Skip to main content
SpringerLink
Log in

A Thermodynamic Perspective on Polymer Glass Formation

  • Perspective
  • Published:
Chinese Journal of Polymer Science Aims and scope Submit manuscript

Abstract

The dynamics of polymeric and other glass-forming liquids dramatically slows down upon cooling toward the glass transition temperature without any obvious significant change in their static structure. A quantitative understanding of this extraordinary dynamic slowdown remains one of the most significant challenges in condensed matter physics. Historically, extensive efforts have been devoted to explaining the dynamics of glass-forming liquids in terms of thermodynamic properties, leading to a number of semi-empirical models emphasizing distinct thermodynamic properties. Here, a thermodynamic perspective is provided on the glass formation of polymeric and other materials. We begin with an overview of the thermodynamic models of glass formation, including the intuitively appealing “free volume” models, enthalpy models originally emphasized by Goldstein and later by others, and the highly influential configurational entropy-based models. The review of these models is followed by a discussion of the advances that attempt to bring together some of the seemingly disparate thermodynamic viewpoints on glass formation by revealing a close interrelation between thermodynamic properties. We conclude this review with remarks on several key topics in this field, along with our viewpoint for future work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Debenedetti, P. G.; Stillinger, F. H. Supercooled liquids and the glass transition. Nature 2001, 410, 259–267.

    CAS  PubMed  Google Scholar 

  2. Ediger, M. D.; Angell, C. A.; Nagel, S. R. Supercooled liquids and glasses. J. Phys. Chem. 1996, 100, 13200–13212.

    CAS  Google Scholar 

  3. Berthier, L.; Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 2011, 83, 587–645.

    CAS  Google Scholar 

  4. Ediger, M. D.; Harrowell, P. Perspective: supercooled liquids and glasses. J. Chem. Phys. 2012, 137, 080901.

    CAS  PubMed  Google Scholar 

  5. Biroli, G.; Garrahan, J. P. Perspective: the glass transition. J. Chem. Phys. 2013, 138, 12A301.

    PubMed  Google Scholar 

  6. Debenedetti, P. G.; Stillinger, F. H. Glass transition thermodynamics and kinetics. Annu. Rev. Condens. Matter Phys. 2013, 4, 263–285.

    Google Scholar 

  7. Parry, B.; Surovtsev, I.; Cabeen, M.; O’Hern, C.; Dufresne, E.; Jacobs-Wagner, C. The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity. Cell 2014, 156, 183–194.

    CAS  PubMed  Google Scholar 

  8. Roos, Y. H. Glass transition temperature and its relevance in food processing. Annu. Rev. Food Sci. Technol. 2010, 1, 469–496.

    CAS  PubMed  Google Scholar 

  9. Xu, Z.; Dai, X.; Bu, X.; Yang, Y.; Zhang, X.; Man, X.; Zhang, X.; Doi, M.; Yan, L. T. Enhanced heterogeneous diffusion of nanoparticles in semiflexible networks. ACS Nano 2021, 15, 4608–4616.

    CAS  PubMed  Google Scholar 

  10. Dai, X.; Zhang, X.; Gao, L.; Xu, Z.; Yan, L. T. Topology mediates transport of nanoparticles in macromolecular networks. Nat. Commun. 2022, 13, 4094.

    CAS  PubMed  PubMed Central  Google Scholar 

  11. Dai, X.; Zhu, Z.; Li, Y.; Yang, B.; Xu, J. F.; Dong, Y.; Zhou, X.; Yan, L.-T.; Liu, D. “Shutter” effects enhance protein diffusion in dynamic and rigid molecular networks. J. Am. Chem. Soc. 2022, 144, 19017–19025.

    CAS  PubMed  Google Scholar 

  12. DiMarzio, E. A. Equilibrium theory of glasses. Ann. N. Y. Acad. Sci. 1981, 371, 1–20.

    CAS  Google Scholar 

  13. Smallenburg, F.; Sciortino, F. Liquids more stable than crystals in particles with limited valence and flexible bonds. Nat. Phys. 2013, 9, 554–558.

    CAS  Google Scholar 

  14. Zhang, G.; Stillinger, F. H.; Torquato, S. The perfect glass paradigm: disordered hyperuniform glasses down to absolute Zero. Sci. Rep. 2016, 6, 36963.

    CAS  PubMed  PubMed Central  Google Scholar 

  15. Ingebrigtsen, T. S.; Dyre, J. C.; Schroder, T. B.; Royall, C. P. Crystallization instability in glass-forming mixtures. Phys. Rev. X 2019, 9, 031016.

