Magnetic Field-Dependent Normal Force of Magnetorheological Gel

Jul 25, 2013 - ABSTRACT: Magnetorheological gel (MRG) is a new kind of MR material, and it ... property, MRF can be applied on dampers,13−15 brakes,...
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Magnetic Field-Dependent Normal Force of Magnetorheological Gel Benxiang Ju, Miao Yu,* Jie Fu, Xing Zheng, and Shuzhi Liu Research Center of Sensing and Instrumentation Technologies, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044, China ABSTRACT: Magnetorheological gel (MRG) is a new kind of MR material, and it can be regarded as the analogue of MR fluid. In this study, a MRG sample based on a polyurethane matrix was fabricated. The normal force of MRG was investigated by using an advanced commercial rheometer under rotational and oscillatory shear modes. The influence of time history, strain amplitude, frequency, shear rate, and temperature in the presence of a variable and constant magnetic field on the normal force of MRG was systematically studied. The experimental results indicated that the magnetic field has a greater impact on the normal force of MRG, and the increment of magnetic field enhanced the normal force obviously. However, the other factors in the presence of a constant magnetic field only have weak effects on the normal force. This behavior can be regard as the magnetic field-dependent normal force, and the mechanism of interaction between the magnetic field and normal force was investigated by microstructure analysis.

1. INTRODUCTION

Apart from shear properties, such as shear stress and shear modulus, the normal force behavior also has attracted considerable attention. Up to now, most studies of normal force behaviors focused on MRF. Vicente et al.26 carried out studies on the normal force of MRF based on a commercial controlled stress parallel plate rheometer and claimed that the normal force can be generated only when two factors are satisfied: the magnetic field must exceed a critical value and the MRF must be under shear strain. See and Tanner25 found that the normal force acted to push the plates apart with a magnitude that increased with magnetic flux density. When MRF was subjected to continuous shearing, the normal force decreased with shear strain. Laun et al.26 proposed that the relationship between the normal force and magnetic field can be expressed as FN ∝ B,24 and the normal force can be increased with shear strain. Chan et al.27 presented that the normal force can be increased by the addition of a steadyrelative speed compared to the stationary plates. Lopez− Lopez28 and Guo29 reported that there were three regions in the normal force vs shear rate or shear strain. In addition, Guo et al.30 measured the normal force of MR suspensions with different iron volume concentrations and found that the dynamic and static normal forces of the MR suspensions are highly dependent on the volume fraction, magnetic field, and shear rates. Jiang et al.31 presented that the normal stress increases considerably with an increase in shear rate and magnetic field and decreases suddenly and significantly upon the onset of shear thickening in MRF. From the above introduction of the present research on the normal force of MRF, it is very important to comprehend the characteristics of the MRF. As a new MR material, MRG shows special magnetic properties, which gives it much potential as an application in dampers, artificial muscles, etc.32,33 Its normal force is also

MR fluid (MRF), MR elastomer (MRE), and MR foam comprise a class of smart material, whose rheological properties can be controlled by the external magnetic field.1−12 The most well-known MR material is MRF, whose yield stress can be changed by an external magnetic field. On the basis of this property, MRF can be applied on dampers,13−15 brakes,16 actuators,17 and so on. A new generation of MR material, known as MR gel (MRG), was proposed by Wilson and Fuchs.18,19 It can be regarded as the analogue of MRF. MRF is a magnetic suspension, which has iron particles with high permeability dispersed in a nonmagnetic carrier fluid. Without an external magnetic field, MRF behavior is similar to that of a Newtonian fluid.20 Upon application of a magnetic field, the mostly iron particles form chain-like structures parallel to the external magnetic field and thus creates a strong and reversible changes in its rheological property. These similar features can also be found in the MRG, and MRG differs from the traditional MRF. For example, the sedimentation of iron particles leads to a significant decrease in the MR effect and application stability of MRF, while the MRG was prepared by polymer gel with high viscosity. A higher viscosity results in controlled initial viscosity and reduces the sedimentation of iron particles in matrix. Thus, this may have an additional effect on the stability of the MRG. For a new kind of MR material, Hu et al.21 investigated the effect of strain amplitude, frequency, and magnetic field strength on the viscoelastic module. The dynamic shear yield stress increased dramatically with the applied external magnetic field. Wei et al.22 studied the rheological properties of MRG under both steady and oscillation shear using a MR rheometer, and the MRG exhibits high static shear yield stress (60.8 kPa at 573mT) and dynamic shear yield stress (83.9 kPa at 573mT), with a wide variation range (static shear yield stress of 6−62 kPa; dynamic shear yield stress of 15−85 kPa). Moreover, a very strong relative increase in storage modulus, up to 6000%, was obtained by An et al.23 © 2013 American Chemical Society

