Design and Simulation of Electrodes for 3D ... - ieee-robio 2015
Design and Simulation of Electrodes for 3D Dielectrophoretic Trapping Minglin Li, Yanli Qu, Zaili Dong, Wen J. Li*, and Yuechao Wang State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, 110016, China
Abstract—Micro- and nano-particles can be trapped in locally strong or weak regions of a non-uniform electric field through the effect of dielectrophoretic principle. Recently, a novel optoelectronic tweezers (OET) based on optically induced dielectrophoresis (DEP) was demonstrated by Chiou et al. [1] for effectively trapping and manipulation of cells and latex particles. The OET allows an optical beam to create a virtual electrode on a photoconductive surface, which produces a highly non-uniform electric field. Here we simulated the electric field distribution produced by a light-induced ring-shaped electrode for particles trapping. Then, we simulated the DEP trapping effects from a real microelectrode that could be fabricated on a glass substrate to replace the virtual light-induced electrode. This is to compare the efficiencies of OET and microelectrode induced DEP effects. We also derived the smallest radiuses of the polystyrene bead which could be potentially trapped in the OET device and the real electrode structure. Finally, we designed and analyzed a 3×3 electrode array to explore the possibility of arbitrarily trapping and manipulating single particles using the real microelectrodes. Index Terms—dielectrophoretic trapping, optoelectronic tweezers, nano-manipulation, DEP.
I. INTRODUCTION trapping and manipulation using PARTICLES dielectrophoresis have been attracting comprehensive attentions in the field of micro/nanotechnology[2], [3]. DEP has been demonstrated by many research groups to trap particles in local strong electric field and in local weak electric field, termed respectively positive DEP and negative DEP. A common electrode configuration used for particles trapping is a planar quadrupole arrangement where four electrodes point towards a central enclosed region [4], [5]. This electrode design may have many advanced varieties, however, these planar traps suffer from the drawback that increasing the field only pushes particles farther out of the trap and does not necessarily increase confinement. To avoid _______________________________________ *Contact author: [email protected]. Wen J. Li is a professor at The Chinese University of Hong Kong and also an affiliated professor at the Shenyang Institute of Automation. Minglin Li is also with College of Mechanical Engineering, Fuzhou University, 350002, China and Graduate University of the Chinese Academy of Sciences, 100049 China. This work is supported in part by the NSFC (Project code: 60635040 and 60675060) and the Chinese National 863 Plan (Project code: 2006AA04Z320 and 2007AA04Z317).
;
them, Voldman et al. [6] designed and demonstrated an extruded quadrupole dielectrophoretic trap with stronger holding forces than those of planar quadrupole. However, the extruded electrode is more difficult to be fabricated. Another way to increase the strength of quadrupole electrode traps is the octopole field cage [7], [8]. Although the octopole field cage only includes two planar quadrupole electrodes simpler fabricated than the extruded quadrupole, they are more complicated to align and package. Recently, a novel optoelectronic tweezers (OET) based on light-induced DEP was demonstrated by Chiou et al. [1] for effectively trapping and manipulation of cells and latex particles. In the OET device, a virtual electrode would form on the surface and generate a highly non-uniform electric field in the liquid layer through an optical beam focused on the photoconductive surface. Since the conductivity of photoconductor linearly increases several orders of magnitude due to the photogenerated charged carriers in the photoconductor, from dark to light, the distribution of the light-induced non-uniform field depends on the profile of the light intensity. Noted that the conductivity of the illuminated photoconductor is still smaller than that of metals [9], so the
(a)
(b) Fig. 1. (a) The simplified system of OET device. (b) The potential contour and the electric field norm distribution at the centric symmetry plane.
