Invited Instructional Review pubs.acs.org/Langmuir

Controlling Colloidal Particles with Electric Fields Tara D. Edwards and Michael A. Bevan* Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States S Supporting Information *

ABSTRACT: In this instructional review, we discuss how to control individual colloids and ensembles of colloids using electric fields. We provide background on the electrokinetic transport mechanisms and kT-scale equilibrium colloidal interactions that enable such control. We also describe the experimental configurations, microscopy methods, image analyses, and material systems for which these mechanisms have been successfully employed. Methods are presented for creating various structures including colloidal chains, quasi-2D colloidal crystals, and 3D colloidal crystals. We also describe electric-field-mediated feedback control of the colloidal crystal size as well as colloidal crystal assembly and disassembly. Finally, we discuss future extensions of these methods that aim to incorporate accurate colloidal crystallization dynamic models into electric-field-mediated feedback control to allow rapid assembly, disassembly, and repair of defect-free colloidal structures.

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INTRODUCTION The ability to control colloidal particles could serve as a basis for the realization of a number of emerging material and device technologies,1−3 such as tunable materials, reconfigurable devices, photonic materials, and meta-materials.4 Current methodologies for structuring colloidal particles include sedimentation, 5−7 depletion interactions, 8−11 magnetic fields,12,13 shear fields,14,15 optical fields,16,17 and electrical fields.18−20 Particles assembled via sedimentation often form irreversible structures with defects that are not easily manipulated after assembly. Depletion attraction can be used to assemble particles via kT-scale interparticle attraction; however, this is a diffusion-limited process and does not provide control over microstructural orientation. Colloidal assembly by means of magnetic fields is material-specific in that it requires the use of magnetic particles. Using shear to order colloidal particles can produce nonequilibrium structures from dissipative fluid forces; however, connections between multibody hydrodynamic interactions and shear-induced colloidal assembly processes are complex. Optical fields as a means of colloidal assembly require a fine balance in the optical contrast between the medium and the particles. Electric-field-mediated colloidal assembly is perhaps the most attractive means of manipulating colloidal ensembles and creating ordered structures in that it is applicable in various electrode geometries at various length scales for both charged and noncharged particles.18,21−24 Many of these approaches are based on steady-state electrokinetic flows to manipulate and/or assemble colloidal particles via dissipative forces.25 The focus of this instructional review is the use of conservative forces due to dipolar interactions to manipulate colloidal particles within electric fields. Unlike many other electric-field-mediated assembly techniques, the methods presented in this review are unique in that these interaction potentials have been directly measured and can therefore be quantitatively tuned to control colloidal particles. We do not attempt an exhaustive © 2014 American Chemical Society

literature review of all related experimental studies or background theory but refer readers to our original papers and the references contained within them for more details.26−32 By using relatively weak fields to assemble particles via kTscale interactions and Brownian motion, the structures that form are reversible equilibrium structures (i.e., when the electric field is turned off, electrostatic repulsion prevents strong van der Waals and dipolar attraction and causes the particles to disassemble via Brownian motion). Dipolar interactions governing electric-field-mediated colloidal assembly are easily tuned by controlling the applied voltage and frequency. These kT-scale dipolar interactions have been directly measured26,28,30 and quantitatively connected to assembled particle microstructures. Because particle migration can be controlled with electric fields, assembly can occur at faster than diffusion-limited rates unlike depletion-mediated colloidal assembly. Colloidal particles assembled or manipulated in the presence of a nonuniform electric field have a net response due to a combination of sedimentation, diffusion, and electric-fieldmediated mechanisms.33−35 Colloidal particles suspended in aqueous media will have a surface charge via dissociated chemical groups, adsorbed ions, crystal lattice defects, or an imbalance in the number of crystal lattice ions necessary to impart colloidal stability.36 The surface charge is screened by solution counterions that concentrate near the surface. Together, the layers of ions and counterions create an electrostatic double layer.37 An inhomogeneous alternating current (ac) electric field applied to colloidal particles near a planar wall surface causes a distortion of the counterions that concentrate near the surface of the colloidal particle to induce a net dipole. Colloidal particles with induced dipoles display Received: January 14, 2014 Revised: February 24, 2014 Published: March 6, 2014 10793

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Figure 1. Au film (A) parallel and (B) quadrupole electrodes on glass microscope slides with PDMS O-rings containing a colloidal dispersion. Electrodes are connected to a function generator operated by computer software. Optical microscopy/charged coupled device images of (C) a single 3.01 μm SiO2 colloid in a 30 μm parallel electrode gap center and (D) a quasi-2D crystal of 3.01 μm SiO2 colloids in a 100 μm quadrupole electrode gap center in high-frequency ac electric fields. Contour plot of the electric field for (E) the xz cross section of two parallel electrodes for a 34 × 34 μm2 area with a linear spectrum scale from 10 to 100 V/mm and (F) 3.01 μm SiO2 colloids in a 1 MHz ac electric field with a linear spectrum scale from E/E0 = 0 to 7. Images A and C are adapted with permission from ref 28, images B, D, and F are adapted with permission from ref 32, and image E is adapted with permission from ref 9.

