Brownian Dynamics Simulation of the Capture of Primary Radicals in

Max Planck Institute of Colloids and Interfaces, Research Campus Golm, Am ... kinetic equation only in colloidal dispersions of very low polymer volum...
0 downloads 0 Views 99KB Size
4480

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

Ind. Eng. Chem. Res., Vol. 46, No. 13, 2007 4485

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.

(15) Einstein, A. Zur Theorie der Brownschen Bewegung. Ann. Phys. 1906, 19, 371. (16) Smoluchowski, M.v. Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen. Ann. Phys. 1906, 21, 756. (17) Ermak, D. L.; McCammon, J. A. Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 1978, 69, 1352. (18) Adamczyk, Z.; Jaszczo´lt, K.; Michna, A.; Siwek, B.; SzykWarszynska, L.; Zembala, M. Irreversible adsorption of particles on heterogeneous surfaces. AdV. Colloid Interface Sci. 2005, 118, 25. (19) Bolton, C. E.; Green, N. J. B.; Harris, R.; Pimblott, S. M. Competition between geminate recombination and reaction with a macromolecule. J. Phys. Chem. A 1998, 102, 730. (20) Green, N. J. B.; Spencer-Smith, R. D. Simulation of geminate recombination in the presence of an absorbing plane. J. Phys. Chem. 1996, 100, 13561. (21) Ulberg, D. E.; Churaev, N. V.; Ilyin, V. V.; Malashenko, G. L. Molecular dynamics simulation of the aggregation of colloidal particles. Colloids Surf., A 1993, 80, 93. (22) Tobita, H. Monte Carlo simulation of emulsion polymerization linear, branched and crosslinked polymers. Acta Polym. 1995, 46, 185. (23) Chern, C. S.; Poehlein, G. W. Polymerization in nonuniform latex particles: Distribution of free radicals. J. Polym. Sci., Part A: Polym. Chem. 1987, 25, 617. (24) Croxton, C. A.; Mills, M. F.; Gilbert, R. G.; Napper, D. H. Spatial inhomogeneities in emulsion polymerizations: Repulsive wall calculations. Macromolecules 1993, 26, 3563. (25) Tobita, H.; Takada, Y.; Nomura, M. Molecular weight distribution in emulsion polymerization. Macromolecules 1994, 27, 3804. (26) O’Driscoll, K. F.; Kuindersma, M. E. Monte Carlo simulation of pulsed laser polymerization. Macromol. Theory Simul. 1994, 3, 469. (27) Willemse, R. X. E. New insights into free-radical (co)polymerization kinetics. Ph.D. Dissertation, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 2005. (28) Schlu¨ssler, K. H.; Walter, L. Computer simulation of randomly packed spheres - A tool for investigating polydisperse materials. Part. Charact. 1986, 3, 129. (29) Kirsch, S.; Pfau, A.; Ha¨dicke, E.; Leuninger, J. Interface and bulk properties in films of phase separated dispersions. Prog. Org. Coat. 2002, 45, 193. (30) Prescott, S. W. Chain-length dependence in living/controlled freeradical polymerizations: Physical manifestation and Monte Carlo simulation of reversible transfer agents. Macromolecules 2003, 36, 9608. (31) Nie, L.; Yang, W.; Zhang, H.; Fu, S. Monte Carlo simulation of microemulsion polymerization. Polymer 2005, 46, 3175. (32) Fitch, R. M. Polymer Colloids: A ComprehensiVe Introduction; Academic Press: London, 1997. (33) Green, N. J. B. On the simulation of diffusion processes close to boundaries. Mol. Phys. 1988, 65, 1399. (34) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. A. Particle deposition and aggregation. Measurement, modelling and simulation; Butterworth-Heinemann: Woburn, 1995. (35) Adcock, S. A.; McCammon, J. A. Molecular Dynamics: Survey of methods for simulating the activity of proteins. Chem. ReV. 2006, 106, 1589. (36) Chen, J. C.; Kim, A. S. Brownian Dynamics, Molecular Dynamics and Monte Carlo modeling of colloidal systems. AdV. Colloid Interface Sci. 2004, 112, 159. (37) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (38) Smoluchowski, M. v. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lo¨sungen. Z. Phys. Chem. 1917, 92, 129. (39) Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Taylor & Francis: Washington, DC, 1989. (40) Kim, A. S.; Chen, H. Diffusive tortuosity factor of solid and soft cake layers: A random walk simulation approach. J. Membr. Sci. 2006, 279, 129. (41) Islam, M. A. Einstein-Smoluchowski Diffusion equation: A discussion. Phys. Scr. 2004, 70, 120. (42) Tyuzyo, K.; Harada, Y. On the distance between particles in synthetic polymer emulsions. Colloid Polym. Sci. 1965, 201, 66.

ReceiVed for reView January 18, 2007 ReVised manuscript receiVed April 2, 2007 Accepted April 18, 2007 IE070115C