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Propagation of Electrooptic Shear Waves in Colloidal Crystals As Studied by Reflection Spectroscopy† Akira Tsuchida, Tomomi Taniguchi, Tomofumi Tanahashi, and Tsuneo Okubo* Department of Applied Chemistry, Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu 501-1193, Japan Received August 31, 1998. In Final Form: January 13, 1999 Electrooptic properties of colloidal crystals of silica spheres (diameter: 103 nm) in an exhaustively deionized aqueous suspension have been studied by electric reflection spectroscopy using the rectangular parallelepiped-shaped cells with electrical membranes inside the cell wall. Acoustic shear waves are induced inside and even outside the electrodes, where the electric field is absent, when sine-wave electric fields ranging 0.01-1000 Hz in frequency and 0.0001-100 V/cm in field strength are applied. Modulation effects such as phase delay, change in the amplitude, and harmonics generation are observed. A significant effect of the optical path length is observed on the shear waves; i.e., the amplitude and phase difference change significantly for the cell of long optical length. The importance of the synchronous fluctuation of the colloidal spheres mediated by the expanded electrical double layers in the crystal lattice is strongly supported for the electrooptic effects observed.
Introduction Optic response in an electric field, i.e., the electrooptic effect, has been investigated extensively for colloidal dispersions.1,2 Recently, we have studied the electrooptic effects of colloidal crystals by electric reflection spectroscopy.3-6 Significant modulation effects in the phase difference, amplitude, waveform transformation, harmonics generation, and acoustic shear waves have been observed. Stoimenova et al. have reported electrooptic effects such as resonance frequencies (harmonic oscillation) and acoustic shear waves for the colloidal crystal systems, for the first time.7-9 These significant electrooptic effects have been clarified mainly due to (a) the synchronous fluctuation of colloidal spheres in the crystal cages and (b) the transformation between two subphases in the lattice structures of colloidal crystal, face-centered cubic (fcc) and body-centered cubic (bcc) lattices, in an electric field. It should be noted here that the dynamics of the extended electrical double layers surrounding the spheres and the intersphere electrostatic repulsive forces play important roles for the synchronous fluctuation and the transformation in colloidal crystal lattices.10-12 The thick* To whom correspondence should be addressed. Phone: +8158-293-2620. Fax: +81-58-293-2628. E-mail: okubotsu@apchem. gifu-u.ac.jp. † Presented at Polyelectrolytes ‘98, Inuyama, Japan, May 31June 3, 1998. (1) Jennings, B. R., Stoylov, S. P., Eds. Colloid and Electrooptics; Inst. Phys. Pub.: Bristol, U.K., 1992. (2) Stoylov, S. P. Colloid Electrooptics. Theory, Techniques, Applications; Academic Press: London, 1991. (3) Okubo, T.; Tsuchida, A.; Okada, S.; Kobata, S. J. Colloid Interface Sci. 1998, 199, 83. (4) Okubo, T.; Tsuchida, A.; Tanahashi, T.; Iwata, A.; Okada, S.; Kobata, S.; Kobayashi, K. Colloid Surf., in press. (5) Okubo, T.; Tsuchida, A.; Iwata, A.; Tanahashi, T. Colloids Surf. 1999, 148, 87. (6) Okubo, T.; Tsuchida, A.; Tanahashi, T.; Iwata, A. J. Colloid Interface Sci. 1998, 207, 130. (7) Stoimenova, M.; Okubo, T. J. Colloid Interface Sci. 1995, 176, 267. (8) Stoimenova, M.; Dimitrov, V.; Okubo, T. J. Colloid Interface Sci. 1996, 184, 106. (9) Stoimenova, M.; Okubo, T. Surfaces of Nanoparticles and Porous Materials; Schwarz, J. A., Ed.; Dekker: New York, 1999; p 103.
