Frequency Dependence of Gold Nanoparticle Superassembly by

Oct 27, 2007 - Dielectrophoresis is an effective method for capturing nanoparticles and assembling them into nanostructures. The frequency of the diel...
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Langmuir 2007, 23, 12450-12456

Frequency Dependence of Gold Nanoparticle Superassembly by Dielectrophoresis Brian C. Gierhart,*,† David G. Howitt,‡ Shiahn J. Chen,§ Rosemary L. Smith,§ and Scott D. Collins§ Department of Electrical and Computer Engineering, and Department of Chemical Engineering and Materials Science, UniVersity of CaliforniasDaVis, DaVis, California 95616, and The MicroInstruments and Systems Laboratory (MISL), Laboratory for Surface Science and Technology (LASST), UniVersity of Maine, Orono, Maine 04469 ReceiVed May 19, 2007. In Final Form: August 6, 2007 Dielectrophoresis is an effective method for capturing nanoparticles and assembling them into nanostructures. The frequency of the dielectrophoretic alternating current (ac) electric field greatly influences the morphology of resultant nanoparticle assemblies. In this study, frequency regimes associated with specific gold nanoparticle assembly morphologies were identified. Gold nanoparticles suspended in water were captured by microelectrodes at different electric field frequencies onto thin silicon nitride membranes. The resultant assemblies were examined by transmission electron microscopy. For this system, the major frequency-dependent influence on morphology appears to arise not from the Clausius-Mossotti factor of the dielectrophoretic force itself, but instead from ac electroosmotic fluid flow and the influence of the electrical double layer at the electrode-solution interface. Frequency regimes of technological interest include those forming one-dimensional nanoparticle chains, microwires, combinations of microwires and nanoparticle chains suitable for nanogap electrode formation, and dense three-dimensional assemblies with very high surface area.

Introduction Fabrication of novel nanostructures and their assembly into nanodevices and nanosystems has recently received considerable attention.1-4 Nanosystems offer advantages over their micro and macro analogs that include decreased size, less power consumption, faster speeds, greater sensitivities, and potentially lower cost. Although biological systems make complex nanoscale proteins with enviable precision and repeatability, synthetic nanotechnology falls considerably short of such sophistication both in complexity and throughput. Currently, the most common method for controlled nanofabrication is electron beam lithography.5 This technique enables nanometer resolution but is limited to thin films, has low throughput, and is prohibitively expensive. Focused ion beam fabrication offers more versatility6 but is similarly limited by throughput and expense. Although scanning probe microscopies such as atomic force microscopy (AFM) offer nanofabrication techniques like dip-pen lithography7 and nanoshaving8 and possess exquisite atomic manipulation abilities, most scanning probes are slow and not well-suited to highthroughput fabrication. Parallel AFM arrays, or millipedes,9 do * Corresponding author. E-mail: [email protected]. † Department of Electrical and Computer Engineering, University of CaliforniasDavis. ‡ Department of Chemical Engineering and Materials Science, University of CaliforniasDavis. § MicroInstruments and Systems Laboratory, University of Maine. (1) Duan, X. F.; Huang, Y.; Cui, Y.; Wang, J. F.; Lieber, C. M. Nature 2001, 409, 66-69. (2) Daniel, M. C.; Astruc, D. Chem. ReV. 2004, 104, 293-346. (3) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787-792. (4) Cui, Y.; Lieber, C. M. Science 2001, 291, 851-853. (5) Fischbein, M. D.; Drndic, M. Appl. Phys. Lett. 2006, 88, 063116. (6) Giannuzzi, L. A.; Stevie, F. A. Introduction to Focused Ion Beams: Instrumentation, Theory, Techniques, and Practice; Springer: New York, 2005. (7) Piner, R. D.; Zhu, J.; Xu, F.; Hong, S. H.; Mirkin, C. A. Science 1999, 283, 661-663. (8) Xu, S.; Liu, G. Y. Langmuir 1997, 13, 127-129.

