Publications

Some of the current members of the research group "Thermodynamic Modeling and Analysis of Phase Transitions" were members of a former group or of RG 1 respectively. Therefore, the corresponding publications can found on the web pages of these groups:

  • former Young Scientists' Group "Modeling of Damage Processes"
  • former Leibniz Group "Mathematical Models for Lithium-Ion Batteries"
  • Research group 1 "Partial Differential Equations"
    • Monographs

      • S. Jachalski, D. Peschka, S. Bommer, R. Seemann, B. Wagner, Chapter 18: Structure Formation in Thin Liquid--Liquid Films, in: Transport Processes at Fluidic Interfaces, D. Bothe, A. Reusken, eds., Advances in Mathematical Fluid Mechanics, Birkhäuser, Springer International Publishing AG, Cham, Switzerland, 2017, pp. 531--574, (Chapter Published), DOI 10.1007/978-3-319-56602-3 .
        Abstract
        We revisit the problem of a liquid polymer that dewets from another liquid polymer substrate with the focus on the direct comparison of results from mathematical modeling, rigorous analysis, numerical simulation and experimental investigations of rupture, dewetting dynamics and equilibrium patterns of a thin liquid-liquid system. The experimental system uses as a model system a thin polystyrene (PS) / polymethylmethacrylate (PMMA) bilayer of a few hundred nm. The polymer systems allow for in situ observation of the dewetting process by atomic force microscopy (AFM) and for a precise ex situ imaging of the liquid--liquid interface. In the present study, the molecular chain length of the used polymers is chosen such that the polymers can be considered as Newtonian liquids. However, by increasing the chain length, the rheological properties of the polymers can be also tuned to a viscoelastic flow behavior. The experimental results are compared with the predictions based on the thin film models. The system parameters like contact angle and surface tensions are determined from the experiments and used for a quantitative comparison. We obtain excellent agreement for transient drop shapes on their way towards equilibrium, as well as dewetting rim profiles and dewetting dynamics.

      • M. Dimian, P. Gurevich, O. Klein, D. Knees, D. Rachinskii, S. Tikhomirov, eds., MURPHYS-HSFS-2014: 7th International Workshop on MUlti-Rate Processes and HYSteresis (MURPHYS) & 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), 727 of Journal of Physics: Conference Series, IOP Publishing, 2016, 252 pages, (Collection Published).

      Articles in Refereed Journals

      • S. Bergmann, D.A. Barragan-Yani, E. Flegel, K. Albe, B. Wagner, Anisotropic solid-liquid interface kinetics in silicon: An atomistically informed phase-field model, Modelling and Simulation in Materials Science and Engineering, 25 (2017), 065015, DOI 10.1088/1361-651X/aa7862 .
        Abstract
        We present an atomistically informed parametrization of a phase-field model for describing the anisotropic mobility of liquid-solid interfaces in silicon. The model is derived from a consistent set of atomistic data and thus allows to directly link molecular dynamics and phase field simulations. Expressions for the free energy density, the interfacial energy and the temperature and orientation dependent interface mobility are systematically fitted to data from molecular dynamics simulations based on the Stillinger-Weber interatomic potential. The temperature-dependent interface velocity follows a Vogel-Fulcher type behavior and allows to properly account for the dynamics in the undercooled melt.

      • W. Dreyer, C. Guhlke, Sharp limit of the viscous Cahn--Hilliard equation and thermodynamic consistency, Continuum Mechanics and Thermodynamics, 29 (2017), pp. 913--934.
        Abstract
        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.

      • M. Eigel, R. Müller, A posteriori error control for stationary coupled bulk-surface equations, IMA Journal of Numerical Analysis, (2017), published online on 9.3.2017, DOI 10.1093/imanum/drw080 .
        Abstract
        We consider a system of two coupled elliptic equations, one defined on a bulk domain and the other one on the boundary surface. Problems of this kind are relevant for applications in engineering, chemistry and in biology like e.g. biological signal transduction. For the a posteriori error control of the coupled system, a residual error estimator is derived which takes into account the approximation errors due to the finite element discretisation in space as well as the polyhedral approximation of the surface. An adaptive refinement algorithm controls the overall error. Numerical experiments illustrate the performance of the a posteriori error estimator and the adaptive algorithm with several benchmark examples.

