Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
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Жанр произведения: Техническая литература
Год издания: 0
isbn: 9781118799499
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      The values are taken from the literature.

      Another puzzling fact has been long ago pointed out by Kauzmann [10] who wondered what would happen if the entropy of a supercooled liquid were extrapolated down to temperatures much lower than the experimentally observed Tg. The conclusion was that it would become lower than that of the isochemical crystal at a temperature TK, thus termed the Kauzmann temperature (Table 2), which could suggest that the liquid undergoes a continuous phase transition toward the crystalline phase at TK analogous to the critical point of fluids.

      One way out of the paradox implies kinetic arguments and assumes that the viscosity of the supercooled liquid diverges at a temperature close to TK. This assumption may be represented by the Vogel–Fulcher–Tammann (VFT) equation (Chapter 4.1):

      (11)equation

      where the temperature T0 of the viscosity divergence is actually close to the Kauzmann temperature (Table 2) even though they may depend on the specific sample and the method of measurement.

      Another way out is to take with great caution the extrapolations of the heat capacity and other thermodynamic functions of the supercooled liquid. As long pointed out [e.g. 11], there is no current theory for these properties in liquid state analogous to the Einstein or Debye models that provide functional forms at all temperatures for heat capacities of crystals.

      As derived from strikingly old questions in glass science, these counterintuitive features indicate that glasses cannot be described by equilibrium thermodynamic states only. Nonequilibrium thermodynamics is, therefore, likely to be useful to characterize glasses and the glass transition.

      The questions raised by the Kauzmann paradox or the PD ratio clearly illustrate the need for a more fundamental thermodynamic description of the glass transition. Following the pioneering work of Tool [12, 13] and Davies and Jones [9], different approaches and phenomenological models have been developed to deal with the glass transition range itself, many within the framework of classical nonequilibrium thermodynamics [4, 11].

      The first physical models have then relied on two different approaches. In free‐volume theories, one generally considers that the dynamics of the system is determined by the free space present around its atoms, which makes configurational rearrangements more or less easy. In entropy theories, among which that of Adam‐Gibbs is the best known [15], the same determining role is attributed to configurational entropy. In other words, these theories assign the strong increase of relaxation times with decreasing temperatures and the eventual structural freezing in to decreases of either free volume or configurational entropy. Other more recent theories of the glass transition rely on mode coupling, random first‐order transitions or energy‐landscape descriptions [e.g. 16]. These different approaches have the common goal of finding the exact expression for the structural relaxation time, or its distribution, as a function of controlling parameters such as temperature or pressure, or structural order parameter.

      For the sake of simplicity, let us consider here conditions of constant pressure. If the additional parameter ξ is taken into account, the total differential of the enthalpy of a system can be written as the sum of two contributions (considering pressure, the generalization to three contributions would be obvious):

      (12)equation

      The isobaric heat capacity is written as:

      When the rate of change of ξ becomes much smaller than the rate of change of temperature, (dξ/dt)P ≪ (dT/dt)P, the configurational contribution is negligible.

      (15)equation

      The