Search

A mathematical model for the total heat flow obtained in differential scanning calorimetry (DSC) experiments from polymers with enthalpic relaxation is proposed. It is limited to the glass transition and enthalpic relaxation range of temperature and to the cases where the enthalpic relaxation is the only non-reversing process taking place. The model consists of a mixture of functions representing the heat capacity heat flow of the glassy and non-glassy fractions, the glass transition progress and the enthalpic relaxation heat flow. Optimal fittings of the model were performed on the experimental total heat flow data, obtained from two thermoplastics with different aging times. Considering which functions of the mixture represent reversing and non-reversing processes, the reversing and non-reversing heat flows were also estimated. The estimated reversing and non-reversing signals were compared with the ones obtained by modulation. On the whole a good match was found, which was even better considering that the estimates are not affected by the frequency effect of the modulated temperature DSC (MTDSC) measurements. The model assumes linear trends for the heat capacity heat flow of the glassy and non-glassy structures. The glass transition progress is represented by a generalized logistic function and the enthalpic relaxation heat flow by the first derivative of another generalized logistic. It brings about a new approach to these phenomena, where the parameters of these functions represent the temperature at which each event is centered, the change of heat capacity (Cp) at the glass transition and the energy involved in the enthalpic recovery. Copyright © 2011 John Wiley & Sons, Ltd.

A goodness-of-fit test statistic for nonlinear regression models based on local polynomial estimation is proposed in this paper. The criterion used to construct the test is the distance between the parametric fit and the nonparametric regression estimation. The good performance of the test is shown via a simulation study. The method is applied to check a logistic mixture regression model for real data coming from a thermal analysis problem. Copyright © 2009 John Wiley & Sons, Ltd.

In this work, an alternative method to the Arrhenius equation for thermogravimetric analysis (TGA) is presented. It is based in performing a logistic regression of the raw TGA data. This model assumes that more than one physical process may be involved in each mass loss step and that each physical process may extend along all the experiment. The logistic mixture obtained explains the complete TGA trace, including as many mass loss steps as the experiment has. The typical asymptotic tendency of the mass loss steps is perfectly reproduced by the model. A discussion of the model from the statistical point of view is presented as well as a comparison with other classical models. Copyright © 2007 John Wiley & Sons, Ltd.