A thermodynamic approach to the fragility of glass-forming polymers

Cangialosi, Daniele; Alegría, Ángel; Colmenero, Juan

doi:10.1063/1.2149853

Cited by 47 publications

(59 citation statements)

References 37 publications

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“…͑7͒ fails in several complex glass formers. It has recently been proposed by Cangialosi et al 8,48 that the reason for such failure can be traced back to the presence of a residual excess entropy at the Vogel temperature T 0 , namely, to the difference between the Kauzmann temperature T K and T 0 . As, according to the AG relation, at T 0 no ␣ relaxation-related excess entropy should be left out, the residual excess entropy at T 0 has been attributed to non-␣ process related relaxational processes arising from internal degrees of freedom.…”

Section: ͑4͒mentioning

confidence: 99%

“…As, according to the AG relation, at T 0 no ␣ relaxation-related excess entropy should be left out, the residual excess entropy at T 0 has been attributed to non-␣ process related relaxational processes arising from internal degrees of freedom. 8,48 In particular, it has been shown that relation ͑7͒ is restored by considering the residual excess entropy related to the structural relaxation only: 8,48…”

Section: ͑4͒mentioning

confidence: 99%

“…Despite decisive theoretical steps forward in the comprehension of the glass transition, 3 the phenomenological relations associating the fragility to other physical properties still play a central role in this field, allowing to shed light on possible deep links among apparently uncorrelated quantities. Among them, ͑i͒ the thermodynamic approach to the fragility 4,5 also in the light of the Adam-Gibbs ͑AG͒ theory [6][7][8] and the random first-order transition; 9 ͑ii͒ the ratio between the maximum and the minimum of the boson peak, i.e., of the bump observed at the Thz frequencies in the Raman-and neutron-scattering spectra of glass-forming materials; 10 ͑iii͒ the degree of stretching in the nonexponential decay of the correlation functions in the liquid close to T g ͑Ref. 11͒; ͑iv͒ the statistics of the minima in a potential energy landscape-based description of the diffusion process in supercooled liquids; 12,13 ͑v͒ the temperature behavior of the high frequency shear elastic modulus in the supercooled liquid; 14 ͑vi͒ the Poisson ratio; [15][16][17][18] ͑vii͒ the mean squared displacement in a glass, which for different systems seems to stand in the same order as they stand in a T g scaled Arrhenius plot.…”

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Universal relation between viscous flow and fast dynamics in glass-forming materials

2010

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The connection between viscous flow and vibrational properties in glass-forming materials is scrutinized examining the fragility of a wide set of liquids and the nonergodicity factor of the corresponding glasses. Building on the same line of reasoning which allows us to extend the connection between viscosity and thermodynamics in complex systems, we show here how the two quantities are strongly correlated once the effect of those secondary relaxation processes due to internal degrees of freedom is correctly accounted for. This result provides a missing thermodynamic rationale for the recently debated universality of the correlation between fast and slow degrees of freedom. Glass-forming liquids can cross the melting line avoiding crystallization, and upon cooling below the melting temperature, their viscosity increases by several orders of magnitude, eventually leading to the glass transition. This is a kinetic transition usually defined by the condition in which the structural relaxation time ͑the ␣ process͒ equals a given value, arbitrarily fixed to 100 s. At the glass transition temperature, T g , the shear viscosity of most systems is in the range of 10 11 Ͻ Ͻ 10 13 poise, values high enough to consider the system as "solid" from the mechanical point of view.The rapidity of the increase in the viscosity when approaching T g from the liquid side led in the scientific community to the classification of glasses into long and short, 1 a concept widespread by Angell introducing the kinetic "fragility" 2 m = limSince Ϸ 10 −4 poise is the "infinite" temperature limit in basically any material and ͑T͒ is always found to be a concave function of T −1 , the lowest fragility value is around m = 17, and the systems in the low m side are named "strong" liquids and show an Arrhenius behavior. Conversely, it is empirically found that for the most "fragile" systems, where a high ͑and T-dependent͒ apparent activation energy is found, m Ͼ 150. Despite decisive theoretical steps forward in the comprehension of the glass transition, 3 the phenomenological relations associating the fragility to other physical properties still play a central role in this field, allowing to shed light on possible deep links among apparently uncorrelated quantities. Among them, ͑i͒ the thermodynamic approach to the fragility 4,5 also in the light of the Adam-Gibbs ͑AG͒ theory 6-8 and the random first-order transition; 9 ͑ii͒ the ratio between the maximum and the minimum of the boson peak, i.e., of the bump observed at the Thz frequencies in the Raman-and neutron-scattering spectra of glass-forming materials; 10 ͑iii͒ the degree of stretching in the nonexponential decay of the correlation functions in the liquid close to T g ͑Ref. 11͒; ͑iv͒ the statistics of the minima in a potential energy landscape-based description of the diffusion process in supercooled liquids; 12,13 ͑v͒ the temperature behavior of the high frequency shear elastic modulus in the supercooled liquid; 14 ͑vi͒ the Poisson ratio; 15-18 ͑vii͒ the mean squared displacement in a glass...

