An effective model for sodium insertion in hard carbons.

Sodium ion batteries (NIBs) are a potential alternative to Lithium ion batteries (LIBs) because of their lower cost and greater availability. As anodes, hard carbons (HCs) seem to be the most promising candidates for NIBs. Previous numerical theoretical research studies have focussed on the general conditions for Na insertion in HCs, while experiments have shown that the properties of Na insertion in HCs depend strongly on specific material properties of HCs. Our target is building an effective model based on experimental data and the volume expansion phenomenon as a base for constructing chemical potentials and free energies efficiently as the starting point for continuum modeling of intercalation in HCs. In our effective model, HC is treated implicitly, while Na is simulated in a confined space, created by the HC. To reproduce the complex intercalation behavior of Na, different intercalation sites at different energy levels must be introduced. The results show good agreement with the experimental data and clarify the contribution of different Na insertion sites and the exchange between different sites of Na to the open circuit voltage as well as their contribution to the reversible and irreversible capacity of Na in HCs.

A volume-based description of transport in incompressible liquid electrolytes and its application to ionic liquids.

Transference numbers play an important role in understanding the dynamics of electrolytes and assessing their performance in batteries. Unfortunately, these transport parameters are difficult to measure in highly concentrated liquid electrolytes such as ionic liquids. Also, the interpretation of their sign and magnitude has provoked an ongoing debate in the literature further complicated by the use of different languages. In this work, we highlight the role of the reference frame for the interpretation of transport parameters using our novel thermodynamically consistent theory for highly correlated electrolytes. We argue that local volume conservation is a key principle in incompressible liquid electrolytes and use the volume-based drift velocity as a reference. We apply our general framework to electrophoretic NMR experiments. For ionic liquid based electrolytes, we find that the results of the eNMR measurements can be best described using this volume-based description. This highlights the limitations of the widely used center-of-mass reference frame which for example forms the basis for molecular dynamics simulations - a standard tool for the theoretical calculation of transport parameters. It shows that the assumption of local momentum conservation is incorrect in those systems on the macroscopic scale.

Origin of Heterogeneous Stripping of Lithium in Liquid Electrolytes.

Lithium metal batteries suffer from low cycle life. During discharge, parts of the lithium are not stripped reversibly and remain isolated from the current collector. This isolated lithium is trapped in the insulating remaining solid-electrolyte interphase (SEI) shell and contributes to the capacity loss. However, a fundamental understanding of why isolated lithium forms and how it can be mitigated is lacking. In this article, we perform a combined theoretical and experimental study to understand isolated lithium formation during stripping. We derive a thermodynamic consistent model of lithium dissolution and find that the interaction between lithium and SEI leads to locally preferred stripping and isolated lithium formation. Based on a cryogenic transmission electron microscopy (cryo TEM) setup, we reveal that these local effects are particularly pronounced at kinks of lithium whiskers. We find that lithium stripping can be heterogeneous both on a nanoscale and on a larger scale. Cryo TEM observations confirm our theoretical prediction that isolated lithium occurs less at higher stripping current densities. The origin of isolated lithium lies in local effects, such as heterogeneous SEI, stress fields, or the geometric shape of the deposits. We conclude that in order to mitigate isolated lithium, a uniform lithium morphology during plating and a homogeneous SEI are indispensable.

Local Volume Conservation in Concentrated Electrolytes Is Governing Charge Transport in Electric Fields.

While ion transport processes in concentrated electrolytes, e.g., based on ionic liquids (IL), are a subject of intense research, the role of conservation laws and reference frames is still a matter of debate. Employing electrophoretic NMR, we show that momentum conservation, a typical prerequisite in molecular dynamics (MD) simulations, is not governing ion transport. Involving density measurements to determine molar volumes of distinct ion species, we propose that conservation of local molar species volumes is the governing constraint for ion transport. The experimentally quantified net volume flux is found to be zero, implying a nonzero local momentum flux, as tested in pure ILs and IL-based electrolytes for a broad variety of concentrations and chemical compositions. This constraint is consistent with incompressibility, but not with a local application of momentum conservation. The constraint affects the calculation of transference numbers as well as comparisons of MD results to experimental findings.

Machine Learning-Based Lifetime Prediction of Lithium-Ion Cells.

