Fluctuation Model for Structural Relaxation and the Glass Transition
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(1)
where AH* is an activation enthalpy, x a constant which parameterizes the nonlinearity, and Tf the fictive temperature. In the TN model the relaxation times differ in their pre-exponential constants T,0. For the fluctuation model an appropriate modification of the TN equation is: lnTr = lnT0 + xAH*/RT + (1
-
x)AH*/RTsi
(2)
Here the distribution arises from a distribution of local "structural" temperatures T81 which reflect local fluctuations in free volume or configurational entropy. The mean value of the TZ, < T. >, is constrained to equal the fictive temperature Tf at any instant. Intrinsic light scattering in a melt is due to local fluctuations in the refractive index n. Since the kinetics of structural relaxation are not precisely identical when measured for different macroscopic properties [1], a calculation of the variation in the light scattering 133 Mat. Res. Soc. Symp. Proc. Vol. 455 ©1997 Materials Research Society
during structural relaxation should use kinetic parameters derived from relaxation experiments in which n is the property which is monitored. Using procedures detailed in Refs. [1-31, Eq. (2) with a KWW distribution was used to fit the data of Boesch et al. [5] for the isothermal relaxation of the refractive index n of B20 3 glass in the transition region. These fits are shown in Figs. 1 and 2, where Tp, is the fictive temperature assessed from the refractive index n. The best fit parameters were:
-o= 3.1 x 10-33S AH*/R = 45,300 K x = 0.51 0 = 0.78 where 3 (0 < p < 1) is the exponent in the KWW or stretched exponential relaxation function, exp[-(t/Tr)-']. These parameters were then used to calculate the variance 2 < A2 TS,. > (= < T2,, > - < T,, >2) in the refractive index "structural" temperature of B2 0 3 glass during rate heating following rate cooling and isothermal annealing just below the transition region for the thermal histories reported by Bokov and Andreev [6]. These 2 < A2 TS,, > curves are compared in Fig. 3 with the corresponding light scattering intensities I (arbitrary units) measured by Bokov and Andreev [6]. Since I is proportional to the mean square fluctuation < A 2 n > in n, it should similarly be proportional to < A2T 8 , >. The agreement between the shapes of the experimental I curves and the calculated < AIT,• > curves in Fig. 3 is excellent, and the changes in the temperatures and heights of the maxima in the experimental I curves with increases in sub-Tg annealing time are accurately reflected in the calculated curves. The principal discrepancy between the experimental and calculated curves in Fig. 3 is that the I curves are displaced toward lower temperatures by about 9K relative to the < A'Ts,, > curves. This discrepancy was neither surprising nor unexpected. The viscosity and structural relaxation times of B20 3 are extremely sensitive to small amounts of water in the melt [7]. The relaxation experiments of Boesch et al. [5] were done on extremely dry specimens, while there is no indication of special drying procedures in the study of Bokov and Andreev [
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