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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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Xu X, Douglas JF, Xu WS. Thermodynamic–Dynamic Interrelations in Glass-Forming Polymer Fluids. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Xiaolei 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
| | - 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
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Novikov VN, Sokolov AP. Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1101. [PMID: 36010765 PMCID: PMC9407199 DOI: 10.3390/e24081101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Revised: 08/05/2022] [Accepted: 08/07/2022] [Indexed: 06/15/2023]
Abstract
Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.
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Affiliation(s)
- Vladimir N. Novikov
- Institute of Automation and Electrometry, Russian Academy of Sciences, 630090 Novosibirsk, Russia
| | - Alexei P. Sokolov
- Department of Chemistry and Joint Institute for Neutron Sciences, University of Tennessee, Knoxville, TN 37996, USA
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
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Roggero A, Caussé N, Pébère N, Dantras E. VFT to Arrhenius crossover at the dynamic glass transition of an epoxy network as revealed by dielectric experiments in continuous immersion. POLYMER 2022. [DOI: 10.1016/j.polymer.2022.124542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Zhang H, Wang X, Yu HB, Douglas JF. Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:56. [PMID: 33871722 DOI: 10.1140/epje/s10189-021-00060-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 03/21/2021] [Indexed: 06/12/2023]
Abstract
We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.
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Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada.
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 1H9, Canada
| | - Hai-Bin Yu
- Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China
| | - Jack F Douglas
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology(NIST), Gaithersburg, MD, 20899, 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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Xu WS, Douglas JF, Xia W, Xu X. Investigation of the Temperature Dependence of Activation Volume in Glass-Forming Polymer Melts under Variable Pressure Conditions. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01268] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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
- Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Wenjie Xia
- Department of Civil and Environmental Engineering, North Dakota State University, Fargo, North Dakota 58108, United States
| | - Xiaolei Xu
- 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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Zykova VA, Adichtchev SV, Novikov VN, Surovtsev NV. Second-order-derivative analysis of structural relaxation time in the elastic model of glass-forming liquids. Phys Rev E 2020; 101:052610. [PMID: 32575277 DOI: 10.1103/physreve.101.052610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 04/23/2020] [Indexed: 06/11/2023]
Abstract
Recently it was shown [V. N. Novikov and A. P. Sokolov, Phys. Rev. E 92, 062304 (2015)10.1103/PhysRevE.92.062304] that the second derivative with respect to inverse temperature of the structural relaxation time in some supercooled molecular liquids has a sharp maximum. It marks the point at which the apparent activation energy begins to saturate with decreasing temperature. The elastic model of glass-forming liquids expresses the temperature dependence of the structural relaxation time through that of the shear modulus. In this paper, we test whether this model is able to predict the maximum of the second derivative. We confirm its presence in the elastic model by analyzing the temperature dependence of the Brillouin light scattering in salol. This is a very subtle feature of the temperature dependence, which is greatly enhanced when taking derivatives. Its presence in the Brillouin data provides strong support to the elastic model of glass-forming liquids.
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Affiliation(s)
- V A Zykova
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
| | - S V Adichtchev
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
| | - V N Novikov
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
| | - N V Surovtsev
- Institute of Automation and Electrometry, Russian Academy of Sciences, Novosibirsk, 630090, Russia
- Novosibirsk State University, Novosibirsk, 630090, Russia
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Ginzburg VV. A simple mean-field model of glassy dynamics and glass transition. SOFT MATTER 2020; 16:810-825. [PMID: 31840706 DOI: 10.1039/c9sm01575b] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.
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Affiliation(s)
- Valeriy V Ginzburg
- Core Research and Development, The Dow Chemical Company, Midland, MI 48674, USA.
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Zhang H, Wang X, Chremos A, Douglas JF. Superionic UO2: A model anharmonic crystalline material. J Chem Phys 2019; 150:174506. [DOI: 10.1063/1.5091042] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Hao Zhang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Xinyi Wang
- Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada
| | - Alexandros Chremos
- Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Jack F. Douglas
- Material Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Niss K, Hecksher T. Perspective: Searching for simplicity rather than universality in glass-forming liquids. J Chem Phys 2018; 149:230901. [PMID: 30579292 DOI: 10.1063/1.5048093] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This article gives an overview of experimental results on dynamics in bulk glass-forming molecular liquids. Rather than looking for phenomenology that is universal, in the sense that it is seen in all liquids, the focus is on identifying the basic characteristics, or "stylized facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner.