hold promise for future higher-throughput nanofabrication but are not yet available. Until systems engineering descends further down the dimensional staircase, simpler and more readily available techniques are needed to create and assemble nanostructures. Dielectrophoresis (DEP) offers an inexpensive and straightforward alternative for both the nanofabrication and assembly of nanostructures and systems.10 Dielectrophoresis describes the force that a nonuniform ac electric field exerts on neutral (uncharged) matter and is widely employed in the manipulation and sorting of both biological and synthetic particles. More recently, dielectrophoresis has been used in the fabrication of molecular electronics,11-14 nanolaminates for novel materials,15 and nanowires and microwires by capturing and fusing nanoparticles.16,17 Dielectrophoresis is also used to make devices from carbon nanotubes18 and semiconductor nanowires1 and to sort, select, and purify19 carbon nanotubes according to their metallic or semiconducting character.20 Of particular importance in the (9) Vettiger, P.; Despont, M.; Drechsler, U.; Durig, U.; Haberle, W.; Lutwyche, M. I.; Rothuizen, H. E.; Stutz, R.; Widmer, R.; Binnig, G. K. IBM J. Res. DeV. 2000, 44, 323-340. (10) Hughes, M. P. Nanoelectromechanics in Engineering and Biology; CRC Press: Boca Raton, FL, 2003. (11) Khondaker, S. I.; Yao, Z. Appl. Phys. Lett. 2002, 81, 4613-4615. (12) Khondaker, S. I.; Yao, Z.; Cheng, L.; Henderson, J. C.; Yao, Y. X.; Tour, J. M. Appl. Phys. Lett. 2004, 85, 645-647. (13) Amlani, I.; Rawlett, A. M.; Nagahara, L. A.; Tsui, R. K. J. Vac. Sci. Technol., B 2002, 20, 2802-2805. (14) Amlani, I.; Rawlett, A. M.; Nagahara, L. A.; Tsui, R. K. Appl. Phys. Lett. 2002, 80, 2761-2763. (15) Trau, M.; Saville, D. A.; Aksay, I. A. Langmuir 1997, 13, 6375-6381. (16) Bernard, L.; Calame, M.; Molen, S. J. v. d.; Liao, J.; Scho¨nenberger, C. Nanotechnology 2007, 235202. (17) Ozturk, B.; Talukdar, I.; Flanders, B. N. Appl. Phys. Lett. 2005, 86, 183105. (18) Chen, Z.; Yang, Y.; Chen, F.; Qing, Q.; Wu, Z.; Liu, Z. J. Phys. Chem. B 2005, 109, 11420-11423. (19) Yamamoto, K.; Akita, S.; Nakayama, Y. J. Phys. D: Appl. Phys. 1998, 31, L34. (20) Krupke, R.; Hennrich, F.; Lohneysen, H. v.; Kappes, M. M. Science 2003, 301, 344-347.

10.1021/la701472y CCC: $37.00 © 2007 American Chemical Society Published on Web 10/27/2007

