Restricted primitive model of dianions and counterions within the mean spherical approximation: Integral equation and thermodynamic perturbation theory

An analytical integral equation theory has been used to obtain the formal solution for the system of anionic dimers and cationic counterions within the mean spherical approximation. Expressions for the contact values of the radial distribution functions, internal energy, Helmholtz free energy, and osmotic pressure of the system have been derived analytically while the radial distribution functions beyond contact have been calculated numerically by using the Perram algorithm. Also, the thermodynamic perturbation theory has been used to calculate the osmotic coefficient of longer anionic chains and counterions. These results compare reasonably well with available simulation data.