ness of the electrical double layers is approximated by the Debye screening length, Dl, given by
Dl ) (4πe2n/kBT)-1/2
(1)
where e is the electronic charge, is the dielectric constant of solvent, kB is the Boltzmann constant, T is the absolute temperature, and n is the concentration of “diffusible” or “free-state” simple ions in suspension. Note that the maximum value of Dl observed for the exhaustively deionized suspension in water is ca. 1 µm and much longer compared with the size of colloidal particles. Since rigidity of the electrical double layers is extremely small and the colloidal spheres are charged negatively in general, lattice spacing changes synchronously when an alternating electric field is applied.13-18 In this report, shear wave propagation effect of colloidal crystals is discussed experimentally in detail by electric reflection spectroscopy using the electrooptic cells of T3, T10 and T20 types. Materials and Methods Materials. Monodispersed colloidal silica spheres (CS-82) were kindly donated by Catalyst & Chemicals Ind. Co. (Tokyo). The diameter was 103 nm (mean diameter) ( 13.2 nm (standard deviation) by electron microscopy (TEM, JEOL, Tokyo, Type JEM2000FX). The polydispersity index given by the standard deviation divided by the mean diameter was 0.13. The charge density of the strongly acidic groups was 0.38 µC/cm2, which was determined by conductometric titration with a Wayne-Kerr autobalance precision bridge, model B331 mark II.19 The sphere sample was further purified carefully several times using an ultrafiltration cell (model 202; membrane, Diaflo XM, Amicon Co., Lexington, MA) and then treated with a mixed bed of cationand anion-exchange resins (Bio-Rad, AG501-X8 (D), 20-50 mesh) (10) Pieranski, P. Contemp. Phys. 1983, 24, 25. (11) Ottewill, R. H. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 281. (12) Okubo, T. Acc. Chem. Res. 1988, 21, 281. (13) Fujita, H.; Ametani, K. Jpn. J. Appl. Phys. 1977, 16, 1907. (14) Fujita, H.; Ametani, K. Jpn. J. Appl. Phys. 1979, 18, 753. (15) Tomita, M.; van de Ven, T. G. M. J. Opt. Soc. Am. 1984, A1, 317. (16) Tomita, M.; van de Ven, T. G. M. J. Phys. Chem. 1985, 89, 1291. (17) Okubo, T. J. Chem. Soc., Faraday Trans. 1 1987, 83, 2487. (18) Okubo, T. J. Chem. Soc., Faraday Trans. 1 1988, 84, 3377. (19) Okubo, T. Colloid Polym. Sci. 1993, 271, 190.
10.1021/la981128l CCC: $18.00 © 1999 American Chemical Society Published on Web 04/03/1999
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Figure 2. Waveforms of the applied (dotted curve) and reflection (solid curve) signals of colloidal crystals of CS-82 spheres at 25 °C: φ ) 0.048; E ) 1.5 V/cm; f ) 0.05 Hz; cell T20; position 3B.
Figure 1. Schematic representation of the cell and apparatus. for more than 4 years in order to delete ionic impurities completely. Water used for sample preparation was obtained from a Milli-Q water system (Milli-RO Plus and Milli-Q Plus, Millipore Ltd., Bedford, MA). Electric Reflection Spectroscopy. Two kinds of spectroscopic measurements on the optical reflection intensity and reflection spectrum were made using T3, T10, and T20 observation cells as is shown in Figure 1. The shape of the cells was rectangular parallelepiped. Optical path lengths were 3, 10, and 20 mm for the T3, T10, and T20 cells, respectively. A pair of transparent NESA electric conducting membranes (10 × 10 mm) were coated on both the top and bottom insides of the glass plates. On the surface of the top observation glass the grid lines were printed at intervals of 5 mm as is shown in the figure. The measurement position (center of the grid lines) was designated by numbers and alphabetical characters named for each section, e.g. 4B. The sample suspension was sealed tightly and repeatedly by Parafilm (American National Can, Greenwich, CT). The suspension in the cell coexisted with the mixed bed of the ionexchange resins (Bio-Rad) at least 7 days before and during the measurements. The sphere concentrations were 0.048 and 0.096 in volume fraction (φ). A halogen light source (PHL-50, Sigma Koki, Saitama) and a Y-type optical fiber cable were used. The focus size on the cell surface was smaller than 1.5 mm in diameter.3 The measurements were made usually parallel but once rectangular to the electric field applied. Intensity of the reflected light was detected by a photomultiplier for the intensity measurements and then recorded on a digital oscilloscope (DL1300, Yokogawa, Tokyo). Time-resolved reflection spectra were measured on a photonic multichannel analyzer (PMA-50, Hamamatsu Photonics, Hamamatsu, Japan) with 1 s time interval. An oscillator (Type 4025, Krohn-Hite Co., Cambridge, MA) was used to apply a sinewave electric field (0.01-1000 Hz and 0-6 V rms). All the experiments were made in a room air conditioned at 25 ( 0.5 °C.
