(259c) A Robust Bayesian Approach for Model Discrimination in Copolymerization Kinetics

A robust Bayesian approach and Markov Chain Monte Carlo (MCMC) simulation is developed for kinetic study of polymerization systems. The method is employed for assessing the power of experimental data in discriminating between different copolymerization models. The simulation algorithm is exact, in the sense that it takes full account of the fluctuations and correlations. To avoid inaccuracies in the results, the time step between successive Monte Carlo (MC) events is adapted to the time scale of the fastest reaction. Two models i.e. Terminal Unit Model (TUM) and Penultimate Unit Model (PUM)) are considered to represent the copolymer composition and the monomer sequences along the copolymer chain. Also three kinetic models i.e. terminal rate model, Implicit Penultimate Unit Model (IPUM) and Explicit Penultimate Unit Model (EPUM) are considered to investigate the kinetic behavior of the copolymerization system. Prior estimates of the model parameters are obtained by L1-norm Robust statistics. Using the structure of the experimental data through a Likelihood function, Bayesian calculations are performed to update the prior estimates. The joint posterior probability regions and shimmer bands are calculated for updated model parameters. The simulation method is validated with reference to the literature data for a number of copolymerization systems with pronounced penultimate effect. By adjusting the number of MC runs and the size of the simulation volume, the accuracy in the order of the experimental error (i.e. ) can be obtained. The major conclusions are:

In contrast to what is observed in low conversion polymerization on the macro-scale, compositional drift can be observed on the molecular scale. Despite a better fit of the four-parameter PUM over the two-parameter TUM in some copolymerization systems, the composition data are not sufficiently sensitive to enable unambiguous discrimination between the different copolymerization models in some systems. Polymerization media can be locally inhomogeneous in the vicinity of a growing chain end, leading to preferential sorption which can be responsible for deviations from the ideal copolymerization behaviour in absence of any penultimate unit effects. In these situations, it is impossible to establish the real source of the deviations and additional measurements such as sequence distribution, molecular weight distribution and copolymerization rate data are required. Even under conditions of moderately small sample sizes, strong correlations, and marked non-normality, the simulation method is found to be quite robust. The statistical analyses of the simulation results justify the accuracy and reliability of the simulation method for kinetic parameter estimation and model discrimination in polymerization systems.