Universal nature of particle displacements close to glass and jamming transitions

MD simulation of concentrated polymer solutions: structural relaxation near the glass transition

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T(g) or critical temperature T(c) of mode-coupling theory (MCT). Both T(g) and T(c) (> T(g)) decrease with increasing solvent concentration φ(S). The decrease is linear for the concentrations studied (up to φ(S) = 25%). Above T(c) we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T(c). Near T(c) we investigate dynamic correlation functions, such as the incoherent intermediate scattering function φ(q)(s)(t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r; t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that φ(q)(s)(t) obeys the time-temperature superposition principle and has α relaxation times τ(q)(s) which are compatible with a power law increase close (but not too close) to T(c). In divergence to MCT, however, the increase of τ(q)(s) depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the α relaxation an analysis of P(ln r; t) reveals a double-peak structure close to T(c). The first peak corresponds to "slow" particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These "fast" particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T(c).

Tracking heterogeneous dynamics during the alpha relaxation of a simple glass former

We study the relaxation process in a simple glass former--the Kob-Andersen lattice gas model. We show that, for this model, structural relaxation is due to slow percolation of regions of cooperatively moving particles, which leads to heterogeneous dynamics of the system. We find that the size distribution of these regions is given by a power law and that their formation is encoded in the initial structure of the particles, with the memory of initial configuration increasingly retained with increasing density.

Anomalous diffusion in heterogeneous glass-forming liquids: temperature-dependent behavior

In a preceding paper, Langer and Mukhopadhyay [Phys. Rev. E 77, 061505 (2008)] studied the diffusive motion of a tagged molecule in an heterogeneous glass-forming liquid at temperatures just above a glass transition. Among other features of this system, we postulated a relation between heterogeneity and stretched-exponential decay of correlations, and we also confirmed that systems of this kind generally exhibit non-Gaussian diffusion on intermediate length and time scales. Here I extend this analysis to higher temperatures approaching the point where the heterogeneities disappear and thermal activation barriers become small. I start by modifying the continuous-time random-walk theory proposed in Langer and Mukhopadhyay and supplement this analysis with an extension of the excitation-chain theory of glass dynamics. I also use a key result from the shear-transformation-zone theory of viscous deformation of amorphous materials. Elements of each of these theories are then used to interpret experimental data for orthoterphenyl, specifially, the diffusion and viscosity coefficients and neutron-scattering measurements of the self-intermediate scattering function. Reconciling the theory with these data sets provides insights into the crossover between super-Arrhenius and Arrhenius dynamics, length scales of spatial heterogeneities, violation of the Stokes-Einstein relation in glass-forming liquids, and the origin of stretched-exponential decay of correlations.

Facilitation, complexity growth, mode coupling, and activated dynamics in supercooled liquids

In low-temperature-supercooled liquids, below the ideal mode-coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. Here, we present a theory that shows explicitly the interplay between the two processes and shows that activated hopping facilitates continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics described here by the mode coupling theory (MCT)] and the activated hopping (described here by the random first-order transition theory). We apply the theory to a specific system, Salol, to show that the theory correctly predicts the temperature dependence of the nonexponential stretching parameter, beta, and the primary alpha relaxation timescale, tau. The study explains why, even below the mean field ergodic to nonergodic transition, the dynamics is well described by MCT. The nonlinear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Furthermore, the theory correctly predicts the observed variation of the stretching exponent beta with the fragility parameter, D. These two predictions also allow the complexity growth to be predicted, in good agreement with the results of Capaccioli et al. [Capaccioli S, Ruocco G, Zamponi F (2008) J Phys Chem B 112:10652-10658].

Dynamical heterogeneity in a model for permanent gels: different behavior of dynamical susceptibilities

We present a systematic study of dynamical heterogeneity in a model for permanent gels upon approaching the gelation threshold. We find that the fluctuations of the self-intermediate scattering function are increasing functions of time, reaching a plateau whose value, at large length scales, coincides with the mean cluster size and diverges at the percolation threshold. Another measure of dynamical heterogeneities-i.e., the fluctuations of the self-overlap-displays instead a peak and decays to zero at long times. The peak, however, also scales as the mean cluster size. Arguments are given for this difference in the long-time behavior. We also find that the non-Gaussian parameter reaches a plateau in the long-time limit. The value of the plateau of the non-Gaussian parameter, which is connected to the fluctuations of diffusivity of clusters, increases with the volume fraction and remains finite at the percolation threshold.

Exploring the potential energy landscape of glass-forming systems: from inherent structures via metabasins to macroscopic transport

In this review a systematic analysis of the potential energy landscape (PEL) of glass-forming systems is presented. Starting from the thermodynamics, the route towards the dynamics is elucidated. A key step in this endeavor is the concept of metabasins. The relevant energy scales of the PEL can be characterized. Based on the simulation results for some glass-forming systems one can formulate a relevant model system (ideal Gaussian glass-former) which can be treated analytically. The macroscopic transport can be related to the microscopic hopping processes, using either the strong relation between energy (thermodynamics) and waiting times (dynamics) or, alternatively, the concepts of the continuous-time random walk. The relation to the geometric properties of the PEL is stressed. The emergence of length scales within the PEL approach as well as the nature of finite-size effects is discussed. Furthermore, the PEL view is compared to other approaches describing the glass transition.