fcm values greater than zero and migrate to the electrode edges (the field maximum). This electrokinetic transport mechanism is termed positive dielectrophoresis (PDEP) and usually occurs at low frequencies where interactions are dominated by differences in the conductivity of the particles and medium. In contrast, when a uniform potential difference is applied across an electrode, electrophoresis (EP) and electroosmosis (EO) electrokinetic transport occur concurrently.39 A direct current (dc) or a low-frequency ac applied electric field causes the ions within the capacitor-like electrostatic double layer to move and the surrounding fluid to be dragged along with the ions. For example, negatively charged SiO2 in a suspension subject to an electric field will move toward the positively charged anode while the surrounding double-layer ions will be drawn toward the cathode. The opposite charge on the boundary of the suspended colloidal particle(s) causes electroosmotic flow of the suspending fluid. This electro-

frequency-dependent capacitive (dielectric charging) or resistive (conductive charging) behavior.38 These induced dipoles interact with the nonuniform electric field and migrate to their net potential energy minimum. This electrokinetic migration is balanced by hydrodynamic drag and is referred to as dielectrophoresis. The Clausius−Mosotti factor, fcm, determines if a particle’s potential energy minimum occurs at the electric field minimum (e.g., at the center of electrode gaps) or at the field maximum (e.g., at electrode edges) (Figure 1E,F). Particles that are less polarizable than the medium in which they are dispersed have fcm values that are less than zero and are transported to the electrode center (the field minimum). This type of electrokinetic transport is known as negative dielectrophoresis (NDEP) and typically occurs at high frequencies where conductive charging does not have time to occur on particles and interactions are thus dominated by differences in the particle and medium permittivities. Particles that are more polarizable than their suspending medium have 10794

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osmotic flow opposes the particle motion and slows its velocity (which is proportional to the applied electric field). In the following section, we review materials and experimental configurations where these electrokinetic phenomena have been employed to manipulate and assemble colloidal particles. Specifically, we detail electrode device microfabrication and the necessary experimental conditions. We describe how to manipulate single colloidal particles and ensembles of colloidal particles utilizing ac electric fields in either a parallel or quadrupole electrode geometry. We discuss the electric-field-mediated colloidal interactions governing these processes and how such interactions can be applied to feedback-controlled colloidal assembly, disassembly, and ensemble size. We conclude with a summary and future directions.

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Batch Fluid Cell Preparation. The batch cells in which all experiments in this review were conducted should consist of a clean electrode device, a poly(dimethylsiloxane) (PDMS) O-ring (Supporting Information, SI), and an 18 mm × 18 mm coverslip (Corning, Corning, NY). Clean electrodes by sonicating in acetone for 30 min, followed by IPA for 30 min. Rinse the electrode with copious amounts of DI water and dry with nitrogen gas. Coat a clean PDMS O-ring with vacuum grease (Dow Corning, Midland, MI) and place it on the electrode surface. Interface 22 gauge magnetic wires (Radio Shack, Fort Worth, TX) with the electrode using conductive carbon tape (Ted Pella, Redding, CA). Fill the O-ring with a colloidal dispersion and seal with a coverslip that has been wiped clean with lens paper. Connect the electrode in series with a function generator (Agilent 33220A, Agilent Technologies, Santa Clara, CA). When the quadrupole electrode is used, attach one lead to the north−south poles and the other to the east−west poles. Particles and Media. Particles that have previously been successfully manipulated using electric fields include nominal 800nm-diameter gold colloids (Alfa Aesar, Ward Hill, MA); nominal 3-, 4-, and 5-μm-diameter sulfate-stabilized polystyrene colloids (PS, Invitrogen, Carlsbad, CA); nominal 1.59-, 2.34-, 3.01-, and 3.13-μmdiameter silica colloids (SiO2, Bangs Laboratories, Fishers, IN); and nominal 1.5-μm-diameter fluorescent SiO2 colloids (Kisker Biotech, Steinfurt, Germany). PS- and 1-octadecanol (Sigma-Aldrich Company, St. Louis, MO)-coated SiO2 particles with adsorbed poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) triblock copolymer (F108 Pluronic, BASF, Wyandotte, MI) with segment molecular weights of 5400/3300/5400 g/mol levitated over PS (∼192 000 Mw, Sigma-Aldrich Company, St. Louis, MO) spin-coated electrodes with the same adsorbed triblock copolymer still allow for particle manipulation using inhomogeneous electric fields. To obtain a monodisperse suspension of colloidal particles, particles should be sedimentation fractionated prior to experimentation (SI). In addition to DI water, dispersion media that have previously been employed that allow for the manipulation of colloidal particles using electric fields include dimethylforamide, sodium chloride, sodium hydroxide, and sodium biocarbonate solutions at ≤1 mM. Optical Microscopy and Image Analysis. All quasi-2D colloidal particle manipulation can be performed using either an inverted or upright optical microscope. In the work presented in this review, all video microscopy (VM) experiments were performed by utilizing an Axio Imager A1m upright or an Axio Observer A1 inverted optical microscope (Zeiss, Germany) with a 63× objective (air N.A.= 0.6) or a 40× objective (air N.A. = 0.65) (Achroplan, Germany). Experimental video images were captured via a 12-bit CCD camera (ORCA-ER, Hamamatsu, Japan). All 3D colloidal particle manipulation was observed using a confocal microscope. We used a mounted Zeiss LSM 5 Pascal scanner (Zeiss, Oberkocken, Germany) with a 63× oilimmersion objective (N.A. = 1.45, Achroplan, Germany) with a 488 nm line excitation source on a 500 mW argon ion laser.29 Image analysis algorithms coded in FORTRAN can then be used to track colloid motion in quasi-2D or 3D VM experiments for further analysis.40−42 VM images can similarly be collected and analyzed using MATLAB.31,32,43 Video capture and image manipulation can be performed using the MATLAB image processing and image acquisition toolboxes that record digital images at a rate of 8 frames/s. The electric field amplitude and frequency can be controlled remotely with a function generator via a device driver written in the MATLAB instrument control toolbox. Image analysis algorithms coded in MATLAB simultaneously locate and track particle centers,42 determine the total number of colloidal particles, and compute order parameters in real time. Instantaneous values of the voltage, frequency, and order parameters are written to ASCII text files, and images are written to TIFF stacks to create movies.

