CONTRIBUTORS RALPH L. AMEY JEAN PIERRE BOON FRANK P. BUFF BENJAMIN CHU U. DAHLBORG H. TED DAVIS P. J. HUNTER K. E. LARSSON R. A. LOVETT I. OPPENHEIM STUART A. RICE M. B. ROBIN J. S. ROWLINSON PAUL W. SCHMIDT K. SKÖLD CLIFFORD W. TOMPSON J. S. WAUGH SIMPLE DENSE FLUIDS EDITED BY H.L. FRISCH ë'Mwimi.'Srr'MV DEPARTMENT THE STATE UMIVERSITY OF MEW YORK AT ALBANY ALBANY, NEW YORK and Z. W. SALSBURG {rMKimSKlUV DEPARTMENT RICE UMIYERSTTY HOUSTON, TEXAS 1968 Θ ACADEMIC PRESS Mew York and London COPYRIGHT © 1968, BY ACADEMIC PRESS INC. ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS. ACADEMIC PRESS INC. Ill Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS INC. (LONDON) LTD. Berkeley Square House, London W.l LIBRARY OF CONGRESS CATALOG CARD NUMBER: 67-23159 PRINTED IN THE UNITED STATES OF AMERICA LIST OF CONTRIBUTORS Numbers in parentheses indicate the pages on which the authors* contributions begin. RALPH L. AMEY (183), Department of Chemistry, Occidental College, Los Angeles, California JEAN PIERRE BOON1 (251), Department of Chemistry and James Franck Institute, The University of Chicago, Chicago, Illinois FRANK P. BUFF (17), University of Rochester, Rochester, New York BENJAMIN CHU (111), Department of Chemistry, University of Kansas, Lawrence, Kansas U. DAHLBORG (119), National Research Council, Stockholm, Sweden H. TED DAVIS (251), Department of Chemistry and Department of Chemical Engineering, The University of Minnesota, Minneapolis, Minnesota P. J. HUNTER2 (1), Department of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, London, England K. E. LARSSON (119), Royal Institute of Technology, Stockholm, Sweden R. A. LOVETT3 (17), Bell Telephone Laboratories, Inc., Murray Hill, New Jersey I. OPPENHEIM (203), Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts STUART A. RICE (251), Department of Chemistry and James Franck Institute, The University of Chicago, Chicago, Illinois M. B. ROBIN (215), Bell Telephone Laboratories, Inc., Murray Hill, New Jersey 1 Permanent address: Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium. 2 Present address: British Petroleum Limited, British Petroleum Research Center, Middlesex, England. 8 Present address: Department of Chemistry, Washington University, St. Louis, Missouri. V VÎ LIST OF CONTRIBUTORS J. S. ROWLINSON (1), Department of Chemical Engineering and Chemi- cal Technology, Imperial College of Science and Technology, London, England PAUL W. SCHMIDT (31, 111), Department of Physics, University of Missouri, Columbia, Missouri K. SKÖLD (119), AB Atomenergi, Studsvik, Sweden CLIFFORD W. TOMPSON (31), Department of Physics, University of Missouri, Columbia, Missouri J. S. WAUGH (203), Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts FOREWORD The statistical mechanical treatment of liquids has, for many years, posed an intriguing challenge. The perfect gas is characterized by complete independence of its molecular constituents. Its properties are readily computable from the average random behavior of single isolated molecules. The behavior of a real, therefore imperfect, gas, can be formulated by a perturbation on the simplified model of the perfect gas. The perfect crystal, at the other extreme, has similar simplifying charac- teristics. The motion of the molecules is limited to very low amplitude excursions from the regular periodic array of the lattice sites. The simplification of assuming the potential to have only quadratic terms in the displacements leads to a model of independent oscillations along the coordinates of the normal modes. The properties of a real crystal follow well from perturbations on this simplified model. The liquid has no such simple model as basis. Nature has separated it from both gas and crystal by first order phase transitions that to the theoretician mean singularities in the functions representing the proper- ties. No really satisfactory results are obtainable by starting with a model that is crystalline in nature or one that is gaseous, although both show some features resembling reality. Neighboring molecules are too closely arranged in three-dimensional proximity to permit convergence of a development based on considerations of the interactions of small numbers at a time. The structure is too disorderly and random to let itself be realistically symbolized by disorder in a geometric lattice. There have, nevertheless, been significant advances made in the statistical mechanics of simple liquids. These advances have usually stemmed from techniques of the highest generality, applicable, in principle, to systems of great complexity. They have, however, usually been methods that present such great numerical difficulty that even for the simplest liquids it is necessary to introduce approximations of doubt- ful validity before numerical comparisons with experimental data are possible. The experimental information with which these results could be compared have been largely nonexistent or at least difficult to find. Whether this aided or hindered the imagination of the theoretician is always questionable. To the theoretical scientist it is always consoling to believe that any lack of agreement can be assigned to experimental vu viii FOREWORD error. However, it has been the initiative of two theoreticians that has brought this present volume to fruition, a compendium of facts on the behavior of simple liquids. Much of the information is quite new, but in addition it has been available in such scattered sources that few scientists have had an adequate conception of how much was available, or of the connection between the different facets of knowledge. The collection of information of this kind in one place has long been a need, expressed frequently at the biannual Gordon Conferences on liquids. The compen- dium will be of tremendous value to many. JOSEPH MAYER PREFACE Throughout the history of science, there has been a vital interplay between experimental and theoretical developments, and the develop- ment of our understanding of the fluid state