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Bidisperse Electrorheological Fluids Using Hydrolyzed Styrene-Acrylonitrile Copolymer Particles: Synergistic Effect of Mixed Particle Size Jung-Bae Jun, Seong-Yong Uhm, Seong-Heun Cho, and Kyung-Do Suh* Division of Chemical Engineering, College of Engineering, Hanyang University, Seoul 133-791, South Korea Received June 17, 2003. In Final Form: November 24, 2003 Monodisperse micron-sized styrene-acrylonitrile copolymer (SAN) particles with three different sizes (about 5, 10, and 15 µm) were prepared by a two-step seeded polymerization and used for a study of bidisperse electrorheological (ER) suspensions. The effect of the particle size and the size-mixing fraction on ER properties was studied with varying the size of these monodisperse copolymer particles. When the two particle sizes were mixed, the suspension generally showed a decrease in the shear yield stress, reaching a minimum value. However, a bidisperse ER suspension of large particles containing a small fraction of fine particles showed an interesting synergy effect of size mixing on ER response, giving enhanced yield stresses over the other size-mixing fractions. This synergistic ER suspension also showed a great increase in the viscoelastic property. The current density of suspensions was maximum at the synergistic bidisperse suspension. This synergy effect in a particular bidisperse suspension was investigated in view of the structure model consideration and was concluded to be due to a close packing and a peculiar structural ordering at an optimum size ratio and mixing fraction.
Introduction The electrorheological (ER) fluids, first reported by Winslow1 in 1949, have been studied widely for a long time and recently have gained much more attention because of their potential applications in many industrial areas. There also have been several mechanisms to explain the origin of ER effect from the attractive forces between dispersed particles in ER suspension. The widely accepted model assumed dielectric polarization of ER fluids arising from the difference between dielectric permittivities of the dispersed particles and the medium liquid.2 In the presence of an electric field, suspended particles polarize and align into chains and consequently aggregate to form a lattice structure of particles, for example, body centered tetragonal (BCT) lattice,3,4 in the columns. In addition, the strength of an individual column increases rapidly with column thickness because of multichain interactions.5 This complexity of the structures formed makes it difficult to fashion theoretical models for the purpose of matching calculations with actual rheological properties to understand and improve ER fluids. However, it is certain that the particle size and size distribution affect the column structure. As stated, because ER effect is strongly affected by the dipole moment of particles and the geometry of the particle chains in the column while forming the chain, it is required to understand further the effect of particle size characteristics on ER properties. Though systematic analyses of the dependence of ER effect on the size characteristics of suspended particles have been performed in recent years, there have been few studies using completely monodisperse particles. Many * To whom correspondence should be addressed. E-mail: kdsuh@ hanyang.ac.kr; telephone: +82-2-2290-0526; fax: +82-2-2295-2102. (1) Winslow, W. M. J. Appl. Phys. 1949, 20, 1137. (2) Klingenberg, D. J.; Zukoski, C. F. Langmuir 1990, 6, 15. (3) Parthasarathy, M.; Klingerberg, D. J. Mater. Sci. Eng., R 1996, 17, 57. (4) Dassanayake, U.; Fraden, S.; van Blaaderen, A. J. Chem. Phys. 2000, 112, 3851. (5) Otsubo, Y.; Edamura, K. Colloids Surf., A 1996, 109, 63.
