Dielectrophoresis and Optoelectronic Tweezers for Nanomanipulation

Jong Min Sung
December 10, 2007

(Submitted as coursework for Physics 210, Stanford University, Autumn 2007)

Fig. 1: Schematic of single-beam optical tweezers. Particle is trapped by optical gradient force. [6]


Over the last decades, a variety of nano-manipulation techniques have developed and played significant roles in various research area, especially biological science and technology. The representative techniques include optical tweezers [1], magnetic tweezers [2], electrokinetic forces (electrophoresis [3], dielectrophoresis [4], travelling-wave dielectrophoresis), acoustic traps and hydrodynamic flows. The conventional tools have their own advantages and they has been selectively used to perform the experiments that meet the purposes. For example, optical tweezers is very useful technique to conduct experiments that require high resolution for trapping single molecules. Magnetic tweezers is advantageous to give a rotational force and analyze the topological structure of single molecules, such as DNA and RNA. Electrokinetic forces are attractive for high throughput cell manipulation. However, none of the previous manipulation techniques has satisfied high resolution and high throughput at the same time. Optoelectronic tweezers is a newly invented nano-manipulation technique, which is the combination of optical tweezers with dielectrophoresis that provides high flexibility, high resolution and high throughput at the same time. In this article, optical tweezers, dielectrophoresis and optoelectronic tweezers are introduced for the basic concepts and biological applications.

Optical Tweezers

Optical tweezers, invented by Arthur Ashkin in 1982 [5], is one of the widely used manipulation techniques for micro- to nano-particles [6], and especially has been successful in studying a variety of biological systems in recent years [7]. Optical tweezers uses a focused laser beam to provide an attractive or repulsive force (typically pN-nN) to physically hold and move microscopic dielectric objects. The force on the dielectric particles can be written as

where E is an electric field and α is a polarizability, which means it is proportional to the gradient along the intensity of the beam. Optical tweezers is very useful technique in confining particles in small area (a few decades of nm). However, it has some limitation of the multiple traps or the trapping of organic particles (e.g., cells) due to its high laser intensity (0.1-10 mWh) and tight focusing requirement in the working area (~ 100×100 µm2). Moreover, it is found that the strong laser intensity can induce photo-damage to the observing biomolecules. Therefore, it might be very advantageous if a new technique offering parallel trapping and no damage to the molecules is applied to the research.


Fig. 2: Schematic illustrating dielectrophoresis (DEP) resulted from electroic force.

Dielectrophoresis (DEP), introduced by Herbert Pohl in 1950's [8], is electrical analog of optical tweezers, which relies on the gradient of an electric field rather than an optical field. In an uniform field, neutral particles do not move due to the zero net force, while charged particles are attracted to the opposite electrode as illustrated in Fig. 2a. DEP force appears when the interaction of the electric field gradient with the induced dipole of neutral particles within the field results in a net force on the particles as shown in Fig. 2b. Note that DEP force can be observed either with AC or DC excitation, because it does not depend on the polarity of the electric field. Also, DEP is most easily observed for particles with diameters ranging from around 1 - 1000 µm2, because gravity (above 1000 µm2) and Brownian force (below 1 µm2) overwhelm the DEP force out of the range.

DEP Force

The typical case is the induced dipole in a lossy dielectric spherical particle as will be explained below [9]. For a homogeneous sphere of radius R with complex permittivity εp* in a medium with complex permittivity &epsilonm* the time-dependent DEP force is given by

Where FDEP is the dipole approximation to the DEP force, ω is the radian frequency of the applied field, r refers to the spatial coordinate, and E is the complex applied electric field. CM is complex Clausius-Mossotti (CM) factor, which, for a lossy dielectric uniform sphere, such as a bead, can be expressed by

Where the complex permittivities are given by ε* = ε + σ/(jω), where ε is the permittivity, σ is the electrical conductivity of the medium or particle, and j is the imaginary number. DEP force can be a positive value (pDEP) that propels the particles toward the electric-field maxima or a negative one (nDEP) toward the minima, depending on the sign of the CM factor. The force equation is considered to be accurate when electric field gradients are not very large compared with the particle size, because it is based on the dipole approximation. When the electric field gradients are large, such as the position close to electrode edges, higher order terms become relevant and result in higher forces, which is expressed by

