Shaping Up Zn-Doped Magnetite Nanoparticles from Mono- and Bimetallic Oleates: The Impact of Zn Content, Fe Vacancies, and Morphology on Magnetic Hyperthermia Performance

The currently existing magnetic hyperthermia treatments usually need to employ very large doses of magnetic nanoparticles (MNPs) and/or excessively high excitation conditions (H × f > 1010 A/m s) to reach the therapeutic temperature range that triggers cancer cell death. To make this anticancer therapy truly minimally invasive, it is crucial the development of improved chemical routes that give rise to monodisperse MNPs with high saturation magnetization and negligible dipolar interactions. Herein, we present an innovative chemical route to synthesize Zn-doped magnetite NPs based on the thermolysis of two kinds of organometallic precursors: (i) a mixture of two monometallic oleates (FeOl + ZnOl), and (ii) a bimetallic iron-zinc oleate (Fe3–yZnyOl). These approaches have allowed tailoring the size (10–50 nm), morphology (spherical, cubic, and cuboctahedral), and zinc content (ZnxFe3–xO4, 0.05 < x < 0.25) of MNPs with high saturation magnetization (≥90 Am2/kg at RT). The oxidation state and the local symmetry of Zn2+ and Fe2+/3+ cations have been investigated by means of X-ray absorption near-edge structure (XANES) spectroscopy, while the Fe center distribution and vacancies within the ferrite lattice have been examined in detail through Mössbauer spectroscopy, which has led to an accurate determination of the stoichiometry in each sample. To achieve good biocompatibility and colloidal stability in physiological conditions, the ZnxFe3–xO4 NPs have been coated with high-molecular-weight poly(ethylene glycol) (PEG). The magnetothermal efficiency of ZnxFe3–xO4@PEG samples has been systematically analyzed in terms of composition, size, and morphology, making use of the latest-generation AC magnetometer that is able to reach 90 mT. The heating capacity of Zn0.06Fe2.94O4 cuboctahedrons of 25 nm reaches a maximum value of 3652 W/g (at 40 kA/m and 605 kHz), but most importantly, they reach a highly satisfactory value (600 W/g) under strict safety excitation conditions (at 36 kA/m and 125 kHz). Additionally, the excellent heating power of the system is kept identical both immobilized in agar and in the cellular environment, proving the great potential and reliability of this platform for magnetic hyperthermia therapies.


INTRODUCTION
The success of magnetic hyperthermia therapies depends on the heating capacity or specific absorption rate (SAR) of the magnetic nanoparticles (MNPs) when they are exposed to an alternating magnetic field (AMF). 1−3 As a matter of course, to achieve the desired therapeutic effect under a safe frequency field product (H × f <10 10 A/m s), the MNP heating power has to be optimized. 4,5 The design of new MNPs with improved magnetothermal efficiency is a challenging task due to the difficulty in controlling and predicting the complex colloidal synthesis of inorganic nanocrystals. 6−8 The preparation of nanostructures with very specific sets of characteristics (size, morphology, homogeneous chemical composition, high purity, and low size/shape dispersity) requires an extremely fine control over the synthetic protocol. 9 In this sense, the thermal decomposition of organometallic precursors opened a new avenue for synthesizing novel iron oxide-based MNPs with a well-defined size and morphology. 10,11 The most commonly used iron oxide MNPs for biomedical applications are of magnetite (Fe 3 O 4 ) due to their high magnetic response, good biocompatibility, chemical stability, and simple compo-sition. 12,13 But interestingly, the introduction of a low quantity of divalent transition-metal ions (M x Fe 3−x O 4 , M = Zn, Co, Mn, Ni, etc.) within the spinel structure of magnetite NPs has proven to be a good strategy to obtain mixed ferrites with tuned magnetic performances, 14−17 although in some cases, there are concerns about their dubious biocompatibility. Particularly, Zn-containing ferrite NPs are considered quite biocompatible because zinc is an essential trace element of the human body that has a relatively high toxic dose, up to 450 mg day −1 . 18 Currently, zinc ferrites are also being explored for biomedical applications due to their higher stability against oxidation. 19,20 Additionally, as it is well-known, the introduction of diamagnetic Zn 2+ ions in the magnetite lattice ([Fe 3+ ] A [Fe 2+ Fe 3+ ] B O 4 ) can produce significant enhancement of the particle′s magnetic moment, compared to pure magnetite. 21 This is because Zn 2+ ions tend to replace Fe 3+ in A sites, reinforcing the already existing unbalance between antiferromagnetically coupled A and B sublattices. Unfortunately, this mechanism holds up, in the bulk state, just until a Zn content of x ≈ 0.4 (Zn x Fe 3−x O 4 ), above which the lack of magnetic moments located at A sites strongly disrupts the exchange interaction between both sublattices, causing a decrease of the total magnetic moment. 22 Another drawback in the preparation of doped ferrite NPs is that the dopant is often assimilated in different positions of the crystal lattice, 23−27 which typically happens due to the nonequilibrium nature of these chemical reactions, making it difficult to achieve the intended theoretical results and running the risk of deriving mistaken conclusions. Thus, the first step in the development of doped ferrite nanomaterials should be the accurate determination of the local geometry of the dopant atoms to ensure reliable properties and trustful potential applications.
