Experimental Comparison of Methods to Evaluate Heat Generated by Magnetic Nanofluids Exposed to Alternating Magnetic Fields

Abstract

The paper aims to compare different methods able to estimate the specific loss power (SLP) generated by three different types of magnetic nanoparticles, MNPs, dispersed in a suspension fluid, e.g., octane or water. The nanoparticles were characterized morphologically in terms of shape and size, chemically for composition and their physical properties like magnetization and SLP were studied. We evidenced the differences in SLP evaluation due to the applied method, particularly in the presence of thermally induced phenomena such as aggregation or precipitation of MNPs that can affect the heating curve of the samples. Then, the SLP determination methods less sensible to this phenomenon appear to be the ones that use the initial slope when the sample is in quasi-adiabatic condition. Finally, we propose a comparison of those methods based on the pros and cons of their use for the SLP determination of magnetic nanofluids. In particular, the analysis of the behavior of the heating curve is useful to evaluate the useful amplitude of the interval analysis for the initial slope methods.

1. Introduction

Magnetic fluid hyperthermia (MFH) uses magnetic nanofluids, i.e., magnetic nanoparticles suspended in a liquid medium, to increase the local temperature in a target area. The magnetic nanoparticles can generate heat when they are exposed to a time-varying magnetic field [1,2,3,4,5,6,7]. Hyperthermia can be an effective anticancer agent, particularly when combined with ionizing radiation or chemotherapy [8]. Thermal stress, depending upon the time of exposure and temperature, can directly initiate cell death or cause intracellular protein damage, denaturation, or degradation. If the affected proteins are enzymes involved in DNA damage repair, hyperthermia can effectively inhibit or abrogate cancer cell recovery from DNA-damaging agents. Further, physiological factors enhance the susceptibility of tumors to combined heat and radiation because mild tissue heating promotes vasodilation which increases blood flow to raise pO₂ which increases the biological effectiveness of the (low linear energy transfer) radiation. In general, an increment of a few degrees with respect to the physiological temperature of 37 °C, i.e., a final temperature between 41 and 43 °C, is able to induce cell death by apoptosis [4,5,9,10,11,12,13,14,15]. A higher temperature can induce necrosis and this effect is used, for instance, in ablation therapy [3,16,17],as it is well known the magnetic field used in the MFH is in the order of <10² kA/m (in a range that corresponds to 50–200 Oe) at 100–400 kHz [1,2,3,18,19,20,21,22]. In general, the maximum frequency and field amplitude are limited by considerations of patient safety due to off-target Joule heating caused by induced eddy currents [23]. In fact, importantly for human exposure, it is pivotal to maintain the product of the magnetic field strength (H) and its frequency (f) below a threshold safety value. This is known as the Brezovich criterion, for which the product C = H × f should remain below 5 × 10⁸ A/(ms) to minimize any collateral effects of alternating magnetic fields on the human body. In recent years this limit was updated and now the safety limit commonly prescribed is set at 5 × 10⁹ A/(ms) [24], even though some authors suggest that it could be raised close to 10¹⁰ A/(ms) [25,26].

The specific loss power, SLP, is used as a parameter to investigate how much energy is absorbed per magnetic nanoparticles mass (NPs) under AMF. Hence, extensive efforts have been made to produce magnetic nanomaterials possessing high SLP values. In fact, different types of magnetic nanoparticles (MNPs) could be synthetized using iron oxide, Mn-Fe oxide, or CoFe compounds [18,27,28,29,30,31]. These types of MNPs could be produced by physical or chemical processes. The most common chemical methods for MNP production include co-precipitation and thermal decomposition [32,33,34,35,36,37]. These different materials show different magnetic characteristics and consequently generate a different power density expressed in terms of SLP. The variation in SLP values can be attributed to several factors including sample size, concentrations, and magnitude and frequency of the applied field [7,38,39,40,41].

