Improving the Heating Efficiency of Iron Oxide Nanoparticles by

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Improving the Heating Efficiency of Iron Oxide Nanoparticles by Tuning Their Shape and Size Zohreh Nemati, Javier Alonso, Irati Rodrigo, Raja Das, Eneko Garaio, Jose Angel Garcia, Iñaki Orue, Manh-Huong Phan, and Hariharan Srikanth J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10528 • Publication Date (Web): 03 Jan 2018 Downloaded from http://pubs.acs.org on January 5, 2018

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The Journal of Physical Chemistry

Improving the Heating Efficiency of Iron Oxide Nanoparticles by Tuning their Shape and Size Zohreh Nemati1, Javier Alonso1,2,*, Irati Rodrigo2, Raja Das1, Eneko Garaio3, José Ángel García2,4, Iñaki Orue5, Manh-Huong Phan1, and Hariharan Srikanth1,*

1 Materials Institute, Department of Physics, University of South Florida, Tampa, FL, 33620, USA 2 BCMaterials, Edificio No. 500, Parque Tecnológico de Zamudio, Derio, 48160, Spain 3 Depto. de Electricidad y Electrónica, Universidad del País Vasco (UPV/EHU), Leioa, 48940, Spain 4 Depto. de Física Aplicada II, Universidad del País Vasco (UPV/EHU), Leioa, 48940, Spain 5 SGIker Medidas Magnéticas, Universidad del País Vasco (UPV/EHU), Leioa 48940, Spain. * corresponding authors: Javier Alonso: [email protected] Hariharan Srikanth: [email protected]

Abstract Magnetic nanoparticles mediated hyperthermia is a very promising therapy for cancer treatment. In this field, superparamagnetic iron oxide nanoparticles (SPIONs) have been commonly employed due to their intrinsic biocompatibility, but they present some limitations 1 ACS Paragon Plus Environment

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that restrict their heating efficiency (SAR). Therefore, we have investigated how tuning the size and shape of these iron oxide nanoparticles can be useful to enhance their hyperthermia responses. Monodisperse and crystalline iron oxide nanoparticles have been synthesized by thermal decomposition in two different shapes (spheres and cubes) in a wide range of sizes, ~10-100 nm. We have thoroughly characterized them both structurally (XRD, TEM) and magnetically (PPMS), and then we have analyzed their heating efficiency using a combination of calorimetric and AC magnetometry measurements (0-800 Oe, 300 kHz). We have been able to delimit a range of optimum sizes to maximize the heating efficiency of these nanoparticles depending on their shape. We find that the nanospheres exhibit the highest heating efficiency for sizes around 30-50 nm, while the nanocubes show a sharp increase in the heating efficiency around 30-35 nm. The SAR variation has been related to the magnetic anisotropy of the nanoparticles that depends on their size, shape, arrangement and dipolar interactions.

1. INTRODUCTION Magnetic nanoparticles (MNPs) are very promising for biomedical applications. Due to their small size, they can interact with living organisms such as cell, bacteria, etc. In addition, their magnetic response allows them to be remotely controlled and guided inside the human body. They can easily be functionalized with therapeutic drugs and ligands. As a consequence, these MNPs have been extensively investigated in the last years with prospective biomedical applications including Magnetic Resonance Imaging (MRI), drug delivery, biosensing, etc. 1– 6

. Among all these applications, magnetic hyperthermia is one of the most promising ones

especially for cancer treatment 1,7,8. Each year in the United States, more than 1.5 million people are diagnosed with cancer, and more than 500,000 die from this disease 9. Current methods for cancer treatment unfortunately can cause severe collateral damage and depending on the type 2 ACS Paragon Plus Environment

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of cancer, their efficiency is relatively limited. Therefore, a search for less aggressive and more effective treatments has become increasingly important. With this idea in mind, magnetic hyperthermia that utilizes MNPs to target, heat and destroy cancer cells in a localized and effective way is of current interest.

During the hyperthermia treatment, MNPs are injected into the patient. These MNPs will target the tumor area and once they are in the vicinity of the tumor, an external AC field with a frequency f and amplitude H is applied, and this makes the MNPs release heat. By reaching a therapeutic window typically between 40-44 ºC, cancer cells can be deactivated (dead or driven to apoptosis) without affecting the healthy ones, since in this range of temperatures, cancer cells have been shown to be more susceptible to heat than healthy tissues 1,10. In addition, it has also been shown that by rising the temperature cancer cells become more susceptible to radio or chemotherapy 11,12, thus improving the efficiency of these therapies. If we raise temperatures higher than 50 ºC (thermal ablation region), a more violent cancer cell death is induced through direct destruction of the cancer cells 1,10,13.

Using MNPs as hyperthermia mediators was first proposed in the 1950s 14. However, the first phase I clinical trials were not performed until the early 2000s in Germany (MagForce Nanotechnologies). Currently, magnetic hyperthermia is being applied for cancer treatment in several countries around the world, including Japan, Germany and China 15–17. Despite all this work, there are still several problems that restrict the clinical realization of hyperthermia. One of these problems is associated with the heating efficiency of the nanoparticles also known as Specific Absorption Rate (SAR) or Specific Loss Parameter (SLP). Traditionally, small superparamagnetic iron oxide nanoparticles (SPIONs) have been favored for magnetic hyperthermia due to their intrinsic biocompatibility, longer life time during blood circulation, lower tendency to agglomerate, etc.

18,19

. Nevertheless, these SPIONs present a series of 3

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limitations, such as relatively low saturation magnetization and coercive field values, which restrict their heating efficiency or SAR. Ideally, one would desire to increase the SAR as much as possible in order to achieve an efficient hyperthermia treatment with low amount of MNPs and small AC field amplitude values. In the last years, different strategies have been proposed in the literature in order to synthesize MNPs that possess enhanced SAR values while retaining the advantages of SPIONs (e.g. biocompatibility)20–24. As was described by Carrey et al. 25, the heating efficiency of the nanoparticles whether the MNPs are in the superparamagnetic regime or in the ferromagnetic regime, is “hysteresis loss” given by the hysteresis loop (magnetization vs magnetic field) area described by the MNPs during the AC field application. Therefore, by increasing the hysteresis loop area one can improve the heating efficiency of the MNPs.

Increasing the saturation magnetization (MS) of the MNPs is often considered a straightforward approach that has been studied for a long time in order to increase the hysteresis losses

26–28

.

The MS of iron oxide based nanoparticles can be enhanced by improving their crystallinity or reducing their surface disorder, but still the maximum attainable MS value is lesser than that of bulk Fe3O4, 92 emu/g

29

. One strategy to overcome this limitation is, for example, to use

Fe/Fe3O4 core/shell nanoparticles, since the MS of bulk iron (220 emu/g) is much greater than Fe3O4, but there can be a major problem relating to the magnetic degradation and consequently the decrease of SAR with time as we have previously discussed in

30

. In addition, one must

take into account that even if a material with high MS value (such as Fe) is employed in order to increase the “height” of the AC hysteresis loops, the “width” of these AC loops (regulated by the magnetic anisotropy of the MNPs) must also be increased to obtain noticeable hysteresis losses and therefore hyperthermic effect, as was demonstrated by Simeonidis et al. 31.

