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Thermal Analysis Bernhard Wunderlich The University of Tennessee at Knoxville, Knoxville, Tennessee and Oak Ridge National Laboratory, Oak Ridge, Tennessee ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers BOSTON SAN DIEGO NEW YORK LONDON SYDNEY TOKYO TORONTO This book is printed on acid-free paper. ® Copyright © 1990 by Academic Press, Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. ACADEMIC PRESS, INC. 1250 Sixth Avenue, San Diego, CA 92101 United Kingdom Edition published by ACADEMIC PRESS LIMITED 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging-in-Publication Data: Wunderlich, Bernhard, Thermal analysis / Bernhard Wunderlich. p. cm. Includes bibliographic references. ISBN 0-12-765605-7 (alk. paper) 1. Thermal analysis. I. Title. QD79.T38W86 1990 543'.086-dc20 90-32796 CIP Printed in the United States of America 90 91 92 93 9 8 7 6 5 4 3 2 1 Preface The subject of Thermal Analysis is described starting with its theories (thermodynamics, irreversible thermodynamics, and kinetics) and covering the five basic techniques: thermometry, differential thermal analysis, calorimetry, thermomechanical analysis and dilatometry, and thermogravimetry. The book is designed for the senior undergraduate or beginning graduate student, as well as for the researcher and teacher interested in this exciting field. Thermal analysis has increased so much in importance in the last 20 years that there is a considerable need for continuing education. Each technique is treated from basic principles and history to instrumen tation and applications. The applications are chosen from all fields of applied and basic research. Quite often, however, I found applications from macro- molecular science, my own field of research, particularly appealing. Extensive references are given throughout to facilitate the entrance into the literature. The problems at the end of each chapter serve as a means to encourage simple calculations, discussion, and extra thought on the material. Some of the problems are neither easy nor short. The solutions to the numerical problems are collected at the end of the book. The unique collection of the figures, equations, and brief summaries on separate pages of blackboard material simplifies review of the material and production of overhead foils for teaching, and finally it will serve as the visual material for an audio course to be produced in 1991/92. This course will be available from the author. This book serves as an aide in the study of thermal analysis. As such, it is designed to meet a wide variety of objectives. One of these is to illustrate applications of thermal analysis; another is to review instrumentation and techniques; and the third is to present the theory which underlies any interpretation. An effort is made to do justice to these topics by permitting anyone interested in only one or two of the topics to bypass the other information. Similarly, the five different techniques of thermal analysis are treated such that they represent independent points of entry into the book. Your personal approach to Thermal Analysis should thus be planned ahead. If you are only interested in applications, you may first bypass the theory (although it probably will become quickly obvious that the theory is the xi xii Preface necessary basis for better understanding of thermal analysis). If you are interested in theory, obviously the instrumentation and applications sections can be skipped. The following examples will illustrate several situations: 1. You want to understand thermal analysis from the ground up. In this case it is best to go through the book the same way as you would study any graduate subject. Since this text is patterned after a one semester, three- credit lecture course, you should reserve about 15 hours each week for a 15- week period for the study. The self-study format lets you compress or extend the study periods as needed. There should be breaks in the flow of the study when you need to review background material or expand on the course material. Both are possible with the extensive references given. 2. You have no prior knowledge of thermal analysis and have been given the task to set up and run, let us say, a commercial differential scanning calorimeter. In this case you may want in the first week to read the literature on your instrument as given by the manufacturer and try out simple opera tions. At the same time you should start the study with sections Heat, Temperature, and Thermal Analysis, (Sect. 1.1), and Principles and History of Chapters 4 and 5, to understand the basics of the field. The sections on Instrumentation (Sects. 