Magnetic-Field Sensitivity of Storage Modulus for Bimodal Magnetic

Article pubs.acs.org/JPCB

Magnetic-Field Sensitivity of Storage Modulus for Bimodal Magnetic Elastomers Jinta Nanpo,†,‡ Kazushi Nagashima,†,‡ Yasuhiro Umehara,† Mika Kawai,†,‡ and Tetsu Mitsumata*,†,‡ †

Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan ALCA, Japan Science and Technology Agency, Tokyo 102-0076, Japan

‡

ABSTRACT: The magnetic-field dependence of the storage modulus for bimodal magnetic elastomers consisting of carbonyl iron with a diameter of 2.8 μm (magnetic) and aluminum hydroxide with a diameter of 1.4 μm (nonmagnetic) was measured, and the effect of nonmagnetic particles on the magnetic-field sensitivity of the storage modulus was investigated. The coefficient of the magnetic-field sensitivity for the monomodal magnetic elastomer increased from 0.018 to 0.026 mT−1 for the bimodal one by embedding nonmagnetic particles of 6.6 vol %. At volume fractions above 5.4 vol %, the bimodal magnetic elastomer exhibited significant nonlinear viscoelasticity at 0 mT and a high storage modulus at 500 mT, simultaneously, the coefficient of the magnetic-field sensitivity demonstrated high values. This strongly indicates that both the particles form a particle network at the off-field, and they make a well-developed chain structure under magnetic fields. The time profiles of the storage modulus for bimodal magnetic elastomers can be fitted by a linear combination of two exponential functions with two characteristic times showing the alignment of magnetic particles. The alignment time for the fast and slow processes was distributed around 3.3 ± 0.3 and 176 ± 12 s, respectively. The alignment time was independent of the volume fraction of the nonmagnetic particles; however, the increment in the storage modulus for the fast process significantly increased at volume fractions above 5.4 vol %. It was also revealed that the coefficient of the magnetic-field sensitivity can be scaled by a power function of the increment in the storage modulus divided by the off-field modulus, ΔG′/G′0, not only for the bimodal magnetic elastomers but also for the monomodal ones.

1. INTRODUCTION Soft materials responsive to external stimuli, such as temperature, pH, and electric fields, have attracted considerable attention as the next-generation actuators, devices with virtual reality, or soft robots, etc. A magnetic elastomer is a soft material responsive to magnetic fields and consists of polymeric matrices and magnetic particles.1−13 When magnetic fields are applied to magnetic elastomers, the magnetic particles align in the direction of the magnetic fields and make a chain structure within the elastomer. The chain structure of the magnetic particles increases the viscoelasticity of the magnetic elastomer due to the stress transfer and the magnetic interaction among the magnetic particles. This is called the magnetorheological (MR) effect. Considering the industrial application of magnetic elastomers, the most important factor on the MR property would be the absolute change in the elastic modulus by magnetic fields. The absolute change in the elastic modulus can be easily varied by raising the volume fraction of the magnetic particles or decreasing the elastic modulus of the matrix. Another important factor evaluating the MR property is the magneticfield sensitivity of the elastic modulus against the magnetic fields. This factor will be very important for practical use as the © XXXX American Chemical Society

magnetic-field sensitivity closely relates to the response time for changing the viscoelastic properties. Here, the magnetic-field sensitivity is defined by the increment in the storage modulus against the magnetic field at low magnetic fields. The value of the coefficient of the magnetic-field sensitivity has a wide range depending on the kind of magnetic particles or matrices. In our previous paper,14 we have briefly reported that the coefficient of the magnetic-field sensitivity, α, at 0% plasticizer (dioctyl phthalate, DOP) was extremely low, ∼1.0 × 10−3 mT−1, suggesting low mobility of the magnetic particles within the hard matrix. The α increased with the DOP content, and it took a maximum value of 1.8 × 10−2 mT−1 at 70 wt % DOP, suggesting that the magnetic particles form a well-developed chain structure within the soft matrix. This value of α was very close to that for carrageenan magnetic hydrogels, 2.0 × 10−2 mT−1, indicating that the mobility of magnetic particles in the polyurethane matrix is comparable to that in physically crosslinked networks of polysaccharide. It was also revealed that the coefficient of the magnetic-field sensitivity can be scaled by a Received: August 26, 2016 Revised: November 29, 2016