      • M. Landstorfer, Boundary conditions for electrochemical interfaces, Journal of The Electrochemical Society, 164 (2017), pp. 3671--3685.
        Abstract
        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 electrocatalysis. 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.

      • E. Meca Álvarez, V. Shenoy , J. Lowengrub, H2-Dependent Attachment Kinetics and Shape Evolution in CVD Graphene Growth, 2D Materials, 4 (2017), DOI 10.1088/2053-1583/aa74f1 .

      • M. Dziwnik, A. Münch, B. Wagner, An anisotropic phase-field model for solid-state dewetting and its sharp-interface limit, Nonlinearity, 30 (2017), pp. 1465--1496.
        Abstract
        We propose a phase field model for solid state dewetting in form of a Cahn-Hilliard equation with weakly anisotropic surface energy and a degenerate mobility together with a free boundary condition at the film-substrate contact line. We derive the corresponding sharp interface limit via matched asymptotic analysis involving multiple inner layers. The resulting sharp interface model is consistent with the pure surface diffusion model. In addition, we show that the natural boundary conditions, as indicated from the first variation of the total free energy, imply a contact angle condition for the dewetting front, which, in the isotropic case, is consistent with the well-known Young's equation.

      • CH. Heinemann, Ch. Kraus, E. Rocca, R. Rossi, A temperature-dependent phase-field model for phase separation and damage, Archive for Rational Mechanics and Analysis, 225 (2017), pp. 177--247.
        Abstract
        In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature (cf., e.g., [C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321--359] and [C. Heinemann, C. Kraus: Existence results for diffuse interface models describing phase separation and damage. European J. Appl. Math. 24 (2013), 179--211]), we encompass in the model thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More in particular, we prove the existence of "entropic weak solutions", resorting to a solvability concept first introduced in [E. Feireisl: Mathematical theory of compressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53 (2007), 461--490] in the framework of Fourier-Navier-Stokes systems and then recently employed in [E. Feireisl, H. Petzeltová, E. Rocca: Existence of solutions to a phase transition model with microscopic movements. Math. Methods Appl. Sci. 32 (2009), 1345--1369], [E. Rocca, R. Rossi: "Entropic" solutions to a thermodynamically consistent PDE system for phase transitions and damage. SIAM J. Math. Anal., 47 (2015), 2519--2586] for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.

      • A. Münch, B. Wagner, L.P. Cook, R.R. Braun, Apparent slip for an upper convected Maxwell fluid, SIAM Journal on Applied Mathematics, 77 (2017), pp. 537--564, DOI 10.1137/16M1056869 .
        Abstract
        In this study the flow field of a nonlocal, diffusive upper convected Maxwell (UCM) fluid with a polymer in a solvent undergoing shearing motion is investigated for pressure driven planar channel flow and the free boundary problem of a liquid layer on a solid substrate. For large ratios of the zero shear polymer viscosity to the solvent viscosity, it is shown that channel flows exhibit boundary layers at the channel walls. In addition, for increasing stress diffusion the flow field away from the boundary layers undergoes a transition from a parabolic to a plug flow. Using experimental data for the wormlike micelle solutions CTAB/NaSal and CPyCl/NaSal, it is shown that the analytic solution of the governing equations predicts these signatures of the velocity profiles. Corresponding flow structures and transitions are found for the free boundary problem of a thin layer sheared along a solid substrate. Matched asymptotic expansions are used to first derive sharp-interface models describing the bulk flow with expressions for an em apparent slip for the boundary conditions, obtained by matching to the flow in the boundary layers. For a thin film geometry several asymptotic regimes are identified in terms of the order of magnitude of the stress diffusion, and corresponding new thin film models with a slip boundary condition are derived.

      • A. Roggensack, Ch. Kraus, Existence of weak solutions for the Cahn--Hilliard reaction model including elastic effects and damage, Journal of Partial Differential Equations, 30 (2017), pp. 111-145, DOI 10.4208/jpde.v30.n2.2 .
        Abstract
        In this paper, we introduce and study analytically a vectorial Cahn-Hilliard reaction model coupled with rate-dependent damage processes. The recently proposed Cahn-Hilliard reaction model can e.g. be used to describe the behavior of electrodes of lithium-ion batteries as it includes both the intercalation reactions at the surfaces and the separation into different phases. The coupling with the damage process allows considering simultaneously the evolution of a damage field, a second important physical effect occurring during the charging or discharging of lithium-ion batteries. Mathematically, this is realized by a Cahn-Larché system with a non-linear Newton boundary condition for the chemical potential and a doubly non-linear differential inclusion for the damage evolution. We show that this system possesses an underlying generalized gradient structure which incorporates the non-linear Newton boundary condition. Using this gradient structure and techniques from the field of convex analysis we are able to prove constructively the existence of weak solutions of the coupled PDE system.

