On the analysis and application of an ion size-modified Poisson–Boltzmann equation

In this paper, an improved electrostatic free energy functional is presented as an extension of the one proposed in Xie and Li (2015) to reflect ion size effects. It is then shown to have a unique minimizer, resulting in the solution existence and uniqueness of one commonly-used ion size-modified Poisson–Boltzmann equation (SMPBE). As for applications, SMPBE is used to calculate the electrostatic solvation free energy with the new derived well-defined formula and simulate an electric double layer numerically to demonstrate the advantage of SMPBE over the classic Poisson–Boltzmann equation in the prediction of ionic concentrations.