64 Journal of Magnetism and Magnetic Materials 39 (1983) 64-66
North-Holland PublishingCompany
EXPERIMENTAL POSSIBILITY TO DETECT AGGREGATES IN MAGNETIC FLUIDS BY
MAGNETO-OPTICAL METHODS
R.V. MEHTA
S. v. RegionalCollege of Engineeringand Technology,Surat-395007, India
Expressions for magneticallyinduced extinction coefficientsof dilute magnetic fluids containing independent particles or
aggregates of 10 to 20 particles or large aggregates are analyzed. Correlations between these coefficientsderived for two
different field configurationsand two different states of polarization of incident light are described. Possibility to ascertain
aggregation is discussed.
1. Introduction
In a magnetic fluid the repulsive energy due to
steric repulsion and the randomizing energy kBT
due to Brownian motion is usually sufficient to
overcome the attraction due to grain-grain inter-
actions, the dipole energy in an applied field H
and the London-Van der Waals' force. Hence the
formation of aggregation may not occur in a well-
stabilized fluid. In spite of this, aggregation is
assumed to be responsible for the difference in
magnetically induced transmission for fresh and
aged colloidal solution of magnetite [1], drift in the
transmitted intensity by ferrofluids [2], and time
variation of magnetization of ferrofluids in pulsed
magnetic fields [3]. Scholten has analyzed the origin
of magnetically induced birefringence and dichro-
ism of light in terms of the orientation of particles,
orientation of chains, spatial ordering of particles,
etc. [4]. In the present paper we explore the possi-
bility of ascertaining the formation of small or
large aggregates by studying magnetically induced
extinction in a dilute magnetic fluid. It should be
noted that barfing a few exceptions [1,2] almost all
authors have studied either dichroism, i.e. the dif-
ference in extinction, or birefringence, i.e. the dif-
ference in refractive indices for the two orthogonal
state of polarizaton of incident light. Here we
would like to bring out the advantage of determin-
ing extinction coefficients individually. In the next
section the relations between extinction coeffi-
cients to be expected due to the orientation of
single particles are described. In section 3 the
theory for small aggregates is discussed. In section
4 the theory for large aggregates is summarized.
The last section deals with the interpretation of the
observed effects.
2. Single particles
Scattering properties of the individual particles
dispersed in a magnetic fluid determines the opti-
cal properties of the fluid as a whole. If turbidity
of the fluid is less than 0.4, then effect of multiple
scattering can safely be neglected. Further, if the
mutual distances between the particles are suffi-
ciently large and there is not spatial ordering in
the medium, then condition of independent
scattering holds. The scattering property of such a
single particle is described by the scattering matrix
S(0, ep). S((0, qb) is to be derived from electromag-
netic theory. In the case of a magnetic fluid the
size of the dispersed particles is much smaller than
the wavelength of the incident light. Hence
Rayleigh theory of scattering is applicable. In this
case the following expressions for the induced
extinctions are derived [5].
C, = -4"rrKN[Ima 2 + Im(a t - a2)L(h)], (1)
C±= -4~rKN[Im(~---~)-Im(~f~--~)L(h)]
(2)
CL = C.L, (3)
Co= -4~KNIm( 2az + al )
3 " (4)
Subscripts II and .1. represent the orientation of
the electric vector of the incident light, parallel
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