Directed Self-Assembly of Colloidal Crystals by Dielectrophoretic

Feb 6, 2012 - the order−disorder transition and particle electrophoretic mobility are correctly ... structures by colloidal self-assembly can be ach...
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Directed Self-Assembly of Colloidal Crystals by Dielectrophoretic Ordering Jason M. McMullan† and Norman J. Wagner* Department of Chemical and Biomolecular Engineering and Center for Molecular and Engineering Thermodynamics, University of Delaware, Newark, Delaware 19716, United States S Supporting Information *

ABSTRACT: In this Article, we report the dielectrophoretic assembly of colloidal particles and show how the kinetics of assembly and degree of ordering depend on the particle size, charge, solution ionic strength, and field strength and frequency. A special dielectrophoresis (DEP) sample cell is constructed and validated to quantitatively measure directed self-assembly via sequential light scattering and optical microscopy measurements. Our results confirm the recently established scaling for the order−disorder transition and extend it to higher scaled frequencies. The limiting scaling of the order−disorder transition and particle electrophoretic mobility are correctly predicted by the standard electrokinetic model (SEKM). In particular, the order−disorder transition line is predicted from the particle properties using a recently proposed empirical scaling law and the SEKM over an order of magnitude in particle size.

1. INTRODUCTION Previous work studied the assembly of large length scale crystalline structures made from colloidal particles.1 These ordered structures have many applications including photonic devices and as materials with consistent mechanical properties dictated by repeating structure.2,3 The formation of crystalline structures by colloidal self-assembly can be achieved by methods including capillary deposition,4 large amplitude oscillatory shear,5−7 magnetic field,8,9 interfacial polarization,10 spin coating,11,12 and surface templating.13 Dielectrophoretic ordering with alternating current electric fields14−19 has attracted attention because a massive number of building blocks can be easily assembled to make millimeter length-scale structures in parallel without templates. Dielectrophoretic selfassembly can also be reversible upon removal of the field to allow for the annealing and dynamical control of the structures. Crystal formation typically occurs within seconds to minutes with this technique, and the electric field strength and frequency applied dictate the final structural properties. Application of an electric field to a colloidal dispersion induces dielectric polarization of the particles in suspension.20,21 Previous work has examined the induced particle polarizability by changing applied field strength, frequency, particle size, and the dielectric constant and conductivity mismatch between the particle and the suspending media.15,21 Colloidal particles in an aqueous suspension can also show induced polarization due to the coupling of the field to the free ions in the double layer surrounding the particle.14,22 The double layer polarization strength depends on many factors including the ion mobility, particle size, double layer size, and the electrical frequency. These length scales lead to two © 2012 American Chemical Society

characteristic relaxation times: the relaxation time for ion diffusion on the scale of the particle size, ωP = Dcounterion/a2, and the relaxation times for ion diffusion over the double layer size, which is characterized by the Debye length, κ−1, leading to ωDL = Dcounterion/κ−2.17 In the frequency regime between these two time scales, the polarization is additive and leads to a higher particle polarization.23 The region of highest polarization for typical aqueous colloidal dispersions is in the ω ≈ kHz range.17 External AC electric fields induce dipoles in the particles leading to the formation of chain structures that can coalesce to two- and three-dimensional crystalline structures with sufficient particle loading.15 With a coplanar electrode geometry, the dielectrophoretic force pulls the colloids to an area of highest field gradient forming chains and crystals in a single plane, which were studied previously with microscopy and light scattering.15,19 Previous work on dielectrophoretically ordered structures manipulated colloids in solution to make many structures including chains, crystals, and wires.15,19,24 Previous work by Lumsdon et al. on DEP ordered colloidal structures tracked the transition from disordered suspensions to chained structures showing a dependence of the threshold field strength on frequency and particle size.15 Mittal et al. identified a method of scaling the data by employing dimensionless group λchain: λchain =

πεsε0 | K (ω)|2 a3E2 k bT

(1)

Received: December 4, 2011 Revised: February 1, 2012 Published: February 6, 2012 4123

