J. Phys. Chem. B 2008, 112, 9903–9908
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Experimental Investigation of Electrostatic Particle-Particle Interactions in Optoelectronic Tweezers Hyundoo Hwang, Jae-Jun Kim, and Je-Kyun Park* Department of Bio and Brain Engineering, KAIST, 335 Gwahangno, Yuseong-gu, Daejeon 305-701, Republic of Korea ReceiVed: April 24, 2008; ReVised Manuscript ReceiVed: June 3, 2008
This paper reports experimental and theoretical investigation of electrostatic attraction and repulsion of microparticles in an optoelectronic tweezers (OET). When we manipulate dielectric particles suspended in a fluid using OET, the electrostatic interactions of the polarized particles occur, limiting the effective manipulation of microparticles using a light-induced dielectrophoresis. In this study, we first demonstrate the electrostatic particle-particle interactions in the OET device using a liquid crystal display. At the same time, the experimental investigation of the dipole interactions between two spherical particles has been performed using the OET device. On the basis of the point-dipole model, simulation studies on the dipole forces acting on the particles and their trajectories by the forces are also performed. The experimental results show good agreement with the previously reported numerical studies as well as the results of our simulation studies. Introduction When we apply electrokinetic mechanisms such as electrophoresis and dielectrophoresis (DEP) to manipulate microparticles in biological and chemical applications, particle motions induced from the electrostatic interactions among the target particles as well as from the external driving forces occur.1,2 Those motions would serve several purposes in a few cases, but they have often interfered with the normal particle movements by canceling intended driving forces. As novel concepts for the DEP-based particle manipulation have been recently proposed in a programmable manner,3–7 the electrostatic particle-particle interactions have become more important phenomena which should be necessarily considered. In optoelectronic tweezers (OET), which is a remarkable technology for parallel manipulation of microparticles using dynamic optical images, a nonuniform electric field for inducing the dielectrophoretic movements of suspended particles is formed by projecting a dynamic image pattern from display device onto a photoconductive material.6,7 We can freely manipulate the suspended microparticles using the image-driven DEP forces in the OET device. The OET has been successfully applied for dynamic manipulation of individual cells8,9 and nanowires.10 The DEP forces result from the dipole moments of dielectric particles induced by the light-induced electric field, which also cause the electrostatic interactions among them. Since the target particles are manipulated without any flows and settled trajectories in the channel-less environment like an OET device, they can be brought very close to each other, increasing the effects by dipole forces among the manipulated particles. In consequence, the electrostatic particle-particle interactions influence the particle behaviors more dominantly in the OET device than in other DEP-based microfluidic systems. Moreover, in the OET environment, the electrostatic forces often become the most dominant than other forces, including hydrodynamic forces and even the light-induced DEP force which is a driving force. The forces make the particles aggregate or repel each * To whom correspondence should be addressed. Telephone: +82 42 869 4315. E-mail:
[email protected].
other, interfering with the effective particle manipulation using OET.11 Therefore, it is important to understand, estimate and control the electrostatic particle-particle interactions,12 especially in the channel-less DEP-based micromanipulator such as OET. Although many researchers have tried to understand the particle-particle interactions under electric field,13–20 the mechanism of the particle interactions is still unclear. Recently, Kang and Li21 have theoretically investigated the relative motion between two spherical particles in electrophoresis based on the extended model of the dipole-dipole interaction mechanism.17,18 On the other hand, Kadaksham et al. have reported the numerical study of the dynamical behavior of electrorheological suspensions subjected to nonuniform electric field.22 They have also considered the DEP force which acts on the particles under nonuniform electric field as well as the electrostatic particleparticle interactions which acts even when the electric field is uniform.23 However, although the experimental investigation of the electrostatic interactions between two dielectric particles should be performed to verify the theoretical models, it has never been shown to date since there were no compatible methods to freely manipulate the dielectric particle one by one and to observe their interaction in an electric field. In this paper, we utilized the OET device to experimentally investigate the electrostatic interactions between two dielectric particles. This is the first study about the particle-particle interactions occurred in the novel particle manipulation technology called OET. By using the OET device, we could manipulate a single particle to demonstrate the particle-particle interactions under the electric field and observe the particle behaviors as well. In this study, we applied the simplest OET platform called lab-on-a-display7 to easily demonstrate the electrostatic particleparticle interactions. We could observe both attractive and repulsive particle motions using the simple experimental setup. We also experimentally measured the velocities and positions of each particle and compared them with the results of numerical study. The numerical calculation of the dipole forces acting on the particles and their behaviors was performed based on the
10.1021/jp803596r CCC: $40.75 2008 American Chemical Society Published on Web 07/23/2008
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Hwang et al. Nikon, Japan). The particle positions and velocities were measured by analyzing the recorded movies using a MATLAB program. Results and Discussion In the OET device, the nonuniform electric field is generated by the projected LCD image, according to previously reported result of the numerical analysis.7 Hence we can manipulate the individual particles using the image-driven DEP forces. However, there are also electrostatic particle-particle interactions generated by the induced dipole of the dielectric particles. To expect the electrostatic forces acting on the polarized particles and their trajectories in an electric field, we applied the force equation based on the point-dipole model as below:22
Fdip )
12πr6εmRe(fCM)2
Figure 1. Experimental setup of lab-on-a-display system for observing electrostatic particle-particle interactions in optoelectronic tweezers (OET).
