Influence of Electrolyte Concentration on the Aggregation of Colloidal

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Influence of Electrolyte Concentration on the Aggregation of Colloidal Particles near Electrodes in Oscillatory Fields Sukhleen Saini, Scott C. Bukosky, and William D. Ristenpart* Department of Chemical Engineering, University of California, Davis, Davis, California 95616, United States S Supporting Information *

ABSTRACT: Micron-scale particles suspended in various aqueous electrolytes have been widely observed to aggregate near electrodes in response to oscillatory electric fields, a phenomenon believed to result from electrically induced flows around the particles. Previous work has focused on elucidating the effects of the applied field strength, frequency, and electrolyte type on the aggregation rate of particles, with less attention paid to the ionic strength. Here we demonstrate that an applied field causes micron-scale particles in aqueous NaCl to rapidly aggregate over a wide range of ionic strengths, but with significant differences in aggregation morphology. Optical microscopy observations reveal that at higher ionic strengths (∼1 mM) particles arrange as hexagonally closed-packed (HCP) crystals, but at lower ionic strengths (∼0.05 mM) the particles arrange in randomly closed-packed (RCP) structures. We interpret this behavior in terms of two complementary effects: an increased particle diffusivity at lower ionic strengths due to increased particle height over the electrode and the existence of a deep secondary minimum in the particle pair interaction potential at higher ionic strength that traps particles in close proximity to one another. The results suggest that electrically induced crystallization will readily occur only over a narrow range of ionic strengths.

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INTRODUCTION Research over the past two decades has clearly established that micron-scale colloids near electrodes will aggregate in response to an applied oscillatory field.1−13 Early work by Trau et al.1,2 attributed the aggregation behavior to the proximity of the particle to the charge polarization layer near the electrode; the particle disrupts the otherwise uniform electric field and creates a tangential field component that results in electrohydrodynamic (EHD) fluid motion directed toward the particle. Neighboring particles are mutually entrained in the respective flows, leading to aggregation. Ristenpart et al.6 expanded on this proposed mechanism via a scaling analysis that treated the particles as point dipoles and predicted that the aggregation rate scales as the square of the applied field strength and inversely with frequency, predictions which are both consistent with experimental observations.4,6,7,9,10 The ability to externally induce aggregation of colloids is of great interest for controlled formation of various structures, including for example colloidal dimers11 and chiral colloidal molecules.13 Many details of the aggregation process, however, remain obscure, and many alternative mechanisms based on various types of electrically generated flow have been proposed to explain the aggregation behavior.15,17−20 In particular, the point dipole model fails to capture the effect of electrolyte type. As originally reported by Kim et al.,14 the same particles that aggregate if suspended in NaCl or KCl will instead separate in NaOH and KOH. Sides and Prieve and co-workers7,8,14−20 considered several models to explain the electrolyte-dependent particle behavior, with a particular emphasis on the phase angle between applied field and the nanometer scale oscillations of © XXXX American Chemical Society

the particle. The effect of electrolyte type is still not entirely clear; however, recent evidence indicates that the rate of aggregation is inversely correlated with the electrolyte-dependent magnitude of the particle zeta potential21 and that particles in some electrolytes can occupy two different average heights above the electrode.22,23 Given the tremendous amount of research to date, a perhaps surprising aspect is that effectively no work has systematically examined the effect of electrolyte concentration. Almost all previous studies have been restricted to concentrations in the range of about 0.1−1 mM. The early work by Trau et al.2 used an approximately 0.1 mM concentration of unspecified electrolytes. Kim et al.14 studied the effect of electrolyte concentration on the separation or aggregation rate of particles in NaOH, KOH, NaCl, and NaHCO3 solutions but limited their examination of the concentration effect to 0.1 and 1 mM NaOH solutions; they concluded the rate of particle separation was independent of the electrolyte concentration. In subsequent work on the phase angle correlation with aggregation/ separation behavior, Sides and Prieve and co-workers7,19,24 restricted attention to 0.15 mM for almost all of their different electrolytes studies. Likewise, Woehl et al.21 studied more than two dozen electrolyte types but performed all experiments with 1 mM solutions. To date, no detailed investigation describing the effect of electrolyte concentration has been conducted. Received: December 18, 2015 Revised: April 6, 2016

