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The Anomalous Einstein-Stokes Behaviour of Oxygen and Other Low Molecular Weight Diffusants

  • Michael McCabe
  • David J. Maguire
  • Nicholas A. Lintell
Conference paper
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 566)

Abstract

Almost a century ago, Einstein and Sutherland independently derived equations that describe the relationship between diffusion of solutes and the molecular parameters of those solutes. In that time it has been recognized that, although the equations adequately describe the diffusion of large and medium-sized molecules, there is deviation from this relationship for small molecules. Many authors have attempted to redefine the equations for diffusion, with varying degrees of success, but generally have not attempted to consider the fundamental events that may be occurring at the molecular level during the diffusion of small molecules. In this presentation, we attempt to provide such an explanation, particularly with respect to the diffusion of oxygen through water. We consider the possibility of a random rotational model that complements the (slower) translational process of traditional diffusion and thereby provides accelerated diffusion of small molecules. It is hoped that our description of this model may provide a basis for the development of mathematical modelling of the process.

Keywords

Translational Diffusion Tritiated Water Hydrogen Fluoride Oxygen Oxygen Water Nitrogen 
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.

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References

  1. 1.
    G. T. Evans, Force correlation and the diffusion coefficient of water, J. Chem. Phys. 117, 11284–11291 (2002).CrossRefGoogle Scholar
  2. 2.
    A. Einstein, Uber die von der molekular-kineticshen theorie der warme geforderte bewegung von in ruhenden flussigkeiten suspendierten teilchen, Ann. Physik. 17, 549–560 (1905).Google Scholar
  3. 3.
    A. Einstein, Elementare theorie der brownschen bewegung, Zeilschrift für Elektochemie XIV, 235–239 (1908).Google Scholar
  4. 4.
    W. Sutherland, A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin, Philos. Mag. 9, 781–785 (1905).Google Scholar
  5. 5.
    R. Mills, Self-diffusion in normal and heavy water in the range 1–45 degrees, J. Phys. Chem. 77, 685–688.Google Scholar
  6. 6.
    A. K. Harrison, and R. Zwanzig, Transport on a dynamically disordered lattice, Phys. Rev. A, 32(2), 1072–1075 (1985).PubMedCrossRefGoogle Scholar
  7. 7.
    G. Phillies, Translational diffusion coefficient of macroparticles in solvents of high viscosity, J. Phys. Chem. 85, 2838–2843 (1981).CrossRefGoogle Scholar
  8. 8.
    L. A. Bunimovitch, and G. S. Ya, Statistical properties of the Lorentz gas with a periodic configuration of scatterers, Comm. Math. Phys. 78, 479–497 (1980).CrossRefGoogle Scholar
  9. 9.
    M. McCabe, and T. C. Laurent, Diffusion of oxygen, nitrogen and water in hyluronate solutions, Biochem. Biophys. Acta. 399, 131–138 (1975).PubMedGoogle Scholar
  10. 10.
    M. McCabe, and D. J. Maguire, The measurement of the diffusion coefficient of oxygen thorough small volumes of viscous solution: implications for the flux of oxygen through tissues, Adv. Exp. Med. Biol. 316, 467–473 (1992).PubMedGoogle Scholar
  11. 11.
    M. McCabe, The diffusion coefficient of caffeine through agar gels containing a hyaluronic acid-protein complex. A model system for the study of the permeability of connective tissues, Biochem. J. 127, 249–253 (1972).PubMedGoogle Scholar
  12. 12.
    R. B. Setlow, and E. C. Pollard, Molecular Physics (Addison-Wesley Publishing Co., Massachusetts, 1962).Google Scholar
  13. 13.
    K. Krynicki, C. D. Green, and D. W. Sawyer, Pressure and temperature-dependence of self-diffusion in water, Faraday Discuss. 66, 199–208 (1978).CrossRefGoogle Scholar
  14. 14.
    H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, and J. Hermans, Interaction models of water in relation to protein hydration. In Intermolecular Forces: Proceedings of the Fourteenth Jerusalem Symposium on Quantum Chemistry and Biochemistry. B. Pullman, editor, (D. Reidel Publishing Company, Dordrecht, The Netherlands) pp. 331–342 (1981).Google Scholar
  15. 15.
    Y. X. Yu, and G. H. Gao, Study on self-diffusion in water, alcohols and hydrogen fluoride by the statistical associating fluid theory, Fluid Phase Equilib. 179, 165–179 (2001).CrossRefGoogle Scholar
  16. 16.
    J. Jordan, E. Ackerman, and R. L. Berger, Polarographic Diffusion Coefficients of Oxygen Defined by Activity Gradients in Viscous Media J. Am. Chem. Soc. 78(13), 2979–2983 (1956).CrossRefGoogle Scholar
  17. 17.
    R. Castillo, C. Garza, and S. Ramos, Brownian Motion at the Molecular Level in Liquid Solutions of C60, J. Phys. Chem. 98, 4188–4190 (1994).CrossRefGoogle Scholar
  18. 18.
    G. L. Pollack, R. P. Kennan, J. F. Himm, and D. R. Stump, Diffusion of xenon in liquid alkanes: Temperature dependence measurements with a new method. Stokes-Einstein and hard sphere theories, J. Chem. Phys. 92, 625–630 (1990).CrossRefGoogle Scholar
  19. 19.
    B. A. Kowert, K. T. Sobush, N. C. Daug, G. L. Seck, C. F. Fukua, and C. L. Mapes, Diffusion of dioxygen in 1-alkenes and biphenyl in perfluoro-n-alkanes, Chem. Phys. Lett. 353, 95 (2002).CrossRefGoogle Scholar
  20. 20.
    R. K. Murarka, S. Bhattacharyya, and B. Bagchi, Diffusion of small light particles in a solvent of large massive molecules, J. Chem. Phys. 117, 10730–10738 (2002).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Michael McCabe
  • David J. Maguire
  • Nicholas A. Lintell

There are no affiliations available

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