Frequency Dependence of Au Nanoparticle DEP

fabrication of useful nanodevices is the dielectrophoresis of metallic nanoparticles, such as gold nanoparticles. Gold nanoparticles are widely available in diameters ranging from 2 to 250 nm. The utility of highly conductive metallic nanostructures has prompted several investigations into applying dielectrophoresis as a means to assemble precision nanostructures to create nanogaps for molecular electronics,12 nanowires and microwires for electrical connection to devices and components,21 and high surface area electrodes for sensor applications.22 Although electrophoretic capture of nanostructures has been recently reviewed,23 less is known about dielectrophoretic capture. For example, several investigators have reported frequency dependence in the assembly of gold nanoparticles, such as increases in the threshold voltage required to initiate assembly for frequencies in the range 10-104 Hz22 and diminishing nanowire growth velocities as frequency is increased.21,24 The dielectrophoresis of carbon nanotubes has also been observed to depend on the frequency of the applied field.25 These observed variations in behavior with frequency have been attributed by some investigators to a variation in the dielectrophoretic force. Others make no comment on the origin of the frequency dependence26 or attribute the effect to particle chain orientation.27 Some have observed what appears to be fluid flow at the growing tips of nanowires and attribute this to electrohydrodynamic forces21 or thermal convective fluid flow.27 Researchers working with colloidal polystyrene have noted frequency-dependent orientation and clustering effects.28 Because of the utility of dielectrophoresis in creating and manipulating nanostructures, a more detailed understanding of the mechanisms governing frequency dependence is desirable. In this study, gold nanoparticles were captured using a variety of frequencies and the resulting assemblies examined using transmission electron microscopy (TEM). Different frequency regimes associated with specific morphologies are identified and explained in terms of electric field gradient and fluid flow velocity calculations. The major frequency-dependent influences on this type of dielectrophoretic assembly are seen to be electrode polarization and ac electroosmotic fluid flow. Materials and Methods Low-pressure chemical vapor deposition was employed to deposit 80 nm of stoichiometric silicon nitride on an oxidized silicon wafer. The silicon was patterned and anisotropically etched, followed by removal of the oxide layer, to form a 100 µm square silicon nitride membrane. This membrane provided a window for TEM visualization. Two gold electrodes (100 nm thick Au/10 nm thick Cr) were photolithographically patterned on the membrane using a liftoff process. The chrome and gold layers were deposited by electron beam evaporation. The gold electrodes were 50 µm wide and separated from each other with a gap of between 3 and 100 µm. The wafers were diced with a diamond blade into 2.1 mm square chips. Each chip was cleaned with acetone and methanol, rinsed with deionized water, and dried with clean nitrogen. Before use, the chips were cleaned for 1 min in an oxygen plasma at 200 W power, 150 mTorr pressure, and 7 sccm oxygen flow; rinsed briefly in 95% ethanol; and dried with clean nitrogen.29 Electrical contact to the (21) Hermanson, K. D.; Lumsdon, S. O.; Williams, J. P.; Kaler, E. W.; Velev, O. D. Science 2001, 294, 1082-1086. (22) Lumsdon, S. O.; Scott, D. M. Langmuir 2005, 21, 4874-4880. (23) Boccaccini, A. R.; Roether, J. A.; Thomas, B. J. C.; Shaffer, M. S. P.; Chavez, E.; Stoll, E.; Minay, E. J. J. Ceram. Soc. Jpn. 2006, 114, 1-14. (24) Bhatt, K. H.; Velev, O. D. Langmuir 2004, 20, 467-476. (25) Dimaki, M.; Boggild, P. Nanotechnology 2005, 16, 759-763. (26) Kretschmer, R.; Fritzsche, W. Langmuir 2004, 20, 11797-11801. (27) Yuan, Y. J.; Andrews, M. K.; Marlow, B. K. Appl. Phys. Lett. 2004, 85, 130-132. (28) Negi, A. S.; Sengupta, E.; Sood, A. K. Langmuir 2005, 21, 1162311627.

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Figure 1. Instrumentation circuit for dielectrophoretic nanoparticle capture showing a drop of nanoparticle solution (a), gold electrodes (b), and silicon nitride surface (c). R2 (normally 15 kΩ) was set so that Vmeas ) Vin/2 (R1 ) 10 kΩ).

gold electrodes on the chip was accomplished using micromanipulators and a probe station. A drop of nanoparticles (Ted Pella) containing either 5, 15, or 20 nm diameter gold nanoparticles30 in deionized water was placed onto the chip by manual pipetting. The nanoparticle supplier specified concentrations of 5.0 × 1013/mL for the 5 nm particles, 1.4 × 1012/mL for the 15 nm particles, and 7.0 × 1011/mL for the 20 nm particles. The circuit for nanoparticle capture is shown in Figure 1. A sinusoidal ac voltage (Vin) was applied to one gold electrode using a function generator (HP3310A), and the voltage at the opposite electrode (Vmeas) was monitored using an oscilloscope (HP54610B).31 A 10 kΩ resistor (R1) was connected in series with the electrodes to limit the current flowing through completed nanowires. A parallel resistor (R2, typically ∼15 kΩ) was added to prevent the voltage across the electrodes from being sensitive to solution impedance changes during nanowire growth. Unless specifically noted, the applied voltage was removed when voltage measurements indicated that a completed nanowire had “shorted” the electrodes, or after 5 min, whichever came first. After nanowire fabrication, the chip was rinsed in deionized water and dried with clean nitrogen. The resistance of completely connected nanowires was measured after drying using a semiconductor parameter analyzer (HP4155A), and nanowires were imaged using a TEM (Phillips CM-12). Measurements of fluid velocity were made using identical devices wire-bonded into a custom package that accommodated the use of a 40× microscope objective. Latex microspheres (2.0 µm, Bangs Laboratories, Inc., Fishers, IN) were dispersed in deionized water by ultrasonication, and a drop of this solution was applied to the chip and covered with a glass coverslip. Video micrographs of the microspheres moving with the fluid were captured at different electrical excitation frequencies using a digital microscope camera (PaxCam, MIS, Inc., Franklin Park, IL) and processed using particle tracking software.32

