- Email: [email protected]
The influence of the magnetic field on the elastic properties of anisotropic magnetorheological elastomers
Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669
Contents lists available at SciVerse ScienceDirect
Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
The influence of the magnetic field on the elastic properties of anisotropic magnetorheological elastomers Ioan Bica West University of Timis¸oara, Faculty of Physics, Bd. V. Paˆrvan, No. 4, 300223 Timis¸oara, Romania
A R T I C L E I N F O
Article history: Received 24 November 2011 Accepted 3 March 2012 Available online 10 March 2012 Keywords: Magnetorheological elastomer Silicone rubber Carbonyl iron Thermal decomposition Microwaves Iron nanoparticles
A B S T R A C T
This paper deals with the process of achievement of anisotropic magnetorheological elastomers (MREs), based on silicone rubber and iron nanoparticles. Plane capacitors are manufactured with MREs. The capacity C of the plane capacitors is measured as function of the intensity H of the magnetic field. By using the approximation of the dipolar magnetic moment and the ideal elastic body model, respectively, the tensions and deformations field and respectively the elasticity module of MREs function of H have been determined, for magnetic field values of up to 1000 kA/m. The obtained results are presented and discussed. ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
1. Introduction Magnetorheological elastomers (MREs) and magnetorheological suspensions (MRSs) are active magnetic materials, consisting of a matrix in which magnetic particles are dispersed. As their mechanical and rheological properties are well controlled by applied magnetic fields, these materials are of interest in various applications. Unlike the MRSs, in which long term particles deposition often occurs [1–4] the stability of the MREs is ensured by inserting the particles in polymer chains [5–14]. The capabilities of MREs have received an increasing interest cluring last decades. Thus, Kaleta et al. [5] produced isotropic and anisotropic MREs based on thermoplastic rubber and iron microparticles, and carried out a study of their static magnetomechanical properties. Fan et al. [6] manufactured MREs based on silicone rubber and carbonyl iron microparticles (in different mass fractions) and studied their both static and dynamic magnetomechanical properties. These MREs’ properties are used in various systems. Thus, Deng et al. [7] proposed magnetomechanical damping devices based on adaptive tuned vibrations (note that the damping mechanism in MREs differs from that in magnetostrictive materials [8,9]). The present author [10–14] made magnetic field-controlled magnetoresistive dipoles and electric quadropoles, based on silicone rubber and iron microparticles. The devices are of interest in developing stress or strain sensors and transducers for chemically agressive environments. Following this research
E-mail address: [email protected].
direction, the present paper deals with fabrication of silicone rubber-based MREs, containing iron nanoparticles formed by thermal decomposition (microwave-assisted) of carbonyl iron dispersed in a viscous mixture of polydimethylsiloxane and silica. The magnetomechanical properties of the as-obtained MREs are studied by means of the plane capacitor method. 2. Experiment The obtaining of MRE as an anisotropic dielectric material in a plane capacitor comprises two steps. During the first step, carbonyl iron powder is mixed with liquid silicone rubber, followed by in situ thermal decomposition; as a consequence anemometric iron particles result. In the second stage the mixture is injected together with catalyst between two parallel copper plates, followed by polymerization in magnetic field. 2.1. In situ obtaining iron nanoparticles The used precursors are: - silicone rubber (SR) of type RTV-3325 (Bluestar Silicones) consisting of a viscous mixture of polydimethylsiloxane and silica; the ignition temperature of the mixture is above 673 K [15], - carbonyl iron (CI), produced by Sigma, as a powder of grain size ranging between 4.5 mm and 5.4 mm and iron content exceeding 97%. It thermally decomposes starting from 503 K [16,17]. Four samples Si (i = 1, 2, 3, 4) with different compositions were
1226-086X/$ – see front matter ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2012.03.006
I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669 Table 1 Samples and microwave heating parameters. Sample
Materials
106 V (m3)
P (W)
t (s)
TS (K)
S1
SR CI SR CI SR CI SR CI
27.0 1.5 25.5 3.0 22.5 6.0 19.5 9.0
440
720
423
264
600
438
264
600
440
136
480
450
S2 S3 S4
Note: SR, silicone rubber; CI, carbonyl iron; P, nominal power of the microwaves; t, time; TS, sample surface temperature.
