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Effect of electric fields on the surface profiles of electrorheological suspensions
Colloids and Surfaces A: Physicochem. Eng. Aspects 324 (2008) 228–233
Contents lists available at ScienceDirect
Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Effect of electric fields on the surface profiles of electrorheological suspensions Kazutoshi Tsuda, Yuji Hirose, Hironao Ogura, Yasufumi Otsubo ∗ Department of Urban Environment Systems, Graduate School of Engineering, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba-shi 263-8522, Japan
a r t i c l e
i n f o
Article history: Received 4 December 2007 Received in revised form 8 April 2008 Accepted 10 April 2008 Available online 23 April 2008 Keywords: Electrorheology (ER) Surface profile Silica suspension Dielectric polarization Electrophoretic migration Comb pattern electrode
a b s t r a c t The surface deformation induced in electric fields is studied on the comb pattern electrodes for silica suspensions. On the application of electric fields, a fine pattern with a waveform is developed from the smooth surface. The surface profiles can be approximated by single sinusoidal waves or their superposition depending on the sample thickness. In electric fields, the silica suspensions shows the viscosity decrease in steady shear and yield stress in the limit of zero shear rates. The viscosity decrease can be attributed to electrophoretic migration of particles to one electrode and the development of yield stress to eletrorheological effects due to chain formation of particles between electrodes. In thick liquid films, the dielectric polarization forces are predominant and the sinusoidal profiles with a wavelength of pitch of electrodes are formed. In thin films, the electrophoretic forces are predominant and the wavelength coincides with twice the pitch of electrodes. At intermediate thicknesses, the surface profiles can be expressed by a superposition of two sinusoidal waves. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In general, the surface of particles dispersed in a liquid carries an electrical charge. Since the charged particles are attracted to one electrode in DC electric fields, the migration and deposition of particles can take place. When the suspension consisting of pigments in a colored solvent is sandwiched in a narrow space between transparent electrodes and the electric field is applied in one direction, the motion of pigment particles toward the electrode is generated. As a result, a passive image is produced due to the scattering and absorption of visible light by the deposited pigments. The application of electric fields in the opposite direction causes the removal of pigments and the electrode is covered with colored solvent. If the optical density of solvent is so high that the light reflection is not influenced by the pigments on the opposite electrode, the color of the solvent can be observed. By the use of the pigments and solvent with contrasting colors, the images can be controlled by deposition and removal of pigments. Recently, on the basis of this mechanism, the electrophoretic displays have received increasing interests as new imaging devices [1–3]. A reversible and rapid change in viscosity of fluids on the application or removal of electric fields is commonly referred to as the electrorheological (ER) effect. Typical ER fluids are suspensions of polarizable particles dispersed in insulating oils [4–9]. In electric
∗ Corresponding author. Tel.: +81 432903128; fax: +81 432903128. E-mail address: [email protected] (Y. Otsubo). 0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2008.04.033
fields, each particle acquires an induced dipole. The dipole–dipole interactions cause the particles to form chain structures in direction parallel to the field vector [10–12]. The chains spanning the electrode gap respond elastically at very low strains. Therefore, the ER suspensions undergo a rapid transition from Newtonian fluids to rigid solids in electric fields. When the applied stress is increased above some critical value that is called yield stress, the steady-flow occurs in the electrified suspensions. After the onset of flow, the shear rate linearly increases with increasing the applied stress. The flow behavior of ER suspensions is represented by a Bingham equation in electric fields [13–16]. Since the local fluidity can be actively controlled by the field strength, the ER fluids are attractive as vehicles in new mechanical devices such as stop valves, clutches, and dampers [17–20]. In both electrophoretic and ER effects, the most important feature is that the distribution of particles in the systems becomes unhomogeneous on the application of electric fields. For fundamental evaluation of these effects, the uniform electric fields are usually applied for suspensions which are sandwiched between two parallel plate electrodes. But the electric forces acting on the particles depend on the local field intensity. Therefore, the nonuniform electric fields can increase the electric forces and in turn enhance the destabilization and structuring of particles. In fact, we have confirmed in previous papers [21,22] that the column formation of particles is enhanced in the honeycomb pattern electrodes and this serves to increase the yield stress of ER suspensions. The present study is designed to understand the particle behavior in nonuniform electric fields. The electric fields are generated by
K. Tsuda et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 324 (2008) 228–233
229
Fig. 2. Creep behavior for suspension at a particle concentration of 7.2 vol% in different electric fields: () 0; () 1.0; () 3.0 kV mm−1 .
Fig. 1. A schematic picture of comb pattern electrodes.
2. Materials and methods
and space. The line thickness and pitch of electrodes are 0.1 and 0.5 mm, respectively. The suspensions were places on the pattern electrodes at thicknesses up to 0.54 mm. A DC voltage in the range of 1.0–3.0 kV was applied to line electrodes on one side and the other electrodes were connected to the ground (E = 0). The bottom of suspensions was strongly electrified, but the top surface was exposed to atmosphere. The surface topography was measured by the use of a laser displacement sensor (LT9010M manufactured by Keyence). By combination with a mechanical stage (KS-1100 manufactures by Keyence), the wide regions of suspension surfaces could be scanned with a vertical accuracy of 0.01 m.
2.1. Materials
3. Results and discussion
The suspensions were composed of silica particles and silicone oil. The silica particles were manufactured by Catalysts and Chemicals Industries Co. Ltd. (Japan), whose diameter and density were 1.3 m and 2.2 × 103 kg m−3 , respectively. The silicone oil with a Newtonian viscosity of 0.12 Pa s and density of 1.0 × 103 kg m−3 at 25 ◦ C was obtained from Toshiba Silicone Co. (Tokyo, Japan) and used as received. The suspensions were prepared at particle concentrations up to 13% by volume. Prior to the sample preparation, the silica particles were heated at 105 ◦ C for more than 1 week to control the conditions of particle surfaces. Owing to the high viscosity of medium, the suspensions showed long term stability against sedimentation. Neither clear supernatant liquids nor sediments were detected after the storage in a quiescent state for several days.
