Cristina Da Cruz

Olivier Sandre

Valérie Cabuil

Phase behavior of nanoparticles in a thermotropic liquid crystal

Keywords: ferronematics, ferrofluids, nanoparticles, liquid crystals, SAXS

In this work we describe the outstanding behavior of a nanocomposite system composed of the thermotropic liquid crystal 5CB doped with nanoparticles of the magnetic iron oxide maghemite (γ-Fe 2 O 3 ). We show that the I-N transition is associated to a reversible gathering of nanoparticles inside droplets of ferronematic phase coexisting with a non magnetic nematic host phase.

Composite systems composed of a liquid crystal (LC) doped by particles have been the subject of numerous famous works in the past 1 and in the last years. 2 LC ordering induces topological defects 3, 4 and additional long-range forces 5 among colloidal particles. These forces can result in the formation of supermolecular structures, 6,7 cellular structures 8, 9 and even soft solids. 10 Due to their anisotropic properties, liquid crystals can be orientated under magnetic or electric fields. [START_REF] De Gennes | The Physics of Liquid Crystals[END_REF] However, the intensity of a magnetic field necessary to align a LC can be too high (> 0.1 Tesla) for practical applications. This limitation could be overcome with ferronematic liquid crystals (FNs) obtained by doping a nematic matrix with ferromagnetic particles. Well before their real experimental synthesis, ferronematics were first introduced theoretically by Brochard and de Gennes 1 to increase the magnetic anisotropy of LCs and to lower the magnetic field intensities required for their orientation. The authors also predicted that a strong anchoring of the mesogen molecules onto the particles would result in a ferromagnetic behavior of the matrix (i.e. a hysteretic magnetization curve). 1 Since then, research on lyotropic 12-15 or thermotropic 16,17 ferronematics have focused on the decrease of the critical field of the so-called Fredericks transition, which originates from the competition between field-induced and surfaceinduced orientations of the nematic director. Until now, the poor solubility of the magnetic grains in thermotropic LCs has restricted their study to either large (0.5 µm long) magnetic needles 16 or to spherical magnetic nanoparticles (with typical dimensions of 100 Å) but volume fractions of 0.05% at most 17 .

Ferrofluids are colloidal suspensions of magnetic nanoparticles that remain stable under whatever intensity of magnetic field or magnetic field gradient. 18 So-called ionic ferrofluids 19,20 are composed of electrically charged magnetic grains in water, which electrostatic repulsion prevents from flocculation. A second type called oily ferrofluids is composed of surfactant coated magnetic nanoparticles, for which the stability of the colloidal solution is provided by a steric repulsion which counterbalances Van der Waals and magnetic dipolar attractions. Ferrofluids in various organic solvents can be derived from ionic ferrofluids by coating the grains with appropriate surfactants. 21 The typical concentration of magnetic grains in a ferrofluid is larger than 10 16 grains / cm 3 .The average magnetic moment of a grain is of the order of 10 4 Bohr magnetons (also the approximate number of iron ions per nanoparticle).

Herein we describe the formulation of a composite material that results from the incorporation of magnetic nanoparticles into a matrix made of a thermotropic liquid crystal (LC) exhibiting a nematic phase at room temperature. A special attention is paid to the dispersion state and to the phase behavior of the magnetic nanoparticles in the matrix in relation with the phase behavior of the LC.

Previous works mentioned dispersing a magnetic powder made of nanometric grains directly into a liquid crystal and then sonicating 17 . Instead of this method, we chose to mix the LC with a ferrofluid constituted of a dispersion of magnetic nanoparticles in a volatile solvent in order to reach higher concentrations in the LC and a proper dispersion state. The choice of the surfactant preventing particles from aggregation is of uppermost importance.

Materials

The nematic liquid crystal used for this work is 5CB i. e. 4pentyl-4'-cyano-biphenyl presented in scheme 1, which exhibits a nematic phase between 21°C and 35°C.

The magnetic nanoparticles are prepared by alkaline coprecipitation of ferric and ferrous salts following a procedure described previously. 20 The obtained magnetic oxide is maghemite γ-Fe 2 O 3 . The surface of the nanoparticles is grafted by Beycostat NE (BNE), 21,[START_REF]Beycostat NE (or N B09) is a commercial product provided by CECA, Courbevoie (France) used to disperse inorganic pigments in aromatic or chlorinated oils (but insoluble in aliphatic solvents). 23 The relationship between molar concentration in iron and volume fraction of nanoparticles is Φ (%)=1[END_REF] which is a commercial anionic surfactant composed of a mixture of mono-and di-esters of phosphoric acid, the chain being an alkylphenol containing nine ethoxy groups. We choose Beycostat NE to coat the nanoparticles because of its affinity for aromatic solvents, whereas oleic acid used in some publications leads to a systematic aggregation of the magnetic nanoparticles. BNE is adsorbed directly onto the precursor cationic maghemite nanoparticles in nitric acid medium. After rinsing some of the ungrafted BNE in excess in a mixture of methanol/ether, the dispersion of the nanoparticles is achieved in dichloromethane. These magnetic nanoparticles exhibit some polydispersity in diameters ranging from 5 to 12 nm. (see supporting information) Scheme 1: Molecular structure and polymorphism of 5CB, the liquid crystal here in study.

Crystal

21°C Nematic 35°C Isotropic T(°C)

Preparation of ferronematic samples

The ferronematics are prepared by simply adding the magnetic nanoparticles suspended in dichloromethane to the liquid crystal in nematic phase at room temperature and then waiting for the solvent to evaporate. The iron concentration in the LC is measured by Atomic Absorption Spectroscopy (AAS) at λ = 480 nm after degradation of iron oxide nanoparticles into ferric ions by concentrated hydrochloric acid. 23

Optical observations

First we see by eye a biphasic state at room temperature, that disappears when we heat carefully our ferronematics until crossing the phase transition to isotropic state. At this T (N-I) temperature and above, a stable dispersion of the nanoparticles is obtained. This homogeneous mixture resulting from the heating to the isotropic phase stays homogeneous even when submitted to a strong magnetic field (around 1 Tesla) as long as temperature remains above T (N-I) . Therefore, it can be considered as a true ferrofluid with the isotropic LC as solvent. Optical microscopy experiments are carried out in order to observe the microphase behavior of the mixture. The FN samples are observed under crossed polarizers using an upright microscope (Leitz, 20X magnification) equipped with a homemade Peltier temperature-controlled stage. Some of the warm isotropic mixture is deposited between two glass slides where it cools down and then it is heated again above the nematic-isotropic transition point. The phenomenon

CN C H 3 (a) (b) (c) (d) (e) (f) (g) (h) (i)
occurring on cooling below the I-N transition appears under the microscope as the formation of dark orange microdroplets, which means rich in iron oxide nanoparticles. In a reversible way, droplets disappear abruptly on heating above T (N-I) , and then are replaced by a diffuse cloud of nanoparticles vanishing slowly (figure 1a). On decreasing again temperature below the I-N transition, the microphase separation again occurs in a reversible way and at the same temperature. After a fluctuating interface has appeared suddenly from the initially homogenous matrix (figure 1b), the new phase concentrates into droplets, that rapidly shrink and turn into a darker color (figure 1c). We observe also that the neighboring droplets originating from the rupture of a larger drop remain aligned together (figure 1d). Under crossed polarizers (figure 1e), the localization of those strings appears somehow superposed with the Schlieren texture. In other words, the droplets of ferronematic phase below T (N-I) are expelled towards the defect lines of the predominant LC (which exhibit typical colors of a nematic LC under crossed polarizers). We notice also that the diameter of the droplets is controlled by the cooling rate of the quench. Qualitatively, the faster is the cooling, the smaller are the droplets (on average). By careful examination of the droplets under crossed polarizers (figure 1f), we become aware that nematic disinclination lines exist also inside the droplets (black crosses), meaning that there are not made of isotropic phase. When the sample is heated again, the sizes of the droplets start to increase (figure 1g). Then we see the front of isotropic phase (black under crossed polarizers) advancing against the nematic region (figure 1h), until it invades the whole space (figure 1i). Furthermore, it is important to point out that no matter how many temperature cycles are applied to the samples, the magnetic nanoparticles never form a solid flocculate, which means that some LC acts as a solvent inside the droplets. Following the variance rule, the existence of a bi-phasic state below T (N-I) is a direct consequence of a multi-component system. Such a case was reported for hydrophilic silica particles (5 nm diameter) in a 5CB host, [START_REF] West | [END_REF] that do not disperse in the nematic phase but are captured by the N-I interface at the transition. In that example, a complete exclusion of the silica particles is observed below the I-N transition, leading to a precipitate forming a "cellular" structure. Such a network formation below T (N-I) has also been reported recently for the same 5CB LC loaded with sterically stabilized colloids made of a polymer (PMMA), of different diameters ranging from 100 nm to 1µm. 25 By using NMR spectroscopy, the authors of this article proved that even 10°C below T (N-I) , 10% of the 5CB molecules were still in the isotropic phase coexisting with the nematic phase, which they explain by a tri-component system (LC / particles / solvent residue). Here on the contrary, the magnetic nanoparticles accumulate inside non isotropic droplets. The formation of the nematic order below T (N-I) tends here to confine the nanoparticles into concentrate ferronematic droplets in coexistence with the apparently unmodified and empty nematic phase.

