Effective interactions in polydisperse systems of penetrable macroions

Abstract

A coarse-graining approach based on the linear response theory is applied to deduce general expressions for the effective pair potentials in a multi-component system of soft macroions. Within the underlying approximations, the effective pair potentials can be written as simple convolutions between the intrinsic macroion charge distributions and a Yukawa-like potential which effectively contains the averaged contributions from the small ions. Two different charge distributions are assigned to the soft macroions: a Gaussian-like diffuse distribution and a uniform charge distribution inside the particle cores. The resulting effective pair potentials are then used in an effective model based on the hyppernetted chain approximation to investigate the structural properties of a two-component system of oppositely charged particles as a function of the various system parameters. It is found that the condensation of counterions is much stronger in the case of particles with a Gaussian charge distribution, leading to much weaker electrostatic interactions and less structured pair correlations in comparison with the system of uniformly charged macroions.