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Du YZ, Li HF, Zhang Y, Zhou XN, Zhao JX. Restricted Phase Space Thermodynamics of Einstein-Power-Yang-Mills AdS Black Hole. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25040687. [PMID: 37190476 PMCID: PMC10137636 DOI: 10.3390/e25040687] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Revised: 03/31/2023] [Accepted: 04/09/2023] [Indexed: 05/17/2023]
Abstract
We consider the thermodynamics of the Einstein-power-Yang-Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton's gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form containing both the pressure and the central charge of the dual conformal field theory, i.e., the restricted phase transition formula. A novel phenomena arises: the dual quantity of pressure is the effective volume, not the geometric one. That leads to a new behavior of the Van de Waals-like phase transition for this system with the fixed central charge: the supercritical phase transition. From the Ehrenfest's scheme perspective, we check out the second-order phase transition of the EPYM AdS black hole. Furthermore the effect of the non-linear Yang-Mills parameter on these thermodynamic properties is also investigated.
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Affiliation(s)
- Yun-Zhi Du
- Institute of Theoretical Physics, Shanxi Datong University, Datong 037009, China
| | - Huai-Fan Li
- Institute of Theoretical Physics, Shanxi Datong University, Datong 037009, China
| | - Yang Zhang
- Institute of Theoretical Physics, Shanxi Datong University, Datong 037009, China
| | - Xiang-Nan Zhou
- College of Physics and Information Engineering, Shanxi Normal University, Taiyuan 030619, China
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2
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Yang M, Li W, Liu X, Wang H, Wu Y, Wang X, Zhang F, Zeng Q, Ma D, Ruan H, Lu Z. Configurational Entropy Effects on Glass Transition in Metallic Glasses. J Phys Chem Lett 2022; 13:7889-7897. [PMID: 35979998 DOI: 10.1021/acs.jpclett.2c01234] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Configurational entropy (Sconf) is known to be a key thermodynamic factor governing a glass transition process. However, this significance remains speculative because Sconf is not directly measurable. In this work, we demonstrate the role of Sconf theoretically and experimentally by a comparative study of a Zr-Ti-Cu-Ni-Be high-entropy metallic glass (HE-MG) with one of its conventional MG counterparts. It is revealed that the higher Sconf leads to a glass that is energetically more stable and structurally more ordered. This is manifested by ab initio molecular dynamics simulations, showing that ∼60% fewer atoms are agitated above Tg, and experimental results of smaller heat capacity jump, inconspicuous stiffness loss, insignificant structural change during glass transition, and a more depressed boson peak in the HE-MG than its counterpart. We accordingly propose a model to explain that a higher Sconf promotes a faster degeneracy-dependent kinetics for exploration of the potential energy landscape upon glass transition.
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Affiliation(s)
- Ming Yang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
- Neutron Science Platform, Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wenyue Li
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Xiongjun Liu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Hui Wang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Yuan Wu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Xianzhen Wang
- Institute for Advanced Materials and Technology, University of Science and Technology Beijing, Beijing 100083, China
| | - Fei Zhang
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
| | - Qiaoshi Zeng
- Center for High Pressure Science and Technology Advanced Research, Pudong, Shanghai 201203, China
| | - Dong Ma
- Neutron Science Platform, Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Haihui Ruan
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
| | - Zhaoping Lu
- Beijing Advanced Innovation Center for Materials Genome Engineering, State Key Laboratory for Advanced Metals and Materials, University of Science and Technology, Beijing, Beijing 100083, China
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3
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Zhao X, Grassia L, Simon SL. Mobility of Pressure-Densified and Pressure-Expanded Polystyrene Glasses: Dilatometry and a Test of KAHR Model. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00983] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiao Zhao
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, United States
| | - Luigi Grassia
- Department of Engineering, University of Campania Luigi Vanvitelli, Aversa 81031, Italy
| | - Sindee L. Simon
- Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States
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Doss K, Mauro JC. Theory of structural relaxation in glass from the thermodynamics of irreversible processes. Phys Rev E 2021; 103:062606. [PMID: 34271756 DOI: 10.1103/physreve.103.062606] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2021] [Accepted: 05/12/2021] [Indexed: 11/07/2022]
Abstract
This work proposes a fundamental thermodynamic description of structural relaxation in glasses by establishing a link between the Prony series solution to volume relaxation derived from the principles of irreversible thermodynamics and asymmetric Lévy stable distribution of relaxation rates. Additionally, it is shown that the bulk viscosity of glass, and not the shear viscosity, is the transport coefficient governing structural relaxation. We also report the distribution of relaxation times and energy barrier heights underpinning stretched exponential relaxation. It is proposed that this framework may be used for qualitative and quantitative descriptions of the relaxation kinetics in glass.
