Soft Matter

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Experimental stu

aPhysics Department, Moscow State Unive

kram@polly.phys.msu.rubEast Bavarian Centre for Intelligent Mater

Hochschule Regensburg, Seybothstr. 2, D-93cState Institute of Chemistry and Technolog

Moscow, RussiadA.N. Nesmeyanov Institute for Organoelem

Russia

Cite this: Soft Matter, 2014, 10, 8765

Received 5th August 2014Accepted 12th September 2014

DOI: 10.1039/c4sm01738b

www.rsc.org/softmatter

This journal is © The Royal Society of C

dy of the magnetic field enhancedPayne effect in magnetorheological elastomers

Vladislav V. Sorokin,a Eva Ecker,b Gennady V. Stepanov,c Mikhail Shamonin,b

Gareth J. Monkman,b Elena Yu. Kramarenko*ad and Alexei R. Khokhlovad

The dynamic modulus and the loss factor of magnetorheological elastomers (MREs) of various

compositions and anisotropies are studied by dynamic torsion oscillations performed in the absence and

in the presence of an external magnetic field. The emphasis is on the Payne effect, i.e. the dependence

of the elastomer magnetorheological characteristics on the strain amplitude and their evolution with

cyclically increasing and decreasing strain amplitudes. MREs are based on two silicone matrices differing

in storage modulus (soft, G0 � 103 Pa, and hard, G0 � 104 Pa, matrices). For each matrix, the

concentration of carbonyl iron particles with diameters of 3–5 mm was equal to 70 and 82 mass% (22

and 35 vol%, respectively) in the composite material. Samples for each filler content, isotropic and

aligned-particles, are investigated. It is found that the Payne effect significantly increases in the presence

of an external magnetic field and varies with the cyclical loading which reaches saturation after several

cycles. The results are interpreted as the processes of formation–destruction–reformation of the internal

filler structure under the simultaneously applied mechanical force and magnetic field. Impacts of matrix

elasticity and magnetic interactions on the filler alignment are elucidated.

1. Introduction

New types of magnetorheological (MR) materials, namely, somagnetic elastomers and magnetic gels have attracted growingattention over the past 18 years. Commencing with a few pio-neering studies in the 1990s1–6 the amount of papers producedeach year has increased exponentially. The interest is mainlyconnected with the industrial potential of the new MR mate-rials. Being solid analogies of magnetorheological uids,7

demonstrating a dramatic change in viscoelastic propertiesunder the inuence of magnetic elds, magnetorheologicalelastomers (MREs) and gels exhibit some new and interestingproperties. In addition to their rheological characteristics (suchas the storage modulus, loss modulus, loss factor) MREs andMR gels are able to signicantly change their dimensions8–11

and demonstrate a shape memory effect10,12,13 in the presence ofrather small magnetic elds (up to 600 mT). These materials arevery promising in many applications, including those tradi-tionally the domain of MR uids: for example, for devices where

rsity, Moscow, 119991, Russia. E-mail:

ials (EBACIM), Ostbayerische Technische

053 Regensburg, Germany

y of Organoelement Compounds, 105118,

ent Compounds RAS, 119991, Moscow,

hemistry 2014

the tunable stiffness and shape are required – dampers, seals,actuators, valves, articial muscles, etc.

The MR effect in MREs and gels, i.e. the increase in visco-elastic properties on the application of a magnetic eld, is themost widely studied aspect – see for instance ref. 14–27. Hith-erto, it has been understood from the literature13,19,22 that theMR effect is due to structuring of the magnetic particles withinthe magnetic eld. While in MR uids, the formation ofmagnetic chains is unrestricted, and the structuring in the MRsolid analogies takes place under the inuence of both polymerelasticity and magnetic interactions. Due to strong couplingbetween particles and the polymer matrix, the particledisplacements are controlled by polymer elasticity. Thus, in astiff polymer matrix no structuring is possible because elasticforces dominate and maintain the particles in their initialpositions. In soer matrices, magnetic forces can overcomepolymer elasticity. The soer the matrix, the more pronouncedthe structuring of the magnetic ller, resulting in a largerchange in material rheology. The MRE with the initial shearmodulus of 10–20 kPa has been shown to demonstrate a 100–500 times increase in the storage and loss moduli.12,13,19,24 Therecently developedMRE with even lower initial storage modulus(between 100 Pa and 2000 Pa) has a colossal magneto-rheological effect of >106%.21

Because the structuring is dened by a balance betweenelastic and magnetic forces, the factors inuencing magneticinteractions such as magnetic properties of the ller, the size ofthe particles and their spatial density also control the MR effect.

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It has been understood that iron with high saturation magne-tization is one of the best candidates for the ller. Usually,micrometer-sized particles are used, although recently the MREbased on even sub-millimeter iron particles has been obtainedwith a more pronounced MR effect.27 The enhancement of theMR effect with increasing ller concentration has beendemonstrated in a number of publications.19,20,22 Furthermore,it has been found that with a xed ller concentration thelargest MR effect is realized in structured composites synthe-sized within a magnetic eld19,20,22 where the mechanicalcompressive force is parallel to the magnetic chain structure. Inthe case of shear force, the force should be perpendicular to theinternal magnetic structure.

Being composite polymer materials, MREs and MR gelsexhibit the so-called Payne effect. The Payne effect is known tobe a particular feature of the stress–strain behavior of rubbercomposites containing llers, in particular, carbon black.29 It ismanifested as a function of storage and loss moduli on theamplitude of the applied strain. Above some critical strainamplitude, the storage modulus decreases rapidly withincreasing amplitude saturating at rather large deformationswhile the loss modulus shows a maximum in the region wherethe storage modulus decreases. The loss tangent (tan d¼ G00/G0)increases in this region which is sometimes called dynamichysteresis in the rubber industry.30 The Payne effect depends onthe ller content of the material and vanishes with unlledelastomers.