II. ELECTRIC FIELDS A. The light-induced electric field For simulation, we considered a simplified model of the OET system, as shown in Fig. 1(a). A liquid containing particles is sandwiched between an upper transparent and conductive ITO-coated glass, and a lower photoconductor. These two surfaces are biased with an ac signal. The upper ITO layer is grounded. The dark part of bottom photoconductor is regarded as insulator, and the ring-shaped bright part is illuminated by a Gaussian laser beam to form a virtual electrode on the surface with a peak potential in the centric circle line. Assumed that the light-induced virtual electrode was activated by a potential with the Gaussian profile along its thickness, given as: 2 ⎛ ( x − x0 ) ⎞ ⎟ U ( x ) = U 0 exp⎜⎜ − 2 w 2 ⎟⎠ ⎝
(1)
where x0 is the position of highest voltage U0 (10V) and defines the average radius of the light-induced virtual ring-shaped electrode, and 2w is the beam diameter and stands here for the width of the virtual electrode. With a set of parameters, w = 6μm, x0 = 10μm, and a chamber of 20μm height, the potential contour line and electric field surface distribution in the centric symmetry plane of the OET device is shown in Fig. 1(b). When the laser beam is focused or defocused on the photoconductor surface, the width of the virtual electrode will change and be able to influence the position of the weak potential energy well, as shown in Fig. 2. The higher value of w reveals that the potential of the virtual electrode declines slowly along with the electrode thickness, which generates the smaller gradient of electric field, and so the DEP trapping force. The smaller value of w creates the stronger vertical confinement and the holding force, though the position of weak well will move a certain extent.
;
5
x 10
w = 6 μm w = 8 μm w = 2 μm
16
Electric field, norm (V/m)
OET would be not able to handle the cell suspensions of high conductivity (several S/m), such as original cell culture media [10]. In addition, the OET requires complicated optical equipments to project and focus the laser beam. In order to generate a similarly high non-uniform field using real microelectrodes instead of OET, herein, we simulated the electric field distribution produced by a light-induced virtual ring-shaped electrode. Then, we substituted a real microelectrode that could be fabricated on a glass substrate in place of the virtual light-induced electrode. We simulated the distribution of the electric field using finite element method and derived the smallest radius of a single polystyrene bead potentially that could be trapped in the OET device and in the microelectrode structure, respectively. Finally, we designed and analyzed a 3×3 electrode array to explore the possibility to arbitrarily trap and manipulate single particles using the microelectrode.
14 12 10 8 6 4 2
0
0.5
1
1.5
2
-5 the vertical position in the centric line (m) x 10
Fig. 2. The electric field norm in the centric line of the OET device and the influence of the parameter w.
B. The electric field of real electrodes When we substituted a real ring-shaped microelectrode which could be fabricated on a glass substrate for the virtual light-induced electrode in Fig. 1, the weak potential energy well will move down to the right above the surface, as shown in Fig.3. When increasing or decreasing the voltage applied on the real electrode, and when changing the width of the real electrode, the position of the weak potential energy well will not deviate in any case except for the magnitude of the DEP trapping force. To obtain the similar trapping position as the OET, we designed a ring-dot-shaped electrode structure as shown in Fig. 4(a). The two electrodes are fabricated in two layers isolated by an insulator, except that the dot extrudes to the ring layer. The average radius of the ring electrode was 10μm, and the width of the ring electrode and the radius of the dot electrode are all of the same value of 5μm. For the simplified two-dimensional simulation, we set the upper ITO layer and the dot electrode grounded and applied an oscillatory voltage 10V on the ring electrode. Then the potential contour and the electric field norm distribution was calculated and shown in Fig. 4(b). Note that the position of the weak potential energy well was similar to that of the OET device. However, the electric field close to the substrate was different. When the bias applied on the dot electrode was changed, the position of the weak potential well would be move up and down as expected, as shown in Fig. 5. If the voltage of the ring electrode and the upper ITO layer is kept constant, then the larger the potential difference between the ring electrode and the dot electrode, the higher the well position. III. DIELECTROPHORETIC TRAPPINGS A. The dielectrophoretic force According to DEP fundamentals, the degree of non-uniform field reflects upon the magnitude of the dielectrophoretic force, as given by [11]:
6
x 10
Electric field, norm (V/m)
2.5
2
ITO
substrate
electrode
ground 3 (V) -3 (V) -10 (V) turn off
1.5
1
0.5
Fig. 3. The potential contour and the electric field norm distribution of the real microelectrode system. channel
dot dot dot dot dot
0
0.5
1
1.5
2
the y position along the centric line (m)x 10-5
Fig. 5. The electric field norm in the centric line of the real electrode structure and the influence of the voltage applied on the dot electrode.
