Determination of Magnetic Parameters of Maghemite (γ-Fe2O3) Core-Shell Nanoparticles from Nonlinear Magnetic Susceptibility Measurements
© The Author(s). 2017
Received: 30 December 2016
Accepted: 6 April 2017
Published: 17 April 2017
Method of determining of magnetic moment and size from measurements of dependence of the nonlinear magnetic susceptibility upon magnetic field is proposed, substantiated and tested for superparamagnetic nanoparticles (SPNP) of the “magnetic core-polymer shell” type which are widely used in biomedical technologies. The model of the induction response of the SPNP ensemble on the combined action of the magnetic harmonic excitation field and permanent bias field is built, and the analysis of possible ways to determine the magnetic moment and size of the nanoparticles as well as the parameters of the distribution of these variables is performed. Experimental verification of the proposed method was implemented on samples of SPNP with maghemite core in dry form as well as in colloidal systems. The results have been compared with the data obtained by other methods. Advantages of the proposed method are analyzed and discussed, particularly in terms of its suitability for routine express testing of SPNP for biomedical technology.
KeywordsSuperparamagnetic nanoparticles Nanoparticles of “core-shell” type Magnetic susceptibility Inductive response Non-harmonic response
PACS75.30.Cr 75.47.Lx 75.50.Dd
There are different applications of biocompatible magnetic nanoparticles (MNP) in biomedical technologies. The MNP can be applied to cell separation, immunoassay, magnetic resonance imaging (MRI), drug and gene delivery, minimally invasive surgery, radionuclide therapy, hyperthermia and artificial muscle applications (see  for example). Most of these applications require superparamagnetic state of MNP. However, nanoparticles agglomerate very easily. By this reason, the production methods of superparamagnetic nanoparticles (SPNP) are being developed. Those nanoparticles should be weakly interactive and as a result incapable to stick together.
One of the different ways to avoiding MNP agglomeration is the production of composite particles of the core-shell type . The particle core made of iron oxide is superparamagnetic, and the polymeric shell does not allow them to agglomerate. The polymeric shell serves also to functionalize nanoparticles for specific applications [1, 2]. The diameter of the nanoparticles has a high impact on the imaging quality in magnetic particle imaging. Thereby, only the magnetic core of the particle contributes to the measured signal. Thus, only the diameter of the magnetic core is important for magnetic particle imaging, but not the total size of particles. Besides, most common techniques measure the total size of the particles. It is important to have instruments for measurement of nanoparticle parameters such as magnetic moment, size and size distribution for their practical use. Complex characterization of MNP usually requires package of measurements, such as scanning- or transmitted electron microscopy (SEM, TEM), vibrating sample method (VSM) and X-ray diffraction (XRD), which is difficult to use in routine investigations. That is why simple and easy express methods are needed in investigation of magnetic nanoparticle properties.
To date, several magnetic detection techniques have been employed to measure the magnetic response of the particles with respect to a magnetic excitation field. One of them is susceptometry, i.e., detection of the response to a magnetic excitation at the fundamental frequency, the technique allowing to determine quantitatively the magnetic particle concentration in a test volume [3, 4]. The other is the relaxometry which is based on recording the time transient of the magnetic response of the particles during the off-time of a pulsed excitation field. The technique allows making a distinction between bound and unbound magnetic particles . Another technique is based on frequency mixing at the nonlinear magnetization curve of superparamagnets. This detection technique for MNP is used in immunoassay and magnetic particles determination in liquids [6–9].
Our approach for SPNP characterization is based on a nonlinear susceptibility measurement . The technique is similar to that of susceptometry, but measurements are made not on fundamental frequency but on the second harmonic of the excitation signal. It was first investigated in . As it was shown, the method allows evaluating of magnetic moment and concentration of particles very easily but it was based not only on the assumption that all the particles are superparamagnetic but also they all were equal in size. The second assumption cannot be realistic since no existing method is capable of producing the monodisperse nanoparticles. In the given work, we analyze the expansion of this approach for determination of the nanoparticle size distribution parameters in the frame of lognormal distribution model.
As one can see, the resulting response signal is composed not only from the fundamental but also from the second harmonic of the excitation being the result of the nonlinearity of the magnetic medium of the core.