Tailoring the magnetic anisotropy of the nanoparticles can provide an alternative and more effective approach to maximize their hysteresis losses and hence their heating efficiencies, and 4 ACS Paragon Plus Environment

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several efforts have been devoted to realizing this in the last few years 32–34. Essentially, it has been pointed out that by increasing the magnetic anisotropy of the nanoparticles (which depends on several contributions, such as surface, shape, magnetocrystalline, etc.), their heating efficiency can be increased provided that the magnitude of the applied AC field is larger than the magnetic anisotropy field 35. Therefore, by changing the shape of the iron oxide nanoparticles or modifying their surface 20,23,32,36–38 one can tune the magnetic anisotropy and improve their heating efficiency. For example, Guardia et al. 36 have shown that the 19 nm iron oxide nanocubes exhibit very high SAR values (~2500 W/g at 360 Oe and 520 kHz), much higher than those typically reported in iron oxide nanospheres of the same volume; and Lee et al.

39

have demonstrated that exchange coupled core/shell [email protected]

with increased magnetic anisotropy can give rise to very high SAR values, up to 4000 W/g at 460 Oe and 500 kHz.

Finally, tuning the size of the MNPs can also help enhance their heating efficiency. However, the dependence of the SAR on the size of the nanoparticles is still not very clear. According to the commonly employed linear response theory 40,41 (Néel and Brownian relaxation), the SAR of the MNPs is supposed to exhibit a maximum around 15-20 nm, but this is only valid for small AC field amplitudes. As the amplitude of the AC field increases, a more complicated evolution of the SAR versus size is obtained, and as a result, apparently contradictory SAR vs. size results have been reported in the literatures 42–46. For examples, Lv et al. 44 and Ma et al. 47

have shown experimentally that the SAR reaches a maximum for sizes above 40 nm, while

Mehdaoui et al. 42 and Levy et al. 48 observed a maximum for an optimal size of about 15 nm. In addition, as the size of the MNPs increases and they depart from the superparamagnetic behavior, the effect of magnetic interactions needs to be taken into account 7,49,50. In general, dipolar interactions have been shown to hinder the heating efficiency of the MNPs, except in specific cases, such as when interparticle dipolar interactions favor specific arrangements of 5 ACS Paragon Plus Environment


the MNPs, such as chain-like structures

34,51–53

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, or when dipolar interactions are established

between different aggregates of MNPs 54. Although magnetic interactions are in principle not desirable, it has been shown that when the MNPs are incorporated in the cancer cells, they tend to be strongly agglomerated

55,56

and therefore dipolar interactions are likely to play an

important role in the clinical hyperthermia treatment.

One of the main problems that restricted a comprehensive comparative size dependent study of the heating properties of MNPs is the intrinsic difficulty of synthesizing “comparable” MNPs in a wide range of sizes using conventional synthesis methods 57–59. As the size of the MNPs varies, their morphology, size distribution, crystallinity, saturation magnetization, etc., also tend to change, hindering the analysis and comparison of experimental results with theoretical predictions.

In an effort to shed more light on this matter, we have employed thermal decomposition processes to synthesize iron oxide based MNPs in a wide range of sizes and with very similar characteristics, and carried out a thorough study on the evolution of the structural, magnetic and heating properties of MNPs as a function of their size (~10-100 nm) and shape (spheres and cubes). Their structural and magnetic properties have been studied using a combination of different techniques, and their heating efficiency has been analyzed using both calorimetric and AC magnetometry methods. This combination of both techniques is quite unusual, due to the lack of commercial systems that can carry out AC magnetometry hyperthermia, and has allowed us not only to analyze which particles heat better (calorimetric method) but also to understand why they heat better (AC magnetometry). This way we have been able to obtain a complete depiction on the evolution of the heating efficiency of these MNPs and the different parameters that control it. To the best of our knowledge, this is the first time that such a thorough experimental study, combining both hyperthermia techniques, has been carried out to 6 ACS Paragon Plus Environment

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follow the size and shape dependence evolution of the heating efficiency of iron oxide based nanoparticles.

2. EXPERIMENTAL SECTION

2.1 Materials Fe(III)-acetilacetonate (Fe-acac, ≥99.9%), oleylamine (OA, 70%), oleic acid (OY, 90%), ethanol (99.5%), hexane (95%), benzyl ether (98%), agarose, and tetramethyl ammonium hydroxide (TMAH, ≥97%) were purchased from Sigma-Aldrich. All materials were used as received.

2.2 Synthesis The magnetic nanoparticles were synthesized by using thermal decomposition method of Fe(III)-acetilacetonate (Fe-acac) in the presence of surfactants and Ar+ H2 gas. A three-necked flask was charged with oleylamine (OY), oleic acid (OA), and Fe-acac. The mixture was stirred magnetically under 95% Ar + 5% H2 gases for 2 hours at 130°C to remove moisture or air from the flask. The temperature was raised subsequently to 220°C. After nucleation, the temperature was raised for reflux up to 350°C, and finally the sample was cooled down to room temperature. Tuning the ratio of OA/OY essentially allowed us to control the shape of the nanoparticles. To form cubic nanoparticles the ratio of OA/OY should be 1 while for spherical nanoparticles a ratio of OA/OY ~ 0.7 was used. The reflux time, nucleation time, and the amount of precursor (Fe-acac) were varied for each sample in order to control their size. Spheres had a nucleation time of 30 min, a reflux time between 90 and 240 min, and the amount of precursor varied between 0.7 and 2.5 g; while for cubes, the nucleation time went from 30 to 60 min, the reflux time was tuned between 60 and 90 min, and the amount of precursor varied between 0.7 and

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1.8 g. The resulting nanoparticles contain a mixture of FeO/Fe3O4. To convert the remnant FeO to Fe3O4, the mixture was annealed at 175 °C for 1.5 hours and washed with a mixture of 3 ml Hexane and 97 ml Ethanol, in all cases. To synthesize the smallest 7 nm nanospheres, a slightly different route was employed: 1,2 hexadecane diol, benzyl ether, oleylamine, oleic acid, and Fe-acac was mixed in a three neck flask. Under nitrogen gas atmosphere, the temperature of the mixture was increased to 200 °C and was kept for 2 h. Subsequently the temperature was raised to 300 °C and refluxed for 1 h. After reflux the sample was cooled down to the room temperature and washed three times with mixture of 3 ml Hexane, and 97 ml Ethanol. Finally, all the samples were coated with tetramethyl ammonium hydroxide (TMAH) to make them hydrophilic and water dispersible. 2.3. Structural Characterization Transmission Electron Microscopy Images were taken by using a FEI Morgagni 268 Transmission electron microscope (TEM) operating at 60 kV. For the preparation, non-coated samples were diluted in hexane and sonicated for a few minutes. Afterwards, one drop of each sample was casted onto a Cu grid and inserted inside the TEM for imaging. X-ray Diffractograms were obtained using a Bruker AXS D8 X-ray diffractometer working in Bragg Brentrano geometry at Cu K-α wavelength. For the preparation, several drops of the each sample (dispersed in hexane) were casted onto a piece of a Si wafer and left to dry until obtaining a homogeneous layer. Dynamic Light Scattering (DLS) measurements were carried out using a Malvern Zetasizer Nano. For the preparation, TMAH coated samples were diluted (50-100 µg/ml) in a disposable 2 ml polystyrene cuvette.

2.4 Magnetic Characterization 8 ACS Paragon Plus Environment

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Magnetic measurements were carried out using a Physical Property Measurement System (PPMS) from Quantum Design, with a vibrating sample magnetometer (VSM) option. All the DC magnetic measurements were carried out with the samples in powder form pressed together inside a gel capsule. The M-T curves were recorded between 5 and 350 K following the zerofield-cooling/field-cooling (ZFC/FC) protocol. During the ZFC, the sample is cooled down in absence of magnetic field down to 5 K, and then a 50 Oe magnetic field is applied, and the magnetization is recorded while increasing the temperature. On the other hand, during FC, the sample is cooled down in presence of the same 50 Oe magnetic field, and then the magnetization is recorded with increasing temperature keeping the field applied. M-H loops were measured at 300 K, applying fields up to 50 kOe.

