Surface Charge Boundary Condition Often Misused in CO₂ Reduction Models

The Poisson-Nernst-Planck equations have been used to model species transport in electrochemical CO2 reduction, where the surface charge boundary condition accounts for the potential drop across the Stern layer. A direct comparison of the published models reveals the relative permittivity inside the Stern layer has been applied inconsistently across the literature, with values ranging from 6 to 80.1. In fact, a majority of studies use the pure water or electrolyte permittivity value inside the Stern layer, implying a Stern layer capacitance in the range of 100-200 mu F cm(-2). This is far higher than the Stern layer capacitances measured in fundamental experiments of the electric double layer, typically in the range of 20-25 mu F cm(-2). Using such a high capacitance supercharges the electric field in the diffuse layer, leading to an overestimate of the electrolyte cation concentration, extreme pH and pOH values, and-if steric effects are included-a vast underestimation of the CO2 concentration at the reaction plane. The discrepancy can be traced back to the surface charge boundary condition, which is explained in detail herein. Previously published CO2R models that used such a high Stern layer capacitance or permittivity are expected to have overpredicted the effects of the electric double layer.