      • CH. Kraus, M. Radszuweit, Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach, Computational Mechanics, 60 (2017), pp. 163--179, DOI 10.1007/s00466-017-1393-4 .
        Abstract
        We present a continuum model that incorporates rate-dependent damage and fracture, a material order parameter field and temperature. Different material characteristics throughout the medium yield a strong inhomogeneity and affect the way fracture propagates. The phasefield approach is employed to describe degradation. For the material order parameter we assume a Cahn Larché-type dynamics, which makes the model in particular applicable to binary alloys. We give thermodynamically consistent evolution equations resulting from a unified variational approach. Diverse coupling mechanisms can be covered within the model, such as heat dissipation during fracture, thermal-expansion-in- duced failure and elastic-inhomogeneity effects. We furthermore present an adaptive Finite Element code in two space dimensions, that is capable of solving such a highly nonlinear and non-convex system of partial differential equations. With the help of this tool we conduct numerical experiments of different complexity in order to investigate the possibilities and limitations of the presented model. A main feature of our model is that we can describe the process of micro-crack nucleation in regions of partial damage to form macro-cracks in a unifying approach.

      • E. Meca Álvarez, A. Münch, B. Wagner, Sharp-interface formation during lithium intercalation into silicon, European Journal of Applied Mathematics, (2017), published online on 28.3.2017, DOI 10.1017/S0956792517000067 .
        Abstract
        In this study we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as a-Si. The governing equations couple a viscous Cahn-Hilliard-Reaction model with elasticity in the framework of the Cahn-Larché system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dynamics of triple points where the sharp interface in the bulk of the layer intersects the free boundary. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model.

      • E. Meca Álvarez, A. Münch, B. Wagner, Thin-film electrodes for high-capacity lithium-ion batteries: Influence of phase transformations on stress, Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 472 (2016), pp. 20160093/1--20160093/15.

      • M. Korzec, A. Münch, E. Süli, B. Wagner, Anisotropy in wavelet based phase field models, Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, 21 (2016), pp. 1167--1187.
        Abstract
        Anisotropy is an essential feature of phase-field models, in particular when describing the evolution of microstructures in solids. The symmetries of the crystalline phases are reflected in the interfacial energy by introducing corresponding directional dependencies in the gradient energy coefficients, which multiply the highest order derivative in the phase-field model. This paper instead considers an alternative approach, where the anisotropic gradient energy terms are replaced by a wavelet analogue that is intrinsically anisotropic and linear. In our studies we focus on the classical coupled temperature - Ginzburg-Landau type phase-field model for dendritic growth. For the resulting derivative-free wavelet analogue existence, uniqueness and continuous dependence on initial data for weak solutions is proved. The ability to capture dendritic growth similar to the results obtained from classical models is investigated numerically.

      • W. Dreyer, C. Guhlke, M. Landstorfer, Theory and structure of the metal/electrolyte interface incorporating adsorption and solvation effects, Electrochimica Acta, 201 (2016), pp. 187--219.
        Abstract
        In this work we present a continuum theory for the metal/electrolyte interface which explicitly takes into account adsorption and partial solvation on the metal surface. It is based on a general theory of coupled thermo-electrodynamics for volumes and surfaces, utilized here in equilibrium and a 1D approximation. We provide explicit free energy models for the volumetric metal and electrolyte phases and derive a surface free energy for the species present on the metal surface. This surface mixture theory explicitly takes into account the very different amount of sites an adsorbate requires, originating from solvation effects on the surface. Additionally we account for electron transfer reactions on the surface and the associated stripping of the solvation shell. Based on our overall surface free energy we thus provide explicit expressions of the surface chemical potentials of all constituents. The equilibrium representations of the coverages and the overall charge are briefly summarized.

