Determination of state-of-charge dependent diffusion coefficients and kinetic rate constants of phase changing electrode materials using physics-based models

The simplified gravimetric intermittent titration technique (GITT) model, which was first proposed by Weppner and Huggins in 1977, remains a popular method to determine the solid-state diffusion coefficient (D1) and the electrochemical kinetic rate constant (k). This is despite the model having been developed on the premise of a single-slab electrode and other gross simplification which are not applicable to modern-day porous battery electrodes. Recently however, more realistic and conceptually descriptive models have emerged, which make use of the increased availability of computational power. Chief among them is the P2D model developed by Newman et al., which has been validated for various porous battery electrodes. Herein, a P2D GITT model is presented and coupled with grid search optimization to determine state-of-charge (SOC) dependent D1 and k parameters for a sodium-ion battery (SIB) cathode. Using this approach, experimental GITT steps could be well fitted and thus validated at different SOC points. This work demonstrates the first usage of the P2D GITT model coupled with optimization as an analytical method to derive and validate physically meaningful parameters. The accurate knowledge of D1 and k as a function of the SOC gives further insight into the SIB intercalation dynamics and rate capability

Overpotential analysis of graphite-based Li-ion batteries seen from a porous electrode modeling perspective

The overpotential of Li-ion batteries is one of the most relevant characteristics influencing the power and energy densities of these battery systems. However, the intrinsic complexity and multi-influencing factors make it challenging to analyze the overpotential precisely. To decompose the total overpotential of a battery into various individual components, a pseudo-two-dimensional (P2D) model has been adopted and used for electrochemical simulations of a graphite-based porous electrode/Li battery. Analytical expressions for the total overpotential have been mathematically derived and split up into four terms, associated with the electrolyte concentration overpotential, the Li concentration overpotential in the solid, the kinetic overpotential, and the ohmic overpotential. All these four terms have been separately analyzed and are found to be strongly dependent on the physical/chemical battery parameters and the reaction-rate distribution inside the porous electrode. The reaction-rate distribution of the porous electrode is generally non-uniform and shows dynamic changes during (dis)charging, resulting in fluctuations in the four overpotential components. In addition, the disappearance of the phase-change information in the voltage curve of the graphite-based porous electrode/Li battery under moderate and high C-rates is ascribed to the Li concentration overpotential among solid particles, resulting from the non-uniform reaction-rate distribution

Physics-based modeling of sodium-ion batteries part II. Model and validation

Sodium-ion batteries (SIBs) have recently been proclaimed as the frontrunner 'post lithium' energy storage technology. This is because SIBs share similar performance metrics with lithium-ion batteries, and sodium is 1000 times more abundant than lithium. In order to understand the electrochemical characteristics of SIBs and improve present-day designs, physics-based models are necessary. Herein, a physics-based, pseudo-two-dimensional (P2D) model is introduced for SIBs for the first time. The P2D SIB model is based on Na3V2(PO4)2F3 (NVPF) and hard carbon (HC) as positive and negative electrodes, respectively. Charge transfer in the NVPF and HC electrodes is described by concentration-dependent diffusion coefficients and kinetic rate constants. Parametrization of the model is based on experimental data and genetic algorithm optimization. It is shown that the model is highly accurate in predicting the discharge profiles of full cell HC//NVPF SIBs. In addition, internal battery states, such as the individual electrode potentials and concentrations, can be obtained from the model at applied currents. Several key challenges in both electrodes and the electrolyte are herein unraveled, and useful design considerations to improve the performance of SIBs are highlighted

A modified pseudo-steady-state analytical expression for battery modeling

© 2019 The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS)method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS)expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS)expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles

From Li-Ion Batteries toward Na-Ion Chemistries: Challenges and Opportunities

© 2020 The Authors. Published by Wiley-VCH GmbH Among the existing energy storage technologies, lithium-ion batteries (LIBs) have unmatched energy density and versatility. From the time of their first commercialization in 1991, the growth in LIBs has been driven by portable devices. In recent years, however, large-scale electric vehicle and stationary applications have emerged. Because LIB raw material deposits are unevenly distributed and prone to price fluctuations, these large-scale applications have put unprecedented pressure on the LIB value chain, resulting in the need for alternative energy storage chemistries. The sodium-ion battery (SIB) chemistry is one of the most promising “beyond-lithium” energy storage technologies. Herein, the prospects and key challenges for the commercialization of SIBs are discussed. By comparing the technological evolutions of both LIBs and SIBs, key differences between the two battery chemistries are unraveled. Based on outstanding results in power, cyclability, and safety, the path toward SIB commercialization is seen imminent

Physics-based modeling of sodium-ion batteries part I: Experimental parameter determination

