arXiv subjects

Andreas Heuer

Publications and source records attributed to Andreas Heuer.

At least 91 records · Page 5Linked to original sources

arXiv2008

Understanding correlation effects for ion conduction in polymer electrolytes

Polymer electrolytes typically exhibit diminished ionic conductivity due to the presence of correlation effects between the cations and anions. Microscopically, transient ionic aggregates, e.g. {\it ion-pairs}, {\it ion-triplets} or higher order ionic clusters, engender ionic correlations. Employing {\it all-atom} simulation of a model polymer electrolyte comprising of poly(ethylene oxide) and lithium iodide, the ionic correlations are explored through construction of elementary functions between pairs of the ionic species that qualitatively explains the spatio-temporal nature of these correlations. Furthermore, commencing from the exact Einstein-like equation describing the collective diffusivity of the ions in terms of the average diffusivity of the ions (i.e. the self terms) and the correlations from distinct pairs of ions, several phenomenological parameters are introduced to keep track of the simplification procedure that finally boils down to the recently proposed phenomenological model by Stolwijk-Obeidi (SO) [N. A. Stolwijk and S. Obeidi, Phys. Rev. Lett. 93, 125901, 2004]. The approximation parameters, which can be retrieved from simulations, point to the necessity of additional information in order to fully describe the correlation effects apart from merely the fraction of ion-pairs which apparently accounts for the correlations originating from only the nearest neighbor structural correlations. These parameters are close to but not exactly unity as assumed in the SO model. Finally, as an application of the extended SO model one is able to estimate the dynamics of the free and non-free ions as well as their fractions from the knowledge of the single particle diffusivities and the collective diffusivity of the ions.

cond-mat.mtrl-sci↗

arXiv2008

Understanding Segmental Dynamics in Polymer Electrolytes: A Computer Study

We study the segmental dynamics of poly(ethylene oxide) (PEO) from microscopic simulations in the neat polymer and a polymer electrolyte (PEO/LiBF$_4$) by analyzing the normal modes. We verify the applicability of the Rouse theory, specifically for the polymer electrolyte where dynamic heterogeneities, arising from cation-polymer interactions, alter the mobility non-uniformly along the chains. We find that the Rouse modes for both the systems are orthogonal despite the presence of non-exponential relaxation of the modes and violation of the Gaussian self-similarity of the chains. The slowdown of the segmental dynamics in the polymer electrolyte is rationalised by an order of magnitude increase in the friction coefficient for those monomers which are bound by cations. In general, for the electrolyte the Rouse predictions for the dynamics of segments (both free and/or bound) agree well except for very short times.

cond-mat.soft↗

arXiv2008

Can the dynamics of an atomic glass-forming system be described as a continuous time random walk?

We show that the dynamics of supercooled liquids, analyzed from computer simulations of the binary mixture Lennard-Jones system, can be described in terms of a continuous time random walk (CTRW). The required discretization comes from mapping the dynamics on transitions between metabasins. This comparison involves verifying the conditions of the CTRW as well as a quantitative test of the predictions. In particular it is possible to express the wave vector-dependence of the relaxation time as well as the degree of non-exponentiality in terms of the first three moments of the waiting time distribution.

cond-mat.dis-nn↗

arXiv2007

Realization of Levy flights as continuous processes

On the basis of multivariate Langevin processes we present a realization of Levy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Levy flights. Our procedure is similar to the treatment of the Kramers-Fokker Planck equation in the Smoluchowski limit. The proposed approach forms a feasible way of tackling Levy flights in inhomogeneous media or systems with boundaries what is up to now a challenging problem.

cond-mat.stat-mech↗

arXiv2007

Generalized superstatistics of nonequilibrium Markovian systems

The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff's diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes. The latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually. Then stationary probability as well as flux distributions are represented as some sums over the channels. The latter construction actually forms the superstatistical description, which, however, deals with a certain superposition of equilibrium subsystems rather then is a formal expansion of the nonequilibrium steady state distribution into terms of the Boltzmann type.

cond-mat.stat-mech↗

arXiv2006

Boundary-reaction-diffusion model for oscillatory zoning in binary crystals grown from solution

Oscillatory Zoning (OZ) is a phenomenon exhibited by many geologically formed crystals. It is characterized by quasi periodic oscillations in the composition of a solid solution, caused by self-organization. We present a new model for OZ. The growth mechanism applied includes species diffusion through the solution bulk, particle adsorption, surface diffusion and subsequently desorption or incorporation into the crystal. This mechanism, in particular, can provide the synchronization effects necessary to reproduce the layered structure of experimentally obtained crystals, lacking in other models. We conduct a linear stability analysis combined with numerical simulations. Our results reproduce the experimental findings with respect to the patterns formed and a critical supersaturation necessary for OZ to occur.

cond-mat.mtrl-sci↗

arXiv2005

Contributions to the mixed-alkali effect in molecular dynamics simulations of alkali silicate glasses