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Affiliation(s)
- Karan Doss
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - John C Mauro
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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5
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Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions. Symmetry (Basel) 2021. [DOI: 10.3390/sym13020256] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
An integro-differential equation describes the non-equilibrium thermal response of glass-forming substances with a dynamic (time-dependent) heat capacity to fast thermal perturbations. We found that this heat transfer problem could be solved analytically for a heat source with an arbitrary time dependence and different geometries. The method can be used to analyze the response to local thermal perturbations in glass-forming materials, as well as temperature fluctuations during subcritical crystal nucleation and decay. The results obtained can be useful for applications and a better understanding of the thermal properties of glass-forming materials, polymers, and nanocomposites.
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6
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Minakov AA, Schick C. Nanoscale Heat Conduction in CNT-POLYMER Nanocomposites at Fast Thermal Perturbations. Molecules 2019; 24:molecules24152794. [PMID: 31370312 PMCID: PMC6696361 DOI: 10.3390/molecules24152794] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Revised: 06/22/2019] [Accepted: 07/26/2019] [Indexed: 11/30/2022] Open
Abstract
Nanometer scale heat conduction in a polymer/carbon nanotube (CNT) composite under fast thermal perturbations is described by linear integrodifferential equations with dynamic heat capacity. The heat transfer problem for local fast thermal perturbations around CNT is considered. An analytical solution for the nonequilibrium thermal response of the polymer matrix around CNT under local pulse heating is obtained. The dynamics of the temperature distribution around CNT depends significantly on the CNT parameters and the thermal contact conductance of the polymer/CNT interface. The effect of dynamic heat capacity on the local overheating of the polymer matrix around CNT is considered. This local overheating can be enhanced by very fast (about 1 ns) components of the dynamic heat capacity of the polymer matrix. The results can be used to analyze the heat transfer process at the early stages of “shish-kebab” crystal structure formation in CNT/polymer composites.
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Affiliation(s)
- Alexander A Minakov
- Prokhorov General Physics Institute of the Russian Academy of Sciences, GPI RAS, Vavilov str. 38, 119991 Moscow, Russia
| | - Christoph Schick
- Institute of Physics and Competence Centre CALOR, University of Rostock, 18051 Rostock, Germany.
- Butlerov Institute of Chemistry, Kazan Federal University, 18 Kremlyovskaya Street, Kazan 420008, Russia.
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Minakov AA, Schick C. Nanometer scale thermal response of polymers to fast thermal perturbations. J Chem Phys 2018; 149:074503. [PMID: 30134667 DOI: 10.1063/1.5044187] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Nanometer scale thermal response of polymers to fast thermal perturbations is described by linear integro-differential equations with dynamic heat capacity. The exact analytical solution for the non-equilibrium thermal response of polymers in plane and spherical geometry is obtained in the absence of numerical (finite element) calculations. The solution is different from the iterative method presented in a previous publication. The solution provides analytical relationships for fast thermal response of polymers even at the limit t → 0, when the application of the iterative process is very problematic. However, both methods give the same result. It was found that even fast (ca. 1 ns) components of dynamic heat capacity greatly enhance the thermal response to local thermal perturbations. Non-equilibrium and non-linear thermal response of typical polymers under pulse heating with relaxation parameters corresponding to polystyrene and poly(methyl methacrylate) is determined. The obtained results can be used to analyze the heat transfer process at the early stages of crystallization with fast formation of nanometer scale crystals.
