Screened Coulomb potential and the renormalized charges of ions and molecules inelectrolyte solutions

Abstract

We consider solutions that consist of solute and solvent molecules of arbitrarysizes, shapes and internal charge distributions. The free energy of interaction(the potential of mean force) between the molecules is analysed in terms of ascreened Coulomb potential and renormalized charge distributions of the molecules.The emphasis in this work is to bring out a simple physical interpretation ofthe theory, but the treatment is based on exact statistical mechanical theorywithout any approximations. The results thereby are the true properties of thesystem for given pair interaction potentials between the constituent particles. Ingeneral, the electric potential from any molecule in the solution can be exactlyobtained for all distances by using a (generalized) screened Coulomb potential,provided the source charges constitute a renormalized charge distribution of themolecule. When charge renormalization is done consistently, macroions, small ionsand solvent molecules are treated in fundamentally the same manner and allparticles acquire renormalized charge distributions that generally are different fromtheir actual (bare) distributions. The electrostatic free energy of interaction isgiven by the interaction between the renormalized charge distributions of themolecules as mediated by the screened Coulomb potential. The exact formalism isalso used for the primitive model of electrolytes. The concepts in the generaltheory are illustrated by expressing the Poisson–Boltzmann and hypernettedchain (HNC) approximations in this alternative framework. Conditions are givenunder which the exact theory predicts the existence of attractive electrostaticinteraction between two identical particles at large distances from each other.