        Our model is then used to describe two examples: (i) a silver single crystal electrode with (100) face in contact to a (0.01M NaF + 0.01M KPF6) aqueous solution, and (ii) a general metal surface in contact to some electrolytic solution AC for which an electron transfer reaction occurs in the potential range of interest. We reflect the actual modeling procedure for these examples and discuss the respective model parameters. Due to the representations of the coverages in terms of the applied potential we provide an adsorption map and introduce adsorption potentials. Finally we investigate the structure of the space charge layer at the metal/surface/electrolyte interface by means of numerical solutions of the coupled Poisson-momentum equation system for various applied potentials. It turns out that various layers self-consistently form within the overall space charge region, which are compared to historic and recent pictures of the double layer. Based on this we present new interpretations of what is known as inner and outer Helmholtz-planes and finally provide a thermodynamic consistent picture of the metal/electrolyte interface structure.

      • W. Dreyer, C. Guhlke, R. Müller, A new perspective on the electron transfer: Recovering the Butler--Volmer equation in non-equilibrium thermodynamics, Physical Chemistry Chemical Physics, 18 (2016), pp. 24966--24983.
        Abstract
        Understanding and correct mathematical description of electron transfer reaction is a central question in electrochemistry. Typically the electron transfer reactions are described by the Butler-Volmer equation which has its origin in kinetic theories. The Butler-Volmer equation relates interfacial reaction rates to bulk quantities like the electrostatic potential and electrolyte concentrations. Since in the classical form, the validity of the Butler-Volmer equation is limited to some simple electrochemical systems, many attempts have been made to generalize the Butler-Volmer equation. Based on non-equilibrium thermodynamics we have recently derived a reduced model for the electrode-electrolyte interface. This reduced model includes surface reactions but does not resolve the charge layer at the interface. Instead it is locally electroneutral and consistently incorporates all features of the double layer into a set of interface conditions. In the context of this reduced model we are able to derive a general Butler-Volmer equation. We discuss the application of the new Butler-Volmer equations to different scenarios like electron transfer reactions at metal electrodes, the intercalation process in lithium-iron-phosphate electrodes and adsorption processes. We illustrate the theory by an example of electroplating.

      • O. Klein, A representation result for rate-independent systems, Phys. B, 486 (2016), pp. 81--83.

      Contributions to Collected Editions

      • J. Fuhrmann, C. Guhlke, A finite volume scheme for Nernst--Planck--Poisson systems with Ion size and solvation effects, in: Finite Volumes for Complex Applications VIII -- Hyperbolic, Elliptic and Parabolic Problems -- FVCA 8, Lille, France, June 2017, C. Cancès, P. Omnes, eds., 200 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2017, pp. 497--505, DOI 10.1007/978-3-319-57394-6_52 .

      • O. Klein, V. Recupero, Hausdorff metric BV discontinuity of sweeping processes, in: MURPHYS-HSFS-2014: 7th International Workshop on MUlti-Rate Processes & HYSteresis (MURPHYS) & the 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), O. Klein, M. Dimian, P. Gurevich, D. Knees, D. Rachinskii, S. Tikhomirov, eds., 727 of Journal of Physics: Conference Series, 2016, pp. 012006/1--012006/12, DOI 10.1088/1742-6596/727/1/012006 .
        Abstract
        Sweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of emphrate independent operator containing as a particular case the so called emphplay operator which is widely used in hysteresis. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide a counterexample showing that the solution operator of the sweeping process is not continuous when its domain is endowed with the strict topology of $BV$ and its codomain is endowed with the $L^1$-topology. This is at variance with the case of the play operator which instead is continuous in this sense.

      Preprints, Reports, Technical Reports

      • M. Landstorfer, On the dissociation degree of ionic solutions considering solvation effects, Preprint no. 2443, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2443 .
        Abstract, PDF (3471 kByte)
        In this work the impact of solvation effects on the dissociation degree of strong electrolytes and salts is discussed. The investigation is based on a thermodynamic model which is capable to predict qualitatively and quantitatively the double layer capacity of various electrolytes. A remarkable relationship between capacity maxima, partial molar volume of ions in solution, and solvation numbers, provides an experimental access to determine the number of solvent molecules bound to a specific ion in solution. This shows that the Stern layer is actually a saturated solution of 1 mol L-1 solvated ions, and we point out some fundamental similarities of this state to a saturated bulk solution. Our finding challenges the assumption of complete dissociation, even for moderate electrolyte concentrations, whereby we introduce an undissociated ion-pair in solution. We re-derive the equilibrium conditions for a two-step dissociation reaction, including solvation effects, which leads to a new relation to determine the dissociation degree. A comparison to Ostwald's dilution law clearly shows the shortcomings when solvation effects are neglected and we emphasize that complete dissociation is questionable beyond 0.5 mol L-1 for aqueous, mono-valent electrolytes.