It is clear, then, that a priori a remarkable improvement of the SAR can be achieved if high-grade Fe 3 O 4 NPs are doped with a suitable amount of Zn 2+ in the proper lattice position. In addition, as has been reported recently, the heating power of magnetite NPs with nonfluctuating magnetic moment (FM-NP), whose average size is over 20 nm, can be significantly greater than that of the superparamagnetic NPs (SP-NPs < 20 nm) if high-enough fields (H > 15−20 mT) are used and dipolar magnetic interactions are minimized. 28,29 However, as one would expect, the synthesis of high-quality Zn-doped magnetite FM-NPs is far more challenging than that of undoped magnetite. In recent years, it has been common to synthesize Zn-doped ferrite NPs by thermal decomposition of metal acetylacetonates 14, 25,30 and by coprecipitation of corresponding metal chloride or nitrate salts, 25,31−33 which in most of the cases gave rise to polydisperse NPs in size and shape. The decomposition of metal oleates has also been explored in some studies on Zn-ferrites, but it usually has the downside of having to deal with the formation of the wustite (FeO)-phase byproduct. 14, 27 Certainly, works describing the synthesis of Zn-doped magnetite NPs with a well-defined morphology, average size larger than 20 nm, and devoid of secondary phases are rather scarce and mostly focused on NPs with a cubic morphology. 20,26,34 There is no doubt that the development of new strategies to prepare Zn-doped ferrites of different sizes and shapes would stimulate the progress of nanoparticle-based platforms for theranostics.
Herein, we present an improved protocol to synthesize highly crystalline Zn x Fe 3−x O 4 NPs with a low size/shape dispersity and enhanced saturation magnetization. We have explored a new synthetic route based on the decomposition of bimetallic iron-zinc oleates, which has been compared to a more common route employing a mixture of monometallic oleates (iron oleate + zinc oleate). To the best of our knowledge, this is the first time that these two approaches are carefully analyzed and compared. By finely modifying the synthesis conditions of both routes, NPs of different sizes (10− 50 nm), shapes (spheres, cubes, and cuboctahedrons), and zinc contents (0.05 < x < 0.25) have been obtained. These samples have been chemically, structurally, and magnetically analyzed with great accuracy making use of X-ray absorption near-edge structure (XANES), DC magnetometry, and Mossbauer spectroscopy. The study has allowed one to determine reliably both the Zn position/content and the Fe distribution/ vacancies, a subject that has not been sufficiently explored even in the most recent works on this topic. 35,36 Additionally, Zn x Fe 3−x O 4 NPs have been specifically PEGylated to avoid NP aggregation in cell environments, and viability assays have been carried out to prove their good biocompatibility.
Finally, the heating efficiency of Zn x Fe 3−x O 4 @PEG NPs has been studied in detail by measuring the dynamical hysteresis loops at different frequencies (up to a field intensity of 90 mT) and in several dispersion environments (distilled water, agar, and cell culture). The optimal excitation parameters to maximize the heating production under clinical safety limits have been determined for each sample.

RESULTS AND DISCUSSION
2.1. Role of Chemical Synthesis on the Size, Shape, Crystalline Structure, and Composition. By carrying out thermolysis of different iron and zinc oleates, Zn x Fe 3−x O 4 NPs of different sizes, shapes, and compositions were obtained. Since our goal is to focus on zinc contents x < 0.4 and the dopant has typically to be added in excess to reach the intended compostion, 23,37,38 Fe/Zn oleates with 5:1 and 2:1 ratios have been used in the preparations, employing both monometallic oleates (FeOl + ZnOl) and bimetallic oleates (Fe 3−y Zn y Ol) (y = 0.5 and 1) (see Section 4 and Figure S1, Table S1 in the Supporting Information). The main structural difference between the mixture of monometallic oleates and bimetallic oleates is the presence of heterometallic bridging coordination in the latter (see Figure S2 and Table S2 in the Supporting Information), which reduces the diffusion distance between Zn−Fe centers, affecting the growth dynamics of the Zn x Fe 3−x O 4 NPs, as will be shown in the following.
The Zn x Fe 3−x O 4 samples present a zinc content (measured by inductively coupled plasma mass spectrometry (ICP-MS)) ranging from x = 0.1 to 0.25 and an average dimension from 10 to 50 nm. With the aim of providing a clear picture of the main synthesis parameters affecting the properties of the NPs, five representative samples have been chosen (see Table 1). Samples have been named according to the composition and size as follows: Zn x -D TEM , where x is the zinc content in the NPs determined by ICP-MS and D TEM is the average dimension obtained by transmission electron microscopy (TEM) analysis.
TEM micrographs in Figure 1 show monodisperse samples with spherical, cubic, and cuboctahedral shapes. When FeOl and ZnOl are reacted together at an Fe/Zn ratio equal to 5:1, using a final T of 320°C and 30 min of annealing, spherical particles of 10 nm diameter (sample Zn 0.15 -10 in Figure 1a) are obtained. By increasing the annealing time to 80 min, the shape of the nanocrystals changes from spheres to cubes and the average dimension increases considerably, from 10 to 48 nm (sample Zn 0.1 -48 in Figure 1b). Samples Zn 0.15 -10 and Zn 0.1 -48 seem to have followed the reaction profile described by Hyeon et al., in which the nucleation process starts between 310 and 320°C and growth takes places gradually from 1 to 20 min of aging, proceeding rapidly afterward and causing the morphology to evolve to the cubic type. 39 On the other hand, when bimetallic Fe 2.5 Zn 0.5 Ol (Fe/Zn = 5:1) is reacted at the same synthesis conditions as those used in sample Zn 0.15 -10 (see sample Zn 0.1 -24 in Table 1), the NPs grow further and present a well-faceted octahedral shape with slight truncation (cuboctahedrons) (Figure 1c). The larger size obtained when the bimetallic Fe 2.5 Zn 0. 5 Ol is used appears to be due to the shorter distance between Zn 2+ and Fe 3+ cations within the metallo-organic complex. The Zn 2+ ions accelerate the transformation of the bimetallic oleate precursor, shifting its decomposition temperature to lower values. 27 Therefore, as could be expected, the reaction of Fe 2.5 Zn 0.5 Ol at higher final T (330°C) produces even larger cuboctahedral nanoparticles (see sample Zn 0.1 -34 Figure 1d). Thus, it also seems reasonable to postulate that the changes in the decomposition profile of the bimetallic Fe 2.5 Zn 0.5 Ol not only speed up the growing stage but also modify the morphology of resulting nanocrystals.