A

DOI: 10.1021/acs.jpcb.6b08622 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B power function of the increment in the storage modulus divided by the off-field modulus, ΔG′/G′0. We have reported bimodal magnetic hydrogels and elastomers consisting of magnetic and nonmagnetic particles. The bimodal magnetic elastomers exhibit a drastic change in the elastic modulus compared to that of monomodal magnetic elastomers. For example, the relative change in Young’s modulus for a monomodal magnetic elastomer is 1.8, and it is raised to 5.8 only by mixing it with the nonmagnetic particles of 9.6 vol %.15 The bimodal magnetic elastomer endures against a compression load of 30 N and thus can be used in actuators working at high loads.16−18 Accordingly, it can be expected that the coefficient of the magnetic-field sensitivity for bimodal magnetic elastomers is higher than that for monomodal ones. In this study, we report the magnetic-field dependence of the storage modulus for bimodal magnetic elastomers consisting of iron and aluminum hydroxide particles and discuss the influence of the mixed particle on the magnetic-field sensitivity for magnetic elastomers.

Figure 1. Magnetic-field dependence of the storage modulus for bimodal magnetic elastomers as a function of the volume fraction of AH particles.

2. EXPERIMENTAL PROCEDURE 2.1. Synthesis of Bimodal Magnetic Elastomers. A prepolymer method was used to synthesize bimodal magnetic elastomers. Poly(propylene glycol) (Mw = 2000, 3000), toluene diisocyanate, carbonyl iron (CI SM grade) particles, nonmagnetic aluminum hydroxide particles (Al(OH)3) (AH), and plasticizers (DOP) were mixed by a mechanical mixer for several minutes. The mixed solution was poured in a silicon mold and cured in an oven for 60 min at 100 °C. The concentration of DOP was defined by the ratio of DOP to the matrix without magnetic particles, and it was kept at 70 wt %; DOP/(DOP + matrix). The weight fraction of the magnetic particles was kept at 70 wt %; CI/(CI + matrix), which corresponds to a volume fraction of ϕ = 0.24. The weight fraction of the nonmagnetic particles was varied up to 6 wt %; AH/(AH + matrix), which corresponds to a volume fraction of 0.066. The median diameter of the AH particles in dry state was measured to be 1.4 ± 0.2 μm, using a particle size analyzer (SALD-2200; Shimadzu). Several kinds of magnetic particles (BASF Japan) have been used in this experiment. The median diameter for SM, CS, and CM particles was 2.8, 6.7, and 7.2 μm, respectively. The magnetic particles were produced by hydrogen reduction, and the minimum weight fraction of iron for SM, CS, and CM particles is 99.0, 99.5, and 99.5, respectively. The saturation magnetization for SM, CS, and CM particles is 245, 190, and 105 emu/g, respectively. The magnetic susceptibility at magnetic fields below 200 mT for SM, CS, and CM particles is 8.71 × 10−2, 6.34 × 10−2, and 3.50 × 10−2 emu/gOe, respectively. 2.2. Rheological Measurements. Dynamic viscoelastic measurements were carried out using a rheometer (MCR301, Anton Paar) at 20 °C, the strain was varied from 10−4 to 1, and the frequency was constant at 1 Hz. The sample was a disk of 20 mm diameter and 1.5 mm thickness.

Table 1. Coefficient of Magnetic-Field Sensitivity α and α′ Using eqs 1 and 2

a

Volume fraction of nonmagnetic particles. content. cCorrelation coefficient.

b

Plasticizer (DOP)

approximately 500 mT. The data for monomodal magnetic elastomers with the same volume fraction of magnetic and nonmagnetic particles are also shown in Figure 1. As seen in the graph, the initial slope for monomodal magnetic elastomers was smaller than that for bimodal ones. It was also found that the change in the storage modulus for monomodal magnetic elastomers was smaller than that for bimodal ones. At low magnetic fields below 200 mT, the storage modulus for bimodal magnetic elastomers can be empirically explained by the following equation G′(B) = G′0 exp(αB)

3. RESULTS AND DISCUSSION Figure 1 shows the magnetic-field dependence of the storage modulus for bimodal magnetic elastomers as a function of the volume fraction of nonmagnetic AH particles. The storage modulus for bimodal magnetic elastomers increased with the magnetic field independently of the volume fraction of the AH particles, and it was saturated at high magnetic fields of

(1)

where B is the magnetic field, G′0 is the storage modulus at 0 mT, the α stands for the coefficient of the magnetic-field sensitivity for magnetic elastomers, and it was determined by the least-squares fitting using the above equation. For comparison, the storage modulus for bimodal magnetic elastomers was fitted by the following quadratic function B


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The Journal of Physical Chemistry B

Figure 4. Relationship between coefficient of magnetic-field sensitivity α and ΔG′/G′0 for monomodal and bimodal magnetic elastomers with various magnetic particles.