prepared, and there were heated in a microwave oven (model MM820CPB-Midea). The compositions and heating parameters are given in Table 1. Using a AX-6520 (AxioMat) pyrometer, the temperature TS of the sample monitored. The magnetic behavoiur of the samples was examined in 50 Hz ac fields, by means of an integrating fluxmeter [18]; in Fig. 1 the hysteresis loop of the sample S4 is shown (similar loops resulted for the lower particles density samples S1, S2 and S3). Since the loop is very close to the anhysteretic, from fitting with a Langevin-type [19] function (the coefficient of determination was r2 = 0.99992), a value dm = 3.5 nm resulted for the mean diameter of the iron particles. The carbonyl iron powder is electroconductive. In microwave field, each microparticle, situated in the liquid matrix, is inductively heated and, at temperatures beyond 503 K, it decomposes thermally [16]; iron atoms and carbon monoxide molecules result. As an effect of pressure as-developed in the liquid matrix, the carbon monoxide is ejected to the surface and then evacuated by the exhauster of the microwave oven. The dispersed Fe atoms move toward colder regions; if in these regions the temperature is close to the dew point, crystal nuclei occur, grow by further condensation and nanoparticles form. Then, complex bonds occur between the surface Fe atoms and the polydimethylsiloxane free radicals, leading to hydrodynamic stabilization of the as-formed nanoparticles [17]. 2.2. MRE-based capacitors Each of the samples Si is mixed and homogenized with 1.5 106 m3 catalyst of type 6H (Bluestar-Silicones). The obtained mixture is injected between two copper plates which are pressed until the distance between them becomes 0.0002 m. The material, in liquid state, is polymerized in a transverse magnetic field of
1667
500 kA/m 10%. The polymerization of the silicone rubber takes place at room temperature (297 K 10%). The reaction is completed within 24 h. Finally, plane capacitors with dielectric material based on silicone rubber and iron nanoparticles are obtained, having volume fractions of w1 = 0.05; w2 = 0.10; w3 = 0.20 and w4 = 0.30. 3. Theory For simplicity, assume that the Fe nanoparticles from the elastic matrix have the same size; let dm be their diameter. Due to the polymerization in a magnetic field, the nanoparticles form linear chain, uniformly distributed within the elastic matrix. The distance between the chains is assumed sufficiently large. This means that when a magnetic field is applied, the interaction between the chains is negligible compared to that between the nanoparticles. The distance between the nanoparticles in the chain is assumed equal with the average initial distance [3]: 1=3
d0 dm ’i
(1)
where wi is the volume function. Under the magnetic field, the nanoparticles from the chain are magnetized, parallel to the field each having the magnetic moment [3]: m ¼ 0:5pd3m H
(2)
Let the relative magnetic permeability of the elastic matrix
me 1 and that of the iron nanoparticles mp me. between two neighboring nanoparticles, an attractive force [3,10–12]: F m1 ¼
3m0 me m2
(3)
pd4
occurs. where m0 is the vacuum permeability, and d < d0 is the distance between the magnetic dipoles centers at H 6¼ 0. The number of Fe nanoparticles from the elastic matrix corresponding to wi is: ni ¼
’i V Vp
¼ 6’i
Ll h0 d3m
(4)
where V is the volume of the dielectric (MRE), Vp is the volume of the nanoparticle, L, l and h0 are the length, width and thickness of the MRE at H = 0, respectively. The average magnetic force which is exerted upon the MRE is: Fm ¼
1 nF 2 i mi
(5)
Introducing (3) and (4) into (5) and taking into account the expression (2) for d dm, we obtain: F m ¼ 2:25pm0 Ll
h0i ’ H2 ; dm i
(6)
The action of Fm will be counter-balanced by the elastic force: F el ¼ kei ðh0 h0i Þ;
(7)
where kei is the elastic constant, while h0 and h0i are the thicknesses of the dielectric for H 6¼ 0 and H = 0, respectively. The equilibrium condition ~ F m ¼ ~ F el leads to: Ll ’i 2 hi ¼ h0i 1 2:25pm0 H ; (8) ke dm According to of Eqs. (6) and (7) the capacity of the plane capacitor is:
Fig. 1. The magnetization curve of the S4.
