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Ind. Eng. Chem. Res. 2007, 46, 4480-4485
Brownian Dynamics Simulation of the Capture of Primary Radicals in Dispersions of Colloidal Polymer Particles Hugo F. Herna´ ndez* and Klaus Tauer Max Planck Institute of Colloids and Interfaces, Research Campus Golm, Am Mu¨hlenberg, D-14424 Potsdam, Germany
The kinetics of collision between primary persulfate radicals and colloidal polymer particles, a key issue in emulsion polymerization modeling, is determined by the simulation of Brownian dynamics using a Monte Carlo random flight algorithm. The results obtained confirm the ideal behavior predicted by Smoluchowski’s kinetic equation only in colloidal dispersions of very low polymer volume fractions (10%) dispersions, is considered. It is also confirmed that only for very diluted dispersions, such as those reported by Lo´pez de Arbina and co-workers,12 can the capture rate coefficient be adequately represented by the diffusion model, which is based on the Smoluchowski equation. 4. Conclusions Significant deviations from the Smoluchowski equation (expressed by the Smoluchowski number) for nonideal concentrated systems were evidenced by the Brownian dynamics
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simulation of the diffusion and collision of primary radicals in polymer dispersions, revealing the importance of polymer volume fraction in the radical capture process when the diffusion of radicals in the aqueous phase is the rate-controlling step and demonstrating the potential use of Monte Carlo methods to simulate and describe the complex processes involved in heterogeneous polymerization. A kinetic expression for the collision between primary radicals and polymer particles considering the effect of polymer volume fraction (eq 10) was obtained from the simulation of Brownian dynamics of radicals and particles using the MCRF method. This expression was able to describe experimental radical capture kinetics obtained in diluted systems as well as in more concentrated dispersions. This is remarkable as several effects were not considered during the simulation, such as the competitive propagation and termination of radicals both in the aqueous phase and inside the polymer particles, the interparticle forces (van der Waals and electrostatic), the nucleation of new particles, and thermodynamic barriers to capture (Gibb’s free energy change). These and many others refinements can be added to the simulation model to obtain a better representation of the capture process and to study many other phenomena in emulsion polymerization such as radical desorption, competitive growth and secondary nucleation of particles, and stability of polymer dispersions. Acknowledgment The authors gratefully acknowledge the Max Planck Society for the financial support of this research. Literature Cited (1) Antonietti, M.; Tauer, K. 90 years of polymer latexes and heterophase polymerization: More vital than ever. Macromol. Chem. Phys. 2003, 204, 207. (2) Tauer, K.; Nozari, S.; Ali, A. M. I. Experimental reconsideration of radical entry into latex particles. Macromolecules 2005, 38, 8611. (3) Herrera-Ordon˜ez, J.; Olayo, R.; Carro, S. The kinetics of emulsion polymerization: Some controversial aspects. J. Macromol. Sci., Part C 2004, 44, 207. (4) Gardon, J. L. Emulsion polymerization. I. Recalculation and extension of the Smith-Ewart Theory. J. Polym. Sci., Polym. Chem. Ed. 1968, 6, 623. (5) Fitch, R. M.; Tsai, C. H. Particle formation in polymer colloids. III. Prediction of the number of particles by homogeneous nucleation theory. In Polymer Colloids; Fitch, R. M., Ed.; Plenum: New York, 1971; pp 73102. (6) Ugelstad, J.; Hansen, F. K. Kinetics and mechanism of emulsion polymerization. Rubber Chem. Technol. 1976, 49, 536. (7) Hansen, F. K.; Ugelstad, J. Particle nucleation in emulsion polymerization. I. A theory for homogeneous nucleation. J. Polym. Sci., Polym. Chem. 1978, 16, 1953. (8) Penboss, I. A.; Gilbert, R. G.; Napper, D. H. Entry rate coefficients in emulsion polymerization systems. J. Chem Soc., Faraday Trans. 1 1983, 79, 2247. (9) Maxwell, I. A.; Morrison, B. R.; Napper, D. H.; Gilbert, R. G. Entry of free radicals into latex particles in emulsion polymerization. Macromolecules 1991, 24, 1629. (10) Tauer, K.; Deckwer, R. Polymer end groups in persulfate-initiated styrene emulsion polymerization. Acta Polym. 1998, 49, 411. (11) Asua, J. M.; de la Cal, J. C. Entry and exit rate coefficients in emulsion polymerization of styrene. J. Appl. Polym. Sci. 1991, 42, 1869. (12) Lo´pez de Arbina, L.; Barandiaran, M. J.; Gugliotta, L. M.; Asua, J. M. Emulsion polymerization: Particle growth kinetics. Polymer 1996, 37, 5907. (13) Liotta, V.; Georgakis, C.; Sudol, E. D.; El-Aasser, M. S. Manipulation of competitive growth for particle size control in emulsion polymerization. Ind. Eng. Chem. Res. 1997, 36, 3252. (14) Bluett, V. M.; Green, J. B. On the competition between scavenging and recombination in solutions of macromolecules J. Phys. Chem. A 2006, 110, 6112.
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ReceiVed for reView January 18, 2007 ReVised manuscript receiVed April 2, 2007 Accepted April 18, 2007 IE070115C
