Surface Charge Boundary Condition Often Misused in CO₂ Reduction Models

Abstract

The Poisson–Nernst–Planck equations have been used to model species transport in electrochemical CO 2 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 μF 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 μF 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 CO 2 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 CO 2 R models that used such a high Stern layer capacitance or permittivity are expected to have overpredicted the effects of the electric double layer.

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