Table Of ContentCONTRIBUTORS
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.
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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
