A transient model of the cathode catalyst layer of a proton exchange membrane fuel cell is presented. The catalyst layer structure can be described as a superposition of the polymer membrane, the backing layer, and some additional platinum particles. The model, which incorporates some of the features of the pseudo-homogeneous models currently present in the literature, considers the kinetics of the electrochemical reaction taking place at the platinum surface, the proton transport through the polymer agglomerates, and the oxygen and water transport within the pores as well as the membrane material of the catalyst layer. Due to the lower porosity of this region and the higher liquid water content, the catalyst layer can be current limiting in the fuel cell. Furthermore, since the cost of the catalyst material is critical, it is important to have a model predicting the effective utilization of this catalyst layer as well as one, which gives insights into how it might be improved. Equations are presented for the mass conservation of reactants and products, the electrical and ionic currents, and the conservation of energy. A discussion of a number of the closure relations such as the Butler-Volmer equation employed is included as is a discussion of the initial and boundary conditions applied. The mathematical model is solved using a finite elements approach developed at the I.U.S.T.I. / Master of Science

La modélisation mathématique des systèmes électrochimiques, et en général la modélisa- tion des systèmes fluidiques réactifs en présence de champs électriques, est un problème d’une complexité telle que des solutions analytiques n’existent que dans des cas très simpli- fiés et la solution numérique est, malgré toute la puissance de calcul moderne, encore très difficile. À ce jour, les avancées dans la modélisation au niveau des modèles d’écoulement sont majeures, mais la modélisation couplée de l’écoulement, avec le champ électrique en présence de solutions concentrées demeure encore un défi de taille. Le couplage des diffé- rents champs décrits par les modèles mathématiques devient critique dans les régions où ont lieu les réactions hétérogènes aux interfaces chargées modélisées par l’équation non linéaire de Butler-Volmer. Les logiciels commerciaux modernes commencent à permettre de coupler les modules d’électrochimie avec la mécanique des fluides numérique (CFD), mais l’ impossibilité d’ac- céder au code source ne permet pas au chercheur de modifier à volonté la formulation des modèles. Par conséquent, le projet de recherche actuel vise le développement d’une plate-forme logicielle ouverte (open-source) comme OpenFOAM, qui peut garantir une complète accessibilité au code-source, la liberté des utilisateurs à faire des modifications, la transparence des détails des modèles, et tous les autres développements qui sont requis pour chaque problème rencontré par les chercheurs. Le développement de modèles reposant sur des lois physiques établies permettra la modéli- sation des systèmes électrochimiques complexes, et la compréhension des phénomènes qui s’y déroulent. Il vise la modélisation du transfert de masse d’une cellule où l’écoulement de la solution concentrée (molten salt) est turbulent, biphasique et incompressible, et les réactions électrochimiques de surface sont calculées en utilisant une distribution tertiaire de densité de courant. Le principal enjeu sur le plan scientifique, dans le cadre de ce projet, demeure donc de développer un modèle qui soit bien calé sur le problème technologique visé afin qu’il puisse reproduire de façon réaliste les systèmes électrochimiques. Il vise éga- lement à amener la modélisation à un point où l’outil pourra être utilisé comme instrument de prédiction et de validation de nouveaux concepts des systèmes électrochimiques. / Abstract: The modeling of electrochemical systems, and in general the modeling of reacting flows ex- posed to electric field, is a complex problem to the point that analytic solutions exist only for simplified cases despite the increasing computer power. The state of art shows major improvements in the fluid-dynamics of electrochemical reactors; but the full coupling of the flow with the electric field in presence of concentrated electrolytic solutions still needs to be properly investigated. The coupling gets even more critical along the charged in- terfaces where heterogeneous reactions are modeled through the non-linear Butler-Volmer equation. Commercial software are slowly try to connect electrochemical modules to the well val- idated CFDs, but most of the time costly licenses, and poor accessibility to the source code, do not allow a deep integration between the two. Instead, this research study pro- poses an open-source code implemented in OpenFOAM, that guarantees full accessibility to the source code, user’s modifications, full transparency of the model’s details, and any possible further developments required by the specificity of the problem. The final code implements the mass transfer of a cell where the concentrated solution (molten salt) is a two-phase turbulent incompressible flow and the electrochemical surface reactions consider tertiary current distributions. The aim of this work is to create an open source platform to predict and analyze industrial reactor’s performances. The advanced modeling can be later exploited and used as a validation instrument for new electrochemical concepts.