Results and Discussion Micrographs of gold nanoparticles captured within a 3 µm gap between two gold electrodes are shown in Figure 2. A wide variation in assembly morphology with frequency is apparent. During their assembly, the applied ac electric field produces forces on both the nanoparticles and the solution. It is instructive to review the form of each of these forces and determine their magnitude and frequency dependence for each set of observed experimental data. Dielectrophoresis. The primary force driving nanoparticle capture is DEP. Uncharged (neutral) dielectrics in a nonuniform (29) This cleaning process was undertaken to improve the repeatability of results in accordance with prior work. (30) Five nanometer particles range from 4.5 to 6.5 nm, 15 nm particles range from 14.0 to 16.5 nm, and 20 nm particles range from 18.5 to 22.5 nm in diameter. (31) A 10× probe was used to prevent loading the circuit unduly with oscilloscope or cable impedance. (32) Abramoff, M. D.; Magelhaes, P. J.; Ram, S. J. Biophoton. Int. 2004, 11, 36-42.

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Figure 2. TEM micrographs of assemblies made with frequencies ranging from 10 Hz to 1 MHz (7.5 V, 3 µm gap, 15.5 nm nanoparticles).

electric field experience a time-averaged dielectrophoretic force given by33

〈F BDEP(t)〉 ) 2πma3Re[K(ω)]∇|E Brms|2

(1)

where m is the permittivity of the medium, a is the radius of the nanoparticle, K(ω) is the Clausius-Mosotti factor, and Erms is the rms value of the electric field. This force is proportional to the volume of the nanoparticle and the gradient of the magnitude of the electric field squared. The frequency-dependent behavior resides in the Clausius-Mosotti factor, K(ω), which represents the complex polarizability of the particle and is given by

j p - m - (σp - σm) ω K(ω) ) j p + 2m - (σp + 2σm) ω

(2)

where p and m are the permittivities of the particle and medium, j is x-1, ω ) 2πf is the angular frequency, and σp and σm are the conductivities of the particle and medium. At low frequencies, the conductivity terms are dominant, while at high frequencies the permittivity terms are dominant. Positive values of the Clausius-Mossotti factor occur at low frequencies when σp > σm and at high frequencies when p > m. This is called positive DEP and corresponds to a time-averaged force pulling the nanoparticle toward areas of high field strength. Negative values of the Clausius-Mossotti factor occur at low frequencies when σp < σm and at high frequencies when p < m. This is called negative DEP and corresponds to time-averaged force pushing the nanoparticle toward areas of low field strength. For conductive nanoparticles in water, this factor typically shows a sharp crossover from +1 at low frequencies (σp > σm) to -0.5 at high frequencies (p < m). The frequency at which this crossover occurs is related to the nanoparticle and medium properties. The crossover frequency will tend to decrease with higher σm, lower σp, higher p, and lower m, and vice versa. A benefit of choosing gold nanoparticles in water for this study is that the Re[K(ω)] crossover occurs at a frequency around 1018 Hz, well above any reasonably obtainable electrical excitation frequency (Figure 3). In this case, Re[K(ω)] may be assumed to be +1 under all experimental conditions. Several factors can reduce this crossover frequency and deserve consideration. For example, residual chemicals from nanoparticle formation, such as sodium citrate, tannic acid, and potassium carbonate will increase the conductivity of the solution. Measurements using a conductivity probe (CON 10, Oakton Instruments) indicate that the solution conductivity is less than 600 µS/cm, and will have little effect on Re[K(ω)]. The permittivity of gold nanoparticles is larger than the permittivity of bulk gold by a (33) Pohl, H. A. Dielectrophoresis: The BehaVior of Neutral Matter in Nonuniform Electric Fields; Cambridge University Press: Cambridge, 1978; pp 38-47.

