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J. Phys. Chem. B 2008, 112, 14132–14139
Particle Dispersibility and Giant Reduction in Dynamic Modulus of Magnetic Gels Containing Barium Ferrite and Iron Oxide Particles Tetsu Mitsumata,*,† Takashi Wakabayashi,† and Takahiko Okazaki‡ Department of Polymer Science and Engineering, Graduate School of Engineering, Yamagata UniVersity, Yonezawa 992-8510, Japan, and Research and DeVeloping Center, Bando Chemical Industries, Ltd., Kobe 652-0882, Japan ReceiVed: July 7, 2008; ReVised Manuscript ReceiVed: September 7, 2008
The particle dispersibility of barium ferrite and iron oxide magnetic particles in carrageenan gels was investigated, and the influence of the dispersibility on the giant reduction in the dynamic modulus of the gels was discussed. The gels containing barium ferrite demonstrated giant reductions in the storage Young’s modulus on the order of 105 Pa due to magnetization; however, small reductions in the storage modulus of less than 104 Pa were observed for the gels containing iron oxide. The storage modulus of gels with barium ferrite did not follow the Krieger-Dougherty equation above volume fractions of 0.06, indicating the heterogeneous dispersion of the magnetic particles; however, the modulus of the gels with iron oxide satisfied the equation at all volume fractions, suggesting the random dispersion of the particles. It was noted that the gels with barium ferrite demonstrated enhanced nonlinear viscoelasticity and a large value of the loss tangent, while the gels with iron oxide exhibited weak nonlinear viscoelasticity and a small value of the loss tangent. Magnetic measurements indicated high values of remanent magnetization for barium ferrite and low values for iron oxide. After magnetization at 1 T, the magnetic gels with barium ferrite became elongated parallel to the magnetic field and shrunk perpendicular to the field. In contrast, the magnetic gels with iron oxide did not undergo a marked deformation. These results strongly indicate that the giant reduction in the storage modulus requires both enhanced nonlinear viscoelasticity and magnetostriction which originate from the particle dispersibility. The relationship between the dispersibility of magnetic particles and the giant reduction in the storage modulus is discussed using rheological and morphological data. 1. Introduction Functional soft materials responsive to physical stimuli have been extensively and thoroughly investigated for the past decade. Magnetic fluids are a functional material for which the viscoelastic property markedly changes upon applying a magnetic field. The phenomenon is called the magnetorheological (MR) effect, which has attracted considerable attention because of its potential use in field-sensitive actuators and dampers. Polymer gels and elastomers containing magnetic fluids or fine magnetic particles also exhibit the MR effect, and they are called MR gels and MR elastomers, respectively. Not only have MR fluids been developed but also MR gels and elastomers for use in vibration control devices because the change in the dynamic modulus leads to a shift of the resonance frequency of the vibration. In general, the effect of a magnetic field on the elastic modulus is positive, that is, the elastic modulus increases in the presence of a magnetic field. For example, a poly(vinyl alcohol) (PVA) gel containing magnetic fluids exhibited a change in Young’s modulus of 31 Pa under a magnetic field of B ) 0.5 T.1 A silicone gel in which iron particles were aligned demonstrated an increase in storage modulus of 18 kPa at B ) 43 kA/m when the volume fraction of the iron particles was φ ) 0.28. The increase in the modulus decreased under large strains of γ > 0.1.2 An elastomer containing aligned carbonyl * To whom correspondence should be addressed. E-mail: tetsu@ yz.yamagata-u.ac.jp. Phone: +81 (0)238 26 3078. Fax: +81 (0)238 26 3101. † Yamagata University. ‡ Bando Chemical Industries, Ltd.
