Dielectrophoresis

Dielectrophoresis (or DEP) is a phenomenon in which a force is exerted on a dielectric particle when it is subjected to a non-uniform electric field.^{[1][2][3][4][5]} This force does not require the particle to be charged. All particles exhibit dielectrophoretic activity in the presence of electric fields. However, the strength of the force depends strongly on the medium and particles' electrical properties, on the particles' shape and size, as well as on the frequency of the electric field. Consequently, fields of a particular frequency can manipulate particles with great selectivity. This has allowed, for example, the separation of cells or the orientation and manipulation of nanoparticles^[2] and nanowires.

Background and Properties

Publications on dielectrophoresis go as far back as the 1950s, by Herbert Pohl.^[6][7] Recently, dielectrophoresis has been revived due to its potential in the manipulation of microparticles,^[2][3][4][8]nanoparticles and cells.

Pohl wrote in his book^[1] defining dielectrophoresis as the translational motion of neutral matter caused by polarization effects in a nonuniform electric field. The phenomenological bases are catalogued below:

1. The dielectrophoresis force can be seen only when particles are in nonuniform electric fields.
2. Since the dielectrophoresis force does not depend on the polarity of the electric field, the phenomenon can be observed either with AC or DC excitation.
3. Particles are attracted to regions of stronger electric field when their permittivity exceeds that of the suspension medium.
4. When the permittivity of the medium is greater than that of the particles, the motion of the particles is to lesser electric field.
5. DEP is most readily observed for particles with diameters ranging from approximately 1 to 1000 μm. Above 1000 μm, gravity overwhelms DEP; below 1 μm, Brownian motion overwhelms the DEP forces.

Phenomena associated with dielectrophoresis are electrorotation and traveling wave dielectrophoresis (TWDEP). Dielectrophoresis can be enhanced using multiple frequencies, in what is known as multiple-frequency dielectrophoresis (MFDEP).

Dielectrophoretic force

For a field-aligned prolate ellipsoid of radius r and length l (r < l) with complex dielectric constant $\varepsilon_p^*$ in a medium with complex dielectric constant $\varepsilon_m^*$ the time-dependent dielectrophoretic force is given by^[3]:

$F_\mathrm{DEP} = \frac{\pi r^2 l}{3}\varepsilon_m \textrm{Re}\left\{\frac{\varepsilon^*_p - \varepsilon^*_m}{\varepsilon^*_m}\right\}\nabla \left|\vec{E}\right|^2$

The complex dielectric constant is $\varepsilon^* = \varepsilon + \frac{\sigma}{j\omega}$, where $\epsilon$ is the dielectric constant, σ is the electrical conductivity, ω is the field frequency, and j is the imaginary number.^[2][3][4]

This equation is accurate for highly elongated ellipsoids when the electric field gradients are not very large (e.g., close to electrode edges). The equation only takes into account the dipole formed and not higher order polarization.^[3] When the electric field gradients are large, higher order terms become relevant,^[3] and result in higher forces. To be precise, the time-dependent equation only applies to lossless particles, because loss creates a lag between the field and the induced dipole. When averaged, the effect cancels out and the equation holds true for lossy particles as well. An equivalent time-averaged equation can be easily obtained by replacing E with E_rms, or, for sinusoidal voltages by dividing the right hand side by 2.

For a homogeneous sphere of radius r and complex permittivity $\varepsilon_p^*$ in a medium with complex permittivity $\varepsilon_m^*$ the (time-averaged) DEP force is^[3]:

$\langle F_\mathrm{DEP} \rangle = 2\pi r^3\varepsilon_m \textrm{Re}\left\{\frac{\varepsilon^*_p - \varepsilon^*_m}{\varepsilon^*_p + 2\varepsilon^*_m}\right\}\nabla \left|\vec{E}_{rms}\right|^2$

The factor in curly brackets is known as the complex Clausius-Mossotti function^[2][3][4] and contains all the frequency dependence of the DEP force.

Applications of Dielectrophoresis

Dielectrophoresis can be used to manipulate, transport, separate and sort different types of particles. Since biological cells have dielectric properties,^[9][10] dielectrophoresis has many medical applications. Prototypes that separate cancer cells from healthy cells have been made.^[11] Platelets have been separated from whole blood with a DEP-activated cell sorter. ^[12]

Dielectrophoresis Field-Flow Fractionation (DEP-FFF)

The utilization of the difference between dielectrophoretic forces exerted on different particles in nonuniform electric fields is known as DEP separation. The exploitation of DEP forces has been classified into two groups: DEP migration and DEP retention. DEP migration uses DEP forces that exert opposite signs of force on different particle types to attract some of the particles and repel others.^[13] DEP retention uses the balance between DEP and fluid-flow forces. Particles experiencing repulsive and weak attractive DEP forces are eluted by fluid flow, whereas particles experiencing strong attractive DEP forces are trapped at electrode edges against flow drag.^[14]

Dielectrophoresis Field-Flow Fractionation, introduced by Davis and Giddings,^[15] is a family of chromatographic-like separation methods. In DEP-FFF, DEP forces are combined with drag flow to fractionate a sample of different types of particles.^{[14][16][17][18]} Particles are injected into a carrier flow that passes through the separation chamber, with an external separating force (a DEP force) being applied perpendicular to the flow. By means of different factors, such as diffusion and steric, hydrodynamic, dielectric and other effects, or a combination thereof, particles (<1 μm in diameter) with different dielectric or diffusive properties attain different positions away from the chamber wall, which, in turn, exhibit different characteristic concentration profile. Particles that move further away from the wall reach higher positions in the parabolic velocity profile of the liquid flowing through the chamber and will be eluted from the chamber at a faster rate.

