Dielectrophoresis

Dielectrophoresis (DEP) is a phenomenon in which a force is exerted on a dielectric particle when it is subjected to a non-uniform electric field. 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 and nanowires. Furthermore, a study of the change in DEP force as a function of frequency can allow the electrical (or electrophysiological in the case of cells) properties of the particle to be elucidated. Dielectrophoresis (DEP) is a phenomenon in which a force is exerted on a dielectric particle when it is subjected to a non-uniform electric field. 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 and nanowires. Furthermore, a study of the change in DEP force as a function of frequency can allow the electrical (or electrophysiological in the case of cells) properties of the particle to be elucidated. Although the phenomenon we now call dielectrophoresis was described in passing as far back as the early 20th century, it was only subject to serious study, named and first understood by Herbert Pohl in the 1950s. Recently, dielectrophoresis has been revived due to its potential in the manipulation of microparticles,nanoparticles and cells. Dielectrophoresis occurs when a polarizable particle is suspended in a non-uniform electric field. The electric field polarizes the particle, and the poles then experience a force along the field lines, which can be either attractive or repulsive according to the orientation on the dipole. Since the field is non-uniform, the pole experiencing the greatest electric field will dominate over the other, and the particle will move. The orientation of the dipole is dependent on the relative polarizability of the particle and medium, in accordance with Maxwell–Wagner–Sillars polarization. Since the direction of the force is dependent on field gradient rather than field direction, DEP will occur in AC as well as DC electric fields; polarization (and hence the direction of the force) will depend on the relative polarizabilities of particle and medium. If the particle moves in the direction of increasing electric field, the behavior is referred to as positive DEP (sometime pDEP), if acting to move the particle away from high field regions, it is known as negative DEP (or nDEP). As the relative polarizabilities of the particle and medium are frequency-dependent, varying the energizing signal and measuring the way in which the force changes can be used to determine the electrical properties of particles; this also allows the elimination of electrophoretic motion of particles due to inherent particle charge. Phenomena associated with dielectrophoresis are electrorotation and traveling wave dielectrophoresis (TWDEP). These require complex signal generation equipment in order to create the required rotating or traveling electric fields, and as a result of this complexity have found less favor among researchers than conventional dielectrophoresis. The simplest theoretical model is that of a homogeneous sphere surrounded by a conducting dielectric medium. For a homogeneous sphere of radius r {displaystyle r} and complex permittivity ε p ∗ {displaystyle varepsilon _{p}^{*}} in a medium with complex permittivity ε m ∗ {displaystyle varepsilon _{m}^{*}} the (time-averaged) DEP force is: The factor in curly brackets is known as the complex Clausius-Mossotti function and contains all the frequency dependence of the DEP force. Where the particle consists of nested spheres - the most common example of which is the approximation of a spherical cell composed of an inner part (the cytoplasm) surrounded by an outer layer (the cell membrane) - then this can be represented by nested expressions for the shells and the way in which they interact, allowing the properties to be elucidated where there are sufficient parameters related to the number of unknowns being sought.For a more general field-aligned ellipsoid of radius r {displaystyle r} and length l {displaystyle l} with complex dielectric constant ε p ∗ {displaystyle varepsilon _{p}^{*}} in a medium with complex dielectric constant ε m ∗ {displaystyle varepsilon _{m}^{*}} the time-dependent dielectrophoretic force is given by: The complex dielectric constant is ε ∗ = ε + i σ ω {displaystyle varepsilon ^{*}=varepsilon +{frac {isigma }{omega }}} , where ε {displaystyle varepsilon } is the dielectric constant, σ {displaystyle sigma } is the electrical conductivity, ω {displaystyle omega } is the field frequency, and i {displaystyle i} is the imaginary unit. This expression has been useful for approximating the dielectrophoretic behavior of particles such as red blood cells (as oblate spheroids) or long thin tubes (as prolate ellipsoids) allowing the approximation of the dielectrophoretic response of carbon nanotubes or tobacco mosaic viruses in suspension.These equations are accurate for particles when the electric field gradients are not very large (e.g., close to electrode edges) or when the particle is not moving along an axis in which the field gradient is zero (such as at the center of an axisymmetric electrode array), as the equations only take into account the dipole formed and not higher order polarization. When the electric field gradients are large, or when there is a field null running through the center of the particle, higher order terms become relevant, 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 Erms, or, for sinusoidal voltages by dividing the right hand side by 2.These models ignores the fact that cells have a complex internal structure and are heterogeneous. A multi-shell model in a low conducting medium can be used to obtain information of the membrane conductivity and the permittivity of the cytoplasm. For a cell with a shell surrounding a homogeneous core with its surrounding medium considered as a layer, as seen in Figure 2, the overall dielectric response is obtained from a combination of the properties of the shell and core.