The mixed-alkali effect on the cation dynamics in silicate glasses is analyzed via molecular dynamics simulations. Observations suggest a description of the dynamics in terms of stable sites mostly specific to one ionic species. As main contributions to the mixed--alkali slowdown longer residence times and an increased probability of correlated backjumps are identified. The slowdown is related to the limited accessibility of foreign sites. The mismatch experienced in a foreign site is stronger and more retarding for the larger ions, the smaller ions can be temporarily accommodated. Also correlations between unlike as well as like cations are demonstrated that support cooperative behavior.

cond-mat.mtrl-sci↗

arXiv2005

Nonlinear Ionic Conductivity of Thin Solid Electrolyte Samples: Comparison between Theory and Experiment

Nonlinear conductivity effects are studied experimentally and theoretically for thin samples of disordered ionic conductors. Following previous work in this field the {\it experimental nonlinear conductivity} of sodium ion conducting glasses is analyzed in terms of apparent hopping distances. Values up to 43 Åare obtained. Due to higher-order harmonic current density detection, any undesired effects arising from Joule heating can be excluded. Additionally, the influence of temperature and sample thickness on the nonlinearity is explored. From the {\it theoretical side} the nonlinear conductivity in a disordered hopping model is analyzed numerically. For the 1D case the nonlinearity can be even handled analytically. Surprisingly, for this model the apparent hopping distance scales with the system size. This result shows that in general the nonlinear conductivity cannot be interpreted in terms of apparent hopping distances. Possible extensions of the model are discussed.

cond-mat.mtrl-sci↗

arXiv2005

Coupling of ion and network dynamics in lithium silicate glasses: a computer study

We present a detailed analysis of the ion hopping dynamics and the related nearby oxygen dynamics in a lithium meta silicate glass via molecular dynamics simulation. For this purpose we have developed numerical techniques to identify ion hops and to sample and average dynamic information of the particles involved. This leads to an instructive insight into the microscopic interplay of ions and network. It turns out that the cooperative dynamics of lithium and oxygen can be characterized as a sliding door mechanism. It is rationalized why the local network fluctuations are of utmost importance for the lithium dynamics.

cond-mat.mtrl-sci↗

arXiv2003

Particle rearrangements during transitions between local minima of the potential energy landscape of a supercooled Lennard-Jones liquid

The potential energy landscape (PEL) of supercooled binary Lennard-Jones (BLJ) mixtures exhibits local minima, or inherent structures (IS), which are organized into meta-basins (MB). We study the particle rearrangements related to transitions between both successive IS and successive MB for a small 80:20 BLJ system near the mode-coupling temperature T_MCT. The analysis includes the displacements of individual particles, the localization of the rearrangements and the relevance of string-like motion. We find that the particle rearrangements during IS and MB transitions do not change significantly at T_MCT. Further, it is demonstrated that IS and MB dynamics are spatially heterogeneous and facilitated by string-like motion. To investigate the mechanism of string-like motion, we follow the particle rearrangements during suitable sequences of IS transitions. We find that most strings observed after a series of transitions do not move coherently during a single transition, but subunits of different sizes are active at different times. Several findings suggest that the occurrence of a successful string enables the system to exit a MB. Moreover, we show that the particle rearrangements during two consecutive MB transitions are basically uncorrelated. Specifically, different groups of particles are highly mobile during subsequent MB transitions. Finally, the relation between the features of the PEL and the relaxation processes in supercooled liquids is discussed.

cond-mat↗

arXiv2003

Complete identification of alkali sites in ion conducting lithium silicate glasses: a computer study of ion dynamics

The available sites for ions in a typical disordered ionic conductor are determined. For this purpose we devised a straightforward algorithm which via cluster analysis identifies these sites from long time ionic trajectories below the glass transition. This is exemplified for a lithium silicate glass (Li_2O)_x (SiO_2)_(1-x) for x = 0.5 and x = 0.1. We find for both concentrations that the number of sites is only slightly bigger than the number of ions. This result suggests a theoretical description of the dynamics in terms of mobile vacancies as most appropriate. Furthermore identification of the ionic sites allows one to obtain detailed characteristics of the ionic motion, e.g. quantification of correlated forward-backward jumps.

cond-mat↗

arXiv2003

What does the potential energy landscape tell us about the dynamics of supercooled liquids and glasses?

