Skip to main content
SpringerLink
Log in

Many-body effects in diffusion-limited kinetics

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We review a novel approach to treating many-body effects in diffusion-limited kinetics. The derivation of the general expression for the survival probability of a Brownian particle in the presence of randomly distributed traps is given. The reduction of this expression to both the Smoluchowski solultion and the wellknown asymptotic behavior is demonstrated. It is shown that the Smoluchowski solution gives a lower bound for the particle survival probability. The correction to the Smoluchowski solution which takes into account the particle death slowdown in the initial process stage is described. The steady-state rate-constant concentration dependence and the reflection of many-body effects in it are discussed in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. von Smoluchowski,Phys. Z. 17:557–585 (1916).

    Google Scholar 

  2. S. A. Rice,Diffusion-Limited Reactions (Elsevier, Amsterdam, 1985).

    Google Scholar 

  3. A. A. Ovchinnikov, S. F. Timashev, and A. A. Belyy,Kinetics of Diffusion-Controlled Chemical Processes (Nova Science Publishers, New York, 1989).

    Google Scholar 

  4. A. Blumen, J. Klafter, and G. Zumofen, inOptical Spectroscopy of Glasses, I. Zschokke, ed. (Reidel, Dordrecht, 1986), p. 199.

    Google Scholar 

  5. A. Szabo,J. Phys. Chem. 93:6929 (1989).

    Google Scholar 

  6. J. Keizer,Chem. Rev. 87:167 (1987).

    Google Scholar 

  7. G. H. Weiss,J. Stat. Phys. 42:3 (1986).

    Google Scholar 

  8. U. M. Gösele,Progr. React. Kinet. 13:63 (1984).

    Google Scholar 

  9. D. F. Calef and J. M. Deutch,Annu. Rev. Phys. Chem. 34:493 (1983).

    Google Scholar 

  10. A. M. Berezhkovskii, Yu. A. Makhnovskii, and R. A. Suris,Khim. Fiz. 8:833 (1989).

    Google Scholar 

  11. A. M. Berezhkovskii, Yu. A. Makhnovskii, and R. A. Suris,Chem. Phys. 137:41 (1989).

    Google Scholar 

  12. A. M. Berezhkovskii, Yu. A. Makhnovskii, and G. E. Chudinov,Chem. Phys. Lett. 161:512 (1989).

    Google Scholar 

  13. A. M. Berezhkovskii and Yu. A. Makhnovskii,Chem. Phys. Lett. 161:512 (1989).

    Google Scholar 

  14. M. Tachiya,Radiat. Phys. Chem. 21:167 (1983).

    Google Scholar 

  15. A. Szabo, R. Zwanzig, and N. Agmon,Phys. Rev. Lett. 61:2496 (1989).

    Google Scholar 

  16. I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur,Vvedenie v Teoriu Neuporyadochennykh System (Nauka, Moscow, 1982).

    Google Scholar 

  17. J. M. Ziman,Models of Disorder (Cambridge University Press, Cambridge, 1979).

    Google Scholar 

  18. B. Ya. Balagurov and V. G. Vaks,Zh. Eksp. Theor. Fiz. 65:1939 (1973) [Sov. Phys. JETP 38:968 (1984)].

    Google Scholar 

  19. M. D. Donsker and S. R. S. Varadhan,Comm. Pure Appl. Math. 28:525 (1975).

    Google Scholar 

  20. A. A. Ovchinnikov and Ya. B. Zeldovich,Chem. Phys. 28:215 (1975).

    Google Scholar 

  21. P. Grassberger and I. Procaccia,J. Chem. Phys. 77:6281 (1982).

    Google Scholar 

  22. R. K. Kayser and J. B. Hubbard,Phys. Rev. Lett. 51:79 (1983).

    Google Scholar 

  23. M. Kac,Probability and Related Topics in the Physical Sciences (Interscience, New York, 1958).

    Google Scholar 

  24. L. S. Shulman,Techniques and Applications of Path Integration (Wiley, New York, 1981).

    Google Scholar 

  25. B. B. Mandelbrot,The Fractal Geometry of Nature (Freeman, New York, 1983).

    Google Scholar 

  26. G. H. Weiss and R. J. Rubin,Adv. Chem. Phys. 52:363 (1983).

    Google Scholar 

  27. A. M. Berezhkovskii, Yu. A. Makhnovskii, and R. A. Suris,J. Stat. Phys. 57:333 (1989).

    Google Scholar 

  28. M. Bixon and R. Zwanzig,J. Chem. Phys. 75:2354 (1981).

    Google Scholar 

  29. W. Feller,An Introduction to the Probability Theory and Its Applications, Vol. 2 (Wiley, New York, 1970).

    Google Scholar 

  30. C. W. Gardiner,Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1985).

    Google Scholar 

  31. M. Abramovitz and I. A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1964).

    Google Scholar 

  32. K. Mattern and B. U. Felderhof,Physica A 135:505 (1986).

    Google Scholar 

  33. A. M. Berezhkovskii and A. Szabo, to be published.

  34. A. M. Berezhkovskii, Yu. A. Makhnovskii, and R. A. Suris, to be published.

  35. A. M. Berezhkovskii, Yu. A. Makhnovskii, and R. A. Suris,Zh. Eksp. Teor. Fiz. 91:2190 (1986) [Sov. Phys. JETP 64:1301 (1986)].

    Google Scholar 

  36. M. Bramson and J. L. Lebowitz,Phys. Rev. Lett. 61:2397 (1988).

    Google Scholar 

  37. M. Bramson and J. L. Lebowitz,Physica A 168:88 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Karpov Institute of Physical Chemistry, K-64, 103064, Moscow, USSR

    A. M. Berezhkovskii, Yu. A. Makhnovskii & R. A. Suris

Authors
  1. A. M. Berezhkovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. A. Makhnovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. A. Suris
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berezhkovskii, A.M., Makhnovskii, Y.A. & Suris, R.A. Many-body effects in diffusion-limited kinetics. J Stat Phys 65, 1025–1041 (1991). https://doi.org/10.1007/BF01049596

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01049596

Key words

Search

Navigation