On the temperature dependence of the nonexponentiality in glass-forming liquids

Using a simple mathematical formalism, we show that temperature dependent nonexponential relaxation found in glass-forming liquids and amorphous polymers, often resulting in a decrease in the stretching exponent when decreasing temperature, can be suitably described assuming the combination of an intrinsic stretched response and the existence of temperature independent heterogeneities. The effect of the latter is incorporated by assuming a Gaussian distribution of Vogel temperatures. Comparison with experimental data of a large number of glass formers showed that this approach is able to quasiquantitatively describes the temperature dependence of the stretching exponent using the width of the distribution as the single fitting parameter. According to this approach, the rapidity of the decrease in the stretching exponent with decreasing temperature depends not only on the magnitude of the standard deviation of Vogel temperatures but also on the value of the intrinsic stretching exponent and on the fragility of the glass former. The latter result is able to rationalize, at least partially, the empirical correlation between the fragility and the stretching exponent at T-g.