A thermodynamic correction to the theory of competitive chemisorption of ions at surface sites with nonelectrostatic physisorption

We resolve a thermodynamic inconsistency in previous theoretical descriptions of the free energy of chemisorption (charge regulation) under conditions where nonelectrostatic physisorption is included, as applied to surface forces and particle-particle interactions. We clarify the role of nonelectrostatic ion physisorption energies and show that a term previously thought to represent physisorbed ion concentrations (activities) should instead be interpreted as a "partial ion activity" based solely on the electrostatic physisorption energy and bulk concentration, or alternatively on the nonelectrostatic physisorption energy and surface concentration. Second, the chemisorption energy must be understood as the change in chemical potential after subtracting the electrostatic energy, not subtracting the physisorption energy. Consequently, a previously reported specific ion nonelectrostatic physisorption contribution to the chemisorption free energy is annulled. We also report a correction to the calculation of surface charge. The distinction in "partial ion activity" evaluated from bulk concentration or from surface concentration opens a way to study nonequilibrium forces where chemisorption is in equilibrium with physisorbed ions but not in equilibrium with bulk ions, e.g., by a jump in ion concentrations.