Although the fall-off of the storage modulus with increasingstrain has already been discussed for MREs in ref. 1 and 2 verylittle attention has been paid to this interesting phenomenonwhich is especially pronounced for MREs in magnetic elds.Only a few groups have recently started to study the non-linearmagnetorheological response of MREs.12,14,24,32–38 In ref. 37 theterm the “magnetic Payne effect” was rst introduced for MRgels to emphasize their strain-soening. In spite of some workalready having been carried out, many fundamental issuesregarding the Payne effect remain poorly understood andrequire further investigation. In particular, the relative impactof the polymer matrix in the process of ller structuring atvarious strains remains unclear. The study of different MREparameters based on rheological properties is hitherto missingand will be claried in this paper. The focus is on the Payneeffect in MR silicone-based elastomers with high iron particlecontent. The study of this effect in detail, depending on theinitial modulus of the matrix and the amount of ller as well asthe ller distribution within MREs, will be discussed.

Other important aspects of MR material behavior ignored inmost papers are hysteresis, strong time dependence and stresshardening. Some features of MRE hysteresis under the simul-taneously applied magnetic eld and external mechanical forcehave been elucidated by us in ref. 12 and 38. It has been shownthat the MRE behaves as a material with the strengtheningeffect, i.e. its modulus increases and then saturates underapplied mechanical stress within a magnetic eld. A series ofinvestigations have been performed by the Mendes group ontriblock copolymer physical gels with embedded magneticparticles.35–37 They have particularly stressed that MR gels are

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intrinsically non-linear systems and studied the effect of alter-nate cyclical strain on the stress–strain behavior of MR gels withdifferent types of magnetic particles and their ordering withingels (either isotropic or chain forming perpendicular andparallel to the shear plane).36

In this paper we show that cyclical strain with increasingstrain amplitude changes the dynamic modulus of MR elasto-mers. Analyzing the behavior of MREs with different matrixmoduli and different ller contents as well as different llerdistributions, the processes of formation–destruction–refor-mation of the internal ller structure under the simultaneouslyapplied stress and magnetic eld is studied. An attempt toestimate the relative impact of polymer elasticity and magneticinteractions on viscoelastic characteristics of MREs is thenmade.

2. Experimental2.1. Material

For the synthesis of MRE samples we used the siliconecompound SIEL produced by the Russian Institute of Chemistryand Technology of Organoelement Compounds (GNIIChTEOS).The composition of the SIEL compound has already beendescribed in detail elsewhere.12,13,19,20,28 The main advantage ofthe SIEL compound is its ability to accommodate a wide varia-tion of mechanical properties of the elastomers obtained. Forexample, the Young's modulus can be varied in the range from0.1–600 kPa, tensile strength from 0.1–4 MPa, and elongation atbreak between 100% and 500%. Furthermore, it does notproduce any by-products during the vulcanization process in aclosed volume, and using SIEL it is possible to control thevulcanization process in the “temperature-time” coordinates. Inaddition, the silicone matrices obtained have a wide workingtemperature range. For the purposes of this study two types ofmatrices were synthesized. We call them “so” and “hard”matrices to emphasize their differences in Young's modulus.

Carbonyl iron particles of 3–5 mm in diameter are used asllers. The particle surface is modied by oligomer silicone oilto prevent particle agglomeration and to enhance theircompatibility with the silicone compound. The detailed proce-dure of MRE preparation is described elsewhere.12,13,19,20 Bothisotropic and anisotropic samples were synthesized (see Table1). Anisotropic samples were prepared by applying a magneticeld perpendicular to the surface of samples during curing. Theformation of chain-like or columnar-like structures parallel tothe magnetic eld lines has been observed in numerouspublications,13,19,22,36,39 in particular, for the MRE compositionsused in this study.13,19 At small iron concentrations the particlealignment within the matrix can be seen by the naked eye due tothe transparency of the silicone rubber. Optical microscopy canbe also used to observe the structures.13,19 At high ller content,iron particles tend to form a three-dimensional network, whichhas a preferential ordering direction while synthesized within amagnetic eld.19 The inner structure of the anisotropic MREsamples has been recently characterized by using computertomography.39

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Table 1 Composition of the MRE samples synthesized

Mass% Matrix 1 (so – S) Matrix 2 (hard – H)

0 S-0 (empty) H-0 (empty)70 S-I-70 (isotropic) S-A-70 (anisotropic) H-I-70 (isotropic) H-A-70 (anisotropic)82 S-I-82 (isotropic) S-A-82 (anisotropic) H-I-82 (isotropic) H-A-82 (anisotropic)

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The composition of the samples under present study issummarized in Table 1. We use the following notations for thesamples. The rst letter refers to the matrix used: “S” – for soersamples and “H” – for harder samples. The next letter indicatesthe ller distribution within the sample obtained by differentcuring procedures: “I” stands for isotropic samples while “A” isused for samples synthesized in the magnetic eld and, thus,having a pre-aligned ller structure. The number in the samplenotation shows the content of the iron in mass%. The llercontent was chosen to be equal to either 70 mass% or 82 mass%(22 and 35 vol%, respectively). We compare rheological char-acteristics of the MREs with those of unlled matrices indexedas “0”.

2.2. Measurements

Rheological measurements were made using a commerciallyavailable rheometer (Anton Paar, model Physica MCR 301), witha measuring “plate–plate” unit and a magnetic cell MRD 170/1T. The magnetic cell has an electromagnet capable of producinga homogeneous magnetic eld perpendicular to the measuringplate. The homogeneity of the magnetic eld in the workingarea is not explicitly specied by the equipment manufacturer.As dened for such a rheometer,40 in a typical measurementconguration with a MR uid the reference value of themagnetic ux density differs from the r2-weighted average uxdensity in the MRF by roughly 13%.

By varying the driving current I in the coil of the electro-magnet in the range of 0–5 A, the magnetic ux density B can bechanged from zero to approximately 700 mT. At a given drivingcurrent I the actual value of B slightly depends on the compo-sition of the MR sample due to the variation of effectivemagnetic properties. Table 2 shows how the magnetic uxdensity changes with I for all samples. In the following wecompare sample behavior at constant current, not at constant B.

