pubs.acs.org/Langmuir © 2010 American Chemical Society
Electric Response of Nonspherical and Spherical Silica Particle Dispersions to Ac Electric Field Satoshi Nishimura,*,† Hideo Matsumura,‡ Katsunori Kosuge,§ and Tomohiko Yamaguchi† †
Nanotechnology Research Institute, ‡Photonic Research Institute, and §Research Institute for Environmental Management Technology, National Institute of Advanced Industrial Science & Technology (AIST), Tsukuba, Higashi1-1-1, Tsukuba, Ibaraki, 305-8565, Japan Received January 29, 2010. Revised Manuscript Received March 30, 2010
For the purpose of revealing unique aspects of the electrical double layer (EDL) around nonspherical particles, we focus on a silica square platelike particle with well-defined shape, i.e., H-ilerite. Impedance measurements for suspensions of silica spherical and square platelike particles are performed to examine ion concentration polarization and its relaxation in their EDLs under ac electric fields that are high enough to orient H-ilerite to electric fields and form pearl chains of particles. For a silica spherical particle, the relaxation frequency of ion concentration polarization in EDL around the particles is independent of applied electric field strength and the volume fraction of the particles in suspension. The conductance ratios of silica particle suspension to its supernatant show a good linear relation against the volume fraction independently of applied electric field strength. For H-ilerite, at low electric field strength where there is neither electric orientation nor pearl chain formation, the conductance ratio also shows a linear relation against the volume fraction. The slope of the conductance ratio to the volume fraction increases and the relaxation frequency decreases as applied electric field strength increases. In addition, two linear relations with different slopes, where the slope becomes steep at higher volume fractions, appear in the plots of the conductance ratio against the volume fraction. Such a unique response of H-ilerite suspension to electric field can be explained by the electric orientation of H-ilerite accompanying pearl chain formation.
Introduction When an electric field is applied to colloidal suspension, counterions in the electrical double layer (EDL) around the colloidal particles accumulate on one side of the EDL and are deficient on the other side.1 Such a nonequilibrium state of EDL has been well-known as the ion concentration polarization of EDL. The ion concentration polarization of EDL causes the pearl chain formation and dielectric phoresis.2-4 These phenomena have been extensively applied to nanoengineering processes such as biosensor,5 DNA manipulation,6 cell separation,7 and laboratoryon-tips8 where various materials ranging from colloidal materials to polymer molecules are targeted. The performances of these applications are significantly dominated by the EDL properties and shape of the targeted materials as well as external factors such as applied electric field, ionic strength, and dielectric property of media surrounding them. Various shapes of targeted materials are manipulated under an ac electric field in the nanoengineering applications, and so it is *To whom correspondence should be addressed. E-mail: s.nishimura@ aist.go.jp. (1) Dukhin, S. S.; Shilov, V. N. Adv. Colloid Interface Sci. 1980, 13, 153. (2) Hughese, M. P. Nanotechnology 2000, 11, 124. (3) Muth, E. Kolloid-Z. 1927, 41, 97. Kruyt, R.; Vogel, J. G. Kolloid-Z. 1941, 95, 2. Matsumura, H. Colloids Surf., A 1995, 104, 343. (4) Pohl, A. H.; Hawk, Ira. Science 1996, 272, 706. Matsue, T.; Matsumoto, N.; Uchida, A. Electrochim. Acta 1997, 42, 3251. (5) Velev, O. D.; Laler, E. W. Langmuir 1999, 15, 3693. (6) Washizu, M.; Kurosawa, O.; Arai, I.; Suzuki, S.; Shimamoto, N. IEEE Trans. Ind. Appl. 1995, 36, 1010. Germishuizen, W. A.; Tosch, P.; Middelberg, P. J.; W€alti, C.; Dacies, A. G.; Writz, R.; Pepper, M. J. Appl. Phys. 2005, 97, 014702. W€alti, C.; Tosch, P.; Germishuizen, W. A.; Kaminski, C. F. Appl. Phys. Lett. 2006, 88, 153901. (7) Pohl, A. H.; Pollock, J. K. In Method of Cell Separation; Castimopoolas, N., Ed.; Plenum Press; New York, 1978; Vol. 1; p67. Pohl, A. H.; Pollock, J. K. In Modern Bioelectrochemistry; Gutmann, F., Keyzer, H., Ed.; Plenum Press; New York, 1986; Chapter 12; p329. (8) Hughes, M. P. Electrophoresis 2002, 23, 2569.
