Glass transition: A unified treatment
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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 Cl(T) = TAsic(T)/Ahic(T) with Ahtc as the excess enthalpy and As[c the excess entropy. (2) Being above Kauzmann's isentropic temperature, the lowest limit Ts is determined by £l(Ts) = 1 — 2/(3y) with y 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 £l(Tg) is found to be bound by a Tg-independent material constant 1 — 2/(3y). (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.
I. INTRODUCTION As one of the most formidable problems in condensed matter physics and despite the strong interest in the glass transition over many decades, a general satisfying description of the glass transition is yet to be established.1 3 There is yet to be an explicit relationship between the required cooling rate and the relevant dynamics of a liquid to support the conventional wisdom that at normal pressure every liquid can become a glass if the cooling rate is sufficiently large. On the other hand, the possible existence of the lowest limit of the observed kinetic glass transition temperature has been speculated since Kauzmann4'5; however, if the observed glass transition actually reflects an underlying transition as speculated, then what is the basic relationship for defining the limit? What is the relationship between the observed kinetic glass transition temperature and the underlying limit? To understand those issues is far from a simple task because of the complexity of the problem, which requires a description that couples microscopic processes with macroscopic behavior; the issues cannot be addressed by the microscopic models6'7"12 alone. Here we take a 1908
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J. Mater. Res., Vol. 9, No. 7, Jul 1994
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