Dielectrophoresis

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.[9][10] Recently, dielectrophoresis has been revived due to its potential in the manipulation of microparticles,[2][4][5][11] 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.[12] For a homogeneous sphere of radius ${\displaystyle r}$ and complex permittivity ${\displaystyle \varepsilon _{p}^{*}}$ in a medium with complex permittivity ${\displaystyle \varepsilon _{m}^{*}}$ the (time-averaged) DEP force is:[4]

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

The factor in curly brackets is known as the complex Clausius-Mossotti function[2][4][5] 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 ${\displaystyle r}$ and length ${\displaystyle l}$ with complex dielectric constant ${\displaystyle \varepsilon _{p}^{*}}$ in a medium with complex dielectric constant ${\displaystyle \varepsilon _{m}^{*}}$ the time-dependent dielectrophoretic force is given by:[4]

${\displaystyle F_{\mathrm {DEP} }={\frac {\pi r^{2}l}{3}}\varepsilon _{m}{\textrm {Re}}\left\{{\frac {\varepsilon _{p}^{*}-\varepsilon _{m}^{*}}{\varepsilon _{m}^{*}}}\right\}\nabla \left|{\vec {E}}\right|^{2}}$

The complex dielectric constant is ${\displaystyle \varepsilon ^{*}=\varepsilon +{\frac {i\sigma }{\omega }}}$, where ${\displaystyle \varepsilon }$ is the dielectric constant, ${\displaystyle \sigma }$ is the electrical conductivity, ${\displaystyle \omega }$ is the field frequency, and ${\displaystyle i}$ is the imaginary unit.[2][4][5] 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.[4] 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,[4] 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. 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.[13] 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.[14]

${\displaystyle \varepsilon _{1eff}^{*}(\omega )=\varepsilon _{2}^{*}{\frac {({\frac {r_{2}}{r_{1}}})^{3}+2{\frac {\varepsilon _{1}^{*}-\varepsilon _{2}^{*}}{\varepsilon _{1}^{*}+2\varepsilon _{2}^{*}}}}{({\frac {r_{2}}{r_{1}}})^{3}-{\frac {\varepsilon _{1}^{*}-\varepsilon _{2}^{*}}{\varepsilon _{1}^{*}+2\varepsilon _{2}^{*}}}}}}$

where 1 is the core (in cellular terms, the cytoplasm), 2 is the shell (in a cell, the membrane). r1 is the radius from the centre of the sphere to the inside of the shell, and r2 is the radius from the centre of the sphere to the outside of the shell.

Dielectrophoresis can be used to manipulate, transport, separate and sort different types of particles. Since biological cells have dielectric properties,[15][16][17] dielectrophoresis has many medical applications. Instruments that separate cancer cells from healthy cells have been made.[18] Platelets have been separated from whole blood with a DEP-activated cell sorter.[19] Dielectrophoresis can be used to manipulate, transport, separate and sort different types of particles. DEP is being applied in fields such as medical diagnostics, drug discovery, cell therapeutics, and particle filtration.

DEP has been also used in conjunction with the semiconductor chip technology for the development of DEPArray technology (Menarini Silicon Biosystems) for the simultaneous management of thousands of cells in a microfluidic device. Single microelectrodes on the floor of a flow cell are managed by the CMOS chip to form thousands of “Dielectrophoretic Cages”, each capable of capturing and moving one single cell under control of a routing software.

The most effort in studying DEP has been directed towards satisfying the unmet needs in the biomedical sciences.

As biological cells have dielectric properties [15][16] dielectrophoresis has many medical applications. Instruments capable of separating cancer cells from healthy cells have been made [18][20][21][22] as well as isolating single cells from Forensic mixed samples.[23] DEP has made it possible to characterize and manipulate biological particles like blood cells, stem cells, neurons, pancreatic β cells, DNA, chromosomes, proteins and viruses. DEP can be used to separate particles with different sign polarizabilities as they move in different directions at a given frequency of the AC field applied. DEP has been applied for the separation of live and dead cells, with the remaining live cells still viable after separation [24] or to force contact between selected single cells to study cell-cell interaction.[25]

• Strains of bacteria and viruses[26][27] red and white blood and cells. DEP can also be used to detect apoptosis soon after drug induction measuring the changes in electrophysiological properties.[28]

• AES Electrophoresis Society - Learning Center
• Biological cell separation using dielectrophoresis in a microfluidic device
• Sandia's dielectrophoresis device may revolutionize sample preparation