Relaxation of the ionic cloud on the basis of a dressed-ion theory

Abstract

The dynamic response of a bulk electrolyte or colloid solution to an external field is investigated on the basis of a dressed-ion theory (DIT) in a hydrodynamic point of view. The radial part of the perturbed electric field acting on a given ion is explicitly calculated in terms of the DIT quantities derived from the linear response function calculated from the modified mean-spherical aproximation (MMSA) and its static and frequency-dependent limits are analyzed. In the static case, the asymptotic behavior is analyzed and Onsager’s result is reformulated in terms of the effective charges and effective screening length and in the limit of vanishing concentration Debye–Falkenhagen–Onsager results are recovered. In the frequency-dependent DIT transport theory a relation between the field frequency and the time of relaxation of the ionic atmosphere is shown to be needed in order to get real renormalized charges and screening lengths. A decay of the perturbed electrostatic field as the inverse square root of the field frequency is obtained at high frequency and vanishing concentration along with a model-independent phase factor between the external and internal fields. The radial dependence of the perturbed average potential in the neighborhood of a quasiparticle is also calculated in the static case and several behaviors ranging from classical Derjaguin–Landau–Verwey–Overbeek colloidal stability theory interaction to pure attraction and repulsion are obtained. The results are analyzed in terms of a splitting of the ionic cloud into three different parts each one contributing to the radial dependence of the perturbed potential.