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fraction of 3 × 10−3. Each suspension was washed three times by centrifugation and resuspension. The electrophoretic mobility was measured via dynamic light scattering (Zetasizer, Malvern Instruments Ltd.), with ostensible zeta potential approximated using the Helmholtz−Smoluchowski relation for small mobilities. To begin an experiment, the colloidal suspension was placed into the spacer, and the particles were allowed to settle near the bottom electrode by gravity for ∼2 h. After the particles settled near the electrode, an ac electric field of 5 Vpp (volts peak-to-peak) and 100 Hz was applied using a 20 MHz function generator (Agilent 33220A). We chose this frequency because it is high enough such that electrolytic reactions should be negligible (a finding corroborated by current density measurements; cf. Figure S1) but low enough that aggregation readily occurs. The resulting particle behavior was observed using either optical microscopy or laser scanning confocal microscopy (Zeiss LSM 700). Lower magnification videos were recorded to observe the overall aggregate morphology of the system, whereas higher magnification images were taken to help quantify the aggregate packing. The resulting aggregate morphology was imaged and analyzed using standard imaging techniques, including image thresholding and Delaunay triangulation (the im2bw and delaunay functions in MATLAB). The experiment was repeated for colloidal solutions of different NaCl concentrations ranging from 0.005 to 3 mM, which corresponded to Debye lengths ranging from 137 to 5.6 nm, respectively. At NaCl concentrations higher than 3 mM, the particles tended to stick irreversibly to the electrode surface upon sedimentation and contact, and hence no aggregation was observed. No special measures were taken to prevent carbon dioxide from saturating the water, so the actual ionic strength of the low NaCl concentration solutions was presumably altered by the presence of carbonic acid. As discussed below, however, we nonetheless observe a large difference in behavior simply with changes in NaCl concentration even at extremely low values. The aggregation behavior was also studied using a laser scanning confocal microscope to correlate the particle height with the observed aggregate structures. To measure the particle height, some particles at a lower concentration (3 × 10−4 volume fraction) were allowed to dry overnight on the surface of the bottom electrode, causing them to irreversibly adhere. To begin an experiment, fresh particle suspensions were added as described above, with a small fraction of stuck particles residing at the electrode surface. The average center of the stuck particles was considered as the zero reference plane; these particles were easily identified as stuck due to their lack of Brownian motion. At each ionic strength, the fluorescent intensities from the aggregates as well as the stuck reference particles were measured systematically as a function of vertical position (a standard z-stack). The peak of the intensity curve corresponded to the average center of the aggregates, and the height was thus the difference between the centers of the mobile and stuck particles. We note that the height measured in this manner represents the “average” height of the particles, averaged over many particles that fluctuate in position due to thermal motion, rather than the “most probable height” one might intuitively inspect based on the minimum in a potential energy profile.25,26

In this article we describe experimental observations of the effect of electrolyte concentration (NaCl) on the aggregation behavior of micron-scale particles at a fixed electric field strength and frequency. Systematic experiments with concentrations ranging from 10−3 to 3 mM reveal an order−disorder transition above a critical concentration of about 0.2 mM, from randomly closed-packed (RCP) to hexagonally closed-packed (HCP) structures. Qualitatively, the order−disorder transition is similar to recent results reported by Dutcher et al.,12 who demonstrated that a reversible transition from a hexatic to disordered structure occurs (at fixed salt concentration and field strength) upon decreasing the frequency from around 500 to 100 Hz; they explained the behavior in terms of an increased particle height and correspondingly increased particle diffusivity at lower frequencies. We present evidence that a similar increase in particle height above the electrode occurs for particles suspended in lower ionic strengths, suggesting an increased diffusivity and tendency for disorder. Moreover, we present calculations indicating that a deep secondary minima in the particle pair interaction potential occurs for salt concentrations above the observed critical value of 0.2 mM. The results suggest that HCP crystallization is a consequence of both decreased diffusivity and decreased double-layer repulsion. The key implication of the work is that electrically induced particle crystallization can only occur over a narrow range of salt concentrations.

