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Effects of Zeta Potential and Electrolyte on Particle Interactions on an Electrode under ac Polarization Junhyung Kim, John L. Anderson,* Stephen Garoff,† and Paul J. Sides Department of Chemical Engineering, and Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received February 28, 2002 The relative motion between two colloidal particles loosely deposited on an electrode passing alternating current was investigated. Parameters such as zeta potential, electrolyte composition, electrolyte concentration, and frequency were varied. At a low frequency (100 Hz), the particles aggregated in both sodium bicarbonate and sodium chloride solutions but separated in sodium hydroxide solutions. At 1000 Hz, the particles separated in both bicarbonate and hydroxide solutions, and the rate of separation was slower than at 100 Hz for the hydroxide solutions. The effect of zeta potential was negligible, indicating a convective mechanism causing the relative motion between the particles. Electrolyte concentration had no appreciable effect on the motion. These results are qualitatively consistent with predictions of a theory based on electrohydrodynamic flow induced by the interaction between a space charge in the liquid adjacent to the electrode’s surface, generated by concentration gradients of the ions, and an electric field tangent to the electrode which is caused by deflection of current around each particle. The interparticle separation velocity in hydroxide solutions predicted from the theory without adjustable parameters is comparable to the experimental values.
Introduction Colloidal particles loosely deposited on an electrode have been observed to move laterally and form clusters in both direct current (dc) and alternating current (ac) electric fields.1-8 In both cases, the interaction between particles occurred on a length scale comparable to the particle size; however, the electric fields in the ac mode were 100 times those in the dc mode to achieve the same relative velocity between pairs of particles. Experimental studies of the interactions between two particles in dc fields5,6 have demonstrated that electroosmotic flow9,10 about each particle is responsible for the relative motion between particles, and the relative velocity between the particles is proportional to ζE where ζ is the zeta potential of the particles and E is the electric field at the electrode’s surface in the absence of the particles. The relative motion of particles in ac fields is not as well understood. The objective of this paper is to present data that can distinguish between electrokinetic and electrohydrodynamic mechanisms for particle motion on electrodes in ac fields. In particular, we test certain features of a recently published electrohydrodynamic theory11 based on fluid convection generated by the ac * To whom correspondence should be addressed. † Department of Physics. (1) Bohmer, M. Langmuir 1996, 12, 5747. (2) Trau, M.; Saville, D. A.; Aksay, I. A. Science 1996, 272, 706. (3) Trau, M.; Saville, D. A.; Aksay, I. A. Langmuir 1997, 13, 6375. (4) Yeh, S. R.; Seul, M.; Shaiman, B. I. Nature 1997, 386, 57. (5) Guelcher, S. A. Investigating the Mechanism of Aggregation of Colloidal Particles during Electrophoretic Deposition. Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, PA, 1999. (6) Guelcher, S. A.; Solomentsev, Y.; Anderson, J. L. Powder Technol. 2000, 110, 90. (7) Sarkar, P.; De, D.; Yamashita, K.; Nicholson, P. S.; Umegaki, T. J. Am. Ceram. Soc. 2000, 83, 1399. (8) Kim, J.; Guelcher, S. A.; Garoff, S.; Anderson, J. L. Adv. Colloid Interface Sci., in press. (9) Solomentsev, Y.; Bohmer, M.; Anderson, J. L. Langmuir 1997, 13, 6058. (10) Solomentsev, Y.; Guelcher, S. A.; Bevan, M.; Anderson, J. L. Langmuir 2000, 16, 9208. (11) Sides, P. Langmuir 2001, 17 (19), 5791.
