Electrically Induced Shear Waves in Colloidal Crystals

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.

184, 106–111 (1996)

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Electrically Induced Shear Waves in Colloidal Crystals MARIA STOIMENOVA,* ,1 VASSIL DIMITROV,*

AND

TSUNEO OKUBO†

*Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria; and †Department of Applied Chemistry, Gifu University, Gifu 501-11, Japan Received February 7, 1996; accepted May 29, 1996

The static light scattering method is used for the detection of acoustic waves induced in colloidal crystals and liquids by lowfrequency electric pulses. The method is sensitive to both density and shear modes and can be applied for the study of the liquidcrystalline phase transitions. At low fields the variations of light scattering intensity follow both the amplitude and the phase variations of the wave motion and enable the determination of resonance parameters, hence of viscoelastic parameters of the colloidal system. q 1996 Academic Press, Inc.

INTRODUCTION

Recently we communicated a series of experimental observations on the induction of density waves in colloidal crystals upon application of ac electric pulses (1). Resonance frequencies were detected, tentatively related to the deformation of the crystal lattice. This paper presents a more detailed study of the phenomenon, which confirms its relation to electrically induced transverse acoustic waves. The propagation of low-frequency shear waves was predicted both for semidilute polymer solutions (2) and for dilute colloidal crystals (3). They were detected experimentally by mechanical resonance techniques (4, 5) and by photon correlation spectroscopy of the thermal diffuse scattering (6) and were used for the determination of the shear modulus in latex suspensions. The application of electric pulses to colloidal crystals provokes the propagation of similar modes. It gives rise to concentration fluctuations which are detected by different experimental techniques. Concentration gradients induced by dc electric pulses were studied by the Bragg diffraction technique (7). Density fluctuations in ac electric fields were observed by time-resolved reflection spectroscopy and transmitted light spectroscopy (8). The side observation of static light scattering turned out also to be sensitive to the electrically induced translational modes (1). In our electric light scattering experiments on silica colloidal crystals we detect both longitudinal and transverse waves, induced by the field pulses. The present paper deals 1

To whom correspondence should be addressed.

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METHODS AND SAMPLES

The electro-optic observations on the acoustic modes were performed on a conventional apparatus applied in numerous experiments on the anisotropic colloidal systems (9, 1). The measuring cell (of volume about 10 ml) is shown schematically in Fig. 1. Attached to a sled, the cell is placed in a metal (thermostated) box. The movement of the sled in the box is restricted in one direction, along the incident light beam. White unpolarized light is incident on the sample parallel to the electrodes. The cell diameter is 1.8 cm, the distance between the front cell wall (of incidence) and the electrodes is about 0.5 cm. The electrodes are platinum plates of area 1 cm2 , distanced at 2.6 mm. The observation plane is perpendicular to the applied electric field. Light scattering is measured at an observation angle of 907 (point a in Fig. 1) using a photomultiplier/oscilloscope registration. The scattered intensity of the unperturbed system (I0 ) is compensated and the field-induced light scattering variations ( DI Å IE 0 I0 ) with time (t) are directly observed on the oscilloscope. The ac component of the effect is determined by the amplitude of the steady-state oscillations and its variations for different volume fractions are shown by normalized curves. The optical arrangement is preserved upon movement of the cell along the incident beam and this permits the comparison of pictures between and outside the electrodes (points a–f in Fig. 1). The variable parameter in the course of this procedure is the optical pathlength. Since the intensity of light scattered by the unperturbed system decreases gradually from the front wall to the electrodes, the observed light scattering variations are followed as relative quantities. The colloidal silica spheres used in the investigation (a product of Catalyst & Chemicals Ind. Co., Tokyo) are the same which were used in our previous paper (1), spheres of mean diameter 103 nm and charge density 0.38 mC/cm2 .

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0021-9797/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.

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with the distinction of the acoustic modes, paying particular attention to the transverse phonons. Since the longitudinal mode is of a more general character, it will be considered in a separate paper.

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FIG. 1. Scheme of the electro-optic measuring cell.