has been no exception. Until recent years the experimentalist and the theoretician were most often one and the same person, with the theoretical emphasis on interpreting and understanding the experimental data. Recent trends and fashions have, however, weakened the connection between theoretical and experimental developments. Most of the theoretical work is now done by the pure theoreticians and many have turned away from the roots of experimental data to concentrate on abstract models and to build theories based upon fundamental physical laws and well-defined approximations. As a result, the growing literature dealing with dense fluids and liquids displays a major lacuna, the testing of theoretical calculations with appro- priate experimental data and the comparison of experimental results with theory. In turning away from intuition and emphasizing rigor, the theoretician relies on the study of simple substances to maintain his connection with the real world. He often finds data on such simple systems to be scarce, widely scattered, and of unknown quality. Moreover, much of these data are found in some reduced form which reflects the ideas and concepts of the man doing the experimental work. The task of finding and then extracting the pertinent experimental facts is often formidable enough to discourage most theoreticians from pursuing this goal. In many cases, experimentalists have ceased to appreciate the attitude of the theoreticians. They fail to see the relevance of certain simple models to experimental systems. The density of formal and mathematical manipulation in most theoretical publications proves to be a great barrier in interpreting the results and understanding the goals of the theoretical work. Lacking a full appreciation of the importance of simple systems, the experimentalist will often concentrate his effort on what are convenient systems experimentally. Moreover, even when he is willing to undertake a study of simple substances, the experimentalist is at a loss to know which data are most important and would be most meaningful to theoretical studies. The question of the accuracy needed to make a meaningful comparison between theory and experiment is also often a difficult question to answer. ix X PREFACE This apparently growing rift between experimental and theoretical development is unquestionably a serious threat to the development of science as a whole. This book is an attempt to reverse this trend in the study of the chemistry and physics of fluid systems. The first objective is to compile the best data available for simple systems. By simple systems, we mean primarily the noble gases, the homonuclear diatomic molecules, and a select group of some polyatomic but spherically symmetrical molecules. By restricting our goals in this manner, we hope to cover most of the systems of interest to the fundamental theoretician and still make it possible to obtain an exhaustive compilation of the data within a reasonable period of time. The second objective is to present these data in convenient graphical and tabular form. In each case, an attempt has been made to obtain the basic data untarnished by involved numerical reduction. The third objective is to give each compilation some theoretical context to indicate the importance of these studies to the development of our current ideas about the liquid state. Moreover, we hope that these theoretical outlines will indicate why certain aspects are emphasized and which important areas are missing. While on the one hand, the scope of this work is limited to a few simple pure systems, we have attempted to include all significant types of data for these systems. The contributors are people conversant with both the current status of fluid theory and the experimental work on the simple fluids. They were asked not only to compile the data but to present it from a critical point of view in the light of present theoretical knowledge. It is not the object herein to summarize current theories of dense fluids. We leave that to the various treatises that are available in this area. Such a theoretical treatise will quite often use experimental data to illustrate the results of the theory by comparison, but this illustration is more often than not given only in graphical form and represents a very special point of view. We believe the present work will supplement such treatises by being complete in its survey and presenting the data for practical use rather than illustration. The reader will also find some overlap with exhaustive handbook compilations of experimental data. However, this volume will supply theoreticians with a current and con- venient survey of the basic experimental data and not bury it in studies of complex systems which are beyond the present interest of the theore- tician. Even a casual survey of this work will reveal how sparse the data actually are for simple systems. The most urgent need in the whole study of the fluid state is for several experimental comprehensive studies of simple fluid systems. We hope the obvious gaps emphasized in this survey will stimulate a number of investigators to explore these problems. The 5M CO mited — Very mited mited d old e Methane Limited Limited Li Good Very limited li Very limited Fair Lian Fluorin Very sparse — — — — — e romin Fair — Very mited — — — ORTED hlorine B Fair — Very mited li — — — L DATA REP Hydrogen C Very limited — — li Very limited Very limited Fair RIMENTA Oxygen Good None Limited Fair Limited — Fair Y OF EXPE Nitrogen Good Very limited Good Fair Very limited Limited Fair QUANTIT Xenon — Very limited Limited Fair Limited Limited Sparse Very sparse Y OF THE Krypton Very limited Limited — — Sparse — Limited SURVE Argon Good Limited Good Good — Limited — Good Neon — Limited and old Good — — — Very sparse m d d Heliu Limite — Fair Limite Fair Fair — System property Thermodynamic orthobaric line Electromagnetic (data reported eince 1950) Surface X-ray scattering Light scattering Spectroscopy Nuclear relaxation Transport