Figure 3. The real part of the Clausius-Mossotti factor Re[K(ω)] versus frequency for gold nanoparticles in water (p ) 6.9 × 0, σp ) 4.5 × 1011 µS/cm, m ) 78 × 0, and σm ) 1.0 µS/cm).

size-dependent factor related to the limitation of the electron mean free path and plasma frequency.34 This decreases the crossover frequency of Re[K(ω)], but the effect is slight and limited to optical frequencies. Gold nanoparticles in colloidal suspension are typically stabilized electrostatically, leading to an interfacial layer of charge in the solution surrounding the particle. This layer also increases effective nanoparticle permittivity, which decreases the crossover frequency of Re[K(ω)]. This interfacial charge layer effect will be more pronounced at lower solution conductivities and lower frequencies. However, even after accounting for these effects, the value of Re[K(ω)] remains very close to +1 for experimentally practical frequencies, i.e., f < 10 GHz. Experimentally, nanoparticle capture was observed over the entire tested frequency range (10 Hz to 1 MHz), indicating positive dielectrophoretic force. Electrode Polarization. Electrodes in solution with an applied voltage attract and repel charged species near the electrode surface, creating image charge in a process known as electrode polarization. This effect screens electrode potential so that the effective field far from the electrode is smaller. If the electrode/solution interface is modeled as a simple capacitance in series with a resistance, the impedance of the interface may be expressed as

Z ) 1/(jωCE) + RS + 1/(jωCE)

(3)

where CE is the interfacial capacitance and RS is the solution resistance. The effective voltage divided across the bulk of the solution is then

Veff/Vrms ) RS/(RS + 2/(jωCE))

(4)

Graphing eq 4 as a function of frequency shows the majority of the voltage drops across the interface at low frequencies while at high frequencies the solution sees the full applied voltage (34) Muskens, O. L.; Fatti, N. D.; Vallee, F.; Huntzinger, J. R.; Billaud, P.; Broyer, M. Appl. Phys. Lett. 2006, 88, 063109.

Frequency Dependence of Au Nanoparticle DEP

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Figure 4. The ratio of the effective bulk solution voltage to the applied electrode voltage (solid line) and of the voltage across the electrode-solution interface to the applied electrode voltage (dashed line) versus frequency (RS ) 100 kΩ, CE ) 5 nF).

(Figure 4). The transition between these two regimes occurs at a frequency of 103 Hz for typical values of RS ) 100 kΩ and CE ) 5 nF. This picture of interfacial impedance is corroborated by measurements of device impedance available in the Supporting Information (Figure S1). Fitting these measurements to a resistance in series with two capacitances yields values for RS and CE of 93 kΩ and 4.4 nF, respectively. Interfacial polarization therefore creates different electrical field distributions for low and high frequencies (Figure 5). At low frequencies, the field gradient is large and extends some distance into solution. At high frequencies, the magnitude of the field gradient is smaller and does not extend as far from the electrode edge. The geometry of planar electrodes causes the gradient to be larger closer to the edge in both cases, because of the high radius of curvature of the edge, as may be seen in the slight curvature of the voltage solid line in the vicinity of the electrode edge in Figure 5. The dielectrophoretic force, which is proportional to the gradient of the field squared, will therefore be larger at low frequencies. This is seen qualitatively in the higher collection rate and greater degree of fusion between nanoparticles at low frequencies. Mutual Dielectrophoresis and Nanoparticle Chain Formation. Particles in an electric field attract one another as they each locally distort electric field lines in a process called mutual dielectrophoresis. Mutual dielectrophoresis is a second-order effect and is generally much weaker than direct DEP. However, pearl-chaining,33 the formation of linear chains of particles in the presence of an electric field, has been attributed to mutual dielectrophoresis. The process has been postulated to occur in solution at some distance from the electrode surface. However, for particles to make contact and form a chain in solution, the mutual dielectrophoretic force must overcome electrostatic or double layer repulsion, a requirement that is met only when the electric field magnitude exceeds a threshold given by35,36

1 |Eth| ≈ 1.7 |K(ω)|

x

kBT

pa3

(5)

This equation gives a threshold field magnitude, |Eth|, for typical gold nanoparticles (15 nm diameter) of about 56 V/µm (5.6 × 107 V/cm). Under normal DEP conditions, such high fields are unlikely to be found in solution at distances remote from the electrode interface. High fields are anticipated at the electrode/ solution interface, particularly at low frequencies. These high fields result in correspondingly high DEP attraction to the electrode itself and depletion of nanoparticles from solution,

Figure 5. Voltage, electric field, and field gradient magnitude profiles inside of a 2 µm electrode gap with no charge in the liquid as expected in the high-frequency case (solid lines) and with some charge in the liquid near the electrode surface as expected in the low-frequency case (dashed lines) calculated using finite element analysis (FlexPDE, PDE Solutions, Inc).

