Thermodynamic consistency in the symmetric Poisson–Boltzmann equation for primitive model electrolytes

A Poisson–Boltzmann equation, which gives symmetric pair-correlation functions, is examined for thermodynamic consistency. The osmotic coefficients via the virial, compressibility and energy routes are obtained for primitive model electrolytes and compared to those predicted by integral equations and available Monte Carlo results. Some comparisons are made of the predicted mean activity coefficients. Analytical solutions and some numerical results are also presented for the linearized Poisson–Boltzmann equation.