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Effects of Nanostructure and Dipolar Interactions on Magnetohyperthermia in Iron Oxide Nanoparticles Juan Manuel Orozco-Henao, Diego Fernando Coral, Diego Muraca, Oscar Moscoso-Londoño, Pedro Mendoza Zélis, Marcela B. Fernández van Raap, Surender K. Sharma, Kleber R. Pirota, and Marcelo Knobel J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00900 • Publication Date (Web): 24 May 2016 Downloaded from http://pubs.acs.org on May 24, 2016

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Effects of Nanostructure and Dipolar Interactions on Magnetohyperthermia in Iron Oxide Nanoparticles J. M. Orozco-Henao,† D. F. Coral,‡ D. Muraca,∗,† O. Moscoso-Londoño,† P. Mendoza Zélis,‡ M. B. Fernandez van Raap,‡ S. K. Sharma,¶ K. R. Pirota,† and M. Knobel†,§ †Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas (UNICAMP), 13083-970 Campinas, SP, Brasil. ‡Instituto de Física de La Plata (IFLP- CONICET), Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), c.c. 67, 1900 La Plata, Argentina. ¶Department of Physics, CCET, Federal University of Maranhão, São Luis, Maranhão, Brasil. §Laboratório Nacional de Nanotecnologia (LNNano/CNPEM), Rua Giuseppe Máximo Scolfaro 10000, 13083-100, Campinas, São Paulo, Brasil. E-mail: dmuraca@ifi.unicamp.br Abstract Magnetohyperthermia properties of magnetic nanoparticle colloids are strongly affected by their intrinsic magnetic properties and dipolar interaction among them. The intrinsic magnetic properties are related to nanoparticles (NPs) size, geometry, phase

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composition, magnetic anisotropy as well as saturation magnetization. The dipoledipole interactions are determined by colloid nanoparticle concentrations and the possible existence of clustering on the colloidal suspension. Here we have observed that oxygen atmosphere and pressure changes during the final stage of thermal decomposition are critical to modify the size of the iron oxide NPs from 8 nm to near 20 nm, and consequently their overall magnetic properties. Size dependent magnetic parameters such as anisotropy, magnetic moment per particle, blocking temperature and dipolar interaction energy were inferred using different phenomenological approaches. A detailed magnetohyperthermia analysis was performed by applying the linear response theory. A good correlation between experimental and theoretical specific absorption rate (SAR) values were obtained for frequency of 260 kHz and applied field of 52 kA/m. These results were observed for the different sizes nanoparticles, nerveless disagreement between the experimental and the model increases at lower frequencies.

Introduction The study of magnetic materials is intrinsically interdisciplinary, combining physics, chemistry, engineering and materials science with many prospective technological applications and several open scientific challenges. In addition, nanoscale science and technology has been growing to become a broad area of knowledge, ranging from organic/inorganic chemistry to condensed matter physics, leading to a fast development of many disrupting applications. The increasing interest in nanoscale studies has both scientific and technological motivations. One of the main interests is owing to the novel physico-chemical properties (such as catalysis, electrical transport, optical, elastic or magnetic properties, among others) that are only observed in materials with at least one characteristic length in the nanometer range, and in many cases still not fully understood. Furthermore, the technological developments respond to a demand of more complex and smaller devices that can be only obtained from technologies emerging from nanoscale materials. In particular, the possible applications of


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nanodevices and/or nanomaterials for biotechnology and health are still incommensurable. Some possible applications are in cancer diagnosis and treatment. For example, in the area of diagnosis for early disease detection there are promising technologies by means of metallic nanoparticles such as gold (using the resonance plasmon), 1 or magnetic nanoparticles (using diverse resonance techniques). 2 In the area of cancer treatments, one important method is to treat a specific area from a tumor by means of raising the local temperature, known as hyperthermia (from hyper (rise) and therme (heat)). Indeed, this is not a new idea: the first hyperthermia paper was published in 1866 3 and from around 3000 B.C. the mankind have already treated illnesses by using heat. 4 The new advance that the nanotechnology introduces is the magnetohyperthermia, i.e., the possibility to heat a tissue in a very specific place of the human body that is difficult to reach by other techniques. Besides the possibility of targeting specific ill cells, the heating occurs in the nanoscale, minimizing side effects usually associated with the death of healthy cells. Both magnetohyperthermia treatments and localized drug delivery can be improved by the combination of magnetic nanoparticles with some proteins as vectors. 5 Magnetohyperthermina strongly depends on mangnetic intrinsec magnetic NPs properties. In order to improve magnetic properties such as anisotropy and/or saturation magnetization for magnetohyperthemia applications, several materials have been studied, starting from pure metallic nanoparticles of Fe, Co, or Ni to possible alloys, being the most common, the ferrite (Fe3−x Mx O4 , with M: Fe, Ni, Co, Mn) type nanoparticles. 6,7 In particular, due to the biocompatible feature of magnetite, the scientific community has been focused to use it, especially by means of core@shell structures with magnetite at the shell. 8 Although many efforts have been devoted to the study of complex nanoparticles, there are still many open questions, even from basic information such as the comprehension of basic parameters (for example size, shape and crystalline degree) on the magnetic properties. It is well known that for nanoparticles the surface effects are strongly relevant, due to the fraction of atoms on the surface in comparison with those in the volume. 9,10 For example,



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for a 10 nm nanoparticle, about 23 % of the atoms are at the surface. Furthermore, owing to an incomplete atomic coordination on the surface of the nanoparticles, the magnetic layer behavior is different from the core, and this certainly affect the overall magnetization and anisotropy of the nanoparticles. For magnetohyperthermia, drug delivery, or any biomedical application using magnetic nanoparticles, it is critical to understand as well as to optimize their physical/chemical properties, such as the composition, crystalline structure, size and shape distribution. Magnetohyperthermia effect is commonly studied by means of the so-called specific absorption rate (SAR) parameter as a merit figure for a given nanoparticle (NP) under a given excitation field condition. The SAR depends on different intrinsic properties of the nanoparticles (volume, anisotropy and saturation magnetization, for example), external field conditions (frequency and amplitude) as well as colloidal properties during the experiments, such as solvent viscosity and concentration, which modulate the magnetic dipolar interactions or possible nanoparticles agglomerations or assembling. 11–14 Different experimental studies were recently carried out trying to understand and determine the crossover between individual and collective effects on colloidal SAR experiments. Results indicate that the effect of dipolar interaction or agglomerations need to be considered for colloids above certain concentrations. 15–17 In this work we report the synthesis, structural, magnetic and magneto hyperthermia characterizations of different iron oxide nanoparticles produced by thermal decomposition method. We found that with a simple modification in the synthesis conditions, sizes and shapes can be tailored, leading to different magnetic properties. The characterization of structure, shape and sizes was performed by conventional X-ray diffraction, small angle Xray scattering and transmission electron microscopy. The magnetic characterization was performed by conventional magnetometry, with data analysis based on classical superparamagnetic theory to obtain relevant parameters of the nanoparticles, namely blocking temperature, magnetic anisotropy, effective magnetic moment distribution. The structural and


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magnetic properties are correlated with magnetocalorimetry results and the SAR values are semiempirically simulated using Linear Response Theory (LRT). 18 The data modeling is aimed on testing its validity, in search of a predictive SAR outcome for a given colloid under a given field, which constitute a powerful tool for a real therapeutic application and probably the ultimate goal of any SAR study.

