Effective screened Coulomb charge of spherical colloidal particles

The application of the well-known DLVO pair potential and its variations in the literature to the evaluation of the charge on macroions routinely resu lts in an "effective" charge considerably smaller than the "bare" surface c harge. Various theories have been proposed for "charge renormalization" on the basis of either surface effects (viz., counterion "condensation") or eq uivalence of linearized and nonlinearized electrostatic potentials at the s urface of a computation cell in the numerical analysis of the Poisson-Boltz mann equation. In the present discourse, a model for the effective charge i s proposed that is based on the equivalence of the screened Coulomb macroio n-counterion interaction to the thermal energy k(B)T. The distance at which these interactions are equal, R-therm, defines a distance partition for th e counterions into two populations: those tightly associated with the macro ion and contributing to the charge reduction and those "free" in solution a nd contributing to the properties of the surrounding medium. The characteri stics of this model are in good agreement with other theoretical approaches based on more elaborate solutions to the Poisson-Boltzmann equation and co mputer simulations. More important, this relatively simple model is in agre ement with the experimentally determined trends relating the effective char ge to the titration charge. Limitations of the proposed model, as well as t he screened Coulomb potential, are also discussed.