Logarithmic Relaxation in a Kinetically Constrained Model

We present Monte Carlo simulations in a modification of the north-or-east-or-front model recently investigated by Berthier and Garrahan [J. Phys. Chem. B 109, 3578 (2005)]. In this coarse-grained model for relaxation in supercooled liquids, the liquid structure is substituted by a three-dimensional array of cells. A spin variable is assigned to each cell, with values 0 or 1 denoting respectively unexcited and excited local states in a mobility field. Change in local mobility (spin flip) for a given cell is permitted according to kinetic constraints determined by the mobilities of neighboring cells. In this work we keep the same kinetic constraints of the original model, but we introduce two types of cells (denoted as "fast'' and "slow'') with very different rates for spin flip. As a consequence, fast and slow cells exhibit very different relaxation times for spin correlators. While slow cells exhibit standard relaxation, fast cells display anomalous relaxation, characterized by a concave-to-convex crossover in spin correlators by changing temperature or composition. At intermediate state points logarithmic relaxation is observed over three time decades. These results display striking analogies with dynamic correlators reported in recent simulations on a bead-spring model for polymer blends.Comment: Major changes. To be published in Journal of Chemical Physic

Atomic motions in the αβ\alpha\beta-region of glass-forming polymers: Molecular versus Mode Coupling Theory approach

We present fully atomistic Molecular Dynamics simulation results on a main-chain polymer, 1,4-Polybutadiene, in the merging region of the $\alpha$- and $beta$-relaxations. A real space analysis reveals the occurrence of localized motions (``$\beta$-like'') in addition to the diffusive structural relaxation. A molecular approach provides a direct connection between the local conformational changes reflected in the atomic motions and the secondary relaxations in this polymer. Such local processes occur just in the time window where the $\beta$-process of the Mode Coupling Theory is expected. We show that the application of this theory is still possible, and yields an unusually large value of the exponent parameter. This result might originate from the competition between two mechanisms for dynamic arrest: intermolecular packing and intramolecular barriers for local conformational changes (``$\beta$-like'').Comment: 10 pages, 6 figure

Static and dynamic contributions to anomalous chain dynamics in polymer blends

By means of computer simulations, we investigate the relaxation of the Rouse modes in a simple bead-spring model for non-entangled polymer blends. Two different models are used for the fast component, namely fully-flexible and semiflexible chains. The latter are semiflexible in the meaning that static intrachain correlations are strongly non-gaussian at all length scales. The dynamic asymmetry in the blend is strongly enhanced by decreasing temperature, inducing confinement effects on the fast component. The dynamics of the Rouse modes show very different trends for the two models of the fast component. For the fully-flexible case, the relaxation times exhibit a progressive deviation from Rouse scaling on increasing the dynamic asymmetry. This anomalous effect has a dynamic origin. It is not related to particular static features of the Rouse modes, which indeed are identical to those of the fully-flexible homopolymer, and are not modified by the dynamic asymmetry in the blend. On the contrary, in the semiflexible case the relaxation times exhibit approximately the same scaling behaviour as the amplitudes of the modes. This suggests that the origin of the anomalous dynamic scaling for semiflexible chains confined in the blend is esentially of static nature. We discuss implications of these observations for the applicability of theoretical approaches to chain dynamics in polymer blends.Comment: 15 pages (single-column), 6 figure

Dynamic Arrest in Polymer Melts: Competition between Packing and Intramolecular Barriers

We present molecular dynamics simulations of a simple model for polymer melts with intramolecular barriers. We investigate structural relaxation as a function of the barrier strength. Dynamic correlators can be consistently analyzed within the framework of the Mode Coupling Theory (MCT) of the glass transition. Control parameters are tuned in order to induce a competition between general packing effects and polymer-specific intramolecular barriers as mechanisms for dynamic arrest. This competition yields unusually large values of the so-called MCT exponent parameter and rationalize qualitatively different observations for simple bead-spring and realistic polymers. The systematic study of the effect of intramolecular barriers presented here also establishes a fundamental difference between the nature of the glass transition in polymers and in simple glass-formers.Comment: 4 pages, 3 figures, 2 table

A Novel Route to Calculate the Length Scale for the Glass Transition in Polymers

The occurrence of glass transition is believed to be associated to cooperative motion with a growing length scale with decreasing temperature. We provide a novel route to calculate the size of cooperatively rearranging regions CRR of glass-forming polymers combining the Adam-Gibbs theory of the glass transition with the self-concentration concept. To do so we explore the dynamics of glass-forming polymers in different environments. The material specific parameter $\alpha$ connecting the size of the CRR to the configurational entropy is obtained in this way. Thereby, the size of CRR can be precisely quantified in absolute values. This size results to be in the range 1 $\div$ 3 nm at the glass transition temperature depending on the glass-forming polymer

The Berry phase and the pump flux in stochastic chemical kinetics

We study a classical two-state stochastic system in a sea of substrates and products (absorbing states), which can be interpreted as a single Michaelis-Menten catalyzing enzyme or as a channel on a cell surface. We introduce a novel general method and use it to derive the expression for the full counting statistics of transitions among the absorbing states. For the evolution of the system under a periodic perturbation of the kinetic rates, the latter contains a term with a purely geometrical (the Berry phase) interpretation. This term gives rise to a pump current between the absorbing states, which is due entirely to the stochastic nature of the system. We calculate the first two cumulants of this current, and we argue that it is observable experimentally

Relaxation Scenarios in a Mixture of Large and Small Spheres: Dependence on the Size Disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and the small particles. Density-density correlators for the small particles become extremely stretched, and display logarithmic relaxation by properly tuning the temperature or the wavevector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated to Mode Coupling transition lines of the types B and A at, respectively, small and very large size disparity. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent Mode Coupling Theory for fluids confined in matrixes with interconnected voids [V. Krakoviack, Phys. Rev. Lett. {\bf 94}, 065703 (2005)].Comment: Journal of Chemical Physics 125, 164507 (2006

Tests of mode coupling theory in a simple model for two-component miscible polymer blends

We present molecular dynamics simulations on the structural relaxation of a simple bead-spring model for polymer blends. The introduction of a different monomer size induces a large time scale separation for the dynamics of the two components. Simulation results for a large set of observables probing density correlations, Rouse modes, and orientations of bond and chain end-to-end vectors, are analyzed within the framework of the Mode Coupling Theory (MCT). An unusually large value of the exponent parameter is obtained. This feature suggests the possibility of an underlying higher-order MCT scenario for dynamic arrest.Comment: Revised version. Additional figures and citation