Non-Debye screening in a formally consistent version of the modified mean spherical approximation

Abstract

The non-Debye decay length of ionic solutions ( κ) is analyzed combining the dressed ion theory route with a new version of the modified mean spherical approximation (MMSA) [Varela et al., J. Chem. Phys. 109, 1930 (1998)]. Seeking formal consistency, the MMSA short-range direct correlation function is naturally extended to include a linear term in radial distance whose effect on the screening predictions is analyzed. This behavior is derived from soft-core considerations and the concentration-dependent slope is related to the penetrability of the ions by means of a Tosi–Fumi-type potential. A limit is established for the slope of c( r) in order to predict the correct behavior of the decay constant in the low concentration regime ( κ→ k D +, k D being Debye's parameter). This limit is shown to be violated by the classical mean spherical approximation (MSA) for a one-component charged spheres fluid. Thus, it is confirmed that the MSA effective decay constant tends to Debye's one from below in the limit of vanishing concentration, in accordance with the recent hypernetted chain (HNC) calculations, a behavior which has been the object of some controversy in the literature. Finally, the HNC calculations of κ are analyzed for various ionic species and the behavior of the calculated slope of c( r) discussed in terms of ionic coupling.