point-dipole model,22 which is one of the most widely used models about the motions of dielectric particles under the electric field. Experimental Details We have utilized a lab-on-a-display platform which is the simplest OET system for microparticle manipulation using a light-induced DEP (Figure 1).7 We used a liquid crystal display (LCD) and an illumination of microscope as an image pattern generator and a backlight source, respectively. An OET device which is directly put on the LCD module contains a photoconductive layer and an indium tin oxide (ITO) layer that is transparent and conductive. The photoconductive layer consists of four materials: a 180 nm-thick ITO for a conductive electrode, a 50 nm-thick n+ doped hydrogenated amorphous silicon (n+ a-Si:H) for the contact resistance reduction, an 800 nm-thick intrinsic hydrogenated amorphous silicon (intrinsic a-Si:H) for a photoconductive material, and a 20 nm-thick silicon nitride (SiNx) for the passivation. These four layers were consecutively deposited by plasma enhanced chemical vapor deposition (PECVD). A liquid sample in which polystyrene microbeads are suspended was sandwiched between the photoconductive and the ITO ground layer. We used 45 µm diameter polystyrene beads (PolySciences, PA) diluted with deionized water as a target sample. The dielectric constants of the particles and the liquid are 3.56 and 78.5, respectively. The applied voltage is 10 V at 100 kHz. On the basis of these experimental conditions, we could simulate the electric field strength using a commercial computational fluid dynamics (CFD) solver (CFD-ACE+; ESI, Huntsville, AL) and calculate the forces acting on the particles. When we project a dynamic LCD image onto the photoconductive layer of the OET device, the partially illuminated area of the photoconductive layer surface becomes a virtual electrode to induce DEP for particle manipulation. We can freely manipulate the suspended particles in the OET device by moving the projected image patterns. When a voltage was applied on the device, we naturally observed the electrostatic interactions among the closely positioned microparticles. We could also move the target particles to an adequate position to intentionally induce and observe the electrostatic particle-particle interactions. The movements of microbeads were observed and recorded using an upright microscope (Zeiss Axioskop 40; Carl Zeiss, Jena, Germany) and a digital camera (Coolpix5400;
d4
[dij(EiEj) + (dijEi)Ej + (dijEj)Ei 5dij(Eidij)(Ejdij)] (1)
where r is particle radius, E is the electric field, and dij is the unit vector in the direction from the center of the ith particle to the center of the jth particle. m ) 0r is the permittivity of the fluid, where r is the relative permittivity of the fluid and 0 is the permittivity of free space. The Claussius-Mossotti factor is fCM ) (p* - m*)/(p* + 2m*), where p* and m* are the complex permittivities of the particle and fluid, respectively. The electric field directions at the center of the particles are strictly varied because the particles are randomly distributed in the initial state and the electric field is nonuniform. For the simplification of the model, however, all simulations are based on the assumption that the electric field around a particle is spatially uniform in z-direction like that in the OET device. The results of experimental observation are also satisfied with the results calculated from the simplified model. In addition, the force induced by the dipole of dielectric particles is much more dominant than the light-induced DEP force at the moment when the electrostatic particle-particle interactions occur. Hence we could apply the simplified equation to explain the particle movements in the OET device. In the uniform electric field, the electrostatic force which is expressed in eq 1 can be simplified in spherical coordinates as follows:24
Fdip(d, θij) )
12πr6εmRe(fCM)2E2 4
d
[(3sin2θij - 1)eˆr + cos2θijeˆθ] (2)
Here θij is the angle between the xy-plane and the vector dij. That is, the electrostatic force between two spherical particles depends on their relative position and the distance between them. Figure 2 shows the electrostatic forces, which is normalized and simply plotted, acting on a particle around the other particle whose position is represented by a circle. Here, we assumed that a particle is located at the particular point considered in space and is acted by the force which is represented in each point of the figure. The positions of each particle were normalized by their radius. Forces acting on the particle along the line x ) 0 are always attractive while those on the particles along the line z ) 0 are always repulsive. This result significantly agrees with the result of elsewhere literature.21 On the basis of this model, we could estimate the motions of multiparticles by the dipole interactions in the OET device. When we manipulate microspheres using an OET device, some unwanted particle motions are appeared due to the electrostatic interactions among the particles. The particles,
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Figure 2. Normalized electrostatic forces acting on a particle around another particle (circle); vectors (left) and magnitudes (right).
