RESUMO
In this paper, we study the effect of a bias dc field on the dynamic response of a moderately concentrated ferrofluid to an ac magnetic field of arbitrary amplitude. The ferrofluid is modeled by an ensemble of interacting moving magnetic particles; the reaction of particle magnetic moments to ac and dc magnetic fields occurs according to the Brownian mechanism; and the ac and dc magnetic fields are parallel. Based on a numerical solution of the Fokker-Planck equation for the probability density of the orientation of the magnetic moment of a random magnetic particle, dynamic magnetization and susceptibility are determined and analyzed for various values of the ac field amplitude, the dc field strength, and the intensity of dipole-dipole interactions. It is shown that the system's magnetic response is formed under the influence of competing interactions, such as dipole-dipole, dipole-ac field, and dipole-dc field interactions. When the energies of these interactions are comparable, unexpected effects are observed: the system's susceptibility can either increase or decrease with increasing ac field amplitude. This behavior is associated with the formation of nose-to-tail dipolar structures under the action of the dc field, which can hinder or promote the system's dynamic response to the ac field. The obtained results provide a theoretical basis for predicting the dynamic properties of ferrofluids to improve their use in biomedical applications, such as, in magnetic induction hyperthermia.
RESUMO
Based on numerical results of dynamic susceptibility, a simple theory of the dynamic response of a ferrofluid to an ac magnetic field is obtained that includes both the effects of interparticle dipole-dipole interactions and the dependence on field amplitude. Interparticle interactions are incorporated in the theory using the so-called modified mean-field approach. The new theory has the following important characteristics: in the noninteracting regime at a weak ac field, it gives the correct single-particle Debye theory results; it expands the applicability of known theories valid for high concentrations [Ivanov, Zverev, and Kantorovich, Soft Matter 12, 3507 (2016)10.1039/C5SM02679B] or large values of ac field amplitudes [Yoshida and Enpuku, Jpn. J. Appl. Phys. 48, 127002 (2009)10.1143/JJAP.48.127002], in accordance with their applicability. The susceptibility spectra are analyzed in detail. It is demonstrated that interparticle dipole-dipole interactions and an increase in field amplitude have an opposite effect on the dynamic response of ferrofluids, so that at certain field amplitudes, relaxation processes in the system of interacting particles are determined by the characteristic relaxation times for an ideal paramagnetic gas. The new theory correctly predicts the dynamic susceptibility and characteristic relaxation times of a ferrofluid at high ac field amplitudes as long as the Langevin susceptibility χ_{L}â²1, which is a complex characteristic of ferrofluid density and the intensity of interparticle dipole-dipole interactions.
