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Xu WS, Sun ZY. A Thermodynamic Perspective on Polymer Glass Formation. CHINESE JOURNAL OF POLYMER SCIENCE 2023. [DOI: 10.1007/s10118-023-2951-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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2
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Douglass IM, Dyre JC. Distance-as-time in physical aging. Phys Rev E 2022; 106:054615. [PMID: 36559484 DOI: 10.1103/physreve.106.054615] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 11/05/2022] [Indexed: 06/17/2023]
Abstract
Although it has been known for half a century that the physical aging of glasses in experiments is described well by a linear thermal-history convolution integral over the so-called material time, the microscopic definition and interpretation of the material time remains a mystery. We propose that the material-time increase over a given time interval reflects the distance traveled by the system's particles. Different possible distance measures are discussed, starting from the standard mean-square displacement and its inherent-state version that excludes the vibrational contribution. The viewpoint adopted, which is inspired by and closely related to pioneering works of Cugliandolo and Kurchan from the 1990s, implies a "geometric reversibility" and a "unique-triangle property" characterizing the system's path in configuration space during aging. Both of these properties are inherited from equilibrium, and they are here confirmed by computer simulations of an aging binary Lennard-Jones system. Our simulations moreover show that the slow particles control the material time. This motivates a "dynamic-rigidity-percolation" picture of physical aging. The numerical data show that the material time is dominated by the slowest particles' inherent mean-square displacement, which is conveniently quantified by the inherent harmonic mean-square displacement. This distance measure collapses data for potential-energy aging well in the sense that the normalized relaxation functions following different temperature jumps are almost the same function of the material time. Finally, the standard Tool-Narayanaswamy linear material-time convolution-integral description of physical aging is derived from the assumption that when time is replaced by distance in the above sense, an aging system is described by the same expression as that of linear-response theory.
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Affiliation(s)
- Ian M Douglass
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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3
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McKenna GB, Chen D, Mangalara SCH, Kong D, Banik S. Some open challenges in polymer physics*. POLYM ENG SCI 2022. [DOI: 10.1002/pen.25938] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Gregory B. McKenna
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
- Department of Chemical and Biomolecular Engineering North Carolina State University Raleigh North Carolina USA
| | - Dongjie Chen
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
| | | | - Dejie Kong
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
| | - Sourya Banik
- Department of Chemical Engineering Texas Tech University Lubbock Texas USA
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Xu WS, Douglas JF, Sun ZY. Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02740] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
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5
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Abstract
This paper generalizes isomorph theory to systems that are not in thermal equilibrium. The systems are assumed to be R-simple, i.e., to have a potential energy that as a function of all particle coordinates R obeys the hidden-scale-invariance condition U(Ra) < U(Rb) ⇒ U(λRa) < U(λRb). "Systemic isomorphs" are introduced as lines of constant excess entropy in the phase diagram defined by density and systemic temperature, which is the temperature of the equilibrium state point with the average potential energy equal to U(R). The dynamics is invariant along a systemic isomorph if there is a constant ratio between the systemic and the bath temperature. In thermal equilibrium, the systemic temperature is equal to the bath temperature and the original isomorph formalism is recovered. The new approach rationalizes within a consistent framework previously published observations of isomorph invariance in simulations involving nonlinear steady-state shear flows, zero-temperature plastic flows, and glass-state isomorphs. This paper relates briefly to granular media, physical aging, and active matter. Finally, we discuss the possibility that the energy unit defining the reduced quantities should be based on the systemic rather than the bath temperature.
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Affiliation(s)
- Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Wang JG, Li Q, Peng X, McKenna GB, Zia RN. "Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics. SOFT MATTER 2020; 16:7370-7389. [PMID: 32696798 DOI: 10.1039/d0sm00999g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.
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Affiliation(s)
- J Galen Wang
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
| | - Qi Li
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Xiaoguang Peng
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Gregory B McKenna
- Department of Chemical Engineering, Texas Tech University, Lubbock, TX 79409, USA
| | - Roseanna N Zia
- Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA.
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7
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Abstract
This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.
