Rheological properties of magneto-responsive copolymer gels

Rheological properties of

magneto-responsive copolymer gels

Rheological properties of

magneto-responsive copolymer gels

 

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 29 oktober 2012 om 12.30 uur

door Haining AN

Master of Science: Sichuan university geboren te China

Dit proefschrift is goedgekeurd door de promotor: Prof. dr. S.J. Picken

Copromotor: Dr. E. Mendes

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. dr. S.J. Picken Technische Universiteit Delft, promotor

Dr. E. Mendes Technische Universiteit Delft, copromotor

Prof. dr. E.H. Brück Technische Universiteit Delft

Prof. dr. J.H. van Esch Technische Universiteit Delft

Prof. dr. F. Schosseler CNRS - Institut Charles Sadron, Strasbourg, France

Prof. dr. C. Creton CNRS - ESPCI ParisTech, France

Dr. J. Groenewold University Utrecht

Prof. dr. A. Schmidt-Ott Technische Universiteit Delft, reservelid

This research forms part of the research programme of the Dutch Polymer Institute (DPI), Technology Area Functional Polymer Systems, DPI project #626.

Cover design & layout by: Ruo Cheng

ISBN: 978-94-6186-061-3

Copyright © 2012 by Haining AN

Printed by Wöhrmann Print Service, Delft, Nederland

All rights reserved. No parts of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the publisher.

Table of contents

Chapter 1 Introduction: Soft magnetorheological copolymer gels

1

Chapter 2 Materials and macro-rheology 15 Chapter 3 Enhanced hardening of soft self-assembled

copolymer gels under homogeneous magnetic fields 23

Chapter 4 Long time response of soft magnetorheological gels 44 Chapter 5 Nonlinear rheological study of magneto responsive

soft gels

72

Chapter 6 Direct observation of particle rearrangement during cyclic stress hardening of magnetorheological gels

89

Chapter 7 Conformation change of a single magnetic particle string within gels

106

Chapter 8 Conclusions 129

Summary and future work 131

Dankwoord 134

Chapter 1

Introduction

Magnetorheological (MR) materials belong to the class of smart materials that respond to external stimuli by changing at least one of their properties. MR materials, similar in principle to electrorheological materials, have their rheological properties altered in the presence of a magnetic field. Conventional MR materials can be fluids or elastomers.1

Developed by Jacob Rabinow at the US National Bureau of Standards in 1948,2 _{MR technology has been the focus of increasing interest for over thirty}

years due to its magnetic field dependent viscosity. Reviews of MR technology can be found in numerous publications.3-5 In this chapter, we focus on what we believe are some of the more significant contributions from the past few years.

1.1 Magnetorheological (MR) fluids

Figure 1.1. Schematic diagram of the microstructure change of MR fluids in the presence of the magnetic field.

MR fluids are a suspension of micron-sized, magnetic particles in an appropriate carrier liquid like water, kerosene or various oils. Prior to the presence of magnetic field, MR fluids behave as normal liquids with a consistency similar to a Newtonian fluid. When exposed to a magnetic field, micron-sized particles suspended in the fluid align parallel to the flux path due to the induced magnetic dipole–dipole interaction. The induced structure can be extremely complicated in terms of shape (chains, columns and clusters). The deformation of those concentrated solid structures hinders the flow of the fluid, hence increasing the effective rheological properties (response) under magnetic field. As a result, the liquid suddenly becomes “harder” and more viscous with a yield stress up to 100 kPa.

MR fluids should not be confused with ferrofluids,6 which usually contain magnetic nanoparticles with sizes of about 10 nm, and only exhibit weak field-dependent rheology properties. Typical filler particles for MR fluids are big enough to support hundreds of magnetic domains.

The candidate of the particles for MR fluids should be relatively inexpensive, and available in large quantities. Spherical carbonyl iron particles7 _{are generally}

used as the filler material to fabricate MR materials. The soft magnetic particles have desired low value of residual magnetisation, a high permeability and high magnetic saturation value. Low remnant magnetization is recommended, as

highly remnant particles tend to stick together when the magnetic field is turned off, and will therefore not yield a completely reversible MR effect.

A good8 _{MR fluid should exhibit "high yield strength" and "non-settling". In}

general, it is not hard to make strong MR fluids with a high yield strength. On the other hand, sedimentation of the carbonyl iron (CI) particles due to the large density mismatch with the carrier liquid and difficulties in re-dispersion after caking have been usually regarded as serious disadvantages of MR fluids regarding their applications. In order to solve these problems, many methods are applied to enhance dispersion stability of MR fluids.

Various submicron fillers (carbon nanotubes, organoclay, and fumed silica) have been introduced to the carbonyl Iron-based MR suspensions to improve the stability of a MR fluids.9-12 _{Water based MR fluids with long-term stability have}

been prepared13 by adding soluble polymers that modify the viscosity of the carrier and adsorb on the particles. The sedimentation can be improved due to the decreased particle density by introducing polymer coating layer on CI particles.14 However, the MR response is also reduced because the polymer coating is non-magnetic. Other additives such as thixotropic agents and surfactants have also been used. The current challenge of MR fluids and the commercial applications requires the development of stable MR fluids with large field-induced rheological changes, and better understanding of the rheology of these materials, particularly under application conditions.

1.2 Magnetorheological (MR) elastomers

MR elastomers include a wide variety of composite materials, which typically consist of magnetic particles in a chemical cross-linked elastomer rather than liquid. It can be regarded as the elastic solid analogues of MR fluids with the expected advantage that magnetic particles do not undergo sedimentation. The rheological properties of a MR elastomer can be altered in response to an applied magnetic field. Furthermore, the matrix freezes the particle distribution after cross-linking. Considering the direction of the magnetic field, shear force, and the initial particle ordering within the sample, MR elastomers have direction dependent rheological properties.

In this new emerging field, dozens of papers have appeared during the last few years reporting on the MR elastomers differing in composition and synthetic conditions. Three components, the matrix, particles and additives are used in MR elastomers. The reported polymer matrix15-26 includes PDMS, poly (vinyl alcohol), silicone elastomers, natural rubber, soft polyurethanes (PU) and even a blend of polymers.

MR elastomers are divided into isotropic and anisotropic (chain-like structure) based on different curing conditions. If no external magnetic field is applied during the crosslinking, the particle network within MR elastomers can be considered as isotropic. For the anisotropic MR elastomers, the tailor-made anisotropy will translate into a directionally dependent rheological response. The anisotropic MR elastomers could have larger rheological response than that of isotropic one under the same magnetic field strength.

MR elastomers also have their own problems, which hinders their application. The complicated pre-manufacture process for rubber or elastomer based MR materials are time & energy consuming. High temperatures and strong magnetic fields are usually needed for a long time. The convention rubber-producing equipment must be modified in order to provide a magnetic field during crosslinking. The manufacture is not yet widespread with standards for production. The MR response (both relative and absolute) of elastomers is generally small compared to that of MR fluids.