Microscopic observations of the 2-phase behavior are also made under an applied magnetic field. At first we cool from isotropic to nematic phase at 2 °C/min without any field: small spherical droplets form as seen on figure 2a. Under the application of a magnetic field of low intensity (0.03 Tesla) parallel to the plane of the sample, the droplets which are close enough to attract each other gather into chains containing between two and fifteen droplets (figure 2b). When the field is released, chains persist for a while but display rotational Brownian motion as can bee seen on figure 2c. Chains also appear flexible as droplets within a given chain can move around and eventually escape from the chain. If we wait longer, all the chains disappear. When heating to isotropic, all droplets disappear and nanoparticles disperse themselves again homogeneously in the isotropic LC.

Another kind of experiment consists in applying the same magnetic field all along the transition from the isotropic to the nematic strate. In that case, the droplets not only chain but although significantly elongate (figure 3a), meaning that they are both magnetic and deformable. However, we never observe droplets coalescing under magnetic dipolar attraction. Observed under crossed polarizers (figure 3b), the nematic host phase still exhibits disinclination lines, which is a clue that it is poor in magnetic nanoparticles and does not benefit from their orienting properties. Contrary to the strings of droplets under zero field connected to the Schlieren texture, this chaining under a magnetic field is ascribable to fieldinduced dipolar attractions between the highly magnetic droplets. After field release, the chains persist and the droplets keep their elongated shape (figure 3c), but they starts to rotate randomly under Brownian motion.

The interpretation of these results is delicate and needs some discussion compared to previously published works on mixtures of nematics with either solid or liquid colloids. With a somehow analogous system consisting of droplets of an aqueous ferrofluid mixed with an immiscible nematic LC, 26 Poulin et al. have observed the spontaneous chaining of the droplets by the interplay of surface and elastic forces, in the absence of magnetic field. This effect is not dictated by the magnetic interactions, and therefore is observed also for pure water droplets as long as an appropriate surfactant is used to determine a normal boundary condition of the LC molecules at the surface of the droplets. 27 When the anchoring energy dominates over the elastic energy (associated to distorsions of the nematic director), each droplet associated to a so-called "hedgehog" defect interacts with the other droplets by (i) long range (dipolar type) attraction and (ii) short range repulsion (of elastic nature, presumably due to the thin nematic layer squeezed when droplets become closer). The situation in the present work is different because 5CB constitutes both the nematic host matrix and the solvent of the dispersed ferronematic phase. Therefore we can imagine that the boundary conditions at the surface of the droplets is rather planar than normal. At least we know that the interfacial cost of the droplets in the nematic matrix must be low, because they are easily deformed into ellipsoids by a weak magnetic field. This point is corroborated by the absence of coalescence, which would be favored by a larger interfacial tension.

To summarize those optical microscopy experiments, we observe: i) a biphasic behavior below T (N-I) with a nematic LC phase poor or empty of nanoparticles and droplets of ferronematic phase rich in nanoparticles; ii) a sensitivity to a weak magnetic field causing the deformation and/or the chaining of the droplets along the field direction, but no coalescence.

DSC experiments

Mixtures with different volume fractions of nanoparticles in 5CB are studied by Differential Scanning Calorimetry in order to determine if the biphasic behavior observed optically leads to an endothermic peak, which is a thermodynamic signature of the nematic to isotropic transition. The curves of the heat flows vs. temperature are collected with a Perkin-Elmer DSC 7 calorimeter coupled with a cryostat at different rates of temperature change. We report here only the results on heating at 1 °C/min, which is also the rate also used in the SAXS experiments. From these thermograms (figure 4), we see that increasing the quantity of nanoparticles incorporated in the liquid crystal matrix causes a decrease of the range of the nematic phase existence together with a widening of the clarification peak. From this series of peaks, T (N-I) measured precisely by DSC is plotted vs. the volume fraction Φ of nanoparticles on figure 5. linear decrease of T (N-I) as a function of Φ, we conclude that some chemical species is more soluble in the isotropic phase than in the nematic phase and perturbs the nematic phase enough to be considered as an impurity. Two possibilities can be considered: on the one hand, a small amount of nanoparticles can be directly soluble inside the nematic matrix (in addition to the droplets which contain most of the nanoparticles); on the other hand, the nanoparticles could be perfectly insoluble in the nematic phase and only the surfactants desorbed from the nanoparticles enter inside the nematic phase. To decide which phenomenon really occurs, we analyze the thermogram of 5CB without nanoparticles but with some added BNE surfactant inside. The transition to isoptropic phase occurs at 34.1°C and 34.7°C respectively with 2.3 % and 0.8 % in weight of BNE, which are the same temperatures as B22 and B25 samples respectively. These values fit really well with the estimates of the final proportion of free BNE inside the ferronematics by dilution of the initial ferrofluid, which contains about 5 wt % BNE for a volume fraction of nanoparticles Φ= 1.2 %. To be entirely sure that the decrease of T (N-I) is due the presence of BNE only, we separate the nematic phase from the magnetic isotropic phase by decantation of the droplets on a strong magnet ( ~0.5 Tesla).

The DSC thermogram of the entire ferronematic and of this separated N phase showing exactly the same T (N-I) temperature lower than for pure 5 CB, we are allowed to conclude that the free BNE is the only parameter that regulates this decrease of transition temperature. As a conclusion, we have proved that the magnetic nanoparticles do not contribute to this decrease of T (N-I) , for which only the free surfactant is responsible. This fact is corroborated by the absence of iron titrated by AAS inside the nematic phase isolated from the droplets by magnetic separation of a ferronematic. If any nanoparticles existed in this nematic phase, the corresponding [Fe] would be less than 10 -5 molL -1 (sensitivity of AAS). Let us note that previous studies on ferronematics with other magnetic nanoparticles coated with surfactants at lower concentrations (< 0.1 vol %) reported a monophasic behavior with no variation of the clarification temperature.

SAXS experiments

Optical microscopy has indicated that the I-N transition is concomitant with the apparition of a dispersed phase dense in magnetic nanoparticles in coexistence with the nematic host phase containing very few particles or even not at all. Such phase separation can be studied using small angle neutron or X-ray scattering, two techniques that are well suited to study the structure and interactions between nanoparticles in ferrofluids and materials derived from them. SAXS is appropriate here because the contrast between the nematic matrix and the ferric oxide is quite important, so that the signal of 5 CB can be considered as a background scattering (supporting information). The cross-correlations between nanoparticles in ferronematics are pointed out by comparing the intensity scattered by the composite systems to the one of the dilute ferrofluid, behaving as an ideal gas. SAXS experiments are performed on two samples at two different volume fractions Φ (equal to about 0.2 and 0.7 % respectively) and at different temperatures to follow the interactions between nanoparticles as a function of temperature. These experiments were done in the LURE laboratory using synchrotron radiation (beamline D24, Orsay, France). The samples are introduced in Lindemann X-ray glass capillaries of 1 mm inner diameter placed horizontally in a Mettler F82 temperature stage. Different scattering patterns in transmission mode are recorded as a function of temperature with increasing or decreasing rates of ± 1 °C/min. The distance from the sample to the detector was 1750 mm enabling to cover the following q-range : 9. 10 -3 -2. 10 -1 Å -1 . Each SAXS curve is the average of four independent frames, each obtained with an acquisition time of 100 s. We notice from the graphs that the intensity is higher when the sample is in the isotropic state and decreases regularly when reaching the isotropic-nematic transition. The opposite phenomenon is observed in the reverse way. We think that it is due to the sedimentation of the droplets to the bottom of the capillary, because they are rich in nanoparticles and thus with a higher mass density than the nematic phase below T C . That would result in a lower concentration of nanoparticles analyzed in the beam, and so a lower scattered intensity. As control experiments, we let first the sample at rest for 24h and we observe the intensity slowly increasing by spontaneous homogenization; then, we rotate the capillary by 180° around its axis, and we check that the intensity further increases by a factor three (see curves at 34 °C). This variation of nanoparticles concentration in the beam due to sedimentation of bi-phasic samples is also responsible for the difference between the plateau value S(q) at large q and the expected value of 1.

First of all we determine the form factor I FF (q) in a stable dilute ferrofluid, which represents intra-particle density correlations due to their shape convolved with the polydispersity of sizes. The background signal I Bk (q) without capillary is also recorded. To take in consideration the contribution I LC (q) of the liquid crystal to the signal I FN (q) of the ferronematics, we record the intensity scattered by pure 5CB at different temperatures between 33°C and 36°C. The signals obtained at all temperatures are strictly identical and thus can be averaged together. In the studied q-range I LC (q) appears independent of temperature on each side of N-I transition because the signature of the nematic order occurs at higher q values. In our experiments, the liquid crystal only contributes to the high-q background and thus can be subtracted (supporting information) to extract the signal of nanoparticles only. All transmitted X-ray intensities T Bk , T LC , T FF and T FN , are measured with an air ionization chamber. As a result, the structure factor is calculated at all temperatures using the following equation: By this way, the structure factor of the nanoparticles is determined as a function of temperature for two samples with a volume fraction of nanoparticles of 0.725 % and 0.195 % respectively. These SAXS experiments being sensitive mainly to the nanoparticles, they provide a signature of the I to N transition specific to the nanoparticles, pointing out the effect of the transition of the LC matrix on their spatial organization.

At high temperature where the sample is in the isotropic and homogeneous state, S(q) is nearly flat except at lowest q values where it slightly decreases, which tells us about repulsive interactions between nanoparticles (low compressibility). When temperature is decreased below a threshold T C , a correlation peak appears suddenly. From the top of this peak at the abscissa q max , we deduce the more likely distance between the particles d max = 2π/q max . Thus we obtain an estimate of the local volume fraction For the more concentrated sample (0.7 %) a local volume fraction of 17 % is obtained and for the less concentrated one (0.2 %), 18 %. The value of Φ local does not vary significantly with the average Φ measured by iron titration and is much higher than Φ. Therefore we deduce that Φ local measured by SAXS is the volume fraction of nanoparticles inside the droplets observed by optical microscopy below T (N-I) . As a consequence, the T C temperature defined as the appearance of the correlation peak is ascribable to the appearance of the droplets and therefore directly related to T (N-I) of the ferronematic.