Precise lifetime predictions for lithium-ion cells are crucial for efficient battery development and thus enable profitable electric vehicles and a sustainable transformation towards zero-emission mobility. However, limitations remain due to the complex degradation of lithium-ion cells, strongly influenced by cell design as well as operating and storage conditions. To overcome them, a machine learning framework is developed based on symbolic regression via genetic programming. This evolutionary algorithm is capable of inferring physically interpretable models from cell aging data without requiring domain knowledge. This novel approach is compared against established approaches in case studies, which represent common tasks of lifetime prediction based on cycle and calendar aging data of 104 automotive lithium-ion pouch-cells. On average, predictive accuracy for extrapolations over storage time and energy throughput is increased by 38% and 13%, respectively. For predictions over other stress factors, error reductions of up to 77% are achieved. Furthermore, the evolutionary generated aging models meet requirements regarding applicability, generalizability, and interpretability. This highlights the potential of evolutionary algorithms to enhance cell aging predictions as well as insights.

Elucidating the Role of Microstructure in Thiophosphate Electrolytes - a Combined Experimental and Theoretical Study of ß-Li3 PS4.

Solid-state batteries (SSBs) are promising candidates to significantly exceed the energy densities of today's state-of-the-art technology, lithium-ion batteries (LIBs). To enable this advancement, optimizing the solid electrolyte (SE) is the key. ß-Li3 PS4 (ß-LPS) is the most studied member of the Li2 S-P2 S5 family, offering promising properties for implementation in electric vehicles. In this work, the microstructure of this SE and how it influences the electrochemical performance are systematically investigated. To figure this out, four batches of ß-LPS electrolyte with different particle size, shape, and porosity are investigated in detail. It is found that differences in pellet porosities mostly originate from single-particle intrinsic features and less from interparticle voids. Surprisingly, the ß-LPS electrolyte pellets with the highest porosity and larger particle size not only show the highest ionic conductivity (up to 0.049 mS cm-1 at RT), but also the most stable cycling performance in symmetrical Li cells. This behavior is traced back to the grain boundary resistance. Larger SE particles seem to be more attractive, as their grain boundary contribution is lower than that of denser pellets prepared using smaller ß-LPS particles.

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 electrolyte on 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, as recently proposed in this context. In this way, we formulate a rigorous multiscale methodology from atomistic quantum chemistry calculations to phenomenological continuum models. We apply our generalized framework to ionic liquids near electrified interfaces and perform analytical 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 as dielectricity, ion size, 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 interactions. Eventually, phase separation of the bulk electrolyte into ionic layers emerges once the molecular repulsion becomes dominant. Our framework predicts the exact phase boundaries among these three phases as a function of temperature, dielectricity, and ion size.

Modeling of Electron-Transfer Kinetics in Magnesium Electrolytes: Influence of the Solvent on the Battery Performance.

The performance of rechargeable magnesium batteries is strongly dependent on the choice of electrolyte. The desolvation of multivalent cations usually goes along with high energy barriers, which can have a crucial impact on the plating reaction. This can lead to significantly higher overpotentials for magnesium deposition compared to magnesium dissolution. In this work we combine experimental measurements with DFT calculations and continuum modelling to analyze Mg deposition in various solvents. Jointly, these methods provide a better understanding of the electrode reactions and especially the magnesium deposition mechanism. Thereby, a kinetic model for electrochemical reactions at metal electrodes is developed, which explicitly couples desolvation to electron transfer and, furthermore, qualitatively takes into account effects of the electrochemical double layer. The influence of different solvents on the battery performance is studied for the state-of-the-art magnesium tetrakis(hexafluoroisopropyloxy)borate electrolyte salt. It becomes apparent that not necessarily a whole solvent molecule must be stripped from the solvated magnesium cation before the first reduction step can take place. For Mg reduction it seems to be sufficient to have one coordination site available, so that the magnesium cation is able to get closer to the electrode surface. Thereby, the initial desolvation of the magnesium cation determines the deposition reaction for mono-, tri- and tetraglyme, whereas the influence of the desolvation on the plating reaction is minor for diglyme and tetrahydrofuran. Overall, we can give a clear recommendation for diglyme to be applied as solvent in magnesium electrolytes.

Solid-Electrolyte Interphase During Battery Cycling: Theory of Growth Regimes.

The capacity fade of modern lithium ion batteries is mainly caused by the formation and growth of the solid-electrolyte interphase (SEI). Numerous continuum models support its understanding and mitigation by studying SEI growth during battery storage. However, only a few electrochemical models discuss SEI growth during battery operation. In this article, a continuum model is developed that consistently captures the influence of open-circuit potential, current direction, current magnitude, and cycle number on the growth of the SEI. The model is based on the formation and diffusion of neutral lithium atoms, which carry electrons through the SEI. Recent short- and long-term experiments provide validation for our model. SEI growth is limited by either reaction, diffusion, or migration. For the first time, the transition between these mechanisms is modelled. Thereby, an explanation is provided for the fading of capacity with time t of the form tß with the scaling coefficent ß, 0≤ß≤1. Based on the model, critical operation conditions accelerating SEI growth are identified.

