JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
207, 130 –136 (1998)
CS985726
Electro-optic Properties of Colloidal Crystals As Studied by Reflection Spectroscopy Tsuneo Okubo,1 Akira Tsuchida, Tomofumi Tanahashi, and Atsue Iwata Department of Applied Chemistry, Gifu University, Gifu 501-1193 Japan Received March 26, 1998; revised June 2, 1998
Electro-optic properties of colloidal crystals of silica spheres in the exhaustively deionized aqueous suspension have been studied by the reflection spectroscopy using a T-type cell. Acoustic shear waves are induced when sine-wave electric fields ranging from 0.01 to 1 Hz are applied. Modulation effects of the crystals on the applied AC fields such as phase delay, change in response intensity, waveform transformation, and harmonics generation are observed. The shear waves propagate outside the electrodes where the electric field is absent. The synchronous fluctuation of the colloidal spheres including expanded electrical double layers in the crystal lattice will be one of the main causes of the electro-optic nature of the crystals. © 1998 Academic Press Key Words: electro-optics; colloidal crystals; reflection spectroscopy; harmonics generation; visco-elastic solid; synchronization.
1. INTRODUCTION
Electro-optic effects such as Pockels and Kerr effects, where the change of refractive index of substances is induced by an applied electric field, have been extensively investigated for many kinds of chemical substances (1, 2). In this paper, the electro-optic effects are discussed in detail for the colloidal crystal systems. When a suspension of monodispersed colloidal spheres is deionized thoroughly in polar solvents such as water, a crystal-like structure is formed by the extended electrical double layers around the spheres and the intersphere repulsive forces (3–5). The width of the electrical double layers is approximated by the Debye screening length, D 1 , given by D 1 5 ~4 p e 2n/ e k BT! 21/ 2,
[1]
where e is the electronic charge, e is the dielectric constant of solvent, k B is the Boltzmann constant, T is the absolute temperature, and n is the concentration of “diffusible” or “freestate” simple ions in suspension. Note that the maximum value of D 1 observed for the exhaustively deionized suspension in water is ca. 1 mm, and much longer compared with the size of colloidal particles. Since the sheath of electrical double layer is 1
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very soft and the colloidal spheres are charged negatively in general, lattice spacing changes reversibly when an alternating electric field is applied (6 –11). Change in the reflection colors also occurs by an electric field. Stoimenova et al. have studied the electro-optic effects of colloidal suspensions using the electric field light scattering technique (12–14). In this method, the electro-optic effect, a 5 (I e 2 I 0 )/I 0 , was measured, where I e and I 0 are the scattered light intensities in the presence and the absence of an electric field, respectively. The electro-optic effects for colloidal crystals such as the resonance frequencies and the acoustic shear waves have been reported, for the first time, by the joint work between Bulgarian groups and ours (15–17). Furthermore, we have studied the electro-optic effects of colloidal crystals by the reflection intensity and the time-resolved reflection spectroscopy using several types of observation cells (18 –20). The significant harmonic generation has been observed using an O-type cell consisting of two parallel glass plates coated with the transparent electrical conducting membranes inside the cell wall (18). The synchronous fluctuation of the colloidal spheres in the crystal lattices and the transformation between two subphases of lattice structures, i.e., face-centered cubic (fcc) and body-centered cubic (bcc), have been clarified as causes of harmonic generation. The propagation of the shear waves induced electrically has been observed using an I-type cell consisting of four electrodes inside (20). The measurements were made from the whole directions around the outside cell wall. Phase differences were substantial and explained by the symmetric nature in the shear waves. It should be mentioned here that the electrohydrodynamic effects have been reported recently in relation to the phase delay induced by the colloidal particles with extended electrical double layers (21, 22). When an AC electric field is applied to an aqueous suspension of colloidal particles, synchronous spinning, lateral transfer, and self-organization of the particles are observed. These phenomena have been analyzed theoretically, and competition between the electric potential energies of mutual polarization of two neighboring particles was proposed to be one of the causes of the electrohydrodynamic effects (23).