Experimental details X-Ray diffraction (XRD) measurements were performed on a Phillips PW1820/1710 diffractometer using Cu Kα radiation with wavelength of 1.54 Å, and 2θ from 10o to 90o with a scan step of 0.01o /s. Thermogravimetry (TG) analysis was used to estimate the composition of the coated NPs i.e., the mass relation of iron oxide to NPs mass. Measurements were carried out on dried powder samples with a Shimatzu TG-50 and DTA-50 systems. During the measurements the samples were kept inside platinum crucibles and heated at a constant rate of 10 K/min under a flux of 50 ml/min of N2 . It was further used to express colloid concentrations as mass of iron oxide/toluene volume, and to normalize magnetization measurements. Small-angle X-ray Scattering (SAXS) experiments in toluene dispersed samples were obtained at the Brazilian Synchrotron Light Laboratory (LNLS), Centro Nacional de Pesquisa em Energia e Materiais (CNPEM), Campinas, Brazil. The measurements were carried out at room temperature using the SAXS2 beamline at a wavelength of λ = 1.822 Å. The scattering intensity was measured as a function of momentum transfer vector q (q = 4π sinθ/λ), from 0.05 to 1.6 nm−1 , where θ is the scattering angle. Transmission Electron Microscopy (TEM) images were acquired by drying a toluene dispersion of the nanoparticles on a carbon coated copper grid. The images were taken at the National Brazilian Nanotechnology Laboratory, by means of transmission electron microscopy (200 keV JEM 2010 microscope, LNNano/CNPEM), Brazil, using a TV (Gatan



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ES500W) and CCD (TVips-16MP). DC Magnetic measurements were performed to study the magnetic properties on dried powder samples using a MPMS SQUID magnetometer with fields up to 1600 kA/m (± 2 T) and temperatures from 2 to 300 K. The temperature dependence of magnetization was performed in the Zero Field Cooling (ZFC) and Field Cooling (FC) modes under an external applied magnetic field of 4 kA/m. The magnetization values are given per mass of iron oxide of the NPs. The ratio of iron oxide mass per NPs mass (including the capping) were obtained by TG measurements (see SI). Specific Absorption Rate (SAR) data from magnetic hyperthermia experiments were obtained from magnetocalorimetric experiments using a resonant R-L-C circuit Hüttinger (2.5/300) radiofrequency (RF) field generator equipped with a water refrigerated five-turn coil of 2.5 cm inner diameter. Samples were dispersed in toluene to a final sample concentration of 10 mg/mL (This concentration is define as the mass of particle (mass of iron oxide core plus organic capping) per volume of solvent). A representative aliquot of 500 μl was poured into a clear glass dewar located in the geometrical center of the coil and subjected to RF fields with frequencies between 113 kHz to 260 kHz and 52 kA/m of amplitude. Heating curves for toluene and other samples were measured using an optical fiber sensor connected to a signal conditioner (Neoptics) with a precision of ±0.1o C. SAR value is calculated as:

SAR =

c dT , [C] dt

(1)

where c is the volumetric heat capacity of toluene (103.7 J/(mol K)), and [C] the magnetic material concentration on the colloidal suspension expressed as mass of iron oxide divided by solvent volume. The relation dT /dt was evaluated, from the heating curves, at a specific temperature Teq , i.e. the temperature at which the medium without NPs reaches the thermal equilibrium under the same RF experimental conditions. For toluene, the equilibrium temperature was T=32o C. Measurements were made in triplicate. Reported values and SAR analysis were done considering the amount of iron oxide on the NPs obtained by TG analysis. 6 ACS Paragon Plus Environment

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Synthesis of magnetic nanoparticles Several chemical routes have been used to obtain iron oxide NPs for hyperthermia treatment, some of these involves the co-precipitation of Fe(II) and Fe(III) salts, 19 Fe(II) water precipitation 20 or thermal decomposition (TD) 21,22 of Fe(acac)3 , Fe(carboxylate)3 , Fe(Co)5 or Fe(oleate). Each route has its advantages and disadvantages related to bio-physicalchemical properties like colloidal stability, bio-compatibility, size distribution control, crystalline phase, shape, saturation magnetization, etc. 11 TD is one of the best synthesis procedures to obtain magnetic iron oxide NPs with narrow size dispersion, excellent size control, good crystallinity and higher saturation magnetization. However, the TD canonical route is rather limited to produce NPs with larger sizes (∼ 12 nm) and generally it is not biocompatible. For biocompatibility the nanoparticle surfaces can be polymerized with various solvents. 23,24 To increase the NPs size, above 12 nm, two or more step based seed mediated syntheses were proposed, but these processes deteriorate the quality of NPs due to the existence of crystalline defects. 25 Hence, a variation in the synthesis parameters during TD route appears to improve NPs properties. For example, Guardia et al 9 studied the influence of surfactant and reducing agent variation on the shape and size distribution. They obtained a narrow size distribution between 4 nm and 20 nm for NPs synthesized with standard TD but using oleic acid as a surfactant. More recently Muscas et. al 26 reported cobalt ferrite NPs obtained with residual oxygen content in the reaction environment during the TD synthesis, opening a new variable that has been less explored. Demortière et al reported a fine control of iron oxide NPs size through the ligand/precursor ratio and the solvent boiling point. 27 We have performed variations in the reducting agents and atmosphere during TD procedure to obtain magnetic nanoparticles displaying distinctive magnetic properties. We followed the standard procedure presented by S. Sun. 22 Iron (III) acetylacetonate (Fe(acac)3 ≥ 99%) was used as the metal organic precursor, 1,2-hexadecanediol 90% as a reducing agent, oleic acid (OA) and oleylamine (OLm) as surfactants to reduce NPs aggregation. The 7 ACS Paragon Plus Environment


