(561c) An Efficient Hybrid Algorithm Combining Kinetic Monte Carlo and Continuum Model for Radical Polymerization

Abstract: The Kinetic Monte Carlo (KMC) algorithm has been widely used in the simulation of polymerization reactions due to its ability to track the finest details of individual molecule sequences. However, the disadvantages of high computational cost and long running time have been difficult to overcome, which is attributed to the large number of molecules that the algorithm needs to simulate to obtain converged result. A scaling approach has been developed to address this issue for free radical polymerization, using the pseudo steady state assumption (PSSA) to correct radical concentration when simulating a small number of molecules. However, PSSA is not always satisfied, and for complicated reaction systems, it might be very difficult to derive a closed-form formula for radical concentration from PSSA. This work proposes a new hybrid algorithm, which circumvents the dependence on PSSA and the associated derivations. Instead, a continuum model is solved in parallel with the KMC simulation to provide the accurate value of radical concentrations for calculating a scaling factor, which recovers the correct results in KMC simulations when using a small number of molecules. As a case study, the algorithm is tested on free radical polymerization (FRP) and living radical polymerization (ATRP) The results show the hybrid method does accurately simulate the system with 100 times fewer molecules than what would have otherwise been required for an accurate full KMC simulation. Key characteristics of the polymerization system (such as conversion and molecular weight distribution) are consistent with a full KMC simulation with sufficiently large number of molecules, with the running time reduced by nearly 96.5%. It is worth stating that by solving for real-time radical concentration using the continuum model, the algorithm avoids the need to assume PSSA, which makes it highly generalizable. While we demonstrated the method on FRP and ATRP as examples, the application of the model can be easily extended to the KMC simulation of any other polymerization, or even any chemical reaction system with highly disparate concentration scales.

References:

[1]Keating, J. J.; Plawsky, J. L. Radical Lifetimes in Atom Transfer Radical Polymerization: A Monte Carlo and Deterministic Investigation. Macromolecules 2020, 53 (17), 7224–7238.

[2]Gao, H.; Oakley, L. H.; Konstantinov, I. A.; Arturo, S. G.; Broadbelt, L. J. Acceleration of Kinetic Monte Carlo Method for the Simulation of Free Radical Copolymerization through Scaling. Ind. Eng. Chem. Res. 2015, 54 (48), 11975–11985.