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Affiliation(s)
- Alexander A Minakov
- Prokhorov General Physics Institute of the Russian Academy of Sciences, GPI RAS, Vavilov St. 38, 119991 Moscow, Russia
| | - Christoph Schick
- University of Rostock, Institute of Physics and Competence Centre CALOR, Albert-Einstein-Str. 23-24, 18051 Rostock, Germany
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Kutcherov V, Chernoutsan A, Brazhkin V. Crystallization and glass transition in crude oils and their fractions at atmospheric and high pressures. J Mol Liq 2017. [DOI: 10.1016/j.molliq.2017.05.056] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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9
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Koperwas K, Grzybowski A, Grzybowska K, Wojnarowska Z, Paluch M. Effects of dynamic heterogeneity and density scaling of molecular dynamics on the relationship among thermodynamic coefficients at the glass transition. J Chem Phys 2015; 143:024502. [DOI: 10.1063/1.4923005] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- K. 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
| | - A. 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
| | - K. Grzybowska
- 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
| | - Z. Wojnarowska
- 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
| | - M. 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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10
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Affiliation(s)
- K. Ramesh
- Department of Physics, Indian Institute of Science, Bangalore 560012, India
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11
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Mo JX, Liu WB. Ehrenfest scheme forP−Vcriticality of higher dimensional charged black holes, rotating black holes, and Gauss-Bonnet AdS black holes. Int J Clin Exp Med 2014. [DOI: 10.1103/physrevd.89.084057] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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12
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13
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Buchenau U. Bulk and shear relaxation in glasses and highly viscous liquids. J Chem Phys 2012; 136:224512. [DOI: 10.1063/1.4726459] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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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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15
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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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16
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Rabochiy P, Lubchenko V. Universality of the onset of activated transport in Lennard-Jones liquids with tunable coordination: Implications for the effects of pressure and directional bonding on the crossover to activated transport, configurational entropy, and fragility of glassforming liquids. J Chem Phys 2012; 136:084504. [DOI: 10.1063/1.3687166] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
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17
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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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18
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Moynihan CT. Two Species/Nonideal Solution Model for Amorphous/Amorphous Phase Transitions. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-455-411] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTA simple macroscopic thermodynamic model for first order transitions between two amorphous phases in a one component liquid is reviewed, augmented and evaluated. The model presumes the existence in the liquid of two species, whose concentrations are temperature and pressure dependent and which form a solution with large, positive deviations from ideality. Application of the model to recent data indicates that water can undergo an amorphous/amorphous phase transition below a critical temperature Tc of 217K and above a critical pressure Pc of 380 atm.
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Wondraczek L, Krolikowski S, Behrens H. Relaxation and Prigogine–Defay ratio of compressed glasses with negative viscosity-pressure dependence. J Chem Phys 2009; 130:204506. [DOI: 10.1063/1.3141382] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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20
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Ribeiro MCC, Scopigno T, Ruocco G. Prigogine−Defay Ratio for an Ionic Glass-Former: Molecular Dynamics Simulations. J Phys Chem B 2009; 113:3099-104. [DOI: 10.1021/jp810934e] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Mauro C. C. Ribeiro
- Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, C.P. 26077, 05513-970, São Paulo, SP, Brazil, and Istituto Nazionale per la Física della Materia (INFM-CNR) and Dipartimento di Fisica, “Sapienza” Universitá di Roma, 00185 Roma, Italy
| | - Tullio Scopigno
- Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, C.P. 26077, 05513-970, São Paulo, SP, Brazil, and Istituto Nazionale per la Física della Materia (INFM-CNR) and Dipartimento di Fisica, “Sapienza” Universitá di Roma, 00185 Roma, Italy
| | - Giancarlo Ruocco
- Laboratório de Espectroscopia Molecular, Instituto de Química, Universidade de São Paulo, C.P. 26077, 05513-970, São Paulo, SP, Brazil, and Istituto Nazionale per la Física della Materia (INFM-CNR) and Dipartimento di Fisica, “Sapienza” Universitá di Roma, 00185 Roma, Italy
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21
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Christensen T, Dyre JC. Solution of the spherically symmetric linear thermoviscoelastic problem in the inertia-free limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021501. [PMID: 18850835 DOI: 10.1103/physreve.78.021501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2008] [Revised: 05/17/2008] [Indexed: 05/26/2023]
Abstract
The coupling between mechanical and thermal properties due to thermal expansion complicates the problem of measuring frequency-dependent thermoviscoelastic properties, in particular for highly viscous liquids. A simplification arises if there is spherical symmetry where--as detailed in the present paper--the thermoviscoelastic problem may be solved analytically in the inertia-free limit, i.e., the limit where the sample is much smaller than the wavelength of sound waves at the frequencies of interest. As for the one-dimensional thermoviscoelastic problem [Christensen et al., Phys. Rev. E 75, 041502 (2007)], the solution is conveniently formulated in terms of the so-called transfer matrix, which directly links to the boundary conditions that can be experimentally controlled. Once the transfer matrix has been calculated, it is fairly easy to deduce the equations describing various experimentally relevant special cases (boundary conditions that are adiabatic, isothermal, isochoric, etc.). In most situations the relevant frequency-dependent specific heat is the longitudinal specific heat, a quantity that is in between the isochoric and isobaric frequency-dependent specific heats.