To have better MR response, the chain direction of the anisotropic MR elastomers must be considered when it is placed in a particular device. If the isotropic MR elastomer can have a relative good performance, it will be quite an advantage.

Although there are already enough matrix materials that can be used in MR elastomers, producing MR elastomers with different properties regarding initial modulus and MR performance is still a great challenge. Furthermore, the deep understanding of the relationship between the viscoelastic properties of the matrix and the performance of the MR elastomers is still lacking.

Upon application of external fields, magnetic particles rapidly form chains which then aggregate into thicker bundles and complex three-dimensional structures. The transition process involves magnetization of particles and spatial rearrangement that is determined by a competition between the dipole-dipole interactions and the viscous drag forces.

Various experimental techniques27-33 and simulation methods34-37 are employed to get the relationship between the chain structure evolutions in magnetic colloidal system. It is well accepted that the aggregation kinetics at low solid fraction is now relatively well understood by the diffusion-limited cluster aggregation (DLCA) theory.38 However, the theory has been less successful for colloidal systems at high concentration and larger particle-particle interactions, which are not strongly affected by thermal fluctuations.

The notion that microstructure formation in MR fluids occurs at multiple time scales has been observed recently. By neglecting thermal motion and applying the field instantaneously, Mohebi39 showed that there are two distinct time scales for the structure formation within MR fluids. They correspond to an initial formation of disparate chain, and then a migration of chains into columns and wall-like structures. The first process was seen to occur on the millisecond time scale and the second process was much slower depending upon the sample thickness. R. Tao40 confirmed the two developmental stages and mention at the final 3D structure, to minimize the energy, every chain must have four mismatched chains as its nearest neighbours. This leads to the body-centered tetragonal (BCT) lattice structure. In some cases, it has been described as consisting of three41 of four42 steps for the aggregation.

High concentration of particles brings great difficulty in observing and quantifying chain structures, although they are more important when larger rheological response is required. Since the stress response of the MR material is closely related to the microstructural evolution of the magnetic particle network, time-dependent rheological response of the MR material can be an indirect method to characterise the aggregation of the chain structure. It will also be crucial in effectively designing MR devices, where the rheological response under DC magnetic field is commonly used. Research has been done to explore particle dynamics with the transient rheological response of MR fluids43-45 and ER fluids.46-49 However, the structure information from rheology experiments is very

limited and usually remains a reasonable guess. Indeed, morphological information of the particle network would be very welcome to help to explain rheological behaviour.

1.4 Models for predicting the rheological properties of MR

materials

The rheological properties of MR materials can be divided into two distinctive regimes: the off-state properties in the absence of the magnetic field and the on-state properties in the presence of the magnetic field. The origin of the field dependence of rheological properties is the existence of field-induced dipole type magnetic forces between the separate particles. The behaviour of MR materials can be considered as a combination of matrix properties and the properties of magnetic particle network inside the matrix.

A few theoretical models 23, 50-52 have already been developed to describe the behaviour of MR elastomers. Most models are based on the magnetic dipole interactions between two adjacent particles in the chain. Magnetic field is applied parallel to the chains. A magnetic field embodies a relation between flux density,B, and magnetic field strength (or intensity) H. In air or in vacuum, the relation is linear.

0

B



H ₍₁₎ where



0 is the permeability of air or vacuum, which equals 4π×10−7 H•m/A. In a ferromagnetic material such as soft iron the relation may be nonlinear.

0(1 ) 0 1

B







H 

 

H 



H ₍₂₎ Where



1 1



is the (dimensionless) relative permeability of the medium

and

  

 0 1is the magnetic permeability. The relative permeability of free space,

or vacuum, is 1.

An external magnetic field strength, H0 will induced magnetic moments, m, in the particles with radius a _{and magnetic susceptibility,}



.

3 0 1 4 3 i m    a H (3) The field Hiis the result of an applied external field H0 and the local field induced by the neighbour particles. Considering the interaction among particles in the same chain after being magnetized, the magnetic field intensity in the particle i can be expressed as:

0 = + i j j i H H H 



( 4 )

Figure 1.2. Dipole particle interaction

The dipole interaction energy between two adjacent particles (point dipoles) is a function of the radius of separation of the particles,r_{, and the angle that they} form relative to the magnetic field,



. The relationship is depicted in Figure 1.2. The dipole interaction energy reaches a maximum when the particles are touching and are in line with the external magnetic field.

2 2 12 3 0 1 (1 3cos ) 4 m E r      (5) Under the external magnetic field, the magnetic energy of particle i can be expressed as Eq.(6). 1 = =2 n i ij ij j i j E E E  





(6) For a MR elastomer in which particle volume percentage and total volume

3 3 n 4 V a    (7) Therefore, the total magnetic energy E and the magnetic energy density U can be estimated as, i n E E ₍₈₎ i UnE V/ ₍₉₎

Therefore the shear stress can be calculated by taking the derivative of the magnetic energy density with respect to the overall strain.

/

U

   _{ (10)} 

MR elastomer magnetic shear modulus can be calculated by taking the derivative of the shear stress with respect to the overall strain.

G  /

   _{ (11)} In general, several assumptions are made to simplify the problem.

1. Particles are aligned in perfect long chains.

2. The particles can be viewed as identically induced dipole moments.

3. Shear strain and associated stress are uniformly distributed over the length of each particle chain.

4. The tilting angle of the magnetic particle string is regarded the same as the overall shear strain



.

Another assumption that they have in common is the fact that they do not take rearrangement of off-state structure into account. The off-state particle network is assumed the same as on-state particle network for MR elastomers. In general, although the absolute values for the increase of G’ of typical elastomers seem to be described by those models, the model sometimes fail to predict the huge rheological response of gels composed of a very soft matrix. A plausible explanation may be the ability of soft gels to allow for a rearrangement of the original particle network, likewise in a magnetic fluids, while such rearrangement is much more difficult to occur in an elastomer. This is a point which we will tackle in the study presented in this book.

1.5 MR technology applications

MR technology has moved out of the laboratory and turned into viable industrial applications. The success is apparent in many disciplines, ranging from the automotive and civil engineering to the biomedical.

The benefit of the controllable yield stress in MR fluids has been realized in many devices for various applications. In many applications the MR fluids is employed in one of three common modes: valve mode, shear mode, or squeeze mode.

For instance, the Lord Corporation has been developing MR fluids and manufacturing MR truck seat dampers53 for a number of years now. Another area of study that has incorporated MR dampers is the stabilization of buildings during earthquakes.54

The use of magnetic fields to control suspension viscosity has many applications in torque and stress transfer devices. An example of such device is a MR clutch, which consists of two parallel disks filled with MR suspension. Torque exerted on one of the disks is partially transmitted to the second disk through the viscous suspension. The fraction of torque transmitted is a function of the suspension viscosity, which may be controlled by the magnetic field.

