In the present paper, a magnetorheological elastomer (MRE) based on silicone rubber, magnetorheological suspension and catalyst, in a magnetic field, is obtained. Using the plane capacitor method, it is shown that the elastic properties of the magnetorheological elastomer are influenced by the intensity and direction of the applied magnetic field. The obtained experimental results are presented and discussed

BICA, I.

BUNOIU, O. M.

CHIRIGIU, L.

CIRTINA, G.

IORDACONIU, L.

English

Studia Universitatis Babeş-Bolyai

STUDIA UBB PHYSICA, Vol. 60 (LX), 1, 2015, pp. 45-52 (RECOMMENDED CITATION)      Dedicated to Academician Professor Dr. Emil Burzo on His 80th Anniversary   MAGNETORHEOLOGICAL ELASTOMER ELASTICITY -  BASED CAPACITOR   O.M. BUNOIU1*, I. BICA1, L. CHIRIGIU2,  G. CIRTINA1, L. IORDACONIU1   ABSTRACT. In the present paper, a magnetorheological elastomer (MRE) based on silicone rubber, magnetorheological suspension and catalyst, in a magnetic field, is obtained. Using the plane capacitor method, it is shown that the elastic properties of the magnetorheological elastomer are influenced by the intensity and direction of the applied magnetic field. The obtained experimental results are presented and discussed.   Keywords: silicone rubber, magnetorheological elastomer, plane capacitor, carbonyl iron, magnetic Young modulus.     INTRODUCTION   Magnetorheological elastomers (MREs) are part of the magnetically active materials category. They consist of an elastic matrix into which magnetizable nano- or microparticles are dispersed or aligned [1-4]. Like in the case of the magnetorheological suspensions [5-9], some physical the physical properties like of the MREs drastically change under the action of the magnetic field. This particular feature is used in mechanical shocks absorbers and dampers [10], (bat the damping mechanism differs from the classical magnetomechanical damping magnetostrictive ferromagnets [11-14]).                                                             1 Department of Physics, West University of Timisoara, Bd. V. Parvan, nr.4, Timisoara 300223, Romania 2 Department of Analytical Chemistry, University of Medicine and Pharmacy, Petru Rares Street, No. 2–4, Craiova, Romania * Corresponding author e-mail: madalin.bunoiu@e-uvt.ro O.M. BUNOIU, I. BICA, L. CHIRIGIU, G. CIRTINA, L. IORDACONIU    46 One property of interest is related to the change of the electric conductivity of MREs in a magnetic field [15, 16], property used in obtaining active or passive electric circuit elements [17-22]. Such devices can be used in the manufacturing of deformations and mechanical tensions sensors and/or transducers. The physical properties of the MREs [1-4, 10, 15-23] strongly depend on the method of preparation. In this context, the obtaining procedure at an anisotropic MRE and the study of its elastic properties by means of the plane capacitor method is presented in the paper.   EXPERIMENT Plane capacitor with MRE  The components used in obtaining the plane capacitor with MRE-based dielectric material are: silicone rubber, RTV-3325 (Bluestar – Silicones), silicone oil (Merck), catalyst, 60R (Merck) and carbonyl iron (Sigma) as microparticles with diameter between 4.5μm and 5.4μm and iron content of min 97%. A liquid mixture, consisting in 2.4cm3 carbonyl iron and 0.2cm3 silicone oil, is brought to the temperature of 573±5% [20] and maintained at this temperature for5 minutes. At the end of the 5 minutes time the mixture is allowed to reach room temperature. Following the thermal decomposition of carbonyl iron, iron nanoparticles with average diameter of 61.2nm are formed inside the liquid matrix [20]. The obtained product is mixed and homogenized with silicone rubber (1.2cm3±10%) and catalyst (0.2cm3±10%). The formed mixture is injected between two parallel copper plates (diameter 30mm), provided on the outline with a spacer so as to maintain the distance between the plates at 3.5mm±10%.The as-formed set was placed between the poles of a type Phylatex (Germany)-Weiss electromagnet. The magnetic field has a normal direction to the surface of the plane capacitor plates and intensity of H=840kA/m±10%. After 24 hours, a plane capacitor with MRE dielectric material based on silicone rubber and iron nanoparticles (60% vol.) is obtained.   