Slow Current or Potential Scanning of Battery Porous Electrodes: Generalized Perturbation Solution and the Merits of Sinusoidal Current Cycling

Abstract

The determination of Open Circuit Voltage (OCV) is required in order to successfully model electrode behavior, and a standard method for doing this is to charge and discharge a cell at very slow current rates while measuring both voltage and State of Charge (SOC). For example, scans at a rate of C/100 (needing 100 h to charge from empty to full) are often used, but faster scans lose accuracy because irreversible losses, including those due to transport phenomena and reaction kinetics, impact the voltage in rough proportion to scan rate. We develop perturbation methods to correct measurements at higher scan rates to make their accuracy comparable to results at slower scan rates. Perturbation corrections are given for cases in which current is scanned (e.g., at different constant C-rates) as well as when voltage is scanned (e.g., linear-sweep voltammetry). Sinusoidal scanning of either voltage or current is proposed to eliminate the discontinuities at scan reversal, increasing the accuracy of these methods. The analytic formulas given here can be combined with a regression analysis of data at multiple scan rates to determine not only the OCV but also other resistances in the electrode, and this is a goal of future work.

Cation Mixing and Capacity Loss in Li||Ni0.6Mn0.2Co0.2O2 Cells: Experimental Investigation and Application of the Multi-Site, Multi-Reaction Model

“…The thermodynamics for the lithium counter electrode at z 0 is simply U Li 0. We model the thermodynamics of the intercalation electrode with the multi-site, multi-reaction (MSMR) model (Verbrugge et al, 2017; 2018; Baker et al, 2019;Baker and Verbrugge, 2021). The mole fraction of sites occupied by lithium in an NMC622 gallery j is x j .…”

“…Thus, we again return to the mole fraction x, instead of x, we consider x TM to be constant over a cycle, and we will drop terms of order α. Our main tool is the perturbation analysis developed in (Baker and Verbrugge, 2021). This starts with the assumption 2 that t 0 is sufficiently large that both γ, γ < < 1.…”

“…Also, we assume that x TM is constant to leading order in α. As was done in (Baker and Verbrugge, 2021), we can expand each dependent variable in, for example, the total mole fraction x of filled Li sites in the NMC622 Li layer expressed as…”

“…Our focus in this work is to model the slow charge of the cell and clarify capacity degradation. We use C/10 charging, where the 1C rate corresponds to the current required to charge a cell from the completely discharged state to the fully, as in fully charged state in 1 h. Because the charge rates are low, as will be shown in the scaling analysis, we can use the perturbation approach recently described in (Baker and Verbrugge, 2021) to treat the data, extract the open-circuit potential of the cell, and clarify degradation, which we find is consistent with cation mixing in the lithiated NMC622 (Li z Ni 0.6 Mn 0.2 Co 0.2 O 2 , where 0≤ z ≤ 1) positive electrode material (Kim et al, 2016a;Li et al, 2018a;Liao et al, 2005). References to early work on cation mixing in metal oxides can be found in the work of Rossen et al (1993b), particularly for LiCoO 2 , Rossen et al (1993a) and Ohzuku et al (1993) for LiCoO 2 and LiCo 0.5 Ni 0.5 O 2 , and Y-Choi et al (1996) for Li 1−δ Co y Ni 1−y O 2 .…”

“…In this work, we show that because the degradation associated with cation mixing is slow, we can average the degradation reaction over each cycle. The perturbation procedure presented in (Baker and Verbrugge, 2021) is used to derive model equations that are simple to implement, which facilitates parameter regression. The remainder of this publication is organized as follows.…”