Size Distribution Of Magnetic Nanoparticles Research Articles

An Improved Method for Estimating the Saturation Magnetization and Core Size Distribution of Magnetic Nanoparticles Based on M-H Curve

An Improved Method for Estimating the Saturation Magnetization and Core Size Distribution of Magnetic Nanoparticles Based on M-H Curve

Synthesis and characterization of magnetic nanoparticles from raffinate of industrial copper solvent extraction plants

Abstract Magnetite nanoparticles successfully produced from the raffinate of an Iranian industrial copper solvent extraction unit. Removal of iron from leach solution is important for successful operation of hydrometallurgical recovery of copper. It includes reduction of Fe3+ to Fe2+ followed by precipitation of Al3+ as Al(OH)3, oxidation of Fe2+ to Fe3+ (the theoretical ratio for stoichiometric, Fe3+/Fe2+ = 2) and finally synthesize of nano-sized magnetite. Two different Fe2+ oxidation agents namely H2O2 and O2 were used. Using XRD, FTIR, FESEM, and TEM analysis, the phase structure, morphology, and size distribution of magnetic nanoparticles, produced under different conditions, were evaluated and compared. Under optimum conditions spherical magnetic nanoparticles with an average size of about 25 ± 3 nm can be produced. The XRD analysis of produced nanoparticles after purification of raffinate showed the slight formation of aluminum hydroxide, goethite and hematite phases. In addition, the VSM results indicate the highly ferromagnetic behavior for samples at the room temperature with a saturation magnetization of 41.25 emu/g.

Finding the magnetic size distribution of magnetic nanoparticles from magnetization measurements via the iterative Kaczmarz algorithm

The characterization of the size distribution of magnetic nanoparticles is an important step for the evaluation of their suitability for many different applications like magnetic hyperthermia, drug targeting or Magnetic Particle Imaging. We present a new method based on the iterative Kaczmarz algorithm that enables the reconstruction of the size distribution from magnetization measurements without a priori knowledge of the distribution form. We show in simulations that the method is capable of very exact reconstructions of a given size distribution and, in that, is highly robust to noise contamination. Moreover, we applied the method on the well characterized FeraSpin™ series and obtained results that were in accordance with literature and boundary conditions based on their synthesis via separation of the original suspension FeraSpin R. It is therefore concluded that this method is a powerful and intuitive tool for reconstructing particle size distributions from magnetization measurements.

AC Magnetic Nanothermometry: An Investigation of the Influence of Size Distribution of Magnetic Nanoparticles

In this paper, we investigate the influence of the size distribution of magnetic nanoparticles (MNPs) on the magnetic signal and mathematical model of ac magnetic nanothermometry (MNTM). Based on the Taylor expansion of the Langevin function, two novel and real-time temperature estimation models that consider the size distribution of MNPs are proposed. These models use the summation and ratio of odd-harmonic amplitudes of signal induced by MNPs in the differential pick-up coil, respectively. The simulation results show that there is a large difference between the harmonic amplitudes of monosized and multisized MNPs. The experiments are performed under low-frequency (117 Hz) and weak (30 Oe) sinusoidal ac magnetic field. Therefore, the influence of magnetic relaxations and truncation error on MNTM can be ignored. Experimental results show that the maximum temperature estimation error of model I is about 0.63 K with a standard deviation of 0.21 K, whereas that of model II is about 0.60 K with a standard deviation of 0.32 K in the measurement time of 1 s. In addition, the problem of relative temperature sensitivity and noise for these two models are discussed.

Investigation of magnetic properties of Fe3O4 nanoparticles using temperature dependent magnetic hyperthermia in ferrofluids

Rate of heat generated by magnetic nanoparticles in a ferrofluid is affected by their magnetic properties, temperature, and viscosity of the carrier liquid. We have investigated temperature dependent magnetic hyperthermia in ferrofluids, consisting of dextran coated superparamagnetic Fe3O4 nanoparticles, subjected to external magnetic fields of various frequencies (188–375 kHz) and amplitudes (140–235 Oe). Transmission electron microscopy measurements show that the nanoparticles are polydispersed with a mean diameter of 13.8 ± 3.1 nm. The fitting of experimental dc magnetization data to a standard Langevin function incorporating particle size distribution yields a mean diameter of 10.6 ± 1.2 nm, and a reduced saturation magnetization (∼65 emu/g) compared to the bulk value of Fe3O4 (∼95 emu/g). This is due to the presence of a finite surface layer (∼1 nm thickness) of non-aligned spins surrounding the ferromagnetically aligned Fe3O4 core. We found the specific absorption rate, measured as power absorbed per gram of iron oxide nanoparticles, decreases monotonically with increasing temperature for all values of magnetic field and frequency. Using the size distribution of magnetic nanoparticles estimated from the magnetization measurements, we have fitted the specific absorption rate versus temperature data using a linear response theory and relaxation dissipation mechanisms to determine the value of magnetic anisotropy constant (28 ± 2 kJ/m3) of Fe3O4 nanoparticles.

