Review on Multi-Scale Models of Solid-Electrolyte Interphase Formation

Electrolyte reduction products form the solid-electrolyte interphase (SEI) on negative electrodes of lithium-ion batteries. Even though this process practically stabilizes the electrode-electrolyte interface, it results in continued capacity-fade limiting lifetime and safety of lithium-ion batteries. Recent atomistic and continuum theories give new insights into the growth of structures and the transport of ions in the SEI. The diffusion of neutral radicals has emerged as a prominent candidate for the long-term growth mechanism, because it predicts the observed potential dependence of SEI growth.Comment: 8 pages, 4 figure

Theory of reactions at electrified interfacess

Interfacial reaction and transport processes are a decisive factor for the overall performance of electrochemical systems. However, existing models rely on phenomenological descriptions of charged interfaces, which yields no deeper insights. We present a generic theory to describe charge and electron transfer reactions at charged interfaces, which is applicable to different electrochemical systems, like fuel cells or batteries with liquid or solid electrolytes. In the present work, our general theory is adopted to the electrochemical double layer at the interface between a solid electrode and a liquid electrolyte. The model allows to describe the intercalation reaction in Li-ion insertion batteries as a two-step process, consisting of a first desolvation and adsorption and a second actual insertion step. It becomes apparent that a charging of the double layer acts as the necessary driving force for the charge transfer across the interface

Modeling of adsorption processes at nanostructured cathodes in lithium-sulfur batteries

Due to its high theoretical energy density lithium-sulfur batteries are one of the most promising candidates for future energy storage. This position is further based on low costs, an intrinsic overload protection, non-toxicity and the natural abundance of its compounds [1]. Nevertheless even after 5 decades of research lithium-sulfur cells are still far away from a commercialization. All occurring challenges in the operation of lithium-sulfur batteries are associated with intermediate species, which are produced when lithium reacts with sulfur [2]. These lithium polysufides differ in their chain length and their solubility. Soluble polysulfides generate a redox shuttle between cathode and anode, while insoluble polysulfides precipitate on the anode. This leads to a reduction of active sulfur and to a corrosion and polarization of the anode. One strategy to overcome this is a structuring of the cathode to retain soluble lithium polysulfides [3]. We present a thermodynamically consistent continuum model for nanostructured sulfur carbon composite cathodes. All polysulfides are assumed to be contained in carbon particles. Particular emphasis is put to the adsorption of Li ions on the carbon surface and covers the influence of the electrochemical double-layer. The surface effects are modeled from electrostatic considerations only, without assuming structural properties of the double-layer. Therefore, the model allows us insight into the chemical and physical processes at the electrode-electrolyte interface as well as their influence on the operation of a Li-S battery. [1] L.F. Nazar et al., J. Mater. Chem., 20, 9821-9826, (2010). [2] S.S. Zhang, J. Power Sources 231, 153-162, (2013). [3] G. Zheng, Nano Lett. 11, 4462-4467, (2011)

Modeling Nucleation and Growth of Zinc Oxide During Discharge of Primary Zinc-Air Batteries

Metal-air batteries are among the most promising next-generation energy storage devices. Relying on abundant materials and offering high energy densities, potential applications lie in the fields of electro-mobility, portable electronics, and stationary grid applications. Now, research on secondary zinc-air batteries is revived, which are commercialized as primary hearing aid batteries. One of the main obstacles for making zinc-air batteries rechargeable is their poor lifetime due to the degradation of alkaline electrolyte in contact with atmospheric carbon dioxide. In this article, we present a continuum theory of a commercial Varta PowerOne button cell. Our model contains dissolution of zinc and nucleation and growth of zinc oxide in the anode, thermodynamically consistent electrolyte transport in porous media, and multi-phase coexistance in the gas diffusion electrode. We perform electrochemical measurements and validate our model. Excellent agreement between theory and experiment is found and novel insights into the role of zinc oxide nucleation and growth and carbon dioxide dissolution for discharge and lifetime is presented. We demonstrate the implications of our work for the development of rechargeable zinc-air batteries.Comment: 16 pages, 8 figures, Supplementary Information uploaded as ancillary fil

B. B. G. K. Y. Hierarchy Methods for Sums of Lyapunov Exponents for Dilute Gases

We consider a general method for computing the sum of positive Lyapunov exponents for moderately dense gases. This method is based upon hierarchy techniques used previously to derive the generalized Boltzmann equation for the time dependent spatial and velocity distribution functions for such systems. We extend the variables in the generalized Boltzmann equation to include a new set of quantities that describe the separation of trajectories in phase space needed for a calculation of the Lyapunov exponents. The method described here is especially suitable for calculating the sum of all of the positive Lyapunov exponents for the system, and may be applied to equilibrium as well as non-equilibrium situations. For low densities we obtain an extended Boltzmann equation, from which, under a simplifying approximation, we recover the sum of positive Lyapunov exponents for hard disk and hard sphere systems, obtained before by a simpler method. In addition we indicate how to improve these results by avoiding the simplifying approximation. The restriction to hard sphere systems in $d$-dimensions is made to keep the somewhat complicated formalism as clear as possible, but the method can be easily generalized to apply to gases of particles that interact with strong short range forces.Comment: submitted to CHAOS, special issue, T. Tel. P. Gaspard, and G. Nicolis, ed