iron particles exhibited an increase in shear modulus of 0.6 MPa at B ) 0.8 T and φ ) 0.3.3 An elastomer made of natural rubber and carbonyl iron particles underwent an increase in shear modulus of 2 MPa at B ) 0.6 T and φ ) 0.27.4 The storage modulus of a silicone elastomer containing carbonyl iron particles increased by 4 MPa upon curing under a magnetic field at B ) 42 kA/m and φ ) 0.3.5 An MR rubber with carbonyl iron powder underwent dynamic modulus changes of 2.5 MPa at B ) 170 kA/m and φ ∼ 0.56 and 3.5 MPa at B ) 525 kA/m and φ ∼ 0.38.7 It was also revealed using a poly(dimethyl siloxane) elastomer with aligned magnetic particles that the MR effect strongly depends on the direction of the magnetic field.8 The positive change in the elastic modulus for these materials can be understood by considering the magnetic energy acting between magnetized particles. In contrast, a material has been used to demonstrate the negative change in the elastic modulus due to magnetization. Our previous studies revealed that a natural polymer gel containing barium ferrite particles demonstrated significant negative changes in the dynamic modulus upon magnetization.9,10 The magnetic gel with a volume fraction of magnetic particles 0.39 exhibited reductions in the storage Young’s modulus of ∼107 Pa and in the loss modulus of ∼106 Pa upon magnetization at B ) 1 T. Magnetic gels demonstrating such a giant reduction in the dynamic modulus had enhanced nonlinear viscoelasticity, which is called the Payne effect.11 This originated from the temporal destruction of particle networks, which were made of many fragile (physical) contacts between the magnetic particles. The contacts are due to a simple physical contact, not to a special
10.1021/jp805955j CCC: $40.75 2008 American Chemical Society Published on Web 10/22/2008
Magnetic Gels Containing BaFe12O19 and Fe3O4 Particles
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Figure 1. SEM photographs of barium ferrite (a,b) and iron oxide (c,d) used in the present study. Magnification: ×10 000 (a,c), ×20 000 (b,d).
force such as magnetic interaction. It was also noted that the magnetic gels exhibited magnetically induced strain, i.e., magnetostriction of as large as 10-3. Magnetostriction was also observed in polyurethane elastomers containing barium ferrite particles.12 The giant reduction in the dynamic modulus is caused by the permanent destruction of the particle network induced by the magnetostriction. Therefore, the modulus change upon magnetization should be affected by both the degree of nonlinear viscoelasticity and the strain induced by the magnetostriction. In this paper, we investigated the effect of magnetic particles on the giant reduction in the dynamic modulus using barium ferrite and iron oxide particles. In a dry state, the barium ferrite and iron oxide particles had mean volume diameters of 1.84 and 1.59 µm, respectively. Both particles showed that the double peaks seen in the dry state were unified in pure water. In pure water, the agglomerate of barium ferrite had a large mean volume diameter of 20.8 µm, although the mean volume diameter of the iron oxide remained 1.58 µm, which is the same value of that in the dry state. This indicates the barium ferrite particles are aggregative and the iron oxide particles are dispersive. From the magnetic point of view, barium ferrite particles have a large remanent magnetization and iron oxide particles have a small remanent magnetization. We investigated how particle dispersibility, particle magnetism, and magnetostriction affect the giant MR effect using rheological, magnetic, and morphological data.
2. Experimental Procedure Synthesis of Magnetic Gel. Magnetic gels consisting of fine magnetic particles and κ-carrageenan, a natural polymer, were synthesized. The carrageenan is a sodium type gel with a molecular weight of 857 kDa, and the sodium content was 0.57 wt %. A pregel solution of the magnetic gel was prepared by mixing a 3 wt % κ-carrageenan (CS-530, San-Ei Gen F.F.I.) aqueous solution and barium ferrite (BaFe12O19, Sigma-Aldrich) or iron oxide (Fe3O4, Wako Chemicals) at 90 °C using a mechanical stirrer for 30 min. The pregel solution was poured into a glass mold of 10 mm thickness and was cooled to 20 °C to obtain the magnetic gel. Scanning electron microscope (SEM) images of these particles in a dry state are shown in Figure 1. The size distributions of the magnetic particles in dry state and in deionized water were obtained using a particle size analyzer (Mastersizer2000, Malvern Instruments) and are shown in Figure 2. In a dry state, the barium ferrite and iron oxide particles had mean volume diameters of 1.84 and 1.59 µm, respectively. In pure water, the agglomerate of barium ferrite had a large mean volume diameter of 20.8 µm, although the mean volume diameter of the iron oxide remained 1.58 µm, which is equal to the value in the dry state. The densities of carrageenan gel and magnetic gel were measured using an electric densimeter (Mirage MD-300S), and the density of magnetic particles was measured using a pycnometer.