MATERIALS AND METHODS

Microfabrication of Electrode Devices. Standard photolithography techniques were employed to create the Au thin film electrodes used in all experiments presented in this review (Figure 1A−D). All microfabrication steps should be conducted in a class 1000 clean room. Wipe clean plain glass microscope slides (24 mm × 75 mm, Fisher Scientific, Pittsburgh, PA) or glass coverslips (24 mm × 60 mm, Corning, Corning, NY) with lens paper, sonicate for 30 min in acetone, sonicate for 30 min in isopropanol, rinse with copious amounts of deionized water (DI), and dry with nitrogen. Prebake the clean microscope slides or coverslips on a hot plate at 120 °C for 10 min and 90 °C for 3 min to dehydrate the glass substrates. To remove any remaining residue or contaminants from the substrates, expose to oxygen plasma for 5 min at 400 W in a plasma etcher (PE II-A plasma system, Technics West Incorporated, San Jose, CA). Transfer the glass substrates to a spin coater (Laurell Technologies Corporation, North Wales, PA) and coat with an S1813 positive photoresist (Shipley Company, Marlboro, MA) at 4000 rpm and an acceleration value of 20 for 1 min. Soft bake the slides at 90 °C for 1 to 2 min and allow to cool to room temperature for 1 min. For the experiments described in this review, two Cr masks were designed using CAD software and fabricated at the University of Minnesota Nanofabrication Center. One mask produces parallel, interdigitated electrodes (Figure 1A,C), and the other mask creates quadrupole electrodes (Figure 1B,D). Depending on the desired electrode pattern, wipe clean the respective Cr mask with acetone and lens paper. Load the mask into the mask aligner (EVG 620, EV Group, Austria) with the Cr side facing down. Center a microscope slide under the mask feature with the photoresist film layer facing up toward the chrome side of the mask and secure with Scotch tape. Expose the photoresist to ultraviolet (UV) light through the Cr mask. Postbake the UV-exposed microscope slides at 95 °C for 1 min to cross-link the unexposed photoresist. Finally, develop the photoresist to remove the photoresist on the exposed portions of the microscope slide that are not cross-linked via agitation in CD26 developer (MicroChem, Newton, MA) for ∼1 min. Rinse the slides with IPA to remove excess developer and dry with compressed air before beginning the metal deposition process. The Au features of the electrode are deposited onto the developed photoresist microscope slides using an electron beam (e-vap CVS-6 6 kW, MDC Vacuum Products Corporation, Hayward, CA). Load the photoresist-developed slides into the chamber with the photoresist side exposed for metal deposition. Deposit Cr as an adhesive layer at a rate of 0.5 Å/s until there is a 15 nm layer. Subsequently, deposit Au at a rate of 1 Å/s until there is a 35 nm layer for a total film thickness of approximately 50 nm. Agitate the slides in remover 1165 (Shipley Company, Marlboro, MA) at 80 °C for approximately 10 min to remove the photoresist from the microscope slides. Sonication of the microscope slides in acetone for about 20 min can also be performed to remove the photoresist. The resulting Au parallel or quadrupole electrode pattern is all that should remain on the microscope slide.

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SINGLE-PARTICLE MANIPULATION Dipole−Inhomogeneous ac Electric Field Interaction. The ability to manipulate, characterize, and sort individual

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Figure 2. Interactions of single colloids with an inhomogeneous ac electric field in a 30 μm parallel electrode gap. (A) SiO2 colloids at an applied 1 MHz frequency and amplitudes of 0.5 V (yellow diamond), 1.0 V (green square), 1.5 V (red triangle), and 2 V (black circle). Nominal particle sizes of 1.59 μm (top), 2.34 μm (middle), and 3.01 μm (bottom) were each measured at the same field conditions. (B) PS colloids at an applied amplitude of Vpp = 300 mV and frequencies of 200 kHz (blue triangles), 300 kHz (yellow diamonds), 375 kHz (green squares), 500 kHz (red inverted triangles), and 1 MHz (black circles). Nominal particle sizes of 3 μm (top), 4 μm (middle), and 5 μm (bottom) were each measured under the same field conditions. Potential energy profiles were fit using eqs 1−6. Separation and energy scales are referenced to their values at the electrode gap midpoint. Adapted with permission from ref 28.

colloidal particles has seen an increase in demand in many developing technologies.38 Inhomogeneous ac electric fields can be employed to transport and trap individual colloidal particles at either the center of an electrode or an electrode’s edge depending on the material properties and the applied field conditions. Applying an inhomogeneous electric field to a single colloidal particle causes the counterions that concentrate near the colloid’s surface to rearrange and induce a dipole. The induced dipole−inhomogeneous electric field interaction potentials, uDEpf(x, z) or uDEpf(R), are given by26

for the interdigitated and quadrupolar electrode geometries, respectively, where E(x, z) and E(R) are the electric field peak magnitude, E0 = 0.5Vpp/dg is the nominal electric field magnitude, Vpp is the applied peak-to-peak voltage, and dg is the distance between the electrodes. λE is the relative dipolar and Brownian energy given as45 λE = πεma3(fcm E0)2 /kT

where εm is the medium permittivity and fcm is the Clausius− Mosotti factor given as

pf −1 uDE (x , z) = −2kTλEf cm E*(x , z)2 pf uDE (R )