For a model glass-former we demonstrate via computer simulations how macroscopic dynamic quantities can be inferred from a PEL analysis. The essential step is to consider whole superstructures of many PEL minima, called metabasins, rather than single minima. We show that two types of metabasins exist: some allowing for quasi-free motion on the PEL (liquid-like), the others acting as traps (solid-like). The activated, multi-step escapes from the latter metabasins are found to dictate the slowing down of dynamics upon cooling over a much broader temperature range than is currently assumed.

cond-mat.stat-mech↗

arXiv2003

A simple harmonic model as a caricature for mismatch and relaxation effects for ion hopping dynamics in solid electrolytes

We formulate a simple harmonic mean-field model with N+1 particles and analyse the relaxation processes following a jump of one of these particles. Either the particle can jump back (single-particle route) or the other N particles adjust themselves (multi-particle route). The dynamics of this model is solved analytically in the linear response regime. Furthermore we relate these results to a phenomenological approach by Funke and coworkers (concept of mismatch and relaxation: CMR) which has been successfully used to model conductivity spectra in the field of ion dynamics in solid electrolytes. Since the mean-field model contains the relevant ingredients of the CMR-approach, a comparison of the resulting rate equations with the CMR-equations becomes possible. Generalizations beyond the mean-field case are discussed.

cond-mat↗

arXiv2002

Finite-Size Effects in a Supercooled Liquid

We study the influence of the system size on various static and dynamic properties of a supercooled binary Lennard-Jones liquid via computer simulations. In this way, we demonstrate that the treatment of systems as small as N=65 particles yields relevant results for the understanding of bulk properties. Especially, we find that a system of N=130 particles behaves basically as two non-interacting systems of half the size.

cond-mat.soft↗

arXiv2002

Backward correlations and dynamic heterogeneities: a computer study of ion dynamics

We analyse the correlated back and forth dynamics and dynamic heterogeneities, i.e. the presence of fast and slow ions, for a lithium metasilicate system via computer simulations. For this purpose we define, in analogy to previous work in the field of glass transition, appropriate three-time correlation functions. They contain information about the dynamics during two successive time intervals. First we apply them to simple model systems in order to clarify their information content. Afterwards we use this formalism to analyse the lithium trajectories. A strong back-dragging effect is observed, which also fulfills the time-temperature superposition principle. Furthermore, it turns out that the back-dragging effect is long-ranged and exceeds the nearest neighbor position. In contrast, the strength of the dynamic heterogeneities does not fulfill the time-temperature superposition principle. The lower the temperature, the stronger the mobility difference between fast and slow ions. The results are then compared with the simple model systems considered here as well as with some lattice models of ion dynamics.

cond-mat.dis-nn↗

arXiv2002

Energy Barriers and Activated Dynamics in a Supercooled Lennard-Jones Liquid

We study the relation of the potential energy landscape (PEL) topography to relaxation dynamics of a small model glass former of Lennard-Jones type. The mechanism under investigation is the hopping betweem superstructures of PEL mimima, called metabasins (MB). From the mean durations $\tauphi$ of visits to MBs, we derive effective depths of these objects by the relation $\Eapp=\d\ln\tauphi/\dβ$, where $β=1/\kB T$. Since the apparent activation energies $\Eapp$ are of purely dynamical origin, we look for a quantitative relation to PEL structure. A consequence of the rugged nature of MBs is that escapes from MBs are not single hops between PEL minima, but complicated multi-minima sequences. We introduce the concept of return probabilities to the bottom of MBs in order to judge whether the attraction range of a MB was left. We then compute the energy barriers that were surmounted. These turn out to be in good agreement with the effective depths $\Eapp$, calculated from dynamics. Barriers are identified with the help of a new method, which accurately performs a descent along the ridge between two minima. A comparison to another method is given. We analyze the population of transition regions between minima, called basin borders. No indication for the mechanism of diffusion to change around the mode-coupling transition can be found. We discuss the question whether the one-dimensional reaction paths connecting two minima are relevant for the calculation of reaction rates at the temperatures under study.

cond-mat.dis-nn↗

arXiv2002

Characterization of the complex ion dynamics in lithium silicate glasses via computer simulations

We present results of molecular dynamics simulations on lithium metasilicate over a broad range of temperatures for which the silicate network is frozen in but the lithium ions can still be equilibrated. The lithium dynamics is studied via the analysis of different correlation functions. The activation energy for the lithium mobility agrees very well with experimental data. The correlation of the dynamics of adjacent ions is weak. At low temperatures the dynamics can be separated into local vibrational dynamics and hopping events between adjacent lithium sites. The derivative of the mean square displacement displays several characteristic time regimes. They can be directly mapped onto respective frequency regimes for the conductivity. In particular it is possible to identify time regimes dominated by localized dynamics and long-range dynamics, respectively. The question of time-temperature superposition is discussed for the mean square displacement and the incoherent scattering function.

cond-mat.dis-nn↗

arXiv2001

How do dynamic heterogeneities evolve in time?

We present simulations of a hard disc system and analyze the time evolution of the dynamic heterogeneities. We characterize the time evolution of slow regions and slow particles individually. The motion of slow clusters turns out to be very restricted, i.e. a cluster is generated and annihilated in a spatial region four times the size of its maximum extent. The residual motion of the cluster can be traced back to subdiffusive motion of the constituent particles and the process of absorption and loss of adjacent particles. The subdiffusive dynamics is independent of how long the particles remain slow. Clusters of fast particles show an even smaller reach, which seems to be due to their short life time.

cond-mat.soft↗