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Continuum electrolyte models represent a practical tool to account for the presence of the diffuse layer at electrochemical interfaces. However, despite the increasing popularity of these in the field of materials science, it remains unclear which features are necessary in order to accurately describe interface-related observables such as the differential capacitance (DC) of metal electrode surfaces. We present here a critical comparison of continuum diffuse-layer models that can be coupled to an atomistic first-principles description of the charged metal surface in order to account for the electrolyte screening at electrified interfaces. By comparing computed DC values for the prototypical Ag (100) surface in an aqueous solution to experimental data, we validate the accuracy of the models considered. Results suggest that a size-modified Poisson-Boltzmann description of the electrolyte solution is sufficient to qualitatively …