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Ultrasound studies on magnetic fluids based on maghemite nanoparticles.


The field of nanotechnology has developed impressively in the last few decades. Therefore, nowadays researchers can fabricate, characterize and customize the functional properties of nanoparticles for a large range of applications [1-5]. Among the great variety of studied nanoparticles, an increased attention has been directed to the study of iron oxide nanoparticles. In nature, the most commonly encountered types of iron oxides are magnetite ([Fe.sub.3][O.sub.4]), maghemite ([gamma]-[Fe.sub.2][O.sub.3]), and hematite ([alpha]-[Fe.sub.2][O.sub.3]) [6, 7]. Currently, iron oxide particles are being used in magnetic storage media, catalysis, or for magnetic ink and pigments [8, 9]. Iron oxide nanoparticles have been also used in a number of biomedical applications for the diagnosis and treatment of many diseases. They have been used as contrast agents for magnetic resonance imaging (MRI) especially for the diagnosis of tumors and soft tissues [1, 10], Recent studies [9-15] highlighted the efficiency of superparamagnetic iron oxide nanoparticles (SPOIONs) in enhancing the image contrast of MRI images of liver and lymph nodes, thus helping physicians and medics all around the world to better diagnose certain disease in the early stages. Due to their superparamagnetic properties, which prevent particle aggregation, magnetite and maghemite nanoparticles are the ideal candidates for many biomedical applications [10, 16], SPIONs have been also used in drug targeted tumor therapies due to their unique ability to be guided by an external magnetic field directly to the affected area, thus enabling a reduction of the treatment dose and minimizing the side effects of the cancer treatment [17, 18].

In order to improve the biological properties of magnetic nanoparticles, researchers have chosen to encapsulate them in different biological polymers. Among them, dextran has been used for this purpose due to its biocompatibility, biodegradability, and its improved transfection efficiency. These qualities make it suitable for its use in biological systems [11]. Other advantages that make dextran a good candidate for encapsulating iron oxide nanoparticles is its nontoxicity, as well as its low price [11, 19]. Furthermore, there are studies [11, 20] proving that dextran-stabilized magnetite particles remain longer in the blood stream, thus allowing access to macrophages located in lymph nodes, liver or kidney tissues.

The United States Food and Drug Administration (FDA) has already approved the use of a number of nanoparticles with iron cores and carbohydrate coatings [21]. In 1996, the first nanoparticle-based iron oxide imaging agent (Feridex I.V.-ferumoxides) has been approved to be clinically used for the detection of liver lesions by the FDA [21]. In this context, it is understandable why dextran coated iron oxide nanoparticles are of great interest for future biomedical applications. A detailed understanding of the properties possessed by dextran coated iron oxide nanoparticles could improve the diagnosis and treatment methods which could in turn help improve the life of patients worldwide.

In this paper, the particle size and morphology of the maghemite and dextran coated maghemite was evaluated by dynamic light scattering (DLS), transmission electron microscopy (TEM), and scanning electron microscopy (SEM).

Moreover, the present research is focused on ultrasound studies on magnetic ferrofluid, such as maghemite and dextran coated maghemite. Ultrasound velocity and attenuation are experimentally determined, for the three solutions. The velocity is used in a finite elements model as target for an inverse problem, providing the elastic constants of the [gamma]-[Fe.sub.2][O.sub.3] nanoparticles.


Dextran. H([[C.sub.6][H.sub.10][O.sub.5]).sub.x] OH (MW ~40,000), was purchased from Merck. Iron dichloridc tetrahydrate (Fe[Cl.sub.2] x 4[H.sub.2]O), iron trichloride hexahidrate (Fe[Cl.sub.3]6[H.sub.2]O), sodium hydroxide (NaOH), hydrochloric acid (HCl), and perchloric acid (HCl[O.sub.4]) were purchased from Merck. Deionized water was used in the synthesis of nanoparticles.

