Date of Award
Open Access Dissertation
Ralph E. White
A solid electrolyte interphase (SEI) growth model is developed in a mixed modethat contains solvent diffusion through the SEI layer and corresponding solvent reduction kinetics at the SEI/electrode interface. The governing equations are solved by the Landau transformation, which makes the moving layer fixed to predict the open circuit potential, SEI layer thickness, and capacity loss. The estimated parameters fitted with experimental data from the literature are computed using COMSOL and MATLAB. Results show that the mixed mode model predicts lower capacity loss and thinner SEI layer due to its growth under open circuit conditions than previously reported by others.
A short-time asymptotic analysis is performed to establish corrections of theIlkovich equation, which describes the polarographic response of a dropping mercury electrode. The convective-diffusion equation governing diffusion-limited reactant flux for small drop times is solved by a regular perturbation based on powers of the sixth root of time. This produces a framework within which higher terms of the Ilkovich equation can be derived systematically. As well as reproducing Ilkovich’s original formula and verifying Newman’s correction of Koutecky’s first-order term, we calculate the second-order term for the first time. The calculation is compared to the Newman–Levich procedure and tested against numerical simulations with finiteelement software.
A method is presented which can be used to obtain analytical solutions for boundaryvalue problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix integration, and matrix inverse methods using Maple. The solution process is illustrated for single and multiple domains with different types of boundary conditions and constraints when necessary due to the boundary conditions. The method is easier to use and could be extended to include partial differential equations (PDEs).
Madi Reddy, S.(2023). Mathematical Analysis of Electrochemical Systems. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/7353