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reaction was performed under a nitrogen atmosphere. Four samples were obtained with slight modifications in the final decomposition temperature, reagent concentrations and atmospheric conditions. Figure 1 shows a schematic representation of different temperature ramps used (left) and a schematic representation of different synthesis parameters and the resulting size and shape variations (right). M8 standard 8 nm NPs sample. These particles were obtained by using 1.05 g of F e(acac)3 mixed with 2.6 g of 1,2 - hexadecanediol, 1.9 mL of OA, 1.97 mL of OLm and 20 mL of benzylether at room temperature. The mixture was stirred magnetically while it was driven to 200o C at a heating rate of 2o C to 4o C per minute under N2 atmosphere. The mixture was heated to 200o C for 1 hour in N2 atmosphere. After the solution was heated to 290o C and kept at this temperature for 1.5 h. Finally the mixture was cooled down to room temperature with addition of 30 mL of ethyl alcohol to stabilize the solution. The black solution obtained was dissolved in toluene and precipitated with ethanol by centrifugation at 3800 rpm for 15 minutes. This procedure was repeated for 6 times. M5T final temperature varied sample, 5 nm NPs. The sample was obtained using the same procedure as for sample M8 . The only difference was the final decomposition temperature. Here the solution mixture was driven to 240o C for 1.5h. The procedure was repeated as mentioned above. M6S surfactant concentrations varied sample, 6 nm NPs. In this case the procedure was same as described above with only difference in the concentration of OLm and OA. Here we have used 3.5mL of OLm which is about 75 % of the standard concentration and 0.5mL of OA representing a reduction of the same amount of its initial concentration.


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O2 M19 pressure variation and presence of oxygen, 19 nm NPs.

The last sample was obtained by changing the final synthesis conditions. We have used the standard process as described above (for M8 ) with a small variation during cooling the solution to room temperature. The three neck flask was opened at 290o C to pass air for some time during cooling to room temperature.

Figure 1: left: schematic representation of the different temperature ramp used in the TD protocol; right: schematic representation of variation in the synthesis conditions and resulting shapes and sizes obtained

Results and discussion Structural and Morphological Characterization The phase purity and composition were checked using powder XRD method. The diffraction patterns for all the samples are shown in Fig. 2. All the diffraction patterns are characteristic of small size particles and confirm the formation of a pure fcc spinel-inverse iron oxide phase. The observed reflections are (220), (311), (400), (511) and (440), according to JCPDS 85O2 sample has an extra reflection at 1436 for F e3 O4 . It can also be observed that the M19

36.2o , which is due to the the presence of FeO (111), JCPDS 75-1550. From TG experiments the estimated mass fraction of iron oxide NPs was about 79 %, 78 %, 81 % and 92 % for O2 M5T , M6S , M8 and M19 respectively (see Supplementary information).



M

8

Intensity (arb. units)

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S

M

6

T

M

5 O2

M

19

Magnetite

30

45

60

75

90

Bragg's Angle (grad)

Figure 2: Diffraction pattern for each sample with magnetite Bragg diffraction at: (220) (30.09o ), (311) (35.44o ), (400) (43.08o ), (511) (56.97o ) and (440) (62.55o ). Purple star stands for a non-magnetite phase present in the sample. Dashed line: magnetite powder diffraction data. 28 O2 Figure 3 (a) shows small angle x-ray scattering patterns of M5T , M8 and M19 samples.

The scattered intensity (I) as function of q displays three main features related to NPs size, size dispersity, interparticle interference and aggregation. First, a knee (indicated with an arrow), is a signature of the primary particle size. The onset of this knee-like feature is O2 observed around q = 1 nm−1 for M5T , and shifts to lower q values for the M8 and M19 samples,

indicating larger particle size. Other intensity bump appears at q close to 0.6 nm−1 only for O2 and it is somehow smooth due to polydispersity. For the other samples this maximum M19

is outside of the measured q range. Second, an intensity depletion due to the destructive O2 interpaticle interference is observed, for sample M19 , between 0.2 and 0.3 nm−1 , providing

information on interparticle interaction nature. This feature is not so clearly observed for the other samples, because it is buried between primary particle Guinier behavior and high q scattering from aggregates, but it will be shown later that it is reflected by the proposed fitting model. The third region provides information about the nanoparticles aggregation in the suspension. At low q values, instead of a Guinier behavior, a power law intensity decrease appears. In order to obtain qualitative information about this complex colloids structure, the


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M

T

1.6

5

fit

1.4

Sphere

S(q)

1.2

10 8

0.8

0.4

S(q)

fit Mass Fractal Hard

M

1.0

0.6

M

I (arb. units)

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Sphere

0.2 0.2

0.4

0.6

0.8

1 M

O2

T

5

M

8

Mass Fractal Hard Sphere

M

0.1

O2

19

0.1

1

q (nm )

1.4 -1

fit

-1

1.2

q (nm )

19

0.1

1.0

-1

1

q (nm )

(a)

(b)

Figure 3: a) Log-Log representation of colloids scattering curves expressed as intensity (I) O2 vs. scattering vector modulus q of M5T , M8 and M19 colloids. Solid lines are the model functions (eq. 2) that best fit the experimental SAXS measures. b) Log-Log plot of the structure function S(q). Inset shows a zoom in which power law and interference between particles dependence can be seen for low and high range q values respectively. SAXS-patterns were well fitted by modeling with two kind of contributions and an incoherent background (bkg) as: ∞ I(q) =

∞ N1 Isp (q, r)SHS (q, r)g(r)dr + Smf (q, ξ)

0

N2 Isp (q, r)g(r)dr + bkg

(2)

0

where N1 and N2 are the weight of each contribution. The first contribution contains the scattered intensity Isp of spherical NPs of radius r with electronic density difference between magnetic core and liquid matrix Δρ

Isp

sin(qr) − qr cos(qr) 4 = πr3 Δρ 3 3 (qr)3

weighted with a Gaussian distribution function g(r) =

2

2 2 √1 e−(r−r0 ) /2s s 2π

(3)

that considers size

dispersity, being r0 the mean particle radius and s the standard deviation. This contribution is plotted as a dashed blue line (labeled as Sphere) in figure 3 (a) for sample M5T . The interparticle interference effects are taken into account using a hard sphere structure



