Langmuir 2001, 17, 2301-2304
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Electrically Switchable Colloidal Ordering in Confined Geometries T. Gong and D. W. M. Marr* Chemical Engineering Department, Colorado School of Mines, Golden, Colorado 80401 Received December 12, 2000. In Final Form: February 5, 2001 A novel field-induced approach has been developed that allows the controlled ordering of colloidal particles in confined systems. In this approach, an electric field is used to create a strong lateral dipole-dipole interaction that induces colloidal crystallization in two-dimensional geometries. Because the particle density is relatively low and the interaction of long range, colloidal mobility is high enough to allow rapid crystallization upon the application of the electric field. The observed phase transitions are fully reversible and can be readily controlled by adjusting either the applied field strength or particle confinement.
Introduction The controlled assembly of colloidal particles has received significant attention in recent years1-3 because of the potential application of nano- and microstructured materials in many fields. Ordered colloidal systems have lattice spacings ranging from nanometers to micrometers and can therefore diffract ultraviolet, visible, and nearinfrared light. One can take advantage of this property for a variety of applications, including sensors,4,5 narrowband optical filters,6 optical switches, photonic band gap materials, waveguides,7-10 and other types of optical and electrooptical devices.3 Photonic crystals, spatially periodic arrays in a medium of different dielectric constant, are of particular interest and are designed to affect the propagation of electromagnetic waves in much the same way that semiconductors influence the movement of electrons. First proposed in 1987,11,12 they could lead to the miniaturization and high-speed performance of integrated circuits13,14 and have profound applications for telecommunications, lasers, fiber optics, data processing, and display technologies.7,13,14 To date, the primary difficulty in the use of colloidal systems for such applications has been the fabrication of large arrays of colloidal particles into specific lattices with specific defect structures and with designed optical properties. Ordering in these systems is thermodynamically driven by colloidal interactions that may be predominantly attractive or repulsive, interactions that can often be readily tuned. For example, in a colloidal * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Grier, D. G. MRS Bull. 1998, 23, 21. (2) Dinsmore, A. D.; Crocker, J. C.; Yodh, A. G. Curr. Opin. Colloid Interface Sci. 1998, 3, 5. (3) Xia, Y.; Gates, B.; Yin, Y.; Lu, Y. Adv. Mater. 2000, 12, 693. (4) Asher, S. A.; Holtz, J.; Weissman, J.; Pan, G. MRS Bull. 1998, October, 44. (5) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829. (6) Sunkara, H. B.; Jethmalani, J. M.; Ford, W. T. Chem. Mater. 1994, 6, 362. (7) Joannopoulos, J. D.; Villeneuve, P. R.; Fan, S. Nature 1997, 386, 143. (8) Yablonovitch, E. J. Opt. Soc. Am. B 1993, 10, 283. (9) Chow, E.; Lin, S. Y.; Johnson, S. G.; Villeneuve, P. R.; Joannopoulos, J. D.; Wendt, J. R.; Vawter, G. A.; Zubrzycki, W.; Hou, H.; Alleman, A. Nature 2000, 407, 983. (10) Weissman, J. M.; Sunkara, H. B.; Tse, A. S.; Asher, S. A. Science 1996, 274, 959. (11) Yablonovitch, E. Phys. Rev. Lett. 1987, 58, 2059. (12) John, S. Phys. Rev. Lett. 1987, 58, 2486. (13) Busch, K.; John, S. Phys. Rev. Lett. 1999, 83, 967. (14) Fairley, P. Technol. Rev. 2000, 103, 38.