4.3 and 5.2) can be gone over lightly, to make comparisons with other instruments. Next, you will want to set up calibration and data reporting routines, which can be accomplished, for example, with the help of the section on Standardization and Technique (Sect. 4.3.3) and the instructions for your specific instrument. The second week should be spent on the various applications. Concentrate on your specific analysis interests and try to expand to related areas. The third week can be spent with the solving of a series of problems. If not before, it will now be obvious to you that deeper understanding requires the theory of DTA and DSC, the theory of matter, and the theory of thermal analysis. After these topics are mastered, which may take six to eight weeks, the related techniques may be of interest (thermometry, thermomechanical analysis and thermogravimetry). These topics would make up the rest of the course. 3. You are a researcher or supervisor with little prior knowledge of thermal analysis who wants to add, let us say, calorimetry to the laboratory. Since time is short and you need to understand the alternatives offered by the instrument salesmen, I would recommend that you start with a quick study of Principles and Instrumentation of Chapters 4 and 5 to gain an overview. This will probably determine whether your second session should go to the applica tions of DTA or calorimetry. Notes should be taken of the possible multiple applications of any instrument and future applications. In the time between Preface xiii the approval, order, and delivery of the instrument, a training program, similar to the one outlined under example 2, above, may be set up for all the staff. 4. You are an experienced worker in the field of thermal analysis and would like to update and expand your knowledge. In this case I would recommend as an easy entry into the subject using Chapter 2, to be followed by the part dealing with your expertise — let us say Thermogravimetry, Chapter 7. After going through these chapters, and doing some of the problems, you should be able to choose among the theory route, the applications route, or the instrumentation route. Combinations are also possible and would show similarities to example 1. Prerequisites for the study have been kept to a minimum. Some knowledge of undergraduate general chemistry, physical chemistry, and materials science is assumed. Parallel review of these subjects is advisable. Occasional update on the subject matters of the Applications may be necessary. Special help, discussion, and also graduate credit for completed work, will be available along with a set of audio tapes on the lecture material. Help in solving the problems can also be obtained through an audio cassette with more detailed discussions of the solutions. It is the goal of this book to help the reader along the road to becoming a professional thermal analyst. Any comments and suggestions for improvements are always welcome. Bernhard Wunderlich Acknowledgments This book has grown through many stages of development. From a first lecture course given during a sabbatical at the University of Mainz, Germany, 1967-68, it was changed between 1973 and 1981 to a senior/graduate, three- credit lecture and audio course dealing only with macromolecules. Then it was expanded to the audio course Thermal Analysis that dealt with a larger range of materials. The present book is a further expansion, completed in 1990. At every stage the book was shaped and improved by many participating students and numerous reviewers. The extensive job of entering the first draft into the text processor was connected with learning the intricacies of a new system. It was cheerfully done by Ms. Joann Hickson. The valuable help of all these persons is gratefully acknowledged. Naturally, I am the source of any remaining errors. Research from the ATHAS Laboratory described in the book was generously supported over many years by the Polymers Program of the Materials Division of the National Science Foundation. Several of the instrument companies have helped by supplying information, and also supported the acquisition of equipment. The continuation of the ATHAS effort since 1988 is also supported by the Science Alliance of the University of Tennessee and the Division of Materials Sciences, Office of Basic Energy Science, US Department of Energy, under Contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc. This book was set by the author in WordPerfect 5.1® with the figures imported from drawings prepared in Microsoft® Windows 386, sometimes based on scans from a Hewlett-Packard ScanJet®. The final proof pages were printed with a Hewlett-Packard LaserJet® II. All illustrations were drawn to fit SI standards. References to the original sources in the literature and acknowlegments are given in the text. C H A P T ER 1 INTRODUCTION 1.1 Heat, Temperature, and Thermal Analysis The most fitting introductory discussion on thermal analysis is perhaps a brief outline of the history and meaning of the two basic quantities: heat and temperature. In Fig. 1.1 some facts about heat are summarized. Heat is quite obviously a macroscopic quantity. One can appreciate it with one's senses directly. The microscopic origin of heat, the origin on a molecular scale, is the motion of the molecules of matter. The translation, rotation, and vibration of molecules thus cause the sensation of heat, and one can summarize: the macroscopically observed heat has its microscopic origin in molecular motion. Temperature, in turn, is more difficult to comprehend. It is the intensive parameter of heat, as is shown in Sect. 2.2.1. Before we can arrive at this conclusion, many aspects of temperature must be considered. 