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factor SHS (q, r) with the Percus and Yevick closure: 29

SHS (q, r) =

1

(4)

1 + 24fp G(fqrp ,qr)

where fp is the local volume fraction of the spherical particles within the clusters and gives information on the probability of finding NPs in the vicinity of each other1 . In this model the local monodisperse approximation is used to include the hard sphere structure factor, i.e., is assumed that a particle of a certain size is always surrounded by particles with the same size. Following this, the scattering is approximated by that of monodisperse sub-systems weighted by the size distribution 30,31 . This contribution is plotted as a continuous purple line (labeled as Hard sphere) in figure 3 (a) for M8 and M19 colloids. A second contribution accounts for the intensity excess at low q. A mass fractal model for NP aggregates following a power law 32,33 is used as a second hierarchical contribution with structure factor:

Smf (qξ) = 1 +

df Γ(df − 1) sin[(df − 1) tan−1 (qξ)] df −1 (qr0 )df (1 + 1/(qξ)2 ) 2

(5)

Here df is the mass fractal exponent (m ∝ rdf ) and ξ is the cluster radius. A monodisperse approach is considered to include the mass fractal structure factor and spherical symmetric interaction potential among particles. This contribution is plotted as a continuous green line (labeled as Mass Fractal) in figure 3 (a) for M8 and M19 colloids. In the proposed model, the first contribution accounts for the interparticle interference into the cluster, while the second contribution comes from the structure of the whole cluster, and gives information about its shape and size. Similar models were successfully used to analyze the x-ray scattered intensity from palladium NPs in a polymer matrix, 34 in SAXS experiments carried out in silica NPs droplets 35 and in SANS studies of pores distribution 2

4

2

) cos A−2 A+(A cos A G(fp , qr) = α sin A−A + β 2A sin A+(2−A + γ −A cos A+4[(3A −6) Acos 5 A2 A3 2 4 2 4 2qr, α = (1 + 2fp ) /(1 − 2fp ) , β = −6fp (1 + fp /2) /(1 − fp ) and γ = αfp /2. 1


3

−6A) sin A+6]

with A =

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in a silica ceramic. 36 For sample M5T only the mass fractal contribution was necessary to fit the entire curve. The structure function S(q) calculations allow the use of a unique contribution for M5T and two contributions for the other samples. Log-Log plots of S(q), derived as the ratio of measured scattering intensity and the intensity scattered corresponding to particles in a diluted state, are shown in figure 3 (b). For sample M5T , S(q) clearly shows a main power law dependence on q −df at lower q-range, whereas for samples M8 and M19 the power law dependence is combined with the oscillating behavior arising from the interference between scattering from particles inside the aggregates. Mean particle radius ro , standard deviation s, mean hard sphere volume fraction f p, cluster size ξ, and fractal dimension df , were used as fitting parameters (Fig 3,b)). Table 1: SAXS parameters. Mean particle radius r0 , standard deviation s (nm), local volume fraction of the spherical particles fp , cluster size ξ (nm), fractal dimension df .

Sample r0 (nm)

s (nm)

fp

ξ (nm)

df

M5T

2.23(1)

0.52(1)

-

20.10(1)

2.36(1)

M8

3.50(2)

0.70(2)

0.31(3)

16.10(2)

1.94(3)

O2 M19

9.28(1)

1.66(3)

0.46(1)

48.66(4)

2.92(8)

The estimated primary particle size from SAXS analysis is consistent with TEM imaging results. The fp values indicate that these colloids have a tendency to aggregate, being this tendency more pronounced as NPs size increase in agreement with the larger NP magnetic O2 moment, i.e for the M19 sample. The cluster shape can be estimated from df exponent

( df ∼4: spherical cluster, df ∼2: planar structures and df ∼ 1: linear structures). Non integer df indicates fractal structures. Fitted df values indicates more compact and dense O2 clusters for M19 and M5 .



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Fig. 4 (a) shows some representative TEM images for each sample. The mean particle size is obtained by simply counting more than 100 particles, and is presented in Fig. 4 (b). The samples M5T and M6S have almost a similar size distribution with mean size of 5 nm and 6 nm, respectively, which are smaller than that for the M8 sample (8 nm with spheroidal shape). The estimated size (the mean diagonal size of a non-spherical particle) for the sample O2 M19 is about 19 nm.

It is well known that for NPs, the magnetic properties are strongly dependent not only on chemical phases, but also on particle sizes and shapes. Indeed, by heating above the decomposition temperature (∼ 180◦ C), the precursors produce a high concentration of monomers (ions, Fe3+ , Fe2+ ) and when it overcomes a threshold limit of supersaturation, the nucleation process is initiated. Afterwards, the NPs grow via monomers addition and the nucleation process is limited when the monomers are below the supersaturation limit. Generally, the NPs solubility increases with the reduction of monomers concentration. After this process an Ostwald Ripening effect occurs, 37 where the NPs below certain critical sizes redissolve in the solution, hence generating new monomers which contributes towards the increasing the size of the larger NPs. In the present synthesis, the surfactant (OA) hinders the NPs aggregation and promotes the steric hindering, whereas the OLm acts as a good reducing and stabilizer agent. 38 Samples M5T and M6S are smaller than M8 . Comparing the synthesis procedure, the size reduction in sample M5T is mainly due to a reduced refluxing temperature in the synthesis process, whereas sample M6S is smaller probably owing to the excess of OLm, which is in a good agreement with previous results. 38 When the ratio of OLm and the solvent (benzyl ether, in the present case) is increased as compared to OA, the NPs size is reduced. Yanglong et. al 39 suggested that the OLm acts as a weaker ligand than oleates during the reaction. This tends to decrease the growth rate and stimulate the nucleation process with a reduction of the amount of monomers at the final growth stage. O2 As mentioned above, M19 sample was synthesized using the same reactant composition


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(a)

(b)

Figure 4: a) Representative TEM images for each sample; b) Size by simple particle counting. LogNormal fitted curve and fitting parameters 15 are given for each case. ACS Paragon Plus Environment


