Advertisement

Bimolecular Diffusion-Limited Reaction Kinetics at Steady-State

  • Eric Clement
  • Leonard Sander
  • Raoul Kopelman
Part of the NATO ASI Series book series (NSSB, volume 258)

Abstract

Physics of condensed matter offers numerous examples of reactive systems where the transport of reactants such as atoms, molecules or any localized excitation, is of the diffusive type. In general these systems exhibit two distinct time scales. One is a typical time of reaction between reactants and the other is a characteristic time associated with the microscopic erratic movements of the particles, often referred to as a time of jump The limiting process is calleddiffusion limited when at the time scale characterizing a microscopic jump, particles seem to react “instantaneously” when they are in contact at a microscopic distance (reaction radius). Bimolecular diffusion-limited reactions of the type Ai+Aj->Product, where Aiand Ajare distinct or similar rectants, are extensively investigated since they represent many important physical situations. The product formed by the reaction can be an aggregate, a third particle Ak, a particle Ai or Aj, or both particles may annihilate in pairs and leave the system. The range of applications spanned by these models covers particle aggregation, gelation of sols, coalescence of aerosols, electron-hole recombination in semi-conductors, soliton-antisoliton annihilation in polymers, exciton fusion in molecular crystals, etc…. Classically, the point of view associated with these different physical situations is essentially the same.

Keywords

Percolation Cluster Conservation Constraint Steady State Density Reaction Radius Distinct Time Scale 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Blumen, J. Klafter and G. Zumofen, inOptical Spectrocopy of glasses, ed. I. Zschokke (Reidel Publ. Co., Dordrecht, Holland(1986)).Google Scholar
  2. 2.
    R. Kopelman, Science241, 1620 (1988).CrossRefGoogle Scholar
  3. 3. a)
    E. Clement, L. M. Sander and R. Kopelman, Phys.Rev.A39, 6455 (1989)CrossRefGoogle Scholar
  4. b).
    E. Clément, L. M. Sander and R. Kopelman, Phys.Rev.A39, 6466 (1989).CrossRefGoogle Scholar
  5. 4.
    E. Clément, L. M. Sander and R. Kopelman, Phys.Rev.A39, 6472 (1989).CrossRefGoogle Scholar
  6. 5.
    E. Clément, L. M. Sander and R. Kopelman, Euro.Phys.Lett.ll (8), 707 (1990).CrossRefGoogle Scholar
  7. 6.
    E. Clement, L. M. Sander and R. Kopelman, to be published in Chemu Phys (1990).Google Scholar
  8. 7. a)
    S. Alexander and R. Orbach, J. Physique Lett.,43, 625 (1982).CrossRefGoogle Scholar
  9. b).
    R. Rammal and G. Toulouse, J. Physique. Lett.,54, 44, L13 (1983).CrossRefGoogle Scholar
  10. 8.
    P. G. de Gennes, J. Chem. Phys.76, 3316 (1982).CrossRefGoogle Scholar
  11. 9.
    Von Smoluckowski, Z.Phys. Chem.29, 129 (1917).Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Eric Clement
    • 1
  • Leonard Sander
    • 2
  • Raoul Kopelman
    • 3
  1. 1.Laboratoire d’Optique de la Matière CondenséeUniv. Pierre et Marie CurieParisFrance
  2. 2.Department of PhysicsUniversity of MichiganAnn ArborUSA
  3. 3.Deparment of ChemistryUniversity of MichiganAnn ArborUSA

Personalised recommendations