In the last decades, the synthesis of iron oxide magnetic nanoparticles (MNPs) has gained much attention,^[1,2] because of their applications in the biomedical area, and particularly magnetic imaging^[3,4] and hyperthermia therapy trials^[5,6] have been studied. In this scope, the magnetite (Fe₃O₄) and maghemite (γ-Fe₂O₃) are the most frequently used MNPs due to their strong magnetic properties, low cytotoxicity, and chemical stability.^[7,8] Nevertheless, in order to carry out in vitro or in vivo experiments using MNPs, it is necessary to suspend them on biological media (i.e., cell culture medium, phosphate buffer saline, isotonic solution, etc.) to ensure a reasonable colloidal stability, thereby forming a stable ferrofluid system.^[9,10]

Ferrofluids of MNPs with controlled diameters and shapes, are typically produced by using the well-known chemical co-precipitation procedure, where a base solution is added to liquid saline solutions of Fe²⁺/Fe³⁺, under an inert environment with adjustable temperature and pH.^[11–15] Furthermore, the surface of the MNPs must be coated with functional groups to achieve the anchoring of targeting agents and possibly the transport of drugs to cells or tissues.^[16,17] For example, ferrofluids with Fe₃O₄ nanoparticles coated with polyacrylic acid have shown a good efficiency for possible cancer therapy applications.^[18] In the same way, the use of oleic acid as stabilizing surface-ligand for aqueous dispersion is achievable by the formation of a double-layer of oleic acid on the surface of MNPs. The formation of a single layer will not allow the MNPs to be dispersed in aqueous solvents, but a large excess of oleic acid used in the synthesis method favors the formation of a double-layer and provides the optimal water dispersibility.^[19,20] Double-layer stabilized nanoparticles can be dispersed in polar and non-polar solvents, and this dual lyophilic character allows us to have MNPs highly stable in aqueous solvents.^[21,22] In another work, tiny nanoparticles capped with oleic acid ligands have shown an innovative application to industrial catalytic process, due to their high polydispersity.^[23]

Superficial modification of the MNPs produces many physical changes, which are exploited to reach a good colloidal stability and diminish the internal dipolar interactions, thus avoiding forming magnetic clusters. Nevertheless, the magnetic properties and monodispersity of the MNPs should not be dramatically modified after this functionalization process. Thus, the main aim of this work is to evaluate the induced changes in the structure and magnetic properties of Fe₃O₄ MNPs which are coated with oleic acid. Later, the power absorption density of the ferrofluid with OAMNP is analyzed to explore its expected performance in magnetic hyperthermia experiment.

The interaction between alternant magnetic field and ferrofluid system can be modeled by using the linear response theory. In this approximation, a linear relationship between the induced magnetization M and H is assumed. Then, the drained power density P on a volume V of ferrofluid is given by Eq. (1).^[24] As observed, P depends on its complex magnetic susceptibility χ″F, in addition to the frequency f, H², and the magnetic permeability of the empty space μ₀ = 4π × 10⁻⁷ N/A²,

$$ \begin{eqnarray}P={\mu }_{0}\pi {{\chi }^{^{\prime\prime} }}_{{\rm{F}}}f{H}^{2}.\end{eqnarray}$$ (1)

Regarding the effective relaxation time τ, this parameter takes into account both the Néel relaxation time (τ_N) and the Brownian relaxation times (τ_B) as expressed in Eq. (3). Thus, τ_N includes the effective magnetic anisotropy constant κ_e of the suspended MNPs through the Arrhenius law (see Eq. (4)), where τ₀ is the characteristic length of time (typically 1 × 10⁻⁹ s). In addition, τ_B includes the viscosity η of the liquid medium and the hydrodynamic diameter D_H of the MNPs, following the Stokes–Einstein law (Eq. (5))

$$ \begin{eqnarray}\begin{array}{lll} & & \tau =\displaystyle \frac{{\tau }_{{\rm{N}}}{\tau }_{{\rm{B}}}}{{\tau }_{{\rm{B}}}+{\tau }_{{\rm{N}}}},\end{array}\end{eqnarray}$$ (3)