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and procedures that M8 , with only difference that during cooling, the solution was exposed to atmosphere oxygen; this exposure resulted in particles with 19 nm size, more than twice the expected value. There are only a few reports in the literature regarding the influence of oxygen or change in the system pressure during the synthesis. Recently, Muscas et al. reported the effect of oxygen amount and pressure variation on sizes and shapes for thermally decomposed CoFe2 O4 NPs. 26 Although the study of the influence of O2 during the heating ramp is quite different from our case, where the oxygen appears only at the final stage of the synthesis their hypothesis 26 is also fully applicable to our case: the smaller NPs with higher surface energy could be redissolved (increasing the amount of monomers on the solution) during the pressure change and favor the growth of the remaining NPs. On the other hand, at first stage, Fe3+ to Fe2+ are reduced in monomers, resulting in the formation of tiny crystallites primarily made of FeO. 40 The presence of FeO in TD method was recently reported and studied. 41 Here, the increase of monomers due to the oxygen presence favors the growth, generating a longer diffusion path from the surface to the core of the NPs, 40 limiting the oxidation process allowing the presence of a certain amount of FeO. Magnetic characterization Figure 5 shows the zero field cooled and field cooled (ZFC/FC) magnetization curves under an external magnetic field of ∼40 kA/m (50 Oe) for M8 , M5T and M6S samples, respectively. These curves display a well defined maximum in the ZFC curves. Above the irreversibility temperature (Ti ), defined as the temperature where the difference between the ZFC and the FC curves is lower than 10 %, the system is considered fully unblocked (superparamagnetic regime). Considering the mean TB (the temperature that separates the blocked regime from the superparamagnetic one) as the maximum of d(ZFC-FC)/dT, 42 the values of TB are 17.8(0.2)K, 27.2(0.4)K and 24.0(0.3)K, obtained for the M5T , M6S and M8 , respectively. From the mean TB and using the functional expression TB ≈ Kef f V/25 kB 43 (where Kef f is the effective anisotropy constant and V the mean NP volume), the calculated value of Kef f are


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3.08(0.13)×104 J/m3 , 9.36(0.16)×104 J/m3 and 8.29(0.15)×104 J/m3 for M8 , M5T and M6S samples, respectively. These values are higher than the room temperature bulk magnetite anisotropy (1.1 × 104 J/m3 ), 44 as expected due to surface anisotropy contribution (increase of Kef f as the NPs size decreases). In our case, for these three samples, the Ti is very close to TB indicating narrow dispersion and low magnetic interaction between the NPs. Above Ti the three samples obey Curie’s Law 44 and the net magnetic moment can be obtained from χ = nμ2 /3kB T, where T is temperature, χ the d.c. magnetic susceptibility, kB the Boltzmann constant, μ the NPs mean magnetic moment and, n the density of particles per mass unit that are in the superparamagnetic state. Applying Curie’s law the obtained values are 6.5×103 μB , 3.2×103 μB and 4.5×103 μB (where μB is the Bohr magneton) with particle density in paramagnetic state of 1 × 1018 kg−1 , 1.8 × 1018 kg−1 and 1.7 × 1018 kg−1 for the M8 , M5T and M6S samples, respectively. As expected, the mean magnetic moment increases as a function of particle size. In addition, if one considers that the magnetite unit cell with 56 ions (24 of Fe2+,3+ and 32 of O2− ) are 8 times the unit formula of Fe3 O4 with 4.5 μB per unit formula, a unit cell will show a magnetic moment of 36 μB and, hence, for a 5 nm diameter NPs, there are approximately 7.1×103 μB (considering the unit cell size as 8.6 Å), which is close to the obtained experimental value. Another procedure to obtain the Kef f and TB values is through the ZFC equations, within the framework of the single domain NP model for ideal non-interacting particles. Due to the proximity on the shape of the experimental ZFC curves with those for ideal systems, we decided to fit the experimental ZFC data using the canonical ZFC equation, given by 45

MZF C (T ) =

μ0 MS2 H 3Ke

∞ τ 1 T m ln TB f (TB )dTB + f (TB )dTB τ0 T 0

(6)

T

where μ0 is the vacuum permeability, f (TB ) is the blocking temperatures distribution; MS is the saturation magnetization; H is the applied magnetic field and; τm and τ0 are the measured and the characteristic time, respectively. As the values of H, MS and τm are



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known or readily determinable, we decided to keep them fixed in the fitting procedure. The fits for the experimental data using equation (6) are shown in figure 5 (continuous lines). The fitted curves are in good agreement with the experimental data. From these fits, the blocking temperature for samples M6S , M5T and M8 were 17K, 15K and 19K, respectively, along with Kef f values of 6 × 104 J/m3 , 8.1 × 104 J/m3 and 2 × 104 J/m3 respectively. The results are of the same order of magnitude than those previously obtained from the Curie law analysis. The characteristic time τ0 is another noteworthy parameter obtained from the fit with values 8 × 10−9 s, 1 × 10−9 s and 1.2 × 10−9 s for the three aforementioned samples and the obtained values lie in the range of weakly interacting superparamagnetic systems, i.e. 10−10 − 10−9 s. 43 Therefore, one can affirm that the three samples are very close to the superparamagnetic behavior. O2 However, a different magnetic trend is observed from ZFC/FC results for M19 sample.

Close to 106 K, the sample clearly exhibits a Verwey transition (VT), typically observed in magnetite, and is related to a first order structural transition at 120 K for the stoichiometric magnetite. No VT is observed for the smaller nanoparticles. This could be due to size effect. Although it is difficult to find any systematic study in the literature on variation of VT with the nanoparticles size. Several report shown, like ours, that for smaller particles (especially where the blocking temperature is below the VT), there is no VT. Below 120 K the crystalline structure is monoclinic, but above this temperature it has a cubic spinel structure (space group F d3m). Hence, the VT crystalline distortion is caused by the Coulomb repulsion +

+

between the Fe2 and Fe3 ions. 46,47 In addition, one can notice a smooth change in the ZFC curve close to 25 K, which is attributed due to surface effect. 48 The shift in the VT temperature might be due to the presence of small iron deficiency in magnetite, 49,50 or size effects on magnetite NPs. 51 Unfortunately, the VT partially overlaps the broad superparamagnetic transition, making it difficult to obtain the TB for this sample. Nevertheless, it is worth noting that Ti temperature is close, but below room temperature. Thus, the NPs are almost unblocked, or near the unblocked regime at room temperature.


