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Mathematical Reformulation of Physics Based Model Predicting Diffusion, Volume Change and Stress Generation in Electrode Materials

Webb, Rebecca Diane
http://orcid.org/0000-0003-2309-1446
http://rave.ohiolink.edu/etdc/view?acc_num=osu1658344480701017

Abstract Details

2022, Master of Science, Ohio State University, Mechanical Engineering.
The development of next generation electrode materials provides the opportunity to significantly increase the energy density of lithium-ion batteries. These materials form alloy compounds with lithium and have specific capacities that are much higher than of graphite. Of these materials, silicon, which has a theoretical capacity of ~4200 mAh/g, is the closest to commercialization. However, silicon experiences large volume changes during the lithiation and delithiation processes. This ultimately leads to stress generation within the particle causing fracture, loss of active material, and rapid loss of cell capacity. The differences in behavior for silicon-based anodes compared to traditional graphite anodes highlights the need for the development of physics-based models to capture the effects of volume change and stress generation on the solid-state diffusion process. One such model proposed by Christensen and Newman describes the effects of diffusion, volume change, and stress generation in a spherical electrode particle. This mathematical model takes the form of an index-2 set of differential and algebraic equations which require implicit numerical methods to obtain a solution. Due to the mathematical complexity and high computational time and memory requirements, this model is not suited for controls or estimation-based applications. This thesis presents a mathematical reformulation of the Christensen-Newman equations using index-reduction to obtain a semi-explicit index-1 version of the model. Index reduction allows for the differential and algebraic equations to be decoupled enabling the use of explicit time marching methods. This reformulation will enable the integration of this model into larger cell level frameworks as well as estimation and controls-based applications. The reduced index model is verified against a fully implicit benchmark solution for a graphite anode. A local sensitivity analysis is performed to ascertain the effects of the mechanical properties as well as the diffusion coefficient on the surface concentration of lithium, particle radius, radial stress, and tangential stress and to facilitate a process for calibrating these parameters.
Marcello Canova (Advisor)
Jung Hyun Kim (Committee Member)
119 p.
Mechanical Engineering
Lithium-Ion Battery Modeling; Lithium-Ion Battery Aging; Silicon Anode; Volume Change; Stress Generation; Index Reduction; Differential and Algebraic Equations

Recommended Citations

Citations

  • Webb, R. D. (2022). Mathematical Reformulation of Physics Based Model Predicting Diffusion, Volume Change and Stress Generation in Electrode Materials [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1658344480701017

    APA Style (7th edition)

  • Webb, Rebecca. Mathematical Reformulation of Physics Based Model Predicting Diffusion, Volume Change and Stress Generation in Electrode Materials. 2022. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1658344480701017.

    MLA Style (8th edition)

  • Webb, Rebecca. "Mathematical Reformulation of Physics Based Model Predicting Diffusion, Volume Change and Stress Generation in Electrode Materials." Master's thesis, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1658344480701017

    Chicago Manual of Style (17th edition)

osu1658344480701017
168
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This open access ETD is published by The Ohio State University and OhioLINK.