The Importance of the Knowledge of Errors in the Measurements in the Determination of Copolymer Reactivity Ratios from Composition Data

Abstract

Often the errors in the measurement of copolymerizations are not accurately determined or included in the calculation of reactivity ratios. Some knowledge of the errors in the initial monomer ratio, conversion, and copolymer composition is however essential to obtain reliable (unbiased) reactivity ratios with a realistic uncertainty. It is shown that the errors serve a trifold purpose; they can serve as weighing factors in the fit, they can be compared with the fit residues to decide whether the chosen model is adequate for the data and they can be used to construct a realistic joint confidence interval for the reactivity ratios. The best approach is to have an estimate of the individual errors in the copolymer composition, either from a thorough error propagation exercise or from replicate measurements. With these errors, the χ²-joint confidence intervals can then be constructed which gives a realistic estimate of the errors in the reactivity ratios. Utilizing the Errors in Variables Method (EVM) is correct and useful, but only if the individual errors in all the variables in each experiment are more or less known.