      • W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes. Part III: Compactness and convergence, Preprint no. 2397, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2397 .
        Abstract, PDF (327 kByte)
        We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convection--diffusion--reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper, which continues the investigations of [DDGG17a, DDGG17b], we prove the compactness of the solution vector, and existence and convergence for the approximation schemes. We point at simple structural PDE arguments as an adequate substitute to the Aubin--Lions compactness Lemma and its generalisations: These familiar techniques attain their limit in the context of our model in which the relationship between time derivatives (transport) and diffusion gradients is highly non linear.

      • W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes. Part II: Approximation and a priori estimates, Preprint no. 2396, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2396 .
        Abstract, PDF (355 kByte)
        We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convection--diffusion--reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper, which continues the investigation of [DDGG17a], we derive for thermodynamically consistent approximation schemes the natural uniform estimates associated with the dissipations. Our results essentially improve our former study [DDGG16], in particular the a priori estimates concerning the relative chemical potentials.

      • W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes. Part I: Derivation of the model and survey of the results, Preprint no. 2395, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2395 .
        Abstract, PDF (343 kByte)
        We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convection--diffusion--reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper we establish the existence of a global--in--time weak solution for the full model, allowing for a general structure of the mobility tensor and for chemical reactions with highly non linear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time. With respect to our former study [DDGG16], we also essentially improve the a priori estimates, in particular concerning the relative chemical potentials.

      • E. Meca Álvarez, A. Münch, B. Wagner, Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity, Preprint no. 2387, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2387 .
        Abstract, PDF (801 kByte)
        We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material flux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material flux, the coherent spinodal decomposition is recovered. In the present problem stability analysis of the time-dependent and non-uniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a flat moving front. The second instability is related to the Mullins-Sekerka instability in the presence of elasticity and arises at the moving front between the two phases when the flux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analysed within the same framework which allows to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting are demonstrated for a system of equations modelling the lithiation/delithiation processes within the context of Lithium ion batteries.

      • E. Meca Álvarez, V.B. Shenoy, J. Lowengrub, H2-dependent attachment kinetics and shape evolution in chemical vapor deposition graphene growth, Preprint no. 2358, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2358 .
        Abstract, PDF (1763 kByte)
        Experiments on graphene growth through chemical vapor deposition (CVD) involving methane (CH4) and hydrogen (H2) gases reveal a complex shape evolution and a nonmonotonic dependence on the partial pressure of H2 (pH2). To explain these intriguing observations, we develop a microkinetic model for the stepwise decomposition of CH4 into mobile radicals and consider two possible mechanisms of attachment to graphene crystals: CH radicals to hydrogen-decorated edges of the crystals and C radicals to bare crystal edges. We derive an effective mass flux and an effective kinetic coefficient, both of which depend on pH2, and incorporate these into a phase field model. The model reproduces both the non-monotonic dependence on pH2 and the characteristic shapes of graphene crystals observed in experiments. At small pH2, growth is limited by the kinetics of attachment while at large pH2 growth is limited because the effective mass flux is small. We also derive a simple analytical model that captures the non-monotone behavior, enables the two mechanisms of attachment to be distinguished and provides guidelines for CVD growth of defect-free 2D crystals.

      • S. Bommer, R. Seemann, S. Jachalski, D. Peschka, B. Wagner, Liquid-liquid dewetting: Morphologies and rates, Preprint no. 2346, WIAS, Berlin, 2016.
        Abstract, PDF (1107 kByte)
        The dependence of the dissipation on the local details of the flow field of a liquid polymer film dewetting from a liquid polymer substrate is shown, solving the free boundary problem for a two-layer liquid system. As a key result we show that the dewetting rates of such a liquid bi-layer system can not be described by a single power law but shows transient behaviour of the rates, changing from increasing to decreasing behaviour. The theoretical predictions on the evolution of morphology and rates of the free surfaces and free interfaces are compared to measurements of the evolution of the polystyrene(PS)-air, the polymethyl methacrylate (PMMA)-air and the PS-PMMA interfaces using in situ atomic force microscopy (AFM), and they show excellent agreement.

