What is Liquid?
The idea of this special issue was derived a year ago. The year 2014 was a significant anniversary both generally and personally. Personally, it was 80 years since the oldest of us, Douglas Henderson, was born. More generally, it was a hundred years since another important paper in the theory of liq...
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Інститут фізики конденсованих систем НАН України
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| Cite this: | What is Liquid? / D.Henderson, M. Holovko, I. Nezbeda, A. Trokhymchuk // Condensed Matter Physics. — 2015. — Т. 18, № 1. — С. 10101: 1–4. — англ. |
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Henderson, D. Holovko, M. Nezbeda, I. Trokhymchuk, A. 2019-06-14T10:43:55Z 2019-06-14T10:43:55Z 2015 What is Liquid? / D.Henderson, M. Holovko, I. Nezbeda, A. Trokhymchuk // Condensed Matter Physics. — 2015. — Т. 18, № 1. — С. 10101: 1–4. — англ. 1607-324X DOI: 10.5488/CMP.18.10101 https://nasplib.isofts.kiev.ua/handle/123456789/153518 The idea of this special issue was derived a year ago. The year 2014 was a significant anniversary both generally and personally. Personally, it was 80 years since the oldest of us, Douglas Henderson, was born. More generally, it was a hundred years since another important paper in the theory of liquids by Ornstein and Zernike appeared. With this in mind, we felt it is timely for a collection of expert contributions to fill at least some of the gaps on the way to answer that magic question What is "liquid"? We are thankful for all colleagues who joined us in this project. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics What is Liquid? Article published earlier |
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Condensed Matter Physics |
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Інститут фізики конденсованих систем НАН України |
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The idea of this special issue was derived a year ago. The year 2014 was a significant anniversary both generally and personally. Personally, it was 80 years since the oldest of us, Douglas Henderson, was born. More generally, it was a hundred years since another important paper in the theory of liquids by Ornstein and Zernike appeared. With this in mind, we felt it is timely for a collection of expert contributions to fill at least some of the gaps on the way to answer that magic question What is "liquid"? We are thankful for all colleagues who joined us in this project.
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1607-324X |
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https://nasplib.isofts.kiev.ua/handle/123456789/153518 |
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What is Liquid? / D.Henderson, M. Holovko, I. Nezbeda, A. Trokhymchuk // Condensed Matter Physics. — 2015. — Т. 18, № 1. — С. 10101: 1–4. — англ. |
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2025-11-26T21:36:21Z |
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2025-11-26T21:36:21Z |
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Condensed Matter Physics, 2015, Vol. 18, No 1, 10101: 1–4
DOI: 10.5488/CMP.18.10101
http://www.icmp.lviv.ua/journal
Foreword
All that doth flow we cannot liquid name
Or else would fire and water be the same;
But that is liquid which is moist and wet
Fire that property can never get.
Then ’its not cold that doth the fire put out
But ’tis the wet that makes it die, no doubt.
The poem “What is Liquid?”
Margaret Cavendish,
Duchess of Newcastle-upon-Tyne,
English aristocrat, philosopher, poet and writer
(1623 – 15 December 1673)
What is Liquid?
Nowadays it is well accepted to divide matter into two major types – solids and fluids. A usual way
to distinct between solid and fluid by analyzing the pictures obtained in diffraction experiments, namely,
sharp Bragg reflections in the case of solids while diffuse rings in the case of fluids is not, generally speak-
ing, entirely obvious. The atoms in glasses and amorphous solids do not possess an ordered arrangement
as well. Fluids can be defined unambiguously as substances that flow under a shear stress, nomatter how
small. This distinction is not so evident, however, between liquids and gases that basically (although not
exclusively) form the subset of fluids. The pioneering theory of van der Waals (1873) of the continuity of
the gaseous and liquid states of matter yielded qualitative interpretation of the vapor-liquid equilibrium
and the existence of a critical point. According to this theory, at temperatures below the critical temper-
ature, the gaseous and liquid phases can coexist in equilibrium. Above the critical temperature, there
is a single fluid phase, i.e., one can proceed continuously from low-density fluid to high-density fluid. It
means that an equilibrium high-density fluid below the critical temperature, that according to van der
Waals theory is a liquid, somehow differs from the fluid of exactly the same density but at temperature
above the critical temperature. In fact, at temperatures above the critical temperature, the coexistence of
fluid phases is not observed; this means that there is no difference between gas and liquid.
In their review article, written for Reviews of Modern Physics in 1976, after a century of effort since
the work of van der Waals, Barker and Henderson asked a question What is “liquid”? They presented
a unified account of the statistical mechanics of condensed phases and did their best to give a compre-
hensive survey of the many approaches to the theory of liquids, examining many possible extensions of
the theories existing at that time. The question What is “liquid”? was just a paraphrase of the questions
that were often asked by aliens in “Star Trek”. As in the television series, with this question they were
echoing the existing puzzlement in the theory of liquids. Curiously, exactly the same question had been
documented even before the van der Waals work, more than three centuries ago as the title of the poem
written by Margaret Cavendish1, the poem that is used as an epigraph to this introduction.
