On the theory of divalent ion binding by polyelectrolytes

Abstract

AbstractThe problem of the binding of a divalent counterion by two adjacent binding sites of a uniform linear polyelectrolyte has been investigated for both finite and infinite chain lengths. Allowance has been made for interactions between adjoining ionized groups and for the presence of a univalent counterion which may also be bound. For the case of finite chain lengths, the partition function is obtained in terms of a 3 × 3 matrix containing the conditional probabilities of the possible states of a polyelectrolyte group. By a novel method, the expression for the partition function is then simplified to a finite polynomial containing only the coefficients of the secular equation, but not its eigenvalues. From this expression for the partition function, the quasi‐grand partition function for the infinitely long chain is calculated. It is shown that for both cases of finite and infinite chain length, closed explicit expressions relating the degrees of ionization and ion binding to the ion activities and the interaction parameter may be obtained from which the eigenvalues of the matrix have been eliminated. The applicability of the new method of calculation to other problems involving finite linear Ising lattices is briefly discussed.