Decision trees as applied to the robust estimation of diffusion coefficients in polyolefins
Résumé
This study dealt with decision trees as used to predict diffusion coefficients (D's) in polyolefins of molecules with molecular weights ranging between 50 and 1200 g/mol at 23 and 40 degrees C. The approach was tested on 657 D's (267 molecules) mainly collected by the European working group SMT-CT98-7513. According to a reptation-like mechanism of transport, three topological molecular descriptors, the Van-der-Waals volume, the gyration radius, and a dimensionless shape parameter, were proposed as both classifiers and regressors. They were calculated from the minimized and oriented structure in the absence of interaction with the polymer matrix. The foreseen ability of regression trees was tested by both cross-validation and bootstrap sampling for a wide number of classes. Optimally pruned trees provided correlation coefficients ranging between 0.74 and 0.96 for each tested polymer. The effects of the volume of diffusing molecules predominated in polyethylene, whereas a combination of the three parameters was required in polypropylene. D overestimates, which are particularly useful for checking the compliance of food contact materials, were derived and validated from the upper percentiles of the D values observed in each terminal class. The use of decision trees as a tool for data assimilation is discussed. We concluded that the proposed descriptors were a priori (without a preliminary fitting) able to gather molecules with similar D values without introducing any significant bias.