Magnetic microparticles can be used as probe particles that undergo a controlled strain imposed by a magnetic field. The microrheology can be used to determine the viscoelastic response of complex fluids.55 _{In microfluids devices,}

field responsive fluids can be used as smart fluids in bio-fluid analysis and DNA separation chips.56

A severe limitation of commercially available MR fluids for many applications is their high cost from the iron particles. In general, there are two ways of solving the problem: either by optimization of the fluidic and the magnetic designs of the considered device or by improving the properties of the MR fluid. In addition, it is especially desirable if these strong MR fluids only require a moderate magnetic field. For a large electromagnet, the delay time controlled by L/R (inductance over resistance) can be as long as several seconds. Only if the required magnetic field is moderate will the size and delay time of electromagnets not become an issue

and MR devices will remain agile.

MR elastomers hold promise in adaptive tuned vibration absorbers, stiffness tunable mounts, and automobile suspensions. Such elastomers may be used to construct tunable mounts, bushings, or vibration absorbers.

In addition to the tunable stiffness, a magnetic field may also result in a fast and reversible deformation in the material. The field-induced deformation is more significant when the matrix is a soft polymeric gel. The high sensitivity and large deformation of MR gels has made them promising candidates for actuators and sensors.

1.6 Motivation

In this thesis, we will study the rheological response of highly swollen physical gels obtained by self-assembling of triblock copolymers containing magnetic particles. Thermo reversible tri-block copolymer gels are inexpensive, easy to use and recycle. The properties of these gels can be easily adjusted by varying the polymer concentration, morphology and molecular weight between cross-links. The primary goal of this work is to develop soft MR gels that will respond with strong increase in the storage and loss moduli in the presence of an external magnetic field.

The soft MR gels provide an easy way to get stable MR material regarding the sedimentation problem of the MR fluids. The presence of the 3-dimensional gel network imparts as a small degree of rigidity to the magneto rheological material and reduces particle settling. However, when a strong shearing force is applied, the polymer network is easily disrupted, encouraging the flow of material and the structuring of particle network under magnetic field. Quantities such as yield stress or storage modulus increment of MR gels under magnetic field remain reasonably high.

Since the viscosity of the matrix is low at high temperature, it is quite easy to align the magnetic particles by a small field in a very short period, as compared with the complicated and energy consuming manufacture process for MR elastomers.

significant anisotropies. Compared with that, the particles in MR elastomer are regarded as “frozen in” after synthesis. The low modulus of the gel matrix might result in the ability for local rearrangements of the particle network in the presence of the magnetic field after synthesis. These unique properties might distinguish the MR gels from their cousin and translate into their unique rheology properties.

For this purpose we will in parallel,

-develop very soft (low elastic modulus) gels containing dispersed (aligned) magnetic particles by using thermo reversible copolymer gels.

- investigate linear, nonlinear, cyclic rheological response of the MR gels in the presence of the magnetic field for various sample geometries.

- relate (or model) the rheological data to parameters such as the particle volume fraction, the elastic modulus of the matrix, and the degree of alignment of particles.

1.7 Outline

In the next chapter, the materials involved in the preparation of MR gels are listed. The construction of homemade magneto device for rheology characterization is presented. Typical dynamic mechanical measurements are also explained.

In Chapter 3, a general investigation of linear rheology study of MR gels is presented. We can conclude that MR gels are an intermediate system between MR elastomers and MR fluids with both directional dependent response and partial rearrangement of the particle network.

In Chapter 4, we investigate the transient rheological responses of MR gels. The storage modulus of MR gels continued to increase with time after a step change of magnetic field. The result was compared with the transient rheological response of equivalent MR fluids (paraffin oil without copolymer) and a MR elastomer (PDMS) and interpreted as the consequence of quiescent rearrangement of the original particle network under magnetic field. The characteristic time is significantly dependent on the magnetic flux density, the matrix viscoelastic property, particle volume fraction and sample’s initial particle distribution.

The next part of this dissertation focuses on the nonlinear rheological properties of MR gels under large amplitude oscillatory shear flow. We show that the strain at onset of nonlinearity depends strongly on magnetic flux density, particle volume fraction, sample’s initial particle distribution and viscoelastic property of the matrix.

In Chapter 6, the cyclic rheological behaviour is discussed. MR gels show cyclic stress hardening behaviour in the presence of the magnetic field and it will be explained by the shear-induced rearrangement of the particle network of MR gels.

The conformation change of a single magnetic particle string within triblock copolymer gels is discussed in Chapter 7. Rearrangement of these magnetic particle strings happen under the combined influence of magnetic field and shear strain.

Finally, Chapter 8 provides a conclusion of the work and highlights the significant results. Recommendations for future work are also presented.

1.8 References

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31 P. Domínguez-García, S. Melle, J. M. Pastor and M. A. Rubio, Phys. Rev. E., 2007, 76, 051403. 32 D. Sohn, J. Magn. Magn. Mater., 1997, 173, 305.

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34 P. D. Duncan and P. J. Camp, J. Chem. Phys., 2004, 121, 11322. 35 P. D. Duncan and P. J. Camp, Phys. Rev. Lett., 2006, 97, 107202. 36 T. Ukai and T. Maekawa, Phys. Rev. E., 2004, 69, 032501.

37 M. Carmen Miguel and R. Pastor-Satorras, Phys. Rev. E., 1999, 59, 826. 38 S. Miyazima, P. Meakin and F. Family, Phys. Rev. A., 1987, 36, 1421. 39 M. Mohebi, N. Jamasbi and J. Liu, Phys. Rev. E., 1996, 54, 5407. 40 R. Tao, J. Phys.: Condens. Matter., 2001, 13, 979.

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Chapter 2

Materials and macro-rheology

The preparation of physically cross-linked MR gels using triblock copolymer polystyrene-block-poly (ethylene-stat-butadiene) –block-polystyrene (SEBS), midblock selective paraffin oil containing carbonyl iron particles is described. The properties of those materials are listed. The construction of homemade magneto devices for rheology characterization is presented and typical dynamic mechanical rheological measurements are explained.

2.1 Materials and sample preparation.

In this work, physical gels were obtained by self-assembling of triblock copolymer SEBS in paraffin oil.

Kraton G-1650E (kindly provided by Kraton Polymers) is a clear linear triblock copolymer based on styrene and ethylene/butylene, S-E/B-S, with bound styrene of 29.2% mass. It can be written as S15EB70S15100, the subscript numbers give the

weight percentage of the corresponding blocks, and the superscript number denotes the overall molecular weight in Kg/mol. The molecular structure of SEBS is shown in Figure 2.1.

