Characterization of Néel and Brownian Relaxations Isolated from Complex Dynamics Influenced by Dipole Interactions in Magnetic Nanoparticles

Abstract

The magnetization dynamics involved in applying an alternating field are composed of a superposition of Neél and Brownian relaxations. To evaluate the mechanisms of magnetic relaxations, it is necessary to individually evaluate the Neél and Brownian regimes. In this study, by applying a fast responding pulse field, the two-step magnetization response of magnetic nanoparticles dispersed in a fluid in the Brownian regime occurred after the Neél regime. We isolated Neél and Brownian relaxations from an experimentally observed superposition relaxation system by fitting the theoretical calculation to the measured time evolution response of the magnetization, which was in agreement with the susceptibility that was measured through applying an alternating magnetic field. The dependence of Neél and Brownian relaxation's dominance in the superposition system on relaxation times was clearly observed. In particular, the effect of dipole interactions on Neél and Brownian relaxation times were confirmed by changing the particle concentration in a magnetic fluid. Elucidation of the transition process from Neél to Brownian relaxation, which is influenced by the proportion between Neél and Brownian relaxation times and the effect of dipole interactions on the individual relaxation processes, allows us to develop optimal magnetic nanoparticles for a variety of biomedical applications.

Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation

“…11 In another set of very recent experiments, the concentration dependence of the magnetization relaxation has been measured and the Brownian and Néel contributions have been identified. 7 While the effective Brownian relaxation time was found to increase with increasing concentration, a weaker, opposite behavior was observed for the effective Néel relaxation time. Furthermore, the corresponding dynamic magnetic susceptibility deviates strongly from the Debye law for noninteracting MNPs and the effective relaxation time (1) is not sufficient to describe the behavior.…”

“…with transition rates w. Equations of the type (5) with (6) and (7) are known in the literature as ''differential Chapman-Kolmogorov'' equations. 33 In order to complete the model, we therefore need to specify the transition rates w in eqn (7). We here follow ref.…”

“…3,6 Therefore, methods for determining their relative importance are currently being explored, helping to find the optimal colloids for the given application. 7,8 For ferrofluids, where MNPs are suspended in a non-magnetic carrier fluid, Rosensweig assumed that both relaxation processes occur independently so that the corresponding rates can be added up to yield an effective relaxation given by 5 1…”

Magnetic Fluid Hyperthermia Based on Magnetic Nanoparticles: Physical Characteristics, Historical Perspective, Clinical Trials, Technological Challenges, and Recent Advances

“…[ 64,66 ] In this linear approximation, the hysteresis loop area is given by where μ 0 is the permeability of free space (4π × 10 −7 m kg s −2 A −2 ), M s is the saturation magnetization, V m is the volume of the particles, k B is the Boltzmann constant (1.38 × 10 −23 J K −1 ), T the absolute temperature (in Kelvin) and τ is the Néel–Brown relaxation time. [ 67 ] The Brownian ( τ B ) and Néel ( τ N ) relaxation times of a single superparamagnetic nanoparticle assuming as sphere can be calculated utilizing the following formulas Where τ N is the Néel relaxation time, τ 0 is the effective relaxation time (≈10 −9 s), K eff is the magnetic anisotropy constant, D m is the magnetic core diameter from TEM, k B is the Boltzmann constant (1.38 × 10 −23 J K −1 ), T is the absolute temperature in Kelvin, τ B is the Brownian relaxation time, η is the dynamic viscosity of the surrounding medium ( η is the 0.7978 × 10 −3 kg m −1 s −1 for water) and D h is the hydrodynamic diameter (the diameter of the particle plus adsorbed surfactant, derived from dynamic light scattering (DLS)). [ 19f ] Considering that these two independently mechanisms take place simultaneously, the effective relaxation time τ eff is given by when τ N ≫ τ B or τ N ≪ τ B , the dominant mechanism as described by τ eff , is determined by the shorter of the two relaxation times.…”

Specific Loss Power of Co/Li/Zn-Mixed Ferrite Powders for Magnetic Hyperthermia

“…This effect was mainly due to the higher operating frequency of the thermometric setup (100 kHz) with respect to the B-H loop tracer (69 kHz) and it also included the contribution to the SLP of the Brown relaxation process that took place only in the magnetic liquid solution and not in the dried sample used for dynamic hysteresis loops measurements [24,87]. In fact, the Brown relaxation mechanism is associated with the physical rotation of the whole particle in the fluid generating heat due to the viscous friction between the rotating particles and the surrounding liquid medium [24,87,88]. However, recent studies, both in vivo and ex vivo, have demonstrated that the particles are generally immobilized when directly injected into the tumor tissues highlighting that the Brown process is largely suppressed during hyperthermia treatments [89][90][91].…”