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where |K(ω)| is the particle polarizability detailed in previous work.17 This dimensionless group relates the balance of forces given by the ratio of particle ordering to particle disruption by Brownian motion.17 Further, Mittal et al. identified the scaling of the field frequency, ω, to the dimensionless frequency, ω/ωP, based on the characteristic time for counterion diffusion around the particle: D ωP = counterion (2) a2 In the above, the counterion diffusivity, Dcounterion, depends on the particle surface charge and the electrolyte in solution. In the presence of added electrolyte, the average ion diffusivity is used for calculating the characteristic time. A plot of the rescaled data can be found in previous work.17 This scaling has been shown to extend to crystallization of submicrometer particles, where small angle neutron scattering was employed to determine the structure in situ.14 Here, we study the formation of dielectrophoretic ordered colloidal crystals observed with a combination of light scattering (LS) and optical microscopy. The particle electrokinetic properties are measured via electrophoretic mobility and confirmed with standard electrokinetic model (SEKM) predictions. The dynamics of crystal formation are examined along with the final crystal structure. The experiments extend the scaling for the order−disorder transition to higher scaled frequencies than previously observed. Further, predictions based on an empirical model for the transition and the SEKM are shown to quantitatively predict the order−disorder transition line from knowledge of the relevant particle properties.

Figure 1. Dielectrophoretic sample cell schematic shown with the light scattering (LS) setup. Note: Image not to scale.

2. MATERIALS AND METHODS A schematic of the custom dielectrophoresis (DEP) sample cell is shown in Figure 1. The DEP cell consists of a colloidal suspension contained between a glass slide (Corning no. 1 1/2, 22 mm) and a custom built Plexiglas top held apart by a nonconductive silicone spacer (Bioptechs Inc.). The spacer sets a sample thickness of 400 ± 5 μm and is sealed with vacuum grease (Dow Corning). A thin sample gap mitigates undesirable electrohydrodynamic flows. A coplanar electric field is generated in the solution using parallel gold electrodes with a separation of 2 mm deposited on the glass cover slide. The electrode is created using negative photolithography with a photomask by deposition from vapor of 10 nm of chromium as a binding layer and then 100 nm of gold (Thermionics, VE Series) followed by mask liftoff. The glass is treated to remove any contaminants in a solution of NoChromix (Godax) and sulfuric acid (Fisher Scientific) then washed and plasma cleaned (Harrick Plasma PDC-32G). Electrical contacts are made with the sample cell through gold spring pins (Digi-Key) and copper tape (3M). The sample is introduced through tubing (Upchurch Scientific) in the Plexiglas top slowly with 1 mL glass syringes (Hamilton) with Luer-Lok connections. Sine wave alternating current (AC) electric fields are generated using a function generator (Agilent 33220A) connected to an amplifier (Tegam 2340, 50×). Any remaining DC component from the circuit is removed with a 1 μF capacitor (Illinois Capacitor) in series, and external electrical noise is reduced via quad-shielded coaxial cables. Electrode polarization is checked with dielectric spectroscopy25 and shown to be an insignificant contribution at these experimental conditions of salt concentration and frequency. All voltages reported are root-meansquared voltages, Vrms. The suspensions consist of sulfonated polystyrene particles in water (Interfacial Dynamics Corp. (IDC) Latex, Eugene, OR) with a diameter of d = 2.9 ± 0.12 μm (IDC). A scanning electron micrograph (SEM) of the d = 2.9 μm particles is shown in Figure 2 taken with a JEOL JSM-7400F. To enable independent quantification of the