Results and Discussion Reflection Intensity inside the Electric Field. Figure 2 shows a typical example of the waveforms of reflected light observed at the edge of the electrode (position 3B) of T20 cell. The dotted curve is the applied waveform, and the solid one shows the reflected response signal. Though the signal was rather noisy, the same
Figure 3. Amplitude (a) and phase difference (b) in the reflection signals of CS-82 spheres at 25 °C: φ ) 0.048, E ) 10 V/cm for cell T3 (O, b); and E ) 1.5 V/cm for cell T20 (4), position 4B.
sinusoidal curve as that of the applied electric field was obtained in the reflected light intensities. Because the colloidal crystals are charged negatively, lattice spacing will change by the electric field. In our experiments large response signals were obtained always on the electrodes inside the electric field. Figure 2 shows clearly the phase differences appeared between the applied and response signals, which may support the viscoelastic nature of the colloidal crystals.10-12,20,21 The waveforms of the response signals were strongly dependent on the frequencies, voltages of the applied sine waves, and sphere concentrations. In some experimental conditions, the waveform showed two peaks separated within a period of one cycle, which means the existence of the higher-order harmonics generation. Rarely, the second-order harmonics has been generated exclusively.6 Figure 3a shows the frequency (f) dependencies of the amplitudes (A) of the reflected responses for the cells T3 and T20 at 4B position. The values decreased sharply when f increased in the range 0.01-100 Hz. At 1000 Hz the response was too small to be detected. The large
Electrooptic Shear Waves in Colloidal Crystals
Figure 4. Amplitude (a) and phase difference (b) in the reflection signals of CS-82 spheres at 25 °C: φ ) 0.048, f ) 0.05 Hz, cell T3 (O, b); cell T20 (4), position 4B.
structural relaxation times (several to several 10 ms) for the colloidal crystals will be one of the most important reasons why the responsible frequency is quite low.22-24 In other words, the slow translational movement of colloidal spheres covered with the highly extended electrical double layers may prevent the fast response of the crystals to follow up the electric fields. The harmonics component given by the solid circles (b) was observed for T3 cell only at f ) 0.5-5 Hz. The A-values for T20 cell were very large compared with those for T3 cell when comparison was made at f < 0.1 Hz. We should note here that the applied electric field was much high for T3 cell (10 V/cm) compared with that for T20 cell (1.5 V/cm). As is shown in Figure 3b, the phase differences, φ, for the T20 cell were not so sensitive to the change of f, whereas those for T3 decreased substantially when f increased from 0.5 Hz to the higher value. These results support that the translational movement of colloidal lattices in thin cell is highly restricted by the cell walls. Figure 4a,b shows the electric field (E) dependencies of the A- and φ-values, respectively, at the 4B position for the T3 and T20 cells. log A increased linearly when log E increased for both cells. The harmonics component (b) was also observed for T3 cell at high voltages only accompanied with the large deformation in the crystal lattice. The φ-values, on the other hand, were rather insensitive to the electric field as is shown in Figure 4b. Reflection Intensity outside the Electric Field. Acoustic shear wave propagation through colloidal crystals has been reported by several researchers25-27 and by our (20) Benzing, D. W.; Russel, W. B. J. Colloid Interface Sci. 1981, 83, 163. (21) Benzing, D. W.; Russel, W. B. J. Colloid Interface Sci. 1981, 83, 178. (22) Clark, N. A.; Ackerson, B. J. Phys. Rev. Lett. 1980, 44, 1005. (23) Okubo, T. J. Colloid Interface Sci. 1987, 117, 165. (24) Okubo, T. J. Chem. Phys. 1987, 87, 3022. (25) Joanny, J. F. J. Colloid Interface Sci. 1979, 71, 622. (26) O’Brien, R. W.; Midmore, B. R.; Lamb, A. L.; Hunter, R. J. Faraday Discuss. Chem. Soc. 1990, 90, 301. (27) Lindsay, H. M.; Chaikin, P. M. J. Chem. Phys. 1982, 76, 3774.