Before use the sample was treated continuously on a mixed bed of cation- and anion-exchange resins (Bio-Rad, AG501X8(D), 20–50 mesh). The same resins were used for the deionization of water needed for the suspension preparation. The suspensions are obtained by dilution of the stock solution (sphere volume fraction f Å 0.08) with water and are further kept in contact with the ion-exchange resins for a week in order to achieve the crystal state (conductivity below 10 06 ohms 01 at 257C). The low volume fractions treated in the paper display beautiful crystal phases consisting of very large single crystals (8). EXPERIMENTAL RESULTS

As already announced (1), the investigated samples of isotropic colloidal particles present electro-optic effects both

FIG. 2. Variations of the scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant field intensity (U Å 20 V) and different frequencies: (a) f Å 0.4 Hz; (b) f Å 0.3 Hz; (c) f Å 0.2 Hz. Sphere volume fraction f Å 0.013.

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FIG. 3. Variations of the scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant field frequency ( f Å 0.6 Hz) and different field intensities: (a) U Å 20 V; (b) U Å 40 V. Sphere volume fraction f Å 0.013.

in the liquid and in the crystal phases of the suspensions. Generally speaking, they are displayed at very low frequencies. The decrease of field frequency below 1 Hz permits their observation at comparatively low field intensities. Figures 2 and 3 present typical electro-optic responses for the liquid state of the samples. Similar to the responses demonstrated for the crystal state (1), at sufficiently low fields (depending on frequency) only an ac component is displayed, which is linear with field intensity and follows field frequency with phase lag p /2. The increase of field intensity introduces a dc component and higher harmonics in the ac response. A basic difference in the behavior of the samples in the liquid and the crystal phases is the appearance of a second mode of lower relaxation time and damping coefficient. In Fig. 4 the variations of the amplitude of the ac component are presented for the two phases. In parallel with the increase of the low-frequency effects (the points remain beyond the scale of the figure) the crystal samples present effects in a wider frequency range, displaying reproducible resonance peaks. The latter effects are of significantly smaller amplitude compared to the low-frequency mode and higher field intensities are required for their observation. Figure 5 shows the field intensity dependence of the frequency curves for a crystal sample. The oscillograms of typical effects obtained at the peak frequencies are presented in Figs. 6 and 7. They display an oscillating decay which indicates the underdamped behavior of this mode. More pronounced is the participation of a

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FIG. 4. Dependencies of the amplitude of the ac component of DI on the electric field frequency (at constant field intensity U Å 70 V) for the liquid and the crystal phases of two volume fractions: ( l, l ) liquid phase; ( L, s ) crystal phase; ( l, L ) f Å 0.007; ( l, s ) f Å 0.013. In the inset: similar curves measured at field intensity U Å 10 V ( f Å 0.013).

slowly relaxing dc component. As illustrated in Fig. 7 this component is strongly dependent on the initial phase of the external field. In parallel, the amplitude of the ac effect rapidly saturates with field intensity. The high ratio of the dc and the ac components hampers the detailed observation of the resonance effects.

FIG. 5. Dependencies of the amplitude of the ac component of DI on the electric field frequency at different field intensities: ( L ) U Å 4 V; ( l ) U Å 7 V; ( n ) U Å 10 V; ( l ) U Å 30 V; ( s ) U Å 50 V. Sphere volume fraction f Å 0.007.

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FIG. 6. Variations of the scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant field frequency ( f Å 17 Hz) and different field intensities: (a) U Å 40 V; (b) U Å 60 V. Sphere volume fraction f Å 0.013.

Due to the low damping, the investigated mode is propagating and can be observed outside the electrode space. This is achieved by moving the measuring cell in the plane of observation, searching for the maximal optical response. Figures 8 and 9 show the comparison of the observed electrooptic responses between and outside the electrodes at equal electric field parameters, for a sample of shorter deionization time (three days). The ratio of the dc and the ac components changes drastically and the linear dependence of the alternating component is preserved up to considerably higher fields. The ac amplitude increases significantly and residual oscillations are obtained in cases when the interelectrode signal does not detect them. Figure 10 illustrates the variations of the electro-optic response obtained by consequent variation of the distance between the observed spot and the electrodes (points b–f in Fig. 1, step 1 mm). Both the amplitude and the phase of the oscillations are varying and, despite the evident signs of ‘‘bad acoustics,’’ they are demonstrating the formation of standing waves. Measuring the ac amplitude at the maximum we obtain its frequency dependence. Although the measuring cell is asymmetric and does not enhance the precise determination of characteristic frequencies, the observed effects are so large that they permit the detection of resonance peaks. Figure 11 presents normalized frequency curves of the ac component (obtained by observation outside the electrodes) for three samples of different sphere volume fractions. They display clearly expressed peaks at frequencies which increase with the volume fraction. Figures 12 and 13 demon-