3.1. ER behavior of suspensions
the use of a single flat plate, on which the electrodes of line and space are coated. When the suspensions placed on the electrodes are electrified, the deformation of surface profiles occurs by the unhomogeneous distributions of particles. The relation between the surface deformation and internal structures will be discussed in terms of electric forces induced on the flat electrodes with a comb pattern.
2.2. Methods Steady-flow and creep properties were measured using a parallel plate geometry on a stress-controlled rheometer (Haake, Rheo-Stress RS100) which was modified for the ER experiments. The diameter of plates was 35 mm and the gap between two plates was 0.5 mm. A DC voltage was applied by a technique of frictionless contact to the upper plate which was insulated from the shaft. The shear rates in steady-flow experiments were from 3.0 to 3.0 × 102 s−1 and the applied stresses in creep experiments were from 1.0 to 10 Pa. The ER behavior was measured in electric fields up to 4.0 kV mm−1 . The current density was less than 2 mA m−2 for all samples in an electric field of 4.0 kV mm−1 . The measuring temperature was 25 ◦ C. For measurements of field-induced surface topography, the flat electrodes with a comb pattern was used, of which the schematic picture is shown in Fig. 1. The glass surface is coated with transparent ITO (indium tin oxide) electrodes in a striped pattern of line
Fig. 2 shows the creep behavior for suspension at a particle concentration of 7.2 vol% in electric fields of 0, 1.0 and 3.0 kV mm−1 . The stress was increased stepwise from 1.0 to 10 Pa in a shearing time of 60 s at each stress. The strain was measured as a function of time. Without electric fields, the strain linearly increases with time and the responses can be approximated as purely viscous. In electric fields, the strain almost instantaneously responds the change in stress and reaches the equilibrium in short periods. Because the creep curve can be expressed by a Voigt model at low stresses, the electrified suspensions are apparently characterized as elastic solids. When the stress is increased beyond some critical level, the constant-rate strain due to viscous flow is suddenly induced. The suspension in electric fields has a yield stress which increases with increasing field strength. The yield stress is estimated to be about 10 Pa at 3.0 kV mm−1 . The creep experiments clearly indicate that the silica suspensions are ER-active and solidified at low stresses. Fig. 3 shows the flow behavior of 7.2 vol% suspension in electric fields of 0 and 3.0 kV mm−1 . The measurements were carried out in the procedure that the shear rate was exponentially increased and decreased in the range of 0.3–300 s−1 in a measuring time of 20 min. Significant differences are not observed between the upcurve and down-curve for suspension without electric fields. But, the down-curve and up-curve cannot be overlapped each other in electric fields. The stress of down-curve is decreased and the hysteresis appears between two curves at low shear rates. Another interesting aspect at low shear rates is that the stress level of downcurve in electric fields is lower than that in zero fields. Although the solidification of suspensions in electric fields is confirmed through creep experiments, the viscosity under steady-flow conditions is decreased. In ER suspensions, the viscosity enhancement is striking
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Fig. 3. Hysteresis behavior of viscosity during a cycle of increasing (filled symbols) and decreasing (open symbols) shear rate for 7.2 vol% suspension in electric fields of () 0 and (, ) 3.0 kV mm−1 .
at low shear rates and the stress curve plotted against the shear rate shows a plateau in the zero shear limit. The height which increases with increasing field strength is generally considered to correspond to the Bingham yield stress. However, the ER responses of sample suspensions are converted from positive to negative during steady shear. The low viscosity in electric fields and hysteresis behavior observed for sample suspensions cannot be explained by simple ER mechanisms. We have already reported [22] that the ER toners for electrophotography show similar flow behavior. In the liquid toners, the charge control agents are added to give the sufficient charges for fast development and high image quality. Since the charged particles are attracted to one electrode in DC electric fields, the migration and deposition of particles can take place. Provided that the particles dispersed in a liquid bear no electrical charges, the chain structures are constructed along the field vector by dielectric polarization forces. When the electrified suspensions are subjected to steady shear, the electric forces are dominant at low shear rates, and the hydrodynamic forces are dominant at high shear rates. In the case of liquid toners, the viscosity behavior is mainly determined by the dielectric polarization forces in low shear fields and electrophretic forces in high shear fields. Therefore, one can expect that the electrophoretic effects, producing a particle-free region near the upper plate, can cause the viscosity decrease. By the additional experiments, it is microscopically observed for sample suspensions that the negative electrode is covered with deposited particles after the electrification by a pair of needle electrodes. The unique ER behavior of silica suspensions can be explained by a combination mechanism in which the dielectric polarization forces give rise to the viscosity increase due to chain formation of particles and electophoretic forces lead to the viscosity decrease due to migration of particles to one electrode. The yield stress generated in electrified suspensions arises from the development of chain structures between electrodes. By assuming that the particles all align into chains of single-particle width and equal spacing, the yield stress can be predicted to linearly increases with particle concentration, because each chain has the same strength and the number of chains per area is proportional to the concentration [23]. For 7.2 vol% suspension with a yield stress of 10 Pa, the polarization forces between two particles in an electric field of 3.0 kV mm−1 is determined to be 1.23 × 10−10 N from the strength of single chain. The electophoretic migration is induced after the chains spanning the electrode gap are ruptured in shear fields. Considering that the viscosity reduction in electric fields is attributed to the
Fig. 4. Three-dimensional image and cross-sectional profile of surface for 9.9 vol% suspension at a sample thickness of 0.135 mm in an electric field of 3.0 kV.
