Dynamics of superparamagnetic nanoparticles in viscous liquids in rotating magnetic fields

Abstract

The dynamics of magnetic nanoparticles in a viscous liquid in a rotating magnetic field has been studied by means of numerical simulations and analytical calculations. In the magneto-dynamics approximation three different modes of motion of the unit magnetization vector and particle director are distinguished depending on frequency and amplitude of the rotating magnetic field. The specific absorption rate of a dilute assembly of superparamagnetic nanoparticles in rotating magnetic field is calculated by solving the Landau–Lifshitz stochastic equation for the unit magnetization vector and the stochastic equation for the particle director. At elevated frequencies an optimal range of particle diameters is found where the specific absorption rate of an assembly in a rotating magnetic field has a maximum. It is shown that with an optimal choice of the particle sizes sufficiently large SAR values of the order of 400–500 W/g can be obtained in a rotating magnetic field with a frequency f = 400 kHz and a moderate magnetic field amplitude H 0 = 100 Oe.

Theory of superlocalized magnetic nanoparticle hyperthermia: rotating versus oscillating fields

“…Of course, in order to look for the most efficient applied field configuration, one can perform further theoretical investigations. For example, open questions motivated by the present theoretical study of the enhancement and superlocalization effects are the inclusion of (i) the interaction between the particles which can results in formation of clusters [63]; (ii) the dependence on the diameter of the nanoparticles; and (iii) the possible rotating motions of the nanoparticle as a whole [35,37,[57][58][59][60]62]. However, we do expect that considerations very likely do not violate our major finding that appropriate combination of rotating and (in-plane) static fields is essentially like an oscillating one but in order to achieve the same heating efficiency, i.e., the same SAR one has to double the applied frequency, so, for the same frequency, the oscillating combination is a better choice.…”

“…[22], where the dynamics and the energy dissipation in the presence of a static and rotating fields have been studied and enhancement effects are reported, however the frequency range is too large to be applicable for hyperthermia. Indeed, the applied external magnetic field is one of the most easily variable parameters to increase the efficiency of heat generation and one finds several attempts in the literature where the case of the rotating external magnetic field has been studied, as an example see the selection [23][24][25][26][27][28][29][30][31][32][33][34][35]37].…”

“…If the applied frequency is high enough (ω 100 kHz) and the diameter of the nanoparticle is appropriately chosen (typically small enough), the mechanical rotation of the nanoparticles in the surrounding medium is restricted and one can estimate the efficiency of the heat transfer by considering the change in the orientation of the magnetization vector, which is called the Neel relaxation process, [35][36][37]39]. On the other hand the applied frequency and the product of the frequency and field amplitude cannot be arbitrarily large due to the biological limitation of hyperthermic treatment of the human body [38][39][40].…”

Polarised superlocalization in magnetic nanoparticle hyperthermia

“…Another issue is the mechanical motion (rotation) of the particles in their environment. If the applied frequency is high enough (ω > ∼ 100 kHz) and the diameter of the nanoparticle is relatively small (∼ 20 nm), the mechanical rotation of the MNPs can be restricted in the surrounding medium, and only the orientation of their magnetic moment has to be taken into account [19,[21][22][23]. Important to note that the frequency cannot be chosen to be too high to minimize eddy currents and to enable the use of the method for hyperthermic treatments.…”

Nanomagnetic Actuation of Hybrid Stents for Hyperthermia Treatment of Hollow Organ Tumors

“…In such simulations, the heating efficiency was determined in dependency of MNP magnetic size and anisotropy energy constants as well as of the AFM parameters. In Monte-Carlo simulations, the effects of MNP immobilization and interactions on MFH were also investigated [ 48 ].…”