    CAS  Google Scholar 

  16. Roland, C. M.; Hensel-Bielowka, S.; Paluch, M.; Casalini, R. Supercooled dynamics of glass-forming liquids and polymers under hydrostatic pressure. Rep. Prog. Phys. 0005, 68, 1405–1478.

    Google Scholar 

  17. Roland, C. M. Relaxation phenomena in vitrifying polymers and molecular liquids. Macromolecules 2010, 43, 7875–7890.

    CAS  Google Scholar 

  18. Cangialosi, D. Dynamics and thermodynamics of polymer glasses. J. Phys.: Condens. Matter 2014, 26, 153101.

    CAS  PubMed  Google Scholar 

  19. Napolitano, S.; Glynos, E.; Tito, N. B. Glass transition of polymers in bulk, confined geometries, and near interfaces. Rep. Prog. Phys. 2017, 80, 036602.

    PubMed  Google Scholar 

  20. McKenna, G. B.; Simon, S. L. 50th Anniversary perspective: challenges in the dynamics and kinetics of glass-forming Polymers. Macromolecules 2017, 50, 6333–6361.

    CAS  Google Scholar 

  21. Dudowicz, J.; Freed, K. F.; Douglas, J. F. Generalized entropy theory of polymer glass formation. Adv. Chem. Phys. 2008, 137, 125–222.

    CAS  Google Scholar 

  22. Xu, W.-S.; Douglas, J. F.; Sun, Z. Y. Polymer glass formation: role of activation free energy, configurational entropy, and collective motion. Macromolecules 2021, 54, 3001–3033.

    CAS  Google Scholar 

  23. Götze, W. in Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory. Oxford University Press, Oxford, 2008.

    Google Scholar 

  24. Pazmiño Betancourt, B. A.; Hanakata, P. Z.; Starr, F. W.; Douglas, J. F. Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 2966–2971.

    PubMed  PubMed Central  Google Scholar 

  25. Goldstein, M. Some thermodynamic aspects of the glass transition: free volume, entropy, and enthalpy theories. J. Chem. Phys. 1963, 39, 3369–3374.

    CAS  Google Scholar 

  26. Caruthers, J. M.; Medvedev, G. A. Quantitative model of super-Arrhenian behavior in glass forming materials. Phys. Rev. Materials 2018, 2, 055604.

    CAS  Google Scholar 

  27. Medvedev, G. A.; Caruthers, J. M. A quantitative model of super-Arrhenian behavior in glass-forming polymers. Macromolecules 2019, 52, 1424–1439.

    CAS  Google Scholar 

  28. Zhao, X.; Simon, S. L. A model-free analysis of configurational properties to reduce the temperature- and pressure-dependent segmental relaxation times of polymers. J. Chem. Phys. 2020, 152, 044901.

    CAS  PubMed  Google Scholar 

  29. Kauzmann, W. The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 1948, 43, 219–256.

    CAS  Google Scholar 

  30. Xu, X.; Douglas, J. F.; Xu, W. S. Teermodnaamic-dynamic interrelations in glass-forming polymer fluids. Macromolecules 2022, 55, 8699–8722.

    CAS  Google Scholar 

  31. Lucretius, In Great Books of the Western World. Hutchins, R. M., Ed.; Encyclopaedia Britannica, Inc.: Chicago, 1952; Book I.

    Google Scholar 

  32. Robertson, R. E. Theory for the plasticity of glassy polymers. J. Chem. Phys. 1966, 44, 3950–3956.

    Google Scholar 

  33. Batschinski, A. J. Untersuchungen über die innere Reibung der Flüssigkeiten. Z. Phys. Chem. 1913, 84U, 643–706.

    Google Scholar 

  34. Hildebrand, J. H. in Viscosity and Diffusivity: A Predictive Treatment. Wiley, New York, 1977.

    Google Scholar 

  35. Hildebrand, J. H.; Lamoreaux, R. H. Fluidity: a general theory. Proc. Natl. Acad. Sci. U. S. A. 1972, 69, 3428–3431.

    CAS  PubMed  PubMed Central  Google Scholar 

  36. Doolittle, A. K. Studies in Newtonian flow. I. The dependence of the viscosity of liquids on temperature. J. Appl. Phys. 1951, 22, 1031–1035.

    CAS  Google Scholar 

  37. FoxJr., T. G.; Flory, P. J. Second-order transition temperatures and related properties of polystyrene. I. Influence of molecular weight. J. Appl. Phys. 1950, 21, 581–591.

