Electrophoresis
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2008-06-29T22:28:20Z
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''For specific types of electrophoresis (for example, the process of administering medicine, [[iontophoresis]]), see [[electrophoresis (disambiguation)]].''
'''Electrophoresis''' is the most known [[electrokinetic phenomena|electrokinetic phenomenon]]. It was discovered by Reuss in 1809.<ref>Reuss, F.F. ''Mem.Soc.Imperiale Naturalistes de Moscow'', 2, 327 1809</ref> 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.<ref> Lyklema, J. “Fundamentals of Interface and Colloid Science”, vol.2, page.3.208, 1995</ref><ref>Hunter, R.J. "Foundations of Colloid Science", Oxford University Press, 1989</ref><ref>Dukhin, S.S. & Derjaguin, B.V. "Electrokinetic Phenomena", J.Willey and Sons, 1974</ref><ref>Russel, W.B., Saville, D.A. and Schowalter, W.R. “Colloidal Dispersions”, Cambridge University Press,1989</ref><ref>Kruyt, H.R. “Colloid Science”, Elsevier: Volume 1, Irreversible systems, (1952)</ref><ref>Dukhin, A.S. and Goetz, P.J. "[[Ultrasound]] for characterizing colloids", Elsevier, 2002</ref> There is an IUPAC Technical Report<ref>”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</ref> prepared by a group of most known world 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]].
[[Image:electrophoresis.gif|thumb|300px|]]
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 water at the interface.<ref>Knecht et al., J. Col. Int. Sc. 318, p. 477, 2008</ref>
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 (physics)|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 excees 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]] μ<sub>e</sub> as coefficient of proportionality between particle speed and electric field strength:
:<math>\mu_e = {v \over E}</math>
Multiple theories were developed during 20th century for calculating this parameter. Ref. 2 provides an overview.
==Theory==
[[Image:retardation.gif|thumb|300px|]]
The most known and widely used theory of electrophoresis was developed by [[Smoluchowski]] in 1903 <ref> M. von Smoluchowski, Bull. Int. Acad. Sci. Cracovie, 184 (1903)</ref>
:<math>\mu_e = \frac{\varepsilon\varepsilon_0\zeta}{\eta}</math>,
where ε is the [[dielectric constant]] of the [[dispersion medium]], ε<sub>0</sub> is the [[Vacuum permittivity|permittivity of free space]] (C² N<sup>-1</sup> m<sup>-2</sup>), 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<sup>-1</sup>. 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.
Detail theoretical analysis proved that Smoluchowski theory is valid only for sufficiently thin DL, when [[Debye length]] is much smaller than particle radius ''a'':
:<math> {\kappa}a >>1 </math>
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]]
:<math> Du <<1 </math>
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:
:<math> {\kappa}a <1 </math>
It is "thick Double Layer" model. Corresponding electrophoretic theory was created by Huckel in 1924 <ref> Huckel, E., ''Physik.Z., 25, 204 (1924)</ref>. It yields following equation for electrophoretic mobility:
:<math>\mu_e = \frac{2\varepsilon\varepsilon_0\zeta}{3\eta}</math>,
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 <ref> Overbeek, J.Th.G., ''Koll.Bith'', 287 (1943)</ref> and Booth <ref> Booth, F. Nature, 161, 83 (1948)</ref>.
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 <ref>Dukhin, S.S. and Semenikhin, N.M. ''Koll.Zhur''., 32, 366 (1970)</ref>. Similar theory was created 10 years later by O'Brien and Hunter <ref>O'Brien, R.W. and Hunter, R.J. ''Can.J.Chem., 59, 1878 (1981)</ref>. Assuming '''thin Double Layer''', these theories would yield results that are very close to the numerical solution provided by O'Brien and White <ref> O'Brien, R.W. and White, L.R. ''J.Chem.Soc.Faraday Trans. 2, 74, 1607, (1978)</ref>.
==Notes==
{{Commons|Electrophoresis}}
<references />
==References==
* http://gslc.genetics.utah.edu/units/activities/electrophoresis/
* Voet and Voet, Biochemistry, John Whiley & sons. 1990.
* Jahn, G. C., Hall, D.W., and Zam, S. G. 1986. A comparison of the life cycles of two ''Amblyospora'' (Microspora: Amblyosporidae) in the mosquitoes ''Culex salinarius'' and ''Culex tarsalis'' Coquillett. J. Florida Anti-Mosquito Assoc. 57, 24–27.
* Khattak MN, Matthews RC. Genetic relatedness of ''Bordetella'' species as determined by macrorestriction digests resolved by pulsed-field gel electrophoresis. Int J Syst Bacteriol. 1993 Oct;43(4):659-64.
* Barz, D.P.J., Ehrhard. P., Model and verification of electrokinetic flow and transport in a micro-electrophoresis device, Lab Chip, 2005, 5, 949 - 958.
* Shim, J., Dutta, P., Ivory, C. F., Modeling and simulation of IEF in 2-D microgeometries, Electrophoresis, 2007, 28, 527-586.
==See also==
*[[Capillary electrophoresis]]
*[[Gel electrophoresis]]
*[[Protein electrophoresis]]
*[[Electrophoretogram]]
*[[Electrophoretic display]]
*[[Isotachophoresis]]
==External links==
* [http://web.med.unsw.edu.au/phbsoft/mobility_listings.htm List of relatives mobilities]
* [http://www.hbcpnetbase.com/ Handbook of Physics and Chemistry]
* [http://www.dispersion.com/ Dispersion Technology]
[[Category:Electromagnetism]]
[[Category:Electrophoresis]]
[[Category:Colloidal chemistry]]
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