Debye-Hückel theory of weakly curved macroions: Implementing ion specificity through a composite Coulomb-Yukawa...

The free energy of a weakly curved, isolated macroion embedded in a symmetric 1:1 electrolyte solution is calculated on the basis of linear Debye-Hückel theory, thereby accounting for nonelectrostatic Yukawa pair interactions between the mobile ions and of the mobile ions with the macroion surface, present in addition to the electrostatic Coulomb potential. The Yukawa interactions between anion-anion, cation-cation, and anion-cation pairs are independent from each other and serve as a model for solvent-mediated ion-specific effects. We derive expressions for the free energy of a planar surface, the spontaneous curvature, the bending stiffness, and the Gaussian modulus. It is shown that a perturbation expansion, valid if the Yukawa interactions make a small contribution to the overall free energy, yields simple analytic results that exhibit good agreement with the general free energy over the range of experimentally relevant interaction parameters.