10064
Langmuir 2002, 18, 10064-10067
Two-Dimensional Electrohydrodynamically Induced Colloidal Phases Tieying Gong,† David T. Wu,†,‡ and David W. M. Marr*,† Chemical Engineering Department and Chemistry Department, Colorado School of Mines, Golden, Colorado 80401 Received July 15, 2002. In Final Form: October 21, 2002 Over the past decade, experiments have shown that applied electric fields can be used to assemble colloids at electrode surfaces via an apparently electrohydrodynamic attractive interaction. Recently however, it has been seen that confinement strongly influences this process, simultaneously suppressing the apparent attractions while increasing the relative importance of field-induced dipole-dipole repulsions. By varying the degree of confinement and the strength of the applied field, one can alter the relative magnitude of these competing effects. We show here that one can take advantage of this interplay for the construction of novel two-dimensional colloidal phases.
Introduction Application of electric fields to colloidal dispersions has gained attention recently for its use in the control of colloidal assembly at electrode surfaces.1-3 In this approach, a dc field is typically used to first translate colloids onto a surface where, once deposited, a number of interesting behaviors can be observed upon the application of a sufficiently large ac or dc field. For example, colloids will translate over distances of many micrometers to form tightly packed two-dimensional domains that then aggregate into larger crystals4,5 (see Figure 1a). This effective attraction runs counter to the expected dipoledipole dominated behavior as theorized by Richetti et al.6 The governing effect in a dc field is electro-osmotic flow7 as first suggested by Bo¨hmer5 and then elaborated upon by Anderson et al.8-10 In this, the normally directed field drives ions and fluid from the deposited particle’s double layer away from the electrode, subsequently drawing fluid across the electrode to maintain mass balance. Attraction is observed when a second particle is entrained by these flow fields created by the first particle’s presence. In ac fields, electrohydrodynamics dominates,2,4,7 where water electrolyzes producing hydronium and hydroxide ions that migrate toward the electrodes. No net production or consumption of ions occurs, but the migration leads to a concentration gradient at each electrode. A colloid near one of the electrodes creates a lateral field disturbance that disrupts the concentration and associated pressure gradients, initiating convective flow, and sweeping particles toward each other across the electrode surface. * To whom correspondence may be addressed. E-mail: dmarr@ mines.edu. † Chemical Engineering Department. ‡ Chemistry Department. (1) Yeh, S.-R.; Seul, M.; Shraiman, B. I. Nature 1997, 386, 57-59. (2) Trau, M.; Saville, D. A.; Aksay, I. A. Langmuir 1997, 13, 63756381. (3) Hayward, R. C.; Saville, D. A.; Aksay, I. A. Nature 2000, 404, 56-59. (4) Trau, M.; Saville, D. A.; Aksay, I. A. Science 1996, 272, 706-709. (5) Bo¨hmer, M. Langmuir 1996, 12, 5747-5750. (6) Richetti, F.; Prost, J.; Clark, N. A. In Physics of Complex and Supermolecular Fluids; Safran, S. A., Clark, N. A., Eds.; Exxon Monograph; Wiley: New York, 1987; pp 387-411. (7) Sides, P. J. Langmuir 2001, 17, 5791-5800. (8) Guelcher, S. A.; Solomentsev, Y.; Anderson, J. L. Powder Technol. 2000, 110, 90-97. (9) Solomentsev, T.; Bo¨hmer, M.; Anderson, J. L. Langmuir 1997, 13, 6058-6068.
