Non-spherical Wigner-Seitz cells in linear Poisson-Boltzmann theory

Abstract

A common approach to calculate the electrostatic potential in a colloidal crystal is to assume that the neighbor distribution around each colloid is isotropic. In this thesis a numerical model is discussed that keeps the explicit non-isotropic neighbor distribution intact while calculating the electrostatic potential in linear Poisson-Boltzmann theory. The data obtained from this model will be compared with the isotropic approximation and with DLVO theory and it will be shown that at high densities the non-isotropic neighbor distribution cannot be neglected. The model also allows us to investigate an energy dominated fcc/bcc phase transition for varying colloid sizes and predicts that the bcc phase for colloids larger than a certain size becomes inaccessible.