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Assembly of Colloidal Particles into Microwires Using an Alternating Electric Field Simon O. Lumsdon and David M. Scott* DuPont Company, Experimental Station E304, Wilmington, Delaware 19880-0304 Received November 5, 2004. In Final Form: March 14, 2005 We have investigated the dielectrophoretic assembly of colloidal gold, carbon black, and carbon nanotubes into electrical wires. The resulting microwires have diameters less than 1 µm, with lengths ranging from 5 µm to 3 mm. Current-voltage curves for these wires indicate an ohmic response, where the resistance is determined by the type of colloid and by the frequency of the alternating field used to grow the wires. The predicted frequency dependence of dielectrophoresis is confirmed by experiment. Measurements of the threshold voltage for initial wire growth are also presented. These experiments demonstrate that a variety of nanoparticles can be assembled into microwires for sensor applications.
be expressed8 as
Introduction It has been known for nearly 200 years that charged particles in a constant (DC) electric field experience electrophoretic forces that cause them to move.1 More recently, it has been observed that colloidal particles can be assembled into a variety of small-scale structures by application of electric fields created by contact electrodes. This effect has been studied previously,2,3,4 and it is envisioned that new functional materials or devices might be constructed via electrophoresis. However, the electrophoretic technique is limited to colloidal systems where a strong surface charge is present on the particles and where the applied voltage is very low (below the threshold for electrolysis). These limitations can be overcome by the use of alternating (AC) fields, which induce a dielectrophoretic force.5,6,7 The application of an AC field across a suspension of colloidal particles produces a time-dependent polarization due to the redistribution of free and bound charges in and on the particles. The sign and magnitude of the resulting induced dipoles depend on the polarizability factor, K, of the particles, which for homogeneous spheres is given by the real part of the Clausius-Mossotti function, K5,6
K*(ω) )
2*(ω) - 1*(ω) 2*(ω) + 21*(ω)
(1)
where 1* and 2* are the frequency-dependent complex permittivities of the fluid and particle, respectively. In the case of metallic particles, K ) 1 because the conduction band electrons continually redistribute themselves to reduce the internal electric field to zero. In the case of a dielectric sphere with ohmic loss (but not dielectric loss), the real part of the Clausius-Mossotti function (eq 1) can * Author to whom correspondence should be addressed. (1) The first observation of this effect is attributed to Ruess, F. F. Mem. Soc. Imp. Nat. Moscou 1809, 2, 327. (2) Trau, M.; Saville, D. A.; Aksay, I. A. Science 1996, 272, 706. (3) Bohmer, M. Langmuir 1996, 12, 5747. (4) Yolomentsev, Y.; Bohmer, M.; Anderson, J. L. Langmuir 1997, 13, 6058. (5) Jones, T. B. Electromechanics of particles; Cambridge University Press: Cambridge, 1995. (6) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Cambridge, 1978. (7) Pethig, R.; Huang, Y.; Wang, X. B.; Burt, J. P. H. J. Phys. D: Appl. Phys. 1992, 24, 881.
Re|K(ω)| )
2 - 1 + 2 + 21 τ
3(1σ2 - 2σ1) MW(σ2
+ 2σ1)2(1 + ω2τ2MW)
(2)
where 1 (and 2) and σ1 (and σ2) are the real dielectric permittivity and conductivity of the fluid and particles, respectively. Here the parameter τMW is the MaxwellWagner charge relaxation time (i.e., the finite time required for the redistribution of charge):9
τMW )
2 + 21 . σ2 + 2σ1
(3)
The dipoles of the polarized particles interact with the applied electric field. The resulting dielectrophoretic (DEP) force F BDEP depends on the field gradient, ∇E B 2 and the radius, r, of the particle5,6
B rms2 F BDEP ) 2π1 Re|K(ω)|r3 ∇E
(4)
The direction of the force is determined by the sign of Re[K(ω)]: metallic particles (with K ) 1) are always attracted to the regions of high field gradient. For dielectric particles with ohmic loss where 1 < 2 and σ1 > σ2 (or 1 > 2 and σ1 < σ2), the force changes from attractive to repulsive at an angular crossover frequency proportional, but not equal, to (1/τMW). Such a frequency-dependent change of sign of the interaction is commonly observed with polymer microspheres in water.7,10 The frequency dependence is discussed in more detail below. The use of alternating voltage allows a wide variety of particles to be manipulated regardless of their charge state, without causing electrolytic decomposition of the fluid or electro-osmotic currents (either of which can disrupt particle motion). Dielectrophoresis has been used as a tool for the assembly of composite particles,11,12 (8) Benguigui, L.; Lin, I. J. J. Appl. Phys. 1982, 53, 1141. (9) Equation 4 corrects the typographical error in eq 3.7 of ref 5 quoted in refs 13-14. (10) Mu¨ller, T.; Gerardino, A.; Schnelle, T.; Shirley, S. G.; Bordoni, F.; DeGasperis, G.; Leoni, R.; Fuhr, G. J. Phys. D: Appl. Phys. 1996, 29, 340. (11) Fuhr, G.; Mu¨ller, T.; Schnelle, T.; Hagedorn, R.; Voigt, A.; Fiedler, S.; Arnold, W. M.; Zimmermann, U.; Wagner, B.; Heuberger, A. Naturwissenschaften 1994, 81, 528. (12) Sides, P. J. Langmuir 2001, 17, 5791.
