A Hybrid Algorithm for Accurate and Efficient Monte Carlo Simulations of Free‐Radical Polymerization Reactions

Abstract

Monte Carlo simulation methods are suitable for free radical polymerizations (FRP) even when there is significant chain length dependence of the reactions. For each simulation step the probability of each possible reaction is determined at that point in time. In FRP modeling most of the computation time is spent on radical propagation. We demonstrate a hybrid simulation method where the propagation reaction is treated using differential equations and other reactions (e.g. termination and initiation reactions) are treated stochastically. This allows significant reductions in simulation time while maintaining the features of complete Monte Carlo methods. This approach can be applied to more complex polymerization reactions like branching and crosslinking using Monte Carlo methods within manageable times.

Monte Carlo Simulations of Free Radical Polymerizations with Divinyl Cross-Linker: Pre- and Postgel Simulations of Reaction Kinetics and Molecular Structure

“…This condition was developed for accurate MC simulations of free-radical polymerization. 32,34 This equation was derived for non-cross-linking homopolymerization reactions considering the number of free radicals in the Figure 10 we can see that for all three simulation volumes the computed results are nearly identical, which suggests that eq 40 is valid for cross-linking reactions as well. This also validates the selected simulation volume of 4.98 × 10 −17 L for the reaction conditions.…”

“…For intramolecular polymer−polymer reactions (eqs 13, 14, and 20−22), the overall respective rate coefficient (K x,ii ) is calculated as 13, 14, 20 22) x ii x x , chem res (32) Equation 32 is similar to eq 27 but without inclusion of the diffusion term. For an intramolecular reaction, translational diffusion is not significant, but other modes of polymer movements such as rotation and bending will affect the possibility of these reactions occurring.…”

Copolymerization of Ethylene with 1,9‐Decadiene: Part I – Prediction of Average Molecular Weights and Long‐Chain Branching Frequencies

“…Thus, the size of the control volume has to be large enough to give accurate results at acceptable computation times and ensure convergence of the polymer properties. Previous publications show how to select the most appropriate control volume for a given system . The most adequate control volume chosen to perform all the MC simulations in the present work was 5 × 10 −15 L. Table summarizes all MC reaction rate expressions and the implemented algorithm.…”

Chain‐by‐Chain Monte Carlo Simulation: A Novel Hybrid Method for Modeling Polymerization. Part I. Linear Controlled Radical Polymerization Systems

“…The key requirement in kMC is that the system should be sufficiently “large” in the sense of thermodynamic limit, where the molecular populations are imagined to go to infinity along with the system volume, V , while the concentrations remain constant . As discussed previously, the problem arises trying to find the sufficiently “large” system size in order to reliably define the system, and there is no general way of specifying the system size . For most polymer systems, the system size is not small and depends on structure and parameters of the reaction mechanism.…”

“…In general, this set of 1000 chains would be considered to provide a poor approximation of the distribution, as much larger ensembles are needed for an accurate description of the actual distributions. So, while MC methods have the advantages of closely mimicking the process of chain development during the course of polymerization, simplicity, and suitability for high dimensionality cases, they have the drawback of requiring a large number of computations to achieve convergence . Another factor to consider in MC methods is that, because of their randomized nature, every simulation started from the same set may end up in a different realization of the distribution.…”