Figure 2. (a) Scanning electron micrograph (SEM) of d = 2.9 μm polystyrene particles. (b) Light scattering intensity versus wave vector (q) of d = 2.9 μm particles in 0.1 mM KCl at ϕ = 0.5% as compared to the Mie prediction28 with no adjustable parameters for q. particle electrokinetic properties, the dispersions are repeatedly cleaned by an established washing process26 using centrifugation (6000g, 10 min). During the washing process, each suspension is diluted to ϕ = 0.5% and centrifuged to obtain a pellet (VWR Galaxy 7D), and the supernatant is removed and exchanged with the solution of interest (95% of the volume per wash). The suspensions are washed five times with deionized water (Millipore Direct-Q: 18.2 MΩ cm) and five times with the electrolyte of interest (0.1 mM Alfa Aesar Puratronic potassium chloride (99.997% pure − Metals Basis)). For the electrophoretic mobility measurements where solvent density matching is required, mixtures of H2O and D2O (Cambridge Isotope Laboratories 99.9%) are used to prevent sedimentation. These suspensions are cleaned in H2O at the proper electrolyte concentration and then diluted into a mixture of H2O/D2O at the correct electrolyte concentration after the final wash. Electrolyte solutions are filtered with a 0.2 μm syringe filter (Nalgene) prior to use. The suspensions are vortex mixed between each centrifugation step and sonicated at the end of the preparation process to remove any particle clusters before use. 4124

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A light scattering (LS) device constructed to interface with the dielectrophoretic sample cell is shown in Figure 1. This experimental configuration examines structures formed parallel and perpendicular to the applied field, but averages information over the field gradient direction, which is parallel to the laser direction. The system uses a red diode laser (VHK, Edmund Optics, λ = 635 nm) brought in on the optical axis of the microscope to facilitate the switch between microscopy and light scattering measurements. The laser is trimmed with a d = 1 mm pinhole (Edmund Optics) to remove any stray light illumination through the sample. The scattered light from the sample is collected on a screen with a beam stop and recorded with a digital camera (Unibrain Fire-I, 8-bit, γ = 1). The camera and lens have a minimum working distance of 100 mm and minimal distortion (−2.1% at full field). The LS system is calibrated with a visible transmission grating (Thorlabs Inc., GT13−03) with evenly spaced grating distances, dgrating, giving sharply defined scattering points obeying the relation: θgrating = sin−1(λ /dgrating) = 10.98°

(3) Figure 3. Particle electrophoretic mobility versus KCl concentration for d = 2.9 μm in density matched H2O/D2O. Lines are constant surface charge density predictions from the standard electrokinetic model22 accounting for dissolved CO2 (C = 1.6 × 10−6 M).

Because the angle observed with the screen is the scattered angle in air, it needs to be corrected to the angle in the water using Snell’s law, assuming a sufficiently thin sample. The water angle is used to calculate the magnitude of the scattering vector, q, with the definition: q = |q ⃗| =

4πn ⎛⎜ θ ⎞⎟ sin ⎝2⎠ λ

behavior is compared against predictions of the standard electrokinetic model (SEKM).22,26 Figure 3 includes predictions for specific constant surface charge densities where the calculations include dissolved carbon dioxide in the water at CCO2 = 1.6 × 10−6 M and the accurate solvent properties for the H2O/D2O mixture.29 The particle mobilities agree well with a line of constant surface charge density. It is of note that particle mobility cannot be predicted using a constant zeta potential because a constant potential with decreasing salt concentration gives a decrease in surface charge density. The SEKM predictions indicate the particles have a surface charge density between σ = −2 to −5 μC/cm2, which is lower than the manufacturer measured value of σ = −6.2 μC/cm2 determined via titration. This discrepancy between the surface charge density determined from fits of the SEKM model and the titration value is expected and agrees with previous literature.26 Titration measures all of the surface charge sites, whereas the electrophoretic mobility measures the zeta potential at the plane of shear, which can be lower due to tightly bound ions in the Stern layer. Ordered colloidal arrays of d = 2.9 μm polystyrene particles in 0.1 mM KCl are formed in the presence of electric fields and monitored with microscopy shown in Figure 4. In these images, a sample of ϕ = 0.5% particles is loaded in a sample cell with a thickness of 400 ± 5 μm, giving enough particles for one monolayer when they are concentrated at the assembly surface. Microscopy images of structures formed after long times of applied electric field are taken as a function of electrical frequency and field intensity. The images taken here show longrange similar order over many particle diameters. Crystal structures are seen clearly at high field strengths, whereas at low field strengths, the structures resemble a disordered structure. This is because the field strength is barely sufficient to overcome the Brownian motion that is disrupting the ordered structure. Also, there is not a large variation in structure as a function of electrical frequency. Crystallization dynamics over large length scales are observed as a function of electric field strengths and frequency as a function of time using light scattering. An image matrix is shown for the long-time light scattering observations under the indicated field conditions in Figure 5. As shown, the sharpness