dispersion, repulsions can be modified by changing solution ionic strength and attractions can be influenced by solvent index matching or by varying salt concentration.15 However, development of technologically relevant colloidal crystals is hindered by the difficulty in uncoupling the variation of colloid-colloid interactions from the lattice structures that do form. Often for a specific application one wishes to manipulate colloidal surface chemistry, intervening fluid, or the specific colloidal material, all of which influence the nature of the crystallization process and may inhibit the formation of a particular lattice structure. A means of ordering colloidal particles that does not rely upon surface or particle chemistry could greatly aid the use of colloidal crystallization for technological applications. Recently, two-dimensional systems have been of particular interest because novel phase behavior16-18 and unique optical properties9,19,20 have been observed. Also, new interactions in confined geometries have been reported; as first discussed by Richetti et al. in 1984,21 electric fields21-25 induce a “lateral attraction” on electrode surfaces that can be used to create local colloidal crystallites. One can adjust the strength of this lateral attraction and the resulting phase behavior by changing the current magnitude. With this approach successful deposition of layer-by-layer colloidal crystals has been accomplished.22 Here we show that for strictly confined systems, however, the application of an electric field instead gives rise to a strong interparticle repulsion that can be used to create relatively large regions of colloidal order. Experimental Section To create the confined systems used in our studies, two glass slides coated with indium tin oxide (ITO) (sheet resistance of 20 (15) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, 1989. (16) Marcus, A. H.; Rice, S. A. Phys. Rev. E 1997, 55, 637. (17) Murray, C. A.; van Winkle, D. H. Phys. Rev. Lett. 1987, 58, 1200. (18) Murray, C. A.; Sprenger, W. O.; Wenk, R. A. Phys. Rev. B 1990, 42, 688. (19) Lin, S. Y.; Chow, E.; Hietala, V.; Villeneuve, P. R.; Joannopoulos, J. D. Science 1998, 282, 274. (20) Leonard, S. W.; Mondia, J. P.; van Driel, H. M.; Toader, O.; John, S.; Busch, K.; Birner, A.; Go¨sele, U.; Lehmann, V. Phys. Rev. B 2000, 61, R2389. (21) Richetti, P.; Prost, J.; Barois, P. J. Phys. Lett. 1984, 45, L1137. (22) Trau, M.; Saville, D. A.; Aksay, I. A. Science 1996, 272, 706. (23) Yeh, S.-R.; Seul, M.; Shraiman, B. I. Nature 1997, 386, 57. (24) Hayward, R. C.; Saville, D. A.; Aksay, I. A. Nature 2000, 404, 56. (25) Bo¨hmer, M. Langmuir 1996, 12, 5747.
10.1021/la001740o CCC: $20.00 © 2001 American Chemical Society Published on Web 03/16/2001
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Figure 1. Experimental schematic. By confining the geometry, one can vary the relative strength of electroosmotically induced attractions and dipole-dipole repulsions.
Letters
ionic current. This hypothesis suggests that lateral variations in concentration polarization induce a spatially varying free charge that induces electroosmotic fluid motion in the presence of an electric field, causing the particles to move together. In our strictly confined systems however, drastically different behavior is observed in the presence of an electric field. Instead of strong lateral attractions, the colloids experience a strong lateral repulsion as shown in Figure 2d, where ordering has occurred within the strictly confining two-dimensional plane. We attribute this result to a change in the nature of the electroosmotically induced fluid flow due to the imposed geometric constraints that either significantly diminishes or completely removes the effective attraction (Figure 1b). The strong lateral repulsion we observe can be described in terms of a dipole-dipole interaction induced by the applied electric field. The strength of this interaction can be expressed as
φ(r,θ) ) -
Figure 2. Series of images captured in a wedge geometry as one moves from (a) three-dimensional to (d) strictly confined two-dimensional regions. The applied field varied from 1.6 to 3.1 V/µm at a frequency of 100 Hz. Ω per square, Delta Technologies, Limited, Stillwater, MN) were sandwiched together and sealed with epoxy resin. Using this approach we have been able to consistently achieve cells with a thickness of approximately 3.5 µm (verified via optical microscopy). In combination with 3 µm polystyrene (PS) latex particles (Interfacial Dynamics Corporation, Portland, OR), strictly confined two-dimensional systems can be created. The dispersions used in these studies consisted of a 1:1 ratio of deionized water (conductivity ∼1 µS/cm) and glycerin (ACS reagent grade, Merck, Albany, GA, used as received) with a small amount of Triton X-100 (Aldrich, Milwaukee, WI) added as a stabilizer. No additional deionization was performed. Our experiments were conducted using an alternating electric field at a frequency of 100 Hz and over an amplitude range of 1 V to 11 V peak to peak.