2.5 Magnetic Hyperthermia

Magnetic hyperthermia studies have been performed using a combination of calorimetric and AC magnetometry methods. The calorimetric hyperthermia was carried out with a commercial 4.2 kW Ambrell Easyheat LI 3542 system. Suspensions of 1 and 2 mg/ml of nanoparticles in water and in water + 2% agar were used for measurements and the magnetic field was tuned from 0 to 800 Oe. The 2% agar solution was used to restrict the physical rotation of the nanoparticles, since this simulates more realistic in vivo conditions 51. AC magnetometry was done using a homemade setup

60

on a suspension of 1 mg/ml of nanoparticles in water. The

magnetic field amplitude was tuned between 0 and 400 Oe. The frequency was kept at 310 kHz in both cases. In our experiments, the maximum product of the frequency by the magnetic field reaches a value of H.f = 1.9 1010 Am-1s-1 for the highest applied field (800 Oe). This value is higher than those considered in the literature within the safety limit, H.f ≤ 5 109 Am-1s

40

,

although there still an ongoing dicussion about this matter, and some works have suggested



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that the safety limit can reach values up to ~1010 Am-1s-1 the same order of magnitude than our measurements 1.

3. RESULTS & DISCUSSION

3.1 Structural Characterization

Monodisperse and crystalline nanospheres and nanocubes made of magnetite in a wide range of sizes (~10-100 nm) were synthesized by thermal decomposition for this study (see further details in the Experimental Section). As seen in Figure 1, for both the nanospheres and nanocubes, uniform MNPs have been successfully obtained at large scale and the sizes are well tuned (the corresponding size distributions are presented in Figure S1). The shape of these nanospheres is in general spherical or quasi-spherical, although for bigger sizes (≥ 54 nm), the nanospheres start to present a more “polyhedric” shape resembling cube-octahedrons. This transformation of the geometry of the MNPs typically happens for bigger sizes of nanoparticles 61

. For the nanocubes, the shape of the cubes is slightly deformed at smaller sizes, resembling

that of the octopods we analyzed in our previous article 33, but as the size increases, the cubic shape becomes better defined and the aspect ratio gets closer to 1. Some of the nanospheres present different contrast areas in their interior that can be related to the presence of lattice defects or facets as has been reported in the literature

62,63

. For the nanocubes instead, the

characteristic contrast areas are very similar to those reported in the case of cubic nanoparticles with concave sides 64. In addition, as we have also indicated in a previous work 65, the sides of the nanocubes correspond to {100} facets.


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Figure 1. TEM images obtained for the spherical and cubic MNPs.

As observed in Figure S1, the size distribution of these nanoparticles follows in all the cases a Log-Normal distribution, with a relatively narrow size dispersion, as it is typical in samples prepared by thermal decomposition 7,66. Only the smallest and biggest MNPs somewhat deviate from this trend. This can also be seen in the obtained values for the average size (‹D›), standard deviation (σ) and coefficient of variation (CV), as indicated in Table 1. From these values, it is clear that the smallest nanospheres, 7 and 13 nm (CV ~20%), and the biggest nanocubes, 107 nm (CV ~15%) present higher relative size distribution than the rest of the samples, and this could affect their magnetic response and heating efficiency. We can also realize from the TEM images that all the MNPs are disaggregated (the individual nanoparticles are not physically “clumped” together), which is a desirable characteristic for their biomedical applicability 67, since large aggregates of nanoparticles are more easily removed from the bloodstream by the reticuloendothelial system and can also cause problems like embolism. However, it is true that our MNPs tend to form arrays. Normally this is due to a competition between attractive (Van der Waals and dipolar) and repulsive (electrostatic) interactions 68. As inferred from the TEM images, these arrays seem to be mostly hexagonal in the case of the nanospheres while the nanocubes tend to organize forming square arrays, as it is has been reported before 69. We have verified by using DLS that this tendency of the MNPs to form arrays or clusters also happens 11 ACS Paragon Plus Environment


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when they are dispersed in water (see Figure S2). Although the samples employed for DLS were very diluted (50-100 µg/ml), it can be seen that in general both the nanospheres and the nanocubes tend to form clusters of up to a few hundred nm (~140 nm for the spheres and ~620 nm for the nanocubes), the average size of these clusters is overall smaller for the nanospheres than for the nanocubes and the evolution of the cluster size as a function of the individual size of the MNPs is quite different depending on their shape. Since the cluster formation is directly linked to the presence of interparticle interactions, these results already suggest that magnetic interactions are going to play an important role in the hyperthermic response of our nanoparticles.

Table 1. Mean size (‹D›), Standard Deviation (σ), Volume (V), Coefficient of Variation (CV), Coercive field (HC), Saturation magnetization (MS), normalized remanence (Mr/MS)

spheres 7 nm 13 nm 26 nm 33 nm 52 nm 97 nm cubes 19 nm 30 nm 36 nm 42 nm 106 nm

‹D› (nm)

σ (nm)

7.0 13.2 25.6 32.9 51.6 97.3

1.4 2.7 2.0 2.1 6.2 10.3

18.7 29.6 35.6 41.9 105.9

1.5 2.7 4.0 3.1 15.9

V (nm3)

HC (Oe)

MS (emu/g)

Mr/MS

20.0 20.4 7.8 6.4 12.0 10.5

179 1149 8780 18807 73585 477630

0 ~0 ~0 32.3 62.0 87.4

58.4 61.1 68.3 64.2 71.2 85.9

0.00 0.02 0.01 0.08 0.15 0.11

8.0 9.1 11.2 7.4 15.0

6859 27000 46656 74088 1191016

~0 33.7 86.2 277.2 327.7

76.1 67.5 67.5 92.1 87.4

0.01 0.04 0.12 0.18 0.25

CV (%)

Next, we have analyzed the crystallinity of these MNPs by XRD (see Figure 2). All the XRD data present well defined peaks, revealing the good crystallinity of the nanoparticles. It is true, however, that with increasing size the peaks become narrower, more evidently in the case of the nanospheres, suggesting some improvement in the crystallinity with increasing size. The position and relative intensities of all of the XRD peaks match well with those of magnetite 12 ACS Paragon Plus Environment

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and maghemite structure (American Mineralogy Crystal Structure Database AMCSD 0000945 and 0007898, respectively). We also tried to obtain some information from these data about the crystalline nature of our MNPs by using the Scherrer formula 70 (see Figure S3). In general, the obtained grain sizes are smaller than the TEM sizes, suggesting that our spherical and cubic MNPs are made of a few small crystallites, corroborating what had been observed in TEM images. In addition, it is important to remark that no other Fe-oxide phases, such as FeO, were observed in any of the X-ray diffractograms. This confirms that the thermal annealing of the MNPs carried out after the synthesis has allowed us to remove any remaining amount of FeO in these nanoparticles, and that they are mostly composed of magnetite/maghemite 71,72. This is important since, in principle, the presence of FeO (or other iron oxide phase different from Fe3O4) would deteriorate the magnetic response (and the heating efficiency) of the nanoparticles by reducing the saturation magnetization, although we have previously demonstrated that by carefully tuning the FeO/Fe3O4 ratio it is possible to improve the hyperthermic response by creating exchange coupled nanoparticles 32.