(4)

where θ is the scattering angle relative to the incident beam, λ is the wavelength of incident radiation, and n is the refractive index of water. The intensity is corrected for the planar detector and the solid angle by the relation:27

Icorr = Iobs/(cos3 θ)

(5)

The length scale calibration is confirmed with the scattering from a disordered, dilute particle suspension as shown in Figure 2. The observed scattering for the sample is then compared to the Mie prediction28 with no fitting parameters except for a constant factor to shift the intensity. The scattering minima line up extremely well with the Mie prediction,28 and the intensity decays at high q due to the loss of intensity at the edge of a planar screen and the bit depth of the camera used. To compliment the LS measurements, bright field optical microscopy was performed on an Axio Observer.A1 (Zeiss) inverted microscope connected to a high speed Phantom v5.1 camera (Vision Research). The observation area of the LS system is the area of the beam, which is about 20 times greater than the observed area via microscopy. Electrophoretic mobility measurements are conducted on a Brookhaven ZetaPALS instrument. This instrument uses a diode laser (λ = 678 nm, 25 mW) with a dip electrode and a photomultiplier tube (PMT) detector at an angle of 15°. The dip electrode is cleaned before use by sonication, ethanol, and water, and then placed in the suspension cuvette and allowed to equilibrate. A zeta potential reference material (Brookhaven Instruments ZR3) was used to check the system operation electrode cleanliness before and after each measurement. The suspensions were prepared at a volume fraction of ϕ = 0.0011% in a density matched solution of D2O/H2O. Predictions of particle electrophoretic mobility and particle polarizability were performed with a standard electrokinetic model (SEKM) code provided by Hill et al.22,26 The details of the model and its validation with electrokinetic measurements are contained in the previous work.22,26 The model includes the double layer polarization with the classic Maxwell−Wagner relaxation at higher frequencies for all colloidal suspension conditions.

3. RESULTS AND DISCUSSION Particle electrophoretic mobility is measured as a function of suspending electrolyte concentration, and the results are shown in Figure 3 for d = 2.9 μm particles. The particle electrokinetic 4125

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techniques. As the electric field is applied, at short times, the particles rapidly associate into chains, which are shown in the scattering image as a horizontal streak at low q. At long times, the particle chains coalesce and form a full two-dimensional colloidal crystal indicated in the scattering image by a welldefined six-spot ordering pattern along with crystalline repeats at higher q values. The time scales of growth from the microscopy and light scattering are the same, allowing either technique to be used to probe the crystalline microstructure. The ordering dynamics of the colloidal crystalline structures observed with scattering are quantified with an alignment factor.5,30 The light scattering images collected were normalized with their initial, disordered state image with In(t) = I(t)/Ibaseline. To characterize the degree of order observed in the normalized scattering patterns as a function of azimuthal angle, φ, the integrated intensity over an annular region at a given q was calculated as 2π

A f (q) =

∫0 I(q , ϕ)cos(nϕ − β)dϕ 2π

n

Figure 4. Long time microscopy images from d = 2.9 μm particles in 0.1 mM KCl at ϕ = 0.5% as a function of field intensity and frequency.

