An analytic structure factor for macroion solutions

Abstract

We assume the time-averaged structure of a macroion solution to be determined only by the repulsive screened Coulomb pair potential between finite macroions. The counter ions and solvent are treated as a uniform neutralizing background which determines the screening of the potential. We slove the Ornstein-Zernike equation in the mean spherical approximation to obtain closed analytic forms for the direct correlation function c(r) and the structure factor S(Q). In the zero charge limit, the Percus-Yevick hard sphere solution is recovered. As charge is added to the macroions at given volume fraction, the isothermal compressibility decreases and S(Q) shows increasing structure, eventually exhibiting solid-like behaviour. The results provide a useful model basis for studying interacting colloidal systems, and finite ion screened one component plasmas in general.