Figure 2.1. Molecular structure of SEBS polymer. X and Y Z represent the polymerization degrees of the hard and soft blocks of SEBS, respectively.

Kraton SEBS polymer is widely used for formulating adhesives and coatings, as base material for compound formulations, as a modifier of thermoplastics and as a modifier of bitumen. The crystalline nature of the soft block (CH2-CH2)n is

effectively suppressed because of their small percentage. Consequently, SEBS is endowed with outstanding elastic behaviour and transparency. Typical properties of the SEBS elastomer are summarized below (manufacturer information).1

Table1. Typical properties of Kraton G-1650E elastomer. Property Test method Units Typical value

Specific gravity ISO2781 0.91

Tensile strength[a] ISO37 MPa 35

Elongation at break[a] ISO37 % 500

300% modulus[a] ISO37 MPa 5.6

[a]

Paraffinic oils (n-alkane mixtures) are selective solvents of the poly(ethylene/butylene) block. The selected paraffin oil (Sigma-Aldrich, 18512) has a zero shear rate viscosity of 130 mPa.s and a density of 0.827-0.89 g/cm3 _at

20 °C. Flash point (the lowest temperature at which it can vaporize to form an ignitable mixture in air) is 215 °C - closed cup. Care should be taken not to exceed the flash point of the oil during the gel preparation process.

At relatively high concentrations of paraffin oil, the incompatible PS blocks aggregate to form spherical micelles, which serve to stabilize the copolymer network and thereby generate a thermoreversible gels. Endblock PS phases play a role of physical crosslinking junctions below Tg of PS. The thermodynamic

incompatibility between blocks induces microphase separation and self-assembly of the insoluble styrenic end blocks into distinct domains with characteristic size scales on the order of ~10 nm.2,3

The thermal transitions, viscoelastic behaviour, swelling behaviour of thermoreversible gels essentially depend on polymer concentration and types of hydrocarbon oil.4-6

The gelation temperature increases with the copolymer concentration for all the hydrocarbon oils. It means that the higher the copolymer concentration in the gel, the higher the gelation temperature will be at which there is minimum number of physical junctions necessary to form the gel.7

The gels are fragile at high hydrocarbon oil content and found to be stronger at higher polymer concentration. The molecular weight and paraffinic hydrocarbon contents in oil have also contributed to the stability of micelles and the incompatibility of hydrocarbon oil in SEBS.8,9

For completeness, we display data on the frequency sweep and strain sweep of a typical pure gel (10 wt% SEBS in paraffin oil) in Figure 2.2.

Under the dynamic strain amplitude of 0.2%, the frequency dependence of G’ and G” is measured. The result shows that the exciting frequency has little influence on the rheological properties. Two noteworthy features of Figure 2.2a support the identification of these triblock copolymer/oil blends as thermoplastic elastomer gels, namely the fact that G’ consistently exceeds G” over the entire frequency spectrum, and G’ is virtually independent of frequency over three orders of magnitude.

(a) (b)

Figure 2.2. Dependences of G’ and G” on the applied (a) frequency and (b) strain in the absence of the magnetic field. G’ and G” are defined later in this chapter.

The dynamic strain sweep (0.1% to 50%) was applied at a fixed frequency (10 rad/s). The self assembled gels behave like an elastomer with a broad linear viscoelastic (LVE) region as shown in Figure 2.2b.

In our work, commercial iron particles (kindly provided by BASF) were used as magnetic filler without further purification. The soft magnetic particles have desired low value of residual magnetisation, a high permeability and high magnetic saturation value. Carbonyl iron Powder (CIP) was also involved in many other applications including inductive electronic components, diamond tools, microwave and radar absorption, metal injection moulding, screening of electromagnetic radiation and even food supplements.10

They are prepared by a thermal decomposition of iron pentacarbonyl (Fe(CO)5).

In the course of the decomposition process, spherical particles form on a nucleus, thereby developing a shell structure. The decomposition conditions determine the main properties, including the particle size distribution of the intermediate products.

Mechanically hard grade of HQ (iron content up to 97.8 %) was chosen because of their desired small particle size distribution. They are spherical and polydisperse, with an average diameter 1 um. The particle has the magnetic saturation around 208 emu/g. Other commercial grades of CIP are also available from BASF. Their magnetic properties and the particle size can be found in reference 11.

2.2 The magneto-rheological device.

Field responsive fluids can be characterized by their rheological and optical properties. Despite the huge potential commercial importance, the current knowledge about MR material is rather small mainly due to the limited availability of appropriate instrument.

A homemade plate-plate (diameter of 25 mm) magneto cell was developed and mounted on a commercial rheometer (ARES, Rheometric Scientific Co.). The use of parallel plate geometry has the advantage of much easier operation and cleaning procedures compared to a concentric cylinder system. The configurations are shown in Figure 2.3, in which a small volume of gels is tested between two coaxial parallel plates.

Figure 2.3. Home made magneto-rheological device.

The lower plate was set to oscillate with a desired frequency. The upper plate was connected to a transducer (100 g force rebalanced transducer in ARES rheometer). The plate-plate is made of brass to prevent the occurrence of radial magnetic forces acting on the shaft. Tests on pure gel without magnetic particles, measured at the maximum available magnetic field strength, proved that there are no interactions between the rheometer’s measuring system and the magneto rheological device.

The magnetic field is generated by an electromagnet, which is composed by three customized solenoid coils (Shanghai Union Electric Factory, each one has a turnover number = 2000, wire diameter, Ø0.80 mm) connected to a DC power

supply (Delta Elektronika, SM300-5 P216) and a soft iron bar to enhance and guide the magnetic field perpendicular to the rheometer plates. The air gap between the iron bars enveloping the rheometer plate-plate is set to 5 mm, ensuring a high flux density on the sample while not interfering with the plate-plate cell. The hole was cleaved through the centre of the yoke to allow the brass plates to be inserted. The pieces can be reassembled with iron screws. Magnetic flux density up to 0.8 Tesla (air gap) can be obtained. A Labview interface allows for control of the coil current and the resulting magnetic flux density. The magnetic flux density can be applied as linear or stepwise. A Hall sensor (magnet-physik, FH 55)12 allows online measurements of the actual magnetic flux density.

After any experiment, the system is demagnetized to keep the remanence lower than 1 mT. The field divergence was small enough (≈ 2%, 10 mT along the Z direction at 500 mT) such that particle migration was not observed during the experiments and the magnetic field can be regarded as homogeneous.

2.3 Rheology characterization.

The MR gels are intended to be used as structural materials in applications, where the load is often of a dynamic type. In cyclic dynamic loading, the applied strain is given by

     



(t)=



0sin(



t) 0



is the strain amplitude, and



is the angular frequency. t is cycle time.

