Generalized Entropy Theory of Polymer Glass Formation

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

doi:10.1002/9780470238080.ch3

Cited by 161 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%

“…Note that the theory identifies the entropy density s c , i.e., the configurational entropy per lattice site, as the essential quantity for use in the AG model. Thus, LCT computations of s c (T ) have enabled the direct determination of three characteristic temperatures of glass formation, [40][41][42][43][44] namely, the "ideal" glass transition temperature T 0 where s c extrapolates to zero, the onset temperature T A which signals the onset of non-Arrhenius behavior of the relaxation time and which is evaluated from the maximum in s c (T ), and the crossover temperature T I which separates two temperature regimes with qualitatively different dependences of the relaxation time on temperature and which is evaluated from the inflection point in T s c (T ). The relaxation time τ is then obtained from s c and the AG relation,…”

Section: A Generalized Entropy Theorymentioning

confidence: 99%

“…(3) The monomer structure and molecular weight enter into the theory through a set of geometrical indices, providing a substantial improvement over the traditional lattice theories. Further information on the generalized entropy theory can be found in recent reviews [39,40]. …”

Section: A Generalized Entropy Theorymentioning

confidence: 99%

“…[39,40] We now consider how the bending energy influences the thermodynamic scaling for a polymer system with the PP structure because its treatment requires only a single backbone bending energy. The cell volume parameter, cohesive energy and chain length are fixed.…”

Section: A Influence Of the Bending Energymentioning

confidence: 99%

“…The previously successful applications [39,40] suggest that the theory could be utilized to investigate more specific details, such as the thermodynamic scaling of polymer melts. Hence, we assess the influence of molecular details on thermodynamic scaling of polymer melts within this molecular theory of polymer glass formation.…”

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: A Generalized Entropy Theorymentioning

confidence: 99%

Section: A Generalized Entropy Theorymentioning

confidence: 99%

Section: A Influence Of the Bending Energymentioning

confidence: 99%

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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The Random First‐Order Transition Theory of Glasses: A Critical Assessment

Biroli

Bouchaud

2012

Structural Glasses and Supercooled Liquids

107

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The aim of this chapter is to summarise the basic arguments and the intuition bolstering the RFOT picture for glasses, based on a finite dimensional extension of mean-field models with an exponentially large number of metastable states. We review the pros and cons that support or undermine the theory, and the directions, both theoretical and experimental, where progress is needed to ascertain the status of RFOT. We elaborate in particular on the notions of mosaic state and point-to-set correlations, and insist on the importance of fluctuations in finite dimensions, that significantly blur the expected cross-over between a Mode-Coupling like regime and the mosaic, activated regime. We discuss in detail the fundamental predictions of RFOT, in particular the possibility to force a small enough system into an ideal glass state, and present several new ones, concerning aging properties or non-linear rheology. Finally, we compare RFOT to other recent theories, including elastic models, Frustration Limited Domains or Kinetically Constrained models.Details that could throw doubt on your interpretation must be given, if you know them. You must do the best you can -if you know anything at all wrong, or possibly wrong -to explain it. If you make a theory, for example, and advertise it, or put it out, then you must also put down all the facts that disagree with it, as well as those that agree with it.

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Entropy Theory of Polymer Glass‐formation in Variable Spatial Dimension

Douglas

Freed

2016

Advances in Chemical Physics

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We explore the nature of glass-formation in variable spatial dimensionality (d) based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established statistical mechanical model. We find that structural relaxation in the fluid state asymptotically becomes Arrhenius in the d → ∞ limit and that the fluid transforms upon sufficient cooling above a critical dimension near d = 8 into a dense amorphous state with a finite positive residual configurational entropy. Direct computations of the isothermal compressibility and thermal expansion coefficient, taken to be physical measures of packing frustration, demonstrate that these fluid properties strongly correlate with the fragility of glass-formation.PACS numbers: 64.70.QGrowing evidence indicates that molecular packing plays an essential role in both the physics of crystallization [1][2][3][4][5] and glass-formation [6][7][8][9][10][11][12][13][14][15][16][17], prompting a consideration of variable spatial dimensionality (d) as a conceptual probe of these solidification processes. In particular, the "decorrelation principle", recently proposed by Torquato and Stillinger [18,19], states that unconstrained correlations in hard hyperspheres diminish with increasing d and vanish in the d → ∞ limit. Likewise, recent simulations [7][8][9] have indicated that certain often cited aspects of glass-formation, such as the dynamic heterogeneity and the decoupling between structural relaxation and diffusion, become diminished at elevated d. While prior studies [11][12][13][14][15] have focused mainly on how critical packing fractions associated with glass-formation in hard hyperspheres vary with d, little is known concerning the d dependence of the characteristic temperatures and fragility of glass-formation in molecular fluids. No prior work has considered complex fluids, such as polymeric liquids, where many molecular parameters may be tuned to control the nature of glass-formation.In this Letter, we consider the glass-formation of a model polymer glass-forming (GF) liquid in d dimensions. Our approach is based on the generalized entropy theory (GET) [20], which is a combination of the lattice cluster theory (LCT) [21] and the Adam-Gibbs (AG) theory [22] linking the configurational entropy s c (i.e., the entropy devoid of the vibrational component) to the structural relaxation time τ α . The LCT employs a ddimensional hypercubic lattice model, whose use facilitates the development of an expansion about the meanfield limit of infinite d. The LCT thus naturally provides * Contribution of the National Institute of Standards and Technology -Work not subject to copyright in the United States. † wsxu@uchicago.edu ‡ jack.douglas@nist.gov § freed@uchicago.edu a framework for considering the d dependence of polymer thermodynamic properties, thereby making the GET suitable for exploring glass-formation in d dimensions.As a primary result, we find that structural relaxation in the fluid st...

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Generalized Entropy Theory of Polymer Glass Formation

Cited by 161 publications

References 303 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 Random First‐Order Transition Theory of Glasses: A Critical Assessment

Entropy Theory of Polymer Glass‐formation in Variable Spatial Dimension

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