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important to understand EDL characteristics of nonspherical particles under an ac electric field. However, it seems to be more complicated than that for spherical particles with isotropic shape due to the presence of asymmetric EDL. For the purpose of investigating asymmetric EDL around nonspherical particles under an ac electric field, we focus on H-ilerite, i.e., silica square platelike particles, because of its own well-defined anisotropic shape and surface charge property. By comparing with silica spherical particles of which symmetric EDL’s properties have been well examined traditionally, it enables one to extract the characteristics of asymmetric EDL around H-ilerite platelike particles. Impedance measurement for colloidal suspensions is one of the most useful techniques to extract nonequilibrium properties of EDL that are unavailable from electrokinetic measurements but have been conducted under low electric field strength of around 0.1 V/cm.9 One reason is to avoid perturbation of experimental system such as electrolysis and polarization of electrodes. Another reason is to assess the EDL properties of isolated and monodispersed particles under the condition that the interaction among neighboring particles can be neglected. However, the strength of applied electric field for the above applications is at least 10 times higher in magnitude than that for the fundamental impedance measurements because it is necessary to induce the response of targeted materials to electric field and/or the interactions among them in order to obtain the optimum performance of the applications. In this study, we investigate nonequilibrium EDL properties such as ion concentration polarization and relaxation of asymmetric (9) Kijlstra, J.; van Leeuwen, H. P.; Lyklema, J. J. Chem. Soc. Faraday Trans. 1992, 88, 3441. (b) Kijlstra, J.; van Leeuwen, H. P.; Lyklema, J. Langmuir 1993, 9, 1625. (c) Kijlstra, J.; Wegh, R. A. J.; van Leeuwen, H. P.; Lyklema, J. J. Electroanal. Chem. 1994, 366, 37.
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Figure 1. Microscopic observations for silica spherical and H-ilerite particles: (a) optical microscopic images of silica particles; (b) SEM images of H-ilerite; (c) schematic diagram for shape and size of silica and H-ilerite particles.
EDL for nonspherical particles by means of impedance measurements performed under ac electric fields that are high enough to orient the platelike particle to the electric fields and form their own pearl chains.
Experimental Section Materials. As a spherical particle, monodispersed silica particle with an average diameter of 1.62 μm and relative density of 2 was supplied from Nippon Shokubai Co., Ltd. (Figure 1a). Prior to use for experiments, the silica particles were dispersed in MilliQ water ultrasonically, followed by rinsing with water repeatedly until the conductance of supernatant reached that of water. We used Hþ-exchanged ilerite (H-ilerite) with a form of square plate as a nonspherical particle (Figure 1b). H-ilerite was prepared from layered sodium silicate ilerite with the molar ratio of 1Na2O:8SiO2:10H2O, that is to say, Na-ilerite, by exchanging Naþ ions in the interlayer of Na-ilerite to Hþ ions. Na-ilerite was hydrothermally synthesized from the mixture of colloidal silica with a SiO2 content of about 80% (Wako gel Q63), sodium hydroxide (Wako, analytical grade) and water in a Teflon-lined autoclave.10 The autoclave was heated at 115 C for 3-4 weeks in an oven. The product of the hydrothermal reaction, i.e., Nailerite, was rinsed with Milli-Q water by centrifugation repeatedly until conductivity of supernatant reached that of water, followed by dispersing Na-ilerite into 2 L of 0.1 M HCl aqueous solution for 8hours to exchange Naþ to Hþ in the interlayer of Na-ilerite crystals. The products were rinsed with water repeatedly until the pH of supernatant reached that of water, and then stored as concentrated suspensions. The products obtained by the hydrothermal reaction and the cation-exchanging treatment were identified as X-ray powder diffraction patterns of Na- and H-ilerite crystals using a diffract meter using CuKR radiation (Rigaku Co. Ltd., RINT 2000), respectively. H-ilerite was sized by centrifugation in polypropylene tubes. H-ilerite with the average size of 3.5 3.5 0.17 μm, which was almost the same volume of a silica spherical particle with a diameter of 1.6 μm (Figure 1c), was obtained with centrifugal force of 400-600G for 5 min in order to compare with the results for the silica particles. The relative density of H-ilerite was estimated to be 2.1 from chemical (10) Brenn, U.; Ernst, H.; Freude, D.; Herrmann, R.; J€ahnig, R.; Karge, H. G.; K€arger, J.; K€onig, T.; M€adler, B.; Pingel, U,-T.; Prochnow, D.; Schwieger, W. Microporous Microporous Mater. 2000, 40, 43. (11) Vortmann, S.; Rius, J.; Siegmann, S.; Hermann, G. J. Phys. Chem. B 1997, 101, 1292.