Figure 2. Storage modulus in the presence and absence of magnetic fields for bimodal magnetic elastomers as a function of the volume fraction of AH particles.

Figure 5. Strain dependence of the storage modulus for bimodal magnetic elastomers as a function of the volume fraction of AH particles.

Figure 3. Coefficient of magnetic-field sensitivity α determined from G′ vs B curves for magnetic elastomers using eq 1 as a function of the volume fraction of AH particles (bottom axis) and the additional volume fraction of magnetic particles (top axis).

G′(B) = G′0 + α′B2

G′EM (B) = G′M, ∞

B2 α″ + B 2

(3)

Here, G′EM(B) and G′M,∞ show the magnetically induced excess modulus and the maximum value of the elastic modulus, respectively. α″ is a material parameter showing the magneticfield sensitivity for magnetic elastomers. By a similar manner, parameter α″ for monomodal (ϕAH = 0.00) and bimodal (ϕAH = 0.06) magnetic elastomers was determined to be 1.6 × 104 and 5.6 × 104 mT2, respectively. However, the fitting was not good, with low values of correlation coefficient: 0.76 for ϕAH = 0.00 and 0.20 for ϕAH = 0.06. Figure 2 depicts the relationship between the storage modulus for bimodal magnetic elastomers and the volume fraction of AH particles. The storage modulus at 0 mT was almost constant, although the volume fraction of AH particles

(2)

where α′ also stands for the coefficient of the magnetic-field sensitivity for magnetic elastomers. The values of the correlation coefficient are listed in Table 1. It can be seen that correlation coefficient α′ was higher than α for bimodal magnetic elastomers, and, in contrast, correlation coefficient α was higher than α′ for monomodal magnetic elastomers. Moreover, we compared a coefficient representing the magnetic-field sensitivity at low magnetic fields using the following phenomenological function reported in a literature19 C


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Figure 3 indicates coefficient of the magnetic-field sensitivity α determined by eq 1 as a function of the volume fraction of AH particles. The coefficient of the magnetic-field sensitivity was almost constant at volume fractions below 0.043, and it increased apparently above this volume fraction. This result coincides with the threshold at ϕAH = 0.043 observed in the storage modulus in Figure 2. The maximum value of α was 2.6 × 10−2 mT−1 at ϕAH = 0.066, which is 1.6 times higher than that of monomodal magnetic elastomers. The relationship between the volume fraction of additional magnetic particles and magnetic-field sensitivity α for monomodal magnetic elastomers is also shown in Figure 3. The volume fraction of additional magnetic particles is equal to the volume fraction of nonmagnetic particles. As shown in the figure, the α for monomodal magnetic elastomers slightly increased below the volume fraction of 0.043, and it increased above this volume fraction. The maximum value of α was 2.3 × 10−2 mT−1 for monomodal magnetic elastomers. Thus, bimodal magnetic elastomers demonstrate high magnetic-field sensitivity compared to that of monomodal magnetic elastomers particularly at high volume fractions of magnetic particles. Figure 4 demonstrates the relationship between coefficient of the magnetic-field sensitivity α and ΔG′/G′0 for monomodal and bimodal magnetic elastomers. Here, ΔG′ was calculated by subtracting the off-field modulus from the on-field modulus at 500 mT. The value of α increased with ΔG′/G′0 for all magnetic elastomers. The experimental values of α were successfully fitted by a power function, α = (ΔG′/G′0)0.31, with a correlation coefficient of 0.986. The correlation coefficients were 0.904 and 0.972 when the fitting was carried out using plots of α versus G′0 and α versus ΔG′, respectively. Hence, ΔG′/G′0 is the best parameter, in which the coefficient of the magnetic-field sensitivity is dominated. The coefficient of the magnetic-field sensitivity for monomodal magnetic elastomers with various diameters of magnetic particles (CS: 6.7 μm, CM: 7.2 μm) and various plasticizer contents is also presented in the same figure. These values appeared on the fitting line of the bimodal magnetic elastomers studied here. Therefore, α is independent of the plasticizer content or the particle diameter, and it can be scaled by a power function of ΔG′/G′0. The G′ versus B curves for magnetic particles with diameters exceeding approximately 100 μm cannot be fitted by eq 1, 2, or 3. Generally, the initial slope of the curves was extremely small compared to that for magnetic particles with diameters of several microns. Figure 5 shows the strain dependence of the storage modulus for bimodal magnetic elastomers as a function of the volume fraction of nonmagnetic AH particles. At 0 mT, the storage modulus for monomodal magnetic elastomers (ϕAH = 0) was constant at low strains below γ < 10−3, and it decreased with the strain at high strains. The storage modulus for bimodal magnetic elastomers with ϕAH = 0.066 was constant at low strains below γ < 10−4, and it decreased with the strain at high strains. This is called the Payne effect indicating that a particle network is destructed by the strain. The storage modulus for bimodal magnetic elastomers obeyed the Guth−Gold formula; however, it is considered that the AH particles make a particle network within the elastomer. The storage modulus for polyurethane elastomers without both magnetic and nonmagnetic particles was independent of the strain, as shown in the same figure. At 500 mT, the storage modulus for monomodal magnetic elastomers (ϕAH = 0) was constant at low strains below γ < 10−4, and it significantly decreased with

