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.

Carboxylic acid monomers are commonly used at low concentrations as functional additives in emulsion polymerization. Being quite water-soluble, they partition between the aqueous and polymer particle phases in complex manners. We have studied of the partitioning behavior of both acrylic (AA) and methacrylic (MAA) acids between water and a variety of individual styrene, acrylate, and methacrylate monomers. The distribution coefficients strongly depend upon the hydrogen-bond acceptor characteristics of the organic phase and the pH of the aqueous phase. AA and MAA behave similarly, but AA distributes much less strongly to the organic phase than does MAA. The logs of the distribution coefficients for both vinyl acids correlate linearly with the molar volume of the (meth)acrylate monomers, and these values decrease as the molecular weight of the monomer increases. Vinyl acid distributions to styrene monomer are nearly completely determined by the dimerization of the acids in the monomer phase and, as such, are quite sensitive to the concentration of the acid in the water phase. The effects of ionic strength and temperature are minimal for the usual emulsion polymerization reaction conditions.

A computationally efficient Monte Carlo method was used to simulate the reaction kinetics and molecular structure development during free-radical copolymerizations with divinyl monomers. A single parameter was used to describe the reduced reactivity of the pendent vinyl groups incorporated within the polymer backbone. The simulation results were compared with published experimental data for the bulk copolymerization of methyl methacrylate with different levels of ethylene glycol dimethacrylate. The model was able to effectively predict the reaction kinetics, the gel point, and sol−gel fractions in both the pre-and postgel regimes, including the swelling index of the gel. In the postgel regime the cross-linked molecule becomes the primary locus of reactions, and all chains eventually become part of this massive cross-linked polymer network. The Monte Carlo method allows the determination of the complete molecular structure as it evolves with time, including properties like cross-linking density, number of free chain ends, primary cycles and loops, and the fraction of unreacted pendent vinyl groups.

We have studied of the partitioning behavior of both acrylic (AA) and methacrylic (MAA) acids between water and a variety of styrene, acrylate and methacrylate co- and ter-monomer phases. As in single monomer phase systems, the distribution coefficients for multicomponent systems strongly depend upon the hydrogen bond acceptor characteristics of the organic phase and the pH of the aqueous phase. These measured distribution coefficients for multicomponent monomer systems can be predicted by applying an appropriate “mixing rule” to the distribution and dimerization coefficients obtained from the single monomer systems. Using a log-based mixing rule, we have been able to accurately predict the water/monomer distribution characteristics of both AA and MAA for a wide variety of styrene/(meth)acrylate multimonomer systems for our own data as well as those developed by others. This includes multicomponent monomer experiments at pH levels at which the vinyl acids are partially or fully ionized in the water phase.

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