(a)
(b) Fig. 4. (a) The ring-dot-shaped microelectrode structure. (b) The potential contour and the electric field norm distribution at the two-dimensional plan.
;
x 10
16
3 2
where υ is the volume of particle, Re[α] is the real part of the complex permittivity of particle, ∇E 2 is the gradient of the norm of electric field and represents the degree of non-uniform field. The gradient of the electric field norm in the OET device with the same parameters to those in Fig.1(b) and that of the real ring-dot shaped electrode structure with the same parameters to those in Fig.4 are shown in the Fig. 6(a) and (b), respectively. Compared with the OET device, the real microelectrode has a larger vertical component of − ∇E 2 around the potential energy well in the centre line—the red line in Fig. 6(a), as shown in Fig. 7. Although the vertical component of − ∇E 2 above the position of 7μm reveals that a particle will be pulled down toward the stable position, the Brownian motion would retard or obstruct the motion.
Fig. 6. The gradient of the electric field (a) in the OET device with the conditions: U0 = 10V, w = 6μm, x0 = 10μm; (b) in the real ring-dot-shaped electrode with the dot and the upper grounded and the ring electrode of 10V.
20
2
（2）
the vertical component of -∇E ( V /m )
1 FDEP = υ Re[α ]∇E 2 4
15 10 5 0 -5 2
4
6
8
10
12
14
16
the y position at the centre line (m) x 10-6
Fig. 7. The gradient of electric field norm in the centric line of the real electrode (the red line) and the virtual electrode (the blue line).
Re[α ] = 3ε m
ω (ε p − ε m ) − j (σ p − σ m ) ω (ε p + 2ε m ) − j (σ p + 2σ m )
(3)
here, j is the root of -1. Then the time-average DEP trap force acting on the bead with the radius of R is given by:
FDEP =
1 4πR Re[α ]∇E 2 = −40πε 0 R 3∇E 2 (4) 4 3 3
From Einstein’s equation, the randomized equivalent force of Brownian motion acting on the bead can be derived [5] and is given by:
FBrw = 6πηR
kT 12πηRkT = t 3πηRt
(5)
where η is the kinetic viscosity of water, k is the Boltzmann’s constant and T is the absolute temperature. For a time interval of 1s and at room temperature, the equivalent force of Brownian motion has to be smaller than the time-average DEP trap force so that the bead can be stably trapped in the weak potential energy well. Thus, the radius of the bead that is able to be strongly trapped must satisfy the following condition:
R≥5
12πηkT
(40πε ∇E )
2 2
(6)
0
Fig. 8 shows the smallest radius of beads along with the y position of the centre line in the both systems. The beads of radius above the lines would be exposed to the larger DEP trap force than that of the Brownian motion. For a bead with a radius of 80nm situated at 8μm above the substrate, the DEP trap force in the real electrode system is strong enough to overcome the Brownian motion and will vertically pull the bead back toward the cross point B. Then the bead would oscillate between the points of A and B for the effect of Brownian motion. However, the 80nm bead in the OET device would not be stably held in a narrow resign and would move randomly away. The beads of radius at the point C and D represent the limitations of the DEP vertical trapping in the ;
OET and the real electrode structure, respectively. x 10
-7
real electrode virtual electrode
x 10 14 The radius (m)
12 10
The radius of bead (m)
B. The DEP compared with the Brownian motion In the OET device, we assumed that the liquid containing the particles is statically sandwiched between two conductive layers before being exposed on an ac electric field. In order to trap single particles, the dielectrophoretic force acting to move the particle into the centre of the trap must overcome the Brownian motion, especially for sub-micrometre particles. Now, we consider a physiological saline (conductivity σm of 1S/m, permittivity εm of 80 ε0) containing polystyrene beads with a permittivity εp and conductivity σp of 2.5ε0, 10-4S/m, respectively [6], where ε0 is the dielectric constant of vacuum. The real part of complex permittivity of beads Re[α] is -120ε0 with the field frequency ω = 20MHz, which is obtained from:
8
B
12
C
A
10 8 6
D
4
6
-8
4
6 8 10 12 -6 the y position (m) x 10
4 2
0
0.5
1
1.5
2
the y position at the centre line (m) x 10-5 Fig. 8. The smallest radius of a bead that can be strongly trapped against the Brownian motion along the centre line.