formation of particle-free region, the rupture of chains may take place near the upper plate. The total electophoretic forces generated in the chain with a length of gap distance (consisting of 385 particles) may be comparable to the dielectric polarization forces between two particles at the breaking point. According to the theory on electophoretic migration of colloids, the surface charge can be calculated from the balance between electophoretic and hydrodynamic forces. The dielectric constant of silicone oil being taken as 2.7, the surface charge of silica in the sample suspension is estimated to be about 0.3 mV. The electric forces dominate at low shear rates, and the hydrodynamic forces dominate at high shear rates. The hydrodynamic force acting on a spherical particle with a radius of r at a shear rate of ˙ is given as 60 r 2 , ˙ where 0 is the viscosity of medium. The obtained value at ˙ = 300 s−1 is 2.87 × 10−10 N. This estimation is acceptable because the shear stresses around 300 s−1 are almost equal to the zero-field values as shown in Fig. 3. When the sufficient hydrodynamic forces are applied to the systems, the flow curves are not influenced by the electric fields. 3.2. Surface profiles in electric fields Fig. 4 shows the three-dimensional image and cross-sectional profile of surface for electrified suspension at a particle concentration of 9.9 vol%. The DC voltage of 3.0 kV was instantaneously applied for suspension placed on the electrodes at a thickness of 0.135 mm in the conditions of no electric fields. In many ER studies, the intensity of electric fields has been generally given by the voltage divided by the electrode separation. However, the electric fields are not uniform in this experimental configuration. The field intensity is expressed by the voltage applied to the line electrodes. On the application of an electric field, a fine pattern with a waveform is formed from the smooth surface in response times of about 100 ms. The cross-sectional profile in direction perpendicular to line electrodes is nearly sinusoidal. The wavelength is 1 mm and this corresponds to twice the pitch of line electrodes. In this study, the degree of surface deformation is evaluated by the topographical depth, that is, twice the amplitude of sinusoidal wave. The topographic depth shown in Fig. 4 is about 50 m. The tops of sinusoidal surfaces are located on the line of negative electrodes. Fig. 5 shows the topographic depth plotted against the sample thickness for 9.9 vol% suspension in different electric fields.
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Fig. 5. Topographic depth plotted against the sample thickness for 9.9 vol% suspension in different electric fields: () 1.0; () 2.0; () 3.0 kV mm−1 .
At 1.0 kV and below the change in surface profiles could not be detected. There exists a critical strength for appearance of waveform surfaces. Beyond the critical strength, the surface deformation is enhanced at higher electric fields. However, the suspensions could not be placed on the electrodes at thicknesses less than 0.1 mm. Because the conductive ITO part and insulating glass part have different surface properties, it is difficult to form the thin liquid films with a smooth surface on the comb pattern electrodes. Although the data are not obtained for thin liquid films, the topographic depth decreases with increasing sample thickness. When the thickness is increased above 0.5 mm, the smooth surfaces are kept even in high electric fields. With respect to the surface deformation in electric fields, the most significant finding is that the sample thickness influences not only the topographic depth, but also the surface profiles. As typical instances, Figs. 6 and 7 show the surface profiles at thicknesses of 0.27 and 0.54 mm, respectively, for 9.9 vol% suspension in an electric field of 3.0 kV. At 0.54 mm, the expression of surface profile by a sinusoidal function may be reasonable, but the wavelength is decreased to about half the value attained at 0.135 mm. It looks likely that the bottoms of sinusoidal surfaces are located on the line of electrodes, irrespective of polarity. As a first approximation, the increase in thickness may lead to a decrease in wavelength. However, it is difficult to accept the
Fig. 6. Three-dimensional image and cross-sectional profile of surface for 9.9 vol% suspension at a sample thickness of 0.27 mm in an electric field of 3.0 kV.
Fig. 7. Three-dimensional image and cross-sectional profile of surface for 9.9 vol% suspension at a sample thickness of 0.54 mm in an electric field of 3.0 kV.
sinusoidal approximation at 0.27 mm. At intermediate thicknesses, the surface profiles can be described by a superposition of two sinusoidal curves with different wavelengths. This suggests that the surface deformation of suspensions in electric fields should be controlled by two kinetic mechanisms. Fig. 8 shows the effect of particle concentration on the topographical depth in different electric fields for suspensions at a thickness of 0.27 mm. As expected from Fig. 5, the degree of surface deformation is pronounced in high electric fields. However, the particle concentration does not significantly influence the overall shapes of surface profiles, which is primarily dominated by the sample thickness. Referring to the result at 3.0 kV, the topographic depth increases, passes through a maximum, and then decreases with increasing particle concentration. If the particle concentration is increased beyond 15 vol%, the surface deformation in electric fields would not be generated. The periodical profile of suspension surfaces is a manifestation of unhomogeneous distribution of particles. Since the field-induced arrangements in the systems are determined by a balance between the electric forces acting on the particles and geometrical hindrance against particle migration, the particle concentration has an appropriate value for formation of surface profile with a maximum topographic depth.
Fig. 8. Effect of particle concentration on the topographic depth for suspensions at a thickness of 0.27 mm in different electric fields: () 1.0; () 2.0; () 3.0 kV mm−1 .
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Fig. 9. Models of particle migration due to different effects: (a) ER effect; (b) electrophoretic effect.