Figure 6. Composite of TEM micrographs of gold nanoparticles captured within 1 min at voltages from 6 to 9 V (20 nm diameter particles, f ) 1 MHz).

both of which mitigate against mutual DEP. At high frequencies, the field extends further into solution, but is also weaker. Therefore, it is highly unlikely in this case that chain formation occurs by mutual DEP. Linear chains of nanoparticles are observed experimentally, but there does not seem to be a threshold voltage associated with their formation (Figure 6). Thermal Effects. Joule heating of the fluid medium in microelectrode dielectrophoresis coupled with removal of heat by thermally conductive electrodes produces temperature and density gradients within the solution. Gradients in fluid density give rise to a buoyancy force, which in turn produces convection.

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Since the nanoparticles move with the fluid, these convective flows also transport nanoparticles and give rise to an apparent force on the nanoparticles. Thermal convection fluid flow velocity in microelectrode structures has been shown to be negligible in magnitude compared to other electrical forces.37 However, fluid density gradients also produce gradients in both the permittivity and conductivity of the medium, and these gradients can couple with the electric field to produce electrohydrodynamic forces. There are two predominant electrohydrodynamic forces in DEP that work in opposition to each other. First, the DEP forces due to dielectric gradients are considered. The cooler, denser medium has a higher dielectric constant than the warmer, less dense medium. The field acts to pull fluid with a higher dielectric constant toward regions of high electric field strength.38 The effect is analogous to DEP, where the cooler fluid represents an extended particle experiencing positive DEP force. Conversely, the warmer, less dense medium may be considered an extended particle experiencing negative DEP force. The second effect is caused by conductivity changes. Increased density concentrates free and paired charges within the fluid medium, which produces an increase in conductivity. The Coulomb force acts on this volume charge produced by the conductivity gradient, pushing cooler fluid away from areas of high field strength. The magnitude of the maximum fluid velocity produced by the balance of these forces in a planar microelectrode configuration may be estimated by37

Vmax ) M(ω,T)

(

)

mσmVrms4 1 π 2π3λTη r 24

(6)

where λ is the thermal conductivity, η is the solution viscosity, r is the radial coordinate with its origin at the center of the electrode gap, and variation with frequency is contained in the dimensionless factor

M(ω,T) )

T ∂σm T ∂m σm ∂T m ∂T 1 + (ωτ)

2

+

1 T ∂m 2 m ∂T

(7)

where the charge relaxation time of the liquid τ ) m/σm. For water, ∂/∂T ) -0.36/°C39 and ∂σ/∂T may vary from 1% to 7%/°C depending on purity level and temperature.40 Interestingly, M(ω,T) demonstrates similar behavior to Re[K(ω)] with a characteristic crossover frequency that depends on the relative values of m, p, σm, and σp. The frequency range in which electrohydrodynamic thermal fluid flow varies is promisingly similar to experimental observations of nanoparticle assembly morphological variation (Figure 7). However, experimental measures of fluid flow indicate much higher velocities and a reduction in velocity at low frequencies that is not consistent with this mechanism. Another explanation for the experimentally observed fluid flow is needed. ac Electroosmosis. For microelectrodes, the electric field at the surface of coplanar electrodes can have a substantial electric (35) Jones, T. B. Electromechanics of Particles; Cambridge University Press: Cambridge, NY, 1995; p 140. (36) Pohl gives this same expression with 1/x2π instead of 1.7. (37) Ramos, A.; Morgan, H.; Green, N. G.; Castellanos, A. J. Phys. D: Appl. Phys. 1998, 31, 2338-2353. (38) Pohl calls this thermally assisted dielectrophoresis (TAD) and discusses its usefulness in stirring and cooling solutions. (39) Lide, D. R. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 1993; pp 6-10. (40) Gray, D. M. In Water Encyclopedia; Lehr, J. H., Keeley, J. W., Lehr, J. K., Kingery, T. B., Eds.; John Wiley & Sons: New York, 2005; pp 429-433.