Solid oxide fuel cells (SOFC) are mainly used as large stationary elec- tricity sources, therefore an every little improvement in their performance leads to considerable savings. In order to understand the fundamentals of the SOFC operation, we have developed a new model describing the main physical processes. The thermodynamical model of SOFC, developed in this thesis, concerns the gas transport, the transport of the charged particles in- cluding the thermoelectric effect and the electrochemical reactions. Linear irreversible thermodynamics is the key modelling framework, in which the dusty gas model and the Butler-Volmer equations are used. A new relation between the electrochemical affinity and the overpotential is introduced into the Butler-Volmer equation. A weakly formulated statinonary system en- dowed with boundary conditions is solved with the finite element method in one dimensional approximation. 1

This thesis primarily focuses on the electrochemical properties of the H₂/H⁺ redox couple, at various metallic electrodes in room temperature ionic liquids. Initially, a comprehensive overview of room temperature ionic liquids, RTILs, compared to conventional organic solvents is presented which identifies their favourable properties and applications, followed by a second chapter describing the basic theory of electrochemistry. A third chapter presents the general experimental reagents, instruments and measurements used in this thesis. The results presented in this thesis are summarized in six further chapters and shown as follows. (1) Hydrogenolysis, hydrogen loaded palladium electrodes by electrolysis of H[NTf₂] in a RTIL [C₂mim][NTf₂]. (2) Palladium nanoparticle-modified carbon nanotubes for electrochemical hydrogenolysis in RTILs. (3) Electrochemistry of hydrogen in the RTIL [C₂mim][NTf₂]: dissolved hydrogen lubricates diffusional transport. (4) The hydrogen evolution reaction in a room temperature ionic liquid: mechanism and electrocatalyst trends. (5) The formal potentials and electrode kinetics of the proton_hydrogen couple in various room temperature ionic liquids. (6) The electroreduction of benzoic acid: voltammetric observation of adsorbed hydrogen at a Platinum microelectrode in room temperature ionic liquids. The first two studies show electrochemically formed adsorbed H atoms at a metallic Pt or Pd surface can be used for clean, efficient, safe electrochemical hydrogenolysis of organic compounds in RTIL media. The next study shows the physicochemical changes of RTIL properties, arising from dissolved hydrogen gas. The last three studies looked at the electrochemical properties of H₂/H⁺ redox couple at various metallic electrodes over a range of RTILs vs a stable Ag/Ag⁺ reference couple, using H[NTf₂] and benzoic acid as proton sources. The kinetic and thermodynamic mechanisms of some reactions or processes are the same in RTILs as in conventional organic or aqueous solvents, but other remarkably different behaviours are presented. Most importantly significant constants are seen for platinum, gold and molybdenum electrodes in term of the mechanism of proton reduction to form hydrogen.

Three mathematical models, two of primary alkaline battery cathode discharge, and one of primary alkaline battery discharge, are developed, presented, solved and investigated in this thesis. The primary aim of this work is to improve our understanding of the complex, interrelated and nonlinear processes that occur within primary alkaline batteries during discharge. We use perturbation techniques and Laplace transforms to analyse and simplify an existing model of primary alkaline battery cathode under galvanostatic discharge. The process highlights key phenomena, and removes those phenomena that have very little effect on discharge from the model. We find that electrolyte variation within Electrolytic Manganese Dioxide (EMD) particles is negligible, but proton diffusion within EMD crystals is important. The simplification process results in a significant reduction in the number of model equations, and greatly decreases the computational overhead of the numerical simulation software. In addition, the model results based on this simplified framework compare well with available experimental data. The second model of the primary alkaline battery cathode discharge simulates step potential electrochemical spectroscopy discharges, and is used to improve our understanding of the multi-reaction nature of the reduction of EMD. We find that a single-reaction framework is able to simulate multi-reaction behaviour through the use of a nonlinear ion-ion interaction term. The third model simulates the full primary alkaline battery system, and accounts for the precipitation of zinc oxide within the separator (and other regions), and subsequent internal short circuit through this phase. It was found that an internal short circuit is created at the beginning of discharge, and this self-discharge may be exacerbated by discharging the cell intermittently. We find that using a thicker separator paper is a very effective way of minimising self-discharge behaviour. The equations describing the three models are solved numerically in MATLABR, using three pieces of numerical simulation software. They provide a flexible and powerful set of primary alkaline battery discharge prediction tools, that leverage the simplified model framework, allowing them to be easily run on a desktop PC.