The thermal behavior of lithium ion batteries has a huge impact on their lifetime and the initiation of degradation processes. The development of hot spots or large local overpotentials leading, ...e.g., to lithium metal deposition depends on material properties as well as on the nano- und microstructure of the electrodes. In recent years a theoretical structure emerges, which opens the possibility to establish a systematic modeling strategy from atomistic to continuum scale to capture and couple the relevant phenomena on each scale. We outline the building blocks for such a systematic approach and discuss in detail a rigorous approach for the continuum scale based on rational thermodynamics and homogenization theories. Our focus is on the development of a systematic thermodynamically consistent theory for thermal phenomena in batteries at the microstructure scale and at the cell scale. We discuss the importance of carefully defining the continuum fields for being able to compare seemingly different phenomenological theories and for obtaining rules to determine unknown parameters of the theory by experiments or lower-scale theories. The resulting continuum models for the microscopic and the cell scale are numerically solved in full 3D resolution. The complex very localized distributions of heat sources in a microstructure of a battery and the problems of mapping these localized sources on an averaged porous electrode model are discussed by comparing the detailed 3D microstructure-resolved simulations of the heat distribution with the result of the upscaled porous electrode model. It is shown, that not all heat sources that exist on the microstructure scale are represented in the averaged theory due to subtle cancellation effects of interface and bulk heat sources. Nevertheless, we find that in special cases the averaged thermal behavior can be captured very well by porous electrode theory.
Silicon-based, high-energy-density electrodes show severe microstructural degradation due to continuous expansion and contraction upon charging and discharging. This mechanical degradation behaviour ...affects the cell’s lifetime by changing the microstructure morphology, altering transport parameters, and active volume losses. Since direct experimental observations of mechanical degradation are challenging, we develop a computer simulation approach that is based on real three-dimensional electrode microstructures. By assuming quasi-static cycling and taking into account the mechanical properties of the electrode’s constituents we calculate the heterogeneous deformation and resulting morphological changes. Additionally, we implement an ageing model that allows us to compute a heterogeneously evolving damage field over multiple cycles. From the damage field, we infer the remaining electrode capacity. Using this technique, an anode blend of graphite particles and silicon carbon composite particles (SiC-C) as well as a cathode consisting of Lithium-Nickel-Manganese-Cobalt Oxide with molar ratio of 8:1:1 (NMC811) are studied. In a two-level homogenization approach, we compute, firstly, the effective mechanical properties of silicon composite particles and, secondly, the whole electrode microstructure. By introducing the damage strain ratio, the degradation evolution of the graphite SiC-C anode blend is studied for up to 95 charge-discharge cycles. With this work, we demonstrate an approach to how mechanical damage of battery electrodes can be treated efficiently. This is the basis for a full coupling to electrochemical simulations.
•1D novel multiphysics model of a PEM water electrolysis anode is developed.•Two-phase flows with charge conservation are simulated in the anode.•Water management in PEM is investigated for its ...effects on ion conductivity.•The properties of the porous transport layer are studied for improving performance.•The factors on oxygen evolution reaction are analyzed in CV test simulations.
1D multiphysics modelling of the PEM water electrolysis anode is benefit for detailed investigation of the joint effects of electrochemical performance and multicomponent multiphase flow transport phenomena. Such a model can be effectively applied for the water electrolysis system design and optimization. Recently, the importance of hydraulic effects and dynamic behavior gradually attracts much focus on this specific issue. In this article, a novel 1D dynamic model has been developed for interpreting the multiphysics processes in the PEM water electrolysis anode, which considers the complex fluid dynamics and electrochemistry in the PEM water electrolyzer (PEMWE) components – PEM, the anode catalyst layer and the porous transport layer. As a result, the hydraulic and electrochemical properties of three components were studied for investigation of their effects on the characterization of electrochemical performance and mass transport processes. It concludes that for the improvement of electrolytic performance, the porous transport layer is suggested to be designed for high permeability and low contact angle. The catalyst layer needs to be optimized for its three-phase interface fraction with high coating mass in the membrane assembly.