electric field interacting with a diffusion layer of ions created by electrode reactions. In a previous paper,8 we presented data for the relative motion of two charged latex particles on a tin-doped indium oxide (ITO) electrode undergoing ac polarization. The electrolyte was sodium bicarbonate, and the root-meansquare (rms) field was about 30 V/cm. At frequencies in the range of 30-500 Hz, pairs of particles approached each other at a speed that decreased as frequency increased, and at 1000 Hz the particles moved apart. Another interesting observation in ac fields was that the particles stopped moving together when the gap between them was about 1/2 the particle radius. (In dc fields, the particles approach each other until they come essentially into contact.5,6) This steady-state gap in ac fields was somewhat dependent on the field strength and frequency. While these results8 provide some insight into the dynamics in ac fields, they are not sufficient to test competing theories for the mechanism behind the twoparticle interactions. Two important system properties that have not yet been examined are the zeta potential of the particles and the type of ions composing the electrolyte. If the mechanism behind the particle interactions in ac fields is dominated by electrokinetics, as it is with dc fields, then the zeta potential would be an important parameter and the relative velocity between particles should be proportional to ζ. In addition, an electrokinetic mechanism should depend only on the Debye screening length and hence would not distinguish between similar-valence electrolytes, that is, between sodium bicarbonate and sodium hydroxide. On the other hand, if the relative two-particle velocity is independent of ζ but dependent on the type of ion in the electrolyte, then electrohydrodynamic convection3,11 might be the cause. Experiments The experimental cell appears in Figure 1. The two ITO electrodes consisted of 100 nm thick films of ITO on glass substrates 25.4 mm in diameter having a sheet resistance of 16
10.1021/la025682d CCC: $22.00 © 2002 American Chemical Society Published on Web 06/13/2002
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Figure 1. Experimental cell used to image trajectories of pairs of particles on an ITO thin-film electrode. Ω. The electrode spacing was 2 mm. Electrical connection was made via a brass ring which distributed current evenly to all points on the edge of the disk. An alternating voltage (sine wave) was applied to the electrode with a Hewlett-Packard 33120A 15 MHz function generator driving an EG&G Potentiostat model 273. The particles used in the experiments were carboxylatemodified polystyrene latex spheres 9.7 ( 0.67 µm in diameter (Interfacial Dynamic Corp., IDC). The particle suspensions were prepared by adding 10-20 µL of the particle suspension supplied by IDC to 25 mL of the test solution. The effective zeta potentials (ζ) of the particles were measured by using a PALS zeta potential analyzer (Brookhaven Instrument Corp.). The cell was filled with the suspensions of particles, and the particles were deposited on the electrode by sedimentation. Some of the particles were coated with the neutral triblock copolymer poly(ethylene glycol)-poly(propylene glycol)-poly(ethylene glycol) (133/50/133 block sizes, MW ) 14 600, Pluronics, BASF Corp.) to reduce the effective zeta potential.
Kim et al. Aqueous solutions of sodium and potassium hydroxide, sodium bicarbonate, and sodium chloride were used to probe the effect of ionic constituents on the particle motion. In most cases, the electrolyte concentration was 0.1 mM. We also compared 0.1 and 1.0 mM sodium hydroxide solutions to test the effect of electrolyte concentration. The electrolyte conductivity was measured before the solution was introduced into the cell by using an Accumet Research AR50 conductivity meter. The conductivity of the electrolyte in the cell was measured before and after the experiments by applying a 300 mV alternating potential at 10 kHz and measuring the current. There was a decrease of about 30% in the conductivity of the 0.1 mM sodium hydroxide solutions over the time of an experiment, presumably due to absorption of carbon dioxide. The conductivities of the other solutions remained constant with time. The particles were deposited on the electrode by sedimentation. Nearly all of the deposited particles were mobile, as indicated by their Brownian motion. Their motion when the field was applied was observed with an Olympus IMT-2 microscope having a 20× objective, a 1.5× intermediate lens, and a Sony XC-77 CCD camera. Images were recorded on videotape by using a Panasonic V-AG735 SVHS recorder, and frames were sampled from the videotape with a Scion LG-3 frame grabber. The location of the center of each particle was determined by using Scion Image 1.62a image analysis software at a rate of one frame per second. Pairs of particles on the electrode were arbitrarily chosen for observation with the requirement that they were at least 10-20 radii from other particles. Trajectories of the two particles in each pair were determined by computing the separation distances between the pairs of particles as a function of time. The clock on each trajectory was set to zero when the particle
Figure 2. Averaged trajectories of five pairs of particles with experimental standard deviations shown as the vertical bars. Dimensionless separation is the center-to-center distance between the particles divided by the particle radius. 100 Hz at an rms potential of 30-35 V. ζ is the measured zeta potential (mV) of the particles. (a) 0.1 mM sodium bicarbonate (ζ ) -81.5 ( 4.0), (b) 0.1 mM sodium chloride (ζ ) -72.5 ( 1.3), and (c) 0.1 mM sodium hydroxide (ζ ) -57.9 ( 1.9).
