Dielectric properties of polyelectrolytes. II. A theory of dielectric increment due to ion fluctuation by a matrix method

The mean square of dipole moment of a linear macromolecule which is responsible for dielectric increment of aqueous polyelectrolyte solutions is calculated by means of a matrix method in which ion binding at discrete sites and the nearest‐neighbor interaction are taken into account. On the basis of the relationship between polarization of poly‐ion and fluctuation of bound counterions the present theory indicates that the loosely bound ions result in larger increment and otherwise smaller increment. Also, the theory predicts that the dielectric increment has a maximum at an intermediate monovalent–divalent ion ratio when both species coexist. These results are consistent with experiments on polyacrylic acid neutralized with NaOH and Ca(OH)2. At large contents of divalent ions the effect of chelation is also discussed.