Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 349

Although the liquid state is generally far from simple, it can be considered as an equilibrium reference at viscosities (η) low enough that flow is easy, i.e. at high‐enough temperatures at the pressure considered. In that case, the diffusion of microscopic entities, be they molecules or atoms, obeys the Stokes‐Einstein relation, which relates the diffusivity D to the temperature and viscosity with:

(5)

where the coefficient C is a geometrical factor fixed by the boundary condition of the flow.

From its position at time t₀, a diffusing entity travels a kind of random walk over an average distance as a function of time. For low‐viscosity liquids and high temperatures, D is high so that entities explore a great many different positions and configurations in a time shorter than that needed to perform a physical measurement. They do it through degrees of freedom that include not only thermal motions of translation, rotation, and vibration but also the complex kinds of atomic motions collectively termed configurational, which are governed by strong short‐range repulsions and long‐range attractions in molecular liquids. The measurement then averages out all these configurations.

Picturing these motions at a microscopic scale is difficult, however, especially for complex liquids or melts with various interacting entities. In various types of glass‐forming liquids [5], local order can nonetheless be described in terms of degree of polymerization, formation of channels or sub‐lattices, or formation of interpenetrating networks. Like the advancement of a chemical reaction, such structural features may be described in terms of the aforementioned parameter ξ. In internal thermodynamic equilibrium, i.e. in the liquid state, ξ is equal to ξ_eq(T,P), but not in the glass transition range where ξ(t) becomes a function of T(t), P(t), and A(t), revealing its nonequilibrium nature. Below the glass transition range, where the relaxation time of the configurational degrees of freedom exceeds the experimental timescale, they cease to contribute to the measured property. At temperature low enough, the structure then eventually freezes in for good in one state defined by one particular value of ξ(t), which becomes independent of the external parameters T and P.

From a practical standpoint, the timescale defined by the viscosity of the material is important to determine the temperature at which the system will fall out of equilibrium when observed at the timescale of a particular experiment. There is not yet a unique model for describing relaxation phenomena in all glass‐forming liquids (Chapter 3.7), whether strong or fragile with Arrhenian or non‐Arrhenian viscosities, respectively [6]. In measurements of macroscopic properties, one nonetheless considers generally that experimental timescales τ_exp are of the order of τ_exp~10² – 10³ seconds. The viscosity should then be of the order of 10¹² Pa.s or 10¹³ P for structural relaxation to be complete under these conditions. To stress the usually tremendous variations of viscosity down to the glass transition, it will suffice to note that the viscosities of stable liquids (i.e. above the melting or liquidus temperature) range from 10⁻³ to 10² Pa.s depending on chemical composition and structural type.