On the contrary, the metal oleate type used in the synthesis (monometallic or bimetallic) does not affect the amount of Chemistry of Materials pubs.acs.org/cm Article zinc incorporated in the NPs. All of the samples synthesized using an initial Fe/Zn ratio of 5:1 give rise to NPs with a similar zinc content (x ≈ 0.1) regardless of the synthetic route employed. The slightly higher zinc content in Zn 0.15 -10 is likely due to its larger surface-to-volume ratio, assuming that the dopant concentration tends to be somewhat higher on the NP surface because of internal diffusion constraints. 27,40 With the aim of increasing the zinc content within the NP lattice while facilitating its diffusion, a bimetallic Fe 2 Zn 1 Ol with a higher zinc concentration has been used (Fe/Zn = 2:1), expanding the annealing time to 60 min. In this way, the resulting NPs have a higher zinc concentration (x = 0.25), but they present an irregular prismatic shape with twinning planes (sample Zn 0.25 -39), as can be seen in Figure 1e. It seems feasible that an increase in Zn 2+ substitution causes lattice strains and, thus, some kind of crystal distortion.
To gain further information on the structural characteristics of the nanoparticles, X-ray diffraction (XRD) has been performed in powder samples. The whole set of Zn x Fe 3−x O 4 samples (see Figure 2a) shows an inverse spinel structure with the space group Fd3m, compatible with the magnetite phase (PDF #880866) and without any trace of the wustite phase, which is a very common byproduct in this kind of iron oxide nanoparticles. 25 After Rietveld refinement, no additional impurity phase has been detected and the observed peaks have been indexed as (111), (220), (311), (400), (422), (511), (440), (620), and (533). The summary of Rietveld refined structural data is displayed in the Supporting Information ( Figure S3 and Table S3), and the estimated lattice parameters (a) have been included in Table 1. The diffractions peaks of Zn 0.25 -39 are the most shifted toward lower angles (see Figure 2b), which give rise to the largest lattice parameter among the samples, i.e., 8.4016 Å, in accordance with its higher zinc content. When the x determined by ICP-MS is taken into account, there is no clear correlation between the lattice parameter and the zinc concentration (see Figure 2c). This seems to suggest that a fraction of zinc may not be within the ferrite lattice. As will be proved in the following (by XANES, magnetometry, and Mossbauer techniques), there are Zn 2+ ions on the NP surface; thus, the Zn content in the ferrite lattice is lower than the total zinc amount determined by ICP-MS. If the corrected zinc content within the ferrite is plotted versus the lattice parameter, a linear-like dependence can be observed (see Figure 2d). In any case, an in-depth study of the physical dimension of unit cells should also account for the possible iron vacancies in the crystal lattice, a matter that will be discussed in more detail later.
In relation to the average crystallite sizes, they have been calculated from (311) ( Figure 2b) and (400) diffraction peaks and are listed in Table 1 (see also Tables S4−S6 in the Supporting Information). In all of the cases, except for Zn 0.25 -39, the average dimensions calculated from TEM measurements match very well with the crystallite sizes, meaning that samples Zn 0.15 -10, Zn 0.1 -48, Zn 0.1 -24, and Zn 0.1 -34 are composed of single crystals. Nevertheless, the crystallite size of Zn 0.25 -39 is smaller than the physical average size determined by TEM, which implies that the NPs of this sample are twinned crystals, in agreement with what is seen in Figure 1e.
2.1.1. X-ray Absorption Near-Edge Structure (XANES). XANES is an element-specific technique that allows one to gain information about the oxidation state and the local symmetry of the absorbing element and can be used to identify and quantify inorganic phases and coordination compounds. 41,42 In the present case, X-ray absorption near-edge structure (XANES) has been performed at both Fe K-edge and Zn K-edge to investigate iron and zinc arrangements within the Zn x Fe 3−x O 4 NPs. Figure 3a shows the Fe K-edge XANES spectra of the set of Zn  appear at the edge energy (see the zoom-in of Figure 3a). In fact, the edge position is a clear-cut indicator of the oxidation state of the absorbing atom. Note that while magnetite is an inverse spinel where the Fe 2+ ions occupy octahedral (B) sites and Fe 3+ ions occupy both octahedral (B) and tetrahedral (A) sites, ZnFe 2 O 4 is a normal spinel in which the Zn 2+ cations occupy the A sites and the Fe 3+ are located in the B ones. Thus, the oxidation state of the Fe ions in magnetite (Fe 2+ / Fe 3+ ratio of 1:2) is lower than that in ZnFe 2 O 4 (exclusively Fe 3+ ) and, consequently, the edge position appears ∼2 eV shifted to lower energies in comparison with the ZnFe 2 O 4 XANES spectrum. 41 In the case of the Zn x  Figure  3a), suggesting that the Zn concentration in the ferrite lattice must be somewhat lower than the Zn content determined by ICP-MS. In contrast, the Zn 0.15 -10 sample shows a larger shift in the edge position toward higher energies (≈0.6 eV), which can be explained by the presence of the maghemite (Fe 2 O 3 ) phase on the surface (see Figure S4 in the Supporting Information). A partial oxidation from magnetite to maghemite is not surprising in the Zn 0.15 -10 sample considering the high surface-area-to-volume ratio in NPs with an average dimension of 10 nm. Additionally, the presence of the maghemite phase in this sample is in accordance with the lower lattice parameter obtained from the Rietveld refinement (see Table 1). Figure 3b displays the Zn K-edge XANES spectra of Zn x Fe 3−x O 4 NPs compared to the ZnFe 2 O 4 reference. The edge position of the synthesized nanoparticles is coincident with that observed in the ZnFe 2 O 4 XANES spectrum, revealing a Zn 2+ oxidation state in the sample. Above the edge position, all spectra present three main peaks. Although the positions of those peaks are comparable with that observed in the ZnFe 2 O 4 XANES spectrum, the relative intensity of the peaks varies among the samples. Indeed, while certain similarities are observed between the Zn K-edge XANES spectra of the Zn x Fe 3−x O 4 samples and ZnFe 2 O 4 , confirming the incorporation of Zn cations in the inner structure of the magnetite in lattice A, an additional contribution is necessary to reproduce the experimental spectra. Therefore, the Zn K-edge XANES spectra of the Zn x Fe 3−x O 4 samples were fitted to a linear combination of ZnFe 2 O 4 and the available standards. The best linear combination fit was found considering the coexistence of Chemistry of Materials pubs.acs.org/cm Article ZnFe 2 O 4 and Zn 2+ adsorbed onto a hydroxyapatite-like structure (see Figure 3c,d), a partially distorted phase in which Zn 2+ favors the tetrahedral coordination. 