Logistic approach to polymer degradation in dynamic TGA Ricardo Cao a , Salvador Naya a , Ramo´n Artiaga b, ) , Ana Garcı´a b , Angel Varela b a Department of Mathematics, University of A Corun ˜a, Facultad de Informa ´tica, Campus Elvin ˜a, A Corun ˜a, Spain b Department of Industrial Engineering II, University of A Corun ˜a, Escuela Polite ´cnica Superior, Esteiro, 15403 Ferrol, Spain Received 17 December 2003; received in revised form 16 February 2004; accepted 17 March 2004 Abstract The method presented in this work allows for fitting an overall TGA curve by generalized logistic regression. It is assumed that overlapping processes may be involved in a single step of a TGA trace. Since the logistic functions reproduce very well the typical asymptoticity at the beginning and end of degradation processes, the authors consider that each single degradation process can be fitted by a single logistic function or by the linear combination of a small number of them. Since the fitting is very good, the generalized function can replace the original TGA curve. This way, it is possible to differentiate directly the overall TGA curve fitted, overcoming the problems of noise and overeunder smoothing, typical in DTG calculation. On the other hand, the separation of overlapping processes in several functions suggests that each single overlapping degradative process could be explained by one or the linear combination of few logistic functions. Particularly, one of the parameters obtained with this kind of logistic mixture represents the point in the time (or temperature) axis where each process is ‘‘centered’’, while another parameter is related to the degradation rate. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Polymer degradation; Logistic mixture; TGA; Fitting; Smoothing 1. Introduction Degradation is usually a complex process involving combinations of random scission, depolymerisation, degradation involving thermally labile defects and other mechanisms [1]. With regard to the assessment of polymer stability, thermogravimetric analysis (TGA) is usually employed to determine the temperature of initial weight loss, which can be viewed as the onset of degradation [2]. TG is also used to identify components in a sample. Nevertheless, in some cases the percentages of the components in a sample cannot be determined directly from the TGA dynamic run because the decomposition of the components occurs simultaneously [3]. Both isothermal and dynamic heating experiments can be used to evaluate kinetic parameters [4]. In dynamic thermogravimetric analysis (TGA), the mass of the sample is continuously monitored while the sample is subjected, in a controlled atmosphere, to a thermal program, where the temperature is ramped at a constant heating rate. Generally, smoothing of TGA curves is performed in order to reduce the noise which makes the data analysis easier. The fitting is usually performed when kinetic analysis is concerned. In that case, sections of the TGA traces, not entire curves, are fitted to different models. Fitting single heating rate data to models does not generally work in order to obtain the kinetics [5,6]. Multiple heating rate methods are considered more appropriate to obtain kinetic parameters than the single heating rate ones [7]. The isoconversional methods such as Ozawa, FlynneWall, or Friedman are generally recommended. Different processes with different depen- dence on the heating rate may be overlapping. Evapora- tion of volatile component is a diffusion controlled weight loss process, heating rate dependent that does not follow the typical single activation energy Arrhenius model. Chemically controlled mass losses may have different activation energy and thus different heating rate dependence. Once the dependence of the activation energy on the conversion was obtained, overlapping ) Corresponding author. Tel.: C34-981337400; fax: C34- 981337410. E-mail address: rartiaga@udc.es (R. Artiaga). 0141-3910/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymdegradstab.2004.03.006 Polymer Degradation and Stability 85 (2004) 667e674 www.elsevier.com/locate/polydegstab