The intrinsic ER mechanism of suspensions is the chain formation of polarized particles. In uniform electric fields generated between parallel plate electrodes, the particles first form chains spanning the electrode gap. When placed near a chain, a particle will be repelled by the nearest particle in the chain. But the particle will be attracted by the chained particles well above and below it. As a result, the chains aggregate to build up the column [24–26]. The column structure must be the configuration which minimizes the dipolar interaction energy. The ideal column structure in electric fields is a body-centered tetragonal lattice [27,28]. Because the equilibrium conformations of individual chains are always aligned with the electric field, the direction of chains is perpendicular to the plate electrodes. The electric fields between two electrodes with the patterns of conductive lines are not uniform. The potential gradient is generated in the direction parallel to the electrode surfaces. Therefore, the force component in direction perpendicular to individual chains is enhanced to build up the closely packed column. We have reported [21] that the nonuniformity of electric field can cause the columns with high particle concentrations. Let us now consider the geometrical situation employed in the present study. Since the silica suspensions are electrified between line electrodes on the single glass plate, the particle–particle attraction which causes the chain structures between electrodes is induced in direction perpendicular to electrode lines. Also, the forces in direction perpendicular to the glass plate are generated by dielectric polarization of particles in nonuniform fields. As the polarization effects are independent of polarity of electrodes, the topographic thickness is increased between electrode lines due to the particle migration and formation of condensed columns. The wavelength of surface profiles is determined by the pitch of striped pattern. Fig. 9(a) shows a schematic picture of forces between polarized particles on comb pattern electrodes. The forces acting on the particles by electric polarization are decreased with increasing distance from the electrodes. Hence, the sinusoidal profiles disappear for thick liquid films. When the sample thickness is decreased to the order of 0.1 mm, the forces in direction parallel to glass plate become predominant. Even at the surfaces of suspensions, the dielectric polarization hardly contributes to the perpendicular forces which result in the particle migration toward the glass surface. However, the silica particles are positively charged in the silicone oil. In electric fields, the particles are attracted to negative electrode and the migration of particles takes place by electrophretic effect. Fig. 9(b) shows a schematic picture of electrophoretic migration of particles on comb pattern electrodes. Because the particles are repelled by the positive electrode and deposited on the negative electrode, the sinusoidal profiles are formed, whose wavelength coincides with twice the pitch of electrodes. The large values of topographic depth are attributed to high field intensity in thin liquid films. In the range of sample thickness studied, the forces causing the surface profile
changes are governed by electrophoretic effect for thin films and by ER effect for thick films. Although the magnitude of forces decreases with increasing sample thickness, the electrophoretic and ER forces acting on particles are comparable at the intermediate thickness. Therefore, the surface profiles are expressed by a superposition of two sinusoidal waves. As a simplified approach, the field strength on comb pattern electrodes is quantitatively evaluated through a model consisting of two wire electrodes. Supposing that the field strength at the surface of suspensions with a thickness of 0.135 mm above the line of negative electrode is unity, the increase of thickness to 0.54 mm causes the field strength to decrease to 0.1. Since the field vector is directed to the electrode, the electrophoretic forces rapidly decreases with increasing thickness. On the other hand, above the center of electrode gap for suspension with a thickness of 0.54 mm, the relative field strength in direction parallel to the suspension surfaces is about 0.2. The electric force contributing chain formation is slowly decreases with increasing thickness. Consequently, the dielectric polarization forces govern the surface profiles at large thicknesses. 4. Conclusions (1) When the electric fields are applied to silica suspensions in a silicone oil, the electophoretic force and dielectric polarization force are generated on the particles. The former results in the viscosity decrease due to migration of particles to one electrode and the latter in solidification of systems due to chain formation of particles. (2) On the application of electric fields to suspensions placed on the comb pattern electrodes, a fine pattern with a waveform is developed from the smooth surface. The surface profiles can be approximated by single sinusoidal waves or their superposition depending on the sample thickness. (3) In thick liquid films, the dielectric polarization forces are predominant and the sinusoidal profiles with a wavelength of pitch of electrodes are formed. In thin films, the electrophoretic forces are predominant and the wavelength coincides with twice the pitch of electrodes. At intermediate thicknesses, the surface profiles can be expressed by a superposition of two sinusoidal waves. Acknowledgements This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan, for which the authors are grateful. References [1] J.R. Harbour, M.L. Hair, Ferrofluids as a contrasting fluid for electrophoretic display, Photogr. Sci. Eng. 26 (1982) 30–32. [2] V. Novotny, Applications of non aqueous colloids, Colloids Surf. 24 (1987) 361–375. [3] D.A. Hays, Paper documents via the electrostatic control of particles, J. Electrostat. 51–52 (2001) 57–63. [4] W.M. Winslow, Induced fibration of suspensions, J. Appl. Phys. 20 (1949) 1137–1140. [5] H. Block, J.P. Kelly, Electrorheology, J. Phys. D, Appl. Phys. 21 (1988) 1661–1677. [6] Y. Otsubo, M. Sekine, S. Katayama, Electrorheological properties of silica suspensions, J. Rheol. 36 (1992) 479–496. [7] Y. Otsubo, K. Edamura, Electrorheological properties of suspensions of inorganic shell/organic core composite particles, J. Colloid Interface Sci. 168 (1994) 230–234. [8] T. Hao, Electrorheological suspensions, Adv. Colloid Interface. Sci. 97 (2002) 1–35. [9] J.B. Yin, X.P. Zhao, Giant electrorheological activity of high surface area mesoporous cerium-doped TiO2 templated by block copolymer, Chem. Phys. Lett. 398 (2004) 393–399.
K. Tsuda et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 324 (2008) 228–233 [10] A. Gast, C.F. Zukoski, Electrorheological fluids as colloidal suspensions, Adv. Colloid Interface Sci. 30 (1989) 153–202. [11] Y. Chen, A.F. Sprecher, H. Conrad, Electrostatic particle-particle interactions in electrorheological fluids, J. Appl. Phys. 70 (1991) 6796–6803. [12] T.C. Halsey, Electrorheological fluids, Science 258 (1992) 761–766. [13] D.L. Klass, T.W. Martinek, Electroviscous fluids. I. Rheological properties, J. Appl. Phys. 38 (1967) 67–74. [14] D.L. Klass, T.W. Martinek, Electroviscous Fluids. II. Electrical properties, J. Appl. Phys. 38 (1967) 75–80. [15] D.J. Klingenberg, F. van Swol, C.F. Zukoski, The small shear response of electrorheological suspensions. I. Simulation in the point-dipole limit, J. Chem. Phys. 94 (1991) 6160–6169. [16] R.T. Bonnecaze, J.F. Brady, Yield stress in electrorheological fluids, J. Rheol. 36 (1992) 73–115. [17] Y.F. Deinega, G.V. Vinogradov, Electric fields in the rheology of disperse systems, Rheol. Acta 23 (1984) 636–651. [18] T.C. Jordan, M.T. Shaw, Electrorheology, IEEE Trans. Electr. Insulation 24 (1989) 849–878. [19] H. Block, J.P. Kelly, A. Qin, T. Watson, Materials and mechanisms in electrorheology, Langmuir 6 (1990) 6–14.
