Highly asymmetric electrolytes in the primitive model: Hypernetted chain solution in arbitrary spatial dimensions

Abstract

The pair-correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model (PM), all ions are approximated as nonoverlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier-Bessel transform introduced by Talman (J. Comput. Phys. 1978, 29, 35), with logarithmically spaced computational grids. Numeric efficiency for arbitrary spatial dimensions is a commonly exploited virtue of this transform method. Here, we highlight another advantage of logarithmic grids, consisting in efficient sampling of pair-correlation functions for highly asymmetric ionic mixtures. For three-dimensional fluids, ion size and charge-ratios larger than 1000 can be treated, corresponding to hitherto computationally not accessed micrometer-sized colloidal spheres in 1-1 electrolyte. Effective colloidal charge numbers are extracted from our PM results. For moderately large ion size and charge-asymmetries, we present molecular dynamics simulation results that agree well with the approximate HNC pair correlations.

Liquid pair correlations in four spatial dimensions: theory versus simulation

“…This gap can be essentially filled in by numerical liquid integral equation solutions as reported in the present article and in Ref. [11]. Figure 2.…”

“…In the present work, we employ a numerical method that we have comprehensively outlined in Ref. [11]. This method, based on techniques that were originally published in Refs.…”

“…There are, however, situations that require a (semi-)analytical statistical mechanical approach as an alternative to computer simulations. In such cases, there is a choice of various liquid integral equations that are based on the Ornstein-Zernike equation, and that have often been proven to predict pair correlations accurately and efficiently [1,2,[7][8][9][10][11][12][13]. The large body of complementary experiments, simulations and analytical theory have resulted in a good understanding of pair correlations in the fluid or liquid state by now.…”

Dynamical density functional theory for the diffusion of injected Brownian particles

“…The presented DDFT equations, as well as the PercusYevick equation, can be numerically efficiently solved for any physically relevant kind of isotropic, pairwise additive particle interactions, and for arbitrary spatial dimension d [26]. However, for simplicity we restrict ourselves here to the generic case of nonoverlapping hard disks in d = 2 dimensions, with pair potential…”

“…In the present work, we therefore rely on the accurate and efficient numerical solution method that we have published in Ref. [26].…”