In this thesis a method is presented for the modelling the effects of the excluded volume (ion-ion) and ion excess polarisability (ion-solvent) interactions in an electrolyte at a smooth planar electrode. The impact of these interactions is studied in terms of the equilibrium state of single and mixed electrolytes, the dynamic response of single electrolytes to a time-dependent applied potential, and their effect on the reaction rate, for both steady and time-dependent applied potentials. For reacting systems, the reaction rate is modelled using a modified form of the Frumkin-Butler-Volmer equation, in which the interactions are explicitly accounted for. At equilibrium, the model offers improvement over models which only account for the excluded volume interaction, in terms of both the predicted electrolyte structure and the electrical properties of the electrode. For example accounting for the polarisability interaction is shown to limit and then reverse the growth in the differential capacitance at the point of zero charge as the bulk concentration increases, an effect is not seen when only the excluded volume interaction is accounted for. Another example is for mixed electrolytes, in which accounting for the polarisability interaction leads to better agreement with experimental data regarding the composition of the double layer. For the response of an electrolyte to a potential step, the two interactions both lead to peaks in the time taken to reach equilibrium as a function of the potential. The effect of the domain length on the equilibration time is qualitatively discussed, together with the differences between the two interaction models. The response to a time-dependent potential is analysed through simulated electrochemical impedance spectroscopy and consideration of the capacitance dispersion effect. Between this and the potential step response data it is shown that the interactions themselves have little direct effect on the dynamic processes beyond the way in which they limit the ion concentrations in the double layer and alter the differential capacitance of the system. The investigation of the effect of the ion interactions on the reaction rate shows that both terms can either increase or decrease the rate, relative to a system with no interactions, depending on the details of the reaction and the applied potential. This is linked to the changes in the electric field within the double layer, which are caused by the interactions, and how this affects the reactant flux in that region. In terms of simulated EIS, deviations are observed relative to the equivalent circuit for the system, the reasons for which are discussed.

Ce travail comprend deux volets. Un premier volet plus « stratégique » concernant l’importance du stockage pour les énergies renouvelables. Un deuxième volet de plus en plus technique et de plus en plus précis concernant le positionnement du stockage électrochimique, la place qu’y tient la batterie Plomb Acide, les variantes technologiques, pour arriver à une modélisation électrochimique détaillée du type de batterie retenu. Dans le premier volet, le chapitre 1 de la thèse met en évidence le bon positionnement du stockage électrochimique pour les besoins des énergies renouvelables. Vis-à-vis des fluctuations aléatoires de la ressource, le temps est un élément important de la discussion : temps de stockage d’une part, temps de mobilisation de l’énergie stocké d’autre part. A cet égard, le cahier des charges pour le lissage de production d’une unité connectée au réseau est bien différent des applications de stockage pour un système de production autonome. Le deuxième chapitre devient plus technique, à l’occasion de la comparaison de la batterie au plomb avec les autres systèmes de stockage. L’idée directrice est d’appuyer cette discussion sur des arguments liés au bases physiques de fonctionnement des composants étudiés : c’est en même temps un prétexte pour commencer l’introduction de principes de bases d’électrochimie qui seront développés et utilisés par la suite. On a raisonné sur trois grandes familles : accumulateurs (exemples batterie au plomb, NiMH, Lithium ion), systèmes de type redox ou plus généralement combustible externe (exemple pile à combustible) et super capacités. Comparaison globalement peu flatteuse pour les performances moyennes de la batterie au plomb, sauvée par son bon rapport performances/prix. Le troisième chapitre entre dans le détail des variantes technologiques, qui démontre une grande flexibilité permettant des compromis pour s’adapter à des besoins spécifiques très variés. On s’est attaché à chercher les aspects spécifiques peu explorés pouvant mener à des améliorations, notamment au niveau de mécanismes réactionnels mis en évidence récemment, 2 En particulier au niveau de l’électrode positive (en liaison notamment avec la mise en évidence par Pavlov d’une phase intermédiaire entre PbO2 et l’électrolyte, de gel Pb(OH)2, aux propriétés mal élucidées). Nous avons placé dans ce chapitre une analyse détaillée de l’hydrolyse, prenant en compte la recombinaison directe de O2 et H2 à l’électrode négative citée également par Pavlov. Ces éléments seront directement repris et complétés au chapitre 4 en modélisation. Le chapitre 4, consacrée à la modélisation et l’expérimentation est l’aboutissement du travail progressif d’introduction de bases d’électrochimie appliquées à la batterie. Il va souligner le rôle central des mécanismes de diffusion/migration dans le fonctionnement. Un premier volet « mathématique » concerne une approximation des équations de diffusion par un réseau de composants discret, optimale du point de vue du nombre de composants. Le modèle global de la batterie peu schématiquement être décomposées en trois grandes fonctions : diffusion, activation, hydrolyse. Ces fonctions sont interconnectées, mais on s’efforcera de les introduire successivement sous forme découplée (au moins de façon approchée). Une première étape est d’obtenir, en grande partie à partir d’expérimentations spécifiques, des valeurs réalistes des paramètres du modèle. Les simulations effectuées démontrent la