Glass transition: A unified treatment

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Abstract
A unified kinetic and thermodynamic description of the glass transition in undercooled liquids at normal pressure is established. The following results are obtained for the first time: (1) The glass transition temperature Tg is determined to be in the range of Ts < Tg < Tn. Both Ts and Tn are material-dependent and each of them is characterized by a different Ω(T) = TΔslc(T)/Δslc(T) with Δhlc as the excess enthalpy and Δslc the excess entropy. (2) Being above Kauzmann's isentropic temperature, the lowest limit Ts is determined by Ω(Ts) = 1 −2/(3γ) with γ being the ratio between the total energy and the free energy of the liquid-crystal interface. (3) Although a glass preserves the entropy and enthalpy values of the liquid at Tg, the ratio Ω(Tg) is found to be bound by a Tg-independent material constant 1 −2/(3γ). (4) Tg increases linearly with the logarithm of the cooling rate and such a linear relationship is found to be not always valid. (5) The observed cooling-rate dependent glass transition at Tg is the kinetically modified reflection of an underlying cooling-rate independent transition at Ts, and the underlying transition at Ts is kinetically equivalent to the sudden and strong divergence of the structure relaxation time of the liquid. (6) It is shown that if the cooling rate exceeds a minimum value determined here as a function of temperature, the atoms of an undercooled liquid will not have sufficient time to rearrange themselves into the corresponding crystalline configuration; consequently, crystalline nucleation can be prevented. The results are supported by the available experimental evidence. A systematic test of the results on different systems is possible since the results are in terms of experimentally accessible quantities.