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Description of a glass transition with immeasurable structural relaxation time

Author

Listed:
  • Chtchelkatchev, N.M.
  • Ryltsev, R.E.
  • Mikheyenkov, A.V.
  • Valiulin, V.E.
  • Polishchuk, I.Ya.

Abstract

A general problem of studying supercooled liquids and glasses is very long relaxation times that do not allow determining explicitly dynamic characteristics. One of the ways to solve this problem is extrapolating values of some dynamical property (e.g. viscosity) from the temperature range where it can be directly measured (simulated) to the low-temperature region. Such extrapolations are usually contradictory because different fitting functions can give substantially different results. Thus, the development of methods for robust extrapolation is an urgent task especially for molecular dynamic study of glassforming liquids. Here we propose a model-free statistical algorithm for a low-temperature extrapolation of liquid viscosity (diffusion coefficient) and apply it to the problem of determination of glass transition temperature and the temperature Tc where the viscosity formally diverges. Our approach is based on numerical analytical continuation of temperature dependence of the viscosity using Padé approximants and error correction procedures using statistical averaging for the treatment of noisy input data. We tested the method on several glass-forming systems and revealed good stability and predictability. Our extrapolation algorithm is suitable for both numerical and experimental studies of glassformers when it is necessary to descend into the parameter range where structural relaxation times of a liquid are too long to be directly obtained.

Suggested Citation

  • Chtchelkatchev, N.M. & Ryltsev, R.E. & Mikheyenkov, A.V. & Valiulin, V.E. & Polishchuk, I.Ya., 2023. "Description of a glass transition with immeasurable structural relaxation time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    • Handle: RePEc:eee:phsmap:v:615:y:2023:i:c:s0378437123001656
    DOI: 10.1016/j.physa.2023.128610
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    References listed on IDEAS

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    1. Hadipeykani, Majid & Aghadavoudi, Farshid & Toghraie, Davood, 2020. "A molecular dynamics simulation of the glass transition temperature and volumetric thermal expansion coefficient of thermoset polymer based epoxy nanocomposite reinforced by CNT: A statistical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 546(C).
    2. Renxuan Xie & Albree R. Weisen & Youngmin Lee & Melissa A. Aplan & Abigail M. Fenton & Ashley E. Masucci & Fabian Kempe & Michael Sommer & Christian W. Pester & Ralph H. Colby & Enrique D. Gomez, 2020. "Glass transition temperature from the chemical structure of conjugated polymers," Nature Communications, Nature, vol. 11(1), pages 1-8, December.
    3. Vasin, M.G. & Vinokur, V.M., 2019. "Description of glass transition kinetics in 3D XY model in terms of gauge field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1161-1169.
    4. Makinde, O.D., 2007. "Hermite–Padé approximation approach to steady flow of a liquid film with adiabatic free surface along an inclined heat plate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 1-7.
    5. Kirchner, Katelyn A. & Goyal, Sushmit & McKenzie, Matthew E. & Harris, Jason T. & Mauro, John C., 2020. "Statistical description of the thermodynamics of glass-forming liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    6. Nuyts, Jean & Platten, Isabelle, 2001. "Phenomenology of the term structure of interest rates with Padé Approximants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(3), pages 528-546.
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