Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669

The influence of the magnetic field on the elastic properties of anisotropicmagnetorheological elastomers

Ioan Bica

West University of Timis oara, Faculty of Physics, Bd. V. Parvan, 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.

� 2012 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights

reserved.

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Journal of Industrial and Engineering Chemistry

jou r n al h o mep ag e: w ww .e lsev ier . co m / loc ate / j iec

1. Introduction

Magnetorheological elastomers (MREs) and magnetorheologi-cal suspensions (MRSs) are active magnetic materials, consisting ofa matrix in which magnetic particles are dispersed. As theirmechanical and rheological properties are well controlled byapplied magnetic fields, these materials are of interest in variousapplications. Unlike the MRSs, in which long term particlesdeposition often occurs [1–4] the stability of the MREs is ensuredby inserting the particles in polymer chains [5–14]. The capabilitiesof MREs have received an increasing interest cluring last decades.Thus, Kaleta et al. [5] produced isotropic and anisotropic MREsbased on thermoplastic rubber and iron microparticles, and carriedout a study of their static magnetomechanical properties. Fan et al.[6] manufactured MREs based on silicone rubber and carbonyl ironmicroparticles (in different mass fractions) and studied their bothstatic and dynamic magnetomechanical properties. These MREs’properties are used in various systems. Thus, Deng et al. [7]proposed magnetomechanical damping devices based on adaptivetuned vibrations (note that the damping mechanism in MREsdiffers from that in magnetostrictive materials [8,9]).

The present author [10–14] made magnetic field-controlledmagnetoresistive dipoles and electric quadropoles, based onsilicone rubber and iron microparticles. The devices are of interestin developing stress or strain sensors and transducers forchemically agressive environments. Following this research

E-mail address: ioanbica50@yahoo.com.

1226-086X/$ – see front matter � 2012 The Korean Society of Industrial and Engineer

doi:10.1016/j.jiec.2012.03.006

direction, the present paper deals with fabrication of siliconerubber-based MREs, containing iron nanoparticles formed bythermal decomposition (microwave-assisted) of carbonyl irondispersed in a viscous mixture of polydimethylsiloxane and silica.The magnetomechanical properties of the as-obtained MREs arestudied by means of the plane capacitor method.

2. Experiment

The obtaining of MRE as an anisotropic dielectric material in aplane capacitor comprises two steps. During the first step, carbonyliron powder is mixed with liquid silicone rubber, followed by insitu thermal decomposition; as a consequence anemometric ironparticles result. In the second stage the mixture is injected togetherwith catalyst between two parallel copper plates, followed bypolymerization 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 polydimethylsiloxaneand silica; the ignition temperature of the mixture is above673 K [15],

- carbonyl iron (CI), produced by Sigma, as a powder of grain sizeranging between 4.5 mm and 5.4 mm and iron content exceeding97%. It thermally decomposes starting from 503 K [16,17]. Foursamples Si (i = 1, 2, 3, 4) with different compositions were

ing Chemistry. Published by Elsevier B.V. All rights reserved.

Table 1Samples and microwave heating parameters.

Sample Materials 106� V (m3) P (W) t (s) TS (K)

S1 SR 27.0 440 720 423

CI 1.5

S2 SR 25.5 264 600 438

CI 3.0

S3 SR 22.5 264 600 440

CI 6.0

S4 SR 19.5 136 480 450

CI 9.0

Note: SR, silicone rubber; CI, carbonyl iron; P, nominal power of the microwaves; t,

time; TS, sample surface temperature.

I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–1669 1667

prepared, and there were heated in a microwave oven (modelMM820CPB-Midea). The compositions and heating parametersare given in Table 1. Using a AX-6520 (AxioMat) pyrometer, thetemperature TS of the sample monitored.

The magnetic behavoiur of the samples was examined in50 Hz ac fields, by means of an integrating fluxmeter [18]; inFig. 1 the hysteresis loop of the sample S4 is shown (similar loopsresulted for the lower particles density samples S1, S2 and S3).Since the loop is very close to the anhysteretic, from fitting with aLangevin-type [19] function (the coefficient of determinationwas r2 = 0.99992), a value dm = 3.5 nm resulted for the meandiameter of the iron particles.

