Role of oscillatory solvent-mediated interactions for the differential capacitance of an electric double layer

Solvent-mediated ion-ion interactions in aqueous electrolytes often exhibit damped oscillations arising from hydration-shell structuring, yet their consequences for electric double-layer behavior remain poorly quantified. Here, we combine canonical Monte Carlo simulations with a generalized Poisson-Helmholtz-Boltzmann mean-field model to determine how oscillatory Yukawa-type hydration forces influence the differential capacitance of a planar electrode in a symmetric electrolyte. By systematically varying the oscillation wavelength and ion size, we map how these interactions reshape the capacitance profile, including the camel-to-bell transition, and delineate the conditions under which mean-field descriptions remain reliable. In the large-ion regime, mean-field theory predicts that strong solvent oscillations may induce the transition. In contrast, Monte Carlo simulations reveal that the capacitance remains bell-shaped and insensitive to solvent structuring. We further show that oscillatory hydration potentials soften short-range interactions, allowing mean-field theory to reproduce simulation trends qualitatively across broad parameter ranges; however, significant deviations arise when ion-ion correlations and excluded-volume effects become dominant. This combined simulation-theory analysis clarifies the microscopic origins of capacitance modulation in hydrated electrolytes and offers a general framework for incorporating oscillatory solvation forces into continuum electric double-layer models.