Measurements of the dynamic modulus were performed inthe dynamic mode of forced torsion oscillations with acontrolled load (torque) varying according to a harmonic law.Disc shaped samples having a diameter of 20 mm and a heightof approximately 2 mmwere secured between a stationary lower

Table 2 Measuredmagnetic flux density B (T) at the reference positionfor different currents I

I, A S-I-70 S-A-70 S-I-82 S-A-82 H-I-70 H-A-70 H-I-82 H-A-82

1.7 0.237 0.235 0.247 0.236 0.238 0.231 0.266 0.2583.4 0.463 0.448 0.489 0.463 0.466 0.447 0.526 0.5025.0 0.626 0.628 0.665 0.631 0.631 0.607 0.715 0.684

This journal is © The Royal Society of Chemistry 2014

plate and an upper plate connected to a rotor subject to forcedtorsion oscillations. The frequency and the amplitude of theoscillations were varied and dependencies of the storagemodulus G0, the loss modulus G00 and the loss factor on theoscillation frequency, strain amplitude as well as the magneticeld were obtained for all samples. The maximum strainamplitude applied was limited to 25%, to avoid any slippagebetween the measuring unit walls and the sample surfaces.

3. Results

We start the discussion of our results with the standardtemperature and frequency tests which are followed by theanalysis of the observed Payne effect.

3.1. Inuence of the temperature

As an example we present in Fig. 1 the results of the test for thesample S-I-82. The strain amplitude was maintained constant atg¼ 0.01% and the strain frequency f¼ 1.6 Hz. The temperatureT was varied in the range of 15–55 �C. In Fig. 1 temperaturedependencies of the moduli in the absence and presence of themagnetic eld are plotted.

It can be observed, that in the magnetic eld, the dynamicmodulus increases signicantly (2–3 orders) but the tempera-ture hardly affects the modulus values. Both the storage andloss moduli only slightly decrease with temperature. The lossmodulus notably uctuates with a standard deviation of 7%which is quite acceptable for rheological measurements.

This result is consistent with recent studies of temperatureeffects on rheological characteristics of MREs based on asimilar silicone compound SIEL38 performed in the absence of amagnetic eld. The rupture tests carried out in ref. 38 haveshown that the stress–strain curves are practically temperature

Fig. 1 Dynamic modulus vs. temperature measured in the absence ofthe magnetic field (a) and in the presence of the magnetic field at I ¼ 5A (b).

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independent in the temperature range �40 to 150 �C. Fig. 1shows that the application of the magnetic eld does not induceany temperature related response. A negligible effect oftemperature on the dynamic modulus is attributed to the strongtemperature stability of the silicone matrix used in our MREwhich widens the range of possible practical applications of thematerials developed.

During all the following measurements the temperature wascontrolled and maintained constant at 20 �C (�2 �C).

3.2. Frequency tests

In these tests the strain amplitude was equal to g¼ 1%, and thefrequency f was varied in the range of 0.01–10 Hz. In Fig. 2frequency dependencies of the storage modulus (Fig. 2a and b)and the loss modulus (Fig. 2c and d) measured in the absence(bold lines) and in the presence (dotted lines) of a magneticeld at I ¼ 5 A are presented. Fig. 2a and c and Fig. 2b and dshow the moduli of the so and hard samples, respectively.Curves corresponding to the samples with equal masspercentages of the ller are shown by one color. G0(f) and G00(f)curves for isotropic and anisotropic samples are presented bycircles and triangles, respectively, while for empty samplescrosses are employed.

Analyzing the results presented in Fig. 2 the followingconclusions can be made:

(i) The initial value of the storage modulus of the hardmatrix is approximately one order of magnitude larger thanthat of the so matrix. The same relationship is valid for theloss modulus.

Fig. 2 Frequency dependencies of storage modulus G0 and lossmodulus G0 0 measured in the absence (bold lines) and presence(dotted lines) of the magnetic field for soft (a and c) and hard (b and d)samples.

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(ii) Both storage and loss moduli monotonically increasewith the frequency for all measured samples with and withoutthe magnetic eld. The maximum increase is observed for theloss modulus of the unlled samples S-0 and H-0. In thefrequency range of 0.01–10 Hz, approximately two orders ofmagnitude increase in G00 takes place. Filling the matrix withmagnetic particles leads to some decrease in the growth rate ofthe loss modulus with frequency. For the samples containing82% iron, less than an order of magnitude increase in G0 0 isobserved. Furthermore, a log–log plot becomes non-linear,deviating from linearity at low frequencies. When the magneticeld is applied the frequency dependence of the modulibecomes less pronounced.

(iii) As one could expect even without the magnetic eld thestorage and loss moduli increase with increasing magnetic llercontent. Reinforcement of the rubber matrix with magneticllers has been reported in numerous publications.14,19,20,22,33

We have studied it for MREs based on SIEL and iron particlespreviously12,13,19 and do not focus on this phenomenon here. It isworth mentioning that this reinforcement is much morepronounced for the soer matrix. An addition of 82 mass% ofiron ller leads to a 20-fold increases in the storage modulus ofthe soermatrix while for the harder matrix this increase is only1.7 times.

(iv) The comparison between isotropic and anisotropicsamples in the absence of the magnetic eld shows that theanisotropic spatial distribution of particles increases storageand loss moduli. The chain-like structures built in duringsample synthesis serve to strengthen the sample. Structuredsamples are originally mechanically anisotropic, and themodulus values measured in two perpendicular directions tothe internal structure axis can differ signicantly.19,20,37

However, the effect of the sample anisotropy is not verypronounced and the change in modulus is less than 100%. It isalso important to mention that the effect of anisotropy is higherfor samples with smaller ller content when the particle struc-ture is less dense.

(v) In the presence of a magnetic eld at I ¼ 5 A, the storageand loss moduli of the so samples increased by 2–3 orders,and those of the hard samples increased by 2 orders ofmagnitude. Because in the absence of the magnetic eld themoduli increase considerably with the frequency and in thepresence of the magnetic eld the frequency dependence isnegligible, the highest magnetic response is realized at lowfrequencies. Signicant changes in moduli due to the magneticeld strength have been reported in a number of publica-tions.12,13,19,21 With the increasing magnetic eld strength theinteractions between the particles increase and they formchains parallel to the eld lines. In initially anisotropic samplessome pre-ordering of the ller already exists without themagnetic eld. Consequently, in the magnetic eld, strength-ening of the chains takes place resulting in an increase in themechanical modulus (G0). Several groups have reported a highermodulus increment in magnetic elds for initially structuredsamples19,20,22,37 where the particle pre-alignment helps thematerial to react to smaller elds. We shall discuss thesephenomena in detail below.

