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We generalize linearized Gouy-Chapman-Stern theory of electric double layerfor nanostructured and morphologically disordered electrodes. Equation forcapacitance is obtained using linear Gouy-Chapman (GC) orDebye-$\rm{\ddot{u}}$ckel equation for potential near complexelectrode/electrolyte interface. The effect of surface morphology of anelectrode on electric double layer (EDL) is obtained using "multiple scatteringformalism" in surface curvature. The result for capacitance is expressed interms of the ratio of Gouy screening length and the local principal radii ofcurvature of surface. We also include a contribution of compact layer, which issignificant in overall prediction of capacitance. Our general results areanalyzed in details for two special morphologies of electrodes, i.e."nanoporous membrane" and "forest of nanopillars". Variations of local shapesand global size variations due to residual randomness in morphology areaccounted as curvature fluctuations over a reference shape element.Particularly, the theory shows that the presence of geometrical fluctuations inporous systems causes enhanced dependence of capacitance on mean pore sizes andsuppresses the magnitude of capacitance. Theory emphasizes a strong influenceof overall morphology and its disorder on capacitance. Finally, our predictionsare in reasonable agreement with recent experimental measurements onsupercapacitive mesoporous systems.

physical review. e, statistical, nonlinear and soft matter physics

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