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FIG. 1.
Schematic representation of the reflection intensity measurements.
In this report, electro-optic properties of colloidal crystals will be discussed in detail using a T-type bridge-shaped cell, where the optical measurements are made perpendicular to the electric field. The significant harmonic generation and the waveform transformation were observed. 2. EXPERIMENTAL
2.1. Materials
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FIG. 3. Waveforms of the applied(dotted curve)- and reflection(solid curve)-signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 3 V and f 5 0.05 Hz.
then treated with a mixed bed of cation- and anion-exchange resins (Bio-Rad, AG501-X8 (D), 20-50 mesh) for more than 4 years in order to delete ionic impurities completely. Water used for sample preparation was obtained from Milli-Q water system (Milli-RO Plus and Milli-Q Plus, Millipore Ltd., Bedford, MA). 2.2. Reflection Spectroscopy
Monodispersed colloidal silica spheres (CS-82) were kindly donated by Catalyst & Chemicals Ind. Co. (Tokyo). Diameter was 103 nm (mean diameter) 6 13.2 nm (standard deviation) by electron microscopy (TEM, JEOL, Tokyo, Type JEM-2000FX). The polydispersity index given by the standard deviation divided by the mean diameter was 0.13. Charge density of the strongly acidic groups was 0.38 mC/cm2, which was determined by conductometric titration with a Wayne–Kerr autobalance precision bridge, model B331 mark II (24). The sphere sample was further purified carefully several times using an ultrafiltration cell (model 202, membrane: Diaflo XM, Amicon Co., Lexington, MA) and
Two kinds of spectroscopic measurements, i.e., the optical reflection intensities and reflection spectra, were made using the T-type observation cell shown in Fig. 1. The cell is made of Pyrex, is bridge shaped, and consists of rectangular parallel plates (11 mm in height, 20 mm in width, and 9 mm in depth) and two cylinders (70 mm in height and 19 mm in diameter). Two platinum electrodes (10 mm 3 12 mm, 27 mm in distance) were set on both sides of the observation cell to cover all the central area of the cell with the electric field. The sample suspension was sealed tightly by Parafilm. The suspension in the cell was coexisted with the mixed bed of the ion-exchange resins at least 7 days before and during the measurements. The
FIG. 2. Waveforms of the applied(dotted curve)- and reflection(solid curve)-signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 3 V and f 5 0.1 Hz.
FIG. 4. Waveforms of the applied(dotted curve)- and reflection(solid curve)-signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 10 V and f 5 0.07 Hz.
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FIG. 5. X-Y plots of the reflection signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 10 V and f 5 0.07 Hz.
sphere concentrations examined were 0.012, 0.048, and 0.096 in volume fraction (f). A halogen light source (PHL-50, Sigma Koki, Saitama) and a Y-type optical fiber were used. The focus size is smaller than 1.5 mm in diameter (18). The measurements were made perpendicular to the cell wall and the electric field in most cases. Intensity of the reflected light was detected by a photomultiplier and then recorded on a digital oscilloscope (DL1300, Yokogawa, Tokyo). An oscillator (Type 4025, Krohn– Hite Co., Cambridge, MA) was used to apply an electric field (10 V rms maximum). Time-resolved reflection spectra were measured on a photonic multichannel analyzer (PMA-50, Hamamatsu Photonics, Hamamatsu) using the same optical fiber cable alignment as the reflection intensity measurements. All the experiments were made at 25°C.
FIG. 7. Reflection signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048 and E 5 3 V.
curve represents the applied waveform and the solid one shows the reflected signal. Though the signal is rather noisy, the same sinusoidal curve as that of the applied electric field is obtained in the reflected light intensities. Because the colloidal crystals are charged negatively, lattice spacing will change by the
3. RESULTS AND DISCUSSION
3.1. Reflection Intensity Measurements Figure 2 shows a typical example of the waveforms of reflected light at the central position of the cell. The dotted
FIG. 6. Waveforms of the applied(dotted curve)- and reflection(solid curve)-signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 5 V and f 5 0.02 Hz.
