Analysis of Vanselow,Gapon, and Davis selectivity coefficients based on simple lattice Statistics

Simple lattice statistics was applied to formulate the monovalent-bivalent cation exchange reaction on lattice surfaces. The Davis and Gapon selectivity coefficients K_D and K_G could be derived for two-dimensional lattices with different reactions between bivalent cations and exchange sites. On the other hand, the Vanselow selectivity coefficient Kv could not be derived for twodimensional surfaces, but was found to be suitable for one-dimensional arrays of exchange sites. These results suggest that the use of K_v should be restricted to one-dimensional exchangers like linear polyelectrolytes and humic substances, while K_D is suitable for general purposes.