=

−1 −2kTλEf cm E*(R )2

fcm = Re[(εp̃ − εm̃ )/(εp̃ + 2εm̃ )]

(4)

where ε̃m and ε̃p are the complex medium and particle permittivities of the form ε̃ = ε − (iσ/ω), where σ is the conductivity and ω is the angular frequency. The particle conductivity is given as σ = 2Kn/a, where Kn is the surface conductance.46 Interaction Dependence on Frequency. As implied by eq 4, the interaction between an induced dipole and an inhomogeneous ac electric field depends on the frequency of the applied electric field. As a result, controlling the applied frequency allows different material types and sizes of colloidal particles to be transported and trapped at either the electrode edge or center. An individual colloidal particle can be transported to and trapped within the center of an electrode

(1)

for the interdigitated and quadrupolar electrode geometries, where x is the position within the parallel electrode gap relative to the center, z = h + a where h is the particle−wall surface-tosurface separation and 2a is the particle diameter, R is the radial distance from the quadrupole center, k is the Boltzmann’s constant, T is the absolute temperature, and E*(x, z) and E*(R) are the electric field in the electrode center given by44 E*(x , z) = E(x , z)/E0 = 8−0.5Vppdg−1 E*(R ) = E(R )/E0 = 4dg−1R

(3)

(2) 10796

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particles i and j, θij is the angle formed between i and j, P2(cos θij) is the second Legendre polynomial, and area-fractiondependent (ϕA) modifications of the local electric field are accounted for by fϕ, given as45,48,49

by applying a high-frequency electric field. Figure 1C shows the configuration for measuring and manipulating dilute nominal 1.59-, 2.34-, and 3.01-μm-diameter SiO2 and nominal 3-, 4-, 5μm-diameter sulfate-stabilized PS in DI water between parallel thin Au film electrodes with approximately 330 μm strips separated by approximately 30 μm.28 Voltages applied between 0.5 and 2.0 V at a 1 MHz frequency cause SiO2 and PS particles to have negative fcm values and experience NDEP regardless of size. Particles are transported to their lateral mechanical equilibrium position at the electrode channel center where the electric field is at a minimum (Figure 1E) and their interaction potential is also at a minimum (Figure 2). Figure 2 also demonstrates that the interaction potential becomes weaker for both particle material types not only as the applied voltage is decreased but also as the colloid size decreases. Consequently, to decrease fluctuations of the colloid from the electrode channel center, the particle size and/or the applied voltage can be increased. To demonstrate how to transport and trap individual particles at electrode edges, Figure 2B shows nominal 3-, 4-, and 5-μm-diameter PS at a voltage of 300 mV and a frequency below their crossover frequency (COF). The COF ranges between 365 and 385 kHz for these three PS colloid particle sizes.28 The high surface conductance of the PS colloids allows for the PS to become more polarizable than the medium and hence a crossover to positive fcm values in eq 4. In Figure 2B, this crossover corresponds to the particle−field interaction transitioning from a single well in the middle of the electrode gap to a double well with minima near the electrode edges. This crossover to PDEP transport mechanisms corresponds to changes in the particle equilibrium position from the center of the electrode at high frequencies to the electrode edges at lower frequencies. To determine the frequency at which fcm shifts from negative to positive values for other particle material types, the field amplitude can be fixed and then the frequency can be decreased from a high value where the particle exhibits NDEP (e.g., 1 MHz). Upon detection of a crossover frequency, the particle will move to an electrode edge. In general, ac EO will be encountered for frequencies approaching 100 kHz at which point strong convective instabilities eject particles from the electrode gap.47

fϕ = [1 − fcm ϕA (1 + I )]−2

(6)

where I is a fitting constant. The correction in eq 6 should be multiplied by the particle-field potentials in eq 1 in concentrated colloidal dispersions. Colloidal Ensembles at Electric Field Minima. As was demonstrated for single particles, when a high-frequency ac electric field is applied to an ensemble of colloidal particles, the particles experience NDEP and will migrate to their potential energy minimum where the electric field gradient is the smallest in the center of the electrode gap. Various structures including quasi-2D chains and hexagonally close-packed (HCP) crystals can be formed between the parallel electrodes depending on the applied field strength and the particle concentration or 2D particle area fraction, ϕA. Figure 3A shows the different particle configurations possible for a 1 MHz ac electric field applied to ensembles of nominal 2.34-μm-diameter SiO2 in DI water at voltages ranging from 0.5 to 2 V and particle area fractions ranging from ϕA = 0.04 to 0.23 within ∼330 μm interdigitated electrode strips separated laterally by 30 μm.26 To confine the colloidal particles weakly as an associated fluid in the electrode channel center, low voltages were applied to induce a weak dipole−inhomogeneous ac electric field interaction. The applied field strength required to confine the particles as a fluid within the gap decreases as ϕA increases. Chains of colloidal silica oriented perpendicular to the electrode gap form from induced dipoles aligning as a result of dipole−dipole interactions between particles. Chaining can be achieved by increasing the particle concentration at a given voltage or the applied field strength for a given concentration. Figure 3A shows that HCP 2D crystal configurations are obtained by further increasing the particle concentration and/ or field strength as the result of lateral interactions between chains and their compression in the inhomogeneous field. Similar results are obtained using 800 nm Au colloids dispersed in aqueous 0.1 mM NaHCO3 over an identical interdigitated electrode.47 Figure 3B shows that by applying an ac electric field between 0.5 and 2.5 V at ω > 100 kHz, Au colloids at ϕA = 0.14 assemble into chains that bridge the electrodes. At a fixed colloid concentration, the colloidal assembly rate increases with increasing ac field amplitude. As was the case with the SiO2 colloids, at high enough field strengths, frequency, and colloidal concentrations, Au linear wire structures form as a result of ac electric fields inducing dipoles on the colloids and their assembly via NDEP transport and dipolar interactions. Colloidal Ensembles at Electric Field Maxima. We previously explained for individual colloids that it is possible for the colloid to become more polarizable than the medium depending on its material properties, which allows the particle to be transported via PDEP to a potential energy minimum at the electrode edges for frequencies below the COF. The same is true for ensembles of colloidal particles. Figure 3C illustrates that ensembles of nominal 3-, 4-, and 5-μm-diameter PS in DI water with ϕA = 0.39, 0.32, and 0.36 within 330 μm interdigitated electrode strips separated laterally by 60 μm can be assembled at either the center of the electrode channel