IV. ELECTRODE ARRAY Microfabricated array-based structures have been wildly used in cell-based applications [12]. Herein, we discuss the design of a 3×3 real microscopic ring-dot-shaped electrode array, as shown in Fig. 9(a). The ring electrodes are interconnected and arranged in parallel rows on the substrate surface. The centric dots are extruded into the lower insulated layer and interconnected to form perpendicular columns, which can be seen in Fig. 4(a) but not drawn in Fig. 9(a). When the centric row of ring electrodes are exposed to5V, and the perpendicular centric column of dot electrodes and the upper layer are all grounded, three weak potential energy wells formed in different positions of different heights as shown in Fig. 9(b).And, if a trapping well is exactly needed at a given position, we can apply certain voltages to the other dot columns and the other ring rows for form the well. Fig. 10(a) shows only one trap generated through the following set of parameters: the centric row ring electrode and the side column dot electrodes are of 5V, and both the centric column dot electrode and the side row ring electrodes are of 0V. Another case of only one trap released with the certain set of parameters is shown in Fig. 10(b). V. CONCLUSIONS We analyzed and compared the electric fields and the DEP forces in the OET device and the real ring-dot-shaped electrode structure for 3D DEP trapping of particles. The smallest radii of polystyrene beads were also explored in the two DEP systems through comparing the DEP trap force and the effect of Brownian motion. In addition, a 3×3 trapping electrode array was designed and simulated to explore the effectiveness of arbitrarily trapping and manipulating single particles.
[4]
(a)
Potential well
Potential well
(b) Fig. 9. (a) The 3×3 electrode array. (b) The potential well in the electrode array.
5V 5V
0V 0V (a) 5V
2V
5V
0V -5 V (b)
Fig. 10. (a) One weak potential energy well generated. (b). One weak potential energy well released.
REFERENCES [1]
[2] [3]
;
P.Y. Chiou, A.T. Ohta, and M.C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature, vol. 436, (no. 7049), pp. 370-372, 2005. M.P. Hughes, “AC electrokinetics: applications for nanotechnology,” Nanotechnology, vol. 11, (no. 2), pp. 124-132, 2000. J. Voldman, “Dielectrophoretic Traps for Cell Manipulation,” in BioMEMS and Biomedical Nanotechnology Volume IV: Biomolecular Sensing, Processing and Analysis, M. Ferrari, R. Bashir and S. Wereley eds.: Springer US, 2006, pp. 159-186.
