Fragility of Glass-Forming Polymer Liquids

Dudowicz, Jacek; Freed, Karl F.; Douglas, Jack F.

doi:10.1021/jp053693k

Cited by 153 publications

(252 citation statements)

References 63 publications

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“…The generalized entropy theory has previously been applied to investigate essential molecular and physical features affecting glass-formation, [40][41][42][43][44][45] studies explain some experimentally observed trends, while many theoretical predictions are confirmed by experiments [39,40], suggesting that the theory correctly captures general trends of glass formation in polymers. We further extend the theory in this paper to investigate thermodynamic scaling of the dynamics of polymer melts, whether the LCT also predicts thermodynamic scaling, how the exponent γ varies with molecular parameters, and the relation of γ to other measurable quantities.…”

Section: A Generalized Entropy Theorymentioning

confidence: 99%

“…Moreover, some striking empirical correlations between the scaling exponent and the fragility parameter [8,12,37,38] also invite theoretical considerations. We address the above issues by employing the generalized entropy theory, [39][40][41][42][43][44][45][46] which has been previously developed to describe both the universal characteristics of glass formation and the specific properties of polymeric glass-forming liquids.…”

Section: Introductionmentioning

confidence: 99%

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

Freed

2013

The Journal of Chemical Physics

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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.

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Section: A Generalized Entropy Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Freed

2013

The Journal of Chemical Physics

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“…The poorer chain packing in turn can lead to an increase in the "fragility", in the context of fragile and strong glass formers. 64 Poor chain packing in fragile glass formers is known to give rise to decreases in the tensile stress at breakage, and so it is reasonable to expect that τ would decrease with increasing N as the fragility of glass formation increases. This interpretation of the trend in τ being related to the fragility of the glass-formation requires further investigation, of course, and we mention this as a tentative explanation of the trend in τ that we and others have observed.…”

Section: Calculation Of τmentioning

confidence: 99%

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Knauert

Douglas

Starr

2007

J Polym Sci B Polym Phys

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212

158

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Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ , which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod-like, and sheet-like model nanoparticles, all at a volume fraction φ ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod-like nanoparticles and least for the sheet-like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass-formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer-particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites.

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“…A second advance is provided by the generalized entropy theory [7][8][9][10][11][12][13][14][15] (GET), whose successes indicate directions for devising the theory. The GET formally combines a thermodynamic theory 16 for the configurational entropy of a polymer melt with Adam-Gibbs theory 17 (AGT) for the structural relaxation time τ (T).…”

Section: Introductionmentioning

confidence: 99%

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

Freed

2014

The Journal of Chemical Physics

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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

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Fragility of Glass-Forming Polymer Liquids

Cited by 153 publications

References 63 publications

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

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

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

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

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