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PARTICLE ENSEMBLES IN PARALLEL ELECTRODES Induced Dipole−Dipole Interactions. Just as inhomogeneous ac electric fields can be utilized to manipulate individual colloid particles within an interdigitated electrode, they can also be employed to transport and assemble ensembles of colloidal particles. Applying an ac electric field to an ensemble of colloids still causes a rearranging of counterions that concentrate near the colloid surfaces to induce a dipole. As a result, concentrated colloidal systems in an ac electric field have induced dipoles that interact with each other while still interacting with the inhomogeneous electric field. These induced dipoles interact with one another with a potential energy, uDDpp(rij, θij, x, z) or uDDpp(rij, θij, R), given by pp uDD (rij , θij , x , z) = −kTλEfϕ P2(cos θij)(2a /rij)3 E*(x , z)2 pp uDD (rij , θij , R ) = −kTλEfϕ P2(cos θij)(2a /rij)3 E*(R )2

(5)

for the interdigitated and quadrupolar electrode geometries, respectively, where rij is the center-to-center separation between 10797

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structures in the middle of the electrode gap as a result of NDEP transport and induced dipole interactions, a frequency of 600 kHz is applied, which is above the COF for PS colloids. Isotropic fluid configurations should be observed at frequencies within the range of the COF (COF = 365−385 kHz) where fcm ≈ 0. However, Figure 3C shows that at a frequency of 350 kHz isotropic fluid configurations are not observed. Instead, chaining in the center of the electrode will occur even though dipole−dipole and dipole−field interactions should be negligible at these conditions. This is believed to occur because of ac EO flow-induced interactions in the absence of induced dipolar interactions. Increasing the particle size enhances the colloidal confinement in both the center of the electrode for NDEP or at the electrode edges for PDEP as a result of stronger dipole−field interactions. Electrophoresis/Electroosmosis for Colloidal Ensembles. In addition to the equilibrium particle microstructures that are obtainable using individual SiO2 and PS particles and ensembles of SiO2 and PS particles resulting from kT-scale dipolar interactions and either NDEP or PDEP transport, Figure 3B shows that additional steady-state microstructures are possible at lower frequencies using nominal 800-nm-diameter Au colloids.47 A 1 kHz frequency can be applied to transport Au colloids out of the electrode gap and concentrate them on top of the electrodes with a depleted area near the electrode edges. This behavior is the result of ac EO created by 3D periodic flows with recirculation on the parallel electrodes. These flows were visible during colloidal transport to assemble over the electrodes. ac EO flows removed colloids from the electrode gap and concentrated them on top of the electrodes in stagnation regions. Applying a frequency of 10 Hz to Au colloids caused them to oscillate as a band within the center of the electrode gap or aggregate above the electrodes (Figure 3B).47 At such low frequencies, the electric field is maintained in a given direction for a longer period of time, allowing the ions in the electrostatic double layer to respond. As a result, conductance dominates permittivity in this electrokinetic transport regime, and both the particle motion and EO are similar to the response in a dc field. Recirculation of EO flows at this low frequency will create stagnation areas on top of and in between the electrodes to concentrate Au colloids in these areas as shown in Figure 3B.

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PARTICLE ENSEMBLES IN QUADRUPOLE ELECTRODES Quasi-2D Crystallization in a Quadrupole Electrode. If an ensemble of colloidal particles is suspended over a quadrupole electrode (Figure 1B), behavior similar to that of ensembles of colloidal particles in a parallel electrode is observed.29,31,43,50 Using a 1 MHz ac electric field, nominal 3.13-μm-diameter SiO2 colloids in DI water or 0.1 or 1 mM NaOH or NaCl over a 100-μm-gap quadrupole electrode are less polarizable than the aqueous medium; as a result, they experience their lowest potential energy at the electric field minimum in the quadrupole center. These particles will be held within the quadrupole center with a force that is proportional to the electric field strength squared (eq 5).51 By using a low voltage, SiO2 colloids are weakly confined in an inhomogeneous fluid configuration within the quadrupole center. For the same number of particles in the quadrupole center, increasing the voltage will cause the particles to become more concentrated ultimately forming a quasi-2D crystal with a circular morphology and HCP microstructure in the center of

Figure 3. (A) VM images of equilibrated 2.34 μm SiO2 colloids within a 34 μm coplanar thin film electrode gap as a function of area fraction and field amplitude. (B) VM images of steady-state configurations of 800 nm gold colloids within a 30 μm gap between interdigitated coplanar gold film electrodes as a function of the applied ac electric field frequency and amplitude. (C) VM images of equilibrated PS colloids within a 60 μm coplanar Au thin film electrode gap as a function of frequency and particle size for a constant field amplitude of 300 mV. Image A is adapted with permission from ref 26, image B is adapted with permission from ref 47, and image C is adapted with permission from ref 30.