10.1021/la0472697 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/09/2005
Assembly of Colloidal Particles into Microwires
colloidal crystals,13,14 microscopic biosensors,15 and electrically functional microwires from gold nanoparticles.16,17 Recently, the use of dielectrophoresis to purify and align carbon nanotubes has been reported.18,19 In this paper, we present results of a study involving dielectrophoretic assembly of colloidal gold, carbon black, and carbon nanotubes into micrometer-scale electrical wires. These wires are flexible and remain intact after the electric field is removed. The purpose of this work was to investigate a variety of experimental conditions and materials and to measure the electrical behavior of the resulting microwires. This work extends the experimental methods previously demonstrated on colloidal gold15 to other materials, notably carbon black and carbon nanotubes. The observation of a threshold voltage in the wire formation process is introduced, and the frequency dependence of wire growth via DEP is also considered. Materials and Methods Materials. Ultrapure water was obtained from a Barnstead Easypure reverse osmosis system. Gold nanoparticles were synthesized by the reduction of gold chloride using sodium citrate and tannic acid.20 The particle diameter had a median size of 25 nm as measured by dynamic light scattering (Malvern Zetasizer Nano S). The concentration of particles, ≈1012 particles/mL, was not sufficient for microwire assembly.16 Therefore, the suspension was centrifuged at 1500g through Millipore BioMax filters (Fisher Scientific), to concentrate the dispersion to ≈1014 particles/mL. The 5 nm gold particles were purchased from Structure Probe, Inc. in an aqueous dispersion that was concentrated via centrifugation to approximately 1014 particles/mL. Carbon black particles, with a median particle diameter of 30 nm, were purchased from Degussa (FW-18, black pigment). Single- and multiwalled carbon nanotubes (SWCNT and MWCNT) were obtained from MER Corporation in Tucson AZ. These nanotubes had an apparent diameter of approximately 15 nm, as observed via scanning electron microscopy (SEM). The physical diameter is probably much smaller than 15 nm,21 but the exact value is not relevant in these experiments. An additional MWCNT sample was obtained from Tsinghua University; these nanotubes had an apparent diameter of 50 nm (by SEM), and their topology was highly branched. The carbon black and CNT particles were dispersed in water using an ultrasonic probe for 2 min at a concentration of approximately 1012 particles/mL (Sonics & Materials Vibra-Cell, operating at 20 kHz and a total output power of about 50 W). Apparatus. The microwires are assembled in an alternating electric field between two electrodes; the gap between these electrodes ranged between 5 µm to 3 mm. As in previous studies,16,17 100 nm thick gold electrodes were deposited onto glass slides, and the gap between the electrodes was determined by the width of a Teflon tape which acted as a mask during the deposition. The same technique was used here to create electrode structures with a gap of approximately 3 mm. In the present experiments, we have also used much smaller electrode structures (with gap sizes ranging from 5 to 100 µm) fabricated on a glass substrate via photolithography. These electrodes were formed by depositing a 100 nm thick layer of gold onto a 10 nm layer of chromium. A photomask defining the size and shape of the electrodes was used to apply an etch-resist layer, and then the (13) Lumsdon, S. O.; Kaler, E. W.; Williams, J. P.; Velev, O. D. Appl. Phys. Lett. 2003, 82, 949. (14) Lumsdon, S. O.; Kaler, E. W.; Velev, O. D. Langmuir 2004, 20, 2108. (15) Velev, O. D.; Kaler, E. W. Langmuir 1999, 15, 3693. (16) Hermanson, K. D.; Lumsdon, S. O.; Williams, J. P.; Kaler, E. W.; Velev, O. D. Science 2001, 294, 1082. (17) Bhatt, K. H. and Velev, O. D. Langmuir 2004, 20, 467. (18) Krupke, R.; Hennrich, F.; v. Lohneysen, H.; Kappes, M. M. Science 2003, 301, 344. (19) Kumar, M. S.; Kim, T. H.; Lee, S. H.; Song, S. M.; Yang, J. W.; Nahm, K. S.; Suh, E. K. Chem. Phys. Lett. 2004, 383, 235. (20) Slot, J. W.; Geuze, H. J. Eur. J. Cell Biol. 1985, 38, 87. (21) Brintlinger, T.; Chen, Y. F.; Du¨rkop, T.; Cobas, E.; Fuhrer, M. S.; Barry, J. D.; Melngailis, J. Appl. Phys. Lett. 2002, 81, 2454.