Figure 3. (a) Captured movie still of electrostatic particle aggregation during the particle manipulation using OET (scale bar ) 100 µm). (b) Captured movie stills and (c) calculated trajectory of electrostatic attractive interaction. They form a chain in the electric field direction. (d) Measured velocities of six pairs of beads moved by attractive forces according to the projected distances between them. The theoretical velocity calculated in part c was also plotted (red, solid line).
which were randomly distributed at the initial state, attract each other and form chains in vertical direction, or broaden the gaps among themsdue to the electrostatic attractive and repulsive forces, respectivelysas soon as voltage is applied. When we select and drag a target particle in a certain direction by controlling the LCD image which induces the light-activated DEP forces, some chance for the moving particle of closing the distances from other ones appears since the particles are exposed to each other without any structural shields such as micro walls and channels in the OET device. Therefore, the electrostatic particle-particle interactions can occur and affect
more dominantly the particle movements in the OET device than those in other electrokinetic microparticle manipulators. Figure 3a indicates the captured movie of attractive interaction of two 45 µm diameter polystyrene beads. When we moved a particle in a certain pathway, the particle was attached to another particle which has been positioned in the middle of the pathway and aligned in the vertical direction. We could favorably observe the attraction between two particles at the upper view with the microscope, since the upper glass layer of OET device is coated with the transparent and conductive material, ITO. To analyze the particle movements in detail, we observed the captured
9906 J. Phys. Chem. B, Vol. 112, No. 32, 2008 movie frame by frame as shown in Figure 3b. According to the observation, one of the target particles was out-of-focus and immediately pulled each other with a strong attractive force. Finally, they formed a chain in the direction of electric field. Figure 3c shows the simulated trajectories of two particles which form a chain by the attractive dipole force. It also represents the cross-sectional view of Figure 3b. The relative initial positions of two particles, which can be represented by an angle θ in eq 2 and Figure 3c, significantly affect to their behaviors by the electrostatic interactions. When the particles are positioned with an angle which is much larger than 0°, they would show the attractive interaction as shown in Figure 3, parts b and c. The movements of particles look like the results of direct numerical simulations which were performed by Wang et al.25 In this case, we assumed that the angle θ is 37.4°. The value was selected by the analysis of the particle movements which are experimentally observed and the result of the trajectory calculation based on the simplified model, because we could not precisely measure the value of the angle. We also considered the device dimension and the experimental conditions for assuming the angle. Figure 3d shows the projected velocities of beads moved by the electrostatic attractive forces according to the projected distances between them. We selected six pairs of target particles and measured their velocity by capturing their positions frame by frame. As we mentioned above, we neglected the other forces such as hydrodynamic and DEP forces except the electrostatic dipole forces, Fdip. Therefore, the velocity, Vdip, can be represented by Stoke’s formula, Vdip ) Fdip/6πηr, where η is the fluid viscosity. According to the velocity measurement and the Stoke’s drag definition, the dipole force would be increased as the projected distance between two particles decreases. These experimental results closely correspond with the theoretical values. The calculated velocity could be obtained from the simulation result in Figure 3c. The attractive interactions would occur when the positions of two beads are close to each other and out of the horizontal with a certain angle θ. In this study, however, since the precise value of the angle could not be determined in our experimental setup, we assumed the angle θ as mentioned above (θ ) 37.4°). According to the numerical study of Kang and Li,21 the particles show the attractive motion if θ is larger than 36.6°. We could roughly determine such a tendency by merely adjusting the microscope focus. In order to more precisely measure the z-position of particles, the further studies about the measurement system such as confocal microscopy are necessary. We could also investigate the “repulsive-to-attractive interaction” between two spherical particles. At first, two suspended particles repelled and immediately pulled each other with a strong attractive force. Finally, the electrostatic particle-particle interaction made the beads to form a chain in the direction of electric field. According to the simulation study, the particles would show the “repulsive-to-attractive interaction” when they are positioned with an angle which is slightly larger than 0°. As the angle θ decreases, both the time that it takes for the repulsive behaviors to appear and the length that the moieties move by the repulsive force become longer (data not shown). As the distance among the particles becomes shorter, these attractive and “repulsiveto-attractive” interactions become more significant than the driving light-induced DEP force in the OET environment. Consequently, they often interfere with the effective particle manipulation using OET. To prevent these attractive motions of particles, we should focus the target particles onto the