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FIG. 7. Variations of the scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant parameters ( f Å 17 Hz, U Å 70 V) and different initial phases. Sphere volume fraction f Å 0.013.

strate the phase variations of the signal around the resonance peaks for one of the samples. The peak frequencies almost coincide with those detected in the inter-electrode space, but

FIG. 9. Variations of scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant parameters ( f Å 9 Hz, U Å 80 V), observed at different points of the sample: (a) between the electrodes; (b) outside the electrodes. Sphere volume fraction f Å 0.013, storage time 3 days.

they are of larger amplitude and can be detected in a wider range of volume fractions. DISCUSSION

FIG. 8. Variations of scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant parameters ( f Å 9 Hz, U Å 40 V), observed at different points of the sample: (a) between the electrodes; (b) outside the electrodes. Sphere volume fraction f Å 0.013, storage time 3 days.

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The electro-acoustic effects in colloidal dispersions (10) have received considerable attention in the last ten years. Theoretical treatment of the phenomena in dilute colloids is performed in the ‘‘thin double layer’’ approximation (11). Despite further extensions of the theories (12), they retain the restriction to gas-like colloids. In our knowledge, colloidal crystals and liquids are not considered in this aspect. The above-presented results demonstrate the propagation of acoustic waves in the plane perpendicular to the external field direction. The large scale of the observed modes (frequencies of the order of hertz and wavelengths of the order of millimeters) enhances the visual observation of the phenomena. One can distinguish with the naked eye the propagating longitudinal (appearance of bright and dark bands) and shear (oscillation of bright spots) acoustic waves. The observed shear oscillations are actually along the electric field, while the concentration fluctuates in the transverse direction. This is the probable cause for the p /2 phase lag of the optical response detected between the electrodes. The field-induced acoustic waves provoke fluctuations of the systems’ dielectric constant, creating optical anisotropy in the sample. Due to the large scale of their wavelengths (of the order of the observed area) and very low characteristic

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FIG. 10. Variations of scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant parameters ( f Å 5.5 Hz, U Å 40 V) observed at different points of the sample pointed out in figure 1. Sphere volume fraction f Å 0.007.

FIG. 12. Variations of the scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant field intensity ( U Å 70 V) and different frequencies: (a) f Å 3.2 Hz; (b) f Å 4.7 Hz; (c) f Å 6 Hz. Sphere volume fraction f Å 0.007.

frequencies they are not averaged in the optical response of the system, but the scattered light intensity follows the local variations of the dielectric constant (the sign of the effect is changing with the compression and the rarefaction of the colloid). This yields the possibility of performing ‘‘electrooptic spectroscopy’’ of the sample and thus of distinguishing the different acoustic modes.