In addition to electric field properties, particle confinement plays a significant role in the effective colloid interactions in these two-dimensional systems.11 The introduction of a second confining wall into a colloid system under an electric field produces a dramatic lateral repulsion under conditions that would lead to a strong attraction in the single electrode case. Under these conditions, two-electrode confinement restricts the movement of fluid, flow fields begin to overlap, and colloids experience a diminished attraction. By variation of the nature of the applied electric field and the degree of particle confinement, the relative strength of attractions and repulsions can be independently varied, providing a way to tune both the strength and range of the effective interaction potential. In doing so we show here that, in addition to the colloidal phases seen in strict twodimensional confinement without applied electric fields, novel phases develop including wormlike phases and honeycomb lattices. Experimental Section Solutions of 4.2 µm diameter, σ, polystyrene colloids (surfactant-free white CML latex, Interfacial Dynamics Corporation, Portland, OR) in a potassium chloride solution of final ionic strength 0.001 M were prepared. The solution consisted of approximately 0.5 wt % Triton X-100 (Aldrich Chemical Co., Inc., Milwaukee, WI) in 50:50 wt % deuterium oxide (d-99.9%, Cambridge Isotope Laboratories, Inc, Andover, MA, added to minimize any sedimentation) to a deionized water/KCl solution. As purchased, the colloids were first centrifuged to high concentration and then added to the solution to obtain the desired dimensionless densities, Fσ2. The polystyrene spheres in the final solution were measured to have a zeta potential of -59.8 ( 1.5 mV (ZetaPlus V.3.52, Brookhaven Instruments Corporation, Holtsville, NY). A wedge cell allows access to colloidal domains of varying degrees of confinement within one experimental system. This cell, as illustrated in Figure 2, is similar to a Hull cell, which has a well-known current distribution.12 The experiments shown here however are done within a limited range within the wedge and no local current deviates more than 15% from the average overall cell current. To create these cells, two indium-tin oxide coated glass slides, 3 in. by 1 in. (Delta Technologies, Limited, Stillwater, MN), were first coated with 0.5 wt % Triton X-100, then placed, (10) Solomentsev, Y.; Guelcher, S. A.; Bevan, M.; Anderson, J. L. Langmuir 2000, 16, 9208-9216. (11) Gong, T.; Marr, D. W. M. Langmuir 2001, 17, 2301-2304. (12) West, A. C.; Matlosz, M.; Landolt, D. J. Appl. Electrochem. 1992, 22, 301-303.
10.1021/la026241x CCC: $22.00 © 2002 American Chemical Society Published on Web 11/27/2002
Letters
Langmuir, Vol. 18, No. 26, 2002 10065
Figure 1. (a) Unconfined (h/σ ) 1.23) vs (b) confined (h/σ ) 1.03) colloids under a 25 V applied ac field.
Figure 2. Wedge cell: (a) side view; (b) top view.
Figure 3. Phase diagrams as a function of density and degree of confinement (h ) plate spacing) under (a) 10 V and (b) 25 V applied fields: b, fluid; 2, crystalline; 9, wormlike; ), aggregates; (, crystalline aggregates; O, honeycomb. Points 7 and 8 correspond to parts a and b of Figure 1, respectively. conductive sides facing in, with a Kapton spacer of 12.5 µm (DuPont High Performance Materials, Circleville, OH) between them at one end. Poly(dimethylsiloxane) (PDMS) (Sylgard Brand, Dow Corning Corporation, Midland, MI) was cured around the slides to seal the edges together leaving channels for sample insertion and air venting. Sample solution was then added to the cell via syringe, and more PDMS was used to seal the channels. Once cured, electrodes were attached to each slide’s conductive surface. Electric fields were applied to the cell using a function generator (DS360 ultralow distortion function generator, Stanford Research Systems, Sunnyvale, CA).
Results and Discussion In the limit of large electrode spacings, we observe, upon application of an ac field, strong aggregation into ordered domains as seen by other authors and shown in Figure
1a. Under the opposite limit of tightly confining geometries, we observe the previously reported repulsively ordered colloidal crystals due to dominating dipole-dipole repulsions11 (Figure 1b). It is between these two limits that novel phases have been observed and are reported here. As discussed above, to conveniently perform experiments under varying degrees of confinement, a wedge cell was created with a slight variation in gap thickness ranging approximately from 12.5 to 4 µm, over a distance of about 1 cm (Figure 2). To generate phase diagrams, a constant voltage was first applied across the cell for approximately 60 min and the various phases and local particle densities were noted by scanning the microscope over regions of different cell thickness. This procedure is then repeated for different
10066
Langmuir, Vol. 18, No. 26, 2002
Letters
Figure 4. Images from various regions of the phase diagrams presented in Figure 3.