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EXPERIMENTAL METHODS

The experimental methods were similar to those described previously.12,22 In brief, the experimental setup (Figure 1) consisted

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RESULTS AND DISCUSSION The optical microscopy images in Figure 2 show the overall aggregation morphology of particle suspensions of varying NaCl concentration, in response to 5 min of a continuously applied 5 V, 100 Hz field. These images were taken at a lower magnification (5×) to look at the overall aggregation behavior, rather than focusing only on a few individual aggregates. The experimental images reveal that the particles tend to aggregate for all NaCl concentrations tested, but there is a distinct change in morphology with the changing concentration. For concentrations ∼0.005 mM and below, the particles form very large and loosely packed aggregates (Figure 2a). There is clearly a long-range attraction, as evidenced by the large regions depleted of particles, but the particles do not stay in close

Figure 1. (a) Schematic of the experimental apparatus (not to scale). (b) Magnification emphasizing the aggregate height with respect to “stuck” particles that are irreversibly adhered to the electrode. of two parallel glass slides coated with ITO (indium tin oxide, 5−15 Ω sheet resistance) separated by a 1 mm thick nonconductive poly(dimethylsiloxane) spacer containing the colloidal suspension. Prior to each experiment, the electrodes were washed with RBS 35 detergent, then ultrasonicated for 10 min each in RBS 35 detergent, acetone, and deionized (DI) water, and finally dried using filtered compressed air. Stock solutions were prepared with reagent grade NaCl at different ionic strengths by diluting 10 mM NaCl solution using DI water (18.2 MΩ cm). Colloidal suspensions were prepared by adding 2 μm diameter fluorescent sulfonated polystyrene (PS) particles (Invitrogen, F8853) to an aqueous NaCl solution to a volume B

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Figure 2. Optical microscopy images of 2 μm diameter particles suspended in aqueous solutions of varied concentrations, taken 5 min after applying an ac electric field (5 Vpp, 100 Hz). Each low-magnification image at the top is 1100 μm wide; each high-magnification image at the bottom is 260 μm wide.

contact; they appear randomly arranged within the cluster and exhibit vigorous Brownian motion. At a slightly larger concentration of 0.05 mM (Figure 2b), the particle aggregates are denser but still randomly packed. At low magnification the aggregates qualitatively appear “wispy”, in that they tend to form long feathery aggregates. The aggregate morphology substantially changes for higher salt concentrations. At 0.2 mM (Figure 2c), the particles form more tightly packed and smaller aggregates. The particles here are arranged much more regularly within the aggregates; i.e., they exhibit HCP ordering. Similar structures are likewise observed at 0.5 mM (Figure 2d), albeit with more evidence of aggregate coarsening. At 1 mM (Figure 2e), HCP aggregates still form, but the average aggregate size is smaller, and there is noticeably less aggregate coarsening. Finally at 3 mM (Figure 2f) the particles tend to irreversibly adhere to the electrode upon contact, so the aggregates do not have much chance to form and are hardly visible. We emphasize that the particle volume fraction, applied frequency, and applied potential are the same in each image in

Figure 2; only the salt concentration was varied. Because the conductivity varies with salt concentration, one possibility is that the actual electric field strength experienced by the particles varies with the salt concentration. Our measurements of the current density, however, indicate that at 100 Hz the salt concentration has almost no effect on the observed current amplitude over several orders of magnitude in the conductivity (cf. Figure S1). This observation is consistent with the expectation that electrolytic effects will be negligible in aqueous systems above approximately 50 Hz,20,27 and hence the electric field magnitude can be approximated here as the ratio of the applied potential difference to the electrode separation distance. Another key point is that the images shown in Figure 2 represent pseudo-steady-state configurations. No further aggregation or crystallization was observed at lower salt concentrations (less than 0.2 mM); the structures persisted indefinitely without noticeable changes in overall morphology until the field was removed. Slow but continued aggregate coarsening occurred at intermediate concentrations, but the overall qualitative appearance with regard to aggregate structure C

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Figure 3. Representive confocal microscopy images of 2 μm diameter sulfonated PS particles at three different NaCl concentrations. The superimposed red circles mark the particle centers, and the red lines depict the connection to the nearest neighbors, as calculated via Delaunay triangulation. The images were taken 5 min after the application of ac electric field of 5 Vpp and 100 Hz.

