Electrochemical capacitors (ECs) serve as promising electrical energy storage systems due to their potential to achieve both high energy and high power densities. They can be classified as either electric double layer capacitors (EDLCs) or pseudocapacitors depending on the charge storage mechanism. EDLCs store charge in the electric double layer (EDL) forming at the electrode/electrolyte interface. Pseudocapacitors store energy both in the EDL and in the redox reactions occurring at or near the electrode surface along with ion intercalation into the electrodes. However, the interpretations of experimental results and the electrode optimization of such systems are made difficult by the coupling effect of EDL formation, redox reactions, and ion intercalation in the multidimensional porous electrode structures. This dissertation presents rigorous physical interpretations of conventional experimental characterization methods and provides design rules for EC electrodes using a multidimensional physicochemical model.

First, electrochemical impedance spectroscopy (EIS) measurements (Nyquist plots) of planar EDLC electrodes and devices were reproduced numerically for different electrode conductivity and thickness, electrolyte domain thickness, as well as ion diameter, diffusion coefficient, and concentrations. The electrode resistance, electrolyte resistance, and the equilibrium differential capacitance were identified from Nyquist plots without relying on equivalent RC circuits. These results and interpretations were then confirmed experimentally for EDLC devices consisting of two identical activated-carbon electrodes in both aqueous and non-aqueous electrolytes. Similarly, EIS measurements of planar redox active electrodes were reproduced numerically for a wide range of electrode electrical conductivity, electrolyte thickness, redox reaction rate constant, and bias potential. The electrode, bulk electrolyte, charge transfer, and mass transfer resistances could be identified from the Nyquist plots. The results were then confirmed experimentally for LiNi0.6Co0.2Mn0.2O2 and MoS2 electrodes in organic electrolytes.

Moreover, multidimensional simulations under cyclic voltammetry were performed for EDLC electrodes of different thicknesses consisting of spherical nanoparticles arranged in either simple cubic (SC) or face-centered cubic (FCC) packing structure. The capacitance under quasi-equilibrium (low charging/discharging rate) and rate-dependent (high charging/discharging rate) conditions were compared for different electrode nanoarchitectures and design suggestions were drawn. Moreover, multidimensional simulations were carried out for pseudocapacitive electrodes consisting of ordered conducting nanorods coated with a thin film of pseudocapacitive material. The contributions of EDL formation and redox reactions were discriminated and an optimum pseudocapacitive layer thickness that maximized total areal capacitance was identified as a function of scan rate and confirmed by scaling analysis.

Finally, commonly used methods to calculate energy and power densities of EDLC and hybrid pseudocapacitors were compared and evaluated. Energy conservation law was applied to the devices to identify the most appropriate method to calculate energy and power densities. The findings were confirmed by experimental measurements on EDLCs made of activated carbon electrodes and organic electrolyte and on hybrid pseudocapacitors made of MnO2-graphene and activated carbon electrodes in aqueous electrolyte.