Hwang et al. xy-plane or increase the distance between particles by reducing their concentration in the liquid sample. Repulsive interactions among the microparticles were also observed as shown in Figure 4a. As time goes by, the randomly distributed particles become arranged with their own equilibrium positions resulted from the electrostatic repulsions among them. We could investigate the repulsive interactions quantitatively by measuring the center-to-center distances among the particles suspended in the fluid with a high concentration. Figure 4b shows the distributions of center-to-center particle spacings of them according to the processing time. When two particles are located closely at first, they repelled each other with a repulsive dipole force until they meet other particles which also repel them in the opposite direction. Consequently, they would be arranged with the regular center-to-center spacing by the electrostatic repulsions and formed a crystalline structure in process of time as shown in Figure 4c. From these phenomena, we could infer that there is a critical distance among the particles at which the electrostatic dipole force, Fdip, is balanced with the light-induced DEP force, when we apply OET for the microparticle manipulation. In this case, the calculated DEP force was about 10 pN, which is in the equilibrium with the dipole repulsive force when the distance between two particles on xy-plane is about 130 µm. This result is well identified with the experimental result in Figure 4b. In Figure 4c, the particles formed chains in the vertical direction by the electrostatic attractive forces. At the same time, they repelled each other and moved until the sum of the forces acting on the particle became zero. Figure 4d shows the effect of electrostatic particle repulsions on the optoelectronic manipulation of microparticles. The particles, which were initially positioned in the critical distance along the x-axis, could not be moved all together by the LCD image moving from left to right. We could manipulate them with the image-driven DEP force only when one or two particles were selected to move. This phenomenon is caused by the repulsive interactions among the particles. These electrostatic repulsive forces often interfere with the effective manipulation of the individual particles. At the same time, however, it can also help the prevention of electrostatic particle aggregation or collisions among them, when we manipulate the particles using OET. This phenomenon can be useful when we manipulate many particles in parallel process using a programmable particle manipulator such as OET. To induce the repulsions, we should focus them onto the same level parallel to the xy-plane perpendicular to the direction of electric field.11 That is, if the angle in Figure 3c, which represents the initial relative positions of two particles, is about 0°, they would show the electrostatic repulsions. We could also experimentally determine that most of the microbeads which show the repulsive interactions are located at the same level by adjusting the microscope focus. The particle behaviors observed with these electrostatic particle-particle interactions would be more complex as the number of particles in the sample liquid increases. When we applied a higher concentration of the particles, the distances among the particles became much closer, resulting in larger and more dipole forces acting on a particle. In consequence, the forces acting on the particles increased and the motions of particles became faster and more complex. Conclusions In this study, we applied the OET device to investigate the electrostatic interactions among the suspended particles. We could demonstrate that the OET, which is a novel
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Figure 4. (a) Captured movie of electrostatic repulsive interaction. (b) Frequency distribution of the center-to-center particle spacings according to the time. (c) The particles which are arranged with the regular spacings in the xy-plane. (d) Only when one or two beads among all beads, which are positioned along the x-axis with a critical distance, were selected to move from left to right, we could succeed to manipulate them (scale bar ) 100 µm). Strong electrostatic repulsive forces among the target particles often interfere with the effective particle manipulation using imagedriven DEP as well as prevent the particle aggregations.
manipulation technology using the light-induced electrokinetic mechanisms, can be a useful tool for the study about particle interactions. In addition, we have successfully investigated the electrostatic attractions and repulsions between two dielectric microparticles through experimental observation and analysis using an LCD-based OET system. We also numerically calculated the dipole forces around the particles and simulated their trajectories to compare with the results of experimental observation. The dielectric particles attracted each other and formed a chain in the direction of electric field when they were closed to each other and out of horizontal with a certain vertical distance. When they are positioned at the almost same level, they also showed the “repulsive-to-attractive interaction”. On the other hand, when they are at the same level, they repelled each other in the direction perpendicular to the electric field until they are kept apart enough from each other or meet other one which repels them in the opposite direction. These electrostatic attractive and repulsive interactions would interfere with the precise control of microparticles using the image-driven DEP in the OET device, since the electrostatic interactions are much more dominant than the DEP forces at the moment when the particles are positioned close to each other. However, we can also utilize these phenomena occurred in the OET device for several applications such as a self-assembled micropattern structure.26 Therefore, we need to try to understand and control these interactions not only for manipulating microparticles freely from the electrostatic interactions in the OET device but also for using these interesting phenomena as a novel particle manipulation principle. Under this point of view, a programmable electrokinetic particle manipulator such as OET can be a useful tool for the study of electrostatic particle-particle interactions.