∫0 I(q , ϕ)dϕ

(6)

where n is an integer indicating the symmetry of order, and β is the angle of alignment relative to the applied field. As defined here with the choice of an appropriate β for each order symmetry to align the cosine function with the intensity, the absolute value of Af can range from 0 to 1 meaning complete disorder or complete order, respectively. Two different azimuthal q values are examined, probing two different length scales. The dynamics of crystallization (6-fold) are observed at high q = 0.0023 ± 0.0001 nm−1, as discussed earlier, and the dynamics of chain formation (2-fold) are observed at low q = 0.0012 ± 0.0001 nm−1. The alignment factor as a function of time, field intensity, and field strength is shown in Figure 6. For reference, long time light scattering images at ω = 100 kHz are shown. The time dependence is broken into two distinct regions; growth, where the electric field is applied, and crystal structures form versus decay, where the electric field is removed and the structures decay back to a random state. In the growth section, the chains, monitored by the 2-fold ordering, form quickly and reach a plateau value. The crystals, observed with the 6-fold ordering, take longer to form and refine toward a plateau at later times. As field intensity is increased, the degree of crystalline order increases, as seen by a 6-fold alignment factor where the strongest ordering is seen for E = 177 V/cm and ω = 75 kHz. At low field intensities, the crystalline order is absent because the applied field strength is not sufficient to overcome Brownian motion. For all cases, the chaining strength grows quickly and reaches a plateau where the height of the plateau is a function of the voltage and frequency applied in the system. The crossover point between the chaining and crystalline order alignment factors is a metric to determine if the system is chained or crystalline state and is also a function of the field strength, frequency, and time. The time dynamics of the growth of the alignment factor, Af n(t), are analyzed with a single exponential model given by

Figure 5. Long time light scattering patterns from d = 2.9 μm particles in 0.1 mM KCl at ϕ = 0.5% as a function of field intensity and frequency (q range is 0 ≤ qx,y ≤ 0.00474 nm−1).

and intensity of the 6-fold scattering peaks are a strong function of electric field intensity and a weak function of electrical frequency. At low field strengths, structures barely form particle chains, whereas crystals are formed at high field strengths. The crystallographic distance, qhkl, of all peaks is the same over all field intensities and frequencies. The microscopy images show the crystals follow the p6mm plane group where the interparticle spacing, dspacing, is given by dspacing = (2π)/(qhkl sin(2θ)), where θ = 60°. In this case, the scattering peak distance is qhkl = 0.0023 ± 0.0001 nm−1, which translates to an interparticle separation of dspacing = 3.15 ± 0.14 μm. This agrees well with the interparticle separation including the characteristic length scale of the double layer, 2(aHS + κ−1) (0.1 mM KCl, κ−1 = 30.4 nm), which is 2.96 μm. The dynamics of crystal formation are probed using microscopy and light scattering as two complementary

A f (t ) = A f n

n,∞

× (1 − e(−t / λ n ,growth))

(7)

where Af n,∞ is the final growth alignment factor (or plateau value), t is the time, and λn,growth is the time constant for 4126

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Figure 6. Alignment factor as a function of time versus electric field intensity and electric frequency for d = 2.9 μm particles in 0.1 mM KCl at ϕ = 0.5% for chaining order (2-fold) and crystalline order (6-fold). Long time light scattering patterns for ω = 100 kHz are shown for reference.

Upon removing the field, the characteristic time for loss of crystalline order, λ6,decay = 9.9 ± 3.1 s independent of electric field conditions, indicates that crystal disruption occurs rapidly. Because the force causing the disorder in these systems is Brownian motion, a natural choice of comparative time scale is the characteristic Brownian time scale, τ = a2/Do. The bare colloid diffusion coefficient is Do = kbT/6πaη, where kb is Boltzmann’s constant, T is the temperature, a is the particle radius, and η is the dynamic viscosity, which for water at 25 °C is 8.9 × 10−4 Pa s. For this system, this characteristic time scale is τ = 12.4 s, which compares well with the observed decay time. Note that the characteristic time scale is a scaling estimate as the diffusivity will depend on the concentration and proximity to a surface, which must be accounted for in a more quantitative calculation.31 This order of magnitude agreement between the experimental decay time and the characteristic time scale for Brownian motion validates the notion that Brownian motion is the primary reason for decay upon removal of the field and provides guidance for understanding the dynamics and longevity of structures upon removal of the field. Previous work by Lumsdon et al.,15 Mittal et al.,17 and McMullan et al.14 documented the order−disorder transition and rescaling for electrically ordered particles. These rescaled data from previous data are shown in Figure 8 with the previous data from Lumsdon et al.,15 and McMullan et al.14 Augmenting the previously established curve is the chaining threshold for the d = 2.9 μm particles at E = 111 V/cm, which is observed at all frequencies. In addition, data for a set of d = 1.3 μm particles, contained in the Supporting Information, show a

ordering. The decay sections are also fit starting with the plateau value with a single exponential of the form: A f (t ) = A f × e(−t / λ n ,decay) n n,∞