    CAS  Google Scholar 

  38. Vogel, H. The law of the relationship between viscosity of liquids and the temperature. Phys. Z. 1921, 22, 645–646.

    CAS  Google Scholar 

  39. Fulcher, G. S. Analysis of recent measurements of the viscosity of glasses. J. Am. Ceram. Soc. 1925, 8, 339–355.

    CAS  Google Scholar 

  40. Tammann, G.; Hesse, W. Die Abhängigkeit der viscosität von der temperatur bie unterkühlten flüssigkeiten. Z. Anorg. Allg. Chem. 1926, 156, 245–257.

    CAS  Google Scholar 

  41. Ferry, J. D. in Viscoelastic Properties of Polymers. Wiley, New York, 1980.

    Google Scholar 

  42. Williams, M. L.; Landel, R. F.; Ferry, J. D. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 1955, 77, 3701–3707.

    CAS  Google Scholar 

  43. White, R. P.; Lipson, J. E. G. Polymer free volume and its connection to the glass transition. Macromolecules 2016, 49, 3987–4007.

    CAS  Google Scholar 

  44. White, R. P.; Lipson, J. E. G. Explaining the T, V-dependent dynamics of glass forming liquids: The cooperative free volume model tested against new simulation results. J. Chem. Phys. 2017, 147, 184503.

    PubMed  Google Scholar 

  45. White, R. P.; Lipson, J. E. G. Pressure-dependent dynamics of polymer melts from Arrhenius to non-Arrhenius: the cooperative free volume rate equation tested against simulation data. Macromolecules 2018, 51, 4896–4909.

    CAS  Google Scholar 

  46. White, R. P.; Lipson, J. E. G. Connecting pressure-dependent dynamics to dynamics under confinement: the cooperative free volume model applied to poly(4-chlorostyrene) bulk and thin films. Macromolecules 2018, 51, 7924–7941.

    CAS  Google Scholar 

  47. Debot, A.; White, R. P.; Lipson, J. E. G.; Napolitano, S. Experimental test of the cooperative free volume rate model under 1D confinement: the interplay of free volume, temperature, and polymer film thickness in driving segmental mobility. ACS Macro Lett. 2019, 8, 41–45.

    CAS  PubMed  Google Scholar 

  48. Xu, W. S.; Douglas, J. F.; Xia, W.; Xu, X. Understanding activation volume in glass-forming polymer melts via generalized entropy theory. Macromolecules 2020, 53, 7239–7252.

    CAS  Google Scholar 

  49. Xu, W. S.; Douglas, J. F.; Freed, K. F. Entropy theory of polymer glass-formation in variable spatial dimension. Adv. Chem. Phys. 2016, 161, 443–497.

    CAS  Google Scholar 

  50. Xu, W.-S.; Douglas, J. F.; Xu, X. Role of cohesive energy in glass formation of polymers with and without bending constraints. Macromolecules 2020, 53, 9678–9697.

    CAS  Google Scholar 

  51. Floudas, G.; Paluch, M.; Grzybowski, A.; Ngai, K. L. in Molecular Dynamics of Glass-Forming Systems: Effects of Pressure. 1st Ed.; Springer-Verlag: Berlin, 2010.

    Google Scholar 

  52. Sanchez, I. C. Dimensionless thermodynamics: a new paradigm for liquid state properties. J. Phys. Chem. B 2014, 118, 9386–9397.

    CAS  PubMed  Google Scholar 

  53. Simha, R.; Boyer, R. F. On a general relation involving the glass temperature and coefficients of expansion of polymers. J. Chem. Phys. 1962, 37, 1003–1007.

    CAS  Google Scholar 

  54. Foreman, K. W.; Freed, K. F. Lattice cluster theory of multicomponent polymer systems: chain semiflexibility and specific interactions. Adv. Chem. Phys. 1998, 103, 335–390.

    CAS  Google Scholar 

  55. Xu, W. S.; Freed, K. F. Lattice cluster theory for polymer melts with specific interactions. J. Chem. Phys. 2014, 141, 044909.

    PubMed  Google Scholar 

  56. Adam, G.; Gibbs, J. H. On the temperature dependence of cooperative relaxation Properties in glass-forming Liquids. J Chem. Phys. 1965, 43, 139–146.

    CAS  Google Scholar 

  57. Stukalin, E. B.; Douglas, J. F.; Freed, K. F. Application of the entropy theory of glass formation to poly(a-olefins). J. Chem. Phys. 2009, 131, 114905.

