(225h) Efficient Kinetic Monte Carlo Simulation Used in the Design of Copolymer Prepared By Free Radical Polymerization
Efficient Kinetic Monte Carlo Simulation Used in the Design of Copolymers Prepared by Free Radical Polymerization
Hanyu Gao, Department of Chemical and Biological Engineering, Northwestern University
Ivan A. Konstantinov, The Dow Chemical Company
Steven G. Arturo, The Dow Chemical Company
Linda J. Broadbelt, Department of Chemical and Biological Engineering, Northwestern University
Key Words: Kinetic Monte Carlo, free radical polymerization, pseudo steady state assumption, minimal number of molecules
Free radical polymerization has a wide range of applications and has constituted more than half of the entire polymer industry. Extensive research effort has been aimed at modeling and simulation of free radical polymerization, in order to reduce the amount of experimental work needed to explore the effect of synthesis conditions on the properties of the polymer product. Kinetic Monte Carlo (KMC)  is a powerful tool for simulating polymeric reactions because of its capability of recording the explicit sequence of every polymer chain, enabling more detailed analysis of polymer properties .
In KMC simulations of polymerization, researchers have noted that there is a minimal requirement on the number of molecules used in the system in order to obtain converged results . Currently, this number is determined through a trial and error process. A sequence of increasing numbers of initial molecules (e.g., 106, 107, 108, …) is used until convergence is reached. This limit is an important barrier for the acceleration of KMC simulations. In this work, we analyzed the cause of this requirement and developed a method to use much fewer molecules and generate a small polymer chain sample . The importance of this work lies in expediting KMC simulations and opening up the possibility of linking KMC simulation with molecular simulation, which can only handle a limited number of atoms.
In a case study of the copolymerization of butyl acrylate/methyl methacrylate, our method reduced the number of molecules from more than 109 to less than 106, which accelerated the simulation by more than 1000 times. This significant reduction in simulation time makes available fast evaluation of multiple synthesis conditions, which can be used for efficiently designing synthesis recipes for desired polymer properties. In addition, rigorous statistical tests showed that this sample conformed to the converged results obtained with much larger chain populations, in terms of the distribution of key measures of polymer chains (e.g. molecular weight distribution, sequence distribution, etc.). This indicates that the small chain sample is a suitable representative of the large population and can be used in molecular simulation in order to calculate macroscopic polymeric physical and chemical properties.
 D. T. Gillespie, "A general method for numerically simulating the stochastic time evolution of coupled chemical reactions," Journal of Computational Physcis, vol. 22, pp. 403-434, 1976.
 V. R. Regatte, H. Gao, I. A. Konstantinov, S. G. Arturo, and L. J. Broadbelt, "Design of copolymers based on sequence distribution for a targeted molecular weight and conversion," Macromolecular Theory and Simulations,vol. 23, pp. 564-574, 2014.
 P. H. M. Van Steenberge, D. R. D’hooge, M. F. Reyniers, and G. B. Marin, "Improved kinetic Monte Carlo simulation of chemical composition-chain length distributions in polymerization processes," Chemical Engineering Science, vol. 110, pp. 185-199, 2014.
 H. Gao, L. H. Oakley, I. A. Konstantinov, S. G. Arturo, L. J. Broadbelt. “On the Minimal Number of Molecules Used in Kinetic Monte Carlo Simulations of Free Radical Polymerization,” Submitted for publication in Chemical Engineering Science.