Structural relaxation time and cooling rate of a melt in the glass transition region

Abstract

The nature of the parameter involved in the Bartenev equation qτg = C relating the cooling rate of a glass-forming melt to its structural relaxation time in the glass transition region is discussed on the basis of the Volkenshtein-Ptitsyn theory using a number of known relationships. It is established that parameter C for amorphous substances with the same fragility is linearly temperature dependent. This parameter is shown to equal the narrow temperature range δTg characterizing the liquid-glass transition region (by Nemilov); i.e., C = δTg. It is concluded that δTg for most glassy systems is only ∼0.7% of the glass transition temperature Tg. The narrowness of temperature range δTg is explained by the small fluctuation volume fraction fg “frozen” at the glass transition temperature. The concept of a close relationship between constant C and the structural order at Tg (i.e., the characteristic of the inner state of a nonequilibrium “frozen” amorphous system) is developed.