    PubMed  Google Scholar 

  58. Yang, Z.; Xu, X.; Xu, W. S. Influence of ionic interaction strength on glass formation of an ion-containing polymer melt. Macromolecules 2021, 54, 9587–9601.

    CAS  Google Scholar 

  59. Starr, F. W.; Sastry, S.; Douglas, J. F.; Glotzer, S. C. What do we learn from the local geometry of glass-forming liquids? Phys. Rev. Lett. 2002, 89, 125501.

    PubMed  Google Scholar 

  60. Hanakata, P. Z.; Douglas, J. F.; Starr, F. W. Local variation of fragility and glass transition temperature of ultra-thin supported polymer films. J. Chem. Phys. 2012, 137, 244901.

    PubMed  PubMed Central  Google Scholar 

  61. Zhang, W.; Starr, F. W.; Douglas, J. F. Reconciling computational and experimental trends in the temperature dependence of the interfacial mobility of polymer films. J. Chem. Phys. 2020, 152, 124703.

    CAS  PubMed  Google Scholar 

  62. Douglas, J. F.; Pazmino Betancourt, B. A.; Tong, X.; Zhang, H. Localization model description of diffusion and structural relaxation in glass-forming Cu-Zr alloys. J. Stat. Mech.: Theory Exp. 2016, 054048

  63. Zhang, H.; Wang, X.; Douglas, J. F. Localization model description of diffusion and structural relaxation in superionic crystalline UO2. J. Chem. Phys. 2019, 151, 071101.

    PubMed  Google Scholar 

  64. Simmons, D. S.; Cicerone, M. T.; Zhong, Q.; Tyagi, M.; Douglas, J. F. Generalized localization model of relaxation in glass–forming liquids. Soft Matter 2012, 8, 11455–11461.

    CAS  PubMed  PubMed Central  Google Scholar 

  65. Sutherland, W. XXXVI. A new periodic property of the elements. London, Edinburgh Dublin Philos. Mag. J. Sci. 1890, 30, 318–323.

    Google Scholar 

  66. Sutherland, W. V. A kinetic theory of solids, with an Experimental Introduction. London, Edinburgh Dublin Philos. Mag. J. Sci. 1891, 32, 31–43.

    Google Scholar 

  67. Sutherland, W. XXIX. A kinetic theory of solids, with an experimental introduction. London, Edinburgh Dublin Philos. Mag. J. Sci. 1891, 32, 215–225.

    Google Scholar 

  68. Sutherland, W. LXIII. A kinetic theory of solids, with an experimental introduction. London, Edinburgh Dublin Philos. Mag. J. Sci. 1891, 32, 524–553.

    Google Scholar 

  69. Larini, L.; Ottochian, A.; De Michele, C.; Leporini, D. Universal scaling between structural relaxation and vibrational dynamics in glass–forming liquids and polymers. Nat. Phys. 2008, 4, 42–45.

    CAS  Google Scholar 

  70. Davies, R. O.; Jones, G. O. The irreversible approach to equilibrium in glasses. Proc. R. Soc. A 1903, 217, 26–42.

    Google Scholar 

  71. Goldstein, M. On the temperature dependence of cooperative relaxation properties in glass–forming liquids—comment on a paper by Adam and Gibbs. J. Chem. Phys. 1960, 43, 1852–1853.

    Google Scholar 

  72. Simon, F. Über den Zustand der unterkühlten Flüssigkeiten und Gläser. Z. Anorg. Allg. Chem. 1931, 203, 219–227.

    CAS  Google Scholar 

  73. Berthier, L.; Ozawa, M.; Scalliet, C. Configurational entropy of glass–forming liquids. J. Chem. Phys. 2019, 150, 160902.

    PubMed  Google Scholar 

  74. Gibbs, J. H.; DiMarzio, E. A. Nature of the glass transition and the glassy state. J. Chem. Phys. 1908, 28, 373–383.

    Google Scholar 

  75. Flory, P. J. Statistical thermodynamics of semi–flexible chain molecules. Proc. R. Soc. Lond. A 1906, 234, 60–73.

    Google Scholar 

  76. DiMarzio, E. A.; Yang, A. J. M. Configurational entropy approach to the kinetics of glasses. J. Res. Natl. Inst. Stand. Technol. 1997, 102, 135–157.

    CAS  Google Scholar 

  77. Bestul, A. B.; Chang, S. S. Excess entropy at glass transformation. J. Chem. Phys. 1964, 40, 3731–3733.

    CAS  Google Scholar 

  78. Glasstone, S.; Laidler, K. J.; Eyring, H. in The Theory of Rate Processes: The Kinetics of Chemical Reactions, Viscosity, Diffusion and Electrochemical Phenomena. International Chemical Series; McGraw-Hill Book Company: Incorporated, 1941.