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In spite of the aforementioned features of frequencydependencies of the moduli, they do not demonstrate anycritical behavior. Thus, in all further measurements the oscil-lation frequency was maintained constant at 1.6 Hz.

3.3. Strain amplitude tests

Following frequency tests, several strain amplitude tests withand without the magnetic eld were performed. The storagemodulus and loss modulus vs. strain amplitude are plotted forall samples as shown in Fig. 3. Curves which correspond toequal mass percentages of the ller are shown in the samecolour. To distinguish between different samples the samesymbols as shown in Fig. 2 are used.

It can be concluded that both moduli are independent ofstrain amplitude for unlled samples. For all lled elastomersthe moduli become strain-dependent.

In the absence of a magnetic eld a slight decrease in G0 andG0 0 of the lled samples with increasing amplitude is observed.For samples with a random ller distribution strain depen-dence is practically negligible, and the linear viscoelastic regionproceeds up to g� 1.0% and the storage modulus decreases 20–30% at strains of up to 25%. However, for initially structuredsamples, the non-linear region starts earlier at g� 0.1% and themodulus decrease with strain amplitude being morepronounced. This is a strong indication of the Payne effect.

The appearance of the Payne effect in anisotropic compos-ites shows that the physical mechanism behind the Payne effectin MREs is most likely related to destruction–reformation of amagnetic ller network. This hypothesis is further conrmed bythe material behavior in a magnetic eld.

Fig. 3 Storage modulus and loss modulus vs. strain amplitude without(solid lines) and with themagnetic field (dashed lines) (I¼ 5 A) for soft (aand c) and hard (b and d) matrices.

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Indeed, the magnetic ller becomes much more active whena magnetic eld is applied. Interactions between magneticparticles and their rearrangement cause not only a hugeincrease in the storage and loss moduli but also a strong straindependence of the moduli. One can say that the magneto-induced Payne effect is observed, apparently caused byprogressive breakdown of the magnetic ller network.

Actually, this phenomenon could be explained by strongmagnetic ller interactions in the magnetic eld. In order tominimize magnetic energy, interacting magnetic particles tendto move from the initial equilibrium positions, forming struc-tures aligned along the eld lines. When the ller content is 82mass% as in our case, the percolation threshold has alreadybeen exceeded. Consequently, what is formed are not simplechains but three-dimensional structures with preferred orien-tation axes. These are magnetic interactions which strengthenthe material in the magnetic eld. For small deformations, theller structure is only slightly disturbed while large deforma-tions tend to destroy the magnetic network resulting in materialsoening. Enhancement of the Payne effect due to the magneticeld has also been reported, particularly, in ref. 37 and 38. Inref. 38 the dependence of the moduli on the strain amplitudewas obtained only for one composition of the silicone MREbased on a mixture of small (3–5 mm) and large (40–80 mm)carbonyl iron particles and it has been found that it becomesmore pronounced with the increasing magnetic eld. Here weanalyze in detail the inuence of the magnetic ller concen-tration as well as the matrix elasticity on G0 and G00 vs. g

dependencies.It can be clearly seen that both the absolute values of the

moduli and magneto-induced Payne effect are enhanced withincreasing ller content within the elastomer and consequentlyas a result of increasing contributions from magnetic interac-tions. Growth in moduli for increasing magnetic particlecontent at xed strain has also previously been reported, forinstance.11,12,36,38

Comparison with so and hard matrix samples reveals thatthe material response to the magnetic eld is somewhat greaterfor the so matrix samples. The storage modulus of the sostructured sample S-A-82 experiences a 50-fold decrease for astrain amplitude increase from 0.01 by 25% while for the hardersample H-A-82 this change is about 28-fold. This fact is closelyconnected to the mobility of particles within the matrix. Parti-cles can shi from their equilibrium positions within somatrices more easily than within hard matrices.

Another important parameter characterizing the respon-siveness of MREs to an external magnetic eld is the ratiobetween the modulus in the eld and its initial value withoutthe eld. An interesting observation is that the maximumrelative increase of the storage modulus for the so compositesis realized at 70 mass% of iron and is equal to 630 at g¼ 0.01%.For the samples with the higher ller content 82 mass% G0(5 A)/G0(0 A) is twice as small. This is because for the so matrix G0(0A) increases considerably with the addition of the ller in theabsence of the magnetic eld. As a result, there is an optimalller content (which does not necessarily correspond to thelargest lling) at which the relative modulus increment is a

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Fig. 4 Cyclic loading of soft sample S-I-70 (a and c) and hard sampleH-I-70 (b and d) in the magnetic field (I ¼ 5 A).

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maximum. In fact, for the harder material the maximum of theratio G0(5 A)/G0(0 A) is reached for the sample H-I-82 with thehighest ller content but it is only 145. It should be noted thateven this value is large compared to others reported in theliterature.1–4,25,26,31–35

Summarizing, it can be seen that the lower the initialmodulus of the matrix, the more pronounced both themagneticresponse and the Payne effect demonstrated by the behaviorof G0.

Concerning the loss modulus G0 0, it is found that all thefeatures mentioned for the storage modulus are also valid forG0 0. In particular, some slight strain dependence has alreadybeen observed for lled samples in the absence of the magneticeld at g > 3% and becomes well pronounced for anisotropicsamples at g > 1%. The Payne effect in the magnetic eld isobviously present and the parameters are highly dependent onG0 0(g). The absolute loss modulus values of the so and hardsamples are close to each other, G0 0 for soer samples beingsomewhat higher. The relative modulus increaseG00(5 A)/G00(0 A)is larger for soer samples in the whole range of strain ampli-tudes (0.01–25%), its maximum value being realized for S-I-70reaching 390 at small g, while the maximum value of G0 0(5 A)/G0 0(0 A) is only about 62 for H-I-82.

