Bulletin of the Korean Chemical Society

Korean Chemical Society (대한화학회)
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Point Particle Approximation for Single and Two Species Diffusion-Influenced Reactions

  • Received : 2013.02.08
  • Accepted : 2013.02.16
  • Published : 2013.05.20
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Abstract

The fluctuations in concentrations of reactants dominate the long-time dynamics of the single (A + A ${\rightarrow}$ 0) and two species (A + B ${\rightarrow}$ 0) diffusion-influenced annihilation reactions. Although hierarchical Smoluchowski approaches can provide a systematic and flexible framework to deal with the fluctuation effects, their results are too complicated to be analytically solved. For the efficient numerical calculation of the complicated fluctuation effect terms, we show that the presented point particle approximation is not only practical but also quite accurate for most conditions in diffusion-influenced reaction systems.

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References

  1. Ovchinnikov, A. A.; Zeldovich, Y. B. Chem. Phys. 1978, 28, 215. https://doi.org/10.1016/0301-0104(78)85052-6
  2. Toussaint, D.; Wilczek, F. J. Chem. Phys. 1983, 78, 2642. https://doi.org/10.1063/1.445022
  3. Kang, K.; Redner, S. Phys. Rev. Lett. 1984, 52, 955. https://doi.org/10.1103/PhysRevLett.52.955
  4. Monson, E.; Kopelman, R. Phys. Rev. Lett. 2000, 85, 666. https://doi.org/10.1103/PhysRevLett.85.666
  5. Waite, T. R. Phys. Rev. 1957, 107, 463. https://doi.org/10.1103/PhysRev.107.463
  6. Lee, S.; Karplus, M. J. Chem. Phys. 1987, 86, 1883. https://doi.org/10.1063/1.452140
  7. Kuzovkov, V.; Kotomin, E. Rep. Prog. Phys. 1988, 51, 1479. https://doi.org/10.1088/0034-4885/51/12/001
  8. Kim, H.; Shin, K. J. Phys. Rev. E 2000, 61, 3426. https://doi.org/10.1103/PhysRevE.61.3426
  9. Kim, H.; Shin, S.; Shin, K. J. J. Chem. Phys. 1998, 108, 5861. https://doi.org/10.1063/1.476502
  10. Kim, H.; Shin, S.; Shin, K. J. Chem. Phys. Lett. 1998, 291, 341. https://doi.org/10.1016/S0009-2614(98)00604-6
  11. Kim, H. Chem. Phys. Lett. 2010, 484, 358. https://doi.org/10.1016/j.cplett.2009.11.033
  12. Smoluchowski, M. Z. Phys. Chem. (Leipzig) 1917, 92, 129.
  13. Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids, 2nd ed.; Oxford University Press: New York, 1986.
  14. Kotomin, E.; Kuzovkov, V.; Frank, W.; Seeger, A. J. Phys. A 1994, 27, 1453. https://doi.org/10.1088/0305-4470/27/5/012
  15. Lee, J.; Sung, J.; Lee, S. J. Chem. Phys. 2000, 113, 8686. https://doi.org/10.1063/1.1318738
  16. Park, J.; Kim, H.; Shin, K. J. J. Chem. Phys. 2003, 118, 9697. https://doi.org/10.1063/1.1570409
  17. Seki, K.; Wojcik, M.; Tachiya, M. J. Chem. Phys. 2011, 134, 094506. https://doi.org/10.1063/1.3560419
  18. Torney, D. C.; McConnell, H. M. J. Phys. Chem. 1983, 87, 1941. https://doi.org/10.1021/j100234a023
  19. McQuarrie, D. A. Statistical Mechanics; Harper and Row: New York, 1976.