  79. Kauzmann, W.; Eyring, H. The Viscous flow of large molecules. J. Am. Chem. Soc. 1940, 62, 3113–3125.

    CAS  Google Scholar 

  80. Kincaid, J. F.; Eyring, H.; Stearn, A. E. The theory of absolute reaction rates and its application to viscosity and diffusion in the liquid state. Chem. Rev. 1941, 28, 301–365.

    CAS  Google Scholar 

  81. Goldstein, M. Viscous liquids and the glass transition: a potential energy barrier picture. J. Chem. Phys. 1969, 51, 3728–3739.

    CAS  Google Scholar 

  82. Stillinger, F. H.; Weber, T. A. Hidden structure in liquids. Phys. Rev. A 1982, 25, 978–989.

    CAS  Google Scholar 

  83. Stillinger, F. H.; Weber, T. A. Packing structures and transitions in liquids and solids. Science 1984, 225, 983–989.

    CAS  PubMed  Google Scholar 

  84. Xu, X.; Douglas, J. F.; Xu, W. S. Influence of side-chain length and relative rigidities of backbone and side chains on glass formation of branched polymers. Mccromolcculs 2021, 44, 6327–6341.

    Google Scholar 

  85. Xu, X.; Xu, W. S. Melt properties and string model description of glass formation in graft polymers of different side-chain lengths. Macromolecules 2022, 55, 3221–3235.

    CAS  Google Scholar 

  86. Xu, W.-S.; Douglas, J. F.; Freed, K. F. Generalized entropy theory of glass-formation in fully flexible polymer melts. J Chem. Phys. 2016, 145, 234509.

    PubMed  Google Scholar 

  87. Chen, D.; McKenna, G. B. Deep glassy state dynamic data challenge glass models: configurational entropy models. J. Non-Cryst. Solids 2021, 566, 120871.

    CAS  Google Scholar 

  88. Kirkpatrick, T. R.; Wolynes, P. G. Stable and metastable states in mean-field Potts and structural glasses. Phys. Rev. B 1987, 36, 8552–8564.

    CAS  Google Scholar 

  89. Kirkpatrick, T. R.; Thirumalai, D.; Wolynes, P. G. Scaling concepts for the dynamics of viscous liquids near an ideal glassy state. Phys. Rev. A 1989, 40, 1045–1054.

    CAS  Google Scholar 

  90. Bouchaud, J. P.; Biroli, G. On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glasses. J. Chem. Phys. 2004, 121, 7347–7354.

    CAS  PubMed  Google Scholar 

  91. Lubchenko, V.; Wolynes, P. G. Theory of structural glasses and supercooled liquids. Annu. Rev. Phys. Chem. 2007, 58, 235–266.

    CAS  PubMed  Google Scholar 

  92. Rosenfeld, Y. Relation between the transport coefficients and the internal entropy of simple systems. Phys. Rev. A 1977, 15, 2545–2549.

    Google Scholar 

  93. Rosenfeld, Y. A quasi–universal scaling law for atomic transport in simple fluids. J. Phys.: Condens. Matter 1999, 11, 5415–5427.

    CAS  Google Scholar 

  94. Dyre, J. C. Perspective: excess–entropy scaling. J. Chem. Phys. 2018, 149, 210901.

    PubMed  Google Scholar 

  95. Weeks, J. D.; Chandler, D.; Andersen, H. C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 1971, 54, 5237–5247.

    CAS  Google Scholar 

  96. Schweizer, K. S.; Saltzman, E. J. Theory of dynamic barriers, activated hopping, and the glass transition in polymer melts. J. Chem. Phys. 2004, 121, 1984–2000.

    CAS  PubMed  Google Scholar 

  97. Saltzman, E. J.; Schweizer, K. S. Universal scaling, dynamic fragility, segmental relaxation, and vitrification in polymer melts. J. Chem. Phys. 2004, 121, 2001–2009.

    CAS  PubMed  Google Scholar 

  98. Chen, K.; Saltzman, E. J.; Schweizer, K. S. Molecular theories of segmental dynamics and mechanical response in deeply supercooled polymer melts and glasses. Annu. Rev. Condens. Matter Phys. 2010, 1, 277–300.

    CAS  Google Scholar 

  99. Mirigian, S.; Schweizer, K. S. Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. I. General formulation and application to hard sphere fluids. J. Chem. Phys. 2014, 140, 194506.