Dynamical heterogeneity in a glass-forming ideal gas

We conduct a numerical study of the dynamical behavior of a system of three-dimensional "crosses," particles that consist of three mutually perpendicular line segments of length sigma rigidly joined at their midpoints. In an earlier study [W. van Ketel, Phys. Rev. Lett. 94, 135703 (2005)] we showed that this model has the structural properties of an ideal gas, yet the dynamical properties of a strong glass former. In the present paper we report an extensive study of the dynamical heterogeneities that appear in this system in the regime where glassy behavior sets in. On the one hand, we find that the propensity of a particle to diffuse is determined by the structure of its local environment. The local density around mobile particles is significantly less than the average density, but there is little clustering of mobile particles, and the clusters observed tend to be small. On the other hand, dynamical susceptibility results indicate that a large dynamical length scale develops even at moderate densities. This suggests that propensity and other mobility measures are an incomplete measure of the dynamical length scales in this system.

From elementary steps to structural relaxation: a continuous-time random-walk analysis of a supercooled liquid

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 yields a quantitative link between the elementary step and the full structural relaxation. The analysis involves a verification of the CTRW conditions as well as a quantitative test of the predictions. The wave-vector dependence of the relaxation time and the degree of nonexponentiality can be expressed in terms of the first moments of the waiting time distribution.

Negative differential mobility of weakly driven particles in models of glass formers

We study the response of probe particles to weak constant driving in kinetically constrained models of glassy systems, and show that the probe's response can be nonmonotonic and give rise to negative differential mobility: increasing the applied force can reduce the probe's drift velocity in the force direction. Other significant nonlinear effects are also demonstrated, such as the enhancement with increasing force of the probe's fluctuations away from the average path, a phenomenon known in other contexts as giant diffusivity. We show that these results can be explained analytically by a continuous-time random walk approximation where there is decoupling between persistence and exchange times for local displacements of the probe. This decoupling is due to dynamic heterogeneity in the glassy system, which also leads to bimodal distributions of probe particle displacements. We discuss the relevance of our results to experiments.

Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: low-temperature behavior

We propose a model of a heterogeneous glass-forming liquid and compute the low-temperature behavior of a tagged molecule moving within it. This model exhibits stretched-exponential decay of the wave-number-dependent, self-intermediate scattering function in the limit of long times. At temperatures close to the glass transition, where the heterogeneities are much larger in extent than the molecular spacing, the time dependence of the scattering function crosses over from stretched-exponential decay with an index b=1/2 at large wave numbers to normal, diffusive behavior with b=1 at small wave numbers. There is a clear separation between early-stage, cage-breaking beta relaxation and late-stage alpha relaxation. The spatial representation of the scattering function exhibits an anomalously broad exponential (non-Gaussian) tail for sufficiently large values of the molecular displacement at all finite times.

Large-amplitude jumps and non-Gaussian dynamics in highly concentrated hard sphere fluids

Our microscopic stochastic nonlinear Langevin equation theory of activated dynamics has been employed to study the real-space van Hove function of dense hard sphere fluids and suspensions. At very short times, the van Hove function is a narrow Gaussian. At sufficiently high volume fractions, such that the entropic barrier to relaxation is greater than the thermal energy, its functional form evolves with time to include a rapidly decaying component at small displacements and a long-range exponential tail. The "jump" or decay length scale associated with the tail increases with time (or particle root-mean-square displacement) at fixed volume fraction, and with volume fraction at the mean alpha relaxation time. The jump length at the alpha relaxation time is predicted to be proportional to a measure of the decoupling of self-diffusion and structural relaxation. At long times corresponding to mean displacements of order a particle diameter, the volume fraction dependence of the decay length disappears. A good superposition of the exponential tail feature based on the jump length as a scaling variable is predicted at high volume fractions. Overall, the theoretical results are in good accord with recent simulations and experiments. The basic aspects of the theory are also compared with a classic jump model and a dynamically facilitated continuous time random-walk model. Decoupling of the time scales of different parts of the relaxation process predicted by the theory is qualitatively similar to facilitated dynamics models based on the concept of persistence and exchange times if the elementary event is assumed to be associated with transport on a length scale significantly smaller than the particle size.

Structural origins of dynamical heterogeneity in colloidal gels

We show by resolving single-particle dynamics as a function of contact number that dynamical heterogeneity in depletion colloidal gels must have more than one structural origin. Although the magnitude of dynamical heterogeneity of weak gels with cluster structure and strong gels with string structure is similar, the dependence of particle localization on contact number differs significantly in each. The observed transition between contact number dependent and independent dynamics for the weak and strong gels is abrupt. The results suggest that spatially heterogeneous dynamics cannot be a complete explanation of the dynamical heterogeneity of colloidal gels.

Decoupling of exchange and persistence times in atomistic models of glass formers

With molecular dynamics simulations of a fluid mixture of classical particles interacting with pairwise additive Weeks-Chandler-Andersen potentials, we consider the time series of particle displacements and thereby determine the distributions for local persistence times and local exchange times. These basic characterizations of glassy dynamics are studied over a range of supercooled conditions and were shown to have behaviors, most notably decoupling, similar to those found in kinetically constrained lattice models of structural glasses. Implications are noted.

Structure and dynamics of glass formers: predictability at large length scales

Dynamic heterogeneity in glass formers has been related to their static structure using the concept of dynamic propensity. We reexamine this relationship by analyzing dynamical fluctuations in two atomistic glass formers and two theoretical models. We introduce quantitative statistical indicators which show that the dynamics of individual particles cannot be predicted on the basis of the propensity or by any structural indicator. However, the spatial structure of the propensity field does have predictive power for the spatial correlations associated with dynamic heterogeneity. Our results suggest that the quest for a connection between the static and dynamic properties of glass formers at the particle level is in vain, but they demonstrate that such a connection does exist on larger length scales.