Measurements   The electric capacity of the plane capacitor at the temperature of the environment (296 K ± 10%) and in the absence of the magnetic field is measured with the capacimeter CM-7115A (Fujian). The capacitor with MRE is introduced in a transverse magnetic field (normal to the plates) and then in a longitudinal magnetic field (in plane). Three sets of measurements are performed with the CM-7115A (Fujian) capacimeter precision. MAGNETORHEOLOGICAL ELASTOMER ELASTICITY - BASED CAPACITOR    47 RESULTS AND DISCUSSION   The average values of the capacity C as a function of the magnetic field intensity H are presented in Fig.1a. At H=0, the capacity of the plane capacitor is fixed to the value C0=96pF. We note with CT the capacity of C in a transverse magnetic field and with CL the capacity of the same C in a longitudinal magnetic field. When applying a transverse magnetic field (0<H(kA/m)≤400), the value of C jumps from C0=96pF to CT=124 pF, for H= 15kA/m. For 15<H(kA/m)≤400, CT has a quasi-linear growth with H. At H=400 kA/m one obtains CT =157pF. In a longitudinal magnetic field, the values CL(H)<CT(H). Here, as Figure 1 shows, two regions of CL=CL(H), namely: 96≤CL(pF) ≤97.5, for: 0≤H(kA/m) ≤100; 97.5<CL(pF)≤131, and for: 100<H(kA/m) ≤400, can be observed. Neglecting the edge effects [27], the capacitance of the plane capacitor with MRE based dielectric may  be approximated to: 0200 4hdC r ,  for H=0   and  hdC r 420 ,  for H≠0  (1) Here 0 =8.85 pF/m, r is the relative permittivity of the MRE; d, h0 and h are the diameter and thicknesses of the MRE.   The linear magnetic strain is:  e =(h-h0)/h0 = [(C0 /C)-1]      (2) where h0 and h can be obtained from  Eqs.(1) .  For C0 si C=C(H), from Fig.1, introduced in (2), on obtained in Fig.2, (eT) transversal magnetic linear strain and (eL) magnetic longitudinal linear strain. 0 50 100 150 200 250 300 350 40090100110120130140150160   CT (transversal)   CL (longitudinal)C(pF)H(kA/m) Fig. 1. Capacitance C of the plane capacitor as a function of the strength magnetic field H. O.M. BUNOIU, I. BICA, L. CHIRIGIU, G. CIRTINA, L. IORDACONIU    48 0 50 100 150 200 250 300 350 400-0,4-0,3-0,2-0,10,0 (eL)longitudinal (eT)transversaleH(kA/m) Fig. 2. The linear magnetic strain e as a function of the strength magnetic field H.  We see from Fig. 2 like MRE is compressed. MRE compression value depends on the strong magnetic field intensity vector direction. From Fig.2, it is observed that for H ≥ 20kA/m, compressing due to the transverse magnetic field is far enlarging compared to that due to the longitudinal magnetic field. In a magnetic field, the nanoparticles from the inside of the elastic matrix are magnetized. We consider that the nanoparticles are of diameter d   dm. Then, their magnetic moment is [25]:  cos63 Hdm m      (3) where dm is the diameter of the magnetizable particles, H is the magnetic field strength and α is the angle between the Hand direction of chains magnetic dipolesm.  The parameter   is the initial magnetic susceptibility of the MRE. For ep   ( p and e are the relative magnetic permeability of the iron nanoparticles and silicone rubber) this may approximated to [25]: 323 epep       (4)  Introducing the expression (4) into Eq. (3) yields:  cos5.0 3 Hdm m       (5) We consider Hconstant. Then, between two neighboring and identical magnetic dipoles, an attractive magnetic force occurs [20, 25]: MAGNETORHEOLOGICAL ELASTOMER ELASTICITY - BASED CAPACITOR    49 4203rmF em         (6) where 0 = 12.56 x 10-7 H/m and r is the distance between the centers of the two dipoles.   The mechanical stress induced in to the MRE by Fm [26]: 223mmmCdFSFN        (7) where Nc/S is the number of columns per transverse cross-section unit of MRE [26] and   is the volume fraction of the iron nanoparticles.  From Eqs. (5), (6) and (7), which for r=dm results mechanical stress induced in to MRE by longitudinal magnetic field, i.e.:  220 cos5.4 HL       (8) Here α  is the angle between vector intensity of magnetic field and the direction of the dipoles columns.  For α=0,  the stress is maximum and has the expression: 205.4 HT         (9) where T  is the stress component corresponding to vector intensity magnetic field normal to the plates.  