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O2 The magnetic behavior for M19 is similar to one reported by Guardia et al. 9 for ∼ 45 nm

magnetite nanoparticles synthesized by TD. They found that the maximum TB was above the room temperature and strongly affected by the interactions among particles. They also studied a set of NPs with sizes comparable to our samples (around (∼ 17 nm), 9 but they O2 sample has a very good did not observed any VT. In fact, the Fe3 O4 phase on the M19

stoichiometry. As it was previously mentioned, a small amount of FeO could be present for O2 the M19 sample. The FeO phase is antiferromagnetic, with possible Néel temperature from

200 K (bulk) to 240 K (in nanostructures), 41,52 whereas the Fe3 O4 is ferrimagnetic. One can notice from ZFC/FC data that only a quite smooth change on FC measure can be observed on that range of temperatures. Figure 6 shows the magnetization as a function of the applied field at different temperatures for all the samples. The inset zooms in low applied fields. No coercive field is observed O2 samat 300 K for the M8 , M5T and M6S , whereas a value of ∼ 557 A/m is found for the M19

ple. The saturation magnetization at 300 K (obtained from Langevin formalism described later) were 54.0 Am2 /kg, 50.6 Am2 /kg, 69.5 Am2 /kg, 84.8 Am2 /kg for the M5T , M6S , M8 and O2 M19 , respectively. The reduction of saturation magnetization with the decrease of NPs size

could be ascribed to surface spin disorder 9,51 or collective oscillation. 53 O2 Magnetization loops for M19 at 2 K show a smooth vertical shift towards higher magne-

tization. This could happen due to the existence of two anisotropy contributions (see inset, change of slope below 39.8 kA/m) because of the presence of two phases (Fe3 O4 and FeO), or an extra energy term owing to the surface anisotropy effect. The first one would arise from part of the spins that are present in the inter-phase between Fe3 O4 -FeO that remain uncompensated 40 and the second one would also be due to uncompensated spins, but with an external surface of the Fe3 O4 . However, no exchange-bias effect is observed by measuring a field dependence magnetization in FC condition from above 300 K in a field of 2 T. Above TB , the magnetic behavior is well described by the superparamagnetic theory, 54 which considers each particle as a set of N atoms that rotate coherently resulting in an



M8

4

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ZFC

0

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Figure 5: ZFC/FC curves for the different samples under an applied field of ∼ 4kA/m (50 Oe). ZFC fitted curves for M8 , M5T and M6S are shown as continuous lines. Verwey transition O2 point is highlighted in figure (d) for sample M19 . effective particle magnetic moment of N μ with negligible anisotropy. As the model considers each particle as a classical magnetic moment, the usual procedure of paramagnetic theory can be used to derive the Langevin function that describe the magnetization of a magnetic NPs system. In order to take into account the particles size polydispersity, a Log-Normal distribution of the moments is usually included in the magnetization function ∞ μL

M (H, T ) = N 0

μ μH 0 f (μ)dμ, kB T


(7)

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Figure 6: Magnetization as a function of applied field for all samples. Results for three different temperatures are shown in a ±2T applied field range. Low field behavior is shown in the insets.



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Page 22 of 40

where N is the number of particles per mass unit in the superparamagnetic regime, μ is the effective magnetic moment, f (μ) magnetic moment distribution, and kB the Boltzmann constant. The Log-Normal distribution function f (μ) is given by f (μ) =

√ 1 e 2πμσ

−

ln(μ/x0 )2 2σ

where σ is the standard deviation, x0 is the median of the distribution and μ = x0 e(σ

2 /2)

the mean magnetic moment. Nevertheless, in real systems the standard superparamagnetic model does not consider any effect on the interactions among particles, such as dipole-dipole interactions, for example. Taking into account the fact that the magnetic measurements were performed on dried samples covered by organic materials, some sort of magnetic dipolar interaction is expected. A phenomenological model that takes into account dipolar interactions was proposed by Allia et al. 55 They suggested an interacting superparamagnetic model (ISP) that considers that the magnetic moments of the particles interact in such way that they create an extra disorder on the system due to the dipolar field. Thus, this long-range interaction (or disorder effect) can be treated as an extra phenomenological temperature, T ∗ , added to the Langevin function argument, i.e T is replaced by T + T ∗ . T ∗ can be straightforwardly related to the dipolar energy using the relation D = kB T ∗ , where D = αμ2 /d3 , d is the distance between magnetic moments (particles) and α is a constant close to the unit. 55 The temperature obtained from ISP model can be written as T ∗ = αMs2 /kB N , considering d3 = 1/N and Ms = N μ. 55 The fact that the system is equally described by the Langevin function with or without the T ∗ in its argument can be used to find the relations between Nap (from eq. 7, Nre from ISP) , μap (from eq. 7 and μre from ISP) through Nap = (1 + T ∗ /T )Nre and μap = (1/(1 + T ∗ /T ))μre . T ∗ takes into account the low field susceptibility for an interacting superparamagnetic system, χ = N μ2 /(3kB (T +T ∗ )) along with a relation of the distributed magnetic moments ρ = μ2 /μ2 , magnetite density ρm and vacuum permeability μ0 : ρ/χ =

3kB N m 53 (T /Ms2 )+ 3ρ . μ0 αμ0

The linear behavior of ρ allows

one to obtain a T ∗ for each temperature in the studied interval. The room temperature T ∗ obtained from this protocol are summarized in table 2. Figure 7 shows the magnetization


Page 23 of 40

curves at 300 K with their respective L(x) function fits.


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M8 MS6 Fit

80

40

MT5 MO2 19

0

-40

-80 -150 -100 -50

0

4

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150

Figure 7: Magnetization as a function of applied field for each sample at 300 K. The dots are experimental data, while continuous lines are the fitted curve for each case by means of equation (7).

Table 2: Magnetic characterization parameters. Saturation magnetization (MS ), coercive field (Hc ), blocking temperature (TB ), dipolar interaction temperature (T ∗ ), dipolar interaction energy ( D ), effective anisotropy (Kef f ) and effective magnetic moment in B¨ ohr magnetons: (1) from Langevin fits and (2) from Curie’s Law. ∗

Expected value considering D = (4/3π)μ0 μ2ef f /d3 .

Sample

Size (±1nm) Ms (±1Am2 kg−1 )

∗∗ From

Hc vs T analysis, not shown here.

