isolated molecules. ESPs can be determined through diffraction measurements or evaluated using quantum mechanical theory, and are often used in identifying reactive sites within molecules. Politzer et a/.59 analyzed patterns of the electrostatic potentials on isosurfaces of electron densities of isolated molecules, and found that correlations exist among certain statistical properties of these potentials with bulk properties of materials that are typically related to intermolecular interactions. These statistical properties

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of the electrostatic potential are used in what is termed a "general interaction properties function" (GIPF), whose form depends on the macroscopic property of interest. Politzer et al.69 had many successes in using the GIPF method to predict aqueous solvation free energies, lattice energies in ionic crystals, diffusion coefficients, solubilities, heats of vaporization, sublimation, and fusion, boiling points, partition coefficients and critical constants. A successful example of the GIPF methodology to energetic materials research is found in the prediction of the solid state heat of formation of an energetic material, a property required to assess potential performance of an energetic material. As shown earlier, the gas-phase heat of formation of an energetic material is one property that can be readily calculated using QM methods. However, the heat of formation in the condensed phase is required to assess the detonation or gun-firing performance of an energetic material. This property cannot be calculated directly using quantum mechanics but if the gas-phase heat of formation and the heats of sublimation or vaporization are known, application of Hess's law, A#(Solid) = AH (Gas) - AF(Sublimation)

(4)

Aff(Liquid) = Atf(Gas) - A H (Vaporization)

(5)

gives the heat of formation in the condensed phase. The heats of sublimation or vaporization cannot be obtained directly from QM calculations; however, these properties can be obtained using the GIPF approach. Politzer et al.59 showed that the statistical descriptors within the GIPF methodology, SA, a\ot and u, are related to the heats of vaporization and sublimation: AiJ(Vaporization) = a v / (SA) + bJa^otu

+c

(6)

AH (Sublimation) = a'(SA) 2 + b'yJa^otv + c'.

(7)

and

In these equations, SA, a\ot and v are global properties of the ESP on the specified isosurface of electron density (Politzer recommends the 0.001 electron/bohr 3 isosurface). The SA is the molecular surface area of the isosurface of electron density and the quantity a^ot reflects the variability of the electrostatic potential on the molecular surface. The quantity v shows the degree of balance between the positive and negative potentials on the molecular surface. The constants a, 6, c, a', 6', and d are determined by least-squares fitting of Eqs. (6) or (7) to experimental values of the heat of vaporization or sublimation.

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Politzer et al. developed a GIPF description of the heats of vaporization and sublimation for organic molecules60 using information for 34 organic compounds, most of which were non-energetic species. The resulting GIPF description of the heat of sublimation was then used, along with DFT predictions of gas-phase heats of formation, to predict the solid-phase heat of formation of five CHNO species, four of which are energetic materials. The results were in good agreement with measurements, and have an average error of 2.8kcal/mol. We performed a subsequent study, 41 except CHNO molecules with functional groups common to energetic materials were used to parameterize the GIPF functions. In our work, the root mean square (rms) deviation of the predicted heats of vaporization from 27 experimental values is 1.7kcal/mol, and the rms deviation of the predicted heats of sublimation from 36 experimental values is 3.6 kcal/mol. The computations using gas-phase heats of formation and the GIPF functions predicted liquid heats of formation for 24 energetic materials with a rms deviation from experiment of 3.3 kcal/mol. Similarly, predicted solid-phase heats of formation for 44 energetic materials have a rms deviation from experiment of 9.0 kcal/mol. Politzer and co-workers also attempted to use the GIPF approach to predict a macroscopic property that is not known to be a direct function of nonbonding interactions in a material: impact sensitivities of an explosive.61 These authors examined 13 nitroaromatic, 8 nitramine and 5 nitroheterocyclic molecules, and found functional relations between impact sensitivities and properties of the electrostatic potential for each class of explosives. The functional descriptions of the correlations were different between the classes, but each correlation was given by descriptors that reflected the degree of imbalance between the positive and negative regions of the surface electrostatic potential. A single functional form could not represent all three classes adequately. An improved predictive methodology using the GIPF would describe the impact sensitivity of any explosive regardless of its structural type; unfortunately, our subsequent study 62 suggests that the current GIPF approach is unable to achieve this goal. Because the most common measure of impact sensitivity, the drop hammer test, sometimes produces widely varying and unreproducible results, use of such results within the GIPF approach might produce erroneous correlations. Therefore, it is important to use measured data under which conditions of the tests were unvarying, well defined and controlled. We 62 performed QM characterizations for a set of 34 polynitroaromatic and benzofuroxan molecules (denoted the training set) for which drop

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weight impact test measurements were performed under the same conditions, using the same machine and the same operator. 63 Initial attempts were made to use only statistical quantities associated with the ESPs of the molecules in establishing correlations with the training set, as prescribed by the GIPF method of Politzer et al.59 Also, in order to assess whether any correlation was maintained with explosives outside the training set, Rice and Hare chose a different set of explosives for which reliable drop weight impact test measurements had been performed (denoted the test set), and applied the new models to them. The test set includes FOX-7 (l,l-diamino-2,2-dinitro-ethylene), methyl picrate (2-methoxy-l,3,5-trinitrobenzene), HNS (2,2',4,4',6,6'-hexanitrostilbene), styphnic acid (2,4,6-trinitroresorcinol), the (3- and £-polymorphs of CL-20 (2,4,6,8,10,12-hexanitrohexaazaisowurtzitane), PETN (pentaerythrityl tetranitrate), HMX, RDX, NTO (5-nitro-2,4-dihydro-3H-l,2,4triazol-3-one), and NQ (nitroguanidine). While there appears to be modest correlations with GIPF models, all of these models had severe deficiencies in describing certain explosives, particularly insensitive explosives {h$Q%> 150cm). The inability of the GIPF models to adequately predict sensitivities of all of the explosives in the training and test sets, particularly the insensitive explosives, suggest that other quantities must be incorporated into these models. For example, one could use measures of the imbalance between the positive and negative potentials on the isosurface of electron density of a molecule. While no correlation using functional description using GIPF parameters or other molecular descriptors was determined that could reproduce all measured data, we observed a particular feature in the ESPs that appeared to be related to sensitivity to impact. 62 These surface potentials show that the most sensitive CHNO explosives have regions of very positive ESPs localized over covalent bonds. This localized region of electron deficiency over covalent bonds is not apparent in the insensitive explosives that were evaluated. Also, this feature in the ESPs of the explosives examined in this study is independent of chemical classification; localized electron deficiencies over covalent bonds were observed in sensitive nitroaromatic, nitrate ester and nitramine systems This feature was also observed by Murray et al.,61 and they used a descriptor of localized charge in the GIPF functionality; however, application of their model to the Rice and Hare test set did not result in a good prediction. Thus, the GIPF approach did not quantitatively predict sensitivity to impact; however, these studies did present evidence that the sensitivity of a system to impact appears to be associated

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with degree of electron deficiency over the skeleton of an explosive molecule. Such information may be useful as indicative of possible sensitivity problems, and also invites further research to establish whether these regions of localized electropositive charge reflect chemical instability of the explosive and whether such features on the ESPs have a mechanistic or physical basis for sensitivity to impact.

3.2. Condensed

Phase

The number of quantum mechanical calculations of properties and processes of condensed-phase energetic materials are growing with the increase in computer speeds and availability of solid-state QM software. Numerous condensed-phase quantum mechanical calculations of explosives were performed by Kunz and Kuklja 64-70 using the periodic Hartree-Fock method with energies adjusted by electron correlation corrections based on manybody perturbation theory. These studies attempted to identify the role of electronic transitions in initiation to detonation, a process in which a material is rapidly compressed. Toward that end, they calculated the band structure of ideal crystals of energetic materials and of crystals that contained different types of defects, including voids, slip planes, and edge dislocations. They also investigated changes to the band structure upon isotropic or uniaxial compression of both perfect and defect-containing crystals. Their work has shown that the gap between the valence and conduction bands of the material is affected by the presence of dislocations, and that compression of the material narrows this band gap. However, many of their studies assumed rigid molecules: therefore, the molecular structure was not allowed to relax. Other calculations using different QM methods were also performed to explore the role of electronic transitions in initiation to detonation. 71 ~ 73 Although not a condensed-phase QM study, a complete-active-space-selfconsistent-field (CASSCF) calculation 71 on a single nitromethane molecule was performed to investigate the role of excited electronic states in initiation processes. These calculations showed that upon bending the NO2 group out of the equilibrium CNO2 plane, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) states cross. Additionally, the energy of this crossing, and the structure of the molecule is near that of nitromethane in the triplet excited state. These results suggest that non-radiative transitions from electronic excited

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states could influence initiation reactions under conditions that produce a significant deformation of the molecular structure. Subsequent static and dynamic DFT calculations 72 of perfect nitromethane crystals and crystals containing defects and voids were performed. Band gaps were calculated for crystals subjected to hydrostatic stress, uniaxial strain and shear strain associated with shock loading. Relaxation of the molecular structure and cell parameters were allowed in these calculations. None of the calculations showed a significant narrowing of the band gap. Rather, structural relaxations occurred that allowed the molecules to maintain geometries close to their low-pressure values. These results, when analyzed in light of the CASSCF calculations on the single molecule,71 suggest that significant distortion of the molecules in the crystal is required to produce a narrowing of the band gap to the point that the thermal conduction band will be populated at conditions of detonation. While these authors provided hypotheses for conditions that would allow for closure of the band gap, 72 additional large scale ab initio dynamic calculations would be required to support these. The effect of pressure and molecular vacancies on the band gap of nitromethane was further explored using the self-consistent charge density functional tight binding (SCC-DFT-TB) scheme, 73 a process that allows for the study of larger supercells than that used by Reed et al.72 and which can accommodate concentrations of molecular voids. The results of these calculations 73 were consistent with the Reed et al. calculations 72 in that the band gap was not significantly lowered with pressure. However, the results indicated that under conditions of both uniaxial and isotropic compression, C-H bonds lengthen with increased pressure to a point at which the hydrogen atom dissociates. This result suggests that transitions from covalent to ionic C-H bonds and chemical reactions precede the closing of the band gap, but that narrowing of the gap would be facilitated by the presence of the dissociated protons. The authors caution that this hypothesis should be explored using more accurate ab initio methods. All of these calculations indicate that complex shock-induced electronic transitions might be involved in the initiation to detonation and thus cannot be precluded from mechanistic arguments. It is imperative that development of high level, computationally tractable QM methods for the solid state be aggressively pursued so that implications emanating from these results can be explored. QM/MD calculations of reactions of energetic materials in the condensed phase have also been performed, but these studies are discussed in the chapter by Fried.

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4. Classical Molecular Simulation Classical molecular simulation methods are the most practical means now available to calculate thermodynamic properties of a condensed-phase energetic material or study its time-dependent processes, due to the modest computational requirements compared to QM calculations. The classical methods are easily implemented, amenable to parallelization and MD and MC methods can treat the various thermodynamic ensembles, such as microcanonical (constant volume, constant energy), isothermaMsochoric (constant temperature, constant volume), and isothermaHsobaric (constant temperature, constant pressure). MP calculations provide a rapid means to obtain optimized crystal structures (and resulting density) and are used in ab initio crystal prediction, a method developed to predict how a molecule will pack in the solid state. One of the most limiting factors of the MD, MC and MP simulations, however, is their dependence on a description of the interactions among all of the atoms in the system. This section will discuss efforts in development of interaction potentials of energetic materials and their application in classical molecular simulations, and then provide examples of how molecular simulations can assist in energetic materials development and design. Because molecular simulations of reactions in both gas and condensed phases are discussed by other contributors to this volume, we will not include those in this section. Rather, we will discuss classical molecular simulations used to predict properties or nonreactive processes associated with performance of the energetic material. A molecular dynamics simulation of the initiation and propagation of a detonation wave through a real explosive crystal is probably the most ambitious and eagerly-awaited simulation in energetic materials research. The interaction potential to describe such a process must correctly describe breaking and formation of covalent bonds in a system containing a large number of molecules. However, it is equally important that the interaction potential of a real explosive correctly describes the weaker non-bonding interactions that govern how the molecules pack in the crystalline state. Further, a good model should accurately predict mechanical and thermodynamic properties of the material over wide temperature and pressure ranges. At this time, no interaction potential of a real explosive exists that accomplishes all of these goals, particularly with regard to reactions of the material in the condensed phase. This bottleneck in model development is due to the lack of detailed information regarding reactions of energetic materials in the condensed phase. This obstacle, however, has not precluded the development of functions that can be used in molecular simulations of

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non-reactive processes of real energetic materials, many of which will be discussed herein. 4.1. Condensed

Phase Interaction

Potentials

A reasonable approach in developing an interaction potential that describes both reactive and non-reactive processes begins with a simple functional description of the system that is parameterized using available data. The function is used in molecular simulation to assess its performance in predicting properties or processes of the material. Adjustments to the functional form or parameters or enhancements of the potential can be made as needed, and the model applied to molecular simulations of processes of ever-increasing complexity including those that precede reaction. By developing the models in this evolutionary approach, one hopes that a model will emerge with the capability to describe a wide range of reactive and non-reactive processes in energetic materials. Because the state of development of reactive potentials of real explosives is given elsewhere in this volume, this section will be limited to describing modeling of non-reactive processes of energetic materials using non-reactive potentials. The models used to describe intermolecular interactions are usually simple pair-additive functions that can be decomposed into van der Waals and electrostatic interactions. The van der Waals interactions are typically described by simple functions such as Lennard-Jones or exponential six, and the electrostatic interaction is usually assumed to have a simple Coulombic form, where the atomic charges are often determined through fitting of atom-centered partial charges to the QM-generated ESP of the explosive molecule, or selected to reproduce measured multipole moments. The models are classified as either rigid or flexible, with the former assuming that the molecular frame is fixed during the simulation (i.e. there are no intramolecular interaction potential terms), thus allowing only the intermolecular distances and relative orientations to vary. Most of the functions that describe intermolecular interactions are parameterized using experimental information about the crystal at room temperature conditions, but QM calculations of interactions between the molecules or between functional groups on the molecules are used to supplement the information used in the parameterization. 74 The flexible models include descriptions of the intermolecular interactions and functions that describe various intramolecular motions. The intramolecular terms are typically common functions such as Morse or

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harmonic oscillators to describe bond stretching, harmonic oscillators to describe bond angle bending or wagging motions, or simple cosine series to describe torsional motions. These functions are parameterized to reproduce experimental vibrational frequencies or fitted to force constant matrices that are generated through quantum mechanical calculations of isolated molecules. Incorporating flexibility into the models increases the computational requirements, but this is necessary to study dynamic processes associated with high temperatures and pressures, or to investigate energy flow within an explosive crystal. At this time, there are only a handful of interaction potentials that describe real explosives, including HMX, 74 RDX, 75 nitromethane, 76-78 l,3,5-triamino-2,4,6-trinitrobenzene (TATB), 79 PETN, 80 FOX-7, 81 ammonium dinitramide (ADN), 82 ammonium nitrate (AN), 83 and NTO. 8 4 Most simulations carried out using these models have assessed their performance in molecular simulation and identified deficiencies. In particular, two models have been subjected to extensive testing through molecular simulation of various processes, and have demonstrated impressive performance in molecular simulations of a variety of properties and processes. 4.2. Results Using the Sorescu, of CHNO Explosives

Rice,

Thompson

Model

4.2.1. Rigid Molecule Approximation A very simple model used to study dynamic processes in a wide variety of solid explosives was developed by Sorescu, Rice and Thompson (SRT) 75 ; its form is a simple atom-atom exponential-six plus Coulombic potential. The partial charges used in the Coulombic interaction terms were determined by fitting atom-centered partial charges to a quantum-mechanically determined electrostatic potential for a single RDX molecule whose structure corresponded to that in the crystal at ambient conditions. The remaining exponential-six parameters were adjusted to reproduce the experimental structure of the RDX crystal at ambient conditions. SRT found that this interaction potential could also describe the geometric parameters and lattice energies of different polymorphic phases of two other nitramine crystals: the polycyclic nitramine CL-20 85 and the monocyclic nitramine HMX. 86 Further investigations exploring the limits of transferability of this interaction potential to other energetic molecular crystals were undertaken by performing MP calculations for 30 nitramine crystals 87 and 51 non-nitramine CHNO crystals. 88 MP calculations using this interaction

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potential reproduced the crystal structures of all of these to within 5% of experiment. All of the simulations applied the rigid molecule approximation. Because the physical and chemical processes of energetic materials that are of most interest occur at high pressures and temperatures, a regime in which conformational molecular changes become important, the next step in model development was to explore the validity of the rigidmolecule assumption in simulations of energetic materials under hydrostatic compression. Therefore, SRT analyzed the dynamics of the important energetic crystals RDX, HMX, HNIW and PETN under hydrostatic compression conditions using NPT-MD simulations and this simple intermolecular potential. 89 In that study, predicted lattice parameters for the RDX, HMX and HNIW crystals were found to be in good agreement with experimental values over the entire range of pressures investigated experimentally. For the PETN crystal, the calculated crystallographic parameters were in acceptable agreement with experimental data only for pressures up to 5 GPa. For higher pressures, the disagreements of predictions with experiment demonstrated the inadequacy of the rigid-body approximation when used in simulations of floppy molecules such as PETN. However, the SRT results suggest that at moderate temperatures and pressures, simulations using the rigid-molecule approximation will provide reasonably accurate results at a significantly reduced computational cost compared to those that use more complex flexible interaction potentials. 4.2.2. Flexible Model: Nitromethane (a) Condensed phase thermodynamic properties SRT next extended their CHNO intermolecular potential to include intramolecular terms for use in simulations of the simple nitroalkane explosive, nitromethane. 78 ' 90 Nitromethane is a popular system for modelers, because of the small number of atoms and because extensive data from numerous experimental investigations of its properties over a wide range of conditions are available to assess a model. SRT performed NPT-MD simulations over the entire solid phase at 1 atm, and at pressures ranging from 0.3 to 7GPa at room temperature. 78 The results indicate that the model is able to reproduce accurately the changes of the structural crystallographic parameters as functions of temperature and pressure for the entire range of values investigated, including an experimentally-observed 45° change in methyl group orientation in the high pressure regime relative to the low-temperature configuration. MD simulations of the liquid

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at ambient pressure in the temperature range 260-374 K and over a wide pressure range at 298 K were also performed, with the majority of liquid properties being reproduced. However, the model gives less accurate predictions of the dielectric permittivity of liquid nitromethane. 90 This was attributed to the lack of polarization effects in the intermolecular interactions. Further studies have used the SRT model to explore more complex processes of explosives, including energy transfer 91 and melting. 92 (b) Energy transfer in the liquid The investigation of energy transfer mechanisms in liquid nitromethane was stimulated from experiments that followed the vibrational energy redistribution of certain molecular vibrational modes in the liquid. Spectroscopic data 9 3 with high time resolution and sensitivity were obtained using antiStokes Raman spectroscopy to study the vibrational excitation and relaxation phenomena after excitation of the CH stretches. The data showed how energy is redistributed in the system, first among the molecular vibrations of the excited molecules and followed by heating of the bath molecules. Constant energy constant volume (NVE) MD simulations of the liquid,91 equilibrated to conditions consistent with the experiment followed by excitation of the CH stretching vibrations of 25% of the molecules in the simulation cell, produce results in qualitative agreement with the experimental data, 9 3 including rapid relaxation of the excited CH stretches into different vibrational modes of the molecules, a multi-stage vibrational cooling process, and excitation of modes of the surrounding unexcited molecules through indirect rather than direct intermolecular vibrational energy transfer processes. Unfortunately, classical molecular dynamics simulations do not reflect quantum effects that might influence the energy transfer process. Therefore, we hope that algorithms and computational advances will soon allow for a quantum description of the energy transfer process in liquid nitromethane. (c) Melting Melting of nitromethane was also explored using the SRT model using two types of MD simulations. 92 The first type of simulation is one in which the crystal is gradually heated until a parameter that monitors the degree of translational order in the crystal abruptly decreases. This change indicates that the system has transitioned from the crystalline to the liquid state, and the temperature at which this occurs is the "transition" temperature. MD simulations using this method for several atomic crystals have shown that

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the transition temperature for a perfect crystal is substantially higher than the true thermodynamic melting temperature, but that the introduction of voids lowers the transition temperature. 94 ~ 96 Further, the studies showed that there is a range of void concentrations in the crystal that will produce a transition temperature near the true thermodynamic melting point. Therefore, the key assumption in this method is that the true thermodynamic melting temperature for any model corresponds to the transition temperature for a crystal containing a critical concentration of voids. The calculated value of the melting temperature for the nitromethane model using this method is in good agreement with experiment; however, because this method of predicting the thermodynamic melting point is empirical, a second melting simulation was performed in which a co-existence of the liquid and solid phases were simulated to confirm the result. For this method of simulating melting, a simulation cell was constructed in which a block of liquid nitromethane was appended to a rectangular block of crystalline nitromethane, and the system equilibrated (using NPT-MD) to the desired temperature and pressure. Once equilibrated, NVE-MD simulations were performed and the temperature and behavior of the system monitored. If the temperature of the system is too high, the solid portion of the crystal will melt. If the temperature of the system is below the melting point, the liquid portion of the cell will solidify. The melting point is the temperature for which the liquid and solid maintain a co-existence. The results for the two methods were in near agreement, with the slight difference being attributed to hysteresis associated with the direct heating process imposed in the void-nucleated melting simulation.

4.3. Results

Using the Smith and Bharadwaj

Model of HMX

A fully-flexible interaction potential for HMX developed by Smith and Bharadwaj 74 has been subjected to extensive testing in molecular simulation. The model has been parameterized using quantum mechanical information generated for four gas-phase conformers of HMX, two of which correspond to molecular structures in the /? and a crystalline polymorphs. Care was taken in parameterizing this potential to correctly describe conformation flexibility associated with nitro group rotation, inversion of the amine nitrogens, and inversions within the ring structure. Because their goal was to use a single function to describe the amorphous phases of HMX and all of its crystalline polymorphs, they performed numerous calculations for geometries associated with changes in the degrees-of-freedom leading

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to the transition from one conformer to another. Parameters for standard functions describing intramolecular motions were fitted using this information. Intermolecular interactions were described by forms reported in the literature or, where absent, parameterized using information generated from QM calculations of HMX or from DMNA or l,3-dimethyl-l,3-dinitro methyldiamine (DDMD). 21 ' 74 Both DMNA and DDMD are moieties within the HMX structure that can be used to calculate valence parameters for HMX at a significantly reduced computational cost (it is assumed that the interactions within these molecules will be similar to those of the same moieties within HMX). The interaction potential also included electrostatic interactions with charges determined by obtaining the set that best reproduced the molecular dipole moment and the total electrostatic potential that was within 4 A of each atom (while excluding points within the van der Waals radius of each atom) from the MP2/6-311G** wave function. Unlike the procedure used by Sorescu et al.,75 Smith and Bharadwaj constrained the fit such that like atoms had equal charges. This model has been used in a variety of molecular simulations, some of which were performed for validation of the model. The validation studies used molecular dynamics to calculate lattice parameters and thermal expansion coefficients of the a-, (3- and £-HMX crystals, heats of sublimation for /3- and <5-HMX, and the room temperature isotherm and elastic tensor for /3-HMX.97'98 Results were in overall good agreement with experimental information. This model has also been applied in several molecular dynamics simulations to generate engineering parameters required for mesoscale simulations of composite explosives that use HMX as the energetic fill." 101 Strong interest in mesoscale simulations of heterogeneous explosives arises from their potential to characterize hot spots (localized regions of high temperature) in the explosive mix. Hot spots are believed to strongly influence (or control) performance and responses of an explosive, however, they have never been observed through experiment and little is known about them. The size of hot spots (thought to be in the millimeter-micron range) precludes evaluation in microscale simulations, but can be treated by mesoscale simulations. However, such simulations require as inputs thermophysical and mechanical properties about the components in the simulation that might be difficult to obtain through measurements. As described by Menikoff and Sewell,101 molecular dynamics simulations can provide data that are lacking or complement existing experimental data to generate the necessary inputs for the mesoscale simulations.

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Although the preceding examples of molecular simulations of energetic materials focused mainly on reproducing measured results, these numerous studies demonstrate the types of properties that should be calculated in validating any new interaction potential.

