GLASS-TRANSITION - A UNIFIED TREATMENT

A unified kinetic and thermodynamic description of the glass transitio n in undercooled liquids at normal pressure is established. The follow ing results are obtained for the first time: (1) The glass transition temperature T(g) is determined to be in the range of T(s) < T(g) < T(n ). Both T(s) and T(n) are material-dependent and each of them is chara cterized by a different OMEGA(T) = TDELTAs(lc)(T)/DELTAh(lc)(T) with D ELTAh(lc) as the excess enthalpy and DELTAs(lc) the excess entropy. (2 ) Being above Kauzmann's isentropic temperature, the lowest limit T(s) is determined by OMEGA(T(s)) = 1 - 2/(3gamma) with gamma being the ra tio between the total energy and the free energy of the liquid-crystal interface. (3) Although a glass preserves the entropy and enthalpy va lues of the liquid at T(g), the ratio OMEGA(T(g)) is found to be bound by a T(g)-independent material constant 1 - 2/(3gamma). (4) T(g) incr eases linearly with the logarithm of the cooling rate and such a linea r relationship is found to be not always valid. (5) The observed cooli ng-rate dependent glass transition at T(g) is the kinetically modified reflection of an underlying cooling-rate independent transition at T( s), and the underlying transition at T(s) 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 u ndercooled liquid will not have sufficient time to rearrange themselve s into the corresponding crystalline configuration; consequently, crys talline nucleation can be prevented. The results are supported by the available experimental evidence. A systematic test of the results on d ifferent systems is possible since the results are in terms of experim entally accessible quantities.