43,44 The presence of this tetrahedral molecular geometry phase suggests that a fraction of Zn cations are located out of the inorganic core, probably on the surface of the NPs as zinc oleate that have not yielded decomposition. The higher decomposition temperature of ZnOl seems to be the reason why at the final T of the synthesis (320−330°C), there are still some zinc centers that have not been completely detached from the oleate ligands (see Figure S6 in the Supporting Information). Since this secondary Zn phase is located at the organic surface coating, it will not affect the magnetic properties of the inorganic ferrite core. The linear combination fits presented in Figures 3c,d and S5 provide the percentage of zinc in the inorganic core (as Zn x Fe 3−x O 4 ) and on the surface (as a metallo-organic structure with tetrahedral coordination); see Table 2. It becomes apparent that the zinc content determined by ICP-MS reflects the total zinc amount in the NP system (ferrite core + organic surface). Thus, to know the real Zn content in the ferrite lattice, the corresponding percentage (second column in Table  2) must be applied to the total zinc amount (ICP-MS data presented in Table 1). The recalculated Zn x Fe 3−x O 4 compositions are listed in Table 2. These corrected x values are in agreement with the slight edge-position variations observed at the Fe K-edge (commented above) and the stoichiometries determined by Mossbauer that will be discussed in the following (and are presented in Figure 2d).  Table 3.
As would be expected, M s values at 5 K reflect the increase of the net magnetic moment of the lattice as the Zn content increases due to the tetrahedral Fe 3+ substitution. As shown in Table 3, M s ranges from 122 Am 2 /kg in the Zn-richest sample (for x ≈ 0.25) to 105−108 Am 2 /kg in the samples with the lowest Zn content (for x ≈ 0.1). Note that these values significantly exceed the saturation magnetization of pure bulk magnetite (98 Am 2 /kg at 5 K). However, another direct consequence of the Zn content increase is the concomitant decrease of the Curie temperature, originated by the weakening of the superexchange interaction between A and B sublattices. Such a temperature reduction may be on the order of 200 K for a Zn content of 0.4 relative to pure magnetite (∼950 K) and affects strongly the room-temperature magnetization values. 45 This effect can be observed by plotting M s as a function of temperature ( Figure S7 Table 3) notably improved when compared with pure magnetite (92 Am 2 /kg at RT).
Additionally, from the hysteresis loops at 5 K shown in Figure 4, it can be stated that the whole set of NPs is basically single magnetic-phase objects whose magnetization reaches saturation at fields smaller than 0.5 T. This is because the curves do not present kinks and/or linear contributions to the total magnetization in the high-field region, which would be expected if paramagnetic and/or different ferro-/ferri-magnetic phases were significant. The shape of the hysteresis loops at 5 K clearly fits with the Stoner−Wohlfart model of uniaxial single domains for all Zn x Fe 3−x O 4 samples (except for Zn 0.25 -39 composed of twinned NPs), as confirmed by simulations of direct hysteresis loops performed with this model (see Model S1 in the Supporting Information). Note that the model predicts a reduced remanence (M r /M s ) of about 0.5 (Table 3). In brief, it suggests that interparticle interactions play a minor role at 5 K, so that the magnetization process results from the addition of randomly distributed rotations of noninteracting superspins located at each individual particle. Below the Verwey transition (VT) (T < 100 K), the effective magnetic  Chemistry of Materials pubs.acs.org/cm Article anisotropy (K eff ) arises from the competition of the uniaxial magnetocrystalline effect, originating from the monoclinic distortion of the magnetite lattice 46 and the shape anisotropy. In this case, the differences in the value of the coercive field (H c ) (or effective magnetic anisotropy, K eff ) seem to be driven by the shape anisotropy contribution, which depends on the particle's morphology. Note that the Zn content, and therefore its possible impact on monoclinic distortion, should be quite similar in samples Zn 0.1 -48, Zn 0.1 -24, and Zn 0.1 -34. Otherwise, the lower H c value of Zn 0.15 -10 at 5 K is due to the nonnegligible thermal fluctuation effects in NPs of 10 nm, which are in the SPM regime at RT. The thermal effects are also visible in the rest of the samples at RT given that the hysterical properties (H c and M r /M s ) are considerably reduced. This happens when the total anisotropy energy K eff v is comparable to the thermal energy k B T and/or the dipolar interaction energy. M(T) curves obtained upon zero-field cooling and field cooling (ZFC and FC) conditions are presented in Figure 5. The most evident shared feature is the large magnetization step observed in the vicinity of 100 K when the sample is warmed up (ZFC) as well as cooled down (FC) across it. This step is usually the fingerprint of the pure magnetite phase and originates from the Verwey transition (VT). In Figure 5, it is also observed that this transition slightly moves up and down in temperature from sample to sample (86 K in sample Zn 0.1 -34 and around 100 K in samples Zn 0.1 -24, Zn 0.1 -48, and Zn 0.25 -39; see Table 3). Even in sample Zn 0.15 -10 composed of smaller NPs (whose blocking T is around 55 K), a bump between 80 and 100 is observed (marked in Figure 5a).
