A brief review of continuous models for ionic solutions: the Poisson–Boltzmann and related theories

The Poisson–Boltzmann (PB) theory is one of the most important theoretical models describing charged systems continuously. However, it suffers from neglecting ion correlations, which hinders its applicability to more general charged systems other than extremely dilute ones. Therefore, some modified versions of the PB theory are developed to effectively include ion correlations. Focused on their applications to ionic solutions, the original PB theory and its variances, including the field-theoretic approach, the correlation-enhanced PB model, the Outhwaite–Bhuiyan modified PB theory and the mean field theories, are briefly reviewed in this paper with the diagnosis of their advantages and limitations. (topical review)