Figure 6. Nonlinear parameter β for bimodal magnetic elastomers as a function of the volume fraction of AH particles.

Figure 7. Relationship between nonlinear parameter β and the loss factor at a strain of 1 for bimodal magnetic elastomers.

was raised. The storage moduli at 500 and 770 mT were almost constant at volume fractions below 0.043, and it increased above this volume fraction. This strongly indicates that the nonmagnetic AH particle is not contributed from the chain structure of the magnetic particles at volume fractions below 0.043. The storage modulus at 770 mT was comparable to that at 500 mT. The broken line in the figure represents the storage modulus for magnetic elastomers obtained by the Guth−Gold formula, which is explained by the following formula 2 G′ = G′0 (1 + 2.5ϕAH + 14.1ϕAH )

(4)

where G′0 is the storage modulus at 0 mT, and ϕAH is the volume fraction of AH particles. The storage modulus for bimodal magnetic elastomers at 0 mT was not significantly raised even at high volume fractions of magnetic particles. D


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Figure 8. Time profiles of (a) the storage modulus and (b) normalized change in the storage modulus for bimodal magnetic elastomers as a function of the volume fraction of AH particles.

Figure 9. Normalized change in the storage modulus for the fast and slow processes of chain formation as a function of the volume fraction of AH particles.

Figure 10. Alignment time for the fast and slow processes of chain formation as a function of the volume fraction of AH particles.

β=1− the strain at high strains. The storage modulus for bimodal magnetic elastomers with ϕAH = 0.066 was constant at low strains below γ < 10−3, and it decreased with the strain at high strains, which was more significant than that for ϕAH = 0. The increase in the liner viscoelastic regime by embedding AH particles indicates that the chain structures reinforced by AH particles are able to endure against high strains. At γ = 1, the storage modulus for bimodal magnetic elastomers at 500 mT was independent of the volume fraction of AH particles. Accordingly, this evidence suggests that the chains consisting of magnetic and nonmagnetic particles are completely destructed by the strain. Figure 6 depicts the nonlinear parameter β for bimodal magnetic elastomers as a function of the volume fraction of AH particles. The nonlinear parameter β was defined by the following equation

G′MS G′L

(5)

where G′MS is the storage modulus at the maximum strain (γ = 1), and G′L is the storage modulus at the linear viscoelastic regime (γ < 10−4 in most cases). At 0 mT, the β increased with the volume fraction of AH particles, and the value was constant at ϕAH = 0.043. It can be considered that the particle network destructed by the strain increased on increasing the volume fraction of AH particles. This result also indicates that the particle network is not further developed at AH volume fractions above 0.043 even when the volume fraction of AH is raised. Thus, the nonlinearity gives us valuable information indicating the dispersibility of magnetic and nonmagnetic particles, which cannot be obtained by the storage modulus at a linear viscoelastic regime. At 500 mT, the β slightly increased with the volume fraction of AH particles, and the value was E


