(346ad) Monomer-Based Kinetic Monte Carlo Simulation for Multifunctional Polymerization

Complex polymer networks are abundant in both nature and art, as their crosslinked structure is exploited for its insolubility and stability. Multifunctional monomers comprised of multiple, diverse functional sites of interest here polymerize into these complex polymer networks through a free-radical mechanism. The heterogeneity of the resulting polymer and products increases via oxidation and scission reactions. Efforts have been made to capture the diverse product distribution, but the nature of radical polymerization leads to a combinatorial explosion of species and limits tractability of solving the time evolution of concentrations with a large system of ordinary differential equations in a deterministic method.[1]

This research utilizes a two-level polymer framework and stochastic kinetic Monte Carlo (kMC) simulation to address the challenges faced with modeling complex polymer systems. Polymers are graph-like: monomer nodes are crosslinked by covalent bond edges. Further, each monomer type is a unique graph with individual atoms and covalent bonds. Chemical reactions transform graphs with specific node patterns or functional groups by making and breaking edges. In literature, Orlova et al. tracked chemistry at the monomer level, generating unique monomer units, but they did not maintain explicit crosslinked species and instead used random graph theory to reconstruct polymer distribution at discrete time points.[2] Kurdikar et al. also used a monomer-based model for multifunctional polymerization, tracking the evolution of unique polymers by the collection of monomer units they contained, but not the polymer topology of how monomers are connected.[3]

This work leverages both monomer approaches while retaining crosslink information. Kinetically informed stochastic selection of reaction type, then species, then functional group are identified and reacted to the product. The graphs of polymer species are stored as an adjacency list of monomer IDs and their respective connections and bond types, such as alkyl, ether, or peroxyl crosslinks. Graph isomorphism allows for species uniqueness checks.

Using an on-the-fly, rule-based kinetic Monte Carlo scheme in which possible reaction events are generated dynamically allows kinetically significant reaction pathways to be tallied in real time, preventing artificial truncations of species size dictated by a pre-populated, finite list of reactions that can lead to a skewed product distribution. The advantage of the dynamic kMC approach is demonstrated using a toy model artificially truncated to dimers compared to one generated using on-the-fly, rule-based product evolution based on free-radical polymerization with representative rate constants involving 15 monomer bases.

Developing a computational tool that captures polymer topology and maintains atomic-level detail for complex, multifunctional polymers allows for deeper exploration of the polymer distributions, their reactivity, and their sensitivity to process parameters in a computationally feasible manner.

[1] Oakley, L. H., Casadio, F., Shull, K. R., & Broadbelt, L. J. (2015). Microkinetic modeling of the autoxidative curing of an alkyd and oil-based paint model system. Applied Physics A,

[2] Orlova, Y., Kryven, I., & Iedema, P. D. (2018). Automated reaction generation for polymer networks. Computers & Chemical Engineering, 112, 37–47.

[3] Kurdikar, D. L., Somvarsky, J., Dusek, K., & Peppas, N. A. (1995). Development and Evaluation of a Monte Carlo Technique for the Simulation of Multifunctional Polymerizations. Macromolecules, 28(17), 5910–5920.