Received: Revised: Accepted: Published: 11583

April 27, 2013 July 12, 2013 July 25, 2013 July 25, 2013 dx.doi.org/10.1021/ie4013419 | Ind. Eng. Chem. Res. 2013, 52, 11583−11589

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The viscosity of the mixture of CO and MDI is low in the second stage of MRG preparation, which is a favorable condition for iron particle distribution. The microstructure of the MRE samples was observed by using a digital microscope (Model: VHX-600, KEYENCE Corporation). Figure 2 shows a

unique for practical application in designing actuators, sensors, magnetic seals, and so on. Therefore, more work should be done to the normal force on MRG under the magnetic field. In this study, the MRG sample was fabricated, and the normal forces under rotational and oscillatory shear mode were systemically tested. The influence of time, strain amplitude, frequency, shear rate, and temperature under variable and constant magnetic field with the normal force of MRG were studied and analyzed.

2. EXPERIMENTAL SECTION 2.1. MRG Sample Preparation. The polyurethane matrix of MRG was mainly synthesized from CO (CO: Sinopharm Chemical Reagent Co. Ltd., China) and MDI (MDI: 4,4≈50%, 2,4- ≈50%, Yantai Wanhua Polyurethanes Co. Ltd., China). There were three steps in the synthesis of the MRG samples. First, CO was distilled at 110 °C in a vacuum drying oven for about 1 h before use with excess water evaporated in this step. Then CO was poured into a beaker, and the temperature was decreased to 80 °C. A few minutes later, MDI was also injected into beaker, and the mixture was stirred for several minutes until mixing well. The mole ratio of MDI and CO was calculated by the following formula m /933 g mol−1 nOH = CO n NCO mMDI /250 g mol−1

Figure 2. Microstructure of MRG sample (1000 ×).

microstructure photograph of the MRG sample in which the bright spots represent the carbonyl iron particles and the yellow background stands for the polyurethane matrix. It shows that the carbonyl iron particles are homogeneously distributed in the matrix, and this indicates that the compatibility between the carbonyl iron particles and the matrix is very good. 2.2. Testing for Normal Force. The normal force of the MRG sample can be tested by using an advanced commercial rheometer (Model: MCR301, Anton paar), and Figure 3 shows

(1)

where nOH represents the mole of the −OH group, nNCO is the mole of the −NCO group, mCO is the weight of CO, mMDI is the weight of MDI, and the value of nOH/nNCO was set to1.57:1. Second, the mixture was mixed with carbonyl iron particles (type: JCF2−2, Jilin Jien Nickel Industry Co. Ltd., China; size distribution : D50 = 5−8 μm). At the same time, stannous octoate (Sinopharm Chemical Reagent Co. Ltd., China) was added into mixture with stirring as catalyst. At last, as soon as the iron particles and the matrix were well mixed, the mixture was placed in a drybox to vulcanization about 1 h at the temperature of 80 °C. After that, the sample was placed several days at room temperature, and then the MRG sample was obtained. A photograph of the MRG sample is shown in Figure 1.

