The electrostatic interaction between a charged sphere and an oppositely charged planar surface and its application to protein adsorption

To calculate the electrostatic interaction between a charged sphere and a charged surface under the condition of constant charge density on the two surfaces is difficult. The theory presented in this paper provides an approximate solution to this problem when the charge of the two bodies is of opposite sign. The proposed calculation model is based on a solution of the Poisson–Boltzmann (P–B) equation for two oppositely charged planar surfaces to which the approximate integration procedure developed by Deryaguin is applied. The obtained expression is rather simple and is in good agreement with retention data for a protein in ion exchange chromatography. The developed model is physically more sound than the previously developed ‘slab’ model for protein retention. Under the experimental conditions of ion exchange chromatography of proteins, the two models give comparable numerical values for the ionic strength dependence of retention.