FIG. 8. Reflection signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048 and f 5 0.05 Hz.
ELECTRO-OPTICS OF COLLOIDAL CRYSTALS
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FIG. 9. Amplitudes of the fundamental (open circle) and harmonics (solid circle) peaks in the reflection signals of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 3 V and f 5 0.05 Hz. Picture inserted shows the positions observed.
electric field. This change must induce the modulation of the waveforms. In our experiments large response signals were obtained always at the central positions between the electrodes. The waveform of the response signal is strongly dependent on the frequency and strength of the applied sine wave and concentration of the spheres. Figure 3 shows an another example of the waveforms at the central position of the cell. The reflection intensity changes periodically, and the waveform observed deviates from the applied sine wave. In the figure the response curve has two peaks, large and small, within a period of one cycle. This shows that the harmonic generation occurs with the nonlinear electro-optic response of the crystal lattice (18). This figure also shows clearly the presence of the phase difference between the applied and response signals, which supports the viscoelastic nature of the colloidal crystals (25, 26). The beautiful second-order harmonics generation was observed for the colloidal crystals by selection of the experimen-
FIG. 10. Fourier transform of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 10 V and f 5 0.07 Hz. Frequency at n 5 1 corresponds to 0.07 Hz.
FIG. 11. Fourier transform of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, E 5 3 V, a: f 5 0.01 Hz (n 5 1: 0.01 Hz), b: 0.02 Hz, c: 0.05 Hz, d: 0.07 Hz and e: 0.1 Hz.
tal parameters such as sine-wave frequency and voltage. Figure 4 is one of the best examples showing the second-order harmonics generation. The response signal is almost sinusoidal, however, the frequency is doubled, 0.14 Hz. X–Y-type plots between the applied electric field intensities I in and the response intensities I out are shown in Fig. 5. A node is observed in the horizontal axis, which confirms the existence of double frequency component, i.e., generation of the second-order harmonics. Figure 6 shows the response waveform when a rectangular wave with low frequency is applied to the crystals. Surprisingly, a triangle wave with the same frequency as that of applied one is observed. The slow translational movement of colloidal spheres covered with the extended electrical double layers is one of the main causes of the waveform transformation. Figure 7 shows frequency ( f ) dependencies of the phase differences (w) and the amplitudes ( A) of the reflected signals. Changes in the w values were rather insensitive to frequencies in the range from 0.01 to 0.1 Hz, whereas A decreased sharply when f increased in the range higher than 0.02 Hz. At frequencies higher than 1 Hz, the response is too small to be detected. The largest amplitude is obtained when the sphere concentration is the highest, f 5 0.096 in our work. Generally speaking, the elastic modulus (G) of colloidal crystals increases proportionally to the number of spheres in a unit volume of suspension (27). It is highly plausible that the large G value of
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3.2. Reflection Intensity Measurements Outside the Electric Field
FIG. 12. Fourier transform of colloidal crystals of CS-82 spheres at 25°C. f 5 0.048, f 5 0.05 Hz (n 5 1: 0.01 Hz), a: E 5 0.7 V, b: 1 V, c: 2 V, d: 5 V and e: 10 V.