C 0i ¼ e0 eni
S ; h0i
for H ¼ 0;
(9)
I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669
1668
S hi
(10)
0.00
where e0 = 8.856 1012 F/m and eri is the relative dielectric permittivity of the MREs. By introducing (8) into (10) one obtains:
-0.05
C 0i ¼ e0 eri
for H 6¼ 0
C 0i Ll ’i 2 ¼ 1 2:25pm0 H ; kei dm Ci
-0.10
ezz
(11)
The elastic constant kei is obtained from (11) and takes the form: kei ¼ 2:25pm0 Ll
’i 1 C 0i =C i
H2 ;
-0.15
ϕ1= 5%
-0.20
(12)
Under the action of Fm, normal tensions are induced in MREs as: F h0 ðs ZZ Þi ¼ mi ¼ 2:25pm0 ’ H2 ; Ll dm i
ϕ2= 10%
-0.25 -0.30
(13)
ϕ3= 20% ϕ4= 30% 0.0
0.1
0.2
0.3
0.4
-3
The linear strain of the MREs is obtained from the relationships: ðeZZ Þi ¼
0.5
0.8
0.9
1.0
(14)
In the linear approximation the relationship between (sZZ)i and (eZZ)i is: ðs ZZ Þi ¼ EðeZZ Þi ;
3
10
2:25pm0 h0 ’i 2 H ; E¼ dm ðC 0i =C i 1Þ
σ(kN/m2)
(15)
where E is the Young modulus. By introducing the expressions (13) and (14) into (15) the Young modulus results as:
2
10
ϕ1 = 5%
(16)
ϕ2 = 10%
1
10
ϕ3 = 20% ϕ4 = 30%
4. Experimental results and discussions The electric capacitor of the manufactured MRE-based capacitors was measured under various transverse magnetic field conditions, by a CM-7115 (Fujian) capacimeter. The magnetic field was generated of a Weiss electromagnet (Phylotex) and measured by a GM-04 (Horst) Gaussmeter. For H = 0 (Fig. 2), the capacity C0i of the plane capacitors is influenced only by wi. As shown in Fig. 2, the ratio C0i/Ci decreases with increasing H and for the same value of H it is sensibly influenced by the volume fraction of the iron nanoparticles, according to the expression in (11). From Eq. (13), a compression of the MRE-based dielectric material results in a magnetic field.
0
10
0
1
2
3
4
-2
5
6
7
8
9
10
10 x H[kA/m] Fig. 4. The tension sZZ as function of the magnetic field intensity H for values of wi as parameter.
Indeed, using the information provided by Fig. 2, in the expression (14), one can determine from Eq. (14) the strain eZZ of MREs as function of H, such as displayed in Fig. 3. The results presented in Fig. 3 confirm that (eZZ)i < 0. The compression of the MRE increases with H and is influenced by wi according to the proposed model. 18
1.00
16
0.95
14 0.90
ϕ1 = 5%
12 10 x E(N/m )
2
0.85 0.80 0.75
ϕ1 = 5% C01=5.34nF
0.70
ϕ1 = 20% C03=7.52nF
-3
C0i/Ci
0.7
Fig. 3. The liniar strain eZZ of MRE as function of H, for wi parameters.
hi h0i C 0i ¼ 1; h0i Ci
0.65
0.6
10 x H[kA/m]
ϕ1 = 10% C02=6.78nF
0.1
0.2
0.3
0.4
ϕ3 = 20%
8
ϕ4 = 30%
6 4 2
ϕ1 = 30% C04=9.72nF
0.0
ϕ2 = 10%
10
0 0.5
0.6
0.7
0.8
0.9
1.0
-3
10 x H[kA/m] Fig. 2. The ratio ai = C0i/Ci as function of the transverse magnetic field intensity H, for wi volume fractions of the iron nanoparticles. Here: C0i and Ci are the capacitances of the plane capacitors at H = 0 and H 6¼ 0.
0
1
2
3
4
5
6
7
8
9
10
-2
10 x H[kA/m] Fig. 5. The elasticity module E as function of the transverse magnetic field intensity H for wi as parameter.