When the strain amplitude is large, the stress response is not always sinusoidal. The shear stress can be adequately represented as a Fourier series of odd harmonics:       N m=1,odd (t)= _msin(m t _m) 



   m



is the shear stress amplitude of the m-th harmonic.



_m is the phase angle of the m-th harmonic, whose range is between (0º- 90º).

Both quantities are influenced by the strain amplitude and by the frequency. The above equation can also be expressed in terms of a series of in-phase and out of phase moduli as follows:

     





N 0 m m=1,odd ( )=t G' sin(_m m t) G" cos(m t)  



  

Where G'_mandG"_mare the m-th storage and loss moduli, respectively.

If the strain and the strain rate are infinitely small, the viscoelastic behaviour is linear behaviour and the time-dependent stress-strain relations can be described by linear differential equations. The amplitude of the stress can be expressed in sinusoidal form:

     



( )=t



0( 'sinG



tG"cos



t) 

The storage modulus, G’, represents the ability of the viscoelastic material to store the energy of deformation, which contributes to the material stiffness. The loss modulus G” represents the ability of the material to dissipate the energy of deformation. The commonly output moduli from commercial rheometers are the first-harmonic moduli G’1 and G”1.

Another term widely used for deformation studies of viscoelastic materials is the ratio between the loss and storage moduli:

      " tan = ' G G 

Where tan



is called the loss angle or the loss factor. It can be used for

2.4 References

1 http://www.kraton.com/

2 Soenen, H.; Berghmans, H.; Winter, H. H.; Overbergh, N. Polymer, 1997, 38, 5653. 3 G. Lattermann and M. Krekhova, Macromol. Rapid Commun., 2006, 27, 1373.

4 J. H. Laurer, J. F. Mulling, S. A. Khan, R. J. Spontak, J. S. Lin and R. Bukovnik, J. Polym. Sci.

Part B: Polym. Phys., 1998, 36, 2379.

5 J. H. Laurer, J. F. Mulling, S. A. Khan, R. J. Spontak, J. S. Lin and R. Bukovnik, J. Polym. Sci.

Part B: Polym. Phys., 1998, 36, 2513.

6 J. H. Laurer, R. Bukovnik and R. J. Spontak, Macromolecules, 1996, 29, 5760. 7 J. R. Quintana, E. Hernaea, and I. Katime, J. Phys. Chem. B., 2001, 105, 2966.

8 J. K. Kim, M. A. Paglicawan, S. H. Lee and M. Balasubramanian, J. Elastomers Plast., 2007, 39, 133.

9 J. K. Kim, Marissa A. Paglicawan and M. Balasubramanian, Macromol. Res., 2006, 14, 365. 10 http://www.inorganics.basf.com/ca/internet/de/

11 A. J. F. Bombard, M. Knobel, M. R. Alcantara and I. Joekes, J. Intell. Mater. Syst. Struct., 2002,

13, 471

Chapter 3

Enhanced hardening of soft self-assembled

copolymer gels

under homogeneous magnetic fields

The rheological properties of highly swollen physical gels obtained by self-assembling of triblock copolymers containing magnetic particles were investigated in the presence of external homogeneous magnetic fields. Three different types of sample with distinctive magnetic particle orderings were investigated: isotropic (no magnetic field present during synthesis), parallel to the plane of the gel film and perpendicular to the plane of the gel film. Both the storage and loss moduli exhibit a strong increase with external magnetic flux density for all geometries. Dependence of the rheological response on volume fraction of particles was also investigated. The strength of such rheological hardening, as well as its saturation behaviour, depends strongly on the relative orientation between particle strings, shear and external magnetic field. In some cases very strong relative increase of storage modulus, up to 6000% was obtained. Further transient rheological studies suggest that strong rearrangement of the particle network is largely responsible for the enormous increase in elastic modulus. Parallel to that, a maximum in the loss factor was observed as a function of the particle volume fraction and the field strength and it was interpreted in terms of a competition between an increase in string (clusters) hardening and a decrease in their ability to deform and flow. These results suggest that Magnetorheological (MR) gels are an intermediate system between MR elastomers and MR fluids with both directional dependent rheological response and partial rearrangement of the particle network.

* Parts of this chapter have been published in: H. N. An, S. J. Picken and E. Mendes, Soft Matter, 2010, 6, 4497.

3.1 Introduction

Active materials are smart materials with properties that can be significantly altered in a controlled fashion by external stimuli, such as stress, temperature, pH, moisture, electric or magnetic fields. Early examples include polyelectrolyte gels with interesting mechano-chemical properties1-3 and liquid crystalline elastomers4,5 that are discussed for applications as actuators and components of artificial muscles. Another important branch of active materials consists of magnetorheological (MR) materials. They include MR fluids, MR elastomers and MR foams.6 Since the discovery in 1940’s of the MR phenomenon,7,8 MR fluids have been studied to a large extent and proven to be suited to many applications. MR elastomers or rubbers are composites where magnetic particles are suspended in a non-magnetic elastic matrix. It can be regarded as the elastic solid analogues of MR fluids with the strong advantage over its fluid counterpart being that in MR elastomers magnetic particles do not undergo sedimentation. Furthermore, the elastic matrix freezes the particle distribution to some extent and the particles can be homogeneously distributed or grouped.

Isotropic magnetic gels, that are gels containing randomly dispersed magnetic particles, are able to react to magnetic field gradients as introduced by Zrinyi’s pioneer work 9,10 in the 90’s. It was just in 2003 that ferrofluid-based anisotropic magnetic gels with frozen-in magnetic order and able to respond to homogeneous fields were reported.11 _{Recently, in 2006, the Hungarian group reported the first}

systematic study on the rheology of PDMS elastomers containing dispersed magnetic particles that exhibit frozen order.12 They named these new materials “Magnetoelasts”. The idea is the following: since magnetic particles tend to align and form piles under a magnetic field, such tailor-made anisotropy will translate into a directionally dependent rheological response of the material. The characteristic response will be influenced by many factors including: the properties of the matrix, the size, size distribution, composition and volume fraction of the ferromagnetic particles and the relative orientation between particle alignment in the system, external field and direction of applied strain.

few years reporting on the MR elastomers differing in composition and synthetic conditions. The reported polymer matrix12-23 _{includes PDMS, poly (vinyl alcohol),}

silicone elastomer, natural rubber, soft polyurethanes (PU) and even a blend of polymers. However, the high storage modulus matrix impedes the application of those materials because they are on one hand difficult to fabricate and on the other hand hinders large MR effects.

Despite of its great potential as a strongly actuating system, only very few attempts have been made to combine reversible physical gelation with magnetic properties.24-28 In principle, thermoreversible gels offer considerable advantages with respect to covalently cross-linked polymer networks. They are reversible and easy to fabricate with their properties and morphology can be tuned by varying the gelator composition, molar mass and concentration. Furthermore, gels are intrinsically not homogeneous systems.29,30 This fact may promote the magnetic particle network’s ability to rearrange under external field.