researchers investigated extensively a variety of particle size and size distribution for ER effect, and their influence on the ER effect is quite diverse.6-13 Monodisperse ER fluids are generally expected to give a stronger ER effect than polydisperse suspensions because the monodisperse particles strengthen particle chain formation because of a greater electrostatic interaction between neighboring particles. Ota and Miyamoto9 disclosed from their theoretical study that a homogeneous ER fluid should give the largest yield stress. Wu and Conrad10 supported this conclusion by experiments where mixed glass spheres of different sizes were used and found that the shear yield stress decreased to a minimum value with the volume fraction of smaller particles. Tan et al.11 explained the reduction of shear stress for two-component ER fluids as follows: when the smaller particles are embedded in the homogeneous large particle chain, the homogeneous chains are weakened because the chain segment, particle in the chain or the column, has weaker internal dipole interaction, producing a larger breaking or deformation. On the other hand, a large enhancement of shear yield stress was observed by Tam et al.12 on adding nanoparticles of lead zirconate titanate or lead titanate to the ER fluid containing 50 µm glass spheres. Their experimental results suggested that the ferroelectric nanoparticles not only modify the dielectric constant of the liquid but also coat the glass spheres to form, effectively, particles with higher dielectric constant. See et al.13 also found the highest ER effect occurring with a mixed suspension of small and large particles (50:50 mixture). It was proposed that the reason for the different stress behaviors is associated with (6) Shih, Y. H.; Conrad, H. Int. J. Mod. Phys. B 1994, 8, 2835. (7) Ahn, K. H.; Klingenberg, D. J. J. Rheol. 1994, 38, 713. (8) Lemaire, E.; Meunier, A.; Bossis, G. J. Rheol. 1995, 39, 1011. (9) Ota, M.; Miyamoto, T. J. Appl. Phys. 1994, 76, 5528. (10) Wu, C. W.; Conrad, H. J. Appl. Phys. 1998, 83, 3880. (11) Tan, Z. J.; Zou, X. W.; Zhang, W. B.; Jin, Z. Z. Phys. Rev. E 1999, 59, 3177. (12) Tam, W. Y.; Wen, W.; Sheng, P. Physica B 2000, 279, 171. (13) See, H.; Kawai, A.; Ikazaki, F. Rheol. Acta 2002, 41, 55.
10.1021/la030248c CCC: $27.50 © 2004 American Chemical Society Published on Web 02/11/2004
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the size ratio influencing the particle aggregate microstructure, which is responsible for the flow resistance. In our previous study,14 we could synthesize highly monodisperse hydrolyzed styrene-acrylonitrile copolymer (SAN) particles by a two-step seeded polymerization showing different ER characteristics with particle compositions. In this study, three different sizes of monodisperse hydrolyzed SAN particles were dispersed in a silicone oil for the study of ER properties of bidisperse suspensions. The effect of the particle size on the ER response was investigated by altering the size level and the mixing volume fraction ratios. The results show an interesting synergistic ER response for a certain mixed size system. Experimental Section 1. Preparation of Hydrolyzed SAN Particles. Monodisperse PS particles with three different sizes were prepared by dispersion polymerization of styrene (St, Aldrich Chemical Co.) with altering the type of dispersion medium and the initiator concentration.14,15 These PS particles were used as seed particles for a two-step seeded polymerization to prepare monodisperse micron-sized SAN particles, and the seeded polymerization procedures are much the same as reported in our previous works.14,16,17 First, the obtained PS seed particles (0.2 g) were redispersed in a 0.25% sodium lauryl sulfate (SLS) aqueous medium and swollen with 1-chlorododecane (CD, Tokyo Chemical Industry (TCI) Co., 0.3 g) at 30 °C for 12 h. Second, an emulsion of a monomer mixture (20 g) of St, acrylonitrile (AN, TCI Co.), and benzoyl peroxide (BPO, Junsei Chemical Co., 1 wt % against total monomers) was poured into the reactor, and the swelling was continued at 30 °C for another 6 h. The swollen particles were then stabilized with a 5 wt % poly(vinyl alcohol) (PVA, Mw ) 8.8 × 104∼9.2 × 104 g‚mol-1, 87∼89% hydrolyzed, Kuraray Chemical Co.) aqueous solution, and the polymerization was carried out under a nitrogen atmosphere at 70 °C for 16 h. The particles produced