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Thomas Voigtmann

Publications and source records attributed to Thomas Voigtmann.

At least 37 records · Page 2Linked to original sources

Solvable Models of Supercooled Liquids in Three Dimensions

We introduce a supercooled liquid model and obtain parameter-free quantitative predictions that are in excellent agreement with numerical simulations, notably in the hard low-temperature region characterized by strong deviations from Mode-Coupling-Theory behavior. The model is the Fredrickson-Andersen Kinetically-Constrained-Model on the three-dimensional $M$-layer lattice. The agreement has implications beyond the specific model considered because the theory is potentially valid for many more systems, including realistic models and actual supercooled liquids.

cond-mat.dis-nn↗

Multiple character of non-monotonic size-dependence for relaxation dynamics in polymer-particle and binary mixtures

Adding plasticizers is a well-known procedure to reduce the glass transition temperature in polymers. It has been recently shown that this effect shows a non-monotonic dependence on the size of additive molecules [The Journal of Chemical Physics 150 (2019) 024903]. In this work, we demonstrate that, as the size of the additive molecules is changed at fixed concentration, multiple extrema emerge in the dependence of the system's relaxation time on the size ratio. The effect occurs on all relevant length scales including single monomer dynamics, decay of Rouse modes and relaxation of the chain's end-to-end vector. A qualitatively similar trend is found within mode-coupling theoretical results for a binary hard-sphere (HS) mixture. An interpretation of the effect in terms of local packing efficiency and coupling between the dynamics of minority and majority species is provided.

cond-mat.soft↗

Arrested dynamics of the dipolar hard-sphere model

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (softcore) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: At low ({$η$} = 0.2) and intermediate ($η$ = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations ({$η$} $\lt$ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid.

cond-mat.soft↗

On the dynamics of reaction coordinates in classical, time-dependent, many-body processes

Complex microscopic many-body processes are often interpreted in terms of so-called `reaction coordinates', i.e. in terms of the evolution of a small set of coarse-grained observables. A rigorous method to produce the equation of motion of such observables is to use projection operator techniques, which split the dynamics of the observables into a main contribution and a marginal one. The basis of any derivation in this framework is the classical (or quantum) Heisenberg equation for an observable. If the Hamiltonian of the underlying microscopic dynamics and the observable under study do not explicitly depend on time, this equation is obtained by a straight-forward derivation. However, the problem is more complicated if one considers Hamiltonians which depend on time explicitly as e.g. in systems under external driving, or if the observable of interest has an explicit dependence on time. We use an analogy to fluid dynamics to derive the classical Heisenberg picture and then apply a projection operator formalism to derive the non-stationary generalized Langevin equation for a coarse-grained variable. We show, in particular, that the results presented for time-independent Hamiltonians and observables in J. Chem. Phys. 147, 214110 (2017) can be generalized to the time-dependent case.

cond-mat.stat-mech↗

Glassy dynamics in asymmetric binary mixtures of hard-spheres

The binary hard-sphere mixture is one of the simplest representations of a many-body system with competing time and length scales. This model is relevant to fundamentally understand both the structural and dynamical properties of materials, such as metallic melts, colloids, polymers and bio-based composites. It also allows us to study how different scales influence the physical behavior of a multicomponent glass-forming liquid; a question that still awaits a unified description. In this contribution, we report on distinct dynamical arrest transitions in highly asymmetric binary colloidal mixtures, namely, a single glass of big particles, in which the small species remains ergodic, and a double glass with the simultaneous arrest of both components. When the mixture approaches any glass transition, the relaxation of the collective dynamics of both species becomes coupled. In the single glass domain, spatial modulations occur due to the structure of the large spheres, a feature not observed in the two-glass domain. The relaxation of the \emph{self} dynamics of small and large particles, in contrast, become decoupled at the boundaries of both transitions; the large species always displays dynamical arrest, whereas the small ones appear arrested only in the double glass. Thus, in order to obtain a complete picture of the distinct glassy states, one needs to take into account the dynamics of both species.

cond-mat.soft↗

Static Structure of Active Brownian Hard Disks

We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems.

cond-mat.stat-mech↗

On the "generalized Generalized Langevin Equation"

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. In contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation, but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows to relate the Taylor expansion of the memory kernel to data that is accessible in MD simulations and experiments, thus allowing to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions, and is shown to be consistent with direct measurements from simulations.