Below, we report on the viscoelasticity of tri-block copolymer physical gels containing frozen-in pre-aligned magnetic particles and focus on the relationship between anisotropic responses when local rearrangements under external fields is allowed by the gel matrix. Triblock physically cross-linked gels of polystyrene-block-poly (ethylene-stat-butadiene)-block-polystyrene (SEBS) were swollen with midblock-selective mineral oil. We show that relative magneto-hardening up to 6000% can be obtained at a small strain (0.2%), depending on the sample geometry and particle volume fraction. A maximum on the loss modulus is reported and samples with originally very different particle distributions can exhibit very similar responses under magnetic field. Both observations added to transient stepwise experiments, are interpreted on the basis that magnetic particles can easily rearrange in the inhomogeneous gel matrix.

3.2 Experimental section

Materials. Physical gels were obtained by self-assembling of triblock copolymer SEBS (Kraton G 1650E, kindly provided by Kraton Polymers). The copolymer was swollen in paraffin oil (Sigma-Aldrich, 18512). This kind of matrix

has been widely studied by different groups.31-35 Commercial carbonyl iron particles (HQ grade, kindly provided by BASF) were used as magnetic filler without further purification. They are spherical and polydisperse, with an average diameter 1 μm.

Sample preparation. Predetermined amounts of copolymer and oil were mixed with the particles under nitrogen at 170 °C and then quickly cooled down to room temperature in the presence of a constant magnetic field (20 mT). Samples were peeled off and the string (bundle) structures of the particles, ensured by the presence of the field during the cooling, are retained in the gel. This procedure ensures the formation of strings (or bundles) of particles contained in the gel. Three different types of magnetic particle orderings were investigated: isotropic (no magnetic field present during synthesis), parallel to the plane of the gel film and perpendicular to the plane of the gel film. In order to name our samples, we use the disk faces as a reference for the direction of the applied field during synthesis. For example, when the columnar arrangements of the particles are perpendicular to the disk-shaped sample face, we call the sample “perpendicular”. The volume fraction of the magnetic particles was varied from 0 vol% to 18 vol%.

The magneto-rheological device. A homemade plate-plate (diameter of 25 mm) magneto cell was developed and mounted on a commercial rheometer (ARES, Rheometric Scientific Co.) as we explained in chapter 2.

(a) (b) (c)

Figure 3.1. Schematic representation of sample geometries with different types of magnetic particle ordering: (a) random; (b) perpendicular to disc surface and (c) parallel to disc surface. Two small arrows indicate the direction of the dynamic shear. The large arrows indicate the direction of magnetic field.

was kept constant as 10 wt%. The range of the external magnetic field is 0–650 mT, the driving frequency is fixed as 1 rad/s, and the dynamic strain amplitude was set to 0.2%. This value has been chosen by first performing a series of stress-strain curves for all samples and many values of the magnetic field, including the maximum one. This ensures that all data fall in the viscoelastic linear regime.

All the experiments reported on this chapter were carried out at room temperature. The relative particle alignment, shear direction and homogeneous field direction during rheological measurements investigated in this chapter are depicted in Figure 3. 1. The shear direction and homogeneous field direction was always kept constant.

3.3 Results and discussion

Samples were prepared according to the procedure described above, during a two step assembling process. First, at high temperature, as soon as a magnetic field (20 mT) is applied to the triblock disordered solution containing dispersed carbonyl iron particles, the interactions due to the induced magnetic dipole moment of the particles assemble them into strings (or bundles) parallel to the direction of the field. As temperature decrease in the presence of the field, a second (self)-assembling process takes place and the end blocks of the copolymer collapse into nano-structures forming a gel around the oriented strings (bundles), freezing the particle assembly structure even after the removal of the magnetic field. These gels are stable over months. Three different types of magnetic particle ordering were produced in this manner: isotropic (no magnetic field present during synthesis), parallel to the plane of the gel disc and perpendicular to the plane of the gel disc.

3.3.1 Optical Microscopy investigations.

It is convenient to first investigate our systems using optical microscopy. Varying particle volume fraction and polymer concentration and preparation conditions during the two steps assembling process described above may lead to

formation of various heterogeneous aggregates consisting of particles, linear strings, bulk dense drops, very dense columns, etc, depending among others in the ability to disperse the particles. For a better transparency of the samples, we start with a very dilute concentration of the particles (Φ = 0.02 vol%).

(a) (b) (c)

(d) (e) (f)

Figure 3.2 String (bundle) of carbonyl iron particles under uniform magnetic field seen by optical microscope from the top of the samples. Particle volume fractions are: (a) 0.02 vol%; (b) 0.04 vol%; (c) 0.1 vol%; (d) 0.5 vol%; (e) 1 vol%; (f) 2 vol%. All scale bars= 20 um.

As shown in Figure 3.2a, the two step assembling process results in the formation of head-to-tail string-like structures aligned parallel to the field direction as expected. The thermal fluctuations of the string shape are weak and they are almost straight rod-like aggregates. The string presents a wide length distribution from 5 μm to 150 μm. A great number of isolated particles, that is, not incorporate into the strings, are also observed because the chance to find their neighbour particles are low at very dilute concentration of particles. With the increase of particle volume fraction (0.04 vol%), the length of the string increases further and can achieve 250 μm while the diameter still remains similar to the particle diameter itself (1 μm). Further increase of the particle volume fraction (0.1 vol%) results in larger string-string interactions that leading to the formation of bundles. Further increase to Φ ~ 0.5-2 vol% results in a decrease of the bundle-bundle distance which lead to bundle overlapping and the formation of more complex 3-D

microstructures. Such overlapping seems to occur at typical inter-bundle distances of 5 to 10 μm. For Φ larger than 2 vol%, images become too dark to be investigated. The well defined structure of magnetic particle string or bundle proves that we can create anisotropic structure even with a small magnetic field (20 mT) for a relatively short time (10 min), as compared with the necessary strong magnetic field for MR elastomers preparation.

3.3.2 Rheological properties in the absence of external magnetic field.

0 5 10 15 20

3 6 9 12

Particle volume fraction [vol%]

G'

0

[kPa]

perpendicular random parallel

Figure 3.3. Dependence of the off-state storage modulus, G’0 on particle volume

fraction, for three different sample geometries as depicted in Figure 3.1.