4.4. Molecular

Packing:

Ab Initio

Crystal

Prediction

Classical interaction potentials can also be used in another molecular simulation technique of importance to energetic materials development: ab initio crystal structure prediction. This type of calculation has the potential to significantly enhance and optimize the design and development of advanced energetic materials because it allows the prediction of a key property associated with performance of the material: its crystal density. The ability to predict the crystal density will allow a designer to assess performance without the need to synthesize the material. In this manner, candidates with densities that will produce less-than-satisfactory performance can be eliminated from further consideration before actual resources are expended on synthesis. Therefore, this important methodology is considered to be a key computational tool in the development of advanced energetic materials research. Ideally, ab initio crystal structure prediction identifies the most thermodynamically and kinetically-favored crystal structure using only theoretical information about a single molecule.102 However, practical limitations on current methodologies preclude an incontrovertible identification. These limitations include an inability to theoretically treat kinetic factors associated with crystal growth, such as solvent effects and crystallization conditions. Additionally, the majority of methods assume that the crystal structure with the lowest lattice energy corresponds to the thermodynamically-favored structure rather than the structure with the lowest free energy. This assumption effectively ignores entropic and vibrational enthalpic contributions to the free energy. Some methods restrict the molecular models used in the structure generation and packing calculations to be rigid. This restriction does not allow for the deformation of the molecular model by crystalline forces, and may affect the final result. Nevertheless, the current methods designed for crystal prediction are still useful because the calculations generate a set of low-energy crystal structures that usually include the experimental (true) structure (assuming good models of the intermolecular interactions and the molecular structure are used). While an indisputable identification of the experimental structure cannot be guaranteed using the current methods, the generation of a

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series of low-energy hypothetical crystal structures will provide a materials designer with a range of density values that will allow screening of the materials. The elimination of less promising materials identified through such a screening will reduce unnecessary synthesis and measurement and will allow time and other resources to be expended on the more promising candidates. Also, a set of hypothetical crystal structures can aid in the determination of crystal structures for cases in which the measurements are ambiguous. This is accomplished through simulation of powder diffraction patterns using the predicted structural information. These simulated spectra are then compared with the experimental data, and used to distinguish among many possibilities. Further, these calculations can be used to assess the quality of an intermolecular interaction potential in its ability to reproduce measured crystallographic parameters. Finally, the method can be used to rapidly examine a wide variety of notional candidate materials for applications in which crystal morphology or density is a critical indicator of behavior, activity and performance once the confidence level of the model is established. 102 Several methods have been developed for ab initio crystal structure prediction, and have been summarized in a report 103 of a study in which the various methods were subjected to a blind test of crystal structure prediction for four compounds. These methods generally follow a threestep prescription of (1) generating a three-dimensional molecular model; (2) creating hypothetical crystal structures using the molecular model; and (3) minimizing the energy of each hypothetical crystal. All of these require a description of interatomic interactions. The generation of the three-dimensional molecular model is now easily and rapidly accomplished using current quantum mechanical methods, described earlier in this chapter. The creation of hypothetical crystal structures using the molecular model can be accomplished in a variety of ways. As described by Gao and Williams, 104 the most general method of generating a hypothetical crystal structure is to place Z images of the molecular model randomly into a cell. In the absence of an imposed space-group symmetry in the cell, it is unlikely that the global energy minimum will be identified during the energy minimization step. Therefore, space-group symmetry of the cell is usually assumed before the creation of the hypothetical cell. Once the choice of space group has been made, a reasonable starting structure for the cell must be obtained. The parameters that must be assigned before energy minimization are the cell parameters and the orientation and location of the molecular model within the crystal. Once these are chosen, the remaining (Z - 1) molecules in the cell are generated using

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the space-group symmetry operations. Typically, several hypothetical crystal structures are generated for each space group for which the molecular orientation of the molecule has been randomly or systematically selected. The larger the number of hypothetical crystals that are generated, the more completely the configuration space is sampled. Most methods are limited to searching the most common crystalline space groups because the generation of large numbers of hypothetical crystals for the possible 230 crystalline space groups within a single calculation becomes too costly. Limiting the configuration space search in this manner is reasonable because a survey of organic compounds by Mighell et al.105 indicates that 90% of organic crystals are described by only 17 space groups. However, in the ideal case, all space groups would be sampled. The energy minimization step of the structural prediction procedure, while conceptually straightforward, possesses the most significant challenges of the calculation. As in any atomistic modeling procedure, the quality of the result is dependent on the accuracy of the description of the interatomic forces. As discussed earlier, the majority of interaction potentials to describe condensed-phase energetic materials are simple pairadditive functions, but even these simple descriptions lead to extremely complex PESs that contain numerous local energy minima. Therefore, in addition to being required to use an accurate description of interatomic forces, one is faced with identifying the global and low-energy minima on this surface. A few procedures have been proposed to address this important problem 106 but the majority of the methods use simple optimization procedures. Further, there is the issue of the energy rankings of the predicted crystals. Currently, lattice energies alone are being used to rank the crystals, and often a number of crystals of different symmetries have similar lattice energies; inclusion of intramolecular energies (i.e. conformational energies) in the ranking process might help distinguish among the candidate crystals. The simplest ab initio crystal prediction methods consider the molecules as rigid entities, and use analytical functional descriptions of non-reactive force fields; however, the validity of the rigid molecule assumption is questionable when considering the packing process. Typical CHNO energetic materials often contain internal rotors allowing for a variety of stable molecular conformers (e.g. HMX or CL-20 conformers). One factor that influences how a molecule will pack into a crystal is the arrangement of its atoms within the molecular structure. Thus, energetic materials that consist of different stable molecular conformers often have different polymorphic

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forms. These polymorphs can belong to different crystalline space groups and have different thermophysical properties, all of which could influence performance. Thus, it is important that the polymorphism be regarded when performing ab initio crystal prediction. This could be accomplished by including at least limited flexibility in the ab initio crystal prediction search. It is not necessary that a full-flexible interaction potential be used in the calculation; it is possible that inclusion of limited flexibility, such as those few degrees-of-freedom that describe transitions from the various molecular conformers would be sufficient. A related limitation is dependence of the calculations on the accuracy of the intermolecular interaction potential. While these models might be sufficient to generate local minima on the PES that correspond to measured crystallographic parameters, the accuracies of the energies might not allow for proper ranking. Further, the assumption of empirical forms always introduces a measure of uncertainty in the results. A more desirable alternative is to use quantummechanical forces in the ab initio crystal prediction calculations in order that more accurate descriptions of the interatomic interactions will be given. Unfortunately, such calculations are extremely time-consuming, and at this time, accurate solid state QM methods can only be used for small systems. The more computationally modest solid state DFT methods do not describe the van der Waals interactions that probably dominate the ways in which the organic crystals pack. Therefore, computationally efficient solid state quantum methods that accurately treat van der Waals interactions in organic crystals should be developed.

4.5. Crystal

Growth

Perhaps the most challenging obstacle in the ab initio crystal prediction method is the proper inclusion of kinetic effects associated with the crystallization process. In the current methods, it is assumed that the most thermodynamically stable phase is the one that will be formed; however, influence of a solvent in the crystallization process could favor formation of a thermodynamically less favored polymorph. Removal of this limitation should be aggressively pursued using theoretical chemistry methods, if possible. Of note are recent MM/MD approaches 107 ' 109 applied to HMX and RDX that are designed to lead to an understanding of effects that influence nucleation of polymorphs. These studies used MM/MD to determine morphologically important crystal surfaces109 and examine effects of solvent on crystal morphology. 107,108 In these studies, molecular simulation is

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used to calculate and rank attachment energies for different crystal faces. Attachment energy is defined as the energy released per growth unit upon adding a surface layer of one interplanar thickness onto a corresponding crystal surface, and has been assumed to be linearly proportional to the growth rate on t h a t surface. This energy should be reduced in the presence of a solvent; thus, calculations of the attachment energy reduced by the presence of solvent could be used to explain solvent effects on crystal morphology. It is encouraging t h a t a t t e m p t s are being made to use theoretical modeling methods to address a most difficult problem in energetic materials synthesis, and it is hoped t h a t advances along this line will be incorporated in ab initio crystal prediction methods. 5. C o n c l u d i n g R e m a r k s Applications of s t a n d a r d theoretical chemistry calculations of real energetic materials have resulted in the development of useful computational procedures t h a t could aid in advanced energetic materials research and development. Although there are several areas t h a t require improvements in m e t h o d s (particularly t h e solid-state q u a n t u m mechanical calculations), the incorporation of atomistic simulation and q u a n t u m mechanical prediction into the design, development, and testing processes of energetic materials is on the horizon. T h e examples described in this chapter not only show the usefulness of theoretical chemistry applications in energetic materials research but suggest t h a t they will lead to a fundamental understanding of the distinctive physicochemical behavior of energetic materials.

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C H A P T E R 12 C O M B U S T I O N A N D I G N I T I O N OF N I T R A M I N E PROPELLANTS: ASPECTS OF MODELING, SIMULATION, A N D ANALYSIS Eun S. Kim and Vigor Yang* Department of Mechanical and Nuclear Engineering The Pennsylvania State University 104 Research Building East University Park, PA 16802, USA * vigor@psu. edu

Contents 1. Nomenclature 2. Introduction 3. Description of Combustion-Wave Structures 3.1. Steady-State Combustion of RDX Monopropellant 3.2. Laser-Induced Ignition of RDX Monopropellant 3.3. Steady-State Combustion of Nitramine/GAP Pseudo-Propellants 4. Theoretical Formulation 4.1. Solid-Phase Region 4.2. Subsurface Multi-Phase Region 4.3. Gas-Phase Region 4.4. Boundary Conditions 5. Numerical Method 6. Discussion of Model Results 6.1. Steady-State Combustion of Nitramine Propellants 6.2. Laser-Induced Ignition of RDX Monopropellant 6.3. Steady-State Combustion of HMX/GAP and RDX/GAP PseudoPropellants 6.3.1. HMX/GAP Pseudo-Propellant 6.3.2. RDX/GAP Pseudo-Propellant 7. Concluding Remarks Acknowledgments References

369

370 371 377 377 378 380 381 382 382 385 388 390 391 391 395 400 401 406 412 413 413

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& V. Yang

1. Nomenclature A = cross-sectional area of propellant sample Ag = fractional cross-sectional area consisting of gas bubbles in two-phase region Aj = pre-exponential factor of rate constant of reaction j As = interface area between bubbles and liquid per unit volume a = pre-exponential factor of burning-rate law Bj = temperature exponent in rate constant of reaction j Ci = molar concentration of species i cpi = constant-pressure specific heat of species i Ej = activation energy of reaction j e = internal energy Hv = enthalpy of vaporization h = enthalpy hc = heat transfer coefficient hi = static enthalpy of species i h{. = heat of formation of species i at standard condition kj = rate constant of reaction j fn" = mass flux N = total number of species n = pressure exponent N-R = total number of reactions p = pressure Po = pre-exponential factor of vapor pressure in Arrhenius form Qlaser

=

rb = i? u = T = s= t = u = Vi = vn = Wi = Wi = WRJ = Xi = x = Yi =

laser

nea

t

n u x

propellant burning rate universal gas constant temperature sticking coefficient time bulk velocity diffusion velocity of species i average normal velocity component of vapor molecule molecular weight of species i mass production rate of species i mass production rate of reaction j molar fraction of species i spatial coordinate mass fraction of species i

Combustion

and Ignition of Nitramine

Propellants

371

Greek Symbols (f> = void fraction p = density A = thermal conductivity to = molar production rate Subscripts 0+ = gas-phase side of propellant surface 0~ = condensed-phase side of propellant surface c = condensed phase c-g = from condensed to gas phase cond = condensation eq = equilibrium condition evap = evaporation f = mass-averaged quantity in subsurface foam layer g = gas phase i = preconditioned state 1 = liquid phase s = propellant surface or solid phase v = vapor 2. Introduction This chapter deals with the state-of-the-art theoretical modeling and numerical simulation of steady-state combustion and laser-induced ignition of nitramine monopropellants, including cyclotrimethylenetrinitramine (RDX) and cyclotetramethylenetetranitramine (HMX), as well as steadystate combustion of RDX/glycidyl azide polymer (GAP) and HMX/GAP pseudo-propellants. The prefix pseudo is used to emphasize that RDX (or HMX) and GAP are mixed physically and no curing agent is used as for operational propellants. These energetic compounds, with their molecular structures shown in Fig. 1, have been widely used in many propulsion and gas-generation systems to meet various stringent performance and environmental requirements. They are highly energetic and produce high impetus and specific impulse for gun and rocket propulsion applications. In comparison with ammonium perchlorate (AP), nitramines produce little smoke, toxicity, and corrosion. Azide-containing energetic binders, such as GAP, 3,3-bis(azidomethly)oxetane (BAMO), and 3-azidomethyl-3-methyloxetane (AMMO), have positive heats of formation but produce relatively lowtemperature flames.

372

E. S. Kim & V. Yang

02N A ,HC CH 2

02N ,N' H C

O ^ V N I O , H2 RDX Fig. 1.

»2 NO, "N C H

1

02N/^C^N02 H

HMX

H-fO-CH-CH, | H2CN-N2

OH

2 GAP

Molecular structures of RDX, HMX, and GAP.

In the past decade, significant progress has been made in the study of combustion-wave structures and ignition characteristics of RDX and HMX monopropellants. Extensive experimental diagnostics 1-23 and theoretical analyses 24-40 were conducted over a broad range of operating conditions. Both self-sustained and laser-assisted combustion, 24 ~ 39 as well as ignition transients, 39,40 have been treated in detail. Studies on the physical properties, sublimation, decomposition, ignition, and self-deflagration of nitramine propellants conducted prior to 1984 are summarized by Boggs41 and Fifer,42 and the state of understanding of steady-state combustion of nitramine propellants up to 1990 is given by Alexander et al.43 Recently, Brill et al. provides a comprehensive overview of various studies on the near-surface chemical kinetics of RDX and HMX.5 A summary of the overall latest development is covered in a volume edited by Yang et al.44 Most of the early theoretical analyses of steady-state combustion of nitramine propellants were based on global reaction schemes for gas-phase processes.45 The first comprehensive model of RDX combustion, accommodating 23 species and 49 reactions in the gas phase, was initiated by Ermolin et al.46 The propellant surface conditions, however, were treated as input parameters in order to match experimentally-measured speciesconcentration profiles. A substantial improvement was made by Melius24 to relax this constraint. His formulation simultaneously took into account the thermal decomposition of RDX and the ensuing chemical reactions to an extent that the key heat-release mechanisms could be identified. Yetter et al.25 refined Melius' model to include the sub-models of reactions among the major intermediate products such as CH2O, NO2, N2O, H2, HCN, and NO, but a significant amount of uncertainties still existed about the pathways of the reduction and associated rates of large fragments departing from the burning surface of these cyclic nitramines. By considering global reactions, Margolis, Williams, Li, and co-workers 26-28 developed an analytical approach, which included the presence of gas bubbles and liquid droplets

Combustion

and Ignition of Nitramine

Propellants

373

in the two-phase region near the propellant surface by means of methods of matched asymptotic expansion. The model, however, provided limited information concerning the chemical processes. Prasad et al. also studied self-sustained and laser-assisted combustion of RDX and HMX. 29 ' 30 Their model differed from the ones described in Refs. 24-28 in that bubble formation within the liquid layer was neglected. In general, these models of RDX and HMX combustion predicted burning rate, surface temperature, and melt-layer thickness reasonably accurately, although some disagreements with experimental data in the near-surface species profiles and the temperature sensitivity of propellant burning rate were noted. Recognizing the important role of the condensed phase, Liau and Yang developed a detailed model of RDX combustion accounting for the foam layer, which is the region between the gas and solid phases. 32 ' 33 Such a foam layer consisted of two phases: liquefied RDX and bubbles containing gaseous RDX and its decomposition products. Davidson and Beckstead 34 further studied the near-surface temperature distribution and pressure sensitivity of burning rate. In the past decade, extensive studies have been conducted to study the chemical kinetics of the near-surface region of RDX and HMX. The similar approach was later extended to study the combustion behavior of HMX. 35 The recent studies have provided great insight into the underlying mechanisms dictating the chemistry of the subsurface region as well as near-surface gas phase. However, more needs to be learned about complex processes involved in the two-phase near-surface region, which includes an array of intricacies such as thermal decomposition, subsequent reactions, evaporation, bubble formation and interaction, and interfacial transport of mass and energy between the gas and condensed phases. An integrated modeling and experimental effort is required to improve the state of knowledge. Similar to the steady-state combustion model development, a series of theoretical ignition modeling efforts has also been carried out in the past to study the ignition behavior of solid propellants and explosives. A comprehensive review of the early work was conducted by Price et al. in 1966.47 The experimental and theoretical literature pertaining to the ignition of solid propellants over the period of 1966 through 1980 was reviewed by Kulkarni et al.48 and Hermance. 49 The state of understanding in Russia up to 1989 was presented by Vilyunov and Zarko, 50 giving a detailed examination of the various ignition models and related experimental approaches. In 1998, a review of laser and radiative ignition of 24 solid energetic materials, with emphasis on work performed in the former Soviet Union, was provided by Strakouskiy et al.51

374

E. S. Kim & V. Yang

Ignition of solid propellants and explosives involves an array of intricate physiochemical processes under energetic stimuli, and has been a subject of extensive research since 1950. In general, ignition models can be broadly divided into four categories: solid-phase (or reactive solid), heterogeneous, gas-phase, and multi-phase reaction models. The solid-phase reaction models 5 2 - 5 5 assume that exothermic reactions in the condensed phase are the dominant mechanism of ignition, while the effects of surface and gasphase processes are secondary and can be neglected. Heterogeneous reaction models 5 6 - 6 4 assume that heterogeneous reactions at the propellant surface are responsible for ignition due to the molecular diffusion of ambient oxidizer species to the propellant surface. The gas-phase reaction models 6 5 - 7 2 presume that exothermic gas-phase reactions and their heat feedback to the propellant surface are the primary mechanism of ignition. In spite of their contributions in correlating experimental data and providing qualitative understanding of ignition behavior, the solid-phase (or reactive solid), heterogeneous, and gas-phase reaction models 5 2 - 7 2 are semi-empirical in nature and do not provide predictive capability at scales sufficient to resolve the detailed ignition mechanisms and flame evolution. A prior understanding of the ignition process is usually required before modeling. This obstacle mainly results from the use of global kinetics schemes derived for steadystate combustion. Moreover, a simple pyrolysis law is often employed to describe the propellant gasification process in terms of propellant surface temperature along with prescribed condensed-phase heat release. Recently, Yang and co-workers developed a multi-phase reaction model by extending the steady-state model described in Refs. 32 and 33 to include the transient development in the entire combustion zone, including the solid-phase, nearsurface two-phase, and gas-phase regions. 39 ' 40 The formulation accommodates detailed chemical kinetics and transport phenomena in the gas-phase region, as well as thermal decomposition and subsequent reactions in the two-phase region. Thermodynamic phase transition and volumetric radiant energy absorption are also considered for a complete description. The model is capable of treating the entire ignition process from surface pyrolysis to steady-state combustion, with the instantaneous burning rate and surface conditions treated as part of the solution. 39 ' 40 A summary of the theoretical formulation and results of this multi-phase model is given in the later sections of this chapter. Unlike the situation with nitramine monopropellants, limited theoretical modeling studies for GAP decomposition and combustion are available. 37,38 ' 73 More effort, however, has been expended on experimental

Combustion

and Ignition of Nitramine

Propellants

375

studies. 3 ' 74 ^ 81 The entire combustion-wave structure can be segmented into three regions: solid-phase, near-surface two-phase, and gas-phase regimes. In the solid phase, the extent of chemical reactions is usually negligible due to the low temperature and short residence time. Thermal decomposition and ensuing reactions, as well as phase transition, take place in the foam layer, generating gas bubbles and forming a two-phase region. Rapid gasification occurs at the burning surface, and further decomposition and oxidation continue to take place and release a significant amount of energy in the near-surface region. The burning surface temperature is greater than 700 K. No visible flame is observed in the gas phase; instead, a large amount of fine powder is formed away from the burning surface and generates a cloud of intense smoke. The final flame temperature of GAP is around 1300-1500 K, which is significantly lower than those of nitramines (~3000K). Recently, gas-phase species and temperature measurements were conducted to investigate CO2 laser-induced pyrolysis of cured GAP at the intensities of 100 and 200 W/cm 2 under atmospheric pressure using a triple quadrupole mass spectrometer (TQMS) with fine-wire thermocouples. 74 The decomposition products observed in that work were N2, HCN, CO, H 2 CO, NH 3 , CH 3 CHO, CH 2 CHCHNH, CH3CHNH, H 2 0 , CH 4 , and C 2 H 4 . Among these, the major species were N 2 , HCN, CO, and H 2 CO. The relative concentrations of these decomposed species were similar to those observed by Arisawa and Brill. 75 Very intense smoke was formed in the gas phase; no carbonaceous residue was observed on the burning surface. The smoke formation was thus assumed to be caused by cold ambient gases, quenching hot condensable gases issuing from the GAP surface. The surface temperature was measured to be 1050 K under both heat fluxes of 100 and 200W/cm 2 , which is considerably higher than those reported in the literature 7 6 - 7 8 (Ts = 700-760 K, 710-750 K, and 813 K) possibly due to differences in sample preparation (cured versus uncured GAP), experimental conditions (self-sustained versus laser-assisted combustion), type of GAP strands used, diagnostic technique, and measurement accuracy. Both the surface temperature and the burning rate of GAP were higher than those of HMX under the same experimental condition. Using TQMS with fine-wire thermocouples, Litzinger et al.3 also conducted gas-phase species and temperature measurements to study the combustion characteristics of several nitramine/azide pseudo-propellants including RDX/GAP and HMX/GAP, all with a mass ratio of 8:2. The experiments were performed at C 0 2 laser heat fluxes of 100-400 W/cm 2 under atmospheric pressure. Emphasis was placed on the effects of nitramine/azide interaction

376

E. S. Kim & V. Yang

and external heat flux. The major decomposition species for HMX/GAP and RDX/GAP were similar to those found for neat HMX and RDX. The species-concentration profiles showed three distinct regions: a primary reaction zone, a dark zone, and a secondary reaction zone. The burning rates of HMX/GAP and RDX/GAP were increased with the addition of GAP, regardless of the laser energy intensity impressed. This finding contradicted the experimental results obtained by Kubota and Sonobe, 76 which showed that the addition of GAP into HMX lowered the burning rate. The discrepancy may arise from the differences in their experimental setups and sample preparation. For instance, the HMX used by Kubota and Sonobe 76 had a bimodal particle size distribution (70% of 2/iim and 30% of 20 /um), compared with an average crystal size of 75 /jm used by Litzinger et al.3 Furthermore, the GAP was cured with hexamethylene diisocyanate (HMDI) and crosslinked with trimethylolpropane (TMP) in Kubota and Sonobe's experiments. The T-jump/FTIR spectroscopy technique was applied to the study of the decomposition characteristics of GAP having one, two, and three terminal -OH groups. 75 Samples were rapidly heated to a temperature range of 500-600 K at 2 atm with a heating rate of 800 K/s. The major decomposition products were CH 4 , HCN, CO, C 2 H 4 , NH 3 , CH 2 0, CH 2 CO, H 2 0 , and GAP oligomer. IR-inactive N 2 was not measured, but is present as one of the major decomposition products of GAP in other studies using mass spectrometry. 74 ' 79 NH3 was found to be formed from the end chain of the azide group. The formation of CO appeared to result from both the parent polymer and secondary reactions. The ratio of HCN to NH3 increased as temperature increased. The intensive heat release during GAP decomposition explains the high burning surface temperature of GAP. 74 Over the past several years, Yang and co-workers 37-39 have established comprehensive numerical analyses of nitramine/GAP pseudo-propellant combustion to predict the propellant burning rate and detailed combustion wave structure over a broad range of pressure, laser intensity, and propellant composition. The steady-state model described in Refs. 32 and 33 was extended to include GAP binder in the nitramine combustion. The model takes into account various fundamental processes at scales sufficient to resolve the microscopic flame-zone physiochemistry. The thermochemical parameters of nitramine and GAP are deduced from existing experimental data. Four global decomposition reactions in the condensed phase as well as subsequent reactions are included. In the gas phase, a detailed chemical kinetics scheme involving 74 species and 532 reactions is employed to describe the heat-release mechanism. The key physiochemical processes

Combustion

and Ignition of Nitramine

Propellants

377

dictating the propellant burning behavior and flame structure were studied over a broad range of ambient pressure, preconditioned temperature, propellant composition, and impressed laser intensity. In the following sections, the combustion-wave structures and burning characteristics of RD x, 32 > 33 . 36 ' 39 > 40 HMX, 39 HMX/GAP, 37 - 39 and RDX/GAP 3 8 will be briefly discussed. The state-of-the-art approaches recently developed in this subject area are then described along with a brief discussion of the numerical techniques. Finally, results of these modeling studies are summarized. 3. Description of Combustion-Wave Structures Three physical problems are considered in this chapter: (1) steadystate combustion of nitramine propellants; (2) laser-induced ignition of RDX monopropellant; and (3) steady-state combustion of nitramine/GAP pseudo-propellants. During the past decade, Yang and co-workers 32 ' 33 ' 36-40 have developed a series of comprehensive numerical models for studying the key physiochemical processes involved in the combustion and ignition of nitramine monopropellant and nitramine/GAP pseudo-propellants. These models accommodated detailed chemical kinetics and transport phenomena in the gas phase, as well as thermal decomposition and subsequent reactions in the condensed phase. The formation of gas bubbles in the molten surface layer due to molecular degradation and thermodynamic phase transition is also included to provide a complete description. The steady-state combustion models 32 ' 33 ' 36 " 39 are capable of resolving the combustion-wave structures in both the gas and condensed phases, with the instantaneous burning rate and surface temperature calculated as part of the solution. The analyses 32,33 were later extended to treat the entire ignition process from surface pyrolysis to steady-state combustion. 39 ' 40 3.1. Steady-State

Combustion

of RDX

Monopropellant

Figure 2 shows the physical model of concern, a strand of RDX monopropellant burning in a stagnant environment with or without the assistance of external laser heat flux. To facilitate formulation, the entire combustionwave structure is conveniently segmented into three regions: (1) solid-phase; (2) near-surface two-phase, and (3) gas-phase. During burning, the propellant remains thermally stable in the solid phase until the temperature approaches the melting point at which thermodynamic phase transition occurs as shown in Fig. 3. Molecular degradation and evaporation of RDX

E. S. Kirn & V. Yang

378

gaseous f 38 species flame 1158 or 178 reactions region { (Melius, Yetter) 2 decomposition pathways , 1 gas-phase reaction foam !ayer< evaporation/condensation " r — > (Brill) preheated region phase transition 300K

RDX

degorrsoeiltoiL HCN+HONO J&™&&±

Fig. 2.

3000K

NO+C€M-N2 « 9 D * O J ! a i »

N2+co+H20

+CH 2 0+N 2 0

+H 2 0+HCN

+G0 2 +H 2

,etc.

,ete.

,etc.

