Association in electrolyte solutions: Rodlike polyelectrolytes in multivalent salts

Abstract

We describe a new approach to determine the degree of association between ionic components in complex electrolyte solutions. We use the electrostatic contribution to the free energy that arises from the exact separation into long and short ranged parts of the correlation functions in a dilute electrolyte solution to determine the effective charge of the various ionic components. We describe the short-ranged direct correlations between different ionic components with delta functions whose strength give the direct association between them. The association is determined self-consistently by minimizing the resulting free energy, which contains long and short range correlations contributions. Association between like charges is mediated by direct association between opposite charges. We analyze rodlike polyelectrolyes in monovalent and/or multivalent salts. We find a broad minimum in the absolute value of effective rod charge at long distances as a function of monovalent salt concentration. This minimum is due to the association of the salt ions among themselves. We also determine the number of multivalent and monovalent ions associated to the rods. The degree of association is a function of the smallest length scale, which determines the electrostatic potential between ionic species at contact.