Inspection of Fig. 3c reveals that the characteristic behaviorof the loss modulus for the sample S-A-82% in the magneticeld differs from that of all other curves. At small strainamplitudes the modulus monotonically increases, then reachesa maximum value and nally monotonically decreases for largestrains. This is typical for materials demonstrating the Payneeffect.29 However, all other curves decrease monotonically withthe strain amplitude without showing any maximum. Thismonotonous behavior has been observed previously for similarMREmaterials38 but the maximum eld was twice as small. Thiscontradiction inspired a deeper study of this phenomenon. Inaddition, it has already been mentioned that MREs under thesimultaneously applied magnetic eld and external mechanicalforce are subject to hysteresis.12,37,38 In ref. 38, for a singlesample, one cycle of increasing–decreasing strain amplitude forfour values of the maximum strain amplitude was carried out.This shows that the difference in the initial and nal G0 valuesincreases with g. In the following Section we study the effect ofrepeatedly increasing strain on material viscoelastic behavior.

3.4. MRE dynamic modulus vs. repeatedly increasing strainamplitude in the maximum magnetic eld

We have studied the moduli behavior at the maximummagnetic eld strength during incremental increases in theoscillation strain amplitude. The experiment has been per-formed in the following way: G0 and G0 0 were measured while thestrain amplitude was changed from 0.01 by 25%. The nextmeasurement was then immediately commenced from theminimum strain amplitude of 0.01 and increasing by up to 25%.These experiments were then repeated several times. In Fig. 4 G0

and G00 are plotted against g as obtained from several consec-utive measurements with increasing strain amplitude for soerand harder specimens of the same composition (S-I-70 and H-I-

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70). It was found that the dynamic modulus distinctly changeswith the number of measurements.

Analyzing the behavior of the storage modulus presented inFig. 4a and b one can conclude that for both samples eachsubsequent G0(g) curve lies above that of the one measuredpreviously. The difference in G0 values is higher at small strainamplitudes and the material becomes stiffer with every subse-quent measurement. For the harder sample some saturation ofthe modulus values takes place following 9 consecutivemeasurements and the resulting modulus value is twice as highas the initial one at g ¼ 0.01%. At strain amplitudes larger than0.1% the modulus increment with measurements decreasesand at g > 10% all curves merge. For the soer sample satura-tion is reached even earlier, following a mere 3 measurementsand again, all curves merge at g > 1%. It should be noted thatthe characteristic behavior of G0(g) is similar in all measure-ments – a decreasing function of g.

The situation with the loss modulus (see Fig. 4c and d) iscompletely different. Unlike the storage modulus, G0 0(g) curveschange their shape with consecutive measurements. During therst measurement for the so sample and four measurementsfor the hard sample, the loss modulus decreases monotonicallywith increasing strain amplitude while during the followingmeasurements a maximum for G0 0(g) appears at 0.3–0.4%strain. Thus, an increase of the strain amplitude up to 0.3–0.4%causes an increase in G0 0 while at strain amplitudes larger than0.4 the loss modulus decreases. Similar non-monotonousbehavior of G0 0 was observed for the sample S-A-82 during therst measurement. Aer 9 cycles the saturation of the lossmodulus of both the hard and the so samples takes place.

Increases in the loss modulus at small g can be explained byenergy needed for continuous rupture of the magnetic coupling

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between ller particles with increasing strain amplitude. Thesubsequent modulus decrease is realized when the structure isalready broken at high g and the particle interactions decreasedue to growing distances between particles with strain.

The appearance of the maximum only aer several cycles canbe understood again from the idea that the simultaneousapplication of mechanical stress and magnetic eld assists theparticle alignment and more compact packing in chains. Withsoer matrices having more labile structure and strongermagnetic interactions, the structuring is easier and its effectmore pronounced (less cycles are needed to produce maximumG0 0).

The behaviour of loss moduli of the so and hard samples issomewhat different. The loss modulus of the harder sampleincreases with repeated cycles throughout the whole region ofstrain amplitudes 0.01–20%while the loss modulus of the soersample drops signicantly, especially in the region of small andlarge strains. This results from the differentmobility of particlesin so and hard matrices and thus, different structuringprocesses.

In order to analyze the relative contributions from the elasticand viscous components, the loss factor (damping factor or losstangent) which is the ratio of the loss modulus to the storagemodulus, tan d¼ G0 0/G0 is presented in Fig. 5. These plots pertainto samples S-I-70 and H-I-70 containing the same amount ofmagnetic ller but having different moduli to those of the initialpolymer matrix. Again, considerable differences in behaviorbetween the so and hard samples can be seen. For the sosample a huge increase in tan d is observed with increasing g

during the rst measurement (Fig. 5a), meaning that dissipationenergy processes dominate. The value of tan d¼ 0.79 is very highat g around 5–6%. High values of tan d were also obtained forMRE containing sub-millimeter magnetic particles, mentionedin ref. 31. However, further measurements show how loss factorvalues decrease throughout the whole strain range while themaximum tan d remains at g¼ 5–6% but the absolute maximumvalue decreases from 0.79 to 0.43.For the hard sample H-I-70 thebehavior of the loss factor changes withmeasurements in a quitedifferent manner (see Fig. 5b). The value of tan d at small strainsdecreases while at high strains it increases with the number ofcycles. Apart from the rst measurement there is a pronouncedintersection point on all the curves at around g ¼ 0.25%. One

Fig. 5 Loss factor vs. strain amplitude on cyclic loadings for sample S-I-70 (a) and sample H-I-70 (b) in a magnetic field (I ¼ 5 A).

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could expect that it is at this strain that the relative contributionsfrom the polymer network and magnetic interactions change. Atsmall strains more compact packing of magnetic particles takesplace and stronger magnetic couplings are formed and littleenergy is dissipated. At higher strains the energy dissipated as aresult of the destruction of chains has a larger impact on G0 0. Thestronger the formed structure, the more energy is needed torupture it. As a result, tan d grows with the number of measure-ments at g > 0.25%.

Consequently, it is this interplay between elastic andmagnetic interactions which denes both the history of thematerial behavior as well as its nal state at saturation. Thus,the matrix contributes much to the processes taking part withinthe MRE in the presence of a magnetic eld.

Summarizing the results it can be concluded that thesimultaneous application of the magnetic eld and oscillatingstrain causes restructuring of the ller particles and one canobtain the following representation for the material behavior.

