Emulsion polymerization is a highly complex dynamic process in which several simultaneous and usually competitive chemical (radical generation, propagation, termination, chain transfer) and physical events (diffusion, absorption, desorption, nucleation, coagulation) occur at very different time scales and dimensions. These events take place in a typical free-radical emulsion polymerization at rates ranging from about 10⁰ to 10⁹ s^-1 and involving entities of very different length scales, such as ions and molecules (< 1 nm), macromolecules (1 – 10 nm), polymer particles (10 nm – 1 μm) and monomer droplets (>1 μm). A precise quantitative model of the kinetics of emulsion polymerization requires the detailed knowledge of the kinetics of all these physical and chemical processes.

In the present work, all these different events are investigated at different time and length scales using suitable simulation methods such as Molecular Dynamics (MD) simulation [1,2], Brownian Dynamics (BD) simulation [3] and kinetic Monte Carlo (kMC) simulation [4]. The use of simulation techniques with spatial resolution such as MD and BD is advantageous when dealing with systems of increased geometrical complexity. This is the case of non-spherical polymer particles, structured polymer particles (e.g. core-shell, multilayered, etc.), non-uniform polymer particles (e.g. gradient in radial monomer composition), polydisperse particles and so on.

Molecular Dynamics (MD) simulation is used to estimate the diffusion coefficients of a given molecular species under very specific conditions. These diffusion coefficients are then used by the Brownian Dynamics (BD) simulation method to describe the molecular motion at a much larger time and length scale. The BD simulation of radicals in emulsion polymerization is used to determine the rate of radical capture by polymer particles [5,6], as well as the rate of radical desorption from the particles to the continuous phase [7]. Similarly, the BD method can be used to simulate the absorption and desorption of monomer molecules by polymer particles, and therefore, to obtain a description of the monomer swelling dynamics. The simulation of polymerization reactions under diffusion control, which usually takes place inside the polymer particles at low monomer volume fraction, is performed using a new modified version [8] of the stochastic simulation algorithm developed by Gillespie [4]. Finally, the integration of all these multi-scale processes into one single simulation is performed using a kinetic Monte Carlo (kMC) algorithm.

References:

[1] Frenkel, D. and B. Smit. "Understanding molecular simulation", Academic Press, San Diego 2002.

[2] Chen, J. C. and A. S. Kim. "Brownian Dynamics, Molecular Dynamics and Monte Carlo modeling of colloidal systems". Adv. Colloid Interf. Sci., 112, 159-173 (2004).

[3] Ermak, D. L. and J. A. McCammon. "Brownian dynamics with hydrodynamic interactions". J. Chem. Phys., 69, 1352-1360 (1978).

[4] Gillespie, D. T. "A general method for numerically simulating the stochastic time evolution of coupled chemical reactions". J. Comp. Phys., 22, 403-434 (1976).

[5] Hernandez, H. F. and K. Tauer. "Brownian Dynamics Simulation of the capture of primary radicals in dispersions of colloidal polymer particles". Ind. Eng. Chem. Res., 46, 4480-4485 (2007).

[6] Hernandez, H. F. and K. Tauer. "Brownian Dynamics Simulation Studies on Radical Capture in Emulsion Polymerization". Macromol. Symp., 259, 274-283 (2007).

[7] Hernandez, H. F. and K. Tauer. "Radical desorption kinetics in emulsion polymerization - Theory and Simulation". Submitted to Ind. Eng. Chem. Res.

[8] Hernandez, H. F. and K. Tauer. "Stochastic simulation of imperfect mixing in free radical polymerization". Macromol. Symp. (2008). In press.