I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669
For m0 = 4p 107 H/m, h0 = 0.002 m, dm = 3.5 nm, from (13) sZZ = sZZ (H) for wi as parameter is obtained as shown in the graphs in Fig. 4. It can be noticed from Fig. 4 that the principal tension, sZZ, increases with H. As expected in for given H, sZZ is sensibly influenced by wi. Using in Eq. (15) the data presented in Figs. 3 and 4, the variation of the Young modulus with H may be determined, as shown in Fig. 5. 5. Conclusions - The Fe nanoparticles are obtained by thermal decomposition in microwave field (Table 1) of carbonyl iron in a mixture with polydimethylsiloxane silicone and silica; - At temperatures T 320 K iron nanoparticles stabilized in the liquid matrix are obtained; - The liquid solution formed by polydimethylsiloxane silicone with silica, iron nanoparticles and catalyst is polymerized between two copper plates in the presence of a transverse magnetic field (H = 500 kA/m 10%) normal to the plates. Plane capacitors are obtained with dielectric based on silicone rubber and iron nanoparticles, with volume fractions w1 = 5%, w2 = 10%, w3 = 20%, w4 = 30%; - The capacitance of the as-obtained capacitors increases with of the magnetic field strength H and is sensibly influenced by wi; - Linear strain and the tensions induced in the MRE, due to the magnetic interactions between the iron nanoparticles, increase with H and are sensibly influenced by wi. - The MRE elastic modulus increases with increasing H and is sensibly influenced by the volume concentration wi of the iron nanoparticles.
1669
Note to the editor As I recently came to the conclusion that the TEM micrograph (made by Dr. M. Lita from the ‘‘Polytechnica’’ University of Timisoara) shown in Fig. 1 of the previous version of the article is of questionable reliability, I decided not to keep it in the actual version of the paper. Instead, I introduced the magnetic hysteresis loop of the MRE, from which the mean diameter of the iron particles was deduced. References [1] J.F. Bombard, J.V.R. Teodoro, Int. J. Mod. Phys. B 25 (2011) 943. [2] Hu, N.M. Wereley, Int. J. Mod. Phys. B 25 (2011) 979. [3] S. Melle, Study of the dynamics MRS subject to external fields by means of optical techniques: aggregation processes, structure formation and temporal evolution, PhD Thesis, Universidad de Madrid, Madrid, 1992. [4] (a) I. Bica, H.J. Choi, Int. J. Mod. Phys. B 29 (2008) 5041; (b) M.J. Hato, H.J. Choi, H.H. Sim, B.O. Park, S.S. Ray, Colloids Surf., A 377 (2011) 103; (c) B.O. Park, B.J. Park, M.J. Hato, H.J. Choi, Colloid. Polym. Sci. 289 (2011) 381; (d) B.J. Park, F.F. Fang, H.J. Choi, Soft Matter 6 (2010) 5246. [5] Kaleta, M. Kro´levicz, D. Lewendowski, Smart Mater. Struct. 20 (2011) 085006. [6] Y. Fan, X. Gong, S. Xnen, W. Zheng, J. Zheng, W. Jiang, Smart Mater. Struct. 20 (2011) 035007. [7] H.-X. Deng, X.-L. Gong, L.-H. Wang, Smart Mater. Struct. 20 (2006) N111. [8] A. Ercuta, I. Mihalca, J. Phys. D: Appl. Phys. 35 (2002) 2902. [9] A. Ercuta, J. Phys.: Condens. Matter 20 (2008) 325227. [10] I. Bica, Mater. Sci. Eng. B 166 (2010) 94. [11] I. Bica, J. Ind. Eng. Chem. 15 (2009) 769. [12] I. Bica, J. Ind. Eng. Chem. 15 (2009) 605. [13] I. Bica, J. Ind. Eng. Chem. 15 (2009) 773. [14] I. Bica, Mater. Lett. 63 (2009) 2230. [15] Rhodorsil RTV 33315, Safety Data Sheet, Version: 1.02, 2002, p. 4. [16] D.W. Llewelyn,, United States Patent Office 3,694,188 (1972). [17] T.W. Smith, United States Patent 4,252,672 (1981). [18] I. Mihalca, A. Ercuta, C. Ionescu, Sens. Actuators A 106 (2003) 61. [19] S. Odenbach, Magnetic Fluids, Springer-Verlag, Berlin Heidelberg, 2002.