Sodium-ion batteries (SIBs) have been heralded as the most promising “beyond lithium” energy storage technology. This proclamation is based on recent technological trends and the outstanding performance of the state-of-the-art prototype 18650 and pouch cells. However, improving the design and performance of SIBs requires an in-depth understanding of the electrochemical behavior of the electrodes from both an experimental and physics-based modeling perspective. In this contribution, experimental characterizations of SIB electrode materials based on Na3V2(PO4)2F3 (NVPF) cathode and hard carbon (HC) anode are presented. The goal of this experimental investigation is to understand the individual electrode behavior and further elucidate relevant parameters for physics-based models. As a result, geometric, thermodynamic, and kinetic parameters are deduced from the two SIB electrodes. Based on the analyses of Na//NVPF and Na//HC half-cells, diffusion mass transport limitations and Ohmic losses are identified for both electrodes. These overpotential losses are equally present in full cell SIBs composed of NVPF and HC electrodes. These results are useful in the setup of SIB physics-based models

A modified pseudo-steady-state analytical expression for battery modeling

The solid-state spherical diffusion equation with flux boundary conditions is a standard problem in lithium-ion battery simulations. If finite difference schemes are applied, many nodes across a discretized battery electrode become necessary, in order to reach a good approximation of solution. Such a grid-based approach can be appropriately avoided by implementing analytical methods which reduce the computational load. The pseudo-steady-state (PSS) method is an exact analytical solution method, which provides accurate solid-state concentrations at all current densities. The popularization of the PSS method, in the existing form of expression, is however constrained by a solution convergence problem. In this short communication, a modified PSS (MPSS) expression is presented which provides uniformly convergent solutions at all times. To minimize computational runtime, a fast MPPS (FMPPS) expression is further developed, which is shown to be faster by approximately three orders of magnitude and has a constant time complexity. Using the FMPSS method, uniformly convergent exact solutions are obtained for the solid-state diffusion problem in spherical active particles

A comprehensive impedance journey to continuous microbial fuel cells

The aim of the present work was to characterize the impedance response of an air-cathode MFC operating in a continuous mode and to determine intrinsic properties that define its performance which are crucial to be controlled for scalability purposes. The limiting step on electricity generation is the anodic electrochemically-active biofilm, independently of the external resistance, Rext, utilized. However, for Rext below 3k? the internal impedance of the bioanode remained invariable, in good correspondence to the power density profile. The hydraulic retention time (HRT) had an effect on the impedance of both the bioanode and the air-cathode and especially on the overall MFC. The lowest HRT at which the MFC was operable was 3h. Yet, the variation on the HRT did not have a significant impact on power generation. A two constant phase element-model was associated with the EIS response of both bioanode and air-cathode, respectively. Consistency was found between the CPE behaviour and the normal power-law distribution of local resistivity with a uniform dielectric constant, which represented consistent values with the electrical double layer, the Nernst diffusion layer and presumably the biofilm thickness. These results have future implications on MFC monitoring and control, as well as in providing critical parameters for scale-up.Grant 180B12A7 from the Environmental and Energy Technology Innovation Platform (MIP2), under the project �Sewage Plus: second life of sewage as a matrix for dilution of organic waste streams�. Surajbhan Sevda gratefully acknowledges a scholarship from the Flemish Government, Department of Higher Education and Scientific Research (Vlaamse Gemeenschap) under the framework of Indo-Belgium fellowship (Academic year 2011�2012)Scopu

An experimental and modeling study of sodium-ion battery electrolytes

Electrolytes play an integral role in the successful operation of any battery chemistry. The reemergence of the sodium-ion battery (SIB) chemistry has therefore rejuvenated the search for optimized SIB salts and solvents. Recent experiments have found that 1 M NaPF6 in ethylene carbonate (EC) and propylene carbonate (PC), EC0.5:PC0.5 (w/w) is the best binary electrolyte for SIBs. However, mathematical models, to elucidate these experimental findings, have so far been lacking. Furthermore, no attempts to understand the effect of EC composition on the conductivity and electrolyte stability have been performed. Herein, the viscosity and conductivity profiles of NaPF6 in EC0.5:PC0.5 electrolyte are unraveled, using experimental and modeling approaches at different temperatures and salt concentrations. The viscosity is measured in a double-wall Couette cell and for the first time, the ionic conductivity is determined using two Pt blocking electrodes in a PAT-Cell electrochemical setup. Modeling is performed using the Advanced Electrolyte Model (AEM), a statistical mechanics software. It is shown that the conductivity and viscosity relationship follows a simple Stokes' law even at a low temperatures and high concentrations. In addition, the stability of binary and ternary electrolytes on hard carbon is shown to correlate with the preferential ion solvation of EC