According to the literature, the lowering of the VT point in bulk magnetite is usually considered as a consequence of either Fe deficit (Fe 3(1−δ) O 4 ) in undoped magnetite and/or 3d transition-metal substitution of Fe 2+ cations (M x Fe 3−x O 4 , with M = Zn, Mn, Co, etc.). 47 Besides, the shifting effect also involves the softening of the transition that becomes gradually one of a second order instead of a first order. 48 The point is that values of δ > 0.03 or x = 3δ > 0.01 are sufficient to remove the Verwey transition in bulk single crystals, from which it would be expected that in our Zn x Fe 3−x O 4 samples, characterized by nominal x ≥ 0.1, the magnetization step should be no longer observed. However, there is clear experimental evidence that the Verwey transition is strongly affected by surface properties, particularly significant at the nanometer scale. 49 In the work of Guigue-Millot et al., the VT shifted toward higher temperatures and did not fit the relation that exists for bulk single crystals. The authors proposed that the number of Fe 2+ /Fe 3+ pairs per formula unit is the driving force that determines the VT in nanometric grains. The number of Fe 2+ /Fe 3+ pairs in our Zn x Fe 3−x O 4 samples will be estimated in the following by gathering together the analysis of  This can be easily achieved from room-temperature spectra in samples above the SPM limit (D > 20 nm), i.e., in the whole set of Zn x Fe 3−x O 4 samples except in Zn 0.15 -10. Figure 6 shows the Mossbauer spectra of Zn 0.1 -48, Zn 0.1 -24, Zn 0.1-34, and Zn 0.25 -39 NPs collected at room temperature together with the Mossbauer fitting parameters. For a better comparison, the area of the spectra has been normalized to the Fe content.
If the thermal fluctuation effect is sufficiently small, Mossbauer spectra of the stoichiometric Fe 3 O 4 magnetite results from the superposition of two well-resolved sextets. The sextet with the higher hyperfine field (I) is ∼49 T, and it is associated with Fe 3+ ions in tetrahedral sites (A), while the component with a lower hyperfine field (II) (∼46 T) is assigned to Fe 2+ Fe 3+ atoms in the octahedral (B) ones. 50 The electron hoping among the Fe 2+ and Fe 3+ atoms in the octahedral (B) position is much faster than the resolution time of the Mossbauer spectroscopy, and the hyperfine values of both Fe 2+ and Fe 3+ cannot be independently determined by this technique. The low hyperfine field sextet is normally considered to be associated with an only component with an Fe 2.5+ intermediate valence representing an Fe 2+ Fe 3+ pair of hopped atoms. The relative resonant area ratio among two components is, thus, S I /S II = 0.5, in accordance with the population of both crystallographic positions A and B in a stoichiometric magnetite.
Spectra of the studied Zn x Fe 3−x O 4 samples have been properly fitted by superposition of two sextets with hyperfine parameters compatible with those expected from a magnetite phase ( Figure 6). The spin relaxation superparamagnetic effects due to reduced sizes of the NPs are not manifested in any spectra. The slightly lower hyperfine fields observed in the spectral components of Zn 0.1 -24, Zn 0.1-34 and Zn 0.25 -39 NPs can be attributed to their relatively smaller sizes and their topological cuboctahedral shapes with lower core/surface Fe atoms in comparison to the cubic-shaped Zn 0.1 -48 sample.
The S I /S II (Fe) relative resonant area ratio of Zn x Fe 3−x O 4studied NPs can be found in Table 4. Assuming that Zn ions are located in A sites, as inferred from XANES, the normalized atomic S I /S II (at.) ratios differ from the 0.5 value in all of the samples, evidencing the different stoichiometric compositions of the NPs. Fe 3+ ions are substituted by Zn 2+ ones in A tetrahedral sites and, to conserve the charge neutrality, a conversion of some Fe 2+ ions in Fe 3+ and/or generation of Fe 2+ vacancies in B octahedral position is provoked. Formally, the nonstoichiometric Zn-doped magnetite NPs can be represented by the following formula where δ and x symbolize the vacancies (0 ≤ δ ≤ 0.33) and zinc concentration, respectively. Following expression 1, there are 5δ + 2x unbalanced Fe 3+ ions in the B octahedral position that, as suggested by some authors, do not contribute to Fe 2+ −Fe 3+ electronic hopping but instead to a high hyperfine I sextet. 51 This fact must be reflected on the relative resonant area ratio, being projected by eq 2 Based on eq 2, the number of Fe 2+ /Fe 3+ pairs per formula unit is given by  In addition, the net magnetic moment in the framework of eq 1 can be calculated as Note that an increase in the Zn content (x) reinforces the net magnetic moment, while octahedral vacancies (δ) tend to reduce it. In such a context, eqs 2 and 4 allow the calculation of x and δ from experimental S I /S II (Fe) and μ values (obtained from the M s data at 5 K; see Table 3). Table 4 summarizes the experimental S I /S II and μ, the obtained δ and x values, the pair number (p), and the corresponding stoichiometry for each sample. Samples Zn 0.1 -24 and Zn 0.1-34 present vacancy concentrations of δ = 0.04 and δ = 0.09, respectively. In contrast, Zn 0.1 -48 and Zn 0.25 -39 give rise to slightly negative numbers, leading us to conclude that in these samples there is an apparent absence of Fe 2+ vacancies, which seems chemically plausible given that Zn 0.1 -48 and Zn 0.25 -39 were synthesized using quite larger annealing times (see Table 1). However, it should be noted that Zn 0.25 -39 NPs present crystal distortions (see Figure 1), so a precise interpretation of S I /S II (Fe) could require a more specific formulation-frame. It is noteworthy to mention that the Verwey transition temperature presents approximately a linear relation with Fe 2+ /Fe 3+ pairs (see Figure  5f), which is in agreement with the hypothesis proposed by Guigue-Millot et al. 49 commented in the previous section.
