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Author: Guhlke, Clemens × Start date: 1984 × Type: Text × Type: report × Subject: phase transitions ×

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Now showing 1 - 5 of 5
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    Hysteresis in the context of hydrogen storage and lithium-ion batteries
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Dreyer, Wolfgang; Guhlke, Clemens; Huth, Robert
    The processes of reversible storage of hydrogen in a metal by loading and unloading and of charging and discharging of lithium-ion batteries have many things in common. The both processes are accompanied by a phase transition and loading and unloading run along different paths, so that hysteretic behavior is observed. For hydrogen storage we consider a fine powder of magnesium (Mg) particles and lithium storage is studied for iron phosphate (FePO_4) particles forming the cathode of a lithium-ion battery. The mathematical models that are established in citeDGJ08 and citeDGH09a, describe phase transitions and hysteresis exclusively in a single particle and on that basis they can predict the observed hysteretic plots with almost horizontal plateaus. Interestingly the models predict that the coexistence of a 2-phase system in an individual particle disappears, if its size is below a critical value. However, measurements reveal that this is qualitatively not reflected by the mentioned hysteretic plots of loading and unloading. In other words: The behavior of a storage system consisting of many particles is qualitatively independent of the fact whether the individual particles itself develop a 2-phase system or if they remain in a single phase state. This apparent paradoxical observation will be resolved in this article. It will be shown that if each of the individual particles homogeneously distributes the supplied matter, nevertheless the many particle ensemble exhibits phase transition and hysteresis, because one of the two phases is realized in some part of the particles while the remaining part is in the other phase.
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    Hysteresis and phase transition in many-particle storage systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Dreyer, Wolfgang; Guhlke, Clemens; Herrmann, Michael
    We study the behavior of systems consisting of ensembles of interconnected storage particles. Our examples concern the storage of lithium in many-particle electrodes of rechargeable lithium-ion batteries and the storage of air in a system of interconnected rubber balloons. We are particularly interested in those storage systems whose constituents exhibit non-monotone material behavior leading to transitions between two coexisting phases and to hysteresis. In the current study we consider the case that the time to approach equilibrium of a single storage particle is much smaller than the time for full charging of the ensemble. In this regime the evolution of the probability to find a particle of the ensemble in a certain state, may be described by a nonlocal conservation law of Fokker-Planck type. Two constant parameter control whether the ensemble transits the 2-phase region along a Maxwell line or along a hysteresis path or if the ensemble shows the same non-monotone behavior as its constituents.
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    Phase transition and hysteresis in a rechargeable lithium battery revisited
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Dreyer, Wolfgang; Gaberscek, Miran; Guhlke, Clemens; Huth, Robert; Jamnik, Janko
    We revisit a model which describes the evolution of a phase transition that occurs in the cathode of a rechargeable lithium battery during the process of charging/discharging. The model is capable to simulate hysteretic behavior of the voltage
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    Sharp limit of the viscous Cahn-Hilliard equation and thermodynamic consistency
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Dreyer, Wolfgang; Guhlke, Clemens
    Diffuse and sharp interface models represent two alternatives to describe phase transitions with an interface between two coexisting phases. The two model classes can be independently formulated. Thus there arises the problem whether the sharp limit of the diffuse model fits into the setting of a corresponding sharp interface model. We call a diffuse model admissible if its sharp limit produces interfacial jump conditions that are consistent with the balance equations and the 2nd law of thermodynamics for sharp interfaces. We use special cases of the viscous Cahn- Hilliard equation to show that there are admissible as well as non-admissible diffuse interface models.
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    Stochastic model for LFP-electrodes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dreyer, Wolfgang; Friz, Peter K.; Gajewski, Paul; Guhlke, Clemens; Maurelli, Mario
    In the framework of non-equilibrium thermodynamics we derive a new model for porous electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by surface fluctuations leading to a system of stochastic differential equations. The model is capable to derive an explicit relation between battery voltage and current that is controlled by thermodynamic state variables. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltagecharge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.