We present an exclusively thermodynamics based derivation of a Butler–Volmer expression for the intercalation exchange current in Li ion insertion batteries. In this first paper we restrict our ...investigations to the actual intercalation step without taking into account the desolvation of the Li ions in the electrolyte. The derivation is based on a generalized form of the law of mass action for non ideal systems (electrolyte and active particles). To obtain the Butler–Volmer expression in terms of overpotentials, it is necessary to approximate the activity coefficient of an assumed transition state as function of the activity coefficients of electrolyte and active particles. Specific considerations of surface states are not necessary, since intercalation is considered as a transition between two different chemical environments without surface reactions. Differences to other forms of the Butler–Volmer used in the literature 1,2 are discussed. It is especially shown, that our derivation leads to an amplitude of the exchange current which is free of singular terms which may lead to quantitative and qualitative problems in the simulation of overpotentials. This is demonstrated for the overpotential between electrolyte and active particles for a half cell configuration.
•Li-ion battery model featuring Solid Electrolyte Interphase growth on reaction interfaces, including carbon-binder pores.•Simulation of inhomogeneous cell degradation processes on resolved 3D ...electrode microstructures.•Convergence and performance comparison of monolithic and novel semi-implicit solver with complex full cell simulation.•Monolithic solver suffers from poor linear solver convergence, due to saddle-point structure.•Semi-implicit solver outperforms monolithic approach, while preserving convergence.
Growth of the Solid Electrolyte Interphase is one of the major degradation processes in Li-ion batteries and yields an increase in cell resistance, as well as a reduction in capacity. In order to facilitate computer-aided design of novel cell concepts and omit costly prototyping, it is crucial to incorporate this mechanism into electrochemical simulations on the microscale and to develop efficient numerical solvers. Electrochemical battery models without degradation are commonly discretized with a fully implicit discretization resulting in a monolithic scheme. Solving the resulting systems with a Newton method allows for quadratic convergence, where the major part of the computational effort is spent on solving the underlying linear systems. Hence, finding a suitable preconditioner for the linear solver is essential for overall solver performance. While an efficient algebraic multigrid preconditioner results in a good performance for the model without degradation, we encounter a noticeable loss in performance of the solver when including the coupled degradation model. We attribute the observed performance issues to the implicitly defined interface currents introduced by the degradation model. By taking into account the slow dynamics of the degradation, we propose an alternative semi-implicit solution approach separating the degradation dynamics and eliminating the implicit interface currents, in order to promote the efficient utilization of the algebraic multigrid preconditioner. The monolithic and semi-implicit solvers are evaluated by performing a series of full cell simulations featuring calendar and cyclic aging scenarios and a complex geometry including the binder domain in each electrode. Based on the results, the semi-implicit solver significantly improves the performance, while maintaining the convergence behaviour.
In this work a phase field method is used for the solution of an electro-chemical diffusion model for a lithium-iron-phosphate particle coupled to a small-strain elasto-plasticity model. This ...coupling takes the mechanical dilatation of the crystal lattice during intercalation into account. The electro-chemo-mechanical coupling is derived from a Helmholtz free energy, resulting in constitutive equations for both the diffusion and the mechanical equilibrium in the electrode material. A new method for the generation of virtual microstructures is given with additional constraints to obtain smooth boundaries. This ensures valid mechanical solutions for grid refinement. The model is then discretized, linearized and solved for various microstructures. Academic results in one and two spatial dimensions are presented as well as results on spherical structures. The versatility of the numerical method is demonstrated for virtual microstructures generated by stochastic models on graphite.
Fast charging is one of the main challenges in Lithium-ion battery applications. Especially at low temperatures and high C-rates, capacity loss due to lithium plating is identified as the main aging ...effect. Electrochemical models are able to predict the lithium plating onset conditions, as they provide information about the local potentials and lithium concentrations within the individual electrodes. Due to the narrow potential window of graphite, a precise determination of the sensitive parameters is needed for an accurate prediction of the plating onset. Experimental parameterization is needed as each cell has a specific geometry and the transport parameters are material and geometry-dependent. Literature values are scattered and often do not provide information on the electrode geometry. In this study, a non-isothermal electrochemical 3D model was experimentally parameterized and used to investigate the lithium plating onset at low temperatures. The whole set of geometrical, transport and kinetic model parameters were determined at different temperatures and states of charge and the results were validated against the individual potentials of a multi-layer pouch cell. Good predictions of lithium plating onset were obtained. The study shows that the model can be used to develop fast-charging strategies for commercial lithium-ion batteries at low temperatures.
