Impedance measurements on kerosene-based ferrofluids

We study the impedance behavior of two ferrofluids, of a similar magnetic material, one constituted by spherical nanoparticles and the other constituted by cubes, both suspended in kerosene. The ferrofluid constituted by cubic nanoparticles has 10% doping of a rare earth ion. The samples were inserted between two parallel disk-like electrodes of area S=2.3cm2 made of surgical steel, separated by d=127μm. The impedance was measured by applying a sinusoidal voltage of amplitude V0=30 mV, from 1 mHz to 100 kHz. To analyze the experimental data, we use a model based on the Poisson–Nernst–Planck equations, with Ohmic boundary conditions. In the analysis, we assume that the ferrofluids contain free ions, originated from the manufacturing process, released by the stabilization layer around the magnetic nanoparticles dispersed in kerosene. The corresponding nanoparticles are charged of opposite signs with respect to these free ions. In the high frequency region, the effective diffusion coefficient coincides with that from the free diffusion coefficients, defined as the mathematical average between the diffusion coefficients of the nanoparticles and the free ions. In the low frequency region, we found the ambipolar diffusion coefficient, defined as their harmonic average. The effect of the electrodes is taken into account by means of surface conductivity to describe the conduction current across the electrode, assumed to be proportional to the surface electric field. In this model, the role of the electrodes is important just in the low frequency region. On the contrary, in the high frequency region, where the electric current is dominated by the displacement current, the role of the electrodes is negligible. The results show that the nanoparticles of the magnetic material have no effects on the higher-frequency range of the impedance spectra. In the low frequency region, our results indicate a difference in the electric response of the two ferrofluids. Due to their similar dimensions and, hence, similar ambipolar diffusion coefficients, we impute the observed different behavior to the charge transfer from the bulk to the external circuit included in the surface conductivity.