Distribution of ions in electrolyte solutions and plasmas. Part 3

Abstract

Using the expression for the binary distribution function (F_ji) obtained in Part 2, the potential of mean force between two ions (W_ji) and the mean electrostatic potential (ψ_j) are determined for dilute solutions to terms of the order ε³ for symmetrical and ε² for unsymmetrical electrolytes. The reason for the failure of the assumption W_ji=e_iψ_j=e_jψ_i beyond the first-order in ε is discussed and it is shown that W_ji=e_iψ_i+(εⁿ) where n= 3 for symmetrical and 2 for unsymmetrical electrolytes. The degree of error in both linearized and non-linearized forms of the Poisson–Boltzmann equation is determined, and it is shown that, although of the same order, the error is more severe in the linearized equation. The Kirkwood closure F_jik=F_jiF_jkF_ik is examined and it is shown that in the limit t→ 0 F_jik=(F_jiF_jkF_ik)[1 +(εⁿ)] where again n= 3 for symmetrical and 2 for unsymmetrical electrolytes. By solving the third equation in the BBGY hierarchy, differential equations are obtained for these higher terms. The ground is prepared for the later investigation of concentrated electrolyte solutions.