Accurate solutions to integral equations describing weakly screened ionic systems

Abstract

A procedure recently developed by Talman for the rapid numerical evaluation of Fourier transforms of slowly decaying functions is applied to the evaluation of convolution integrals appearing in integral equations describing pair correlations in ionic systems. The correlation functions are tabulated at uniformly spaced intervals in a variable ρ=lnr, where r is the interparticle distance. In the regime of weak screening, this procedure permits simultaneous efficient sampling of both the rapidly varying part of the functions near particle contact and the long range slowly decaying portion. The effectiveness of the procedure is demonstrated by evaluating accurate solutions to the hypernetted chain equation for a model of a 2–2 aqueous electrolyte at 25 °C over the range of salt concentrations from 10⁻⁷ to 10⁻² M. Comparison of these results to those obtained from other approximate integral equations shows that significant differences persist to exceedingly small concentrations.