Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 298

In 1999, Gupta [6] extended the notion of T‐dependent bond constraints to glass‐forming supercooled liquids: “Since the structure of a glass formed by cooling a liquid is the same as the structure of the liquid at the glass transition (or fictive) temperature, T_g , it follows that if the glass structure is an extended TD network, then such a network must also exist in the super‐cooled liquid state at T_g .” More importantly, he argued that the configurational entropy, ΔS(T), of a supercooled liquid is approximately proportional to the average degrees of freedom per vertex, f(T). This result, later substantiated by Naumis [32], leads to several important consequences:

1 At the Kauzmann temperature, TK, defined by ΔS(TK) = 0, the degrees of freedom vanish:(15)

1 From the Adam–Gibbs theory of viscosity, it follows that the temperature‐dependence of viscosity is simply related to that of f(T):(16)

Here, A is a constant independent of T.

1 The fragility, m, of a liquid defined as(17)

is related to the temperature‐dependence of f as follows:

(18)

The value of log [η_g/η_∞] is about 16. The variation of the degrees of freedom, f(T), with T, for good, poor, and non‐glass‐forming liquids is shown schematically in Figure 3. From Eq. (16), one then concludes that the cause of the non‐Arrhenian nature of the viscosity is the temperature‐dependence of bond constraints.

Figure 3 Schematic variation of degrees of freedom (f) in three supercooled liquids with increasing temperature normalized with respect to the Kauzmann temperature (T_K). Curve (a) represents a strong glass former, curve (b) a fragile glass former, and curve (c) a non‐glass former for which a TD network cannot exist

(Source: From [6]).