A Fundamental Question About Electrical Potential Profile in Interfacial Region of Biological Membrane Systems

  • V. S. Vaidhyanathan


It is generally presumed, that if a plane plate is positively charged, its potential is positive and that if a plate contains an excess of negative charges, its potential is negative. One may assume that the distribution of positive and negative ions, near a surface with an excess of fixed negative charges, is similar to the schematic representation presented in Figure 1a. In Figure 1 b, are presented the corresponding plots of charge density, and a function \( Y(x) = - 4\pi e\sum\limits_{\sigma } {{z_{\sigma }}{c_{\sigma }}(x)} \), where Zσ is the signed valence charge number of ions of kind σ, and cσ(x) is its number density (concentration in a small volume element) at location x. e is the protonic charge and \( Y(x) = \in (x)\phi ''(x) + \in '(x) \), where <Emphasis Type=“NonProportional”>E</Emphasis>(x) is the value of the dielectric coefficient at x, and <Emphasis Type=“NonProportional”>E</Emphasis>′(x) = [d<Emphasis Type=“NonProportional”>E</Emphasis>/dx] is its first differential with respect to position variable x. ∅(x) is the value of electric potential felt by a unit charge placed at x. ∅′(x) and ∅″(x) are respectively the first and second differentials of ∅, with respect to x. If the above stated statements are valid, then one may presume that the electric potential profile in interfacial regions, will be similar to the schematic plot ∅(x), presented in Figure 1 c.


Interfacial Region Electrolyte System Taylor Coefficient Inhomogeneous Region Molecular Integral 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J.G. Kirkwood and I. Oppenheim, ‘Chemical Thermodynamics’ McGraw Hill Book Co. New York, (1961).Google Scholar
  2. 2.
    T.L.Hill, in ‘Membrane Phenomena’ Disc. Faraday Society, (1956) p.31.Google Scholar
  3. 3.
    R.H.Fowler and E.A.Guggenheim, ‘Statistical Thermodynamics’ Cambridge University Press, New York, (1939).Google Scholar
  4. 4.
    E.J.W.Verwey and Th.G.Overbeek, ‘Theory of Stability of Lyophobic Colloids’ Elsevier Publishing Co. New York (1945) p. 31.Google Scholar
  5. 5.
    N.Lakshminarayaniah, ‘Transport Phenomena in Membranes’ Academic Press, New York, (1969).Google Scholar
  6. 6.
    S.Rice and M.Nagasawa, ‘Polyelectrolyte Solutions’ Academic Press, New York, (1961).Google Scholar
  7. 7.
    D.Agin, in ‘Foundations of Mathematical Biology’ R.Rosen editor, Academic Press, New York, (1971) vol. 1.Google Scholar
  8. 8.
    H.R.Leuchtag and H.M.Fishman, in ‘Structure and Function in Excitable Cells’ edited by Chang, Tasaki, Adelman and Leuchtag, Plenum Publishing Copn. New York, (1983).Google Scholar
  9. 9.
    H.R.Kruyt, ‘Colloid Science’ Elsevier Publ.Corpn. Amsterdam, (1952).Google Scholar
  10. 10.
    D.C.Grahame, Chem. Reviews, 41 441 (1947).CrossRefGoogle Scholar
  11. 11.
    V.S.Vaidhyanathan, Colloids and Surfaces, 6 291–306 (1983).CrossRefGoogle Scholar
  12. 12.
    F.J.Booth, J.Chem. Phys., 19, 39, 327 (1951).Google Scholar
  13. 13.
    V.S.Vaidhyanathan, J. Biol. Phys., 10, 153, 167 (1982).CrossRefGoogle Scholar
  14. 14.
    V.S.Vaidhyanathan, in ‘Topics in Bioelectrochemistry and Bioenergetics’ G.Milazzo, editor, John Wiley & Sons, London, (1976) vol.1, p.287–378. also, Bioelectrochemistry and Bioenergetics, 5 754–775 (1978).Google Scholar
  15. 15.
    T.L.Hill, ‘Introduction to Statistical Thermodynamics’ Addison Wesley Publishing Co., Reading, Mass. (1960).Google Scholar
  16. 16.
    W.G.McMillan and J.E.Mayer, J. Chem. Phys., 13, 276 (1945).CrossRefGoogle Scholar
  17. 17.
    J.G.Kirkwood and F.P.Buff, J. Chem. Phys., 19 774 (1951).CrossRefGoogle Scholar
  18. 18.
    V.S.Vaidhyanathan, Bioelectrochemistry and Bioenergetics, 12, 105–118 (1984).CrossRefGoogle Scholar
  19. 19.
    V.S.Vaidhyanathan, Bioelectrochemistry and Bioenergetics, 7, 25–30 (1980).CrossRefGoogle Scholar
  20. 20.
    V.S.Vaidhyanathan, in ‘Bioelectrochemistry:Ions, Surfaces and Membranes’ M.Blank, editor, Advances in Chemistry Series, 188, 313–336 (1980).CrossRefGoogle Scholar
  21. 21.
    V.S. Vaidhyanathan, Bull. Math. Biology, 41, 365–385 (1979).Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • V. S. Vaidhyanathan
    • 1
  1. 1.Department of Biophysical Sciences School of MedicineState University of New York at BuffaloBuffaloUSA

Personalised recommendations