Contents lists available at SciVerse ScienceDirect
Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec
The influence of the magnetic field on the elastic properties of anisotropic magnetorheological elastomers Ioan Bica West University of Timis¸oara, Faculty of Physics, Bd. V. Paˆrvan, No. 4, 300223 Timis¸oara, Romania
A R T I C L E I N F O
Article history: Received 24 November 2011 Accepted 3 March 2012 Available online 10 March 2012 Keywords: Magnetorheological elastomer Silicone rubber Carbonyl iron Thermal decomposition Microwaves Iron nanoparticles
A B S T R A C T
This paper deals with the process of achievement of anisotropic magnetorheological elastomers (MREs), based on silicone rubber and iron nanoparticles. Plane capacitors are manufactured with MREs. The capacity C of the plane capacitors is measured as function of the intensity H of the magnetic field. By using the approximation of the dipolar magnetic moment and the ideal elastic body model, respectively, the tensions and deformations field and respectively the elasticity module of MREs function of H have been determined, for magnetic field values of up to 1000 kA/m. The obtained results are presented and discussed. ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved.
1. Introduction Magnetorheological elastomers (MREs) and magnetorheological suspensions (MRSs) are active magnetic materials, consisting of a matrix in which magnetic particles are dispersed. As their mechanical and rheological properties are well controlled by applied magnetic fields, these materials are of interest in various applications. Unlike the MRSs, in which long term particles deposition often occurs [1–4] the stability of the MREs is ensured by inserting the particles in polymer chains [5–14]. The capabilities of MREs have received an increasing interest cluring last decades. Thus, Kaleta et al. [5] produced isotropic and anisotropic MREs based on thermoplastic rubber and iron microparticles, and carried out a study of their static magnetomechanical properties. Fan et al. [6] manufactured MREs based on silicone rubber and carbonyl iron microparticles (in different mass fractions) and studied their both static and dynamic magnetomechanical properties. These MREs’ properties are used in various systems. Thus, Deng et al. [7] proposed magnetomechanical damping devices based on adaptive tuned vibrations (note that the damping mechanism in MREs differs from that in magnetostrictive materials [8,9]). The present author [10–14] made magnetic field-controlled magnetoresistive dipoles and electric quadropoles, based on silicone rubber and iron microparticles. The devices are of interest in developing stress or strain sensors and transducers for chemically agressive environments. Following this research
E-mail address: [email protected].
direction, the present paper deals with fabrication of silicone rubber-based MREs, containing iron nanoparticles formed by thermal decomposition (microwave-assisted) of carbonyl iron dispersed in a viscous mixture of polydimethylsiloxane and silica. The magnetomechanical properties of the as-obtained MREs are studied by means of the plane capacitor method. 2. Experiment The obtaining of MRE as an anisotropic dielectric material in a plane capacitor comprises two steps. During the first step, carbonyl iron powder is mixed with liquid silicone rubber, followed by in situ thermal decomposition; as a consequence anemometric iron particles result. In the second stage the mixture is injected together with catalyst between two parallel copper plates, followed by polymerization in magnetic field. 2.1. In situ obtaining iron nanoparticles The used precursors are: - silicone rubber (SR) of type RTV-3325 (Bluestar Silicones) consisting of a viscous mixture of polydimethylsiloxane and silica; the ignition temperature of the mixture is above 673 K [15], - carbonyl iron (CI), produced by Sigma, as a powder of grain size ranging between 4.5 mm and 5.4 mm and iron content exceeding 97%. It thermally decomposes starting from 503 K [16,17]. Four samples Si (i = 1, 2, 3, 4) with different compositions were
1226-086X/$ – see front matter ß 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jiec.2012.03.006
I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669 Table 1 Samples and microwave heating parameters. Sample
Materials
106 V (m3)
P (W)
t (s)
TS (K)
S1
SR CI SR CI SR CI SR CI
27.0 1.5 25.5 3.0 22.5 6.0 19.5 9.0
440
720
423
264
600
438
264
600
440
136
480
450
S2 S3 S4
Note: SR, silicone rubber; CI, carbonyl iron; P, nominal power of the microwaves; t, time; TS, sample surface temperature.
