Entropic model for the relaxation in vitreous systems. Estimation of uncertainty in the calculation of the conformational relaxation times

Differential scanning calorimetry experiments were conducted on a thermotropic polyester. The experimental results consists of a series of thermograms measured on heating after different thermal histories that contained (or not) an isothermal stage at a temperature Ta below the glass transition with a duration ta. The thermogram showed the characteristic peak in the region of the glass transition. The calculation of the relaxation times of the co-operative conformational rearrangements related to the glass transition and structural relaxation phenomena has been conducted by curve fitting using a phenomenological model. The curve fitting procedure was conducted simultaneously on a fixed number n of experimental thermograms. The aim of the paper is to present a method to estimate the uncertainty in the calculation of the model parameter. The results show how the computer simulated thermograms agree quite well to the experimental data. The uncertainty in the model parameters and through them the uncertainty in the calculated relaxation times is quite important when the number of experimental curves n is small but rapidly decreases as n increases and if more than five curves are used simultaneously in the fitting routine both the values of the model parameters and their uncertainty become independent on the number and thermal histories of the experimental thermograms.