Generalized equation of state for fluids: From molecular liquids to colloidal dispersions

Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

A Simple Equation for the Free Energy of Liquids

A simple, three-parameter equation is proposed for the free energy of classical fluids composed of molecules which are not hydrogen bonded. Agreement with experiment is much the same as has been obtained from more complicated three-parameter equations. For spherical and nearly spherical molecules, semiquantitative relations between intermolecular pair potential parameters and the parameters of the proposed equation were found. For alkanes, relations between the parameters and carbon number were noted. These relationships contribute to the understanding of fluid state properties in terms of the properties of the molecules of which they are composed.