•Non-isothermal electrochemical model for Lithium ion batteries.•Model validation using a reference electrode inside the commercial cell.•Experimental model parameterization at different temperatures and SOCs.•Lithium plating prediction experimentally validated against the anode potential voltage and by means of post-mortem analysis.
To predict the temperature profile in an ohmic reactor, it is essential to know the thermal and electrical conductivity of the reactor geometry. Those properties can be considered on different ...modeling scales: On the detailed (resolved) scale, the reactor consists of a packed bed structure, where the properties of each substance are considered. On the effective (continuum) scale, the packed bed is considered as effective medium with composite properties. In this contribution, we consider both scales and compare the results. Based on the detailed description with a resolved microstructure, the bed's effective thermal and electrical conductivity are computed. These properties are compared with analytical formulas. The electrical conductivity is the basis for the electrical field and the current density. Finally, these properties are used to evaluate the ohmic heating of the packed bed exposed to flow and to compute the temperature distribution within the reactor.
The modeling and simulation of ohmic heating in a packed bed reactor is presented. Two different modeling scales are considered and compared. Therefore, effective properties of the detailed scale and analytical formulas of the effective scale are investigated. Those properties are used to compute the temperature distribution.
A nonlinear initial boundary value problem for the lithium ion concentration, the electric potential and the electrode-electrolyte interface currents is introduced on the microscale. The model ...enables the resolution of porous electrode microstructures. Different exchange current densities for Butler–Volmer interface conditions are evaluated. The Cahn–Hilliard equation is used to describe the phase transition from solid-solution diffusion to two-phase dynamics. The resulting phase-field model is then discretized on a regular mesh. A first-order finite-volume scheme with an adaptive time integration method is applied. The parameters and their effects in the non-convex Helmholtz energy are investigated and explained. Furthermore, the numerical convergence of the scheme is examined. In order to illustrate the method, the charging process of several single-particles and a complex structure is numerically simulated.
•All-solid-state lithium batteries using TiS2 diffusion-dependent cathode are presented.•Morphological change of TiS2 is critical to enhancing interparticle lithium-ion diffusion.•The proposed ...electrode delivers specific energy densities of 414 Wh/kgelectrode and 1155 Wh/Lelectrode.
All-solid-state lithium batteries require a well-designed electrode structure to efficiently charge and discharge active materials. Mimicking electrodes impregnated with liquid electrolyte in lithium-ion batteries, composite-type all-solid-state electrodes have been widely utilized. An alternative electrode configuration is the diffusion-dependent electrode, which consists mostly of active material. Unlike the composite electrode, which uses lithium-ion transport via a percolated solid electrolyte, the diffusion-dependent electrode uses interparticle lithium-ion diffusion through active material particles with a seamless interface. In this design, the energy density dramatically increases owing to the increased content of active material in the electrode. Herein, titanium disulfide (TiS2) is systematically explored as an appropriate material applicable as a diffusion-dependent cathode owing to its outstanding mechanical and electrochemical properties. Based on the morphology-based study of TiS2 particles, the diffusion-dependent cathode composed of spherical TiS2 nanoparticles stably delivers high areal and volumetric capacities of ~ 9.43 mAh/cm2 and ~ 578 mAh/cm3, respectively, at a loading level of 45.6 mg/cm2, which corresponds to specific energy densities of 414 Wh/kgelectrode and 1155 Wh/Lelectrode. The proposed TiS2 electrode, which can be fabricated by a practical slurry-based process using a conventional binder and solvent, is a strong candidate as a cathode for commercially available all-solid-state lithium batteries.
High-performance all-solid-state lithium batteries employing TiS2 diffusion-dependent cathode are proposed. This novel electrode, which consists mostly of TiS2 active material, can deliver high areal and volumetric capacity of ~ 9.43 mAh/cm2 and ~ 578 mAh/cm3 at a loading level of 45.6 mg/cm2, utilizing the morphology-induced facile lithium-ion diffusion between TiS2 particles. Display omitted
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