      • M. Landstorfer, The partial molar volume and area of solvated ions and some aspects of partial charge transfer, Preprint no. 2337, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2337 .
        Abstract, PDF (10181 kByte)
        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 ceF- and ceClO4- 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.

      • M. Dziwnik, S. Jachalski, Existence of solutions to an anisotropic degenerate Cahn--Hilliard-type equation, Preprint no. 2332, WIAS, Berlin, 2016.
        Abstract, PDF (278 kByte)
        We prove existence of solutions to an anisotropic Cahn-Hilliard-type equation with degenerate diffusional mobility. In particular, the mobility vanishes at the pure phases, which is typically used to model motion by surface diffusion. The main difficulty of the present existence result is the strong non-linearity given by the fourth-order anisotropic operator. Imposing particular assumptions on the domain and assuming that the strength of the anisotropy is sufficiently small enables to establish appropriate auxiliary results which play an essential part in the present existence proof. In addition to the existence we show that the absolute value of the corresponding solutions is bounded by 1.

      • W. Dreyer, P. Friz, P. Gajewski, C. Guhlke, M. Maurelli, Stochastic model for LFP-electrodes, Preprint no. 2329, WIAS, Berlin, 2016.
        Abstract, PDF (1531 kByte)
        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.

      • W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Existence of weak solutions for improved Nernst--Planck--Poisson models of compressible reacting electrolytes, Preprint no. 2291, WIAS, Berlin, 2016.
        Abstract, PDF (638 kByte)

        We consider an improved Nernst-Planck-Poisson model for compressible electrolytes first proposed by Dreyer et al. in 2013. The model takes into account the elastic deformation of the medium. In particular, large pressure contributions near electrochemical interfaces induce an inherent coupling of mass and momentum transport. The model consists of convection-diffusion-reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity and the Poisson equation for the electrical potential. Cross-diffusion phenomena occur due to the principle of mass conservation. Moreover, the diffusion matrix (mobility matrix) has a zero eigenvalue, meaning that the system is degenerate parabolic. In this paper we establish the existence of a global-in- time weak solution for the full model, allowing for cross-diffusion and an arbitrary number of chemical reactions in the bulk and on the active boundary.
      • O. Klein, Uncertainty quantification for hysteresis operators and a model for magneto-mechanical hysteresis, Preprint no. 2246, WIAS, Berlin, 2016.
        Abstract, PDF (708 kByte)
        Many models for magneto-mechanical components involve hysteresis operators. The parameter within these operators have to be identified from measurements and are therefore subject to uncertainties. To quantify the influence of these uncertainties, the parameter in the hysteresis operator are considered as functions of random variables. Combining this with the hysteresis operator, we get new random variables and we can compute stochastic properties of the output of the model. For two hysteresis operators corresponding numerical results are presented in this paper. Moreover, the influence of the variation of the parameters in a model for a magneto-mechanical component is investigated.

      Talks, Poster

      • S. Bergmann, Phase-field modeling of Si thin-film growth via liquid-phase crystallization, Winter Workshop on Microstructure Characterization and Modeling for Solar Cells, February 12 - 16, 2017, Schliersee-Spitzingsee, February 13, 2017.

      • B. Wagner, Phase-field modeling of Si thin-film growth via liquid-phase crystallization, Winter Workshop on Microstructure Characterization and Modeling for Solar Cells, February 13 - 16, 2017, Schliersee-Spitzingsee.

      • W. Dreyer, J. Fuhrmann, P. Gajewski, C. Guhlke, M. Landstorfer, M. Maurelli, R. Müller, Stochastic model for LiFePO4-electrodes, ModVal14 - 14th Symposium on Fuel Cell and Battery Modeling and Experimental Validation, Karlsruhe, March 2 - 3, 2017.

      • P.-É. Druet, mit Vortrag?, Seminar ``Compressible and Incompressible Multiphase Flows: Modelling, Analysis, Numerics'', June 4 - 10, 2017, Mathematisches Forschungsinstitut Oberwolfach.

      • M. Landstorfer, Theory, structure and experimental justification of the metal/electrolyte interface, Universität Münster, Fachbereich Mathematik und Informatik, Institut für Analysis und Numerik, July 11, 2017.

      • R. Müller, A posteriori analysis for coupled bulk-surface problems, Oberseminar ``Angewandte Analysis und Numerische Simulation'', Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation, June 1, 2017.