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Affiliation(s)
- Jeppe C Dyre
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Schmelzer JWP, Tropin TV. Glass Transition, Crystallization of Glass-Forming Melts, and Entropy. ENTROPY 2018; 20:e20020103. [PMID: 33265194 PMCID: PMC7512596 DOI: 10.3390/e20020103] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2017] [Revised: 01/22/2018] [Accepted: 01/26/2018] [Indexed: 11/16/2022]
Abstract
A critical analysis of possible (including some newly proposed) definitions of the vitreous state and the glass transition is performed and an overview of kinetic criteria of vitrification is presented. On the basis of these results, recent controversial discussions on the possible values of the residual entropy of glasses are reviewed. Our conclusion is that the treatment of vitrification as a process of continuously breaking ergodicity with entropy loss and a residual entropy tending to zero in the limit of zero absolute temperature is in disagreement with the absolute majority of experimental and theoretical investigations of this process and the nature of the vitreous state. This conclusion is illustrated by model computations. In addition to the main conclusion derived from these computations, they are employed as a test for several suggestions concerning the behavior of thermodynamic coefficients in the glass transition range. Further, a brief review is given on possible ways of resolving the Kauzmann paradox and its implications with respect to the validity of the third law of thermodynamics. It is shown that neither in its primary formulations nor in its consequences does the Kauzmann paradox result in contradictions with any basic laws of nature. Such contradictions are excluded by either crystallization (not associated with a pseudospinodal as suggested by Kauzmann) or a conventional (and not an ideal) glass transition. Some further so far widely unexplored directions of research on the interplay between crystallization and glass transition are anticipated, in which entropy may play—beyond the topics widely discussed and reviewed here—a major role.
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Affiliation(s)
- Jürn W. P. Schmelzer
- Albert-Einstein-Strasse 23-25, 18059 Rostock, Germany
- Correspondence: ; Tel.: +49-381-498-6889; Fax: +49-381-498-6882
| | - Timur V. Tropin
- Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Russia
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9
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Cangialosi D. Glass Transition and Physical Aging of Confined Polymers Investigated by Calorimetric Techniques. RECENT ADVANCES, TECHNIQUES AND APPLICATIONS 2018. [DOI: 10.1016/b978-0-444-64062-8.00013-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
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10
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Zhavoronok ES, Senchikhin IN, Roldughin VI. Physical aging and relaxation processes in epoxy systems. POLYMER SCIENCE SERIES A 2017. [DOI: 10.1134/s0965545x17020109] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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11
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Sanditov DS, Darmaev MV, Mantatov VV. Estimation of the parameter of the main equation of the glass transition of amorphous polymers and other amorphous substances. POLYMER SCIENCE SERIES A 2016. [DOI: 10.1134/s0965545x16020176] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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12
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Koperwas K, Grzybowski A, Tripathy SN, Masiewicz E, Paluch M. Thermodynamic consequences of the kinetic nature of the glass transition. Sci Rep 2015; 5:17782. [PMID: 26657017 PMCID: PMC4674716 DOI: 10.1038/srep17782] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2015] [Accepted: 11/03/2015] [Indexed: 01/18/2023] Open
Abstract
In this paper, we consider the glass transition as a kinetic process and establish one universal equation for the pressure coefficient of the glass transition temperature, dTg/dp, which is a thermodynamic characteristic of this process. Our findings challenge the common previous expectations concerning key characteristics of the transformation from the liquid to the glassy state, because it suggests that without employing an additional condition, met in the glass transition, derivation of the two independent equations for dTg/dp is not possible. Hence, the relation among the thermodynamic coefficients, which could be equivalent to the well-known Prigogine-Defay ratio for the process under consideration, cannot be obtained. Besides, by comparing the predictions of our universal equation for dTg/dp and Ehrenfest equations, we find the aforementioned supplementary restriction, which must be met to use the Prigogine-Defay ratio for the glass transition.