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Figure 1. (a) Photograph of the electrode assembly used to grow microwires. In the middle of the glass substrate are four pairs of microscopic parallel electrodes (see inset) that form four gaps. The 30 µm width of these electrodes is greatly exaggerated in (b), which shows a schematic of the circuit used to grow the microwires in the gap between the electrodes. A glass cover slip is typically placed on the electrode assembly to prevent the dispersions from drying during the experiment. excess metal was removed. A photograph and schematic of a typical electrode configuration is shown in Figure 1. Due to the small size of these structures, we were able to make dozens of identical electrode assemblies from a single glass substrate. This abundance enabled us to use a fresh electrode set for each experiment. To assemble a microwire, a drop of the colloidal suspension is placed on the electrode gap and covered with a glass cover slip. An alternating electric field is applied using a function generator (Wavetek Model 23) and the electrical circuit shown in Figure 1. The resistor in Figure 1 limits the surge of current when the wires bridge the gap, and the capacitor blocks any DC bias produced by the function generator. It should be noted that the use of such small gaps lowers the applied voltage necessary to grow a microwire, so there is no need for an external linear amplifier (as used in the previous work). The frequency of the applied field was varied between 100 and 1000 Hz, and the applied voltage and current were measured using digital multimeters (Fluke Model 87). In an alternative experimental arrangement (not shown), we have also grown microwires between two electrode probes that were inserted into a well slide filled with colloidal solution. This approach is useful for experimenting with very large gaps (over 3 mm) that could not be achieved with the small-scale electrodes discussed here. Experimental Methods. Experiments were conducted by preparing an aqueous colloid (gold, carbon, or CNT) and placing a drop on the electrode assembly described above. This assembly was placed on an optical microscope stage and connected to the circuit shown in Figure 1, which supplies a sinusoidal voltage to the electrodes. The growth of the microwires was observed through the microscope. The applied root-mean-square (RMS) voltage was held constant during the growth of the microwire. A number of experimental parameters can be varied: particle size, concentration, composition, electrode gap, RMS voltage applied to the electrodes, and the frequency. Observations include the RMS current passing through the colloid during wire growth, the threshold voltage required to initiate wire growth, growth rate, the diameter and morphology of the assembled microwire, and the electrical resistance of the completed microwire. The wire is known to span the electrode gap when at least 1 µA of current registers on the ammeter in Figure 1b and a completed wire can be seen through the microscope. Resistance is estimated by injecting an alternating current through the wire and recording the corresponding voltage drop between the two electrodes. These measurements are made at the same AC frequency used to grow the wire. These data are used to construct an I-V (i.e., current versus voltage) curve for the wire; the inverse slope of the resulting line is the resistance of the wire. The measurement is made after the microwire spans
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the electrode gap, thus completing the circuit of Figure 1b, while the microwire remains in the partially depleted colloidal suspension. The presence of the colloid undoubtedly affects the result, and in fact many of the intended applications of this work require that the wire be sensitive to its chemical surroundings. An analysis of the mechanism of conduction through these wires is outside the scope of this scouting study, but we believe direct conduction through the dispersion to be small because the current flowing through the circuit increases significantly (typically by 2 orders of magnitude in the case of carbon black) when the microwire connects the two electrodes. These measurements were made in situ because the amount of time required to clean and dry the microwires (while maintaining the electrical connection) was deemed to be prohibitively expensive. The microwires formed in this study are strong enough to be manipulated with tweezers. A few of the wires were removed from the electrode assembly and mounted on a metal stub for SEM.