1.1.1 History Knowledge about heat and temperature was not available, let us say, two hundred years ago. Much confusion existed at that time about the nature of heat. Since language had its origin even earlier than that, a considerable share of this confusion is maintained in our present-day language. Let us look, for example, at the excerpt from a dictionary reproduced in Fig. 1.1. Several different meanings are listed there for the noun heat. A good number of these have a metaphorical meaning and can be eliminated immediately for scientific applications (entries 4, 6, and 8 -15). Taking out duplications and trying to separate the occasionally overlapping meanings, one finds that there remain four principally different uses of the word heat. The first and primary meaning of heat is given in entry 1: it describes the heat as a physical entity, energy, and derives it from the quality of being hot which, in turn, describes 1 2 Thermal Analysis MacroscopicaUy observed heat heat has its microscopic orign in heat, #.[ME. bette, bete; AS. A*to, hut, fron molecular motion bit, hot.] 1. tht quality of being hot; hotness: in physios, heat is considered a forn of energy whose effect is produced by the accelerated vibration of nolecules: theoretically, at -273*C, all Molecular notion would stop and there would be no heat. Llmi/m j/rnn Ik UÀ (1789) 2. Mich hotnessj great warnth; as, the beat of this roon is unbearable. 3. degree of hotness or uarnth; as, hou nueh beat shall I apply? ELEMENTS OF CHEMISTRY 4. the sensation produced by heat, the sensation experienced uhen the body is sub jected to heat fron any source. Translated by R Ken. Edinburgh 1789. pages 4-6. about heat: 5. hot weather or clinate; as, the beat of the tropics; the beat of the day. This substance, whatever it is, being the cause (. indication of high tenperature, as the of heat, or, in other words, the sensation which condition or color of the body or part of the body; redness; high color; flush. we call wamth being caused by the accumulation It has raised aninosities in their hearts, of this substance, we cannot, in strict language be*ts in their faces. -Addison. distinguish it by the term heat; because the 7. the warning of a roon, house, etc., as same name would then very improperly express by a stove or furnace; as, his rent includes beet, light, and gas. both cause and effect.... 8. a burning sensation produced by spices, nustard, etc. ... Wherefore, we have distinguished the 9. fever. cause of heat, or that eiquisitely elastic fluid 1·. strong feeling or intensity of feeling; which produces it, by the term of caloric. Be ex11c. itetnheen pt,e raiordd oor,r acnognedri,t iosne alo,f etecx.c itenent, sides, that this expression fulfils our object intensity, stress, etc.; nost violent or in in the system which we have adopted, it posses tense point or stage; as in the beat of ses this farther advantage, that it accords with battle. 12. a single effort, round, bout, or trial; every species of opinion, since, strictly speak especially, any of the preliminary rounds of ing, we are not obliged to suppose this to be a a race, etc., the winners of which conpete a real substance; it being sufficient, as will in the final round. more clearly appear in the sequel of this work, se1x3u.(aal ) esxecxiuteanl enetx ciitne naennitn;a ls(;b )r tuhte o pre erisotdr uosf. that it be considered as the repulsive cause, 14. in netallurgy, (a) single heating of whatever that may be, which separates the parti netal, ore, etc. in a furnace or forge; (b) cles of matter from each other; so that we are the anount processed in a single heating. still at liberty to investigate its effects in 15. (a) intense activity; (b) coercion, as by torture; (c) great pressure, as in crin- an abstract and mathematical manner. inal investigation. [Slang.] &αηα& (ÈQÛMI (l620 )l thev erye ssence ofh eat,o rt rie substantial self ofh eat, ism otiona ndn othinge lse. .. byC ount Rumford (1798, boilingo fw ater by friction) and by Davy (1799,m eltingb yr ubbingt wo blocks ofi ce against each other) aren otc ompletely satisfying. 