were repeatedly washed by decantation in water and ethanol and dried under a vacuum at ambient temperature. To obtain SAN particles with various sizes, the size of seed latex particles was varied. To increase the polarizability of particles for the ER effect, hydrolyzed SAN particles were prepared and used. Hydrolysis of the SAN particles was carried out according to a Radziszewski reaction.18 SAN particles were dispersed into the mixture of hydrogen peroxide, water, acetone, and potassium sulfide, and the hydrolysis reaction was performed at 50 °C for 12 h. Then, hydrolyzed SAN particles were thoroughly washed with water and dried in a vacuum at 80 °C for 24 h. 2. Characterization and Viscometry. The particle morphology was observed by scanning electron microscopy (SEM, JSM-6330, JEOL) and the diameter of particles was determined by Coulter Counter Multisizer II. The permittivity of the SAN particles was measured at a range of 100-106 Hz with a dielectric spectrometer (Concept 40, NOVOCONTROL). The ER fluids with a 20% volume fraction were prepared by dispersing particles with different sizes at various particle volume ratios in a silicone oil (KF-96, 50cS, Shinetsu) with mechanical stirring. Rheological properties of the suspensions were measured at room temperature by an ARES concentric cylindrical rheometer (ARES4, Rheometric Scientific, Inc.) equipped with a high-voltage power generator (EL5P8L, Glassman High Voltage, Inc.). A dc electric field was applied for 3 min to obtain an equilibrium structure before applying the shear, and the flow curves were obtained with the rheometer operating in the controlled strain mode. An oscillatory shear experiment was also performed in the frequency sweep test mode from 10-1 to 102 rad/s at the (14) Jun, J. B.; Uhm, S. Y.; Suh, K. D. Macromol. Chem. Phys. 2003, 204, 451. (15) Tuncel, A.; Tuncel, M.; Salih, B. J. Appl. Polym. Sci. 1999, 71, 2271. (16) Kim, J. W.; Suh, K. D. Macromol. Chem. Phys. 2001, 202, 621. (17) Park, J. G.; Kim, J. W.; Suh, K. D. Colloid Polym. Sci. 2001, 279, 638. (18) Payne, G. B.; Deming, P. H.; Williams, P. H. J. Org. Chem. 1961, 26, 569.
Figure 1. SEM photograph of monodisperse hydrolyzed SAN particles used (M-SAN). Table 1. Particle Characteristics of the Hydrolyzed SAN Microspheres with Different Sizes and Same Dielectric Property
name
number average diameter, Dn (µm)
particle size distribution, Dw/Dn
dielectric constant at 100 Hz
S-SAN M-SAN L-SAN
5.31 9.52 14.96
1.01 1.01 1.01
15.82
strain amplitude 0.1%. The dc current density under a static (no shear) condition was measured using a Keithley 196 system.
Results Highly monodisperse PS seed particles were produced by dispersion polymerization, and with these seed particles, monodisperse micron-sized SAN particles were also produced through the two-step seeded polymerization. Then, SAN particles were hydrolyzed in a basic medium, maintaining the size monodispersity and the spherical shape unchanged. The properties of hydrolyzed SAN particles produced are listed in Table 1. All the particles were highly monodisperse in size and particle size was successfully controlled by the seeded polymerization method. Figure 1 shows the SEM photograph of typical hydrolyzed SAN particles with a medium size (M-SAN in Table 1). Therefore, it was possible to prepare completely monodisperse and bidisperse ER fluids for the study of relation between the ER effect and the size-mixing fraction. Figure 2 shows the relation between the diameter of hydrolyzed SAN particles and the yield stress for homogeneous ER fluids as a function of the electric field strength. As the diameter increased, the dynamic yield stress of the ER fluids also increased. Additionally, as the applied electric field strength was increased, the yield stress increased gradually. From the result, the shear yield stress is largely dependent on the particle size, and this follows our previous experimental results14,19 and also is in agreement with the results of Shih and Conrad6 and Tan et al.11 It is seen that the dependence of the shear yield stress on the field strength is slightly stronger for the large particle ER suspension than for the small particle suspension. Figure 3 gives the shear yield stress versus the mixing fraction ratio of particles, where φm and φs are the volume (19) Jun, J. B.; Lee, C. H.; Kim, J. W.; Suh, K. D. Colloid Polym. Sci. 2002, 280, 744.
