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Modeling and simulations of electrical energy storage in electrochemical capacitors


The present study investigates transport and electrochemical phenomena in electrochemical capacitors (ECs) for electrical energy storage applications. Modeling of such systems is made difficult by the complex multidimensional and multiscale porous electrode structures along with the coupled physical phenomena and redox reactions. This study is unique in that it presents rigorous development of physical models for electric double layers and redox reactions in ECs. These models were used to gain insights into the coupled transport and electrochemical phenomena involved. Finally, the results were used to identify the dominant design parameters.

First, this study identified the important physical phenomena that must be accounted for when simulating electric double layer capacitors (EDLCs). It established that the Stern and diffuse layers, the finite ion sizes, and the field-dependent electrolyte permittivity must all be accounted for. To account for the Stern layer for 3D electrode structures along with all the other phenomena, a new set of boundary conditions was derived. In fact, this study presents the first simulations of EDLCs with 3D electrode structures including (i) ordered mesoporous carbon sphere arrays and (ii) ordered bimodal mesoporous carbons, respectively. The model and numerical tools were validated successfully against experimental data.

Second, this study derives a scaling law for the integral areal capacitance of carbon-based EDLCs supported by rigorous analysis and experimental data for various mesoporous carbon electrodes with different electrolytes. It establishes that the integral areal capacitance of porous electrodes can be expressed as the product of the capacitance of planar electrodes and a semi-empirical function to correct for the porous electrode morphology. To maximize the integral areal capacitance, the electrolyte should have small ion effective diameter and large dielectric constant. The electrode pore diameter should be tailored as monodispersed as possible to match the ion diameter.

Third, this study presents dynamic modeling of EDLCs accounting for charge transport in both the electrode and electrolyte. It provides rigorous physical interpretations of experimental observations from electrochemical impedance spectroscopy and cyclic voltammetry (CV) experiments based on physics-based numerical simulations. Moreover, a generalized modified Poisson-Nernst-Planck (GMPNP) model was derived from first principles to simulate electric double layer dynamics valid for asymmetric electrolytes and/or in the presence of multiple ion species. For the first time, a self-similar behavior was identified for the electric double layer integral capacitance estimated from CV measurement simulations.

Finally, this study presents dynamic modeling of asymmetric supercapacitors in CV measurements by rigorously and simultaneously accounting for electric double layers and redox reactions as well as ion insertion in the electrode. It establishes that in CV measurements of pseudocapacitive materials: (i) the capacitive current varies linearly with scan rate $v$ and (ii) the Faradaic current is proportional to $v^{1/2}$.

The models and results could help develop the optimum electrode architecture to achieve maximum energy and power densities. Moreover, these models will also be useful for simulating and designing various practical electrochemical, colloidal, and biological systems for a wide range of applications.

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