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Figure 3. Density of magnetic gels vs weight concentration of magnetic particles.
Figure 2. Particle size distributions of barium ferrite and iron oxide used in the present study in a dry state (a) and in deionized water (b).
Rheological Measurements. Dynamic viscoelastic measurements were carried out using a rheometer (MCR301, Anton Paar) with measuring plates having coarse surfaces, which are special plates for the measurement of wet gels. The frequency was kept at 1 Hz, and the oscillation amplitude was varied from 10-6 to 10-2. The normal force was maintained at approximately 2 N. The temperature was controlled at 25.0 °C during viscoelastic measurement. The samples were obtained by the similar way as described in Synthesis Of Magnetic Gel and were disks with dimensions of 25 mm diameter and 5 mm thickness. First, we placed a sample in the rheometer and measured its complex modulus before magnetization; then the sample was placed in an electromagnet to magnetize it under a magnetic field of 1 T at room temperature. Afterward, the modulus was measured again. Note that the viscoelastic measurement was carried out in the absence of a magnetic field. Each modulus was determined from the average of three measurements using different samples. Magnetic Measurements. Magnetization measurements in fields up to 1 T were carried out using a vibrating sample magnetometer (VSM-P7, Toei Industrial) at room temperature. The samples were obtained by the similar way as described in Synthesis Of Magnetic Gel and were disks with dimensions of 2 mm diameter and 1 mm thickness. Each sample was wrapped in a thin film of poly(vinyl chloride) to prevent the evaporation of water from the sample. The magnetization was calibrated using a Ni disk to eliminate the demagnetizing effect of ferromagnetic substances. Microscope and SEM Observations. Observations were carried out using an upright microscope (Axio Imager M1m, Carl Zeiss) with transmitted light illumination at room temperature. Magnetic gels with volume fractions of 1.4 × 10-3 and 4.7 × 10-3 were prepared on a glass by mixing small amounts of magnetic particles and 3 wt % κ-carrageenan aqueous
solutions (total weight was ∼0.1 g), while heating by a hot stage at 90 °C. When the samples with high volume fractions of magnetic particles such as the samples used in the rheological measurement, the light transmitted from a microscope was completely blocked by the samples. Magnetic gels with φ < 0.01 were suitable for the observation of particle dispersibility. The thickness of each sample was approximately 100 µm. The shape and size of the magnetic particles were observed using a SEM with an accelerating voltage of 15 kV (S-800, Hitachi High-Technologies). Measurement of Magnetostriction. The samples were obtained by the similar way as described in Synthesis Of Magnetic Gel and were cubic with dimensions of 10 × 10 × 10 mm3. The dimensions of the magnetic gels parallel and perpendicular to the magnetization direction were measured before and after magnetization at 1 T using a laser displacement sensor with a maximum resolution of 0.01 µm (ZS-HLDS5, Omron). 3. Results and Discussion Density. The density of the magnetic gels as a function of the particle concentration in weight is shown in Figure 3. The concentration was calculated from the amounts of chemical agents in the synthesis. The densities of both magnetic gels increased with particle concentration. In our previous papers,9,10 we showed that gels with barium ferrite can be synthesized up to a concentration of 75 wt %. However, a gel with an iron oxide concentration of above 40 wt % was not obtained, because the pregel solutions lost flowability and could not be poured in the mold. The volume fraction of magnetic particles was determined using the following equation:
φ)
dMG - dCG dMP - dCG
(1)
Here, dMG denotes the density of the magnetic gel, dCG is the density of the carrageenan gel matrix, and dMP is the density of the magnetic particles. The density of 3 wt % carrageenan gel was measured to be 1.033 g/cm3. The measured densities of barium ferrite and iron oxide particles used in this study were 5.122 and 2.552 g/cm3, respectively, by Archimedes’ principle. Rheology of Magnetic Gels before Magnetization. The strain dependence of the storage modulus of magnetic gels with various volume fractions of magnetic particles is shown in Figure 4a,b. The storage modulus of the carrageenan gel without
Magnetic Gels Containing BaFe12O19 and Fe3O4 Particles
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Figure 5. Volume fraction dependence of storage modulus for magnetic gels: (O) barium ferrite and (0) iron oxide. The solid line represents the Krieger-Dougherty equation.
