Mono- and divalent competitive adsorption to a charged membrane in a closed system: A comparative study

Competitive adsorption to a negative surface between monovalent and divalent cations is studied in a closed system. A self-consistent theory is presented for the cases when the divalent cation binds to two negative sites (1:2 binding) and to one negative site (1:1 binding). It is demonstrated that these two cases are distinguishable when the relative difference in total divalent concentrations determined at fixed bulk divalent concentrations is plotted as a function of the bulk monovalent concentration. The 1:2 binding case yields a sigmoidal curve while the 1:1 binding curve is hyperbolic. The comparison between the 1:2 and 1:1 binding cases of the divalent cation is extended to include; (1) the existence of a surface charge to which no binding occurs, and (2) the case when an additional non-binding monovalent cation is present.