For the magnetic tension, Eqs. (8) and (9), the elastic matrix reacts with the longitudinal elastic tension σeL and the transverse elastic tension σeT, respectively.  At equilibrium are available equalities σeL = σL and σeT = σT  or: 205.4 H = kL d0/S [(h/h0)-1]L cos2α= kL h0/S [(C/C0)-1]L cos2α = EL eL     (10) 205.4 H = kT d0/S [(h/h0)-1]T  =  kT h0/S [(C/C0)-1]T = ET eT  (11) where  kL and kT  are MRE elastic constant, eL=[(C/C0)-1]L and  eT = [(C/C0)-1]T  are the longitudinal and the transversal linear strain, S is surface aria and:  ET = kT d0/S and EL = kL d0/S cos2α    (12) is the magnetic elasticity module (ET) for transversal magnetic field and (EL) is the magnetic elasticity module for longitudinal magnetic field. From Eqs. (10) and (11) results: O.M. BUNOIU, I. BICA, L. CHIRIGIU, G. CIRTINA, L. IORDACONIU    50 EL = 205.4 H /[(C/C0)-1]L   and ET = 205.4 H /[(C/C0)-1]T (13)  The angle of α is obtained from the Eqs. (12) and (13), namely: α = arcos [(ET/ EL)0.5]     (14)  For φ = 0.60, µ0 = 12.56 x 10-7 H/m and (C/C0)L,T, from Fig. 1, and the Eqs. (13) can be obtained EL,T =  EL,T(H), plotted in Fig. 3. 0 50 100 150 200 250 300 350 4000,00,51,01,5(ET) transversal  magnetic Young  modulus (EL) longitudinal magnetic Young  modulus E(MN/m2 )H(kA/m) Fig. 3. Magnetic module ET and EL function of the magnetic strength field H.  Introducing EL,T = EL,T(H) from Fig. 3 in Eqs. (14), and obtained α = α(H), plotted in Fig. 4. Shall see from Fig.4, as the angle α are shrinking as the H increase, corresponding with the modification of EL, from Fig. 3. Introducing C=C(H) values (Fig. 1a) and C0=96pF into Eq. (10) and the dependence e=e(H) is obtained as shown in Fig. 2. It can be noticed the linear strain e increases with the magnetic field Hand it is sensibly dependent its direction. For α=0 (transverse magnetic field) expression (11) can be rewritten as TT eE . Then, using Eq. (7) for  =0.60, 0≤H(kA/m) ≤440 and )(Hee TT   from Fig. 2 one obtains E=E(H) as plotted in Fig. 3. It can be noticed from Fig. 3 that the magnetic Young modulus E sensibly increases with H, in accord with the model proposed in Refs. [28, 29]. The columns formed by the iron nanoparticles have the same direction as H. At the moment of a longitudinal magnetic field application (Hin plane) the chains formed by the iron nanoparticles MAGNETORHEOLOGICAL ELASTOMER ELASTICITY - BASED CAPACITOR    51 tend to orient towards H . An angle α will occur between the direction of H and that of the chains. We intend to determine α with the growth ofH . For this, we use the expression (6), E=E(H) from Fig. 3 and eL= eL(H) from Fig. 2. Then, for  =0.60 and 0 ≤ H (kA/m) ≤ 440,the dependence  α= α(H) will be obtained as plotted in Fig.4.  It can be seen from Fig. 4 that the angle α decreases with the increase of H. According to Refs. [28, 29] the value of α depends on  Fm ~Hn  (where n   2).  0 50 100 150 200 250 300 350 40088,288,488,688,889,089,289,489,689,890,0(grad)H(kA/m) Fig. 4. The angle α between H  and the direction of the dipoles columns m   as a function of the longitudinal strength magnetic field H.   CONCLUSIONS   Anisotropic MRE was obtained by magnetic field polymerization of the mixture formed by silicone rubber with catalyst and magnetorheological suspension based on silicone oil and Fe nanoparticles;  The electric capacitance C of the plane capacitor with the MRE, the magnetic field – induced linear strain e  and the stress σ  depend on the strength and direction of H ;  The magnetic Young modulus E  of the MRE is strongly influenced by H ;  The angle α between by H  and the direction of the chains formed by iron particles decreases rapidly within the field range 20 ≤H(kA/m) ≤240 and becomes constant for higher field values.    O.M. BUNOIU, I. BICA, L. CHIRIGIU, G. CIRTINA, L. IORDACONIU    52  REFERENCES  1. Yu L. Raikher, O.V. Stolbov, and G.V. Stepanov, J. Phys. D: Appl. Phys. 41, 152 002 (2008).  2. X. Zheng, S. Peng, W. Wen, and W. 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MAGNETORHEOLOGICAL ELASTOMER ELASTICITY - BASED CAPACITOR

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MAGNETORHEOLOGICAL ELASTOMER ELASTICITY - BASED CAPACITOR

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