The rheological properties of MR gels due to the presence of magnetic particles can be divided into two distinctive contributions: the off-state composite-like properties due to purely mechanical reinforcement, that is, without the presence of magnetic field and the magneto-response due to induced dipole interactions integrated over the sample in the presence of external magnetic field (on-state). Figure 3.3 shows the dependences of off-state storage modulus (G’0)

on the particle volume fraction for three different sample geometries. As the particle volume fraction, Φ, increases, the field free modulus also increases slightly. Larger amounts of particles results in larger “off-state” storage modulus. Since G’0 on particle volume fraction is relatively small for all three geometries, we

can conclude that without external field the magnetic particles are not really sintered into strong strings. This result is much different from what is expected from mechanical reinforcement of very long rods. We may conclude that bundles are composed by loose packing of magnetic strings with gel matrix probably

trapped in between them rather than a close packed hard phase. Therefore, without external field, strings and bundles can follow the shear easily.

3.3.3 Rheological properties in the presence of external magnetic field.

The rheological response of the system in the presence of an external magnetic field depends on the sample morphology and the relative direction of applied shear, external magnetic field and alignment of strings.

Isotropic gel: 0 100 200 300 400 500 600 0 5 10 15 20 25

G"[kPa]

B[mT]

G'[kPa]

Storage modulus Loss modulus Loss factor 0.05 0.10 0.15 0.20 0.25

Loss factor

Figure 3.4. Dependence of G’, G’’ and the loss factor (tanδ= G”/ G’) on homogeneous magnetic flux density, for a randomly dispersed sample with particle volume fraction of Φ = 3 vol%.

The effect of the magnetic flux density on the storage modulus and loss modulus for a MR sample (Φ=3 vol%) with randomly dispersed particles, that is, the one prepared without magnetic field, is displayed in Figure 3.4. G’ increases monotonically from 5 kPa to 20 kPa while G” increases from 200 Pa to 3 kPa, when the field is varied from 0 to 650 mT. No saturation of G’ is observed even up to 650 mT, while there is a weak saturation of G”. The loss factor (tanδ= G’’/ G’) is also plotted in the Figure 3.4. It shows a maximum point for high field values and it represents a change in strength between the loss and storage modulus. The relative small loss factor demonstrates that the elastic behaviour of the composite is more dominant in comparison to the viscous behaviour all over the magnetic flux density variation. From now on, in order to clearly demonstrate the effect of

the magnetic field on the storage modulus and loss modulus, we will display data in absolute increment of the storage modulus or magneto-induced storage modulus: ∆G’= G’-G’0, that is the storage modulus under magnetic field subtracted

by the off-state value. The same holds for ∆G” = G”-G”0.

0 100 200 300 400 500 600 0 50 100 150 200 G' -G ' 0 [kP a] B[mT] 2 vol% 3 vol% 6 vol% 10 vol% 18 vol% 0 100 200 300 400 500 600 0 10 20 30 40 2 vol% 3 vol% 6 vol% 10 vol% 18 vol% G" -G" 0 [kPa ] B[mT] (a) (b)

Figure 3.5. Magneto-induced increment of G’ (a) and G" (b) with applied magnetic flux density for different particle volume fraction (random dispersion).

In Figure 3.5, the volume fraction of the magnetic particles was varied from 2 vol% to 18 vol%. The field-induced modulus of each sample exhibits an increasing trend with increasing particle volume fraction and magnetic flux density. For example, the magneto-induced storage modulus, ∆G’ B=650 mT, is 15 kPa when the

particle content is 3 vol% compared to 200 kPa when the particle content is 18 vol%. The magneto-induced loss modulus ∆G”B=650 mT is 3 kPa when the Φ= 2

vol% compared to 42 kPa when Φ=18 vol%.

Anisotropic gel: Figure 3.6a and 3.6b display the effect of the magnetic flux

density on the field-induced storage modulus and loss modulus for samples with columnar ordering of the particles perpendicular to the disk plane, which is parallel to the direction of the external magnetic field during rheological measurement.

0 100 200 300 400 500 600 0 150 300 450 600 G' -G ' 0 [kP a ] B[mT] 2 vol% 3 vol% 6 vol% 10 vol% 18 vol% 0 100 200 300 400 500 600 0 40 80 120 G" -G " 0 [kP a] B[mT] 2 vol% 3 vol% 6 vol% 10 vol% 18 vol% (a) (b) 0 100 200 300 400 500 600 0.0 0.1 0.2 0.3 0.4 Loss factor B[mT] 2 vol% 3 vol% 6 vol% (c)

Figure 3.6. Magneto-induced increment of G’ (a), G" (b) and tanδ (c), with applied magnetic flux density for different particle volume fractions (magnetic particle ordering perpendicular to the plane of the gel disc).

The volume fraction of the particles was varied from 2 vol% to 18 vol%. The field-induced modulus shows a much larger increase with magnetic field compared with the random geometry. At higher field intensities, the storage modulus and loss modulus tends to level off. In some cases, the field-induced modulus reaches a maximum. It is interesting to note that ∆G’ and ∆G” have different saturation magnetic flux density values. For example, the loss modulus saturates much earlier (400 mT) with the field than the storage modulus (600 mT) for Φ =18 vol%. This effect is further shown on Figure 3.6c, where the loss factors exhibiting a maximum with field strength are displayed. The off-state loss factor increases with particle volume fraction. The loss factor exhibits a maximum value at an intermediate value of the field (Figure 3.6c). For the lowest particle volume fraction (2 vol%), the loss factor first increases with the magnetic field while it saturates at larger field values. For higher particle volume fractions (6 vol%), a

maximum value of the loss tangent becomes very prominent and appears for weaker fields as the particle volume fraction is increased.

The clear maximum point of loss tangent with increasing magnetic field in MR elastomers was recently reported by L. Chen19 and H. Bose13. It is natural to be understood based on the competition of loss modulus and storage modulus. Figure 3.6 corresponds to the situation where the applied magnetic field is parallel to the magnetic strings, and shear perpendicular to them. G’ depends mainly on the strength of the string that relies on the magnetic flux density. With the increase of the magnetic field, the average particle-particle interaction increases. This will result in an increase in mechanical stiffness due to hardening of the filler strings with respect to the polymer matrix.

Interpretation of the loss modulus is much more subtle. As the particle-particle interaction increases with magnetic field, it will restrict the movement of the strings and the ability of the system to follow the strain. When there is no magnetic field, the network structure of magnetic aggregates (strings) can be easily deformed, evidenced by the small off-state storage and loss moduli. As the strength of the string increases with magnetic field, it will be more difficult for the strings to follow the strain. The loss of mobility of the strings compromise the hardening of strings, resulting in an early saturation of the loss modulus compared with storage modulus, which was further shown as a maximum point of the loss factor.

