Brownian Relaxation Research Articles

Agglomeration Dynamics of Magnetite Nanoparticles at Low Magnetic Field Gradient

Agglomeration of magnetite nanoparticles in the aqueous solution is studied at the low magnetic field gradients of 23–34 T/m by monitoring the temporal change of magnetic weight. A conventional electronic balance is used to measure the magnetic weight that is the magnetic force on the magnetic sample by the magnetic field gradient. The magnetic weight grows slowly following the stretched exponential after the instantaneous jump by the Neel and Brown relaxation. Magnetization of the magnetite nanoparticles is estimated from the magnetic weight and compared with the Langevin function. The magnetization is close to the saturation in the studied magnetic field range and the saturation magnetization of the agglomerate of nanoparticles is about 60% of that of the bulk magnetite. Kinetic parameters of the stretched exponential show little the magnetic field dependence in the investigated range. Complex energy landscape is involved in the agglomeration as the stretched exponential dynamics indicates. The half‐life of the response function for the magnetic weight change suggests that the pathways of low energy barriers are activated by magnetic field at the early stage of agglomeration.

Iron oxide nanoparticles modified with silanes for hyperthermia applications

Fe3O4-HDTMS nanocomposites were prepared and studied using Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy, X-ray analysis, thermal analysis (TGA), dynamic light scattering analysis, magnetic and specific loss power (SLP) measurements. FTIR results showed that during the modification, the formation of the silane coating occurs due to the appearance of the magnetite–O–Si–R bond. According to TGA results, the mass loss in the range of temperatures 410–650 °C is due to the destruction of covalent bonds Fe–O–Si. The Si–O–R coating leads to the decrease in the absolute value of the effective saturation magnetization due to the presence of a non-magnetic phase (coating) in the sample, but the coercivity increases with the coating thickness due to higher effective values of the magnetic anisotropy of the magnetostrictive nature. The thermal response of NP-based dispersions in silicone and oleic acid was shown that SLP value is higher for magnetic material dispersions in Lipiodol and oleic acid compared to silicone-based dispersions. This can be explained by the contribution of both Neel and Brownian relaxation processes. However, in the case of silicone-based dispersion, Brownian relaxation is negligible because of NP immobilization in viscous silicone matrix. As it is to the effect of coating on SLP, this is clearly evident in the case of silicone dispersions. The study of the heating ability of dispersions based on HDTMS-modified Fe3O4 NPs showed that the coating does not significantly decrease the SLP values.

INFLUENCE OF SATURATION MAGNETIZATION AND VISCOSITY ON SPECIFIC LOSS POWER FOR CoFe2O4 AND MnFe2O4 MAGNETIC NANOPARTICLES

Magnetic nanoparticles absorb energy from external alternating magnetic field to create ananosized heating source. Specific loss power (SLP) is affected strongly by several magneticparameters of material and viscosity of nanofluid. In this study, the specific loss power asdependent on saturation magnetization was calculated for hard ferrite CoFe2O4 (K = 290 kJ/m3)and soft ferrite MnFe2O4 (K = 3 kJ/m3) with two values of viscosity in biological range 1-2 mPas.Besides, we investigated the experimental dependence SLP on their saturation magnetizationwhile changing viscosity using agar powder. A large change of slopesSLPMwas found for CFOwhen the viscosity changes; whereas it remained almost unaffected by the variation of viscosityfluid of MFO. All calculation and experimental results are discussed via the competitionbetween Néel and Brown relaxation.

Bifunctional CoFe2O4/ZnO Core/Shell Nanoparticles for Magnetic Fluid Hyperthermia with Controlled Optical Response

Conjugation of optical and magnetic responses in a unique system at the nanoscale emerges as a powerful tool for several applications. Here, we fabricated bifunctional CoFe2O4-core/ZnO-shell nanoparticles with simultaneous photoluminescence in the visible range and ac magnetic losses suitable for hyperthermia. The structural characterization confirms that the system is formed by a ≈7 nm CoFe2O4 core encapsulated in a ≈1.5-nm-thick semiconducting ZnO shell. As expected from its high anisotropy, the magnetic losses in an ac magnetic field are dominated by the Brown relaxation mechanism. The ac magnetic response of the core/shell system can be accurately predicted by the linear response theory and differs from that one of bare CoFe2O4 nanoparticles as a consequence of changes in the viscous relaxation process due to the effect of the magnetostatic interactions. Concerning the optical properties, by comparing core/shell CoFe2O4/ZnO and single-phase ZnO nanoparticles, we found that the former exhibits a broade...