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compositions and crystal structure data.11 The side length and thickness of the H-ilerite were estimated by Normarskitype differential interference optical microscope (Olympus Co., Ltd., Japan, BH-2) and an atomic force microscope system (Digital Instrument Co. Ltd., Nanoscope III), respectively. Sodium chloride (Wako, analytical grade) was used as a supporting electrolyte without further purification. For all measurements and sample preparations, Milli-Q water was used in this study. Impedance Measurements. Impedance measurements for suspensions and their supernatant were performed using two different electronic measuring units in order to cover a wide range of applied electric field strength. At a root mean squared values of an electric field strength (Erms) of 1.41-14.1 V/cm (low electric fields), the impedance measurements were performed by connecting two Pt electrodes immersed in a small glass tube of either suspension or its supernatant (Figure 2c) with a impedance and phase analyzer (Solartron Co., Ltd., S1260) through an impedance interface (Solartron Co. Ltd., 1294) shown in Figure 2a. At Erms of 14.1-141 V/cm (high electric fields), the impedance measurements were performed by connecting the same electrode configuration as described above (Figure 2c) with another electronic measuring unit shown in Figure 2b. Ac electric fields with frequencies ranged from 10 kHz to 10 Hz were applied between the two Pt electrodes by a frequency generator (IWATSU Co., Ltd., Japan, model SG-4101) through an operational amplifier (Tektronix Co., Ltd., TM502). Current input/voltage output preamplifier (NF Corporation, LI-76) was connected in series with one of the two Pt electrodes, and then current passed through the medium between the two electrodes was monitored as an amplified voltage output. The electric response of colloidal suspensions to ac electric field is described by complex impedance, Z^ ¼ Zðcos θ - j sin θÞ
ð1Þ
where Z and θ are magnitude and phase components of complex impedance, respectively. For measurements under low electric field (Figure 2a), control of equipments and data collection for magnitude and phase of complex impedance were operated via a personal computer. For measurements under high electric field (Figure 2b), magnitude and phase of complex impedance were estimated from a Lissajous’s figure described by an applied electric field and amplified voltage signal corresponding to the current passed between the two electrodes. Microscopic Observations. The microscopic observations for suspensions of H-ilerite and silica particles were performed under ac electric fields using the same equipments and procedure as reported previously.12,13 In brief, we describe them here. Two Pt-wire electrodes with a diameter of 0.5 mm were placed with a gap of 1 mm in a rectangular hollow of a silica vessel (W 10 mm L 34 mm D 0.5 mm) (see Figure 2d) and connected with the configuration of electronic instruments shown in Figure 2b. As soon as a small amount of suspension was placed in the gap of the two electrodes and covered with a cover glass plate, we observed particles present at the middle of the cell depth under a Normarskitype differential interference optical microscope (Olympus Co., Ltd., Japan, BH-2). Electrophoresis Measurements. Electrophoretic mobility of H-ilerite and silica particles was measured at two stationary layers in a rectangular microelectrophoresis cell under the applied DC electric field with strength of 2-4 V/cm (Microtec Nition Co., Ltd., Japan, ZEECOM). The mobility was obtained as the average of values measured at two stationary layers. All of the experiments were conducted at a room temperature of 23-25 C. (12) Nishimura, S.; Matsumura, H.; Kosuge, K.; Yamaguchi, T. Langmuir 2007, 23, 6567. (13) Nishimura, S.; Matsumura, H.; Kosuge, K.; Yamaguchi, T. Langmuir 2007, 23, 8789.
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Figure 2. Schematic diagrams of apparatus for impedance measurements: (a) electronic measuring units for low electric field strength; (b) electronic measuring units for high electric field strength; (c) electrodes configuration for impedance measurements; (d) glass cell with electrodes for microscopic observation.
compared ζ potentials of silica and H-ilerite particles. Using the numerical calculation presented by O’Brien and White,14 ζ potential of -76 ( 4 mV was calculated for silica particle in 10-5 M NaCl aqueous solution (κa ∼ 9) at 25 C. We observed the electrophoretic mobility of H-ilerite orienting the side edge surface to electric field with random rotation. This is analogous to the case for electrophoretic mobility of cylindrical (rod-like) particle which long axis is oriented vertical to electric field. We tentatively converted the mobility of H-ilerite to ζ potential using an equation for electrophoresis of cylindrical particle. Ohshima’s equation based on Henry’s function for cylindrical particle15 is given by 2 Figure 3. Electrophoretic motility of silica spherical and H-ilerite particles as a function of NaCl concentration at pH5.4-5.8.
Results and Discussions Electrophoretic Mobility of Silica Particle and H-Ilerite. From chemical composition and crystallographic structure of H-ilerite,11 we can consider that the negative surface charges of H-ilerite originate from Si-O- sites on the face and edge surfaces of H-ilerite crystal as a result of the dissociation and binding of Hþ from Si-OH in the same way as the origin of surface charges on silica particle. Figure 3 shows electrophoretic mobility of H-ilerite and silica particles at concentrations of from 10-5 to 10-2 M NaCl at natural pH of 5.4-5.8. H-ilerite and silica particles in aqueous solution of NaCl are negatively charged. The mobility of H-ilerite particles decreases in magnitude as the NaCl concentration increases from 10-5 to 10-2 M, similar to the case for silica particle, but they are somewhat smaller in magnitude than those of silica particles. At a concentration of 10-5 M NaCl where impedance measurements and microscopic observations were mainly conducted in this study, we (14) O’Brien, R. W.; White, L. R. J. Chem. Soc. Faraday Trans. 2 1978, 74, 1607.
