Grzegorz Szamel

Computer simulation study of the structure and dynamics of ring polymers

We study the equilibrium structure and dynamics of unconcatenated, unknotted polymer rings in the melt. In agreement with earlier studies we find that rings in the melt are more compact than linear chains. In addition, we show that the “correlation hole” in the equilibrium correlation functions is deeper and wider for rings than for linear chains. This suggests that there is less interpenetration in the melt of rings compared to the melt of linear chains. We also find that rings diffuse faster than linear chains. For smaller rings this result agrees with the earlier work of Muller, Wittmer, and Cates [Phys. Rev. E 53, 5063 (1996)]. The main result of this study is that faster ring diffusion persists up to ring size at least ten times greater than the entanglement crossover of linear chains. Furthermore, we show that, for all ring sizes studied, the dependence of the single-chain relaxation time on ring size is weaker than for linear chains. Finally, we find that both faster diffusion and faster relaxation...

Structure and dynamics of ring polymers

We study the equilibrium structure and dynamics of unconcatenated unknotted polymer rings in the melt. In accordance with earlier studies we find that rings in the melt are more compact than linear chains. We show that rings interpenetrate less and, perhaps as a result, diffuse faster than linear chains. Ring diffusion is faster for all ring sizes studied, the largest ring having numbers of monomers approximately ten times greater than the entanglement crossover of linear chains.

Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation

We solved the mode-coupling equations for the Kob-Andersen binary mixture using structure factors calculated from Brownian dynamics simulations of the same system. We found, as was previously observed, that the mode-coupling temperature T(c) inferred from simulations is about two times greater than that predicted by the theory. However, we find that many time-dependent quantities agree reasonably well with the predictions of the mode-coupling theory if they are compared at the same reduced temperature epsilon = (T - T(c))/T(c), and if epsilon is not too small. Specifically, the simulation results for the incoherent intermediate scattering function, the mean square displacement, the relaxation time, and the self-diffusion coefficient agree reasonably well with the predictions of the mode-coupling theory. We find that there are substantial differences for the non-Gaussian parameter. At small reduced temperatures the probabilities of the logarithm of single particle displacements demonstrate that there is hopping-like motion present in the simulations, and this motion is not predicted by the mode-coupling theory. The wave-vector-dependent relaxation time is shown to be qualitatively different from the predictions of the mode-coupling theory for temperatures where hopping-like motion is present.

Increasing the density melts ultrasoft colloidal glasses

We use theory and simulations to investigate the existence of amorphous glassy states in ultrasoft colloids. We combine the hypernetted chain approximation with mode-coupling theory to study the dynamic phase diagram of soft repulsive spheres interacting with a Hertzian potential, focusing on low temperatures and large densities. At constant temperature, we find that an amorphous glassy state is entered upon compression, as in colloidal hard spheres, but the glass unexpectedly melts when density increases further. We attribute this reentrant fluid-glass transition to particle softness and correlate this behavior to previously reported anomalies in soft systems, thus emphasizing its generality. The predicted fluid-glass-fluid sequence is confirmed numerically.

Relaxation in a glassy binary mixture : Mode-coupling-like power laws, dynamic heterogeneity, and a new non-gaussian parameter

We examine the relaxation of the Kob-Andersen Lennard-Jones binary mixture using Brownian dynamics computer simulations. We find that in accordance with mode-coupling theory the self-diffusion coefficient and the relaxation time show power-law dependence on temperature. However, different mode-coupling temperatures and power laws can be obtained from the simulation data depending on the range of temperatures chosen for the power-law fits. The temperature that is commonly reported as this systems mode-coupling transition temperature, in addition to being obtained from a power law fit, is a crossover temperature at which there is a change in the dynamics from the high-temperature homogeneous, diffusive relaxation to a heterogeneous, hopping-like motion. The hopping-like motion is evident in the probability distributions of the logarithm of single-particle displacements: approaching the commonly reported mode-coupling temperature these distributions start exhibiting two peaks. Notably, the temperature at which the hopping-like motion appears for the smaller particles is slightly higher than that at which the hopping-like motion appears for the larger ones. We define and calculate a new non-Gaussian parameter whose maximum occurs approximately at the time at which the two peaks in the probability distribution of the logarithm of displacements are most evident.

