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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in taking into account the time dependence of ξ at every temperature through the temperature dependence of the relaxation time τ. The simplest way to do this is to assume a simple exponential decay for ξ at fixed temperature and pressure:

      where ξeq(P,T) is the equilibrium value of the order parameter, i.e. a variable characterizing the liquid structure that depends only on P and T. Although the relaxation time itself has been given different temperature dependences with Arrhenius, VFT, or others laws (Chapter 3.7), the important point is that they are all of an exponential nature with respect to T or P to ensure the structural freezing‐in of the system.

Graph depicts the simulated affinities of o-terphenyl in the glass transition range upon cooling and heating as calculated from the lattice-hole model. Solid circle for -0.3 K/min and solid square for -0.5 K/min; empty circle for +0.3 K/min and empty square for +20 K/min. The horizontal line represents equilibrium. Inset: entropy production rates calculated from the previous affinities. Solid circle upon cooling and empty circle upon heating.

      The rate of entropy production thus reflects the spontaneous or irreversible microscopic processes that take place within the system during relaxation. As dictated by the Second Law of thermodynamics, it is always positive whether upon cooling or heating (Figure 5, inset). Physically, it can be thought of the heat irreversibly generated by friction at a microscopic scale. The resulting thermal power Pi = i, where σi is the entropy creation in Eq. (4), is produced much too quickly to be compensated instantaneously by an exchange of heat with the surrounding heat bath. Under this circumstance, this is why an effective or fictive temperature can be defined. This surrounding heat bath is sometimes called the phonon bath since it is characterized by fast or vibrational modes.

      On the contrary, the change in configurational entropy is a reversible process related to the heat exchanged with the surrounding heat bath whose relevant thermal power is:

      (18)equation

      Because the configurational entropy becomes constant upon vitrification, its variations have vanished (i.e. the configurational heat capacity) below the glass transition range. Above this range, in the supercooled liquid state, they of course differ from zero as indicated by

      (19)equation