(8)

where Af n,∞ is the same value from the growth analysis, and λn,decay is the time constant for decay. The time-dependent alignment factors from Figure 6 are analyzed, and the plateau values are shown in Figure 7. Both plateau alignment factors for the chain and crystalline structures are shown as a function of field strength and frequency. The chaining and crystal alignment factors show an increase in plateau height with increasing electric field intensity. The linear behavior of Af n,∞ versus electric field intensity is shown in the inset of each figure. When the Af n,∞ is divided by the field strength, a scaled plateau value is obtained to collapse the data onto a single curve. The scaled Af n,∞ is nearly independent of frequency, with only a small decrease at the highest frequency. For the data in the crystalline state, the E = 111 V/cm is not included because this field strength is still at the point where the chaining behavior is greater than the crystal behavior. The time scale for chaining order, λ2,growth, is rapid and occurs at an average λ2,growth = 4.0 ± 0.9 s showing rapid particle association into chain structures. The time scale for crystallization, λ6,growth, takes much longer with the highest field strength on the order of 30−90 s. This indicates that initial particle chaining occurs rapidly, followed by crystallization on a longer time scale. 4127

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chaining threshold at E = 265 V/cm. For each condition, the symbol shown is the experimental observed point for chaining and the error bar is the next observed field strength, which in some cases also results in a crystalline structure. These data collapse onto and extend the master curve over an order of magnitude in particle size and to higher scaled frequencies than previously investigated. This scaling of the data results in a chaining threshold line where, below, no ordered structure can form, and, above, chain structures begin to form. This master curve gives the field intensity and frequency required for particle ordering for polystyrene particles over a large range of experimental conditions. Extensions to smaller, nanoparticle sizes and higher concentrations such that multilayers form have been demonstrated,14 while extension to larger particles should be possible if gravitational effects do not dominate over the dielectrophoretic force. Semipredictive modeling of the order−disorder state transition is achieved using the standard electrokinetic theory provided from Hill et al.22 to calculate the particle polarization, accounting for the double layer contribution. Here, we are primarily interested in determining the source of the empirically observed scaling shown in Figure 8, whereby the product of particle size to the 3/2 power times the electric field increases apparently linearly as the logarithm of the scaled frequency for values greater than one. For purposes of this comparison, we assume no added electrolyte with a characteristic surface charge density σ = −1 μC/cm2 and a concentration of dissolved carbon dioxide of CCO2 = 1.6 × 10−6 M.26 The calculated polarizability |K(ω)| is then used in the rearranged force balance in eq 1 so as to predict the behavior shown in Figure 8. Equation 1 is rearranged to the form of ⎛ ai ⎞1.5⎛ Ei ⎞ ⎜ ⎟ ⎜ ⎟= ⎝ a 0 ⎠ ⎝ E0 ⎠

Figure 7. Plateau alignment factor scaled with field intensity for d = 2.9 μm particles in 0.1 mM KCl at ϕ = 0.5%. (a) Scaled Af 2,∞ as a function of frequency with an inset of the linear behavior of Af 2,∞ with field intensity. (b) Scaled Af6,∞ as a function of frequency with an inset of the linear behavior of Af6,∞ with field intensity.

ai3Ei2 a03E02

=

λk bT

1

πεm | K (ω)|2 a03E02

(9)

