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

TL;DR

This paper develops an efficient spectral hypernetted chain (HNC) method to compute pair-correlation functions in highly asymmetric ionic mixtures across arbitrary dimensions, enabling analysis of colloidal-scale electrolytes previously computationally inaccessible.

Contribution

It introduces a Fourier-Bessel transform-based spectral HNC solver with logarithmic grids for arbitrary dimensions, allowing treatment of extreme ion size and charge asymmetries in ionic fluids.

Findings

Able to handle ion size- and charge-ratios over 1000 in 3D

Accurately predicts pair-correlation functions for asymmetric electrolytes

Validates results with Molecular Dynamics simulations

Abstract

The pair-correlation functions for fluid ionic mixtures in arbitrary spatial dimensions are computed in hypernetted chain (HNC) approximation. In the primitive model, all ions are approximated as non-overlapping hyperspheres with Coulomb interactions. Our spectral HNC solver is based on a Fourier-Bessel transform introduced by Talman [J. Comput. Phys., 29, 35 (1978)], 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 one thousand 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 primitive model results. For moderately large ion size- and charge-asymmetries, we present Molecular Dynamics simulation results that agree well with the approximate HNC pair correlations.