$$ \begin{eqnarray}\begin{array}{lll} & & {\tau }_{{\rm{N}}}={\tau }_{0}\exp \left(\displaystyle \frac{{\kappa }_{{\rm{e}}}{V}_{{\rm{p}}}}{{K}_{{\rm{B}}}T}\right),\end{array}\end{eqnarray}$$ (4)

$$ \begin{eqnarray}\begin{array}{lll} & & {\tau }_{{\rm{B}}}=\displaystyle \frac{3\eta }{{K}_{{\rm{B}}}T}\displaystyle \frac{4\pi }{3}{\left(\displaystyle \frac{{D}_{{\rm{H}}}}{2}\right)}^{3}=\displaystyle \frac{\pi \eta {D}_{{\rm{H}}}^{3}}{2{K}_{{\rm{B}}}T}.\end{array}\end{eqnarray}$$ (5)

$$ \begin{eqnarray}{\kappa }_{{\rm{e}}}=\displaystyle \frac{25{T}_{{\rm{B}}}{K}_{{\rm{B}}}}{{V}_{{\rm{p}}}}.\end{eqnarray}$$ (6)

$$ \begin{eqnarray}\begin{array}{lll} & & P={\rho }_{{\rm{F}}}\cdot SAR,\end{array}\end{eqnarray}$$ (7)

$$ \begin{eqnarray}\begin{array}{lll} & & SAR=\displaystyle \frac{{C}_{{\rm{v}}}}{{m}_{{\rm{np}}}}\displaystyle \frac{{\rm{d}}T}{{\rm{d}}t}.\end{array}\end{eqnarray}$$ (8)

The ferrofluid of uncoated MNPs is prepared following a co-precipitation methodology. First, 30 ml of deionized water (previously deoxygenated with N₂) is deposited in a glass test tube and 15-ml deionized water in another one, both are isolated from the atmosphere to avoid absorbing oxygen. A Schlenk flask is depressurized to 500 mm of Hg within 8 min and then, it is filled with N₂. Afterwards, 0.4867 g of FeCl₃ (Sigma Aldrich) is dissolved in the first test tube and 0.417 g of FeSO₄ ⋅ 7H₂O (Fermont) in the second tube. Subsequently, both solutions are deposited in the flask. The blend is heated at 30 °C under continuous stirring at 400 rpm. At this point a chronometer is started in order to control the addition sequence of the reactants and heating periods. Right after 5 min, 3 ml of 5-M NH₄OH is added by using a peristaltic pump at a volumetric rate of 1.5 ml/min. After 15 min, a syringe needle is inserted into the septum of the flask. 30 min later, the synthesis is finished. A blackish suspension is obtained, indicating the formation of MNPs. The suspension of MNPs is washed four times with deionized water to eliminate the remaining by-products of the synthesis. Finally, a ferrofluid of MNP dispersed in water is obtained.

In the same sense, the procedure to obtain the ferrofluid of OAMNPs includes the aforementioned steps, followed by the addition of oleic acid. After 10 min, the dispersion is maintained at 80 °C for 10 min, and then, at 90 °C for 10 min. Then, 300 μl of oleic acid (Fluka Analytics, reagent grade) is added into the dispersion and kept stirring for 20 min. Afterwards, the stirring is stopped, and a colloidal dispersion of OAMNPs is obtained. The excess of oleic acid is eliminated by centrifugation at 1.2 × 10⁴ rpm for 1 h and 10 °C. The supernatant is removed and the OAMNPs are resuspended in deionized water. The centrifugation and resuspension in deionized water steps are repeated four times, and finally, the obtained ferrofluid of OAMNP is dialyzed by using a cellulose membrane (Sigma-Aldrich, MWCO 12 kDa, 1 Da = 1.66054 × 10⁻²⁷ kg).

The core diameter of the MNPs is estimated through x-ray diffraction (XRD) measurements by using a Panalytical Empyrean system and its goniometer covers the angular displacement 5° ≤ 2θ ≤ 80°. Then, Δθ = 0.02° is the programmed angular increment and t = 30 s is the sampling time for data acquisition. For this purpose, dried samples with 50 mg of coated and uncoated MNPs are placed on specials glass sample holders for XRD. Additionally, dried samples are analyzed through Fourier transform infrared (FTIR) spectroscopy measurements by using a Thermo Scientific Nicolet iS5 spectrometer in an ATR mode.

