Development of a mathematical model to study the impact of state of charge dependent exchange current density on the generated voltage hysteresis of silicon anode-based lithium half cells

Abstract

In this work, three different types of Silicon (porous, nano and bulk) anode-based coin cells are manufactured and lithiation-delithiation battery cycling tests are conducted. During the experiment, a capacity difference is witnessed at the beginning and the end point of the battery cycling loop. This capacity difference during battery cycling is reduced by implementing side-reaction correction technique on the exchange current density using Tafel kinetics formula. A huge voltage gap known as voltage hysteresis is generated during the battery cycling experiment of all three type cells. Here, a physics based mathematical model is developed to identify the main reason behind this voltage hysteresis generation. The impact of hydrostatic stress is checked on this generated voltage hysteresis. The stress induced voltage values are found significantly low to have impact on voltage hysteresis. Next, key parameters are identified which can control this stress. Then, new sets of exchange current density equation (average, linear and logarithmic) as a function of State of Charge (SOC) are developed. It is observed that, with the application of logarithmic SOC dependent exchange current density equation, voltage curve is fitted the best with the experimental result and the generated hysteresis can be minimized by controlling this SOC based exchange current density equation. Details of this study will provide more explanation.

A mathematical model development to investigate the impact of key parameters on the generated voltage hysteresis of silicon anode based lithium half cells

“…In case of 𝛺, constant values were used throughout the lithiation-delithiation cycling. Some impacts from 𝛺 were seen, but this parameter is also connected with diffusivity as reported by various researchers at their work (Verbrugge et al, 2015;Verbrugge and Cheng, 2019;Sethuraman et al, 2010;Sethuraman et al, 2012;Hossain, 2021), so again it suggests that solid diffusivity has influence on voltage hysteresis.…”

“…Here, 𝜎 ℎ Ω is called the stress induced voltage. Cheng and Verbrugge (2018), Jin et al (2019) and Hossain (2021) and Zhang et al (2007) all indicated how important it is to include this additional term in BV equation. 𝑖 0 is called the exchange current density.…”

Study of risk factors in adolescence in terms of demographic changes

“…We studied different types of reports/models/data sheets such as medical, mathematical, simulation, experimental, statistical, economical, engineering, socio economic etc. (Hossain, 2021;Cousens et al, 2011;Pedicelli et al, 2022;Hossain et al, 2020a;Fiorentino et al, 2018;Morshed et al, 2019;Hossain et al, 2020b;Romanenko et al, 2022;Pereira et al, 2019;Hossain et al, 2022a;Lobstein et al, 2019;Quek et al, 2017;Hossain et al, 2022b;Park et al, 2012;Inchley et al, 2020;Masud et al, 2021;Wijnhoven et al, 2014;van Ekris et al, 2016;Hossain, 2020;Waters et al, 2011;Homer et al, 2019;Hossain and Kim, 2020;Rutter et al, 2017;Finegood et al, 2010;Hossain, 2023;Savona et al, 2021;Malik et al, 2013;Idris et al, 2023;Monzani et al, 2019). We tried to figure out what would be the best-suited model/report to represent our investigation.…”