How powerful are composition data in discriminating between the terminal and penultimate models for binary copolymerization?

Abstract

The terminal model for binary copolymerization is often accepted simply on the grounds that it provides a satisfactory fit to a set of experimental data. The penultimate (and other) models are often not considered or are rejected as making no significant improvement. It is argued that such inferences are invalid unless reference is made to the power of the experiments in estimating penultimate unit effects. A method for assessing the possible magnitude of penultimate unit effects in binary copolymerization is offered. This involves using a nonlinear least-squares method to fit the penultimate model and constructing an approximate 95% joint confidence interval for r1/r1’ and r2/r2’. The method is illustrated with reference to literature data for methyl methacrylate/styrene copolymerization. An analysis of the composition data of Fukuda et. al. for this system shows that while the terminal model is a possible solution, the size of the 95% joint confidence interval shows that penultimate unit effects could be substantial and the model may still give an adequate fit to the experimental composition data (0.4 ≤ r1/r1’≤ 2.7 and 0.3 ≤ r2/r2’ ≤ 2.2). Design criteria for evaluation of reactivity ratios which take into account the need for model discrimination are discussed. © 1989, American Chemical Society. All rights reserved.