The SLP generated by an MNP fluid could be estimated from calorimetric data using different methods as largely discussed in the literature [7,40,42,43,44,45,46,47]. The simplest method includes the evaluation of the fit of a long acquisition of the temperature vs time curve using an exponential model (named in some literature reference as the Box-Lucas model [46,47,48]), typical of heating phenomena for which the initial part of the curve has a quasi-adiabatic behavior. This method requires time for each acquisition and a stable environmental temperature [45,48]. The other two methods involve the computation of the slope of the temperature curve considering the interval in which temperature rises linearly and in which the quasi-adiabatic condition is valid [9,43,44,45,48,49,50,51,52,53,54]. These methods require less time for data acquisition since the quasi-adiabatic interval is within the first few minutes of the fluid heating curve. In this paper, we compare the SLP values obtained using these three different computation methods to a variety of MNP samples. The SLP evaluation using the fit of the exponential model was performed at a single frequency and a single magnetic field intensity (e.g., see [48]); whereas the two methods that involve the slope of the temperature curve were used to characterize the different MNPs in terms of SLP at three different frequencies and different magnetic field intensities [44,45,48,55]. We also provide the data obtained from the physical characterizations of the MNPs to highlight the similarities and differences arising from the synthesis methods. In particular, the samples are different in terms of size, magnetic properties, metal ions content, and generated power density. In our study, we considered three MNPs based either on iron-oxide prepared by co-precipitation, C5 sample, or by thermal decomposition, sample C12, and a sample based on Mn-Fe oxide, labeled C26. All the NPs powders were suspended in water while one, C5, was also suspended in octane.

2. Materials and Methods

Iron(III) acetylacetonate (99.9%), manganese(II) acetylacetonate (99.9%), oleylamine (≥98%), oleic acid (≥99%), 1,2-tetradecanediol (90%), benzyl ether (98%), cetyltrimethylammonium bromide (≥98%), iron(II) chloride tetrahydrate (≥99%), iron(III) chloride hexahydrate (≥99%), ammonium hydroxide solution (28.0–30.0% NH₃ basis), n-octane (98%), and solvents were purchased from Sigma-Aldrich and used without further purification.

2.1. Synthesis of the Nanoparticles

The magnetic nanoparticles used in this study have been prepared by common thermal decomposition of organometallic precursors or coprecipitation by slight modification of reported methods [34,56].

2.1.1. Synthesis of C26

In a typical preparation, 2.80 g (7.90 mmol) of iron(III) acetylacetonate, [Fe(acac)₃], and 1.00 g (3.95 mmol) of manganese(II) acetylacetonate, [Mn(acac)₂], were mixed in an inert atmosphere (N₂) with oleylamine (6.40 g, 24.0 mmol), oleic acid (6.80 g, 24.0 mmol), and 1,2-tetradecanediol (9.20 g, 36.0 mmol) in 100 mL of benzyl ether as solvent. The dark red homogeneous mixture was magnetically stirred and heated at 200 °C for 120 min and then at 300 °C for 60 min. After cooling the system to room temperature, the black suspension was poured into a 3-fold volume of ethanol and mechanically stirred. The NPs were magnetically separated, washed three times with ethanol (50 mL), and dried under vacuum. For dispersion in water, an equal mass of cetyltrimethylammonium bromide (CTAB) was ground with the NPs until a homogeneous mixture was obtained and dispersed in deionized water.

2.1.2. Synthesis of C12

In a similar procedure as for C26, 2.80 g (7.90 mmol) of iron(III) acetylacetonate, [Fe(acac)₃], were mixed in an inert atmosphere (N₂) with oleylamine (6.40 g, 24.0 mmol), oleic acid (6.80 g, 24.0 mmol), and 1,2-tetradecanediol (9.20 g, 36.0 mmol) in 100 mL of benzyl ether as solvent. Reaction time, temperature, purification procedure, and dispersion in water were performed as in the synthesis of C26.

2.1.3. Synthesis of C5

This sample was prepared by a coprecipitation method starting from inorganic salts in basic solution. Typically, iron(II) chloride tetrahydrate (4.97 g, 25.0 mmol) and iron(III) chloride hexahydrate (13.52 g, 50.0 mmol) are dissolved in deionized water (150 mL) and treated with a solution of ammonium hydroxide (24% in water). The base is added under vigorous mechanical stirring until pH 11 (controlled with litmus paper) and subsequently, 7.5 mL of oleic acid (6.70 g, 23.7 mmol) is added to the black suspension and the temperature is increased to 60 °C and maintained for 30 min. The black solid is separated magnetically, washed with water several times and then three times with ethanol (50 mL), and dried under vacuum.