Optical Dielectrophoresis

The use of photoconductive materials (for example, in lab-on-chip devices) allows for localized inducement of dielectrophoretic forces through the application of light. In addition, one can project an image to induce forces in a patterned illumination area, allowing for some complex manipulations. When manipulating living cells, optical dielectrophoresis provides a non-damaging alternative to optical tweezers, as the intensity of light is about 1000 times less.^[19]

References

1. ^ ^{a b} Pohl, H. A., 1978. Dielectrophoresis the behavior of neutral matter in nonuniform electric fields. Cambridge University Press. Cambridge.
2. ^ ^{a b c d e} Morgan, H. and Green, N. AC Electrokinetics: Colloids and Nanoparticles.
3. ^ ^{a b c d e f g h} T. B. Jones, Electromechanics of particles (Cambridge University Press, Cambridge, 1995).
4. ^ ^{a b c d} Kirby, B.J. (2010). Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices.. Cambridge University Press. ISBN 978-0521119030. http://www.kirbyresearch.com/textbook. 
5. ^ Chang, H.C. and Yao, L. (2009). Electrokinetically Driven Microfluidics and Nanofluidics. 
6. ^ H. A. Pohl, "The Motion and Precipitation of Suspensoids in Divergent Electric Fields", J. Appl. Phys. 22(7), 869–871 (1951).
7. ^ Pohl, H. A., 1958, "Some effects of nonuniform fields on dielectrics", J. Appl. Phys., 29(8), 1182 - 1188.
8. ^ Tathireddy, P.; Choi, Y-H, Skliar, M (2008). "Particle AC electrokinetics in planar interdigitated microelectrode geometry". Journal of Electrostatics 66 (11-12): 609–619. doi:10.1016/j.elstat.2008.09.002. 
9. ^ Pethig R. Dielectric Properties of Biological Materials, 1979.
10. ^ Choi, J.W., Pu, A. and Psaltis, D. (2006). "Optical detection of asymmetric bacteria utilizing electro orientation". Optics Express 14: 9780–9785. Bibcode 2006OExpr..14.9780C. doi:10.1364/OE.14.009780. http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-14-21-9780. 
11. ^ Micro-fluidics cut cancer test from a day to an hour - IMEC Tech Forum
12. ^ Pommer, MS et al., 2008. "Dielectrophoretic separation of platelets from diluted whole blood in microfluidic channels", Electrophoresis, 29(6), 1213-1218.
13. ^ http://alexwg.org/Nanotechnology2006.pdf Wissner-Gross, A.D., 2007. "Dielectrophoretic reconfiguration of nanowire interconnects". Nanotechnology 17, 4986-4990.
14. ^ ^{a b} Gascoyne, P.R.C., Y. Huang, R. Pethig, J. Vykoukal and F.F. Becker, 1992. "Dielectrophoretic separation of mammalian cells studied by computerized image analysis". Meas. Sci.Technol. 3, 439-445.
15. ^ Davis, J.M. and J.C. Giddings, 1986. "Feasibility study of dielectrical field-flow fractionation". Sepa. Sci. and Tech. 21, 969-989.
16. ^ Giddings, J.C., 1993. "Field-Flow Fractionation: Analysis of macromolecular, colloidal, and particulate materials". Science. 260, 1456-1465.
17. ^ Huang, Y., X.B. Wang, F.F. Becker and P.R.C. Gascoyne, 1997. "Introducing dielectrophoresis as a new force field for field-flow fractionation". Biophys. J. 73, 1118-1129
18. ^ Wang, X.B., J. Vykoukal, F.F. Becker and P.R.C. Gascoyne, 1998. "Separation of polystyrene microbeads using dielectrophoretic/gravitational field-flow-fractionation". Biophysical Journal. 74, 2689-2701.
19. ^ Dongqing Li, ed. "Encyclopedia of Microfluidics and Nanofluidics". Springer, New York, 2008.

External links

• The American Electrophoresis Society: Dielectrophoresis
• Dielectrophoresis: a spherical shell model
• On the Relationship of Dielectrophoresis and Electrowetting
• Biological cell separation using dielectrophoresis in a microfluidic device
• Sandia’s dielectrophoresis device may revolutionize sample preparation
• Institute of Bioelectronic and Molecular Microsystems: Dielectrophoresis