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¨ ¨ [20] D. Klein, H. Freimuth, G.J. Monkman, S. Egersdorfer, A. Meier, H. Bose, M. Baumann, H. Ermert, O.T. Bruhns, Electrorheological tactel elements, Mechatronics 15 (2005) 883–897. [21] Y. Otsubo, Effect of electrode pattern on the column structure and yield stress of electorheological fluids, J Colloid Interface Sci. 190 (1997) 466–471. [22] Y. Otsubo, Y. Suda, Electrorheological toners for electrophotography, J. Colloid Interface Sci. 253 (2002) 224–230. [23] L. Marshall, C.F. Zukoski, J.W. Goodwin, Effects of electric fields on the rheology of non-aqueous concentrated suspensions, J. Chem. Soc. Faraday Trans. I 85 (1989) 2785–2795. [24] Y. Otsubo, K. Edamura, Relation between yield stress and column thickness in electrorheological fluids, Colloids Surf. A: Phys. Eng. Aspects 109 (1996) 63–69. [25] J.E. Martin, J. Odinek, T.C. Halsey, Evolution of structure in a quiescent electrorheological fluid, Phys. Rev. Lett. 69 (1992) 1524–1527. [26] T. Chen, R.N. Zitter, R. Tao, Laser diffraction determination of the crystalline structure of an electrorheological fluid, Phys. Rev. Lett. 68 (1992) 2555–2558. [27] R. Tao, J.M. Sun, Three-dimensional structure of induced electrorheological solid, Phys. Rev. Lett. 67 (1991) 398–401. [28] R. Tao, J.M. Sun, Ground state of electrorheological fluids from Monte Carlo simulations, Phys. Rev. A 44 (1991) 6181–6184.
Contents lists available at ScienceDirect
Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa
Effect of electric fields on the surface profiles of electrorheological suspensions Kazutoshi Tsuda, Yuji Hirose, Hironao Ogura, Yasufumi Otsubo ∗ Department of Urban Environment Systems, Graduate School of Engineering, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba-shi 263-8522, Japan
a r t i c l e
i n f o
Article history: Received 4 December 2007 Received in revised form 8 April 2008 Accepted 10 April 2008 Available online 23 April 2008 Keywords: Electrorheology (ER) Surface profile Silica suspension Dielectric polarization Electrophoretic migration Comb pattern electrode
a b s t r a c t The surface deformation induced in electric fields is studied on the comb pattern electrodes for silica suspensions. On the application of electric fields, a fine pattern with a waveform is developed from the smooth surface. The surface profiles can be approximated by single sinusoidal waves or their superposition depending on the sample thickness. In electric fields, the silica suspensions shows the viscosity decrease in steady shear and yield stress in the limit of zero shear rates. The viscosity decrease can be attributed to electrophoretic migration of particles to one electrode and the development of yield stress to eletrorheological effects due to chain formation of particles between electrodes. In thick liquid films, the dielectric polarization forces are predominant and the sinusoidal profiles with a wavelength of pitch of electrodes are formed. In thin films, the electrophoretic forces are predominant and the wavelength coincides with twice the pitch of electrodes. At intermediate thicknesses, the surface profiles can be expressed by a superposition of two sinusoidal waves. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In general, the surface of particles dispersed in a liquid carries an electrical charge. Since the charged particles are attracted to one electrode in DC electric fields, the migration and deposition of particles can take place. When the suspension consisting of pigments in a colored solvent is sandwiched in a narrow space between transparent electrodes and the electric field is applied in one direction, the motion of pigment particles toward the electrode is generated. As a result, a passive image is produced due to the scattering and absorption of visible light by the deposited pigments. The application of electric fields in the opposite direction causes the removal of pigments and the electrode is covered with colored solvent. If the optical density of solvent is so high that the light reflection is not influenced by the pigments on the opposite electrode, the color of the solvent can be observed. By the use of the pigments and solvent with contrasting colors, the images can be controlled by deposition and removal of pigments. Recently, on the basis of this mechanism, the electrophoretic displays have received increasing interests as new imaging devices [1–3]. A reversible and rapid change in viscosity of fluids on the application or removal of electric fields is commonly referred to as the electrorheological (ER) effect. Typical ER fluids are suspensions of polarizable particles dispersed in insulating oils [4–9]. In electric
∗ Corresponding author. Tel.: +81 432903128; fax: +81 432903128. E-mail address: [email protected] (Y. Otsubo). 0927-7757/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2008.04.033
fields, each particle acquires an induced dipole. The dipole–dipole interactions cause the particles to form chain structures in direction parallel to the field vector [10–12]. The chains spanning the electrode gap respond elastically at very low strains. Therefore, the ER suspensions undergo a rapid transition from Newtonian fluids to rigid solids in electric fields. When the applied stress is increased above some critical value that is called yield stress, the steady-flow occurs in the electrified suspensions. After the onset of flow, the shear rate linearly increases with increasing the applied stress. The flow behavior of ER suspensions is represented by a Bingham equation in electric fields [13–16]. Since the local fluidity can be actively controlled by the field strength, the ER fluids are attractive as vehicles in new mechanical devices such as stop valves, clutches, and dampers [17–20]. In both electrophoretic and ER effects, the most important feature is that the distribution of particles in the systems becomes unhomogeneous on the application of electric fields. For fundamental evaluation of these effects, the uniform electric fields are usually applied for suspensions which are sandwiched between two parallel plate electrodes. But the electric forces acting on the particles depend on the local field intensity. Therefore, the nonuniform electric fields can increase the electric forces and in turn enhance the destabilization and structuring of particles. In fact, we have confirmed in previous papers [21,22] that the column formation of particles is enhanced in the honeycomb pattern electrodes and this serves to increase the yield stress of ER suspensions. The present study is designed to understand the particle behavior in nonuniform electric fields. The electric fields are generated by
K. Tsuda et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 324 (2008) 228–233
229
Fig. 2. Creep behavior for suspension at a particle concentration of 7.2 vol% in different electric fields: () 0; () 1.0; () 3.0 kV mm−1 .