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Affiliation(s)
- Tage Christensen
- DNRF Centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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22
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Wondraczek L, Behrens H. Molar volume, excess enthalpy, and Prigogine-Defay ratio of some silicate glasses with different (P,T) histories. J Chem Phys 2007; 127:154503. [DOI: 10.1063/1.2794745] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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23
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Abstract
The phenomenology of the laboratory glass transition is examined in the enthalpy landscape framework. It is shown that a generic description of the glassy state based on partitioning of the phase space caused by the finiteness of the time of observation explains all universal features of glass transition. Using this description of glass, which is referred to as the extrinsically constrained liquid, expressions are derived for properties of glass and for property changes at the laboratory glass transition. A model enthalpy landscape is used to illustrate the basic concepts of this description. Additional new consequences of this description, such as the role of complexity in glass transition and the zero residual entropy of a glass, are discussed.
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Affiliation(s)
- Prabhat K Gupta
- Department of Materials Science and Engineering, Ohio State University, Columbus, Ohio 43210, USA
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24
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Ellegaard NL, Christensen T, Christiansen PV, Olsen NB, Pedersen UR, Schrøder TB, Dyre JC. Single-order-parameter description of glass-forming liquids: A one-frequency test. J Chem Phys 2007; 126:074502. [PMID: 17328615 DOI: 10.1063/1.2434963] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear dynamic Prigogine-Defay ratio" LambdaTp(omega) with the property that if LambdaTp(omega)=1 at one frequency, then LambdaTp(omega) is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter (which may be nonexponential in time). Generalizations to other cases of thermodynamic control parameters than temperature and pressure are also presented.
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Affiliation(s)
- Niels L Ellegaard
- DNRF Centre Glass and Time, IMFUFA (27), Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark
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25
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26
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Javaheri MRH, Chamberlin RV. A free-energy landscape picture and Landau theory for the dynamics of disordered materials. J Chem Phys 2006; 125:154503. [PMID: 17059268 DOI: 10.1063/1.2354471] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Landau's theory of phase transitions [Nature (London) 138, 840 (1936); Statistical Physics (Pergamon, London, 1959)] is adapted to treat independently relaxing regions in complex systems using nanothermodynamics. The order parameter we use governs the thermal fluctuations, not a specific static structure. We find that the entropy term dominates the thermal behavior, as is reasonable for disordered systems. Consequently, the thermal equilibrium occurs at the internal-energy maximum, so that the potential-energy minima have negligible influence on the dynamics. The dynamics involves normal thermal fluctuations about the free-energy minimum, with a time scale that is governed by the curvature of the internal-energy maximum. The temperature dependence of the fluctuations yields Vogel-Tamman-Fulcher-type [Phys. Z. 22, 645 (1921); J. Am. Ceram. Soc. 8, 339 (1925); Z. Anorg. Allg. Chem. 156, 245 (1926)] relaxation rates and approximate time-temperature superposition, consistent with the Williams-Landell-Ferry [J. Am. Chem. Soc. 77, 3701 (1955)] procedure for analyzing the dynamics of complex fluids, while the size dependence of the fluctuations provides an explanation for the distribution of relaxation times and heterogeneity that are found in glass-forming liquids, thus providing a unified picture for several features in the dynamics of disordered materials.