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Affiliation(s)
- Kristine Niss
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
| | - Tina Hecksher
- Glass and Time, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark
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Bhadauriya S, Wang X, Pitliya P, Zhang J, Raghavan D, Bockstaller MR, Stafford CM, Douglas JF, Karim A. Tuning the Relaxation of Nanopatterned Polymer Films with Polymer-Grafted Nanoparticles: Observation of Entropy-Enthalpy Compensation. NANO LETTERS 2018; 18:7441-7447. [PMID: 30398875 PMCID: PMC6537094 DOI: 10.1021/acs.nanolett.8b02514] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Polymer films provide a versatile platform in which complex functional relief patterns can be thermally imprinted with a resolution down to few nanometers. However, a practical limitation of this method is the tendency for the imprinted patterns to relax ("slump"), leading to loss of pattern fidelity over time. While increasing temperature above glass transition temperature ( Tg) accelerates the slumping kinetics of neat films, we find that the addition of polymer-grafted nanoparticles (PGNP) can greatly enhance the thermal stability of these patterns. Specifically, increasing the concentration of poly(methyl methacrylate) (PMMA) grafted titanium dioxide (TiO2) nanoparticles in the composite films slows down film relaxation dynamics, leading to enhanced pattern stability for the temperature range that we investigated. Interestingly, slumping relaxation time is found to obey an entropy-enthalpy compensation (EEC) relationship with varying PGNP concentration, similar to recently observed relaxation of strain-induced wrinkling in glassy polymer films having variable film thickness. The compensation temperature, Tcomp was found to be in the vicintity of the bulk Tg of PMMA. Our results suggest a common origin of EEC relaxation in patterned polymer thin films and nanocomposites.
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Affiliation(s)
- Sonal Bhadauriya
- Department of Polymer Engineering, University of Akron, Akron, Ohio 44325 United States
| | - Xiaoteng Wang
- Department of Polymer Engineering, University of Akron, Akron, Ohio 44325 United States
| | - Praveen Pitliya
- Department of Chemistry, Howard University, Washington, District of Columbia 20059, United States
| | - Jianan Zhang
- Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Dharmaraj Raghavan
- Department of Chemistry, Howard University, Washington, District of Columbia 20059, United States
| | - Michael R. Bockstaller
- Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States
| | - Christopher M. Stafford
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States
| | - Alamgir Karim
- Department of Polymer Engineering, University of Akron, Akron, Ohio 44325 United States
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Agapov AL, Novikov VN, Hong T, Fan F, Sokolov AP. Surprising Temperature Scaling of Viscoelastic Properties in Polymers. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00454] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alexander L. Agapov
- Department of Chemistry, University of Tennessee, 1420 Circle Drive, Knoxville, Tennessee 37996, United States
| | - Vladimir N. Novikov
- Department of Chemistry, University of Tennessee, 1420 Circle Drive, Knoxville, Tennessee 37996, United States
- Institute of Automation and Electrometry, Russian Academy of Sciences, 1 Koptyug ave., Novosibirsk 630090, Russia
| | - Tao Hong
- Department of Chemistry, University of Tennessee, 1420 Circle Drive, Knoxville, Tennessee 37996, United States
| | - Fei Fan
- Department of Chemistry, University of Tennessee, 1420 Circle Drive, Knoxville, Tennessee 37996, United States
| | - Alexei P. Sokolov
- Department of Chemistry, University of Tennessee, 1420 Circle Drive, Knoxville, Tennessee 37996, United States
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
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Chung JY, Douglas JF, Stafford CM. A wrinkling-based method for investigating glassy polymer film relaxation as a function of film thickness and temperature. J Chem Phys 2018; 147:154902. [PMID: 29055329 DOI: 10.1063/1.5006949] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
We investigate the relaxation dynamics of thin polymer films at temperatures below the bulk glass transition Tg by first compressing polystyrene films supported on a polydimethylsiloxane substrate to create wrinkling patterns and then observing the slow relaxation of the wrinkled films back to their final equilibrium flat state by small angle light scattering. As with recent relaxation measurements on thin glassy films reported by Fakhraai and co-workers, we find the relaxation time of our wrinkled films to be strongly dependent on film thickness below an onset thickness on the order of 100 nm. By varying the temperature between room temperature and Tg (≈100 °C), we find that the relaxation time follows an Arrhenius-type temperature dependence to a good approximation at all film thicknesses investigated, where both the activation energy and the relaxation time pre-factor depend appreciably on film thickness. The wrinkling relaxation curves tend to cross at a common temperature somewhat below Tg, indicating an entropy-enthalpy compensation relation between the activation free energy parameters. This compensation effect has also been observed recently in simulated supported polymer films in the high temperature Arrhenius relaxation regime rather than the glassy state. In addition, we find that the film stress relaxation function, as well as the height of the wrinkle ridges, follows a stretched exponential time dependence and the short-time effective Young's modulus derived from our modeling decreases sigmoidally with increasing temperature-both characteristic features of glassy materials. The relatively facile nature of the wrinkling-based measurements in comparison to other film relaxation measurements makes our method attractive for practical materials development, as well as fundamental studies of glass formation.