Fig. 1. A schematic picture of comb pattern electrodes.
2. Materials and methods
and space. The line thickness and pitch of electrodes are 0.1 and 0.5 mm, respectively. The suspensions were places on the pattern electrodes at thicknesses up to 0.54 mm. A DC voltage in the range of 1.0–3.0 kV was applied to line electrodes on one side and the other electrodes were connected to the ground (E = 0). The bottom of suspensions was strongly electrified, but the top surface was exposed to atmosphere. The surface topography was measured by the use of a laser displacement sensor (LT9010M manufactured by Keyence). By combination with a mechanical stage (KS-1100 manufactures by Keyence), the wide regions of suspension surfaces could be scanned with a vertical accuracy of 0.01 m.
2.1. Materials
3. Results and discussion
The suspensions were composed of silica particles and silicone oil. The silica particles were manufactured by Catalysts and Chemicals Industries Co. Ltd. (Japan), whose diameter and density were 1.3 m and 2.2 × 103 kg m−3 , respectively. The silicone oil with a Newtonian viscosity of 0.12 Pa s and density of 1.0 × 103 kg m−3 at 25 ◦ C was obtained from Toshiba Silicone Co. (Tokyo, Japan) and used as received. The suspensions were prepared at particle concentrations up to 13% by volume. Prior to the sample preparation, the silica particles were heated at 105 ◦ C for more than 1 week to control the conditions of particle surfaces. Owing to the high viscosity of medium, the suspensions showed long term stability against sedimentation. Neither clear supernatant liquids nor sediments were detected after the storage in a quiescent state for several days.
3.1. ER behavior of suspensions
the use of a single flat plate, on which the electrodes of line and space are coated. When the suspensions placed on the electrodes are electrified, the deformation of surface profiles occurs by the unhomogeneous distributions of particles. The relation between the surface deformation and internal structures will be discussed in terms of electric forces induced on the flat electrodes with a comb pattern.
2.2. Methods Steady-flow and creep properties were measured using a parallel plate geometry on a stress-controlled rheometer (Haake, Rheo-Stress RS100) which was modified for the ER experiments. The diameter of plates was 35 mm and the gap between two plates was 0.5 mm. A DC voltage was applied by a technique of frictionless contact to the upper plate which was insulated from the shaft. The shear rates in steady-flow experiments were from 3.0 to 3.0 × 102 s−1 and the applied stresses in creep experiments were from 1.0 to 10 Pa. The ER behavior was measured in electric fields up to 4.0 kV mm−1 . The current density was less than 2 mA m−2 for all samples in an electric field of 4.0 kV mm−1 . The measuring temperature was 25 ◦ C. For measurements of field-induced surface topography, the flat electrodes with a comb pattern was used, of which the schematic picture is shown in Fig. 1. The glass surface is coated with transparent ITO (indium tin oxide) electrodes in a striped pattern of line
Fig. 2 shows the creep behavior for suspension at a particle concentration of 7.2 vol% in electric fields of 0, 1.0 and 3.0 kV mm−1 . The stress was increased stepwise from 1.0 to 10 Pa in a shearing time of 60 s at each stress. The strain was measured as a function of time. Without electric fields, the strain linearly increases with time and the responses can be approximated as purely viscous. In electric fields, the strain almost instantaneously responds the change in stress and reaches the equilibrium in short periods. Because the creep curve can be expressed by a Voigt model at low stresses, the electrified suspensions are apparently characterized as elastic solids. When the stress is increased beyond some critical level, the constant-rate strain due to viscous flow is suddenly induced. The suspension in electric fields has a yield stress which increases with increasing field strength. The yield stress is estimated to be about 10 Pa at 3.0 kV mm−1 . The creep experiments clearly indicate that the silica suspensions are ER-active and solidified at low stresses. Fig. 3 shows the flow behavior of 7.2 vol% suspension in electric fields of 0 and 3.0 kV mm−1 . The measurements were carried out in the procedure that the shear rate was exponentially increased and decreased in the range of 0.3–300 s−1 in a measuring time of 20 min. Significant differences are not observed between the upcurve and down-curve for suspension without electric fields. But, the down-curve and up-curve cannot be overlapped each other in electric fields. The stress of down-curve is decreased and the hysteresis appears between two curves at low shear rates. Another interesting aspect at low shear rates is that the stress level of downcurve in electric fields is lower than that in zero fields. Although the solidification of suspensions in electric fields is confirmed through creep experiments, the viscosity under steady-flow conditions is decreased. In ER suspensions, the viscosity enhancement is striking
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Fig. 3. Hysteresis behavior of viscosity during a cycle of increasing (filled symbols) and decreasing (open symbols) shear rate for 7.2 vol% suspension in electric fields of () 0 and (, ) 3.0 kV mm−1 .
at low shear rates and the stress curve plotted against the shear rate shows a plateau in the zero shear limit. The height which increases with increasing field strength is generally considered to correspond to the Bingham yield stress. However, the ER responses of sample suspensions are converted from positive to negative during steady shear. The low viscosity in electric fields and hysteresis behavior observed for sample suspensions cannot be explained by simple ER mechanisms. We have already reported [22] that the ER toners for electrophotography show similar flow behavior. In the liquid toners, the charge control agents are added to give the sufficient charges for fast development and high image quality. Since the charged particles are attracted to one electrode in DC electric fields, the migration and deposition of particles can take place. Provided that the particles dispersed in a liquid bear no electrical charges, the chain structures are constructed along the field vector by dielectric polarization forces. When the electrified suspensions are subjected to steady shear, the electric forces are dominant at low shear rates, and the hydrodynamic forces are dominant at high shear rates. In the case of liquid toners, the viscosity behavior is mainly determined by the dielectric polarization forces in low shear fields and electrophretic forces in high shear fields. Therefore, one can expect that the electrophoretic effects, producing a particle-free region near the upper plate, can cause the viscosity decrease. By the additional experiments, it is microscopically observed for sample suspensions that the negative electrode is covered with deposited particles after the electrification by a pair of needle electrodes. The unique ER behavior of silica suspensions can be explained by a combination mechanism in which the dielectric polarization forces give rise to the viscosity increase due to chain formation of particles and electophoretic forces lead to the viscosity decrease due to migration of particles to one electrode. The yield stress generated in electrified suspensions arises from the development of chain structures between electrodes. By assuming that the particles all align into chains of single-particle width and equal spacing, the yield stress can be predicted to linearly increases with particle concentration, because each chain has the same strength and the number of chains per area is proportional to the concentration [23]. For 7.2 vol% suspension with a yield stress of 10 Pa, the polarization forces between two particles in an electric field of 3.0 kV mm−1 is determined to be 1.23 × 10−10 N from the strength of single chain. The electophoretic migration is induced after the chains spanning the electrode gap are ruptured in shear fields. Considering that the viscosity reduction in electric fields is attributed to the
Fig. 4. Three-dimensional image and cross-sectional profile of surface for 9.9 vol% suspension at a sample thickness of 0.135 mm in an electric field of 3.0 kV.