Application of Image Processing to Determine Size Distribution of Magnetic Nanoparticles

Digital image processing has increasingly been implemented in nanostructural analysis and would be an ideal tool to characterize the morphology and position of self-assembled magnetic nanoparticles for high density recording. In this work, magnetic nanoparticles were synthesized by the modified polyol process using Fe(acac)3 and Pt(acac)2 as starting materials. Transmission electron microscope (TEM) images of as-synthesized products were inspected using an image processing procedure. Grayscale images (800 × 800 pixels, 72 dot per inch) were converted to binary images by using Otsu’s thresholding. Each particle was then detected by using the closing algorithm with disk structuring elements of 2 pixels, the Canny edge detection, and edge linking algorithm. Their centroid, diameter and area were subsequently evaluated. The degree of polydispersity of magnetic nanoparticles can then be compared using the size distribution from this image processing procedure.

Experimental and simulation studies on the behavior of signal harmonics in magnetic particle imaging

Our purpose in this study was to investigate the behavior of signal harmonics in magnetic particle imaging (MPI) by experimental and simulation studies. In the experimental studies, we made an apparatus for MPI in which both a drive magnetic field (DMF) and a selection magnetic field (SMF) were generated with a Maxwell coil pair. The MPI signals from magnetic nanoparticles (MNPs) were detected with a solenoid coil. The odd- and even-numbered harmonics were calculated by Fourier transformation with or without background subtraction. The particle size of the MNPs was measured by transmission electron microscopy (TEM), dynamic light-scattering, and X-ray diffraction methods. In the simulation studies, the magnetization and particle size distribution of MNPs were assumed to obey the Langevin theory of paramagnetism and a log-normal distribution, respectively. The odd- and even-numbered harmonics were calculated by Fourier transformation under various conditions of DMF and SMF and for three different particle sizes. The behavior of the harmonics largely depended on the size of the MNPs. When we used the particle size obtained from the TEM image, the simulation results were most similar to the experimental results. The similarity between the experimental and simulation results for the even-numbered harmonics was better than that for the odd-numbered harmonics. This was considered to be due to the fact that the odd-numbered harmonics were more sensitive to background subtraction than were the even-numbered harmonics. This study will be useful for a better understanding, optimization, and development of MPI and for designing MNPs appropriate for MPI.

Measurement of Brownian Relaxation of Magnetic Nanoparticle by a Multi-Tone Mixing-Frequency Method

A detection scheme for hydrodynamic size distribution of magnetic nanoparticles (MNPs) is demonstrated by a mixing-frequency method in this paper. MNPs are driven into the saturation region by a low frequency sinusoidal magnetic field. A multi-tone high frequency sinusoidal magnetic field is then applied to generate mixing-frequency signals that are highly specific to the Brownian relaxation of MNPs. These highly sensitive mixing-frequency signals from MNPs are picked up by a pair of balanced built-in detection coils. The relation between MNPs' hydrodynamic size distribution and phase delays of the mixing-frequency signals behind the applied field are derived, and are experimentally verified. Iron oxide MNPs with the core diameter of 30 nm are used for the measurement of Brownian relaxation. The results are fitted well with Debye model. This study provides a volume-based magnetic sensing scheme for the real-time measurement of MNPs hydrodynamic size distribution.

Effect of the size distribution of magnetic nanoparticles on metastability in magnetization relaxation

We theoretically examine metastability occurring in magnetization relaxation for magnetic nanoparticles with size distributions. An array of magnetic nanoparticles is simulated using a spin $S=1$ ferromagnetic Blume-Capel model on a square lattice. The particle size distributions give rise to distributions of magnetic anisotropy. Including the distributions, we perform kinetic Monte Carlo simulations of magnetization relaxation at low temperatures for the Blume-Capel model. We compute the average lifetime of the metastable state from the simulations and the absorbing Markov chains method in the low-temperature limit. We also carry out similar simulations and calculations for a constant value of magnetic anisotropy for comparison. Our results suggest that the lifetime of the metastable state is determined by the smallest particle for a given system, and that the lifetime with size distributions obeys a modified Arrhenius-like law, where the energy barrier depends on even temperature and standard deviation of the distributions as well as magnetic field and magnetic anisotropy.

How the size distribution of magnetic nanoparticles determines their magnetic particle imaging performance

Spatial and temporal resolution of magnetic particle imaging (MPI), a powerful technique for biomedical imaging, depends crucially on the magnetic properties of the magnetic nanoparticle (MNP) tracer. The authors establish the relation of the static and the dynamic magnetization behavior of various MNP preparations to their MPI performance. While MNPs with a mean diameter of 6 nm achieve only 0.2% of the theoretical maximum amplitude of the third harmonic (at 25 kA/m drive field strength), those with 19 nm diameter attain 57%. The good performance of Resovist, a clinically approved contrast agent for magnetic resonance imaging, is explained by the presence of MNP aggregates.

