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http://dx.doi.org/10.5012/jkcs.2008.52.3.217

Kinetics of Catalytic Reactions Occurring in a Small Reaction Volume  

Kim, Jung-Han (Department of Chemistry, Chung-Ang University)
Sung, Jae-Young (Department of Chemistry, Chung-Ang University)
Publication Information
Abstract
We investigate the kinetics of diffusion-influenced catalytic reactions occurring in small reaction volume. From a simple exact model study, we find that the reaction rate coefficient decreases with the size of reaction volume. The explicit expression for the average reaction rate constant is presented, which can be regarded as a generalization of well-known Collins-Kimball rate constant into the reactions occurring in a small reaction volume. It turns out that the traditional diffusion influenced reaction dynamics is followed by a single exponential relaxation phase with a rate constant dependent on the reaction volume for the catalytic reactions occurring in small reaction volumes.
Keywords
Diffusion-Influenced Kinetics; Small Reaction Volume; Size Effects; Catalytic Reactions
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1 E. M. Ozbudak et al., Regulation of noise in the expression of a single gene. Nature Genetics. 2002, 31, 69-73   DOI   ScienceOn
2 J. T. Mettetal et al. Predicting stochastic gene expression dynamics in single cells. Proc. Natl. Acad. Sci. 2006, 103, 7304-7309   DOI   ScienceOn
3 N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992
4 D. T. Gillespie, The chemical Langevin equation J. Chem. Phys. 2000, 113, 297-306   DOI   ScienceOn
5 D. A. McQuarrie. Stochastic Approach to Chemical Kinetics, J. Appl. probab. 1967, 4, 413-478   DOI   ScienceOn
6 H. H. McAdams and A. Arkin. Stochastic mechanism in gene expression. Proc. Natl. Acad. Sci. USA 1997, 94, 814-819   DOI   ScienceOn
7 J. I. Steinfeld, Chemical Kinetics and Dynamics 2nd. Ed. (Prentice-Hall, New York: Plenum, 1999)
8 T. Dwars, E. Paetzold, and Gunther Oehme, Reactions in Micellar Systemsl. Angew. Chem. Int. Ed. 2005, 44, 7174-7199   DOI   ScienceOn
9 J. T. Mettetal and A. van Oudenaarden, Science 2007, 317, 463-464   DOI   ScienceOn
10 H. H. McAdams and A. Arkin. Genetic regulation at the nanomolar scale. Trends Genet. 1999, 15, 65-69   DOI   ScienceOn
11 T. S. Gardner, C. R. Cantor, and J. J. Collins. Construction of a genetic toggle switch in Escherichia coli. Nature, 2000, 403, 339-342   DOI   ScienceOn
12 K. Jahnisch, V. Hessel, H. Lowe, and M. Baerns, Chemistry in Microstructured Reactors. Angew. Chem. Int. Ed. 2004, 43, 406-446   DOI   ScienceOn
13 D. T. Gillespie. A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. J. Comput. Phys. 1976, 22, 403-434   DOI   ScienceOn
14 M. Thattai and A. van Oudenaarden, Intrinsic noise in gene regulatory networks. PNAS. 2001, 98, 8614-8619   DOI   ScienceOn
15 S. A. Rice, in Diffusion-Limitted Reactions, edited by C. H. Bamford, C. F. H. Tipper, and R. G. Compton, Comprehensive Chemical Kinetics Vol. 25 (Elsevier, Amsterdam, 1985)
16 H. Song, J. D. Tice, and R. F. Ismagilov, A Microfluidic System for Controlling Reaction Networks in Time. Angew. Chem. Int. Ed. 2003, 42, 767-772