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, 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