capacité du modèle à décrire correctement le comportement de la batterie dans les situations les plus variées. / This work has two parts. A first more "strategic" part concerning the importance of storage for renewable energies. An increasingly technical and increasingly precise part concerning the positioning of the electrochemical storage, the position of the Lead Acid battery, the technological variants, to arrive at a detailed electrochemical modeling of the type of battery retained.In the first section, Chapter 1 of the thesis highlights the good positioning of electrochemical storage for the needs of renewable energies. With respect to the random fluctuations of the resource, time is an important element of the discussion: storage time on the one hand, time of mobilization of stored energy on the other hand. In this respect, the specification for the production smoothing of a unit connected to the network is quite different from the storage applications for a stand-alone production system.The second chapter becomes more technical, when comparing the lead-acid battery with the other storage systems. The guiding idea is to support this discussion on arguments related to the physical basis of functioning of the components studied. At the same time, it is a pretext to begin the introduction of basic principles of electrochemistry that will be developed and used by the after. There are three main families: accumulators (examples lead acid battery, NiMH, Lithium ion), redox systems or more generally external fuel (example fuel cell) and super capacitors. Overall comparison unflattering for the average performance of the lead battery, saved by its good performance / price ratio.The third chapter explains the technological variants, which shows a great flexibility that allows compromises to adapt to a wide variety of specific needs. Attention has been given to identifying specific aspects which have not been explored and which can lead to improvements, in particular in the context of recent reaction mechanisms, 2In particular, at the positive electrode (linked in particular with the Pavlov demonstration of an intermediate phase between PbO 2 and the electrolyte, of Pb (OH) 2 gel, with poorly elucidated properties). In this chapter we have placed a detailed analysis of the hydrolysis, taking into account the direct recombination of O2 and H2 at the negative electrode also cited by Pavlov. These elements will be taken up and completed in Chapter 4 in modeling.Chapter 4, devoted to modeling and experimentation, is the culmination of the progressive work of introducing electrochemical bases applied to the battery. It will underline the central role of dissemination / migration mechanisms in the functioning.A first "mathematical" aspect concerns an approximation of the diffusion equations by a discrete component network, optimal in terms of the number of components. The overall model of the battery schematically be broken down into three main functions: diffusion, activation, hydrolysis. These functions are interconnected, but efforts will be made to introduce them successively in decoupled form (at least in an approximate manner). A first step is to obtain, largely from specific experiments, realistic values of the parameters of the model.

The subject of this thesis is the application of magnetic resonance methods to the characterization and quantification of lithium-ion transport in a wide range of lithium-ion battery electrolyte materials relevant to the electromobility and energy storage sectors. In particular, field-gradient magnetic resonance techniques, in the form of PFG-NMR diffusivity measurements of both liquid- and solid-state electrolytes and in situ MRI of electrochemical cells, comprise the core means by which these characterizations were performed. PFG-NMR and ionic conductivity studies of a range of liquid-state electrolyte mixtures were performed, as a function of temperature, to assess how key mass and charge transport properties reflect differences in composition. In situ MRI was used to study the effect of temperature on steady-state concentration gradient formation in polarized liquid electrolytes, with the results quantitatively compared to model predictions. This approach was then extended, using a combination of MRI and spatially-resolved PFG-NMR, to study the interlinked effects of temperature and current density on concentration gradient formation, and to attempt a comprehensive characterization of the ion transport parameters with spatial resolution. Finally, PFG-NMR and MAS-NMR were applied in a solid-state electrolyte context to investigate compositional effects on ion transport in the argyrodite family of lithium-sulphide ion conductors, and the influence of macroscopic sample format (glass, crystalline powder, compressed crystalline pellet) on micro-scale ion transport in a thio-LISICON ion conductor. Taken together, the studies demonstrate the effectiveness of magnetic resonance methods for the robust elucidation of the means by which material properties impact ion transport in technologically-relevant lithium-ion electrolyte systems. / Dissertation / Doctor of Science (PhD) / Lithium-ion batteries are a critical component of the ongoing efforts to transition the global automobile fleet to electric vehicles and integrate renewable energy sources into the electricity grid. An important aspect of designing and optimizing lithium-ion batteries is a comprehensive understanding of the factors which impact the ability of the electrolyte in the battery to ferry the lithium ions from one electrode to the other, the process which enables them to release energy into the circuit to power a device. This thesis describes results obtained from measuring the diffusion of the ions within the electrolyte for both conventional liquid-state electrolytes, and emerging solid-state electrolyte materials. It also includes studies which make use of MRI to image the flow of ions within the liquid-state electrolyte of an operating battery mimic, and monitor the concentration changes of the ions across the electrolyte as a current is applied to it.

