Effect of particle size distribution on the magnetization of ferrofluid

Abstract

The effect of particle size distribution on the initial susceptibility of ferrofluids was studied. Magnetization and initial susceptibility were calculated for Uniform, Lognormal and Gaussian distributions. Using statistical mechanics, the magnetization and initial susceptibility of a dimer model were written. Dimer model consists of  particles, each particle interacts only with one adjacent particle. The system is exposed to an external magnetic field so the total energy of the system is the sum of the dipole-dipole interaction energy and the particles-field interaction energy. After writing the magnetization and the initial susceptibility it was multiplied by the particle size distribution at two different values of standard deviation. Using Mathematica, the integration over diameter was evaluated. Magnetization curve, Curie-Weiss law and initial susceptibility versus temperature at high fields were investigated for all of the three size distributions. The results were compared with experimental values and we found that Gaussian distribution was the best.