1 Introduction 3 a state of matter. An early, fundamental observation was that in this primary meaning, heat describes an entity in equilibrium. Heat is passed from hot to cold bodies, to equilibrate finally at a common, intermediate degree of hot ness. This observation led in the seventeenth and eighteenth centuries to the theory of the caloric. Heat was given in this theory a physical cause. It was assumed to be an indestructible fluid that occupies spaces between the mole cules of matter. When one looks at the description of heat in the excerpts from the famous book by Lavoisier published in 1789, Elements of Chemistry, that are reprinted in Fig. 1.1, one can read: "This substance (meaning the caloric), whatever it is, being the cause of heat, or, in other words, the sensation which we call warmth being caused by the accumulation of this substance, we cannot, in strict language, distinguish it by the term heat; because the same name would then very improperly express both cause and effect." Lavoisier thus recognized very clearly that there are difficulties in our language with respect to the word heat. To resolve these without detailed knowledge, Lavoisier suggests a few pages later: "Wherefore, we have distinguished the cause of heat, or that exquisitely elastic fluid which produces it, by the term of caloric. Besides, that this expression fulfills our object in the system which we have adopted, it possesses this farther advantage, that it accords with every species of opinion, since, strictly speaking, we are not obliged to suppose this to be a real substance; it being sufficient, as will more clearly appear in the sequel of this work, that it be considered as the repulsive cause, whatever that may be, which separates the particles of matter from each other; so that we are still at liberty to investigate its effects in an abstract and mathematical manner." This second portion of Lavoisier's statement points out that one may, after the introduction of this new word caloric into our language, go ahead and investigate the effects of heat without the problems inconsistent nomenclature causes. Indeed, the mathematical theories of conduction of heat and calori metry were well developed before full knowledge of heat as molecular motion was gained. Unfortunately common usage oflanguage was not changed by this discovery of Lavoisier, nor was it changed after full clarification of the meaning of heat and temperature. As a result, each child is first exposed to the same wrong and confusing language, and only a few learn at a later time the proper nomenclature. Turning to the other meanings of the word heat listed in the dictionary excerpt of Fig. 1.1, one finds that a degree of hotness is implied by entries 2 and 5. This actually indicates that heat has an intensive parameter. Today one should apply for these uses the proper the term temperature. The 4 Thermal Analysis example "the heat of this room is unbearable" is expressed correctly only by saying "the temperature of this room is unbearable." A more detailed description of the term temperature will be given in Sect. 1.1.3 (Figs. 1.3 and 1.4) and in the introduction to Chapter 3. The third meaning of heat involves the quantity of heat as given by entries 3 and 7 of the dictionary excerpt of Fig. 1.1. This reveals that heat actually is an extensive quantity, meaning that it doubles if one doubles the amount of material talked about. Two rooms will take twice the amount of heat to reach the same degree of hotness (temperature). Finally, a fourth meaning connects heat with radiation. This meaning is not clearly expressed in th2e dictionary. Let me again turn to Lavoisier. He said elsewhere in his book , "In the present state of our knowledge we are not able to determine whether light be a modification of caloric, or caloric be, on the contrary, a modification of light." People experienced very early that the sun had something to do with heat, as expressed in terms like "the heat of the sun." The inference of a connection between heat and color also indicates a link between heat and radiation (red-hot, white-hot). Even entries 6 and 9 from the dictionary express a similar physiological link between heat and color. Today, one should have none of these difficulties since we know that heat is just one of the many forms of energy, and radiant energy can, like any other type of energy, be converted to heat, which, in turn, is the energy involved in molecular motion. How did one progress beyond the early idea of caloric? The old theory is so workable that many discussions in this course on thermal analysis could be carried out with the concept of caloric. Another explanation of the phenomenon of heat could be found already in the writings of Francis Bacon in 1620. He writes, after a long di3scourse summarizing philosophical and experimental knowledge, in his book Novum Organum that "the very essence of heat, or the substantial self of heat is motion and nothing else." The types of motion discussed do not always link with molecular motion as we know it today, and, obviously, Bacon also did not convince all of his peers. One had to wait for additional experimental evidence for major progress. It is very interesting that the ultimate experiments that supposedly proved the theory of caloric in error are experiments which one would not fully accept today. A difficulty in the caloric theory was, in particular, the explanation of friction. It seemed to be an 4inexhaustible source of caloric. For "measurement" Count Rumford in 1798 used a blunt drill "to boil" 26.5 pounds of water in two and one half hours. The only effect he produced on the metal was to shave off 4.145 grams. Next he could prove that the capacity