Simulation of Chemical Potentials and Phase Equilibria in Two- and Three-Dimensional Square-Well Fluids:  Finite Size Effects

Abstract

We study the simulation cell size dependence of chemical potential isotherms in subcritical square-well fluids by means of series of canonical ensemble Monte Carlo simulations with increasing numbers of particles, for both three-dimensional bulk systems and two-dimensional planar layers, using Widom-like particle insertion methods. By estimating the corresponding vapor/liquid coexistence densities using a Maxwell-like equal area rule for the subcritical chemical potential isotherms, we are able to study the influence of system size not only on chemical potentials but also on the coexistence properties. The chemical potential versus density isotherms show van der Waals-like loops in the subcritical vapor/liquid coexistence range that exhibit distinct finite size effects for both two- and three-dimensional fluids. Generally, in agreement with recent findings for related studies of Lennard-Jones fluids, the loops shrink with increasing number of particles. In contrast to the subcritical isotherms themselves, the equilibrium vapor/liquid densities show only a weak system size dependence and agree quantitatively with the best-known literature values for three-dimensional fluids. This allows our approach to be used to accurately predict the phase coexistence properties. Our resulting phase equilibrium results for two-dimensional square-well fluids are new. Knowledge concerning finite size effects of square-well systems is important not only for the simulation of thermodynamic properties of simple fluids, but also for the simulation of models of more complex fluids (such as aqueous or polymer fluids) involving square-well interactions.

Mean-field description of ionic size effects with nonuniform ionic sizes: A numerical approach

“…The ionic size effect is more profound in the ion channel selectivity, see, e.g., [4, 12]. Detailed Monte Carlo simulations and integral equations calculations also confirm some of these experimentally observed properties due to the non-uniformity of ionic sizes [13, 14, 15]. …”

“…In a variational setting, such distributions are the conditions for equilibrium concentrations that minimize a mean-field electrostatic free-energy functional of ionic concentrations where the potential is determined by Poisson’s equation [27, 28, 29, 30, 31]. Despite its success in many applications, the classical PB theory is known to fail in capturing well the ion-ion correlations and ionic size effects [32, 33, 13, 14, 15]. …”

Fast Method for Computing Chemical Potentials and Liquid–Liquid Phase Equilibria of Macromolecular Solutions

“…42 (Similar forms of fitting were used by Lomakin et al 17 and Vörtler et al 36 ) The first coefficient, b 1 , in theory is equal to twice the more commonly known second-order coefficient B 2 of the virial expansion of the pressure ( P ). The latter coefficient in turn is given by a Mayer cluster integral, $$B_2=-2\pi true\int dr{r}^{2}false[\text{exp}false(-\beta ufalse(rfalse)false)-1false]$$ …”

Phase diagram of a square-well model in two dimensions

“…There are some early simulation studies 30 to understand the clustering and nucleation in the vapor-liquid transition, a calculation of the critical point, 31 grand canonical Monte Carlo (GCMC) simulations 32 for the liquid-vapor interphase. Other works report the vapor-liquid coexistence in a quasi 2D Stockmayer potential 33 and the nucleation of a 2D Lennard-Jones potential.…”