A model for association in electrolytes. Analytic solution of the hypernetted-chain/mean spherical approximation

We study the structural and thermodynamic properties of electrolytes in which the association between oppositely charged ions (A++B−⇄AB) is represented by a sticky electrolyte model (SEM) which allows positive and negative ions of diameter σ to be bonded at a distance L≤σ/2. The model is solved for a 2–2 electrolyte at concentrations up to 2 M and for L=σ/2 using the hypernetted-chain (HNC) approximation for the correlation functions within the spherical core and the mean spherical (MS) approximation outside. The number of AB dimers at a separation L is found to increase with concentration while there is a reduction in the number of contact ion pairs below that predicted by the restricted primitive model (RPM) from which stickiness is absent. The structural and thermodynamic properties of the SEM and RPM prove to be significantly different and sufficiently interesting to justify future applications of the SEM to molten salts and molecular solvents, especially if the ion–ion interactions can be treated with greater accuracy. The equilibrium properties of the fully associated system of extended dipoles with charges separated at a distance L=σ/2 are also given in the mean spherical approximation.