Results and Discussion Frequency Dependence of DEP. It should be understood that the form of the Clausius-Mossotti function in eq 2 does not make the frequency dependence entirely explicit because permittivity and conductivity are in general functions of frequency. The appearance of angular frequency in eq 2 is merely the result of treating the ohmic loss term as an imaginary number where conductivity is divided by frequency. However, it is a useful approximation (and in many cases not far from the reality) to assume that and σ are essentially constant over the frequency range of interest. With the preceding caveat in mind, the frequency dependence of Re[K(ω)] can be seen more clearly by reexpressing eq 2 in the following form:
Re[K(ω)] ) K∞ + (K0 - K∞)(1 + ω2τ2MW)-1
(5)
where
K∞ )
2 - 1 2 + 21
(6)
K0 )
σ2 - σ1 σ2 + 2σ1
(7)
and
Clearly in the high-frequency limit where ω . (τMW)-1, eq 5 reduces to the constant defined by eq 6. At low frequencies where ω , (τMW)-1, the limit of eq 5 becomes the constant defined by eq 7. This result may appear counterintuitive because it predicts that at low frequencies a dielectric particle’s conductivity, rather than permittivity (dielectric constant), determines the DEP force. When ω ) (τMW)-1, the polarizability factor is the average of the high- and low-frequency limits, (K0 + K∞)/2. As noted above, when 1 < 2 and σ1 > σ2 (or 1 > 2 and σ1 < σ2), there exists a crossover frequency, ωc, where the sign of K changes, reversing the direction of the DEP force. Except in extraordinary situations where the limits given by eqs 6 and 7 are equal in magnitude but opposite in polarity, this crossover frequency is not equal to (τMW)-1 as some authors have assumed. Setting Re[K(ω)] ) 0 in eq 5 and solving for the angular frequency, ω, one can show that
ωc )
x
-K0 (τ )-1 K∞ MW
(8)
Figure 2. Scanning electron microscope images of microwires: (a) the tip of a microwire grown from 25 nm gold, (b) the midsection of the wire grown from 25 nm diameter gold, and (c) a wire grown from 30 nm diameter carbon black. The scale bar on (a) is 1 µm, and the scale bar on (b) and (c) is 500 nm.
The explicit form of the crossover frequency, νc (in Hz), that one observes experimentally is therefore
νc )
x
ωc 1 ) 2π 2π
-(σ22 + σ2σ1 - σ12) (22 + 21 - 12)
(9)
Equation 9 was verified experimentally by observing the crossover frequency for dielectrophoresis of TiO2 (rutile) in water. The TiO2 particles were aggregates several micrometers in diameter that could easily be tracked with an optical microscope. A 0-50 MHz Wavetek frequency generator connected across two metallic strips deposited at right angles on a glass substrate (one of several types of electrode assemblies made using photolithography) provided the divergent electric field. A drop
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Figure 3. Gold microwires grown in a 20 µm electrode gap. (a) Before the threshold voltage is reached, there is no wire growth. (b) A single wire starts to grow when the voltage is raised to 5 V RMS at 250 Hz. After 30 s, the wire spans the gap and no additional wires are formed. (c) Increasing the voltage to 7 V RMS results in the formation of additional wires.