The synthesis of [gamma]-[Fe.sub.2][O.sub.3] ferrofluid was carried out as reported in other papers [22, 23]. The ferrous chloride tetrahydrate (Fe[Cl.sub.2]-4[H.sub.2]O) in 2 M HCl and ferric chloride hexahydratate (Fe[Cl.sub.3]-6[H.sub.2]O) were mixed ([Fe.sup.2+]/[Fe.sub.3+] = 1/2). The final ion concentration (0.38 mol [L.sup.-1]) of maghemite ferrofluid was determined by redox titration [24], The precipitate was centrifuged and treated repeatedly with perchloric acid (3 mol [L.sup.-1]) solution until the [Fe.sub.2+]/[Fe.sub.3+] ratio in the solid was ca. 0.05. After the last separation by centrifugation, the particles were dispersed into dextran (10 g in 100 mL of water) in agreement with the previous reported studies [25].


Particle Size and Morphology

The particle size was measured using TEM and DLS. The DLS measurements were conducted at 25[degrees]C [+ or -] 1[degrees]C using a SZ-100 Nanoparticle Analyzer from Horiba. Before DLS analysis, the samples were diluted in distilled water. The hydrodynamic diameter of the particles was determined from the diffusion coefficient using the Stokes-Einstein equation for the diffusion of spherical particles through a liquid [26].

The mean hydrodynamic diameter and the size distribution profile of the [gamma]-[Fe.sub.2][O.sub.3] and DMNp determined using DLS technique are presented in Fig. 1. For both samples, the intensity distribution of particle sizes obtained by DLS showed one populations. Therefore, we can say that the aggregation state of the particles was minimal. The particle size distribution of [gamma]-[Fe.sub.2][O.sub.3] and DMNp determined by DLS technique revealed that the particle size distribution of [gamma]-[Fe.sub.2][O.sub.3] nanoparticles ranges from approximately 8 to 34 nm with a mean particle size of 17 nm (Fig. 1a), while the particle size distribution of DMNp nanoparticles ranges from approximately 12 to 40 nm with a mean particle size of 21 nm (Fig. lb).

By the TEM technique, we can easily distinguish only the maghemite cores from carbon-coated copper grids (Fig. 2). Because of low electron density, the dextran was not visualized. The TEM investigations were performed using a FEI Tecnai 12 (FEI Company, Hillsboro. OR) equipped with a low-dose digital camera from Gatan Inc. (Pleasanton. CA). For the preparation of the samples, a drop of solution used for DLS measurements was deposited on a copper grid previously coated with carbon film.

The higher magnification TEM images (Fig. 2a and c) showed that the nanoparticles are uniform with a spherical shape. The size distribution for [gamma]-[Fe.sub.2][O.sub.3] was determined from TEM micrographs by measuring the mean diameter of approximately 600 particles. The average grain size of the monodisperse magnetic ferrofluid estimated from TEM was 9.5 [+ or -] 0.5 nm (Fig. 2b).

The morphology of the particles was also investigated by SEM. The SEM measurements were performed using a Quanta Inspect F microscope (FEI Company), equipped with an energydispersive X-ray spectrometer (EDS). The morphological analysis of the maghemite and DMNp has been investigated by SEM technique (Fig. 3).

The analysis of the SEM image of synthesized [gamma]-[Fe.sub.2][O.sub.3] and DMNp presented a clear picture with dense nanoparticles for both samples. On the other hand, the nanoparticles were spherical in size for both samples. The average grain size of the maghemite evaluated from SEM was 10.7 [+ or -] 0.5 nm. These values were in good agreement with the results obtained by TEM. The hydrodynamic diameter determined for [gamma]-[Fe.sub.2][O.sub.3] and DMNp exceeded the particle size of the magnetite core visualized by TEM and SEM in two and three times, respectively. According to the studies conducted by Barbosa-Barros et al. [27], the superior value of the hydrodynamic diameter in comparison with the size noticed by TEM could be explained by an agglomeration process as a consequence of high ratios of iron/polymer.

Ultrasonic Measurements and Results

Ultrasonic Measurements. The measurements were performed using a H5K transducer (General-Electric, Krautkramer), having a central frequency of 5 MHz and a very short burst. In order to acquire the ultrasonic signals, a Tektronix DPO 4014B oscilloscope was used (Fig. 4). For these measurements. 100 mL of tested solutions were kept at constant temperature during the measurements.