or the electrode edges using a voltage of 300 mV and frequencies above and below the COF.30 To form condensed structures near the electrode gap edges as a result of PDEP transport and induced dipolar interactions, a frequency of 100 kHz, which is well below the COF for PS colloids, is applied so that fcm > 0. To form condensed 10798

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strength. Using this method with the system in Figure 4 at an applied ac voltage of 10 V and a frequency of 1 MHz, it is possible to obtain 13 crystalline lateral layers (∼21 μm in the normal direction).29 At distances greater than 21 μm, the particles remain in distinct lateral layers under gravitational confinement, but with a fluid particle microstructure.

the electrode (Figure 1D, SI Figure S1). When using a smaller (larger) number of particles, stronger (weaker) applied field strengths are required to crystallize the particles, which we have previously quantified (SI).32 3D Crystallization in a Quadrupole Electrode. In addition to creating quasi-2D colloidal crystals, the quadrupole electrode geometry can also be used to assemble 3D colloidal crystals.29 The resulting 3D crystals can be imaged using confocal microscopy by employing nominal 1.5-μm-diameter fluorescent SiO2 colloids dispersed in dimethylformamide for index matching. As was seen using larger SiO2 colloids, when a weak ac electric field is applied to the ensemble, the particles will be confined to the center of the quadrupole in a fluid configuration. Similarly, the particles will be compressed into quasi-2D crystals as the voltage is increased. By using smaller particles and operating at higher voltages, the compression due to dipole−field interactions is comparable to gravity so that particles adopt 3D configurations. Figure 4 illustrates with

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PARTICLE ENSEMBLES WITH FEEDBACK CONTROL Controlling Ensemble Size. The use of electric-fieldmediated feedback control allows for the manipulation of colloidal ensembles in an informed manner. Electric-fieldmediated feedback control can be employed to remove particles from the center of the quadrupole electrode to specify the size of the colloidal crystal.31 Specifically, Figure 5 shows how the

Figure 5. Matrix of images for four target crystal sizes. In each case, (top row) the initial configuration is a fluid weakly held by NDEP, (second and third rows) EPEO and NDEP are cycled via feedback control to remove and concentrate particles iteratively, and (bottom row) NDEP is increased to compress particles into quasi-2D colloidal crystals. The inset scale bar is 20 μm. Reproduced with permission from ref 31. Figure 4. CSLM images and MC renderings of 1.5 μm fluorescent SiO2 colloids in a DMF medium displaying 3D hemispherical morphology with a crystalline interior and a thin fluid surface layer in a quadrupole electrode at 10 V and 1 MHz. (A) Projected view of the 3D CSLM XYZ stack and cross-sectional view from the 2D CSLM XZ slice. (B) Projected view and cross-sectional renderings of a 3D MC simulation of the experiment in A. An 8-bit white-blue color scheme indicates ⟨C6⟩ values for each particle between 0 and 6. (C) Projected view of the 3D CSLM XYZ stack rotated through 360° to illustrate the 3D microstructure and morphology. Reproduced with permission from ref 29.

number of 3.13 μm colloidal particles dispersed in DI water or 0.1 mM NaOH over a 100 μm quadrupole electrode can be reduced in a controlled fashion to a smaller user-defined value within 10 particles. Standard particle-tracking algorithms42 are used to detect the total number of colloids, n, within the quadrupole electrode device at a given time. If the total number of particles is greater than the user-specified value, then EP/EO actuation via a dc field between the east−west poles is used to remove particles from the quadrupole center. The flow field, v(R), induced by the simultaneous occurrence of EP and EO is linearly proportional to the applied electric field,39

confocal images and Monte Carlo simulation renderings that the compression of SiO2 colloids in the quadrupole produces a hemisphere of HCP particles. The microstructure is crystalline within the hemisphere center and is encased by a thin fluidphase layer where the density profile vanishes in both the normal and radial directions. The applied voltage can be varied to tune the field-mediated compression relative to gravity, which changes the relative height and radius of the hemisphere crystal. The number of layers achievable by this method depends on the size and number particles in the system as well as the applied field

v (R ) =

εm(ζp − ζw ) 4πμ

E (R )

(7)

where μ is the medium viscosity and ζp and ζw are the zeta potentials on the particles and wall, respectively. For negatively charged colloidal SiO2 particles, this leads to a saddle-shaped flow field with a stagnation point at the quadrupole center.31 To control the number of colloids in the quadrupole, the number can be reduced by making step changes to the applied ac and dc voltages on the basis of the current number of 10799

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Figure 6. (Left) Dynamic-feedback-controlled assembly and disassembly of a colloidal crystal of ∼130 particles using ⟨C6⟩ as the order parameter. Experimental optical video microscopy images and particle trajectories for the assembly process with ⟨C6⟩SP values of (A) 2, (B) 3, (C) 4, (D) 5, and (E) 6. The top image pane in each case shows individual particle C6 values by marking their centers using an 8-bit white-blue color scale with white for C6 = 1 and blue for C6 = 6. Below each experimental image in A−E are 40 s particle trajectories represented by a linear spectrum scale with red for t = 0 s and violet for t = 40 s. (F) Dynamic assembly and disassembly trajectories showing (top) ⟨C6⟩SP (solid blue line) and ⟨C6⟩PV (shaded blue points) vs time and (bottom) electric field voltage, V, (green) and frequency, ω, (orange) vs time. Labels A−E indicate corresponding particle-scale images and trajectories. The proportional controllers had K = 4 V. (Right) Dynamic-feedback-controlled assembly and disassembly of a colloidal crystal of ∼200 particles using Rg as the order parameter. Experimental optical video microscopy images and particle trajectories for the disassembly process with Rg,SP/μm values of (G) 18.8, (H) 19.6, (I) 20.4, (J) 21.2, and (K) 22. The top image pane in each case shows the value of Rg for each ensemble by marking all particle centers using an 8-bit white-red color scale with white for Rg/μm = 18.8 and blue for R g/μm = 22. Below each experimental image in G−K are 40 s particle trajectories represented by a linear spectrum scale with red for t = 0 s and violet for t = 40 s. (L) Dynamic assembly and disassembly trajectories showing (top) Rg,SP (solid red line) and Rg,PV (shaded red points) vs time and (bottom) electric field voltage, V, (green) and frequency, ω, (orange) vs time. Labels G−K indicate corresponding particle-scale images and trajectories. The proportional controller had K = 5.9 V. Copyright © 2012 Wiley. Adapted with permission from ref 27.

