Modern Theories of Carbon-Based Electrochemical Capacitors: A Short Review

Theoretical models for electrochemical capacitors range from the original Helmholtz model and mean-field continuum models, to the surface curvature-based post-Helmholtz models, and to modern atomistic simulations. Here, we review current theoretical models that have been useful at shedding light on experimental findings but also provide predictive capabilities that are needed to achieve the optimization of supercapacitors. Due to the non-planar surface of materials at the nanoscale, the original Helmholtz model is gradually found to be outdated, in particular for carbon materials. We show that the surface curvature-based models provide a better description of the interfacial behavior of carbon materials.