Eduardo Waisman

The radial distribution function for a fluid of hard spheres at high densities

A radial distribution function for hard spheres is obtained, which improves at high densities on the Percus-Yevick function. This is achieved by solving the mean spherical integral equation for a Yukawa form, adjusted to satisfy the Carnahan-Starling equation of state. The solution to the related problem of the mean spherical model approximation for a model fluid which interacts via the hard sphere potential plus the Yukawa potential is reported.

Mean Spherical Model Integral Equation for Charged Hard Spheres. II. Results

We continue our investigation of the solution of the mean spherical model integral equation for systems of charged hard spheres and charged hard sheets (in one dimension). The general method of solution was presented in Paper I of this series. This paper contains explicit expressions for the structure functions and thermodynamic properties of a variety of such systems in one and three dimensions. The results all have a very simple form and are in good agreement with various machine computations. When the charges on the particles vanish our results coincide with those obtained from the Percus—Yevick equation for hard spheres while in the limit of zero hard core diameters the results go over into those obtained from the linearized Debye—Huckel theory.

Solution of the mean spherical approximation for the density profile of a hard-sphere fluid near a wall

We investigate the density profile of a fluid of hard spheres in the vicinity of a (container) wall. Our analysis is based on the solution of an integral equation satisfied by this density profile in the Lebowitz-Percus mean spherical approximation or its generalization. The latter leads to a density profile in very good agreement with machine computations.

Ornstein–Zernike equation for the direct correlation function with a Yukawa tail

The Ornstein–Zernike (OZ) equation with a core condition h (x) = −1 for x<1 and a direct correlation function of Yukawa form c (x) = K exp[−z (x−1)]/x for x≳1 was solved analytically by one of us recently [E. W., Mol. Phys. 25, 45 (1973)]. The equation is of interest (i) as the mean‐spherical approximation for a potential that is the sum of hard‐sphere and Yukawa terms; (ii) as a generalized mean‐spherical approximation for a hard‐sphere system; and (iii) as the key ingredient in the generalized mean‐sphrerical approximations for ionic and polar fluids of Ho/ye, Lebowitz, and Stell, J. Chem. Phys. 61, 3253 (1974). Here we analyze the solution of the above equation to give a quantitatively useful picture of its character. A rapidly convergent expansion in K is obtained. In addition, a general cluster expansion for the solution of the OZ equation with arbitrary c (x) previously derived by one of us (G.S.) is applied to the equation to yield a complementary representation of its solution. Detailed numerical ...

A comparison of perturbative schemes and integral equation theories with computer simulations for fluids at high pressures

We test some refined perturbation and integral equations theories for predicting the equilibrium properties of spherical fluids, with nonstandard interactions at high densities and temperatures. The perturbation theories are fast and convenient to use and give good results for the thermodynamic properties, but not for the structure. The integral equations require more computer time, but yield thermodynamics and structure that are in very good agreement with simulations. In fact there appears to be no need for computer simulations of classical systems of particles interacting with spherical potentials in the fluid regime—at least away from transitions.

Solution of the mean spherical model for a mixture exhibiting phase separation

We have solved analytically the Lebowitz‐Percus Mean Spherical Model (MSM) approximation for a symmetric mixture of two species of particles, constrained to have an equal number of particles of species 1 and 2. In this mixture, like particles interact via a hard sphere potential for r R; unlike particles interact via the same hard spheres potentials (same diameter) and an opposite Yukawa potential Ae −κr/r. We find that for A>0, corresponding to an attraction between particles of the same kind and a repulsion between particles of different kind, that there are no spatially homogeneous solutions of the MSM when θ>θc,θ≡βξe, where β is the reciprocal temperature, ξ the total reduced density of hard spheres and e≡ Ae−κ R/R. We interpret this to mean the existence of phase separation when θ is above its critical value θc We are able to calculate θc analytically as a function of A, κ, and R. We also find that when A<0 there are always homogen...

Thermodynamics of homonuclear diatomic fluids from the angular median potential

The use of the angular median potential as a temperature‐independent spherical reference system for approximating molecular fluids is tested for its predictions of thermodynamics. Calculations have been carried out for a wide range of homonuclear diatomics with continuous atom–atom potentials believed to be representative of the full range of simulation data available for such systems. The results for the pressure are surprisingly good both in the detonation regime and around the triple point. In the latter case, however, the internal energies for highly elongated molecules with attractive potential wells are considerably too positive. Comparison with other perturbation theories indicates that the median reference system gives better pressures but poorer energies than RAM, and that in many cases, especially for purely repulsive potentials, it gives results of comparable accuracy to those obtained with nonspherical reference systems.

Statistical mechanics of simple fluids: beyond van der Waals

Dense fluids, defined to include both dense gases and liquids, have the reputation of being especially difficult to deal with theoretically. This reputation is not undeserved. Unlike dilute gases and crystalline solids, which can be thought of as deviants from well understood ideal states, the ideal gas and the ideal harmonic crystal, the dense fluid lies far from any recognizable landmark. This rules out the use of straightforward, convergent or asymptotic, expansions—the all‐purpose tool of the theoretical physicist—and makes even the hardy wince.

Van der waals one-fluid theory : justification and generalisation

Abstract We describe an approach to van der Waals one-fluid theory based on thermodynamic consistency and propose a method for generalising it to non-conformal fluids.

The mean spherical approximation for a Yukawa fluid interacting with a hard planar wall with an exponential tail

Results, which supplement those of Thompson et al. (preceding paper), are given for a Yukawa fluid interacting with a hard planar wall with an exponential tail. It is argued that density profiles calculated in a mean spherical approximation treatment of this system are only qualitatively reliable.