Figure 3. Testing system of MRG performance and schematic diagram of the MR device.

the testing system. A parallel-plate rotor and MR device were installed in a rheometer, which can test MRG with different conditions. The MRG sample was placed between the rotating disk and the base, and when the rotor rotated or oscillated, the MRG sample worked in rotational or oscillatory shear mode. The parallel-plate rotor can be set to rotate and oscillate with a desired parameter. The testing magnetic field was generated by an electromagnet, and a metal cover enhanced and guided the magnetic circuit perpendicular to the surface of MRG. The range of magnetic flux density was 0−1 T by adjusting the DC power supply from 0 A to 5 A. The MRG can also be tested under different temperatures, which were controlled by a water bath, and the testing temperature can reach as high as 95 °C. The normal force of MRG under rotational and oscillatory shear mode was studied, and the as-prepared sample was initially sheared without the external magnetic field at 10(1/s) for several minutes to ensure good dispersion. In the

Figure 1. Sample of MRG.

It is shown in Figure 1 that the statuses of MRG under a different tilt angle were recorded at room temperature by using photographs. The surface of MRG remained in a horizontal position when the beaker was placed on the desktop (Figure 1(a)). If the beaker was tilted, the surface of MRG was also parallel to the bottom of the beaker at the beginning (Figure 1(b)). However, the surface can adapt to gravity and become level to the horizontal plane about several minutes later (Figure 1(c)). On the basis of the above observation, it is very clear that MRG is a kind of intermediate material between MRE and MRF and is are analogues of MRF. 11584

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rubber. The variation of the MR effect reaches as high as 700%, and the magneto-induced modulus is around 2.2 MPa. Furthermore, MRG has the nature of MRF, whose shear stress was also tested under different magnetic fields, as shown in Figure 4. The above results indicate that the magnetic field has a great effect on the magnetic properties of MRG. 3.1. Effect of Magnetic Field Sweep on Normal Force. In combination with the experimental results above, MRG was sensitive to the external magnetic field. Furthermore, studies on the normal force can further evaluate and understand the characteristics of MRG. The magnetic field-dependent normal force under rotational and oscillatory shear mode were systematically investigated and analyzed below. A typical experiment was done to illustrate the interaction force of MRG along the direction of the magnetic field. As shown in Figure 5, a constant magnetic field was imposed perpendicular to the aluminum plate. The surface morphology of MRG significantly changed under a constant magnetic field of 0.3 T. Many peak structures were formed, and the direction paralleled the external magnetic field (Figure 5(b)). If no magnetic field was applied, the iron particles were randomly suspended in a polymer matrix, and the MRG was in free state, as shown in Figure 5(a). Compared with Figure 2, lots of ordered structures can be formed and paralleled to the magnetic field direction, which is represented by red arrows, as shown in Figure 5(c). Thus, experimental results clarified that the normal force was generated due to the appearance of peak structures in the presence of a magnetic field, and the microstructures change leads to the variation in the normal forces under the magnetic field. The normal force of MRG was first measured by using a magnetic field sweep. The strain amplitude of 1% and frequency of 1 Hz was applied to the MRG sample under an oscillatory shear mode, and the shear rate was set at 50(1/s) under rotational shear mode. Testing of the magnetic flux density from 0 to 1 T was selected. When the magnetic field was applied, the normal force was generated. The results are shown in Figures 6 and 7. The normal force shows that the reactive force from the MRG sample tended to push apart the rotating disk. In Figure 6, the normal force increases with an increasing magnetic field. MRG can be seen as a simulation of MRF. When a magnetic field is externally applied, the particles were driven by the magnetic force to align in the direction of magnetic field, and

experiment, the diameter of the rotating disk was 20 mm, and the following tests were all executed at the gap of 1 mm to avoid the influence of the testing gap on results.

