Non-electrostatic interactions as random fields in charged liquids

We derive an equation capable of treating both the electrostatic and non-electrostatic interactions in the charged liquids. The equation derived is a complex version of the Poisson-Boltzmann equation, in which the non-electrostatic interactions are transformed to complex random fields by the field theory. Thus, the non-electrostatic interactions of the ions in the charged liquids can be simulated easily by generating random numbers according to the random fields. To solve the equation, the finite element method has been applied. The non-electrostatic interactions treated in the equation are general. In this study, we take the steric effect of ions as an example. Results show that the steric effect can be clearly caught by the equation.