Y. Huang and R. Pethig, “Electrode design for negative dielectrophoresis,” Measurement Science and Technology, vol. 2, (no. 12), pp. 1142-1146, 1991. [5] M.P. Hughes and H. Morgan, “Dielectrophoretic trapping of single sub-micrometre scale bioparticles,” Journal of Physics D: Applied Physics, vol. 31, (no. 17), pp. 2205-2210, 1998. [6] J. Voldman, M. Toner, M.L. Gray, and M.A. Schmidt, “Design and analysis of extruded quadrupolar dielectrophoretic traps,” Journal of Electrostatics, vol. 57, (no. 1), pp. 69-90, 2003. [7] T. Schnelle, R. Hagedorn, G. Fuhr, S. Fiedler, and T. Muller, “Three-dimensional electric field traps for manipulation of cells -calculation and experimental verification,” Biochimica et Biophysica Acta (BBA) - General Subjects, vol. 1157, (no. 3), pp. 127-140, 1993. [8] T. Schnelle, T. Muller, and G. Fuhr, “Trapping in AC octode field cages,” Journal of Electrostatics, vol. 50, (no. 1), pp. 17-29, 2000. [9] P.Y. Chiou, W. Wong, J.C. Liao, and M.C. Wu, “Cell addressing and trapping using novel optoelectronic tweezers,” Micro Electro Mechanical Systems, 2004. 17th IEEE International Conference on. (MEMS), pp. 21-24, 2004. [10] G. Fuhr, H. Glasser, T. Muller, and T. Schnelle, “Cell manipulation and cultivation under ac electric field influence in highly conductive culture media,” Biochim Biophys Acta, vol. 1201, (no. 3), pp. 353-60, 1994. [11] Morgan, H. and N.G. Green, AC electrokinetics: colloids and nanoparticles, 2003, Philadelphia: PA Research Studies Press. [12] B.M. Taff and J. Voldman, “A scalable addressable positivedielectrophoretic cell-sorting array,” Anal Chem, vol. 77, (no. 24), pp. 7976-83, 2005.
Abstract—Micro- and nano-particles can be trapped in locally strong or weak regions of a non-uniform electric field through the effect of dielectrophoretic principle. Recently, a novel optoelectronic tweezers (OET) based on optically induced dielectrophoresis (DEP) was demonstrated by Chiou et al. [1] for effectively trapping and manipulation of cells and latex particles. The OET allows an optical beam to create a virtual electrode on a photoconductive surface, which produces a highly non-uniform electric field. Here we simulated the electric field distribution produced by a light-induced ring-shaped electrode for particles trapping. Then, we simulated the DEP trapping effects from a real microelectrode that could be fabricated on a glass substrate to replace the virtual light-induced electrode. This is to compare the efficiencies of OET and microelectrode induced DEP effects. We also derived the smallest radiuses of the polystyrene bead which could be potentially trapped in the OET device and the real electrode structure. Finally, we designed and analyzed a 3×3 electrode array to explore the possibility of arbitrarily trapping and manipulating single particles using the real microelectrodes. Index Terms—dielectrophoretic trapping, optoelectronic tweezers, nano-manipulation, DEP.
I. INTRODUCTION trapping and manipulation using PARTICLES dielectrophoresis have been attracting comprehensive attentions in the field of micro/nanotechnology[2], [3]. DEP has been demonstrated by many research groups to trap particles in local strong electric field and in local weak electric field, termed respectively positive DEP and negative DEP. A common electrode configuration used for particles trapping is a planar quadrupole arrangement where four electrodes point towards a central enclosed region [4], [5]. This electrode design may have many advanced varieties, however, these planar traps suffer from the drawback that increasing the field only pushes particles farther out of the trap and does not necessarily increase confinement. To avoid _______________________________________ *Contact author: [email protected]. Wen J. Li is a professor at The Chinese University of Hong Kong and also an affiliated professor at the Shenyang Institute of Automation. Minglin Li is also with College of Mechanical Engineering, Fuzhou University, 350002, China and Graduate University of the Chinese Academy of Sciences, 100049 China. This work is supported in part by the NSFC (Project code: 60635040 and 60675060) and the Chinese National 863 Plan (Project code: 2006AA04Z320 and 2007AA04Z317).
