On the measurement of the width of the distribution of relaxation times inpolymer glasses

A new method to determine the width of the distribution of relaxation times (DRT) based on calorimetric measurements by temperature modulated differen tial scanning calorimetry (TMDSC) is presented. The simulation of the glass transition by TMDSC, taking into account a DRT, shows that the inflectiona l slope of the complex heat capacity, C-p* depends sensitively on the stret ched exponential parameter beta of the Kohlrausch-Williams-Watts equation, which is inversely related to the width of the DRT (0 less than or equal to beta less than or equal to 1). Furthermore, it is shown that the normalise d inflectional slope of C-p*, defined as: (S) over bar = 1/DeltaC(p)* dC(p)*/dT is independent of the nonlinearity parameter, but depends on the apparent a ctivation energy, Deltah*, implying that it should be normalised also with respect to this. The procedure proposed here for the evaluation of beta is to consider the dimensionless quantity (S) over bar/theta, where theta = De ltah*/RTg2 is the equivalent of an apparent activation energy in the KAHR m odel. For example, the value of (S) over bar/theta increases from 0.05 to 0 .26 in the simulations as beta increases from 0.2 to 0.8. The method was applied to three epoxy resins obtained with different stoich iometric ratios (r = 0.8, 1 and 1.5), for which the values of the parameter beta were previously estimated by conventional DSC, using the method of in trinsic cycles, being in the range 0.3 < beta < 0.4. The values of the norm alised and dimensionless inflectional slope (S) over bar/theta were found e xperimentally 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 beta values close to 0.4, which agree very well with the earlier estimated values. (C) 2001 Elsevier Science Ltd. All rights reserved.