    PubMed  Google Scholar 

  100. Mirigian, S.; Schweizer, K. S. Elastically cooperative activated barrier hopping theory of relaxation in viscous fluids. II. Thermal liquids. J. Chem. Phys. 2014, 140, 194507.

    PubMed  Google Scholar 

  101. Mirigian, S.; Schweizer, K. S. Dynamical theory of segmental relaxation and emergent elasticity in supercooled polymer melts. Macromolecules 2010, 48, 1901–1913.

    Google Scholar 

  102. Xie, S. J.; Schweizer, K. S. Nonuniversal coupling of cage scale Hopping and collective elastic distortion as the origin of dynamic fragility diversity in glass–forming polymer liquids. Macromolecules 2016, 49, 9655–9664.

    CAS  Google Scholar 

  103. Varotsos, P.; Alexopoulos, K. Decisive importance of the bulk modulus and the anharmonicity in the calculation of migration and formation volumes. Phys. Rev. B 1981, 24, 904–910.

    CAS  Google Scholar 

  104. Varotsos, P.; Alexopoulos, K. Calculation of diffusion coefficients at any temperature and pressure from a single measurement. I. Self diffusion. Phys. Rev. B 1980, 22, 3130–3134.

    CAS  Google Scholar 

  105. Khonik, V. A.; Mitrofanov, Y. P.; Lyakhov, S. A.; Vasiliev, A. N.; Khonik, S. V.; Khoviv, D. A. Relationship between the shear modulus G, activation energy, and shear viscosity q in metallic glasses below and above Tg: direct in situ measurements of G and q. Phys. Rev. B 2009, 79, 132204.

    Google Scholar 

  106. Sjögren, L. Temperature dependence of viscosity near the glass transition. Z. Phys. B-Condensed Matter 1990, 79, 5–13.

    Google Scholar 

  107. Dyre, J. C. Colloquium: The glass transition and elastic models of glass-forming liquids. Rev. Mod. Phys. 2006, 78, 953–972.

    CAS  Google Scholar 

  108. Douglas, J. F.; Xu, W. S. Equation of state and entropy theory approach to thermodynamic scaling in polymeric glass-forming liquids. Macromolecules 2021, 54, 3247–3269.

    CAS  Google Scholar 

  109. Novikov, V. N.; Sokolov, A. P. Qualitative change in structural dynamics of some glass-forming systems. Phys. Rev. E 2015, 92, 062304.

    CAS  Google Scholar 

  110. Angell, C. A. Relaxation in liquids, polymers and plastic crystals-strong/fragile patterns and problems. J. Non-Cryst. Solids 1991, 131–133, 13–31.

    Google Scholar 

  111. Angell, C. A. Formation of glasses from liquids and biopolymers. Science 1995, 267, 1924–1935.

    CAS  PubMed  Google Scholar 

  112. Tanaka, H. A new scenario of the apparent fragile-to-strong transition in tetrahedral liquids: water as an example. J. Phys.: Condens. Matter 2003, 15, L703.

    CAS  Google Scholar 

  113. Tanaka, H. Bond orientational order in liquids: towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization. Eur. Phys. J. E 2012, 35, 113.

    PubMed  Google Scholar 

  114. Shi, R.; Russo, J.; Tanaka, H. Origin of the emergent fragile-to-strong transition in supercooled water. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, 9444–9449.

    CAS  PubMed  PubMed Central  Google Scholar 

  115. Zhang, C.; Hu, L.; Yue, Y.; Mauro, J. C. Fragile-to-strong transition in metallic glass-forming liquids. J. Chem. Phys. 2010, 133, 014508.

    PubMed  Google Scholar 

  116. Zhang, H.; Wang, X.; Yu, H. B.; Douglas, J. F. Fast dynamics in a model metallic glass-forming material. J. Chem. Phys. 2021, 154, 084505.

    CAS  PubMed  Google Scholar 

  117. Zhang, H.; Wang, X.; Yu, H. B.; Douglas, J. F. Dynamic heterogeneity, cooperative motion, and Johari-Goldstein β-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition. Eur. Phys. J. E 2021, 44, 56.

    CAS  PubMed  Google Scholar 

  118. Schmidtke, B.; Petzold, N.; Kahlau, R.; Hofmann, M.; Rössler, E. A. From boiling point to glass transition temperature: transport coefficients in molecular liquids follow three-parameter scaling. Phys. Rev. E 2012, 86, 041507.

