doi:10.1016/j.jcis.2005.11.024
Copyright © 2005 Elsevier Inc. All rights reserved.
The role of electrode impedance and electrode geometry in the design of microelectrode systems
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Hao Zhoua, Robert D. Tiltona, b and Lee R. Whitea, 
, 
aDepartment of Chemical Engineering, Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
bDepartment of Biomedical Engineering, Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Received 11 August 2005;
accepted 9 November 2005.
Available online 5 December 2005.
Abstract
Microelectromechanical systems (MEMS) employing spatially and/or temporally nonuniform electric fields have been extensively employed to control the motion of suspended particles or fluid flow. Design and control of microelectromechanical processes require accurate calculations of the electric field distribution under varying electrolyte conditions. Polarization of electrodes under the application of an oscillating voltage difference produces dynamic electrical double layers. The capacitive nature of the double layers significantly inhibits the penetration of the electric field through the double layer and into the surrounding bulk electrolyte at low frequencies. This paper quantitatively discusses the effect of electrode impedance on the electric field distribution as a function of field frequency, electrolyte composition, and electrode zeta potential in microelectrode systems. The design principles for the electrode geometry and configuration are also discussed in terms of their effects on the electric field magnitude and nonuniformity.
Graphical abstract
This paper quantitatively discusses the effect of electrode impedance and electrode geometry and configuration on the electric field distribution in microelectrode systems.
Keywords: MEMS; Electrode impedance; Microelectrode arrays; AC electric field
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Fig. 2. Electric field calculation model used for the microelectrode systems. (a) Calculation model for 
configuration, shown in Fig. 1a. Electric potentials are applied to two parallel electrode strip surfaces, left (L) and right (R), which are positioned at y=0. The lengths lL and lR are the half strip widths of L and R electrode strips, respectively. S stands for the symmetry plane. The characteristic separation width between two connected electrode strips, hw, equals the dielectric strip width lD. The top dielectric surface is positioned at y=1 mm. (b) Calculation model for 
configuration, shown in Fig. 1b. Electric potentials are applied normally to the electrode strip surfaces, T, L, and R. The L and R electrode strips are positioned at y=0. The lengths lL and lR are the half strip widths of L and R electrode strips, respectively. S strands for the symmetry plane. The edges of the strips L and R are separated by a dielectric surface of length lD. The length of the top electrode lT equals lL+lR+lD. The characteristic separation width between two connected electrode strips, hw, equals the microelectrode cell thickness.
Fig. 3. The electric field intensity distribution calculated at y=0.2l=3 μm from the electrode surface without electrode impedance (Zel=0) and with the electrode double layer impedance at 5, 10, 20, 60, 300 Hz, and 20 kHz in the configuration (hw=66.7l=1 mm). The electrode zeta potentials are ζT=ζL=ζR=−80 mV. The electrolyte is 0.1 mM NaHCO3.
Fig. 4. The electric field intensity distribution calculated at various heights, y=0.1l, 0.2l, 0.4l, 0.6l, 0.8l, and 1l, above the electrode surface at 20 Hz in the configuration (hw=66.7l=1 mm). The electrode zeta potentials are ζT=ζL=ζR=−80 mV. The electrolyte is 0.1 mM NaHCO3.
Fig. 5. The electric field intensity distribution calculated at y=0.2l=3 μm above the electrode surface for various electrode zeta potentials in the configuration (hw=66.7l=1 mm). The electrolyte is 0.1 mM NaHCO3. (a) ζT=ζL=−80 mV, ζR=−80, −100, −120, and −140 mV at 5 Hz. (b) ζT=ζL=−80 mV, ζR=−100 mV at 5, 10, 20, 60, 300 Hz, and 20 kHz. (c) ζT=ζL=ζR=−80 mV; ζT=ζL=−80 mV, ζR=−140 mV; ζT=−80 mV, ζL=ζR=−140 mV; ζT=−140 mV, ζL=ζR=−80 mV; ζT=ζL=−140 mV, ζR=−80 mV; and ζT=ζL=ζR=−140 mV at 5 Hz.
