The Calorimetric Glass Transition in a Wide Range of Cooling Rates and Frequencies

  • T. V. Tropin
  • J. W. P. Schmelzer
  • G. Schulz
  • C. SchickEmail author
Part of the Advances in Dielectrics book series (ADVDIELECT)


The glass transition at common laboratory scan rates (K/min) has been a highly debated topic for the last decade. The continuous increase in the variety of available glass-forming materials and methods to characterize them maintains a research interest, as well as opens new perspective applications. In parallel, many different theoretical methods aimed at describing the glass transition have been proposed in the last 70 years. A general theory has yet to be developed and carefully tested. In the present chapter, we describe the results of theoretical and experimental investigations of the glass transition of a model polymer—polystyrene. State-of-the-art scanning calorimetry allows for measuring the temperature dependence of the isobaric heat capacity in an exceedingly wide range of cooling rates. Besides providing novel data on the glass transition of polymers at fast cooling rates, this allows for one to test the capabilities of convenient theoretical methods in modelling the kinetics of the glass transition under very different vitrifying conditions. The glass transition of atactic polystyrene was investigated at different cooling rates in the range of qc = 10−6–104 K/s. Dependencies of the glass transition temperature, Tg, and the shape of heat capacity, Cp, curves on qc were obtained. Furthermore, we have applied a number of different theoretical methods to test their capability to model the glass transition kinetics for such a wide range of control parameter qc. The list of investigated theoretical methods consists of the Tool–Narayanaswamy–Moynihan approach, Adam–Gibbs theory, an irreversible thermodynamics-based approach and some of their modern modifications. As a first step, we show that most of these methods are capable of fitting the cooling rate dependencies of the glass transition parameters (Tg and others). The model parameters in this case are close to literature data. Furthermore, we show that while fitting the Cp(T) curves for a single cooling–heating experiment bears acceptable results, the parameters have to be changed with respect to qc, with their difference becoming significant for very slow or very fast cooling rates. Thus, none of the methods can be applied successfully to model and predict the kinetics of glass transition in a wide range of q. We compare the results of different methods and propose an expression for the relaxation time dependence on model parameters within an irreversible thermodynamics approach. Thus, we extend the experimental results for polystyrene and state that the presently applied theoretical methods are incapable of accurately describing the heat capacity temperature curves Cp(T) for a wide range of cooling/heating rates, q. The present methods and expressions for relaxation time τ do not account for a certain additional effect spanning over different rates of temperature change, which has yet to be discovered.


Glass transition Polymers Polysterene (PS) Calorimetry Glass transition kinetics 





Advanced thermal analysis system (data bank)


Alternating current (calorimetry)


Adam–Gibbs (theory)


Cooperatively rearranging regions


Differential fast-scanning calorimetry


Differential scanning calorimetry


Fast-scanning (chip) calorimetry


Gutzow–Schmelzer (method)


Kovacs–Aklonis–Hutchinson–Ramos (method)




Tool–Narayanaswamy–Moynihan (method)


Temperature-modulated differential scanning calorimetry


Vogel–Fulcher–Tammann (law)



CS acknowledges the financial support from the Ministry of Education and Science of the Russian Federation, grant 14.Y26.31.0019. T. V. and J. W. P. acknowledge the financial support by the Heisenberg-Landau program of the German Federal Ministry of Education and Research (BMBF, Germany).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • T. V. Tropin
    • 1
  • J. W. P. Schmelzer
    • 2
  • G. Schulz
    • 2
  • C. Schick
    • 2
    • 3
    Email author
  1. 1.Frank Laboratory of Neutron PhysicsJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Institute of Physics and Competence Center CALORUniversity of RostockRostockGermany
  3. 3.Butlerov Institute of ChemistryKazan Federal UniversityKazanRussia

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