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u ¼
6 εr ε0 6 ζ61 þ 2η 4
3 7 7 2 7 5 2:55 1þ Kað1 þ expð - KaÞÞ 1
ð2Þ
where u is electrophoretic mobility for a cylindrical particle, εr is the relative permittivity of water, ε0 is the permittivity of a vacuum, η is the viscosity of water, ζ is the ζ potential of the cylindrical particle, κ is the Debye-H€uckel parameter, and a is the radius(short axis) of the cylindrical particle, respectively. Assuming that a corresponds to half of the average thickness, ζ potential of -73 ( 8 mV is calculated for H-ilerite in 10-5 M NaCl aqueous solution (κa ∼ 1) at 25 C. There is little difference in ζ potential between H-ilerite and silica particles, suggesting that the amount of surface charge in diffuse EDL for H-ilerite are almost as large as that for silica particle. Microscopic Observations for Suspensions of H-Ilerite and Silica Particles under an Ac Electric Field. In this study, we focused on particles present at the middle of cell depth to examine only the EDL properties of particles in the absence of (15) Ohshima, H. J. Colloid Interface Sci. 1996, 180, 299. Henry, D. C. Proc. R. Soc. London 1931, A133, 106.
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Figure 5. Conductance ratio, i.e., conductance of suspension of silica spherical particles (K*)/conductance of the supernatant solution of the suspension (K), measured using a impedance and phase analyzer through an impedance interface at the electric field strengths (Erms) of 1.41 V/cm with the volume fraction of silica particles in suspension (Φ) of 0.135 as a function of frequency of applied electric fields. The inset magnifies the frequency region of the decrease in the conductance ratios.
Figure 4. Microscopic images of suspensions of silica and H-ilerite particles taken with changing the strength of the applied electric field with a frequency of 1 kHz at the volume fraction of the particles in suspension (Φ) of 0.002.
electro-osmosis at the cell bottom because we have found that pearl chain formation of particles settling at the bottom of the cell is enhanced by electro-osmotic flow at the cell bottom as reported previously.13 Figure 4 shows the microscopic images of suspensions of silica particles and H-ilerite taken by changing the strength of the applied electric field at the volume fraction of 0.002, which is a limit of microscopic observation. Glaring interference from particles, especially H-ilerite, increased with increasing number of particles, preventing us from taking clear microscopic images. Although the volume fraction for the microscopic observations is somewhat smaller than that for impedance measurements, the microscopic images are helpful for the understanding of the results for impedance measurements. At Erms < 14.1 V/cm, vigorous Brownian motion of H-ilerite and silica particles is observed. They are monodispersed and isolated. For H-ilerite, their orientations randomly fluctuate (see circle area shown in Figure 4a). At Erms = 28.2 V/cm, the side edge surfaces of H-ilerite particles are slightly oriented to the direction of electric field but still fluctuate due to Brownian motion (see circle area shown in Figure 4b). For silica particles, the increase of electric field reduces their Brownian motion a little. At Erms = 28.2-70.7 V/cm, H-ilerite particles are more firmly oriented to electric field with increasing the electric field strength and the attractive interactions between neighboring particles appear. At Erms > 70.7 V/cm, pearl chains of H-ilerite particles grow up to the length of 20-40 μm (follow arrows shown in Figure 4c). For silica particles, pearl chains are consist of 2-3 particles but most of them are still isolated at Erms > 70.7 V/cm (see the arrow in circle area of Figure 4c). Such a difference in the dependence of pearl chain formation on electric field strength indicates that the magnitude of induced dipole moments resulting from ion con10360 DOI: 10.1021/la100433f
centration polarization of EDL for H-ilerite should be larger than that for silica particle at the corresponding electric field strength. This observation will be justified further from impedance measurements for silica and H-ilerite suspensions as described later. Pearl chains observed in this study are transient structure in which particles are linked to other particles in a direction to electric field at separations of submicromrters.13 The pearl chains easily collapse and particles disperse when the applied electric field is switched off. Impedance Measurements for Suspension of H-Ilerite and Silica Particles. The impedance measurements for suspensions of H-ilerite and silica particle and their supernatants were conducted in the frequency region from 10 Hz to 100 kHz at a root mean squared values of electric field strength (Erms) of 1.41-141 V/cm. In such a range of frequency, we mainly focused on the resistive component of complex impedance for suspensions because dielectric component with frequency is remarkably smaller than that for resistive component. In Figure 5, the conductance ratios, i.e., the conductance of suspension 1 K ¼ Z cos θ to the conductance of its supernatant solution suspension 1 K ¼ Zcos θ for the suspensions of silica particles are shown as a function of frequency at Erms = 1.41 V/cm at the volume fraction(Φ) of silica particles in suspension of 0.135. The change in the conductance ratio (K*/K) is observed as the frequency is lowered from 1 kHz to 100 Hz. It is small effect but clearly recognized as shown in the inset of Figure 5. This reflects that the relaxation of the ion concentration polarization of EDL would be caused by the diffusion effect of counterions in the EDL. The relaxation frequency of counterions is given by D ð3Þ πa2 where f0 is the relaxation frequency, D is the diffusion constant for the counterion and a is the radius of a particle.16 Substituting f0 ¼
(16) Shwaltz, G. J. Phys. Chem. 1962, 12, 2636. Shilov, V. N.; Dukhin, S. S. Kolloid Zh. 1969, 31, 706.