For a given sample, reproducible results for T C were obtained when increasing and decreasing temperature several times, independently of the sample history. Besides, the two samples do not indicate the same temperature T C : for the more concentrated sample T C = 32.8-33 °C (figure 7), whereas for the less concentrated sample, T C = 34-34.5 °C (the range of transition is not broader but we recorded less spectra around the transition, figure 8). This dependence of T C with the average concentration of particles is in agreement with the variation of the clarification temperature obtained by DSC thermograms : T (N-I) =34.1 °C at Φ=0.7 % and T (N-I) =34.7 °C at Φ=0.2 % (figure 5). Even though the slight differences (0.4-1 °C) between T C and T (N-I) are likely ascribable to an experimental difference between the temperature stages used for each method, we cannot conclude for sure to the equivalence of T C and T (N-I) . Nevertheless, the results of these two techniques converge to the same conclusion that both temperatures T C and T (N-I) decrease simultaneously. These temperature shifts are related to the concentration of free BNE soluble in the nematic phase.

CONCLUSION

Colloidal dispersions of small particles in nematic liquid crystals are an interesting type of soft matter. The difference from ordinary colloids arises from the orientational ordering of the calamitic molecules and the resulting structure in the colloid. In this work, we present a detailed study of the phase behavior of 5CB with incorporated magnetic nanoparticles by different techniques including optical microscopy, DSC, and SAXS. We have found a multi-scale organized system: magnetic nanoparticles of maghemite confined inside ferronematic droplets, themselves dispersed in a nematic host. By introducing a large amount of magnetic nanoparticles in a nematic host, we have found indeed a phase separation between droplets rich in nanoparticles and a continuous nematic LC empty of nanoparticles and containing unadsorbed surfactant. This 2-phase behavior has never been reported in previous works, certainly because authors used much lower particles concentrations as ours (Φ of 5×10 -4 % at most against Φ > 0.2 % here). We have demonstrated that the transition temperatures T (N-I) measured by DSC and T C by SAXS are both affected by the presence of nanoparticles and surfactant concentration in a similar way, which is a decrease. The DSC measurements show a decrease of the T (N-I) temperature linear with Φ as well as a widening of the corresponding peak. These two elements lead us to conclude on the partial solubilization of some species in the liquid crystal in the nematic phase, which we have identified to be pure surfactant. Concerning the possible discrepancy between T C associated to the presence of droplets and T (N-I) related to the nematic host phase, experiments could be attempted in future on an experimental set-up combining SAXS and DSC simultaneously. Other perspectives to be explored could be: using the dipolar forces between the magnetic droplets under field to probe the elasticity of the nematic matrix; checking the existence of a hysteresis loop in the magnetization curve of ferronematics as predicted theoretically, 1 obtaining true homogeneous ferronematics by controlling the anchoring of the LC on the nanoparticles. This last goal could be reached by grafting mesogenic molecules resembling to the matrix. More generally, the role of the interaction between the "surfactant" molecules covering the nanoparticles and the thermotropic molecules of the matrix is of prime importance and will be clarified in a forthcoming study; this needs to coat the magnetic nanoparticles by several types of molecules that will interact differently with 5CB.

Supporting information:

The distribution of the diameters of the nanoparticles used in this study is determined by fitting either the magnetization curve or the form factor of the dilute ferrofluid. As ferrofluids are giant paramagnetic liquids indeed, their magnetization curve versus the applied magnetic field follows a Langevin's law, 28,29 as long as their interactions are negligible i. e. for small volume fractions Φ < 1 %. The measured magnetization is highly sensitive to the distribution of diameters of the magnetic nanoparticles in the sample, 30, [START_REF] Chantrell | [END_REF] for which we assume a Log-normal distribution law calculated from: Supporting information 1: Magnetization curve of the ferrofluid in dichloromethane measured with a homemade vibrating sample magnetometer. The magnetization M is normalized by the value at saturation M s = 42 Oe is plotted vs. the applied magnetic field H (Oe). The plateau value corresponds to a volume fraction Φ=M s /m s =1.2% where m s =3400 Oe is the specific magnetization of colloidal maghemite. 32 The two parameters d 0 and σ describing the size polydispersity enable to fit the magnetization at both high (a) and low (b) fields. the empty beam, the dilute ferrofluid and the liquid crystal 5CB alone at different temperatures around T (N-I) .

                -

Figure 1 :

 1 Figure 1: Observation of the microphase separation of a typical ferronematic sample of this study by optical microscopy under parallel (a, b, c, d,) or crossed polarizers (e, f, g, h, i). Pictures (a), (h) and (i) are above T (N-I) (and all the other ones are below). The scale is 50µm. (a): isotropic phase above T(N-I) in an almost completely homogeneous state, the orange color being slowly disappearing; (b): sudden apparition of an interface at T(N-I); (c): formation of round droplets; (d): shrinking of the droplets and concentrating of the magnetic materials inside; (e): observation of the strings of droplets superposed with the disinclination lines of the nematic matrix; (f): observation of black crosses inside the droplets; (g): growth of the droplets when the temperature is increased; (h): above T(N-I), dissolution of the droplets into the nematic and advance of the isotropic (black) phase; (i): homogeneous isotropic state almost everywhere.

Figure 2 :Figure 3 :

 23 Application of a magnetic field (B=0.03 Tesla) to the droplets after the demixing. Polarizers are parallel. The scale bar is 50 µm. (a): Before application of the field, spherical droplets are present, with diameters ranging from 1 to 7 µm (with a maximum of the distribution around 4 µm); (b): after 9 min of field application, most droplets are found within chains formed by magnetic dipolar attractions; (c): after switching off the field, the droplets remain attached but the orientation of the chains have started to randomize. Application of a magnetic field (B=0.03 Tesla) since the beginning of the demixing below T(N-I) observed under parallel (a) and crossed polarizers (b, c). (a): the droplets are not only forming chains, but they are also elongated as prolate ellispoids; (b): under crossed polarizers, the orientation of the chains appears independent of the Schlieren texture of the nematic environment; (c): after release of the magnetic field, both chaining and ellipsoidal deformation persist, but they exhibit random orientations.

Figure 4 :

 4 Figure 4: DSC thermograms on heating at 1°C/min for 5CB ferronematic with different volume fractions of maghemite nanoparticles.

Figure 5 :

 5 Figure 5: Dependence of the phase transition temperature T(N-I) from the nematic phase to the isotropic phase (determined on heating at 1 °C/min) with the volume fraction on nanoparticles. The horizontal lines represent the two control experiments made without nanoparticles but with the indicated concentration of BNE surfactant.We see that the decrease of T (N-I) starts from the lowest value of Φ, which proves that no threshold concentration of particles is required for the 2-phase behavior. From the almost

1 )Figure 6 :

 16 Figure 6: Curves showing the dependence of the structure factor of nanoparticles at different temperatures with a rate of 1 °C/min as a function of increasing (INC) or decreasing (DEC) temperature for the more concentrated sample (volume fraction = 0.725 %). * capillary turned around its symmetry axis N. B.:We notice from the graphs that the intensity is higher when the sample is in the isotropic state and decreases regularly when reaching the isotropic-nematic transition. The opposite phenomenon is observed in the reverse way. We think that it is due to the sedimentation of the droplets to the bottom of the capillary, because they are rich in nanoparticles and thus with a higher mass density than the nematic phase below T C . That would result in a lower concentration of nanoparticles analyzed in the beam, and so a lower scattered intensity. As control experiments, we let first the sample at rest for 24h and we observe the intensity slowly increasing by spontaneous homogenization; then, we rotate the capillary by 180° around its axis, and we check that the intensity further increases by a factor three (see curves at 34 °C). This variation of nanoparticles concentration in the beam due to sedimentation of bi-phasic samples is also responsible for the difference between the plateau value S(q) at large q and the expected value of 1.

1 Figure 7 : 1 Figure 8 :

 1718 Figure 7: Zoom close to the Isotropic-Nematic transition for the more concentrated sample (volume fraction = 0.725 %).

  the characteristic diameter of the nanoparticles that we estimate by d 0 SAXS obtained from the form factor (see Supporting information).

  diameter d 0 = exp <ln d> and a standard deviation σ. Combining the Langevin's law with the distribution P(d) provides us with two parameters d 0 and σ used to fit the experimental curves. The same Log-normal distribution law is also used to compute the theoretical form factor of the dilute ferrofluid, assumed to be a polydisperse assembly of spherical nanoparticles. By adjusting the magnetization curve and the experimental form factor of the ferrofluid used in this study, the characteristic diameters d 0 mag =6.3 nm and d 0 SAXS =7.6 nm are found respectively, both with σ =0.4 corresponding to a relatively broad distribution. The discrepancy between the two methods originates from the magnetically disordered shell at the surface of the grains, which contributes to X-rays scattering but not to magnetization. In other words, the magnetic core of the nanoparticles is somehow smaller than their geometrical volume

1 )information 2 :

 12 Supporting SAXS intensities corrected by sample transmission as a function of the scattering vector q for

Acknowledgements:

We wish to thank C. Bourgaux as our local contact in the LURE synchrotron facility and D. Talbot who performed the AAS measurements. C. Da Cruz also thanks J. Malthête for the access to DSC technique at the Curie Institute.