Figure 4. Strain dependence of storage modulus for magnetic gels with various volume fractions: (a) barium ferrite and (b) iron oxide.
particles was ∼1.5 × 105 Pa and exhibited little sensitivity to strain. For both types of magnetic gel, the storage modulus at low strains increased with the volume fraction. However, the storage modulus at high strains had the same value for all magnetic gels, independent of the volume fraction or the type of particle. This means that the enhanced nonlinear viscoelastic response is caused by the contact between magnetic particles; this phenomenon has been called the Payne effect.11 This originates from the temporary destruction of the contacts between magnetic particles which starts to occur from extremely small strains. In the linear viscoelastic regime, the increase in the storage modulus for gels with barium ferrite was much higher than that for gels with iron oxide. Note that the scale of the G′ axis in Figure 4b is narrower than that in Figure 4a. It is worth mentioning that the onset strain of the nonlinear viscoelasticity shifted to a low value when the volume fraction was increased. Moreover, the onset for gels with barium ferrite was 1 order of magnitude lower than that for gels with iron oxide. These results suggest that the gels with barium ferrite particles have a fragile structure that is easily broken by small strains, in contrast to the gels with iron oxide. Figure 5 displays the storage modulus of magnetic gels as a function of the volume fraction of magnetic particles. As described in Figure 4, the filler effect of gels with barium ferrite was more significant than that of gels with iron oxide. The solid line in the figure represents the modulus G′, calculated by the following Krieger-Dougherty equation, for a random dispersion of particles:13
(
G′ ) G′0 1 -
φ φm
)
-(5/2)φm
(2)
Figure 6. Storage modulus at γ ) 10-2 normalized with respect to maximum modulus vs volume fraction for magnetic gels: (O) barium ferrite and (0) iron oxide.
where G′ and G′0 are the storage moduli of the magnetic gel and carrageenan gel, respectively. φm is the maximum volume fraction of the particles, which is approximately 0.63 for hard spheres.14 For magnetic gels with barium ferrite, the storage modulus obeyed eq 2 below a volume fraction of ∼0.03, but had higher than the theoretical values above this volume fraction. This result was in good agreement with the data obtained from an experiment in the compressive mode.9,10 We consider that barium ferrite particles come in contact with each other and form a structure with a high modulus. On the other hand, the storage modulus of magnetic gels with iron oxide followed eq 2 over the whole range of volume fractions. Thus, the barium ferrite particles were heterogeneously dispersed and the iron oxide particles were dispersed randomly in the carrageenan gel. Figure 6 shows the volume fraction dependence of the value of G′/G′m showing the degree of nonlinear viscoelasticity. G′/ G′m is the storage modulus divided by maximum storage modulus G′m in the linear viscoelastic regime shown in Figure 4. G′/G′m for carrageenan gel without magnetic particles had a value of approximately 0.7. For both particles, the value of G′/ G′m below a volume fraction of 0.03 was the same as that of the carrageenan gel, although the data were unstable in the vicinity of φ ∼ 0.01. Above φ ) 0.03, G′/G′m markedly decreased for both types of particle. The volume fraction at the onset of enhanced nonlinear viscoelasticity coincided with the volume fraction at which a high modulus, larger than the theoretical value for a random dispersion, was observed. A further increase in the volume fraction resulted in a gradual decrease in G′/G′m. The lowest values of G′/G′m for gels with
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Figure 8. Volume fraction dependence of loss tangent at γ ) 10-2 for magnetic gels: (O) barium ferrite and (0) iron oxide.
Figure 7. Strain dependence of loss tangent for magnetic gels with various volume fractions: (a) barium ferrite and (b) iron oxide.
