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Author: Landstorfer, Manuel × Has files: Yes ×

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    On the Differential Capacitance and Potential of Zero Charge of Au(111) in Some Aprotic Solvents
    (Weinheim : Wiley-VCH, 2021) Shatla, Ahmed S.; Landstorfer, Manuel; Baltruschat, Helmut
    Voltammetric and Gouy-Chapman capacitance minimum measurements were conducted on Au(111) and roughened Au(111) electrodes in aprotic electrolytes in the absence and presence of specifically adsorbed ions for concentrations ranging from 0.001 to 0.5 M. Negative of the point of zero charge (pzc), the capacitance maximum increases in the order Ca2+
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    Modeling Polycrystalline Electrode-electrolyte Interfaces: The Differential Capacitance
    (Bristol : IOP Publishing, 2020) Müller, Rüdiger; Fuhrmann, Jürgen; Landstorfer, Manuel
    We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter dfacet →0 we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit 1[nm] < dfacet, an ensemble of non-interacting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces. © 2020 The Author(s). Published on behalf of The Electrochemical Society by IOP Publishing Limited.
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    A discussion of the cell voltage during discharge of an intercalation electrode for various C-rates based on non-equilibrium thermodynamics and numerical simulations
    (Bristol : IOP Publishing, 2020) Landstorfer, Manuel
    In this work we discuss the modeling procedure and validation of a non-porous intercalation half-cell during galvanostatic discharge. The modeling is based on continuum thermodynamics with non-equilibrium processes in the active intercalation particle, the electrolyte, and the common interface where the intercalation reaction Li+ + e- ↔ Li occurs. The model is in detail investigated and discussed in terms of scalings of the non-equilibrium parameters, i.e. the diffusion coefficients DA and DE of the active phase and the electrolyte, conductivity sA and sE of both phases, and the exchange current density e0L, with numerical solutions of the underlying PDE system. The current density i as well as all non-equilibrium parameters are scaled s with respect to the 1-C current density iC A of the intercalation electrode. We compute then numerically the cell voltage E as function of the capacity Q and the C-rate Ch. Within a hierarchy of approximations we provide computations of E(Q) for various scalings of the diffusion coefficients, the conductivities and the exchange current density. For the later we provide finally a discussion for possible concentration dependencies. © The Author(s) 2019. Published by ECS.
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    Boundary conditions for electrochemical interfaces
    (Bristol : IOP Publishing, 2017) Landstorfer, Manuel
    Consistent boundary conditions for electrochemical interfaces, which cover double layer charging, pseudo-capacitive effects and transfer reactions, are of high demand in electrochemistry and adjacent disciplines. Mathematical modeling and optimization of electrochemical systems is a strongly emerging approach to reduce cost and increase efficiency of super-capacitors, batteries, fuel cells, and electro-catalysis. However, many mathematical models which are used to describe such systems lack a real predictive value. Origin of this shortcoming is the usage of oversimplified boundary conditions. In this work we derive the boundary conditions for some general electrode-electrolyte interface based on non-equilibrium thermodynamics for volumes and surfaces. The resulting equations are widely applicable and cover also tangential transport. The general framework is then applied to a specific material model which allows the deduction of a current-voltage relation and thus a comparison to experimental data. Some simplified 1D examples show the range of applicability of the new approach.
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    Galilean Bulk-Surface Electrothermodynamics and Applications to Electrochemistry
    (Basel : MDPI, 2023) Müller, Rüdiger; Landstorfer, Manuel
    In this work, the balance equations of non-equilibrium thermodynamics are coupled to Galilean limit systems of the Maxwell equations, i.e., either to (i) the quasi-electrostatic limit or (ii) the quasi-magnetostatic limit. We explicitly consider a volume (Formula presented.), which is divided into (Formula presented.) and (Formula presented.) by a possibly moving singular surface S, where a charged reacting mixture of a viscous medium can be present on each geometrical entity (Formula presented.). By the restriction to the Galilean limits of the Maxwell equations, we achieve that only subsystems of equations for matter and electromagnetic fields are coupled that share identical transformation properties with respect to observer transformations. Moreover, the application of an entropy principle becomes more straightforward and finally helps estimate the limitations of the more general approach based the full set of Maxwell equations. Constitutive relations are provided based on an entropy principle, and particular care is taken in the analysis of the stress tensor and the momentum balance in the general case of non-constant scalar susceptibility. Finally, we summarise the application of the derived model framework to an electrochemical system with surface reactions.