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Figure 2. X-ray Diffractograms corresponding to the spherical and cubic MNPs

3.2. Magnetic Characterization

In order to analyze the magnetic response of these MNPs, we have carried out DC magnetization measurements both as a function of temperature (M-T) and magnetic field (MH) (see Figure 3). The M-T curves were measured following the typical zero-fieldcooling/field-cooling (ZFC/FC) protocol. As mentioned before, during these measurements, the samples were in powder form and therefore much more agglomerated than when they were dispersed in water for the hyperthermia experiments, but these DC magnetic measurements can still provide us some useful feedback on the magnetic response and hysteresis losses of the MNPs.


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Figure 3. M-T and M-H curves for the spherical and cubic MNPs

As depicted in Figure 3, there are some clear differences in the magnetic response of the MNPs depending on their shape and size. In case of the nanospheres, the smallest 7 nm MNPs present a magnetic behavior typical of superparamagnetic (SPM) systems, with a low blocking temperature, around 55 K. The room temperature M-H loop for these 7 nm spheres also exhibits typical superparamagnetism (zero coercivity and remanence) 73, and a very good fitting of the M-H loop can be obtained using a Langevin expression with a mean size of 6.7 nm (see Figure S4). However, with increasing size, the blocking temperature displaces towards higher temperatures and a SPM behavior is no longer observed around room temperature, indicating that all the nanospheres with sizes > 13 nm are in a magnetically blocked state during the hyperthermia experiments. On the other hand, in the case of the nanocubes, even the smallest ones with a side of 19 nm, are in the magnetically blocked state at room. In addition, we can see in the M-T curves for both the nanospheres and the nanocubes that, with increasing size, a 15 ACS Paragon Plus Environment


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characteristic shoulder related to the Verwey Transition appears around 120-130 K, more pronouncedly for the biggest sizes (≥52 nm for nanospheres and ≥42 nm for nanocubes). The Verwey Transition is typically observed in bulk magnetite, and in the case of magnetite MNPs, the Verwey transition tends to become more evident as the crystallinity and stoichiometry of the MNPs are improved 74,75. Therefore, these results suggest that the structural and magnetic “quality” of the MNPs improves with increasing size, as was already inferred from XRD measurements. This improvement can also be deducted from to the clear increase of the saturation magnetization, MS, of these MNPs as they become bigger (see Table 1 and Figure S5), reaching values close to bulk magnetite (92 emu/g) 76 for the largest ones. As we discussed above, MS is one of the key parameters to improve the heating efficiency of the MNPs. This improvement in the magnetic response of the MNPs with increasing size is typical, and can be related to the lower surface to volume ratio and the smaller surface disorder and number of defects that happen in the MNPs as their size increases 71.

Other two important parameters that determine the hysteresis losses, and thereby the heating efficiency of the MNPs, are the coercive field (HC) and the remanence (Mr/MS) (see Table 1 and Figure S5).

Concerning the remanence, the obtained Mr/MS values are similar for nanospheres and nanocubes, but they are very small, Mr/MS ≤ 0.25, much smaller than those expected for noninteracting randomly oriented nanoparticles with uniaxial Mr/MS ~ 0.5 or cubic magnetic anisotropy Mr/MS ~ 0.83 at low temperatures, according to the Stoner-Wohlfarth model. This reduction in the remanence of the nanoparticles can be attributed, apart from the obvious thermal disorder, to the effect of dipolar interactions between the nanoparticles 77,78.


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Regarding the coercivity, HC tends to increase with increasing size, reaching a maximum value of ~87 Oe for the 97 nm spheres and 327 Oe for the 106 nm cubes. The obtained HC values for our nanocubes are appreciably higher than those reported in the literature for Fe3O4 nanocubes of similar size 79, and also higher than those obtained for our nanospheres. In fact, the increase of HC with increasing size is much more pronounced for the nanocubes than for the nanospheres, especially for nanocubes with sizes ≥ 36 nm (vol ≥ 46500 nm3, see Figure S5). The evolution of HC with the size seems to tend to saturate for the bigger MNPs, as can be seen in Figure S5. This suggests that for sizes around 100 nm we are close to the multi-domain limit (a value of 128 nm has been previously reported in the literature for nanospheres

80

). For

biomedical applications, MNPs below the multi-domain limit, such as ours, have been traditionally favored 81. The coercive field is directly related to the “magnetic” or “effective” anisotropy, Keff, and to the saturation magnetization, MS, of the nanoparticles: HC = Keff/MS in the case of uniaxial non-interacting MNPs. Since the changes in HC as a function of the shape and size of our MNPs are appreciably greater than the changes in MS (as can be easily observed in Figure S5), this would suggest that the differences in HC values are mainly related to changes in the magnetic anisotropy. Therefore, the magnetic anisotropy is going to play a crucial role in the heating efficiency of these nanospheres and nanocubes.

Bulk magnetite has a cubic magnetic anisotropy at room temperature and the first order magnetocrystalline anisotropy constant has a negative value (K1 ≈ - 1·105 erg/cm3). However, in the case of magnetite MNPs, other contributions such as shape and surface anisotropy become more relevant, as was explained in the Introduction. These contributions usually favor a uniaxial type anisotropy

82

although other additional contributions can appear if dipolar

interactions are present, as in our case

83

. Hence, dipolar interactions will also affect the

magnetic anisotropy value. From these measurements, we can state that the magnetic anisotropy seems to increase with increasing size and that the nanocubes present, in general, a 17 ACS Paragon Plus Environment


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bigger magnetic anisotropy than the nanospheres, but obtaining a more accurate and precise information about the evolution of the magnetic anisotropy is not such an easy task. Here we can mention that in the literature there is still some controversy about which MNP geometry gives rise to a higher magnetic anisotropy, if spheres or cubes

34,84

. We believe that the

difficulty in addressing this matter is related to the complex task of disentangling the different contributions to the magnetic anisotropy of these MNPs (surface, shape, magnetocrystalline, interactions, etc.). In addition, the different methods employed to determine the magnetic anisotropy from DC magnetization measurements (law of approach to saturation, fitting of MT curves, coercive field, etc.) tend to simplify the role of these different contributions and do not normally contemplate the problematic effect of interactions 49,85,86. Here we consider that a more precise way to determine the magnetic anisotropy and study its role in the magnetic response and heating efficiency of our MNPs during the hyperthermia experiments is through measuring the AC hysteresis loops. As we will show later, the area of the AC hysteresis loop directly represents the hysteresis losses of the MNPs, and the shape of these loops strongly depends on the magnetic anisotropy. In this regard, some studies have tried to get a preliminary idea about the hysteresis losses of the MNPs from the area of the DC hysteresis loops measured at low field values 87. Although this can be certainly useful, only AC hysteresis loops can give correct hysteresis losses values. Nevertheless, and for sake of comparison, we have also represented the DC M-H loops in the low field region (see Figure S5) and these reveal that the nanocubes present a bigger area than the nanospheres, and that in both cases, it increases with increasing size, suggesting a better heating efficiency.

3.3 Magnetic Hyperthermia

As we commented in the Introduction, in order to analyze the heating efficiency of the MNPs we have employed a combination of calorimetric and AC magnetometry measurements. 18 ACS Paragon Plus Environment

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3.3.1 Calorimetric hyperthermia

Calorimetric measurements are very useful in order to get an idea about the heating efficiency (and heating rate) of the MNPs. By measuring the heating rate of the MNPs in a solution, the SAR can be easily determined. Most of the magnetic hyperthermia commercial equipments available are based on this kind of technique

88

. But calorimetric methods cannot provide

insight into the mechanisms behind the heating of the MNPs. For this point, AC magnetometry presents itself as an excellent complementary technique, since it directly reveals us the characteristics of the AC hysteresis loops from which the heating losses are derived. By analyzing these hysteresis loops, we can discover which parameters are controlling the heating efficiency of our MNPs and how these parameters change from one sample to another.