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Figure 5. Amplitude (a) and phase difference (b) in the fundamental (O, 4) and harmonics (b, 2) in the reflection signals of CS-82 spheres at 25 °C: φ ) 0.048; E ) 1.5 V/cm; f ) 0.05 Hz; cell T20; position 4.
group.5 The purpose of this work was much a more quantitative discussion on a millimeter scale. For all the observation cells in this work the electrooptic responses were observed outside the electric fields. Figure 5 shows the A- and φ-values plotted against distance, l (unit: mm), from the cell edge for the T20 cell. The position of the incident light was shifted every 0.1 mm along the position 4. Measurements from 0 to 10 mm in the abscissa were made on the electrode, whereas the values larger than 10 mm were outside the electrode. The A-values inside the electric fields were large but rather scattered. A decreased sharply when l increased beyond 10 mm. The electrooptic response was, however, still observed clearly in the range of l smaller than 25 mm as is shown in the figure. It is interesting to note that the A-values from fundamentals in the response curve at l ranging 10-15 mm were smaller than those at l ranging 15-20 mm. This will be ascribed to the fact that the harmonics components (b) coexisted often in the former area may consume the wave energy of the fundamentals. The harmonics generation was often observed outside but close to the electric field (10-17 mm of l). The φ-values were quite small on the electrode (l < 10 mm). However, they decreased substantially and linearly as l increased outside the electric field. From the slope the apparent propagation rate was estimated to be 0.18 mm/s. Preliminary electric field pulse propagation experiments by us revealed that the rate was larger than 10 mm/s.28 The reason the rate estimated in this work is very small is not clear yet. However, this work may support the existence of a significant wall effect; i.e., the movement of the spheres in the crystal cages is highly restricted in the region close to the cell wall, where the reflection intensities were observed. Figure 6 shows the influence of the optical path length on the reflection signals along the position 4 using the cells T3 and T10. Surprisingly, A increased substantially (28) Tsuchida, A.; Okubo, T.; Tanahashi, T.; Kuzawa, M. Publication in preparation.
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Figure 6. Amplitude (a) and phase difference (b) in the reflection signals of CS-82 spheres at 25 °C: φ ) 0.048, f ) 0.05 Hz, E ) 10 V/cm for cell T3 (O, b); E ) 3 V/cm for cell T10 (4, 2), position 4.
Figure 7. Amplitude (a) and phase difference (b) in the fundamental (O, 4) and harmonics (b, 2) in the reflection signals of CS-82 spheres at 25 °C: φ ) 0.048; E ) 1.5 V/cm; f ) 0.05 Hz; cell T20; left of position B.
