# Classification of Magnetic Nanoparticle Systems—Synthesis, Standardization and Analysis Methods in the NanoMag Project

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## Abstract

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## 1. Introduction

**Figure 1.**Biomedical applications of magnetic nanoparticles. Both single- and multi-core magnetic nanoparticle systems as shown in the TEM images are used in the applications.

**Figure 2.**Analysis techniques used in the NanoMag project for the characterization and analysis of synthesized single- and multi-core nanoparticles shown in the TEM (transmission electron microscopy) images in the middle of the figure.

**Figure 3.**Schematic pictures of magnetic (

**a**) multi-core particles and (

**b**) single-core particles. The definitions of the size parameters of the two different particle types are also shown in the figure. See the text for an explanation of the compartments.

_{0}is the intrinsic relaxation time of the magnetic nanocrystals, K the magnetic anisotropy, V

_{C}the volume of the nanocrystals, k the Boltzmann constant and T is the temperature.

_{H}is the hydrodynamic volume (given by 4πr

_{H}

^{3}/3, where r

_{H}is the hydrodynamic radius) of the magnetic nanoparticles (taking into account the particle surface layer and the volume of carrier liquid the particles drags along when rotating) of the particles and η is the viscosity of the carrier liquid in which the particles are dispersed. The total relaxation time, τ

_{eff}, the magnetic nanoparticles will undergo is given by the effective relaxation time combining both the Néel and Brownian relaxation time according to:

_{R}can be defined as

_{R}, can approximately be seen in the AC susceptibility vs. excitation frequency, i.e., AC susceptometry (ACS) response in the same frequency range as the peak in the out of phase component and a decrease in the in-phase component. Figure 4 shows calculated values of the Néel, Brownian and effective relaxation frequencies vs. nanocrystal diameter for a single-core particle with a physical size equal to the magnetic size and a physical size equal to 100 nm, respectively. The parameters determining whether Néel or Brownian relaxation dominates for a magnetic nanoparticle system dispersed in a carrier liquid at a given temperature, are the mean sizes, size distribution, the magnetic material properties (through the magnetic anisotropy) and the viscous properties of the liquid (through the viscosity of the carrier liquid). At a specific temperature, the Néel relaxation depends mainly on the intrinsic properties of the nanocrystals (size and magnetic anisotropy) whereas the Brownian relaxation depends mainly external properties (carrier liquid viscosity). Both the Néel and Brownian relaxation mechanisms are affected by nanocrystal interactions and by the magnitude of the applied external measurement field (which is not taken into account in Figure 4).

**Figure 4.**Magnetic relaxation time vs. the nanocrystal size (D is the diameter of the nanocrystals) for an iron oxide based nano-sized particle system dispersed in water at room temperature, showing the Néel relaxation frequency (red), Brownian relaxation frequency (blue) and the effective relaxation frequency (green). The figure also shows the Brownian relaxation frequency of a particle with diameter 100 nm (black) and the effective relaxation (magenta) a nanocrystal will undergo positioned in that particle matrix. The parameters of nano-sized iron oxide nanocrystals used in this figure were K = 20 kJ/m

^{3}, τ

_{0}= 10

^{−9}s, η = 10

^{−3}Pa·s and zero shell thickness of the nanocrystals.

_{C}) is the number-weighted nanocrystal size distribution (log-normal function is used), r

^{H}= r

^{C}+ δ where r

_{C}is the magnetic nanocrystal radius,, ω = 2πf where f is the excitation frequency and C is a pre-factor (including temperature, intrinsic saturation magnetization and particle density), δ is the thickness of the shell surrounding the nanocrystals, and χ

_{high}is the high frequency value of the in-phase part of the susceptibility. This high frequency relaxation process is probably due to the intra-potential-well contribution of the nanocrystals to the AC susceptibility [5,7].

_{0B}>, in the Debye model. The mean value of <χ

_{0B}> is then the average DC susceptibility value of the multi-core particle system. Thus, we picture each multi-core particle as a magnetic site with a mean value susceptibility <χ

_{0B}>. Since we use a mean value of the susceptibility, <χ

_{0B}>, we make the approximation that all multi-core particles contributes equally to the DC susceptibility. The AC susceptibility response can then be expressed as [8]:

_{H}) is the hydrodynamic particle size distribution (log-normal function is used). It has been shown in many earlier studies that using the above model that the determined hydrodynamic size distribution and mean particle sizes by fitting data to Equation (7), resembles very well the intensity weighed size distribution and the Z-average size as determined by DLS analysis [5,6,7,9].

_{0N}gives the Néel DC susceptibility contribution, and α is the Cole–Cole parameter for the Néel relaxation part (0 < α < 1) that sets the width of the relaxation distribution. In addition, also in this case, it has been shown in earlier studies that using the above equation that the determined size distribution resembles very well the intensity weighed size distribution as determined by dynamic light scattering analysis.