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Affiliation(s)
- Kajetan Koperwas
- Institute of Physics, University of Silesia, Uniwersytecka
4, 40-007
Katowice, Poland
- Silesian Center for Education and Interdisciplinary
Research, 75 Pulku Piechoty 1A, 41-500
Chorzow, Poland
| | - Andrzej Grzybowski
- Institute of Physics, University of Silesia, Uniwersytecka
4, 40-007
Katowice, Poland
- Silesian Center for Education and Interdisciplinary
Research, 75 Pulku Piechoty 1A, 41-500
Chorzow, Poland
| | - Satya N. Tripathy
- Institute of Physics, University of Silesia, Uniwersytecka
4, 40-007
Katowice, Poland
- Silesian Center for Education and Interdisciplinary
Research, 75 Pulku Piechoty 1A, 41-500
Chorzow, Poland
| | - Elzbieta Masiewicz
- Institute of Physics, University of Silesia, Uniwersytecka
4, 40-007
Katowice, Poland
- Silesian Center for Education and Interdisciplinary
Research, 75 Pulku Piechoty 1A, 41-500
Chorzow, Poland
| | - Marian Paluch
- Institute of Physics, University of Silesia, Uniwersytecka
4, 40-007
Katowice, Poland
- Silesian Center for Education and Interdisciplinary
Research, 75 Pulku Piechoty 1A, 41-500
Chorzow, Poland
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13
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Hecksher T, Olsen NB, Dyre JC. Communication: Direct tests of single-parameter aging. J Chem Phys 2015; 142:241103. [DOI: 10.1063/1.4923000] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tina Hecksher
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Niels Boye Olsen
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Jeppe C. Dyre
- DNRF Center “Glass and Time,” IMFUFA, Department of Sciences, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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14
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Tombari E, Johari GP. Change in entropy in thermal hysteresis of liquid-glass-liquid transition and consequences of violating the Clausius theorem. J Chem Phys 2014; 141:074502. [PMID: 25149796 DOI: 10.1063/1.4892588] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Change in the entropy, dS, with change in the temperature T, with or without phase transformation, is determined only if the thermal path is reversible. For an irreversible thermal path, dS > dqirrev/T, an expression known as inequality in the Clausius theorem. In the glass formation range, Cp and enthalpy show a time-dependent hysteresis between the cooling and heating paths and the two Cp paths cross each other. We provide new data on Cp of poly(styrene) and use the previous Cp data [E. Tombari, C. Ferrari, G. Salvetti, and G. P. Johari, Phys. Rev. B 78, 144203 (2008)], both data obtained from measurements performed on cooling from melt to glass and heating from glass to melt at unusually slow rates, and show that violation of the Clausius theorem in such cases has insignificant consequences for determining the entropy of glass. We also report Cp of the samples annealed for different times at different temperatures in which the enthalpy spontaneously decreased. These measurements also show that violation of the Clausius theorem is relatively inconsequential for interpreting the entropy of the glassy state.
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Affiliation(s)
- Elpidio Tombari
- Istituto per i Processi Chimico-Fisici del CNR, via G. Moruzzi 1, 56124 Pisa, Italy
| | - G P Johari
- Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario L8S 4L7, Canada
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Matsko NB, Mittal V. Thermotropic dynamic processes in multiphase polymer systems by (cryo-)AFM. SOFT MATTER 2014; 10:5478-5488. [PMID: 24948389 DOI: 10.1039/c4sm00458b] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The structural (volume and enthalpy) relaxation of polymers during physical aging has a great relevance in materials science and engineering as it significantly changes the long-term material performance. In this article, we propose a methodological approach of (cryo-)atomic force microscopy (AFM) monitoring of macromolecular rearrangements which accompany structural relaxation within bulk of the polymer during physical aging. In contrast to conventional spectroscopic, scattering and thermal analysis techniques, high resolution topographical/phase imaging of the bulk cross-section over a large period of time and within a wide range of temperatures (-120 °C to +20 °C) yields unique information about the evolution of the polymer ultrastructure as a function of time and temperature in situ.
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Affiliation(s)
- N B Matsko
- Graz Centre for Electron Microscopy and Institute for Electron Microscopy and Nanoanalysis, Graz University of Technology, Steyrergasse 17, A-8010 Graz, Austria.