2.2. Nanofluid

The nanofluids were obtained by suspending the NPs powder in either an apolar solvent (n-octane) or deionized water. Due to the use of lipophilic surface functionalization of the NPs, they are easily dispersible in apolar solvents such as hydrocarbons, while the use of a surfactant is necessary for their dispersion in polar solvents and water. For this reason, the dispersion in n-octane (chosen for its relatively low volatility, to reduce the effect of vaporization on its temperature measurements) was obtained by simple mixing of the powder with the solvent to obtain a 10 mg/mL suspension. 3 mL of the suspension was collected for analysis. In the case of deionized water, the suspension was obtained by treating 60 mg of 1:1 MNP/CTAB mixture powder with 3 mL of water to obtain a 10 mg/mL suspension of magnetic nanoparticles. The concentration in both cases was referred to as the weight of MNPs. Finally, all the suspensions were treated in an ultrasound bath for few minutes for better dispersion prior to analysis.

2.2.1. TEM Analysis for Shape and Size

Dried NPs were dispersed in fluid in order to perform the analysis of the morphology with the aim of investigating the shape and the size by means of transmission electron microscopy (TEM), model TECNAI FEI G2 (FEI company, Hillsboro, OR, USA). A drop of well-mixed fluid was deposited on the TEM grid and analyzed at a suitable magnitude. In this case, the NPs were dispersed in octane or hexane. For each sample, at least 10 representative pictures are acquired using the camera of the instrument. These pictures were elaborated by means of the software ImageJ, version 1.53v 21 (public domain Java image processing program developed by NIH, National Institutes of Health, Bethesda, MD, USA [57]). The nanoparticle shape was identified, and the diameters were measured using the measurement tools. For each sample, a few hundred of nanoparticles were measured, and the average diameter and the corresponding standard deviation were evaluated. The histogram of the diameters was also obtained, and eventually different populations of diameters were identified. In case different sub-populations were identified in the entire population, the average diameter and the frequency of each sub-population were evaluated.

2.2.2. Hydrodynamic Radius

The NPs hydrodynamic diameter was determined by Dynamic light scattering (DLS) measurements using a Malvern Zetasizer 3000HS (Malvern Panalytical, Malvern, UK). All the samples (10 μL of NP_{[10 mg/mL]}) were analyzed in 1 mL of water or octane at 25 °C after 15 minutes sonication in an ultrasonic bath [58].

2.2.3. Magnetic Properties

The magnetic properties of the samples were measured using a Quantum Design superconducting quantum interference device (SQUID, Quantum Design Inc., San Diego, CA, USA) magnetometer operating in the 5–300 K temperature range (maximum applied field 50 kOe) [59].

2.2.4. ICP-MS Characterization

The composition of the MNPs in terms of Fe and Mn content was determined by inductively coupled plasma mass spectrometry (ICP-MS) (Element-2; Thermo-Finnigan, Rodano (MI), Italy) at medium mass resolution. Sample digestion was performed with 1 mL of concentrated HNO₃ (70%) using a high-performance Microwave Digestion System (ETHOS UP Milestone, Bergamo, Italy). A natural abundance iron standard solution was analyzed during sample runs in order to check changes in the systematic bias. The calibration curve was obtained using four Fe and Mn absorption standard solutions (Sigma-Aldrich, St. Louis, MO, USA) in the range 0.2–0.01 μg/mL [58].

From the ICP-MS data, the mass of nanoparticles, m_{NP_P}, corresponding to the mass of powder dispersed in the suspension fluid was determined [51,58,59].

2.3. Temperature vs. Time Characterization

2.3.1. Nanofluid Heating

The nanofluids were heated by means of an inductor connected to a generator EASYHEAT 10.0 kW (manufactured by Ambrell Corporation, Rochester, NY, USA) that generates a time-varying magnetic field at 177 kHz or 245 kHz. The cylindrical inductor in air was formed by 7 turns with an internal diameter of 8 cm. The supply current was varied between 100 A to 500 A which corresponds to a magnetic field between 4.5 to 21.0 kA/m (between 56 and 263 Oe) [60,61]. The temperature of each sample was recorded for different values of magnetic field amplitude and frequency. Temperature measurements were repeated more than three times. The measurement set-up is represented in Figure 1 [61].