The reference signal is obtained by partly filling the cup with distilled water. Due to the bottom plate thickness, the first reflected signal is made of a series of closely packed re-emitted attenuated signals caused by the waves in the aluminum bottom plate. The second echo is preceded by small amplitude echoes, which are coming from waves propagating in the aluminum cup and re-emitted in the fluid. The main echo is, however, clearly visible with its succession of echoes from the flat bottom of the cup. The third echo is similar to the second but is preceded by two series of secondary echoes due to internal reflections in the cup. The time lapse between the main three echoes is used to calibrate the setup. Using the known velocity of ultrasonic waves in pure water at the given temperature, the distance d = 24.53 mm between the transducer face and cup bottom can be determined with an accuracy better than 0.01 mm. The samples are successively filled in the aluminum cup, to the same level as the reference distilled water. The three echoes are determined for each sample. For best results, the time lapses are determined between each pair of corresponding echoes in pure water and in the inspected fluid respectively. In this way, changes in the signal due to the setup are the affecting the signals in the same manner, so only the fluid is influencing the echoes (Fig. 5). By using proprietary software, we have determined the time lapse by using the cross-correlation method, with an accuracy of [+ or -] 1 ns. Samples' velocity can provide information on the concentration of solutions if information exists for the pure components of the solution. The attenuation was determined based on the maximum amplitude (Al, A2, and A3) of the echoes and the distance traveled in the fluid (2d) according to the formula:

[alpha] = 1/2d ln [A.sub.2]/[A.sub.1] (Np/m). (1)

The measured parameters are presented in Table 1. The presence of [gamma]-[Fe.sub.2][O.sub.3] nanoparticles in water reduces the ultrasonic velocity by 12.44 m [s.sup.-1] (0.8% reduction) compared to deionized water at room temperature (23.2[degrees]C) but increases signal attenuation 3.6 times compared to water.

Dextran. on the contrary, increases the ultrasonic wave velocity by 24 m [s.sup.-1] (1.6% increase) compared to water, and the attenuation is only thre times higher.

The mixture of dextran and [gamma]-[Fe.sub.2][O.sub.3] has, as expected, a velocity between those of the separate solutions, with only 19.43 m [s.sup.-1] higher than the velocity in water (1.3% increase) but a considerably higher attenuation.

The ultrasound velocity of dextran 10% is in good agreement with Akashi et al. [28], proving that the fluid medium is nondispersive. It is well known that acoustic attenuation is proportional to the square of the frequency, so that no comparison can be made with the attenuations presented in the same reference at 200 MHz. For this reason, the attenuation of dextran 10% can be compared with good accuracy against the results of Hawley et al. [29], at comparable frequencies. These results confirm the methodology and further investigations have been performed.

Finite Elements Simulation of Ultrasound Propagation. The plane wave propagation in a liquid, in which ultrasound propagates with a velocity c, is defined by the following partial differential equation, written for the acoustic wave pressure [p.sub.a]:

[[partial derivative].sup.2]/[partial derivative][t.sup.2] = [c.sup.2] p-d. (2)

The acoustic pressure variation produces local harmonic motion of the liquid particles. The local velocity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], can be related to the local acoustic pressure by the formula:

[[rho].sub.0][partial derivative][[??].sub.a]/[partial derivative] = - [nabla][p.sub.a], (3)

which in fact relates the local acceleration to the pressure gradient.

Elastic wave propagation in solids produces small displacements [bar.U]=u[bar.i] + v[bar.j] + w[bar.k], which depend on position, producing thus strain and according to the constitutive equations of the material, generate mechanical stresses. The differential equation of motion is

([lambda] + [mu]) [nabla]([nabla] x [bar.U]) + [mu][nabda][bar.U]=[rho][??], (4)

in which [lambda] and [mu] are the Lame coefficients of the material, which can be related to the engineering constants E (Young modulus) and [upsilon] (Poisson coefficient) by the formulas:

[lambda] = Ev/(1+v)(1-2v), [mu] = E/2(1+v). (5)

The finite element method (FEM) can be applied to solve for the interaction between elastic waves propagating in the fluid and in the immersed elastic solid nanoparticles. Our model is three dimensional compared to a similar two-dimensional approach by Galaz et al. [30],

The first major issue is the small size (~10 nm diameter) of the nanoparticles compared to the wavelength of the ultrasonic waves in water (~0.3 mm at 5 MHz). A domain 50 nm X 50 nm x 1,000 nm has proven to be adequate for 0.1% accuracy in velocity computations and reasonable computing resources.

