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

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.