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Figure 2. The relation between the diameter of hydrolyzed SAN particles and the yield stress for homogeneous ER fluids as a function of electric field strength.
Figure 4. Storage moduli obtained from the dynamic frequency sweep test for the bidisperse ER fluids using M-SAN (a) and S-SAN (b) particles at an electric field of 3 kV/mm.
Figure 3. The shear yield stress vs the ratio of volume fractions of M-SAN particle φm (a) and S-SAN particle φs (b) to the total particle volume fraction φ for applied fields E ) 1, 2, and 3 kV/mm.
fraction of the M-SAN and S-SAN particles, respectively, and φ ) 0.2 is the total particle volume fraction. For
bidisperse ER suspensions of L-SAN particles mixed with M-SAN particles (Figure 3a), the shear yield stress decreased over all the size-mixing fractions. This result is in good agreement with the result of Wu and Conrad,10 indicating that uniform-size ER suspension as well as an appropriately large size is required to provide a higher ER property. It is also in good agreement with the theoretical prediction of Ota and Miyamoto.9 For a more detailed description of synergistic effect by particle mixing ratios on the shear yield stress, two additional measurements at mixing fractions of small particles φs/φ ) 0.1, 0.3 were added to Figure 3b. For bidisperse ER suspensions of L-SAN particles mixed with S-SAN particles (Figure 3b), yield stresses at φs/φ > 0.2 showed a similar result like in M-SAN bidisperse suspensions, a negative effect with the mixing of particle sizes. However, an interesting result was found in the size-mixing fraction, φs/φ ) ∼0.2. At φs/φ ) 0.1, the yield stresses were as high as or nearly equal to those at φs/φ ) 0.2; besides, at φs/φ ) 0.3, the yield stress dropped significantly. It is obvious from the results that the highest yield stress appears when a small amount of fine particles are added in the range φs/φ ) 0.1-0.2. These synergistic ER suspensions showed much higher yield stresses than those of each homogeneous ER suspension of large and small particles. See et al.13
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Figure 6. A schematic diagram of the sphere pair geometry. Rij is the center-to-center separation and θij is the angle between the line of centers and the applied electric field.
strongly affected both by the mixing fraction ratio and by the size ratio, giving different ER behaviors such as in the steady shear tests. The current density passing through the ER fluid can be characterized by two components, the absorption current density due to the surface charge and the leakage current density due to the charge transfer between the dielectric particle and the electrode. Figure 5 shows the current density versus the particle mixing fraction ratio for mixed ER fluids. Current densities decreased at most mixing conditions, showing a similar trend to the shear yield stress. However, the synergistic ER fluid gave higher current densities than the other ER fluids. Discussion
Figure 5. Current density vs the ratio of the volume fraction of M-SAN particle (a) and S-SAN particle (b) to the total particle volume fraction φ for applied field E ) 1, 2, and 3 kV/mm.