particles. After starting with a confined fluid state in a 1 MHz ac field, step changes for ac and dc voltages, Vac and Vdc, were programmed on the basis of empirical expressions that depend on the time, t, and the current total number of particles, n, given by

Vdc(t ) = 0.4C1(t1 − t0) + C1(t1 − t ) for NT − 10 ≤ n ≤ NT + 10 Vac(t ) = 2C2 + 10C1(t − t1) for NT − 10 ≤ n ≤ NT + 10

(9)

where t1 is the time after n is within ±10 particles of the userspecified target value, NT. Colloids removed from the quadrupole center by EPEO did not re-enter the quadrupole when NDEP was actuated to concentrate and crystallize the particles. Figure 5 shows VM images of the particle removal and assembly process for four different crystal target sizes. Initially, a large number of particles greater than the desired crystal size are weakly held in the quadrupole center using NDEP with a 1 MHz frequency, 50 mV ac electric field. To reduce the number of particles in the quadrupole center to NT, EPEO is actuated with NDEP by ramping Vdc to transport particles out of the quadrupole. As NT is approached to within the allowed tolerance, NDEP is actuated by ramping up Vac at 1 MHz to concentrate the remaining number of particles within the center of the quadrupole electrode. In experiments conducted in >1 mM media, EPEO electrokinetic transport is insufficient to remove particles. Controlling Colloidal Assembly. Electric-field-mediated colloidal interactions can also be used to control the temporal assembly and disassembly of colloidal crystals. Colloidal assembly typically occurs via nonequilibrium kinetic pathways that require waiting for the structure to relax. The ability to control the dynamic evolution of colloidal ensembles from

Vdc(t ) = C1(t − t0) for n > NT + 10 Vac(t ) = C2 for n > NT + 10

(8)

where t0 is the time at which control is initiated to achieve a user-specified target number of colloidal particles, NT, C1 = 0.04 V/s is the rate at which the dc voltage is changed, and C2 = 0.05 V is the constant applied ac voltage. The constant, C1, denotes the 0.005 V increase in Vdc every 125 ms (i.e., the CCD camera frame rate). This scheme can be actuated numerous times until NT is reached. Control algorithms were designed to remove particles from the quadrupole in batches of 50) using EP/EO to transport particles away from the quadrupole center results in particle aggregation near the electrode edges. After reaching the target total number of particles within the quadrupole, NDEP is used to concentrate and assemble colloidal crystals in the quadrupole center. To perform this step, the dc voltage is decreased incrementally while the ac voltage is simultaneously increased at 1 MHz frequency to a maximum value equal to the voltage required for particle assembly, V(n, κ−1) (eq S10).32 These voltages are given by the empirical expressions 10800

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disordered fluid configurations into ordered crystals allows colloidal crystals to be obtained in an efficient manner. Colloidal particles suspended over a quadrupole electrode can be manipulated using the electrokinetic transport mechanisms already discussed thus far (i.e., NDEP and PDEP).43 Closedloop feedback control schemes have been based on the realtime sensing of order parameters (SI). When particle centers are tracked, order parameter(s), x, can be computed in real time to actuate an applied voltage by means of a proportional control algorithm given by

approach 6, unless an extremely large system size is used, the change in the maximum achievable value is negligible (e.g., ⟨C6⟩ = 5.4 for the ∼130 particle system in Figure 6A−E and ⟨C6⟩ = 5.5 for the particle system in Figure 6G−K; see eq S19). Moreover, the edge particles of ordered colloidal assemblies will have ⟨C6⟩ < 6 because these particles will always have less than six nearest neighbors. A more reasonable set-point value for ⟨C6⟩ can be estimated using eq S19, which predicts ⟨C6⟩HEX, the 6-fold connectivity order for 2D HCP particles with hexagonal morphology. Similarly, eq S12 for Rg,HEX, the radius of gyration for 2D HCP particles within regular polygon morphologies, can be utilized to predict a reasonable set-point value for Rg. However, Brownian motion also causes excursions of particles from within and especially on the edge of the colloidal assembly from the crystal lattice, also resulting in ⟨C6⟩ and Rg process values less than set-point values in Figure 6F,L. Finally, simply decreasing the actuated voltage while remaining at a frequency of 1 MHz limits the maximum disassembly rate to the rate of particle diffusion. However, decreasing the frequency from 1 to 0.1 MHz allows crystals to be disassembled at faster than diffusion-limited rates as a result of PDEP that pulls particles toward the electrode edges.