Regarding the x values, they are quite compatible with the ones obtained from the XANES study (see Tables 2 and 4), which supports the conclusion drawn previously about being a minor fraction of Zn (out of the ferrite inorganic core) forming part of the organic coating.
Additionally, the stoichiometries determined by Mossbauer spectroscopy and listed in Table 4 are highly consistent with the lattice parameters (a) estimated by Rietveld refinement in the foregoing section (see Figure 2c). Given that vacancies generate local electrostatic repulsion among the remaining ions, which in turn induces an increment of the lattice parameter, 52 Table S7 in the Supporting Information) following a previously published protocol that minimizes collective coatings. 29 Sample Zn 0.1 -24 was functionalized using 10 kDa PEG, and samples Zn 0.1 -34, Zn 0.1 -48, and Zn 0.25 -39, which are composed of larger NPs, were coated using longer PEG molecules (20 kDa) to better counterbalance the dipolar interaction among NPs. Due to the small size of the NPs forming the Zn 0.15 -10 sample and, thus, its low potential as a magnetothermal actuator, from here on, this sample will no longer be a part of the discussion.
The cytotoxicities of Zn 0.1 -48@PEG, Zn 0.1 -24@PEG, Zn 0.1 -34@PEG, and Zn 0.25 -39@PEG after 96 hours have been studied. Figure 7 shows that human colorectal cancer cells (HCT116) incubated with Zn x Fe 3−x O 4 @PEG NPs grow at the same rate as cells without NPs (white bar), with no significant differences between the two NP concentrations (C 1 and C 2 , grey and black bars, respectively). The zinc content (0.05 < x < 0.25), size (24−48 nm), and morphology (cuboctahedral, cubic, or prismatic) of the samples did not affect the viability, concluding that these Zn x Fe 3−x O 4 @PEG formulations are not toxic for the cells.

Magnetic Hyperthermia Efficiency of Zn x Fe 3−x O 4 @ PEG Formulations.
The potential of MNPs to produce heat depends critically on a number of factors, such as intrinsic properties (morphology, size distribution, magnetization, effective magnetic anisotropy, etc.), as well as "extrinsic" ones (collective assemblies, viscosity of the medium, etc.). Additionally, it is well-known that any potentially efficient magnetic colloid can produce poor results if the radiofrequency excitation is far from certain optimal conditions. 54 The hyperthermia study developed in this work takes into account most of these issues, with the aim of analyzing the impact of zinc doping and the NP shape on the performance of magnetite-based NPs. The specific absorption rate (SAR) was extracted from the analysis of the hysteresis loops obtained at three different frequencies (133, 305, and 605 kHz), which are in the range usually employed in the hyperthermia technique. The data are summarized in Figure 8 and Table 5.
AC hysteresis loops of samples composed of single crystals (Zn 0.1 -48@PEG, Zn 0.1 -24@PEG, Zn 0.1 -34@PEG), in Figure 8, are similar to those obtained in pure magnetite FM-NPs prepared following a similar synthetic route. 29,55,56 Importantly, these loops are typical of nearly isolated magnetic single domains whose easy axes are oriented at random relative to the externally applied AC magnetic field. In consequence, the Stoner−Wohlfarth-based approach 57 fits reasonably with most of the hysteresis loops presented in Figure 8d(123). The simulations (see Model S1 in the Supporting Information) have been obtained by assuming a Gaussian distribution of the uniaxial effective anisotropy constants, following the same line of thought as that used in the literature 29,55 for comparable magnetite particles. In this approach, the magnetic anisotropy standard deviation is understood as reflecting a morphological disorder, that is to say, irregularities originated by crystallographic directions growing at different rates. Note that hysteresis loop areas of samples Zn 0.1 -48@PEG and Zn 0.1 -34@PEG, which are composed of comparatively large particles, are frequency-independent (as predicted by the model), while in sample Zn 0.1 -24, with smaller particles of 24 nm, the area    Table 3), while most of the magnetite nanoparticles reported in the literature hardly exceed 80 Am 2 /kg. However, this increase alone cannot account for the total SAR improvement. According to the mentioned model, the maximum SAR (or saturation SAR) should increase with particle size, but this is not observed in our case. On the contrary, the saturation SAR reaches the maximum value for sample Zn 0.1 -24 that is composed of smaller NPs. This result seems to reflect the variations in the particles' morphology and, in consequence, in the shape magnetic anisotropy. 58 Some of these differences are quite evident from the TEM analysis, as Zn 0.1 -48 is composed of nearly pure cubic particles, while samples Zn 0.1 -34 and Zn 0.1 -24 have a more faceted NP cuboctahedral-like morphology (see Figure 1). However, the SAR performance is smaller in sample Zn 0.1 -34 (see Figure 8 and Table 5) even though the particle size in Zn 0.1 -34 is on average larger. AC hysteresis loops of Zn 0.1 -34 in Figure 8 show a slight "wasp-waist" effect, typical of bimodal magnetic contributions that seem to have originated in this case from a certain dispersion of morphologies, i.e., octahedrons with different truncation degrees that lead to a distribution of aspect ratios. These features are reflected in the quantitative estimation of the effective anisotropy constant (K eff ), made by modeling the SAR versus field curve. The results indicate that the K eff of sample Zn 0.1 -24 is on average much greater (22 kJ/m 3 ) than those of samples Zn 0.1 -48 and Zn 0.1 -34 (12 kJ/m 3 ), and particularly for the latter, the distribution spreads significantly (σ K = 8, compared with σ K = 5 for the other two samples). With regard to sample Zn 0.25 -39, composed of twinned NPs, the magnetic response to AC fields does not fit to a simple Stoner−Wohlfarth-based model. Most likely, these particles are not magnetic single domains, as DC magnetometry at 5 K suggested, and the hysteresis area is also dependent on frequency (as happens with the much smaller Zn 0.1 -24 NPs). It is also clear that at a maximum AC amplitude of 90 mT and at 133 kHz, sample Zn 0.1 -39 is still quite far from saturation: the SAR versus field curve in Figure 8d 3 keeps growing significantly at the top of the available field range. Zn 0.25 -39 NPs become clearly less efficient as heat producers than the other three samples.