First we present the hyperthermia results corresponding to the calorimetric measurements. For each sample we have recorded the temperature as a function of the time, while the AC field is applied, by inserting a fiber optic sensor inside the vial containing the sample that is placed in the middle of the AC coil. Some examples of the typically obtained heating curves are presented in Figure 4. The heating curves clearly differ from one sample to another, indicating that the heating efficiency of these MNPs strongly depends on their shape, size, and also on the magnitude of the applied AC field. As can be seen, if we consider an initial temperature inside the human body of 37ºC, either the therapeutic window (∆T = 3-7 ºC) or the thermal ablation region (∆T ≥ 13ºC) for cancer treatment can be easily reached in less than 5 min by tuning the size of the MNPs and the magnitude of the applied field.



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Figure 4. Heating curves for the (a-c) 7, 33, and 97 nm nanospheres, and for the (d-f) 19, 36 and 106 nm nanocubes. The measurements were carried out in water, 1 mg/ml, under AC magnetic fields of 0-800 Oe and 300 kHz.

From these heating curves, we have obtained the heating efficiency of the MNPs or SAR, by using the initial slope method 88:

𝑆𝑆𝑆𝑆𝑆𝑆 =

𝑚𝑚𝑠𝑠 ∆𝑇𝑇 𝐶𝐶 𝑚𝑚𝑛𝑛 𝑝𝑝 ∆𝑡𝑡

(1)

where Cp is specific heat of the solvent, ms is mass of the solvent, mn is mass of the nanoparticles, and ΔT/Δt is the initial slope of the heating curves.

The SAR vs. size curves are plotted in Figure 5, and although the range of SAR values reached is similar in both nanospheres and nanocubes (0-800 W/g), there are some clear differences in the evolution of the SAR depending on the shape. In case of the nanospheres, the SAR describes a small shoulder at low sizes (≥ 26 nm), being nearly negligible for sizes ≤ 13 nm, but with 20 ACS Paragon Plus Environment

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increasing size the SAR greatly increases describing a broad maximum around 52 nm (depending on the field) reaching a maximum SAR of ~650 W/g at 800 Oe. This evolution is qualitatively similar to what has been reported in the literature for other systems of MNPs

44

and resembles some of the SAR vs. size curves predicted by theoretical models, such as those proposed by Hergt et al

89

. The very low SAR values that are displayed by the smallest

nanospheres could be related to their broader size distribution, as was discussed above. However, for the nanocubes, the heating efficiency describes a very different picture; the size evolution of the SAR abruptly increases at 30 nm up to ~800 W/g at 800 Oe and then rapidly decays with increasing size, reaching a minimum for the 42 nm sample. Guardia et al.

36

reported a similar abrupt jump of the SAR in their iron oxide nanocubes, but in their case, it reached a maximum at smaller sizes than in our nanocubes, around 19 nm. They attributed this behavior to this particular 19 nm sample being the one presenting the best control over shape and size distribution. We will discuss below some possible explanation for this behavior.

We must remark that this abrupt jump of the SAR vs. size is more noticeable at high fields > 200 Oe and is clearly different from what we are obtaining for the nanospheres. For example, 26 nm nanospheres and 19 nm nanocubes have similar volume and size distribution (see Table 1) but the SAR values are ~390 W/g for the cubes while for the spheres are much smaller, only ~130 W/g. However, if we focus on bigger sizes, 52 nm spheres and 42 nm cubes also present similar volume and size distribution but this time the nanospheres, ~650 W/g, heat much better than the nanocubes, ~180 W/g. This difference in the heating efficiency of the nanoparticles depending on their size and shape was already noted in our previous article

37

, in which 2

different sizes of spheres and cubes were analyzed, but only through this thorough study we can clearly follow the evolution of the SAR with the size.



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Figure 5. SAR vs size curves for the nanospheres (a-c) and nanocubes (d-f) measured in water - 1 mg/ml, water - 2 mg/ml, and agar - 1 mg/ml under AC magnetic fields of 0-800 Oe and 300 kHz.

If we increase the concentration of MNPs, we see even more differences between the nanospheres and the nanocubes; for the nanospheres there was nearly no change in the heating efficiency of the MNPs when increasing the concentration from 1 to 2 mg/ml, but the nanocubes experience appreciable changes in their heating efficiency when increasing the concentration, as can be seen by comparing Figures 5 c and d. In principle, an important dependence of the SAR on the concentration of nanoparticles can be expected, especially in the low concentrations regime (0-2 mg/ml): see for example Conde-Leborán et al. Bakoglidis et al.

43

86

or

. By increasing the concentration of nanoparticles we are basically

strengthening the magnetic dipolar interactions and cluster formation

54

. We already saw by

DLS (see Figure S2) that the nanocubes tended to form bigger clusters than the nanospheres and this could explain why the nanocubes seem to be more affected by the increase in 22 ACS Paragon Plus Environment

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concentration. This could also explain why the SAR for the nanocubes drops at smaller sizes than for the nanospheres: stronger interparticle interactions between the nanocubes would tend to kill the SAR faster with increasing size than for the nanospheres.

Apart from measuring the samples in water, we have also embedded them in a 2% agar solution in order to restrict their movement. In recent years, attention has been brought towards assessing the heating efficiency of the MNPs in media that immobilize them instead of other media where they can freely move/rotate (such as water), since similar immobilizing processes are supposed to take place in vivo 90. As a result of embedding the MNPs in agar, SAR values globally decrease. This is especially noticeable when applying low fields (200 Oe), since SAR values drop to practically zero. However, with increasing field magnitude, the differences between the results in water and in agar tend to become smaller, as expected. Nevertheless, there are some interesting differences between the SAR of nanospheres and nanocubes in water and in agar, as can be seen in Figure S6. For the nanospheres, the differences between water and agar become more noticeable for sizes ≥ 33 nm, being the SAR values in agar sometimes even less than 50% the values in water. It is well known that the Brownian contribution becomes more important with increasing size of the nanoparticles

91

, and therefore it is

reasonable that the immobilization effect of agar affects more the bigger MNPs. However, for the nanocubes the samples in water and in agar present very similar SAR values, except for the case of the 30 nm nanocubes, which are the ones that precisely exhibit an abrupt increase in the SAR. For these 30 nm cubes, the SAR values in agar can be as low as 30% the SAR values in water. As it happened in the previously mentioned article by Guardia et al.

36

, these

nanocubes present slightly better aspect ratio and cubic shape than the rest, although the differences are not remarkable. A possible explanation for why the results in agar and in water are similar for the rest of the nanocubes is that their physical rotation is restricted even in water. It is well known that nanocubes tend to organize in ordered assemblies more easily than 23 ACS Paragon Plus Environment


Page 24 of 46

nanospheres and we already saw by DLS. The cubes inside the clusters will have their physical motion heavily restricted even in water, and therefore the results in water and in agar will be similar.