The carbonyl iron powder is electroconductive. In microwavefield, each microparticle, situated in the liquid matrix, isinductively heated and, at temperatures beyond 503 K, it decom-poses thermally [16]; iron atoms and carbon monoxide moleculesresult. As an effect of pressure as-developed in the liquid matrix,the carbon monoxide is ejected to the surface and then evacuatedby the exhauster of the microwave oven. The dispersed Fe atomsmove toward colder regions; if in these regions the temperature isclose to the dew point, crystal nuclei occur, grow by furthercondensation and nanoparticles form. Then, complex bonds occurbetween the surface Fe atoms and the polydimethylsiloxane freeradicals, leading to hydrodynamic stabilization of the as-formednanoparticles [17].

2.2. MRE-based capacitors

Each of the samples Si is mixed and homogenized with1.5 � 10�6 m3 catalyst of type 6H (Bluestar-Silicones). The obtainedmixture is injected between two copper plates which are presseduntil the distance between them becomes 0.0002 m. The material,in liquid state, is polymerized in a transverse magnetic field of

Fig. 1. The magnetization curve of the S4.

500 kA/m � 10%. The polymerization of the silicone rubber takes placeat room temperature (297 K � 10%). The reaction is completed within24 h. Finally, plane capacitors with dielectric material based on siliconerubber and iron nanoparticles are obtained, having volume fractions ofw1 = 0.05; w2 = 0.10; w3 = 0.20 and w4 = 0.30.

3. Theory

For simplicity, assume that the Fe nanoparticles from the elasticmatrix have the same size; let dm be their diameter.

Due to the polymerization in a magnetic field, the nanoparticlesform linear chain, uniformly distributed within the elastic matrix.The distance between the chains is assumed sufficiently large. Thismeans that when a magnetic field is applied, the interactionbetween the chains is negligible compared to that between thenanoparticles.

The distance between the nanoparticles in the chain is assumedequal with the average initial distance [3]:

d0 � dm’�1=3i (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 0:5pd3mH (2)

Let the relative magnetic permeability of the elastic matrixme � 1 and that of the iron nanoparticles mp� me. between twoneighboring nanoparticles, an attractive force [3,10–12]:

Fm1¼ �3m0mem2

pd4(3)

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’iV

V p¼ 6’i

Ll

d3m

h0 (4)

where V is the volume of the dielectric (MRE), Vp is the volume ofthe nanoparticle, L, l and h0 are the length, width and thickness ofthe MRE at H = 0, respectively.

The average magnetic force which is exerted upon the MRE is:

Fm ¼1

2niFmi (5)

Introducing (3) and (4) into (5) and taking into account theexpression (2) for d � dm, we obtain:

Fm ¼ �2:25pm0Llh0i

dm’iH

2; (6)

The action of Fm will be counter-balanced by the elastic force:

Fel ¼ keiðh0 � h0iÞ; (7)

where kei is the elastic constant, while h0 and h0i are thethicknesses of the dielectric for H 6¼ 0 and H = 0, respectively.

The equilibrium condition ~Fm ¼ �~Fel leads to:

hi ¼ h0i 1 � 2:25pm0Ll

ke

’i

dmH2

� �; (8)

According to of Eqs. (6) and (7) the capacity of the planecapacitor is:

C0i ¼ e0eniS

h0i; for H ¼ 0; (9)

1.00.90.80.70.60.50.40.30.20.10.0

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

ϕ1= 5%

ϕ2= 10%

ϕ3= 20%

ϕ4= 30%

ezz

10-3

x H[kA/m]

Fig. 3. The liniar strain eZZ of MRE as function of H, for wi parameters.

10987654321010

0

101

102

103

ϕ1 = 5%

ϕ2 = 10%

ϕ3 = 20%

ϕ4 = 30%

σ (k

N/m

2)

10- 2

x H[kA/m]

Fig. 4. The tension sZZ as function of the magnetic field intensity H for values of wi as

parameter.