One empirical value of the critical ratio of forces at the transition, λ, is then used for all particle sizes. A value of λ = 400 is found to yield the quantitative predictions shown in Figure 8, which are in good quantitative agreement at high scaled frequencies with the experimental data. This empirical value for λ ≫ 1 is expected for the relatively large double layer sizes, as discussed in previous literature.22,26 The increased polarizability is also due to the increased mobility of the counterion, H3O+, which is the determining ion in the system. It is of note that in this comparison, matching the surface charge density, σ, is not extremely sensitive in this range of electrolyte concentration. The limiting behavior of the predictions is a semilog slope of 0.88 above a scaled frequency of 1. Thus, the frequency dependence of the empirical master curve for the order−disorder transition observed in colloidal DEP directed self-assembly can be understood quantitatively from the SEKM, showing ordering is a consequence of the induced particle double layer polarization.

4. CONCLUSION Formation and kinetics of DEP directed self-assembled ordered structures are reported with a combination of microscopy and light scattering over an extended range of particle sizes and electrokinetic properties. Electrophoretic mobility measurements confirm that particle electrokinetics follow constant surface charge density predictions. Light scattering measurements give quantitative results for length and time scales of structural formation along with final crystalline and chaining

Figure 8. Order−disorder transition plot scaling of DEP ordering parameters over electric field strength, frequency, and particle size for polystyrene particles. Previous data from Lumsdon et al.,15 McMullan et al.,14 and rescaling from Mittal et al.17 Note: a0 = 1 μm, E0 = 100 V/ cm, ωP = Dcounterion/a2, Dcounterion = DK+ = 1.96 × 10−9 m2/s. SEKM predictions from Hill et al.22 with parameters of σ = −1 μC/cm2, CKCl = 0 mM, CCO2 = 1.6 × 10−6 M, λ = 400. 4128

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(4) Ye, Y. H.; LeBlanc, F.; Hache, A.; Truong, V. V. Self-assembling three-dimensional colloidal photonic crystal structure with high crystalline quality. Appl. Phys. Lett. 2001, 78, 52−54. (5) McMullan, J. M.; Wagner, N. J. Directed self-assembly of suspensions by large amplitude oscillatory shear flow. J. Rheol. 2009, 53, 575−588. (6) Ackerson, B. J. Shear induced order and shear processing of model hard-sphere suspensions. J. Rheol. 1990, 34, 553−590. (7) Mock, E. B.; Zukoski, C. F. Investigating microstructure of concentrated suspensions of anisotropic particles under shear by small angle neutron scattering. J. Rheol. 2007, 51, 541−559. (8) Eisenmann, C.; Keim, P.; Gasser, U.; Maret, G. Melting of anisotropic colloidal crystals in two dimensions. J. Phys.: Condens. Matter 2004, 16, S4095−S4102. (9) Zahn, K.; Lenke, R.; Maret, G. Two-stage melting of paramagnetic colloidal crystals in two dimensions. Phys. Rev. Lett. 1999, 82, 2721−2724. (10) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. N. Compression and structure of monolayers of charged latex particles at air/water and octane/water interfaces. Langmuir 2000, 16, 1969−1979. (11) Jiang, P.; McFarland, M. J. Large-scale fabrication of wafer-size colloidal crystals, macroporous polymers and nanocomposites by spincoating. J. Am. Chem. Soc. 2004, 126, 13778−13786. (12) Shereda, L. T.; Larson, R. G.; Solomon, M. J. Local stress control of spatiotemporal ordering of colloidal crystals in complex flows. Phys. Rev. Lett. 2008, 101, 038301. (13) vanBlaaderen, A.; Ruel, R.; Wiltzius, P. Template-directed colloidal crystallization. Nature 1997, 385, 321−324. (14) McMullan, J. M.; Wagner, N. J. Directed self-assembly of colloidal crystals by dielectrophoretic ordering observed with small angle neutron scattering (SANS). Soft Matter 2010, 6, 5443−5450. (15) Lumsdon, S. O.; Kaler, E. W.; Velev, O. D. Two-dimensional crystallization of microspheres by a coplanar AC electric field. Langmuir 2004, 20, 2108−2116. (16) Lele, P. P.; Mittal, M.; Furst, E. M. Anomalous particle rotation and resulting microstructure of colloids in AC electric fields. Langmuir 2008, 24, 12842−12848. (17) Mittal, M.; Lele, P. P.; Kaler, E. W.; Furst, E. M. Polarization and interactions of colloidal particles in ac electric fields. J. Chem. Phys. 2008, 129, 064513. (18) Gangwal, S.; Cayre, O. J.; Velev, O. D. Dielectrophoretic assembly of metallodielectric Janus particles in AC electric fields. Langmuir 2008, 24, 13312−13320. (19) Lumsdon, S. O.; Kaler, E. W.; Williams, J. P.; Velev, O. D. Dielectrophoretic assembly of oriented and switchable two-dimensional photonic crystals. Appl. Phys. Lett. 2003, 82, 949−951. (20) Pohl, H. A. Dielectrophoresis: The Behavior of Neutral Matter in Nonuniform Electric Fields; Cambridge Monographs on Physics, Cambridge University Press: Cambridge, 1978. (21) Jones, T. B. Electromechanics of Particles; Cambridge University Press: Cambridge, 1995. (22) Hill, R. J.; Saville, D. A.; Russel, W. B. Electrophoresis of spherical polymer-coated colloidal particles. J. Colloid Interface Sci. 2003, 258, 56−74. (23) Hill, R. J.; Saville, D. A.; Russel, W. B. Polarizability and complex conductivity of dilute suspensions of spherical colloidal particles with uncharged (neutral) polymer coatings. J. Colloid Interface Sci. 2003, 268, 230−245. (24) Hermanson, K. D.; Lumsdon, S. O.; Williams, J. P.; Kaler, E. W.; Velev, O. D. Dielectrophoretic assembly of electrically functional microwires from nanoparticle suspensions. Science 2001, 294, 1082− 1086. (25) Morgan, H.; Green, N. G. AC Electrokinetics: Colloids and Nanoparticles; Research Studies: Philadelphia, PA, 2003. (26) Hollingsworth, A. D.; Saville, D. A. Dielectric spectroscopy and electrophoretic mobility measurements interpreted with the standard electrokinetic model. J. Colloid Interface Sci. 2004, 272, 235−245.