Strand of RDX burning in a stagnant environment.

gas phase <--> ^-^

o o Oo

o

O

CD

foam layer o o o

gasproducts

RDX vapor

CD

solid phase Fig. 3.

Schematic diagram showing various regions in RDX combustion-wave structure.

then take place in the liquid layer, generating bubbles and forming a two-phase region. The propellant subsequently undergoes a sequence of rapid evaporation and decomposition in the near field immediately above the foam layer. Oxidation reactions continue to occur and to release an enormous amount of energy in the gas phase, with the final temperature reaching the adiabatic flame temperature. A detailed description of the theoretical model can be found in Refs. 32 and 33. 3.2. Laser-Induced

Ignition

of RDX

Monopropellant

The physical problem of concern is the ignition of a strand of RDX monopropellant induced by a continuous and radially-uniform C 0 2 laser. The physiochemical processes involved are schematically illustrated in Fig. 4. The propellant and the ambient gas are initially at room temperature.

Combustion

and Ignition of Nitramine

Gas Phase Ambient —-| Gas a_

Propellants

RDX I Temperature

'/flux

melt Fig. 4.

Physiochemical processes involved in laser-induced ignition of RDX.

379

380

E. S. Kim & V. Yang

Once the laser is activated, volumetric absorption of laser energy in the solid phase takes place, as shown in Fig. 4(a). In the gas phase, only certain gaseous species, such as vapor RDX, absorb a noticeable amount of laser energy at the wavelength of 10.6 /jm; thus, the gas-phase absorption is negligible during the inert heating period. When the solid reaches its melting temperature, the absorbed radiant energy cannot further raise the temperature without first melting the solid. Since the radiant energy absorbed is insufficient for instantaneous melting of all of the solid in a short period, partial melting of the solid occurs, which leads to the formation of a mushy zone consisting of both solid and liquid (Fig. 4(b)). When a pure liquid layer is formed, the solid-liquid interface starts to move due to conductive and radiative heat transfer (Fig. (4c)). In the liquid, thermal decomposition and subsequent reactions, as well as phase transition, take place, generating gas bubbles and forming a two-phase region. The propellant then undergoes a sequence of rapid evaporation at the surface (Fig. (4d)). Ignition occurs if the heat flux is sufficiently large to initiate the subsequent self-accelerated exothermic reactions which result in substantial heat release (in the gas phase) and emission of light (Fig. 4(e)). A luminous flame is produced, regresses toward the surface, and finally reaches a stationary position corresponding to its steady-state condition (Fig. 4(f)). A comprehensive description of the theoretical model is given in Refs. 39 and 40.

3.3. Steady-State Combustion of Pseudo-Propellants

Nitramine/GAP

Figure 5 shows schematically the physiochemical processes involved in the HMX/GAP pseudo-propellant combustion. A physical model for RDX/GAP pseudo-propellant combustion is available in Ref. 38. The entire combustion-wave structure is segmented into three regions: solid-phase, near-surface two-phase, and gas-phase. In the solid-phase region, HMX powder and GAP are physically mixed. The former melts at 558 K with negligible chemical reactions taking place, due to the low temperature and short residence time. Thermal decomposition and phase change of HMX occurs in the liquid phase to form a foam layer. The propellant surface (x = 0) is defined herein as the interface between the foam layer and gas-phase region, at which rapid gasification of HMX prevails. Since the surface temperature of HMX/GAP pseudo-propellant (^700 K) is lower than that

Combustion and Ignition of Nitramine Propellants - 2800 K

Rapid Consumption of HCN and NO

I!

Major Species in Dark Zone: N 2 , H A NO, CO, HCN, H2CO,N20, H2, CO,

381

[Secondary \ ! Flame Zone

^

Dark Zone

1250 K (GAP Polymer [Residue

Decomposition, Evaporation, and Gas-Phase Reactions (Bubble)

Primary Flame Zone (HMX Vapor /Liquid Interface)

(HMX MeltFront)

HMX

GAP

Fig. 5. Combustion-wave structure of HMX/GAP pseudo-propellant at 1 atm. of pure GAP, G A P leaves the surface as aerosol surrounded with vapor H M X and its decomposed gaseous products. In this region, G A P remains as a condensed species and continues to decompose. A significant amount of carbonaceous residue may be present on the surface during combustion. To facilitate analysis, t h e coordinate system is fixed at t h e propellant surface. A quasi one-dimensional model is formulated as a first approximation of the problem. B o t h t h e subsurface and near-surface regions require a multi-phase t r e a t m e n t because of t h e presence of G A P a n d other condensed species in these zones. A detailed derivation of the theoretical model is available in Refs. 37 and 39. A similar model approach has been applied for studying R D X / G A P pseudo-propellant combustion. 3 8

4. T h e o r e t i c a l F o r m u l a t i o n T h e theoretical formulation of physiochemical processes in various regions during the ignition and combustion of H M X / G A P pseudo-propellant is summarized below. 3 7 For monopropellants, t h e model can be simplified by removing the G A P terms in the following governing equations and are

382

E. S. Kim & V. Yang

described in Refs. 32, 33, 39, and 40. The steady-state combustion can be treated as a limiting case by neglecting all the time-varying terms. 4 . 1 . Solid-Phase

Region

Thermal decomposition of HMX and GAP and in-depth radiation absorption are ignored in modeling the solid-phase process. Thus, only heat conduction governed by the following equation is considered: dT

dTc

d (

drc\

The thermal conductivities and specific heat capacities of solid HMX and liquid GAP were recently obtained as a function of temperature by Hanson-Parr and Parr. 17 Measurements of these properties for liquid HMX, however, represent a much more challenging task, because decomposition usually takes place while melting. Thus, they are assumed to be identical to those at the solid state due to the lack of reliable data. The thermodynamic and transport properties used in the present work are given in Ref. 37. The properties of the mixture are estimated as follows. pccc =

FHMXPHMXCHMX

+

(2)

^GAPPGAPCGAP

Ac = ^HMXAHMX + ^GAPAGAP-

(3)

A closed-form solution to Eq. (1) at steady state is available subject to appropriate boundary conditions and the propellant burning rate. 4.2. Subsurface

Multi-Phase

Region

The physiochemical processes in this region are extremely complex, involving an array of intricacies such as thermal decomposition, evaporation, bubble formation, gas-phase reactions in bubbles, and interfacial transport of mass and energy between the gas and condensed phases. A two-phase fluid dynamic model based on a spatial averaging technique is employed to formulate these complicated phenomena. 32 With the assumption that mass diffusion is negligible, the conservation equations for both the condensed and gas phases can be combined and written as follows: Mass d[(l-^)P+M

+

d

[(1

_

0 f

^ ^

+

^

^

= 0.

(4)

Combustion

Condensed-Species

and Ignition of Nitramine

383

Propellants

Concentration

d[(l - {)pcucYCi]=wCi, dt dx Gaseous-Species Concentration d(4>iPgYSi) dt

d(
wSt,

i = l,2,...,Nc;

i = l,2,...,Ng;

(5)

(6)

Energy dTf

dp

dTf

-di+PfU(C{^x--

d (

dT \

\

/

' /^

hgjYgjWc-g

J"=l

Ne

Ne

j=i

j=\

—_ 2_^

hcjYcjWc-g

(7)

J=l

where u>c-g represents the rate of mass conversion from liquid to gas. The properties are mass-averaged as follows. PfCf PfUfCf

Af

= ( 1 -~ f)Pc,C+c ^ f P g C g , = ( 1 -- 4>f)p u Cc +
= L(i ~ 0f)Pc^;CAC

(8)

+ (pfPgi^ g A g J / L ( l - 4>i)PcUc + (/)fPgUgJ

(9) (10)

where Cc =

•.YCi:

c

Si * g * '

Ac

, and Ag :

:

i=l

Ygi. t=l

(lla-d) The mass and energy production terms depend on the specific chemical reaction mechanisms used and can be formulated as described below. The model accommodates the thermal decomposition of HMX and GAP, as well as subsequent reactions in the foam layer. The formation of gas bubbles due to evaporation and thermal degradation is also considered for completeness. Two global-decomposition pathways are employed for HMX, as listed in Table 1. The first reaction (Rl) is an exothermic, lowtemperature pathway, whereas the second reaction (R2) is an endothermic, high-temperature pathway. Unfortunately, uncertainties still exist about the kinetic rates of (Rl) and (R2). A parametric study is thus performed to assess the role of the condensed-phase kinetics of HMX in the overall combustion process of HMX/GAP pseudo-propellant. Two different sets of rates are available in the literature for (Rl) and (R2): one estimated by Davidson and Beckstead 34 using their combustion model and the other obtained by Brill 12 from the T-jump/FTIR experiment. Subsequent reactions among

384

E. S. Kim & V. Yang Table 1.

Subsurface chemical reactions and rate parameters.

No.

Reaction

A&'c

Eh'c

Ref.

Rl

HMX (1) ^ 4 C H 2 0 + 4 N 2 0

5.81 x 10 1 0 1.00 x 10 1 3

34,000 34,400

34 12

R2

HMX (1) -v 4HCN + 2 ( N 0 2 + NO + H 2 0 )

1.66 x 10 1 4 1.00 x 10 16 - 6

44,100 44,100

34 12

R3 R4

GAP56 ( 1 ) - • GAP56^ } + 56N 2 GAP56*1} -> 25.6HCN + 15.8CO + 14.4NH 3 + 17.8CH 2 0 + I6CH3CHO + H 2 0 + 6.4C 2 H 3 CHO + I.5C2H4 + 8CH3CHNH + 8CH 2 CHCHNH + 14.6C ( s )

5 x 10 1 5

41,500

38

1.28 x 10 1 9

53,000

38

R5

HMX(|) «• HMX ( g )

See Ref. 5

—

38

R6

C H 2 0 + N 0 2 ^ C O + NO + H 2 0

802 x T 2 - 7 7

13,730

16

R7

CH3CHO + M = C H 3 + HCO + M

81,770

38

R8

C2H3CHO + M = C 2 H 3 + H C O + M

10 1 6

97,600

38

CH 3 CHNH + M = C H 3 + H 2 CN + M

10 1 6

63,700

38

16

66,900

38

R9 R10 a

CH 2 CHCHNH + M = C 2 H 3 + H 2 CN + M

7 x 10 1 5

10

A = pre-exponential factor; ^°E = activation energy; c Units are in mol, cm, s, K, and cal.

the products of (Rl) and (R2) may occur to provide the thermal energy to sustain pyrolysis. Brill 12 examined several plausible secondary reactions and their reaction rates. Results indicate that reaction (R6) between C H 2 0 and N 0 2 is probably the most important one in the foam layer if it indeed does occur. The rate parameter of reaction (R6) was determined with shock-tube experiments. 16 Thermodynamic phase transition consisting of both evaporation and condensation of HMX, (R5), is considered to provide a complete description of the mass transfer process. The GAP sample considered in the present study is composed of 56 monomer units and is denoted "GAP56". A global, condensed-phase decomposition mechanism for GAP was established based on the experimental data reported in Refs. 74,75 and 81. There is universal agreement that GAP decomposition is initiated by the bond cleavage of the azide group releasing N 2 . 74 ~ 80 This process proceeds rapidly over a temperature range from 260 to 290°C, and has an activation energy of about 41 kcal/mol. 75 There are, however, uncertainties as to how the bond-breaking process occurs. We assume a first-order reaction with the pre-exponential factor and activation energy deduced by Sysak et al.,81 as given by reaction (R3) in Table 1. The subsequent step in the decomposition of GAP releases NH 3 . Its concentration in the gas phase increases with increasing number of -OH end groups in the polymer. It appears that H-atom abstraction involving

Combustion

and Ignition of Nitramine

Propellants

385

the -OH end group is an important channel for NH 3 formation. At this time, there are no mechanistic details which allow one to quantify the NH3 evolution as a global reaction, and thus a rate expression cannot be formulated. Since NH3 is an important source for H-atoms in the gas phase, the deficiency in predicted species concentrations caused by neglecting this step in the decomposition of GAP must be noted. Finally, a rapid, highly exothermic event takes place and releases HCN, CO, CH2O, CH2CO, CH4, C 2 H 4 , H 2 0 , and GAP oligomers, in addition to NH3. 75 In the laser-assisted combustion study of GAP polyol by Tang et al.74 the surface temperature approached 1050 K, which was about 400 K higher than those treated by Arisawa and Brill. 75 Because of this higher temperature, Tang et al.74 identified several different large molecular species using TQMS. The major ones were acetaldehyde (CH3CHO), acrolein (C2H3CHO), and different imines (CH3CHNH and CH 2 CHCHNH). In comparing the results of Arisawa and Brill 75 with those of Tang et al.,74 it appears that the GAP oligomers identified by Arisawa and Brill are likely candidates to form the imines identified by Tang et al. A species balance of the data acquired by Tang et al.74 leads to a global reaction model for the decomposition of GAP56*, which is the polymer unit that has released N 2 , as given by reaction (R4) in Table 1. Most of the gaseous decomposition products from GAP are hydrocarbons or common gases whose chemical kinetic details are readily available. However, the available information about aldehydes (CH3CHO and C2H3CHO) and imines (CH3CHNH and CH 2 CHCHNH), as well as their interactions with either HMX or its decomposition products, appears to be limited. To allow for a reduction of these species, bimolecular decomposition reactions have been formulated, with the activation energies about the differences in enthalpy between products and reactants. 38 The pre-exponential factors are assigned values that are typical for such a process. The reactions considered are listed as reactions (R7-R10) in Table 1. Note that the condensed species GAP56(i), GAP56^, and C(s) are dissolved in liquid HMX, whereas all other species are gaseous and exist in bubbles. Based on the chemical mechanism given by (R1-R6), the species production terms in Eqs. (5) and (6) can be expressed and are listed explicitly in Refs. 37 and 39.

4.3. Gas-Phase

Region

The species evolved from the propellant surface into the gas phase include vapor HMX, decomposition products of HMX and GAP, and unreacted

386

E. S. Kim & V. Yang

GAP. Since condensed and gaseous species both exist in this region, a twophase treatment similar to that described in the preceding section is employed to formulate the problem. The effect of laser absorption in the gas phase on the ignition and combustion processes of nitramine monopropellants has been extensively investigated in Ref. 40. Results indicate that only vapor RDX may absorb an appreciable amount of CO2 laser energy in the gas phase. None of the major gaseous decomposition products of RDX exhibits a noticeable absorption at a wavelength of 10.6 /jm of CO2 laser. Thus the fraction of the laser energy absorbed in the gas phase appears quite limited (less than 10%). The heat release from exothermic reactions is much more pronounced than the laser energy absorbed by the gas phase. The same argument applies to HMX as well since the decomposition species of HMX and RDX are similar With the assumption that body force, viscous dissipation, and radiation emission/absorption effects are ignored, the isobaric conservation equations for both the condensed and gas phases can be combined and written as follows: Mass dl(l-
^)APcYCt]

(12)

Concentration +

J L [ ( 1 _ ^)APcucYCt}

= AwCi,

(i =

l,2,...,Nc); (13)

Gaseous-Species Concentration ,

dYK.

A

,

dYg.

A

= Awgi - YgiAwc_g,

dUgApgVg.Yg.)

(i = 1,2,..., JVg);

(14)

Energy

pc A? dA

+ puc A&

- t~ wV

- A^2

- t

/

j=i

wCjhcj + A]PhgjYgjWc-g

j=i

- A^2

hcjYcjwc-g.

(15)

Combustion

and Ignition of Nitramine

387

Propellants

The thermophysical properties used in Eq. (15) are mass-averaged as follows. PCV = (1 - g)pcCc + 0gPgCg,

(16)

pucp = (1 - 4>s)pcuccc + 0gPgUgcg, A

= S

(17)

[(1 ~ 4>S)PcUcXc + ^gpg%Ag] [(1 - 0S)PcUc + 0gPsUg}

The enthalpy of gaseous or condensed species i in Eq. (15) is defined as

hi= J

cPtdT + h°u.

(19)

The mass diffusion velocity Vi consists of contributions from both concentration and temperature gradients,

Finally, the equation of state for a multi-component system is used to close the formulation, Ng y

P = PsRuTe £^Ti=l

Y

(21) Si

The chemical reactions can be written in the following general form ^ ^ O ^ i / M ; , t=l

j = l,2,...,iVR

(22)

1=1

where v[, and v"^ are the stoichiometric coefficients for the zth species appearing as a reactant in the j t h forward and backward reactions, respectively, and Mi is the chemical symbol for the ith species. The reaction rate constant kj (either kfj or fcbj ) is given by the Arrhenius expression kj = AjT13* e x p ( ^ | ) •

(23)

The rate of change of molar concentration of species i by reaction j is

(

JVg

^g

kijUCfi-k^UC^')•

\

( 24 )

The total mass production rate of gaseous species i in Eq. (14) is then obtained by summing up the changes due to all gas- and condensed-phase

388

E, S. Kim & V. Yang

reactions: JVR

<% = ^gWSi J2 C*j + ™c-g,gl

(25)

3=1

where w c _ gjg . represents the mass conversion rate from liquid to gas of gaseous species i. The gas-phase chemical kinetics scheme is composed of four submodels: (1) the HMX combustion mechanism;30 (2) the additional reactions, recently proposed by Chakraborty and Lin, 4 involving the consumption of H 2 CNN0 2 , H 2 CNNO, H 2 CNO, H 2 CNOH, and H 2 CN; (3) the initial decomposition reactions of GAP including, among others, aldehydes and imines; and (4) the hydrocarbon combustion mechanism 82 containing 49 species and 279 reactions. Bimolecular decomposition reactions for the aldehydes (CH 3 CHO and C2H3CHO) and imines (CH3CHNH and CH 2 CHCHNH) are assumed, and their kinetic rates are estimated, as indicated by reactions (R7-R10) in Table 1. In total, the gas-phase chemical kinetics scheme involves 74 species and 532 reactions. The mass production rates of species generated by condensed-phase reactions in Eqs. (13) and (14) are described by reactions (R3) and (R4) of condensed species such as GAP and its intermediate product. The rate expressions of reactions listed in Refs. 37-39 are utilized to calculate the mass production rates of species generated from GAP decomposition in the gas phase. 4.4. Boundary

Conditions

The physical processes in the gas phase and foam layer must be matched at the propellant surface to provide the boundary conditions for each region. This procedure requires balances of mass and energy, and eventually determines propellant surface conditions and burning rate. With the neglect of mass diffusion in the condensed phase, the conservation laws at the propellant surface can be written as follows: Mass [(1 -
(26)

Species [(1 - t)pcucYCi + (pfpgugYgi}0-

= [(1 - e)pcucYCi + gPg(ug +

Vgz)Ygt}0+; (27)

Combustion

and Ignition of Nitramine

389

Propellants

Energy dT{ Af —

H (1 -

<^f)p c WclHMX c /lHMX 1 _g

As

dx

. o-

Q'L laser *

^

(28)

o+

The temperature is identical on both sides of the interface, but the void fraction and species mass fractions might be different. The treatment of surface absorption of incident radiative energy, Q,'{&sex, is given in Ref. 40. Since the propellant surface is defined as the interface where rapid phase transition occurs, the evaporation law of HMX is assumed to prevail at the interface, 32 ' 33 ' 37 ~ 40 giving [(1 -

^PCUCYHUXJO-

SVUCHMX,

v,eq

(29)

IHM)

V o+ It has been shown that pcuc = pgug is a good assumption for the twophase model. 3 2 ' 3 3 ' 3 7 - 4 0 Equation (26) becomes trivial and Eq. (27) can be written as follows:

[(1 - fa)YCi + faYgi}0-

'1

1

z)YCi

Vs.

(30)

Y„. o+

A summation of the above equations for all the condensed species GAP(i), GAPfjw and C(s) gives [(i - & ) ( i - yRoxJlo- = [(i - 0 g )] o + •

(3i)

Equations (28)-(31) are sufficient to solve the set of unknowns (u, T, Yi,(j>) at the propellant surface and provide the boundary conditions for the foam layer and gas phase. The boundary conditions at the interface (melt front) between the solid phase and foam layer are TC = T{ = T melt Ac

dTc dx

and fa = 0

at x — = ^melt xmeit

PCWCYHMX^HMXS^!

A,

<m~ dx

(32) (33)

The far-field conditions for the gas phase require the gradients of flow properties to be zero at x = oo: dYi dT dp du -T— = — = 0 at a; (34) dx d ox ax The condition at the cold boundary for the condensed phase (x = —oo) is Tc = 1]

a s x - i —oo

(35)

where T\ is the pre-conditioned temperature of the propellant. The initial mass fractions of HMX and GAP are also provided as input parameters.

390

E. S. Kim & V. Yang

5. Numerical Method The theoretical formulation established in the current work requires a robust computational scheme due to the numerical stiffness caused by chemical reactions and transport processes. All the conservation equations and associated boundary conditions are coupled and solved by a doubleiteration procedure which treats the propellant surface temperature Ts and burning rate r^ as eigenvalues. The procedure continues with Ts adjusted by an inner loop while r\, is corrected by the outer iteration. The conservation equations for the subsurface region are solved first and the resulting species concentrations at the surface are used as the boundary conditions for the gas-phase region through the interfacial matching conditions. The next step involves integration of the gas-phase conservation equations to provide the temperature and species-concentration profiles. The non-equilibrium evaporation equation (29) is then employed to check the convergence of T s . If this is not successful, another inner iteration is repeated using an updated value of Ts. The outer iteration follows the same procedure as the inner loop, except that r^ is used as the eigenvalue to check the interfacial energy continuity, Eq. (28). Since only the burning rate and surface temperature, and not the interfacial species composition, are involved in the iterative procedure, the present algorithm performs quite well and significantly reduces the computational burden. The conservation equations (4)-(7) for the subsurface region are fully coupled. They are, however, solved by an uncoupled-iteration method. The method starts with an estimated temperature profile obtained by solving an inert energy equation, and then the conservation equations of mass and species concentrations are integrated using a fourth-order Runge-Kutta method. Equation (7) is subsequently solved with the newly-obtained void fraction and species concentrations to obtain another temperature profile. Since the equations are solved separately, iteration is required to ensure a converged solution that satisfies all the conservation laws and boundary conditions. The governing equations (12)-(15) for the gas phase are fully coupled, but solved by an uncoupled-iteration method similar to the subsurfaceregion solver. Equation (13) is first solved using a fourth-order RungeKutta method to get the void fraction and the mass fractions of condensed species. Equations (12), (14) and (15) are then solved using the ChemkinPremix 83 package with some modifications since the governing equations have been changed to account for a two-phase system. The grid systems of

Combustion

and Ignition of Nitramine

391

Propellants

the two solvers are different and direct interpolation is used to match the grid information. 6. Discussion of Model Results In the past decade, a significant amount of effort has been spent in modeling and simulating steady-state combustion of nitramine monopropellants, 32,33 laser-induced ignition of RDX, 39 ' 40 and steady-state combustion of nitramine/GAP pseudo-propellants. 37-39 These models 3 2 ' 3 3 , 3 7 - 4 0 are based on the theoretical formulation and numerical method outlined in this chapter. Various important burning and ignition characteristics were investigated over a broad range of operating conditions. The roles of the subsurface multi-phase region in the propellant deflagration and ignition processes have been investigated by simulating complete combustion wave structures using the detailed reaction mechanism and updated thermophysical properties. 6.1. Steady-State

Combustion

of Nitramine

Propellants

Predicted temperature profiles of self-sustained RDX combustion over a pressure range from 1 to 90 atm 3 3 are shown in Fig. 6. The temperature increases monotonically from its initial value of 293 K, and levels off

-0.0

0.5

1.0

Distance above propellant surface, mm Fig. 6.

Temperature profiles of self-sustained RDX combustion at various pressures.

392

E. S. Kim & V. Yang

at a value close to the prediction by the chemical equilibrium analysis. The final flame temperature increases with increasing pressure, whereas the flame-standoff distance exhibits an opposite trend owing to enhanced chemical-reaction rates at high pressures. No evidence is obtained of the existence of a temperature plateau in the dark zone regardless of pressure, which is consistent with the experimental observations of self-sustained combustion of RDX monopropellant. 36 However, a dark-zone temperature plateau (at T ~ 1500 K) was present in the laser-assisted combustion of RDX, while the existence of the dark zone was not evident in the selfassisted combustion. Liau and Yang 36 indicated that the chemical preparation and fluid transport times of the intermediate species produced in the primary flame must be comparable in order to form a dark zone. Figure 7 shows the burning rate as a function of pressure. Good agreement between predictions and measurements is obtained. A power law of the burning rate as a function of pressure is observed, (36)

r b = ap"

where the pressure exponent n is about 0.83 (with p in atm), and the preexponential factor a equal to 0.3cm/s for 2] = 293 K. The increased burning rate with pressure is attributed mainly to fast gas-phase exothermic

- ' ' i i

—x—

o

•

o

:e, cm/sec

IU

' 'T

i —i

r-i-F

6

Prediction

O ^^'

Zimmer-Galler(1968)

O

Glaskov(1974)

•

Zenin(1995)

^ OJ

^

(5 '•

•jf*^ o

Burning

QC

T

<' s' '~r

10°

inltlal=293K

... i

101

.

.

.

10"

Pressure, atm Fig. 7. Effect of pressure on strand burning rate of RDX monopropellant; self-sustained combustion.