0 100 200 300 400 500 600 0 50 100 150 200 G' -G' 0 [kP a] B[mT] 2 vol% 3 vol% 6 vol% 10 vol% 18 vol% 0 100 200 300 400 500 600 0 10 20 30 40 2 vol% 3 vol% 6 vol% 10 vol% 18 vol% G" -G " 0 [kPa] B[mT] (a) (b)

0 100 200 300 400 500 600 0.0 0.1 0.2 0.3 0.4 Loss factor B[mT] 2 vol% 3 vol% 6 vol% 0 100 200 300 400 500 600 0.0 0.1 0.2 0.3 0.4 Loss factor B[mT] 2 vol% 3 vol% 6 vol% (c) (d)

Figure 3.7. Magneto-induced increment of G’ (a) and G” (b) with applied magnetic flux density for different particle volume fractions (magnetic particle ordering parallel to the plane of the gel disc). The loss factor for the parallel sample geometry (c) and for the random geometry (d) corresponding to Figure 3.5 is also displayed.

The effect of the uniform magnetic field on the field-induced storage modulus (∆G’) and loss modulus (∆G”) was reported in Figure 3.7 when the magnetic particle ordering was parallel to the plane of the gel disc. The dependence of the rheological response is very different from the perpendicular geometry. In addition, the saturation of the response is very different being absent or much weaker as compared with perpendicular geometry. In the present case, ∆G” tends to level off at 500 mT, while ∆G’ saturation with magnetic field is not observed even for the highest particle volume fraction.

Despite of a much lower rheological response than in the perpendicular geometry (Figure 3.8), the loss factors in Figures 3.6c, 3.7c, 3.7d are very similar. A maximum of the loss factor for a finite value of the magnetic field, dependent on the sample geometry, is also observed. The interpretation of this effect remains the same as for the perpendicular sample as described above but a full mathematical description of the response in relation to the experimental geometry remains to be written.

0 100 200 300 400 500 600 0 50 100 150 200 250 B[mT] G'-G' 0 [kPa] perpendicular random parallel 0 100 200 300 400 500 600 0 15 30 45 60 B[mT] G"-G " 0 [kPa] perpendicular random parallel (a) (b)

Figure 3.8. Dependence of the increment of G’ (a) and G” (b) on magnetic flux density for different sample geometries (particle volume fraction =10 vol%).

The saturation of the rheological response with the magnetic field is also related to the sample geometry. For example, with the same magnetic field (650 mT) and the same particle volume fraction (10 vol%), the saturation of the induced loss modulus (∆G’’) can only be observed when the cluster is perpendicular to the plane of the gel film as evidenced by Figure 3.8. When the magnetic field intensity is small (before the saturation range of the perpendicular geometry), the difference between these three geometries is the largest. However, for magnetic field larger than the saturation value of the perpendicular geometry (500 mT), the induced loss modulus of the other two geometries still increase, decreasing the modulus difference between three geometries. In conclusion, when comparing the rheological response of samples with different geometries, relative orientational rheological responses are similar to those of elastomers, implying that the off-state structures are still kept in a very large extent under magnetic field.

A few theoretical models have already been developed to describe the behaviour of MR elastomers. Jolly et al36 proposed a dipole model based on the magnetic interactions between two adjacent particles. Davis37 calculated the field-induced shear modulus by assuming that the particles form an infinite string in a soft matrix. A finite-column model was used to describe much more realistic string structure formed in high fields and low particle concentration.20 _An

assumption that they have in common is the fact that no take rearrangement of off-state structures (whether it is infinite chain or more realistic string structures) into account. In general, although the absolute values for the increase of G’ of

typical MR elastomers seem to be described by those models, the model sometimes fail to predict the huge rheological response of gels composed of a very soft matrix.25 _{A plausible explanation may be the ability of soft MR gels to}

allow for a rearrangement of the original particle network, likewise in a magnetic fluids, while such rearrangement is much more difficult to occur in an elastomer.

0 200 400 600 800 0 50 100 150 200 250 650mT G'-G ' 0 [kPa] Time[s] perpendicular random parallel 0 200 400 600 800 0 20 40 60 650mT G" -G " 0 [kP a] Time[s] perpendicular random parallel (a) (b)

Figure 3.9. Evolution of the increment of G’ (a) and G” (b) with time in response to stepwise magnetic field for different sample geometries (particle volume fraction = 10 vol%).

A possible way to investigate the rearrangement process of MR gels is to examine the rheology response to a stepwise magnetic field increase, from 0 to 650 mT as displayed in Figure 3.9. The increase of storage modulus can be decomposed into at least two processes, clearly seen from the perpendicular geometry. First, G’ shows an immediate increase to around 50 kPa-100 kPa that takes about 2 to 5 s (time resolution of magnetic field establishment ~2 s). Second, a slower process is observed with characteristic time of about ~10 min with G’ saturating at 240 kPa. This strongly suggests that rearrangement of the particle network occurs in the MR gels. These two processes contribute to the hardening in distinctive manners. First, after the field is turned on, the induced dipole-dipole interactions will on one hand bring a remarkable change in the storage modulus immediately and on the other hand decrease the distance between neighbouring particles inside a string slowly. Rearrangement occurs due to formation of bundles and/or rotation of aggregates. The rearrangement from off-state structures to on-state structures brings further increment of the storage modulus because short distance or closed packing of the strings also implies larger dipole-dipole

interactions.

A rough estimation of the rearrangement process time can be obtained by inspection of data on Figure 3.9a. If we associate distinct amplitude contributions to the fast and slow processes, the contribution of the slow process to the increment in G’ is around 50%, in the time scale of 10 min. After shut down of the magnetic field, the initial distribution of the particles is restored due to elastic forces of polymer matrix and the experiment can be repeated again, where superimposing curves are observed suggesting that rearrangements are reversible.

G” shows a decreasing trend with the time as shown in Figure 3.9b. As we

already explained above in the loss factor discussion, the decrease of loss modulus may come from the decrease in particle network’s ability to deform and flow with strain, as the dipole-dipole interaction become too strong. These interactions increase even further with the process of the rearrangement towards closed packing of strings under magnetic field.

All the three sample geometries show remarkable rearrangement with magnetic field. We believe that the observed similarity between rheological properties of random and parallel geometries (Figure 3.8 and Figure 3.9) might come from a similar partial rearrangement of these two geometries under magnetic field, at least to some extent. In other words, it is very probable that they change to a similar locally anisotropic geometry (like the perpendicular geometry with shorter strings parallel to the magnetic field) once the magnetic field is turned on. 0 5 10 15 20 0 150 300 450 600

G"-G"

0

[kPa]

Particle volume fraction[vol%]

G'-G'

0

[kPa]

perpen G' perpen G" random G' random G" parallel G' parallel G"

Figure 3.10. Dependence of the maximum increment of G’ and G” on particle volume fraction for different sample geometries.

Finally, the dependence of the rheological response on particle volume fraction for different sample geometries is illustrated in Figure 3.10. It is very clear that the most significant effect on ∆G’ and ∆G” is found for the perpendicular geometry, while the other two geometries exhibit almost the same response.