formation of particle-free region, the rupture of chains may take place near the upper plate. The total electophoretic forces generated in the chain with a length of gap distance (consisting of 385 particles) may be comparable to the dielectric polarization forces between two particles at the breaking point. According to the theory on electophoretic migration of colloids, the surface charge can be calculated from the balance between electophoretic and hydrodynamic forces. The dielectric constant of silicone oil being taken as 2.7, the surface charge of silica in the sample suspension is estimated to be about 0.3 mV. The electric forces dominate at low shear rates, and the hydrodynamic forces dominate at high shear rates. The hydrodynamic force acting on a spherical particle with a radius of r at a shear rate of ˙ is given as 60 r 2 , ˙ where 0 is the viscosity of medium. The obtained value at ˙ = 300 s−1 is 2.87 × 10−10 N. This estimation is acceptable because the shear stresses around 300 s−1 are almost equal to the zero-field values as shown in Fig. 3. When the sufficient hydrodynamic forces are applied to the systems, the flow curves are not influenced by the electric fields. 3.2. Surface profiles in electric fields Fig. 4 shows the three-dimensional image and cross-sectional profile of surface for electrified suspension at a particle concentration of 9.9 vol%. The DC voltage of 3.0 kV was instantaneously applied for suspension placed on the electrodes at a thickness of 0.135 mm in the conditions of no electric fields. In many ER studies, the intensity of electric fields has been generally given by the voltage divided by the electrode separation. However, the electric fields are not uniform in this experimental configuration. The field intensity is expressed by the voltage applied to the line electrodes. On the application of an electric field, a fine pattern with a waveform is formed from the smooth surface in response times of about 100 ms. The cross-sectional profile in direction perpendicular to line electrodes is nearly sinusoidal. The wavelength is 1 mm and this corresponds to twice the pitch of line electrodes. In this study, the degree of surface deformation is evaluated by the topographical depth, that is, twice the amplitude of sinusoidal wave. The topographic depth shown in Fig. 4 is about 50 m. The tops of sinusoidal surfaces are located on the line of negative electrodes. Fig. 5 shows the topographic depth plotted against the sample thickness for 9.9 vol% suspension in different electric fields.
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Fig. 5. Topographic depth plotted against the sample thickness for 9.9 vol% suspension in different electric fields: () 1.0; () 2.0; () 3.0 kV mm−1 .
At 1.0 kV and below the change in surface profiles could not be detected. There exists a critical strength for appearance of waveform surfaces. Beyond the critical strength, the surface deformation is enhanced at higher electric fields. However, the suspensions could not be placed on the electrodes at thicknesses less than 0.1 mm. Because the conductive ITO part and insulating glass part have different surface properties, it is difficult to form the thin liquid films with a smooth surface on the comb pattern electrodes. Although the data are not obtained for thin liquid films, the topographic depth decreases with increasing sample thickness. When the thickness is increased above 0.5 mm, the smooth surfaces are kept even in high electric fields. With respect to the surface deformation in electric fields, the most significant finding is that the sample thickness influences not only the topographic depth, but also the surface profiles. As typical instances, Figs. 6 and 7 show the surface profiles at thicknesses of 0.27 and 0.54 mm, respectively, for 9.9 vol% suspension in an electric field of 3.0 kV. At 0.54 mm, the expression of surface profile by a sinusoidal function may be reasonable, but the wavelength is decreased to about half the value attained at 0.135 mm. It looks likely that the bottoms of sinusoidal surfaces are located on the line of electrodes, irrespective of polarity. As a first approximation, the increase in thickness may lead to a decrease in wavelength. However, it is difficult to accept the
Fig. 6. Three-dimensional image and cross-sectional profile of surface for 9.9 vol% suspension at a sample thickness of 0.27 mm in an electric field of 3.0 kV.
Fig. 7. Three-dimensional image and cross-sectional profile of surface for 9.9 vol% suspension at a sample thickness of 0.54 mm in an electric field of 3.0 kV.
sinusoidal approximation at 0.27 mm. At intermediate thicknesses, the surface profiles can be described by a superposition of two sinusoidal curves with different wavelengths. This suggests that the surface deformation of suspensions in electric fields should be controlled by two kinetic mechanisms. Fig. 8 shows the effect of particle concentration on the topographical depth in different electric fields for suspensions at a thickness of 0.27 mm. As expected from Fig. 5, the degree of surface deformation is pronounced in high electric fields. However, the particle concentration does not significantly influence the overall shapes of surface profiles, which is primarily dominated by the sample thickness. Referring to the result at 3.0 kV, the topographic depth increases, passes through a maximum, and then decreases with increasing particle concentration. If the particle concentration is increased beyond 15 vol%, the surface deformation in electric fields would not be generated. The periodical profile of suspension surfaces is a manifestation of unhomogeneous distribution of particles. Since the field-induced arrangements in the systems are determined by a balance between the electric forces acting on the particles and geometrical hindrance against particle migration, the particle concentration has an appropriate value for formation of surface profile with a maximum topographic depth.