The magnetic particles interact with the polymer networkdue to polymer adsorption on the particle surface. In addition,the upper estimate of the polymer network mesh-size gives thevalue of 0.05 mm which is two orders smaller than the particledimensions and the particles are built into the polymer matrix.When there is no external magnetic eld, the main contributionto the material viscoelasticity is due to the polymer network.Having practically no residual magnetization, so magneticiron particles do not interact with each other magnetically andcontribute to the polymer matrix reinforcement effectively inthe same manner as non-magnetic llers.

When an external magnetic eld is applied, the particlesbecome magnetized and commence the interaction with oneanother. In this case the MRE material can be viewed as twointerpenetrating networks, the rst one being the polymernetwork and the second one being the network formed bymagnetic particles in a magnetic eld. The structure of themagnetic ller network in the magnetic eld does not coincidewith the initial ller distribution. When the magnetic eld isapplied, the particles shi from their initial positions tending toform chains to minimize magnetic eld energy. However, theirmovements are limited by (i) the elasticity of the polymernetwork and (ii) neighboring magnetic particles (at high lldensity). Thus, at the instant the magnetic eld is applied, thestructure formed does not correspond to the free energyminimum. The applied mechanical force (shear oscillations)helps the particles to restructure. In particular, at higher strainamplitudes the distances between particles in clusters increaseand more dense magnetic structures can be formed when thestrain is decreased again, resulting in a modulus growth atsmall strains following several repeated cycles of increasingstrain amplitude. For low degrees of ll, direct microscopicobservations of particle restructuring under shear loading andunloading have been performed35 and it has been concludedthat indeed shear cyclic stress serves to remove defects in theparticle strings.

Initiating magnetic interactions leads to magnetic particleclustering resulting in immobilization of a part of the elasticallyactive polymer network, giving contribution to a huge increase

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of the modulus at small strains. The soer the polymer, thelarger the achievable particle movements resulting in higherstructuring (clustering). This leads to a strong increase inmodulus but at the same time more energy is needed to destroythis structure. At higher strain amplitudes, the couplings breakand moduli of the resulting structure are mainly dened by theinterplay of magnetic and elastic interactions.

The same conclusion can be drawn from the saturationbehavior of the loss factor. In Fig. 6 the saturation curves fordifferent samples obtained in the absence of the magnetic eldare plotted and following several consecutive measurements inthe maximum eld as previously shown in Fig. 5. In the absenceof the applied magnetic eld, the loss factor for the isotropicsamples does not depend on the sample composition. Anisot-ropy plays a more signicant role which can clearly be seen bycomparison of the so samples S-I-70 and S-A-70.

The synthesis of the so MR with 70% iron content in themagnetic eld reduces the loss factor by a half. For the sosamples with a higher ller content (S-A-82) and the hardersamples (H-A-70 and H-A-82) the ller structuring upon curingin a magnetic eld is partly hindered by either dense packing ofthe particles or a more rigid matrix and the difference in tan d

for isotropic and anisotropic counterparts becomes smaller. Forall samples the loss factor only slightly increases withincreasing strain amplitude. tan d values lay between 0.18 and0.44 for the whole range of g and sample compositions.

Behavior of the loss factor in the magnetic eld is dramati-cally different. Now it is the strain amplitude effect that is mostpronounced. The change in tan d with g is extreme; the value ofthe loss factor grows more than one order of magnitude fromroughly 0.025 at small g up to around 0.5 at large g. Theapplication of the magnetic eld causes structuring of themagnetic ller and formation of magnetic couplings betweenmagnetic particles which are strong enough to resist breakageat small strain amplitudes, reducing energy dissipation andthus resulting in a decrease in tan d compared with initialvalues obtained in the absence of the magnetic eld. At g ¼0.01% the values of tan d become more than one order ofmagnitude smaller in the magnetic eld than in the absence ofthe eld for all samples. Increasing the strain amplitude causesbreaking of the magnetic coupling which demands energy andtan d begins to grow.

Fig. 6 Saturation dependences of the loss factor on the strainamplitude for all samples in the absence (a) and presence (b) of amagnetic field (at I ¼ 5A).

8772 | Soft Matter, 2014, 10, 8765–8776

Another feature of the tan d(g) function is the appearance ofa maximum. Themaxima of the loss factor for different samplesare realized at g ¼ 4–6% which are one order bigger than the g

values at G0 0 maxima. At high g, the loss factor values tend tothose obtained in the absence of the magnetic eld.

The general character of the tan d(g) function is almost thesame for all the samples. However, in a magnetic eld thecurves corresponding to anisotropic MR lay above the corre-sponding curves for isotropic samples. Thus, in cases of particlepre-alignment upon curing, the interactions are stronger andenergy dissipation is correspondingly higher when compared tothose of the initially isotropic material.

3.5. MRE dynamic modulus under cyclical increasing–decreasing strain amplitude in various magnetic elds

Several additional measurements of the dynamic modulusunder cycles of increasing–decreasing strain amplitudes weremade in various magnetic elds. For sample H-A-70, therespective storage and loss moduli are shown in Fig. 7 and 8.Measurements were carried out in two consecutive stages.During the rst stage the strain amplitude was increasedfrom 0.01% to 50% (upward paired arrows in the gurelegends). When the strain amplitude reached the maximumvalue of 50% the second stage was performed. At the secondstage the strain amplitude was decreased from 50% to 0.01%(downward paired arrows in the gure legends). Twoconsecutive cycles were held at different driving currentsapproximately corresponding to the following magneticux densities: 0.0 T, 0.2 T, 0.4 T and 0.6 T (Fig. 7 and 8, graphs(a–d), respectively).

Fig. 7 Storagemodulus after cyclical loading–unloading of sample H-A-70 at different driving currents: (a) – 0.0 A, (b) – 1.7 A, (c) – 3.4 A, and(d) – 5.0 A.

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Fig. 8 Loss modulus after cyclical loading–unloading of sample H-A-70 at different driving currents. (a)– 0.0 A, (b)– 1.7 A, (c)– 3.4 A, and (d)– 5.0 A.

