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Magnetoelastic behavior of a ferrogel in a homogeneous magnetic field

S. Monz1, A. Tschope1, R. Birringer 1

1Universit at des Saarlandes, FR. 7.3 Technische Physik, Postfach 15 11 50, 66041 Saarbrucken

Introduction

A gel ist a cross-linked polymer network

which is swelled by a fluid. If a gel is

filled with a ferrofluid it will become sen-

sitive to an external magnetic field and it is

called a ferrogel [1]. It has been demon-

strated that such ferrogels exhibit a signif-icant change in shape under the influence

of an inhomogeneous magnetic field [1, 2].

However, only few studies exist concerning

the influence of a homogeneous field on a

ferrogel. It has been shown, for instance,

that the compressive modulus changes in a

homogeneous field [3].

In a homogeneous magnetic field, a mag-

netic torque induces the alignment of the

magnetic moments parallel to the applied

field. The magnetic anisotropy energy KV,where K is the anisotropy constant of thematerial and V the particle volume, maycounteract this alignment, depending on the

particle orientation and the magnitude of

KV. If thermal energy kBT is larger thanthe anisotropy energy, the magnetization

can fluctuate independent of the particle lat-

tice (Neel relaxation), and the relaxation

time constant is given as [4]:

N = 0 exp

KV

kBT

, (1)

with 0 109 s. However, if K V >>

kBT, the rotation of the magnetization isblocked. In the case of a ferrofluid, there is

still a possible mechanism to align the mag-

netic moments by rotation of the entire par-

ticle (Brown relaxation). The corresponding

time constant

B = 3V kBT

(2)

depends on the viscosity of the parti-cle environment. A prominent related phe-

nomenon is the change in shear viscosity of

a ferrofluid in a homogeneous external field

[5].

The objective of the present study is to

investigate the anchorage of the magnetic

particles in the ferrogel polymer networkand the resulting mechanical torsion of an

macroscopic anisotropic ferrogel under the

influence of a homogeneous magnetic field.

Experimental

The ferrogel in the present study is based

on polyvinyl alcohol (PVA, [PVA] =1, 6mol/l) and crosslinked by glutardialde-hyde (GDA, [PVA] / [GDA] = 40 4000)[1]. Ferrogels with macroscopic magnetic

anisotropy were prepared by applying a ho-

mogeneous field of 10kOe during gela-tion. The particle size distribution of this

ferrofluid was determined by transmission

electron microscopy (TEM) and small-angle

X-ray scattering. Both the ferrofluid and fer-

rogels were characterized by vibrating sam-

ple magnetometry.

Results and Discussion

The particle size distribution, as determined

by TEM, could be well described by a log-

normal distribution with a median D0 =7 nm and = 1.5. Similar values were ob-tained from the analysis of small angle X-

ray scattering data.

The magnetization curve of the ferrofluid

shows superparamagnetic behaviour, as ex-

pected (Fig.1, inset). In the fluid matrix, all

magnetic particles will exhibit either Neel or

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- 3 - 2 - 1 0 1 2 3

- 1 . 0

- 0 . 5

- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5

- 1 . 0

- 0 . 5

M

/

M

S

F i e l d [ k O e ]

p e r p e n d i c u l a r

p a r a l l e l

M

/

M

S

F i e l d [ k O e ]

Figure 1: Magnetization curves of a fer-

rogel mesured at room temperature, paral-lel (triangles) and perpendicular (squares) to

the introduced macroscopic anisotropy axis.

For comparisation the used ferrofluid ex-

hibits superparamagnetic behavior (see in-

set).

Brown relaxation, depending on their size

and the magnitude of their anisotropy en-

ergy KV. In contrast, a significant hystere-

sis was found for the ferrogel, which sug-gests that the Brownian rotation of the larger

particles (KV >> kBT) is prevented by thesurrounding gel matrix.

Furthermore, VSM measurements revealed,

that is possible to introduce a magnetic

anisotropy into the ferrogel. The different

shape of the hysteresis loops in Fig.1 are due

to the alignment of the particles along their

easy axis during gel formation [6]. As a re-

sult, the magnetization curves are different

when measured parallel to the anisotropy

axis (triangles) or perpendicular (squares).

This magnetic anisotropy can be used to

transfer a net magnetic torque on the ensem-

ble of magnetic particles leading to a macro-

scopic torsion of the ferrogel. A ferrogel

cylinder of about 15mm length and 4 mmdiameter was prepared with an macroscopic

anisotropy axis perpendicular to the cylin-

der axis. A torsion of 90 was achieved

by applying a homogeneous field of about

500 Oe. A rotation by 90 equals the max-imum possible value because all the mag-

netic particles are aligned parallel to the

field.

In addition, the analysis of the torque bal-

ance revealed that for particles with suffi-

ciently high magnetic anisotropy energy, the

magnetic susceptibility is proportional to

the shear modulus of the gel so that the mag-

netic particles could be used as nanoscopic

probes for the viscoelastic properties of the

matrix.

Acknowledgments

SFB 277: Grenzflachenbestimmte Materi-

alien for the financial support.Dr. R. N. Viswanath, INT Karlsruhe

F. Dobrich, A. Michels

References

[1] M. Zrnyi, L. Barsi, A. Buki, Polymer

Gels and Networks 5, 415 (1997)

[2] M. Zrnyi, Colloid Polym. Sci. 278, 98

(2000)

[3] T. Mitsumata et al., J. Appl. Phys. 85,

8451 (1999)

[4] R. E. Rosensweig, Ferrohydrodynam-

ics, Dover (1997)

[5] S. Odenbach, J. Phys.: Condens. Mat-

ter 15, 14971508 (2003)

[6] D. Collin et al., Macromol. RapidCommun. 24, 737741 (2003)