Independence of the relaxation of a supercooled fluid from its microscopic dynamics: Need for yet another extension of the mode-coupling theory

Using Brownian dynamics computer simulations, we show that the relaxation of a supercooled Brownian system is qualitatively the same as that of a Newtonian system. In particular, near the so-called mode-coupling transition temperature, dynamic properties of the Brownian system exhibit the same deviations from power law behavior as those of the Newtonian one. Thus, similar dynamical events cut off the idealized mode-coupling transition in Brownian and Newtonian systems. We discuss implications of this finding for extended mode-coupling theory. In addition, we point out and discuss the difference between our findings and experimental results, and present an alternative interpretation of some of our simulation data.

Fundamental differences between glassy dynamics in two and three dimensions

The two-dimensional freezing transition is very different from its three-dimensional counterpart. In contrast, the glass transition is usually assumed to have similar characteristics in two and three dimensions. Using computer simulations, here we show that glassy dynamics in supercooled two- and three-dimensional fluids are fundamentally different. Specifically, transient localization of particles on approaching the glass transition is absent in two dimensions, whereas it is very pronounced in three dimensions. Moreover, the temperature dependence of the relaxation time of orientational correlations is decoupled from that of the translational relaxation time in two dimensions but not in three dimensions. Last, the relationships between the characteristic size of dynamically heterogeneous regions and the relaxation time are very different in two and three dimensions. These results strongly suggest that the glass transition in two dimensions is different than in three dimensions.

Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture.

We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction ϕ(c). First, we characterize the systems dynamics. Then, we utilize a method [Phys. Rev. Lett. 105, 217801 (2010)] to extract and analyze the ensemble-independent dynamic susceptibility χ(4)(t) and the dynamic correlation length ξ(t) for a range of times between the β and α relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction-independent master curve ξ(t)~ln(t). For longer times, ξ(t) departs from this master curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation τ(α)~exp[ξ(τ(α))] between the α relaxation time, τ(α), and the dynamic correlation length at this time, ξ(τ(α)), we also find a similar correlation for the diffusion coefficient D~exp[ξ(τ(α))(θ)] with θ≈0.6. We discuss the relevance of these findings for different theories of the glass transition.

Thin films of asymmetric triblock copolymers: A Monte Carlo study

We study the morphology of asymmetric A8B48A8 triblock copolymer thin films confined between two homogeneous surfaces (walls). Morphology is investigated as a function of the film thickness and the strength of the wall–polymer interaction. For very thin films we observe cylinders perpendicular to the walls for a wide range of wall–polymer interaction. With increasing film thickness other morphologies are becoming more stable. We observe wetting layers of short, end blocks, cylinders parallel to the walls, and perforated lamellae. For thick films perpendicular cylinders remain stable only for a very narrow range of wall–polymer interaction.

Self-propelled particle in an external potential: existence of an effective temperature.

We study a stationary state of a single self-propelled, athermal particle in linear and quadratic external potentials. The self-propulsion is modeled as a fluctuating internal driving force evolving according to the Ornstein-Uhlenbeck process, independently of the state of the particle. Without an external potential, in the long time limit, the self-propelled particle moving in a viscous medium performs diffusive motion, which allows one to identify an effective temperature. We show that in the presence of a linear external potential the stationary state distribution has an exponential form with the sedimentation length determined by the effective temperature of the free self-propelled particle. In the presence of a quadratic external potential the stationary state distribution has a Gaussian form. However, in general, this distribution is not determined by the effective temperature of the free self-propelled particle.