that ⟨d⟩ decreases from about 3.5 particle diameters at the lowest salt concentrations to near contact at higher salt concentrations. Likewise, the particles are also clearly more disordered at lower concentrations. To quantify this behavior, we calculated the standard orientational bond order parameter, ψ6 = (1/N)∑i[|(1/Nij)∑jexp(i6θij)|] where θij is the angle between a fixed axis and the bond separating the particles i and j.12 The bond order parameter ranges from 0 to 1, where 0 denotes no ordering and 1 denotes perfect hexagonal ordering. The lowest degree of order is observed at the lowest concentrations, with ψ6 ≈ 0.4. The ordering begins to increase slightly at concentrations above 5 × 10−2 mM, increasing steadily with concentration until the highest degree of ordering (ψ6 ≈ 0.9 is observed at 1 mM (Figure 4b)). (The order parameter does not reach unity due to the presence of grain boundaries or point defects.) Note that the bond order increases in a manner roughly commensurate with the decrease in interparticle separation ⟨d⟩/2a (Figure 4a). Measurements of both the interparticle spacing and orientational bond parameter versus time confirm that the aggregate morphology has achieved a pseudo-state state; i.e., the structure changes little with time after the initial transient aggregation (cf. Figure S2). Having demonstrated that the salt concentration affects the morphology strongly, the key question is why? We first note that a qualitatively similar order−disorder transition was observed by Dutcher et al.,12 who showed that changes in the applied frequency (at constant field strength and ionic strength) could induce a reversible RCP−HCP transition. They demonstrated that the RCP structures observed at lower frequencies were correlated with an increased height of the particles over the electrode (believed to be due to an increased EHD lift force) and that the larger height effectively increased the particle diffusivity via decreased viscous hindrance due to the electrode. Here we held the frequency constant while altering the ionic strength, but one hypothesis would be that lower ionic strengths are associated with an increased electrostatic repulsion with the electrode, leading to a similar increase in the average height of the particles above the electrode. To test this idea, we used confocal microscopy to measure the average height of the particles. Although the particles might appear to all be at the same height (i.e., in exactly the same plane) in the optical microscopy images, the height of individual particles actually fluctuates slightly because of Brownian motion. Confocal microscopy allows the average

remained the same. To quantify the effect of NaCl concentration on the colloidal packing behavior, we measured the interparticle spacing and an orientational bond order parameter at different ionic strengths. For these experiments, we used confocal microscopy of individual aggregates to obtain higher spatial resolution. A Delaunay triangulation method was used to calculate the average interparticle distance within an aggregate (Figure 3). The red circular marks are the detected centers of individual particles, while the straight lines connect nearest neighbors as determined via the Delaunay triangulation. The average of these distances within any given cluster is taken as ⟨d⟩, the mean interparticle separation. As depicted in Figures 2 and 3, the mean interparticle separation significantly decreases as the salt concentration increases. This effect is quantified in Figure 4a, which shows

Figure 4. (a) Average center-to-center interparticle separation, normalized by the particle diameter, versus the concentration of NaCl. (b) Orientational bond order parameter versus NaCl concentration, acquired from confocal images like those shown in Figure 3. Error bars are 2 standard deviations of the mean of at least four different aggregates in each trial, with three unique trial replicates (N = 12). D

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Figure 5. Representatitive fluorescent intensity curves versus vertical position, obtained via confocal microscopy, of 2 μm diameter particles at 5 Vpp and 100 Hz. The solid colored lines are running averages for each intensity profile. The “mobile” particles exhibited Brownian motion, while the “stuck” particles were the smaller subset previously adhered to the electrode. The difference in peak intensity locations gives the absolute height of the mobile particles over the electrode.

significantly alters the average height, with large increases at lower ionic strengths and large decreases at high ionic strengths (black points in Figure 6). In other words, the data in Figure 6 demonstrate that the particles move closer to the electrode in response to the field at high ionic strengths but move f urther from the electrode in response to the field at lower ionic strengths. Near 10−2 mM, the average height remains unchanged. A key implication of the data in Figure 6 is that the effective particle diffusivity will be higher at lower ionic strengths because the particles are further away from the electrode. The diffusivity of an unhindered particle infinitely far from a wall is given by the Stokes−Einstein equation D∞ = kBT/6πμa, where μ is the fluid viscosity and a is the sphere radius. As discussed by Goldman et al.,29 however, a correction must be included when the particle is in close proximity to a solid surface due to the no-slip boundary condition imposed on the solid surface. The force required to move a sphere diverges logarithmically as it approaches contact; equivalently, the diffusivity decays to zero. This dependence implies that particles higher above the electrode will have higher diffusivity, consequently hindering their ability to form ordered structures. Changes in the ionic strength clearly alter the electrode/ particle interaction, so a natural question is whether they also change the particle/particle interaction. A full treatment of the effect of ionic strength on the particle/particle interaction in response to the applied field (included EHD and/or other electrically generated fluid flows) is complicated. As a starting point, however, we can consider the effect of ionic strength on the colloidal interaction energy using the classic Derjaguin− Landau−Verwey−Overbeek (DLVO) formulation, which balances double layer repulsion and van der Waals attraction.30 Using the Derjaguin approximation, the interaction potentials for double layer repulsion and van der Waals attraction between a sphere and wall are respectively