This thesis investigates novel algorithms for enabling the use of first-principle electrochemical models for battery monitoring and control in advanced battery management systems (BMSs). Specifically, the fast solution and state estimation of a high-fidelity spatially resolved thermal-electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional (P2D) model are investigated. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the P2D model is then used in combination with an extended Kalman filter (EKF) algorithm modified for differential-algebraic equations (DAEs) to estimate the states of the model, e.g. lithium concentrations, overpotential. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1% in less than 200s despite a 30% error on battery initial state-of-charge (SoC) and additive measurement noise with 10mV and 0.5°C standard deviations. The parameter accuracy of such first-principle models is of utmost importance for the trustworthy estimation of internal battery electrochemical states. Therefore, the identifiability of the simpler single particle (SP) electrochemical model is investigated both in principle and in practice. Grouping parameters and partially non-dimensionalising the SP model equations in order to understand the maximum expected degrees of freedom in the problem reveals that there are only six unique parameters in the SP model. The structural identifiability is then examined by asking whether the transfer function of the linearised SP model is unique. It is found that the model is unique provided that the electrode open circuit voltage curves have a non-zero gradient, the parameters are ordered, and that the behaviour of the kinetics of each electrode is lumped together into a single parameter which is the charge transfer resistance. The practical estimation of the SP model parameters from frequency-domain experimental data obtained by electrochemical impedance spectroscopy (EIS) is then investigated and shows that estimation at a single SoC is insufficient to obtain satisfactory results and EIS data at multiple SoCs must be combined.

The present work is aimed at investigating the mechanisms of nanowire growth from aqueous solutions through a physical and chemical modeling. Based on this modeling, deriving an optimized process control is intended. The work considers two methods of nanowire growth. The first is the dielectrophoretic nanowire assembly from neutral molecules or metal clusters. Secondly, in the directed electrochemical nanowire assembly metal-containing ions are reduced in an AC electric field in the vicinity of the nanowire tip and afterwards deposited at the nanowire surface. To describe the transport and growth processes, continuum models are employed. Furthermore, it has been necessary to consider electro-kinetic fluid flows to match the experimental observations. The occurring partial differential equations are solved numerically by means of finite element method (FEM). The effect of the process parameters on the nanowire growth are analyzed by comparing experimental results to a parameter study. The evaluation has yielded that an AC electro-osmotic fluid flow has a major influence on the dielectrophoretic nanowire assembly regarding the growth velocity and morphology. In the case of directed electrochemical nanowire assembly, the nanowire morphology can be controlled by the applied AC signal shape. Based on the nanowire growth model, an optimized AC signal has been designed, whose parametrization allows to adjust to the chemical precursor and the desired nanowire diameter. / Ziel der vorliegenden Arbeit ist es, mittels physikalischer und chemischer Modelle die Mechanismen des Nanodrahtwachstums aus wässrigen Lösungen zu erforschen und daraus eine optimierte Prozesskontrolle abzuleiten. Dabei werden zwei Verfahren des Nanodrahtwachstums näher betrachtet: Dies sind die dielektrophoretische Assemblierung von neutralen Molekülen oder Metallclustern sowie die gerichtete elektrochemische Nanodrahtabscheidung (engl. directed electrochemical nanowire assembly), bei der metallhaltige Ionen im elektrischen Wechselfeld an der Nanodrahtspitze zunächst reduziert und anschließend als Metallatome abgeschieden werden. Zur Beschreibung der Transport- und Wachstumsprozesse werden Kontinuumsmodelle eingesetzt. Darüber hinaus hat es sich als notwendig erwiesen, elektrokinetische Fluidströmungen zu berücksichtigen, um die experimentellen Beobachtungen zu reproduzieren. Die auftretenden partiellen Differenzialgleichungen werden mittels der Finiten Elemente Methode (FEM) numerisch gelöst. Die Auswirkungen der Prozessparameter auf das Nanodrahtwachstum werden durch den Vergleich von experimentellen Ergebnissen mit Parameterstudien analysiert. Die Auswertung hat ergeben, dass für das dielektrophoretische Wachstum ein durch Wechselfeldelektroosmose (engl. AC electro-osmosis) angetriebener Fluidstrom die Drahtwachstumsgeschwindigkeit und -morphologie maßgeblich beeinflusst. Im Falle der gerichteten elektrochemischen Nanodrahtabscheidung lässt sich die Drahtmorphologie über das angelegte elektrische Wechselsignal steuern. Unter Verwendung des Wachstumsmodells ist ein optimiertes Signal generiert worden, dessen Parametrisierung eine gezielte Anpassung auf den chemischen Ausgangsstoff und den gewünschten Drahtdurchmesser erlaubt.

