PARTICLE INTERACTION EFFECTS IN FERROFLUIDS

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PARTICLE INTERACTION EFFECTS IN

FERROFLUIDS

N. Ayoub, B. Abu-Aisheh, N. Laham, M. Dababneh, J. Popplewell, K.

O’Grady

To cite this version:

(2)

JOURNAL DE PHYSIQUE

Colloque C8, Supplkment au no 12, Tome 49, dkcembre 1988

PARTICLE INTERACTION EFFECTS IN FERROFLUIDS

N. Y. Ayoub (I), B. Abu-Aisheh ( I ) , N. Laham ( I ) , M. Dababneh (I), J. Popplewell (2) and K. OIGrady (2)

( I ) Department of Physics, Yarmoub University, Irbid, Jordan

( 2 ) University College of North Wales, Bangor, G . B .

Abstract. - An analysis of particle interactions in a magnetite ferrofluid has enabled an interpretation to be made of a nonlinear variation of initial susceptibility with concentration, Curie-Weiss behaviour with a negative temperature intercept and a change in position of the spin-glass peak to lower temperatures as the ferrofluid concentration is reduced.

I n t r o d u c t i o n r 7

A ferrofluid is a stable colloidal system containing single domain ferro- or ferrimagnetic fine particles.

A

study of the initial susceptibility allows the strength and nature of the interparticle coupling to be deter- mined. In this paper we carry out three sets of exper- iments which will indicate that the nature of the interparticle coupling is antiferromagnetic like, and not ferromagnetic.

Experimental

A ferrofluid containing magnetite (Fe304) particles

v

,

a

,

_;

,

A

suspended in Isopar

M

as carrier and coated with oleic PACYILIC FRhCTlDN L. ~ l d '

acid as surfactant was used. From this initial sample

(saturation magnetization I, = 40 ~ ~ r n - l ) we diluted Fig. 1. - Variation of the initial susceptibility [ ~ m ~ / ( K ~ T ) ] the sample into seven different concentrations. The with packing fraction at T = 298 K.

measure of the concentration of any sample is done through measuring the volumetric packing fraction E .

The initial susceptibility was measured from the lin-

ear part of the magnetization versus field curve at low the for a nOn-interacting superparamagnetic fields (i.e. H

<

50 Oe where pH

<

k T p = average fine particle system as given by [l]

magnetic moment,

kT

= thermal energy) after cor-

recting the field for demagnetizing effects. An Oxford (1) Instruments Faraday balance equipped with a contin- . - .

uous flow cryostat that can go down t o 70 K (using liquid nitrogen) and can reach up to 500 K was used. The Faraday balance was calibrated in the high field region using palladium and in the low field region (O- 75 Oe) gave identical results t o those obtained using a Princeton Applied Research vibrating sample mag- netometer. Applying the method of Chantrell et al.

[I] we found a median magnetic particle diameter of D, = (74

f

4) A and a relative standard deviation of

a = 0.5.

R e s u l t s and discussion

Figure 1 shows the variation of the initial susceptibility with packing fraction E, a t room temperature. A

linear variation between the initial susceptibility and

concentration is seen in the range 0

<

E

<

0.04 (which

corresponds to dilute samples). This is consistent with

I

where

xi

is the initial susceptibility, I, is the saturation magnetization of bulk Fe304,

D,

is the magnetic median particle diameter, k is Boltzmann's constant, T

is the absolute temperature, y = DID, is the reduced diameter and

f

(y) is the particle size distribution. For

E larger than 0.04 (as in Fig. 1) the curve deviates from

its expected linear behaviour for a non-interacting system towards lower values

xi.

This behaviour can be understood if the nature of the interparticle coupling is antiferromagnetic like. Our results displayed in figure 1 agree with the measurements obtained by Holmes

et

at. [2]. Ignoring the demagnetizing field would lead to an increase in the non-linearity observed in figure 1 a t large E .

The variation of the inverse of the initial susceptibility ( 1 / ~ ; ) with temperature above the freezing point

(< 200

K)

of the carrier fluid (Isopar M) and up to

(3)

JOURNAL DE PHYSIQUE

T ( TEMPERATURE I N K

Fig. 2. - Variation of initial susceptibility with temperature for the three samples (a), (b) and (c) in the solid state and

it shows the spin-glass type behaviour.

300 K has been obtained for three different concentrations, E = 0.01, 0.04, 0.08. The measurements obey the Curie-Weiss Law

Extrapolation of the plot of 1 / ~ , with T to a zero

1 / ~ , gives the value of 8 appearing in equation (2), where 8 is a measure of the interparticle interaction and its sign gives the nature of the interparticle coupling. A negative 8 shows that the coupling is analo- gous to antiferromagnetic-like order. A positive 8 as observed by O'Grady et al. [3] indicates ferromagnetic coupling. From our results for aggregated systems with large interparticle interactions the coupling gives rise t o a negative value of 8'.

Figure 2 shows the variation of X, with T in the temperature range (70-180) for the same three samples, which are now frozen. The behaviour shown in figure 2 for each sample is typical of fine particle behaviour [4]. The maxima in

X,

for samples "a"

,

"b" and "c" occur a t 80 K, 110 K, and 120 K respectively. The temperature at which the peak in the susceptibility curve occurs (T,)

,

is directly related to the energy barrier of the particle's moment to reversal. The energy barrier to rotation of the particle moments into the direction of the applied field will be reduced by that field but will also be modified by the effective interaction field due to the moments of the neighbour- ing particles. If the interactions were ferromagnetic in character then we would expect a reduction in the

value of T with increasing E . However the value of T, is observed to rise with an increase in E indicating

that the interactions oppose the applied field, again indicating antiferromagnetic-like behaviour.

Of course the dipolar coupling is not antiferromagnetic in the strictest sense of the term, but is a man- ifestation of the tendency of the particle moments to lie along directions so as to produce flux-closure con- figurations. This result is consistent with the mea- surements of el-Hilo et al. [5] where a more detailed analysis of this behaviour is presented.

Acknowledgment

The authors wish to,acknowledge the support given by the Deanship of Research at Yarmouk University in promoting this research.

[l] Chantrell, R. W., Popplewell, J. and Charles, S. W., IEEE Trans. Magn. MAG-14 (1978) 975. [2] Holmes, M., O'Grady, K., Chantrell, R.

W.

and

Bradbury, A., To be published in Proc. EMMA (1988).

[3] O'Grady, K., Bradbury, A., Charles, S. W., Me- near, S., Popplewell, J. and Chantrell, R. w . , J.

Magn. Magn. Mater. 31-34 (1983) 958.

[4] Tari, A., Popplewell, J. and Charles, S. W., J.

Magn. Magn. Mater. 15-18 (1980) 1125.