barium ferrite and iron oxide at φ ∼ 0.25 were 0.09 and 0.56, respectively. The strain dependence of the loss tangent for the magnetic gels with various volume fractions is shown in Figure 7. Both types of magnetic gel exhibited a significant increase in the loss tangent at the strain of which the storage modulus decreased rapidly. The loss tangent of gels with barium ferrite was much larger than that of gels with iron oxide. In addition to the nonlinear viscoelasticity shown in Figure 4, the onset strain for gels with barium ferrite was 1 order of magnitude lower than that for gels with iron oxide. The significant increase in the loss tangent is caused by the enhanced nonlinear viscoelasticity resulting from the mechanical loss owing to the destruction of the particles network.11 The relationship between the loss tangent at γ ) 10-2 and the volume fraction of magnetic particles is presented in Figure 8. Although the strain is in the nonlinear viscoelastic region, the value of loss tangent is considered to indicate the energy loss originating from the destruction of magnetic particles. The loss tangent in the linear viscoelastic region is dominated by the friction energy among magnetic particles. On the other hand, the loss tangent in the nonlinear region is attributed to the destruction energy of the particle network; therefore, the loss tangent in the nonlinear region gives us the information relating to the brittleness or the number of contact of the particle network. The loss tangent for carrageenan gel without magnetic particles was approximately 0.24. For both types of gel, the loss tangent below a volume fraction of 0.03 remained low and was nearly equal to the value for carrageenan gel, although the data were scattered. The scattering of data at low volume fractions was reproducible and might be caused by the nonlinear viscoelasticity; however, the reason is now unclear. Above a
volume fraction of 0.03, the loss tangent increased rapidly and then gradually increased with volume fraction. This critical volume fraction was in good agreement with the volume fraction at which significant nonlinear viscoelasticity occurred. At high volume fractions, the loss tangent for magnetic gels with barium ferrite was two times higher than that for gels with iron oxide. The agreement in the onset volume fractions observed for the nonlinear viscoelasticity and loss tangent indicates the particles are in contact at φ ∼ 0.03 despite the particle dispersibility; barium ferrite is heterogeneously dispersed and iron oxide is randomly dispersed in the gels. It was also observed in PVA gels containing non magnetic aluminum hydroxide particles that the particles started to come in contact at φ ∼ 0.04 and percolated at φ ∼ 0.18.15 Figure 9 shows microphotographs of magnetic gels containing barium ferrite or iron oxide at volume fractions of 1.4 × 10-3 and 4.7 × 10-3, which are enough lower than the onset volume fraction of particle contact determined by the nonlinear viscoelasticity and the loss tangent. One can clearly observe the difference in particle dispersibility between barium ferrite and iron oxide in carrageenan gel. It can be seen from Figure 9a that barium ferrite particles formed aggregates with a size of approximately 10 µm. There was no contact between the aggregated particles at the volume fraction of 1.4 × 10-3. As shown in Figure 9b, the aggregated particles made contact, and the size of the clusters was as large as 50 µm. Figure 9c shows that iron oxide particles are dispersed randomly in the gels while maintaining the diameter of the primary particles of ∼1.1 µm. It is clear from Figure 9d that the iron oxide particles are locally connected at φ ) 4.7 × 10-3 but do not form large clusters such as those of barium ferrite. Slightly above this volume fraction, the light transmitted from a microscope was completely blocked by the samples. Therefore, it is quite natural that both types of magnetic particles form contacts between the particles at φ > 0.03. The direct microscopic observation supports the idea that isolated magnetic particles develop into a local particle network in the vicinity of φ ∼ 0.03. This network is a partial network consisting of aggregated magnetic particles and is not a percolated network throughout the gel. The critical volume fraction was not affected by the types of particle, although the dispersibility was considerably different for barium ferrite and iron oxide particles. The gelation took place within 20 s and was faster as the volume fraction. In the present experiment, the gelation time was much shorter than the precipitation of magnetic particles. Therefore, the influence of precipitation is considered to be less for these samples although the agglomerate of barium ferrite particles was very large. Actually, the
Magnetic Gels Containing BaFe12O19 and Fe3O4 Particles
J. Phys. Chem. B, Vol. 112, No. 45, 2008 14137
Figure 9. Microphotographs of magnetic gels containing barium ferrite (a,b) and iron oxide (c,d) at φ ) 1.4 × 10-3 (a,c) and φ ) 4.7 × 10-3 (b,d).