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Figure 7. Relaxation frequency (f0) estimated for the suspensions of H-ilerite and silica particles as a function of applied electric field strength (Erms).
Figure 6. Conductance ratios, i.e., conductance of suspension of H-ilerite s (K*)/conductance of the supernatant solution of the suspension (K), measured at the volume fraction of H-ilerite in suspension (Φ) of 0.135 as a function of frequency of applied electric fields: (a) Erms = 1.41 V/cm; (b) Erms = 141 V/cm.
diffusion constants of D = 1.1-1.6 10-9 m2/sec for Naþ ion17 into eq 3, the relaxation frequency for Naþ ions in EDL was calculated to be 550-800 Hz. The relaxation frequency was estimated by fitting the Debye single relaxation9 to the data in Figure 5 using regression analysis: K Bðf =f0 Þ2 ¼ Aþ K 1 þ ðf =f0 Þ2
ð4Þ
where A and B are fitting parameters, f0 is the relaxation frequency and f is the frequency of applied electric field. In the regression analysis, appropriate values of the above fitting parameters were initially assumed without any restriction and the fitting parameters were determined using algorithm installed in graphic software (KaleidaGraph) so as to fit the calculated value to data within the errors of 0.1%. As shown in the inset of Figure 5, f0 is found to be 748 Hz. In our previous study, f0 was estimated to be around 600 Hz.12 These relaxation frequencies observed for the impedance measurements are within the range of those calculated from eq 3. This supports that the slight change in conductance ratio for silica particles at the frequencies ranging from100 Hz to 1 kHz is due to the relaxation of the ion concentration polarization of EDL as a result of the diffusion
(17) Robinson, R. A.; Stokes, R. H. Electrolyte Solution; Butterworth: London, 1959; p513-515. Mills, R. Rev. Pure Appl. Chem. 1961, 11, 78.
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effect of Naþ (counterions) in the EDL. For silica particles, f0 is independent of Erms and Φ as will be shown in Figure 7. Figure 6 shows K*/K for H-ilerite measured at Φ =0.135 as a function of the frequency of the applied electric field. In Figure 6a, f0 is found to be around 420 Hz at Erms = 1.41 V/cm where orientations of H-ilerite particles are random due to vigorous Brownian motion as seen in Figure 4a. The range of change in K*/K is observed at frequencies ranging from 10 Hz to 10 kHz. It is much larger than that for silica particles At Erms = 141 V/cm, where H-ilerite particles are oriented to electric field and formed a long pearl chain as seen in Figure 4c, the values of K*/K are larger than that observed at Erms = 1.41 V/cm in the entire range of frequency. The value of f0 decreases to 149 Hz from 420 Hz. These changes of K*/K and f0 with Erms suggest the increase in the size of H-ilerite is parallel to electric field as a result of the electric orientation. This will be specified in the discussion of Figure 7. The bulk concentration of H3Oþ ions at pH5.6-5.8 is 15-25% of that of Naþ ions in 10-5 M NaCl aqueous solution. Substituting D = 8 10-9 m2/sec17 for H3Oþ ion into eq 3, the relaxation frequency for H3Oþ ions in EDL for silica particle and H-ilerite was calculated to be about 2-4 kHz. In this frequency region, a clear relaxation change in K*/K cannot be recognized in either the case of the silica particle or H-ilerite as seen in Figures 5 and 6. But, in Figure 6a, K*/K for H-ilerite tends to deviate from the fitting curve to only a slightly higher values in the range 510 kHz. There is a possibility that such a small deviation may reflect the relaxation for H3Oþ ions in EDL. Considering that Naþ in EDL around particles is dominant in EDL, it is likely that the relaxation change of K*/K for H3Oþ ions in EDL would be smaller than that for Naþ ions. Another argument is that the diffusion of H3Oþ ions in EDL would be as slow as that of Naþ ion in bulk solution. According to voltammeteric measurements in dilute dispersion of polystyrene particles (Φ = 0.02), the diffusion constant for H3Oþ ions is only 1/40 of that in simple acidic solution.18 In this case, the diffusion constant of H3Oþ ions in EDL around particles is ∼1/5 of that for Naþ ions in bulk solution. However, the relaxation corresponding to such a slow diffusion could not be found at all in this study. In Figure 7, the relaxation frequency (f0) estimated from impedance measurement is plotted as a function of electric field strength (Erms). The relaxation frequency for silica particles show almost equal values, independent of electric field strength. The values of f0 for H-ilerite decrease with increasing electric field strength. This reflects that the effective charge separation distance (18) Robert, J. M.; Linse, P.; Osteryoung, J. G. Langmuir 1998, 14, 204.