Results and Discussion As discussed above, an interparticle attraction strong enough to form stable two-dimensional crystals can be induced on an electrode surface by application of an alternating electric field normal to the plane of translation. This effect is illustrated schematically in Figure 1a and shown in Figure 2a where colloidal particles form tight two-dimensional crystals in the presence of a strong 3.1 V/µm ac field. On the basis of a simple model of aligned dipoles, however, one would expect these colloids to repel one another quite strongly. Trau et al.,22 Yeh et al.,23 and Bo¨hmer 25 have proposed that the lateral attraction results from electrohydrodynamic effects arising from charge accumulation near the electrodes due to the passage of
u2 (2 cos2 θ - sin2 θ) 3 4π0r
(1)
for aligned point dipoles,26 where φ(r,θ) is the interaction energy, u is the induced dipole moment, and 0 are the dielectric permittivity of the medium and free space, respectively, r is the separation distance, and θ is the angle between the field and dipole center line. The strength of the dipole can be related to the electric field strength E via u ) RE, where R is the electric polarizability of the colloid. This equation illustrates that the interaction is most repulsive when colloids are in the same plane (θ ) 90°). To illustrate the influence of geometry on the effective colloid interaction in the presence of an electric field, we have constructed cells of a wedge geometry which provide a linear spatial variation from strictly two to three dimensions. In this cell, the wedge angle is very small, ∼0.1°, and the voltage applied is of constant peak-to-peak magnitude, leading to an applied field varying from 3.1 to 1.6 V/µm as one moves from the two- to threedimensional cell regions. Figure 2 shows a series of images captured as the stage was translated from regions of 7-3.5 µm thickness. As the field varies linearly during this translation, the nature of the interaction clearly changes dramatically. In regions where the plate separation allows colloids to move slightly in the third dimension, the colloidal particles experience an effective attraction and form tight colloidal crystals. As one moves to strictly confined two-dimensional regions, however, the gradual transition from interparticle attractions to repulsions can clearly be seen. In fact, one observes a full range of phase behavior, from attraction-induced colloidal crystallization to a two-phase system to entropy-driven repulsive colloidal ordering. This fully reversible behavior is clearly demonstrated as the dispersions revert to disordered fluids when the electric field is turned off. If instead of using a wedge geometry one strictly confines a relatively concentrated suspension to two dimensions, then the colloidal ordering can be controlled solely by varying electric field strength. Figure 3 illustrates this transition from ordered solid to fluid-solid coexistence to fluid as the field strength is lowered from 3.1 to 0.3 V/µm. This approach provides a convenient means of investigat(26) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain Where Physics, Chemistry, Biology, and Technology Meet; Wiley-VCH: New York, 1999.
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Figure 4. Variation of electric field strength required to induce ordering with colloid size and density. The colloid radius was varied from 1.5 to 11 µm, the units on the plot are arbitrary, and the line is best fit with slope ) -3.