height of the individual particles to be extracted from a vertical stack of images (a standard z-stack). Representative curves of fluorescent intensity versus vertical position are shown in Figure 5. At each ionic strength, the two curves represent respectively the small population of stuck (nonmobile) particles that serve as a reference for the electrode position or the mobile particles within the aggregates. The difference in the vertical position of the peak intensity yields the center-to-center separation of the stuck and mobile particles (or equivalently the distance between the electrode surface to the bottom of the mobile particles). The intensity curves show that the height of the aggregates indeed decreases with ionic strength. At 0.001 mM (Figure 5a), the mobile particles are separated by about 2.75 μm, a difference which decreases to 0.65 μm at 0.05 mM (Figure 5b) and vanishes almost to zero at 1 mM (Figure 5c). Systematic measurements at different NaCl concentrations corroborate this trend (Figure 6) and also demonstrate that

Figure 6. Average height of the aggregates as a function of salt concentration with or without applied electric field (100 Hz, 5 Vpp). Error bars are 2 standard deviations of the mean of three trial replicates with three unique regions per trial (N = 9).

⎛ eζp ⎞ ⎛ eζ ⎞ ⎛ k T ⎞2 Φdl (h) = 64πaε0εc⎜ B ⎟ tanh⎜ e ⎟ tanh⎜ ⎟ exp(− κh) ⎝ e ⎠ ⎝ 4kBT ⎠ ⎝ 4kBT ⎠

which way the particles move vertically in response to the field depends strongly on the ionic strength. Control experiments without any applied electric field confirm that the mobile particles tend to reside on average near the gravitational height, hg = kBT/Fg, where Fg = (4/3)πa3Δρg is the gravitational force and kBT is the thermal energy.28 For our 2 μm polystyrene particles in water, hg is approximately 1 μm (dashed line Figure 6, shown as the surface-to-surface separation distance). This simple calculation ignores electrostatic and dispersion effects but nonetheless captures the magnitude of the average particle height over the electrode in the absence of the field (red points in Figure 6). The key point here is that application of the field

(1)

ΦVdW (h) = −A

a ⎡ h h ⎛ h ⎞⎤ ⎟⎥ + ln⎜ ⎢1 + ⎣ 6h 2a + h a ⎝ 2a + h ⎠⎦

Φtotal (h) = φdl + φVdW

(2) (3)

Here kB is Boltzmann’s constant, T is the temperature, e is the elementary charge, and ζe and ζp are the zeta potentials of the electrode and particle, respectively. Since ζp depends on the E

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Langmuir electrolyte concentration, the double-layer repulsion will also vary with NaCl concentration.31 Our measurements indicate that ζp for 2 μm sulfonated PS increases from about −30 to about −55 mV as the NaCl concentration increases from 10−3 to 1 mM (Figure 7), results similar to that reported by Zukoski

Figure 8. (a) Particle pair interaction potential energy as a function of surface to surface separation distance, in the absence of electric field, calculated using eq 3, for varied NaCl concentration. (b) Location of the secondary minimum as a function of NaCl concentration. (c) Depth of potential energy secondary minima as a function of NaCl concentration with dashed blue line showing the concentration where |φmin/kBT| = 1.

Figure 7. Electrophoretic mobility and corresponding approximate zeta potential (approximated using the Helmholtz−Smoluchowski equation) for 2 μm sulfonated PS particles suspended in aqueous NaCl as a function of NaCl concentration. Error bars are 2 standard deviations of the mean of three trial replicates.

et al.31 Parameters used for calculating the interaction potentials are shown in Table 1. We emphasize that these DLVO calculations completely omit the influence of the applied oscillatory field and are thus at best an approximation.