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Cangialosi D. Dynamics and thermodynamics of polymer glasses. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:153101. [PMID: 24675099 DOI: 10.1088/0953-8984/26/15/153101] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
The fate of matter when decreasing the temperature at constant pressure is that of passing from gas to liquid and, subsequently, from liquid to crystal. However, a class of materials can exist in an amorphous phase below the melting temperature. On cooling such materials, a glass is formed; that is, a material with the rigidity of a solid but exhibiting no long-range order. The study of the thermodynamics and dynamics of glass-forming systems is the subject of continuous research. Within the wide variety of glass formers, an important sub-class is represented by glass forming polymers. The presence of chain connectivity and, in some cases, conformational disorder are unfavourable factors from the point of view of crystallization. Furthermore, many of them, such as amorphous thermoplastics, thermosets and rubbers, are widely employed in many applications. In this review, the peculiarities of the thermodynamics and dynamics of glass-forming polymers are discussed, with particular emphasis on those topics currently the subject of debate. In particular, the following aspects will be reviewed in the present work: (i) the connection between the pronounced slowing down of glassy dynamics on cooling towards the glass transition temperature (Tg) and the thermodynamics; and, (ii) the fate of the dynamics and thermodynamics below Tg. Both aspects are reviewed in light of the possible presence of a singularity at a finite temperature with diverging relaxation time and zero configurational entropy. In this context, the specificity of glass-forming polymers is emphasized.
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Affiliation(s)
- D Cangialosi
- Materials Physics Center, Paseo Manuel de Lardizabel 5 20018 San Sebastian, Spain
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17
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Kucera SA, Felton LA, McGinity JW. Physical aging in pharmaceutical polymers and the effect on solid oral dosage form stability. Int J Pharm 2013; 457:428-36. [DOI: 10.1016/j.ijpharm.2013.01.069] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2012] [Revised: 01/28/2013] [Accepted: 01/30/2013] [Indexed: 11/25/2022]
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18
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Gujrati PD, Aung PP. Nonequilibrium thermodynamics. III. Generalization of Maxwell, Clausius-Clapeyron, and response-function relations, and the Prigogine-Defay ratio for systems in internal equilibrium. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041129. [PMID: 22680441 DOI: 10.1103/physreve.85.041129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2011] [Revised: 08/01/2011] [Indexed: 06/01/2023]
Abstract
We follow the consequences of internal equilibrium in nonequilibrium systems that has been introduced recently [Gujrati, Phys. Rev. E 81, 051130 (2010) and Gujrati, Phys. Rev. E 85, 041128 (2012).] to obtain the generalization of the Maxwell relation and the Clausius-Clapeyron relation that are normally given for equilibrium systems. The use of Jacobians allows for a more compact way to address the generalized Maxwell relations in the presence of internal variables. The Clausius-Clapeyron relation in the subspace of observables shows not only the nonequilibrium modification but also the modification due to internal variables that play a dominant role in glasses to which we apply the above relations. Real systems do not directly turn into glasses (GL) that are frozen structures from the supercooled liquid state L; there is an intermediate state (gL) where the internal variables are not frozen. A system possesses several kinds of glass transitions, some conventional (L→gL; gL→GL) in which the state changes continuously and the transition mimics a continuous or second-order transition, and some apparent (L→gL; L→GL) in which the free energies are discontinuous so that the transition appears as a zeroth-order transition, as discussed in the text. We evaluate the Prigogine-Defay ratio Π in the subspace of the observables at these transitions. We find that it is normally different from 1, except at the conventional transition L→gL, where Π=1.
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Affiliation(s)
- P D Gujrati
- Department of Physics, Department of Polymer Science, University of Akron, Akron, Ohio 44325, USA.
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Tropin TV, Schmelzer JWP, Gutzow I, Schick C. On the theoretical determination of the Prigogine-Defay ratio in glass transition. J Chem Phys 2012; 136:124502. [PMID: 22462869 DOI: 10.1063/1.3694531] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In a recent analysis [J. W. P. Schmelzer and I. Gutzow, J. Chem. Phys. 125, 184511 (2006)] it was shown for the first time that--in contrast to earlier belief arising from the works of Prigogine and Defay [Chemical Thermodynamics (Longman, London, 1954), Chap. 19; The first French edition of this book was published in 1950] and Davies and Jones [Adv. Phys. 2, 370 (1953); and Proc. R. Soc. London, Ser. A 217, 26 (1953)]--a satisfactory theoretical interpretation of the experimentally observed values of the so-called Prigogine-Defay ratio Π, being a combination of jumps of thermodynamic coefficients at glass transition, can be given employing only one structural order parameter. According to this analysis, this ratio has to be, in full agreement with experimental findings, larger than one (Π > 1). Its particular value depends both on the thermodynamic properties of the system under consideration and on cooling and heating rates. Based on above-mentioned analysis, latter dependence on cooling rates has been studied in detail in another own preceding paper [T. V. Tropin, J. W. P. Schmelzer, and C. Schick, J. Non-Cryst. Solids 357, 1303 (2011)]. In the present analysis, an alternative general method of determination of the Prigogine-Defay ratio is outlined, allowing one to determine this ratio having at ones disposal the generalized equation of state of the glass-forming melts under consideration and, in particular, the knowledge of the equilibrium properties of the melts in the glass transformation range. Employing, as an illustration of the method, a particular model for the description of glass-forming melts, theoretical estimates are given for this ratio being, again, in good agreement with experimental data.
