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Analysis of the minimal model for the enthalpy relaxation and recovery in glass transition: application to constant-rate differential scanning calorimetry

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Abstract

The so-called minimal model is formulated for describing the enthalpy relaxation and recovery in glass transition. The model is based on the Arrhenius law for the enthalpy relaxation, which uses two-dimensional parameters, namely the activation energy and the so-called pre-factor (relaxation time at relatively high temperature). A numerically effective exact analytical solution is obtained for the case of constant-rate differential scanning calorimetry. The developed model is analyzed according to the logic of the model itself without introducing additional simplifying assumptions of thermodynamic nature. For typical range of the model parameters, the resulting differential equation contains a large parameter, which offers an opportunity for the application of asymptotic and approximate techniques. A number of simple approximations have been provided for some thermodynamic quantities of interest.

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Acknowledgements

IA is grateful to the Biofilms center for the hospitality during his stay at the Malmö University, where this research was carried out.

The authors would like to express their gratitude to the Referee for the valuable comments and suggestions.

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Authors and Affiliations

  1. Institut für Mechanik, Technische Universität Berlin, Berlin, Germany

    Ivan Argatov

  2. Biofilms – Research Center for Biointerfaces, Malmö University, Malmö, Sweden

    Ivan Argatov & Vitaly Kocherbitov

  3. Faculty of Health and Society, Malmö University, Malmö, Sweden

    Vitaly Kocherbitov

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  1. Ivan Argatov
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  2. Vitaly Kocherbitov
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Correspondence to Ivan Argatov.

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Communicated by Andreas Öchsner.

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Argatov, I., Kocherbitov, V. Analysis of the minimal model for the enthalpy relaxation and recovery in glass transition: application to constant-rate differential scanning calorimetry. Continuum Mech. Thermodyn. 33, 107–123 (2021). https://doi.org/10.1007/s00161-020-00891-3

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  • DOI: https://doi.org/10.1007/s00161-020-00891-3

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