Figure 3. Different phases achieved by varying the electric field strength in a strictly confined two-dimensional geometry. The ac field was applied at a frequency of 100 Hz and at strengths of (a) 3.1, (b) 2.0, (c) 0.6, and (d) 0.3 V/µm.
ing phase transitions in two dimensions as one can easily tune the interactions and move throughout the phase diagram. If, as we expect, the interaction is dominated by dipoledipole interactions induced by the electric field, then particle size will play a large role in determining the field strengths required for colloidal ordering. This is due to the proportionality of the electric polarizability R to particle volume via26
(
)
n2 - 1 R ) 4π0a 2 n +2 3
(2)
where a is the particle radius and n its index of refraction. We begin by defining an effective area fraction ηeff ) η*(reff/a)2 where η is the true colloid area fraction and reff is an effective radius that grows with dipole-dipole interaction strength. If reff is based on a particular interaction energy φeff, then
[
(
)]
4π0a3E2 n2 - 1 reff ) a φeff n2 + 2
1/3
(3)
and
[ ( )]
ηeff ) ηa2E4/3
4π0 n2 - 1 φeff n2 + 2
2/3
(4)
If one then assumes that there is a specific ηeff at which the disorder-order transition occurs,27 then the electric field required for ordering, E, is proportional to (ηa2)-3/4 or (F1/4a)-3 where F is the number density. The electrostatic origin of these repulsive forces indicates a dependence of the overall interaction strength on solution ion concentration. Because we do not strictly account for this here, our experiments were conducted at constant ionic strength. (27) Alder, B. J.; Wainwright, T. E. Phys. Rev. 1962, 127, 359.
Figure 5. Small-angle scattering patterns observed by varying the field strength in a strictly confined two-dimensional geometry. The ac field was applied at a frequency of 100 Hz and at strengths of (a) 3.1, (b) 2.0, (c) 0.6, and (d) 0 V/µm.
Despite the simplicity of this approach, the behavior observed experimentally is indeed consistent with this scaling analysis; as the particle size increased, the electric fields required to induce order decreased significantly. Figure 4 shows the field strengths required to induce order for systems of different particle size and density. The behavior follows the expected power law dependence indicating that the dipole-dipole interaction is indeed dominating the observed phase behavior. This new approach to order colloidal systems can be used as a route to the controlled assembly of macroscopic colloidal phases in confined geometries. To emphasize this, small-angle light scattering was used where a laser beam is passed through the sample perpendicular to the plane of colloidal order. A solid-state diode-pumped Spectra Physics Millenia V laser operated at minimum intensity and subsequently attenuated supplied green light at 532 nm. The beam was slightly focused and was approximately 1 mm in diameter when passed through the sample. A sample to detector distance of 12 cm was employed, and images were digitized using a Macintosh G3 for subsequent analysis. Initially, rings associated with a disordered colloidal fluid were readily observable as seen in Figure 5d where the sample consisted of 3 µm colloidal polystyrene particles
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dispersed in water within a strictly confining twodimensional geometry. Upon application of the electric field, both powder-type diffraction patterns (indicating the presence of crystals of varying orientation) and single crystal patterns (as shown in Figure 5a) were quickly seen. The location of spots within the diffraction pattern indicates a hexagonal lattice with nearest neighbor distances of 4.3 µm. To illustrate the reversibility of the transition, Figure 5 shows the change in the scattering pattern as the voltage was reduced from a maximum in Figure 5a to zero applied field in Figure 5d. It has been shown that electric field induced repulsive dipole-dipole interactions can be used to cause ordering of colloidal particles in confined geometries. Because these forces are strong and long-ranged, they can dominate other colloidal interactions and be used to induce colloidal order where crystallization otherwise would not occur. In addition, colloidal mobility remains relatively high after
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crystallization, allowing the rapid formation of large ordered domains. Such electrically switchable colloidal arrays could find use in a variety of photonic applications, including optical switches, waveguides, and band gap materials. Other applications include the creation of patterned arrays in soft lithographic techniques, as masks to fabricate regular arrays of micro- or nanostructures, or as optical microlenses in image processing.3 Finally, such tunable colloidal systems will provide excellent model systems for the direct observation of fundamental phenomena such as crystallization, melting, and phase transitions in two dimensions.16,18,28 Acknowledgment. We thank the NSF for support of this research under CAREER Award CTS-9734136. LA001740O (28) van Winkle, D. H.; Murray, C. A. Phys. Rev. A 1986, 34, 562.