previously reported the synergy effect of mixing particle sizes; their work found that the highest ER effect occurred with the same mixing amount of small and large particles (50:50). They explained that the difference could be that the ratio of particle sizes (3.3:1 in their work) influences the packing of the particles and hence the microstructure of the columns or particle aggregates. Though the ratio of particle sizes of our ER fluid showing a synergy effect is about 3:1 similar to that of See et al.’s, the highest yield stress was observed at the mixture volume fraction ratio of ∼0.2. Moreover, when the mixture volume fraction ratio is about 0.5 (same as 50:50), the shear yield stress of our study reached a minimum value. This is a totally different result from that of See et al. and a possible reason for our particular synergistic effect will be considered in the discussion section. The effect of particles size mixing on the storage modulus of ER fluids is shown in Figure 4. Also in the dynamic test, the storage moduli of homogeneous suspensions were larger than those of bidisperse suspensions, except for the suspensions with small volume fraction ratios of S-SAN particles φs/φ ) 0.1-0.2. This reveals that the synergistic ER fluids have more rigid and stronger particle chains or columns, which are responsible for the higher viscoelastic property. From the results, it is expected that the geometry of the particle chain or column under an electric field be
In this study, we consider only the electrostatic contribution to the stress because the electrostatic force on spheres is one of the most important factors that govern the motion of spheres not near an electrode. The shear stress acting in the x direction on a plane normal to the z direction is the total electrostatic plus short-range repulsive force acting on sphere i in the x direction (See Figure 6). To explain bidisperse suspensions in steady-shear flow, Ahn and Klingenberg7 employed an extended model of idealized electrostatic polarization model for ER suspensions that has been previously developed for simulations of monodisperse suspensions of hard, dielectric spheres.20 In these cases, ER fluids are suspensions of dielectric spherical particles (dielectric constant p) dispersed in a dielectric continuous phase (dielectric constant c). All the particles possess the same dielectric constant but have different diameters. Colloidal and Brownian forces are negligible for large particles under large electric fields. They depicted the electrostatic force on sphere i (diameter σi) at the origin of a spherical coordinate system because of sphere j (diameter σj) at (Rij, θij) by point-dipole limit:
Felif (Rif, θif) ) Fs(σi, σj)
( )
where Rmin ) (σi + σj)/2,
Fs(σi, σj) )
Rmin 4 [(3 cos2 θij - 1)er + Rif sin 2θifeθ] (2)
(
)
16λif3 3 π0cβ2E02 σj2 16 (1 + λif)4
(3)
0 )8.854 × 10-12F/m, β ) (p - c)/(p + 2c), and λif ) σi/σj. (20) Klingenberg, D. J.; Swol, F. V.; Zukoski, C. F. J. Chem. Phys. 1991, 94, 6160.
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Figure 7. Schematic simple configurations of the structure of bidisperse ER suspensions.
According to the above equation, as the ratio of particle diameters (λ) increases, the electrostatic force on particles decreases. Providing the larger particle (L-SAN) is sphere i; it can be simply calculated from eq 3 that for the bidisperse ER fluid with S-SAN, Fs on an L-SAN particle becomes about 36 times smaller than that of an L-SAN particle pair. Though this calculation is a very simplified one, it is easily thought from this theoretical consideration that a monodisperse system is more effective to give higher ER effect. In practice, our results except for one formulation (S-SAN/L-SAN ) 2/8, v/v) agree well with the above theoretical model. However, how can this exceptional case showing a synergistic ER effect be explained? If the particle volume fraction is constant, the ER response of suspensions will be strongly governed by the structural stability and the rigidity of particle chains and columns formed under electric fields. Thus, we consider three simple two-dimensional configurations as shown in Figure 7. Each chain consists of random particle configuration: (a) large particle rich, (b) equal portion of the two particle sizes, and (c) fine particle rich system. In b and c, the two particle sizes cannot form individual chains but acted together to form chains or clusters containing a mixture of the two. Because each particle size acts as a defect in generating homogeneous particle chains, these structures should give a weaker shear strength than that of monodisperse suspensions. In reality, steady shear curves and yield stresses of these two cases well followed the theoretical prediction of Ota and Miyamoto,9 where the ER properties of bidisperse suspensions depend on the particle configuration of two sizes, that is, the ER fluid consisting of only the same particles gives the largest yield stress. This is much the same result of Wu and Conrad. However, an interesting point of this model is that case a exhibits a homogeneous chain of large particles, whereby small particles are attached to the large particles. In the configuration a, when an electric field is applied, large particles occupying most of the particle volume predominantly form a homogeneous chain because of their greater dipole moment. Thereafter, small particles attach to the chain between large particles. However, this large particle-rich case also showed totally different results according to the size ratio of two particles, and the reason cannot be simply explained by two-dimensional consideration. Therefore, we consider a three-dimensional structure of particle chains. In general, under an electric field, particles align between two electrodes, usually as a group of chains or clusters predicted and verified to have the BCT structure.3,4 The unit cell of the BCT lattice is schematically illustrated in Figure 8. When the lattice is composed of monodisperse particles with a radius r, one center particle would have eight nearest neighbor particles of the interparticle distance 2r, which belongs to the different chain class, whereas one center particle also has six other nearest neighbor center particles also of the
Figure 8. A schematic illustration of the unit cell of the BCT lattice formed by the ER particles under an electric field. The radius of the large particle is r.