cond-mat.stat-mech↗

How Glassy Relaxation Slows Down by Increasing Mobility

We investigate how structural relaxation in mixtures with strong dynamical asymmetry is affected by the microscopic dynamics. Brownian and Newtonian dynamics simulations of dense mixtures of fast and slow hard spheres reveal a striking trend reversal. Below a critical density, increasing the mobility of the fast particles fluidizes the system, yet, above that critical density, the same increase in mobility strongly hinders the relaxation of the slow particles. The critical density itself does not depend on the dynamical asymmetry and can be identified with the glass-transition density of the mode-coupling theory. The asymptotic dynamics close to the critical density is universal, but strong pre-asymptotic effects prevail in mixtures with additional size asymmetry. This observation reconciles earlier findings of a strong dependence on kinetic parameters of glassy dynamics in colloid--polymer mixtures with the paradigm that the glass transition is determined by the properties of configuration space alone.

cond-mat.soft↗

Mode-Coupling Theory for Active Brownian Particles

We present a mode-coupling theory (MCT) for the high-density dynamics of two-dimensional spherical active Brownian particles (ABP). The theory is based on the integration-through-transients (ITT) formalism and hence provides a starting point for the calculation of non-equilibrium averages in active-Brownian particle systems. The ABP are characterized by a self-propulsion velocity $v_0$, and by their translational and rotational diffusion coefficients, $D_t$ and $D_r$. The theory treats both the translational and the orientational degrees of freedom of ABP explicitly. This allows to study the effect of self-propulsion of both weak and strong persistence of the swimming direction, also at high densities where the persistence length $\ell_p=v_0/D_r$ is large compared to the typical interaction length scale. While the low-density dynamics of ABP is characterized by a single Péclet number, $Pe=v_0^2/D_rD_t$, close to the glass transition the dynamics is found to depend on $Pe$ and $\ell_p$ separately. At fixed density, increasing the self-propulsion velocity causes structural relaxatino to speed up, while decreasing the persistence length slows down the relaxation. The theory predicts a non-trivial idealized-glass-transition diagram in the three-dimensional parameter space of density, self-propulsion velocity and rotational diffusivity. The active-MCT glass is a nonergodic state where correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.

cond-mat.soft↗

Clearing out a maze: The hungry random walker and its anomalous diffusion

We study chemotaxis in a porous medium using as a model a biased ("hungry") random walk on a percolating cluster. In close resemblance to the 1980s arcade game Pac-Man, the hungry random walker consumes food, which is initially distributed in the maze, and biases its movement towards food-filled sites. We observe that, on the percolating cluster, the mean-squared displacement of the pacman process shows anomalous dynamics, which follow a power law with a dynamical exponent different from both that of a self avoiding random walk as well as that of an unbiased random walk. The change in dynamics with the propensity to move towards food is well described by a dynamical exponent that depends continuously on this propensity, and results in slower differential growth when compared to the unbiased random walk.

cond-mat.stat-mech↗

Anomalous dynamics of intruders in a crowded environment of mobile obstacles

Many natural and industrial processes rely on constrained transport, such as proteins moving through cells, particles confined in nanocomposite materials or gels, individuals in highly dense collec- tives and vehicular traffic conditions. These are examples of motion through crowded environments, in which the host matrix may retain some glass-like dynamics. Here we investigate constrained transport in a colloidal model system, in which dilute small spheres move in a slowly rearranging, glassy matrix of large spheres. Using confocal differential dynamic microscopy and simulations, we discover a critical size asymmetry at which anomalous collective transport of the small particles appears, manifested as a logarithmic decay of the density autocorrelation functions. We demonstrate that the matrix mobility is central for the observed anomalous behaviour. These results, crucially depending on size-induced dynamic asymmetry, are of relevance for a wide range of phenomena ranging from glassy systems to cell biology.

cond-mat.soft↗

On The Nature of the Glass Crossover

Stochastic Beta Relaxation (SBR) is a model for the dynamics of glass- forming liquids close to the glass transition singularity of the idealized mode- coupling theory (MCT) that has been derived from generic MCT-like theories by applying dynamical field-theory techniques. SBR displays a rich phenomenology common to most super-cooled liquids. In its simplest version it naturally explains two prominent features of the dynamical crossover: the change from a power-law to exponential increase in the structural relaxation time and the violation of the Stokes-Einstein relation between diffusion and viscosity. The solution of the model in three dimensions unveils a qualitative change at the crossover in the structure of dynamical fluctuations from a regime characterized by power-law increases of their amplitude and size to a regime dominated by strong Dynamical Heterogeneities: rare regions where dynamics is relatively much faster than in the rest of the system. While the relaxation time changes by orders of magnitude, the size of these regions does not change significantly and actually decreases below the crossover temperature. SBR cannot sustain too large fluctuations and could fail well below the crossover temperature. There it could be replaced by non-conventional activated dynamics characterized by elementary events with intrinsic time and length scales of an unusual large (but not necessarily increasing) size (mesoscopic vs. microscopic).

