The decay of correlations in ionic fluids

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Abstract
The asymptotics of structural correlations in binary ionic fluids are investigated using an extension of the pole analysis of the Ornstein-Zernike equation developed earlier for neutral mixtures. We show that because of electrostatic screening, the presence of long-ranged Coulomb forces does not alter the conclusion that all total pairwise correlation functions rhij (r), with i, j referring to positive or negative ions, exhibit the same exponential decay length α-1 0 and, where applicable, oscillatory wavelength 2π/α1. Moreover, the hij (r) in an ionic fluid exhibit the same amplitude and phase relations as in a neutral mixture. However, since the pole structure of the ĥij (q) is richer than for the neutral case, a wider variety of asymptotic regimes is found. We investigate these using the restricted primitive model treated within the generalized mean spherical approximation (GMSA). Two types of pole arise. These are associated with total number density and with charge density, respectively. Depending on which pole has the smaller imaginary part, different regimes of asymptotic decay are exhibited by hij (r). As the density of ions is increased at fixed temperature, cross-over from monotonic charge to damped oscillatory charge dominated decay (termed Kirkwood cross-over) occurs at a certain value. This is followed, at higher densities, by further (Fisher-Widom) cross-over from monotonic density to damped oscillatory density dominated decay. By combining results obtained for the two types of pole we map out cross-over lines separating regimes in the reduced density-reduced temperature (ρ*, T*) plane where hij (r) exhibit different types of asymptotic decay. This enables us to describe asymptotic correlations for models of various ionic fluids within a single ‘phase diagram’. We find that 1:1 primitive model electrolytes exhibit a different sequence of cross-over, as ρ* is increased at fixed T*, from 2:2 electrolytes. This sequence is, in turn, different from that found in the subcritical molten salt regime. In the case of electrolytes we compare our GMSA results with those of very recent hypernetted chain (HNC) calculations. Such comparisons indicate that the GMSA accounts for all the main features displayed by the HNC results. The implications of our results for weakly asymmetric binary ionic fluids are discussed and we comment briefly on the critical behaviour of such systems.