E Garaio

J M Collantes

J A Garcia

F Plazaola

Stéphane Mornet

Franck Couillaud

Olivier Sandre

A wide-frequency range AC magnetometer to measure the specific absorption rate in nanoparticles for magnetic hyperthermia

Keywords: Specific Absorption Rate, Maghemite Nanoparticles, Magnetic hyperthermia, AC magnetometer

Measurement of specific absorption rate (SAR) of magnetic nanoparticles is crucial to assert their potential for magnetic hyperthermia. To perform this task, calorimetric methods are widely used. However, those methods are not very accurate and are difficult to standardize. In this paper, we present AC magnetometry results performed with a lab-made magnetometer that is able to obtain dynamic hysteresis-loops in the AC magnetic field frequency range from 50 kHz to 1 MHz and intensities up to 24 kA.m -1 . In this work, SAR values of maghemite nanoparticles dispersed in water are measured by AC magnetometry. The so obtained values are compared with the SAR measured by calorimetric methods. Both measurements, respectively by calorimetry and magnetometry, are in good agreement. Therefore, the presented AC magnetometer is a suitable way to obtain SAR values of magnetic nanoparticles.

Introduction

Hyperthermia based therapies are medical practices that consists of rising the temperature of living tissue above the physiological values. They are useful for cancer treatment (i) to damage and kill cancer cells (thermo-ablation), (ii) to change their sensitivity to radiation or drugs (thermo-sensitization) or to (iii) induce local drug release from thermo-sensitive vehicles. As hyperthermia could be performed locally, therapy essentially affects the targeted tumor avoiding damage to surrounding tissues and limiting systemic effects [START_REF] Dickson | Hyperthermia in the treatment of cancer[END_REF][START_REF] Moyer | The role of hyperthermia in optimizing tumor response to regional therapy[END_REF]. Photons (Laser), microwaves, radio-frequency or focused ultrasound are energy sources used for local hyperthermia. Magnetic nanoparticles that release heat while activated in an alternating magnetic field have also been proposed to induce tumor hyperthermia [START_REF] Palazzi | The role of hyperthermia in the battle against cancer[END_REF][START_REF] Habash | Performance analysis of a multicast system in wdm single-hop broadcast-and-select optical network[END_REF]. Such magnetically activated nanoparticles have been shown to enhance efficacy of radiotherapy and chemotherapy against cancer [START_REF] Jordan | Magnetic fluid hyperthermia (mfh): Cancer treatment with ac magnetic field induced excitation of biocompatible superparamagnetic nanoparticles[END_REF][START_REF] Quesson | A method for mri guidance of intercostal high intensity focused ultrasound ablation in the liver[END_REF]. This approach passed a phase II clinical trial in conjunction with conventional radiotherapy [START_REF] Maier-Hauff | Efficacy and safety of intratumoral thermotherapy using magnetic iron-oxide nanoparticles combined with external beam radiotherapy on patients with recurrent glioblastoma multiforme[END_REF] and is authorized for cancer treatment since 2011.

To further assess the potential of magnetic nanoparticles for magnetic hyperthermia, accurate measurement of their heat dissipation rate is necessary. In other words, their specific absorption rate (SAR), which corresponds to the absorbed energy per unit of mass of nanoparticle, has to be determined. This parameter, is quite dependent on magnetic field frequency and intensity as well as on nanoparticle size, shape, material, agglomeration rate and dispersion media [START_REF] Hergt | Magnetic particle hyperthermia: nanoparticle magnetism and materials development for cancer therapy[END_REF][START_REF] Rosenweig | Heating magnetic fluid with alternating magnetic field[END_REF][START_REF] Ma | Size dependence of specific power absorption of fe3o4 particles in ac magnetic field[END_REF].

At the present, mainly calorimetric methods [START_REF] Hergt | Magnetic particle hyperthermia: nanoparticle magnetism and materials development for cancer therapy[END_REF][START_REF] Ma | Size dependence of specific power absorption of fe3o4 particles in ac magnetic field[END_REF][START_REF] Fortin | Size-sorted anionic iron oxide nanomagnets as colloidal mediators for magnetic hyperthermia[END_REF][START_REF] Kita | Heating characteristics of ferromagnetic iron oxide nanoparticles for magnetic hyperthermia[END_REF] are used to measure SAR values of magnetic nanoparticles. For nanoparticles dispersed in a fluid medium, the specific absorption rate is obtained experimentally by the following formula [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF]:

SAR = m d C p,d m N P dT dt t=0 (1)
where m d and C p,d are the mass and heat capacity of the dispersion medium respectively while m N P is the mass of nanoparticles. However, there are many factors that affect the accuracy of calorimetric methods [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF][START_REF] Huang | On the measurement technique for specific absorption rate of nanoparticles in an alternating electromagnetic field[END_REF]. For samples with high absorption power, fast heating causes large temperature gradients into the sample and thus, the recorded SAR can be very dependent on temperature sensor positioning [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF]. The method and time interval used to determine initial temperature slope in eq. ( 1) also adds uncertainties [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF].

In addition, thermal losses also cause under-estimating the SAR value, thus properly designed adiabatic conditions for the experiment are needed [START_REF] Natividad | Adiabatic vs. non-adiabatic determination of specific absorption rate of ferrofluids[END_REF]. Therefore the volume and geometry of the sample are important to specify, for reasons related to the homogeneity of the applied magnetic field and to the surfaceto-volume ratio, determining the heat transfers. SAR measurements by calorimetry are indeed based on the measurement of the maximum slope of the temperature increase, eq. ( 1), but the extension of the linear regime is always limited (except for ideal adiabatic conditions) by a plateau value ∆T max , after a duration that increases with the sample volume. This maximum temperature increment that can be reached by magnetic field hyperthermia (MFH ) directly depends on the surface area of the sample, as demonstrated by the square dependence with diameter on magnetic droplets in a microfluidic circuit [START_REF] Habault | Droplet microfluidics to prepare magnetic polymer vesicles and to confine the heat in magnetic hyperthermia[END_REF].

In order to find a more accurate method to obtain the SAR of magnetic nanoparticles, different ways are proposed in the literature. Ahrentorp et al [START_REF] Ahrentorp | Sensitive high frequency ac susceptometry in magnetic nanoparticle applications[END_REF] obtained SAR values by combining AC magnetic susceptibility and static magnetization curves. Also, methods based on Faraday's law of induction to obtain the dynamic magnetization, M (t), are proposed. Cobos et al. [START_REF] Cobos | High resolution system for nanoparticles hyperthermia efficiency evaluation[END_REF] measured the power dissipated by the nanoparticles through the determination of their in-quadrature magnetic moment. In other works, however, the SAR was obtained directly from AC hysteresis loops area in a small [START_REF] Bekovic | Determination of the heating effect of magnetic fluid in alternating magnetic field[END_REF] and large [START_REF] Veverka | Magnetic heating by cobalt ferrite nanoparticles[END_REF][START_REF] Mehdaoui | Influence of a transverse static magnetic field on the magnetic hyperthermia properties and high-frequency hysteresis loops of ferromagnetic feco nanoparticles[END_REF][START_REF] Gudoshnikov | Hysteresis losses in a dense superparamagnetic nanoparticle assembly[END_REF][START_REF] Gudoshnikov | Ac magnetic technique to measure specific absorption rate of magnetic nanoparticles[END_REF] applied magnetic field regime. In these works based on Faraday's induction law, the applied magnetic field frequency was always below 130 kHz.

In this article, we present an AC magnetometer to measure dynamic hysteresis cycles of magnetic nanoparticle dispersions, which extends the range of measurement up to 1 MHz. This gives valuable information on their dynamic magnetic behavior. Furthermore, the SAR value can be directly obtained from the area of the hysteresis cycles. The device is based on Faraday's induction law and works in the frequency range 50 kHz to 1 MHz. To calibrate the system at high frequencies (above 250 kHz), a personal computer (PC) performs a Fourier analysis of the signal induced by the sample. In the present work, SAR values of maghemite (γ -Fe 2 O 3 ) nanoparticles dispersed in water are measured and compared to the values obtained by calorimetric methods.

Experimental

Magnetic Nanoparticles

The magnetic nanoparticles are synthesized by the aqueous alkaline co-precipitation route of Fe 2+ and Fe 3+ salts, also called Massart's synthesis [START_REF] Massart | Preparation of aqueous magnetic liquids in alkaline and acidic media[END_REF]. The resulting nanoparticles of magnetite (Fe 3 O 4 ) are oxidized by iron nitrate into the pure Fe +III isomorphous maghemite phase [START_REF] Tourinhoa | Synthesis and magnetic properties of manganese and cobalt ferrite ferrofluids[END_REF]. Compared to other syntheses at high temperature in non-aqueous media, the co-precipitation route has the advantage of providing large quantity (hundreds of g) but the drawback of a very large size-dispersity (typically from 5 to 20 nm). Therefore a size-grading method based on successive phase separation by adding electrolyte in excess was applied [START_REF] Massart | Preparation and properties of monodisperse magnetic fluids[END_REF]. Briefly, after synthesis the maghemite nanoparticles are dispersed in water in a nitric acidic medium (pH ∼ 2). Their dipolar attractions (Van der Waals and magnetic) are counterbalanced by electrostatic (double-layer) repulsion arising from the cationic charges at their surface. The addition of an excess of HNO 3 (pH ∼ 0.7-0.8) causes the screening of the charges and the destabilization of the suspension into two phases, respectively concentrated ("liquid-like") and diluted ("gas-like"). After magnetic sedimentation, the concentrated phase (C) is separated from the dilute supernatant (S), that is enriched in nanoparticles of smaller diameters (on the contrary, the C phase is enriched with the larger diameters). The process is repeated to isolate different fractions with much narrower size distribution than the initial suspension. In this work we need nanoparticles of the largest possible diameters to achieve a high SAR value, thus we study the C 1 C 2 C 3 fraction (after three separation steps). The exact procedure of phase separation and washing steps is detailed in the supporting information of several references [START_REF] Arosio | Hybrid iron oxide-copolymer micelles and vesicles as contrast agents for mri: impact of the nanostructure on the relaxometric properties[END_REF][START_REF] Vuong | A universal scaling law to predict the efficiency of magnetic nanoparticles as mri t2-contrast agents[END_REF].