Fig. 8. Effect of particle concentration on the topographic depth for suspensions at a thickness of 0.27 mm in different electric fields: () 1.0; () 2.0; () 3.0 kV mm−1 .
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Fig. 9. Models of particle migration due to different effects: (a) ER effect; (b) electrophoretic effect.
The intrinsic ER mechanism of suspensions is the chain formation of polarized particles. In uniform electric fields generated between parallel plate electrodes, the particles first form chains spanning the electrode gap. When placed near a chain, a particle will be repelled by the nearest particle in the chain. But the particle will be attracted by the chained particles well above and below it. As a result, the chains aggregate to build up the column [24–26]. The column structure must be the configuration which minimizes the dipolar interaction energy. The ideal column structure in electric fields is a body-centered tetragonal lattice [27,28]. Because the equilibrium conformations of individual chains are always aligned with the electric field, the direction of chains is perpendicular to the plate electrodes. The electric fields between two electrodes with the patterns of conductive lines are not uniform. The potential gradient is generated in the direction parallel to the electrode surfaces. Therefore, the force component in direction perpendicular to individual chains is enhanced to build up the closely packed column. We have reported [21] that the nonuniformity of electric field can cause the columns with high particle concentrations. Let us now consider the geometrical situation employed in the present study. Since the silica suspensions are electrified between line electrodes on the single glass plate, the particle–particle attraction which causes the chain structures between electrodes is induced in direction perpendicular to electrode lines. Also, the forces in direction perpendicular to the glass plate are generated by dielectric polarization of particles in nonuniform fields. As the polarization effects are independent of polarity of electrodes, the topographic thickness is increased between electrode lines due to the particle migration and formation of condensed columns. The wavelength of surface profiles is determined by the pitch of striped pattern. Fig. 9(a) shows a schematic picture of forces between polarized particles on comb pattern electrodes. The forces acting on the particles by electric polarization are decreased with increasing distance from the electrodes. Hence, the sinusoidal profiles disappear for thick liquid films. When the sample thickness is decreased to the order of 0.1 mm, the forces in direction parallel to glass plate become predominant. Even at the surfaces of suspensions, the dielectric polarization hardly contributes to the perpendicular forces which result in the particle migration toward the glass surface. However, the silica particles are positively charged in the silicone oil. In electric fields, the particles are attracted to negative electrode and the migration of particles takes place by electrophretic effect. Fig. 9(b) shows a schematic picture of electrophoretic migration of particles on comb pattern electrodes. Because the particles are repelled by the positive electrode and deposited on the negative electrode, the sinusoidal profiles are formed, whose wavelength coincides with twice the pitch of electrodes. The large values of topographic depth are attributed to high field intensity in thin liquid films. In the range of sample thickness studied, the forces causing the surface profile
changes are governed by electrophoretic effect for thin films and by ER effect for thick films. Although the magnitude of forces decreases with increasing sample thickness, the electrophoretic and ER forces acting on particles are comparable at the intermediate thickness. Therefore, the surface profiles are expressed by a superposition of two sinusoidal waves. As a simplified approach, the field strength on comb pattern electrodes is quantitatively evaluated through a model consisting of two wire electrodes. Supposing that the field strength at the surface of suspensions with a thickness of 0.135 mm above the line of negative electrode is unity, the increase of thickness to 0.54 mm causes the field strength to decrease to 0.1. Since the field vector is directed to the electrode, the electrophoretic forces rapidly decreases with increasing thickness. On the other hand, above the center of electrode gap for suspension with a thickness of 0.54 mm, the relative field strength in direction parallel to the suspension surfaces is about 0.2. The electric force contributing chain formation is slowly decreases with increasing thickness. Consequently, the dielectric polarization forces govern the surface profiles at large thicknesses. 4. Conclusions (1) When the electric fields are applied to silica suspensions in a silicone oil, the electophoretic force and dielectric polarization force are generated on the particles. The former results in the viscosity decrease due to migration of particles to one electrode and the latter in solidification of systems due to chain formation of particles. (2) On the application of electric fields to suspensions placed on the comb pattern electrodes, a fine pattern with a waveform is developed from the smooth surface. The surface profiles can be approximated by single sinusoidal waves or their superposition depending on the sample thickness. (3) In thick liquid films, the dielectric polarization forces are predominant and the sinusoidal profiles with a wavelength of pitch of electrodes are formed. In thin films, the electrophoretic forces are predominant and the wavelength coincides with twice the pitch of electrodes. At intermediate thicknesses, the surface profiles can be expressed by a superposition of two sinusoidal waves. Acknowledgements This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan, for which the authors are grateful. References [1] J.R. Harbour, M.L. Hair, Ferrofluids as a contrasting fluid for electrophoretic display, Photogr. Sci. Eng. 26 (1982) 30–32. [2] V. Novotny, Applications of non aqueous colloids, Colloids Surf. 24 (1987) 361–375. [3] D.A. Hays, Paper documents via the electrostatic control of particles, J. Electrostat. 51–52 (2001) 57–63. [4] W.M. Winslow, Induced fibration of suspensions, J. Appl. Phys. 20 (1949) 1137–1140. [5] H. Block, J.P. Kelly, Electrorheology, J. Phys. D, Appl. Phys. 21 (1988) 1661–1677. [6] Y. Otsubo, M. Sekine, S. Katayama, Electrorheological properties of silica suspensions, J. Rheol. 36 (1992) 479–496. [7] Y. Otsubo, K. Edamura, Electrorheological properties of suspensions of inorganic shell/organic core composite particles, J. Colloid Interface Sci. 168 (1994) 230–234. [8] T. Hao, Electrorheological suspensions, Adv. Colloid Interface. Sci. 97 (2002) 1–35. [9] J.B. Yin, X.P. Zhao, Giant electrorheological activity of high surface area mesoporous cerium-doped TiO2 templated by block copolymer, Chem. Phys. Lett. 398 (2004) 393–399.
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