(Figure 8b). Notably, however, the depth of the energy well is small compared to kBT for concentrations smaller than about 10−1 mM (Figure 8c). If we choose 1 kBT as a critical energy well depth, then a significant secondary minimum only occurs for salt concentrations greater than 0.20 mM. Importantly, this critical concentration exactly coincides with the order−disorder transition demonstrated in Figure 4. We emphasize that the interaction energies depicted in Figure 8 are approximations since they neglect the contribution of the longranged attractive force (presumably electrically generated fluid flow). Nonetheless, the key implication is that that at lower salt concentrations the naturally occurring potential energy minimum is too shallow to capture particles and that there is a tremendous electrostatic repulsion that effectively prevents close contact. At higher salt concentrations, in contrast, a relatively deep secondary minimum exists, even prior to application of the field, that helps lock the particles into position.

Table 1. Global Parameters Used for All Calculations particle radius, a (m) elemental charge, e (C) Boltzmann’s constant, kB (J/K) dielectric permittivity of vacuum, ε0 (F/M) dielectric constant of water, εc temperature, T (K) density of fluid, ρf (kg/m3) density of particle, ρp (kg/m3) electrode zeta potential, ζe (mV) Hamaker constant, A (J)

10−6 1.6 × 10−19 1.38 × 10−23 8.854 × 10−12 80 298 997 1050 −80 10−20

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Nonetheless, the calculations of the particle pair interaction potential reveal a striking correlation with our experimental observations. Taking into account the observed zeta potential, the total interaction potential between the particles (eq 3) was calculated for each salt concentration (again, neglecting any influence of the applied field). Representative curves are shown in Figure 8a for different salt concentrations. At this scale, the primary minimum and primary maximum are not visible; instead, we focus on the “secondary minimum” that can result when van der Waals forces significantly exceed electrostatic repulsion at larger separations.30 At the highest ionic strength of 3 mM, a deep secondary minimum (∼6 kBT) occurs near a particle−particle separation of 50 nm. Decreasing the NaCl concentration decreases the depth of the secondary minimum and simultaneously increases the separation distance (Figure 8a); at lower ionic strengths the double-layer repulsion effectively dominates over the van der Waals attraction. For example, at 0.005 mM the secondary minimum is too small to be observed at this scale, but there is a steep energy barrier at about 1 μm separation, suggesting the particles at this ionic strength will have a difficult time approaching any closer. A secondary minimum does occur over all ionic strengths calculated here, at increasingly large separation distances

SUMMARY We demonstrated the effect of NaCl concentration on the aggregate morphology of micron-scale colloidal particles. Our work revealed a transition in aggregate structure from HCP to RCP at critical electrolyte concentration near 0.2 mM. We explain the transition in terms of particle height above the electrode, which increases at lower salt concentrations resulting in increased diffusivity and Brownian motion. Furthermore, the transition is commensurate with the onset of a deep secondary minimum in the particle−particle interaction potential, implying that van der Waals forces help drive the observed crystallization of HCP aggregates. The observations regarding the height above the electrode raise an obvious question: why does the particle height change with ionic strength? One interpretation can be that the EHD flow pushes the particles farther from the electrode due to the impingement of the flow on the particle, potentially balanced by a dipole attraction to the image dipole. Importantly, previous models6,20 were made under the assumption that the Debye length is much smaller than the particle length scale (κa ≫ 1), but in our experiments for very low salt concentrations this F