The present work is aimed at investigating the mechanisms of nanowire growth from aqueous solutions through a physical and chemical modeling. Based on this modeling, deriving an optimized process control is intended. The work considers two methods of nanowire growth. The first is the dielectrophoretic nanowire assembly from neutral molecules or metal clusters. Secondly, in the directed electrochemical nanowire assembly metal-containing ions are reduced in an AC electric field in the vicinity of the nanowire tip and afterwards deposited at the nanowire surface. To describe the transport and growth processes, continuum models are employed. Furthermore, it has been necessary to consider electro-kinetic fluid flows to match the experimental observations. The occurring partial differential equations are solved numerically by means of finite element method (FEM). The effect of the process parameters on the nanowire growth are analyzed by comparing experimental results to a parameter study. The evaluation has yielded that an AC electro-osmotic fluid flow has a major influence on the dielectrophoretic nanowire assembly regarding the growth velocity and morphology. In the case of directed electrochemical nanowire assembly, the nanowire morphology can be controlled by the applied AC signal shape. Based on the nanowire growth model, an optimized AC signal has been designed, whose parametrization allows to adjust to the chemical precursor and the desired nanowire diameter. / Ziel der vorliegenden Arbeit ist es, mittels physikalischer und chemischer Modelle die Mechanismen des Nanodrahtwachstums aus wässrigen Lösungen zu erforschen und daraus eine optimierte Prozesskontrolle abzuleiten. Dabei werden zwei Verfahren des Nanodrahtwachstums näher betrachtet: Dies sind die dielektrophoretische Assemblierung von neutralen Molekülen oder Metallclustern sowie die gerichtete elektrochemische Nanodrahtabscheidung (engl. directed electrochemical nanowire assembly), bei der metallhaltige Ionen im elektrischen Wechselfeld an der Nanodrahtspitze zunächst reduziert und anschließend als Metallatome abgeschieden werden. Zur Beschreibung der Transport- und Wachstumsprozesse werden Kontinuumsmodelle eingesetzt. Darüber hinaus hat es sich als notwendig erwiesen, elektrokinetische Fluidströmungen zu berücksichtigen, um die experimentellen Beobachtungen zu reproduzieren. Die auftretenden partiellen Differenzialgleichungen werden mittels der Finiten Elemente Methode (FEM) numerisch gelöst. Die Auswirkungen der Prozessparameter auf das Nanodrahtwachstum werden durch den Vergleich von experimentellen Ergebnissen mit Parameterstudien analysiert. Die Auswertung hat ergeben, dass für das dielektrophoretische Wachstum ein durch Wechselfeldelektroosmose (engl. AC electro-osmosis) angetriebener Fluidstrom die Drahtwachstumsgeschwindigkeit und -morphologie maßgeblich beeinflusst. Im Falle der gerichteten elektrochemischen Nanodrahtabscheidung lässt sich die Drahtmorphologie über das angelegte elektrische Wechselsignal steuern. Unter Verwendung des Wachstumsmodells ist ein optimiertes Signal generiert worden, dessen Parametrisierung eine gezielte Anpassung auf den chemischen Ausgangsstoff und den gewünschten Drahtdurchmesser erlaubt.