The scanning electron microscopy (SEM) measurements are obtained by using an MIRA3 (LMU) device of TESCAN company, with 1 nm of resolution capability. Samples are prepared by diluting 10 μl of ferrofluid with coated and uncoated MNPs in 1 ml of deionized water; subsequently, 10-μl aliquot is placed on a carbon conductive tape (5 mm × 20 mm), which is adhered to the special sample holder for SEM. During the next 35 min, this sample is dried at 45 °C inside an oven and then they are covered via gold sputtering.

In order to analyze the colloidal stability of water suspended coated and uncoated MNPs, Zeta potentials are determined at different pH values by means of a Zetasizer SZ90 (Malvern) through using polystyrene folded capillary disposable cells. First, a 0.01-M NaCl solution is prepared with deionized water, then, 100 μl of MNP at 15 mg/ml is added into 10 ml of NaCl solution. Afterwards, the pH of the dilutions is adjusted to a desired value by adding NaOH or HCl. Dispersions with pH values ranging from 2 to 11 are measured three times to determine the mean values and standard deviation. Additionally, the corresponding Z-average hydrodynamic diameter (D_H) and polydispersity index (PDI) are measured by using polystyrene disposable cuvettes (10-mm path length, four clear sides).

To determine the fraction of oleic acid covering the surface of the MNPs, thermo-gravimetric (TGA) measurements are realized with the help of a high-resolution Cahn Versa Therm Analyzer and two sample containers with 1.5-g capacity. A container is filled with 60 mg of dried coated MNPs while the second container is filled with the same mass of uncoated MNPs. Then, both samples are separately heated by sweeping the temperature interval 40 °C < T < 850 °C, at 10 °C/min of heating rate. During the experiments, the uncoated MNPs are always heated under an inert N₂-atmosphere (at 25 ml/min of flux) and the coated samples are heated up to 750 °C under N₂-atmosphere, but in the last interval (750 °C < T < 850 °C) the N₂ is replaced by oxygen.

The magnetization loops (at room temperature 300 K) of the MNPs are obtained using a VersaLab vibrating sample magnetometer (VSM) of quantum design. Hence, 5 mg of dried coated and uncoated MNPs are placed into diamagnetic containers and uniform magnetic fields from –30 kOe–30 kOe (1 Oe = 79.5775 A/m) are applied. Magnetization traces following the ZFC–FC protocol are registered establishing H = 100 Oe, while the temperature covers the interval 50 K < T < 400 K.

To determine the power absorption density of the OAMNP ferrofluid, a previously reported induction heater is used.^[27,28] The system is an alternating magnetic field generator equipped with a fluoroptic thermometer, which is used to determine the ferrofluid heating. This generator is suitable for modifying the applied frequency covering the interval 185 kHz < f < 530 kHz and the amplitude H can be increased up to 35 mT. Three Eppendorf tubes, each with 2 ml of capacity and 1 ml of ferrofluid (at 1 mg/ml each) are prepared. The procedure to obtain the P of each sample begins by placing them one at the time inside an adiabatic cavity in the inner space of the induction coil where the magnetic field is exactly uniform. Hence, while a sample is irradiated by fixing f and H, its temperature is registered and stored using the thermometer connected to a PC. Later, the temperature slope is analyzed offline to estimate the SAR by applying Eq. (8), which is substituted into Eq. (7) to determine the corresponding P. Following a systematic increasing of f and H, the respective dependence Pversusf and PversusH can be determined. In this work, the mean values of P are plotted using the measurements of the three samples including their corresponding standard deviations.

The typical XRD spectra obtained from uncoated (dark line) and OAMNP (gray line) samples are displayed in Fig. 1(a), and both measurements show the characteristic peaks of the magnetite structure. Thus, the Miller indices (2 2 0), (3 1 1), (4 0 0), (4 2 2), (3 3 3), and (4 4 0) are clearly distinguished, which correspond to the respective phases 2θ = 30.16°, 35.52°, 43.17°, 53.56°, 57.10°, and 62.70° (JCPDS file, No. 19-0629). Using the Scherrer formula (in radian units) σ = kλ(β(2θ)cos(θ))⁻¹, the estimated average crystallite sizes of uncoated σ_uc and coated σ_OAMNP samples are σ_uc=(13 ± 1) nm and σ_OAMNP = (15 ± 1) nm respectively. For this estimation a shape factor k = 0.94 is considered, the x-ray wavelength is λ = 1.54 × 10⁻¹⁰ m, and the determined parameters β(2θ) and θ are obtained from Fig. 1(b), which represent the close-up of the main peaks displayed in Fig. 1(a). In order to determine the standard deviation of σ_uc and σ_OAMNP, an experiment is performed three times, hence an approximated increase of 13% is observed in the magnetic core of OAMNP, these discrepancies can be attributed to random effects of the preparation processes.

