The electrostatic free energy of polyelectrolyte solutions. I. Randomly kinked macromolecules

Abstract

(1) The electrostatic free energy of randomly kinked, ionized, macromolecules was calculated for polyelectrolyte solutions of finite ionic strenght. A detailed analysis of the charging process and the reference state of the free energy is given. The mutual electrostatic repulsion of the fixed charges on the macromolecule is the main part of the electrostatic free energy. Its calculation is based on two main assumptions: the validity of Kuhn's statistics and of Debye's approximation. (2) The electrostatic contribution per macromolecule to the free energy of the solution is found to be Fe = (v2 ϵ 2/Dh)ln {1 + (6 h/κ h)}, where v is the number of charged groups per polymolecule, ϵ the unit of charge, D the dielectric constant, κ Debye's inverse radius, based on the number of free ions in solution, h the end‐to‐end distance of the charged molecule, and h0 the corresponding end‐to‐end distance in and uncharged reference state. (3) Activity coefficients of free ions in polyelectrolyte solutions have been derived from the theory. The calculated values compare favorably with the activity coefficients from measurements on Donnan distribution of salt.