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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is slower when the sample was previously equilibrated at a lower than at a higher temperature. Hence, the rate at which these changes occur depends not only on temperature but also on the thermal history of the sample, i.e. on the instantaneous structure as well. Because thermodynamic equilibrium is reached when the structure has adjusted to the new intensive parameters, the process is termed structural relaxation.

      To characterize the rate at which the shear viscosity (η) or any other property Y approaches a new equilibrium value, Ye, one defines the relaxation time, τY, as

      (1)equation

      where Yt is the value actually measured at time t. If τY were constant, the relaxation would be exponential:

      (2)equation (.2)

      where Y0 is the initial Y value, so that after a time τY, the variation of Y would be a fraction 1/e of the initial departure from the equilibrium value. Regardless of the actual non‐exponential nature of relaxation, measurements, for example, made on window glass at 777 K point to relaxation times much higher than one hour (Figure 6b). A measurement performed in only a few minutes would thus refer to a fixed configuration, i.e. to a glass. Depending on the timescale of the experiment, one observes that the nature of response is thus either liquid‐ or solid‐like.

      The glass transition range is that temperature interval where, depending on the timescale of the experiment performed, time‐dependent observations are made. It signals the change from the liquid state, where a great many different atomic configurations are unceasingly explored, to another state where atoms become trapped in fixed positions and properties become again time independent. In statistical–mechanical jargon, this change is said to represent the loss of ergodicity and, thus, of internal thermodynamic equilibrium.

      Experimentally, the loss of equilibrium can be readily followed by viscometry. Over an interval as wide as 10–1015.5 Pa.s, the viscosity of a glass‐forming melt can be reproduced empirically with the Vogel–Fulcher–Tammann (VFT) equation (Chapters 4.1 and 10.11):

      (3)equation

      (4)equation

Graph depicts the viscosity of window glass; solid line VFT fit to the data; dashed line: Arrhenius fit made to the high-temperature measurements, arrow: onset of departure from the equilibrium viscosity; solid squares and line: isostructural viscosities.

      Source: Data from [26, 27].

      2.3 The Glass Transition

      2.3.1 Standard Glass‐Transition Temperature

      For the experimental timescales of the order of a few minutes typical of measurements of macroscopic properties, one observes that, regardless of chemical composition, time‐dependent results begin to be observed when the viscosity becomes higher than about 1012 Pa. For convenience and comparison purposes, one defines the standard glass‐transition temperature, Tg, as the temperature at which the viscosity of the liquid reaches this value of 1012 Pa.s.

      2.3.2 Volume Effects

Graphs depict the volume effects of the glass transition. (a) Linear thermal expansion coefficient of E glass heated at 10 K/min; l = sample length. (b). Dependence of the volume of a glass on its fictive temperature.

      (Source: Data from [28]).

      (b). Dependence of the volume of a glass on its fictive temperature.

      In dilatometry experiments, one usually defines the glass‐transition temperature as the intersection of the tangents to the lower‐ and higher‐temperature curves. This temperature generally differs somewhat from the standard Tg simply because the glass transition depends on the particular experimental conditions of the experiment. With respect to enthalpimetry, dilatometry has the advantage of yielding absolute values of the property of interest, namely, the volume (and density). The influence of thermal history on density can thus be readily determined (which is why it was observed as early as in 1845, cf. Chapter 10.11). In contrast, the thermal expansion coefficient of glasses generally does not markedly depend on thermal history. At least above room temperature. The volumes of glasses produced at different cooling rates will then plot as a series of parallel lines (Figure 8b). To characterize the state of the glass, it suffices to know the temperature at which equilibrium was lost, which is directly given by the intersection of the glass and supercooled volumes (Figure 8b). This parameter