I. Bica / Journal of Industrial and Engineering Chemistry 18 (2012) 1666–16691668

C0i ¼ e0eriS

hifor H 6¼ 0 (10)

where e0 = 8.856 � 10�12 F/m and eri is the relative dielectricpermittivity of the MREs.

By introducing (8) into (10) one obtains:

C0i

Ci¼ 1 � 2:25pm0

Ll

kei

’i

dmH2; (11)

The elastic constant kei is obtained from (11) and takes the form:

kei ¼ 2:25pm0Ll’i

1 � C0i=CiH2; (12)

Under the action of Fm, normal tensions are induced in MREs as:

ðsZZÞi ¼Fmi

Ll¼ �2:25pm0

h0

dm’iH

2; (13)

The linear strain of the MREs is obtained from the relationships:

ðeZZÞi ¼hi � h0i

h0i¼ C0i

Ci� 1; (14)

In the linear approximation the relationship between (sZZ)i and(eZZ)i is:

ðsZZÞi ¼ EðeZZÞi; (15)

where E is the Young modulus.By introducing the expressions (13) and (14) into (15) the

Young modulus results as:

E ¼ � 2:25pm0h0’i

dmðC0i=Ci � 1ÞH2; (16)

4. Experimental results and discussions

The electric capacitor of the manufactured MRE-based capa-citors was measured under various transverse magnetic fieldconditions, by a CM-7115 (Fujian) capacimeter. The magnetic fieldwas generated of a Weiss electromagnet (Phylotex) and measuredby 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 volumefraction of the iron nanoparticles, according to the expression in(11). From Eq. (13), a compression of the MRE-based dielectricmaterial results in a magnetic field.

1.00.90.80.70.60.50.40.30.20.10.0

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

ϕ1 = 5% C

01 =5.34nF

ϕ1 = 10% C

02 =6.78nF

ϕ1 = 20% C

03 =7.52nF

ϕ1 = 30% C

04 =9.72nF

C0

i/Ci

10- 3

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.

Indeed, using the information provided by Fig. 2, in theexpression (14), one can determine from Eq. (14) the strain eZZ ofMREs as function of H, such as displayed in Fig. 3. The resultspresented in Fig. 3 confirm that (eZZ)i < 0. The compression of theMRE increases with H and is influenced by wi according to theproposed model.

109876543210

0

2

4

6

8

10

12

14

16

18

ϕ1 = 5%

ϕ2 = 10%

ϕ3 = 20%

ϕ4 = 30%

10

- 3 x

E(N

/m2)

10-2 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 1669

For m0 = 4p � 10�7 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 graphsin 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 sensiblyinfluenced by wi. Using in Eq. (15) the data presented in Figs. 3 and4, 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 inmicrowave field (Table 1) of carbonyl iron in a mixture withpolydimethylsiloxane silicone and silica;

- At temperatures T � 320 K iron nanoparticles stabilized in theliquid matrix are obtained;

- The liquid solution formed by polydimethylsiloxane silicone withsilica, iron nanoparticles and catalyst is polymerized betweentwo copper plates in the presence of a transverse magnetic field(H = 500 kA/m � 10%) normal to the plates. Plane capacitors areobtained with dielectric based on silicone rubber and ironnanoparticles, with volume fractions w1 = 5%, w2 = 10%, w3 = 20%,w4 = 30%;

- The capacitance of the as-obtained capacitors increases with ofthe magnetic field strength H and is sensibly influenced by wi;

- Linear strain and the tensions induced in the MRE, due to themagnetic interactions between the iron nanoparticles, increasewith H and are sensibly influenced by wi.

- The MRE elastic modulus increases with increasing H and issensibly influenced by the volume concentration wi of the ironnanoparticles.

Note to the editor

As I recently came to the conclusion that the TEM micrograph(made by Dr. M. Lita from the ‘‘Polytechnica’’ University ofTimisoara) shown in Fig. 1 of the previous version of the article is ofquestionable reliability, I decided not to keep it in the actualversion of the paper. Instead, I introduced the magnetic hysteresisloop of the MRE, from which the mean diameter of the ironparticles was deduced.

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