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 0304-8853/83/0000-0000/$03.00 © 1983 North-Holland