Where n refers the force order (e.g., n=1 is the dipole and n=2 is the quadrupole), pn indicates the multipolar induced-moment tensor, and [ · ]n and (∇)n means n dot products and gradient operations [10]. This equation can be more explicitly expressed for the time-averaged force in the i-th direction as

For the dipole (n=1) and the quadrupole (n=2), where multipolar CM factor for a uniform lossy dielectric sphere is given by

Fig. 3: Schematic of DEP-FFT method

Particle Separation by DEP

In the frequency range 5-200 kHz, it has been shown that the dielectric properties of cells are determined by Maxwell-Wagner polarization at membrane interfaces which are affected by cell membrane morphologies, internal conductivities, and size [11]. Therefore, DEP force can be applied to separate mixed particles based on the specific conditions, and basically they can be classified into two groups: DEP migration and DEP retention [9]. First, separation of particles is easy if one particle has positive CM factor and the other has negative value. We can readily separate and collect them from each electrode, because they are trapped to the opposite electrodes. Second, the mixed particles can be separated when their sizes are significantly different. Due to the size dependence of the DEP force (FDEP) the particles are repelled to the electrodes with different forces. However, this method has some limitations if the mixed particles are not distinctive in the properties of CM factor and size. Dielectrophoresis Field-Flow Fractionation (DEP-FFF) technique, introduced by Davis and Giddings [12], is one of the methods to increase the efficiency of the separation. As shown is Fig. 3, DEP-FFF uses not only DEP force but also other factors such as sedimentation force (Fgrav ~ mg), which is proportional to the gravity. When particles are injected into a flow channel, each particle flows at different height where the DEP force and gravitational force make balance. Usually, particles that flow near the center reach higher positions in the parabolic velocity profile and it will be discharged from the channel at a faster rate. In addition to the gravitional force, there are many factors that affect the position of the particles, such as diffusion, steric repulsion, drag force, hydrodynamic, dielectric and other effects [9]. Therefore, DEP-FFF technique provides more specific, faster, and continuous performance of particle separation. Current research shows the application of these separation techniques, such as the purification of leukemia cells [13] and collection of bacteria in blood [14].

Optoelectronic Tweezers

Despite the advantages of DEP as shown above, the conventional DEP lacks the flexibility due to the fixed patterns of electrodes. Optoelectronic Tweezers (OET) is a new optical manipulation technique that combines the advantages of both optical tweezers and DEP, resulting in optically-induced dielectrophoresis [16]. OET is composed of external light, digital micromirror display (DMD), objective lens, photosensitive electrodes and applying AC source. First, the light beam arrived on DMD microdisplay excites the patterned area which was previously programmed. Then, the patterned beam from DMD can be collected through the objective lens and reach the photosensitive electrode. Since the pattern on DMD can be changed in a short time resolution, it is possible to produce dynamic beam patterns on the electrode. When the photosensitive electrode is exposed to the light beam, the electric conductivity of the area increases suddenly and significantly. The photosensitive electrode, then, forms virtual electrodes and creates non-uniform electric field that produces the DEP force on particles (Fig. 4). Compared with optical tweezers and DEP, OET has much more advantages as follows [15]. First, OET provides high flexibility in the manipulation of the particles because the virtual electrode can be changed in a short time period through the dynamic control of the programmable DMD. Second, OET is a noninvasive technique for the manipulation of the biomolecules, whereas the photo-damage induced from strong laser power is considered to be a negative effect of optical tweezers. Third, OET is very economic method because it requires low-power for the excitation of the photosensitive electrode. OET can be operated by using incoherent light, such as LED or halogen lamp, thus resulting in the optical power densities 100,000 times less than optical tweezers. Finally, OET enables parallel manipulation of the particles on a wide area, such as 15,000 individually addressable optical traps over an area of 1.3 mm × 1.0 mm. Recently, OET has been widely used for the practical applications, e.g., massively parallel transportation of single particles [15], integrated virtual optical machine including optical sorter path and conveyors, trapping of single semiconductor nanowires, and selective collection of live cells from a mixture of live and dead ones [17].

Fig. 4: Schematic of Optoelectronic tweezers. [15]

Concluding Remarks

In this report, the basic concept and applications of optical tweezers, dielectrophoresis, and finally optoelectronic tweezers are described and explained. Optoelectronic tweezers is highly useful tool that provides the benefits of optical tweezers and dielectrophoresis together. Anyway, they are all pretty useful techniques and it will be very exciting to perform experiments that no one has ever tried before by using these techniques.

© 2007 Jong Min Sung. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


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