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(13) Ma, F. D.; Wang, S. J.; Wu, D. T.; Wu, N. Electric-field-induced assembly and propulsion of chiral colloidal clusters. Proc. Natl. Acad. Sci. U. S. A. 2015, 112 (20), 6307−6312. (14) Kim, J.; Anderson, J. L.; Garoff, S.; Sides, P. J. Effects of zeta potential and electrolyte on particle interactions on an electrode under ac polarization. Langmuir 2002, 18 (14), 5387−5391. (15) Fagan, J. A.; Sides, P. J.; Prieve, D. C. Vertical Oscillatory Motion of a Single Colloidal Particle Adjacent to an Electrode in an ac Electric Field. Langmuir 2002, 18 (21), 7810−7820. (16) Fagan, J. A.; Sides, P. J.; Prieve, D. C. Calculation of ac Electric Field Effects on the Average Height of a Charged Colloid: Effects of Electrophoretic and Brownian Motions. Langmuir 2003, 19 (17), 6627−6632. (17) Fagan, J. A.; Sides, P. J.; Prieve, D. C. Vertical motion of a charged colloidal particle near an AC polarized electrode with a nonuniform potential distribution: Theory and experimental evidence. Langmuir 2004, 20 (12), 4823−4834. (18) Fagan, J. A.; Sides, P. J.; Prieve, D. C. Mechanism of rectified lateral motion of particles near electrodes in alternating electric fields below 1 kHz. Langmuir 2006, 22 (24), 9846−9852. (19) Wirth, C. L.; Rock, R. M.; Sides, P. J.; Prieve, D. C. Single and pairwise motion of particles near an ideally polarizable electrode. Langmuir 2011, 27 (16), 9781−91. (20) Wirth, C. L.; Sides, P. J.; Prieve, D. C. Electrolyte dependence of particle motion near an electrode during ac polarization. Phys. Rev. E 2013, 87 (3), 032302. (21) Woehl, T. J.; Heatley, K. L.; Dutcher, C. S.; Talken, N. H.; Ristenpart, W. D. Electrolyte-Dependent Aggregation of Colloidal Particles near Electrodes in Oscillatory Electric Fields. Langmuir 2014, 30 (17), 4887−94. (22) Woehl, T. J.; Chen, B. J.; Heatley, K. L.; Talken, N. H.; Bukosky, S. C.; Dutcher, C. S.; Ristenpart, W. D. Bifurcation in the Steady-State Height of Colloidal Particles near an Electrode in Oscillatory Electric Fields: Evidence for a Tertiary Potential Minimum. Phys. Rev. X 2015, 5 (1), 011023. (23) Bukosky, S. C.; Ristenpart, W. D. Simultaneous Aggregation and Height Bifurcation of Colloidal Particles near Electrodes in Oscillatory Electric Fields. Langmuir 2015, 31 (36), 9742−9747. (24) Hoggard, J. D.; Sides, P. J.; Prieve, D. C. Electrolyte-dependent pairwise particle motion near electrodes at frequencies below 1 kHz. Langmuir 2007, 23 (13), 6983−6990. (25) Wirth, C. L.; Sides, P. J.; Prieve, D. C. The imaging ammeter. J. Colloid Interface Sci. 2011, 357 (1), 1−12. (26) Rock, R. M.; Sides, P. J.; Prieve, D. C. Ensemble average TIRM for imaging amperometry. J. Colloid Interface Sci. 2013, 403, 142−150. (27) Prieve, D. C.; Sides, P. J.; Wirth, C. L. 2-D assembly of colloidal particles on a planar electrode. Curr. Opin. Colloid Interface Sci. 2010, 15 (3), 160−174. (28) Prasad, V.; Semwogerere, D.; Weeks, E. R. Confocal microscopy of colloids. J. Phys.: Condens. Matter 2007, 19 (11), 113102. (29) Goldman, A. J.; Cox, R. G.; Brenner, H. Slow viscous motion of a sphere parallel to a plane wallI Motion through a quiescent fluid. Chem. Eng. Sci. 1967, 22 (4), 637−651. (30) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, UK, 1991. (31) Zukoski, C. F.; Saville, D. A. An experimental test of electrokinetic theory using measurements of electrophoretic mobility and electrical conductivity. J. Colloid Interface Sci. 1985, 107, 322−333.

assumption is no longer valid. Hence, more detailed modeling is required to take into account all the forces involved. These observations indicate that crystallization is limited to a specific range of electrolyte concentrations. At higher concentrations the particles adhere to the electrode, and no aggregation is observed; at lower concentrations, there is too much thermal motion and too high of an energy barrier to allow crystallization. Our work focuses only on NaCl as an electrolyte, but the qualitative behavior is expected to extend to other electrolytes which result in particle aggregation. Further work is needed to corroborate this prediction and elucidate the underlying mechanism.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b04636. Figures S1 and S2 (PDF) Movie showing aggregation of randomly closed packed structures in response to an electric field (AVI)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (W.D.R.). Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.langmuir.5b04636 Langmuir XXXX, XXX, XXX−XXX