of dispersion could be captured between the glass substrate and a cover slip for observation under the microscope. Handbook values22 of rutile and water are 1 ) 810, 2 ) 1100, 0 ) 8.85 x 10-12 F/m, and σ2 ) 10-11 S/m; the conductivity of the water was measured with a VWR Scientific Model 2052 m to be σ1 ) 0.10 S/m. The predicted crossover frequency (eq 9) is 28.6 MHz, with a repulsive force (eq 7) at lower frequencies and an attractive force (eq 6) at higher frequencies. The observed motion of the TiO2 aggregates is consistent with these expectations, with the change from repulsion to attraction occurring in the range of 26-29 MHz. Mechanism of Wire Assembly. When colloidal particles are well dispersed, the repulsive interactions between them prevent agglomeration. In the presence of an electric field gradient, the dielectrophoretic force acting on the particles drives them toward the region of maximum field intensity, which is at the tip of the growing wire (shown in Figure 2a). There the dielectrophoretic force is strong enough to overcome the repulsive interactions, causing additional particles to agglomerate onto the wire tip. In these experiments, we observed that wire growth did not appear to occur at very low applied voltages. By slowly increasing the RMS voltage from zero and observing the electrodes through the microscope, we found that wire growth appeared to start spontaneously at a specific and reproducible voltage. This observation of a “threshold voltage” suggests that there is a minimum DEP force required for wire formation. This result is discussed in the next section. Figure 2b and c shows SEM images of microwires grown from gold and carbon black colloids under similar conditions (at an applied voltage of about 6 V RMS at 250 Hz). The gold microwire has a diameter of approximately 400 nm, and its particles are packed closely together. In contrast, the microwire grown from carbon black of approximately the same particle size has a larger diameter (900 nm) and a more loosely packed structure; a significant amount of porosity is evident in Figure 2c. This observation demonstrates that the DEP forces are stronger for the gold particles. This result may be understood by considering that carbon is far less conductive than gold (which is assumed to have K ≈ 1). In the low-frequency limit (eq 7), the polarizability is determined by the contrast in conductivity between particle and fluid, and it follows that gold would experience a stronger DEP force than carbon. Once the threshold voltage is reached for 25 nm gold particles in a 20 µm gap (Figure 3a), a single microwire grows rapidly between the planar electrodes (Figure 3b). Other wires are visible on the surface of the electrode, but they do not continue to grow because of the depletion of (22) Lide, D. R. CRC Handbook of Chemistry and Physics, 72nd ed.; CRC Press: Boca Raton, FL, 1991.
Figure 4. The growth of carbon black wires in a 20 µm electrode gap. The wires shown here have not yet spanned the electrode gap. The wires are more numerous and have a more dendritic structure than in the case of gold (compare with Figure 3).
particles from the surrounding medium. When the wire connects, the conductivity is so high that the system is effectively short-circuited, and no further wire growth occurs at this voltage. However, if the voltage is increased, additional wires may assemble provided enough particles are available in the dispersion (Figure 3c). In contrast, dispersions of carbon black tend to grow multiple wires (see Figure 4) as soon as the threshold voltage is reached. Increasing the voltage above the threshold causes the wires to grow faster. The wires have a dendritic structure that is not observed in the case of gold. This disparity in growth behavior is probably due to the substantial difference in electrical conductivity of the particles. Threshold Voltage for Wire Growth. As noted above, microwire growth was observed to start at a “threshold voltage”, suggesting that there is a minimum DEP force required for wire formation. Clearly there is still a DEP force acting on the colloidal particles at lower applied voltages, but it is too weak to overcome the repulsive interparticle forces that stabilize the dispersion. We postulate that the colloidal particles must overcome the interparticle repulsive potential with sufficient vigor to fuse onto the wire tip. Since the kinetic energy is a function of the particle velocity, which in turn is determined by the balance between the dielectrophoretic force and the drag force imposed by the suspension (and any other forces), it follows that a minimum DEP force is needed to grow microwires. The minimum voltage required to initiate wire growth is dependent on a number of variables. According to eqs 2 and 4, the dielectrophoretic force is a function of the frequency of the applied field, the particle radius, and the conductivity and dielectric permittivity of the particles and the surrounding medium. In Figure 5, the threshold voltage is plotted as a function of frequency of the applied
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Lumsdon and Scott Table 1. Ratio of the Observed Threshold Voltage Measured for a 50 µm Gap to the Threshold Measured for a 5 µm Gap (Averaged over the Frequency Range 10 Hz to 10 KHz) material
ratio of threshold voltages
25 nm gold 5 nm gold carbon black MER MWCNT
2.0 ( 0.1 1.7 ( 0.1 2.5 ( 0.2 1.6 ( 0.2
Figure 5. (a) Threshold voltage required for wire growth across a 5 µm electrode gap as a function of applied frequency, with 25 nm gold ([), 5 nm gold (0), 30 nm carbon black (4), MER MWCNT (×), MER SWCNT (b), and Tsinghua MWCNT (O). (b) Threshold voltage for wire growth across a 50 µm electrode as a function of applied frequency, with 25 nm gold ([), 5 nm gold (0), 30 nm carbon black (4), and MER MWCNT (×).