as the optical path length increased both inside and outside the electric field when we take the strengths as the electric fields per unit path length. The A-values were in the order
T3 cell < T10 cell < T20 cell
(2)
This will be again ascribed to the fact that the fluctuation (translational movement) of the respective spheres composing the crystal lattice close to the cell wall is highly restricted compared with the movement in the region far from the cell wall. The phase differences observed for the thin cell were also quite small compared with the broad cell keeping the same order as eq 2. Figure 7a,b shows A- and φ-values observed as a function of distance at the position B of the cell top. In a first glance, the results were quite similar to those shown in Figure 5. The shear wave propagation rate was found to be ca. 0.21 mm/s, which is quite similar to that found in Figure 5, 0.18 mm/s. The apparent propagation rates were not sensitive to direction of the propagation in the same plane. Figure 8 shows the results observed along the side plane just between the electrodes. A always decreased as l increased, when we take into account the factor that coexistence of the fundamentals and the harmonics lowered each of the values significantly as was discussed above. The apparent propagation rate was estimated to be 0.075 mm/s from the initial slope at the positions close to the electrodes in the φ-l plots. It should be mentioned here that the measurements at the vertical direction between the electrodes along the side plane of the cell were omitted in this work. However, we may predict from our previous work6 that the magnitudes of A are rather large, whereas the φ-values outside the electrodes do not decrease with l. The magnitude of the A-values was strongly dependent to the shape of the cell.6 Time-Resolved Reflection Spectroscopy. Figure 9 shows the time-resolved reflection spectra for the T3 cell at the position 4B. The thick solid curve indicates
Figure 8. Amplitude (a) and phase difference (b) in the fundamental (O, 4) and harmonics (b, 2) in the reflection signals of CS-82 spheres at 25 °C: φ ) 0.048; E ) 1.5 V/cm; f ) 0.05 Hz; cell T20; left of side position.
the spectrum without an electric field. Clearly, the reflection peaks shifted slightly toward shorter and then longer wavelengths periodically in the electric field. Figure 10 shows the changes of the peak wavelengths and integrated intensities in the reflection peak profiles. Clearly, the two parameters had the same period as applied frequency. Their magnitudes were not so large for the thin cell. Figures 11and 12 show the spectra for the T10 and T20 cells, respectively, at the same 4B position. Clearly, the
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Figure 9. Reflection spectra of CS-82 spheres at 25 °C: φ ) 0.048, E ) 10 V/cm, f ) 0.05 Hz, (1) t ) 0 s, (2) 3 s, (3) 7 s, (4) 19 s; thick solid line, spectrum at E ) 0 V/cm, cell T3, position 4B.
Figure 11. Reflection spectra of CS-82 spheres at 25 °C: φ ) 0.048, E ) 3 V/cm, f ) 0.05 Hz, (1) t ) 0 s, (2) 4 s, (3) 8 s, (4) 16 s; thick solid line, spectrum at E ) 0 V/cm, cell T10, position 4B.
Figure 10. Integrated intensity (O) and peak wavelength (×) of reflection spectra of CS-82 spheres: E ) 10 V/cm; f ) 0.05 Hz; φ ) 0.048; cell T3; position 4B.
Figure 12. Reflection spectra of CS-82 spheres at 25 °C: φ ) 0.048, E ) 1.5 V/cm, f ) 0.05 Hz, (1) t ) 0 s, (2) 4 s, (3) 8 s, (4) 12 s, (5) 16 s; thick solid line, spectrum at E ) 0 V/cm, cell T20, position 4B.
spectra changed more significantly for the cell having longer path lengths. The largest change in the peak profiles was observed for the thickest cell. These results support strongly the advantage of a thick cell in order to get large electrooptic responses avoiding the wall effect discussed in the preceding section. Integrated intensities obtained from the reflection spectra given in Figures 11 and 12 were also plotted as a function of time, though the graphs showing these were omitted in this work. The higher order harmonics was not observed in these graphs. Conclusions Electrooptic shear waves propagated even outside the electrodes. The viscoelastic shear waves were induced by the synchronous oscillation of the colloidal spheres in a crystal cage. The propagation of the waves was restricted largely by the cell walls. Recently, Stoimenova et al. have reported the existence of the field-induced acoustic waves
in colloidal crystals from the electric light-scattering measurements,15,16 where damping oscillation and the resonance effects were observed. The important role of the viscoelastic properties of the colloidal crystals was supported strongly from the electrooptic effects observed in this work. Theoretical discussion on these electrooptic effects is now in progress in our laboratory. Acknowledgment. This work was supported partly by a Grant-in-Aid for Scientific Research (C) (No. 10650884) from the Ministry of Education, Science, and Culture of Japan and a Grant-in-Aid from the Murata Science Foundation. Dr. M. Komatsu and Dr. M. Hirai of Catalyst & Chemical Ind. Co. (Tokyo and Kita Kyusyu, Japan) are thanked for providing the samples of colloidal silica spheres. LA981128L
