(435c) Acceleration of Kinetic Monte Carlo Simulations Combining a Hybrid Approach with Scaling of Kinetic Parameters for Free Radical Copolymerization

Authors: 
Gao, H., Northwestern University
Konstantinov, I., The Dow Chemical Company
Arturo, S. G., The Dow Chemical Company
Broadbelt, L. J., Northwestern University
In recent years, there has been growing interest in kinetic Monte Carlo (KMC) methods applied to polymerization systems [1]. KMC is favored mainly for two reasons. First, KMC maintains information on the instantaneous length of each propagating radical, which enables convenient modelling of chain-length dependent rate coefficients [2]. The other reason is that polymer molecules can have different microstructures, including sequence distribution, branching and crosslinking. In KMC simulations, since reactions are explicitly simulated, it is relatively straightforward to construct and record the microstructure for each polymer chain [3].

Despite its power, KMC is computationally much more costly than deterministic modelling. Therefore, research efforts have been put forth to increase the computational efficiency of KMC algorithms. Recently there were two newly emerging methods, both of which showed strong performance in accelerating KMC simulations. Tripathi and Sundberg [4] reported a hybrid simulation method where propagation events are treated deterministically while initiation and termination events are treated stochastically, which can reduce simulation time by more than 100 times. This method was demonstrated on MMA homopolymerization, modelled with chain length dependency, and results agreed well between the hybrid algorithm and complete Monte Carlo simulations. Gao et al. [5] discovered a scaling relationship that could be applied to polymerization rate coefficients which enables the usage of a much smaller control volume than what was previously defined as the minimal volume. The method was demonstrated on copolymerization with a wide range of simulating conditions.

While the hybrid algorithm significantly accelerates KMC simulations, it treats propagation steps continuously, so in each iteration hundreds or thousands of monomers are consumed. As a result, it is only able to provide information on the chain lengths and monomer compositions on each chain, but the full sequence information is lost. Recovering sequence using information directly from a hybrid approach, however, is not a trivial task. In this work, we developed a combined model in which the hybrid approach is enhanced by the scaling method, and further extended to copolymerization with the ability to simulate the explicit polymer sequence. In a case study of the copolymerization of butyl acrylate/methyl methacrylate, we demonstrated that our model is able to combine the acceleration capability of both the hybrid approach and the scaling method, reducing the simulation time from 17.8 seconds to 0.50 seconds. Molecular weight distribution and sequence length distribution are compared between the combined model and a complete KMC simulation, and good agreement is observed for both. This method enables fast KMC simulations of free radical polymerization, which is of great help to the development of an optimization model for controlling free radical polymerization processes.

References

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[2] J. Stubbs, R. Carrier, and D. C. Sundberg, "Monte Carlo simulation of emulsion polymerization kinetics and the evolution of latex particle morphology and polymer chain architecture," Macromolecular Theory and Simulations, vol. 17, pp. 147-162, 2008.

[3] A. K. Tripathi, J. G. Tsavalas, and D. C. Sundberg, "Monte Carlo Simulations of Free Radical Polymerizations with Divinyl Cross-Linker: Pre-and Postgel Simulations of Reaction Kinetics and Molecular Structure," Macromolecules, vol. 48, pp. 184-197, 2014.

[4] A. K. Tripathi and D. C. Sundberg, "A Hybrid Algorithm for Accurate and Efficient Monte Carlo Simulations of Free-Radical Polymerization Reactions," Macromolecular Theory and Simulations, vol. 24, pp. 52-64, 2015.

[5] H. Gao, L. H. Oakley, I. A. Konstantinov, S. G. Arturo, and L. J. Broadbelt, "Acceleration of Kinetic Monte Carlo Method for the Simulation of Free Radical Copolymerization through Scaling," Industrial & Engineering Chemistry Research, vol. 54, pp. 11975-11985, 2015.