;
them, Voldman et al. [6] designed and demonstrated an extruded quadrupole dielectrophoretic trap with stronger holding forces than those of planar quadrupole. However, the extruded electrode is more difficult to be fabricated. Another way to increase the strength of quadrupole electrode traps is the octopole field cage [7], [8]. Although the octopole field cage only includes two planar quadrupole electrodes simpler fabricated than the extruded quadrupole, they are more complicated to align and package. Recently, a novel optoelectronic tweezers (OET) based on light-induced DEP was demonstrated by Chiou et al. [1] for effectively trapping and manipulation of cells and latex particles. In the OET device, a virtual electrode would form on the surface and generate a highly non-uniform electric field in the liquid layer through an optical beam focused on the photoconductive surface. Since the conductivity of photoconductor linearly increases several orders of magnitude due to the photogenerated charged carriers in the photoconductor, from dark to light, the distribution of the light-induced non-uniform field depends on the profile of the light intensity. Noted that the conductivity of the illuminated photoconductor is still smaller than that of metals [9], so the
(a)
(b) Fig. 1. (a) The simplified system of OET device. (b) The potential contour and the electric field norm distribution at the centric symmetry plane.
II. ELECTRIC FIELDS A. The light-induced electric field For simulation, we considered a simplified model of the OET system, as shown in Fig. 1(a). A liquid containing particles is sandwiched between an upper transparent and conductive ITO-coated glass, and a lower photoconductor. These two surfaces are biased with an ac signal. The upper ITO layer is grounded. The dark part of bottom photoconductor is regarded as insulator, and the ring-shaped bright part is illuminated by a Gaussian laser beam to form a virtual electrode on the surface with a peak potential in the centric circle line. Assumed that the light-induced virtual electrode was activated by a potential with the Gaussian profile along its thickness, given as: 2 ⎛ ( x − x0 ) ⎞ ⎟ U ( x ) = U 0 exp⎜⎜ − 2 w 2 ⎟⎠ ⎝
(1)
where x0 is the position of highest voltage U0 (10V) and defines the average radius of the light-induced virtual ring-shaped electrode, and 2w is the beam diameter and stands here for the width of the virtual electrode. With a set of parameters, w = 6μm, x0 = 10μm, and a chamber of 20μm height, the potential contour line and electric field surface distribution in the centric symmetry plane of the OET device is shown in Fig. 1(b). When the laser beam is focused or defocused on the photoconductor surface, the width of the virtual electrode will change and be able to influence the position of the weak potential energy well, as shown in Fig. 2. The higher value of w reveals that the potential of the virtual electrode declines slowly along with the electrode thickness, which generates the smaller gradient of electric field, and so the DEP trapping force. The smaller value of w creates the stronger vertical confinement and the holding force, though the position of weak well will move a certain extent.
;
5
x 10
w = 6 μm w = 8 μm w = 2 μm
16
Electric field, norm (V/m)
OET would be not able to handle the cell suspensions of high conductivity (several S/m), such as original cell culture media [10]. In addition, the OET requires complicated optical equipments to project and focus the laser beam. In order to generate a similarly high non-uniform field using real microelectrodes instead of OET, herein, we simulated the electric field distribution produced by a light-induced virtual ring-shaped electrode. Then, we substituted a real microelectrode that could be fabricated on a glass substrate in place of the virtual light-induced electrode. We simulated the distribution of the electric field using finite element method and derived the smallest radius of a single polystyrene bead potentially that could be trapped in the OET device and in the microelectrode structure, respectively. Finally, we designed and analyzed a 3×3 electrode array to explore the possibility to arbitrarily trap and manipulate single particles using the microelectrode.
14 12 10 8 6 4 2
0
0.5
1
1.5
2
-5 the vertical position in the centric line (m) x 10
Fig. 2. The electric field norm in the centric line of the OET device and the influence of the parameter w.