In any case, what is essential for the development of an efficient magnetic hyperthermia therapy is to ensure that the field-frequency conditions used for the treatment are clinically safe and avoid any resistive heating in the biological tissues. Unfortunately, this issue is not sufficiently considered in the literature, and some of the works that account for it differ in the maximum field-frequency product (H × f) that is acceptable to prevent harmful Eddy currents. The Atkinson− Brezovich limit (H × f ≤ 4.85 × 10 8 A/m s)) has been for several years the most acceptable threshold. 59 Recently, different safety limits have been proposed as the Hergt approach (H × f = 5 × 10 9 A/m s) 60 62 In any case, beyond calling into question the most suitable limit, it is very important to investigate the optimal magnetic excitation conditions to reach the admissible maximum SAR on samples with different features. For instance, by considering the Hergt criterion for a given field amplitude (H), the maximum acceptable frequency is determined by 63 = × f H H ( ) 5 10 / This argumentation has been applied to samples Zn 0.1 -24@ PEG, Zn 0.1 -34@PEG, and Zn 0.1 -48@PEG, which are very effective as heat producers at moderate fields (<40 mT) and whose behavior is well-explained by the Stoner−Wohlfarthbased approach. In general, SAR/f (proportional to the hysteresis area) will be a function of the frequency and the The black dashed curve is the acceptable maximum frequency, f limit (H) = 5 × 10 9 /H, for a given magnetic field intensity. The intersection of the black dashed curve and the colored bar of each sample shows the optimal frequency for obtaining the maximum SAR limit value. (b) Experimental SAR versus field curves for the Zn 0.1 -24@PEG sample (AC loops in Figure S10, Supporting Information) in aqueous colloid, agar, and cell media at different cell densities (C 1 and C 2 ; see Section 4).
Chemistry of Materials pubs.acs.org/cm Article field. Given that SAR/f has been only measured at three frequencies, it should be interpolated for the rest of the frequency points in the studied interval (100 kHz and 1 MHz). In this way, it has been obtained the curve presented in Figure  9a for sample Zn 0.1 -24@PEG. On the contrary, for samples Zn 0.1 -48@PEG and Zn 0.1 -34@PEG, the SAR/f is independent of frequency so the calculation is straightforward. The three SAR limit curves of Figure 9a peak at some optimal magnetic field amplitude, and the dashed curve (the hyperbolic function of f limit , eq 5) reveals which frequency corresponds to the maximum SAR limit . Table 5 summarizes the optimal SAR limit values and the corresponding excitation conditions for each sample. Zn 0.1 -24@PEG presents the higher optimal SAR limit of 600 W/g (at 47 mT and 125 kHz), while the rest of the samples peak at slightly minor fields with significantly lower optimal SAR limit values. Since all of the data indicate that sample Zn 0.1 -24@PEG is ideal to carry out magnetic hyperthermia treatment even under strict H × f restrictions, its biomedical suitability was further studied by measuring the AC response in very different dispersion media (agar and cell culture at different cell densities; see Figure 9b). The SAR(H) curves presented in Figure 9b show the high reliability and reproducibility of the magnetothermal actuation of sample Zn 0.1 -24@PEG in environments where the viscosity and the ionic strength of the media are dramatically changed. This fact also reflects the success of the polymer-coating process to avoid strong dipolar interactions among the NPs. It should be highlighted the importance of this feature for the practical use of MNPs in vivo because it demonstrates that regardless of the changes in the biological surroundings the excellent hyperthermia performance of the sample will be kept constant.