Figure 9 shows the reflection amplitudes measured from the whole directions around the cell wall. The strong responses are observed in the area between the electrodes (positions 1 to 3 1 and 11 to 13 in the figure). Interestingly, about 10 of the magnitude of response inside the electric field is still observed outside the field (positions 4 to 10 and 14 to 20). This shows that the shear waves propagate synchronously as acoustic shear waves even to the area where no electric field is applied. An acoustic shear wave and its propagation for the colloidal crystals have been discussed by several researchers (8, 9, 22, 28 –30). Our observation here is believed strongly to be ascribed to the elastic nature of the colloidal crystals. It should be mentioned here that most of the waveforms outside are sinusoidal when sine-wave field is applied. Interestingly, second-order and higher harmonics generations are observed in the areas between the electrodes. The strength of the harmonics is highly dependent on the positions observed. The synchronous and elastic movements of the constituent spheres in the crystal, which is induced by the electric field, are essential for the harmonics generation. 3.3. Fourier Transform Analyses
colloidal crystals compared with the viscosity of the suspension is preferable for the shear wave propagation, though the quantitative discussion is not easy at present. Figure 8 shows the applied field (E) dependencies of the w and A values. The former keep constant, ca. 2270° irrespective of the E values from 0 to 3 V, but decrease as E increases. On the other hand, the latter increase almost linearly when E increases from 0 to 3 V, but exponentially for E-values higher than 3 V.
FIG. 13.
For further quantitative analysis on the harmonics generation, Fourier-transformed spectra are taken in Fig. 10. The horizontal axis denotes the order of the harmonics, e.g., n 5 1 for the fundamental and n 5 2 for the second-order harmonics. Clearly, the component of the second-order harmonics (0.14 Hz) is quite substantial. Causes of the harmonics generation have been discussed in a previous paper from the time-resolved reflection spectroscopy (18). The synchronous fluctuation of each colloidal spheres coated with the expanded electrical
Peak wavelengths of reflection spectra of CS-82 spheres as a function of time at 25°C. f 5 0.048, E 5 10 V and f 5 0.02 Hz.
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FIG. 14.
Integrated intensity of reflection spectra of CS-82 spheres as a function of time at 25°C. f 5 0.048, E 5 10 V and f 5 0.02 Hz.
double layers in the crystal cage and the transformation between two subphases of the lattice structures, fcc and bcc, are very important. Again, the nonlinear electro-optic properties must originate from the viscoelastic nature of the colloidal crystals. Figure 11 shows the Fourier-transformed spectra when f changes from 0.01 to 0.1 Hz. At f 5 0.01 Hz the largest second-order harmonics appears. The second-order component decreases rapidly as f increases. Large signal noises observed in Fig. 11e are due to the small response amplitudes at high frequencies. Figure 12 shows the Fourier transforms at various E values from 0.7 to 10 V. Clearly, large second-order harmonics generates at high voltages. In conclusion, the large second-order harmonics generations are observed at the low applied frequencies and/or high applied voltages. The large magnitude of the deformation in the crystal lattice will be important for the modulation effect. 3.4. Time-Resolved Reflection Spectroscopy Figure 13 shows the change of the peak wavelengths in the time-resolved reflection spectra. The periodical peak shifts are observed with the same period as applied frequency. Figure 14 shows the integrated intensities of the reflection peak profiles for the same time range as is shown in Fig. 13. Clearly, two peaks appear in one cycle of the applied field, indicating the second-order harmonics generation. Transformation between the subphases fcc and bcc was not observed under this experimental condition (18). Therefore, one of the main causes for the harmonics generation must be the nonlinear nature of the colloidal crystals themselves. In conclusion, propagation of the shear waves causes the waveform transformation. The viscoelastic shear wave must be
induced by the synchronous oscillation of the colloidal spheres in a crystal cage. Recently, Stoimenova et al. have reported the existence of the field-induced acoustic waves in colloidal crystals by the electric light-scattering measurements (15, 16), where the damping oscillation and the resonance effects were observed. The important role of the viscoelastic properties of the colloidal crystals is clear for the nonlinear electro-optics. ACKNOWLEDGMENTS This work was supported partly by a grant-in-aid to A.T. from the Housou Bunka Kikin (Japan). Drs. M. Komatsu and M. Hirai of Catalyst & Chemical Ind. Co. (Tokyo and Kita Kyusyu) are thanked for providing the sample of the colloidal silica spheres. The authors acknowledge Professor Dr. M. Stoimenova, Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia, Bulgaria, for her stimulating discussion on the electro-optic properties of colloidal suspensions.
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