Bayesian Modeling and Markov Chain Monte Carlo Simulations for a Kinetic Study of Homo‐ and Co‐ Polymerization Systems

Abstract

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 L1‐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.magnified image

Sequence Distribution and Cumulative Composition of Gradient Latex Particles Synthesized by a Power-Feed Technique

“…Linear graphical methods, such as Fineman–Ross (FR), Kelen–Tüdõs (KT), YBR, and nonlinear least-squares method (NNLS), are used to determine the reactivity ratio. The results are summarized in Table where the dependence of the reactivity ratios on different methods is clearly shown.…”

Progress in Computer Simulation of Bulk, Confined, and Surface‐initiated Polymerizations

“…Efficient accounting algorithms78 are necessary for this purpose, given the large amount of data processed. Copolymerization systems studied by the GSSA include statistical copolymerization with terminal and penultimate termination models,79 multiblock copolymerization,80 and gradient copolymerization 81–85. The bivariate distribution of copolymer composition and molecular weight can be obtained by combining GSSA with simultaneous property accounting algorithms by means of a two‐dimensional fixed pivot technique 86.…”

Modeling of the Penultimate Unit Effect in Chain-Growth Copolymerizations

“…Typically, polymerization systems comprising styrene/acrylonitrile [15][16][17][18][19][20], methyl methacrylate/n-butyl acrylate [21], ethylene/styrene [22], dimethyl itaconate/styrene [23], ethylene/4-methyl-1-pentene [24], α-alkylstyrenes/acrylonitrile [25], styrene/methyl methacrylate [26], p-chlorostyrene/methyl acrylate [27], styrene/isobutylene [28], methyl α-(trifluoromethyl)acrylate and α-(trifluoromethyl) acrylonitrile with styrene, p-chlorostyrene and methyl methacrylate [29], styrene/maleic anhydride [30], isobutyl methacrylate/lauryl methacrylate [31], and styrene/fumaronitrile [32,33] demonstrate a strong penultimate unit effect, representing good examples of the successful implementation of the penultimate model [9,34].…”