Electrostatic forces for monovalent colloids in low and high salt solutions

A novel approach for calculating the interaction energy and electrostatic force between charged spherical colloidal particles in aqueous electrolyte solutions is proposed. The formulation is based upon an integration of the McCartney-Levine force approach in an appropriately modified nonlinear Poisson-Boltzmann equation. The resulting analytical expression for the electrostatic force provides a framework capable of accurate predictions across a wide spectrum of ionic concentrations-from dilute to high ionic strength-without requiring empirical parameter adjustments. Compared to existing approaches, the present formulation demonstrates superior consistency with experimental data for monovalent salts (NaCl and KCl), successfully capturing interaction energies at both short and intermediate separation distances under high ionic strength conditions, thus providing a useful tool for handling colloidal interactions in fields such as materials science and colloid chemistry.