A hierarchical data analysis of a replicate experiment in polyethylene synthesis with high-temperature gel permeation chromatography

We present the results of a 3 x 4 x 4 hierarchical experiment using high-te mperature gel permeation chromatography (GPC) to analyze the molecular weig ht distribution (MWD) of replicate ethylene polymerizations with metallocen e/methylalumoxane (MAO) catalysts. Our aim was to decompose the variance im parted to the MWD by a) GPC analysis itself (sigma(T)(2)), b) heterogeneity in the polymerization reactor (sigma(S)(2)), and c) random fluctuations in conditions between polymerizations (sigma(P)(2)). This variance component analysis was performed on several measures used to characterize the centre, breadth and skewness of MWDs. Using analysis of variance tables, significa nce tests and contrast tests, we were able to reveal statistically signific ant differences in the MWD of polyethylene synthesized in replicate polymer izations at identical conditions, as well as differences between samples dr awn from the same polymerization. By comparing the results of this analysis using different measures of MWD, we were able to draw conclusions regardin g the suitability of various indicators conventionally used to characterize the MWD. The techniques discussed are very general and applicable to almos t any experimental scenario.