Acknowledgment. This work was supported by the Korea Science and Engineering Foundation (KOSEF) NRL Program grant funded by the Korea government (MEST) (No. R0A-2008000-20109-0), and by the Nano/Bio Science and Technology Program (2005-01291) of the MEST, Korea. The authors also thank the CHUNG Moon Soul Center for BioInformation and BioElectronics, KAIST. The microfabrication works for photoconductive layer were performed at the TFT-LCD Research Center, Kyung Hee University. References and Notes (1) Radko, S. P.; Chrambach, A. Electrophoresis 2002, 23, 1957–1972. (2) Maekarian, N.; Yeksel, M.; Khusid, B.; Farmer, K. Appl. Phys. Lett. 2003, 82, 4839–4841. (3) Altomare, L.; Borgatti, M.; Medoro, G.; Manaresi, N.; Tartagni, M.; Guerrieri, R.; Gambari, R. Biotechnol. Bioeng. 2003, 82, 474–479. (4) Manaresi, N.; Romani, A.; Medoro, G.; Altomare, L.; Leonardi, A.; Tartagni, M.; Guerrieri, R. IEEE J. Solid-State Circ. 2003, 38, 2297– 2305. (5) Borgatti, M.; Altomare, L.; Baruffa, M.; Fabbri, E.; Breveglieri, G.; Feriotto, G.; Manaresi, N.; Medoro, G.; Romani, A.; Tartagni, M.; Gambari, R.; Guerrieri, R. Int. J. Mol. Med. 2005, 15, 913–920. (6) Chiou, P. Y.; Ohta, A. T.; Wu, M. C. Nature 2005, 436, 370–372. (7) Choi, W.; Kim, S.-H.; Jang, J.; Park, J.-K. Microfluid. Nanofluid. 2007, 3, 217–225. (8) Hwang, H.; Choi, Y.-J.; Choi, W.; Kim, S.-H.; Jang, J.; Park, J.K. Electrophoresis 2008, 29, 1203–1212. (9) Ohta, A. T.; Pei-Yu, C.; Han, T. H.; Liao, J. C.; Bhardwaj, U.; McCabe, E. R. B.; Fuqu, Y.; Ren, S.; Wu, M. C. J. Microelectromech. Syst. 2007, 16, 491–499. (10) Jamshidi, A.; Pauzauskie, P. J.; Schuck, P. J.; Ohta, A. T.; Chiou, P.-Y.; Chou, J.; Yang, P.; Wu, M. C. Nat. Photon. 2008, 2, 86–89. (11) Hwang, H.; Oh, Y.; Kim, J.-J.; Choi, W.; Park, J.-K.; Kim, S.-H.; Jang, J. Appl. Phys. Lett. 2008, 92, 024108. (12) Aubry, N.; Singh, P. Europhys. Lett. 2006, 74, 623–629. (13) Reed, L. D.; Morrison, F. A., Jr. J. Colloid Interface Sci. 1976, 54, 117–133. (14) Keh, H. J.; Anderson, J. L. J. Fluid Mech. 1985, 153, 417–439.
9908 J. Phys. Chem. B, Vol. 112, No. 32, 2008 (15) Chen, Y.; Sprecher, A. F.; Conrad, H. J. Appl. Phys. 1991, 70, 6796–6803. (16) Kang, S.-Y.; Sangani, A. S. J. Colloid Interface Sci. 1994, 165, 195–211. (17) Shramko, O.; Shilov, V.; Simonova, T. Colloids Surf., A 1998, 140, 385–393. (18) Simonova, T. S.; Shilov, V. N.; Shramko, O. A. Colloid J. 2001, 63, 108–115. (19) Yariv, E. Phys. Fluids 2004, 16, L24-L27. (20) Swaminathan, T. S.; Hu, H. H. J. Colloid Interface Sci. 2004, 273, 324–330. (21) Kang, K. H.; Li, D. Langmuir 2006, 22, 1602–1608.
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