For experimental tests, a sample of 3 mL of the nanofluid, at 10 mg/mL in NP powder, was placed in a 5 mL test tube. The test tube was placed in a holed Teflon cylinder, with an external diameter of 7 cm and an internal hole with diameter of 3 cm, equipped with a threaded cap where the test tube, with a diameter of 1 cm, can be screwed. This way a layer of air is interposed between the test tube and the Teflon cylinder. The cap was equipped with a hole for the temperature sensor. The aim of the cylinder is to maintain the adiabatic conditions in the first few minutes of the heating process. The nanofluid temperature in a predefined time interval was recorded using a fiber optic thermometer Fo-temp (manufactured by Optocom, Stendal, Germany).

Time-temperature data were collected and used to evaluate the SLP by means of three different methods. In the considered samples in a preliminary experiment, we evidenced that the temperature increment of the fluid due to the induced current in the suspension fluid was negligible. Moreover, in our measurement system, the vial with the sample was placed in a hole cylinder with an air layer 2 cm thick. This way the temperature inside the sample was less influenced by external temperature. Then, the temperature data were used as collected.

2.3.2. SLP Obtained by Exponential Function Analysis

In case of the temperature of the nanofluid recorded in a time interval 2400 s long, the SLP was evaluated as in [43,44]. In this case, the temperature versus the time shows an exponential behavior where the temperature evolution in the time T(t) is, can be described by means of the exponential function typical of heating phenomena based on the maximum temperature gap between the initial time step and the temperature at the steady state condition considered the final time step, $∆T_{max}$ as described by Andreu and Natividad in [44]:

$$T\left(t\right)=T_0+∆T_{max}\left(1-e^{-\frac{t}{\tau }}\right)$$

(1)

where T₀ is the initial temperature at the time step 0 s, t is the time and τ is the time constant of the exponential function that represents the heating process as evidenced in Figure 2. From the initial slope, the SLP was evaluated in a time interval lower than half of the time constant.

Fitting the time-temperature curve by means of the minimum least squares method using Matlab fitting tool the values of T₀, $∆T_{max}$ and τ were evaluated. Given the fitting parameters of Equation (1), according to [44], the SLP could be evaluated as:

$$SLP\left(A\right)=\frac{C}{m_{MNP}}·\frac{∆T_{max}}{\tau }$$

(2)

where m_MNP is the mass of NPs, $∆T_{max}$ and τ were the maximum temperature gap and the time constant of the heating curve, respectively, and C, in [J K⁻¹], is the heat capacity of the suspensions approximated to the specific heat of the fluid (4.18 [J g⁻¹ K⁻¹] for water and 2.238 [J g⁻¹ K⁻¹] for octane) multiplied by the mass of the fluid. In fact, the contribution of the heat capacity of the mass of dispersed NPs is negligible with respect to that of the fluid alone and is approximated by that of the fluid as in [9] since the contribution of the MNPs to the C constant, evaluated as in [44], is less than 1% (considering a specific heat for magnetite close to 0.67 [Jg⁻¹K⁻¹] [7] and NPs mass of 10 mg). The values $∆T_{max}$ and τ were evaluated fitting the temperature curve.

The SLP evaluated as in Equation (2) was computed considering the frequency of 177 kHz and considering the peak of the magnetic field at 170 Oe.

2.3.3. SLP Obtained by Initial Slope Method

The SLP could be computed also considering the initial slope of the temperature curve evaluated by means of the ratio between the temperature increment, ΔT(Δt), evaluated in a time interval, Δt, with Δt = 60 s [43,44]:

$$SLP\left(B\right)=\frac{C}{m_{MNP}}·\frac{∆T\left(∆t\right)}{∆t}$$

(3)

In this evaluation, the first 10 s of the temperature curve were discarded. In this method, the quasi-adiabatic interval has to be identified. In particular, other authors evaluate the slope of the temperature rise in different intervals discarding the first 10 s of the temperature curve. The intervals 20 s, 30 s, 60 s, and 90 s were considered and the temperature vs. time slope was computed. Homogeneous values of slope identify linear heating that corresponds to a quasi-adiabatic condition [44,45,48]. In the examined cases the interval Δt = 60 s fit with all the samples examined.