field for a number of particle sizes and types. Across a 5 µm gap (Figure 5a) the field strength is high and the particles assemble at a relatively low voltage. For these particles, we find that the threshold voltage increases with the frequency of the applied field, which is consistent with previous data.16 This observation suggests that K0 > K∞ in eq 5. At a fixed frequency and field strength, increasing the particle size increases the DEP (see eq 4); therefore, the threshold voltage is lower for larger particles, as observed here in the case of gold. The higher conductivity of the gold particles does not cause them to assemble at lower voltages than the larger carbon black particles, confirming that particle size has the most impact on dielectrophoresis. The two MWCNT samples exhibited significantly different threshold behavior, suggesting that they have very different mobility and (probably) conductivity. While eq 4 may not be entirely applicable to carbon nanotubes, it predicts that the larger particle would have a higher DEP and therefore a lower threshold for assembly. The fact that the Tsinghua MWCNT has the highest threshold may indicate that it has lower conductivity, but the effects of particle size and shape may also account for a higher threshold. It should also be noted that CNT materials tend to contain amorphous carbon, and the differences observed between the MWCNT samples may simply be due to differences in composition. Figure 5b shows the results obtained when the same particles are assembled across a 50 µm electrode gap. Since
Figure 6. Current-voltage response of gold microwires grown in electrode gaps of (a) 5 µm and (b) 3 mm. The responses of microwires grown from other materials in a 25 µm gap are shown in (c). Due to the wide range of resistance values, each graph requires a different scale.
the electric field strength is reduced by the increase in gap size, a higher threshold voltage is required to assemble the wires. It was observed that, for a given material, the ratio of the threshold voltages observed for the two gap sizes is essentially independent of the applied frequency over the range 10 Hz to 10 kHz. Table 1 shows the average ratio of the threshold voltages observed for the 50 µm gap to that for the 5 µm gap. The estimated uncertainty shown in Table 1 is the standard deviation of the ratios calculated at each frequency. There appears to be a systematic difference between the various materials. In addition, all of these ratios are much smaller than expected for a 10-
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Figure 7. A montage of optical micrographs showing a microwire assembled from carbon nanotubes and nearly 3 mm in length.
fold increase in gap width. These observations suggest that some other mechanism, either electrochemical or electronic in origin, diminishes the effectiveness of the applied voltage. This aspect is an area for further study. Electrical Properties of Microwires. The potential application of microwires in self-assembled devices depends greatly on their electrical properties. In Figure 6, the current-voltage response of microwires bridging the electrode gap has been recorded. As noted above, these measurements were made in situ after the wire was observed to complete the circuit of Figure 1b. In Figure 6a, 25 nm gold particles were assembled in a 5 µm gap at three different applied frequencies. For simplicity, the electrical measurements were taken at the same AC frequency used to grow the wire. At these low frequencies, the resistance is expected to be independent of the measurement frequency. The data in Figure 6a clearly depict a linear relationship between current and voltage. The fact that the lines do not intersect the origin is probably due to the electrochemical effect that we postulated in the previous section. It appears that over the voltage range shown the wires themselves exhibit nearly Ohmic behavior, by which we mean that they behave as simple resistors. Recently published work on DEP assembly of gold nanoparticles confirms this finding.23 The resistance (i.e., the inverse slope of the plot) does not differ greatly for wires grown at different frequencies. Therefore, in the range of 100-1000 Hz, the resistance of the gold microwires is relatively independent of the frequency used to assemble them. The current-voltage response of 25 nm gold particles assembled in a 3 mm electrode gap is shown in Figure 6b. The wide gap required a relatively high applied voltage (about 100 V) to initiate wire growth. In contradistinction to the results of Figure 6a, it appears that, for the larger electrode gap, the frequency of the applied field affects the resistance of the microwires. As the frequency is increased, the conductance of the wires is also observed to increase. This result may be due to an increase in either wire thickness or density, but these measurements were not made at the time the study was conducted. It is known from previous work17 that increasing the frequency decreases the linear growth rate, which possibly allows more time for additional colloidal particles to be incorporated into the wire structure. It is assumed that a higher packing density would provide more contact points to conduct the current. Evidently, the results of Figure 6a suggest that this effect is not observed in very small electrode gaps and relatively low applied voltages. The I-V measurements of wires grown from carbon black and carbon nanotubes (using the Tsinghua MWCNT sample) are shown in Figure 6c. As in the case of the other materials, the wires remain intact after formation, and the I-V curve is linear over the observed voltage range. For ease of comparison, the equivalent resistances of the wires are shown in Table 2. The AC resistance of the dispersions in the absence of the completed wire (on the order of 5 MΩ in the case of the 25 µm gap) in all cases was found to exceed the estimated resistance of the wire. (23) Kretschmer, R.; Fritzsche, W. Langmuir 2004, 20, 11797.