B. The electric field of real electrodes When we substituted a real ring-shaped microelectrode which could be fabricated on a glass substrate for the virtual light-induced electrode in Fig. 1, the weak potential energy well will move down to the right above the surface, as shown in Fig.3. When increasing or decreasing the voltage applied on the real electrode, and when changing the width of the real electrode, the position of the weak potential energy well will not deviate in any case except for the magnitude of the DEP trapping force. To obtain the similar trapping position as the OET, we designed a ring-dot-shaped electrode structure as shown in Fig. 4(a). The two electrodes are fabricated in two layers isolated by an insulator, except that the dot extrudes to the ring layer. The average radius of the ring electrode was 10μm, and the width of the ring electrode and the radius of the dot electrode are all of the same value of 5μm. For the simplified two-dimensional simulation, we set the upper ITO layer and the dot electrode grounded and applied an oscillatory voltage 10V on the ring electrode. Then the potential contour and the electric field norm distribution was calculated and shown in Fig. 4(b). Note that the position of the weak potential energy well was similar to that of the OET device. However, the electric field close to the substrate was different. When the bias applied on the dot electrode was changed, the position of the weak potential well would be move up and down as expected, as shown in Fig. 5. If the voltage of the ring electrode and the upper ITO layer is kept constant, then the larger the potential difference between the ring electrode and the dot electrode, the higher the well position. III. DIELECTROPHORETIC TRAPPINGS A. The dielectrophoretic force According to DEP fundamentals, the degree of non-uniform field reflects upon the magnitude of the dielectrophoretic force, as given by [11]:
6
x 10
Electric field, norm (V/m)
2.5
2
ITO
substrate
electrode
ground 3 (V) -3 (V) -10 (V) turn off
1.5
1
0.5
Fig. 3. The potential contour and the electric field norm distribution of the real microelectrode system. channel
dot dot dot dot dot
0
0.5
1
1.5
2
the y position along the centric line (m)x 10-5
Fig. 5. The electric field norm in the centric line of the real electrode structure and the influence of the voltage applied on the dot electrode.
(a)
(b) Fig. 4. (a) The ring-dot-shaped microelectrode structure. (b) The potential contour and the electric field norm distribution at the two-dimensional plan.
;
x 10
16
3 2
where υ is the volume of particle, Re[α] is the real part of the complex permittivity of particle, ∇E 2 is the gradient of the norm of electric field and represents the degree of non-uniform field. The gradient of the electric field norm in the OET device with the same parameters to those in Fig.1(b) and that of the real ring-dot shaped electrode structure with the same parameters to those in Fig.4 are shown in the Fig. 6(a) and (b), respectively. Compared with the OET device, the real microelectrode has a larger vertical component of − ∇E 2 around the potential energy well in the centre line—the red line in Fig. 6(a), as shown in Fig. 7. Although the vertical component of − ∇E 2 above the position of 7μm reveals that a particle will be pulled down toward the stable position, the Brownian motion would retard or obstruct the motion.
Fig. 6. The gradient of the electric field (a) in the OET device with the conditions: U0 = 10V, w = 6μm, x0 = 10μm; (b) in the real ring-dot-shaped electrode with the dot and the upper grounded and the ring electrode of 10V.
20
2
（2）
the vertical component of -∇E ( V /m )
1 FDEP = υ Re[α ]∇E 2 4
15 10 5 0 -5 2
4
6
8
10
12
14
16
the y position at the centre line (m) x 10-6
Fig. 7. The gradient of electric field norm in the centric line of the real electrode (the red line) and the virtual electrode (the blue line).
