A MODIFICATION OF DEBYE-HUCKEL THEORY BASED ON LOCAL THERMODYNAMICS

The basic assumption of Debye-Huckel theory is that the linearised form of the Poisson-Boltzmann equation applies, This assumption is replaced here by the more general postulate that the charge density-rho is proportional to the electrical potential psi. It is shown that to obtain thermodynamic consistency the corresponding dependence of number densities on psi must include terms up to psi-2. A new expression for the decay length of electrostatic effects, K-1, is obtained which is related to the classical Debye length, kappa-1, by the expression. K2 = kappa-2(exp Ka divided-by 1 + Ka) where a is the distance of closest approach or unlike ions. This equation gives real solutions for Ka in terms of kappa-a only up to kappa-a = 1.346 which corresponds to Ka = 1 + square-root 3. This limit could be associated with the onset of oscillations in the charge density as a function of distance from the central ion. For symmetrical electrolytes the replacement of kappa by K (a) leads to improved agreement with the Stillinger-Lovett second moment condition, (b) preserves the agreement of expressions for activity coefficients obtained via a charging process with those obtained via application of Kirkwood-Buff solution theory up to terms linear in concentration. However for asymmetrical electrolytes including terms in psi-2 leads to inconsistencies.