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Section: ͑4͒mentioning

confidence: 99%

Section: ͑4͒mentioning

confidence: 99%

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confidence: 99%

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Universal relation between viscous flow and fast dynamics in glass-forming materials

2010

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“…9,10 It has been realized that behavior of structural (segmental) relaxation in many polymers deviates from regularities known for structural (R-) relaxation in small molecular liquids. 4,[11][12][13] There seems to be a "polymer specific" contribution to fragility of polymeric systems. 13 Understanding the structural parameters of polymers that control their fragility and differentiate them from other glass-forming systems remains a challenge.…”

Section: Introductionmentioning

confidence: 99%

Role of Chemical Structure in Fragility of Polymers: A Qualitative Picture

et al. 2008

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Understanding microscopic parameters that control steepness of the temperature variations of segmental relaxation (fragility) and the glass transition phenomenon remains a challenge. We present dielectric and mechanical relaxation studies of segmental dynamics in various polymers with different side groups and backbone structures. The results have been analyzed in terms of flexibility of backbone and side groups of polymeric molecules, as suggested by the recent theoretical works by Dudowicz et al. A comparison of structures with identical backbones and varying side groups and identical side groups but different backbones reveals that the flexibility of side groups relative to the flexibility of the backbone is the most important factor controlling fragility in polymers, while the glass transition temperature T g depends primarily on the backbone flexibility and the side group bulkiness (occupied volume). Based on these results and analysis of literature data we formulated a modified approach to understand the role of chemical structure in segmental dynamics: (i) Polymers with stiff backbones always have high T g and fragility, while (ii) polymers with flexible backbones and no side groups are the strongest; (iii) however, for the most common type of polymeric structure, C-C or Si-O backbone with side groups, fragility increases with increasing "relatiVe" stiffness of side groups versus the backbone. In this class of polymers, lowest fragility is expected when the side groups are of similar chemical structure (or flexibility) as the backbone, as in the case of polyisobutylene, one of the strongest polymers known.

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“…16 The relation to the nonergodicity factor is understandable because a low nonergodicity factor means a low level of density fluctuations, which in turn means that one is close to the ideal glass of the Kauzmann paradoxon and expects a high thermodynamic fragility. 17 Very recently, 18 it has been pointed out that there are exceptions from the nonergodicity rule due to a strong influence of secondary relaxations, 19 a reasoning which is parallel to the one in the present work, a second fragility influence which requires not only a knowledge of the fast motion but also of the relaxations themselves.…”

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confidence: 48%

Fragility and elasticity: Description of flow in highly viscous liquids

Buchenau

2009

Phys. Rev. B

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The fragility ͑the abnormally strong temperature dependence of the viscosity͒ of highly viscous liquids is shown to have two sources. The first is the temperature dependence of the barriers between inherent states considered earlier. The second is the recently discovered asymmetry between the actual inherent state and its neighbors. One needs both terms for a quantitative description. DOI: 10.1103/PhysRevB.80.172201 PACS number͑s͒: 64.70.QϪ, 77.22.Gm Though there is as yet no generally accepted explanation of the flow in highly viscous liquids, 1-3 it seems clear that its description requires the passage of high-energy barriers between inherent states, i.e., local structural minima of the potential energy. 4 According to the elastic models, 2 the fragility stems from a proportionality of the height V of these barriers to the infinite-frequency shear modulus G, which in the highly viscous liquid decreases strongly with temperature.The present Brief Report shows that this is only part of the truth. There is a second source of fragility in the newly discovered 5 asymmetry of about 4k B T between the actual inherent state and its neighbors, possibly due 6 to the elastic distortion accompanying a structural rearrangement ͑the "Eshelby backstress" 7 ͒. As will be seen, the quantitative explanation of the fragility of six different glass formers requires just this specific explanation of the asymmetry.The usual measure of the fragility of a glass former is the logarithmic slope of the relaxation time ␣ of the flow process,where the glass temperature T g is defined as the temperature with ␣ = 1000 s. It is useful to relate ␣ to a critical barrier V c via the Arrhenius relationwhere the microscopic attempt frequency is at 10 −13 s, 16 decades faster than the flow process at the glass temperature.The fragility index I is defined 2 by the logarithmic derivativewhere the factor reflects the sixteen decades between microscopic and macroscopic time scales. I is a better measure of the fragility than m because it does not contain the trivial temperature dependence of any thermally activated process. The elastic models 2 postulate a proportionality between the flow barrier V c and the infinite-frequency shear modulus G. One can again define a dimensionless measure ⌫ for the temperature dependence of G in terms of the logarithmic derivative ⌫ =−d ln G / d ln T at T g . Then the elastic models 2 postulate I = ⌫.In order to check this relation, one needs measurements of both quantities. The flow relaxation time ␣ is relatively easy to measure but the determination of the high-frequency shear modulus is by no means trivial. It requires the measurement of the density and the high-frequency transverse sound velocity v t . Consequently, the logarithmic derivative ⌫ is a sum of two terms, a larger one from the sound velocity and a smaller one from the density.In a liquid, well-defined transverse sound waves do only exist at frequencies which are markedly higher than the inverse 1 / ␣ of the flow relaxation time. With increasing tem...

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A thermodynamic approach to the fragility of glass-forming polymers

Cited by 47 publications

References 37 publications

Universal relation between viscous flow and fast dynamics in glass-forming materials

Universal relation between viscous flow and fast dynamics in glass-forming materials

Role of Chemical Structure in Fragility of Polymers: A Qualitative Picture

Fragility and elasticity: Description of flow in highly viscous liquids

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