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Specific absorption rate of magnetic nanoparticles: nonlinear AC susceptibility

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 Added by Francois Vernay
 Publication date 2020
  fields Physics
and research's language is English




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In the context of magnetic hyperthermia, several physical parameters are used to optimize the heat generation and these include the nanoparticles concentration and the magnitude and frequency of the external AC magnetic field. Here we extend our previous work by computing nonlinear contributions to the specific absorption rate, while taking into account (weak) inter-particle dipolar interactions and DC magnetic field. In the previous work, the latter were shown to enhance the SAR in some specific geometries and setup. We find that the cubic correction to the AC susceptibility does not modify the qualitative behavior observed earlier but does bring a non negligible quantitative change of specific absorption rate, especially at relatively high AC field intensities. Incidentally, within our approach based on the AC susceptibility, we revisit the physiological empirical criterion on the upper limit of the product of the AC magnetic field intensity $H_{0}$ and its frequency $f$, and provide a physicists rationale for it.

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We address the issue of inter-particle dipolar interactions in the context of magnetic hyperthermia. More precisely, the main question dealt with here is concerned with the conditions under which the specific absorption rate is enhanced or reduced by dipolar interactions. For this purpose, we propose a theory for the calculation of the AC susceptibility, and thereby the specific absorption rate, for a monodisperse two-dimensional assembly of nanoparticles with oriented anisotropy, in the presence of a DC magnetic field, in addition to the AC magnetic field. We also study the competition between the dipolar interactions and the DC field, both in the transverse and longitudinal configurations. In both cases, we find that the specific absorption rate has a maximum at some critical DC field that depends on the inter-particle separation. In the longitudinal setup, this critical field falls well within the range of experiments.
We have calculated the low-field magnetic susceptibility $chi$ of a system consisting of non-interacting mono-dispersed nanoparticles using a classical statistical approach. The model makes use of the assumption that the axes of symmetry of all nanoparticles are aligned and oriented at a certain angle $psi$ with respect to the external magnetic field. An analytical expression for the temperature dependence of the susceptibility $chi(T)$ above the blocking temperature is obtained. The derived expression is a generalization of the Curie law for the case of anisotropic magnetic particles. We show that the normalized susceptibility is a universal function of the ratio of the temperature over the anisotropy constant for each angle $psi$. In the case that the easy-axis is perpendicular to the magnetic field the susceptibility has a maximum. The temperature of the maximum allows one to determine the anisotropy energy.
The role of dipolar interactions among Ni nanoparticles (NP) embedded in an amorphous SiO2/C matrix with different concentrations has been studied performing ac magnetic susceptibility Chi_ac measurements. For very diluted samples, with Ni concentrations < 4 wt % Ni or very weak dipolar interactions, the data are well described by the Neel-Arrhenius law. Increasing Ni concentration to values up to 12.8 wt % Ni results in changes in the Neel-Arrhenius behavior, the dipolar interactions become important, and need to be considered to describe the magnetic response of the NPs system. We have found no evidence of a spin-glasslike behavior in our Ni NP systems even when dipolar interactions are clearly present.
We compute the AC susceptibility of a weakly dipolar-interacting monodisperse assembly of magnetic nanoclusters with oriented anisotropy. For this purpose we first compute the relaxation rate in a longitudinal magnetic field of a single nanomagnet taking account of both dipolar interactions in the case of dilute assemblies and surface anisotropy. We then study the behavior of the real and imaginary components of the AC susceptibility as functions of temperature, frequency, surface anisotropy and inter-particle interactions. We find that the surface anisotropy induces an upward shift of the temperature at the maximum of the AC susceptibility components and that its effects may be tuned so as to screen out the effects of interactions. The phenomenological Vogel-Fulcher law for the effect of dipolar interaction on the relaxation rate is revisited within our formalism and a semi-analytical expression is given for the effective temperature is given in terms of inter alia the applied field, surface anisotropy and dipolar interaction.
The dipolar interaction is known to substantially affect the properties of magnetic nanoparticles. This is particularly important when the particles are kept in a fluid suspension or packed inside nano-carriers. In addition to its usual long-range nature, in these cases the dipolar interaction may also induce the formation of clusters of particles, thereby strongly modifying their magnetic anisotropies. In this paper we show how AC susceptibility may be used to obtain important information regarding the influence of the dipolar interaction in a sample. We develop a model which includes both aspects of the dipolar interaction and may be fitted directly to the susceptibility data. The usual long-range nature of the interaction is implemented using a mean-field solution, whereas the particle-particle aggregation is modeled using a distribution of anisotropy constants. The model is then applied to two samples studied at different concentrations. One consists of spherical magnetite nanoparticles dispersed in oil and the other of cubic magnetite nanoparticles embedded on PLGA nanospheres. We also introduce a simple technique to access the importance of the dipolar interaction in a given sample, based on the height of the AC susceptibility peaks for different driving frequencies. Our results help illustrate the important effect that the dipolar interaction has in most nanoparticle samples.
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