Fig. 6. The electric field intensity distribution calculated at y=0.2l=3 μm above the electrode surface for 0.1, 1, and 10 mM NaHCO3 at (a) 5 Hz and (b) 300 Hz in the configuration (hw=66.7l=1 mm). The electrode zeta potentials are ζT=ζL=ζR=−80 mV.
Fig. 7. The electric field intensity distribution calculated at y=0.2l=3 μm from the electrode surface for 0.1 mM NaHCO3, NaCl, KCl, and HCl at (a) 5 Hz and (b) 300 Hz in the configuration (hw=66.7l=1 mm). The electrode zeta potentials are ζT=ζL=ζR=−80 mV.
Fig. 8. The electric field intensity distributions calculated at y=0.2l=3 μm above the electrode surface for characteristic separation width hw=6.67l=0.1 mm, hw=33.33l=0.5 mm, and hw=66.67l=1 mm at (a) 5 Hz and (b) 300 Hz in the configuration. The electrode zeta potentials are ζT=ζL=ζR=−80 mV. The electrolyte is 0.1 mM NaHCO3.
Fig. 9. (a) The electric field intensity distributions, (b) lateral field intensity, and (c) normal field intensity calculated at y=0.2l=3 μm above the electrode surface in the configuration and the configuration with characteristic interelectrode spacing width hw=8l=120 μm at 300 Hz in the configuration. The electrode zeta potentials are ζT=ζL=ζR=−80 mV. The electrolyte is 0.1 mM NaHCO3.
Fig. 10. The electric field intensity distributions calculated at y=0.2l=3 μm above the electrode surface for various voltage configurations, ΦL=0, ΦR=1 in the configuration (where ΦT is not applicable as there is no top electrode); ΦT=ΦL=0, ΦR=1; ΦT=1, ΦL=ΦR=0; and ΦT=ΦR=1, ΦL=0 in the configuration. All at 300 Hz. The electrode zeta potentials are ζT=ζL=ζR=−80 mV and hw=8l=120 μm. The electrolyte is 0.1 mM NaHCO3.
Fig. 11. The electric field intensity distributions calculated at y=0.2l=3 μm above the electrode surface for various dielectric spacings lD=l, 2l, 4l, 6l, and 8l between two electrode strips (a) in the configuration (hw=66.7l=1 mm) and (b) in the configuration; all at 60 Hz. The electrode zeta potentials are ζT=ζL=ζR=−80 mV and the electrode widths are fixed at lL=lR=l. The electrolyte is 0.1 mM NaHCO3.
Fig. 12. The electric field intensity distributions calculated at y=0.2l=3 μm above the electrode surface for various electrode strip widths lL=lR=l, 2l, 3l, and 4l and fixed dielectric spacing lD=2l (a) in the configuration (hw=66.7l=1 mm) and (b) in the configuration; all at 60 Hz. The electrode zeta potentials are ζT=ζL=ζR=−80 mV. The electrolyte is 0.1 mM NaHCO3.
Fig. 13. The electric field intensity distributions calculated at y=0.2l=3 μm above the electrode surface for various left electrode strip widths lL=l, 2l, 3l, 4l, 5l, 6l, 7l, and 8l with fixed lR=l and lT=10l (a) in the configuration (hw=66.7l=1 mm) at 5 Hz, (b) in the configuration at 5 Hz, (c) in the configuration (hw=66.7l=1 mm) at 60 Hz, and (d) in the configuration at 60 Hz. The electrode zeta potentials are ζT=ζL=ζR=−80 mV. The electrolyte is 0.1 mM NaHCO3.
Fig. 14. Representative patterning results for PS 9.6/44 colloids obtained after 10 min of applying an electric field. (a) 60 Hz, 0.17 V. (b) 60 Hz, 0.51 V. (c) 1 kHz, where 0.17 or 0.51 V produced similar results.
Fig. 15. The DEP force that a PS 9.6/44 particle experiences near a single strip electrode of width 2l at an applied voltage of 0.51 V in the configuration. A lateral position of zero indicates the electrode strip center. Lateral DEP force FDEP_x as a function of normalized lateral distance from a single strip center at elevations of 3, 6, 9, and 12 μm above the surface at (a) 60 Hz and (b) 1 kHz.
Table 1.
Parameters used in the calculations in this paper
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