prepared, and there were heated in a microwave oven (model MM820CPB-Midea). The compositions and heating parameters are given in Table 1. Using a AX-6520 (AxioMat) pyrometer, the temperature TS of the sample monitored. The magnetic behavoiur of the samples was examined in 50 Hz ac fields, by means of an integrating fluxmeter [18]; in Fig. 1 the hysteresis loop of the sample S4 is shown (similar loops resulted for the lower particles density samples S1, S2 and S3). Since the loop is very close to the anhysteretic, from fitting with a Langevin-type [19] function (the coefficient of determination was r2 = 0.99992), a value dm = 3.5 nm resulted for the mean diameter of the iron particles. The carbonyl iron powder is electroconductive. In microwave field, each microparticle, situated in the liquid matrix, is inductively heated and, at temperatures beyond 503 K, it decomposes thermally [16]; iron atoms and carbon monoxide molecules result. As an effect of pressure as-developed in the liquid matrix, the carbon monoxide is ejected to the surface and then evacuated by the exhauster of the microwave oven. The dispersed Fe atoms move toward colder regions; if in these regions the temperature is close to the dew point, crystal nuclei occur, grow by further condensation and nanoparticles form. Then, complex bonds occur between the surface Fe atoms and the polydimethylsiloxane free radicals, leading to hydrodynamic stabilization of the as-formed nanoparticles [17]. 2.2. MRE-based capacitors Each of the samples Si is mixed and homogenized with 1.5 106 m3 catalyst of type 6H (Bluestar-Silicones). The obtained mixture is injected between two copper plates which are pressed until the distance between them becomes 0.0002 m. The material, in liquid state, is polymerized in a transverse magnetic field of
1667
500 kA/m 10%. The polymerization of the silicone rubber takes place at room temperature (297 K 10%). The reaction is completed within 24 h. Finally, plane capacitors with dielectric material based on silicone rubber and iron nanoparticles are obtained, having volume fractions of w1 = 0.05; w2 = 0.10; w3 = 0.20 and w4 = 0.30. 3. Theory For simplicity, assume that the Fe nanoparticles from the elastic matrix have the same size; let dm be their diameter. Due to the polymerization in a magnetic field, the nanoparticles form linear chain, uniformly distributed within the elastic matrix. The distance between the chains is assumed sufficiently large. This means that when a magnetic field is applied, the interaction between the chains is negligible compared to that between the nanoparticles. The distance between the nanoparticles in the chain is assumed equal with the average initial distance [3]: 1=3
d0 dm ’i
(1)
where wi is the volume function. Under the magnetic field, the nanoparticles from the chain are magnetized, parallel to the field each having the magnetic moment [3]: m ¼ 0:5pd3m H
(2)
Let the relative magnetic permeability of the elastic matrix
me 1 and that of the iron nanoparticles mp me. between two neighboring nanoparticles, an attractive force [3,10–12]: F m1 ¼
3m0 me m2
(3)
pd4
occurs. where m0 is the vacuum permeability, and d < d0 is the distance between the magnetic dipoles centers at H 6¼ 0. The number of Fe nanoparticles from the elastic matrix corresponding to wi is: ni ¼
’i V Vp
¼ 6’i
Ll h0 d3m
(4)
where V is the volume of the dielectric (MRE), Vp is the volume of the nanoparticle, L, l and h0 are the length, width and thickness of the MRE at H = 0, respectively. The average magnetic force which is exerted upon the MRE is: Fm ¼
1 nF 2 i mi
(5)
Introducing (3) and (4) into (5) and taking into account the expression (2) for d dm, we obtain: F m ¼ 2:25pm0 Ll
h0i ’ H2 ; dm i
(6)
The action of Fm will be counter-balanced by the elastic force: F el ¼ kei ðh0 h0i Þ;
(7)
where kei is the elastic constant, while h0 and h0i are the thicknesses of the dielectric for H 6¼ 0 and H = 0, respectively. The equilibrium condition ~ F m ¼ ~ F el leads to: Ll ’i 2 hi ¼ h0i 1 2:25pm0 H ; (8) ke dm According to of Eqs. (6) and (7) the capacity of the plane capacitor is:
Fig. 1. The magnetization curve of the S4.