1Margaret Cavendish was a poet, philosopher, writer of prose romances, essayist, playwright and, some say, a tireless
self-publicist. Her writing addressed a number of topics, including gender, power, manners, scientific method, and ani-
mal protection. Her romance, The Blazing World, is one of the earliest examples of science fiction. She rejected the Aris-
totelianism and mechanical philosophy of the seventeenth century. She criticized and engaged with the members of the
Royal Society of London and the philosophers Thomas Hobbes, René Descartes, and Robert Boyle. The titles of some
other poems by Cavendish that are relevant to the topic of this paper include “The World Made by Atomes”, “A Warr
D. Henderson, M. Holovko, I. Nezbeda, A. Trokhymchuk, 2015 10101-1
http://dx.doi.org/10.5488/CMP.18.10101
http://www.icmp.lviv.ua/journal
Despite some clear faults, the van der Waals theory had a potential to serve as the basis of a sat-
isfactory theory. Unfortunately, this was not understood at the time, and nearly a century was wasted
by attempting to adjust the van der Waals parameter a instead of refining the concept of an excluded
volume. The beginning of a modern understanding of the liquid state in the direction originated by
van der Waals occurred when the theory of hard-sphere fluid was formulated and when the comput-
ers and simulations were being developed. This made it possible to separate the questions of the ap-
propriateness of a model for the intermolecular potentials and the accuracy of the theoretical approxi-
mations. In 1964 Longuet-Higgins and Widom published an important paper that indicated that the van
der Waals theory was not merely an interesting pedagogical tool but was the basis of a useful theory.
However, a real development of our understanding of the liquid state began in 1967 with two papers
published in The Journal of Chemical Physics by Barker and Henderson and the review article in Science
by Widom. This was continued by the already mentioned seminal article in Reviews of Modern Physics
by Barker and Henderson (1976) and by a review article in Science by Chandler, Weeks, and Andersen
(1983).
The idea of this special issue was derived a year ago. The year 2014was a significant anniversary both
generally and personally. Personally, it was 80 years since the oldest of us, Douglas Henderson, was born.
More generally, it was a hundred years since another important paper in the theory of liquids by Ornstein
and Zernike appeared. With this in mind, we felt it is timely for a collection of expert contributions to fill
at least some of the gaps on the way to answer that magic questionWhat is “liquid”? We are thankful for
all colleagues who joined us in this project.
In total, we have collected thirteen contributions, which provide an insight into the selected develop-
ments, as well as some new concepts that emerged recently when studying the liquid matter. The issue is
opened by a reminiscence of Douglas Henderson on the influence of Henry Eyring and John Barker upon
his life and work, reminding all of us about these two outstanding scientists and fine men.
As it was already admitted, to a very great degree, the success of the Barker-Henderson perturbation
theory was due to analytical results for the hard-sphere fluid widely used as the reference system in the
theory of fluids. In a variety of applications of the perturbation theory, the main problem was to find a
way to relate the hard-sphere reference to a particular fluid system of interest. In this connection, it is
rather interesting to note the first article written by Myroslav Holovko, Taras Patsahan and Volodymyr
Shmatolokha where among others, the analytical results are presented for thermodynamics of a hard-
sphere fluid in a hard-sphere matrix, that were obtained within the scaled particle theory. These results
are further used as the reference system in the framework of the Barker-Henderson perturbation the-
ory to study the vapor-liquid coexistence in the Lennard-Jones fluid adsorbed into a hard-sphere porous
media.
Within the content of the issue, there are two more contributions that concern an extension of the ap-
plication of the Barker-Henderson perturbation theory, that originally was formulated for simple fluid,
on the so-called complex fluid systems. Namely, the article by Taras Hvozd and Yuri Kalyuzhnyi that con-
cerns generalization of the second-order Barker-Henderson perturbation theory for description of the
vapor-liquid phase behaviour in a polydisperse mixture, and the article by Roman Melnyk towards com-
bined application of the mean spherical approximation, second-order Barker-Henderson perturbation
theory and Wertheim thermodynamic perturbation theory to study the structural properties and phase
behaviour of the protein solutions.
The article by Søren Toxvaerd as well as the one by Andrij Trokhymchuk, Roman Melnyk and Ivo
Nezbeda, both discuss the role of repulsive and attractive interactions in the fluid and liquid matter
in general, and within the van der Waals theory, in particular. The results presented in these studies
bring a new insight into the consequences of the short-range and long-range attractive forces for the
physical properties of fluids, and ultimately could result in a revision of an existing common approach to
the separation of pair interaction energy into two parts – a necessary attribute behind the perturbation
theory methodology towards understanding the liquid state of matter.