The weight concentration of this C 1 C 2 C 3 fraction is c 0 = 99 g.L -1 = 9.9 ×10 4 g.m -3 as measured by magnetometry (Fig. 2.1) and UV-Vis spectroscopy (Fig. 2). It was diluted 3 times (c= 33 g.L -1 ) to perform both the calorimetry and dynamic hysteresis measurements. The accurate determination of concentration of iron oxide in the suspension is a pre-requisite for a proper SAR measurement. Regarding colloidal stability, the hydrodynamic diameter of the C 1 C 2 C 3 fraction diluted 400 times in HNO 3 at pH ∼ 2 is 32 ± 0.8 nm (from 5 successive measurements by dynamic light scattering at 90 • C with a NanoZS90 instrument, Malvern, UK), with a low polydispersity index (PDI = 0.137). These nanoparticles are thus perfectly stable, as expected from the electrostatic repulsions created by their positive surfaces charges in acidic medium. It is in this diluted state that the iron oxide concentration was checked by a non destructive method consisting in recording the whole UV-Vis absorption spectrum from 240 to 800 nm and comparing it to a calibration curve derived from standards [START_REF] Galimard | Thirty-femtogram detection of iron in mammalian cells[END_REF]. ). The deviation between the experimental spectra and the calibration curve towards large wavelengths is ascribed to a light scattering background (since the nanoparticles are particularly large in this study). The plateau for the larger light path (L=10 mm) is an artifact due to the lower limit of the detector.

1 E + 0 0 1 E + 0 1 1 E + 0 2 1 E + 0 3 1 E + 0 4 F F J F 1 -C 1 C 2 C 3 H N O 3 d i l 4 0 0 2 m m F F J F 1 -C 1 C 2 C 3 H N O 3 d i l 4 0 0 1 0 m m C a l i b r a t i o n A b s ( m o l / L / c m ) ، | ( n m )

Description of the AC magnetometer

The AC magnetic field is generated by an air-coil connected in parallel with a resonant circuit fed by a linear power amplifier [START_REF] Plazaola | Specific absorption rate of magnetite nanoparticle powders with and without surrounding organic ligands[END_REF]. The system that acquires the dynamic magnetization of the sample, M (t), consists of tree pickup coils (see figure 3). Inside the air-coil, two concentric and oppositely wounded pickup coils connected in series are placed, one on top of the other (coils 1 and 2 in figure 3). The upper coil surrounds the sample holder located in the center of the coil and the lower one, called compensation coil, is located in such a way that without any sample in the sample-holder, the induced voltage is minimal. The third pickup coil, placed outside the air-coil, measures the applied magnetic field intensity and phase (coil 3 in figure 3). It has been checked that the signal induced in this coil is exactly in phase with the magnetic field intensity applied to the sample for all frequencies. The magnetization M (t) is obtained by:

V (t) = ξ • f • M (t) ( 2
)
where f is the magnetic field frequency and ξ a coupling constant calculated numerically from the setup geometry. The signal V (t) induced by the sample into the pick-up coils is recorded by a data acquisition system and sent to a PC.

Temperature of the sample is recorded by a fiber optic thermometer insensitive to RF magnetic fields with a narrow tip of 0.4 mm (Opsens, Qubec, QC, Canada). In order to avoid thermal dilatation and minimize heat flow out of the sample, the sample-holder is made of ceramic material.

The sample holder is cylindrical with a volume of 1.5 mL and aspect ratio L/d of 3 (this parameter is important to specify both for the surface area and the demagnetization factor of the magnetized sample). Due to the lack of perfect symmetry of the two pick-up coils connected in series, a non-zero voltage is recorded even when there is no magnetic sample. To calibrate it, the induced voltage magnitude and phase in the absence of the sample are stored. Then, these values are used to vectorially compensate the signal measured when the sample is present. As it can be appreciated on the AC hysteresis loops present in figure 4, the magnetization curves at different applied magnetic field intensities do not cross each other, which confirms the correct compensation.

At high frequencies (above 250 kHz), the contribution of higher order harmonics generated by the power amplifier that feeds the system, tend to distort the AC hysteresis loops. In order to increase the maximum operational frequency, a spectral Fourier analysis of the signal is preformed in the calibration step (with no sample) to measure the distribution of non-desired harmonics. Next, the high frequency harmonic contribution is removed from each measurement. This is an essential point in order to get reliable measurements up to 1 MHz.

SAR measurements

The power volume density P vd and SAR are obtained from the following equations:

P vd = f • T M t • dH t (3) SAR = f c • T M t • dH t (4)
where M t is the instantaneous magnetization (A.m -1 ) at time t, H t the field intensity (A.m -1 ) at time t, f (Hz) the applied magnetic field frequency and c (kg.m -3 ) the nanoparticle weight concentration of iron oxide in the dispersing medium of volume V d . In equations ( 3) and ( 4), the units of P vd and SAR values are given in W.m -3 and W.kg -1 respectively (although in this text, for convenience, W.cm -3 and W.g -1 are used). The integration is done over a period of the oscillating magnetic field, T = 2π/f .

To obtain the SAR values from the calorimetric method, equation ( 1) has been also used, for comparison.

The specific heat capacity of water has been assumed to be 4.18 J.g -1 K -1 . To obtain the initial temperature slope in eq. ( 1), the temperature evolution curve has been fitted to a second order polynomial law [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF], eq.

( 5), and to an exponential relaxation law [START_REF] Bekovic | Determination of the heating effect of magnetic fluid in alternating magnetic field[END_REF], eq. ( 6). Here we aim at comparing both methods with two different measurement time intervals: T meas = 6 and 12 seconds (defined as the total duration of the applied magnetic field). In addition, the maximum derivative of temperature over time along the measurement period has been taken as initial slope of the curve, eq. ( 7), too.

∆T = dT dt t=0 • t -at 2 (5) ∆T = τ • dT dt t=0 • 1 -exp - t τ ( 6
)
dT dt t=0 = dT dt max (7)

Result and Discussions

Figure 4 shows the dynamic hysteresis cycles of the maghemite nanoparticles sample at applied magnetic field frequencies of 394 and 785 kHz as well as the SAR values obtained from the integration of their area according to eq. ( 4). The dependence of SAR with the applied magnetic field intensity, Happ, is almost quadratic below 10 kA • m -1 , while above this value, it is almost linear. The SAR values at 394 kHz are in good agreement with values measured by calorimetry on similar large size-sorted maghemite nanoparticles [START_REF] Ahrentorp | Sensitive high frequency ac susceptometry in magnetic nanoparticle applications[END_REF], respectively 72 W/g (compared to 70.4 W/g here) under a field of 11 kA • m -1 and 200 W/g (vs. 193 W/g here) under a field of 24 kA • m -1 . In the same reference, the SAR values were estimated from AC susceptometry: the corresponding values were 70 W/g and 215 W/g for field values of 11 and 24 kA • m -1

respectively. The deviation between calorimetry and AC susceptometry for the larger field value in this previous work [START_REF] Ahrentorp | Sensitive high frequency ac susceptometry in magnetic nanoparticle applications[END_REF] is likely ascribed to the use of eq. ( 4) in a linearized form (with some correction factor), introducing the susceptibility χ" = M t /H t . Here we compute the whole integral on a field period T without simplification, therefore our setup can be named "AC magnetometer" rather than "AC susceptometer".

SAR measurement

For applied magnetic field frequencies of 70, 394, 785, 958 kHz and intensities of 11 and 24 kA•m -1 , SAR has been measured by both calorimetry and AC magnetometry. To obtain the initial time slope in eq. ( 1), the different three procedures described in the previous section are used. Table 1 and figure 5 compare the so obtained SAR values. In order to distinguish between the SAR values obtained from different methods,

-3 0 -2 0 -1 0 0 1 0 2 0 3 0 -4 0 -3 0 -2 0 -1 0 0 1 0 2 0 3 0 4 0 M / c ( A m 2 . k g -1 ) H a p p ( k A . m -1 ) f = 3 9 4 k H z (b) -3 0 -2 0 -1 0 0 1 0 2 0 3 0 -4 0 -3 0 -2 0 -1 0 0 1 0 2 0 3 0 4 0 M / c ( A m 2 . k g -1 (a)
) SAR area represents the values obtained from hysteresis loop area. SAR 2poly has been obtained fitting the temperature evolution curve to the second order polynomial of eq. ( 5), whereas SAR expo has been obtained by fitting to the exponential of eq. ( 6), with time intervals of 6 and 12 seconds. Finally, SAR DT max is obtained by the maximum temperature derivative over time, eq. ( 7), along measurement time. As it can be observed in table 1 and figure 5, when P vd is above 1 both calorimetry and AC magnetometry differ the less (below 6%). When the temperature measurement time interval is 6 seconds, however, the obtained SAR 2poly and SAR expo values are smaller than SAR area .

H a p p

On the other hand, when the maximum time derivative is taken SAR DT max values are larger.