      • R. Müller, A posteriori error analysis for coupled bulk-surface diffusion, Matheon Workshop RMMM 8 - Berlin 2017, Reliable Methods of Mathematical Modeling, July 31 - August 3, 2017, Humboldt-Universität zu Berlin, July 31, 2017.

      • R. Müller, Consistent coupling of charge transport and fluid flow with application to nanopores, ACOMEN 2017 - 7th International Conference on Advanced Computational Methods in ENgineering, Minisymposium: Electrokinetic and electrochemical flows for batteries and fuel cells: Analysis, simulation, upscaling, September 18 - 22, 2017, Ghent University, Belgium, September 21, 2017.

      • A. Roggensack, Damage processes in lithium-ion batteries, Workshop ``Recent Trends and Future Developments in Computational Science & Engineering, March 22 - 24, 2017, Plön, March 23, 2017.

      • B. Wagner, Mathematical opportunities and challenges in sustainable energies, SIAM Annual Meeting, July 10 - 14, 2017, Pittsburgh, USA, July 14, 2017.

      • B. Wagner, mit Vortrag?, Leibniz Symposium ``Biomaterial-based Approaches in Personalized Medicine'', Berlin, March 22, 2017.

      • C. Guhlke, Gefahr erkannt, Gefahr gebannt! - Mathematische Modelle machen Lithium-Ionen-Batterien sicherer, Symposium 25 Jahre Forschungsverbund Berlin e.V., Urania, Berlin, May 18, 2017.

      • C. Guhlke, Modelling of ion transport in electrolytes - A thermodynamic approach, 2nd Dresden Battery Days, Dresden, September 18 - 20, 2017.

      • C. Guhlke, Vom Luftballon zur Lithium-Ionen-Batterie, Lange Nacht der Wissenschaften, Technische Universität Berlin, Haus der Mathematik, June 24, 2017.

      • O. Klein, Uncertainty quantification for models involving hysteresis operators, Summer School on Multi-Rate Processes, Slow-Fast Systems and Hysteresis MURPHYS-HSFS-2017, June 19 - 20, 2017, DISMA Dipartimento di Scienze Matematiche ``Giuseppe Luigi Lagrange'', Politecnico di Torino, Italy.

      • CH. Merdon, Pressure-robust mixed finite element methods for the Navier--Stokes equations, scMatheon Workshop RMMM 8 - Berlin 2017, Reliable Methods of Mathematical Modeling, July 31 - August 3, 2017, Humboldt-Universität zu Berlin, August 2, 2017.

      • S. Jachalski, Structure formation in thin liquid-liquid films, SPP 1506 Kolloquium, May 9 - 10, 2016, Aachen, May 9, 2016.

      • M. Landstorfer, Towards a model based understanding of cyclic voltammetry, Electrochemistry 2016, Gesellschaft Deutscher Chemiker e.V. (GDCh), Goslar, September 26 - 28, 2016.

      • M. Maurelli , P. Gajewski, Stochastic methods for lithium-ion batteries, Matheon Center Days, April 11, 2016.

      • E. Meca Álvarez, Si electrodes for Li-ion batteries: Phase-field modeling, University of Oxford, Mathematical Institute, UK, February 18, 2016.

      • E. Meca Alvarez, Thin-film electrodes for high-capacity lithium-ion batteries: Influence of phase transformations on stress, ECMI 2016 - The 19th European Conference on Mathematics for Industry, CT04 Numerical simulation of batteries, June 13 - 17, 2016, Santiago de Compostela, Spain, June 17, 2016.

      • R. Müller, W. Dreyer, J. Fuhrmann, C. Guhlke, New insights into Butler--Volmer kinetics from thermodynamic modeling, The 67th Annual Meeting of the International Society of Electrochemistry, Den Haag, Netherlands, August 21 - 26, 2016.

      • R. Müller, A-posteriori error control for stationary coupled bulk-surface equations, Joint Annual Meeting GAMM und DMV, March 7 - 11, 2016, TU Braunschweig, March 10, 2016.

      • R. Müller, Adaptive FEM and a posteriori error control for stationary coupled bulk-surface PDEs, 2nd Applied Mathematical Symposium Münster, Workshop: Numerical Schemes for Surface PDEs, February 22 - 24, 2016, Westfälische Wilhelms-Universität Münster, February 22, 2016.

