Structural relaxation in supercooled liquid around the glass transition

A typical way of preparing glass is by cooling a viscous supercooled liquid fast enough to avoid crystallization. Although this way of preparation is known for several thousands of years, an underlying molecular mechanism is not fully understood. Fig. 1 shows the specific volume or enthalpy as a function of temperature for a typical glass-forming liquid. Upon cooling from high temperatures, a liquid may crystallize at Tm. This first order phase transition results in a decrease of enthalpy and usually also of specific volume. Contrary, if the cooling through this temperature interval is fast enough to avoid the nucleation and crystal growth, a supercooled liquid state is attained. The specific volume and other thermodynamic properties of the supercooled liquid can be extrapolated from the properties of the liquid above Tm.

Fig. 1: The change in volume and enthalpy during the glass formation and structural relaxation. Inset shows hysteresis between cooling and heating in the glass transition range.

As a supercooled liquid is cooled to lower temperatures, its viscosity increases and the molecular motions start to slow down. At sufficiently low temperatures, the characteristic time for these molecular rearrangements becomes comparable to the time scale of a macroscopic experiment (e.g. 100 s). For shorter time scales, the supercooled liquid is structurally arrested and exhibits solid-like properties. It has a modulus, but similarly like a liquid it lacks long-range order. Thermal expansion coefficient α =(dV/dT)p or heat capacity Cp = (dH/dT)p in the glassy and crystalline state are similar as they are dominated by atomic vibrations which are similar in these two states.
The glass transition temperature Tg can be defined in many different ways. A convenient definition uses the change in the heat capacity or thermal expansion coefficient. Tg varies with cooling rate. Therefore, the glass transition is not a true thermodynamic phase transition but rather a kinetic event which depends upon the crossing of an experimental timescale and the time scales for molecular rearrangements. As a consequence, there is not a single glassy state and the properties of the glass depend upon how it was obtained. A clear manifestation of this „material memory“ is a hysteresis of cooling and heating curves observed at Tg (see Fig.2).

Fig. 2: Volume relaxation data corresponding to temperature jump experiments for a-Se from different initial temperatures T0 (indicated by numbers) to the same final temperature T = 32°C (points). Solid lines represent TNM fit and broken lines represent AGS fit.

If a supercooled liquid in the transition region is subjected to a sudden change in temperature (temperature jump), a time dependent change in volume and enthalpy occurs. This process associated with slow molecular rearrangement has been called structural relaxation. Understanding this behavior is very important for precise control of macroscopic properties of glassy materials. The dependence of the structural relaxation on viscosity causes that the properties of the supercooled liquid and glass in transformation range depend on the thermal history. This leads to hysteresis in volume or enthalpy during cooling or reheating. The importance of thermal history is also revealed by the fact that the relaxation behavior at a given temperature depends on whether the liquid was quenched or reheated to that temperature. There are phenomenological theories of structural relaxation that allow quite precise prediction of properties of glasses and supercooled liquids as a function of their thermal history. A remarkable feature of structural relaxation is its universality. It can be seen in a large variety of glass-forming systems ranging from inorganic glasses to organic polymers. It seems, therefore, that the structural relaxation is not closely associated with specific details of chemical structure of these materials and probably reflects more general features of a glassy state. Moreover, it seems that the bulk properties of glasses are strongly controlled by the supercooled liquid dynamics. A genuine understanding of clues between long-timescale structural relaxation in glasses and short-timescale molecular dynamics in their supercooled liquids is of fundamental importance for glass science.

Fig. 3: Non-exponentiality β and non-linearity σ for volume and enthalpy relaxation of inorganic glasses and organic polymers.

The structural relaxation is important in the processing of optical fibres, plastics engineering industry, food processing and preservation of biomaterials or living organisms under extreme cold or dehydration. It seems that it is not limited to these terrestrial applications as the interstellar water in the Universe may likely be in glassy state.

Our research is focused on detailed study of structural relaxation in chalcogenide glasses by means of dilatometric and calorimetric methods as well as to the description of non-linearity and non-exponentiality features of this intriguing but fascinating phenomenon.

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