Combustion

and Ignition of Nitramine

Propellants

393

reactions at high pressures and their influence on heat transfer to the condensed phase. The temperature sensitivity of burning rate defined in Eq. (37) is also examined: _

~(drh)/rb

<9(lnrb) dTi

(37)

The temperature sensitivity ap stays around 0.0028 K _ 1 for most cases. At elevated pressures, the heat feedback from the gas phase to the condensed phase is higher, and thus the effect of initial temperature on the interfacial energy balance becomes less important. A numerical analysis on the temperature sensitivity for low-pressure conditions was further performed by Beckstead and co-workers.34 The predicted temperature sensitivity was determined to be too low compared to the measurements, mostly due to the uncertainties associated with the treatment of the condensed phase in the model. The calculated species-concentration profiles were validated against experimental data, 22 which was obtained by means of a time-of-flight mass spectrometry technique at 0.5 atm, as shown in Fig. 8. Good agreement was obtained except for the region next to the surface. The discrepancy may arise from the ambiguity in determining the location of the propellant surface in experiments. Due to the limitation of the spatial resolution (500//m), the diagnostic work defined the surface as the location where RDX was completely consumed. This analysis, however, predicted that an appreciable amount of RDX still existed at the surface since only limited RDX decomposition occurred in the subsurface region. If the spatial distribution of the calculated data was artificially shifted upward to the location where NO and HCN attained their peak values, then an improved agreement between the prediction and the measurement could be achieved. The species-concentration profiles revealed that the overall reaction mechanisms globally consist of three steps: (1) decomposition of RDX to CH2O, HCN, NO2, etc. near the surface; (2) first-stage oxidization which includes formation of NO and H2O as well as removal of NO2; and (3) second-stage oxidization which includes conversion of HCN and NO to the final products such as CO, N 2 , and H2. It is worth noting that the highly exothermic reductions of HCN and NO usually occur at elevated temperature (T ~ 2000 K) owing to the large activation energies required to initiate these reactions, which provide the major heat source for raising the flame temperature to its final adiabatic value. The calculated molar fractions of the final product

E. S. Kim & V. Yang

394

Theoretical Calculation 0.40

. i

i

I

i

I

i

'

i

i

I

i

i

i

i

|"i

i

i

i T

'

'

• •'"I

' i l l |

i - i - r - i •_

0.35

N2 ;

Mole Fraction

0.30

/

0.25 0.20

/

/

••'

.

/

"

"

>

'

-

H2Q ;

-

/

/ v . >' *••• y ^ '•• ^

* '

/'''

-

:

"

\e-

/ /

0.05

0.00

/

%/

•i i

•

co:

y ^

•••-•.

;

0.15 0.10

.

• •

.

'•.

HCNV

i

• •

-0.5

, .

i

/

0.0

0.5

1.0

1.5

2.0

.

.

.

2.5

•

.

3.0

Exp. Measurement (Korobeinichev, 1985) 0.40

.,.,,..

• • i •

'

1

•

.

'

1 1 1 . . .

1

0.35 0.30

—o-.

o

H20

•2 0.25

\°

~~

/

i t 0.20 •"•*.

0.10

/ '-

0.00 r i -0.5

o'' i i i

\ :

// \ \\o.. \

rJ3

\

y/P

\\; / C 0

"5 0.15 -

0.05

0

.^-°~ 0 ^

•.

HCNT-

NO

O ^ 6-^-• ^ - A - ' - ^ - M ^ ^ - . . -4-6-^-i-

0

- o t i~T-i-ih 6 i

i I i1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance above propellant surface, mm

Fig. 8. Distributions of major species concentrations of self-sustained combustion of RDX at 0.5 atm.

species are quite consistent with the chemical-equilibrium predictions, with the deviation being less than 2%. The combustion wave structure at 100 atm was also predicted 33 and showed a close similarity to that at 1 atm except for the shorter flame-standoff distance (6 versus 600 /zm) and molten-layer thickness

Combustion

and Ignition of Nitramine

Propellants

395

(2.1 versus 66/mi). The major difference lies in a smaller void fraction. The shorter molten-layer thickness and higher burning rate yield a shorter residence time for condensed-phase reaction. Also, high pressure tends to retard the RDX evaporation, which dominates the gasification process in the two-phase layer. As evidenced by the large ratio of HCN to CH 2 0 mole fraction, the endothermic decomposition, (R2), appears more profound at high-pressure conditions. This can be attributed to the higher surface temperature and heat transfer into the condensed phase. A similar modeling approach was applied to study the combustion characteristics of HMX monopropellant. In this chapter, the model results pertaining to the combustion-wave structure of RDX monopropellant are focused. A comprehensive description of theoretical formulation and results for combustion of HMX monopropellant can be found in Refs. 37 and 39.

6.2. Laser-Induced

Ignition

of RDX

Monopropellant

By extending the state-state model to include the transient behavior, the entire laser-induced ignition process of RDX in an argon environment has also been studied. 39,40 Figure 9 shows the predicted temporal evolution of the temperature field at an incident laser heat flux of 400 W/cm 2 under atmospheric pressure. The initial temperature is 300 K. The interface

3500 3000 X 2500

I 2000 at

ex

I 1500 H 1000 500 1 ms 0.0

0.5 x, cm

1.0

Fig. 9. Evolution of temperature field during laser-induced ignition of RDX in argon at p = 1 atm and Q'^eT = 400 W / c m 2 .

396

E. S. Kim & V. Yang

between the subsurface and gas-phase regions is set to be x = 0, with negative and positive values of the x-coordinate representing the subsurface and gas phase, respectively. The surface temperature is rapidly increased to 475 K within 1 ms, due to the high intensity of laser heat flux. The profiles for t < 1 ms represent inert heating of the thin surface layer with conductive heat losses to both the solid- and gas-phase regions. The temperature rises in the gas phase at t = 2 ms are primarily caused by radiant energy absorption rather than exothermic reactions, because the extent of RDX decomposition in the gas phase is very limited at this stage of the event. At t = 2.9 ms, exothermic gas-phase reactions start to occur, and a flame appears near the propellant surface at t = 3 ms. During the time period between 3 and 6 ms, the temperature continues to increase to around 1500 K, as a consequence of the heat release by exothermic reactions. As time further elapses, a luminous flame appears, and the temperature rises to its adiabatic temperature. The luminous flame is not stationary but regresses toward the surface. There is a time lag (about 4 ms) between the first appearances of the primary and secondary flames. Figure 10 shows a close-up view of the temperature evolution in the condensed phase near the propellant surface. The transient development of thermal-wave penetration into the subsurface region is clearly observed.

550 - Ambient Gas: Ar 500

g

450

3
t

400

H 350

""-"100

-75

-50 x, |im

-25

0

Fig. 10. Close-up view of temperature evolution in subsurface region during laserinduced ignition of RDX at p = 1 atm and Q['aseT = 400 W / c m 2 .

Combustion

and Ignition of Nitramine

397

Propellants

The characteristic thickness of the thermal layer in the subsurface region is much thinner than that in the gas-phase region. Phase transition from solid to liquid can be indicated by the distinct change of temperature gradient at Tm = 478 K. Since most of the C 0 2 laser heat flux is absorbed by the thin surface layer due to the high absorption coefficient (2800 c m - 1 ) of RDX at the wavelength of 10.6 fxia, the formation of the mushy zone can be safely ignored. However, some propellants, including RDX, are quite transparent to plasma irradiation in the UV/visible wavelength range; thus, the appearance of the mushy zone may be evident in that situation. Figure 11 shows the distributions of void fraction and species concentrations in the subsurface two-phase region when ignition is achieved at t = 7 ms. The extent of RDX decomposition in the condensed phase is very limited during the laser-induced ignition process up to 7 ms over the range of conditions studied, due to the short residence time and low temperature conditions. The molten layer in the subsurface region is not fully established within this time frame under atmospheric pressure. As indicated in the previous subsection, the steady-state combustion model predicts that the gas bubbles occupy about 45% of the volume at the surface under atmospheric pressure during self-sustained RDX combustion as a result of RDX evaporation and decomposition. 33 However, the surface void fraction during

1.2

;

RDX x 1000

1.0 0.8 -

^^^

Liguid Solid

550

500

.

;

Melting Point = 478 K

0.6

-

;

450 £ 3

CH 2 0, N 2 0. 1 400 t

.2 0.4 :

HCNsV/

0.2

N0 2

- Ambient Gas Ar 0.0

J&*

.

1

-20

'

i

,

,

,

' -—_^i^>;

-10

-15

NO, npyQy/(

, •

350 300

x, !im Fig. 11. Close-up view of temperature and species-concentration profiles in subsurface region at t = 7 ms (p = 1 atm and Q £ = 400 W / c m 2 ) .

398

E. S. Kim & V. Yang

the self-sustained RDX combustion decreases significantly with increasing pressure. 33 The overall gaseous RDX ignition process can be divided into five distinct stages: thermal decomposition, first oxidation, chemical preparation, second oxidation, and completion stages. In stage I, RDX decomposes to low-molecular weight species, such as CH2O, N 2 0 , NO2, HCN, and HONO. This decomposition process is slightly endo-/exothermic or thermally neutral depending on the initial temperature. In stage II, oxidation reactions occur and release a significant amount of energy with the temperature reaching about 1500 K. The heat release in stage II is mainly caused by the conversion of CH2O and NO2 to H2O, NO, and CO, and to a lesser extent by the reactions of HCN and HONO. Stage III represents the chemical preparation time before the second oxidation reactions (stage IV) take place. The species formed in stage II are relatively stable, due to the high activation energies of their associated reactions, and require a finite time to oxidize further. The reduction of HCN and NO to N 2 , CO, H 2 0 , and H2 is largely responsible for the heat release in stage IV. Finally, all the final products are formed; no further reactions occur in stage V. A parametric study for investigating the effect of the absorption coefficient of vapor RDX on the overall ignition process has been performed by varying the absorption coefficient by 15%. The gas-phase temperature is rapidly increased by more than 300 K at t = 2 ms, with a small amount of the laser energy absorbed by the gas phase. At t = 2.9 ms, the gas-phase temperature rises to more than 800 K, caused by the heat release from the exothermic decomposition reactions in the gas phase. After the inert heating, the heat release from the exothermic reactions becomes much more pronounced than the laser energy absorbed by the gas phase. Since only a small amount of the laser energy was absorbed by the gas phase, a change by 15% in absorption coefficient did not influence the inert heating time significantly. Overall, the effect of the absorption coefficient of vapor RDX on the CO2 laser-induced ignition was not noticeable over the parameter range studied herein. Figure 12 shows the calculated and measured ignition delays of RDX induced by C 0 2 laser under atmospheric pressure. Excellent agreement is achieved between the predicted and experimental data for laser intensities less than 200 W/cm 2 . For 400 W/cm 2 , the predicted ignition delay matches the measurements by Parr and Hanson-Parr, 23 and Lee and Litzinger. 84 However, the measured data of Vilyunov and Zarko 50 do not agree with

Combustion

and Ignition of Nitramine

Propellants

1

|

1

1

1 | 1 III

TIM

10u ;

399

1

-

" ">>

*

10- rr Q

1

K

R O

• -

10:

Fig. 12.

• >

A

>

Viyunov and Zarko Parr and Hanson-Parr 23 Lee and Litzinger84 Current Work ,

,

,

• -

>

50

1

•

$ V

10"'

•

I

60

•

,

!

,

,

,

l l l l

,,!,,,,

" l l l l "

100 200 300 400 500600 Laser Intensity (W/cm)

Effect of CO2 laser intensity on ignition delay of RDX monopropellant.

the model prediction for laser intensities above 200W/cm 2 . Vilyunov and Zarko showed that the ignition delay increases with increasing laser intensity above 200W/cm 2 , whereas the results of the current model as well as those of Parr and Hanson-Parr 23 and Lee and Litzinger 84 revealed the opposite trend. Vilyunov and Zarko 50 stated that the RDX ignition was controlled by the solid-phase kinetics at low laser intensities (below 200W/cm 2 ), whereas the gas-phase kinetics along with the liquid-phase decomposition governed the ignition process at high laser intensities. The current model, however, predicted that the gas-phase chemistry controlled the ignition process over the laser intensity range studied. Thus, the ignition delay became shorter at higher laser intensities, because the gasification rate at the propellant surface increased with increasing laser intensity. Vilyunov and Zarko 50 performed their experiment in both nitrogen and air under atmospheric pressure and found that the ignition delays were about the same within the measurement accuracy. Lee and Litzinger 84 used argon as an inert gas, whereas Parr and Hanson-Parr 23 perform the experiment in air. The differences in ignition delay among these three sets of measured data, especially those above 200 W/cm 2 , may be caused by the variation in RDX sample preparation in each experiment. The RDX samples used by Parr and Hanson-Parr 23 and Lee and Litzinger 84 were pressed military-grade RDX.

400

E. S. Kim & V. Yang

Information about the samples used by Vilyunov and Zarko 50 was not available. In the experiment by Parr and Hanson-Parr, 23 a significant time lag was obtained between the first light and go/no-go times (about 85 ~ 100 ms). First light was defined as the time when the luminous flame was first detected, whereas go/no-go was the time when a stable flame was achieved without the laser-assisted heating. The model predictions for the first light and go/no-go times, however, were about the same. In the experiments, 23 the luminous flame progressed toward the surface immediately after the first light and moved away from the surface after the maximum temperature gradient was achieved near the surface. The model, however, did not predict this type of flame movement. The luminous flame continuously progressed toward the surface until steady-state deflagration was achieved. The discrepancy between model predictions and experimental observations may be attributed to the heat loss to the ambience. The entire ignition process was treated as adiabatic in the model, whereas heat losses from both the gas-phase flame and the condensed-phase region to the surrounding might be significant in the experiments, in which continuous laser heating was required in order to achieve self-sustained combustion by fully establishing the condensed flame. This suggests that during the ignition stage, heat loss in the condensed phase was too rapid compared to the heat transfer from the gas-phase flame to the surface. The discrepancies among the existing experimental results may be attributed to the uncertainties associated with measurements under different types of experimental conditions. It is clearly evident that more measured data is needed for model validation. Nonetheless, the present model provides detailed insight into the key physiochemical processes involved in the laser-induced ignition of RDX, and can be effectively used to estimate ignition delay, heat release mechanisms, and flame structure.

6.3. Steady-State RDX/GAP

Combustion of HMX/GAP Pseudo-Propellants

and

Recently, Yang and co-workers performed numerical analyses to investigate the combustion characteristics of HMX/GAP and RDX/GAP pseudopropellants over a broad range of pressure and laser intensity with various compositions. 37 " 39 Summaries of the model results for both HMX/GAP and RDX/GAP are given below.

Combustion

6.3.1. HMX/GAP

and Ignition of Nitramine

Propellants

401

Pseudo-Propellant

Figure 13 shows the temperature and species-concentration profiles in the gas phase during HMX/GAP pseudo-propellant combustion at a CO2 laser intensity of 100 W/cm 2 under atmospheric pressure. The ratio of HMX to GAP mass fraction is 8:2. Reasonable agreement was achieved with the experimental data reported in Ref. 3. The temperature rises rapidly from 677 K at the surface, levels off around 1200-1600 K, and further increases to its final value at 2780 K. The flame can be divided into three regions: (1) the primary flame; (2) the dark zone; and (3) the secondary flame. The dark zone is a non-luminous region between the primary and the secondary flame, and is characterized with a temperature plateau. The concentrations of HCN, NO, and H2O in the dark zone appeared to be similar to those of pure nitramine propellants. 3 The rapid conversion of HCN and NO to N2 and CO in the secondary flame zone were successfully predicted. These reactions are highly exothermic and usually take place at high temperatures due to their large activation energies. The predicted flame stand-off distance of 3 mm is slightly shorter than the measured value of 4 mm, partly because of the ambiguity in defining the propellant surface during experiments. Figure 14 shows a close-up view of the primary flame immediately above the propellant surface, which extends over a length of 100 j«m. The dominant reactions in this oxidation stage are R1-R3. The prediction of N2O concentration was satisfactory compared with the measurement; 3 however, NO2 and CH2O appear to be consumed too fast. Intermediate reactions forming C H 2 0 and NO2 are still lacking in the near-surface region in order to yield better agreement with experimental results. Conversion of GAP and GAP* to N 2 , HCN, CO, NH 3 , CH 2 0, CH 3 CHO, H 2 0 , C 2 H 3 CHO, C 2 H 4 , CH3CHNH, and CH 2 CHCHNH occurs in a very short distance (~ 10^m). The GAP decomposition is a highly exothermic process releasing a significant amount of energy in the gas phase. However, at the same time, the heat feedback from the gas phase to the surface is reduced due to the dilution of reactive species by the GAP pyrolysis gases. The decomposed fuel fragments, such as CH 2 CHO, C 2 H 3 CHO, CH3CHNH, and CH 2 CHCHNH, further react to form CH 3 , HCO, C 2 H 3 , and H 2 CN. The species-concentration and temperature profiles in the foam layer are shown in Fig. 15. An appreciable amount of HMX evaporates to form gas bubbles in this region, but the extent of decomposition through the pathways (Rl) and (R2) appears to be limited. On the other hand, most of the GAP compound is consumed to become GAP* and N 2 , releasing

402

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2

3 4 x, mm Distance above Propellant Surface, mm (b) 0.40

Distance above Propellant Surface, mm Fig. 13. (a) Calculated and (b) measured 3 species-concentration profiles of gas-phase flame of H M X / G A P pseudo-propellant (mass ratio 8:2) at 1 atm and laser intensity of 100W/cm 2 .

heat to support pyrolysis in the condensed phase. Further decomposition of GAP* according to (R4), however, is constrained due to the low temperature condition. The predicted surface temperature and foam-layer thickness are 677 K and 30 /im, respectively.

Combustion

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403

Propellants

1500

1200

900

i 6

600

x, m Distance above Propellant Surface, urn Fig. 14. Temperature and species-concentration profiles in near-surface region of H M X / G A P pseudo-propellant (mass ratio 8:2) combustion at 1 atm and laser intensity 100W/cm2.

0.5

800

750 i*t 700

650

S

600

x, m Distance underneath Propellant Surface, urn Fig. 15. Temperature and species-concentration profiles in subsurface of H M X / G A P pseudo-propellant (mass ratio 8:2) combustion at 1 a t m and laser intensity of 100 W / c m 2 .

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Figure 16 presents the corresponding temperature sensitivity of burning rate, which appears to be independent of pressure and has a value twice greater than that of pure HMX. In general, the effect of preconditioned temperature on propellant burning rate diminishes with increasing pressure and impressed laser intensity. The enhanced heat transfer to the propellant surface due to large energy release and reduced flame standoff distance in the gas phase at elevated pressure overrides the influence of preconditioned temperature in determining the energy balance at the surface, and consequently decreases the temperature sensitivity of burning rate. Figure 17 shows the effect of propellant composition on burning rate at various pressures. The burning rate in general decreases with the addition of GAP, which releases a substantial amount of N2 through the C-N3 bond breaking in the near-surface region. Although the process is exothermic, the presence of N2 and large fuel fragments dilute the concentrations of surface reactive species, and consequently reduces the rate of energy release from HMX reactions. The heat feedback to the surface decreases accordingly, rendering a lower burning rate. Another factor contributing to this phenomenon is the blowing effect of the GAP compound, which tends to push the primary flame away from the surface. The situation is, however, different at high pressures. The burning rate of HMX/GAP pseudopropellant with a mass ratio of 9:1 is greater than that of pure HMX for p > 30 atm.

Ut

o

40

60 p, atm

Fig. 16. Temperature sensitivity of burning rate of H M X / G A P pseudo-propellant (mass ratio 8:2); self-sustained combustion.

Combustion

and Ignition of Nitramine

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405

p, atm Fig. 17. Effect of propellant composition on burning rate at various pressures; selfsustained combustion.

The effect of laser intensity on the burning rate for several mixture ratios has been examined at 10 and 100 atm, respectively. At 10 atm, the burning rate increases with increasing C 0 2 laser intensity. Although GAP decomposition is highly exothermic, the burning rate decreases with increasing GAP concentration because the fuel-rich pyrolysis products of GAP reduce the flame temperature and move the flame away from the surface. At a high pressure of 100 atm, the intensive heat transfer from the flame to the surface overrides the effect of surface radiant energy absorption. The burning rate thus appears to be insensitive to the impressed laser intensity. The influence of GAP concentration on burning rate exhibits a different trend from that at 10 atm due to the variation of surface temperature, a phenomenon that has been elaborated in connection with the discussion of Fig. 17. The effects of laser heat flux and pressure on the burning rate, melt-layer thickness, and surface void fraction of HMX/GAP pseudo-propellant (mass ratio 8:2) have been studied. The impressed laser flux causes a substantial increase in burning rate at low pressures (e.g., 1 and 10atm). The effect, however, diminishes at high pressure, since the heat feedback from the gas phase overshadows the surface laser absorption in determining the energy balance at the surface. The heat transfer to the burning surface increases almost linearly with pressure. The melt-layer thickness and surface void fraction decrease with increasing radiant heat flux at low pressure, but

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remain almost fixed at high pressure. It should be noted that the bubble formation rate can be enhanced with increasing temperature, but may also be reduced by the decreased residence time resulting from the increased burning rate at high temperature. The present case shows a net decrease in the surface void fraction with increasing pressure.

6.3.2. RDX/GAP

Pseudo-Propellant

The flame structure observed in experiments using TQMS 3 was reasonably well predicted by the model. Figure 18 shows the predicted and measured 3 species-concentration profiles in the gas phase at 1 atm and 100W/cm 2 . Similar to the HMX/GAP combustion, it is found that HCN, NO, and H 2 0 are the major intermediate products in the dark zone. The conversion of HCN and NO to N 2 and CO dominates the luminous flame while the consumption of formaldehyde, NO2, and N 2 0 accounts for the primary flame above the surface. In contrast to RDX combustion, a noticeable amount (1-2%) of CH3CHO was observed near the surface. Here, the agreements between the predicted and measured concentration profiles of CO, C 0 2 , and formaldehyde are not as good as the others. Chemical equilibrium calculation was also performed. This calculation result matches the model output but not the experimental data. Even though the agreement between measured and computed burning rates is reasonably good, further investigations into the combustion wave are suggested to resolve the discrepancy in flame structure. In the foam layer, Fig. 19 shows that the predicted temperature rises from the melt point of RDX at 478 K to around 590 K at the propellant surface. The mass fraction of liquid RDX originates at 0.8 and decreases slightly mostly through evaporation and partially through decomposition. The void fraction increases from 0 to almost 9% due to the formation of bubbles containing vapor RDX and a small amount of decomposed gases. Consistent with the condensed-phase kinetics, the extent of GAP decomposition is negligible at temperatures lower than 600 K. The mass fraction of GAP remains at 0.2 throughout the foam layer, and then evolves into the gas phase. Figure 20 shows the predicted temperature, void fraction, and condensed species-concentration profiles in the region immediately above the propellant surface. GAP starts to decompose in the gas phase when the temperature reaches 700 K. At this stage, GAP* is immediately formed due to the elimination of N 2 and reaches its maximum concentration within a short distance (less than 0.004 cm). The peak value of GAP* mass fraction

Combustion

(3)

0.4

and Ignition of Nitramine

Propellants

407

i—i—i—i—i—1—i—i—i—i—I—i—i—i—i—I—i—i—i—r—i—i—i—i—r

0

1

2

3

4

x, mm Fig. 18. (a) Calculated and (b) measured 3 species profiles of the gas-phase flame of R D X / G A P pseudo-propellant (mass ratio 8:2) at 1 atm and laser intensity 1 0 0 W / c m 2 .

is less than 10%. The calculated concentration of carbon residue in this case is negligible. If the propellant surface is defined as the location where all condensed species are gasified, the surface temperature would be around 1000 K, consistent with GAP combustion.

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600

0.1 RDX„/10

580 *

560

£

540

oi" CD Q.

O

520

r-

500 480

-20

Fig. 19. Predicted flame structure in the foam layer of R D X / G A P pseudo-propellant (mass ratio 8:2) at 1 a t m and laser intensity 1 0 0 W / c m 2 .

1500

Fig. 20. Predicted temperature, void fraction, and condensed species-concentration profiles in the near-surface region of R D X / G A P pseudo-propellant (mass ratio 8:2) at 1 atm and laser intensity 100 W / c m 2 .

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and Ignition of Nitramine

409

Propellants

Figure 21 shows the predicted pressure dependence of burning rate for a RDX/GAP pseudo-propellant with a mass ratio of 8:2. It is found that the burning rate-pressure relation follows a power law which is applicable to many propellants with the exponent n = 1, whereas n = 0.83 for pure RDX. The exponent value n = 1 indicates that the addition of GAP does alter the combustion characteristics of RDX. Figure 22 shows the temperature sensitivity defined in Eq. (35) of burning rate at various pressures. The temperature sensitivity of burning rate decays at high pressures since the heat feedback is more profound than the effect of initial temperature on the burning rate. Similar to results of the HMX/GAP analysis, the combustion characteristics of RDX/GAP pseudo-propellant at various pressures and initial temperatures were investigated. 38 The surface temperature increases linearly with increasing pressure on the logarithmic scale, but it is not very sensitive to the initial temperature. This is understandable because the surface temperature is resolved by an energy balance, and the heat flux is strongly dependant on the pressure but not the initial temperature. The adiabatic flame temperature increases with both increasing pressure and initial temperature. The increase is not linear due to the limitation of grid resolution and the non-linearity of chemical kinetics. The melt-layer thickness

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i , , , ,

75 100

p, atm Fig. 21. Predicted pressure dependence of burning rate of R D X / G A P pseudo-propellant (mass ratio 8:2).