Relating Magnetic Properties and High Hyperthermia Performance of Iron Oxide Nanoflowers

We investigated, in depth, the interrelations among structure, magnetic properties, relaxation dynamics and magnetic hyperthermia performance of magnetic nanoflowers. The nanoflowers are about 39 nm in size, and consist of densely packed iron oxide cores. They display a remanent magnetization, which we explain by the exchange coupling between the cores, but we observe indications for internal spin disorder. By polarized small-angle neutron scattering, we unambiguously confirm that, on average, the nanoflowers are preferentially magnetized along one direction. The extracted discrete relaxation time distribution of the colloidally dispersed particles indicates the presence of three distinct relaxation contributions. We can explain the two slower processes by Brownian and classical Neel relaxation, respectively. The additionally observed very fast relaxation contributions are attributed by us to the relaxation of disordered spins within the nanoflowers. Finally, we show that the intrinsic loss power (ILP, ma...

Threshold heating temperature for magnetic hyperthermia: Controlling the heat exchange with the blocking temperature of magnetic nanoparticles

La0.75Sr0.25MnO3 nanoparticles with average diameter close to 20.9nm were synthesized using a sol-gel method. Measurements showed that the heating process stops at the blocking temperaturesignificantly below the Curie temperature. Measurements of Specific Absorption Rate (SAR) as a function of AC magnetic field revealed a superquadratic power law, indicating that, in addition to usual Néel and Brown relaxation, the hysteresis also plays an important role in the mechanism of heating. The ability to control the threshold heating temperature, a low remanent magnetization and a low field needed to achieve the magnetic saturation are the advantages of this material for therapeutic magnetic hyperthermia.

Magnetic nanoparticle thermometry independent of Brownian relaxation

An improved method of magnetic nanoparticle (MNP) thermometry is proposed. The phase lag ϕ of the fundamental f0 harmonic is measured to eliminate the influence of Brownian relaxation on the ratio of 3f0 to f0 harmonic amplitudes applying a phenomenological model, thus allowing measurements in high-frequency ac magnetic fields. The model is verified by simulations of the Fokker–Planck equation. An MNP spectrometer is calibrated for the measurements of the phase lag ϕ and the amplitudes of 3f0 and f0 harmonics. Calibration curves of the harmonic ratio and tanϕ are measured by varying the frequency (from 10 Hz to 1840 Hz) of ac magnetic fields with different amplitudes (from 3.60 mT to 4.00 mT) at a known temperature. A phenomenological model is employed to fit the calibration curves. Afterwards, the improved method is proposed to iteratively compensate the measured harmonic ratio with tanϕ, and consequently calculate temperature applying the static Langevin function. Experimental results on SHP-25 MNPs show that the proposed method significantly improves the systematic error to 2 K at maximum with a relative accuracy of about 0.63%. This demonstrates the feasibility of the proposed method for MNP thermometry with SHP-25 MNPs even if the MNP signal is affected by Brownian relaxation.

Zn and Zr co-doped M-type strontium hexaferrite: Synthesis, characterization and hyperthermia application

In the present study, hard ferromagnetic (M-type strontium hexaferrite) SrFe12O19 was co-doped by Zn and Zr for magnetic hyperthermia applications. As a result of the high concentration of single domain SrFe12O19 nanoparticles (suspended in the ferrofluid), they found a large hydrodynamic diameter, which caused a long-time Brownian relaxation under the AC magnetic field. On the other hand, increasing the Zn-Zr content (low concentration of SrFe12O19) led to a drop in anisotropy, which coincided with a short-time N´eel relaxation. All of the substituted samples with a multi-disperse state in ferrofluid exhibited an almost equal amount of the N´eel and Brownian effects. Consequently, the magnetic saturation (Ms) was considered as the dominant factor in the specific absorption rate (SAR) of the substituted samples. Transformation to the mono-disperse state was followed by the decrease of the Brownian relaxation time and hence the increase of the SAR. The interesting point in mono-disperse state was the heat generation of pure SrFe12O19 under the AC magnetic field as a result of the decrement of the Brownian relaxation time.