Particle Interactions on an Electrode
Figure 3. Effect of particle zeta potential (ζ) in 0.1 mM sodium chloride. (a) ac field, 35 V/cm, 100 Hz, mean of five trajectories for each ζ. (b) dc field, 0.28 V/cm, one trajectory at each ζ. Filled circles: bare particles (ζ ) -53.2 ( 4.7 mV); open circles: polymer-coated particles (ζ ) -14.7 ( 1.5 mV). centers were 4 radii apart if the particles approached each other or when the centers were slighter greater than 2 radii apart if the particles separated.
Results The effect of electrolyte composition is demonstrated in Figure 2. The data represent the average and standard deviations of particle positions from measurements repeated five times on different pairs of particles. At 100 Hz, the particles approached each other in both chloride and bicarbonate solutions at a rate consistent with previous experiments with bicarbonate, and a steady-state gap occurred as previously reported.8 The steady-state gap was 0.6 of the particle radius for sodium bicarbonate and 0.3 radius for sodium chloride; this difference was reproducible. However, in the case of sodium hydroxide (Figure 2c) the particles moved away from each other. Figure 3 shows that the tendency of the particles to separate in sodium hydroxide remained even when the frequency was increased to 1000 Hz, albeit at a slower rate. In contrast to the behavior in hydroxide solutions, with bicarbonate solutions, two particles approach each other at a rate that decreases with increasing frequency and begin to separate at 1000 Hz.8 Figure 4 shows that there was no significant effect of the concentration of sodium hydroxide on the relative velocity between the particles at 100 Hz. Whether there was attraction (bicarbonate and chloride) or separation (hydroxide) between the pairs of particles at 100 Hz, the relative velocity decreased substantially
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Figure 4. Effect of particle zeta potential (ζ) in 1.0 mM potassium hydroxide. (a) ac field, 35 V/cm, 100 Hz, mean of five trajectories for each ζ. (b) dc field, 0.28 V/cm, one trajectory at each ζ. Filled circles: bare particles (ζ ) -57.0 ( 4.4 mV); open circles: polymer-coated particles (ζ ) - 24.5 ( 4.2 mV).
when the center-to-center separation exceeded 4-5 particle radii, and Brownian motion was more important at these larger separations. To make quantitative comparisons of our data, we have determined the mean relative velocity between the particles at each condition when the center-to-center separation was 3.5 particle radii. To compute this velocity, each trajectory (out of the five for a given set of conditions) was fit to the following empirical equation:
r(t) ) r0 + b1t1/2 + b2t
(1)
where r0 ) 4 (aggregation) or 3 (separation) and r is the center-to-center separation divided by the particle radius (4.85 µm). This equation fit each trajectory over the entire range of data. The relative velocity (v) of a single trajectory equals dr/dt evaluated at the time when r ) 3.5. The values of v for the five individual trajectories were then averaged to get the mean relative velocity reported in Table 1. The effects of particle zeta potential on pair trajectories are shown in Figures 5 and 6. In Figure 6, the electrolyte was potassium hydroxide; in our experiments, we saw no significant difference in the results between sodium and potassium hydroxide. Only one pair of particles was studied in the dc case; there are abundant data in the literature5,6,10 showing that the relative velocity between two particles is proportional to ζ. The important result here is that there is essentially no effect of zeta potential on the relative velocity in the ac case. The “bare” latex
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Table 1. Quantitative Comparison of Predicted and Measured Interparticle Velocitiesa electrolyte NaHCO3 NaHCO3 NaCl NaOH NaOH NaOH
concentration (mM)
frequency (Hz)
v (nm/s) theory
v (nm/s) experiment
number of trajectories
steady-state gap (a)
0.1 0.1 0.1 0.1 1.0 0.1
100 1000 100 100 100 1000
N/A N/A NA +90 +64 +24
-320 ( 87 NA -360 ( 147 +150 ( 50 +120 ( 65 +94 ( 36
5 5 5 5 5 5
0.6 NA 0.3 NA NA NA
a v ) dr/dt at r ) 3.5 radii, where r is the center-to-center distance between the pair of particles. v listed is the average over the trajectories. The applied electric fields were 30-35 V/cm. The steady-state gap equals (r - 2a)/a where r is the separation at long times.