cond-mat.dis-nn↗

Dissipation in a Crystallization Process

We discuss the crystallization process from the supersaturated melt in terms of its non-equilibrium properties. In particular, we quantify the amount of heat that is produced irreversibly when a suspension of hard spheres crystallizes. This amount of heat can be interpreted as arising from the resistance of the system against undergoing phase transition. We identify an intrinsic compression rate that separates a quasi-static regime from a regime of rapid crystallization. In the former the disspated heat grows linearly in the compression rate. In the latter the system crystallizes more easily, because new relaxation channels are opened, at the cost of forming a higher fraction of non-equilibrium crystal structures. In analogy to a shear-thinning fluid, the system shows a decreased resistance when it is driven rapidly.

cond-mat.stat-mech↗

Qualitative Features at the Glass Crossover

We discuss some generic features of the dynamics of glass-forming liquids close to the glass transition singularity of the idealized mode-coupling theory (MCT). The analysis is based on a recent model by one of the authors for the intermediate-time dynamics ($β$ relaxation), derived by applying dynamical field-theory techniques to the idealized MCT. Combined with the assumption of time-temperature superposition for the slow structural ($α$) relaxation, the model naturally explains three prominent features of the dynamical crossover: the change from a power-law to exponential increase in the structural relaxation time, the replacement of the Stokes-Einstein relation between diffusion and viscosity by a fractional law, and two distinct growth regimes of the thermal susceptibility that has been associated to dynamical heterogeneities.

cond-mat.stat-mech↗

Nonlinear rheology of dense colloidal systems with short-ranged attraction: A mode-coupling theory analysis

The nonlinear rheology of glass-forming colloidal suspensions with short-ranged attractions is discussed within the integration-through transients framework combined with the mode-coupling theory of the glass transition (ITT-MCT). Calculations are based on the square-well system (SWS), as a model for colloid-polymer mixtures. The high-density regime featuring reentrant melting of the glass upon increasing the attraction strength, and the crossover from repulsive glasses formed at weak attraction to attractive glasses formed at strong attraction, are discussed. Flow curves are found in qualitative agreement with experimental data, featuring a strong increase in the yield stress, and, for suitable interaction parameters, the crossover between two yield stresses. The yield strain, defined as the position of the stress overshoot under startup flow, is found to be proportional to the attraction range for strong attraction. At weak and intermediate attraction strength, the combined effects of hard-core caging and attraction-driven bonding result in a richer dependence on the parameters. The first normal-stress difference exhibits a weaker dependence on short-ranged attractions as the shear stress, since the latter is more sensitive the short-wavelength features of the static structure.

cond-mat.soft↗

Channel Flow of a Tensorial Shear-Thinning Maxwell Model: Lattice Boltzmann Simulations

We introduce a nonlinear generalized tensorial Maxwell-type constitutive equation to describe shear-thinning glass-forming fluids, motivated by a recent microscopic approach to the nonlinear rheology of colloidal suspensions. The model captures a nonvanishing dynamical yield stress at the glass transition and incorporates normal-stress differences. A modified lattice-Boltzmann (LB) simulation scheme is presented that includes non-Newtonian contributions to the stress tensor and deals with flow-induced pressure differences. We test this scheme in pressure-driven 2D Poiseuille flow of the nonlinear generalized Maxwell fluid. In the steady state, comparison with an analytical solution shows good agreement. The transient dynamics after startup and cessation of the pressure gradient are studied; the simulation reproduces a finite stopping time for the cessation flow of the yield-stress fluid in agreement with previous analytical estimates.

cond-mat.soft↗

On the Bauschinger effect in supercoooled melts under shear: results from mode coupling theory and molecular dynamics simulations

We study the nonlinear rheology of a glass-forming binary mixture under the reversal of shear flow using molecular dynamics simulations and a schematic model of the mode-coupling theory of the glass transition (MCT). Memory effects lead to a history-dependent response, as exemplified by the vanishing of a stress-overshoot phenomenon in the stress--strain curves of the sheared liquid, and a change in the apparent elastic coefficients around states with zero stress. We investigate the various retarded contributions to the stress response at a given time schematically within MCT. The connection of this macroscopic response to single-particle motion is demonstrated using molecular-dynamics simulation.

cond-mat.soft↗

Dynamic arrest in model porous media -- intermediate scattering functions

Heterogeneous media constitute random disordered environments where transport is drastically hindered. Employing extensive molecular dynamics simulations, we investigate the spatio-temporal dynamics of tracer particles in the Lorentz model in the vicinity of the localization transition. There transport becomes anomalous and non-gaussian due to the presence of self-similar spatial structures, and dynamic scaling behavior is anticipated. The interplay of different time and length scales is revealed by the intermediate scattering functions, which are sensitive both to the underlying spatial fractal as well as the anomalous transport. We compare our numerical results in the transition regime to a mode-coupling approach, and find that certain aspects are surprisingly well predicted.

cond-mat.stat-mech↗