Table 2. Resistances of Microwires Assembled via Dielectrophoresis, Determined from I-V Curves Including Those of Figure 6 material
gap (µm)
resistance (kΩ)
gold gold carbon black Tsinghua MWCNT MER MWCNT MER SWCNT
5 3000 25 25 25 25
7.2-10 3-11 400 476 2500-2800 2500-3200
The resistance, rather than the resistivity, is shown because the cross sectional area of the wires was not measured. Table 2 shows a range of resistance values for several types of wire; these data represent the observed equivalent resistance for several replicate experiments, which for clarity are not shown in Figure 6. The variation in the observed resistance of various materials is probably due to differences in packing density and conductivity of the nanoparticles within the wire. It was observed that wires grown from carbon black and carbon nanotubes (see Figure 6c) have a significantly higher resistance than gold microwires. This observation could be used in sensor applications, where an equivalent percentage change in resistance would be more detectable. Wires Grown from Carbon Nanotube Dispersions. The fabrication and application of carbon nanotubes is of great interest to both industry and academia. However, applications require pure samples, and most sources tend to produce a mixture of metallic and semiconducting types with some residual amorphous carbon. Krupke et al.18 have described a process for refining carbon nanotube dispersions by using high frequency (10 MHz) alternating electric fields. Given the differences in conductivity between metallic and semiconducting nanotubes, it follows that dielectrophoresis could be used to separate nanotubes by type or mobility. The implication for the present set of experiments is that the microwires formed from dispersions of CNTs may be composed predominantly of one component from the original dispersion. Therefore, the electrical properties of the microwire may be useful for characterizing the sample. It is interesting to note in Table 2 above that the wire formed from the Tsinghua sample has nearly the same resistance as that formed from carbon black, whereas the MER samples have a much higher resistance. This concept of using the wire’s resistance to assess the composition of the initial dispersion merits additional work. The microwires can become quite long. Figure 7 shows a result from one of our earliest CNT experiments, in which a wire grown from the Tsinghua sample reached nearly 3 mm in length. This wire may be the longest example of a microwire grown from a CNT dispersion via dielectrophoresis. This result suggests that wires of arbitrary length can be generated. Conclusions The experiments presented here have produced a wealth of new information about the formation of microwires via dielectrophoresis. Previous work13-17,23 was focused on gold dispersions. In this paper, we have extended the method to additional materials, including carbon nanotubes. The
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results of this study indicate that a threshold voltage exists below which microwire growth is not observed. An explanation for this threshold voltage is that a minimum DEP force is needed to overcome the repulsive interparticle potential and fuse with the other nanoparticles. The scaling of the threshold voltage with gap distance indicates that there is a loss mechanism reducing the electric field that produces the DEP force. These results are not yet fully understood, but further work along these lines will surely elucidate the mechanism of microwire formation. The explicit frequency dependence of the DEP force has been derived in terms of the high- and low-frequency limits. The crossover frequency in an aqueous suspension of TiO2 was observed to conform to the prediction of eq 9. Measurements of crossover frequency could be used to determine the conductivity of the colloid particles. We explored the electrical properties of microwires grown from gold, carbon black, and carbon nanotubes. They all appear to be ohmic materials, which is consistent with a recent study on gold microwires.23 The gold wires grown in a 5 µm gap appear to have a resistance that is
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independent of the formation frequency. It is seen that the material composition of the wires influences their resistance, and one application of this work could be in the characterization of CNT dispersions. The microfabricated electrode structures worked very well in this study and provided the most reproducible data. We recommend the use of such devices in this area of research. Acknowledgment. We thank our colleagues Jim Ryley and J. Scott McCracken for the plating and microfabrication of the electrodes and Rick Nopper for helpful discussions on the frequency dependence of *. Prof. Fei Wei at Tsinghua University in Beijing, China kindly provided a multiwalled carbon nanotube sample used in this study. We also thank Prof. Orlin Velev (North Carolina State University) for reading and commenting on the manuscript. The comments and suggestions of the reviewers were greatly appreciated. LA0472697