Modeling of Ion Agglomeration in Magnesium Electrolytes and its Impacts on Battery Performance.

The choice of electrolyte has a crucial influence on the performance of rechargeable magnesium batteries. In multivalent electrolytes an agglomeration of ions to pairs or bigger clusters may affect the transport in the electrolyte and the reaction at the electrodes. In this work the formation of clusters is included in a general model for magnesium batteries. In this model, the effect of cluster formation on transport, thermodynamics and kinetics is consistently taken into account. The model is used to analyze the effect of ion clustering in magnesium tetrakis(hexafluoroisopropyloxy)borate in dimethoxyethane as electrolyte. It becomes apparent that ion agglomeration is able to explain experimentally observed phenomena at high salt concentrations.

Analysis of Interfacial Effects in All-Solid-State Batteries with Thiophosphate Solid Electrolytes.

All-solid-state batteries (ASSBs) present a promising route toward safe and high-power battery systems in order to meet the future demands in the consumer and automotive market. Composite cathodes are one way to boost the energy density of ASSBs compared to thin-film configurations. In this manuscript, we investigate composites consisting of ß-Li3PS4 (ß-LPS) solid electrolyte and high-energy Li(Ni0.6Mn0.2Co0.2)O2 (NMC622). The fabricated cells show a good cycle life with a satisfactory capacity retention. Still, the cathode utilization is below the values reported in the literature for systems with liquid electrolytes. The common understanding is that interface processes between the active material and solid electrolyte are responsible for the reduced performance. In order to throw some light on this topic, we perform 3D microstructure-resolved simulations on virtual samples obtained via X-ray tomography. Through this approach, we are able to correlate the composite microstructure with electrode performance and impedance. We identify the low electronic conductivity in the fully lithiated NMC622 as material inherent restriction preventing high cathode utilization. Moreover, we find that geometrical properties and morphological changes of the microstructure interact with the internal and external interfaces, significantly affecting the capacity retention at higher currents.

The electrochemical double layer and its impedance behavior in lithium-ion batteries.

Interfacial reaction and transport processes contribute crucially to the overall performance and impedance of electrochemical systems. The influence of the electrochemical double layer and the interfacial reactions on the impedance of lithium intercalation batteries is investigated with a modeling approach. Our generic theory for charge and electron transfer reactions at electrified interfaces and its simplified adaptation, a reduced interface model, are compared with the standard for electrochemical interface modeling, the Butler-Volmer ansatz, in terms of numerically simulated impedance spectra. Both of our interface models inherently provide significant impedance characteristics that go beyond the standard approach due to their theoretically consistent derivation. We discuss resistant and capacitive contributions of the double layer to impedance spectra and analyze the effect of strongly correlated interfacial dynamics.

Modeling of the electrochemical double layer and its impact on intercalation reactions.

We deduce a generic interface theory to describe charge and electron transfer reactions at electrified interfaces based on fundamental principles. Considering the contact between a solid electrode and a liquid electrolyte, the model allows the consistent determination of emerging electric fields and space charge layers at the interface. The interaction between charge transport and the electrochemical double layer at the boundary between the electrode and electrolyte is investigated. Time scales of interfacial reaction and transport processes are analyzed. Further, we present a reduced bulk model of the electrochemical interface, which allows us to incorporate properties of the electrochemical double layer as extended boundary conditions in transport models of lithium-ion batteries. Numerically less intensive, the reduced model builds a bridge between our detailed description of reactions at electrified interfaces and commonly used modeling approaches for electrode reactions. With both the full and the reduced model, we simulate the impedance response of an electrochemical cell.

High Capacity Garnet-Based All-Solid-State Lithium Batteries: Fabrication and 3D-Microstructure Resolved Modeling.

The development of high-capacity, high-performance all-solid-state batteries requires the specific design and optimization of its components, especially on the positive electrode side. For the first time, we were able to produce a completely inorganic mixed positive electrode consisting only of LiCoO2 and Ta-substituted Li7La3Zr2O12 (LLZ:Ta) without the use of additional sintering aids or conducting additives, which has a high theoretical capacity density of 1 mAh/cm2. A true all-solid-state cell composed of a Li metal negative electrode, a LLZ:Ta garnet electrolyte, and a 25 µm thick LLZ:Ta + LiCoO2 mixed positive electrode was manufactured and characterized. The cell shows 81% utilization of theoretical capacity upon discharging at elevated temperatures and rather high discharge rates of 0.1 mA (0.1 C). However, even though the room temperature performance is also among the highest reported so far for similar cells, it still falls far short of the theoretical values. Therefore, a 3D reconstruction of the manufactured mixed positive electrode was used for the first time as input for microstructure-resolved continuum simulations. The simulations are able to reproduce the electrochemical behavior at elevated temperature favorably, however fail completely to predict the performance loss at room temperature. Extensive parameter studies were performed to identify the limiting processes, and as a result, interface phenomena occurring at the cathode active material/solid-electrolyte interface were found to be the most probable cause for the low performance at room temperature. Furthermore, the simulations are used for a sound estimation of the optimization potential that can be realized with this type of cell, which provides important guidelines for future oxide based all-solid-state battery research and fabrication.