410

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i

u.uuo

^ ^

,

i

,

i

i

i i i 1 1 1 i i i i i_

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iti

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i

10

25

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50

75 100

p, atm Fig. 22. Predicted temperature sensitivity of burning rate of R D X / G A P pseudopropellant (mass ratio 8:2).

decreases with increasing pressure but is not sensitive to the initial temperature. In general, the melt-layer thickness decreases with increasing burning rate, but increases with the higher values of thermal conductivity of the propellant. As shown in Fig. 21, the burning rate is linearly dependant on pressure, and thus the pressure dependence of melt-layer thickness is also linear. The initial temperature of propellant does not exhibit a strong effect on the melt-layer thickness, because both the burning rate and thermal conductivity are not very sensitive to the initial temperature. The surface void fraction decreases with increasing pressure, but increases with increasing initial temperature. It is not surprising because the bubble formation strongly depends on the evaporation process, which is retarded at high pressures but enhanced at high initial temperatures. The effects of laser heat flux on the burning rate, surface heat flux, surface temperature, melt-layer thickness, and surface void fraction at pressure levels of 1, 10, and 100 atm were numerically investigated. The burning rate and surface temperature increase with increasing laser heat flux. The effect decays with increasing pressure because the heat feedback from the gas phase increases with increasing pressure. The melt-layer thickness exhibits an opposite trend; it decreases with increasing burning rate, and its decreasing rate is consistent with the increasing rate of burning

Combustion

and Ignition of Nitramine

Propellants

411

rate. In contrast to the heat feedback from the gas phase at high pressures, the laser heat flux increases bubble formation, up to 50% at the surface at l a t m a n d 300W/cm 2 . The final set of results show the effects of binder mass fraction on combustion characteristics over a broad range of pressure and initial temperature. Here, it is possible to utilize the model to describe experimental observations. For example, the burning rate of pure GAP is higher than that of HMX, but the addition of GAP into HMX lowers the burning rate. 24 In contrast, recent measurements 3 show the enhancement of burning rate by adding GAP into RDX or HMX. Both observations have been reproduced by the model. Figure 23 shows the effects of initial composition and pressure on the burning rate of RDX/GAP pseudo-propellants. The burning rate decreases in the case of higher GAP composition because GAP decomposition produces inert gases that dilute the concentrations of surface reactive species, and thus retard the heat feedback from the gas phase. It is evident that the heat feedback is a controlling factor for the burning rate in all the cases without laser, because the pressure dependence of burning rate follows the same trend as that of heat feedback. The addition of GAP modifies the slopes (pressure dependencies) in Fig. 23, but not in a consistent manner. A small amount of GAP (10% by weight) increases the slope and makes the system unstable, while more GAP (30% by weight) restores the

T

1

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1

1

1—I

I |

no laser" '

10°

i

i

101

1 — i

i

i

i

i

i

102

p, atm Fig. 23.

Predicted effect of propellant formulation on burning rate at various pressures.

E. S. Kim & V. Yang

412

0.45

i

i

i

i

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r

"1

T"

p = 10 atm 0.40 "g 0.35 O

3Z 0.30 CO

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'c = 0.20 CD

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0.15 0.10

_1

I

I

I

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100

'

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150

i

1_

200

i

i

i

'

v

8:2

&--

7:3

.

250

i

i

I

i

300

Radiant Energy Flux, W/cm 2 Fig. 24. Predicted effect of propellant formulation on burning rate at various laser and composition levels.

slope to the pure RDX case but reduces the burning rate by more than 50%. Figure 24 shows the burning rates at 10 atm with various compositions and laser levels. The profiles of mass ratios 10:0 and 9:1 are very close, indicating the burning-rate change due to the addition of a small amount of GAP is negligible for laser heat fluxes ranging from 100 to 300 W/cm 2 . For higher GAP compositions (20 and 30% by weight), the burning rates decrease at 100 W/cm 2 , but increase at 200 and 300 W/cm 2 . The effect is more profound at low pressures since the conductive heat feedback from the gas phase is of less importance in the case of laser-assisted combustion. More experimental data, however, is required for model validation as well as an improved chemical kinetics mechanism of GAP decomposition. 7. Concluding Remarks In the past decade significant progress has been made in modeling the steady-state combustion and transient ignition behavior of nitramine monopropellants and nitramine/GAP pseudo-propellants. The theoretical formulation is based on the conservation equations of mass, energy, and species for both the condensed and gas phases, and takes into account finite-rate chemical kinetics and variable thermophysical properties. These models have been applied to a broad range of operating conditions. Various important

Combustion

and Ignition of Nitramine

Propellants

413

burning and ignition characteristics were investigated systematically, with emphasis placed on the detailed combustion-wave structure and the effect of the subsurface two-phase layer on propellant deflagration and ignition behavior. For pseudo-propellants, the effect of propellant composition on the burning rate at various pressures and heat fluxes was studied. In general, good agreement was achieved between the predicted and measured species-concentration and temperature profiles. Burning rates and their temperature and pressure sensitivities were reasonably predicted over a broad range of operating conditions. The complete ignition process from surface pyrolysis to steady-state combustion of RDX monopropellant was also investigated using the ignition model. Emphasis was placed on the ignition delay and key physiochemical processes responsible for achieving ignition. The predicted ignition delay shows good agreement with experimental data. In spite of the accomplishments achieved so far, several challenges remain. One major difficulty in both experimental and theoretical investigations lies in the treatment of the two-phase near-surface region, which includes an array of intricacies such as thermal decomposition, subsequent reactions, evaporation, bubble formation and interaction, and interfacial transport of mass and energy between the gas and condensed phases. The lack of reliable thermophysical properties poses another limitation in model accuracy. Nonetheless, the existing models provide a solid basis for investigating various underlying processes involved in the combustion and ignition of energetic materials.

Acknowledgments This work was supported partly by the Pennsylvania State University, partly by the Army Research Office under Contract DAAL 03-92-G-0118, and partly by the California Institute of Technology Multidisciplinary University Research Initiative under ONR Grant No. N00014-95-1-1338. The authors are indebted to Dr. Yeong Cherng (John) Liau for his contributions in developing the RDX ignition and combustion models.

References 1. T. P. Parr and D. M. Hanson-Parr, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 381.

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2. O. P. Korobeinichev, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 335. 3. T. A. Litzinger, Y.-J. Lee and C.-J. Tang, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 355. 4. D. Chakraboty and M. C. Lin, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 33. 5. T. B. Brill, M. C. Beckstead, J. E. Flanagan, M. C. Lin, T. A. Litzinger, R. H. W. Waesche and C. A. Wight, J. Propul. Power 18, 824 (2002). 6. B. C. Beard, Propellants, Explosives, and Pyrotechnics 16, 81 (1991). 7. H. H. Krause, N. Eisenreich and A. Pfeil, Propellants, Explosives, and Pyrotechnics 17, 179 (1992). 8. R. Behrens, Jr. and S. N. Bulusu, J. Phys. Chem. 96, 8877 (1992). 9. C. A. Wight and T. R. Botcher, J. Amer. Chem. Soc. 114, 8303 (1992). 10. R. R. Botcher and C. A. Wight, J. Phys. Chem. 97, 9149 (1993). 11. A. Zenin, J. Propul. Power 11, 752 (1995). 12. T. B. Brill, J. Propul. Power 11, 740 (1995). 13. E. S. Kim, H. S. Lee, C. F. Mallery and S. T. Thynell, Combust. Flame 110, 239 (1997). 14. T. A. Litzinger, B. L. Fetherolf, Y.-J. Lee and C.-J. Tang, J. Propul. Power 11, 698 (1995). 15. S. T. Thynell, P. E. Gongwer and T. B. Brill, J. Propul. Power 12, 933 (1996). 16. C. Y. Lin, H. I. Wang, M. C. Lin and C. F. Williams, Int. J. Chem. Kinetics 22, 455 (1990). 17. D. M. Hanson-Parr and T. P. Parr, J. Energetic Mater. 17, 1 (1999). 18. R. A. Isbell and M. Q. Brewster, Propellants, Explosives, and Pyrotechnics 23, 218 (1998). 19. T. B. Brill, Prog. Energy Combust. Sci. 18, 91 (1992). 20. R. A. Isbell and M. Q. J. Brewster, Thermophys. Heat Transfer 11, 65 (1997). 21. A. I. Atwood, T. L. Boggs, P. O. Curran, T. P. Parr and D. M. Hanson-Parr, J. Propul. Power 15, 740 (1999). 22. O. P. Korobeinichev, L. V. Kuibida, V. N. Orlov, A. G. Tereshchenko, K. P. Kutsenogii, R. V. Mavliev, N. E. Ermolin, V. M. Fomin and I. D. Emel'yanov, Mass-Spektrom. Khim. Kinet. 73 (1985). 23. T. P. Parr and D. M. Hanson-Parr, 27th Symp. (Int.) on Combustion, 2301 (1998). 24. C. F. Melius, in Chemistry and Physics of Energetic Materials, ed. S. Bulusu (Kluwer Academic, Norwell, MA, 1990), p. 21. 25. R. A. Yetter, F. L. Dryer, M. T. Allen and J. L. Gatto, J. Propul. Power 11, 666 (1995).

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32. 33. 34. 35. 36. 37. 38.

39. 40. 41.

42.

43.

44.

45. 46. 47. 48.

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S. C. Li, F. A. Williams and S. B. Margolis, Combust. Flame 80, 329 (1990). S. B. Margolis and F. A. Williams, J. Propul. Power 11, 759 (1995). S. C. Li and F. A. Williams, J. Propul. Power 12, 302 (1996). K. Prasad, R. A. Yetter and M. D. Smooke, Combust. Sci. Tech. 124, 35 (1997). K. Prasad, M. Smooke and R. A. Yetter, Combust. Flame 115, 406 (1998). M. S. Miller and W. R. Anderson, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 501. Y.-C. Liau, The Pennsylvania State University, Department of Mechanical Engineering, Ph.D. Diss. (1996). Y.-C. Liau and V. Yang, J. Propul. Power 11, 729 (1995). J. E. Davidson and M. W. Beckstead, J. Propul. Power 13, 375 (1997). J. E. Davidson and M. W. Beckstead, 26th Symp. (Int.) on Combustion, 1989 (1996). Y.-C. Liau and V. Yang, AIAA Paper 97-0589 (1997). E. S. Kim, V. Yang and Y.-C. Liau, Combust. Flames 131, 227 (2002). Y.-C Liau, V. Yang and S. T. Thynell, in Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, Reston, VA, 2000), p. 477. E. S. Kim, The Pennsylvania State University, Department of Mechanical Engineering, Ph.D. Diss. (2000). Y.-C. Liau, E. S. Kim and V. Yang, Combust. Flames 126, 1680 (2001). T. L. Boggs, in Fundamentals of Solid Propellant Combustion, Progress in Astronautics and Aeronautics, Vol. 90, eds. K. K. Kuo and M. Summerfield (1984), p. 121. R. A. Fifer, in Fundamentals of Solid Propellant Combustion, Progress in Astronautics and Aeronautics, Vol. 90, eds K. K. Kuo and M. Summerfield (1984), p. 177. M. H. Alexander, P. J. Dagdigian, M. E. Jocox, C. E. Kolb, C. F. Melius, H. Rabitz, M. Smooke and W. Tsang, Prog, in Energy Combust. Sci. 17, 263 (1991). V. Yang, T. B. Brill and W. Z. Ren (eds.), Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185 (AIAA, Reston, VA, 2000). M. Benreuven, L. H. Caveny, R. J. Vichnevetsky and M. Summerfield, 16th Symp. (Int.) on Combustion, 1223 (1976). N. E. Ermolin, O. P. Korobeinichev, L. V. Kuibida and V. M. Formin, Fizika Goreniya I Vzryva 22, 54 (1986). E. W. Price, H. H. Bradley, G. L. Dehority and M. M. Ibiricu, AIAA J. 4, 1153 (1966). A. K. Kulkarni, M. Kumar and K. K. Kuo, AIAA J. 20, 243 (1982).

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49. C. E. Hermance, in Fundamentals of Solid Propellant Combustion, Progress in Astronautics and Aeronautics, Vol. 90, eds. K. K. Kuo and M. Summerfield (1984), p. 239. 50. V. N. Vilyunov and V. E. Zarko, Ignition of Solids (Elsevier Science Publishers, NY, 1989). 51. L. Strakouskiy, A. Cohen, R. Fifer, R. Beyer and B. Forch, Laser Ignition of Propellants and Explosives (ARL-TR-1699, Army Research Laboratory, Aberdeen Proving Ground, MD, 1998). 52. S. D. Baer and N. W. Ryan, AIAA J. 6, 872 (1968). 53. H. H. Bradley, Combust. Sci. Technol. 2, 11 (1970). 54. A. Linan and F. A. Williams, Combust. Sci. Technol. 3, 91 (1971). 55. A. Linan and F. A. Williams, Combust. Flame 18, 85 (1972). 56. F. A. Williams, AIAA J. 4, 1354 (1966). 57. C. H. Waldman and M. Summerfield, AIAA J. 7, 1359 (1969). 58. C. H. Waldman, Combust. Sci. Technol. 2, 81 (1970). 59. H. H. Bradley and F. A. Williams, Combust. Sci. Technol. 2, 41 (1970). 60. W. H. Andersen, Combust. Sci. Technol. 2, 23 (1970). 61. W. H. Andersen, Combust. Sci. Technol. 5, 43 (1972). 62. W. H. Andersen, Combust. Sci. Technol. 5, 75 (1972). 63. A. Linan and A. Crespo, Combust. Sci. Technol. 6, 223 (1972). 64. T. Niioka, Combust. Sci. Technol. 18, 207 (1978). 65. C. E. Hermance, R. Shinnar and M. Summerfield, Astronautica Acta 12, 95 (1966). 66. T. Kashiwagi, B. W. MacDonald, H. Isoda and M. Summerfield, 13th Symp. (Int.) on Combustion, 1073 (1971). 67. C. E. Hermance and R. K. Kumar, AIAA J. 8, 1551 (1970). 68. R. K. Kumar and C. E. Hermance, AIAA J. 9, 615 (1971). 69. R. K. Kumar and C. E. Hermance, Combust. Sci. Technol. 4, 191 (1972). 70. R. K. Kumar and C. E. Hermance, Combust. Sci. Technol. 14, 169 (1976). 71. M. Kindelan and F. A. Williams, Combust. Sci. Technol. 16, 47 (1977). 72. S. Ritchie, S. Thynell and K. K Kuo, J. Propul. Power 13, 367 (1997). 73. K. Puduppakkiam and M. W. Beckstead, 31th JANNAF Combustion Subcomm. Meeting, (CPIA Publ., 2000). 74. C.-J. Tang, Y. Lee and T. A. Litzinger, Combust. Flame 117, 244 (1999). 75. H. Arisawa and T. B. Brill, Combust. Flame 112, 533 (1998). 76. N. Kubota and T. Sonobe, 23rd Symp. (Int.) on Combustion, 1331 (1990). 77. G. Lengelle, B. Fourest, J. C. Godon and C. Guin, AIAA Paper 93-2413 (1993). 78. J. E. Flanagan, D. O. Woolery and R. L. Kistner, AFAL-TR-87-107 (Air Force Astronautics Laboratory, Edwards AFB, CA, 1987). 79. M. Faber, S. P. Harris and R. D. Srivastava, Combust. Flame 55, 203 (1984). 80. A. A. Zenin and S. V. Finjakov, AIAA Paper 2000-1032 (2000). 81. G. S. Sysak, E. S. Kim and S. T. Thynell, 35th JANNAF Combustion Subcomm. Meeting (CPIA Publ., 1998). 82. M. Frenklach, T. Bowman, G. Smith and B. Gardiner, GRI-MECH 1.2, http://euler.berkeley.edu/gri_mech/index.html.

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83. R. J. Kee, J. F. Grcar, M. D. Smooke and J. A. Miller, A Fortran Program for Modeling Steady, Laminar, One-Dimensional (Premixed Flames, Sandia Report SAND85-8240, Sandia National Laboratories, Albuquerque, NM, 1985). 84. Y. J. Lee and T. A. Litzinger, The Pennsylvania State University, University Park, PA, 1995, private communication.

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C H A P T E R 13 BURNING-RATE MODELS A N D THEIR SUCCESSORS, A PERSONAL PERSPECTIVE Martin S. Miller Attn: AMSRL-WM-BD Army Research Laboratory Aberdeen Proving Ground, MD 21005, USA

Contents 1. Introduction 2. Phenomena 3. Concepts 3.1. Intra-Phase Conservation Equations 3.1.1. Solid Phase 3.1.2. Liquid Phase 3.1.3. Gas Phase 3.2. Phase-Matching Continuity Conditions 3.2.1. Species-Flux Continuity at Solid/Liquid Boundary, x = —^Liq 3.2.2. Energy-Flux Continuity at Solid/Liquid Boundary, x = —^Liq 3.2.3. Species-Flux Continuity at Liquid/Gas Boundary, x = 0 3.2.4. Energy-Flux Continuity at Liquid/Gas Boundary, x = 0 3.3. Surface-Regression Mechanism 3.3.1. Single-Component Evaporation Mechanism 3.3.2. Multi-Component Evaporation Mechanism 3.4. Mathematical Closure of the 3-Phase Problem 4. Models 4.1. Frozen Ozone 4.2. Deficiencies in the Idealization 4.2.1. Multi-Component Evaporation 4.2.2. Liquid-Phase Difussion 4.2.3. Real-Gas Equation of State 4.2.4. Phase Separation 4.3. RDX 419

420 421 423 424 425 426 427 427 428 429 429 429 429 430 431 431 433 434 439 439 440 441 442 442

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M. S. Miller

4.4. Multi-Ingredient Propellant Mixtures, A New Approach 5. Challenges and Opportunities 5.1. "Molecular" Continuum Model of Multi-Component Evaporation 5.2. Molecular-Dynamics Simulations of the Condensed Phase 6. Conclusions Appendix References

446 459 460 465 467 469 469

1. Introduction The capability to calculate the burning rate of propellants from their ingredients has long been recognized as desirable though, until recently, not realizable. Even today, this capability is limited to classes of energetic materials that have been fairly extensively studied experimentally. So far, the goal of computing all the properties of propellants with ingredients that have never actually been synthesized is still beyond our reach. However, considerable progress towards obtaining properties of notional materials such as heats of formation, density, and detonation sensitivity has been made in the last ten years. Over the same period of time, fledgling ability to compute the burning rate for unstudied formulations within known classes of propellants has emerged. What is it that makes the burning-rate calculations so difficult? The combustion of energetic materials involves coupling physical and chemical phenomena in the condensed phase, the gas phase, and at the interface between the two. Our greatest knowledge and experience is centered in the gas phase. We now know that many dozens of chemical species reacting by many hundreds of elementary reactions should be considered there in concert with the physical processes of molecular diffusion, convection, and thermal conduction. Even by itself, the gas phase presents us with a daunting array of nonlinear phenomena to understand. Fortunately, general scientific progress over the last several decades has armed us with the experimental and theoretical tools to approach this problem in a systematic way. Though many uncertainties remain, the conceptual means, if not always the resources, are available to resolve them. Such is not the case in dealing with the condensed-phase and interfacial processes. In these cases we truly do not know what we do not know. It would seem that the best hope for breaking this impasse lies in molecular-dynamics simulation using reactive potentials, but this approach is fairly said to be in its infancy. Thus far, only continuum-mechanics models have been developed to describe the 2- or 3-phase combustion process, and arguments are easily mounted to suggest that one will always

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want to use a continuum model to describe the gas phase. Yet, I believe that mating these two descriptions will not be a trivial task. Anticipation of the coming need for communication between practitioners of these two approaches is what motivates this discourse. Accordingly, emphasis is placed on the mathematical framework and concepts behind the continuummechanics approach, the history of model development, their current status, and unsolved problems.

2. Phenomena Before approaching the issues surrounding the mathematical modeling of propellant burning rates, one should become familiar with the range of phenomenological behaviors associated with the combustion of propellants and propellant ingredients. Solid propellants are of two basic types: homogeneous and composite. Single- and double-base propellants are examples of homogeneous propellants. Homogeneous propellants are considered to be well mixed on a molecular scale, although this may not be strictly true because of the practical constraints on mixing. Single-base propellant consists almost exclusively of nitrocellulose (NC), which becomes increasingly less soluble in the manufacturing solvents as its nitration level increases above about 13% N, leading to a very viscous liquid during mixing and extrusion. My first experience in measuring burning rates was with six-inch long strands of M10. (Propellant formulations are given in the Appendix.) Based on the measurement technique and degree of control over known variables such as pressure, I was expecting a standard error of about 1%. Instead, the standard deviation in measured burning rates using dozens of one-inch-long specimens was as large as 25%. These large deviations arose from inhomogeneities in the propellant material itself due to imperfect mixing of the highly viscous feedstock material. This was a most inauspicious introduction to my new field! Fortunately, this would become the worst case I would ever encounter in my career. Most other homogeneous propellants benefit from the plasticizing properties of NG (propellant ingredient abbreviations are listed in the Appendix) and burn very reproducibly. However, one must always be aware, particularly with experimental propellants, that manufacturing procedures may influence the combustion properties in unexpected and non-reproducible ways. Composite propellants comprise a heterogeneous mixture of crystalline oxidizers and polymeric binders. Double-base propellant with crystalline nitroguanidine (M30) added is an example. Only in the last 15 years have composite propellants involving RDX come into use for guns. The use of

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M. S. Miller

such a secondary explosive as a major ingredient in gun propellant required considerable testing to pass safety criteria for use in the field. Composites utilizing RDX, HMX, and CL20 coupled with various energetic polymeric binders are currently under active investigation. The propellant type can have important consequences for modeling the burning rate. In many cases it is found that the oxidizer particle size strongly influences the burning rate. If this is so, a one-dimensional model may not be suitable. On the other hand, observations of burning surfaces of nitramine-composite propellants 1 at pressures in the order of 1 MPa indicate that a melt layer exists at the surface. This melt layer provides an opportunity for the solid ingredients to become intimately mixed prior to gasification, potentially restoring a one-dimensional character to the combustion phenomena. Despite their uniform morphology, one cannot necessarily assume that homogeneous propellants burn one-dimensionally. The following description of double-base propellant combustion is enough to give pause to the most intrepid model builder: "It can be observed visually that the burning surface exhibits a wave-like mode of consumption. It appears as if glowing filaments of carbonaceous material periodically move over the surface consuming a thin layer of propellant. Cine photography of the propellant surface shows that a smooth area on this surface appears to darken and to roughen. This area is then consumed by a wave of combustion which moves across the surface and leaves behind a network of carbon filaments which are blown off the surface by the steady evolution of gas. The consumption of the reacting surface layer leaves a smooth surface which subsequently repeats this sequence. It seems probable that the overall, average rate of burning is the result of two components: a steady rate analogous to the burning of a liquid propellant and a surface or condensed-phase reactive wave moving laterally across the surface."2 It is clear that any one-dimensional model of homogeneous or composite propellant combustion is to be understood as an idealization of the phenomena and not as an exact description. Despite all of the aforementioned complexities, propellants burn, at least on a macroscopic scale, in "parallel layers", i.e., in a direction normal to the local surface curvature. This is the property that allows for interiorballistic control of the net gasification rate through intricate and ingenious propellant-grain geometries. It is also the property that gives the model builder some basis for hope. Another source of encouragement is that most propellants burn with a very simple power-law pressure dependence, despite

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radical changes in the appearance of the visible flame attached to the burning surface. At pressures below about 1 MPa, there is no visible flame above the burning surface of homogeneous and many composite propellants. As the pressure increases, a weak flame appears a centimeter or more distant from the surface. With further pressure increases, the visible flame resides closer and closer to the surface, under steady-state, constant-pressure conditions. At 10 MPa or more, the flame appears attached directly to the surface. In most cases, this evolving flame behavior does not perturb the power-law pressure dependence of the burning rate. The non-luminous zone between the visible flame and the surface is known as the dark zone, which is now known to be a consequence of the relatively slow reduction of NO to N 2 (and slow reactions involving HCN in the case of nitramines). All this suggests that burning-rate control resides in a thin gas layer close to the surface, an inference that further encourages the one-dimensional idealization.

3. Concepts To date, there have been no molecular-dynamics models of multiphase combustion. This may change in the distant future; however, a nearer-term prospect is that molecular-dynamics submodels of the condensed-phase and/or interface processes will be developed and that these submodels will be used to supplement the continuum-mechanics combustion models. Anticipating the need to merge these two viewpoints, I develop in this section the mathematical formulation of the continuum paradigm. Studying Fig. 1 will provide the reader with some appreciation of the range of phenomena that are involved in the combustion of propellants. No model exists which has treated all of the processes suggested in the figure; the list is intended as a conceptual transition from nature to mathematics. Some propellants are known to exhibit a liquid layer at the burning surface and some may not. I shall assume that, in the general case, a 3-phase (solid, liquid, gas) problem must be solved. The photograph in Fig. 1 is of an RDX composite propellant (M43) burning in the steady state at a pressure of 1.6 MPa. In this case the dark zone is clearly defined and one can see that the idealization of a one-dimensional semi-infinite solid does not appear to be unreasonable. Getting now to the formalism, I consider a semi-infinite solid combusting in the steady state at constant pressure. The spatial coordinate, taken as x, extends from — oo, deep in the solid at an initial temperature of T0, to the

424

M. S. Miller

Fig. 1. Photograph of an RDX-composite propellant (M43) deflagrating at 1.6 MPa at left along with a caricature of the three-phase molecular processes involved.

solid/liquid interface at — £ij q , to the liquid/gas surface at x = 0, and finally to the region of equilibrium gas products at the adiabatic flame temperature Tf at x = oo. Equations conserving mass, atomic species, and energy must be solved in each phase subject to the boundary conditions for that phase. The intra-phase solutions must also satisfy the equations of continuity at each phase boundary and whatever additional constraints are imposed by the surface-regression mechanism.

3.1. Intra-Phase

Conservation

Equations

The conservation equations within each phase are developed and discussed elsewhere3 but will be summarized for convenience and completeness here. The + and — superscripts on the location superscripts indicate the side of the boundary where the values are taken, e.g., — x£- means evaluated at the liquid side of the interface at the coordinate ,r -<'Liq-

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Models and Their

425

Successors

3.1.1. Solid Phase Species conservation: m^=C}kWk, k = l,2,...,N, (1) ax assuming molecular diffusion is negligible on a combustion timescale; rh is the total mass flux and an eigenvalue for the problem, Yk is the mass fraction of the feth species, Cok is the net rate of production of species fc due to chemical reactions, Wk is the molecular weight of the feth species, and N is the total number of distinct species in all three phases. These equations are subject to the domain boundary conditions: Yk = Ykr°°

k = l,2,...,N

a t x = -oo.