CONCLUSIONS
Bimetallic iron-zinc oleates (Fe 3−y Zn y Ol, 0.5 ≤ y ≤ 1) have been innovatively used as precursors to synthesize Zn-doped magnetite NPs (Zn x Fe 3−x O 4 ) with x ranging from 0.06 to 0.2 and with sizes between 25 and 40 nm. It has been proved that when Fe 2.5 Zn 0.5 Ol is used the resulting NPs grow at a higher rate and present more facets (slightly truncated octahedrons), whereas the mixture of monometallic oleates (FeOl + ZnOl) leads to less-faceted NPs (spheres and cubes) with a clear slower growth. The XANES study has revealed that most of the Zn 2+ ions are located at the A sites of the ferrite lattice, and a minor fraction of Zn 2+ remains as zinc oleate adsorbed on the surface as part of the organic coating. Mossbauer spectroscopy has allowed not only for the determination of the Zn content in the inorganic core (which totally agrees with XANES results) but also for the quantification of the Fe 2+ vacancies in the crystal lattice, leading to a precise determination of the stoichiometry in each sample. Samples synthesized using longer annealing times (≥ 60 min) have presented nearly zero iron vacancies, and samples with x ≈ 0.1 have shown the largest saturation magnetization at RT (≈97 Am 2 /kg). By coating the Zn x Fe 3−x O 4 NPs with high-molecular-weight PEG, biocompatible and highly stable colloids have been obtained, whose heating efficiency has been thoroughly analyzed by means of AC magnetometry at different frequencies and at a maximum field amplitude of 90 mT. Simulations of the dynamical hysteresis loops have revealed the decisive role played by morphology in magnetic hyperthermia performance. Zn-doped NPs (x ≈ 0.1) with a low shape dispersion and an average dimension of 25 nm have shown excellent heating capacity under clinically safe excitation conditions. Additionally, the dynamical magnetic response remains constant even when the dispersion media of NPs are very different, i.e., when the NPs are immobilized in agar or embedded in very confluent cell cultures. These novel achievements in the synthesis control of Zn-doped ferrite NPs together with the suitable surface PEGylation, good colloidal stability, biocompatibility, and great magnetothermal reliability will very likely contribute to the development of next-generation medical nanodevices for anticancer therapies.

Preparation of Bimetallic Iron-Zinc
Oleate. Two bimetallic iron-zinc oleates were prepared with different Fe/Zn ratios (5:1 and 2:1) keeping the total metal amount to 40 mmol and adding the corresponding sodium oleate to maintain electroneutrality. The process described above was followed to obtain less viscous redbrownish waxy products (Fe 2.5 Zn 0.5 Ol and Fe 2 Zn 1 Ol).
4.3. Synthesis of Zn x Fe 3−x O 4 NPs. Zn x Fe 3−x O 4 of different compositions, sizes, and morphologies were obtained by modifying the metal oleate precursors, the Fe/Zn ratio, the final synthesis temperature, and the annealing time.
In a typical synthesis, metal oleate (total metal amount 5 mmol) was dissolved in a 2:1 mixture of organic solvents (10 mL 1octadecene + 5 mL dibenzyl ether) together with oleic acid (10 mmol). The mixture was heated in two steps under N 2 (g): first, at 10°C /min from RT to 200°C and, second, at 3°C/min from 200°C to a final T (in the 320−330°C range). The final T was kept from 30 to 80 min (depending on the preparation), and then, the product was cooled to RT. The entire synthesis was carried out under mechanical stirring (at 120 rpm). The final product was cleaned by centrifugation (20 000 rpm) using THF and EtOH as explained in a previous work. 55 The stock solution was dispersed in CHCl 3 and stored in the fridge.
Second, the as-synthesized Zn x Fe 3−x O 4 NPs were coated by PMAO-g-PEG by a recently optimized protocol, 29 64 • Mossbauer spectroscopy measurements were performed at room temperature in transmission geometry using a conventional constant-acceleration spectrometer with a 57 Co-Rh source. The isomer shift values were taken with respect to an α-Fe calibration foil measured at room temperature. The NORMOS program developed by Brand et al. was used for fitting the spectra. • Quasi-static magnetization measurements as a function of magnetic field, M(H), and temperature M(T) were carried out using a SQUID magnetometer (MPMS3, Quantum design). These measurements were performed by drying aqueous colloids of PMAO-coated NPs (∼0.1 mg/mL) on semipermeable filter paper. The saturation magnetizations, M s , at RT and 5 K were obtained from dried as-synthesized samples (powder) and normalized per unit mass of inorganic matter by subtracting the weight percentage of organic matter determined by thermogravimetry. • Specific absorption rate (SAR) measurements were performed by AC magnetometry in a home-made device that generates a high magnetic field able to saturate the samples. 56 This device is capable of working at a wide frequency range (100−950 kHz) with large field intensities: up to 90 mT at low frequencies and up to 31 mT at high frequencies. The dynamic hysteresis loops were measured at room temperature (25°C) at selected frequencies of 133, 305, and 605 kHz. These measurements were carried out in PMAO-PEG-coated NPs dispersed in distilled water, agar (2%), and cell culture with NP concentration c ∼ 0.5 mg/mL in a solution volume of 100 μL.
4.6. In Vitro Study. 4.6.1. Cytotoxicity Assay. The human colorectal cancer cell line HCT116 (ATCC) was cultured in Dulbecco's modified Eagle's medium (DMEM) (Gibco) and supplemented with 10% FBS and antibiotics (Gibco) at 37°C and a 5% CO 2 atmosphere. Cells were seeded in 96-well plates at a density of 1000 cells per well and were allowed to attach to the plate before the addition of nanoparticles. After attachment, 0.1 μg (C 1 = 0.1 ng NP /cell) and 1 μg (C 2 = 1 ng NP /cell) of NPs per well [UdMO1] were added. Proliferation was measured the same day and after 96 h using a crystal violet assay. In brief, cells were fixed in 4% paraformaldehyde and stained with 0.1% crystal violet. After staining, cells were washed with water and 10% acetic acid was added. Absorbance was measured at 590 nm. 4.6.2. Hyperthermia Measurements In Vitro. Cells at two different concentrations (5 × 10 5 and 5 × 10 4 cells) were mixed with 0.05 mg of NPs (C 1 = 0.1 ng NP /cell and C 2 = 1 ng NP /cell) and transferred to 100 μL vials to perform the dynamical hysteresis loops at an NP concentration of 0.5 mg NP /mL using the AC magnetometer described above.
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