Bayesian modeling and Markov chain Monte Carlo simulations for a kinetic study of homo-and Co-polymerization systems

摘要

A Bayesian modeling and Markov Chain Monte Carlo simulation was developed for a kinetic study of homopolymerization and copolymerization systems at the molecular scale. Two copolymerization models - the terminal unit model and the penultimate unit model - were considered. Prior estimates of the kinetic parameters were obtained by L-1-norm robust statistics. Using the structure of experimental data through a likelihood function, Bayesian modeling was employed to update the prior estimates. The joint posterior probability regions and shimmer bands were calculated for updated reactivity ratios. A method for assessing the power of experimental data in discrimination between copolymerization models is presented. This method was validated for free radical polymerization in binary systems. The evolution of species and radical populations during the course of polymerization were determined. The computational time was considerably decreased by calculating the propagation step from lifetime of the polymer chain and local monomer concentration. To avoid inaccuracies in the results caused by poor choice or false computation of the time step, the time step between successive Monte Carlo events was adapted to the time scale of the fastest reaction. The simulation algorithm is exact, in the sense that it takes full account of the fluctuations and correlations.