Effect of orientational ordering of magnetic nanoemulsions immobilized in agar gel on magnetic hyperthermia

Magnetic nanoemulsions of droplet size ∼200 nm, loaded with single domain superparamagnetic nanoparticles (MNP), are potential candidates for multimodal hyperthermia due to availability of large loading volume and enhanced permeation and retention (EPR) in the cancerous tissues. In such nanoemulsions, radio frequency alternating magnetic field induced heating occur at two entirely different length scales, viz. Neel-Brown relaxation of the dispersed MNP and Brownian relaxation of emulsion droplets. Here we study the effects of orientation ordering or texturing of droplets, immobilized in a tissue mimicking agar matrix, on the field induced heating efficiency. A higher specific absorption rate (maximum ∼73 ± 2 W/gFe) is observed for droplets orientated parallel to the direction of the alternating magnetic field because of the enhancement of effective uniaxial anisotropy energy density and increased effective relaxation time. For identical and non-interacting MNP oriented parallel to the external DC magnetic field, a threefold increase in the effective uniaxial anisotropy energy density and ∼20–30% increased specific absorption rate are observed as compared to those oriented perpendicular to the magnetic field. Magnetic force microscopy images showed that the spherical morphology of the droplets remains intact even after orientational ordering and average topographic height of the droplets are found to be ∼220 (±17) nm, which is in good agreement with the most probable size obtained from dynamic light scattering. The residual volume magnetization of the emulsion droplets is found to be 1.1 × 10−6 emu/cc, indicating the superparamagnetic nature of the droplets in tissue equivalent environment. The observed increase in heating efficiency of the immobilized and oriented emulsion droplets shows promising applications in multimodal hyperthermia therapy because of the requirement of lower dose of MNP and shorter treatment time.

Magnetic Field Dependence of Ni Nanorod Brownian Relaxation

AC magnetic susceptibility and optical transmission measurements were performed on Ni nanorod suspensions for ac and superimposed dc magnetic fields up to 9 mT. With the comparably large magnetic moment per nanorod, these field values correspond to Langevin parameters $\xi$ up to about 80. These wide range of $\xi$ values, the narrow size distribution, and the absence of Neel relaxation make these single-domain ferromagnetic nanorods ideally suited for the experimental verification of the dependence of the Brownian relaxation time on ac and dc magnetic fields. Consistent results for the magnetic moment m and the zero-field Brownian relaxation time $\tau _{B,0}$ were obtained for all measurement modalities and the valid field range of alternative models for the ac susceptibility was evaluated.

Concentration-dependent zero-field magnetic dynamic response of polydisperse ferrofluids

In this contribution, we discuss the experimental results obtained for seven ferrofluid samples with the same particle size distribution that differ only in concentration of magnetic material. The dynamic response to a weak linearly-polarised probing AC field is measured for each sample at five different temperatures. We investigate Cole-Cole diagrams and phase shifts in order to describe the impact of ferroparticle concentration on the initial magnetic susceptibility. Our findings show that the main contribution comes from the increasing effective viscosity of the ferrofluid that results in the growth of the Brownian relaxation time. This mechanism is very important for the systems containing even a small portion of large magnetic colloids. The influence of dipolar correlations was separately analysed using computer simulations.

Diopside-magnetite; A novel nanocomposite for hyperthermia applications.

In the present work, the releasing heat, scaffold apatite formation, and magnetic behavior of a novel diopside-magnetite nanocomposite with various contents of magnetite (Fe3O4) were evaluated. The N´eel and Brown relaxations did not have a significant effect on the specific absorption rate (SAR) of the composite samples. Indeed, magnetic saturation, Ms, indicated a crucial effect on the heat release of the samples. The sample with 30wt% magnetite had the highest value of SAR, while the sample with 20wt% magnetite, in the form of scaffold, allowed the high amount of apatite formation on its surface.

Computer simulations of equilibrium magnetization and microstructure in magnetic fluids