However, from this analysis, a clear question emerges: what happens then with the 30 nm nanocubes, why the differences between the SAR values in water and in agar are so large? As indicated by DC magnetic measurements, XRD and TEM, the magnetic response and crystallinity of these 30 nm nanocubes is not the best among all the nanocubes studied, and therefore the answer must lie somewhere else. Since we have seen that the cluster formation is playing a role in the heating efficiency of our MNPs, in order to better understand this divergence, we have obtained TEM images of the clusters of 30 and 36 nm nanocubes (see Figure S7) after applying a magnetic field of 1 kOe. Notice that both nanocubes are apparently similar in size, shape and saturation magnetization, but the heating efficiency is very different (the SAR values for the 30 nm nanocubes are up to ~2.5 times bigger than the SAR values for the 36 nm nanocubes). As depicted in Figure S7, for the 36 nm nanocubes we can clearly see some 2D clusters oriented in the direction of the field, but for the 30 nm nanocubes, we observe a predominance of long 1D chains of nanocubes with some ring-like formations. This kind of quasifractal formations are typical of MNPs, as has been recently reported both in intracellular and extracellular aggregates 92. In the same line, it has been pointed that MNPs aggregates with low fractal dimension, forming chain-like structures, as in the case of the 30 nm nanocubes, presents higher hysteresis losses and therefore better heating efficiency, than clusters of MNPs with higher fractal dimension, like the 36 nm nanocubes 93. In addition, different works in the literature have reported that the formation of chains of MNPs is an efficient way to increase their heating efficiency

34,94,95

. This could explain why the sudden increase in the heating

efficiency of the nanocubes around this size, although we cannot discard other possibilities, as will be discussed during the AC hyperthermia measurements. The formation of the 1D chain 24 ACS Paragon Plus Environment

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like structures for these 30 nm nanocubes, not for the other sizes, could be related to an small improvement in the shape and aspect ratio of the 30 nm; it can be observed in Figure S7 that the 36 nm nanocubes also tend to arrange in chains, but small deviations of some of the individual nanocubes from a cubic shape breaks their parallel alignment leading to the formation of large 2D agglomerates. We also observed by DLS that the 30 nm nanocubes were the ones with the smallest cluster size. Therefore, these results suggest that during the magnetic hyperthermia experiments in water, the 30 nm nanocubes tend to align with the AC field forming chains more easily than the rest of the nanocubes, more evidently for higher fields, and this improves their heating efficiency. This would also explain why the SAR for these 30 nm nanocubes drastically decreases when embedded in agar: it is expected that due to the higher viscosity of agar, the 30 nm nanocubes can no longer form these chain like structures, and therefore, the heating efficiency diminishes with respect to the water. In fact, the heating efficiency of the 30 nm and 36 nm nanocubes is very different in water but quite similar in agar (Figure S6), supporting this argument. Overall, it can be observed that in agar, the differences between the heating efficiency of nanospheres and nanocubes are not so appreciable, but still at sizes < 40 nm, the nanocubes seem to heat better (up to ~700 W/g and ~550 W/g for the 36 nm nanocubes and 32 nm nanospheres, respectively) while for bigger sizes the nanospheres give better results (up to 150 W/g and 400 W/g for the 42 nm nanocubes and 52 nm nanospheres, respectively).

Before continuing, we should recall that agglomeration and immobilization of MNPs, although in principle detrimental for their heating efficiency, as we have explained, reproduce more realistically in vivo conditions than when the MNPs are very well dispersed in water. Experimental in vivo studies consistently reveal that injected nanoparticles tend to get immobilized in the tumor tissue forming agglomerates 92,96–98. Therefore, reporting very high SAR values in low concentrated highly dispersed MNPs can be misleading when trying to 25 ACS Paragon Plus Environment


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assess their actual heating capacity during the clinical hyperthermia treatment. In fact, several studies have shown that MNPs that apparently heat extremely well in water, unfortunately perform poorly when the final in vivo studies are carried out 97.

Before concluding the calorimetric analysis of hyperthermia, we must also remark that with the fields and frequencies we are employing, we are not working in the linear response theory (LRT) regime typically described in the literature. In this regime, only valid for low fields and non-interacting SPM nanoparticles, the SAR evolves as H2, and the SAR vs size evolution typically reaches maximum around 15-20 nm and then drops above that size as has been reported in other systems of nanoparticles working in the LRT regime 46,99. In fact, Hergt et al. already demonstrated years ago that by increasing the magnitude of the applied field (and therefore working outside the LRT regime) the maximum SAR value not only increases but also the optimum size displaces towards bigger values. As a matter of fact, some of the largest SAR values have been reported in the literature for big and highly crystalline nanoparticles (40-60 nm), such as those synthesized by magnetotactic bacteria 100–102.

Therefore, the SAR vs. size curves clearly reveal very different behaviors depending on the shape of the MNPs. In the studied field range (200-800 Oe) nanocubes seem to provide better heating efficiency than the nanospheres (up to ~800 W/g), but their size must be more carefully tuned (30-35 nm) in order to maximize their SAR. This seems related to the tendency of the nanocubes to arrange in chains for these sizes, which helps increasing their heating efficiency. On the other hand, the nanospheres provide remarkable heating in a wider range of sizes (up to ~650 W/g), around 40-60 nm. In addition, our measurements in water and in agar indicate that agglomeration and physical rotation restriction can have a strong role on the heating efficiency of the MNPs, depending also on their shape and size.


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3.3.2 AC magnetometry hyperthermia

In order to gain a better understanding about the differences in the heating efficiency between the nanospheres and nanocubes, we have carried out additional AC magnetometry hyperthermia measurements. In AC magnetometry, the AC hysteresis loops described by the magnetic moments of the MNPs during the hyperthermia experiments are measured and the heating efficiency is directly obtained from the area of these AC hysteresis loops. The AC hysteresis loops measured for the MNPs dispersed in water are presented in Figure 6. The equivalent measurements in agar are included in Figure S8. Note that with the home-made setup we are using for the AC hyperthermia measurements, the maximum field we can reach is 400 Oe instead of the 800 Oe that we could attain with the previously employed commercial system for our calorimetric measurements.



Page 28 of 46

Figure 6. AC hysteresis loops and corresponding SAR vs field curves for the spherical (ad) and cubic (e-h) MNPs measured in water (1 mg/ml) under AC magnetic fields up to 400 Oe and 310 kHz.

The SAR values (in W/g) were directly obtained from the area (A) of the AC hysteresis loops, according to the equation 41:

𝑊𝑊

𝑓𝑓

𝑓𝑓

𝑆𝑆𝑆𝑆𝑆𝑆 � 𝑔𝑔 � = 𝑐𝑐 ∙ 𝐴𝐴 = 𝑐𝑐 ∙ ∮ 𝜇𝜇0 𝑀𝑀𝑡𝑡 𝑑𝑑𝐻𝐻𝑡𝑡

(2)

Mt being the instantaneous magnetization at time t, Ht the sinusoidal magnetic field of frequency f at time t, and c the magnetite weight concentration in the dispersing medium. The integration is done over a period of the oscillating magnetic field, T = 2π/f. In Figure S9 we present a comparison between the SAR values measured at 400 Oe with calorimetric and AC magnetometry methods. As can be seen, the obtained heating efficiency values are relatively similar, independently of the method.

As can be seen, with the maximum field we can apply (400 Oe) we cannot saturate the AC hysteresis loop and we are obtaining in all the cases minor loops. This basically means that if we applied higher fields we would obtain higher SAR values (as can be easily checked by comparing the SAR values obtained here with those measured before from the calorimetric measurements at H > 400 Oe). In addition, the shape of the AC hysteresis loops changes appreciably both as a function of the morphology and size of the MNPs. From a qualitative point of view, for both nanospheres and nanocubes, the area of the AC loops first increases with increasing size and then, above a certain value, starts to decrease. In particular, at very small sizes, when the nanoparticles are in the SPM regime, the AC loops are extremely narrow, with low squareness and low maximum magnetization, Mmax, values, and therefore the heat losses are very small (see Table 2). As the size of the particles increases, Mmax increases up to 28 ACS Paragon Plus Environment

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~40 emu/g and the AC loops become increasingly wider and more squared, thereby increasing the SAR values. This is especially noticeable for the 30 nm nanocubes as it also happened in the case of the calorimetric hyperthermia measurements. However, by increasing the size even more (above 52 nm for the nanospheres and 36 nm for the nanocubes) the AC loops start to become again more tilted and lean, finally resembling Rayleigh lancets for the biggest sizes (~100 nm). A similar evolution has been obtained for the measurements made in agar (Figure S8) although in this case the area of the loops is smaller than in water. Analogous experimental and simulated AC loops have been described in the literature for systems of dipolar interacting MNPs with randomly oriented anisotropy axis

103–105

. In fact, we have checked that our AC

loops are in general more tilted and lean than those expected for an ensemble of non-interacting randomly oriented magnetite nanoparticles with uniaxial anisotropy

25,35,86

(see Figure S10),

confirming that clustering and interactions are playing an important role in the shape of the AC loops, and therefore, in the heating of our MNPs.

