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The free energy of a weakly curved, isolated macroion embedded in a symmetric1:1 electrolyte solution is calculated on the basis of linear Debye-H\"uckeltheory, thereby accounting for non-electrostatic Yukawa pair interactionsbetween the mobile ions and of the mobile ions with the macroion surface,present in addition to the electrostatic Coulomb potential. The Yukawainteractions between anion-anion, cation-cation, and anion-cation pairs areindependent from each other and serve as a model for solvent-mediatedion-specific effects. We derive expressions for the free energy of a planarsurface, the spontaneous curvature, the bending stiffness, and the Gaussianmodulus. It is shown that a perturbation expansion, valid if the Yukawainteractions make a small contribution to the overall free energy, yieldssimple analytic results that exhibit good agreement with the general freeenergy over the range of experimentally relevant interaction parameters.

Debye-H\"uckel Theory of Weakly Curved Macroions: Implementing Ion Specificity through a Composite Coloumb-Yukawa Interaction Potential