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Affiliation(s)
- Timur V Tropin
- Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, 141980 Dubna, Russia
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20
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Schmelzer JWP. Kinetic criteria of glass formation and the pressure dependence of the glass transition temperature. J Chem Phys 2012; 136:074512. [DOI: 10.1063/1.3685510] [Citation(s) in RCA: 63] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
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Cangialosi D, Boucher VM, Alegría A, Colmenero J. Free volume holes diffusion to describe physical aging in poly(mehtyl methacrylate)/silica nanocomposites. J Chem Phys 2011; 135:014901. [DOI: 10.1063/1.3605600] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dynamics of Thermotropic Liquid Crystals Across the Isotropic-Nematic Transition and Their Similarity with Glassy Relaxation in Supercooled Liquids. ADVANCES IN CHEMICAL PHYSICS 2009. [DOI: 10.1002/9780470431917.ch6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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23
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Abstract
One of the basic characteristics of the glass transition, the Prigogine-Defay ratio, connecting jumps of the thermal expansion coefficient, isothermal compressibility, and isobaric specific heat capacity in vitrification is rederived in the framework of the thermodynamics of irreversible processes employing the order-parameter concept introduced by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)]. In our analysis, glass-forming liquids and glasses are described by only one structural order parameter. However, in contrast to previous approaches to the derivation of this ratio, the process of vitrification is treated not in terms of Simon's simplified model [Z. Anorg. Allg. Chem. 203, 219 (1931)] as a freezing-in process proceeding at some sharp temperature, the glass transition temperature T(g), but in some finite temperature interval accounting appropriately for the nonequilibrium character of vitrifying systems in this temperature range. As the result of the theoretical analysis, we find, in particular, that the Prigogine-Defay ratio generally has to have values larger than 1 for vitrification in cooling processes. Quantitative estimates of the Prigogine-Defay ratio are given utilizing a mean-field lattice-hole model of glass-forming melts. Some further consequences are derived concerning the behavior of thermodynamic coefficients, in particular, of Young's modulus in vitrification. The theoretical results are found to be in good agreement with experimental data.
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Möller J, Gutzow I, Schmelzer JWP. Freezing-in and production of entropy in vitrification. J Chem Phys 2006; 125:094505. [PMID: 16965095 DOI: 10.1063/1.2346673] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Following the classical concepts developed by Simon [Z. Anorg. Allg. Chem. 203, 219 (1931)], vitrification in the cooling of glass-forming melts is commonly interpreted as the transformation of a thermodynamically (meta)stable equilibrium system into a frozen-in, thermodynamically nonequilibrium system, the glass. Hereby it is assumed that the transformation takes place at some well-defined sharp temperature, the glass transition temperature Tg. However, a more detailed experimental and theoretical analysis shows that the transition to a glass proceeds in a broader temperature range, where the characteristic times of change of temperature, tauT=-(TT), and relaxation times, tau, of the system to the respective equilibrium states are of similar order of magnitude. In this transition interval, the interplay of relaxation and change of external control parameters determines the value of the structural order parameters. In addition, irreversible processes take place in the transition interval, resulting both in an entropy freezing-in as well as in an irreversible increase of entropy and, as a result, in significant changes of all other thermodynamic parameters of the vitrifying systems. The effect of entropy production on glass transition and on the properties of glasses is analyzed here for the first time. In this analysis, the structural order-parameter concept as developed by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)] and Prigogine and Defay [Chemical Thermodynamics (Longmans, London, 1954)] is employed. In the framework of this approach we obtain general expressions for the thermodynamic properties of vitrifying systems such as heat capacity, enthalpy, entropy, and Gibbs' free energy, and for the entropy production. As one of the general conclusions we show that entropy production has a single maximum upon cooling and two maxima upon heating in the glass transition interval. The theoretical concepts developed allow us to explain in addition to the thermodynamic parameters also specific features of the kinetic parameters of glass-forming melts such as the viscosity. Experimental results are presented which confirm the theoretical conclusions. Further experiments are suggested, allowing one to test several additional predictions of the theory.