(2)

The set of mass fractions {^7°°} reflect the composition of the unreacted propellant. Energy conservation: -i-f Asoi-j-J -"icsoi-i x \ xj x

^tokWkhk

= 0.

(3)

fe=i

Both the thermal conductivity Asoi and the average specific heat of the solid mixture csoi are, in general, functions of the independent variable x. Wk is the molecular weight and hk is the enthalpy of species fc. This equation is subject to the domain boundary conditions: T =

TQ

at x = —oo

(4)

at x = -iE L i q

(5)

and T = Tm

where To is the initial temperature of the propellant, T m is the melting point of the propellant compound, and — xuq is the coordinate of the solid/liquid boundary, which will be an eigenvalue of the complete combustion problem. It should be noted here that these conservation equations for the solid phase and liquid phase in the next section embody precepts deriving from long experience with low-pressure gas-phase processes and may not be as general as presumed. In the gas phase at sufficiently low densities each reaction event takes place in essential isolation. Thermal reaction coefficients, obtained by averaging over velocities and reaction cross-sections, can therefore be used to characterize reaction events anywhere and everywhere. In the condensed phase, on the other hand, reactive events do not take place

426

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Miller

in isolation but in a dielectric field produced by the close proximity of many "spectator" molecules. This dielectric field will evolve as a function of the instantaneous configuration of all the molecules in the vicinity of the reacting molecules during the course of the reaction. The potential therefore exists that there will be too many variables to make the notion of thermal rate coefficients an adequate and useful idealization. Of course, at present the issue is moot in the case of energetic materials as the reactions are virtually unknown. A MD approach, in principle, would handle these complexities in a natural way.

3.1.2. Liquid Phase All models to date have neglected molecular diffusion in the liquid phase as well, but I retain it in the general formulation here because I later show that it may be of some importance. Species conservation in liquid phase: ~(ftuqYkVk)

+ m^-LukWk

= 0,

k=l,2,...,N,

(6)

where pLiq is the liquid density and Vk is the diffusion velocity of species k. These equations are subject to the boundary conditions: • y

+ ""Lid

,

+ __ + -"Liqy "Liq _

y

- y,

- i i

-Liq

k = 1,2,..., N

at x = -xUq

(7)

and y*=y f c °",

k = l,2,...,N

ata; = 0.

(8)

Energy conservation in liquid phase:

Tx ( S S ) - ^ q f - X > ^ c £ - E^Wkhk = 0 (9) ^

'

k

fe=l

subject to the boundary conditions: T = Tm

at x = -x^

(10)

at x = 0.

(11)

and T = TS

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427

3.1.3. Gas Phase Species conservation in gas phase: ~(pGasYkVk)+rhd^--wkWk

= 0,

k = l,2,...,N

(12)

k = l,2,...,N

at x = 0 (13)

subject to the boundary conditions: mYf

+ pUqYf

Vf

= mYk0+ + pGasYk0+ Vk°\

and — = 0, fc = l , 2 , . . . , i V dx Energy conservation in gas phase:

T x ( A G a s f U ) " ^ ^ % ~Y.p^YkVkckp ^

'

a t x = oo.

(14)

- J 2 ^ W k h k = ° (15)

k

fc=l

subject to the boundary conditions: T = TS

at x = 0

(16)

and dT —— = 0 at x = oo. dx There is, finally, the mass conservation equation dm

* T = °'

. , (17)

< 18 >

which has the trivial solution, rh = constant = p®r

(19)

through all three phases. In particular, at T0, the solid-phase density is p° and the linear burning rate is r. 3.2.

Phase-Matching

Continuity

Conditions

Some of the above boundary conditions are expressed in quantities that are unknown at the outset and coupled to solutions in adjacent domains. These initially unknown quantities, m, Ts, xuq_, and {Yk° } are the eigenvalues for the complete problem. The final solutions for the temperature and mass fractions in each domain must satisfy the conservation equations with their respective boundary conditions in each phase for

428

M. S. Miller

z*c*r

2^ihY*'hi' Convection

ln , »7«

£,Y?v; h°t Diffusion Conduction -T(x)

Convection "O^y*"' itx*

Conduction-^.,

SOLID

LIQUID

GAS .v = 0

>x

Fig. 2. Energy fluxes at the phase boundaries arising from convection, molecular diffusion, and thermal conduction.

unique values of the eigenvalues. In order to accomplish this, one needs further constraints on the problem. These are to be found in the interphase equations of continuity, discussed in this section, and in the surfaceregression mechanism, discussed in the next section. Figure 2 shows the contributions to the energy fluxes across the phase boundaries. The meaning of the subscripts and superscripts will be clear from the figure contexts. The continuity conditions at each phase interface are constructed by equating the summed contributions on each side of a particular interface. In the figure I have neglected contributions from the kinetic energy, as these are very small for typical propellant burning rates (of order 0.01% of the starting enthalpies), and also contributions from molecular diffusion in the solid phase, because it will be too slow on the timescale of importance to combustion. The boundary conditions can now be shown to be: 3.2.1. Species-Flux Continuity at Solid/Liquid Boundary, x = — a;L;q This relation is the same as Eq. (7) and thus is not a new constraint.

Burning-Rate

Models and Their

429

Successors

3.2.2. Energy-Flux Continuity at Solid/Liquid Boundary, x = - £ L i q (dT\-x^ N

"

+

r Liq

+™E r

-,L-, iV

+

C

L,q

,.+

-xL"iq _

/ d T \ - ^

+

_

+

y Liqy Liq

+PL i q £ r

r

_

C

+

Liq

-

(20)

3.2.3. Species-Flux Continuity at Liquid/Gas Boundary, x = 0 This relation is the same as Eq. (13) and thus is not a new constraint. 3.2.4. Energy-Flux Continuity at Liquid/Gas Boundary, x = 0 N

Q-

N

+rhJ2Yk0-hl-+pLiqY/YfVfh'

-A Liq f^)

k 0+

g) 3.3. Surface-Regression

N

N

+m£yf/zf +p Gas Eyr^ 0+ ^ + -

(2i)

Mechanism

In general, one might consider that many mechanisms contribute to surface regression during combustion: evaporation or desorption of surface species without change of identity, reaction of surface species to produce different gas-phase species, reaction of gas-phase species with surface species to produce other gas-phase species, and, possibly, physical ejection of molecular aggregates due to explosive reaction in the surface. It is also possible that some combination of these mechanisms might be active in the condensed phase below the surface, creating bubbles which are subsequently convected to the surface and released. Obviously, it will be a very great challenge to include all of these processes in a full combustion model, although attempts have been made to model RDX using a mix of evaporation and bubble formation. 4,5 In these treatments, one-dimensionality was preserved through the artifice of continuous porosity, though with unknown accuracy. In my opinion, the only surface-regression mechanism that has been treated with reasonable rigor is evaporation, and even this has been approximate with unknown accuracy. The remainder of this section will be devoted to a discussion of the approach taken to an evaporative mechanism and its potential shortcomings.

430

M. S. Miller

3.3.1. Single-Component Evaporation Mechanism To date, the only evaporation mechanism used in published burning-rate model developments is based on the following reasoning. Consider a pure liquid substance in equilibrium with its vapor at some temperature Ts. I will refer to the multiphase presence of a single chemical species as "single component". At equilibrium, the mass flux impinging on the surface is given by the kinetic-theory result \nvW where n is the molar number density in the vapor, v is the mean molecular velocity at Ts, and W is the molecular weight of the species being considered. If a is the fraction of impinging molecules that are absorbed into the surface, i.e., the accommodation coefficient, then the mass flux actually absorbed into the surface is \anvW. Under equilibrium conditions, the mass flux escaping the surface equals the mass flux being absorbed. Thus the escaping mass flux can be expressed in terms of the number density at equilibrium or, through the equation of state, the equilibrium vapor pressure pe. Under combustion conditions, the vapor pressure at the surface is less than the equilibrium value due to depletion by reactions and molecular diffusion. Thus, one can express the net regression rate of the surface during combustion in terms of the equilibrium vapor pressure at Ts, the total pressure, and the mole fraction of the mother-liquor species on the gas-phase side of the surface, X° . These arguments are summarized graphically in Fig. 3 and in the following equation, which expresses the net flux of evaporating molecules as the difference between the gross escaping flux and the gross condensing flux, i.e., W

m(X0+,Ts)

2TTRT^

EQUILIBRIUM

,i

Liquid

[pe(Ts) - X0+ Ptotal

(22)

NON-EQUILIBRIUM

.

Equilibrium vapor pressure p*

-aW\,nv\

Liquid

Vapor pressure reduced from p8 by reactions

= Q„.-I_elY8«ZLV escaping

Surface Regression: m = m''escaping i Fig. 3.

4

R T

I

xW

condensing

Single-component evaporative surface-regression mechanism.

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Models and Their

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431

3.3.2. Multi-Component Evaporation Mechanism On the face of it, there is no problem with the rigor of the arguments just presented. The difficulty comes when applying it to even the simplest combustion problem. Take the self-deflagration of pure frozen ozone, for instance. This case will be developed more fully later, but it serves to illustrate the problem with single-component evaporation. Under combustion conditions, by definition, there will be chemical species other than ozone in the gas phase. These will be products and intermediates of ozone decomposition, viz., O2 and O. These other species will also impinge upon and be absorbed to some extent in the surface. Thus, the surface will have a multi-component nature, and the equilibrium vapor pressure of pure ozone will no longer determine the mass flux of ozone escaping the surface but also be a function of the mole fractions and molecular properties of the other molecules present. In addition the mass flux leaving the surface will include contributions from the surface-absorbed products and intermediates originating from the gas-phase reactions. In principle, then, the single-component evaporation mechanism is intrinsically inappropriate for a problem involving combustion. Of course, as an approximation, it may turn out to be useful, but its accuracy is impossible to assess a priori.

3.4. Mathematical

Closure of the 3-Phase

Problem

To illustrate the final posing of the 3-phase mathematical problem, I adopt single-component evaporation as the surface-regression mechanism and assume that molecular diffusion in the liquid phase can be neglected. Neglect of molecular diffusion means that only one boundary condition in the liquid-phase domain is required and I choose this to be Yk = Ykx^\

k = l,2,...,N

at a: = - a : L l q .

(23)

Note that, in the absence of diffusion, Yk~ Liq = Y~ Liq . This single boundary condition replaces Eqs. (7) and (8). Neglect of diffusion, through replacement of Eq. (8), also greatly simplifies the problem by reducing the number of eigenvalues to three, xUq, Ts, and rh. One begins by providing starting estimates for these three eigenvalues of the coupled boundary-value problems; call them a^Liq, Ts, and rh. The solid-phase conservation equations are then solved using the estimated values xuq and rh. This solution will

432

M. S. Miller

provide values of {Vfe_a:Liq} needed by the liquid-phase boundary condition equation (23). After solving the liquid-phase conservation equations, test to see if Asoi(^

2 A L iiq q

Lx) V

/

. X= — X-L

N

h):\Tm)-hf\Tm)\.

(24)

k

This is Eq. (20) rewritten for the neglect of liquid-phase diffusion. The quantity in brackets is the latent heat of fusion for simple substances. If the equality is not met at some chosen level of approximation, then choose another value of xuq and repeat until Eq. (24) is satisfied. When Eq. (24) is satisfied, solve the gas-phase conservation equations using the liquid-phase solutions just obtained for {Y"fc° }, then test to see if the surface-regression mechanism is satisfied, i.e., if i 0+

MX ,fs)

la(-W-Y V 2,-KKI

[p e (f s )-X°V,tai]. S

(25)

J

Normally Eq. (25) will not be satisfied at this point. Choose another value of rh and solve the solid, liquid, and gas phases again, iterating until both Eqs. (24) and (25) are satisfied. Then test to see if

k N

+PGasj2yk0+vko+hi+.

(26)

k

This is Eq. (2) rewritten for the neglect of liquid-phase diffusion. Normally, Eq. (26) will not be satisfied at this point, so choose another value of Ts and iterate all of the above until Eqs. (24)-(26) are all satisfied to the required degree of accuracy. At this point one will have determined the eigenvalues of the problem, xuq, Ts, and rh. The whole process can be more easily visualized as a logic flow chart in Fig. 4. Actually, the process is straightforward and successive guesses for the eigenvalues can be based on physical reasoning depending on the results of each energy-flux equality test so that convergence of each eigenvalue can be approached

Burning-Rate

Models and Their

Successors

Choose trial values 0 f

-^Liq. TS> a

n d

™

Solve conservation eqns. in solid & liquid phases

Solve conservation eqns. in gas phase

Fig. 4. Flow chart illustrating the logic for determining the eigenvalues for the threephase problem for single-component evaporation.

with monotonic decreasing error. The solution process is obviously more complicated if molecular diffusion in the liquid phase is not neglected. 4. Models The quantitative modeling of the burning rate of solid energetic materials really began in the dark hours of World War II with, predominantly, the efforts of Parr and Crawford6 at the University of Minnesota, and Rice and Ginell7 at the University of North Carolina. These and related wartime

434

M. S. Miller

works were published in a special issue of the (then) Journal of Physical and Colloid Chemistry, Vol 54 (1950). At that time virtually all propellants, gun and rocket, used some combination of NC and NG as their energetic ingredient. Since that time composite propellants consisting of ammonium perchlorate in rubber binders (e.g., in the space-shuttle boosters) have dominated the solid rocket propellant applications, with solid composites based on HMX in polymeric binders also in use. Fielded gun propellants are still dominated by nitrate-ester propellants although composites of these conventional propellants with nitroguanidine are common. The variety of propellant ingredients exacerbates the difficulties faced by combustion modelers both because of their different mechanisms and because of the paucity of detailed experimental data available for many of them. Recent trends are toward even more rapid proliferation of new chemical ingredients such as oxetanes, with their functional-group tailorability, and azides, with their attractive environmental advantages. In addition to enhanced performance and safety, the new constraints of minimal environmental impact in manufacture, use, and demilitarization are now driving concerns in the development of new propellants. Coincident with the emergence of many promising new energetic materials, with attendant dilution of experimental characterization, is the growing urgency for theoretical guidance in the formulation of propellants incorporating these materials. It is generally true that the higher the performance required of the weapon system, the smaller will be the margin of safety in the functioning of all the components of the system, including the propellant. If having a burning-rate model was deemed important fifty years ago, it is considerably more so with today's new mix of developmental constraints and advanced ingredients. In this section, our aim is not to give a comprehensive history of burningrate modeling but, rather, to provide a sense of the conceptual development of modeling approaches. This background is essential to an assessment of future avenues of progress in the field. Three subtopics will be addressed: frozen ozone, RDX, and multi-ingredient propellants. This progression of increasing system complexity allows us to illustrate some of the detailed mechanistic challenges facing the model builder and some new approaches to realizing a workable tool for the propellant formulator.

4.1. Frozen

Ozone

Frozen ozone is the simplest chemical system falling within the scope of 3-phase self-sustained deflagration. Though simple from a theoretical point

Burning-Rate

Models and Their

Successors

435

of view, it is anything but a straightforward subject for experimental investigation. Its propensity to detonate is legendary and the attendant dangers have undoubtedly inhibited the kind of extensive measurements of burning rate that one would like for comparison with model outputs. On the other hand, a wealth of high-quality experimental data has been obtained on thermophysical properties such as specific heat, thermal conductivity, melting and boiling points, latent heats, reaction paths and rates, and equations of state. This comprehensiveness and reliability of the input database on frozen ozone, coupled with its simplicity, makes it an attractive subject for modeling despite the paucity of burning-rate data. Its conceptual simplicity encourages and enables a more thorough study of mechanisms than with any other energetic material. Frozen ozone melts at about 80 K and has a normal boiling point of 161.3 K. The rate of reaction in the condensed phase is known to be very slow compared to the timescale of self-sustained deflagration. Thus, all of the uncertainties of describing condensed-phase reactions are conveniently (and legitimately!) sidestepped. The gas-phase reaction mechanism is known with good confidence to consist of the following three reactions. 03 + M ^ 0

2

+0 + M

A # ° 9 8 15 K = +25.65 kcal/mol

(I)

0 3 + O <-• 0 2 + 0 2

A

#298.is K = -93.41 kcal/mol

(II)

0 + 0 + M^0

A f f ° 9 8 1 5 K = - 1 1 9 . 0 6 kcal/mol.

(Ill)

2

+ M

If one is considering a pure ozone feedstock, then Eq. (22) describes the mass flux resulting from evaporation. The only measurement of the linear deflagration rate of condensed-phase ozone was made by Streng 8 for a liquid mixture of 90% 0 3 with 10% 0 2 . The total mass flux leaving the surface in this multi-component case is m = rh(l-y^)+mo3,

(27)

9

an equation first used by Ben-Reuven et al. in connection with an RDX evaporation model. rho 3 is the mass flux of 0 3 alone. Assuming that YQ « ^03°°, i-e., no liquid-phase reactions or molecular diffusion, this expression reduces to ™ ^ ~ (28) J o3 This mass-fraction-equivalency assumption is not strictly true for a number of reasons to be discussed subsequently, but it may be an adequate approximation. rho3 may be computed using a modification of Eq. (22) in

436

M. S. Miller

which the equilibrium vapor pressure term pe is replaced by the O3 partial pressure, which may be approximated by XQ3PQ3, an expression of Raoult's law for ideal solutions. XQ is the O3 mole fraction at the surface, which is assumed to be approximated by XQ°°, consistent with Eq. (28). Of course, Raoult's law is only an approximation which can sometimes result in considerable error. An example of a calculation 10 of the burning rate of pure frozen ozone at 0.1 MPa and initial temperature 40 K is given in Fig. 5. As indicated in the figure, the computed linear burning rate is 0.25 cm/s at 0.1 MPa and an initial temperature of 40 K. By comparison, pure RDX burns about an order of magnitude more slowly at a seven-fold higher initial temperature!

FROZEN OZONE COMBUSTION AT 1 ATM & 40 K r (cm/s) = 0.2526 x N q (micron) = 24.07 T s (K) = 158.06 1.0 -

r- 2200

0.9 -

- 2000

°2 ."' /' ^^-—

0.8 -

- 1800 - 1600

0.7 -

c

B 0.6-

0 CD LL 0.5-

_CD O S

•

I

O

\

9

_l

O

\

CO - 1200

<

v/ ij

_i

V)

. , , - 1400

\

\

ZJ

O

//

0

- 1000

0.4 \

i

0.3 -

- 800

\

i

^°3

0.2 -

\

i

'

i

'

— I

0

]

I

I

10 20

CD E 1-

600

- 400

\

-50 -40 -30 -20 -10

1.

\

0.1 -

0.0 -

1

CO

c u Q.

•

•'/

CD

I

0 I

I

I

30 40

I

j

I

I

- 200

1 I

-0

50 60 70

Distance from Surface ( microns ) Fig. 5. Computed eigenvalues and profiles 10 for the steady-state deflagration of frozen ozone at 0.1 MPa and an initial temperature of 40 K.

Burning-Rate

Models and Their

Successors

437

It is interesting that the surface temperature is about 3 K lower than the boiling point at this pressure. An earlier model 11 assumed that the surface temperature is equal to the boiling point; evidently, in this case, it is not a bad assumption. Unlike any of the burning-rate calculations for more complex systems, such as RDX, the calculations in Ref. 10 include the effects of thermal diffusion in the gas phase, although the burning rate is changed by only a few percent if this process is neglected. Another mechanism investigated in Ref. 10 and unique to this ozone study, is the possibility of a heterogeneous reaction in which an oxygen atom from the gas phase reacts with a surface ozone molecule resulting in two gas-phase O2 molecules: O(gas) + 0 3 (liq) — 20 2 (gas),

Aff 2 Vi5K = -93.41 kcal/mol.

(IV)

This reaction apparently has never been measured but seems not only plausible but probable. It was assumed that the probability is unity in order to determine the maximum effect. Surprisingly, the burning rate increased only 1% at 0.1 and 2.0 MPa despite this highly exothermic reaction occurring at the surface, where it adds directly to the heat feedback. In addition to the enhanced heat feedback, this reaction contributes to the destruction of ozone on the surface and should thereby contribute directly to the regression rate. It turns out that the O atoms near the surface that are consumed by the heterogeneous reaction would be consumed anyway in the reaction zone between 1 and 10 microns from the surface in the gas phase, and reactions this close to the surface contribute their heat with high efficiency to the heat feedback. (See Fig. 6.) The analysis leading to this conclusion is based on an important concept in steady-state combustion that can be gained from a study of the conservation equations above. Starting with Eq. (15) and assuming that the mixture thermal conductivity is constant and that the specific heats for all species are equal and constant, one can show12 that fdT\ f°° , , ™*v x A Gas \-T~) = q{x)e ^xdx, (29) ax V J x=Q+ JO where q(x) is the net volumetric rate of heat release in the gas phase. This expression indicates that heat released within a characteristic transport distance, Asp, will contribute to the heat feedback with high efficiency. Equation (29) is valuable in very complex reaction mechanisms to sort out which reactions are materially affecting the burning rate. The characteristic distance is about 10 microns in Figs. 5 and 6.

438

M. S. Miller

Gas-Phase Species-Production Rates in Frozen-Ozone Combustion

0.1

1

10

100

1000

Distance from Surface (microns) Fig. 6. Rates of production of each species in a pure frozen-ozone problem 1 0 at 0.1 MPa and 40 K initial temperature. The f and b suffixes indicate that the reaction identified is predominantly proceeding in the forward and backward directions, respectively. The whole flame is divided into zones based on the predominant reactions there.

The ozone problem is simple enough to achieve a complete and unambiguous analysis of the chemistry in each part of the flame. The monotonic behavior of the temperature profile in Fig. 5 belies the underlying complexity of parallel and sequential reactions, which switch directions during the course of the flame, as seen in Fig. 6. A curiosity indicated in Fig. 6 is that spatially the first reaction step in the ozone decomposition flame is the production of ozone by Reaction (I) running in reverse. In more complex reaction mechanisms with dozens of species and hundreds of reactions, it is impossible to completely analyze the chemistry. In those cases sorting tools such as PREAD, 1 3 ChemPlot, 14 and Elemap 15 coupled with considerable experience are essential to gain insights into the mechanisms affecting both the burning rate and the flame features such as the dark zone. The lone measurement of a condensed-phase burning rate involving ozone, to which I previously alluded, was for a liquid mixture of 90% O3 and 10% O2. The result was ~0.4cm/s; our calculation, utilizing Eq. (28) and

Burning-Rate

Models and Their

Successors

439

Raoult's law, produced 0.30 cm/s. Sandri 11 has speculated that Streng's measured rate is too high because of heating of the liquid by the flame via conduction through the containing-vessel walls and by radiation from the flame. Plausible as they might be, however, the degree to which errors from these sources affected the burning-rate measurement is not possible to determine. Thus, there may remain a significant error in our burning-rate model, and it is worthwhile to look for shortcomings in the idealization which might account for the discrepancy. If such shortcomings matter to the ozone case, they may well matter in more complex systems as well.

4.2. Deficiencies

in the

4.2.1. Multi-Component

Idealization

Evaporation

As pointed out in Sec. 3.3.2, any combustion problem driven by an evaporative surface-regression mechanism is multi-component in essence since product species will co-exist in the liquid surface either as a result of the presence of more than one ingredient, condensed-phase reaction or molecular diffusion of gas-phase reaction products back to and adsorption onto the surface. This issue is most easily discussed within the context of the O3/O2 mixture problem. Let us assume that there will be no atomic oxygen in the liquid surface due to its high reactivity. The attractive intermolecular forces dominate the heats of vaporization, and the strength of that interaction is ordered as follows: O3-O3 > O3-O2 > O2-O2. The heat of vaporization of an O3 molecule from a surface of both O3 and O2 molecules will therefore be less than that from a surface of pure O3 because the latent heat is just a measure of the work required to remove an O3 from the surface. On the other hand, the heat of vaporization of an O2 molecule from the same surface mixture will be greater than that for O2 from a pure O2 surface. These modifications, in turn, alter the equilibrium partial pressures of both 0 3 and O2 outside the mixture surface, and the equilibrium vapor pressure is a key determinant of the surface-regression rate by Eq. (22). Thus, O3 will escape at a faster rate and O2 at a slower rate from a surface mixture of the two substances than would be expected using the single-component evaporation formulation coupled with Eq. (28). Beyond the greater difficulty of computing the rates of escape of each of the molecules in a multi-component description, there are now fundamental consequences to the posing of the mathematical problem. Though the mass fluxes of O3 and O2 leaving the surface are different, in order to maintain a

440

M. S. Miller

steady state, the linear rates of regression of both species must be equal, i.e., ro3 = ro2 •

(30)

Since "03=^03^03,

(31)

rh

(32)

and o2 =Yg2pro2,

then wp3

_

TOQ2

(33) x o3 o2 I have assumed that the liquid surface is composed only of O3 and O2. This means that x

Y

o2

= 1 " ^o3~

(34)

rho3 and rho2 can be obtained from Eq. (22), modified as previously described, using the proper multi-component equilibrium partial pressures for each species, of course. Ideally, one would also dispense with Raoult's law by computing the partial pressures based, for example, on model potentialenergy functions as described in Sec. 5.1. However, I am now left with a new unknown or eigenvalue of the problem, YQ. , with Eq. (33) as a new constraint. I now must add a new nested loop to the flow chart in Fig. 4. While this is a serious increase in computational complexity for the ozone problem, it becomes an overwhelming increase in complexity for a compound like RDX which has dozens of potential species in the surface. Taking the general case where there are n chemical species on the surface, the number of eigenvalues, and hence nested loops, will be (n + 2). Solution of a complex set of equations like this may be possible, but it will undoubtedly require a different approach than nested loops, possibly a global optimization scheme in which trial values of all of the variables are changed after each iteration. 4.2.2. Liquid-Phase Diffusion In the O3/O2 mixture case, the inclusion of multi-component evaporation will mean that the mass fractions of O3 and O2 at the liquid side of the surface are different from the proportions in the feedstock at —00. This is illustrated in Fig. 7. Since there are no reactions in the liquid phase (by justifiable assumption) the discontinuity in feedstock/surface mass fractions

Burning-Rate

Models and Their

Successors

LIQUID

GAS

441

LOW RATE OF ESCAPE

O3 Diffusional Flow of O3

Diffusional Flow of O2

(h

HIGH RATE OF ESCAPE

Fig. 7. Multi-component mixture of O3 and O2 illustrating how the differing rates of evaporation of the two components results in depletion of O2 mole fraction and enrichment of the O3 mole fraction a t the surface necessitating the consideration of liquid-phase molecular diffusion to ensure species continuity.

will be resolved in nature by molecular diffusion, which must be considered as an attendant consequence of treating multi-component evaporation. Because diffusion is generally slow in liquids, it will manifest itself in this case as very steep gradients in the species just below the surface. Obviously, a whole new class of supportive date will be required.

