1. INTRODUCTION

If a direct current (D.C.) electric field of uniform intensity is applied to a system consisting of a particle suspended in an aqueous medium, at least three effects are likely to occur:

1. The particle moves!
2. The electrical double layer surrounding the particle is distorted.
3. Electrical charges are induced to appear at the interfaces that define the particle's structure.

Let us briefly go through these effects in order:

The observed lateral movement of the particle will most likely result from the fact that it carries a net electrical charge Q on its surface (at neutral pH this charge will be negative for pro- and eukaryotic cells, negative for DNA, either negative or positive for proteins). When exposed to an electric field E, a charged particle will experience a force F (F=Q.E) and the resulting motion is known as electrophoresis. This well known phenomenon (the first publication we are aware of is that by Reuss [1] describing the effect for clay particles) has for some time been extensively exploited for investigating the surface properties of cells (e.g. Coulter [2]).

When suspended in an electrolyte, a particle carrying a net electrical charge will attract around itself ions of opposite electrical polarity, forming an electrical double layer. As shown in Figure 1(a) on the next page, the symmetry of this double layer can be expected to be distorted in the presence of an applied electric field [3].

It will also usually be the case that the electrical properties of the particle (i.e. its electrical conductivity and dielectric constant) will differ from those of the suspending medium. As a result of this, and as first described by Maxwell [4] and further elaborated by Wagner [5], the action of an applied electric field will also be to induce electrical charges to appear at the boundary between the particle and the surrounding medium. This is depicted in Figure 1(b).

The distortion of the electrical double layer and the creation of Maxwell-Wagner interfacial charges lend to the particle the properties of an electric dipole moment. The magnitudes of these induced dipoles are very large in comparison to those usually associated with molecular species because, although the magnitude of the charges involved may not be large, the distance between their oppositely charged poles is large. Thus, for the situation shown in Figure 1(b) the induced dipole moment arising from the two induced charges + and - located at r^- and r⁺ respectively, is given by:

(1)

where r is the particle radius. Even when the separated charge q is equivalent to just one electronic charge, then for a cell of diameter 5 microns the dipole moment will be of value around 2.5x10⁵debye units (c.f. 1.84 debye for a water molecule).

Figure 1 (a) Distortion of electrical double layer caused by an applied electric field E. (b) Interfacial charges induced at the particle boundary. These two effects produce large electrical dipole moments.

If the D.C. field is replaced by one of alternating current (A.C.), then because of the particle's inertia the electrophoretic effect becomes vanishingly small for frequencies above around 1 kHz. Also, distortions of the electrical double layer have a finite relaxation time and become negligible above about 50 kHz. However, dipole moments associated with Maxwell-Wagner interfacial polarisations can exert their influence up to frequencies of 50 MHz and beyond [6].

For a spherical particle of radius r, suspended in a medium of absolute dielectric permittivity , then following the theories of Maxwell and Wagner it can be shown that the magnitude of the dipole moment arising from the induced interfacial charges is given by:

(2)

where and are the complex conductivities of the particle and suspending medium, respectively. These complex conductivities take into account the fact that the particle and suspending medium exhibit both conduction (energy loss) and dielectric (field energy storing) properties when exposed to electrical fields, and have the mathematical form:

(3)

where is the angular frequency of the applied field ( , f being the frequency) and the symbol j () signifies that the dielectric displacement current leads the conduction current by a phase angle of 90^o. The conduction current is determined by the real component of the complex conductivity, whilst the imaginary component determines the magnitude of the dielectric displacement current. Evaluation of equation (2) reveals that the magnitude and polarity of the induced dipole moment depends in quite a complicated manner on the frequency of the applied field and on the relative values of the conductivities and permittivities of the particle and surrounding medium. Thus, if the polarisability of the particle exceeds that of the surrounding medium (i.e. || > || ) the arrangement of the induced charges produces a dipole moment directed with the applied field, as depicted below in figure 2(a). However, if the reverse is true (i.e. || < || ) then as shown in figure 2(b) the moment is directed against the field.

Figure 2 The distribution of electric charges induced at the surface of a particle and the direction of the resulting dipole moment m for: (a) the case where the polarisability of the particle exceeds that of the surrounding medium, and (b) where the particle is less polarisable than the surrounding medium.

The appearance of the interfacial charges (and hence of the induced dipole moment) does not occur immediately on application of the electric field, but at an exponential rate of characteristic time constant given by:

(4)

Taken together equations (2) and (3) describe the magnitude, polarity and time response of the dipole moment induced in a particle in an imposed electric field, and provide the basis for understanding how various forms of A.C. fields may be used to selectively manipulate bioparticles using such phenomena as:

• Dielectrophoresis
• Electrorotation
• Travelling Field Effects
  

2. BIBLIOGRAPHY

1. Reuss, F. F. (1809) Memoires de la Société Imperiales de Naturalistes de Moskou 2, 327-336
2. Coulter, C. B. (1920) J. Gen. Physiol. 3, 309-406
3. Hartley, G. S. (1935) Trans. Faraday Soc. 31, 31-50
4. Maxwell, J. C. (1891) A Treatise on Electricity and Magnetism, 3rd. ed., Vol.1, Ch.ix, Clarendon Press, Oxford.
5. Wagner, K. W. (1914) Archiv. Elektrotechnik 2, S.371-389