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Affiliation(s)
- Jörg Möller
- scitecon, Bayreuther Strasse 13, 01187 Dresden, Germany
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Feeney MR, Debenedetti PG, Stillinger FH. A statistical mechanical model for inverse melting. J Chem Phys 2003. [DOI: 10.1063/1.1593018] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Cangialosi D, Schut H, van Veen A, Picken SJ. Positron Annihilation Lifetime Spectroscopy for Measuring Free Volume during Physical Aging of Polycarbonate. Macromolecules 2002. [DOI: 10.1021/ma021214z] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- D. Cangialosi
- Department of Polymer Materials and Engineering, Delft University of Technology, Julianalaan 136, 2628 BL, Delft, The Netherlands, and Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB, Delft, The Netherlands
| | - H. Schut
- Department of Polymer Materials and Engineering, Delft University of Technology, Julianalaan 136, 2628 BL, Delft, The Netherlands, and Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB, Delft, The Netherlands
| | - A. van Veen
- Department of Polymer Materials and Engineering, Delft University of Technology, Julianalaan 136, 2628 BL, Delft, The Netherlands, and Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB, Delft, The Netherlands
| | - S. J. Picken
- Department of Polymer Materials and Engineering, Delft University of Technology, Julianalaan 136, 2628 BL, Delft, The Netherlands, and Interfaculty Reactor Institute, Delft University of Technology, Mekelweg 15, 2629 JB, Delft, The Netherlands
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Affiliation(s)
- Frank H. Stillinger
- Agere Systems, Murray Hill, New Jersey 07974, Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544, Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, and Department of Pharmaceutical Chemistry, University of California San Francisco, San Francisco, California 94118
| | - Pablo G. Debenedetti
- Agere Systems, Murray Hill, New Jersey 07974, Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544, Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, and Department of Pharmaceutical Chemistry, University of California San Francisco, San Francisco, California 94118
| | - Thomas M. Truskett
- Agere Systems, Murray Hill, New Jersey 07974, Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544, Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544, and Department of Pharmaceutical Chemistry, University of California San Francisco, San Francisco, California 94118
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Abstract
Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.
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Affiliation(s)
- P G Debenedetti
- Department of Chemical Engineering, Princeton University, New Jersey 08544, USA.
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Theory of supercooled liquids and glasses: Energy landscape and statistical geometry perspectives. ACTA ACUST UNITED AC 2001. [DOI: 10.1016/s0065-2377(01)28003-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Johari GP. An equilibrium supercooled liquid’s entropy and enthalpy in the Kauzmann and the third law extrapolations, and a proposed experimental resolution. J Chem Phys 2000. [DOI: 10.1063/1.481850] [Citation(s) in RCA: 73] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gutzow I, Ilieva D, Babalievski F, Yamakov V. Thermodynamics and kinetics of the glass transition: A generic geometric approach. J Chem Phys 2000. [DOI: 10.1063/1.481733] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Richet P, Neuville DR. Thermodynamics of Silicate Melts: Configurational Properties. THERMODYNAMIC DATA 1992. [DOI: 10.1007/978-1-4612-2842-4_5] [Citation(s) in RCA: 51] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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Spezifische WÄrme, spezifisches Volumen, Temperatur- und WÄrmeleitfÄhigkeit von Hochpolymeren. Colloid Polym Sci 1951. [DOI: 10.1007/bf01512276] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Ahlberg JE, Blanchard ER, Lundberg WO. The Heat Capacities of Benzene, Methyl Alcohol and Glycerol at Very Low Temperatures. J Chem Phys 1937. [DOI: 10.1063/1.1750072] [Citation(s) in RCA: 37] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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