Expression (4) allows to determine magnetic moment μ p of SPNP from the dependency U (2)(H) at given n, V, ω, h 0 and T.
Mean value of diameter d p and the standard deviation s d of the SPNP from the mean value can then be found from the parameters of particle distribution by diameter.
To investigate possibility of experimental determination of magnetic moment and dimensions of SPNP, the core-shell nanoparticles with core made of maghemite (γ-Fe2O3) and a polymeric shell were used. The particles were produced by homogeneous nucleation method with oligoperoxide modificator. Polymerization of monomer mixture of N-vinyl pyrrolidone (NVP) and glycidyl methacrylate (GMA) was performed initiated from the surface of the maghemite by means of peroxide fragments of polymeric modificator to obtain the polymeric shell on the surface of the MNP. The process is described in more details in [14, 15]. Three types of samples, obtained in two different ways, were investigated: one of the samples—M-12 in the form of dry powder, the second—M-13 in the form of water colloidal suspension after synthesis and the third one—M-13 after drying the suspension. The masses of the samples were 10.6, 4.1 and 61.1 mg. The part of dry substance in the colloidal suspension was 3% of the total mass of the sample.
Average magnetic moment of the ensemble of SPNP was defined by both fitting the experimental data using (4) and (7). Parameters of distribution of nanoparticle moment and consequently diameter were determined from the fit of experimental data by (7) by Levenberg-Marquardt method in assumption that nanoparticles are spherical and have equal saturation magnetization.
Results and Discussion
Results of determination of average magnetic moment and diameter of investigated nanoparticles M12, M13 and colloidal solution of M13 by different methods
Colloidal solution of M13
μ p , [μ B ]
d p , [nm]
μ p , [μ B ]
d p , [nm]
μ p , [μ B ]
d p , [nm]
Widening of X-ray diffraction peaks (Sherrer method) 
12.1 ± 0.6
4.8 ± 0.4
Transmission electron microscopy 
10.0 ± 2.2
Magnetization curve approximation in a field range 0.8 T 
9.4 ± 3.9
Approximation by U (2)(H) in a field range 0.2 T considering lognormal distribution of particles moment and diameter
8.5 ± 2.5
6.5 ± 2.4
7.6 ± 2.5
As we can see, the method of determination of SPNP magnetic moment and diameter proposed in the present work gives results that conform well with results obtained by other known methods. On the other hand, the method has some advantages. The main is the possibility to determine both the magnetic properties as well as dimensions of SPNP simultaneously together with parameters of magnetic nanoparticles distribution by size. The method is applicable to the sample in shape of dry powder as well as colloidal solutions of SPNP. This method does not require independent methods of particle size determination, but it simplifies routine measurements and permits to perform express analysis of SPNP at a stage of manufacturing as well as at stage of application. The other advantage of the proposal method is simplicity. The method does not require sophisticated and costly equipment. It can be implemented with the use of much less sophisticated magnetization system when comparing to the system used in determining of magnetic nanoparticle parameters. One of the reasons of that fact is the feature of the second harmonic response dependence on the applied bias field. Since the second harmonic response is the magnetization second field derivative, all characteristic changes of the dependency take place in a narrower field region. One of the key advantages of the method when comparing with widely used method of dynamic light scattering is the possibility to determine the core of the particle when applied to the core-shell particles.
The new method of the superparamagnetic nanoparticle size lognormal distribution parameter determination is proposed. Its advantage is the relative simplicity of measurement in limited field range and higher sensitivity for narrow distributions than approximation of magnetization curve. It allows obtaining a size distribution parameters of magnetic core for composite core-shell particles that is more difficult to do by means of electron microscopy  or dynamic light scattering  techniques. If this method is applied to recurring magnetic nanoparticles characterization, it does not need involving other techniques like X-ray or neutron diffraction line profile analysis .
There are no acknowledgements.
The idea of the study was conceived by IIS, LPP and SBU. ISS, LPP and HVS carried out the magnetic measurement of nanoparticles. IIS, LPP, SBU and OAB interpreted the experiments, and IIS and LPP wrote this manuscript. NYM and OSZ fabricated the maghemite core-shell nanoparticles. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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