Double layer interaction between charged parallel plates using a modified Poisson–Boltzmann equation to include size effects and ion specificity

We present calculations of double layer interaction between charged plates taking into account size effects on colloidal systems. Those are modeled using a modified version of Poisson–Boltzmann equation, including non-electrostatic interactions due to the size and the polarizability of each ion. The van der Waals interactions and size effects can properly describe ion specificity as observed experimentally in many colloidal systems. The differential-algebraic mathematical structure is used to solve the modified Poisson–Boltzmann equation. The DASSL code is recursively applied using a Newton–Raphson method to solve the corresponding boundary-value problem. Density profiles around colloidal particles are calculated for different charged-particles immersed in various electrolytes aqueous solutions. From these profiles, we could calculate the pressure (interaction) between the plates. The influence of charge and size asymmetries of ions on density profiles are studied in different solutions. Results show the adequacy of this modified form of the Poisson–Boltzmann equation and the proposed mathematic procedure to solve the needed equations, describing several properties of colloidal systems and ion size correlation.