TB

T ∗ (±1K)

μef f (μB )1

μre (μB )2

D (1×10−21 J) Kef f (×104 Jm−3 )

8474(344)

1.80(0.04)

M8

8

69

24.0(0.3)

130.7(14.2)

6067(39)

M5T

5

53

17.8(0.2)

39.2(4.6)

2671(3)

2837(45)

0.54(0.02)

9.36(0.16)

M6S

6

50

27.2(0.4)

47.4(6.3)

3618(6)

3967(178)

0.65(0.09)

8.29(0.15)

O2 M19

19

85

∼300

—

11503(86)

—

5.58

∗

3.08(0.13)

1.06∗∗

By considering d as the mean magnetic dipolar interaction distance and using α and T ∗ values obtained from the Langevin fits at 300K, d were estimated to be ∼ 6 nm, ∼ 4.7 nm and ∼ 5nm for M8 , M5T and M6S , respectively. This results are close to the expected ones, considering the NPs sizes and that they were dried to do the magnetic measurements. In addition, it is worth noting that for M8 , M5T and M6S samples the μre values (obtained form 23 ACS Paragon Plus Environment


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O2 ISP model) and μef f values (obtained from Curie’ s law) are rather similar. For the M19 , even

though it is possible to fit the experimental results with a Langevin function, the obtained parameters do not have physical meaning for ISP; ZFC/FC magnetization behavior shows a blocked state for this sample even at room temperature, so the usual superparamagnetic model is not a good approximation in this case. The dipolar energy interaction for the O2 sample reported in table 2 was obtained considering the distance between the particles M19

equal to their diameter, and the effective magnetic moment was then theoretically obtained. The parameters reported in the table are in a good agreement with previously published works. 53,55,56

Magnetic hyperthermia O2 SAR measurements were performed for M8 , M5T and M19 samples by dispersing them in

toluene (colloid concentration mass of iron oxide/volume of toluene, of 7.9 mg/ml, 8.1 mg/ml O2 and 9.2 mg/ml for the M5T , M8 and M19 ). Figure 8 shows the temperature increase as a

function of time for the three samples under an a.c. magnetic field of 52 kA/m and a frequency of 260 kHz. The obtained values are 7.2(0.5) W/g, 3.9(0.1) W/g and 101.8(8.5) O2 , respectively (Eq.(1)). The calculated SAR values are in a good W/g for M8 , M5T and M19

agreement with those reported for iron oxide NPs with similar size distribution. 9,11,15 A O2 more detailed study has been further performed for sample M19 at different frequencies and

applied magnetic fields by modifying the RLC circuit configuration. It is worth noticing that under very similar synthesis condition (the only difference was the final oxygen atmosphere O2 increases approximately 14 times when compared with or pressure), the SAR value for M19

M8 . SAR properties are analyzed by means of the magnetic relaxation of single domain magnetic nanoparticles dispersed in a liquid matrix. 18 The relaxation time for magnetic NPs are governed by Neél and Brown processes, depending on the NPs characteristics and medium viscosity. The former is mainly due to the switching of the nanoparticle‘s magnetic moment 24 ACS Paragon Plus Environment

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Temperature (oC)

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Figure 8: Temperature as a function of time for the studied samples. Applied magnetic field of 52kA/m with a 260 KHz frequency. between stable states and is described by τN = τ0 exp(Kef f V/kB T), where τ0 is the attempt time of the material (commonly taken as 1 × 10−10 s − 1 × 10−9 s). 43 The Brown relaxation process is mainly due to NPs physical rotation and it is described by τB = 3ηVH /kB T, where η is the solvent viscosity and VH the hydrodynamic volume of the particles. As the dynamics of particle dipole is governed by the effective relaxation time τ , where 1/τ = 1/τN + 1/τB the smaller reversal time dominates the dynamics. Table 3 shows the theoretical Neél and Brown relaxation times calculated for our samples using parameters listed in table 2. It is infered that the reversal characteristic time τ in the present case is determined by the O2 Néel relaxation mechanism. Hence Kef f V determines the highest SAR values of the M19 ,

influenced by the nanoparticles magnetic sizes and anisotropy. Also, the nanoparticle shape (non-spherical) could affect the hyperthermia response of this sample. But considering the anisotropy values (see table 2), we expect that the SAR increase is more related to sizes than anisotropy. Under the presence of an alternating magnetic field, the NPs, due to the magnetization dynamics lag, show an out-of-phase susceptibility χ . For low enough magnetic field, χ is



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Table 3: Calculated Brown and Néel relaxation times. τ0 taken as 10−9 s. VH was obtained by considering that the organic shell of the MNPs is around 2 nm, due to the length of organic chain (AO or Olm). 57 Sample

τB

τN

M8

2.01 × 10−6 s

6.30 × 10−10 s

M5T

6.9 × 10−8 s

2.75 × 10−10 s

M6s

1.03 × 10−7 s

8.67 × 10−10 s

O2 M19

1.86 × 10−6 s

9.80 × 10−7 s

independent of the magnetic field strength. Under this condition, the so-called linear response theory (LRT) relates the system characteristic relaxation time with the energy loss due to the hysteresis loop and the out-of-phase susceptibility, 58,59 defined as χ (f, τ ) = 2πf τ χ0 /(1 + (2πf τ )2 ). Here f is the applied field frequency and χ0 the equilibrium susceptibility. The SAR value for an assembly of magnetic NPs with randomly oriented magnetic anisotropy directions is given by SAR = μ0 πf H02 χ (f, τ ), where μ0 is the vacuum permeability and H0 is the applied field amplitude. O2 experimental SAR results as a function of the squared Figures 9 (a) and (b) show the M19

applied field amplitude at a fixed frequency and as a function of frequency at a fixed applied field, respectively. Quadratic dependence on applied field is expected from the LRT theory. It is clearly seen in figure 9 (a) that, for our experimental condition, the system does not respond as predicted by the LRT theory. As already mentioned by Rosensweig, 18 under this condition it is necessary to take into account the dependence of the equilibrium magnetic susceptibility on the magnetic field. To this end, we use the field dependence magnetization curves (presented in figure 6) to extract the low field magnetic susceptibility. The SAR dependence on the applied field obtained using the approach described above is also shown in figure 9 (a). The model reproduces rather well the experimental SAR behavior.