4.2.3. Real-Gas Equation of State Since our calculations of the burning rate of frozen ozone and the liquid O3/O2 mixtures assumed an ideal-gas equation of state, it is worth considering if real-gas effects play a role. The critical pressure and temperature of ozone are 5.46 MPa and 261.1 K, so the shortfall in computed burning rate at 0.1 MPa cannot be attributed to this source. However, calculations in Ref. 10 for frozen ozone were performed for pressures up to 2 MPa. At 2 MPa and 40 K initial temperature, the computed surface temperature is 217 K. Using standard tables, 16 one finds that ozone gas at the surface has

442

M. S. Miller

a compressibility factor ( ^ , where v is the molar volume) of about 0.75. At these conditions, the attractive molecular forces are dominating and number densities are higher than ideal, speeding up the reactions. At the same time, for pressures near the critical point, the heat of vaporization is decreasing rapidly; this means that a given amount of heat feedback will vaporize more surface molecules. Thus, it is possible that use of a real-gas equation of state could have significant impact on a burning-rate calculation. To our knowledge, there are no published burning-rate calculations using a real-gas equation of state. 4.2.4. Phase Separation Below about 93 K, mixtures of O3 and O2 separate into two phases, the upper one being O2 rich and the lower one O3 rich. The proportion in each phase depends on the temperature. At the boiling point of liquid O2, 90.2 K, for example, a starting mixture of 50% O3 by weight, 0 3 in the upper layer ultimately settles to 12% by weight and 38% by weight in the lower phase. Streng's measurement of the burning rate of a 90% 03/10% O2 mixture was conducted in a 9-mm Pyrex tube cooled on the outside by liquid oxygen. No mention is made of the presence of two phases during combustion of the mixture, but if the temperature were actually 90.2 K, two liquid phases may have been present. It is possible that this phenomenon could explain the discrepancy between his measured rate and our computed one, since the 02-rich upper layer might be expected to evaporate faster. On the other hand, this would lead to a progressively richer mixture as the O2 selectively escaped; in turn, the specimen would not burn at a steady rate. It also might have been the case that the mixture surface regressed too fast to establish this phase separation. Finally, the presence of the flame inside the tube may have warmed the liquid mixture a few Kelvins, reaching the point where O3 and O2 are miscible in all proportions. 4.3.

RDX

By far, the most intensive efforts to compute burning rate based on elementary gas-phase reactions have been directed towards neat RDX. It is known that RDX chemically decomposes both in the solid and liquid phases, but the solid-phase reaction is slow and probably not relevant to combustion timescales. 17 RDX also has a relatively high vapor pressure and was hypothesized to gasify during steady combustion by evaporation first by Ben-Reuven et al.,9 whose model employed global reactions in the gas

Burning-Rate Models and Their Successors

443

phase. The first use of the evaporation mechanism in a model with elementary gas-phase reactions was by Melius,18 who also assumed the single condensed-phase reaction, RDX(Liq) - • 3CH 2 0 + 3N 2 0.

(V)

His calculated burning rates at 0.1 and 2MPa are in excellent agreement with experimental data. Other elementary-gas-phase-reaction RDX models combining evaporation and liquid-phase reactions include those of Liau and Yang4 (L&Y), Davidson and Beckstead 5 (D&B), and Prasad, Yetter, and Smooke.19 The last of these works, though sharing most of the same condensed- and gas-phase reactions as the first two, is a semi-empirical model, requiring the experimental value of the surface temperature to obtain the burning rate, and will not be discussed here. Both L&Y and D&B assume that Reaction (V) occurs and one other liquid-phase RDX decomposition reaction. In the L&Y model, this other reaction is RDX(Liq) - • 3HCN + ^NO + ^ N 0 2 + ^ H 2 0 ,

(VI)

whereas in the D&B model, it is RDX(Liq) -> 3H2CN + 3N0 2 .

(VII)

Both models assume that RDX can form bubbles in the liquid layer and that the following secondary reaction takes place in the bubbles, N 0 2 + C H 2 0 -> NO + CO + H 2 0 .

(VIII)

The reaction parameters chosen by each of the authors are given in Table 1. Both models describe the melt region as two-phase, consisting of liquid and bubbles; however, since both models are one-dimensional, this "twophase" character is treated in the conservation equations as a continuous "porosity", (j>, defined as the ratio of the cross-sectional area occupied by the gas to the total cross-sectional area. The rate of evaporation into "bubbles", or more accurately, into the porosity, is computed using Eq. (22) at the local subsurface temperature instead of the surface temperature and the "surface area" of bubbles defined by L&Y as ^bubbles = (367TO) 1 /3^/3 ;

^ < I

Abubbles = (367rn)1/3(i_0)2/3i

<j>>±

(35)

where n is the bubble number density. These equations were given without explanation, except to say that n was to be determined empirically. D&B,

444

M. S. Miller

Table 1. Condensed-phase reaction-rate coefficient parameters assumed by different models for RDX in the Arrhenius form k = ATBe~E/RT. Burning-rate calculations based on these models are given in Fig. 8. The Miller 10 3-phase model, assuming no condensed-phase reactions is applied to RDX and its results are also shown in Fig. 8. A is in appropriate cm, mole, K, s units. REACTION — >

V

VI

VII

VIII

— — —

— — —

1.6 x 10 1 7 0 45 kcal/mol

802 2.77 13.73 kcal/mol

— — —

802 2.77 13.73 kcal/mol

A B E

4.66 x 10 0 47.8 kcal/mol

Liau & Yang 4

A B E

6.0 x 10 1 3 0 36 kcal/mol

— — — — — —

Davidson & Beckstead 5

A B E

4.88 x 10 1 1 0 36 kcal/mol

6.5 x 10 1 4 0 45 kcal/mol

Melius

18

18

who used these same equations, evidently understood that n would be a constant, independent of pressure, and they chose l x l O 1 3 as the appropriate value without further explanation. L&Y provide no value for n used in their calculations. The consequences of these varied assumptions and data on the computed burning rate are shown in Fig. 8. For comparison, I applied our 3-phase code used in the ozone case 10 to RDX using the same input data and reaction mechanism employed by L&Y with the exception that no condensed-phase reactions were considered. This model thus assumes that surface regression is by evaporation at the surface only, driven by the heat feedback from reactions in the gas phase whereas in the L&Y model some RDX decomposes in the condensed phase and some RDX evaporates into the liquidphase porosity (representing bubbles). The close agreement between all of these models and the experimental burning rates 20 ^ 26 is nothing short of astonishing. Given the varied inputs and assumptions, one is tempted to conclude that the single common element is the evaporative mechanism and that the condensed-phase reactions are not playing a significant role in the burning rate. However, D&B use a substantially lower vapor pressure (vapor over solid) than that used by L&Y (vapor over liquid) and find a low sensitivity of the burning rate to vapor pressure. Moreover, D&B predict a fairly large amount of the RDX decomposes in the liquid state, unlike L&Y (see Table 2). Unfortunately, Melius did not report the vapor-pressure expression used in his model, and his results are not otherwise directly comparable to the other models because his model used an earlier gas-phase

Burning-Rate

Models and Their

445

Successors

en e

pq o.i

o.oi 1000

Pressure (atm) 4 6,10 18

Fig. 8. Several three-phase models ' ' compared to experimental RDX burning r a t e s . 2 1 - 2 6 The last model is the result of applying our ozone code (no condensed-phase reactions) to RDX with otherwise the same input data used by Liau & Yang. 4

Table 2.

Comparisons among RDX models of selected features at 1 atm.

Model 18

Melius Liau & Yang 4 Davidson & Beckstead 5 Miller 10

T s (K)

Vapor Pressure (atm) at 600 K

Sensitivity of Burning Rate to Vapor Pressure

RDX Fraction Decomposed in Liquid Phase

549 573 595 633

not reported 0.69 0.17 0.69

not reported high low high

4.7% <1% 25% 0

reaction mechanism. All the other models used a mechanism developed by Yetter et al.27 based on Melius's but extended with new reactions thought important. In the final analysis, no definitive comparison is possible because of the incomplete reportage of input data used in the Melius, L&Y, and D&B models. Although each of the models based their solution of the gas-phase conservation equations on the PREMIX code 28 developed at Sandia, they

446

M. S. Miller

each implemented the 3-phase numerical solution in different ways. None of the authors described these methods in sufficient detail to enable others to reconstruct them unambiguously. One is left with the inescapable conclusion that the close agreement between models and experiment in Fig. 8 is not as astonishing as it first seems but the result of finding a combination of input parameters that works. In the end, reconciliation of these various model assumptions, input data, and numerical approaches is probably not productive because of the fundamental and, so far, irreducible uncertainties associated with the condensed-phase processes, principally, but not limited to, the chemical reactions. Modeling the condensed phase in the kind of detail attempted by L&Y and D&B is not currently supported by the availability of adequate experimental measurements and may never be.

4.4. Multi-Ingredient Propellant A New Approach

Mixtures,

In view of the situation described above, how can one go beyond a relatively simple propellant ingredient like RDX, which has been the subject of the most extensive modern research to date, to treat multi-ingredient propellants? I asked this question of myself half-a-dozen years ago and in seeking an answer had an idea which became the basis for launching a new approach. The idea was to construct a hybrid-rigor model in which the gas phase would be treated in full elementary-reaction detail but the condensed phase and surface gasification would be treated in semi-empirical fashion using the Arrhenius-like expression first used by Rice and Ginell7 and known in the propellant community as the "pyrolysis law", rh(Ts) = Ase-^k,

(36)

coupled with a set of hypothesized decomposition products from each propellant ingredient. The decomposition products would conform to proper chemical balance and be selected according to available experimental results and theoretical reasoning. Furthermore, each propellant ingredient would be assumed to decompose without interference from other ingredients, i.e., non-interactively. A full development of this model for nitrate-ester propellants is given elsewhere 29 ' 30 but the basic concepts will be discussed here. Of course, if one had to measure a pyrolysis law for every combination of ingredients, there would be no hope of predictive capability from such a model. However, Anatoli Zenin, having spent the last 40+ years refining the technique of measuring surface temperatures of numerous propellant

Burning-Rate

Models and Their

Successors

447

10

p\n

S

« W A

"3D

a

Pi a o u ex o

A )

•

*

*

•

O

X*

0.1

o * •

Zenin Double-Base Pyrolysis Law Zenin Pyrolysis-Law Data Zenin 20-atm Data (-150,140C) Zenin 1-atm Data (-190,100C)

1 11 M 10.01 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024

l/Ts(K) Fig. 9. Zenin's universal pyrolysis law with sampling of his experimental d a t a 2 3 for a wide range of double-base propellant ingredient proportions.

mixtures and single propellant ingredients with micro-thermocouples, discovered that a single, universal pyrolysis law 23 (Fig. 9) holds for a wide range of double-base propellant formulations with NG content from 0-50% and NC with percent nitration from about 11.5-13.5%. As seen in Fig. 9, even extreme initial temperature data are reasonably well accommodated by the same pyrolysis law. Furthermore, the same double-base pyrolysis law also works for additions of HMX. 23 I wondered if other classes of ingredients, e.g., nitramine-binder systems, might display this same universality. If so, this idea might lead to a predictive tool, at least for members of these classes. To test this hypothesis, Zenin applied his embedded microthermocouple technique to a wide range of nitramine-oxidizer/polymericbinder combinations (Table 3). Figure 10 shows the results of this work 3 1 - 3 3 to date. First of all, notice that there is little difference between RDX and HMX materials with the same binder. Also, most binders with RDX and HMX oxidizers group closely about the pyrolysis law labeled RDXBA, which was obtained as a least-squares fit to the RDX/BAMO-AMMO data alone. It is of great interest that the CL20/PUNE results, while closely adhering to the form of the pyrolysis law, occupies a very different region

448

M. S. Miller

Table 3.

Zenin's nitramine/binder test-material formulations. 3 1 ~ 3 3

Test-Mixture Designation RDX RDX RDX RDX RDX CL20

(or (or (or (or (or (or

HMX)*/BAMO- AMMO HMX)*/BAMO- T H F HMX)/CBIH HMX)/GAP1U HMX)/GAP2 HMX)/PUNE

Binder-Ingredient Proportions 50:50 50:50

— — — 20:80

Oxidizer-Binder Proportions 80 80 80 80 80 70

20 20 20 20 20 30

*50% by weight of particle sizes <50 microns, 50% in range 150-300 microns, 99% purity of RDX and HMX.

on the graph. HMX/PUNE, on the other hand, is in excellent accord with the RDXBA pyrolysis law. The reason for this difference is not known; perhaps, the rate-limiting step in the decomposition of CL20 is significantly different than for RDX and HMX. The tentative conclusion from these measurements is that propellants composed of RDX or HMX in both inert and energetic polymeric binders do indeed follow a universal pyrolysis law. CL20 clearly follows such a law for one energetic binder and may for other binders as well. Other binders are currently being investigated. The parameters for these pyrolysis laws along with Zenin's double-base law are given in Table 4. It would be of considerable practical interest to explore the theoretical basis for the existence of these universal pyrolysis laws; they seen to suggest a common rate-limiting step associated with the condensed phase and/or interfacial region for each family. An understanding of this behavior could well lead to a predictive capability for pyrolysis laws, thereby removing a large empirical component in the present model. By way of reinforcing the general applicability of the form of the pyrolysis law, Eq. (36), it is worth noting that neat RDX, HMX, and ADN all may be well described by this same functional relationship, as can be seen in Fig. 11. In addition to the experimental data, I have plotted in Fig. 11 the results of a least-squares fitting of the pyrolysis law to results calculated using our 3-phase code for both frozen ozone and neat RDX. It can be seen that the relation between the calculated surface temperatures and burning rates are in excellent accord with the form of Eq. (36). In view of all the foregoing evidence, there is considerable support for the general applicability of the pyrolysis law, and this should encourage efforts to calculate the parameters from first principles, an important step in removing the empiricism from this modeling approach and opening the door to much wider prediction capability.

Burning-Rate

Models and Their

449

Successors

1 ao

SD

I 0.01 0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0.0022

1/TS(K) • • A

• 0 Q

• •

•

n

• • •

•

RDX/BAMO-AMMO @ 20C RDX/BAMO-AMMO @ -100C RDX/BAMO-AMMO @ 90C HMX/BAMO-AMMO @ 20C RDX/BAMO-THF @ 20C HMX/BAMO-THF @ 20C RDX/CBIH @ 20C HMX/CBIH @ 20C RDX/GAP1U (g 20C HMX/GAP1U @) 20C RDX/GAP2 @ 20C HMX/GAP2 @ 20C HMX/PUNE @ 20C CL20/PUNE @ 20C - CL20/PUNE Pyrolysis Law (CL20PUNE) - RDX/BAMO-AMMO Pyrolysis Law (RDXBA) - Nilramine/Bindcr Pyrolysis Law (NTRB)

Fig. 10. Zenin's d a t a for a wide variety of nitramine/binder combinations. 3 1 3 3 T h e pyrolysis law identified as NTRB is a least-squares lit to all of the RDX/ and HMX/binder data. The RDXBA pyrolysis law is a fit to the RDX/BAMO-AMMO data alone and the CL20PUNE pyrolysis law is the LS-fit to the CL20/PUNE data alone.

As previously indicated, the model requires the identity and mole fractions of the chemical species resulting from the condensed-phase processes, i.e., the gases leaving the surface. These species will be far from the equilibrium distribution, and, therefore, one has only chemical balance to

450

M. S. Miller Table 4. Parameters for various pyrolysis laws, Eq. (36). Designation

Aa (g/cm 2 -s)

Es (cal/mol)

DB RDXBA NTRB CL20PUNE

1800 10470 2004 1.868 x 10 6

9935 1371 11827 16032

10000 A

. ;S.".'

•

1000 ..-'-s.: r ' = ^

y

;••••••• 1- ••

100

...

- ^ - j . .

--

-

;-

#

-•

". z :: ^..y,-,.: . +

=

10

i —v::r

••••.•.A;_;AT---f —

o

- ^ J-.."&*,.:•..•••.

RDX Zenin Experimental Data RDX Zenin Data Fit RDX Miller 3-Phase Model RDX Miller 3-Phase Model Fit HMX Zenin Experimental Data HMX Zenin Data Fit ADN Zenin Experimental Data ADN Zenin Data Fit O, Miller3-Phase Model O, Miller3-Phase Model Fit

• . . r - i : : : . - ^ ^•:.::T..;.v' NExp.

:

-RDXpExp.

AY \ RI)X 0.01

^HMXExi

,

•

-

.

.

"."r.-:-.'..\\X"

0.0010

0.0020

0.0030

0.0040

0.0050

0.0060

l/Ts(K) Fig. 11. Pyrolysis laws for a number of neat energetic materials. The RDX Miller calculation was performed with the three-phase model previously used for frozen ozone 1 0 using the same input data for RDX as Liau and Yang (with the exception of no condensedphase reactions). All data and calculations are for an initial temperature of 293 K except for frozen ozone, which was at 40 K.

constrain the set of surface products absolutely. With ingredients as complex as those for propellants, this means that there are usually very many possible product sets to consider. Experimental thermal decomposition studies may be useful guides to selecting an appropriate product set but not perfect since those experiments may not accurately mimic the conditions of the burning surface (temperature and heating rate) and probably all suffer from significant unknown changes in the surface products as a result of very fast reactions close to the surface. Use of general theoretical reasoning can also help limit the number of probable product sets. In the end,

Burning-Rate

Models and Their

Successors

451

however, an important selection criterion must be whether the proposed product set results in a calculated burning rate close to the experimental one. Use of this criterion, of course, assumes that the pyrolysis law, the gasphase reaction mechanism, and all the other input data the model needs are accurate. The predictive ability of the model for the whole propellant is redeemed by insisting that the decomposition products from each ingredient, "calibrated" ideally for that ingredient alone, remain consistent for all propellant formulations using that ingredient. This strategy is probably the best-compromise approach, but one should recognize that the assumption of non-interactivity in decomposition might be a better approximation for some systems than others. Since all fielded gun propellants include at least some NC and certain propellants, such as M10, have 98% NC, any burning-rate model of practical importance will have to deal with NC as an ingredient. Not only is NC a complex long-chain polymer, but the repeat units vary among four different types depending on whether the glucose ring is triply, doubly, singly nitrated or un-nitrated altogether. Figure 12 shows a triply nitrated repeat unit. NC is characterized for propellant use by its average percent nitrogen (%N) by weight, and this quantity varies typically from about 11.5% N to about 13.5% N. Pure cellulose trinitrate, cellulose dinitrate, and cellulose mononitrate have %N of 14.14, 11.11, and 6.76, respectively. The work of Leider and Seaton 34 showed that a 12.3% N NC has all three nitration states present but no un-nitrated sites. We developed a Monte Carlo

6

H

CH 2 ON0 2 C H

C

CH I

Fig.;. 12.

H

H

-2C I

o

O

N02

N02

Triply nitrated nitrocellulose repeat unit.

452

M. S. Miller

model 29 ' 30 to determine for an NC specimen of given %N what the distribution among these three nitration states is. Predictions of this model are compared to the NMR data of Todd and Glasser 35 in Fig. 13. The burningrate model then assumes that NC consists of three separate, hypothetically 0.6 «

0.5

Monte-Carlo Code T&G 1996 (P7 L-334)

0.4

£

12.6 %N

0.3

0.1

m

0.0

0.8

•s p -*J

s a c

XS P *3 s o

•>•s a >to

0.7 0.6 0.5

Monte-Carlo Code T&G 1996 (L10683Y) T&G 1996 (F10692Y) T&G 1996 (W10673Y)

13.15 %N

0.4 0.3 0.2 0.1 0.0

Mil

di

0.8

nit

m

0.7

*« &

0.6

et "sS

0.4 0.3

i

•** H « u

0.2

i

0.5

a

o

to

i i Monte-Carlo Code EZZ2 T&G 1996 (PI L-333)

T&G: Todd & Glasser Virginia Tech NMR Data

13.4 %N

i

0.1 0.0

1

XL

mono

di

tri

Substitution Level Fig. 13. Monte-Carlo model for distribution of repeat units among cellulose tri-, di-, and mono-nitrates for an NC specimen of given %N. Comparison is made of the model predictions with the NMR data of Todd and Glasser. 35

Buniing-Rate

Models and Their

Successors

453

pure ingredients corresponding to cellulose tri-. di-. and mononitrate in the proportion indicated by the Monte-Carlo model. The densities of these liypotlietically pure nitrates are obtained from a MD calculation 36 using the COMPASS force field. The model handling of multi-ingredient propellants is summarized graphically for JA2 in Fig. 14. This figure does not represent the current decomposition-product sets but. serves to illustrate the principles behind the method. The CYCLOPS 29,30 code, named for the mythical race of creatures who forged thunderbolts for Zeus, is the computer-code embodiment of the burning-rate model under discussion. CYCLOPS accepts the weight percents of each ingredient and checks to see if NC is among them. If so, then the Monte-Carlo subroutine is called and the nitrate state distribution determined. The ingredient list is then expanded to include the three NC sub-ingredients (cellulose tri-, di-, and mononitrate). The condensed-phase decomposition products for each of the ingredients on the expanded list are then obtained from the decomposition-products database, and the netset of products computed according to the proportion of each ingredient. A trial value for the linear burning rate is then read in from the problem input file and converted to mass flux using the code-computed propellant

Gas Flame

Condensed Phase

_ffi^N

NASCENT GAS-PIIASi HI U I W i s (mole factions)

••

Dinitrat8:19w% Cv| <£

NC(13.1%N): 60 w%

;/ g

,

0.288 N02

~ Xt - 2 m « «S W !r — 0.070 HONO *i % S— 0.061 CHOCHO V, C —

Trinitrate: 75 w%

-« X i_

0.285 CH20

^Sg^j^n^y^^^

__•

^VH

«o . 2

^^TM

0.083 HCO

DEGDN:25w%

^ /

MONTE-CARLO CALC. OF NITRATE-STATE DISTRIBUTION FOR GIVEN %N

.Si t j

________________ DECOMPOSITION PRODUCTS DATABASE

__,

0.045 CH2

_

0.076 CH

Qs

" i

— — —

_

M

0.092 CO

Fig. 14. Conceptual deconstruction of a propellant containing NC into sub-ingredients and then into net condensed-phase decomposition products entering the gas phase.

454

M. S. Miller

density. The surface temperature for this mass flux is then computed from the pyrolysis law, and these values are passed to a modified version of the PREMIX 28 code, which is called as a subroutine to solve the gas-phase conservation equations. From this solution the heat feedback to the surface is computed and compared with the heat feedback required to transform the propellant ingredients at their initial temperature to the condensed-phase decomposition products at the trial surface temperature using the trial mass flux. New trial values are automatically provided by the code until the two heat fluxes are in satisfactory agreement. The criterion for convergence is actually expressed in terms of acceptable changes in successive guesses of the mass flux, which is the unknown sought. Results for the burning rate of M10 and JA2 are shown in Figs. 15 and 16 compared to the experimental data of Juhasz, 37 Miller,22 and Atwood et al.38 for M10 and Miller22 and Juhasz et al.39 for JA2. An extensive analysis 29 ' 30 of the chemical-kinetic origin of the inflection in the M10 curve has been made. It was discovered that those reactions controlling the dark-zone length at low pressures (<10MPa) have little influence over 100 O O • —•—

w

Experiment, M10: Miller (1985) Experiment, M10: AFATL (1982) Experiment, M10: Atwood, et al. (1988) CYCLOPS Code

10

53 M

a 'a u

a s«

41

M10

C

)

; • : ;:

0.1 0.1

1

10

100

1000

Pressure (MPa) Fig. 15. Comparison of CYCLOPS code calculations of burning rate of M10 propellant with experimental d a t a . 2 2 ' 3 7 ' 3 8

Burning-Rate

100

Models and Their

455

Successors

','•;'' :

JA2

//

10

;

^ •

a Pi

;

:

:

:

:

-

SJD

s

"3 u S

pa u a

<

-0.1 -

•

0.01 0.1

•o o

.