In this work, Monte Carlo and Brownian Dynamics simulations are developed to compute the equilibrium magnetization of a magnetic fluid under action of a homogeneous applied magnetic field. The particles are free of inertia and modeled as hard spheres with the same diameters. Two different periodic boundary conditions are implemented: the minimum image method and Ewald summation technique by replicating a finite number of particles throughout the suspension volume. A comparison of the equilibrium magnetization resulting from the minimum image approach and Ewald sums is performed by using Monte Carlo simulations. The Monte Carlo simulations with minimum image and lattice sums are used to investigate suspension microstructure by computing the important radial pair-distribution function go(r), which measures the probability density of finding a second particle at a distance r from a reference particle. This function provides relevant information on structure formation and its anisotropy through the suspension. The numerical results of go(r) are compared with theoretical predictions based on quite a different approach in the absence of the field and dipole-dipole interactions. A very good quantitative agreement is found for a particle volume fraction of 0.15, providing a validation of the present simulations. In general, the investigated suspensions are dominated by structures like dimmer and trimmer chains with trimmers having probability to form an order of magnitude lower than dimmers. Using Monte Carlo with lattice sums, the density distribution function g2(r) is also examined. Whenever this function is different from zero, it indicates structure-anisotropy in the suspension. The dependence of the equilibrium magnetization on the applied field, the magnetic particle volume fraction, and the magnitude of the dipole-dipole magnetic interactions for both boundary conditions are explored in this work. Results show that at dilute regimes and with moderate dipole-dipole interactions, the standard method of minimum image is both accurate and computationally efficient. Otherwise, lattice sums of magnetic particle interactions are required to accelerate convergence of the equilibrium magnetization. The accuracy of the numerical code is also quantitatively verified by comparing the magnetization obtained from numerical results with asymptotic predictions of high order in the particle volume fraction, in the presence of dipole-dipole interactions. In addition, Brownian Dynamics simulations are used in order to examine magnetization relaxation of a ferrofluid and to calculate the magnetic relaxation time as a function of the magnetic particle interaction strength for a given particle volume fraction and a non-dimensional applied field. The simulations of magnetization relaxation have shown the existence of a critical value of the dipole-dipole interaction parameter. For strength of the interactions below the critical value at a given particle volume fraction, the magnetic relaxation time is close to the Brownian relaxation time and the suspension has no appreciable memory. On the other hand, for strength of dipole interactions beyond its critical value, the relaxation time increases exponentially with the strength of dipole-dipole interaction. Although we have considered equilibrium conditions, the obtained results have far-reaching implications for the analysis of magnetic suspensions under external flow.

Evaluation of easy-axis dynamics in a magnetic fluid by measurement and analysis of the magnetization curve in an alternating magnetic field

An understanding of the magnetic relaxation mechanism is critical to the medical application of magnetic nanoparticles. The temporal change in magnetization caused by an applied field can be evaluated by measuring the magnetization curves in the alternating fields. When magnetic nanoparticles are dispersed in a liquid, owing to magnetic torque, the Brownian relaxation influences the magnetization dynamics, in addition to the Néel relaxation. In this study, by evaluating the magnetization curve obtained by subtracting the magnetization curve corresponding to the solid from that of the liquid, the dynamics of the easy axis are observed with respect to the superparamagnetic nanoparticles.

Influence of suspension viscosity on Brownian relaxation of filler particles

Brownian relaxation caused by Brownian movement of particles in suspensions can macroscopically be probed by small-amplitude oscillatory shear experiments. Phenomenological considerations suggest a direct proportionality between suspension viscosity and Brownian relaxation times. To verify this relation experimentally, a set of nanocomposite suspensions with viscosities varying over five decades is presented. The suspensions are chosen in a way to ensure that particle-particle interactions and average particle-particle distances are identical so that they can be used as a model system to study the mere influence of suspension viscosity on Brownian relaxation. The suggested linear relationship between suspension viscosity and Brownian relaxation time can be confirmed. Moreover, a verification of a recently introduced characteristic timescale for Brownian relaxation is presented.

Characterization: Characterizing Physical Properties of Superparamagnetic Nanoparticles in Liquid Phase Using Brownian Relaxation (Small 22/2017)

Characterization: Characterizing Physical Properties of Superparamagnetic Nanoparticles in Liquid Phase Using Brownian Relaxation (Small 22/2017)

Magnetic hyperthermia in magnetic nanoemulsions: Effects of polydispersity, particle concentration and medium viscosity

Magnetic fluid hyperthermia (MFH) is a promising cancer treatment modality where alternating magnetic field is used for heating cancerous cells loaded with magnetic nanofluids. Of late, it is realized that magnetic nano-carriers in the size range ∼100–200nm (e.g. magnetic nanocomposites, magnetic liposomes and magnetic nanoemulsions) are ideal candidates for multimodal MFH coupled with drug delivery or photodynamic therapy due to enhanced permeation and retention (EPR) in the leaky vasculature of cancerous tissues. Here, we study the radiofrequency alternating magnetic field induced heating in magnetically polarizable oil-in-water nanoemulsions of hydrodynamic diameter ∼200nm, containing single domain superparamagnetic nanoparticles of average diameter ∼10nm in the oil phase. We probe the effects of size polydispersity of the droplets and medium viscosity on the field induced heating efficiency. The contribution of Neel and Brown relaxation of the magnetic nanoparticles on specific absorption rate (SAR) of the magnetic nanoemulsions, was found to increase linearly with the square of the applied field, with a maximum value of 164.4±4.3W/gFe. In magnetic nanoemulsions, the heating is induced by the Neel-Brown relaxation of the MNP over a length scale of 10nm, and the whole scale Brownian relaxation of the emulsion droplets has over a length scale of 200nm. The magnetic nanoemulsion sample with lower polydispersity (σ=0.2) exhibited a significantly higher SAR value (3.3 times higher) as compared to the sample with larger polydispersity (σ=0.4). The SAR values of the samples with 4.6 and 1.7 wt.% of MNP loading with σ values 0.4 a 0.3, respectively were comparable, suggesting a higher heating efficiency in nanofluid containing particles of lower size polydispersity even at lower particle loading. The emulsion droplets, immobilized in an agar matrix (4wt.%), gave a maximum SAR value of 41.7±2.4W/gFe as compared to 111.8±3.4W/gFe in the case of droplets dispersed in water, which indicate a ∼40–50% drop in SAR due to abrogation of whole scale Brownian relaxation of the emulsion droplets. This suggests the need for improving the heating efficiency during actual therapy in tissues. The residual SAR of the immobilized sample correlates well with the SAR of the magnetic nanofluid, albeit under a lower external field amplitude due to demagnetization effect of the clusters of MNP loaded inside the droplets. The observed heating efficiency of larger sized magnetic nanoemulsion offer new possibilities for multimodal therapy due to availability of large volume for loading anti-cancer drug or photodynamic agents.