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In order to obtain better predictions we have calculated SAR taking into account the particles size distribution obtained from TEM analysis. Hence, we calculate SAR as:

SAR =

∞ 2 0 V (D)P (D)χ (D)dD μ0 πf H0 ∞ V (D)P (D)dD 0

,

(8)

where V (D) is the NP volume and P (D)dD is volume distribution of NPs with sizes between D and D + dD. This approach allows one to obtain the dissipated energy of an arrange of a polydisperse ensemble of single domain nanoparticles by using basic characterization parameters derived from d.c. magnetization and structural properties. This model does not consider any interparticle interactions effects. Thus, for a polydisperse ensemble of non interacting magnetic NPs SAR values can be obtained by considering Eq.(8) and magnetic characterization parameters obtained on previous section. 16 In figure 9 (b) the SAR dependence on the field frequency predicted by the model is compared with the experimental results. As expected, the disagreement between the experimental and the model increases at lower frequencies. At lower frequencies, the smaller NPs are no longer in the blocked regime and linear response is less probable, and more complex magnetization process takes place, with a mixture of nanoparticles in blocked and superparamagetic regime. SAR experimental values of M8 and M5T samples were acquired for comparison. Figure 10 (a) shows the SAR values obtained at 260kHz as a function of the NPs size for samples O2 . Also, SAR values predicted by the model are shown. One observes a M5T , M8 and M19

better agreement between experimental and theoretical values for the bigger NPs. Figure 10 (b) shows the obtained out-of-phase susceptibility at various frequency values and NPs size O2 distribution function for the samples M5T , M8 and M19 , respectively. It can be seen that

for bigger NPs, the peak of overlap between the out-of-phase susceptibility and the NPs size distribution increases. This behavior explains why the SAR increases with NPs size as seen un figure 10 (b). From the observed differences between the experimental and theoretical predictions, one



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O2 Figure 9: M19 SAR. (a) SAR values as a function of squared applied field (H20 ) amplitudes for a fixed 260 kHz frequency; (b) SAR values as a function of frequency for a fixed 52 kA/m applied field. Also, in both figures the SAR dependencies predicted by Eq.(8) are shown. Volume and anisotropy obtained from d.c. measurements were used.

could consider that dipolar interactions affect the heat efficiency through τ variations. Although there are some recent and relevant scientific contributions related to magnetostatic interactions and their effect on SAR response on colloidal systems, there are still many open questions. Recently, Conde-Leboran et al. 17 reported the heating performance of magnetic NPs as a function of field amplitude and sample concentration. They observed that in collective particle regime competition between the local dipolar field observed by the particles and the applied field amplitude generates a SAR reduction, and occurs above a certain values of concentration, depending on NPs properties and field conditions. It is expected that for 10 mg/mL these effects would begin to be observed. Also, Coral et al. observed a reduction of expected SAR for similar NPs under the same experimental conditions. 60 The standard deviation of the particle size distribution function also plays a key role in order to obtain optimized SAR values. Figure 11 shows a theoretical SAR calculation O2 dependence with the deviation of the size distribution function for the M19 , M8 and M5T

samples. A similar behavior to the one reported by Reza Barati et al for MgFe2 O4 NPs 61 O2 is observed for the M19 sample in the present study. Also, for certain sizes and extremely

narrow particle size distributions, the SAR values would be optimized, as reported in previous 28 ACS Paragon Plus Environment

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Experimental data Theoretical

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Figure 10: (a) Sample nanoparticles size distribution function (continuous line) and out of phase susceptibility (dotted line) at a fixed frequency of 260 kHz and applied field of 52 kA/m; (b) experimental and theoretical SAR results obtained as a function of mean nanoparticle size. Theoretical calculations were obtained with an assumed τ0 ∼ 10−9 s.

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Figure 11: Inferred SAR values as functions of the standard deviation (σ) of the particle size O2 distribution for samples M8 and M5T and M19 works. 18,62,63 This behavior was also discussed by Coral et al. 16 by claiming that the decrease in SAR as the particles size distribution increases occurs only when the mean sizes of the NPs are fitted to maximize the heat dissipation at working condition (2πf τ (D) = 1). Otherwise the increase on polydispersity could lead to an increase in SAR. In other words, O2 one can infer that in the present work M19 is close to the optimal size range to improve the

SAR response.



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Conclusions Iron oxide nanoparticles with particle sizes from 5-19 nm were prepared using a modified thermal decomposition method. Four different samples were investigated in terms of their magnetic and magnetohyperthermia properties. We have shown that the oxygen atmosphere and pressure change during the final stage of thermal decomposition are critical to modify the size of the iron oxide NPs from 8 nm to 20 nm, and consequently their overall magnetic properties. This is in fact interesting in developing the synthesis protocols for iron oxide nanoparticles to tune the particles size, and also to improve the magnetic and magnetohyperthermia properties. The size modification was explained by considering that smaller NPs are redissolved allowing the presence of excess of monomers which leads to an increase in the sizes of the remaining ones. The measured SAR values for the nanoparticles prepared under oxygen was found to increase, mainly owing to size increase, in comparison with those obtained under similar synthesis conditions, but grown under N2 atmosphere. Considering the predicted values of SAR dependence with standard deviation of the particle size distribution, we observed that O2 nanoparticle indeed maximize the heat dissipation in our working the mean sizes of M19

conditions. From the dc magnetic properties it was possible to infer the magnetic anisotropy (1.06 ×104 J/m3 to 9.91 ×104 J/m3 ), magnetic moment per nanoparticle (2618 μB to 11500 μB ), blocking temperature (18 K to above 300 K) and magnetic dipolar interaction energy (0.55 ×10−21 J to 5.5 ×10−21 J). These magnetic results were used as an input to a theoretical model based on LRT, and good correlation between experimental and theoretical specific absorption rate values were obtained for frequency of 260 kHz and applied field of 52 kA/m, for NPs of different sizes. Our results show that LRT does not reproduce SAR data dependence in the whole studied range of frequencies and field amplitudes, reinforcing the idea that there is a need of improved analytical expression to analyze SAR data taking into account dipolar interaction and aggregation.


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Supporting Information Additional material related to thermogravimetric analysis (TG). This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement This work has been supported by the Brazilian agencies FAPESP, FAPEMA and CNPq. We thank TEM facilities of the Brazilian Nanotechnology National Laboratory (LNNano) at Centro Nacional de Pesquisa em Energia e Materiais (CNPEM)/MCTI (14825 and 14827). O. M. L. acknowledges FAPESP grant 2014/26672-8 and D.M acknowledges FAPESP grant 2011/01235-6. SAXS were measured at beam line of Brazilian Synchrotron Light Laboratory (LNLS) at Centro Nacional de Pesquisa em Energia e Materiais (CNPEM)/MCTI under proposal D11A-SAXS2 (14355). D.M. and J.M.O.H. thanks to Maria Eugenia Fortes Brollo for help during the synthesis. This work has been funded by CONICET (PIP 00720), UNLPX11/680 grants of Argentina. P. Mendoza Zélis, and M. B. Fernández van Raap are members of IFLP-CONICET, and D.F. Coral is a fellows of CONICET, Argentina.

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