Other spurious uncertainties of the average σ can be intrinsically involved in the Scherrer equation when the sample has a polydispersed diameter below 10 nm and a crystal structure with superficial strain.^[30] The strain is important if the synthesis method uses high energy and/or temperatures, but it can be neglected when the preparation is based on chemical reactions or liquid-to-solid phase transitions^[31] This last characteristic can explain no larger discrepancies in the sizes reported for several polydispersed nanocomposites from XRD, SEM or TEM.^[32–34] Therefore, the SEM micrograph of OAMNP in Fig. 1(c) clearly shows that the clusters possess almost spherical shapes, and that some small clusters. The diameter sizes (n = 400) are extracted from a set of SEM images and the distribution is represented in Fig. 1(d). After fitting the data to a normal distribution function, the mean diameter is σ_OAMNP = (20 ± 4) nm. Whereas, for uncoated samples the corresponding SEM micrograph of Fig. 1(e) and its plotted distribution of diameters in Fig. 1(f) indicate σ_uc = (15.5 ± 3) nm. By comparing the values of σ_OAMNP and σ_uc from XRD and SEM, the discrepancies of 25% and 16% are respectively evidenced, which are probably related to the polydispersion of the samples omitted in the Scherrer equation. Moreover, 23% is the computed discrepancy through the formula 100(1 – σ_uc / σ_OAMNP), and this difference is mainly related to the oleic acid shell.

In relation to the superficial modification of the MNPs, the FTIR spectra of pure oleic acid, uncoated and coated MNP are displayed in Fig. 2. In the dark waveform, the presence of Fe₃O₄ is corroborated due to the vibrations observed at 577 cm⁻¹ which corresponds to the Fe–O bond, as well as those at 1622 cm⁻¹ and 3209 cm⁻¹ of the O–H groups.^[14] Also, the spectrum of the OA shows its characteristic signals at 3005 cm⁻¹ due to the CH stretch at C = CH, 2922 cm⁻¹ and 2853 cm⁻¹ associated with the asymmetric and anti-symmetric stretch of the CH₂ groups, and an intense signal at 1707 cm⁻¹ due to the stretch of the group C = O. The signal observed at 1284 cm⁻¹ corresponds to the CO stretch; the signals at 1457 cm⁻¹ and 935 cm⁻¹ are associated with the OH stretch in the plane and out of the plane respectively; the signal at 722 cm⁻¹ corresponds to the CH₂ balance and the signal at 1412 cm⁻¹ refers to the vibration of the CH₃ umbrella-like mode of oleic acid.^[35] In addition, the spectrum of OAMNP clearly overlaps the last two FTIR spectra and no other structural changes of magnetite are observed. It shows two characteristic signals at 1428 cm⁻¹ and 1516 cm⁻¹ due to asymmetric and symmetric stretches of the carboxyl group (–COO⁻) respectively; other signal at 1705 cm⁻¹ is due to stretch of group C = O, which corresponds to the characteristic signal of the second layer on the magnetite nanoparticles coated with oleic acid; and finally, the signals at 2847 cm⁻¹ and 2915 cm⁻¹ are associated with the asymmetric and anti-symmetric stretches of the CH₂ groups, respectively.^[14,19] Accordingly, the spectra demonstrate a surface modification of magnetite nanoparticles with an AO double layer coating. Thus, it is expected that the diamagnetic organic coating deposited on MNPs may affect their magnetic properties in comparison with those of uncoated MNPs.