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Table 1. Comparison between Calculated and Observed Relaxation Frequency (f0) and the List of Parameters Required for Calculation of f0a f0, Hz a, μm edge oriented to E
D 109, m2/sec
1
1.8 ( /2 of side length)
calculated
observed
110-160
149
290-420
404-423
1.1-1.6 not oriented 1.1 (effective (random) radius Æaæ) a E is electric field.
in the ion concentration polarization of EDL, which corresponds to a in eq 3 for a spherical particle, increase as a result of the orientations of H-ilerite to electric field. In other words, it takes more time to restore the ion concentration polarization in EDL due to the diffusion of counterions. Table 1 shows the comparison between calculated and observed values of f0 for H-ilerite. The parameters required for the calculation of f0 using eq 3 were also listed in Table 1. For H-ilerite oriented to electric field, eq 3 gave the calculated values of 110-160 Hz for f0. The observed relaxation frequency of 149 Hz for Erms = 141 V/cm is within the range of the values calculated form eq 3. At Erms < 14.1 V/cm where the orientations of H-ilerite particles are random (Figure 4 a), the effective radius Æaæ of H-ilerite is estimated to be around 1.1 μm (see Appendix). Equation 3 gives the values of 240420 Hz for f0 using a = 1.1 μm. The observed relaxation frequencies of 404-423 Hz for Erms = 1.41-14.1 V/cm are also within the range of the calculated values. From these observations, it is evident that the change in the relaxation frequency with electric field strength is due to the orientation of H-ilerite to electric fields. At Erms = 24.2-70.7 V/cm, f0 values are observed in the range 340-400 Hz. These values are close to the relaxation frequency for random orientation of H-ilerite rather than H-ilerite oriented to electric field, implying that the orientation of H-ilerite would remain fluctuating. At Erms = 70.7-141 V/cm, where pearl chains are observed, the relaxation frequency decreases to ∼150 Hz, which corresponds to the size of fully oriented H-ilerite. Fluctuation of electric orientation of H-ilerites would be restrained in pearl chains by local electric fields of neighboring dipole moments in comparison with that of isolated H-ilerite. At Erms = 141 V/cm where long pearl chains are clearly observed, the relaxation frequency corresponding to the length of pearl chain can not be observed. Considering the fact that particles in pearl chains are linked to other particles at small separations under electric field and break into monodispersed particle in the absence of electric field, it is likely the relaxation of ion concentration polarization in EDL would take place within the ranges of a particle and/or between neighboring particles in pearl chain. In Figure 8, K*/K is shown as a function of Erms at the frequencies of 100 Hz and 1 kHz and Φ = 0.135. The values of K*/K at 100 Hz are totally lower than those at 1 kHz. This is due to the relaxation of ionic concentration polarization in EDL as discussed above. For the silica particle, K*/K is independent of the electric field strengths in the whole range of 1.41-141 V/cm. For the H-ilerite, K*/K keeps constant at Erms < 14.1 V/cm. In the range of 28.2-106 V/cm, K*/K increases remarkably and shows values of ∼3 at Erms > 106 V/cm. When electric field was switched to Erms = 1.41 V/cm, K*/K decreased back to the original value of ∼1.8 for Erms = 1.41 V/cm after several seconds. A similar response of K*/K to electric field was observed at Φ = 0.0150.135 although K*/K decreased totally with decreasing the volume fraction of particles in suspension. Such an electric response of K*/K coincides with that of the relaxation frequency shown in 10362 DOI: 10.1021/la100433f
Figure 8. Conductance ratios (K*/K) measured for H-ilerite and silica particles at the volume fraction of H-ilerite s in suspension (Φ) of 0.135 as a function of applied electric field strength (Erms).
Figure 9. Conductance ratios(K*/K) measured for H-ilerite and silica particles as a function of the volume fraction of particles in suspension (Φ) with changing the applied electric fields (Erms).
Figure 7. The electric response of K*/K for H-ilerite and silica particles can be explained by the difference in the electric orientation between nonspherical and spherical particles. Assuming the cross section of particle vertical to the electric field, the cross sectional area and its outline correspond to nonconductive and conductive regions, respectively. The conductive region is dominated by surface conduction of EDL. For H-ilerite, the cross sectional area, i.e., the nonconductive region, decreased more than conductive region and outlined the area as the edge surface of H-ilerite is oriented to the electric field. For silica particle, nonconductive and conductive regions are unchanged because of a spherical particle. In addition, we need consider the increase in K*/K resulting from pearl chain formation. We reported that pearl chain formation of silica particles increase K*/K.12 At Erms > 70.7 V/cm, the contribution of pearl chain formation to the increase in K*/K could be included as will be discussed later. In Figure 9, the values of K*/K for the suspensions of H-ilerite and silica particles are shown as a function of the volume fractions of particles in suspension (Φ). For silica particles, the dependence of K*/K on Φ shows a good linear relation. The slope of K*/K against Φ is independent of Erms. At Erms = 14.1 V/cm, the plots of K*/K against Φ for H-ilerite particles also shows a good linear relation but the slope for H-ilerite is higher than that for silica (19) Dukhin, S. S. Adv. Colloid Interface Sci. 1993, 44, 1. Dukhin, S. S.; Derjaguin, A. A. Equilibrium Double Layer and Electrokinetic Phenomena. In Electrokinetic phenomena; Matijevic, E., Ed.; Surface and Colloid Science 7; John Wiley & Sons; New York, 1974; Chapter 2; pp 217-218.