Figure 5. Effect of electrolyte concentration. Averaged trajectories of five pairs of particles in sodium hydroxide at 100 Hz and an rms potential of 35 V. (a) 0.1 mM (ζ ) -57.9 ( 1.9); (b) 1.0 mM (ζ ) -44.2 ( 5.3).
particles had a zeta potential that was about 3.5 times greater in magnitude (both were negative) than the polymer-coated particles, yet the mean trajectories of five pairs of each were almost the same. One significant effect of zeta potential is on the steady-state separation in sodium chloride (see Figure 5): the bare particles had a smaller long-time gap (0.4 particle radius) than the polymer-coated particles (0.7 particle radius). In summary, our data at 100 Hz show that particles separate in hydroxide solutions and come together in bicarbonate and chloride solutions, and the zeta potential and electrolyte concentration are of little or no consequence in ac fields. Our results are compared with an electrohydrodynamic theory in the following section. Discussion Comparison of Experiment and Theory. The electrohydrodynamic theory proposed by Sides11 assumes a binary electrolyte having one ion that participates in the electrode reaction transferring charge between the solution and the ITO film. For example, in the case of hydroxide solutions the reaction would likely be
anodic: cathodic:
1 2OH- f H2O + 2e- + O2 2 2H20 + 2e- f H2 + 2OH-
(2)
However, the cathodic reaction might also involve the reduction of dissolved oxygen. Assuming the above reactions occur, then OH- is consumed on the positive cycle of a period and it is produced on the negative cycle. The reaction of OH- creates a concentration gradient because
Figure 6. Effect of frequency. Averaged trajectories of five pairs of particles at an rms potential of 30-35 V. (a) 0.1 mM sodium bicarbonate (ζ ) -81.5 ( 4.0); (b) 0.1 mM sodium hydroxide (ζ ) -57.9 ( 1.9). Filled circles: 100 Hz; open triangles: 1000 Hz.
the counterion, which is not reacting, must be at a zeroflux condition.12 The length scale of the concentration polarization layer that develops due to the zero-flux of the counterion is of the order of (D/ω)1/2 where D is the mean diffusion coefficient of the electrolyte and ω is the frequency (rad/s). Since D is typically about 10-5 cm2/s, this length scale is of the order of micrometers at 100 Hz, which is comparable to the particle radius in our experiments. Within the concentration polarization layer, there develops a small but finite space charge (Fe), which is to a good approximation proportional to the difference (tˆ) in ion transference numbers (t+ or t- for the two ions):
t + tˆt ≡ + z+ z-
ti )
zi2Di z+2D+ + z-2D-
(3)
Particle Interactions on an Electrode
zi is the valence of the ion (+1 for the cations and -1 for anions of our experiments), and Di is the diffusion coefficient of the ion. The space charge is also proportional to the faradaic current density (if), that is, the current that converts charge from ions to electrons in the electrode. If we assume that the faradaic current stays in phase with the applied electrical potential, then Fe ∼ ˆtif. The above argument is made neglecting the presence of a particle. Near a deposited particle, the electric field lines are diverted because charge cannot flow through the particle. This creates a disturbance electric field with a component (Ep) directed parallel to the electrode surface and pointing toward the center of the particle. When Ep interacts with the space charge, a force density (Fr ) FeEp) acts on the fluid near the electrode to produce convection of the fluid toward the particle. When averaged over one cycle of the sine-wave potential applied to the electrodes, a finite force density (〈Fr〉) survives; 〈Fr〉 drives liquid toward or away from the particle near the electrode, with a circulatory flow to conserve fluid mass farther from the electrode. Neighboring particles on the electrode are convected by the flow toward or away from the central particle; likewise, all other particles attract or repel their neighbors. This theory11 predicts 〈Fr〉 ∼ -tˆifE0 where E0 is the rms electric field in the liquid at the electrode surface. The relative velocity between two particles (v ) dr/dt) is proportional to 〈Fr〉. Note that the faradaic current is not necessarily proportional to the electric field, and hence v is