    CAS  Google Scholar 

  119. Schmidtke, B.; Petzold, N.; Kahlau, R.;; Rössler, E. A. Reorientational dynamics in molecular liquids as revealed by dynamic light scattering: from boiling point to glass transition temperature. J. Chem. Phys. 2013, 139, 084504.

    CAS  PubMed  Google Scholar 

  120. Schmidtke, B.; Hofmann, M.; Lichtinger, A.; Rössler, E. A. Temperature dependence of the segmental relaxation time of polymers revisited. Macromolecules 2015, 48, 3005–3013.

    CAS  Google Scholar 

  121. Johari, G. P.; Goldstein, M. Viscous liquids and the glass transition. II. Secondary relaxations in glasses of rigid molecules. J. Chem. Phys. 1970, 53, 2372–2388.

    CAS  Google Scholar 

  122. Johari, G. P.; Goldstein, M. Viscous liquids and the glass transition. III. Secondary relaxations in aliphatic alcohols and other nonrigid molecules. J. Chem. Phys. 1971, 55, 4245–4252.

    CAS  Google Scholar 

  123. Johari, G. P. Intrinsic mobility of molecular glasses. J. Chem. Phys. 1973, 58, 1766–1770.

    CAS  Google Scholar 

  124. Xu, W. S.; Douglas, J. F.; Freed, K. F. Influence of cohesive energy on relaxation in a model glass-forming polymer melt. Macromolecules 2016, 49, 8355–8370.

    CAS  Google Scholar 

  125. Xu, W. S.; Douglas, J. F.; Freed, K. F. Influence of pressure on glass formation in a simulated polymer melt. Macromolecules 2017, 50, 2585–2598.

    CAS  Google Scholar 

  126. Xu, W. S.; Douglas, J. F.; Xu, X. Molecular dynamics study of glass formation in polymer melts with varying chain stiffness. Macromolecules 2020, 53, 4796–4809.

    CAS  Google Scholar 

  127. Wang, X.; Xu, W.-S.; Zhang, H.; Douglas, J. F. Universal nature of dynamic heterogeneity in glass-forming liquids: a comparative study of metallic and polymeric glass- forming liquids. J. Chem. Phys. 2019, 151, 184503.

    PubMed  Google Scholar 

  128. Singh, M.; Agarwal, M.; Dhabal, D.; Chakravarty, C. Structural correlations and cooperative dynamics in supercooled liquids. J. Chem. Phys. 2012, 137, 024508.

    PubMed  Google Scholar 

  129. Banerjee, A.; Sengupta, S.; Sastry, S.; Bhattacharyya, S. M. Role of structure and entropy in determining differences in dynamics for glass formers with different interaction potentials. Phys. Rev. Lett. 2014, 113, 225701.

    PubMed  Google Scholar 

  130. Yang, Z. Y.; Nie, W. J.; Liu, L. Y.; Xu, X. L.; Xia, W. J.; Xu, W. S. Applications of machine learning methods in the studies of polymer glass formation. Acta Polymerica Sinica (in Chinese) 2023, 54, 432–450.

    Google Scholar 

  131. Cubuk, E. D.; Schoenholz, S. S.; Rieser, J. M.; Malone, B. D.; Rottler, J.; Durian, D. J.; Kaxiras, E.; Liu, A. J. Identifying structural flow defects in disordered solids using machine-learning methods. Phys. Rev. Lett. 2015, 114, 108001.

    CAS  PubMed  Google Scholar 

  132. Schoenholz, S. S.; Cubuk, E. D.; Sussman, D. M.; Kaxiras, E.; Liu, A. J. A structural approach to relaxation in glassy liquids. Nat. Phys. 2016, 12, 469–471.

    CAS  Google Scholar 

  133. Cubuk, E. D.; Schoenholz, S. S.; Kaxiras, E.; Liu, A. J. Structural properties of defects in glassy liquids. J. Phys. Chem. B 2016, 120, 6139–6146.

    CAS  PubMed  Google Scholar 

  134. Cubuk, E. D.; Ivancic, R. J. S.; Schoenholz, S. S.; Strickland, D. J.; Basu, A.; Davidson, Z. S.; Fontaine, J.; Hor, J. L.; Huang, Y. R.; Jiang, Y.; Keim, N. C.; Koshigan, K. D.; Lefever, J. A.; Liu, T.; Ma, X. G.; Magagnosc, D. J.; Morrow, E.; Ortiz, C. P.; Rieser, J. M.; Shavit, A.; Still, T.; Xu, Y.; Zhang, Y.; Nordstrom, K. N.; Arratia, P. E.; Carpick, R. W.; Durian, D. J.; Fakhraai, Z.; Jerolmack, D. J.; Lee, D.; Li, J.; Riggleman, R.; Turner, K. T.; Yodh, A. G.; Gianola, D. S.; Liu, A. J. Structure-property relationships from universal signatures of plasticity in disordered solids. Science 2017, 358, 1033–1037.