3. RESULTS AND DISCUSSION Figure 4 displays the effect of the magnetic field on the shear storage modulus and shear stress for MRG under oscillatory

Figure 4. Shear storage modulus and shear stress under different magnetic flux density.

and rotational shear mode. Shear storage modulus and shear stress show an increasing tendency with an increasing magnetic field. Taking oscillatory shear for example, the initial modulus of MRG is only 0.027 MPa, while the maximum modulus can reach up to 2.19 MPa at a magnetic field of 1 T. In this study,the magneto-induced modulus is defined as the absolute difference between the maximum modulus and initial modulus. It is indicated that MRG has an obvious magneto-induced modulus under the effect of the magnetic field and can achieve up to 2.16 MPa. Moreover, the MR effect is also a key parameter for evaluating MR material performance, which is the ratio of the magneto-induced modulus and initial modulus.34 The MR effect of the as-prepared MRG sample can reach up to 8000%, which is better than that for MRE. In previous reports, the magneto-induced modulus of MRE based on natural rubber can reach up to 3.6 MPa, but the MR effect (only 133%) is very small.35 MRE with high MR effect can be prepared by a silicone rubber matrix. Liao et al.36 fabricated MRE with HTV silicone

Figure 5. (a) Photograph of MRG. (b) MRG under the influence of permanent magnets. (c) Microstructure of MRG under a magnetic field (100 ×). (d) Schematic diagram of iron particles movement under a magnetic field. 11585

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Figure 6. Normal force of MRG under a magnetic field sweep (oscillatory shear mode).

Figure 8. Viscosity of MRG under a shear rate sweep.

motion resistance of iron particles was obtained. After the magnetic field was turned on, the rearrangement of the particle’s structures occurred in the MRG. The movement of iron particles was mainly determined by the interaction between magnetic force and resistance. Iron particles can be moved easily under the matrix with lower viscosity. In this case, the larger particle−particle interaction can be generated under rotational shear to further the increment of normal force. The fitting curves for normal force versus the oscillatory and rotational shear mode are shown in Figures 6 and 7. The normal force can be estimated by the following consistent formula

FN = kB2

Figure 7. Normal force of MRG under magnetic field sweep (rotational shear mode).

(2)

where B is magnetic flux density, and k is the coefficient. With the magnetic field, the shear-enhanced normal force phenomenon of excited MR fluid was explained by Vicente.24 When particle chains are sheared, the chains are tilted and form an angle to the field direction. If the tilted particle chain is restrained, the normal forces or reactions acting on the two ends of the chain are related to the field-induced magnetic torque. The normal force was considered the vertical component of the resistance force generated by the magnetic torque, and the k can be expressed as27 3 k = πa 2μ0 μ1β 2 sin 2θ sin θ (3) 4

the chains or columnar structures were formed in the MRG sample. Tang et al.37 have proposed that magnetic attractive forces were generated among the particles under the effect of the magnetic field. The particles are assembled to form chains, columnar, or network structures aligned parallel to the magnetic field direction. The magnetic attractive force pushes the particles forward of the existing chain or column structures, as shown in Figure 5(d). Moreover, a higher magnetic field strength means that a higher magnetic attractive force was exerted between the particles and strengthens the interaction force between the particles. Compared with the oscillatory shear mode, Figure 7 shows that the magnetic field has a greater impact on the normal force under the rotational shear mode. For example, the maximum normal force is 20.8 N under oscillatory shear mode, while the maximum normal force can reaches 38.1 N under rotational shear mode. The difference was mainly due to the different shear mode. Similar to the MRF,38 the viscosity decreases with an increase in the shear rate, indicating that this kind of material also exhibits a typical shear thinning behavior. The viscosity of MRG can be characterized by using a rheometer (Figure 3). The viscosity of MRG in the absence of a magnetic field under a shear rate sweep is shown in Figure 8. In Figure 8, the shear rate sweep was carried out under the rotational shear mode with shear rate of from 1 to 100(1/s); the lower shear rate led to a higher viscosity. The viscosity of the MRG matrix with the oscillatory shear is higher than that of the rotational shear mode. Compared with a shear rate of 50(1/ s), when the MRG worked in a strain amplitude of 1% with a frequency of 1 Hz under oscillatory shear mode, the stronger

