Generalization of Linearized Gouy-Chapman-Stern Model of Electric Double Layer for Nanostructured and Porous Electrodes: Deterministic and Stochastic Morphology

TL;DR

This paper extends the Gouy-Chapman-Stern model to account for complex nanostructured electrode surfaces, incorporating surface curvature and disorder effects to better predict electric double layer capacitance.

Contribution

It introduces a generalized theoretical framework that includes surface morphology and stochastic effects, improving understanding of capacitance in nanostructured electrodes.

Findings

Capacitance depends on local surface curvature and morphology.

Surface disorder enhances pore size dependence of capacitance.

Predictions align with experimental data on mesoporous supercapacitors.

Abstract

We generalize linearized Gouy-Chapman-Stern theory of electric double layer for nanostructured and morphologically disordered electrodes. Equation for capacitance is obtained using linear Gouy-Chapman (GC) or Debye-$\rm{\ddot{u}}$ckel equation for potential near complex electrode/electrolyte interface. The effect of surface morphology of an electrode on electric double layer (EDL) is obtained using "multiple scattering formalism" in surface curvature. The result for capacitance is expressed in terms of the ratio of Gouy screening length and the local principal radii of curvature of surface. We also include a contribution of compact layer, which is significant in overall prediction of capacitance. Our general results are analyzed in details for two special morphologies of electrodes, i.e. "nanoporous membrane" and "forest of nanopillars". Variations of local shapes and global size variations due to residual randomness in morphology are accounted as curvature fluctuations over a reference shape element. Particularly, the theory shows that the presence of geometrical fluctuations in porous systems causes enhanced dependence of capacitance on mean pore sizes and suppresses the magnitude of capacitance. Theory emphasizes a strong influence of overall morphology and its disorder on capacitance. Finally, our predictions are in reasonable agreement with recent experimental measurements on supercapacitive mesoporous systems.