The presented results confirm our preliminary assumption (1) that the oscillating decay of the electro-optic responses in colloidal crystals is related to the propagation of electrically induced shear waves in the sample. As predicted by Joanny (3) and proved experimentally by a number of authors (4, 5) the propagation of this mode is enhanced at low frequencies (hertz range) due to the low damping. For wavelengths much larger than the interparticle distance the dispersion equation of the transverse waves is (4): v 2 / i( h / r )k 2v 0 (E/ r )k 2 Å 0, where r ( Å1 g/cm2 ) is the mass density, h ( Å10 02 poise) is the viscosity of the solvent (water), and E is the shear modulus of the sample. For a dilute colloidal crystal E is of the order of 10 dyn/cm and the sound velocity V ( ÅYE/ r ) à 1 4 5 cm/s. Respectively, the microscopic relaxation time t ( Åh /E) à 1 4 10 ms and the attenuation length l ( Å (Imk) 01 Å 2 V/ v 2t ) à 1 4 10 cm. Hence for frequencies much smaller than 1 kHz the dissipation is small and the shear waves are propagating. A cell of dimensions of the order of centimeters enhances the formation of standing waves. From the variation of the peaks in Fig. 11 we can deduce speculatively a quadratic dependence of the shear elastic modulus on the sphere volume fraction in the diluted range. An adequate measuring cell is needed for a precise determination of the absolute values of the elastic modulus. The relaxation time of the longitudinal mode is estimated to be several orders of magnitude lower (4): t long ( Åtah 2 /b 3 ) à 10 4 t, where t ( à1 4 10 ms) is the microscopic relaxation time, a ( à100 nm) is the sphere diameter, b ( à500 nm) is the interparticle distance, h is a distance of the order

FIG. 11. Dependencies of the amplitude of the ac component of DI on the electric field frequency (at constant field intensity U Å 50 V) for different volume fractions: ( l ) f Å 0.007; ( n ) f Å 0.01; ( l ) f Å 0.013.

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FIG. 13. Variations of the scattered light intensity ( DI, arbitrary units) upon application of ac electric pulses ( – rrrr) of constant field intensity (U Å 70 V) and different frequencies: (a) f Å 6.4 Hz; (b) f Å 8.2 Hz; (c) f Å 10.2 Hz. Sphere volume fraction f Å 0.007.

of the longitudinal wavelength ( à1 4 10 mm). Despite the very low relaxation time of this mode, it is important to notify, on one hand, the enormous electro-optic responses obtained at low frequencies in the field intensity range conventionally used in colloidal electro-optics (Figs. 1 and 2) and, on the other hand, the strong asymmetry of the obtained signals resulting in a large dc component. With the increase of field intensity the tail of this component could reach the kilohertz range. Since the density waves concern all the phase states of the colloidal dispersions, it deserves particular attention in the electro-optic studies of colloids. The nature of the double frequency of the electro-optic responses appearing with the increase of field intensity (which is of particular interest due to its similarity to the responses of electrically induced anisotropy fluctuations) is still under investigation. Evidently it reflects the interference of nonlinear effects (products of the perturbations of the involved quantities and interaction of acoustic waves). Since higher harmonics could induce resonance-like behavior, the interpretation of the detected peaks (Fig. 11) requires attentive verification. The observed phenomena could be a topic of interest in different aspects: Since the field-induced acoustic waves create optical anisotropy in the sample, they could be observed by any optical method conventionally used in the electrooptic studies of colloidal dispersions (birefringence, dichroism, fluorescence, etc.). Particular expectations could be related to light depolarization effects. The electro-optic methods could be applied to the determination of the shear elastic

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modulus and other viscoelastic parameters of the colloidal crystal, as well as of their variation in the course of phase transitions. A symmetrical measuring cell convenient for theoretical treatment (i.e., for precise determination of the wavenumber) would be sufficient for the purpose. An evident advantage of the method is the possibility of observing simultaneously the electro-optic responses between and outside the electrodes. Technically this could be achieved by a single pulse and might help to obtain the precise relation of the electric (surface charge and z potential) and the viscoelastic parameters of the colloidal systems by the testing of different theoretical schemes. The necessity for investigation of the translational modes in anisotropic colloidal systems is obvious. In semidilute colloids the concentration and anisotropy fluctuations are correlated and this could explain at least part of the curious low-frequency effects widely studied in colloidal electro-optics. Since the acoustic modes in semidilute polymers and colloids are quite similar (2, 3), the above phenomena can also be observed in polymer solutions, particularly in gels. This might help to achieve the control of gel electrophoresis. Other practical applications of the obtained effects could also be expected. A simple example is their application for teaching purposes concerning wave motion and phase transitions. The light modulation properties of the method deserve attention as well. ACKNOWLEDGMENTS Financial support from the Bulgarian National Fund ‘‘Scientific Studies’’ (Project No. X-451) is gratefully acknowledged. Catalyst & Chemicals Co., Tokyo, is appreciated for kindly providing the silica spheres.

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