Identifying the Mechanism of Continued Growth of the Solid-Electrolyte Interphase.

Continued growth of the solid-electrolyte interphase (SEI) is the major reason for capacity fade in modern lithium-ion batteries. This growth is made possible by a yet unidentified transport mechanism that limits the passivating ability of the SEI towards electrolyte reduction. We, for the first time, differentiate the proposed mechanisms by analyzing their dependence on the electrode potential. Our calculations are compared to recent experimental capacity-fade data. We show that the potential dependence of SEI growth facilitated by solvent diffusion, electron conduction, or electron tunneling qualitatively disagrees with the experimental observations. Only diffusion of Li interstitials results in a potential dependence matching the experiments. Therefore, we identify the diffusion of neutral radicals, such as Li interstitials, as the cause of long-term SEI growth.

Influence of a silver salt on the nanostructure of a Au(111)/ionic liquid interface: an atomic force microscopy study and theoretical concepts.

Ionic liquids (ILs) form a multilayered structure at the solid/electrolyte interface, and the addition of solutes can alter it. For this purpose, we have investigated the influence of the silver bis(trifluoromethylsulfonyl)amide (AgTFSA) concentration in 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide ([Py1,4]TFSA) on the layering using in situ atomic force microscopy. AFM investigations revealed that the Au(111)/electrolyte interface indeed depends on the concentration of the salt where a typical " IL" multilayered structure is retained only at quite low concentrations of the silver salt (e.g. ≤200 µM). However, at 200 µM AgTFSA/[Py1,4]TFSA and above this "IL" multilayered structure is disturbed/varied. A simple double layer structure was observed at 500 µM AgTFSA in [Py1,4]TFSA. Furthermore, the widths of the innermost layers have been found to be dependent on the concentration and on the applied electrode potentials. Our AFM results show that the concentration of solutes strongly influences the structure of the electrode/electrolyte interface and can provide new insights into the electrical double layer structure of the electrode/ionic liquid interface. We also introduce a semi-continuum theory to discuss the double layer structure.

Rational Development of Neutral Aqueous Electrolytes for Zinc-Air Batteries.

Neutral aqueous electrolytes have been shown to extend both the calendar life and cycling stability of secondary zinc-air batteries (ZABs). Despite this promise, there are currently no modeling studies investigating the performance of neutral ZABs. Traditional continuum models are numerically insufficient to simulate the dynamic behavior of these complex systems because of the rapid, orders-of-magnitude concentration shifts that occur. In this work, we present a novel framework for modeling the cell-level performance of pH-buffered aqueous electrolytes. We apply our model to conduct the first continuum-scale simulation of secondary ZABs using aqueous ZnCl2 -NH4 Cl as electrolyte. We first use our model to interpret the results of two recent experimental studies of neutral ZABs, showing that the stability of the pH value is a significant factor in cell performance. We then optimize the composition of the electrolyte and the design of the cell considering factors including pH stability, final discharge product, and overall energy density. Our simulations predict that the effectiveness of the pH buffer is limited by slow mass transport and that chlorine-containing solids may precipitate in addition to ZnO.

Dynamics and morphology of solid electrolyte interphase (SEI).

We develop a novel theory for the continuous electrochemical formation of porous films to study the solid electrolyte interphase (SEI) on lithium ion battery anodes. Existing SEI studies model a homogeneous morphology and a single relevant transport mechanism. Our approach, in contrast, is based on two transport mechanisms and enables us to track SEI porosity in a spatially resolved way. SEI thickness evolution agrees with existing studies and is validated with experiments. This consistent approach is unprecedented in SEI modeling. We predict a non-zero SEI porosity and the dependence of morphology on transport properties. Additionally, we capture dual-layer chemistry and morphology. Analytic expressions which describe the parameter dependence of all key properties are derived and discussed.

Theory of reactions at electrified interfaces.

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.

Multiscale modeling of lithium ion batteries: thermal aspects.

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.