Length-Scale Dependence of Hydration Free Energy: Effect of Solute Charge

Size and curvature are important determinants of particle wettability, in addition to surface chemistry and texture. Hydration free energy of a nonpolar solute scales with volume for small solutes and with surface area for larger ones. If the solute acquires a surface charge, the scaling regimes can be affected, with size-dependence of the charge playing a critical role. For isolated particles grown at fixed surface charge density, the Born approximation gives scaling of hydration free energy with volume. We consider a distinctly different but practically important scenario, where the charged solute and surrounding counterions are dissolved together. For this process, our molecular simulations demonstrate the electrostatic contribution to the solvation free energy, calculated per unit area of the solute, to be virtually independent of solute size. We explain this behavior in terms of counterion shielding effect on the curvature-dependent solute energy in the dehydrated state, an effect closely balanced by the influence of dielectric screening in water. As a result, for moderate surface charge densities of the solute, the net electrostatic contribution is dominated by counterion solvation, and scales with solute surface area independently of the ionic strength in the solution.