A specialized algorithm was implemented in Matlab [31] to insert "random" spherical nanoparticles at the given volumetric ratio in the selected parallelepiped. A number of 223 spheres were thus inserted, without touching or intersections between spheres. A variance in the nanoparticles radius can also be implemented. The result is shown in Fig. 6. The geometry thus obtained for the elastic spheres and the surrounding water and was transferred to a dedicated FEM software [32] for acoustic fluid-solid interaction.

The acoustic problem is solved in the frequency domain. All time variations are assumed to be harmonic. For example, a plane acoustic wave propagating along the Oz axis, produces a pressure: [p.sub.a] = P exp[i(kz-[omega]t)], (6)

in which P is the acoustic pressure amplitude, k=[omega]/c is the wavenumber, and [omega]=2[pi]f is the angular frequency for the frequency/. Equation f. is thus transformed into

-[[omega].sup.2][p.sub.a] = [c.sup.2][p.sub.a]) (7)

and Eq. 4 consequently:

([lambda]+[mu])[nabla]([nabla] x [bar.U])+[mu][lambda][bar.U] = -[[omega].sup.2][rho][bar.U]. (8)

The continuity conditions between the two domains are set as continuity in displacements (or accelerations) and pressure in the fluid transferred as normal stress to the solid particles.

At one end of the slab is applied a harmonic pressure P at a frequency f = 5 MHz. At the opposite end, we have selected "radiation boundary condition" for a plane wave. This radiation condition allows an outgoing plane wave to leave the modeling domain with minimal reflections, when the angle of incidence is near to normal:

[bar.n]([nabla][p.sub.a])+ik[p.sub.a]=0. (9)

The main issue remains with the four lateral rectangular surfaces. Each solid sphere is acted by the incident pressure in the fluid, but perturbed by the many surrounding scattering surfaces represented by the rest of the spheres. For this reason, through these lateral surfaces are transiting scattered pressure fields produced by each sphere. Under these conditions, usual rigid wall boundary conditions are not well suited. Rigid walls produce nonrealistic reflections of the scattered fields and producing an effect of fluid waveguide with rigid boundaries, for which the wave velocity can be affected. We impose periodicity boundary conditions between opposed side surfaces. This choice coupled with the random distribution of spheres corresponds best to the theoretically infinite domain in the lateral direction (perpendicular on the propagation direction). Periodicity in two orthogonal directions generates an ambiguity along the four long edges of the parallelepiped. Our solution was to make very small chamfers along the four edges. Thus, the normal cross-section becomes an octagon with four very small faces. The very small size of the chamfers makes negligible their influence on the solution, so that reflecting boundary conditions were imposed for these surfaces. The mesh of tetrahedral finite elements covers the domain with sufficient detail for the spheres (Fig. 7).

The following results are for [gamma]-[Fe.sub.2][O.sub.3] nanoparticles of radius 4.75 nm, concentration 0.4 mol [L.sup.-1]. At a given temperature, the plane wave in pure water propagates with a velocity c0, which is known with very good accuracy as function of temperature. Consequently, the pressure at a distance L, the length of the FEM model, according to Eq. 6 is

[p.sub.a] = P cos ([omega]/[c.sub.0] L . (10)

The inverse procedure is applied for the nanoparticle suspension. The pressure [p.sub.a] is determined form the FEM solution at the opposite side (z = L), from which the equivalent velocity in the diphasic medium:

c = [omegea]L/arccos ([p.sub.a]/P). (11)

The ratio [p.sub.a]/P along the axis is plotted in stared line in Fig. 8. An iterative procedure can fit the velocity in the diphasic medium, providing the elastic properties (E,v) of the dispersed nanoparticles, by a minimization algorithm in two variables.