Figure 10. Schematic illustrations representing particle dispersibility in carrageenan gels. Barium ferrite (top), iron oxide (bottom).
maximum experimental error within the volume fraction for these samples was only 7%. Schematic illustrations representing the dispersibility of magnetic particles in carrageenan gel are shown in Figure 10. Below a volume fraction of 0.03, the barium ferrite particles form secondary particles because the particle is aggregative. The particle forms an organized local network in the gel above this volume fraction. This local network is the origin of the enhanced nonlinear viscoelasticity and the large values of the loss tangent. Below a volume fraction of 0.03, iron oxide, which is a dispersive particle, is dispersed randomly in the gel. The particles are in partial contact at φ > 0.03, but do not develop into a local network such as that in barium ferrite. According to the measurement of surface potential, the average values of ζ-potential for barium ferrite and iron oxide were determined to be +32.9 and +9.78 mV, respectively. An aqueous solution of κ-carrageenan is a polyelectrolyte with sulfonate groups of negative charges. The ζ-potential of the barium ferrite is considered to be large enough to attract the carrageenan molecules, as a result the particle forms Stern layer of carrageenan molecules. Therefore, the electric potential at the Stern layer is considered to be approximate to the neutral. The barium ferrite particle which lost electric charges aggregates in carrageenan gel. On the other hand, the ζ-potential of iron oxide particle is considered to be insufficient to attract carrageenan molecules on the particle surface. Accordingly, weak charges
Figure 11. Magnetization curves of magnetic gels with various volume fractions of magnetic particles: (a) barium ferrite and (b) iron oxide.
on the particle surface remain and contribute to the repulsion force between the particles. Another factor of the random dispersion of iron oxide is considered to be an increase in the affinity between the particle and water due to hydroxyl groups on the surface of iron oxide. Magnetism. Magnetization curves of the magnetic gels containing barium ferrite and iron oxide particles are shown in Figure 11. Magnetic gels with barium ferrite exhibited a wide magnetic hysteresis, which is a characteristic of a hard ferrite. The magnetic hysteresis originates from the large values of
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Figure 12. Remanent magnetization vs volume fraction of magnetic particles: (O) barium ferrite and (0) iron oxide.
Figure 13. Change in storage modulus due to magnetization vs volume fraction of magnetic particles: (O) barium ferrite, (0) iron oxide.
remanent magnetization and coercive force. The remanent magnetization is the magnetization at zero magnetic field, and the coercive force is the magnetic field at zero magnetization. Magnetic gels with iron oxide showed no magnetic hysteresis, which is a characteristic of a soft ferrite. Figure 12 shows the volume fraction dependences of the remanent magnetization of the magnetic particles. The remanent magnetization was proportional to the volume fraction with good linearity. The slopes of the solid lines in the figure represent the remanent magnetization of each type of particle per unit volume. The remanent magnetizations of barium ferrite and iron oxide were estimated to be 1.96 × 105 and 3.88 × 104 A/m, respectively. These values are nearly equal to those of 2.10 × 105 and 4.02 × 104 A/m for barium ferrite and iron oxide in the powder state, respectively. The remanent magnetization of barium ferrite was higher than that of iron oxide. Magnetization Effect on Storage Modulus. Figure 13 shows the relationship between the change in the storage modulus before and after magnetization at 1 T as a function of the volume fraction of the magnetic particles. As described in the introduction, the storage modulus of magnetic gels decreases upon magnetization, which is opposite to the general MR effect. Both types of magnetic gel exhibited an increased change in the storage modulus with increasing volume fraction. The change in the storage modulus for barium ferrite at φ ) 0.24 was 5.03 × 105 Pa, which corresponds to a modulus change of 45% with respect to the initial modulus of 1.12 × 106 Pa. On the other hand, the change in the storage modulus for gels with iron oxide was on the order of 104 Pa and the maximum change was 2.57 × 104 Pa, which corresponds to a modulus change of 8.6% with
Mitsumata et al.
Figure 14. Magnetic field dependence of magnetostriction for magnetic gels: (O) barium ferrite and (0) iron oxide. Open and closed symbols represent the magnetostriction in parallel and perpendicular to the magnetization, respectively.