Re[α ] = 3ε m
ω (ε p − ε m ) − j (σ p − σ m ) ω (ε p + 2ε m ) − j (σ p + 2σ m )
(3)
here, j is the root of -1. Then the time-average DEP trap force acting on the bead with the radius of R is given by:
FDEP =
1 4πR Re[α ]∇E 2 = −40πε 0 R 3∇E 2 (4) 4 3 3
From Einstein’s equation, the randomized equivalent force of Brownian motion acting on the bead can be derived [5] and is given by:
FBrw = 6πηR
kT 12πηRkT = t 3πηRt
(5)
where η is the kinetic viscosity of water, k is the Boltzmann’s constant and T is the absolute temperature. For a time interval of 1s and at room temperature, the equivalent force of Brownian motion has to be smaller than the time-average DEP trap force so that the bead can be stably trapped in the weak potential energy well. Thus, the radius of the bead that is able to be strongly trapped must satisfy the following condition:
R≥5
12πηkT
(40πε ∇E )
2 2
(6)
0
Fig. 8 shows the smallest radius of beads along with the y position of the centre line in the both systems. The beads of radius above the lines would be exposed to the larger DEP trap force than that of the Brownian motion. For a bead with a radius of 80nm situated at 8μm above the substrate, the DEP trap force in the real electrode system is strong enough to overcome the Brownian motion and will vertically pull the bead back toward the cross point B. Then the bead would oscillate between the points of A and B for the effect of Brownian motion. However, the 80nm bead in the OET device would not be stably held in a narrow resign and would move randomly away. The beads of radius at the point C and D represent the limitations of the DEP vertical trapping in the ;
OET and the real electrode structure, respectively. x 10
-7
real electrode virtual electrode
x 10 14 The radius (m)
12 10
The radius of bead (m)
B. The DEP compared with the Brownian motion In the OET device, we assumed that the liquid containing the particles is statically sandwiched between two conductive layers before being exposed on an ac electric field. In order to trap single particles, the dielectrophoretic force acting to move the particle into the centre of the trap must overcome the Brownian motion, especially for sub-micrometre particles. Now, we consider a physiological saline (conductivity σm of 1S/m, permittivity εm of 80 ε0) containing polystyrene beads with a permittivity εp and conductivity σp of 2.5ε0, 10-4S/m, respectively [6], where ε0 is the dielectric constant of vacuum. The real part of complex permittivity of beads Re[α] is -120ε0 with the field frequency ω = 20MHz, which is obtained from:
8
B
12
C
A
10 8 6
D
4
6
-8
4
6 8 10 12 -6 the y position (m) x 10
4 2
0
0.5
1
1.5
2
the y position at the centre line (m) x 10-5 Fig. 8. The smallest radius of a bead that can be strongly trapped against the Brownian motion along the centre line.
IV. ELECTRODE ARRAY Microfabricated array-based structures have been wildly used in cell-based applications [12]. Herein, we discuss the design of a 3×3 real microscopic ring-dot-shaped electrode array, as shown in Fig. 9(a). The ring electrodes are interconnected and arranged in parallel rows on the substrate surface. The centric dots are extruded into the lower insulated layer and interconnected to form perpendicular columns, which can be seen in Fig. 4(a) but not drawn in Fig. 9(a). When the centric row of ring electrodes are exposed to5V, and the perpendicular centric column of dot electrodes and the upper layer are all grounded, three weak potential energy wells formed in different positions of different heights as shown in Fig. 9(b).And, if a trapping well is exactly needed at a given position, we can apply certain voltages to the other dot columns and the other ring rows for form the well. Fig. 10(a) shows only one trap generated through the following set of parameters: the centric row ring electrode and the side column dot electrodes are of 5V, and both the centric column dot electrode and the side row ring electrodes are of 0V. Another case of only one trap released with the certain set of parameters is shown in Fig. 10(b). V. CONCLUSIONS We analyzed and compared the electric fields and the DEP forces in the OET device and the real ring-dot-shaped electrode structure for 3D DEP trapping of particles. The smallest radii of polystyrene beads were also explored in the two DEP systems through comparing the DEP trap force and the effect of Brownian motion. In addition, a 3×3 trapping electrode array was designed and simulated to explore the effectiveness of arbitrarily trapping and manipulating single particles.
[4]
(a)
Potential well
Potential well
(b) Fig. 9. (a) The 3×3 electrode array. (b) The potential well in the electrode array.
5V 5V
0V 0V (a) 5V
2V
5V
0V -5 V (b)
Fig. 10. (a) One weak potential energy well generated. (b). One weak potential energy well released.
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