The measured data, such as particle average size and shape, mass density of [gamma]-[Fe.sub.2][O.sub.3] nanoparticles and the volume ratio, allow to deduce other mechanical parameters. The ultrasonic waves new information obtained from the FEM model, coupled with velocity measurements, concern the elastic constants of the nanoparticles. The two constants (Young modulus and Poisson coefficient) are obtained in pairs, and not as two separate values. Even so, the range of pairs representing solutions to the FEM model, are useful in estimating the stiffness and brittleness of the nanoparticles. For the investigated samples, the Young modulus is the range 0.5-0.9 GPa, whereas the Poisson ratio is between 0.33 and 0.2. The best fit corresponds to a Young modulus of 0.9 GPa and a Poisson coefficient of 0.2.


The surface functionalization of maghemite nanoparticles can introduce additional functionality, which can be successfully used widely in various fields of medicine. The average grain size of the maghemite coated with dextran evaluated from SEM was in good agreement with that calculated by TEM. More than that, the superior value of the hydrodynamic diameter in comparison with the size noticed by TEM and SEM could be explained by an agglomeration process.

This paper focuses on the recent studies on ultrasound characterization of surface functionalized maghemite nanoparticles in solution. The ultrasonic experiments at 5 MHz are capable to identify important characteristics of the tested suspensions, such as the velocity and attenuation, in accordance with other authors. The FEM model allows to simulate the effective wave propagation in the fluid with dispersed nanoparticles. This is a three-dimensional model, more accurate than other existing models. The inverse problem tested in this case has provided a series of pairs of elastic constants, from which the pair offering the best fit was extracted.

Future studies will focus on the research of the toxicity contributing to the development of new industrial applications as well as ameliorate the quality of life in the population.


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Daniela Predoi, (1) Cristina L. Popa, (1) Mihai V. Predoi (2)

(1) National Institute of Materials Physics, 405A Atomistilor Street, Magurele, Romania

(2) Department of Mechanics, University Politechnica of Bucharest, Bucharest, Romania

Correspondence to: M. V. Predoi, e-mail:

Contract grant sponsor: National PN II 131/2014 project.

DOI 10.1002/pen.24501

Caption: FIG. 1. The particle size distribution of [gamma]-[Fe.sub.2][O.sub.3] (a) and DMNp (b) determined by DLS technique.

Caption: FIG. 2. The higher magnification TEM images of [gamma]-[Fe.sub.2][O.sub.3] (a) and DMNp (c). The average grain size of the monodisperse magnetic ferrofluid of [gamma]-[Fe.sub.2][O.sub.3], (b).

Caption: FIG. 3. The morphology of the particles investigated by SEM technique: [gamma]-[Fe.sub.2][O.sub.3] (a) and DMNp (b).

Caption: FIG. 4. Experimental setup.

Caption: FIG. 5. Acquired reference signal (top) and signal from Dextran 10% and [gamma]-[Fe.sub.2][O.sub.3] in water (bottom).

Caption: FIG. 6. Random distributed nanoparticles of given mean radius and volumetric ratio solid/fluid.

Caption: FIG. 7. FEM mesh used for the diphasic domain (left). Detail (right).

Caption: FIG. 8. Acoustic pressure in diphasic medium (continuous line with star markers) and in pure water (continuous line), along the central line of the domain.
TABLE 1. Measured ultrasonic properties of the three samples and water
(as reference).

                      Temperature           Velocity
Fluid                 ([degrees]C)       (m [s.sup.-1])

Water                     23.2       1,492.07 [+ or -] 0.01
[gamma]-[Fe.sub.2]        23.2       1,479.63 [+ or -] 0.03
 [O.sub.3] in water
Dextran 10%               23.2       1,516.06 [+ or -] 0.17
Dextran 10% and           23.2        1,511.5 [+ or -] 0.31
 [O.sub.3] in water

Fluid                 (Np [m.sup.-1])

Water                       0.6
[gamma]-[Fe.sub.2]          4.0
 [O.sub.3] in water
Dextran 10%                 3.3
Dextran 10% and             8.6
 [O.sub.3] in water
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Author:Predoi, Daniela; Popa, Cristina L.; Predoi, Mihai V.
Publication:Polymer Engineering and Science
Article Type:Report
Date:Jun 1, 2017
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