Electrophoresis

Electrophoresis is the most well-known electrokinetic phenomenon. It was discovered by Reuss in 1807.[1] He observed that clay particles dispersed in water migrate under influence of an applied electric field. There are detailed descriptions of Electrophoresis in many books on Colloid and Interface Science.[2][3][4][5][6][7] There is an IUPAC[[1]]] Technical Report[8] prepared by a group of well known experts on the electrokinetic phenomena. Generally, electrophoresis is the motion of dispersed particles relative to a fluid under the influence of an electric field that is space uniform. Alternatively, similar motion in a space non-uniform electric field is called dielectrophoresis.

Electrophoresis.gif

Electrophoresis occurs because particles dispersed in a fluid almost always carry an electric surface charge. An electric field exerts electrostatic Coulomb force on the particles through these charges. Recent molecular dynamics simulations, though, suggest that surface charge is not always necessary for electrophoresis and that even neutral particles can show electrophoresis due to the specific molecular structure of waterer at the interface.[9]

The electrostatic Coulomb force exerted on a surface charge is reduced by an opposing force which is electrostatic as well. According to double layer theory, all surface charges in fluids are screened by a diffuse layer. This diffuse layer has the same absolute charge value, but with opposite sign from the surface charge. The electric field induces force on the diffuse layer, as well as on the surface charge. The total value of this force equals to the first mentioned force, but it is oppositely directed. However, only part of this force is applied to the particle. It is actually applied to the ions in the diffuse layer. These ions are at some distance from the particle surface. They transfer part of this electrostatic force to the particle surface through viscous stress. This part of the force that is applied to the particle body is called electrophoretic retardation force.

There is one more electric force, which is associated with deviation of the double layer from spherical symmetry and surface conductivity due to the excess ions in the diffuse layer. This force is called the electrophoretic relaxation force.

All these forces are balanced with hydrodynamic friction, which affects all bodies moving in viscous fluids with low Reynolds number. The speed of this motion v is proportional to the electric field strength E if the field is not too strong. Using this assumption makes possible the introduction of electrophoretic mobility μe as coefficient of proportionality between particle speed and electric field strength:

\mu_e = {v \over E}

Multiple theories were developed during 20th century for calculating this parameter. Ref. 2 provides an overview.

Contents

Theory

Retardation.gif

The most known and widely used theory of electrophoresis was developed by Smoluchowski in 1903 [10]

\mu_e = \frac{\varepsilon\varepsilon_0\zeta}{\eta},

where ε is the dielectric constant of the dispersion medium, ε0 is the permittivity of free space (C² N-1 m-2), η is dynamic viscosity of the dispersion medium (Pa s), and ζ is zeta potential (i.e., the electrokinetic potential of the slipping plane in the double layer).

Smoluchowski theory is very powerful because it works for dispersed particles of any shape and any concentration, when it is valid. Unfortunately, it has limitations of its validity. It follows, for instance, from the fact that it does not include Debye length κ-1. However, Debye length must be important for electrophoresis, as follows immediately from the Figure on the right. Increasing thickness of the DL leads to removing point of retardation force further from the particle surface. The thicker DL, the smaller retardation force must be.

Detailed theoretical analysis proved that Smoluchowski theory is valid only for sufficiently thin DL, when Debye length is much smaller than particle radius a:

{\kappa}a >>1

This model of "thin Double Layer" offers tremendous simplifications not only for electrophoresis theory but for many other electrokinetic theories. This model is valid for most aqueous systems because the Debye length is only a few nanometers there. It breaks only for nano-colloids in solution with ionic strength close to water

Smoluchowski theory also neglects contribution of surface conductivity. This is expressed in modern theory as condition of small Dukhin number

Du <<1

Creation of electrophoretic theory with wider range of validity was a purpose of many studies during 20th century.

One of the most known considers an opposite asymptotic case when Debye length is larger than particle radius:

{\kappa}a <1

It is called the "thick Double Layer" model. Corresponding electrophoretic theory was created by Huckel in 1924 [11]. It yields the following equation for electrophoretic mobility:

\mu_e = \frac{2\varepsilon\varepsilon_0\zeta}{3\eta},

This model can be useful for some nano-colloids and non-polar fluids, where Debye length is much larger.

There are several analytical theories that incorporate surface conductivity and eliminate restriction of the small Dukhin number. Early pioneering work in that direction dates back to Overbeek [12] and Booth [13].

Modern, rigorous theories that are valid for any Zeta potential and often any κa, stem mostly from the Ukrainian (Dukhin, Shilov and others) and Australian (O'Brien, White, Hunter and others) Schools.

Historically the first one was Dukhin-Semenikhin theory [14]. Similar theory was created 10 years later by O'Brien and Hunter [15]. Assuming thin Double Layer, these theories would yield results that are very close to the numerical solution provided by O'Brien and White [16].

Notes

  1. ↑ Reuss, F.F. Mem.Soc.Imperiale Naturalistes de Moscow, 2, 327 1809
  2. ↑ Lyklema, J. “Fundamentals of Interface and Colloid Science”, vol.2, page.3.208, 1995
  3. ↑ Hunter, R.J. "Foundations of Colloid Science", Oxford University Press, 1989
  4. ↑ Dukhin, S.S. & Derjaguin, B.V. "Electrokinetic Phenomena", J.Willey and Sons, 1974
  5. ↑ Russel, W.B., Saville, D.A. and Schowalter, W.R. “Colloidal Dispersions”, Cambridge University Press,1989
  6. ↑ Kruyt, H.R. “Colloid Science”, Elsevier: Volume 1, Irreversible systems, (1952)
  7. ↑ Dukhin, A.S. and Goetz, P.J. "Ultrasound for characterizing colloids", Elsevier, 2002
  8. ↑ ”Measurement and Interpretation of Electrokinetic Phenomena”, International Union of Pure and Applied Chemistry, Technical Report, published in Pure Appl.Chem., vol 77, 10, pp.1753-1805, 2005
  9. ↑ Knecht et al., J. Col. Int. Sc. 318, p. 477, 2008
  10. ↑ M. von Smoluchowski, Bull. Int. Acad. Sci. Cracovie, 184 (1903)
  11. ↑ Huckel, E., Physik.Z., 25, 204 (1924)
  12. ↑ Overbeek, J.Th.G., Koll.Bith, 287 (1943)
  13. ↑ Booth, F. Nature, 161, 83 (1948)
  14. ↑ Dukhin, S.S. and Semenikhin, N.M. Koll.Zhur., 32, 366 (1970)
  15. ↑ O'Brien, R.W. and Hunter, R.J. Can.J.Chem., 59, 1878 (1981)
  16. ↑ O'Brien, R.W. and White, L.R. J.Chem.Soc.Faraday Trans. 2, 74, 1607, (1978)

References

See also

External links