Dynamic susceptibility of a concentrated ferrofluid: The role of interparticle interactions

The dynamic susceptibility of concentrated ferrofluids of magnetite-kerosene type is studied experimentally to clarify the effect of interparticle interactions on the magnetization reversal dynamics and the ferrofluid relaxation time spectrum. We synthesize six ferrofluid samples, four of which have the same wide particle size distribution with a high (more than 2kT) average energy of magnetic dipole interactions. These samples differ in particle concentration and dynamic viscosity. The two remaining samples have a lower content of large particles and a moderate energy of magnetic dipole interactions. For all samples, we measure the dynamic susceptibility in the weak probing field at frequencies up to 160 kHz and the field amplitude dependence of the susceptibility at a frequency of 27 kHz. The results show that the susceptibility dispersion at frequencies up to 10 kHz is due to the rotational diffusion of colloidal particles and aggregates. Steric and hydrodynamic interparticle interactions are the main reason for the strong concentration dependence of the viscosity and so they also strongly influence the frequency dependence of the susceptibility. The influence of van der Waals and magnetic dipole interactions on the susceptibility is manifested indirectly, through the formation of multiparticle clusters. The contribution of clusters to the low-frequency susceptibility reaches 80%. Their large sizes (about 100 nm) shift the dispersion region to frequencies of 1-100 Hz, depending on the temperature and particle concentration. Experiments at 27 kHz demonstrate the increase in the dynamic susceptibility with increasing field amplitude. This growth is unexpected since all spectral amplitudes in the Debye function expansion of the dynamic susceptibility decrease monotonically with increasing field. To clarify the situation, the auxiliary problem of the magnetodynamics of a uniaxial particle in the alternating field is solved numerically. The Fokker-Planck-Brown rotational diffusion equation is used. It is shown that an increase in the field amplitude reduces the anisotropy barrier and the Néel relaxation time of particles and increases the dynamic susceptibility by one to two orders of magnitude compared to the weak-field limit. The calculation results are in qualitative agreement with the experimental data and allow us to propose a consistent interpretation of these data. We find that the increase in dynamic susceptibility with increasing amplitude is observed when two necessary conditions are met: (i) The suspension viscosity and the field frequency are high enough to cause the blocking of the rotational degrees of freedom of particles and aggregates and (ii) particles with a large magnetic anisotropy are present in the ferrofluid.