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Analyzing the dependence of the storage modulus on strain,one can see that in the absence of a magnetic eld the G0(g)curve obtained in the second stage with decreasing strain liesbelow the corresponding curve measured in the rst stageunder increasing strain both for the rst and the second cycle(Fig. 7a). Thus, applying stress causes some soening of thematerial. From this it can be deduced that the anisotropicstructure formed during sample curing in a magnetic eld ispartially destroyed when mechanical stress is applied.

When subject to a magnetic eld, the character of the G0(g)function under consecutive increasing–decreasing strainamplitude changes (Fig. 7b–d). In the eld of 0.2 T (at a drivingcurrent of 1.7 A) at g > 0.1% all the curves tend to coincide, thelargest difference being observed at small strains, and themodulus grows signicantly aer consecutive increasing–decreasing strain amplitudes at each cycle. As a result, aer twocycles a 1.5 times increase of the modulus at the minimum g ¼0.01% takes place. In higher magnetic elds (Fig. 7c and d),following the initial increase in strain amplitude, the followingthree curves (obtained in the second stage of the rst cycle andduring the both stages of the second cycle) merge. One canconclude that, given large enough magnetic elds, the satura-tion of G0 is very quickly reached aer the cyclical increase anddecrease of the strain amplitude. During subsequent measure-ments with increasing strain amplitude (Fig. 4) more test cycleswere needed to achieve saturation. However, what is importantis that the saturation curve does not depend on the way it isobtained. Thus, it appears that these saturation curves charac-terize the MRE correctly.

Somewhat similar behavior is found for the loss modulus(see Fig. 8). Namely, in the absence of a magnetic eld, a

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modulus decrease with cycles takes place. G00(g) is a mono-tonically decreasing function at all stages of measurement. Inmagnetic elds G0 0(g) reaches a maximum and the value of G0 0 atthe maximum increases with cycles while the modulus value atthe smallest strain amplitude g ¼ 0.01% decreases. As in the G0

case, at magnetic ux densities of 0.4 and 0.6 T saturation ispractically achieved aer the rst stage.

Consequently, a shear induced change in the viscoelasticproperties of the material must be considered when dealingwith MRE materials. The nal working regime can be achievedonly aer several cycles of loading.

It should also be noted that for the materials under study,the linear regime where G0 and G0 0 are strain independent, ispractically absent in a magnetic eld. Even at strain amplitudessmaller than 5 � 10�4, the dynamic modulus is strain depen-dent.38 This means that the structures formed by the magneticller are very labile.

The gap between 1st-up and 2nd-down cycles observed inFig. 7 and 8 is attributed to the transient relaxation of thematerial between the measurement points. These results areconsistent and repeatable. It is seen that in the absence of themagnetic eld this relaxation may be somewhat longer.

Another important aspect which should be emphasized isthat the material recovers its properties aer some relaxationperiod. This means that following several cycles of loading tosaturation, leaving the sample unloaded will result in themodulus values reverting and again following the initial loadingcurve. In our experiments samples were le to relax for 10 minin order to recover their initial modulus. The detailed study ofthe relaxation time of the moduli is the subject of a futurepaper.

3.6. Fitting of the experimental results

One of the rst models examining the behavior of MRmaterialshas been presented in ref. 1 and 2. The model is based on thedipolar interaction of magnetic particles in chain structures andsimulates the shear stress of chains caused by interparticlemagnetic forces. Unfortunately, it cannot t experimentally tothe modulus values as a function of strain amplitude, and thetheoretical yield strain at which the MR effect falls off has beenshown to be much higher than that indicated by the experi-mental data. Other models, usually limited to composites with asmall amount of ller particles41–45 deal mainly with purelymagnetorheological effects. Furthermore, the present modelsdo not include considerable particle rearrangement as a basicassumption, mainly due to the enormous mathematicalcomplexity of such a consideration in the frame of analyticaland FEM approaches. Presumably neglecting the particle rear-rangements does not help in the prediction of the effectivestrength in the modern theoretical developments.

A large amount of work concerning the theoretical inter-pretation of experimental results has been conducted in theeld of rubber with embedded active llers such as carbonblack or silica.46–48 It has been shown that spherical particlesform clusters with a fractal structure joining into a network athigh particle concentrations. It is important to note that this

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Table 5 Fitting of saturation curves in the magnetic field (I ¼ 5 A)

S-I-70 S-A-70 S-I-82 S-A-82 H-I-70 H-A-70 H-I-82 H-A-82

gc 0.094 0.233 0.153 0.178 0.199 0.157 0.278 0.245m 0.480 0.541 0.485 0.565 0.476 0.491 0.535 0.577

Table 4 Fitting of the first curves in the magnetic field (I ¼ 5 A)

S-I-70 S-A-70 S-I-82 S-A-82 H-I-70 H-A-70 H-I-82 H-A-82

gc 0.202 0.275 0.241 0.387 0.303 0.263 0.191 0.266m 0.310 0.341 0.329 0.367 0.289 0.382 0.270 0.318

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fractal network is not stable but breaks into smaller units withincreasing mechanical strain. It is widely accepted that it is theformation of ller networks that is responsible for the non-linear viscoelastic behavior of lled rubbers. The Payne effect isinterpreted as a dynamic break-up of the ller network.

One of the most widely used phenomenological modelsapplied to the tting of experimental results was proposed byKraus.46 It is based on the assumption that the ller networkbreaks and reforms with various rates which depend on thestrain amplitude and on some rate constants. The result claimsthat the decline of the storage modulus G0 with growing strainamplitude has a characteristic functional form,

G0 � G0N

G00 � G0

N

¼ 1

1þ ðg=gcÞ2m(1)

where gc and m are the tting parameters. It was shownexperimentally that for carbon black lled rubber, the exponentm z 0.6 is universal while the constant gc is different fordifferent samples. Huber48 suggested that the parameter m isrelated to the connectivity exponent C. This relationship opensthe way for the physical interpretation of m.

We have tried to t our experimental results using eqn (1).For tting we used saturation curves measured in the absence ofa magnetic eld and at the maximum magnetic eld with acurrent of I ¼ 5 A. In addition, we tted the initial loadingcurves for all samples.

As an example, in Fig. 9 we plot the measured G0(g) satura-tion function together with the tting curves. One can see thatthe t is quite good. The obtained values of the tting param-eters gc and m for all the samples are shown in Tables 3–5.