Figure 7. Electrohydrodynamic thermal fluid flow factor M(ω,T) versus frequency (left y-axis) and maximum velocity (calculated from eq 6) imparted by thermal fluid flow (right y-axis) (r ) 1.5 µm, 3 µm gap, Vrms ) 5 V).

Figure 8. Surface-bound interfacial charge induced by electrodes (spheres) interacts with the tangential component of electric field (curved lines) and moves fluid along the electrode surface away from the electrode gap. Field lines originate on positive charge and end on negative charge and represent the force experienced by positive charge, so negative charge experiences force opposite the direction of field lines.

field component tangential to the electrode surface. The Coulomb force of this field on the solution interfacial charge (Figure 8) leads to fluid flow along the electrode surface away from the gap in a process termed ac electroosmosis.41 ac electroosmosis has been exploited in microfluidics to pump fluid in microcapillaries where surface forces preclude traditional pumping by pressure differentials. The ac electroosmotic effect can impart fluid velocities as high as 500 µm/s in some cases.42 For symmetrical, coplanar microelectrode gaps such as those used in this study, ac electroosmosis produces fluid flow along the electrode surface directed away from the center of the electrode gap. Fluid velocity43 near the electrode surface is given by

〈V〉 )

2 2 1 V0 Ω 8 ηx(1 + Ω2)2

(8)

where x is the coordinate axis along the electrode surface with its origin at the center of the electrode gap and the dimensionless frequency Ω is given by

π Ω ) ωx κ σ2

(9)

where κ is the Debye-Hu¨ckel length. A reasonable estimate for (41) Green, N. G.; Ramos, A.; Gonzalez, A.; Morgan, H.; Castellanos, A. Phys. ReV. E: Stat., Nonlinear, Soft Matter Phys. 2000, 61, 4011-4018. (42) Ramos, A.; Gonzalez, A.; Castellanos, A.; Green, N. G.; Morgan, H. Phys. ReV. E: Stat., Nonlinear, Soft Matter Phys. 2003, 67, 056302. (43) This velocity is always in the same direction, because the image charge and tangential field both change sign simultaneously as the ac electric field is applied.

Frequency Dependence of Au Nanoparticle DEP

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Figure 9. Calculated ac electroosmosis induced fluid velocity (solid line) and measured fluid velocity (circles) versus frequency. Calculations are from eq 8 (κ ) (15 nm)-1, x ) r,  and σ are as above, η ) 0.008904 P, Vrms ) 5 V) and measurements are video microscopy observations of 2 µm latex spheres in deionized water (Vrms ) 7.5 V).

κ from solutions with similar conductivities is about (50 nm)-1. For typical DEP conditions, this gives a maximum velocity at the electrode edge of 4.1 mm/s, more than enough to considerably influence nanoparticle distribution and assembly morphology. This velocity is small at low frequencies when most of the electric field is inside the interfacial double layer and the tangential field does not extend very far into the solution. The velocity is also small at high frequencies when the interfacial double layer is small because the charged species in solution are not fast enough to follow the rapidly changing polarities of the electrodes. Between these two regimes, the velocity can be quite large (Figure 9). The electrode gap width divided by half the time it takes electrically conducting nanowires to meet in the center of the gap is termed the nanowire growth velocity. Nanowire growth velocity plotted against frequency shows a clear decrease centered on the peak of ac electroosmotic flow, and nanoparticle flux measurements plotted against frequency show an increase centered on the same peak (Figure 10). Observation by optical microscopy and TEM shows assemblies formed around high ac electroosmotic flow, i.e., 1 kHz and 7.5 V, are very thick (Figure 2) and connections between electrodes consistently form near their edges (Figure S2 in the Supporting Information). The increased density of assemblies and corresponding decrease in growth velocity under high flow conditions is likely caused by a combination of mutual attraction between particles due to hydrodynamic forces,44 replacement of diffusion by fluid flow as the primary long-range transport mechanism for fresh nanoparticles, and replacement of medium-range dielectrophoretic forces by fluid flow, preventing the formation of nanoparticle chains. Applications. Several regimes of nanoparticle assembly are of particular technological interest (Figure 11). When two wires meet and make electrical contact, the voltage difference becomes very small and assembly stops, often leaving a chain with single nanoparticle width at their meeting. At 7.5 V and 10 kHz, the ac electroosmotic flow causes most of the wire to be dense and several hundred nanometers thick, except at the meeting point, where a chain of only a few nanoparticles makes the connection. Stereomicroscopic investigation of this connection shows it is very close to the substrate surface. The low resistance of thick connecting wires combined with a nanoscale constriction makes this structure suitable for the formation of a nanogap for molecular (44) Gong, T. Y.; Wu, D. T.; Marr, D. W. M. Langmuir 2002, 18, 1006410067.

