Physical Review B

We review the current state of knowledge of phase separation and phase equilibria in porous materials. Our emphasis is on fundamental studies of simple fluids (composed of small, neutral molecules) and well-characterized materials. While theoretical and molecular simulation studies are stressed, we also survey experimental investigations that are fundamental in nature. Following a brief survey of the most useful theoretical and simulation methods, we describe the nature of gas‐liquid (capillary condensation), layering, liquid‐liquid and freezing/melting transitions. In each case studies for simple pore geometries, and also more complex ones where available, are discussed. While a reasonably good understanding is available for phase equilibria of pure adsorbates in simple pore geometries, there is a need to extend the models to more complex pore geometries that include effects of chemical and geometrical heterogeneity and connectivity. In addition, with the exception of liquid‐liquid equilibria, little work has been done so far on phase separation for mixtures in porous media.

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Phase separation in confined systems

Several methods are available for calculating shear viscosities of liquids from molecular dynamics simulations. There are equilibrium methods based on pressure or momentum fluctuations and several nonequilibrium methods. For the nonequilibrium method using a periodic shear flow, all relevant quantities, including the accuracy, can be estimated before performing the simulation. We compared the applicability, accuracy and efficiency of this method with two equilibrium methods and another nonequilibrium method, using simulations of a Lennard-Jones fluid and the SPC and SPC/E [(extended) simple point charge] water models.

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Determining the shear viscosity of model liquids from molecular dynamics simulations

Studies of the thermal expansion of solids in the temperature range 1–100 K are reviewed. Effects due to thermal vibrations of the lattice, electrons, magnetic interactions and defects are fully discussed. The survey of experimental data is intended to be comprehensive. From the large volume of theoretical work in recent years the authors have aimed to select for discussion the most significant contributions.

Thermal expansion of solids at low temperatures

A semi-empirical `universal' corresponding-states relationship, for the dimensionless transport coefficients of dense fluids as functions of the reduced configurational entropy, was proposed more than twenty years ago and established by many simulations. Here it is shown analytically, by appealing to Enskog's original results for the inverse-power potentials, that the quasi-universal entropy scaling can be extended also to dilute gases. The analytic form and the possible origin for the entropy scaling for dense fluids are discussed in view of this unexpected result. On the basis of the entropy scaling we predict a minimum in the shear viscosity as a function of temperature for all soft inverse-power potentials, in quantitative agreement with the available simulations.

https://iopscience.iop.org/article/10.1088/0953-8984/11/28/303/pdf

A quasi-universal scaling law for atomic transport in simple fluids

The anharmonic contributions to the energy, specific heat, frequency-wave-vector dispersion relations and damping of phonons in a crystal have been studied using the recent technique of thermodynamic Green's functions based on field-theoretic methods. General expressions for these quantities have been deduced. It has been shown that at absolute zero the number of density is finite for the anharmonic solid and it is of the same order as the square of the fractional change in the normal-mode frequencies. The cases of a linear chain and a simple model of a crystal have been studied in detail. The normal modes of a linear chain exhibit some unusual but interesting features for different amounts of anharmonicity. The half-width of the phonons of the anharmonic chain has been evaluated for all temperatures for both normal and umklapp processes. For a solid, the complicated integrals that occur because of anharmonicity are simplified by an approximation scheme suggested by us. Within the scope of this approximation it is found that the frequency-wave-vector dispersion curves for a solid show a dip at the maximum wave number, quite similar to that observed for solids like lead and copper. The width of phonons is proportional to the square of the wave number, and the thermal conductivity is seen to be finite at low temperatures and to vary inversely with temperature at high temperatures.

Theory of Anharmonic Crystals

A theory of electron correlations based on a generalized random-phase approximation is presented An expression for the local-field correction is obtained using the third frequency moment of the spectral function of the electron-density response function The local field is a functional of the structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ which in turn is related to the imaginary part of the dielectric function via the fluctuation-dissipation theorem The equations are self-consistently solved to determined $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ as originally suggested by Singwi et al The pair-correlation function, compressibility, plasma dispersion, and correlation energy of electron liquid at metallic densities have been calculated

Electron correlations and moment sum rules

Expressions for the selfdiffusion coefficient have been obtained using the memory function formalism and the frequency moments of the velocity autocorrelation function. The fourth and the sixth frequency moments of the velocity autocorrelation function have been calculated using a low-order decoupling and the superposition approximation for the static quadruplet and the triplet correlation functions, respectively. These results have been used to calculate the diffusion coefficients of Lennard-Jones fluids over a wide range of densities and temperatures. The predicted results are found to be in good agreement with recent molecular dynamics data.

http://iopscience.iop.org/article/10.1088/0022-3719/20/34/012/pdf

Self-diffusion coefficients of Lennard-Jones fluids

In this paper we study the static and dynamic electron density and spin-density correlation functions of a two-dimensional electron fluid in the quantum Singwi-Tosi-Land-Sjolander theory. The static density and spin-density structure factors S(q) and S ~ (q) and their corresponding pair-correlation functions g(r) and g ~ (r) have been calculated and compared with the available Monte Carlo (MC) simulation data. It is found that the results for S(q) are in good agreement with the MC data except at large values of q for the larger electron density parameter r s . The pair-correlation function g(r) remains positive in the density range examined (1≤r s ≤8) and matches closely with the MC data except at small separations. The spin-dependent pair-correlation functions g ↑↓ (r) and g ↑↑ (r) also satisfy the positive-definite condition. The behavior of the dynamic properties studied is found to be qualitatively similar to the three-dimensional case except for the important difference in the behavior of the dynamic structure factor S(q,ω). It is seen that S(q,ω) exhibits a double-peak structure in the intermediate wave-vector region beyond the plasmon cutoff wave vector. We have also calculated the spin-dependent effective dynamic potentials by combining the spin-symmetric and spin-antisymmetric effective dynamic potentials. The results are compared with the classical Singwi-Tosi-Land-Sjolander theory wherever possible.

Static and dynamic correlation functions of a two-dimensional quantum electron fluid

The sixth frequency moment of the spectral functions of both the longitudinal and transverse current correlations along with their self-parts has been derived for a system of particles interacting through a two-body potential. The first two frequency moments of the spectral function of the energy-density fluctuation, and the first four frequency moments of the spectral function of the kinetic-energy-density fluctuation-correlation functions have also been derived. Numerical estimates for the fourth and sixth frequency moments of the spectral function of the longitudinal current correlations have been made for liquid argon. From this some information about the behavior of the contributions of triplet and quadruplet correlation functions to the frequency moments of liquid argon have been obtained. Numerical estimates have also been made for the first four frequency moments of the kinetic-energy-density fluctuation-correlation function in the long-wavelength limit for liquid argon.

K. N. Pathak

Papers

Theory of Anharmonic Crystals

Electron correlations and moment sum rules

Self-diffusion coefficients of Lennard-Jones fluids

Static and dynamic correlation functions of a two-dimensional quantum electron fluid

Sum rules and atomic correlations in classical liquids