      • R. Müller, The Lippmann equation for liquid metal electrodes, 11th DFG-CNRS Workshop ``Micro-Macro Modeling and Simulation of Liquid-Vapor Flows'', March 2 - 4, 2016, Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, Paris, France, March 3, 2016.

      • C. Guhlke, Modeling of LiFePO4-Electrode, VII European Congress on Computational Methods in Applied Sciences and Engineering - ECCOMAS 2016, Minisymposium ``Advanced Computational Modeling of Batteries and Fuel Cells'', June 5 - 10, 2016, Kreta, Greece, June 7, 2016.

      • B. Wagner, Concentrated suspensions: A multiscale analysis, University of Limerick, Mathematics Applications Consortium for Science and Industry, Ireland, April 1, 2016.

      • B. Wagner, Dewetting patterns of viscoelastic liquid bi-layers, Workshop ``Non-equilibrium dynamics of thin films -- solids, liquids and bioactiv materials'', September 20 - 23, 2016, CECAM-HQ-EPFL, Lausanne, Switzerland, September 20, 2016.

      • B. Wagner, Models for the two-phase flow of concentrated suspensions, British Applied Mathematics Colloquium, April 5 - 8, 2016, University of Oxford, Mathematical Institute, UK, April 6, 2016.

      • B. Wagner, Thin films and complex liquids for industrial application, Leibniz-Kolleg for Young Researchers: Challenges and Chances of Interdisciplinary Research, Thematic Workshop ``Models and Modelling'', Leibniz-Gemeinschaft, Berlin, November 9, 2016.

      • W. Dreyer, Models of lithium-ion-batteries: A paradigm for consistent modelling, 1st Leibniz MMS Days, January 27 - 29, 2016, WIAS, Berlin, January 28, 2016.

      • J. Fuhrmann, W. Dreyer, C. Guhlke, M. Landstorfer, R. Müller, A. Linke, Ch. Merdon, Modeling and numerics for electrochemical systems, Micro Battery and Capacitive Energy Harvesting Materials -- Results of the MatFlexEnd Project, Universität Wien, Austria, September 19, 2016.

      • J. Fuhrmann, A. Linke, Ch. Merdon, W. Dreyer, C. Guhle, M. Landstorfer, R. Müller, Numerical methods for electrochemical systems, 2nd Graz Battery Days, Graz, Austria, September 27 - 28, 2016.

      • C. Guhlke, W. Dreyer, R. Müller, M. Landstorfer, J. Fuhrmann, Beyond Newman's battery model, 2nd Graz Battery Days, Graz, Austria, September 27 - 28, 2016.

      • C. Guhlke, W. Dreyer, R. Müller, M. Landstorfer , Models of lithium-ion batteries: A paradigm for consistent modelling, 1st Leibniz MMS Days, WIAS Berlin, January 27 - 29, 2016.

      • C. Guhlke, J. Fuhrmann, W. Dreyer, R. Müller, M. Landstorfer, Modeling of batteries, Batterieforum Deutschland 2016, Berlin, April 6 - 8, 2016.

      • C. Guhlke, Continuum thermodynamics in the immediate vicinity of an electrode-electrolyte interface, Soft Matter at Interfaces 2016, February 28 - March 2, 2016, Schloss Ringberg, Kreuth, February 28, 2016.

      • C. Guhlke, Impact of stress on the electrical double layer, 2016 MRS Spring Meeting & Exhibit, Symposium EE7 ``Mechanics of Energy Storage and Conversion -- Batteries, Thermoelectrics and Fuel Cells'', March 28 - April 1, 2016, Phoenix, USA, March 31, 2016.

      • O. Klein, On uncertainty quantification for hysteresis operators, Silesian University, Mathematical Institute, Opava, Czech Republic, December 7, 2016.

      • O. Klein, Uncertainty quantification for hysteresis operators, 7th European Congress of Mathematics (7ECM), Minisymposium 29 ``Nonsmooth PDEs in the Modeling Damage, Delamination, and Fracture'', July 18 - 22, 2016, Technische Universität Berlin, July 22, 2016.

      • O. Klein, Uncertainty quantification for hysteresis operators and models for magneto-mechanical hysteresis, Conference ``Advances in Magnetics'' (AIM) 2016, March 14 - 16, 2016, Bormio, Italy, March 14, 2016.