C 0i ¼ e0 eni
S ; h0i
for H ¼ 0;
(9)
I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669
1668
S hi
(10)
0.00
where e0 = 8.856 1012 F/m and eri is the relative dielectric permittivity of the MREs. By introducing (8) into (10) one obtains:
-0.05
C 0i ¼ e0 eri
for H 6¼ 0
C 0i Ll ’i 2 ¼ 1 2:25pm0 H ; kei dm Ci
-0.10
ezz
(11)
The elastic constant kei is obtained from (11) and takes the form: kei ¼ 2:25pm0 Ll
’i 1 C 0i =C i
H2 ;
-0.15
ϕ1= 5%
-0.20
(12)
Under the action of Fm, normal tensions are induced in MREs as: F h0 ðs ZZ Þi ¼ mi ¼ 2:25pm0 ’ H2 ; Ll dm i
ϕ2= 10%
-0.25 -0.30
(13)
ϕ3= 20% ϕ4= 30% 0.0
0.1
0.2
0.3
0.4
-3
The linear strain of the MREs is obtained from the relationships: ðeZZ Þi ¼
0.5
0.8
0.9
1.0
(14)
In the linear approximation the relationship between (sZZ)i and (eZZ)i is: ðs ZZ Þi ¼ EðeZZ Þi ;
3
10
2:25pm0 h0 ’i 2 H ; E¼ dm ðC 0i =C i 1Þ
σ(kN/m2)
(15)
where E is the Young modulus. By introducing the expressions (13) and (14) into (15) the Young modulus results as:
2
10
ϕ1 = 5%
(16)
ϕ2 = 10%
1
10
ϕ3 = 20% ϕ4 = 30%
4. Experimental results and discussions The electric capacitor of the manufactured MRE-based capacitors was measured under various transverse magnetic field conditions, by a CM-7115 (Fujian) capacimeter. The magnetic field was generated of a Weiss electromagnet (Phylotex) and measured by a GM-04 (Horst) Gaussmeter. For H = 0 (Fig. 2), the capacity C0i of the plane capacitors is influenced only by wi. As shown in Fig. 2, the ratio C0i/Ci decreases with increasing H and for the same value of H it is sensibly influenced by the volume fraction of the iron nanoparticles, according to the expression in (11). From Eq. (13), a compression of the MRE-based dielectric material results in a magnetic field.
0
10
0
1
2
3
4
-2
5
6
7
8
9
10
10 x H[kA/m] Fig. 4. The tension sZZ as function of the magnetic field intensity H for values of wi as parameter.
Indeed, using the information provided by Fig. 2, in the expression (14), one can determine from Eq. (14) the strain eZZ of MREs as function of H, such as displayed in Fig. 3. The results presented in Fig. 3 confirm that (eZZ)i < 0. The compression of the MRE increases with H and is influenced by wi according to the proposed model. 18
1.00
16
0.95
14 0.90
ϕ1 = 5%
12 10 x E(N/m )
2
0.85 0.80 0.75
ϕ1 = 5% C01=5.34nF
0.70
ϕ1 = 20% C03=7.52nF
-3
C0i/Ci
0.7
Fig. 3. The liniar strain eZZ of MRE as function of H, for wi parameters.
hi h0i C 0i ¼ 1; h0i Ci
0.65
0.6
10 x H[kA/m]
ϕ1 = 10% C02=6.78nF
0.1
0.2
0.3
0.4
ϕ3 = 20%
8
ϕ4 = 30%
6 4 2
ϕ1 = 30% C04=9.72nF
0.0
ϕ2 = 10%
10
0 0.5
0.6
0.7
0.8
0.9
1.0
-3
10 x H[kA/m] Fig. 2. The ratio ai = C0i/Ci as function of the transverse magnetic field intensity H, for wi volume fractions of the iron nanoparticles. Here: C0i and Ci are the capacitances of the plane capacitors at H = 0 and H 6¼ 0.
0
1
2
3
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10 x H[kA/m] Fig. 5. The elasticity module E as function of the transverse magnetic field intensity H for wi as parameter.