•

•

'

•

-

Strand Burner: Miller (1993) 200cc Closed Bomb: Juhasz (1999) —•— CYCLOPS Code Prediction

'

•

'

-

O

10

100

-

1000

Pressure (MPa) Fig. 16. Comparison of CYCLOPS code calculations of burning rate of JA2 propellant with experimental data. 2 2 , 3 9

the burning rate at low pressures, but, to our surprise, have a major effect on the burning rate at high pressures, where a dark zone does not even exist. Thus, studies of the dark-zone chemistry experimentally accessible at low pressures are actually probing those reactions with critical influence over the burning rate at high pressures. This finding provides new impetus to experimental dark-zone investigations, especially for nitramine propellants because their dark-zone chemistry is less well known than that of nitrateester propellants. How well CYCLOPS predicts the structure of the dark zone is shown in Fig. 17, where the temperature and NO profiles are seen to compare very favorably with experiment. Table 5 gives a comparison of predicted and measured major species for a double-base propellant similar to M9; again, the agreement is excellent. The experimental measurements used for comparison are those of Heller and Gordon, 40 Lengelle et al.,41 and Vanderhoff et al.,42 and they were renormalized for direct comparability by Vanderhoff et al.42 A final example is given of more recent work 43 on RDX in an energetic thermoplastic elastomer (ETPE) binder. The excellent comparison with experimental burning-rate data shown in Fig. 18 is tempered by the poor

M. S. Miller

456

3000

JA2 @ 1.6 MPa 2500

3

a s-

O

2000 •

» Q. 1500

a H

*

CYCLOPS Code Prediction Vanderhoff, et al. (1992) by NO Absorption Vanderhoff, et al. (1992) by OH Absorption

o

>

A

1000

a

500 0.1

0.01

Distance from Surface in Gas (cm) Fig. 17. Comparison of CYCLOPS-code predictions of dark-zone thermal structure compared with the experimental data of Vanderhoff et al.42

Table 5. Comparison of major species mole fraction in the dark zone of double-base propellant with various experimental measurements. 4 0 _ 4 2

Parameters P (MPa) Dark-Zone Temperature (K) NO CO H2 N2 H20 C02 HCN CH 4 C2H4

Heller & Gordon (1955)

Lengelle et al. (1984)

Vanderhoff et al. (1991)

1.6 1600

0.9 1500

1.7 1500

0.24 0.33 0.08 0.04 0.20 0.10 0.004 0.008 0.008

0.21 0.38 0.08 0.02 0.20 0.09 0.026 0.008

0.24

CYCLOPS (Present Model) 1.7 1543 0.25 0.32 0.08 0.004 0.19 0.10 0.004 0.009 0.001

prediction of the thermal structure in Fig. 19. This inconsistency might at first be thought to suggest that the good burning-rate prediction is simply fortuitous, but this is not necessarily the case. As we learned in the case of M10, the burning rate and the dark-zone length at low pressure may be controlled by different sets of reactions, so it is possible that the good burning-rate prediction and poor thermal structure prediction may be due

Burning-Rate

Models and Their

457

Successors

RDX/TPE Propellant @ 293K: 80% RDX, 20% BAMO/AMMO (50/50 Mix) 10

.-.

:• . . . . . : . . . : : . . |.

- . - . - - . .-.-.'.

::i ..••...•"_~v\:|..:"

—•— Data of Zenin (2000) - • - CYCLOPS: with NTRB pyrolysis law - # - CYCLOPS: with R0X/BA pyrolysis law

E u a

0.1

;:-.:.: : : . * ^ (

1 0.01 0.1

1

10

100

Pressure (MPa) Fig. 18. Comparison of CYCLOPS-code calculations of the burning rate of and R D X / T P E propellant using two different pyrolysis laws with the experimental data of Zenin. 32 2500

:

vp\

2000

U

;/

; //

U

O.

£

1000

/

-^

H

500

..

Zenin Embedded-Thermo couple Data CYCLOPS: NTRB pyrolysis law -—'

0.0

i

... . ., .;

RDX/BAMO-AMMO (10 atm, 20 C)

/ '• s"

/ / / >

o

. . . . . .

s

1500

0.5

'

1—'

1.0

•—'—'

1 '

1.5

•

'

>—

2.0

Distance from Surface (mm) Fig. 19. Comparison of CYCLOPS-code predictions of dark-zone thermal structure for an R D X / T P E propellant with the microthermocouple data of Zenin. 32

to imperfections in the chemical mechanism describing the nitramine darkzone chemistry. In all propellants with RDX, we assume that the RDX evaporates unchanged, just as I had assumed for neat RDX; however, binder ingredients are assumed to decompose in the condensed phase.

458

M. S. Miller

The foregoing examples give evidence of the promise of the CYCLOPS code in providing both reasonable predictions of burning rate as well as details of the gas-phase flame structure and detailed chemistry. At present the code is limited to certain families of propellant ingredients, but the number of families will likely increase as other systems are studied. However, perhaps more important is the growing probability that one might be able to predict pyrolysis laws from first principles considerations. Certainly, greater theoretical capabilities to predict the final condensed-phase decomposition products of propellant ingredients can be brought to bear. Thus, the CYCLOPS code may well provide the best computational vehicle for incorporating results of new theoretical approaches to the condensed-phase and surface processes. How this might be accomplished while maintaining mathematical tractability of the code is suggested in Sec. 5. In summary, the CYCLOPS code is based upon a few simple propositions. (1) The surface regression may be adequately idealized as onedimensional. This condition is probably met for most homogeneous propellants. It may also be approximately true for many composite propellants where the burning rate is not a strong function of oxidizer particle size. Surface melt layers, for example, may provide effective premixing of ingredients where the oxidizer particle sizes are not too large. (2) The surface regression may be described by a pyrolysis law, Eq. (36). I have shown that this condition has been met by a large number of neat energetic materials and mixtures of typical propellant ingredients. (3) The overall products of condensed-phase decomposition may be estimated with sufficient accuracy. Chemical balance and results of thermal decomposition experiments are sources of guidance here, though only the former can be considered as an absolute constraint because of the high probability of secondary reactions in decomposition experiments. (4) The decomposition of one propellant ingredient does not affect the decomposition of other ingredients, i.e., the decomposition of a multi-ingredient propellant may be described as the superposition of the independent decompositions of each of its ingredients. This may well be a better approximation for some ingredients than for others. Short of describing the mixture decomposition theoretically on a molecular scale, there is little recourse to this assumption. However, it is often found that significant changes in detailed combustion mechanisms have a remarkably weak influence on the burning rate, that quantity being a highly integrated consequence of myriad underlying details. CYCLOPS exploits this relative insensitivity to mechanistic details.

Burning-Rate

Models and Their

Successors

459

Finally, since the CYCLOPS code is the first code of its kind (though still undergoing development to improve robustness for general use), one can anticipate ways in which it might be put to practical use even at its current stage of development. First, the CYCLOPS code can be used to optimize ingredient proportions to achieve a target burning rate. Also, CYCLOPS could be used to explore subtle, previously unexplained effects of formulation on burning rate. For example, German-made JA2 burns about 20% faster than US-made JA2 with identical ingredient proportions. However, the two differ by different specifications on the nitrocellulose component. While the average %N for the two propellants is the same, the two materials are made from blends of two lots of NC with different %N. Because our nitrate-state-distribution Monte-Carlo code predicts that the surface products for these two propellants will be different, it will be worthwhile to see if CYCLOPS can predict the burning rate difference. Further, CYCLOPS could be used to help set manufacturing tolerances in the specifications of ingredient proportions in military propellants. The CYCLOPS code could be used to determine how any given set of tolerances will map into variations of the burning rate and these burning-rate variations could be judged by using them as inputs to interior-ballistic codes. The burning rate at low pressure has been shown to be sensitive to the heats of formation of propellant ingredients in certain cases. 29,30 To the extent that ingredient purity is reflected in the heat of formation, e.g., due to dinitroglycerine impurity in trinitroglycerine, the CYCLOPS code could be used to determine how ingredient purity affects the burning rate, thereby enabling rationalization of quantitative tolerances for these ingredients. Finally, the CYCLOPS code could determine the effect of chemical modifiers on the burning rate without mixing chemicals. Though not replacing the need to mix and test, using the code as a screening agent and test bed for ideas could improve efficiency and possibly suggest new compounds to test.

5. Challenges and Opportunities The semi-empirical aspects of the CYCLOPS code need be tolerated only until theoretical advances obviate their necessity. The next level of improvement may well come from MD descriptions of the condensed phase and surface phenomena. However, this more fundamental level of treatment will have its own set of approximations and limitations. In order to deal with condensed-phase reactions, for example, considerable progress will have to be made in the parameterization of, and experience with, reactive

460

M. S. Miller

force fields. In my judgment, one will never want to treat the gas phase, with its dozens of species and hundreds of reactions, in this way. To do so would discard more than 50 years of hard-won kinetics research gains. One will, therefore, be faced with merging the discrete and continuous descriptions into a single, tractable mathematical entity. I believe that this will be no easy task, as the MD approach is inherently time-dependent with (computationally-intensive) explicit statistical averaging and the steadystate continuum-mechanics approach outlined earlier in this work is inherently time-independent with implicit statistical averaging. The most fruitful approach may be to develop simple, idealized continuum submodels calibrated to stand-alone MD models of a limited set of phenomena. For example, a reactive-MD model of the condensed phase would provide a set of condensed-phase decomposition products needed by the CYCLOPS code. Similarly, an MD model of multicomponent evaporation and/or pyrolysis could be used to determine a pyrolysis law for CYCLOPS. Results of the continuum submodels, depending on their scope, could then be easily incorporated into either a 3-phase model or a code such as CYCLOPS, retaining mathematical tractability and efficiency. Since, prior to the development of CYCLOPS, I had made a start on incorporating multi-component evaporation into our three-phase code, it will be used as an example here of the proposed approach. 5.1. "Molecular" Continuum Model of Multi-Component Evaporation I consider that a molecule evaporating from a liquid surface (Fig. 20) is at some distance d above the surface. I further assume that the molecule

zN>

*H fF ,

LIQUID

Fig. 20. Model for continuous-phase molecular forces experienced by a molecule evaporating from a liquid surface.

Burning-Rate

Models and Their

461

Successors

follows a tubular path from deep within the liquid to points outside the liquid; the tube has radius a 0 . The conception here is that the radius of the tube is of the order of the "radius" of the escaping molecule, and what is a tortured path geometry in reality is idealized as straightened to a cylindrical path. Since the escaping molecule is at a distance r from all the molecules in the differential volume element, dV = 2nadadz, the potential energy of interaction is d<& = <j)(r)ndV, where n is the number density of liquid molecules (Fig. 20). If I assume a Lennard-Jones (L J) interaction potential, where s is the well depth and a is the collision diameter, 12

(r) = 4e

(37)

and integrate over all the molecules in the liquid, one obtains: $(rf) = 87r?iLiq£o-2

f\-
10V«o

9[x{d)}}>

(38)

where x(d) =

(39) ao

9

63

/(*) = 9 2 8(1 + x2"\4 )

+

5(1 + a ; 2 ) 3

H»Ca»W +

315 945 192(1 + x2)2 384(1 + x2)

1057T

(40)

768

and 9(x)

1

2(1 +x2)

7T

(41)

- arctan(x) + —.

Two important extensions can be made to this formulation. The first is to add the effects of interaction between the escaping molecule and the gas-phase molecules. This modifies the potential to $(d) = 87r(nLiq - nGas)ea2 \ — ( ~ J f[x(d)\ - -

g[x(d)]\.

(42)

The other important extension is to the multicomponent case. This requires a sum over the interactions between the escaping molecule of species i with the other species j , of total different kinds, N. Thus the multicomponent version of the interaction potential between an evaporating molecule of

462

M. S. Miller

species i at a distance d from the surface and all other species both in the liquid and in the gas phase is N

9

$i(d) = 87r(nLiq - n G a s ) ] T /c 3= 1

1 fa,

/Wd)1

'-°'>\hUf'

g[x(d)}

(43)

a0 with its ancillary definitions in Eqs. (39)-(41). These equations may seem awkward but are easily and quickly evaluated in a computer code and represent, in a very general way, enormously complex phenomena. For example, they describe quantitatively how the heat of vaporization goes to zero at the critical point, where the liquid- and gas-phase densities become indistinguishable. A necessary test of the model is the accuracy with which the above equations predict the heats of vaporization of pure substances. The heat of vaporization is obtained by taking the limit in the above equations as d —> oo in Eq. (38). The result is ffvap = 7 r n L i q £ c r " I —

1

32 V ao

(44)

Application of this model is made to 61 data sets for polar and non-polar molecules using the compilation of LJ parameters in Reid and Sherwood44 and Prausnitz, Reid, and Sherwood.45 Calculation results shown in Fig. 21 are obtained by performing a nonlinear least-squares fit of the heat-ofevaporation experimental data to Eq. (44) using Pe, defined as follows, as an adjustable parameter to mediate between the raw theoretical result Hca\c and the best estimate value iJ e s t . -nest. — PpH,calc-

(45)

Assuming that ( ^ ) is unity, the best-fit value of Pe turns out to be 1.10. Its proximity to unity suggests that the physical basis of model assumptions are reasonable. The standard deviation of the error using the optimized value of Pe is about ±12%. This error is surprisingly small considering that the LJ potential is not generally as faithful as an exponential-6 potential for nonpolar molecules and has even worse fidelity for polar molecules, which are abundantly represented in the data set. In fact, even without the adjustment parameter Pe, the standard deviation of the prediction of Hvap is about 16%. This good performance might be improved upon by either using another,

Burning-Rate

Models and Their

40

1

1

30 20 •

Ne

s

m

•

*

•

Polar Molecules

oj§

C 2 H,

.9

1

CH,< OCH3

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HBr

KT

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1

Nonpolar Molecules

if6 • HCI

10

1

•

|co,

S a

463

Successors

H,Br CH ,COOCH,

.:H,CI,»C»1»<:HJCOOC2

CH.CCH tfsH««ifct.uVf

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-10

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-30

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• ° -40

3

C2H5OH

• 4

5

6

7

8

10

H v a p (kcal/mole) Fig. 21. Accuracy of the simple heat-of-vaporization theory using 61 Lennard—Jones parameter sets for both polar and non-polar molecules.

better interaction potential or by possibly modifying the model to recognize the discrete nature of close-neighbor molecular interactions. By itself, the above model is not sufficient to treat the multi-component evaporation problem. One needs also to describe the dynamics of the evaporative escape mechanism. Drawing upon kinetic theory to construct the flux of molecules leaving the liquid surface, r ou t> one obtains 1 /

_ ^vap RT

Tout = ~ ( ^ L i q e

*

(46)

where the quantity in parenthesis is the density of molecules with energies greater than Hvap, and ve is the average velocity of those molecules with enough energy to escape the heat-of-vaporization barrier. Assuming that the molecules in the surface are equilibrated at the surface temperature, Ts, it may be shown that the average escape velocity is •0 V )

0

2

(3ve -P vi

-f>*v'.

v ^

(47)

rM0Ve)\

464

M. S. Miller

where / W

^te

(48)

W is the molecular weight of the escaping molecules, and the minimum velocity for escape ve is

The equilibrium vapor pressure is determined by equating the outward and inward fluxes at equilibrium (see arguments of Sec. 3.3.1.), viz., 4RTsrout

(50)

8RTS TW

To test the predictions of this part of the model apart from imperfections in the predicted value of the heat of vaporization, I use the experimental value of Hv&p in the vapor-pressure formulas. With no adjustment parameters at all, the standard deviation of the predicted from experimental values is 95%. Evidently, there are more serious shortcomings in the vapor-pressure model. I experimented with several empirical modifications of the model and got interesting results by using an adjustable parameter to scale the value of iJvap in computing the escape velocity of Eq. (49). This strategy results in a standard deviation of about 36%, a much improved accuracy but possibly not sufficient for use in the multi-component evaporation code. The best-fit scaling factor has a value of 0.68, i.e., the calculation is significantly improved by assuming that only 68% of the full heat of vaporization must be overcome in order to escape the liquid surface. These results are illustrated in Fig. 22. Noting the slight downward tendency of the error with increasing -Hvap in the figure, I tried using a two-parameter fit to the fraction of Hvap used to compute ve. This improved the standard deviation slightly to 30%. The model may well be further improved and placed on a more sound theoretical basis by doing molecular-dynamics studies to help inform the assumptions. For example, perhaps decreasing the minimum escape velocity improves the idealized model because molecules tend to equilibrate, on average, at a value of potential energy somewhat above that in the bulk by means of collisions in the interfacial region closest to the bulk liquid. A great advantage of this bootstrapping partnership between discrete and continuum descriptions is that, by using the same model potential in both, the physics of the evaporation process can be studied and built into the continuum model apart from the behavior of any real substance. Separate

Burning-Rate

1

1

80

»

60

«

40

• •

Models and Their

1

1

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Nonpolar Molecules Polar Molecules

465

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Heat of Vaporization (kcal/mole) Fig. 22. Accuracy of the simple vapor-pressure model using 61 Lennard—Jones parameter sets for both polar and non-polar molecules.

studies can then address the issue of the best potential model to use. It goes without saying that the continuum models described above can be implemented with any potential-energy function while still preserving the relatively rapid computational qualities essential to incorporation into a multi-component burning-rate model. One might argue that empirically-based engineering correlations could do considerably better at predicting vapor pressures. In fact, I applied the Reidel method 44 ' 45 based on the corresponding-states principle to the same database of molecules used above and found that the standard deviation was only 4%. However, these methods are apparently much less successful when applied to molecule mixtures. This may be an important limitation for energetic-material combustion, where the surface is multi-component even for the simplest case of ozone as explained in Sec. 4.2.

5.2. Molecular-Dynamics Condensed Phase

Simulations

of the

Another fruitful area where the MD approach has played a role and enjoys bright future prospects is in the condensed phase. An example of past use is in determining the idealized mass densities 36 of putatively pure polymers

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of cellulose mono-, di-, and til-nitrate. These values are needed in the semiempirical burning-rate model discussed above for nitrate-ester propellants. In addition, the method was also applied 30 to the unreacting solid form of JA2 propellant to check the accuracy of the JA2 mass density computation by additive molar volumes, the method employed by the CYCLOPS 29 ' 30 code. Figure 23 shows a particular relaxed configuration of JA2, believed to be the first published '•anatomically correct" molecular view of a real propellant. The CYCLOPS-computed value of the density is 1.56g/cc, which compares very well with the MD-computed value of 1.59 ± 0.02 g/cc, which, in turn, compares very well with the experimental value of 1.57 ± 0.01 g/cc.

Fig. 23. One view of a relaxed configuration of .JA2 propellant computed by a molecular-dynamics simulation 3 6 consisting of 2 chains of 15 monomers representing NC, 16 molecules of DEGDN, and 10 molecules of NG. Oxygen atoms are in red, nitrogen in blue, carbon in grey, and hydrogen in white. A number of the component molecules can be identified as indicated. This is believed to be the first computed molecular representation of a real propellant formulation.

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Besides the purpose just described, such a MD simulation could be used to determine propellant heats of formation that properly account for molecular interactions between dissimilar ingredients. Currently, all such interactions are ignored for lack of computational capability and the expectation that heats of solution will generally be small, but we previously found 29 ' 30 that small changes in the heats of formation of propellant ingredients can have surprisingly large effects on the burning rate at low and intermediate pressures. This effect disappears at maximum gun pressures, and therefore will not affect thermodynamic equilibrium calculations, which presently must make the same assumption (that heats of mixing are negligible). The reasons for this unexpected sensitivity of the burning rate to ingredient heats of formation cannot be neatly isolated because it is a highly integrated effect, but it probably arises from a close competition between energy release by reactions and the locally dissipative processes of convection, conduction, and molecular diffusion. Finally, I will express my belief that, while a full molecular-dynamics description of the gas phase will never be able to compete with the continuum description in terms of calculational efficiency and accuracy (for reasons discussed at the beginning of Sec. 5), neither will a continuum description ultimately be able to compete with a discrete molecular description of the condensed-phase processes. It may be a long time before this promise is fulfilled, but if a complete description of propellant combustion is to be realized, there appears to be little choice but to pursue the molecular-dynamics approach tenaciously. In my discussions with molecular dynamicists, I have often observed an irrepressible optimism that the method can be made to work for phase changes, for subtle transport effects such as thermal diffusion, and even for reactive processes. However, examples given are usually for systems that are idealized in the extreme. To be applicable to a practical propellant burning-rate model, these simulations will have to be made to work for very general systems, even particularly difficult cases involving very large numbers of particles. Perhaps it is best that the dynamicists not fully understand the difficulties that await them!

6. Conclusions In this work I have made a reasoned attempt to predict the most promising course of future research aimed at predicting the burning rates of solid propellants from their ingredients. The last fifteen years has seen the rise

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to dominance of models that treat the gas phase on the level of elementary reactions with full multi-component transport. This explicit recognition of chemical specificity has been a necessary precursor to predictive capability. Energetic materials used as propellants are designed to produce gas pressure to accomplish work, and any model of burning rate must include descriptions of the condensed phase and the gasification mechanism. However, attempts to treat the condensed-phase and surface processes at the same level of rigor as the gas phase have been stymied by formidable difficulties in both experimental and theoretical approaches. It is possible that experiments may never be devised to provide the kind of accuracy and detail that we have come to expect in the gas phase; at the least, it will probably be a very long time in coming. Despite this sobering possibility, we have shown that some degree of predictability may be possible using the semi-empirical approach embodied in the CYCLOPS code. At present, this predictability appears to be limited to members of well-studied classes of propellants, such as double-base and RDX/HMX/binder propellants. However, as continuing research encompasses ever wider classes of ingredients, generalizations for the semi-empirical aspects of the code may well enable wider applicability. For example, it has been suggested that a single pyrolysis law for most propellants might prove sufficient if the sensitivity of the burning rate to this law is low. In my opinion, the greatest hope for treating the condensed-phase and surface processes in a full 3-phase, first-principles model lies with the developing field of reactive molecular dynamics. Many obstacles, both known and unknown, will have to be overcome in treating condensedphase reactions by this approach. It is not clear that reactive force fields with sufficient generality can be developed. It is not clear that methods for treating the many-body interactions can be developed with sufficient generality. However, there are ideas in the community about how to proceed; only time and effort will prove their value. It is worth remembering that burning rate is a highly-integrated macroscopic consequence of almost unfathomably numerous microscopic processes. Because of this, the burning rate has often proved to be extraordinarily insensitive to the underlying processes. Thus, one may be justifiably hopeful that even an imperfect description of the detailed processes may lead to predictions of macroscopic phenomena that will provide insights and guidance of a practical nature in the development of new and optimized propellant formulations.

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Appendix — Propellant Ingredients and Formulations Propellant Ingredients: ADN: AMMO: BAMO: CBIH: CL20: DEGDN: GAP1U: GAP2: HMX: PU: PUNE: NC: NCI: NC2: NC3: NE: NG RDX THF

a m m o n i u m dinitramide poly 3-azidomethyl-3-methyl oxetane poly 3,3-bisazidomethyl oxetane co-polymer of butadiene and isoprene with hydroxyl terminated groups 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane, rectangular crystal size 5 x 3 x 3 microns diethylene glycol dinitrate glycidyl azide-polyurethane co-polymer glycidyl azide polymer (molecular mass of 2000) cyclotetramethylenetetranitramine polyurethane mixture of P U and N E nitrocellulose (cellulose nitrate) cellulose mononitrate cellulose dinitrate cellulose trinitrate mixture of two nitroesters (dinitratdietileneglycole and dinitrattrietileneglicole) nitroglycerin (glycerin trinitrate) cyclotrimethylenetrinitramine tetrahydrofuran

Nominal Propellant Formulations A s s u m e d by C Y C L O P S Code: JA2: 60% NC (13.1% N), 25% D E G D N , 15% NG M9: 5 9 . 1 % N C (13.25%N), 40.9% N G M10: 100% NC (13.15% N)

References 1. M. S. Miller and J. A. Vanderhoff, Burning Phenomena of Solid Propellants, U.S. Army Research Laboratory Technical Report ARL-TR-2551, July (2001). 2. G. K. Adams, in Mechanics and Chemistry of Solid Propellants, eds. A. C. Eringen, H. Liebowitz, S. L. Koh and J. M. Crowley (Pergamon Press, 1967).

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3. M. S. Miller and W. R. Anderson, in Solid Propellant Combustion Chemistry, Combustion, and Motor Interior Ballistics, Progress in Astronautics and Aeronautics, Vol. 185, eds. V. Yang, T. B. Brill and W. Z. Ren (AIAA, New York, 2000), pp. 501-531. 4. Y.-C. Liau and Vigor Yang, J. Propul. Power 11, 729-739 (1995). 5. J. E. Davidson and M. W. Beckstead, J. Propul. Power 13, 375-383 (1997). 6. R. G. Parr and B. L. Crawford, Jr., J. Phys. & Colloid Chem. 54, 929-952 (1950). 7. O. K. Rice and Robert Ginell, J. Phys. & Colloid Chem. 54, 885-917 (1950). 8. A. G. Streng, Explosivstoffe 10, 218-225 (1960). 9. M. Ben-Reuven and L. H. Caveny, MAE Report 1455 (Princeton University, Princeton, NJ, 1980). 10. M. S. Miller, in Proc. of the Materials Research Society Symp.: Decomposition, Combustion and Detonation Chemistry of Energetic Materials, eds. T. B. Brill, T. P. Russell, W. C. Tao and R. B. Wardle (Materials Research Society, Pittsburgh, PA, 1996), pp. 169-180. 11. R. Sandri, Combust. Flame 2, 348-352 (1958). 12. M. S. Miller, Combust. Flame 46, 51-73 (1982). 13. W. R. Anderson, S. W. Haga, J. F. Nuzman, A. J. Kotlar and R. J. Anderson, PREAD Computer Code: A Versatile, Portable FORTRAN Computer Code for Interpreting the Complex Chemical Kinetics and Transport Properties of a Premixed, Laminar, Steady-State Flame, U.S. Army Research Laboratory, developed 1990-2002, unpublished. 14. R.