Determining the size distribution of magnetic nanoparticles based on analysis of magnetization curves

This study develops a direct scheme that is based on the magnetization curve of magnetic nanoparticles in the medium-field region above the blocking temperature to extract information on the size of particles and the uniformity thereof. The magnetization curve was fitted with a computer software that was developed in-house and based on the linear addition of the Langevin functions that correspond to particles of different sizes. Numerically generated curves demonstrate that a standard deviation in volume of 10% generates a variation in magnetization of approximately 1%. The fitting program was tested on a series of generated curves for magnetic nanoparticles with various average volumes and standard deviations, yielding results with errors of around 3%. The program was also justified using the data obtained from several published articles, and the results herein were found to agree closely with those in the articles. Magnetite nanoparticles were monodispersed in a polymer matrix and magnetic measurements were made. The obtained results were compared with transmission electron microscopy observations to further validate the developed scheme.

Estimation of the size distribution of magnetic nanoparticles using modified magnetization curves

We herein describe several practical improvements to the method of obtaining the size distribution of magnetic nanoparticles (MNPs) using the magnetization curves obtained from a water-based MNP sample. A vibration sample magnetometer (VSM) was used in place of a superconducting quantum interference device (SQUID), to reduce MNP agglomeration and sedimentation by means of vibration during the measurements. A signal preprocessing method using background rejection was applied to improve the measurement technique for lower concentrations of water-based MNPs, because of the significance of the diamagnetic effect of water in dilute solutions. We further present the results of detailed studies using singular value decomposition (SVD) and the Tikhonov-regulated SVD method to reconstruct the size distribution of the original sample. The experiments show that the controlled use of SVD produces consistent results. Artificial oscillation found using both SVD and the Tikhonov-SVD methods indicates that the characterization of MNP using a magnetization curve could be subject to an upper limit to its accuracy for measuring size distribution.

Gravitational and magnetic separation in self-assembled clay-ferrofluid nanocomposites

We report on experimental observations of self-assemblies in colloidal dispersions of clay nanoplatelets and magnetic nanoparticles. Visual observations have been combined with small angle X-ray scattering (SAXS) in the study of several composites at a fixed clay concentration in the dilute regime, and varying ferrofluid concentrations. Our visual observations which encompass macroscopic separation in gravitational- and magnetic field, indicate that all samples present a concentrated phase and a diluted one. SAXS data obtained from each phase are consistent with the interpretation that the scattering contribution from the clay nano-platelets in the samples can be neglected in comparison with the magnetic particle contribution. The analysis of the scattered intensity is performed combining two models, one based on the global scattering function and the other allowing the extraction of the structure factor of the mixtures. The parameters of the size distribution of magnetic nanoparticles determined by both methods are in good agreement. The structure factor of the mixtures shows that on a local scale, the mixtures behave like a gas of isolated magnetic nanoparticles. It also indicates the presence of interactions between magnetic nanoparticles mediated by the presence of Laponite platelets. Such interactions could be attributed with a progressive partial phase separation between spheres and discs rather than to the formation of dense aggregates.

Linear unbiased estimators for particle size distribution of magnetic nanoparticles

We present two statistical analytical approaches to estimate the particle size distribution of magnetic nanoparticles. They are termed best linear unbiased estimator and linear minimum mean square error estimator. These approaches are implemented and quantified within the formalism of linear unbiased estimation theory. To illustrate the efficiency of the proposed approaches, we give two examples of the application to the particle size distribution analysis in ferrofluids with normal and lognormal samples. In both cases we compare the reconstruction distributions using our methods with those calculated via the electron microscopy images of the ferrofluid particles.

HTS SQUID Microscopy for Measuring the Magnetization Relaxation of Magnetic Nanoparticles

HTS SQUID microscopy is applied for measuring the magnetization relaxation of the ensembles of noninteracting Fe/sub 3/O/sub 4/ nanoparticles dispersed in rigid polymer matrix preventing nanoparticles from agglomeration. Transmission electron microscopy (TEM) is used to determine the size distribution of magnetic nanoparticles and to control the homogeneity of their spatial distribution in the matrix. High sensitivity of SQUID microscope allows us to study samples at low contents of the magnetic component (0.1-0.5 vol%) magnetized in low magnetic field (/spl sim/10/sup -4/ T) produced by a low-inductance coil with short switching time (20 /spl mu/s). A low content of the magnetic component provides the absence of interparticle dipolar interactions, thus simplifying significantly the theoretical description of the magnetization relaxation process. The detection of magnetization relaxation starts after the external magnetizing field is switched off and proceeds for several minutes. A series of samples with a mean size of nanoparticles of about 7 nm possessing relaxation times less than 5 min was measured at a temperature of 77 K. The calculation formula based on the Stoner-Wohlfarth model for single-domain particles with a size distribution as determined from the TEM images will enable to obtain reliable data on the anisotropy constant and the saturation magnetization of Fe/sub 3/O/sub 4/ nanoparticles studied.