I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669
For m0 = 4p 107 H/m, h0 = 0.002 m, dm = 3.5 nm, from (13) sZZ = sZZ (H) for wi as parameter is obtained as shown in the graphs in Fig. 4. It can be noticed from Fig. 4 that the principal tension, sZZ, increases with H. As expected in for given H, sZZ is sensibly influenced by wi. Using in Eq. (15) the data presented in Figs. 3 and 4, the variation of the Young modulus with H may be determined, as shown in Fig. 5. 5. Conclusions - The Fe nanoparticles are obtained by thermal decomposition in microwave field (Table 1) of carbonyl iron in a mixture with polydimethylsiloxane silicone and silica; - At temperatures T 320 K iron nanoparticles stabilized in the liquid matrix are obtained; - The liquid solution formed by polydimethylsiloxane silicone with silica, iron nanoparticles and catalyst is polymerized between two copper plates in the presence of a transverse magnetic field (H = 500 kA/m 10%) normal to the plates. Plane capacitors are obtained with dielectric based on silicone rubber and iron nanoparticles, with volume fractions w1 = 5%, w2 = 10%, w3 = 20%, w4 = 30%; - The capacitance of the as-obtained capacitors increases with of the magnetic field strength H and is sensibly influenced by wi; - Linear strain and the tensions induced in the MRE, due to the magnetic interactions between the iron nanoparticles, increase with H and are sensibly influenced by wi. - The MRE elastic modulus increases with increasing H and is sensibly influenced by the volume concentration wi of the iron nanoparticles.
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Note to the editor As I recently came to the conclusion that the TEM micrograph (made by Dr. M. Lita from the ‘‘Polytechnica’’ University of Timisoara) shown in Fig. 1 of the previous version of the article is of questionable reliability, I decided not to keep it in the actual version of the paper. Instead, I introduced the magnetic hysteresis loop of the MRE, from which the mean diameter of the iron particles was deduced. References [1] J.F. Bombard, J.V.R. Teodoro, Int. J. Mod. Phys. B 25 (2011) 943. [2] Hu, N.M. Wereley, Int. J. Mod. Phys. B 25 (2011) 979. [3] S. Melle, Study of the dynamics MRS subject to external fields by means of optical techniques: aggregation processes, structure formation and temporal evolution, PhD Thesis, Universidad de Madrid, Madrid, 1992. [4] (a) I. Bica, H.J. Choi, Int. J. Mod. Phys. B 29 (2008) 5041; (b) M.J. Hato, H.J. Choi, H.H. Sim, B.O. Park, S.S. Ray, Colloids Surf., A 377 (2011) 103; (c) B.O. Park, B.J. Park, M.J. Hato, H.J. Choi, Colloid. Polym. Sci. 289 (2011) 381; (d) B.J. Park, F.F. Fang, H.J. Choi, Soft Matter 6 (2010) 5246. [5] Kaleta, M. Kro´levicz, D. Lewendowski, Smart Mater. Struct. 20 (2011) 085006. [6] Y. Fan, X. Gong, S. Xnen, W. Zheng, J. Zheng, W. Jiang, Smart Mater. Struct. 20 (2011) 035007. [7] H.-X. Deng, X.-L. Gong, L.-H. Wang, Smart Mater. Struct. 20 (2006) N111. [8] A. Ercuta, I. Mihalca, J. Phys. D: Appl. Phys. 35 (2002) 2902. [9] A. Ercuta, J. Phys.: Condens. Matter 20 (2008) 325227. [10] I. Bica, Mater. Sci. Eng. B 166 (2010) 94. [11] I. Bica, J. Ind. Eng. Chem. 15 (2009) 769. [12] I. Bica, J. Ind. Eng. Chem. 15 (2009) 605. [13] I. Bica, J. Ind. Eng. Chem. 15 (2009) 773. [14] I. Bica, Mater. Lett. 63 (2009) 2230. [15] Rhodorsil RTV 33315, Safety Data Sheet, Version: 1.02, 2002, p. 4. [16] D.W. Llewelyn,, United States Patent Office 3,694,188 (1972). [17] T.W. Smith, United States Patent 4,252,672 (1981). [18] I. Mihalca, A. Ercuta, C. Ionescu, Sens. Actuators A 106 (2003) 61. [19] S. Odenbach, Magnetic Fluids, Springer-Verlag, Berlin Heidelberg, 2002.