⎡⎛ V − V ⎞ ⎤ min V (t ) = Vmin + ⎢⎜ max ⎟xSP(t )⎥ + e(t ) ⎢⎣⎝ xmax − xmin ⎠ ⎥⎦ e(t ) = KP[xSP(t ) − x PV(t )] ω(t ) =

106 Hz if e(t ) ≥ 0 105 Hz if e(t ) < 0

(10)

where V(t) is the applied ac voltage, t is the time, Vmin = 0.05 V is the minimum applied ac voltage, Vmax is the maximum applied ac voltage, x is the order parameter of interest, max and min are the maximum and minimum order parameter set point values, SP and PV denote the set point and process values, Kp is the proportional control constant, and ω(t) is the applied frequency. During colloidal assembly, the control algorithm uses NDEP to drive crystal assembly at the potential energy minimum in the quadrupole center, whereas PDEP drives disassembly by transporting particles to the electrode edges. Figure 6 shows the results using this control algorithm based on the average local 6-fold order, ⟨C6⟩, and radius of gyration, Rg (SI). These results show how the voltage is actuated to assemble and then disassemble the particles in a stepwise fashion in two separate experiments using either ⟨C6⟩ or Rg for assembly and disassembly (Figure 6F,L). It should be noted that either order parameter can be utilized to control the assembly and disassembly of colloidal particles, and Figure 6 simply demonstrates an example of each. To execute this control strategy practically, a 50 mV minimum is chosen because this voltage with a 1 MHz frequency prevents both of these system sizes of nominal 3.13-μm-diameter SiO2 colloids in DI water from escaping a 100 μm gap quadrupole electrode but also allows particles to remain in a disordered fluid configuration. Similarly, a 4 V maximum is chosen to avoid 2D crystals buckling into 3D configurations, as in Figure 4. Again, this voltage will depend on the total number of particles, and eq S10 should be employed to determine Vmax correctly (SI).32 The voltage is actuated using eq 10 every 500 ms so that the rate of actuation is faster than the diffusion-limited selfassembly trajectory of the order parameter of interest. Figure 6 displays several general features that are likely to be encountered when using feedback control to assemble and disassemble colloids in quadrupole electrodes. First, steadystate errors show that the process value consistently falls short of the set-point value. This is an inherent characteristic of proportional control that can easily be corrected with an offset or other control schemes. In addition, fluctuations of the process value around the set point occur as a result of the Brownian motion of the particles. The process value does not achieve a maximum set point value of ⟨C6⟩ = 6 (Figure 6E,F) or its minimum set point value of Rg (Figure 6G,L). Whereas having a larger system size would give ⟨C6⟩ values that better

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SUMMARY AND OUTLOOK

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ASSOCIATED CONTENT

The ability to manipulate colloidal particles using electric fields has been systematically described and demonstrated. Specifically, we reviewed the manipulation of single colloids in interdigitated electrode geometry as well as the manipulation of colloidal ensembles using both interdigitated and quadrupole electrodes. In addition, we discussed several variations including the assembly of 3D colloidal crystals and feedback control of the colloidal ensemble size and assembly/disassembly processes. Current and future directions are focused on implementing dynamic models to perform feedback control on nonequilibrium colloidal assembly trajectories to reconfigure colloidal ensembles rapidly within devices and active materials. Such dynamic models are necessary to cope with the stochastic nature of colloidal assembly and to inform actuation when a simple proportionality does not exist between the voltage and desired states. For example, we are currently developing landscape models to provide transition rates between various colloidal configurations encountered during the assembly/ disassembly process with the goal of using feedback to assemble colloidal wires in reconfigurable antennas and for optimal control of defect-free colloidal-based meta-materials.

S Supporting Information *

Materials and methods for fabricating O-rings, fractionating colloidal particles, manipulating single particles and particle ensembles, and modeling system size effects. 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]. Notes

The authors declare no competing financial interest. 10801

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Biographies

(PDMS) poly(dimethylsiloxane); (PS) polystyrene; (UV) ultraviolet; (VM) video microscopy

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REFERENCES

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Tara D. Edwards is a postdoctoral fellow in chemical and biomolecular engineering at Johns Hopkins University with principle investigator Professor Michael A. Bevan. She graduated summa cum laude from Widener University with a B.S in chemical engineering in 2007. Her Ph.D. was earned from Johns Hopkins University in 2013. Her current research interests focus on reconfigurable colloidal assembly via tunable interactions.

Michael A. Bevan is an associate professor of chemical and biomolecular engineering at Johns Hopkins University. He received his Ph.D. from Carnegie Mellon University in 1999. After postdoctoral appointments at the University of Melbourne, Australia, and the University of Illinois at Urbana−Champaign, he joined Texas A&M University in 2002 and Johns Hopkins University in 2008. Bevan’s research investigates interactions, dynamics, and structure in interfacial colloidal systems.

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ACKNOWLEDGMENTS We acknowledge financial support provided by AFOSR (FA9550-08-1-0329, FA9550-12-1-0090), DARPA (W911NF06-1-0050, FA9550-07-C-00020), NIST (70NANB10H198), an NSF CAREER award and PECASE (CTS-0346473), NSF Cyber Enabled Discovery and Innovation grants (CMMI0835549 and CMMI-1124648), NSF unsolicited grants (CBET-0932973 and CBET-1234981), and ONR (N000141210134).

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ABBREVIATIONS (2D) two-dimensional; (3D) three-dimensional; (ac) alternating current; (COF) crossover frequency; (dc) direct current; (DI) deionized; (EO) electroosmosis; (EP) electrophoresis; (HCP) hexagonally close-packed; (IPA) isopropanol; (NDEP) negative dielectrophoresis; (PDEP) positive dielectrophoresis; 10802

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