One can indeed see that, while the scatter in gc values isquite wide, some tendency in m behavior can be found. In theabsence of the magnetic eld, the values of m decrease with anincreasing concentration of the magnetic ller. Furthermore,

Fig. 9 Fitting of the G0(g) saturation function obtained in the absenceof the magnetic field (a) and at the maximummagnetic flux density (b).

Table 3 Fitting of saturation curves in the absence of the magneticfield

S-I-70 S-A-70 S-I-82 S-A-82 H-I-70 H-A-70 H-I-82 H-A-82

gc 45.0 57.0 54.0 20.4 124.0 33.3 16.0 1.35m 0.399 0.230 0.368 0.286 0.341 0.218 0.307 0.275

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anisotropy in the particle distribution upon curing causes aconsiderable decrease in m. Its effect is even more pronouncedthan the effect of the matrix and magnetic ller content. Thedifference in m values for the S-I-70 and S-A-70 samples is 42%.At the same time the inuence of the matrix is only 15% (forsamples S-I-70 and H-I-70) and the ller content is 8% (for S-I-70and S-I-82) which is even less. According to ref. 48 the exponentm is determined entirely by the ller network. Thus, the changein m for MREs synthesized in different ways must be due tosome difference in the fractal structure of the magnetic llernetwork obtained.

Applying a magnetic eld causes a considerable increase inm. In contrast to the case without the eld, the m values aresomewhat larger for anisotropic samples but the difference issmall. It is important that for the saturation curves (Table 5) thevalues of m are higher than for the initial ones (Table 4), it isobvious that there is considerable further restructuring of theller fractal clusters under the simultaneously appliedmagneticeld and mechanical force.

It should be noted that in nonmagnetic composites thePayne effect is primarily determined by the ller structureeffects. The elastomer is considered to act merely as adispersing medium that inuences the magnitude of agglom-eration and distribution of the ller. On the other hand, it is theelastomermatrix which allows the ller structure to reform aerbreakdown with increasing strain amplitude. In contrast tocarbon black, in the case of magnetic llers, there is a long-range magnetic interaction between particles giving rise tocluster interactions even when magnetic couplings are broken.However, this interaction could probably be described as somerenormalized contribution from polymer elasticity. There is abig challenge to generalize the theories proposed for compos-ites with nonmagnetic llers to cases concerning those havingmagnetic interactions.

4. Conclusions

In this paper an extensive experimental investigation of thePayne effect in MREs has been performed. We study andcompare silicone composites based on two silicone matricescharacterized by different initial elastic moduli and lled with

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carbonyl iron particles of 3–5 mm in diameter. The concentra-tion of the magnetic ller was varied (70 and 82 mass%). Inaddition, MRE with isotropic and anisotropic ller distributionshave been synthesized.

It has been shown that lled matrices demonstrate a smallPayne effect in the absence of a magnetic eld, the ller beingmore active, i.e. strongly interact, in composites having pre-aligned particle structures.

When subject to a magnetic eld, both the storage modulusincreases and the Payne effect become signicant. The llerparticles magnetize and start to interact via magnetic interac-tions thus strengthening the solid ller structure within thepolymeric matrix. The role of the matrix is to allow particles tostructure themselves under the inuence of the magnetic eld.The particle arrangements and thus, stronger magnetic llernetwork formations, are more pronounced in soer polymermedia resulting in increases in G0 of over two orders ofmagnitude for small strain amplitudes g. This nding isunambiguous evidence that the effect of ller restructuringwhich is extremely pronounced, especially in so matrices, isresponsible for huge MR and Payne effects and deserves closertheoretical attention and appropriate adjustment of theoreticalmodels.

With increasing g the ller structure starts to disintegrate,the clusters break into smaller ones leading to material so-ening. More than an order of magnitude change of the modulusvalue with an increasing strain amplitude from 0.01 to 25% isobserved. In contrast to nonmagnetic composites, whosemodulus tends to hydrodynamic values upon aggregatedestruction, the modulus value of MREs by far exceeds themodulus of the material in the absence of the eld even at 25%strain amplitude due to long-range magnetic interactions.

The consecutively repeated measurements of the storagemodulus in a magnetic eld as a function of strain amplitudeshow that the mechanical stress applied simultaneously withthe magnetic eld serves to strengthen the ller structure. Thisin turn enhances the modulus value at low g and increases thePayne effect. At the same time, the loss modulus reaches amaximum aer several cycles, similar to cases concerning lledrubber.

The experiments implemented with consecutivelyincreasing–decreasing strain amplitude clearly show thatalmost all dynamic stress soening is achieved in the rst strainamplitude increase and only minor effects take place insubsequent cycles. Also, for all dynamic parameters the effect ofthe maximum strain appears to be more important than thenumber of cycles.

The obtained results show that real MRE properties shouldbe characterized by saturation curves rather than merely theinitial one. Hysteresis is an intrinsic property of MRE andshould be also taken into account.

The research presented provides an insight into theprocesses of structuring of the magnetic ller under simulta-neously applied stress and magnetic eld. Good tting of theexperimental results with the theoretical models developed fornonmagnetic lled rubbers shows some similarity betweenmagnetic and nonmagnetic composites and opens new

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possibilities for a universal theoretical description of MREbehavior based on fractal ller structure concepts.

The results are very important for further design of devicesbased on MREs, namely, tunable vibration absorbers, some ofwhich have already been developed and patented.49–53

It should be noted that the structuring of the magnetic llerhas also been recently found to affect the electromagneticproperties of the MR materials, in particular, giant magneto-dielectric54 andmagnetoresistive effects55,56 have been observed.And both of these effects are characterized by hysteresis. Thisaspect should be the subject of further investigation.

Acknowledgements

Financial support of the Russian Foundation for Basic Research(grants no. 13-03-00914, 13-03-12147), the German FederalMinistry of Education and Research (BMBF grants no.01DJ13006, 17PNT021) and the Bavarian Academic Centre forCentral, Eastern and Southeastern Europe (BAYHOST) isgratefully acknowledged. The authors thank Matthias Mayer M.Eng. for valuable help with the experimental setup.

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