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Figure 8a shows the time profiles of the storage modulus for bimodal magnetic elastomers as a function of the volume fraction of AH particles. A magnetic field of 500 mT was applied at 30 s. The storage modulus for all bimodal magnetic elastomers suddenly increased by applying the magnetic field, and it was constant at approximately 300 s. The time to reach the equilibrium storage modulus was independent of the volume fraction of AH particles. Figure 8b shows the time profiles of (G′(t) − G′0)/ΔG′ for bimodal magnetic elastomers as a function of the volume fraction of AH particles. The storage modulus at a certain time G′(t) for bimodal magnetic elastomers can be explained by the following equations ⎡ ⎛ t ⎞⎤ G′(t ) = G′0 + ΔG′1⎢1 − exp⎜ − ⎟⎥ ⎢⎣ ⎝ τ1 ⎠⎥⎦ ⎡ ⎛ t ⎞⎤ + ΔG′2 ⎢1 − exp⎜ − ⎟⎥ ⎢⎣ ⎝ τ2 ⎠⎥⎦ ΔG′ = ΔG′1 + ΔG′2

(6) (7)

where G′0 is the storage modulus at t = 0 (0 mT). ΔG′1 and ΔG′2 are the change in the storage modulus for the fast and slow processes, respectively. τ1 and τ2 are the alignment time for the fast and slow processes, respectively. Analysis using three characteristic time constants has been recently reported;22 however, we carried out the fitting using two characteristic times because the correlation coefficient for the present magnetic elastomers ranged above 0.98. The (G′(t) − G′0)/ ΔG′ for bimodal magnetic elastomers with volume fractions of ϕAH = 0.054 and 0.066 quickly reached the equilibrium compared to that of the other bimodal magnetic elastomers. The change in the storage modulus and the alignment time for the fast and slow processes were determined by the fitting under a condition in which the correlation coefficient is higher than 0.90. An et al. reported that the evolution of the storage modulus with time for a physical magnetic gel can be well fitted by a two-exponential function with fast and slow characteristic times.23 Figure 9 shows the relationship between the values of ΔG′1/ ΔG′ and ΔG′2/ΔG′ against the volume fraction of AH particles. The value of ΔG′1/ΔG′ was almost constant at volume fractions ϕAH < 0.043, and it increased with the volume fraction. ΔG′1/ΔG′ was saturated at ϕAH = 0.054. At volume fractions ϕAH < 0.043, the values of ΔG′1/ΔG′ and ΔG′2/ΔG′ were approximately 0.8 and 0.2, respectively. This means that most of the chain structure was formed in the fast process. Attention should be paid to the fact that the chain structure consists of only magnetic particles. At volume fractions ϕAH > 0.054, the value of ΔG′1/ΔG′ increased to 0.9, indicating that the AH particles contribute effectively to the chain structure of magnetic particles. Figure 10 shows the alignment time for the fast and slow processes of chain formation as a function of the volume fraction of AH particles. The alignment time of the fast process was independent of the volume fraction of AH particles, and the averaged alignment time of the fast process was determined to be 3.3 ± 0.3 s. The alignment time of the slow process was also independent of the volume fraction of AH particles, and the averaged alignment time of the slow process was determined to be 176 ± 12 s. It can be considered that the moving distance of the magnetic particles to make a chain

Figure 11. SEM photographs for (a) magnetic CI particles, (b) nonmagnetic AH particles, and (c) distribution of particle diameter.

constant at ϕ = 0.043. It can be considered that the chain structure of magnetic and nonmagnetic particles destructed by the strain increased on increasing the volume fraction of AH particles. This result also indicates that the chain structure of magnetic and nonmagnetic particles is not further developed at AH volume fractions above 0.043 even when the volume fraction of AH is raised. Figure 7 shows the relationship between the nonlinear parameter β and the loss factor at a strain of 1 for bimodal magnetic elastomers. The nonlinear parameter at 0 and 500 mT was roughly proportional to the loss factor. The loss factor at 0 mT was reported as 0.15−0.20 for a magnetic gel with 10 vol % magnetic particles20 and 0.45−0.50 for a magnetic elastomer with 82 wt % magnetic particles.21 The loss factor in the presence of magnetic fields was reported as ∼0.3 for a magnetic gel20 and ∼5.0 for a magnetic elastomer.21 F


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Figure 12. Schematic illustrations representing the particle dispersibility and the chain structure for bimodal magnetic elastomers.