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Table 2. Linear Regression Analysis for the Plots of K*/K against Φ Shown in Figure 9 Erms, V/cm
Φ
silica 1.41-141 0-0.135 H-ilerite 1.41-14.1 0-0.135 28.2 0-0.045 0.045-0.135 70.7-141 0-0.045 0.045-0.135
slope of K*/K to Φ
intercept of K*/K
Ra
2.33 6.07 9.12 13.45 11.36 18.72
1.01 0.99 0.98 0.77 1.00 0.69
0.99450 0.99894 0.99999 0.99895 0.99982 0.99588
a
R is a correlation coefficient obtained as a result of linear regression analysis.
particles. Dukhin et al. presented the following equations concerning the relations between K*/K and Φ:19 " # K 1 3 Du ¼ 1 þ 3Φ - þ , K 2 2 1 þ Du " # K 1 3 Du ¼ 1 þ 3Φ - þ , K 2 2 1 þ 2Du
f .f0
ð5Þ
f , f0
ð6Þ R ¼
ð7Þ
In the above equations, Du is the Dukhin number, a is the radius of the particle, kδ is the surface conductivity and kb is the conductivity of a bulk medium, respectively. Table 2 shows the results of linear regression analysis for the plots of K*/K against Φ in Figure 9. The intercept of K*/K shows a value of ∼1 as predicted from eq 5 except for the case for H-ilerite in the region of Φ > 0.045 and Erms > 28.2 V/cm. The slope of K*/K and Φ is related to the magnitude of induced dipole moment caused by ion concentration polarization of EDL: therefore, the magnitude of induced dipole moment of ion concentration polarization in EDL for H-ilerite is larger than that of silica particles. This is consistent with the microscopic observation for the difference in pearl chain formation (see Figure 4c). As Erms increases, the slope of K*/K against Φ becomes steep. More interestingly, it should be noticed that another linear region with steeper slope appears at Erms > 28.2 V/cm in the plots of K*/K against Φ. At Φ < 0.045, the increase of the slope can be explained by the electric orientation of H-ilerite. To understand the increase in the slopes of K*/K to Φ at Φ > 0.045, we need consider other contribution to the increase of K*/K besides the electric orientation. A possible explanation is that the increase in K*/K is induced by pearl chain formation.12 As seen in Figure 4(c), H-ilerite particles form longer pearl chains than silica particles. Qualitatively we recognized that the number and length of pearl chains tend to increase with increasing Φ. The contribution of pearl chain formation to K*/K must be enhanced by the increase in the number and length of pearl chains. The increase of K*/K caused by pearl chain formation would be negligible for silica particles: accordingly the slope of K*/K to Φ is constant independently of Erms. In Figure 5 and 6, we noticed that the range of change in K*/K for H-ilerite is much larger than that for silica particle. The range (20) Matsumura, H. In Electrical Phenomena at Interfaces. Fundermentals, Measurements, and Applications; Ohshima, H., Furusawa, K., Ed.; Marcel Dekker, Inc.; New York, 1998; p 305.
Langmuir 2010, 26(12), 10357–10364
K ¼ 1 þ Φ½R - 1 K
ð8Þ
where
where 2πa kδ 2kδ 2Du ¼ 2 b ¼ b πa k ak
of change in K*/K, that is caused by the relaxation of ion concentration polarization of EDL, is given by subtracting eq 5 from eq 6. We verified the range of change in K*/K enlarge as the value of Du increases.20 The maximum range of change in K*/K is estimated to be 0.30 from eqs 5 and 6 for Du f ¥ at Φ = 0.135. However, this value is lower than experimental values (a fitting parameter, B in Figure.6) of 0.45 and 0.34 for Erms = 14.1 and 141 V/cm, respectively. The slope of eq 5 converges to the maximum value of 3 but the slopes of K*/K against Φ for H-ilerite exceed it: the slopes ofK* /K to Φ for H-ilerite and silica particle suspensions give values of 6.07 and 2.33 at Erms < 14.1 V/cm, respectively. Equations 5-7 were derived for the case of spherical particles, and consequently, they cannot fully account for the case of nonspherical particles. We assume that the relation between K*/K and Φ is simply given by
L kδ A kb
ð9Þ
In the above equations, Φ is the volume fraction of the particles in the suspension, L is the outline length of a cross section of a particle, A is the cross sectional area of a particle vertical to electric field kδ is the surface conductivity and kb is the conductivity of a bulk medium, respectively. Considering that the ζ potential of H-ilerite is close to that of silica particle, the ratio of surface to bulk conductivity for H-ilerite particle, i.e., kδ/kb, can be assumed to be equal to that for silica spherical particle. So we easily estimated the value of r for H-ilerite from geometrical parameters (L/A) for H-ilerite (Figure 1c) and the experimental value for the slope of K*/K to Φ (2.33), i.e., [R - 1] in eq 8, for silica particles (see Table 2). Table 3 shows the slope of K*/K to Φ estimated for three modes of orientation of H-ilerite: rotation of square plate with the radius of Æaæ (not oriented); face and edge oriented to electric field (E), respectively. The slope of K*/K to Φ for the three modes of orientation of H-ilerite shows the values of 1.45(not oriented to electric field), 0.54(face oriented