Modelling the Double Layer of Polycrystalline Electrodes: Capacitance, Potential of Zero Charge, and Parsons-Zobel Plot.

The double layer capacitance is a central tool to gain insight into the electrical double layer (EDL), yet its interpretation remains challenging. This is true in particular in the presence of surface heterogeneity and specific adsorption. Using a mean-field model, we discuss how these factors shape capacitance curves, affect the potential of zero charge (PZC), and alter the Parsons-Zobel (PZ) plots. The model reveals four distinct regimes of interfacial capacitance behaviour, determined by the facet size and ratio, the Debye length, and differences in PZC and Helmholtz capacitance between facets. These regimes define clear conditions under which capacitance curves exhibit either one or two minima, with the single minimum either coinciding with or deviating from the global PZC. We further demonstrate how adsorption on low-coordinated facets modifies the symmetry and magnitude of capacitance profiles and suppresses PZ slopes. Overall, this work provides a simple yet useful theoretical basis for recognizing and disentangling the respective roles of surface heterogeneity and adsorption in the EDL of polycrystalline electrodes, aiding in the interpretation of experimental results.