interparticle distance 2r, which belongs to the same chain class. However, most bidisperse suspensions cannot produce complete BCT structure because of the inhibiting of different particle sizes. However, assuming the size ratio of particles is high and fine particle volume fraction is low, it is possible BCT structure of only large particles can be produced. This phenomenon is similar to configuration a in Figure 7. Thus, the synergy effect of S-SAN/ L-SAN bidisperse fluid can be explained by this lattice concept. For the synergy effect of a bidisperse ER fluid, a fine particle/coarse particle ratio should be small as a fine particle can enter the gap in the large particle lattice (see Figure 8). For example, for the BCT lattice of L-SAN particles (diameter ) 14.96 µm) in the bidisperse system, fine particles should be smaller than ∼8.7 µm to exhibit an enhancement in ER effect. The size of S-SAN particle satisfies this size limit, but the M-SAN particle does not. Moreover, embedded fine particles between the coarse lattice particles enhance the volume-packing fraction of a unit cell, making the particles hold together tightly with electrostatic interactions. Here, the volume-packing fraction is another factor that affects the chain strength. In bidisperse suspensions, the general feature is an increase in the packing fraction as the size ratio is increased, with a maximum of the packing fraction even more pronounced as the size ratio is larger.21,22 Although mixing of L-SAN with M-SAN particles slightly increases the packing fraction of a unit cell, the microstructure of lattices is strongly deformed because of the very low size ratio (1.6: 1); besides, homogeneous chains of L-SAN particles will hardly be formed. That is, M-SAN particles are caught as a lattice-forming particle, behaving as a structural defect and inhibiting the homogeneous ordering. This model assumption is also supported by the current density profile of bidisperse suspensions. Current density profiles with the mixing ratio of particles in Figure 5 are almost similar to the yield stress curves in Figure 3. This fact shows that the current density is largely dependent on the microstructure of particle chains or columns. Close packing by mixing a small amount of fine particles as well as strong interparticle attraction in the large particlebased lattice structure will increase the current flow along the chain structure. Consequently, the higher current density at the same electric field is due to the close particle formation and the strong particle interaction that causes more chains to draw into thicker columns spanning the two electrodes. (21) Gupta, R. K.; Seshadri, S. G. J. Rheol. 1986, 30, 503. (22) Probstein, R. F.; Sengun, M. Z.; Tseng, T. C. J. Rheol. 1994, 38, 811.
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Conclusions Highly monodisperse spherical SAN particles of three different sizes have been used to investigate the effect of mixing different sizes on the ER response at moderate shear rates. In most cases, bidisperse ER fluids exhibited lowered shear yield stresses than the homogeneous ER fluid of large particles. The negative effect of size mixing on ER properties was considered as the result of interfering chains or column structures of suspended particles by a different size, especially by smaller particles embedded between large particles. These results of mixed systems are in good agreement with those of other previous bimodal systems giving the reduced yield stresses. However, the great enhancement in the yield stress was peculiarly obtained when a small faction (φs/φ ) 0.2) of small S-SAN particles were mixed with large L-SAN particles. The reason for this synergistic ER effect can be suggested from
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the model considerations that the ratio of particle sizes strongly affects the particle microstructure, ordering and packing, and hence the stiffness of the chains or columns responsible for the stress buildup. From the results, it is concluded that for higher ER properties the suspension should have optimum particle size distribution, either a monodisperse or a bidisperse system in case-by-case. Additionally, it is required to understand more the effect of the size and size mixing on the ER property, with varying the size range (extending from nanoscale to a hundred micrometer), the size ratios, and the total volume fractions. Acknowledgment. This study was supported by a grant of the Korea Health 21 R&D Project, Ministry of Health & Welfare, Republic of Korea (03-PJ1-PG1-CH140001). LA030248C