There is an exception to this general trend, and it happens precisely for the 30 nm nanocubes that we were discussing in the previous section. As can be observed in Figure 6, there is a clear and abrupt change in the shape of the AC loops obtained for the 30 nm nanocubes in water; they become completely squared and adopt a shape close to that obtained in systems with cubic anisotropy 106 or in systems with the anisotropy axis oriented in the direction of the field such as oriented chains of MNPs

34,53,107

. This change in the shape of the AC loop for the 30 nm

cubes gives rise to a great increase of the SAR (see Figure 6), as was also observed in the calorimetric measurements. However, the interesting thing is that this change in the shape of the AC loop for the 30 nm nanocubes is not observed when the MNPs are embedded in agar (see Figure S8). When in agar, the shape of the AC loops for the 30 nm nanocubes is similar to the ones obtained for the other nanocubes. These results match well with what we obtained in the calorimetric measurements and in principle, seem to corroborate the critical impact of 29 ACS Paragon Plus Environment


Page 30 of 46

the chain formation of the 30 nm nanocubes in increasing the hysteresis losses and improving the SAR of these MNPs when they are dispersed in water. When the nanocubes are embedded in agar, the SAR still describes a maximum (although not so abrupt) around 30-35 nm, indicating that these are the optimum sizes to increase the heating efficiency in the case of the nanocubes. Nevertheless, and considering the “particular” shape of the AC loops obtained for these 30 nm nanocubes, we cannot completely rule out a possibility that these nanocubes mainly present a cubic anisotropy instead of a uniaxial one, which would also explain the characteristic highly squared AC loops obtained.

Table 2. Maximum coercive field, Hc-max, maximum magnetization, Mmax, maximum normalized remanence, Mr/Mmax, and hyperthermic coercive field, magnetic anisotropy (Keff) and the point of highest slope of the SAR vs. H curves (HC-hyp) as obtained from the AC hysteresis loops measured in water.

Hc-max (Oe) spheres 7 nm 26 nm 33 nm 52 nm 97 nm cubes 19 nm 30 nm 36 nm 42 nm 106 nm

Mmax (emu/g)

Mr/Mmax

Keff (105 erg/cm3)

HC-hyp (Oe)

46 63 123 121 70

4.2 27.8 33.0 36.7 26.2

0.13 0.28 0.41 0.37 0.20

>23.8 9.9 12.2 12.8 >18.6

>400 175 300 320 >400

85 175 155 62 36

25.8 40.2 32.9 19.1 13.6

0.36 0.86 0.45 0.16 0.08

13.4 8.2 14.2 >20.4 >18.9

211 191 370 >400 >400

In Table 2 we have indicated some of the main magnetic parameters extracted from the AC hysteresis loops (measured at Hmax ≈ 400 Oe), including maximum coercive field, Hc-max, maximum magnetization, Mmax, and the maximum normalized remanence, Mr/Mmax.


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It can be observed (see Figure 7) that the evolution of these parameters with increasing size is coincident with the evolution of the SAR: both Hc-max and Mr/Mmax simultaneously increase when the SAR increases and vice versa. This indicates that both parameters are strongly correlated. In addition, we have included the coercive field values obtained from the SAR vs. H curves, the so called HC-hyp. These are derived from the position of the point of the highest slope of the SAR vs. H curves. As can be seen, HC-hyp tends to displace towards higher values with increasing size of the MNPs, independently of their shape. As has been described in the literature

50,108,25

, this HC-hyp parameter plays a crucial role in the heating efficiency of the

MNPs: for applied fields below HC-hyp, the power absorption is mainly caused by viscous losses in the system, and this regime is characterized by a sharp decrease in the hysteresis loop area; however, when H >> HC-hyp, the hysteresis losses dominate and the area of the hysteresis loops appreciably increases, eventually tending to saturate to its maximum value.

In order to get a better understanding about the evolution the AC hysteresis loops and their corresponding SAR values, we have analyzed the evolution of the magnetic anisotropy, Keff, of these MNPs as a function of their shape and size. As we commented before, the magnetic anisotropy plays a crucial role in the heating efficiency of the MNPs and the AC loops can give us an estimation of this parameter. For this task, we have used the same approach described in Ref 53. In this article, Mehdaoui et al. used an equation obtained from numerical simulations in order to estimate Keff in systems of interacting MNPs using the results from AC hysteresis loops. According to this model, assuming randomly oriented anisotropies for the MNPs, the coercive field obtained from the SAR vs field measurements is given by the following equation:

𝐻𝐻𝐶𝐶−ℎ𝑦𝑦𝑦𝑦 = 0.48𝐻𝐻𝐾𝐾 (1 − 𝜅𝜅 0.8 )

(3)

where: 31 ACS Paragon Plus Environment


𝑘𝑘 𝑇𝑇

𝜅𝜅 = 𝐾𝐾 𝐵𝐵

𝑒𝑒𝑒𝑒𝑒𝑒 𝑉𝑉

ln �4𝐻𝐻

𝑘𝑘𝐵𝐵 𝑇𝑇

𝑚𝑚𝑚𝑚𝑚𝑚 𝑀𝑀𝑆𝑆 𝑉𝑉𝑉𝑉𝜏𝜏

0

Page 32 of 46

� (4)

Being τ0 = 10-10 s, V the MNP volume, MS is the experimental saturation magnetization obtained from VSM measurements at high fields (see Table 1), Hmax the maximum applied field (400 Oe) and T is the temperature. Using this expression, we can estimate the magnetic anisotropy, Keff, for our MNPs. For some of these samples, HC-hyp is bigger than the maximum field we can apply (HC-hyp > 400 Oe), and in those cases, a lower limit for Keff is provided.

It is important to remark that the magnetic anisotropy values calculated here, Keff, are not the magnetic anisotropy values of the individual MNPs, but the magnetic anisotropy of the MNPs inside the clusters. This means that Keff incorporates the effect of dipolar interactions. As can be observed (see Table 2), all the obtained Keff values (Keff ≈ 8-24·105 erg/cm3) are relatively high and confirm the enhanced magnetic anisotropy for the nanocubes that our DC magnetization measurements already suggested. In general, it can be observed that with increasing size, Keff first decreases and then increases being inversely proportional to the SAR evolution (see Figure 7), describing a broad minimum around 26-52 nm for the nanospheres, while for the nanocubes there is a sharp decay of Keff around 30 nm. In Figure S11 we have also compared the size dependent evolution the Hc-max and Mr/Mmax with Keff. There is a distinct evolution of both coercivity and remanence, and therefore the squareness of the AC loops, with the magnetic anisotropy, Keff: in the case of nanospheres, Hc-max and Mr/Mmax first increase with increasing Keff, reaching a maximum around Keff ≈ 12·105 erg/cm3, and then decrease. For the nanocubes, the evolution is similar (maximum around Keff ≈ 14·105 erg/cm3) with the exception of the increase of Hc-max and Mr/Mmax for the lowest Keff value, which corresponds to the 30 nm nanocubes. This would suggest that in principle, maximum squareness of the minor AC loops that have been obtained for these samples can be obtained for Keff values around 12-14·105 erg/cm3, again with the exception of the 30 nm nanocubes. For this sample, 30 nm nanocubes, 32 ACS Paragon Plus Environment

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the final Keff value is probably smaller than the one calculated here. If considering the results from Figure S7, we assume a 1D magnetic anisotropy for the 30 nm nanocubes, instead of a random 3D magnetic anisotropy, the obtained Keff is nearly half, Keff ≈ 4.7·105 erg/cm3 (see Ref. 53).