    CAS  PubMed  PubMed Central  Google Scholar 

  135. Boattini, E.; Marín-Aguilar, S.; Mitra, S.; Foffi, G.; Smallenburg, F.; Filion, L. Autonomously revealing hidden local structures in supercooled liquids. Nat. Commun. 2020, 11, 5479.

    CAS  PubMed  PubMed Central  Google Scholar 

  136. Boattini, E.; Smallenburg, F.; Filion, L. Averaging local structure to predict the dynamic propensity in supercooled liquids. Phys. Rev. Lett. 2021, 127, 088007.

    CAS  PubMed  Google Scholar 

  137. Alkemade, R. M.; Boattini, E.; Filion, L.; Smallenburg, F. Comparing machine learning techniques for predicting glassy dynamics. J. Chem. Phys. 2022, 156, 204503.

    CAS  PubMed  Google Scholar 

  138. Bapst, V.; Keck, T.; Grabska-Barwińska, A.; Donner, C.; Cubuk, E. D.; Schoenholz, S. S.; Obika, A.; Nelson, A. W. R.; Back, T.; Hassabis, D.; Kohli, P. Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 2020, 16, 448–454.

    CAS  Google Scholar 

  139. Li, H.; Jin, Y.; Jiang, Y.; Chen, J. Z. Y. Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning. Proc. Natl. Acad. Sci. U. S. A. 2021, 118, e2017392118.

    CAS  PubMed  PubMed Central  Google Scholar 

  140. Zhang, K.; Li, X.; Jin, Y.; Jiang, Y. Machine learning glass caging order parameters with an artificial nested neural network. Soft Matter 2022, 18, 6270–6277.

    CAS  PubMed  Google Scholar 

Download references

Acknowledgments

W.S.X. acknowledges the support from the National Natural Science Foundation of China (Nos. 22222307 and 21973089). Z.Y.S. acknowledges the support from the National Natural Science Foundation of China (Nos. 21833008 and 52293471) and the National Key R&D Program of China (No. 2022YFB3707303). The authors are grateful to Dr. Jack F. Douglas for a critical reading of the manuscript. Z.Y.S. thanks Professor Li-Jia An for helpful discussions on glass formation over the years. W.S.X. thanks Dr. Jack F. Douglas for the long-term collaborations and Professor Karl F. Freed for numerous discussions on polymer thermodynamics and glass formation over the years. W.S.X. also thanks Professors Li-Jia An and Zhao-Yan Sun for their support and encouragement at every stage of his academic career.

Author information

Authors and Affiliations

  1. State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, 130022, China

    Wen-Sheng Xu & Zhao-Yan Sun

Authors
  1. Wen-Sheng Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhao-Yan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Wen-Sheng Xu or Zhao-Yan Sun.

Ethics declarations

The authors declare no interest conflict.

Additional information

Biographies

Wen-Sheng Xu received his Ph.D. degree from Changchun Institute of Applied Chemistry, Chinese Academy of Sciences in 2012. From 2013 to 2018, he was a postdoctoral scholar first with Professor Karl F. Freed at the University of Chicago and then with Dr. Yangyang Wang at Oak Ridge National Laboratory. He is currently a professor in the State Key Laboratory of Polymer Physics and Chemistry at Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, where he has been a faculty member since 2019. His research group utilizes theoretical methods and computer simulations to investigate the dynamics of noncrystalline polymer materials.

Zhao-Yan Sun received her Ph.D. degree from Jilin University in 2001. She was a postdoctoral fellow at University of Dortmund from 2001 to 2002. Since 2003, she has been a faculty member in the State Key Laboratory of Polymer Physics and Chemistry at Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, initially as an assistant professor and then an associate professor, before becoming a full professor in 2010. She was awarded the Young Chemistry Award of the Chinese Chemical Society in 2005. Her research group focuses on the structure and dynamics of polymers and nanocomposites and the development of computer simulation methods.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, WS., Sun, ZY. A Thermodynamic Perspective on Polymer Glass Formation. Chin J Polym Sci 41, 1329–1341 (2023). https://doi.org/10.1007/s10118-023-2951-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10118-023-2951-1

Keywords

Search

Navigation