Figure 10. Nanowire growth velocity, determined from measured time to electrical connection, and nanoparticle flux, derived from optical density measurements of TEM micrographs, versus frequency for 7.5 V, 3 µm gap (O), 15 V, 6 µm gap (×), and 10 V, 3 µm gap (]) (all 15 nm diameter particles).

Figure 11. Plan-view TEM micrographs of nanoparticles assemblies formed at 10 kHz (a), 1 MHz (b) (both 7.5 V, 3 µm gap), and at high fluid flow (c) (10 kHz, 5 V, 2 µm gap; R2 not connected, R1 ) 70 kΩ) (all 15.5 nm nanoparticles).

electronics. At 7.5 V and 1 MHz, there is virtually no ac electroosmotic fluid flow, allowing the dielectrophoretic force to dominate. Single nanoparticle wide pearl chains frequently bridge the entire gap and electrically connect both electrodes. TEM stereomicroscopy again shows this structure to be very

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close to the underlying substrate. This type of one-dimensional nanostructure is suitable for large-scale preservation of quantum effects associated with constituent nanostructures, such as optical and electrical properties for light emission or detection. For example, gold nanoparticle chains have been used as plasmon waveguides45 and CdSe nanoparticle chains have been shown to electroluminesce.17 Another desirable nanoparticle assembly is the thick, dense assembly formed very rapidly under high flow conditions. This assembly has a very high surface area and may be useful in sensors or catalysis. An additional parameter in the formation of nanostructures in this way is the degree to which the nanoparticles fuse together and, for connected nano- and microwires, their resistance. For most microelectrode applications, a low resistance is desirable. For sensor applications, a high surface area may be desirable. The resistance of our nanowires ranged from less than 100 Ω to greater than 1 kΩ. The current that flows through the nanostructure at completion, set by choice of R1 to approximately Vrms/R1, seems to be inversely proportional to the postformation resistance of the completed nanostructure. This process of forming nanowires from dielectrophoretically captured nanoparticles was recently studied in detail.16

Gierhart et al.

depends sensitively on the frequency of the applied field. The influence of ac electroosmotic fluid flow may be seen in the increased density of assemblies and the slowing of nanowire growth velocities around the maximum ac electroosmotic flow frequency. Interfacial layer effects cause thicker nanowires, increased fusion between particles, and increased assembly density at low frequencies, where the electric field gradient is largest adjacent to the electrode surface. Long nanoparticle chains form at high frequencies, probably because of the absence of fluid flow. Understanding these frequency-dependent mechanisms should enable the design of a wide variety of dielectrophoretically assembled precision nanostructures, including one-dimensional nanowires, nanogap electrodes, and high surface area electrodes. Acknowledgment. This study was supported by grants from the National Institutes of Health (NIH/NHGRI Grant 5 R01 R01HG03565) and the David and Lucille Packard Foundation (Interdisciplinary Science Grant 2002-22776A). The authors thank Dwight Howard for assistance with experimental setup, and Prof. Wayne Current and Kelvin Yuk for helpful comments on the same. Fabrication work was carried out at the Northern California Nanotechnology Center and TEM inspection at Materials Science Central Facilities, both of the University of CaliforniasDavis.

Conclusions Dielectrophoretic capture of gold nanoparticles provides a powerful means of creating unique and useful nanostructures. The morphology of nanoparticle assemblies formed in this way (45) Maier, S. A.; Kik, P. G.; Atwater, H. A.; Meltzer, S.; Harel, E.; Koel, B. E.; Requicha, A. A. G. Nat. Mater. 2003, 2, 229-232.

Supporting Information Available: Measured admittance and calculated fit for device with drop of nanoparticle solution and plan view TEM of connection formed under high fluid flow conditions showing connection formation near electrode edge. This material is available free of charge via the Internet at http://pubs.acs.org. LA701472Y