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Affiliation(s)
- Jun Young Chung
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Christopher M Stafford
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Coslovich D, Ozawa M, Kob W. Dynamic and thermodynamic crossover scenarios in the Kob-Andersen mixture: Insights from multi-CPU and multi-GPU simulations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:62. [PMID: 29774433 DOI: 10.1140/epje/i2018-11671-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Accepted: 04/25/2018] [Indexed: 05/23/2023]
Abstract
The physical behavior of glass-forming liquids presents complex features of both dynamic and thermodynamic nature. Some studies indicate the presence of thermodynamic anomalies and of crossovers in the dynamic properties, but their origin and degree of universality is difficult to assess. Moreover, conventional simulations are barely able to cover the range of temperatures at which these crossovers usually occur. To address these issues, we simulate the Kob-Andersen Lennard-Jones mixture using efficient protocols based on multi-CPU and multi-GPU parallel tempering. Our setup enables us to probe the thermodynamics and dynamics of the liquid at equilibrium well below the critical temperature of the mode-coupling theory, [Formula: see text]. We find that below [Formula: see text] the analysis is hampered by partial crystallization of the metastable liquid, which nucleates extended regions populated by large particles arranged in an fcc structure. By filtering out crystalline samples, we reveal that the specific heat grows in a regular manner down to [Formula: see text] . Possible thermodynamic anomalies suggested by previous studies can thus occur only in a region of the phase diagram where the system is highly metastable. Using the equilibrium configurations obtained from the parallel tempering simulations, we perform molecular dynamics and Monte Carlo simulations to probe the equilibrium dynamics down to [Formula: see text]. A temperature-derivative analysis of the relaxation time and diffusion data allows us to assess different dynamic scenarios around [Formula: see text]. Hints of a dynamic crossover come from analysis of the four-point dynamic susceptibility. Finally, we discuss possible future numerical strategies to clarify the nature of crossover phenomena in glass-forming liquids.
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Affiliation(s)
- Daniele Coslovich
- Laboratoire Charles Coulomb, Université de Montpellier, CNRS, Montpellier, France.
| | - Misaki Ozawa
- Laboratoire Charles Coulomb, Université de Montpellier, CNRS, Montpellier, France
| | - Walter Kob
- Laboratoire Charles Coulomb, Université de Montpellier, CNRS, Montpellier, France
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McKenna GB, Simon SL. 50th Anniversary Perspective: Challenges in the Dynamics and Kinetics of Glass-Forming Polymers. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b01014] [Citation(s) in RCA: 102] [Impact Index Per Article: 14.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Gregory B. McKenna
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409-3121, United States
| | - Sindee L. Simon
- Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409-3121, United States
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Xu WS, Douglas JF, Freed KF. Generalized entropy theory of glass-formation in fully flexible polymer melts. J Chem Phys 2016; 145:234509. [DOI: 10.1063/1.4972412] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Wen-Sheng Xu
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - Jack F. Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Karl F. Freed
- James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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18
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Novikov V. Connection between the glass transition temperature T and the Arrhenius temperature T in supercooled liquids. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2016.07.003] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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