Figure 6, represents the temperature evolution of the sample after the magnetic field is switched on for different measured P vd . As it can be observed, when P vd is 5.38 and 6.8 W.cm -3 , the temperature initially rises slowly and after 0.5 seconds, it starts to increase rapidly. Similar behaviour can be found in Wang et al. [START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF] but 5 second after the field is applied. Therefore, when a small temperature measurement time interval is considered, the obtained initial temperature slope in eq. ( 1) can be underestimated due to this phenomenon that can be ascribed to thermal inertia of the measuring system.

When P vd is below 1 W.cm -3 , however, the difference between both methods increases up to 80% (see figure 5). In this case, however, calorimetric methods are less accurate due to the heat flux coming out the sample holder. As it can be observed in figure 6, the temperature increase is very small when P vd is 0.27 W.cm -3 . Moreover, fitting the temperature evolution curve to the exponential in eq. ( 6), gives a total power of 0.13 W flowing out of the sample when ∆T is 1 • C. This outgoing power is comparable with the total power generated by the sample (0.4 W), corresponding to the plateau temperature reached when the created and lost power compensate.

Conclusions

This paper presents an AC magnetometer built to measure dynamic hysteresis cycles of magnetic nanoparticle dispersions, which extends the range of measurement from 50 kHz to 1 MHz, giving valuable information on their dynamic magnetic behaviour. By means of this device, the SAR of quasi spherical maghemite nanoparticles with a distribution of the magnetic core sizes around 12 nm in size has been measured by integrating the area of the AC hysteresis loop. The obtained values are comparable to previously measured values in maghemite nanoparticles with similar characteristics (synthesis route and distribution of sizes).

To check the method, the SAR of the same sample has been measured also by calorimetric methods.

In general, the values obtained by both types of methods are similar within an error of 12%. However the values obtained by calorimetry depend on the curve fitting procedure to obtain the initial time slope in eq.

(1). The uncertainties arise from non-linearity in the initial temperature evolution curve (see figure 6). On the other hand, when the dissipated power density P vd is too small (be it from a not optimal frequency or a too low concentration) the non-adiabatic behaviour of the sample holder increases the differences between calorimetric methods.

Due to a smaller measurement uncertainty, AC magnetometry results in a more accurate and direct method to measure SAR values of nanoparticle dispersions than calorimetric methods. This advantage is true for applied magnetic field frequencies from 50 kHz to 1 MHz and intensities up to 24 kA.m -1 . Moreover, the time required in the measurement process is shorter because a previous thermalization is not required.

M 1 )

 1 Figure 1: a) TEM image of the size-sorted fraction C 1 C 2 C 3 (scale bar length is 100 nm). The image is processed with ImageJ with a threshold and a watershed filter in order to detect the border lines of the nanoparticles and enable an automatic counting; b) Histogram built by processing 5 images with a statistics on N ∼ 1600 nanoparticles; the solid line is a Log-normal distribution of median d T EM 0

Figure 2 :

 2 Figure 2: Non destructive determination of the iron oxide concentration by UV-Vis spectroscopy. The spectrum of the sample diluted 400 times in HNO 3 at pH∼2 (for colloidal stability) is recorded between 240 and 800 nm. The extinction coefficient e(l)calculated after normalization by the light path L (cm) and the equivalent iron concentration (1.24 mol • L -1 as determined here) is fitted to a calibration curve obtained from measurements on samples at concentrations titrated by atomic emission spectroscopy[START_REF] Galimard | Thirty-femtogram detection of iron in mammalian cells[END_REF]. Then the weight concentration c 0 = 99 g • L -1 is simply deduced by multiplying by 80 g • mol -1 (∼half the molar mass of γ -Fe 2 O 3 ). The deviation between the experimental spectra and the calibration curve towards large wavelengths

Figure 3 :

 3 Figure 3: Schematic of the experimental setup.

Figure 4 :

 4 Figure 4: Hysteresis cycles of maghemite nanoparticles a) at 394 kHz, b) at 785 kHz. c) SAR values obtained from the area of the cycles, versus applied magnetic field at 394 and 785 kHz. Sample volume is V d = 1.5 mL and maghemite concentration c = 33 g • L -1 .

Figure 5 :

 5 Figure 5: Relative difference between the SAR values obtained from calorimetric methods and AC magnetometry as a function of power volume density P vd (logarithmic scale).

Figure 6 :

 6 Figure 6: Sample's temperature increase evolution with time for different measured P vd . The inset displays the non-linearities of temperature evolution during the first second.

Table 1 :

 1 W • cm -3 , the SAR values obtained by thermal and electromagnetic methods differ by less than 12%. However, SAR values obtained by calorimetric methods depend on the procedure used to obtain the initial time slope in eq. (1). When temperature evolution is fitted to a second order polynomial with a time interval of 12 seconds, values obtained from AC Magnetometry Calorimetric method. SAR thermal (W.g -1 ) Measured SAR values with AC magnetometry (SARarea) and calorimetric methods, see text.

	Happ	F req.	P vd	SARarea	SAR 2poly	SARexpo	SAR DT max
	(kA.m -1 ) (kHz)	(W.cm -3 )	(W.g -1 )	6 seconds 12 seconds 6 seconds 12 seconds
	11	75	0.22 ± 0.01	8.3 ± 0.2	13 ± 1	10.3 ± 0.5	15 ± 2	10.8 ± 0.6	10 ± 1
	11	394	1.91 ± 0.02 70.4 ± 0.7	67 ± 1	70.6 ± 0.5	67 ± 1	70.8 ± 0.5	77 ± 1
	11	785	4.41 ± 0.05	163 ± 2	157 ± 1	171 ± 1	157 ± 1	172 ± 1	178 ± 1
	11	958	5.6 ± 0.2	207 ± 4	193 ± 2	209 ± 1	193 ± 1	210 ± 1	217 ± 1
	24	394	5.27 ± 0.07	193 ± 2	186 ± 2	192 ± 1	185 ± 2	193 ± 1	202 ± 1
	24	785	12.8 ± 0.2	472 ± 5	442 ± 6	474 ± 2	442 ± 6	478 ± 2	502 ± 1
	24	958	16.1 ± 0.2	595 ± 5	570 ± 6	629 ± 2	570 ± 6	640 ± 2	667 ± 1


Harmonic phases of the nanoparticle magnetization: an intrinsic temperature probe

Eneko Garaio, 1, a) Juan-Mari Collantes, 1 Jose Angel Garcia, [START_REF] Dutz | Magnetic nanoparticle heating and heat transfer on a microscale: Basic principles, realities and physical limitations of hyperthermia for tumour therapy[END_REF][START_REF] Laurent | Magnetic iron oxide nanoparticles: Synthesis, stabilization, vectorization, physicochemical characterizations, and biological applications[END_REF] Fernando Plazaola, [START_REF] Hergt | Magnetic particle hyperthermia: nanoparticle magnetism and materials development for cancer therapy[END_REF] and Olivier Sandre 4, b) 1) Elektrizitatea eta Elektronika Saila, UPV/EHU, 644.48080 Bilbao. Spain [START_REF] Dutz | Magnetic nanoparticle heating and heat transfer on a microscale: Basic principles, realities and physical limitations of hyperthermia for tumour therapy[END_REF] Fisika Aplikatua II Saila, UPV/EHU, 644.48080 Bilbao. Spain Magnetic fluid hyperthermia is a promising cancer therapy in which magnetic nanoparticles act as heat sources activated by an external AC magnetic field. The nanoparticles, located near or inside the tumor, absorb energy from the magnetic field and then heat up the cancerous tissues. During the hyperthermia treatment, it is crucial to control the temperature of different tissues: too high temperature can cause undesired damage in healthy tissues through an uncontrolled necrosis. However, the current thermometry in magnetic hyperthermia presents some important technical problems. The widely used optical fiber thermometers only provide the temperature in a discrete set of spatial points. Moreover, surgery is required to locate these probes in the correct place. In this scope, we propose here a method to measure the temperature of a magnetic sample. The approach relies on the intrinsic properties of the magnetic nanoparticles because it is based on monitoring the thermal dependence of the high order harmonic phases of the nanoparticle dynamic magnetization. The method is non-invasive and it does not need any additional probe or sensor attached to the magnetic nanoparticles. Moreover, this method has the potential to be used together with the magnetic particle imaging technique to map the spatial distribution of the temperature. a) eneko.garayo@ehu.eus b) olivier.sandre@enscbp.fr

I. INTRODUCTION

Tumor destruction with magnetic nanoparticles (MNPs) under an applied human tolerable AC magnetic field is a promising cancer therapy called magnetic fluid hyperthermia (MFH) or sometimes called magnetic hyperthermia [START_REF] Hergt | Magnetic particle hyperthermia: nanoparticle magnetism and materials development for cancer therapy[END_REF][START_REF] Dutz | Magnetic nanoparticle heating and heat transfer on a microscale: Basic principles, realities and physical limitations of hyperthermia for tumour therapy[END_REF] . The most common used heat-sources are superparamagnetic iron oxide nanoparticles. These nanoparticles are also used as contrast agents in magnetic resonance imaging (MRI) [START_REF] Laurent | Magnetic iron oxide nanoparticles: Synthesis, stabilization, vectorization, physicochemical characterizations, and biological applications[END_REF][START_REF] Pankhurst | Applications of magnetic nanoparticles in biomedicine[END_REF] and their spatial distribution can also be acquired by the magnetic particle imaging (MPI) technique [START_REF] Gleich | Tomographic imaging using the nonlinear response of magnetic particles[END_REF][START_REF] Rahmer | First experimental evidence of the feasibility of multi-color magnetic particle imaging[END_REF] , especially for in-vivo diagnostics, where this information is key for a proper magnetic hyperthermia treatment.