where a is the particle radius, μ0 is the vacuum permeability, μ1 is the relative permeability of MRG, θ is the angle of tilt relative to the field direction, and β can be defined as μp − μ1 β= μp − 2μ1 (4) where μp is the iron particle permeability. Equation 2 reflects the relationship between the external magnetic field and the normal force of MRG. 3.2. Effect of Time History on Normal Force. Influence of time history with different constant magnetic fields on the normal force of MRG was experimentally studied. The strain amplitude of 1% and frequency of 1 Hz was selected. The testing time was 400 s, and the magnetic field was fixed at 0, 0.2, 0.4, 0.6, 0.8 T. The time-scanning normal force under the different constant magnetic fields was obtained, as shown in Figure 9. It can be found that normal force increases with time first and then reached a steady-state value in the presence of a magnetic field. 11586

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Figure 11. Normal force of MRG under a strain amplitude sweep.

Figure 9. Normal force of MRG with time under different constant magnetic fields.

when the strain amplitude is smaller than the critical value, the normal force increases significantly with an increase in strain amplitude, especially under higher magnetic field. This critical value is mainly determined by the magnetic force. The particles are driven by the magnetic field to align with the field and form a large number of chain structures with different lengths, and this assumption is clarified in Figure 5(C). Figure 12 shows the

There must be a competition between the interaction force of iron particles and the viscous force of MRG under a magnetic field. When the applied magnetic field is zero, the value of the initial normal force is only −0.12 N, which is due to the interaction between the surface tension and gravity of MRG. Thus, the positive normal force cannot be generated in the absence ofa magnetic field. If a magnetic field is applied, the particles are constrained by the magnetic field and then rearranged to form structures parallel to the direction of the magnetic field, and a higher magnetic field gives a stronger magnetic force. However, the higher magnetic field also leads to a higher viscosity. The magnetic field sweep was carried out under a shear rate of 1(1/s), and the result is shown in Figure 10.

Figure 12. Scheme of microstructure. (a) Microstructure without a magnetic field. (b) Microstructure under the effect of a magnetic field.

scheme for the formation of the chain structures. If no magnetic field is applied, the particles are randomly dispersed in the matrix, and the normal force could hardly be found. As soon as the magnetic field is applied, the particles are rearranged to form lots of chains with different lengths, which can generate a normal force to push a rotating disk. Above the critical value, the normal force increases to a relatively steady-state value with an increasing strain, and the weak growth trend is extended under a higher constant magnetic field. This phenomenon can be attributed to the microscopic structure transformation of MRG at strain sweep. When the strain was applied on the MRG, the microstructures would be destroyed by strain. However, with increasing of the magnetic field, the breaking and rebuilding microstructures can reach new balance. It can be seen from Figure 5(c) that the intensive chain structures exist in MRG sample after applying the magnetic field. When the magnetic field increased to a higher value, the microstructures rebuilding ability can slightly exceed the breaking effect and new structures can enhance the normal force. Due to the differences of the matrix, the above result is inconsistent with Guo’s experiments of MRF.29 The comparison proves that normal force of MRG is more stable than MRF under the influence of strain and magnetic field. 3.4. Effect of frequency and shear rate on normal force. The frequency effect on the normal force was measured under an oscillatory shear mode, as shown in Figure13. The frequency sweep is utilized to measure the normal force under different constant magnetic fields, and the frequency was

Figure 10. Viscosity of MRG under a magnetic field sweep.

Increasing the magnetic field leads to a stronger magnetic interaction between particles and the rearrangement of the particles inside the MRG. At the same time, the viscosity of the MRG also increases to a higher value quickly, as shown in Figure 10. The particles moved with difficulty in the matrix under high viscosity. When the new balance was formed between the viscous force and interaction force of particles, it needs to spend more time on keeping the normal force stable. 3.3. Effect of Shear Strain on Normal Force. The normal force of MRG was characterized in the presence of different constant magnetic fields under a strain amplitude sweep. The shear strain was swept from 0.1 to 100%, and the frequency was 1 Hz. The result is shown in Figure 11. In this section, the magnetic field is set at several constant values. The relationship between the normal force and strain amplitude can be divided into two regions. In the first region, 11587

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Figure 13. Normal force of MRG under a frequency sweep.