2.3.4. SLP Obtained by Quasi-Adiabatic Calculation

The temperature of the nanofluid was recorded in a time interval of 160 s long (150 s AMF ON and 10 s AMF OFF). The SLP related to the nanofluid was evaluated as in [48]. Briefly, before turning the AMF power ON, temperature of the IONP colloid was monitored for a few minutes to ensure the temperature was stable (variation ≤0.1 °C) and the colloid was in thermal equilibrium with the environment. Next, the AMF power was turned ON and temperature was recorded for 160 s. Temperature vs. time was also recorded for water blanks for the same AMF settings (H, f). This measurement was performed three times the first day of the experiment. From this data, excluding the first 10 s from analysis and considering the value until 110 s, the net temperature increase, and incremental temperature increase were calculated for IONP colloids. The net temperature increase of the samples was calculated by subtracting the temperature collected in the first sample at time 0 s. Next, the heating rate, evaluated as the slope of the net temperature increase curve in predefined time intervals, e.g., between 10 and 60 s or between 10 and 110 s, which satisfied quasi-adiabatic conditions [33,35], was used to calculate SLP using methods previously described and will be labeled as QA-SLP method, Quasi Adiabatic-SLP [45,48]. In the considered measurement set-up, the interval 10–60 s is approximately adiabatic.

The SLP values were computed considering the NP total mass (10 mg/mL) for a volume of 3 mL of water or octane.

The SLP using adiabatic method was evaluated at 177, 215, and 245 kHz and considering different magnetic field intensities with peak-to-peak between 113 and 263 Oe (9 to 21 kA/m, peak value).

3. Results

3.1. Magneto-Fluid Characterization

3.1.1. Size Analysis from TEM Image

The TEM images of the analyzed nanoparticles and the histogram of the diameter distributions were reported in Figure 3. The shape of the nanoparticles is approximately cube-shaped for sample C26, irregular with round and triangular elements for C12, and irregular with approximately sphere-shaped for the C5 sample. The average diameter of the magnetic core of the nanoparticles was measured and reported in

Table 1. NP size in terms of magnetic core and hydrodynamic diameter (water suspension). * The hydrodynamic mean diameter was obtained by the number-weighted distributions that represent the number of molecules in each bin in a given histogram, derived from the intensity distribution using the Mie theory [62,63]. Std = standard deviation, PDI = polydispersity index.

	Magnetic Core Diameter		Hydrodynamic Diameter *
	Average [nm]	Std [nm]	Average [nm]	Std [nm]	PDI
C26	29.2	±10.2	109(100%)	±8	0.43
C12	8.8	±3.7	132(97%) 486 (3%)	±15 ±94	0.51
C5	9.5	±3.1	132 (95%) 610 (5%)	±28 ±198	0.46

. The Anderson-Darling test verifies that the null hypothesis (the distribution of the diameters of the nanoparticles is normal) is not true (p-value < 0.005) for all the samples considered. Only for sample C12 is a Lognormal distribution (p-value = 0.2) identified.

3.1.2. Size Analysis: Hydrodynamic Diameter

Table 1 also shows the hydrodynamic diameter of the nanoparticles which also include the non-metallic external shell. The mean diameter was obtained by the number-weighted distributions that represent the number of molecules in each bin in a given histogram (as in Figure 3h–l, derived from the intensity distribution using the Mie theory [62,63]. From the hydrodynamic and magnetic diameters, the thickness of the external shell was evaluated in the case of NP dispersed in octane. The hydrodynamic and magnetic diameters for the NPs in water are related to the size of the NP aggregate.

3.1.3. Magnetic Properties

The magnetic loops measured at temperatures T = 5 K and 300 K are shown in Figure 4. The magnetization has been obtained by dividing the magnetic moment, measured by SQUID, by the mass of the MNPs alone (i.e., excluding the oleate).