Figure 7. Size dependent evolution of the heating efficiency, SAR, and the magnetic anisotropy, Keff of the a) nanospheres and b) nanocubes, as obtained from the AC magnetometry measurements.

It can be observed that the nanocubes heat better than nanospheres at smaller sizes, < 35 nm, when their Keff is low (8·105 erg/cm3); while for bigger sizes, > 35 nm, the Keff of the nanocubes rapidly increases (up to 20·105 erg/cm3) and since the nanospheres present lower Keff, they exhibit better heating efficiency. The increase of the magnetic anisotropy with increasing size of the MNPs can be easily ascribed to the stronger effect of dipolar interactions with increasing volume, V, and saturation magnetization, MS, (Edip ≈ (𝑀𝑀𝑆𝑆 𝑉𝑉)2 ). To this respect, Conde-Leborán et al.

50

have shown that with increasing strength of dipolar interactions, the effective

anisotropy increases and the AC hysteresis loops tend to become leaner and more tilted, which is precisely what we qualitatively observe in our MNPs with increasing size.



Page 34 of 46

These results clearly reveal that, when working at low “non-saturating” AC fields, the best strategy to improve the heating efficiency of the MNPs is, in general, to try to reduce their magnetic anisotropy so that the hysteresis loops can be saturated and become squared, giving rise to high hysteresis losses and SAR values. However, we must remind here that lower magnetic anisotropies also restrict the maximum width of the hysteresis loop that can be obtained when increasing the field, and therefore, if the applied AC field during the hyperthermia experiments is high enough to overcome the magnetic anisotropy barrier, the particles with higher magnetic anisotropy would give rise to wider AC loops and better heating results, as has already been discussed in previous works 22,50,108.

4. CONCLUSIONS

We have successfully synthesized crystalline and monodisperse Fe3O4 MNPs with two different shapes, spheres and cubes, in a wide range of sizes, ~10-100 nm by using thermal decomposition methods. We have observed that their magnetic response changes as a function of their size and shape, and we have related this to the effects of the magnetic anisotropy, arrangement, and dipolar interactions.

The heating efficiency of these MNPs has been analyzed by using a combination of calorimetric and AC hyperthermia methods. This has allowed us to get a deeper understanding about the mechanisms controlling the heating of the MNPs. In particular, the main conclusions reached are:

•

In this range of sizes (~10-100 nm), both nanospheres and nanocubes tend to form clusters due to dipolar interactions, and this effect is more noticeable for the nanocubes whose physical rotation is highly restricted even in water.


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•

By tuning the shape of the MNPs, we can change the range of sizes that optimizes the heating efficiency: around 30-50 nm for the nanospheres (~650 W/g), and around 3035 nm for the nanocubes (~800 W/g), as measured at 800 Oe and 310 kHz.

•

The chain-like arrangement of nanocubes is an ideal way to improve their heating efficiency, as demonstrated by the 30 nm nanocubes, which present the best heating results among all the samples analyzed. This particular arrangement is facilitated by the shape and aspect ratio of the nanocubes.

•

The magnetic anisotropy of the MNPs directly controls the shape of the hysteresis loops and hence the heating efficiency of the MNPs; below ~35 nm, the nanocubes present lower magnetic anisotropy and heat better as compared to the nanospheres; however, with increasing size, the magnetic anisotropy of the nanocubes rises faster due to the stronger effect of dipolar interactions, and this makes the nanospheres better heating agents, in comparison with the nanocubes, above ~35 nm.

•

In order to maximize the heating efficiency of these MNPs, we need to apply high AC fields > 400 Oe at 300 kHz, and therefore we would need to work above the commonly accepted limits (H.f ≤ 1 109 Am-1s-1). To this respect, the nanocubes are more demanding and require higher fields than the nanospheres in order to increase the SAR, although they can exhibit better heating values than the nanospheres.

•

Our results clearly reveal that big iron oxide MNPs (> 30 nm) can yield greater heating efficiencies than smaller ones that have been typically considered in the literature for hyperthermia treatment (15-20 nm), provided that enough field is applied. Moreover, when working under conditions of agglomeration and movement restriction, typically observed in in vivo experiments, we need to increase both the size of the MNPs and the AC field in order to optimize their heating efficiency. And by altering the shape and arrangement of these MNPs we can also improve their heating performance. 35 ACS Paragon Plus Environment


Page 36 of 46

Therefore, we believe that the present findings not only provide important insights into the heating mechanisms of MNPs but also direct the focus of the current hyperthermia research towards using bigger MNPs with different shapes that can provide better in vivo results.

Supporting Information The Supporting Information is available. Content: Size distributions for the nanoparticles as obtained by TEM. DLS analysis of the spheres and the cubes. Scherrer analysis of the spherical and cubic MNPs as derived from XRD. Fitting of the M-H loops using a Langevin based model. Evolution of HC, MS and Mr/MS, together with the low field region of the DC M-H loops. Comparison of the SAR vs field in water and in agar. TEM images of the 30 and 36 nm nanocubes under a DC field of 1kOe. AC hysteresis loops and corresponding SAR values for the MNPs measured in agar. Comparison of SAR values obtained by AC hyperthermia and calorimetric measurements. Simulated AC loops for the 33 nm spheres considering a StonerWohlfarth model for an ensemble of non-interacting randomly oriented uniaxial nanoparticles. Size dependent evolution of HC, Mr/MS, and Keff of the MNPs, as obtained from the AC magnetometry measurements

Acknowledgments Research at the University of South Florida was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-FG02-07ER46438. The Basque Government is acknowledged for Grant No. IT-100516 and Irati Rodrigo's fellowship.

Author Contributions


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Zohreh Nemati synthesized all the nanoparticles (except 7 nm spheres), carried out their structural analysis (TEM) and magnetic and some of colorimetric hyperthermia measurements (ZFC/FC and M-H loops), and wrote the Synthesis section. Javier Alonso carried out DLS measurements and TEM measurements for agglomeration studies, mainly contributed to the analysis of the results, and wrote the rest of the article. Irati Rodrigo carried out the AC hyperthermia measurements and assisted with the evaluation of the corresponding results. Raja Das synthesized the 7 nm nanospheres, carried out XRD measurements and contributed to the discussion. Eneko Garaio and José Ángel García coordinated and managed the AC hyperthermia experiments and assisted in the interpretation of the results. Iñaki Orue carried out the numerical simulation studies, devised several supporting experiments to better understand the results, and greatly contributed to the Results and Discussions. Manh Huong Phan and Hariharan Srikanth assisted in the interpretation the results of this manuscript, coordinated and managed the structural, magnetic and calorimetric hyperthermia experimental work and guided the overall preparation of the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

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1000 spheres 800 600 400 200 SAR (W/g)

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Improving the Heating Efficiency of Iron Oxide Nanoparticles by

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