ordering. Examination of the conditions and dynamics of the transitions between disordered suspensions, chained structures, and colloidal crystals shows that the dynamics are dependent on the applied field strength and frequency. The order parameter or alignment factor builds quickly and saturates, and scales with electric field strength. Brownian motion is confirmed as the mechanism opposing electric field ordering and is shown to govern the decay time constants, λn,decay. The measurements reported here support and extend a recently proposed master scaling for the field strength and frequency required to induce particle chaining. To generate ordered crystal structures from colloidal building blocks, the field strength required to make these structures keeps increasing with decreasing particle size as E ∝ a−3/2, with a frequency dependence that scales with the ion diffusion time in the double layer. This parameter scaling is observed to hold over a large range of experimental conditions. Future experiments can extend the scaling to colloids of different sizes and of increasing volume fraction where more than a single monolayer is formed. A quantitative prediction of the order−disorder state transition is shown by using the standard electrokinetic model to calculate the particle polarizability | K(ω)| along with an empirical value for the critical polarizability ratio that is independent of the system. The experimental results and the SEKM predictions provide a master curve that can be used for identifying suitable conditions to achieve DEPdriven self-assembly.

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ASSOCIATED CONTENT

S Supporting Information *

Data for d = 1.3 μm particles in 0.1 mM KCl used in Figure 8. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

ExxonMobil Research and Engineering, Process Research Laboratories, 1545 Route 22 East, Annandale, New Jersey 08801, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the National Science Foundation − Nanoscale Interdisciplinary Research Team (Grant No. CTS-0506701). We thank Reghan Hill for supplying the SEKM code. We thank our NSF-NIRT team including Eric Furst, Eric Kaler, Orlin Velev, John Brady, Pushkar Lele, Manish Mittal, Sumit Gangwal, and James Swan for useful discussions.

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REFERENCES

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