Figure 15. Normal force of MRG for various temperatures.

swept from 1 to 80 Hz under a shear strain amplitude of 1%. In Figure13, the normal force keeps almost steady values under a constant magnetic field, and the normal force is only influenced by the magnetic field under a frequency sweep. It is observed that the normal force increases with an increasing magnetic field at constant frequency. It should be noted that this result is different from Gong’s conclusion about MRF, where the normal force fluctuates at different frequency under a stable field.39 This frequency sweep property, which only can be controlled by a magnetic field, will make the MRG a broader prospect in applications. Furthermore, Figure 14 shows the shear rate sweep was utilized to measure the normal force under rotational shear

matrix will decrease and the Brownian motion will become severe. This increases the opportunity to change the location of particles and strengthen the interaction between the particles, which will enhance the normal force. Below a magnetic flux density of 0.4 T, the attractive forces between iron particles are not so strong, and the normal force keeps an almost steady state at different temperatures. When the magnetic field further increases, a growing number of particles are constrained to form a chain structure at higher temperature, which further strengthens the normal force. Taking a temperature sweep under a magnetic field of 0.8 T as an example, the normal force increases 40%, while the magnetic field of 0.6 and 0.4 T are only increased by 26.2% and 20.5%. On the basis of the above research, temperature with a constant magnetic field has a limited impact on the normal force of MRG.

4. CONCLUSIONS In this work, a MRG sample based on a polyurethane matrix was fabricated, and a systemically experimental investigation on the normal force behavior of MRG was performed. As-prepared MRG is a sensitive MR material under a magnetic field, and the MR effect of the as-prepared MRG sample can reach up to 8000%. Moreover, the external magnetic field has a decisive impact on the normal force, and the normal force increases with an increasing magnetic field. When the magnetic field is applied, the maximum normal force is 20.8 N under oscillatory shear mode and can reach up to 38.1 N under rotational shear mode. The relationship between the normal force and external magnetic field can be expressed as FN = kB2. However, the influence of time, strain amplitude, frequency, shear rate, and temperature on the normal force of MRG were also studied and analyzed; it is found that these factors have very small effects on the normal force of MRG. On the basis of these results, this work is expected to provide guidance for many potential applications.

Figure 14. Normal force of MRG under a shear rate sweep.

mode, and the shear rate was swept from 10(1/s) to 100(1/s). It was observed that shear rate has no effect on the normal force under a constant magnetic field. With further increase in the shear rate, the structures in MRG were destroyed. However, lots of new structures were rebuilt under the influence of a magnetic field. Hence, a new balance was also formed under the effect of the interaction between the rotational shear and magnetic field to keep the normal force at steady values. 3.5. Effect of Temperature on Normal Force. In some cases, MRG would work in some special conditions, such as wide temperature ranges. Thus, the temperature-dependent behavior and its influence on the normal force have been investigated; testing was carried out at a temperature from 25 to 80 °C, as shown in Figure 15. Figure 15 shows that the normal force exhibits a steady state under a lower magnetic field but increases slowly with an increasing temperature under a high magnetic flux density. In this case, with an increasing temperature, the viscosity of the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +86 23 65111016. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support is acknowledged from the NSFC (No. 51073179) and NSFY (No. 61203098), National Technology R&D Program of the Ministry of Science and Technology (No. 11588

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2012BAF06B04), and The Fundamental Research Funds for the Central Universities (No. CDJZR11128801).

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dx.doi.org/10.1021/ie4013419 | Ind. Eng. Chem. Res. 2013, 52, 11583−11589