On the other hand, the relative mass dependent temperatures of uncoated (dark line) and OAMNP (gray line) are shown in Fig. 3(a). These measurements are obtained via TGA analysis and two clear different behaviors are observed. After a careful observation of the mass registers, the uncoated MNP sample has 2.87 % of mass loss at 39 °C < T < 296 °C and also has 0.45% of mass loss at temperatures above of 296 °C. This decrease is caused by evaporation of water adsorbed on the particle’s surfaces. Nevertheless, the sample of OAMNP decreases by 4.4% at 30 °C < T < 165 °C, followed by a 54.4-% mass loss at 165 °C < T < 337 °C. Also, 6.5 % of mass loss at 338 °C < T < 576 °C is observed, and finally, a 3-% decrease above 577 °C. At the end, 31.7% of iron oxide is reached above 750 °C. In the same sense, the derivative of the relative mass loss is shown in Fig. 3(b), where the characteristic peaks of the mass loss rate are highlighted. Hence, the peak at 77 °C of the OAMNP is associated with the water evaporation (4.4% of mass loss), the peaks at 340 °C and 541 °C are related to the boiling point of the oleic acid (60.9% of mass loss) and the last peak at 758 °C to the oxidation of iron oxide (34.7% of relative mass plus resultant material). With the change of atmosphere at T > 750 °C, clearly can be corroborated the expected phase transition from magnetite to hematite.^[36] By analyzing the ratio of relative mass proportions between oleic acid and magnetite, 4 nm is the estimated coating thickness. Thus, 19.0 nm is the total diameter of OAMNP which matches the mean value obtained from SEM in Fig. 1(d).

The measurements of Zeta potential over the pH interval 2.2 < pH < 11 are displayed in Fig. 4(a). For OAMNP, an initial negative decrease of the Zeta potential is observed to reach a minimum value (–80 mV) at pH = 8; this value increases with the systematic increase of pH and it is maintained below –45 mV for 9 < pH < 11. Thus, for pH > 4 a good colloidal stability of the OAMNP ferrofluid is achieved. In contrast, the ferrofluid with uncoated MNPs shows a low stability behavior for pH > 4, an incipient stability at 6 < pH < 7 and a good stability only for pH > 9. Additionally, the dependence of hydrodynamic diameters D_H on pH is shown in Fig. 4(b). In general, the higher D_H is observed in uncoated MNPs. Indeed, the largest diameter D_Hmax = 5720 nm is registered at pH = 8, but the Zetasizer cannot determine the corresponding D_H for pH > 8, even on its higher resolution scale. When the ferrofluid of OAMNP is analyzed the behavior notably changes, because this parameter systematically decreases with the increase of pH, reaching up to 140 nm at pH = 11. The remarkable differences between the σ_OAMNP via SEM and the σ_OAMNP via D_H are explained by the formation of islands of OAMNP in the ferrofluid, which are probably due to electrostatic and Van Der Waals interactions. A similar trend is observed on the PDI, where the higher values are observed in uncoated MNPs (see Fig. 4(c)). Indeed, for uncoated MNPs, the lowest value PDI_min = 0.6 is reached at pH = 2, which indicates a completely polydisperse behavior over the studied pH range. For OAMNP, the measured PDI indicates some polydispersity for pH > 8 and pH = 6. Nevertheless, an acceptable monodispersity is observed at pH < 6 and pH = 7.4; indeed, the best stability values are reached for pH = 4 (PDI = 0.13 7#x00B1; 0.2) and pH = 7.4 (PDI = 0.18 ± 0.2).