New Reduced‐Order Lithium‐Ion Battery Model to Account for the Local Fluctuations in the Porous Electrodes

Numerical simulations of microscopic transport processes in porous electrodes of lithium‐ion batteries demonstrate the presence of spatially localized fluctuations of physical quantities on the microstructure scale. They can influence the macroscopic battery characteristics (for example, the degradation rates). These fluctuations cannot be captured in a straightforward manner by the widely used porous electrode theory by Doyle, Fuller, and Newman (DFN model). The latter treats the porous electrodes as macroscopically homogeneous composite materials; it reduces the computational costs of numerical simulations. Herein, a modification of the DFN model that incorporates the local fluctuations but preserves the computational efficiency is proposed. Numerical simulation examples are presented that test the accuracy of the reproduction of the local fluctuations. The main new feature lies in the mathematical representation of the slow transport processes in the active material and their influence on the macroscopic reaction rates. The model is rooted in the rigorous mathematical analysis of the transition from a microscopic, microstructure‐resolving transport and reaction description to a macroscopic, volume averaging‐based one. The model construction methodology is open for further modifications for the applications in which some of the assumptions should be dropped, or description of new processes, reactions, phases, etc. should be incorporated

Modelling and Simulation of Zinc-Air Batteries with Aqueous Electrolytes

Primary zinc-air batteries have long been an industry standard for low-power applications like hearing aids. Their high theoretical specific energy (1086 Wh ∙ kg-1), use of cheap and non-hazardous materials, and superior operational safety make secondary zinc-air batteries desirable for emerging markets such as electric vehicles or grid storage. But effects including poor cycling stability of the anode, carbonate formation in the alkaline electrolyte, and the lack of a suitable bi-functional air catalyst have limited their use. The Horizon 2020 project Zinc Air Secondary (ZAS!) aims to develop a high-performance rechargeable zinc-air battery capable of achieving more than 1000 cycles. Modelling and simulation of novel cell materials and architectures provides crucial support towards achieving this goal. We have developed a 1D finite volume continuum model implemented in MATLAB. Our model includes a thermodynamically consistent description of mass transport in concentrated ternary electrolytes, multi-phase coexistence in porous media, and reaction kinetics with considerations for anode passivation due to types I and II ZnO, among other effects. Within this framework, we simulate cell performance and lifetime considering various material com-positions and cell architectures. Initial results show that inhomogeneous Zn dissolution and ZnO precipitation in 32 wt% KOH may lead to significant mass transport limitations, particularly at higher current densi-ties. Furthermore, under certain operating conditions type II ZnO may form on the zinc elec-trode surface, permanently shutting down the cell. To address these issues and improve overall performance the effect

The Role of Energy Scales for the Structure of Ionic Liquids at Electrified Interfaces: A Theory-Based Approach

Ionic liquids offer unique bulk and interfacial characteristics as battery electrolytes. Our continuum approach naturally describes the electrolyte on a macroscale. An integral formulation for the molecular repulsion,which can be quantitatively determined by both experimental and theoretical methods, models the electrolyteon the nanoscale. In this article, we perform a systematic series expansion of this integral formulation, derive a description of chemical potentials in terms of higher-order concentration gradients, and rationalize the appearance of fourth-order derivative-operators in modified Poisson equations, recently proposed in this context. In this way, we formulate a rigorous multi-scale methodology from atomistic quantum chemistry calculations to phenomenologic continuum models. We apply our generalized framework to ionic liquids near electrified interfaces and perform analytic asymptotic analysis. Three energy scales describing electrostatic forces between ions, molecular repulsion, and thermal motion determine the shape and width of the long-ranging charged double layer. We classify the charge screening mechanisms dependent on the system parameters dielectricity, ionsize, interaction strength, and temperature. We find that the charge density of electrochemical double layers in ionic liquids either decays exponentially, for negligible molecular repulsion, or oscillates continuously. Charge ordering across several ion-diameters occurs if the repulsion between molecules is comparable with thermal energy and Coulomb interaction. Eventually, phase separation of the bulk electrolyte into ionic layers emerges once the molecular repulsion becomes dominant. Our framework predicts the exact phase boundaries between these three phases as function of temperature, dielectricity and ion-sizes