introduced particle concentrations. Figure 3 presents two phase diagrams, one taken at an average applied field of 0.73 V/µm (10 V peak to peak) and the other at an average field of 1.8 V/µm (25 V peak to peak). In addition to the crystalline aggregate and repulsive ordered phases previously observed, both wormlike and honeycomb lattices are observed under intermediate confinement. This is illustrated in Figure 4 where images correspond to the observed phases measured under different conditions. Image 4 illustrates one example of the extended honeycomb morphology which is observed under higher applied fields. In this image, lines are drawn connecting colloids to allow better recognition of the structure. As discussed previously, varying the level of confinement provides an effective tune of the relative strength of the competing flow-induced attractions and dipole-induced repulsions in these systems. Although electrohydrodynamic flows are assumed to be the source of the dominant attraction we observe, we have found it useful to interpret these experiments in terms of an effective interaction
potential. This quasi-thermodynamic approach is motivated primarily by two observations. First, all of the phases formed are fully reversible; if the electric field is switched off, colloidal phases immediately relax into their initial homogeneous, fluidlike distributions. Once the field is reapplied, the phases reappear. Second, the observed structures form quickly and appear stable over long periods of time. Despite this, it is certainly possible that the formation of large-scale morphologies is kinetically limited. Evidence of such limitation has been seen in the relatively small domains formed by the honeycomb lattice. As a general rule, we observe that an increase in field strength increases the dipole-dipole repulsion and an increase in plate spacing increases the magnitude of the effective attraction. In this way, the dimensionless plate spacing, h/σ, plays a role analogous to that of the inverse temperature, 1/T, in the structural phase diagram. Full confinement corresponds to high temperature, where strong repulsions dominate weak attractions, as evidenced by the single order-disorder transition characteristic of
Letters
hard spheres observed at h/σ f 1.0 (Figure 3). Increasing the plate spacing then becomes a means of lowering the temperature until the onset of phase separation as h/σ f 1.3 (Figure 3). Because increasing the field strength increases the magnitude of the dipole-dipole repulsion, its increase leads to an effective increase in the colloid “size”. Voltage therefore provides an approximate means of tuning the effective system density. Since the nature of the attractive interactions is yet to be quantitatively characterized, we present a hypothesis on the mechanism of formation of the observed structures. Inspection of the worm phases (images 5 and 6 in Figure 4) shows that particles participate in two types of local geometries: part of a continuing chain, or part of a 3-fold joint. Similarly, the honeycomb structure can result naturally from particles with a preference to form a 3-fold joint. The observed honeycomb structure (image 4) shows a preponderance of 3-fold joints, with some chainlike portions interrupting the regular honeycomb structure. Additionally, careful inspection of the wormlike phase under the somewhat larger plate spacings of image 6 reveals what appears to be an up-down alternation of the colloids, relative to the direction of the field. This is likely due to a lowering of the dipole-dipole energy in this configuration relative to an all in-plane positioning of the colloids. Given that the dipole-dipole repulsion, including the image charges due to confinement, can be relatively wellunderstood, we postulate that in changing the confinement, the attractive interactions in the wormlike and honeycomb phases are reduced to the point where the total interaction potential is such that it favors the two local arrangements, chainlike and jointlike, described above. While it is possible to invoke three-body interactions to explain the 3-fold coordination of the joints, it is difficult to provide a physical mechanism for such a multibody interaction. Instead, we note that a simple pairwise potential with preferred distances (such as at the contact length and at the next-nearest neighbor length) can favor such local arrangements. These preferred distances in the potential can be modulated by a balance between the attractive and repulsive potentials. Thus as we consider in succession images 4, 5, and then 6, we see that the
Langmuir, Vol. 18, No. 26, 2002 10067
relative fraction of 3-fold to 2-fold (chainlike) joints increases steadily. The ability to reversibly create a variety of twodimensional morphologies may have important technological application. For example, colloidal systems have shown the ability to alter the propagation of light, a property one can take advantage of for a variety of applications, including sensors,13 narrow-band optical filters,14 optical switches, and other types of optical and electrooptical devices.15 The required colloidal lattices however, are typically difficult to create and cannot be switched on and off. A technique that allows the reversible formation of colloidal structures with the simple application of an electric field could have significant advantages over previous approaches. Honeycomb lattices have, for example, been suggested as a morphology that could show enhanced photonic band gap properties.16 One additional advantage not shown here is that colloids of different size can be readily chosen. Though relatively large particles were used in this study for convenience, much smaller systems could be incorporated for applications requiring very fast kinetics or the manipulation of light of visible wavelengths. A more systematic study of the nature of the attractive and repulsive attractions can be performed by a quantitative analysis of the structures observed. This inverse problem, which can be treated either via simulation or by approximate analytical methods, may provide guidance for the design of desired structures and will be the subject of a subsequent article. Acknowledgment. This work was supported by NSF Grant CTS-9734136. We thank Laura Schafer for useful discussions. LA026241X (13) Asher, S. A.; Holtz, J.; Weissman, J.; Pan, G. MRS Bull. 1998, October, 44-50. (14) Sunkara, H. B.; Jethmalani, J. M.; Ford, W. T. Chem. Mater. 1994, 6, 362-364. (15) Xia, Y.; Gates, B.; Yin, Y.; Lu, Y. Adv. Mater. 2000, 12, 693-713. (16) Joannopoulos, J. D.; Meade, R. D.; Winn, J. N. Photonic Crystals; Princeton University Press: Princeton, NJ, 1995.