Magnetic properties of uncoated and coated MNPs under the action of static magnetic field are discussed now. In Fig. 5(a), the curves of magnetization M versus magnetic field of the uncoated MNP (dark line) and coated MNP (gray line) are plotted, which are obtained at room temperature. The magnetic saturation of the OAMNP is clearly diminished, reaching M_s = 24 emu/g, which is 2.92 times lower than the same parameter obtained for the uncoated sample. Regarding to the magnetic cohercivity H_c, a similar result is observed, reaching 11 Oe and 25 Oe for coated and uncoated samples respectively. Also, the low magnetic remanence M_r = 0.25 emu/g of OAMNP reaches up to 6.8 times less than the measured in uncoated samples. Hence, those significant differences in the magnetization loop are caused by the lower concentration of magnetite in the OAMNP sample (only 31.7%), in addition, the coating shell helps to diminish the internal dipolar interactions between neighboring particles. Likewise, the dependence of M on temperature following the ZFC–FC protocol (at H = 100 Oe) is shown in Fig. 5(b). Notable differences between both curves can be clearly seen, but the ZFC trace of uncoated samples does not exhibit any maximum value with null slope, indicating the magnetic blocking state of M. Whereas the magnetization of OAMNP exhibits a blocking temperature T_B = 303 K, evidencing a superparamagnetic ordering. Despite a low H_c observed on coated samples, the inset of Fig. 5(a) shows some of ferrimagnetic ordering, but the obtained T_B indicates a predominate superparamagnetic behavior above room temperature. These mixed magnetic properties are the consequence of the polydispersity of the samples, which coincides with the measured PDI of Fig. 4(c). Several studies have reported the modulation of T_B as a consequence of a decrease in the dipolar interactions,^[37–40] because this potential energy is proportional to r⁻³ and the thickness of the shells increases the distance between nearby magnetic cores. Thus, while the ZFC trace is registered, these weakened interactions do not screen the thermal fluctuations originating from the Néel relaxation of the magnetic moments.

Using the core size σ_OAMNP obtained via XRD and the observed blocking temperature T_B, we can obtain κ_e ≈ 9.1 × 10⁻⁴ J/cm³ from Eq. (6), which is the estimated effective anisotropy constant of OAMNP. In consequence, τ_N ≈ 88 s is the effective Néel relaxation time, which is computed by substituting κ_e into Eq. (4). Therefore, the reached Brownian relaxation time τ_B ≈ 2.7 ms is computed from Eq. (5) under the assumption of a water viscosity of η = 8.9 ° 10⁴ N ⋅ s/m² and D_H ≈ 200 nm. This value is four orders of magnitude less than τ_N, and then τ ≈ τ_B. Thus, the effective relaxation time τ described by Eq. (3) is dominated by the rotation of the OAMNP.

The induced heating on the OAMNP ferrofluid is shown in Fig. 6(a). In this experiment, H = 25 mT is the constant amplitude applied during 2 min, while f has been increased in five steps from 182 kHz to 530 kHz. The five traces of the temperature increment over time exhibit an almost linear behavior, where the slope d T / d t systematically grows at each frequency. Indeed, those slopes are computed using data linear regressions in the time interval 20 s < t < 40 s, and also they are used to determine the dependence Pversus time at each value of f as displayed in Fig. 6(b). Moreover, the parameter P is determined first by computing the corresponding SAR values from Eq. (8), which later is introduced into Eq. (7). For these purposes, are used are the specific heat C_v = 4.186 kJ/(K ⋅ kg), density ρ = 1000 kg/cm³, and the suspended fraction of OAMNP m_np = 0.1. The delineated solid line on the plot of Fig. 6(b) is the best linear data fit, which reaches the slope m_f = 0.047 ± 0.004 W/cm³ per kHz and it is characterized by the quality factor χ² = 0.94. This statistical parameter evidences good accordance with P corresponding to the linear response model Eq. (1). Then, P ≈ 22 W is the maximum power dissipated by OAMNP to 1 cm³ of water when H = 25 mT and f = 530 kHz. This magnitude is a very important parameter for future applications in the induction heating of biologic agents.

In other assays, the OAMNP ferrofluid is heated using the constant frequency f = 330 kHz, whereas the amplitude H is increased from 10 mT to 30 mT in steps of 5 mT. In Fig. 7(a), the five traces of the temperature increment during 2 min are shown and the gradual increase of d T / d t with H is evidenced. The same procedure described above (Fig. 6(a)) is used to determine the dependence of P on H and it is displayed in Fig. 7(b). There, the solid line is the best quadratic data fit estimated using the formula P = m_h ⋅ H², where

 1

The linearity condition for P is given by the expression μ₀HV_pM_s < k_BT, and this inequality can be computed using the employed parameters

 1

 1

In this work, the physical changes of a ferro-colloid system of superficially modified iron oxide MNPs are analyzed. Three principal changes must be highlighted as a consequence of the oleic acid coating, i.e. the high colloidal stability related to a low polydispersity index, the modulation of the magnetic properties which leads the magnetization to go up to a superparamagnetic ordering, and the good accordance of its power absorption density with the linear response theory.