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Field dependent transition to the non-linear regime in magnetic hyperthermia experiments: Comparison between maghemite, copper, zinc, nickel and cobalt ferrite nanoparticles of similar sizes
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Image of FIG. 1.

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FIG. 1.

(a) The X-ray powder diffractograms of the synthesized sample and patterns of magnetite and maghemite bulk standards. (b) Rietveld refinement pattern of the copper-ferrite sample. The lower curve represents the difference between the observed and calculated profiles. Plus (+) marks represent the collected data and tic marks show the positions for the allowed reflections. The agreement factors for X-ray diffraction obtained from the Rietveld analysis were: Rp = 4.42%, Rwp = 5.69% and χ2 = 9.454.

Image of FIG. 2.

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FIG. 2.

Morphological characterization. TEM micrographs for cobalt ferrite (b) and maghemite (d); the inset illustrates data from X Ray diffraction. The corresponding size distribution histograms are shown in images (a) and (c) respectively, together with a lognormal distribution fit.

Image of FIG. 3.

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FIG. 3.

(a) Vibrating sample magnetometry for cobalt ferrite and maghemite nanoparticles. (b) Magnification of image (a) at small fields. The inset in Fig. 2(b) shows ferromagnetic resonance data for both samples, measured at the X-band.

Image of FIG. 4.

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FIG. 4.

(a) X-band room temperature ferromagnetic resonance spectra of the ferrite-based nanoparticles. (b) Quasi-static room temperature magnetization curves of all the powder samples. The inset shows a schematic representation of a core-shell nanoparticle.

Image of FIG. 5.

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FIG. 5.

(a) Temperature variation data for cobalt ferrite (solid lines) and maghemite (dashed lines) for different values of the applied field amplitude. (b) Temperature variation data for cobalt ferrite (circles) and maghemite (triangles) together with a bidose fit (solid line) for a field of 133Oe; (inset) heating rate time dependence obtained from the bidose fit.

Image of FIG. 6.

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FIG. 6.

(a) SAR vs. applied field amplitude for the powder cobalt ferrite (asterisks) and maghemite samples (open triangles) at 500kHz using the bidose model. Also shown is the SAR for cobalt ferrite estimated from the initial slope (open circles). In the inset we present SAR as function of magnetic field for both colloidal samples at higher field amplitudes and lower frequency (300kHz) (b) Efficiency, vs. the applied field amplitude.

Image of FIG. 7.

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FIG. 7.

Dynamic hysteresis simulations for different values of σ and h 0 = H 0/H A , with fτ0 = 10−4.

Image of FIG. 8.

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FIG. 8.

Similar to Fig. 5 but for fτ0 = 10−2.

Image of FIG. 9.

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FIG. 9.

Dynamic hysteresis simulations of the efficiency (Ω) vs. σ for different values of fτ0 and h 0 = H 0/H A . The latter ranges from 0.02 (higher; darker) to 0.2 (shorter; lighter) in steps of 0.02.

Image of FIG. 10.

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FIG. 10.

Simulated SAR and efficiency vs. the applied field amplitude for different values of σ. (a) and (b) fτ0 = 10−2 and σ = 3, 5 and 7.(c) and (d) fτ0 = 10−3 and σ = 5, 7 and 9. (e) and (f) fτ0 = 10−4 and σ =8, 10 and 12.

Image of FIG. 11.

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FIG. 11.

Simulated (a) SAR and (b) efficiency vs. (σ, h 0), with fτ0 = 10−2.

Image of FIG. 12.

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FIG. 12.

(a) SAR vs. applied field amplitude for the powder of ferrite-based nanoparticles (symbols) at 500kHz. The solid lines are just guide to the eye. In the inset we present temperature variation data as function of time for all the samples for a field of 133Oe. (b) Efficiency, vs. the applied field amplitude for all the ferrite-based nanoparticles. Symbols represent experimental data, while the solid lines are just guide to the eye.


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Table I.

Estimated parameters for cobalt, copper, nickel, zinc ferrite and maghemite nanoparticles. Exp. correspond to experimentally estimated values, while Bulk is related to calculations using the reported bulk values. M S is the saturation magnetization, H C the coercivity, D RR the particle diameter estimated from Rietveld analysis, x the degree of cationic distribution, H R the electron magnetic resonance field, δH R the resonance linewidth, D TEM modal diameter and δ D size dispersity from Log-normal size distribution, α the damping factor, effective magnetic anisotropy, dipolar anisotropy parameter, anisotropy parameter, anisotropy field, characteristic time, f magnetic field frequency and anisotropy parameter value with maximum hyperthermia. Values in brackets were estimated taking into account the polidispersity of the sample.

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Table II.

Estimated parameters using the core-shell model for maghemite, copper, cobalt and nickel ferrite nanoparticles. CS-Diam correspond to calculations using the value of the core fraction (f core ) estimated from the combination of Rietveld and TEM analysis, while CS-Magn correspond to calculations using the core fraction estimated from magnetization data (see discussion in the text). Some parameters had already been defined in Table I, however others are defined as: core magnetization, experimentally determined particle magnetization, f core fraction of core atoms, κ non-crystalline shell thickness, *D MODAL modal particle size estimated from the core-shell model and *δ D size dispersity assumed in the calculations of the relevant parameters.


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Further advances in magnetic hyperthermia might be limited by biological constraints, such as using sufficiently low frequencies and low field amplitudes to inhibit harmful eddy currents inside the patient's body. These incite the need to optimize the heating efficiency of the nanoparticles, referred to as the specific absorption rate (SAR). Among the several properties currently under research, one of particular importance is the transition from the linear to the non-linear regime that takes place as the field amplitude is increased, an aspect where the magnetic anisotropy is expected to play a fundamental role. In this paper we investigate the heating properties of cobaltferrite and maghemite nanoparticles under the influence of a 500 kHz sinusoidal magnetic field with varying amplitude, up to 134 Oe. The particles were characterized by TEM, XRD, FMR and VSM, from which most relevant morphological, structural and magnetic properties were inferred. Both materials have similar size distributions and saturation magnetization, but strikingly different magnetic anisotropies. From magnetic hyperthermia experiments we found that, while at low fields maghemite is the best nanomaterial for hyperthermia applications, above a critical field, close to the transition from the linear to the non-linear regime, cobaltferrite becomes more efficient. The results were also analyzed with respect to the energy conversion efficiency and compared with dynamic hysteresis simulations. Additional analysis with nickel, zinc and copper-ferrite nanoparticles of similar sizes confirmed the importance of the magnetic anisotropy and the damping factor. Further, the analysis of the characterization parameters suggested core-shell nanostructures, probably due to a surface passivation process during the nanoparticle synthesis. Finally, we discussed the effect of particle-particle interactions and its consequences, in particular regarding discrepancies between estimated parameters and expected theoretical predictions.


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Scitation: Field dependent transition to the non-linear regime in magnetic hyperthermia experiments: Comparison between maghemite, copper, zinc, nickel and cobalt ferrite nanoparticles of similar sizes