to electric field) and 15.64 (edge oriented to electric field). Taking into account the orientation of H-ilerite, we can provide justification for the fact that the slopes of K*/K against Φ for H-ilerite exceed the value of 3 for spherical particles.. The estimated slope of 1.45 for H-ilerite which is not oriented to electric field is much smaller than the experimental value of 6.07 for Erms = 14.1 V/cm. This discrepancy suggests that the edge surface of H-ilerite must be actually more oriented to electric field than predicted. The slope of 11.36, which was observed at Φ 70.7 V/cm. The slope of 18.72, which was observed at Erms > 70.7 V/cm and Φ=0.045-0.135, is larger than the calculated value of 15.64 (see Table 3). This can not be explained by only the effect of electric orientation, suggesting that there exist contribution of pearl chain formation to the increase in K*/K. By the way, we described that the range of relaxation change in K*/K for H-ilerite is much larger than that for silica particles but could not explain it in terms of the subtraction from eq 5 from 6 for Du f ¥. If the relaxation of ionic concentration polarization of EDL accompanies the change in the electric orientation of DOI: 10.1021/la100433f
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Article
Nishimura et al.
Table 3. Calculated Values of r - 1 (Slope of K*/K to Φ) for Three Modes of Orientation of H-Ilerite s Using Geometrical Parameters and Experimental Values of r - 1 for Silica Particles R-1 orientation silica H-ilerite
L/A 106,m
RH-ilerite/Rsilica
R
2.47 not oriented (random) face oriented to E edge oriented to E
1.82 1.14 12.34
estimated
3.33 0.74 0.46 5.00
2.45 1.54 16.64
observed 2.33 6.07-18.72
1.45 0.54 15.64
increased, the slope of K*/K to Φ for H-ilerite increased as a result of the orientation of H-ilerite to the electric field. In addition, at higher volume fractions, the slope of K*/K to Φ for H-ilerite became steeper and could not be expressed by a simple linear relation. Such a unique response of H-ilerite suspension to electric field could be explained by the electric orientation of H-ilerite accompanying pearl chain formation.
Figure 10. Schematic diagram of side length (long axis) of a square.
H-ilerite, the relaxation change in K*/K for H-ilerite would include the decrease in K*/K resulting from the alleviation of electric orientation. It is likely that the range of relaxation change in K*/K for H-ilerite could exceed 0.3 for silica particle (Φ = 0.135).
Acknowledgment. Financial support of AIST is acknowledged (subject: Control of orientation and alignment for anisotropic colloids, 2005-2007). This work was also performed as a part of Grant-in-Aid for Scientific Research on Innovative Areas FY2008-2009 supported by the ministry of education, culture, sports, science and technology (MEXT). S. N. acknowledges Japan Society for Promotion of Science (JSPS) Core-to-core program (Advanced Particle Handling Science) FY2009 for organizing the opportunity for valuable discussions. S.N. also thanks Dr. K. Ooi for helpful suggestions and discussions.
Conclusion We have investigated response of the suspensions of silica spherical particle H-ilerite (silica square platelike particle) to an ac electric field in order to reveal the unique aspects of EDL for nonspherical particles under ac electric fields. For silica spherical particle, the conductance and relaxation frequency of ion concentration polarization in EDL were independent of electric field strength. However, for H-ilerite platelike particle, the relaxation frequency decreased and the conductance ratios (K*/K) increased with increasing the applied electric field strength because of the orientation of H-ilerite to electric field. For silica particles, the plots of K*/K against volume fraction of particles in suspension (Φ) were described by a good linear relation independently of the strength of applied electric field. For H-ilerite, at low electric field strength where there was no response of H-ilerite to the electric field, the plots of K*/K against Φ showed a good linear relation in the same way as for silica particles but the slope was higher than that for silica particles. As the electric field strengths
10364 DOI: 10.1021/la100433f
Appendix Dukhin et al. described that the characteristic frequency of suspension of a rod-like particle of 2a length and the sphere of such a diameter practically coincide.1 We consider that 2a of a rod-like particle would correspond to the side length (long axis) of a square plate for the electric orientation of H-ilerite as observed in Figure 4. When H-ilerite particles fluctuate vigorously, the effective radius can be described by the schematic diagram shown in Figure 10. The effective radius of the square plate Æaæ was calculated as follows. R π=2 Æaæ ¼
0
ða cos θ þ d sin θÞ dθ 2 ¼ ða þ dÞ R π=2 π dθ 0
ð10Þ
where a is the half of side length, d is the thickness of the edge, and θ is the angle of the side to the electric field, respectively.
Langmuir 2010, 26(12), 10357–10364