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Affiliation(s)
- Mohammad Reza H Javaheri
- Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
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27
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Affiliation(s)
- L. Ferrari
- a Gruppo Nazionale di Struttura della Materia , Unità di Bologna Dipartimento di Fisica , via Irnerio 46, 40126 , Bologna , Italy
| | - G. Russo
- a Gruppo Nazionale di Struttura della Materia , Unità di Bologna Dipartimento di Fisica , via Irnerio 46, 40126 , Bologna , Italy
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28
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Affiliation(s)
- J. Jäckle
- a Fakultät für Physik , Universität Konstanz , D-7750 , Konstanz , F. R. , Germany
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Havlíček I, Ilavský M, Hrouz J. Effect of pressure on the cooperative relaxation properties and glass transition temperature of amorphous polymers. J MACROMOL SCI B 2006. [DOI: 10.1080/00222348208018793] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- I. Havlíček
- a Institute of Macromolecular Chemistry Czechoslovak Academy of Sciences , 162 06, Prague 6, Czechoslovakia
| | - M. Ilavský
- a Institute of Macromolecular Chemistry Czechoslovak Academy of Sciences , 162 06, Prague 6, Czechoslovakia
| | - J. Hrouz
- a Institute of Macromolecular Chemistry Czechoslovak Academy of Sciences , 162 06, Prague 6, Czechoslovakia
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Nieuwenhuizen TM. Formulation of thermodynamics for the glassy state: Configurational energy as a modest source of energy. J Chem Phys 2001. [DOI: 10.1063/1.1399036] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] 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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Takahara S, Ishikawa M, Yamamuro O, Matsuo T. Structural Relaxations of Glassy Polystyrene and o-Terphenyl Studied by Simultaneous Measurement of Enthalpy and Volume under High Pressure. J Phys Chem B 1999. [DOI: 10.1021/jp983801l] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shuichi Takahara
- Department of Chemistry and Microcalorimetry Research Center, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
| | - Mariko Ishikawa
- Department of Chemistry and Microcalorimetry Research Center, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
| | - Osamu Yamamuro
- Department of Chemistry and Microcalorimetry Research Center, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
| | - Takasuke Matsuo
- Department of Chemistry and Microcalorimetry Research Center, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan
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Stillinger FH, Debenedetti PG, Sastry S. Resolving vibrational and structural contributions to isothermal compressibility. J Chem Phys 1998. [DOI: 10.1063/1.476997] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Cowie JMG, Harris S, McEwen IJ. Physical Aging in Poly(vinyl acetate). 2. Relative Rates of Volume and Enthalpy Relaxation. Macromolecules 1998. [DOI: 10.1021/ma970287t] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- J. M. G. Cowie
- Department of Chemistry, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
| | - S. Harris
- Department of Chemistry, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
| | - I. J. McEwen
- Department of Chemistry, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland
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Cowie J, Ferguson R, Harris S, McEwen I. Physical ageing in poly(vinyl acetate)—3. Structural relaxation and its effect on the stress relaxation modulus. POLYMER 1998. [DOI: 10.1016/s0032-3861(97)10034-9] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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38
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Zhang Y, Gangwani KK, Lemert RM. Sorption and swelling of block copolymers in the presence of supercritical fluid carbon dioxide. J Supercrit Fluids 1997. [DOI: 10.1016/s0896-8446(97)00031-4] [Citation(s) in RCA: 110] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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39
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Kalospiros NS, Paulaitis ME. Molecular thermodynamic model for solvent-induced glass transitions in polymer—supercritical fluid systems. Chem Eng Sci 1994. [DOI: 10.1016/0009-2509(94)85012-7] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Bengtzelius U, Sjögren L. Changes of thermodynamic quantities at the glass transition. J Chem Phys 1986. [DOI: 10.1063/1.450473] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Viscoelasticity of Glass. ACTA ACUST UNITED AC 1986. [DOI: 10.1016/b978-0-12-706703-2.50004-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Naoki M, Owada A. Factors determining glass transition temperature and relaxation time of poly(vinyl chloride). POLYMER 1984. [DOI: 10.1016/0032-3861(84)90270-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Jäckle J. The relation between the changes of thermodynamic quantities at the glass transition and the long‐wavelength fluctuations of glass structure. J Chem Phys 1983. [DOI: 10.1063/1.446332] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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A simple phenomenological model for the order parameter description of glass transition. Polym Bull (Berl) 1982. [DOI: 10.1007/bf00256096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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The connection between the measured glass transition temperature and the time dependent order parameter description of the glass transition. Polym Bull (Berl) 1981. [DOI: 10.1007/bf00255298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Moynihan CT, Lesikar AV. COMPARISON AND ANALYSIS OF RELAXATION PROCESSES AT THE GLASS TRANSITION TEMPERATURE. Ann N Y Acad Sci 1981. [DOI: 10.1111/j.1749-6632.1981.tb55658.x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Moynihan CT, Lesikar AV. COMPARISON AND ANALYSIS OF RELAXATION PROCESSES AT THE GLASS TRANSITION TEMPERATURE. Ann N Y Acad Sci 1981. [DOI: 10.1111/j.1749-6632.1981.tb55448.x] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Lesikar AV, Moynihan CT. The order parameter model of liquids and glasses with applications to dielectric relaxation. J Chem Phys 1980. [DOI: 10.1063/1.440330] [Citation(s) in RCA: 16] [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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50
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Lesikar AV, Moynihan CT. Some relations connecting volume and enthalpy relaxation in the order parameter model of liquids and glasses. J Chem Phys 1980. [DOI: 10.1063/1.439141] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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