On the one hand, the control and mapping of temperatures in the tumor and the surrounding tissues is crucial during any hyperthermia treatment. The desired therapeutic effect may not be achieved with a temperature increment lower than expected. On the contrary, an excessive temperature increment can produce undesired damage to healthy tissues or too many necrotic cells [START_REF] Dutz | Magnetic particle hyperthermia -a promising tumour therapy?[END_REF] . There exist only few systems to measure and control the temperature in hyperthermia treatment. The use of optical fiber thermometry in magnetic hyperthermia provides a good way to acquire in situ local temperature through the luminescence of a semiconducting crystal (e.g. GaAs). However, it only provides the temperature in a discrete set of spatial points and, in addition, the minimum size of the fiber tip is around 200 µm (and it is very fragile and sensitive to mechanical stresses). Moreover, surgery is needed to place the tip in the desired place through a catheter, which may be extremely complicated.

Therefore, alternative remote sensing methods are subject of investigation. Some of them are based on MRI techniques that exploit the change with temperature of proton density, of T1 (longitudinal) water proton relaxation times, of water molecular diffusion coefficient or of proton resonant frequency through a phase signal analysis [START_REF] Quesson | Magnetic resonance temperature imaging for guidance of thermotherapy[END_REF] . Moreover, measurements of T1 relaxation times that are accurate enough to infer the temperature can be very time consuming and very sensitive to mechanical factors such as animal breathing. Another proposed method to control the temperature during magnetic hyperthermia treatment is the use of self-regulated magnetic nanoparticles as heat sources [START_REF] Epherre | Manganite perovskite nanoparticles for self-controlled magnetic fluid hyperthermia: about the suitability of an aqueous combustion synthesis route[END_REF][START_REF] Barati | Extraordinary induction heating effect near the first order Curie transition[END_REF] . The use of a lanthanide complex absorbed on the nanoparticles for thermometry as molecular thermometric probe [START_REF] Piñol | Joining Time-Resolved Thermometry and Magnetic-Induced Heating in a Single Nanoparticle Unveils Intriguing Thermal Properties[END_REF] , or the anchoring of a thermo-sensitive polymer at the surface or outer shell of the nanoparticles to modulate the MRI contrast 12 are also subjects of investigation. For the same thermometry purpose but not necessitating a chemical modification of the MNPs, Weaver et al. [START_REF] Weaver | Magnetic nanoparticle temperature estimation[END_REF] proposed a method based on the ratio of the 5 th and 3 rd harmonics of the magnetization generated by magnetic nanoparticles, varying the amplitude of the sinusoidal field at a fixed frequency of 1.47 kHz.

On the other hand, one of the most important parameters of magnetic nanoparticles design for magnetic fluid hyperthermia is their specific absorption rate (SAR). Two different approaches are used for SAR measurements. The most commonly used approach is the calorimetric method, consisting in measuring heating rates from the initial slope of temperature versus time [START_REF] Ma | Size dependence of specific power absorption of Fe 3 O 4 particles in AC magnetic field[END_REF][START_REF] Fortin | Size-sorted anionic iron oxide nanomagnets as colloidal mediators for magnetic hyperthermia[END_REF][START_REF] Kita | Heating characteristics of ferromagnetic iron oxide nanoparticles for magnetic hyperthermia[END_REF] . However, there are many factors that affect the accuracy of these methods [START_REF] Huang | On the measurement technique for specific absorption rate of nanoparticles in an alternating electromagnetic field[END_REF][START_REF] Wang | Potential sources of errors in measuring and evaluating the specific loss power of magnetic nanoparticles in an alternating magnetic field[END_REF] . An alternative approach consists in the measurement of the dynamic magnetization versus applied magnetic field [START_REF] Connord | An air-cooled Litz wire coil for measuring the high frequency hysteresis loops of magnetic samples-A useful setup for magnetic hyperthermia applications[END_REF][START_REF] Garaio | A multifrequency electromagnetic applicator with an integrated AC magnetometer for magnetic hyperthermia experiments[END_REF] . This method permits precise and quick SAR measurements, allowing multi-parametric study for different frequencies, field intensities and as a function of temperature [START_REF] Regmi | Temperature dependent dissipation in magnetic nanoparticles[END_REF][START_REF] Garaio | Specific absorption rate dependence on temperature in magnetic field hyperthermia measured by dynamic hysteresis losses (ac magnetometry)[END_REF] . Using the fundamentals and advantages of this last technique, we propose here an accurate, simple and fast method for monitoring and controlling the temperature of magnetic nanoparticles during magnetic hyperthermia. The method does not need any additional probe or sensor attached to the magnetic nanoparticles.

Fundamentally, it is based on the thermal dependence of the phase of the high order harmonics of the nanoparticles response to the magnetic field variation. Also, the method can be easily implemented to study the heat transfer between nanoparticles and the surrounding medium or other phenomena related to magnetic nanoparticles, for instance magnetic field induced drug-delivery.

Moreover, this method could be used together with the magnetic particle imaging technique to map the temperature. MPI measures the spatial distribution of the high order harmonics (see references [START_REF] Gleich | Tomographic imaging using the nonlinear response of magnetic particles[END_REF][START_REF] Rahmer | First experimental evidence of the feasibility of multi-color magnetic particle imaging[END_REF] ). In this case, the spatial distribution of the harmonic phases could be measured in order to map the temperature in the areas where the magnetic particles are placed.

II. EXPERIMENTAL

The magnetic iron oxide nanoparticles are identical to those used in a previous work on the comparison of SAR measurement by calorimetry and by AC magnetometry [START_REF] Garaio | A wide-frequency range ac magnetometer to measure the specific absorption rate in nanoparticles for magnetic hyperthermia[END_REF] . Briefly, a water dispersed maghemite nanoparticle sample was prepared by the alkaline co-precipitation route. This method usually leads to well crystalline and magnetic iron oxide nanoparticles but having a broad range of diameters. Therefore a size-grading process based on successive phase separation by an added electrolyte was applied [START_REF] Massart | Preparation and properties of monodisperse magnetic fluids[END_REF] , in order to isolate a fraction with the largest diameters i.e. around 15-20 nm, still below the threshold size above which iron oxide MNPs have their magnetic moments blocked at ambient temperature [START_REF] Salas | Controlled synthesis of uniform magnetite nanocrystals with high-quality properties for biomedical applications[END_REF] . This sample consists of water dispersion in acidic conditions (pH ≈ 1.9) of maghemite nanoparticles.

The iron oxide concentration was measured at 12 mg•mL -1 from a UV-vis measurement compared to a calibration spectrum. The equivalent concentration of iron is 0.15 mol•L -1 and the solid volume fraction is 0.24 %.

The DC magnetization of the water dispersed nanoparticles was measured by vibrating sample magnetometry (VSM). Fitting the Langevin function to the experimental DC magnetization, the mean size of the particles was obtained: 15 nm with a standard deviation, σ, of 4 nm. The zero field cooling -field cooling (ZFC-FC) curve of the sample was also measured by SQUID magnetometer (H = 10 Oe). From the ZFC-FC curve, the blocking temperature T B of the water dispersed sample was obtained: 78 K, as calculated from the maximum derivative of the subtraction of ZFC and FC branches over temperature. Clearly, the iron oxide nanoparticle sample is in superparamagnetic regime around and above room temperature.

When applying an AC magnetic field to a sample of magnetic nanoparticles:

H AC = H app e j•ω•t (1)
the sample magnetization is given by:

M (t) = ∞ ∑ n=1 M n e j•ω•n•t (2)
where the M n coefficients are complex numbers that depend on magnetic field intensity (H app ) and frequency (ω):

M n = |M n | e j•φn (3)
M n is defined as the n th order harmonic component of the magnetization with their corresponding magnitudes |M n | and phases φ n . The first term, n = 1, is called the fundamental harmonic and the coefficient of proportionality between the field and the magnetization defines the usual magnetic susceptibility. Terms of n ≥ 2, correspond to the high order harmonics. Usually, the magnitude of the harmonics decrease with their order (n) and only the ones below a certain order are considered. Because the dynamic magnetization is antisymmetric versus the applied magnetic field (H AC ), the even order harmonics (n = 2, 4, 6, ...) are null.

In order to obtain the spectrum of the MNP sample magnetization, first the AC hysteresis loops or dynamic magnetization, M (t), were measured by the lab-made AC magnetometer descried in an earlier work [START_REF] Garaio | A multifrequency electromagnetic applicator with an integrated AC magnetometer for magnetic hyperthermia experiments[END_REF] . Afterward, the Fast Fourier Transform (FFT) of the M (t) signal was performed in order to obtain the complex harmonics M n with their corresponding magnitudes |M n | and phases φ n (see equation ( 3)). The whole process takes around 0.5 seconds. To measure the thermal dependence of the harmonics, the temperature of the sample was varied in the biological range between 30 • C and 50 • C and the values of M n from n = 1 to n = 7 were measured continuously. The actual temperature of the sample was measured by an optical fiber thermometer with the probe in direct contact with the colloidal suspension.

III. RESULTS

In this scope, the dynamic magnetization of the prepared nanoparticle sample was measured at different frequencies (75 kHz, 302 kHz, 676 kHz and 1030 kHz) for different applied magnetic field intensities. From the dynamic magnetization, M(t), the different harmonic components (first 7 harmonics) were calculated by FFT. In figure 1 the magnitude |M n | of different harmonics are displayed for different applied magnetic field intensities. As expected, only odd harmonics (1 st , 3 rd , 5 th , 7 th ,...) are present since the dynamic magnetization is antisymmetric. In addition, the phases and magnitudes of all the harmonics vary with field intensity: above 5 kA•m -1 field intensity, the high order harmonics are large enough to be measured by the used AC magnetometer, otherwise the signal is too noisy.

