On the measurement of the width of the distribution of relaxation times in polymer glasses

Abstract

A new method to determine the width of the distribution of relaxation times (DRT) based on calorimetric measurements by temperature modulated differential scanning calorimetry (TMDSC) is presented. The simulation of the glass transition by TMDSC, taking into account a DRT, shows that the inflectional slope of the complex heat capacity, Cp∗ depends sensitively on the stretched exponential parameter β of the Kohlrausch–Williams–Watts equation, which is inversely related to the width of the DRT (0≤β≤1). Furthermore, it is shown that the normalised inflectional slope of Cp∗, defined as:S̄=1ΔCp∗dCp∗dTis independent of the nonlinearity parameter, but depends on the apparent activation energy, Δh∗, implying that it should be normalised also with respect to this. The procedure proposed here for the evaluation of β is to consider the dimensionless quantity S̄/θ, where θ=Δh∗/RTg2 is the equivalent of an apparent activation energy in the KAHR model. For example, the value of S̄/θ increases from 0.05 to 0.26 in the simulations as β increases from 0.2 to 0.8.The method was applied to three epoxy resins obtained with different stoichiometric ratios (r=0.8, 1 and 1.5), for which the values of the parameter β were previously estimated by conventional DSC, using the method of intrinsic cycles, being in the range 0.3<β<0.4. The values of the normalised and dimensionless inflectional slope S̄/θ were found experimentally by TMDSC to be 0.128 (for the resin r=1), 0.132 (for r=1.5) and 0.113 (for r=0.8), all corresponding to β values close to 0.4, which agree very well with the earlier estimated values.