Does equilibrium polymerization describe the dynamic heterogeneity of glass-forming liquids?

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Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio ρ γ /T , where ρ is the density, T is the temperature, and γ is a material dependent constant. Interest in the scaling is also heightened because the exponent γ enters prominently into considerations of the relative contributions to the dynamics from pressure effects (e.g., activation barriers) vs. volume effects (e.g., free volume). Although this scaling is clearly of great practical use, a molecular understanding of the scaling remains elusive. Providing this molecular understanding would greatly enhance the utility of the empirically observed scaling in assisting the rational design of materials by describing how controllable molecular factors, such as monomer structures, interactions, flexibility, etc., influence the scaling exponent γ and, hence, the dynamics. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodynamic scaling in polymer melts. The predictions of theory are in accord with the appearance of thermodynamic scaling for pressures not in excess of ∼ 50 MPa. (The failure at higher pressures arises due to inherent limitations of a lattice model.) In line with arguments relating the magnitude of γ to the steepness of the repulsive part of the intermolecular potential, the abrupt, square-well nature of the lattice model interactions lead, as expected, to much larger values of the scaling exponent. Nevertheless, the theory is employed to study how individual molecular parameters affect the scaling exponent in order to extract a molecular understanding of the information content contained in the exponent. The chain rigidity, cohesive energy, chain length, and the side group length are all found to significantly affect the magnitude of the scaling exponent, and the computed trends agree well with available experiments. The variations of γ with these molecular parameters are explained by establishing a correlation between the computed molecular dependence of the scaling exponent and the fragility. Thus, the efficiency of packing the polymers is established as the universal physical mechanism determining both the fragility and the scaling exponent γ.

Section: A Generalized Entropy Theorymentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Thermodynamic scaling of dynamics in polymer melts: Predictions from the generalized entropy theory

Freed

2013

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“…Many simulated properties of these cooled fluids, including, the string length distribution, the inverse proportionality L ∼ 1/S c between the average string length L and the fluid configurational entropy S c , etc., are found 3 to be quantitatively described by an equilibrium self-assembly model, in accord with a previous suggestion that these models describe glass formation. 5 However, the justification of the scaling of the high temperature activation free energy by the string length L ∼ 1/S c is only heuristic and thus represents a weak point of the analysis. One purpose of the present work is to justify this ansatz using transition state theory to derive AGT, an analysis that also produces a self-assembly model for the excitations of the fluid describing the thermal activation process underlying the relaxation.…”

Section: Derivation Of Adam-gibbs Theorymentioning

confidence: 99%

“…Here, we use the observed properties of the dynamical strings [2][3][4][5] to motivate a derivation of the AGT from first principles, thereby combining together the aforementioned advances. The derivation places the assumptions of AGT on a more fundamental, testable level that suggests new roles for simulations and that should enable further extensions.…”

Section: Derivation Of Adam-gibbs Theorymentioning

confidence: 99%

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion

Freed

2014

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A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions. © 2014 AIP Publishing LLC. [http://dx

“…38 We now examine the extent to which we can understand the changes in relaxation that we observe in in aging fluid based on a dynamical extension of the Adam-Gibbs theory where the evolving magnitude of the string length, L(t), is incorporated into the description.…”

Section: Asymmetric Approach To Equilibriummentioning

confidence: 99%

Evolution of collective motion in a model glass-forming liquid during physical aging

Shavit

Douglas

Riggleman

2013

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At temperatures moderately below their glass transition temperature, the properties of many glassforming materials can evolve slowly with time in a process known as physical aging whereby the thermodynamic, mechanical, and dynamic properties all drift towards their equilibrium values. In this work, we study the evolution of the thermodynamic and dynamic properties during physical aging for a model polymer glass. Specifically, we test the relationship between an estimate of the size of the cooperative rearrangements taking the form of strings and the effective structural relaxation time predicted by the Adam-Gibbs relationship for both an equilibrium supercooled liquid and the same fluid undergoing physical aging towards equilibrium after a series of temperature jumps. We find that there is apparently a close correlation between a structural feature of the fluid, the size of the string-like rearrangements, and the structural relaxation time, although the relationship for the aging fluid appears to be distinct from that of the fluid at equilibrium.