not in general proportional to E02. Our experiments confirm the theory’s predicted dependence on ˆt. If one accepts that OH- ions participate in the electrode reactions, the particles should separate because ˆt ) -0.60 for sodium hydroxide. The comparison between theory and experiment is unclear for the bicarbonate and chloride solutions because the ions of these electrolytes probably did not participate in the electrode reaction (which produces if). This would mean any faradaic current would have to result from contaminants such as dissolved oxygen, and the ionic composition would involve at least three species instead of just two. The buffering action of bicarbonate would further complicate the modeling. Therefore, the result that the particles approached each other in both sodium bicarbonate (tˆ ) +0.94) and sodium chloride (tˆ ) -0.21) has little or no relevance to assessing the validity of the theory. Another important prediction of the theory is that the zeta potential of the particles is irrelevant because neither Fe nor Ep depends on the charge on the surface of the particles. Our data bear this out (Figures 5 and 6). In fact, this result is a strong indication that the mechanism behind the relative motion of particles in ac fields is not electrokinetic; rather it is a convective mechanism based on electrohydrodynamic flows. This is an important result of our work. Furthermore, the theory also predicts that (12) Newman, J. S. Electrochemical Systems; Prentice Hall: Englewood Cliffs, NJ, 1973.
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electrolyte concentration should not affect the relative particle velocity (see Table 1). Our data for sodium hydroxide bear this out. If we assume that the faradaic current equals the total current, then we can predict an upper bound for the interparticle velocity (v) from the electrohydrodynamic theory11 and compare it with our data for NaOH. These theoretical predictions (without adjustable parameters) are listed in Table 1. The agreement at 100 Hz is remarkably good. While the theory correctly predicts a reduction in relative particle velocity at 1000 Hz, it underpredicts the magnitude of v compared to the experimental result at 1,000 Hz. The Stationary State Gap. The mechanism responsible for the gap between aggregating particles at long times, as shown in Figures 2 and 3 and reported previously,8 is not known. Neither the electrohydrodynamic11 nor electrokinetic10 theories by themselves predict this gap at long times, and the gap does not exist in aggregation by dc fields. One must keep in mind that the steady-state gap has only been observed in ac fields for electrolytes that do not participate in the electrode reaction (since the particles separate in hydroxide solutions), and hence any electrohydrodynamic theory would have to consider a ternary or quaternary ion system involving H+ and/or OH-. The zeta potential dependence of the gap (see Figure 5a) suggests an electrokinetic component to the interparticle dynamics. The complex electrohydrodynamic and electroosmotic flow patterns that must exist in this problem might superimpose to form a hydrodynamic node where the particle is captured, but demonstrating the existence of such a node is not currently possible. Summary The two most important results of this work are (1) the particles separated in sodium and potassium hydroxide solutions and (2) the relative velocity between the particles was independent of the zeta potential. Both results are predicted by the electrohydrodynamic theory developed by Sides.11 The theory also correctly predicts that the interparticle velocity is independent of electrolyte concentration and becomes smaller as frequency is increased. The quantitative comparison between theory and experiment is good for sodium hydroxide at 100 Hz, but the theory significantly underpredicts the interparticle velocity at 1000 Hz. The existence of the steady-state gap between particles, observed between particles in all ac experiments with nonreactive electrolytes (bicarbonate and chloride), and its apparent dependence on the zeta potential of the particles are still unexplained. Acknowledgment. This work was supported by NSF Grant CTS-0089875, Carnegie Mellon University, and Philips Research (Eindhoven, The Netherlands). LA025682D