The AC hysteresis loop area and SAR values vary with temperature as reported in the literature [START_REF] Regmi | Temperature dependent dissipation in magnetic nanoparticles[END_REF][START_REF] Garaio | Specific absorption rate dependence on temperature in magnetic field hyperthermia measured by dynamic hysteresis losses (ac magnetometry)[END_REF][START_REF] Beković | An experimental study of magnetic-field and temperature dependence on magnetic fluid's heating power[END_REF] . This thermal dependence is the direct result of the variation with temperature of the phase between magnetization M and applied magnetic field H. Hence, one can deduce that the harmonic phases of magnetization signal must vary with temperature as well. Therefore, the harmonic spectrum of the magnetization of water dispersed maghemite 5 As shown in figure 2, the phase increases with rising temperature in almost linear manner for all the harmonics at 10 kA•m -1 and 20 kA•m -1 applied magnetic field intensities. At 5 kA•m -1 and 25 kA•m -1 field intensities (not shown in figure 2) the harmonic phases exhibit the same behavior, that is, their phase also increases with raising temperature in almost linear manner. In this scope, we propose here the measurement of the harmonic phases as a non-invasive method to obtain the sample temperature which depends on the intrinsic properties of the nanoparticles. In this way, the temperature would be obtained via the previously measured temperature dependence of harmonic phase (see figure 2).

In order to obtain the temperature from the harmonic phases, it is necessary to fit the measured data by a phenomenological expression. At a first approach, the measured phase shifts can be fitted to a linear function. To estimate the fitting quality, the R squared coefficients were calculated (see equation ( 4)). Note that these R 2 coefficients are 1 for a perfect fit and zero for a null correlation. In table I, the calculated R 2 coefficients are written for different frequencies, intensities and harmonic orders. a R squared coefficient between 0.999 and 1, the green color a coefficient between 0.990 0.999 and the red ones indicates a coefficient smaller than 0.990.

R 2 = 1 - ∑ i (y i -f i ) 2 ∑ i (y i -ȳ) 2 (
As it can be appreciated in table I, the errors increase with the harmonic order: for the 3 rd harmonic, R 2 coefficient values are higher. This difference is more noticeable at very small applied magnetic field intensities (see table I at 5 kA•m -1 ). Clearly, this fact is an instrumental (statistical) error caused by too low magnitudes of higher order harmonics, compared to the fundamental harmonic magnitude (low signal-to-noise ratio, see figure 1).

On the other hand, the error increases at 25 kA•m -1 . This error can be induced by the power amplifier that feeds our particular resonant circuit and generates the magnetic field [START_REF] Garaio | A multifrequency electromagnetic applicator with an integrated AC magnetometer for magnetic hyperthermia experiments[END_REF] . At high field intensities, the amplifier works near its own saturation and tends to add harmonics to the output signal. Hence, high order harmonics appear in the applied magnetic field, H(t), and although their magnitude is very small, they can add errors to the measurements.

Considering the fittings with higher squared R values, temperature measurements and the control of temperature can be well performed by using the 3 rd harmonic. The temperature setup scheme in figure 3 can be followed to control the temperature of a nanoparticle sample.

The dynamic magnetization of MNP suspension is measured by pick-up coils and then FFT is performed to obtain the 3 rd harmonic phase. Using the previously measured data, the phases can be converted into temperatures and control the intensity of the applied magnetic field (H app ) to set the sample temperature at T through a proportional integral differential (PID) feedback loop.

Finally, the following experiment was made in order to check the sensitivity of the proposed thermometric method: an AC magnetic field of 302 kHz was applied to the tested magnetic nanoparticle sample by means of the used electromagnetic applicator. The sample holder consisted of a 2 cm length and 1 cm diameter cylindrical vessel. While the temperature was rising, the 3 rd order harmonic phases were measured and recorded every 1

second by means of the used AC magnetometer. Then, the harmonic phases were converted to temperature by means of the previous measurements and linear regressions (see figure 2 and table I). The so obtained temperatures were compared with the ones measured by the optical fiber thermometer (OpSens, Québec City, Canada) whose sensor tip was in direct contact with the sample. Figure 4 shows the temperature evolution curves measured by both methods. As it can be appreciated, the temperature obtained by the proposed method is in good agreement with the one measured by the commercial thermometer. The calculated root-mean-square error (RMSE) is 0.39 and 0.34

IV. CONCLUSIONS

The thermal dependence of the high order harmonics of a water dispersed maghemite nanoparticle sample was studied. From measured data, it was observed that the high order harmonic phases (3 rd , 5 th and 7 th ) increase with temperature in an almost linear way. The phase increment ranges between 1 and 3.5 degrees when sample temperature varies from 30 to 50 • C, which is easily measured.

We propose here the measurement of high order harmonic phase as a non-invasive method to obtain the temperature of a magnetic nanoparticle sample. This method has the potential to be only dependent on the intrinsic properties of the magnetic nanoparticles. Therefore once the method is calibrated (i.e. the linear regression slopes of 3 rd harmonic phases versus temperature) for a given set of magnetic nanoparticles, it allows acquiring and controlling the temperature of the tissues at a constant predetermined value (e.g. 43 • C) during magnetic hyperthermia therapy. We propose the 3 rd harmonic as a good system from which the temperature of a nanoparticle sample can be obtained and controlled.

The use of higher than fundamental harmonics to obtain the temperature has many potential advantages. First, the paramagnetic and diamagnetic signals of the sample are removed, since they are linear with applied field intensity and they are only present in the fundamental harmonic. For the same reason, the error from an uncompensated pickup coil 20 vanishes as well. Secondly, these harmonics are measured in magnetic particle imaging technique, although at somewhat lower frequency, typically in 25-100 kHz range.

But the method proposed here is still applicable (see the 75 kHz line in table I). Therefore, this non-invasive thermometry method specific to magnetized volumes could be combined with MPI to obtain the spatial distribution of particles and their temperature inside and around tumor (everywhere magnetic NPs are localized). Besides, due to the relatively low frequencies (lower than for MRI) involved with magnetic hyperthermia at which the body is transparent, the magnetization harmonics and thus temperature of nanoparticles located in deep tissues could be recorded. The method could be also implemented to study the heat transfer between nanoparticles and the surrounding media or other thermal phenomena related to magnetic nanoparticles.

3 ) 4 )

 34 BC Materials (Basque Center for Materials, Application and Nanostructures) 48040 Leioa. Spain Laboratoire de Chimie des Polymères Organiques, UMR 5629 CNRS/Université de Bordeaux, Bordeaux. France (Dated: 8 September 2015)

1 )FIG. 1 .FIG. 2 .

 112 FIG. 1. The magnitude of different harmonics (1 st , 3 rd , 5 th and 7 th ) for different applied magnetic field intensities at each frequency measured at 25 • C. The high order harmonics start to rise above 5 kA•m -1 .

FIG. 4 .

 4 FIG. 4. Temperature evolution measured with the optic fiber thermometer and the temperature obtained from the harmonic phases. The calculated root mean square error, √ ⟨(T harmonics -T probe ) 2 ⟩, is 0.39 and 0.34 • C at 10 kA•m -1 and 20 kA•m -1 respectively.

  This document is the Accepted Manuscript version of a Published Work that appeared in final form in Appl. Phys. Lett. 107, 123103 (2015) © AIP Publishing LLC (American Institute of Physics, USA) after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1063/1

  This document is the Accepted Manuscript version of a Published Work that appeared in final form in Appl. Phys. Lett. 107, 123103 (2015) © AIP Publishing LLC (American Institute of Physics, USA) after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1063/1.4931457

  4)

	Freq. Intensity		Linear fit
	(kHz) kA•m -1	3 rd	5 th	7 th
		5	0.99457 0.99485 0.99479
	75	10	0.99924 0.99952 0.99888
		20	0.99934 0.99864 0.99866
		25	0.98718 0.98889 0.98796
		5	0.99932 0.93364 0.00148
	302	10	0.99381 0.99445 0.97488
		20	0.99389 0.99531 0.99475
		25	0.99457 0.99485 0.99479
		5	0.99714 0.75294 0.04553
	676	10	0.99908 0.99654 0.98639
		20	0.99888 0.99872 0.99808
		5	0.99788 0.78314 0.79162
	1030	10	0.99918 0.99423 0.93086
		20	0.9989	0.99892 0.99882
	Averaged		0.99664	0.9589	0.83553

TABLE I .

 I R squared coefficients of the linear fittings of the measured phase versus temperature curves. Each column represents different harmonic order (3 rd , 5 th and 7 th ). The blue color indicates

PID 3 rd harmonic phase Convert to Temperature Set H app + -

  • C for 10 kA•m -1 and 20 kA•m -1This document is the Accepted Manuscript version of a Published Work that appeared in final form in Appl. Phys. Lett. 107, 123103 (2015) © AIP Publishing LLC (American Institute of Physics, USA) after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1063/1.4931457

	AC Magnet
	NP
	Sample
	Pick-up
	Coils
	Set T	Hyperthermia Experiment
		Pick-up
		Coils
	FFT	Measure MNP dynamic
		magnetization
	FIG. 3. One possible temperature control scheme for magnetic hyperthermia experiments.
	respectively.
	8

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Appl. Phys. Lett. 107, 123103 (2015) © AIP Publishing LLC (American Institute of Physics, USA) after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1063/1.4931457

ACKNOWLEDGMENTS

The authors thank the European COST action TD1402 "Multifunctional Nanoparticles for Magnetic Hyperthermia and Indirect Radiation Therapy" (RADIOMAG). This work has been financed by the Basque Government under grant IT-443-10.

Supplementary Information:

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