## 2. Results and Discussion

#### 2.1. Single-Core Particle System with Néel Relaxation

^{3}, yields a nanocrystal core size in the range of 11 nm, consistent with the TEM analysis. MRX measurements on particles in a liquid carrier medium (deionized water in this case) as well as in a solid matrix confirm that Néel relaxation dominates in this particle system. Analysis by DLS resulted in a hydrodynamic diameter of 91 nm (Z-average size) indicating that some agglomeration of the coated particles had taken place, although an overestimation in DLS size due to intensity weighted statistics being dominated by a few large particles cannot be ruled out, since the obtained size distributions from the TEM images are number weighted. As a comparison, we can transform the DLS Z-average size to a particle number weighed size distribution and obtain a mean particle size of 54 nm. As seen in Figure 4, this particle system, with a nanocrystal size of 11 nm, shall undergo Néel relaxation. This is in agreement with the results of the ACS analysis.

**Figure 5.**(

**a**) AC (dynamical) susceptibility vs. frequency at room temperature of a magnetic single-core particle system (CSIC01) that shows Néel relaxation (particles dispersed in water). The solid line in the figure is from the fitting procedure to the single-core model; (

**b**) TEM image of the particle system.

#### 2.2. Single-Core Particle System with Brownian Relaxation

**Figure 6.**(

**a**) AC susceptibility vs. frequency at room temperature of a magnetic single-core particle system (CSIC04) that shows Brownian relaxation (particles dispersed in water). The solid line in the figure is from the fitting procedure to the single-core model; (

**b**) TEM image of the particle system.

**Figure 7.**MRX (magnetorelaxometry) data at room temperature of a magnetic single-core particle system (CSIC04) that shows Brownian relaxation when particles are suspended in liquid (in red), and long Néel relaxation when the particles are immobilized (in blue).

#### 2.3. Multi-Core Particle System with Néel Relaxation

**Figure 8.**(

**a**) AC susceptibility vs. frequency at room temperature of a magnetic multi-core particle system (SP02) that shows fast Néel relaxation; (

**b**) TEM image of the particle system.

#### 2.4. Multi-Core Particle System with Brownian Relaxation

**Figure 9.**(

**a**) AC susceptibility vs. frequency at room temperature of a magnetic multi-core particle system (CSIC05) that shows Brownian relaxation with a relaxation frequency at about 300 Hz. The solid line in the figure is from the fitting procedure to the multi-core model; (

**b**) TEM image of the particle system.

**Figure 10.**MRX data at room temperature of a magnetic multi-core particle system (CSIC05) that shows Brownian relaxation when particles are suspended in liquid (in red), and long Néel relaxation when the particles are immobilized (in blue).

#### 2.5. Mixed Particle Systems

**Figure 11.**(

**a**) AC susceptibility vs. frequency at room temperature of a magnetic nanoparticle system (NPG3311) that exhibits a mixture of Brownian and Néel relaxation. The solid line in the figure is from the fitting procedure to the extended multi-core model; (

**b**) TEM image of the particle system. Nanocrystals not belonging to a multi-core structure (e.g., upper right in image) are likely to give the Néel response signal.

## 3. Experimental Section

_{2}O

_{3}) in acid media. These particles were dextran coated under high pressure homogenization (HPH) conditions and magnetically fractionated to obtain CSIC04 and CSIC05. Sample NPG3311 is a suspension of citrate-coated multi-core particles synthesized by aqueous co-precipitation of Fe(II) and Fe(III). SP02 sample consists of magnetic nanoparticles encapsulated in solid polymer spheres dispersed in water. It was prepared by a controlled precipitation process of the polymer that traps the nanoparticles in emulsion droplets by solvent evaporation.

## 4. Conclusions

- Identify analysis and characterization methods that can be used to standardize measurements of magnetic nanoparticles.
- Provide valuable tools in the manufacturing process of magnetic nanoparticles and when comparing results from different labs.
- Promote the standardization techniques for both research and industrial processes.
- Provide new metrological standards for magnetic nanoparticles.

- Correlate magnetic and structural properties of magnetic nanoparticles.
- Develop new analysis methods and models for magnetic nanoparticles.
- Improve the ability to follow the whole life cycle of magnetic nanoparticle systems from synthesis stage to specific applications.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Bogren, S.; Fornara, A.; Ludwig, F.; Del Puerto Morales, M.; Steinhoff, U.; Hansen, M.F.; Kazakova, O.; Johansson, C.
Classification of Magnetic Nanoparticle Systems—Synthesis, Standardization and Analysis Methods in the NanoMag Project. *Int. J. Mol. Sci.* **2015**, *16*, 20308-20325.
https://doi.org/10.3390/ijms160920308

**AMA Style**

Bogren S, Fornara A, Ludwig F, Del Puerto Morales M, Steinhoff U, Hansen MF, Kazakova O, Johansson C.
Classification of Magnetic Nanoparticle Systems—Synthesis, Standardization and Analysis Methods in the NanoMag Project. *International Journal of Molecular Sciences*. 2015; 16(9):20308-20325.
https://doi.org/10.3390/ijms160920308

**Chicago/Turabian Style**

Bogren, Sara, Andrea Fornara, Frank Ludwig, Maria Del Puerto Morales, Uwe Steinhoff, Mikkel Fougt Hansen, Olga Kazakova, and Christer Johansson.
2015. "Classification of Magnetic Nanoparticle Systems—Synthesis, Standardization and Analysis Methods in the NanoMag Project" *International Journal of Molecular Sciences* 16, no. 9: 20308-20325.
https://doi.org/10.3390/ijms160920308