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    A Redlich-Kister type free energy model for Li-intercalation compounds with variable lattice occupation numbers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Landstorfer, Manuel
    One of the central quantities of a lithium ion intercalation compound is the open circuit potential, the voltage a battery material delivers in thermodynamic equilibrium. This voltage is related to the chemical potential of lithium in the insertion material and in general a non-linear function of the mole fraction of intercalated lithium. Experimental data shows further that it is specific for various materials. The open circuit voltage is a central ingredient for mathematical models of whole battery cells, which are used to investigate and simulate the charge and discharge behavior and to interpret experimental data on non-equilibrium processes. However, since no overall predictive theoretical method presently exists for the open circuit voltage, it is commonly fitted to experimental data. Simple polynomial fitting approaches are widely used, but they lack any thermodynamic interpretation. More recently systematically and thermodynamically motivated approaches are used to model the open circuit potential. We provide here an explicit free energy density which accounts for variable occupation numbers of Li on the intercalation lattice as well as RedlichKister-type enthalpy contributions. The derived chemical potential is validated by experimental data of Liy(Ni1/3Mn1/3Co1/3)O2 and we show that only two parameters are sufficient to obtain an overall agreement of the non-linear open circuit potential within the experimental error.
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    Thermodynamic models for a concentration and electric field dependent susceptibility in liquid electrolytes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Landstorfer, Manuel; Müller, Rüdiger
    The dielectric susceptibility $chi$ is an elementary quantity of the electrochemical double layer and the associated Poisson equation. While most often $chi$ is treated as a material constant, its dependency on the salt concentration in liquid electrolytes is demonstrated by various bulk electrolyte experiments. This is usually referred to as dielectric decrement. Further, it is theoretically well accepted that the susceptibility declines for large electric fields. This effect is frequently termed dielectric saturation. We analyze the impact of a variable susceptibility in terms of species concentrations and electric fields based on non-equilibrium thermodynamics. This reveals some non-obvious generalizations compared to the case of a constant susceptibility. In particular the consistent coupling of the Poisson equation, the momentum balance and the chemical potentials functions are of ultimate importance. In a numerical study, we systematically analyze the effects of a concentration and field dependent susceptibility on the double layer of a planar electrode electrolyte interface. We compute the differential capacitance and the spatial structure of the electric potential, solvent concentration and ionic distribution for various non-constant models of $chi$.
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    Modeling polycrystalline electrode-electrolyte interfaces: The differential capacitance
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Fuhrmann, Jürgen; Landstorfer, Manuel; Müller, Rüdiger
    We present and analyze a model for polycrystalline electrode surfaces based on an improved continuum model that takes finite ion size and solvation into account. The numerical simulation of finite size facet patterns allows to study two limiting cases: While for facet size diameter $d^facet to 0$ we get the typical capacitance of a spatially homogeneous but possible amorphous or liquid surface, in the limit $L^Debye << d^facet$ , an ensemble of non-interacting single crystal surfaces is approached. Already for moderate size of the facet diameters, the capacitance is remarkably well approximated by the classical approach of adding the single crystal capacities of the contributing facets weighted by their respective surface fraction. As a consequence, the potential of zero charge is not necessarily attained at a local minimum of capacitance, but might be located at a local capacitance maximum instead. Moreover, the results show that surface roughness can be accurately taken into account by multiplication of the ideally flat polycrystalline surface capacitance with a single factor. In particular, we find that the influence of the actual geometry of the facet pattern in negligible and our theory opens the way to a stochastic description of complex real polycrystal surfaces.
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    A mixture theory of electrolytes containing solvation effects
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Dreyer, Wolfgang; Guhlke, Clemens; Landstorfer, Manuel
    In this work we present a new mixture theory of a liquid solvent containing completely dissociated ions to study the space charge layer of electrolytes in contact with some inert metal. We incorporate solvation shell effects (i) in our derivation of the mixing entropy and (ii) in the pressure model. Chemical potentials of ions and solvent molecules in the incompressible limit are then derived from a free energy function. For the thermodynamic equilibrium the coupled equation system of mass and momentum balance, the incompressibility constraint and the Poisson equation are summarized. With that we study the space charge layer of the electrolytic solution for an applied half cell potential and compare our results to historic and recent interpretations of the double layer in liquid electrolytes. The novelties of the new model are: (i) coupling of momentum- and mass-balance equations, (ii) calculation of entropic contributions due to solvated ions and (iii) the potential and pressure dependence of the free charge density in equilibrium.
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    The partial molar volume and area of solvated ions and some aspects of partial charge transfer
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Landstorfer, Manuel
    The double layer capacity is one of the central quantities in theoretical and experimental electrochemistry of metal/electrolyte interfaces. It turns out that the capacity is related to two central thermodynamic quantities, i.e. the partial molar volume of an ionic constituent and the partial molar area of the respective adsorbate. Since ions in solution (or on the surface) accumulated solvent molecules in their solvation shell, the partial molar volume and area are effected by this phenomena. In this work we discuss several aspects of the relationship between the molar volume and area of an ion, the solvation number and the charge number. In addition, we account for partial charge transfer on the metal surface which explains naturally the difference of the capacity maxima between F and ClO 4 on silver. We provide simple yet validated analytical expressions for the partial molar volume and area of multi-valent ions and parameter values for aqueous solutions.