A correct determination of magnetic nanoparticle (MNP) properties is important for determining their best field of application [1]. These properties must be studied directly in the supporting matrix containing the MNP, because inter-particle interactions (such as dipolar magnetic, electrostatic or steric), can produce MNP structuring. In this way MNP properties, influenced by the environment, are modified, and must be taken into account especially if the MNP will be used for biomedical applications [2-4].

The imaging techniques usually used to characterize the morphology of MNP, such as Transmission Electronic Microscopy (TEM), Scanning Electronic Microscopy (SEM) or Atomic Force Microscopy (AFM), don’t provide direct evidence of the particle structuring, especially when the MNP are supported in a liquid matrix as used for biomedical applications. In microscopy techniques, the sample is diluted and dropped in a sample-holder and dried to evaporate the liquid matrix, inducing particle aggregation in a different way than that expected in concentrated suspensions. A better alternative could be Cryo-TEM, in which the sample is quickly frozen using liquid nitrogen, keeping the MNP structuring [5], nevertheless, as with TEM, the sample must be diluted, diminishing the influence of the distance-dependent interactions among particles [6-8].

The presence of MNP structures in liquid suspensions can be estimated using scattering techniques, where the scattering pattern can be modelled using a form factor that gives information about particle size and morphology, and a structure factor, that gives information about how particles are spatially assembled [9].

In this context, the Small Angle X-ray Scattering (SAXS) technique is a powerful tool to investigate the MNP structuring in a viscous liquid matrix. In this technique, the sample is illuminated with a monochromatic x-ray beam of wave-length λ. The x-rays interact with the particle’s electrons producing scattered radiation. The intensity of the scattered radiation (I) depends on the scattering angle θ, usually between 0.01 and 0.07 rad, as expressed in eq. (1).

where the scattering vector , and the electronic scattered intensity where is the electronic density difference and V _p is the particle volume, and V _p is the form factor.

Assuming spherical particles with a size distribution g(R) the scattered intensity, including a structure factor S(q) can be written as expressed in eq. (2):

This way to take into account the structure factor is called a monodisperse approach and is the simplest way to include a structure factor in the analysis. This approach simply multiplies the size-averaged form factor with the structure factor. Here it is assumed that the interaction potential between particles are spherical symmetric and independent of the particle size [10].

The use of eq. (2) has been successfully used to fit the SAXS data retrieved from scattering patterns produced by nanoparticles in suspension. In addition to the particle shape and particle size distribution, the MNP structuring also can be inferred from the correct choice of S(q) and analysis. [9,11-13].

The correct determination of aggregation using SAXS depends on choosing the correct mathematical model, this means that all the -parameters used must have physical significance and their value must be consistent with the measurement range in use.

The aim of this work is to understand the structuring of magnetic nanoparticles in colloidal suspensions using SAXS. Additionally, a methodology to analyze SAXS patterns is also proposed.

SAXS patterns obtained from two different Fe₃O₄ nanoparticles colloidal suspensions are used to determine the particle shape and size distribution. The structure is determined using two different mathematical models for S(q): mass fractal and hard sphere. While the mass fractal mode gives information about how particles are structured (chain, planar or spherical), the hard sphere model gives information about how compacted the aggregates are.

Results are compared and used to determine how interactions among particles structure the colloidal suspension and could be applied for understanding the structure of nanoparticles in different viscous matrices, providing a useful method for studying SAXS patterns in which the use of structure factors is necessary.

Fe₃O₄ nanoparticles were synthesized using the co-precipitation method [1] at 60ºC. To stabilze them in an aqueous medium, a citric acid solution (0.2 g/ml) was added to the as-synthesized particles until pH = 4.6 was reached. The mixture was stirred for 90 minutes at 60ºC. The pH of the final solution was around 7 and the volume was fixed at 50 ml.

The colloid was gravitationally decanted, resulting in two different samples, the first, labeled as S1, corresponds to the supernatant, composed of the smaller and better-stabilized particles in suspension, and the second, labeled as S2 corresponds to the pellet, composed of the bigger and less-stabilized particles precipitated at the bottom of the vessel. The shape and size of the particles was first determined using transmission electronic microscopy (TEM).

SAXS patterns were taken in the National Laboratory of Synchrotron Light (LNLS) at Campinas-Brazil, using monochromatic x-ray radiation with λ = 1.822 Å. The 2-D scattering patterns were recorded using a MAR165-CCD camera. In order to achieve a q-range of 0.06-4 nm^-1 two sample-detector lengths were used (975 and 1977 mm). SAXS pattern of water was used to join the data coming from the two lengths and to express data in absolute units (cm^-1) of the differential scattering cross section (dΣ(q)/dΩ).

SAXS patterns were fitted using Eq. (2) and the size distributions g(r) were retrieved. In order to analyze the particle structure of the samples, two procedures were employed. In the first one, global scattering functions were used for data modeling. This model, named the Beaucage model, considers approximations of Eq. (2) when q → 0 and q → ∞, resulting in a sum of Guinier and Porod functions. The second method consists in fitting Eq. (2) using two different S(q) models: a mass fractal structure factor (S _f (q)) and a hard sphere structure factor (S _HS (q)).

In Fig. 1, TEM images of both samples are shown. Images reveal that particles are mostly spherical. After counting around 100 particles the radius (R±s.d, s.d. being the standard deviation) of sample S1 is 4.5±1.0 nm and for sample S2 is 5.5±1.1 nm. As expected, the decantation process results in two different mean size samples.

Figure 1 Source: The Authors.

SAXS patterns were taken for both samples following the procedure described in the previous section. Typical two dimensional scattering patterns are shown in Fig. 2.

Figure 2 Source: The Authors.

The intensity is azimuthally integrated in order to obtain a one-dimensional SAXS pattern as shown in Figure 3. Water scattering patterns were used to express SAXS intensity data (originally expressed in arbitrary units) in the units of differential scattering cross section (dΣ(q)/dΩ).

Figure 3 Source: The Authors.

Knowledge of the nanoparticle structuring in aqueous suspensions is necessary in order to determine the applicability of such suspensions. Small Angle X-ray Scattering patterns are a good tools, widely used to determine nanoparticle structuring. Its success relies on the correct selection of the mathematical model used to fit scattering data. SAXS patterns analysis of both colloidal suspensions reveals that the better stabilized colloid is composed of smaller nanoparticles in comparison with the less stabilized colloid. The results show that the aggregation is higher in the less-stabilized colloid having bigger particles, this because the bigger the particle the stronger the magnetic dipolar interaction. For the better-stabilized colloid, particles are aggregated in 2-dimensional structures, for the less-stabilized colloid an almost spherical aggregation was determined. The fitted hard sphere radius values, determined with hard sphere model, confirm that the particles in colloid S1 are more separated and that particles in colloid S2 are more compacted. The structural data obtained with SAXS modelling are in agreement with the parameters measured using TEM, validating their use.