The modern developments in our understanding of fluid state of matter show a tendency to rely
more and more on the use of computer simulations machinery. Despite some controversy and scepticism
with Atomes”, “Motion is the Life of all things” , “The Infinites of Matter”. This information is provided courtesy of Po-
emHunter.Com
10101-2
in the community from the point of view of the consequences for a future of the field, the applications of
molecular dynamics and Monte Carlo to study the fluid systems, both simple and complex, have become
today an essential attribute for each respectful research project. Regarding the case of simple fluids, this
issue presents the article by Taras Bryk, Tullio Scopigno and Giancarlo Ruocco, where these authors ap-
ply the molecular dynamics simulations to obtain the autocorrelation functions of the energy, heat and
entropy densities of the supercritical argon fluid. A nice correspondence of the long-wavelength region
behavior of these time correlation functions with that predicted by hydrodynamics, enables the estima-
tion of the wavenumber-dependent specific heats of this fluid system, which in the macroscopic limit
perfectly agree with experimental data. Such an approach is a good example to promote the advantage
of a combination of the theory and computer simulations, which in this particular case serves for the fur-
ther understanding of the collective dynamics in the supercritical state of matter, which promises many
interesting features observed recently in the scattering experiments.
The issue consists of five other contributions that concern the application of computer simulations
in the field of fluid systems. Two of these articles form a pair and discuss the application of molecular
dynamics simulations to the classical complex fluid system – pure water. The article by Tomaz Mohoric,
Barbara Gribar-Lee and Vojko Vlachy is devoted to the application of the non-equilibrium molecular dy-
namics to the study of the structure of the SPC/E water under non-equilibrium conditions due to different
temperatures for the translational and rotational degrees of freedom. By contrast, in the article by Edgar
Galicia-Andres, Hector Dominguez and Orest Pizio, the authors have applied the constant pressure molec-
ular dynamic simulation to investigate temperature trends of the microscopic structure of the same SPC/E
water as well as TIP4P-Ew water model.
The other two contributions, that concern the application of computer simulations, are dealing with
really complex fluid systems. Namely, the article by Dezso Boda, Gary Leaf, Jim Fonseca and Bob Eisen-
berg reports the application of Grand Canonical Monte Carlo simulations to the study of the energetics of
ionic selectivity in the neuronal sodium channels. The results obtained in such a way show the key role
that entropic hard-core excluded volume plays to distinguish between one or another ion, the issue of a
primary importance to understand the mechanism of ion channels selectivity. In turn, in the article by
Ivo Nezbeda, Jan Jirsak, Filip Moucka andWilliam Smith, the authors have performed molecular dynam-
ics simulations on pure liquid water, aqueous solutions of sodium chloride, and polymer solutions when
these samples are exposed to a strong external electric field with the goal of gaining a molecular insight
into the structural response to the field.
A rather distinct example of the application of computer simulations can be found in the article by
William and Carol Hoover. This contribution is devoted to the Hamiltonian liquids and the so-called “Lya-
punov instability” or the “sensitive dependence on initial conditions” that these systems display. Although
Hamilton’s equations are thoroughly time-reversible, the forward and backward Laputa instabilities can
differ qualitatively. As an example, these authors consider the many-body inelastic collisions in two di-
mensions. Two mirror-image colliding crystallites can either bounce, or not, giving rise to a single liquid
drop, or to several smaller droplets, depending upon the initial kinetic energy and the interparticle forces.
The difference between the forward and backward evolutionary instabilities can be correlated with the
dissipation andwith the Second Law of Thermodynamics, providing an “Arrow of Time” that is illustrated
for two small crystallites colliding so as to make a warm liquid.
Finally, there is one more contribution that was inspired by the slogan What is “liquid”? but will be
printed in the forthcoming issue of Condensed Matter Physics. We are referring here to the article by An-
driy Kovalenko, where this author and his colleagues are dealing with computations as well, but tribute
is paid to another powerful tool of the statistical mechanics modelling in the world of molecular fluids
– the Ornshtein-Zernike integral equation theory. In particular, the article discusses a rather promising
application of this theory as an essential part of the multiscale methodology for chemical and biomolec-
ular nanosystems in solutions. The author is arguing that for real systems, solving the three-dimensional
reference interaction site model (3D-RISM) integral equations is far less computationally expensive than
running the equivalent molecular computer simulations, which must be long enough to sample the rele-
vant exchange and binding events in the sample system. As a result, the 3D-RISM integral equation the-
ory, complemented with an appropriate closure relation, naturally yields the solvation structure around
a solute (supra)molecule of an arbitrary shape in terms of 3D maps of correlation functions. The latter
includes the density distributions of solvent interaction sites, and at once the solvation thermodynam-
10101-3
ics analytically in terms of the correlation functions all with fully consistent account for the effects of
chemical functionalities of all species in the solution.
All together, we hope that this special issue will be of interest and will provide new insights for those
working in the front line of fluid and liquid state statistical physics modelling, as well as for those who
are interested in new developments in condensed matter physics in general.
Douglas Henderson,
Brigham Young University,
84604 Provo, Utah, USA
Myroslav Holovko,
Institute for Condensed Matter Physics,
National Academy of Sciences of Ukraine,
79011 Lviv, Ukraine
Ivo Nezbeda,
Institute of Chemical Process Fundamentals,
Academy of Sciences of Czech Republic,
16505 Prague 6, Czech Republic
Andrij Trokhymchuk,
Institute for Condensed Matter Physics,
National Academy of Sciences of Ukraine,
79011 Lviv, Ukraine
10101-4
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