Characterizing Physical Properties of Superparamagnetic Nanoparticles in Liquid Phase Using Brownian Relaxation

Superparamagnetic iron oxide nanoparticles (SPIONs) have been extensively used as bioimaging contrast agents, heating sources for tumor therapy, and carriers for controlled drug delivery and release to target organs and tissues. These applications require elaborate tuning of the physical and magnetic properties of the SPIONs. The authors present here a search-coil-based method to characterize these properties. The nonlinear magnetic response of SPIONs to alternating current magnetic fields induces harmonic signals that contain information of these nanoparticles. By analyzing the phase lag and harmonic ratios in the SPIONs, the authors can predict the saturation magnetization, the average hydrodynamic size, the dominating relaxation processes of SPIONs, and the distinction between single- and multicore particles. The numerical simulations reveal that the harmonic ratios are inversely proportional to saturation magnetizations and core diameters of SPIONs, and that the phase lag is dependent on the hydrodynamic volumes of SPIONs, which corroborate the experimental results. Herein, the authors stress the feasibility of using search coils as a method to characterize physical and magnetic properties of SPIONs, which may be applied as building blocks in nanoparticle characterization devices.

Thermal performance of Fe-Cr-Nb-B systems in magnetic hyperthermia

In magnetic hyperthermia, the temperature control within the malignant tissues is an important step to increase the efficiency of the therapy. A temperature analysis is a good method to improve the heating process of the magnetic particles injected within tissues. This paper analyzes the thermal effects induced within malignant tissues by the magnetic systems like: magnetite and Fe-Cr-Nb-B when an external time-dependent magnetic field is applied. The heat generation by Néel and Brown relaxations was modeled using the thermal and magnetic properties of the Fe-Cr-Nb-B particles experimentally determined. A lognormal particle size distribution was considered for these magnetic systems with dimensions from 5 nm to 30 nm. After their injection at the center of the tumor, according to the solution of the transient convection-diffusion equation in a porous medium, the mass concentration of the particles within ferrofluid has a spatial and temporal distribution. The ferrofluid injection process was modeled using the Brinkman equations. The ferrofluid injection rate during the injection process influences significantly the spatial distribution of the particle concentration and temperature field within tumor. Higher values of the ferrofluid flow rate determine a strong convection of the particles to the tumor center. As a consequence, the temperature gradients within tumor are smaller. The performance in Magnetic Hyperthermia of Fe-Cr-Nb-B magnetic systems is discussed.

Design and validation of magnetic particle spectrometer for characterization of magnetic nanoparticle relaxation dynamics.

The design and validation of a magnetic particle spectrometer (MPS) system used to study the linear and nonlinear behavior of magnetic nanoparticle suspensions is presented. The MPS characterizes the suspension dynamic response, both due to relaxation and saturation effects, which depends on the magnetic particles and their environment. The system applies sinusoidal excitation magnetic fields varying in amplitude and frequency and can be configured for linear measurements (1 mT at up to 120 kHz) and nonlinear measurements (50 mT at up to 24 kHz). Time-resolved data acquisition at up to 4 MS/s combined with hardware and software-based signal processing allows for wide-band measurements up to 50 harmonics in nonlinear mode. By cross-calibrating the instrument with a known sample, the instantaneous sample magnetization can be quantitatively reconstructed. Validation of the two MPS modes are performed for iron oxide and cobalt ferrite suspensions, exhibiting Néel and Brownian relaxation, respectively.