modulus and the nonlinear parameter at 500 mT showed high values. According to our previous results by electric conductivity measurements,18 it was found that the increase in the electric conductivity for bimodal magnetic elastomers levels off on increasing the volume fraction of nonmagnetic particles with low electric conductivity. As the bimodal magnetic elastomers demonstrated significant increase in Young’s modulus compared to that of the monomodal ones, it can be considered that the nonmagnetic particles intercept the chain of the magnetic particles. Assuming one-dimensional electric conductivity, it is considered for a strand of chains that 27% of the magnetic particles were replaced by the nonmagnetic particles. It was revealed that magnetic elastomers having a bimodal structure demonstrate high coefficient of magnetic-field sensitivity α.

structure becomes short by embedding the nonmagnetic AH particles, at least at volume fractions ϕAH > 0.054. However, alignment times for both the slow and the fast processes were constant against the volume fraction of AH particles. Accordingly, the diffusion coefficient of magnetic particles in the polyurethane matrix is considered to be reduced by embedding the nonmagnetic AH particles. Figure 11a,b shows the SEM photographs for magnetic CI particles and nonmagnetic AH particles, respectively, used in the present study. It was observed that the magnetic CI particles had a spherical shape with a diameter of approximately 3 μm. The distribution of the particle diameter is shown in Figure 11c. It was also recognized that the nonmagnetic AH particles had an irregular shape with a relatively wide distribution of particle diameter compared to that of CI particles. Figure 12 presents the schematic illustrations representing the particle dispersibility and the chain structure for bimodal magnetic elastomers at ϕAH = 0.010 and 0.066. For bimodal magnetic elastomers at ϕAH = 0.010 without magnetic fields, it can be considered that neither magnetic particles nor nonmagnetic particles form a particle network within the polyurethane matrix, as the storage modulus at 0 mT or the value of the nonlinear parameter (=0.568) was comparable to that for the monomodal magnetic elastomer (=0.529). Under magnetic fields, the AH particles do not participate in forming a chain structure, as the storage modulus at 500 mT or the value of the nonlinear parameter (=0.973) was comparable to that for the monomodal magnetic elastomer (=0.972). For bimodal magnetic elastomers at ϕAH = 0.066 without magnetic fields, it can be considered that both magnetic and nonmagnetic particles form a particle network within the polyurethane matrix, as the storage modulus at 0 mT becomes high, and the value of the nonlinear parameter (=0.710) was remarkably higher than that for the monomodal magnetic elastomer (=0.529). Under magnetic fields, the AH particles effectively contribute to a chain structure because both the storage

4. CONCLUSIONS The magnetic-field dependence of the storage modulus for bimodal magnetic elastomers consisting of magnetic and nonmagnetic particles was measured, and the effect of nonmagnetic particles on the magnetic-field sensitivity of the storage modulus was investigated. The coefficient of magneticfield sensitivity for magnetic elastomers increased from 1.8 × 10−2 to 2.6 × 10−2 mT−1 by mixing with nonmagnetic particles of 6.6 vol %. At this volume fraction, the bimodal magnetic elastomer exhibited a high storage modulus under magnetic fields and exhibited a high nonlinear parameter independently of the magnetic fields, indicating that the magnetic and nonmagnetic particles form a particle network in the absence of magnetic fields, and they make a well-developed chain structure in the presence of magnetic fields. Although the magnetic-field sensitivity was successfully improved by the present bimodal method, the method is found to be ineffective to accelerate the mobility of magnetic particles within the polyurethane matrix, according to the dynamic analysis of chain formation. Further improvements to enhance the strength of the fast process for G


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chain formation would be effective to raise the magnetic-field sensitivity of magnetic elastomers. It was also revealed that the coefficient of the magnetic-field sensitivity can be scaled by a function of the increment in the storage modulus divided by the off-field modulus ΔG′/G′0 not only for monomodal but also for bimodal magnetic elastomers. We firmly believe that this research is useful for the development of haptic devices in the next generation using soft materials.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone/Fax: +81 (0)25 262 6884. Department of Materials Science and Engineering, Faculty of Engineering, Niigata University, Niigata 950-2181, Japan. ORCID

Tetsu Mitsumata: 0000-0002-1355-6775 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was partially supported by Sasaki Environment Technology Foundation, NAGAI N-S Promotions Foundation for Science of Perception, and UNION TOOL foundation.

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REFERENCES

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Magnetic-Field Sensitivity of Storage Modulus for Bimodal Magnetic

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