respect to the initial modulus of 2.98 × 105 Pa. The change in the storage modulus was not marked for magnetic gels with iron oxide and barium ferrite for volume fractions below φ ) 0.03. These gels have weak nonlinear viscoelasticity (G′/G′m > 0.6) and small values of the loss tangent (tan δ < 0.3). This strongly indicates that the giant reduction in the storage modulus is caused by the destruction of the local network of magnetic particles. Magnetostriction. As reported previously,10 magnetic gels exhibiting the giant reduction in dynamic modulus undergo magnetostriction, which is deformation by magnetization. We pointed out in the previous paper that magnetostriction can destroy the local particle networks, because they are broken by small strains. Figure 14 shows the magnetic field dependence of magnetostriction for magnetic gels with barium ferrite and iron oxide. The gels with barium ferrite elongated parallel to the magnetic field and contracted perpendicular to the magnetic field. The change in length in the perpendicular direction was approximately half of that in the parallel direction, suggesting isovolumetric deformation. The solid lines for barium ferrite in the figure represent the relationship in which the deformation ∆l is proportional to the square of the magnetic field B2. The deformation of gels with barium ferrite closely fitted the relationship ∆l ∝ B2; therefore, the magnetically induced deformation can be interpreted as the magnetic interaction between magnetized particles. Indeed, the gels recovered to their original length (∆l ) 0) when demagnetization was intentionally carried out (Mr ) 0). As described below, the magnetostriction can be quantitatively understood by considering the magnetic energy acting on the magnetic particles. The strain induced by the magnetic interaction γmag can be written by the following equation since the magnetically induced modulus can be written as µ0(Mrφ)2:10
γmag ∼
µ0(Mrφ)2 G′0
(3)
Here, G′0 is for the storage modulus before magnetization, µ0 represents the magnetic susceptibility in vacuum, Mr is the remanent magnetization of the magnetic particles, and φ is the volume fraction of the magnetic particles. The change in the storage modulus for gels with barium ferrite at φ ) 0.20 was estimated to be 1.9 × 103 Pa using a value of Mr ) 1.96 × 105 A/m. Accordingly, the magnetically induced strain γmag
Magnetic Gels Containing BaFe12O19 and Fe3O4 Particles was determined to be 2.4 × 10-3 using a value of G′0 ) 8.0 × 105 Pa. The observed magnetostriction was 80 µm (γ ) 8.0 × 10-3), which has the same order as the theoretical value estimated using eq 3. The storage modulus of magnetic gels with barium ferrite at φ ) 0.24 in Figure 4 showed that the difference between the storage moduli at γ ) 2.4 × 10-3 and that in the linear viscoelastic region was approximately 6 × 105 Pa. The giant reduction in the storage modulus observed for gels with barium ferrite is probably caused by magnetostriction on the order of 10-3. On the other hand, no clear change in length was observed for gels with iron oxide, both perpendicular and parallel to the magnetic field. The change in the storage modulus for gels with iron oxide at φ ) 0.20 was estimated to be 76 Pa using a value of Mr ) 3.88 × 104 A/m. Similar to the gels with barium ferrite, the magnetically induced strain γmag of gels with iron oxide was determined to be 2.5 × 10-4 using a value of G′0 ) 3.0 × 105 Pa. The observed magnetostriction was 5 µm (γ ) 5.0 × 10-4), which, similar to the case of barium ferrite, corresponds to the theoretical value estimated using eq 3. Although magnetic gels with iron oxide also exhibit magnetostriction, a strain on the order of 10-4 is not sufficient to cause the giant reduction in the storage modulus. Furthermore, the gels with iron oxide have a wide range of linear viscoelasticity from 10-6 to 3 × 10-4, which is another reason why the magnetic gels with iron oxide did not exhibit a giant reduction in the storage modulus. Thus, the magnetostriction plays an important role to cause the giant MR effect although the dispersibility of magnetic particles is intrinsic. It can be considered the magnetostriction occurs by the demagnetizing effect that is frequently seen in the magnetization of a ferromagnetic substance. There arises an inner magnetic field within the magnetic gel oppositely to the direction of the applied field, and these magnetic fields produce the instability of magnetic energy. To minimize the