(492c) Kinetic Monte Carlo Simulation of Miniemulsion Polymer Particles

Miniemulsion polymerization allows for the production of uniformly-sized nanoparticles, and is thus useful in a wide variety of applications, ranging from drug delivery [1] to the disposal of toxic substances [2]. Miniemulsion particles are typically 50-200 nm in diameter, so continuum variables such as concentration are not sufficient to describe individual polymer molecules at this scale, or to capture radial non-uniformities in the particle structure, such as core-shell or hollow morphologies. Realizing a single particle on a face-centered cubic lattice using the kinetic Monte Carlo algorithm enables resolution of the individual monomers while accurately predicting the particle structure. This coarse-grained approach allows the simulation to execute significantly faster than traditional molecular dynamics simulations, which require continuous spatial resolution.

Each lattice site is assigned a type such as monomer, polymer, or radical. Both reactive and diffusive events are executed within the simulation, with the time for each event determined randomly based on the cumulative rate of all possible events at a given iteration. The rates for diffusive events are 10⁷ times higher than the reaction rates, so the 'tau-leaping' algorithm of Gillespie [3] is applied to reduce the order of magnitude of the diffusive rates to that of the reaction rates, to make the simulation computationally tractable. Due to the nanoscopic size of the particle, its state does not change measurably during the time interval between reactive events, and a sufficiently large number of diffusive events would occur between reactive events, so both of Gillespie's requirements are satisfied.

For the KMC model to accurately simulate the particle morphology, one of the key benchmarks is to achieve a realistic molecular weight distribution. The MWD is largely dependent on the rate of termination, for which center-of-mass diffusion of the radicals is the rate-limiting step, since two radicals must diffuse together for termination to occur. The diffusion rates in the KMC simulation have been adjusted so that the simulated MWD agrees with data taken from Asua [4], at early conversion, while the simulation remains computationally tractable. The MWD's produced by the simulation will also be compared with Asua's data [4] at higher conversions.

The KMC model provides a powerful tool to simulate various mechanisms surrounding miniemulsion polymerization. Localized properties, such as monomer availability around radicals, or particle-level mechanisms, such as nucleation, can be directly simulated. For nucleation using oil-soluble initiators, two primary theories exist. Asua proposes that one of the two radicals formed by an oil-soluble initiator molecule must exit the particle before recombining with the other radical [5], while Nomura theorizes that single radicals enter the particle from the aqueous phase, produced from the small fraction of oil-soluble initiator partitioned in the aqueous phase [6]. Such mechanisms are investigated here using our coarse-grained simulations.

References

[1] B. B. C. Youan, T. L. Jackson, L. Dickens, C. Hernandez, and G. Owusu-Ababio. Protein release profiles and morphology of biodegradable microcapsules containing an oily core. Journal of Controlled Release, 76(3):313-326, 2001.

[2] A. J. P. van Zyl, R. D. Sanderson, D. de Wet-Roos, and B. Klumperman. Core/shell particles containing liquid cores: Morphology prediction, synthesis, and characterization. Macromolecules, 36(23):8621-8629, 2003.

[3] D. T. Gillespie. Approximate accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics, 115(4):1716-1733, 2001.

[4] J. A. Alduncin and J. M. Asua. Molecular-weight distributions in the miniemulsion polymerization of styrene initiated by oil-soluble initiators. Polymer, 35(17):3758-3765, 1994.

[5] J. M. Asua, V. S. Rodriguez, E. D. Sudol, and M. S. El-Aasser. The free-radical distribution in emulsion polymerization using oil-soluble initiators. Journal of Polymer Science Part A-Polymer Chemistry, 27(11):3569-3587, 1989.

[6] M. Nomura and K. Suzuki. The kinetic and mechanistic role of oil-soluble initiators in micro- and macroemulsion polymerizations. Industrial & Engineering Chemistry Research, 44(8):2561-2567, 2005.