Magnetite has an inverse spinel structure in which the trivalent ions Fe³⁺ (bearing a magnetic moment of 5 µ_B) are equally distributed in the tetrahedral (A) and octahedral (B) sites and the divalent ions Fe²⁺ (magnetic moment of 4 µ_B) are placed in the B sites, as expressed by the notation [Fe³⁺]_A[Fe²⁺ Fe³⁺]_BO₄. A net magnetic moment is provided by the Fe²⁺ ions since those associated with the Fe³⁺ ions annihilate reciprocally, being the superexchange interaction between A and B sites antiferromagnetic in nature. Hence, the predicted magnetic moment per unit cell is 4 µ_B and the expected value of saturation magnetization at T = 5 K is M_S ~98 emu/g [64].

However, a lower M_S is measured on the investigated samples at T = 5 K (

Table 2. Magnetization at different temperatures.

	MS at T = 5 K (emu/g) ±2%	MS at T = 300 K (emu/g) ±2%
C26	86	72
C12	73	65
C5	80	69

). In particular, M_S decreases with decreasing the mean size of the MNPs (Table 1). This is a finite-size effect often reported for ferrite MNPs and ascribed to the spin canting phenomenon, i.e., a lack of spin collinearity in the spinel structure. The effect of spin canting is strictly associated with the presence of structural disorder, therefore low crystallinity, at the surface and/or in the core of the MNPs. In fact, it is due to reduced and modified atomic coordination and the presence of topological defects, resulting in altered super-exchange bonds [59,65,66,67,68].

The highest M_S (~86 emu/g) is measured in C26 MNPs. This is consistent with the fact that they have the largest mean size and quite a regular cubic shape. The latter feature has been shown to imply a higher degree of crystallinity, compared to the spherical shape [69,70]. Moreover, in Mn-doped magnetite, which is the case of this type of MNP, the possible substitution of Fe²⁺ ions with Mn²⁺ ions (isoelectronic with Fe³⁺ and hence with a magnetic moment of 5 µ_B) brings about an increase of the magnetic moment per unit cell and therefore of the saturation magnetization [71,72,73].

In all the samples the coercivity H_C is in the 200–300 Oe range at T = 5 K; at T = 300 K, H_C ~36 Oe in C26 whereas the absence of magnetic hysteresis (i.e., null coercivity and remanent magnetization) in C12 and C5 is in favor of a superparamagnetic behavior of the whole MNPs assemblies.

In fact, it is well known that MNP can exhibit magnetization relaxation, possibly culminating in the superparamagnetic behavior when the thermal energy is comparable to the anisotropy energy barrier for the reversal of its magnetic moment [74].

The blocking temperature T_B above in which an isolated single-domain MNP enters the superparamagnetic regime is expressed by the relation:

$$T_B=\frac{K V}{k_B\ln \left(t_m{f}_0\right)}$$

(4)

where KV is the magnetic anisotropy energy barrier (K anisotropy coefficient, V volume of the MNP), k_B is the Boltzmann constant, t_m is the measuring time characteristic of the used investigating technique, and f₀ is a frequency factor [74]. A value of ln(t_mf₀) ~25 is usually considered for SQUID measurements, which assumes t_m= 100 s and f₀ = 10⁹ s⁻¹ [71,75].

To gain more information in this respect, we have performed magnetization measurements as a function of increasing temperature (heating rate 3 K/min) in a static magnetic field H_appl = 50 Oe, after cooling the sample from room temperature down to T = 5 K without (zero-field-cooling, ZFC) and with H_appl (field-cooling, FC). The results for the three samples are shown in Figure 5. The magnetic irreversibility effect (difference between the values of M_FC and M_ZFC) is consistent with the relaxation processes of the magnetic moments of the MNPs.

In an assembly of size-distributed MNPs, a distribution of T_B also exists. If the MNPs can be assumed as non-interacting, M_ZFC is expected to show a peak at a temperature T_max that represents an average blocking temperature and can be estimated from Equation (4), considering the mean volume of the assembly; the M_FC branch is expected to decrease with increasing T and to collapse on M_ZFC at a temperature T_irr, corresponding to the blocking temperature of the largest MNPs of the assembly [74].