instability, the magnetic gel may deform under magnetic fields. It was revealed in this study that the giant reduction in the storage modulus is caused by the destruction of local networks of magnetic particles, which is induced by the magnetostriction and/or the rotation of magnetic particles within the gel. 4. Conclusion The effect of particle dispersibility on the rheology of magnetic gels containing barium ferrite and iron oxide has been investigated by dynamic viscoelastic measurements. The magnetic gel containing barium ferrite at φ > 0.06 demonstrated a giant reduction in the storage modulus on the order of 105 Pa due to magnetization. However, a small reduction in the storage modulus on the order of 104 Pa was observed for the magnetic gel with iron oxide at all volume fractions. The magnetic gel exhibiting the giant reduction in the dynamic modulus had the following rheological features. The storage modulus significantly deviated from the Krieger-Dougherty equation at φ > 0.06, suggesting the heterogeneous dispersion of barium ferrite particles in the gel. In addition, nonlinear viscoelasticity, i.e., the Payne effect, was enhanced and the loss tangent increased
J. Phys. Chem. B, Vol. 112, No. 45, 2008 14139 at φ > 0.06. This indicates that aggregated particles of barium ferrite are connected with each other and form a local particle network in the gel. On the other hand, the storage modulus for magnetic gels with iron oxide satisfied the Krieger-Dougherty equation at all volume fractions, suggesting the random dispersion of the magnetic particles. Small increases in the nonlinear viscoelasticity and the loss tangent were observed above a volume fraction of approximately φ ∼ 0.03. This means that iron oxide particles form a particle network, although the particles are dispersed randomly in the magnetic gel. The iron oxide particles are in contact with each other but do not form a local network such as that of barium ferrite. After magnetization at 1 T, the magnetic gel with barium ferrite elongated along the magnetic field direction and shrunk perpendicular to the field. However, the magnetic gel with iron oxide did not exhibit a marked deformation. This behavior can be interpreted in terms of the magnetic features of these particles, that there is a large remanent magnetization in barium ferrite and a small remanent magnetization in iron oxide. Thus, the giant reduction in dynamic modulus occurs by destructing the local network which was formed by the heterogeneous dispersion of magnetic particles. The negative MR effect presented here should appear in all soft materials containing aggregative particles with particle volume fractions sufficiently high for significant nonlinear viscoelasticity to occur. The negative MR effect reduces the increase in elasticity that is induced by a simple magnetic interaction. To control of these two opposite effects is expected to be important in the fabrication of MR soft materials with high efficiency. Acknowledgment. We are grateful to San-Ei Gen F.F.I., Inc. for the offer of κ-carrageenan. This research is partially supported by a Grant-in-Aid for Encouragement of Young Scientist from Japan Society for the Promotion of Science (Proposal No. 18750184) and Bando Chemical Industries. References and Notes (1) Mitsumata, T.; Ikeda, K.; Gong, J. P.; Osada, Y.; Szabo, D.; Zrinyi, M. J. Appl. Phys. 1999, 85, 8451. (2) Shiga, T.; Okada, A.; Kurauchi, T. J. Appl. Polym. Sci. 1995, 58, 787. (3) Jolly, M. R.; Carlson, J. D.; Munoz, B. C.; Bullions, T. A. J. Intell. Mater. Syst. Struct. 1996, 7, 613. (4) Ginder, J. M.; Clark, S. M.; Schlotter, W. F.; Nichols, M. E. Int. J. Modern Phys. B. 2002, 16, 2412. (5) Bossis, G.; Bellan, C. Int. J. Modern Phys. B. 2002, 16, 2447. (6) Lokander, M.; Stenberg, B. Polym. Test. 2003, 22, 245. (7) Lokander, M.; Stenberg, B. Polym. Test. 2003, 22, 677. (8) Varga, Z.; Filipcsei, G.; Zrinyi, M. Polymer 2006, 47, 227. (9) Mitsumata, T.; Nagata, A.; Sakai, K.; Takimoto, J. Macromol. Rapid Commun. 2005, 26, 1538. (10) Mitsumata, T.; Sakai, K.; Takimoto, J. J. Phys. Chem. 2006, 110, 20217. (11) Payne, A. R. J. Appl. Polym. Sci. 1960, 3, 127. (12) Mitsumata, T.; Okazaki, T. Jpn. J. Appl. Phys. 2007, 46, 4220. (13) Krieger, I. M.; Dougherty, T. J. Trans. Soc. Rheol. 1959, 3, 137. (14) Onoda, G. Y.; Liniger, E. R. Phys. ReV. Lett. 1990, 64, 2727. (15) Mitsumata, T.; Hachiya, T.; Nitta, K. Eur. Polym. J. 2008, 44, 2574.
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