Quantitative Model for Clusters of String-like Cooperative Motion in a Coarse-Grained Glass-Forming Polymer Melt
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Quantitative Model for Clusters of String-like Cooperative Motion in a Coarse-Grained Glass-Forming Polymer Melt Beatriz A Pazmiño Betancourt1, Jack F. Douglas 2 and Francis W. Starr1 1
Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA Materials Science and Engineering, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899. 1,2
ABSTRACT We apply a living polymerization theory to describe cooperative stringlike particle rearrangement clusters observed in simulations of a coarsegrained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly ĭ without free parameters. Combining this theory with the Adam-Gibbs (AG) model allows us to predict the relaxation time IJ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann ‘entropy crisis’. INTRODUCTION While the understanding of the fundamental factors controlling glass-forming (GF) liquids has continually improved, there is no generally accepted theory of glass formation based on a fundamental statistical mechanical model. In addition to the familiar phenomenology relating to the macroscopic properties of GF liquids, such as the dramatic and nearly universal temperature T dependence of diffusion and fluid viscosity 1, experimental and computational studies have shown a tendency for particle clusters of excessively high and low mobility to grow upon cooling toward the glass transition temperature T , a phenomenon termed ‘dynamical g heterogeneity’ 2-5. The related notion of ‘cooperative rearranging regions’ (CRR) forms the foundation of Adam-Gibbs theory of relaxation in glass-forming liquids (AG) 6, a model frequently shown to describe the T dependence of relaxation in both experimental 7, 8 and computational studies of GF systems 9-16. Specifically, AG argue that the growth of the activation free energy ǻG for molecular rearrangement is proportional to the CRR size (defined by the number of units rather than their length scale). A similar notion of dynamic clusters of cooperatively rearranging particles is central to the Random First-Order Transition theory 17 (where the emphasis is given to the CRR length scale rather than their mass). Although AG offer no molecular definition of these CRR, recent studies have shown that the growth of cooperative motion on cooling, taking the form of nearly string-like particle rearrangements, parallels the growth of the activation free energy ǻG 18-20, suggesting the
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‘strings’ are a concrete realization of the CRR. The proportionality between the average string length L and ΔG was found to hold even when the fragility of the GF fluid was varied over a broad range in a model polymer-nanoparticle composite.18,19 Additionally, the relation of L to ΔG can account for the dynamical changes in supported polyme
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