Thus, for C5 and C12 MNPs, having a mean size around 10 nm (even less, Table 1), setting K equal to that of bulk magnetite (1.1 × 10⁵ erg/cm³) gives an average blocking temperature of ~20 K. However, the temperature T_max, at which M_ZFC reaches a sort of very broad peak, is definitely higher (Figure 5b,c; as an example, T_max and T_irr are indicated for C5). This is to be ascribed mainly to magnetic dipolar interactions between the MNPS, which result in an increase of their effective anisotropy energy barriers [41,71,74,75,76,77,78,79,80,81].

Other features revealing that interparticle dipolar interactions affect the magnetic relaxation of the nanoparticles are: (i) the trend of M_FC, which tends to become constant below T_max; (ii) the observation that, in spite of the wide size distribution of the C12 and C5 MNPs (Figure 3f,g), T_irr is very close to T_max because magnetic interactions act so as to narrow the distribution of effective anisotropy energy barriers, being the relaxation of the MNPs no longer fully independent [74]. However, Figure 5b,c confirm that the C5 and C12 MNPs are in the full superparamagnetic state at T = 300 K, in agreement with the null values of coercivity and remanent magnetization (inset of Figure 4b).

The relaxing behavior of the C26 MNPs appears more complex. The M_ZFC and M_FC branches are not seen to merge even at T = 300 K, which indicates that the superparamagnetic state of the whole MNPs assembly is not achieved under the adopted experimental conditions, in line with the fact that H_C does not annihilate (inset of Figure 4b). This indicates that higher anisotropy energy barriers are associated with the C26 MNPs, compared to C5 and C12, certainly due to their larger mean size and wide size distribution, good crystallinity, and stronger dipolar interactions also by virtue of the higher M_S. In this last respect, the abrupt decrease of M_ZFC below ~40 K is reminiscent of a long-range collective freezing of the MNPs magnetic moments under the action of dipolar interactions, probably involving the smaller MNPs of the assembly [82,83,84]. Above T ~40 K, the linear rising trend of M_ZFC, typical of a ferromagnet, confirms the presence of non-relaxing MNPs, which coexist with the fraction of relaxing ones.

3.1.4. ICP-MS Analysis

Table 3. Iron and Manganese content evaluated on a sample of 10 mg of NP powder and the mass of the metallic oxide. ICP-MS method.

	Fe Fe/10 mg NP [mg]	Mn Mn/10 mg NP [mg]	Fe3O4 /10 mg NP [mg]	MnxFe3−xO4 /10 mg NP [mg]
C26	5.54 ± 0.28	0.86 ± 0.04	-	8.85
C12	5.76 ± 0.29	-	7.96	-
C5	7.07 ± 0.35	-	9.77	-

reports the Iron and Manganese content measured in a sample of 10 mg in weight of NP powder using ICP-MS.

The mass of magnetic core material in the samples based on ICP-MS analysis (Table 3) is based on the magnetite formula (Fe₃O₄) for samples C12 and C5, while for C26 has been determined on the hypothesis of a Mn-doped ferrite spinel of general formula Mn_xFe_3−xO₄. Based on the experimental Mn/Fe ratio an average formula of Mn_0.41Fe_2.59O₄ can be proposed, in agreement with our previous findings [71]. In the NPs obtained by thermal decomposition (C26 and C12), the relative amount of stabilizing agent (oleate w% = 11.5% and 20.4%, respectively) is higher than that in the coprecipitated ones (C5 with 2.3%), suggesting a more efficient surface functionalization in the treatment at high temperature.

3.2. Temperature vs. TIME Characterization

3.2.1. Evaluation of the SLP by Means of the Exponential Method and Initial Slope

Figure 6 shows an example of a typically normalized temperature increment as a function of the time related to the different nanofluids analyzed at a given frequency and magnetic field intensity.

Table 4. SLP value evaluated applying the three methods, SLP(A), i.e., exponential method, SLP(B), i.e., Initial slope method, and QA-SLP, i.e., Quasi-Adiabatic method, to the long-time data (three series) and average value for a sinusoidal magnetic field with maximum value 170 Oe at 177 kHz. Samples with volume 30 mL with 10 mg/mL of NP powder.

NP	C5o#1 *	C5o#2 *	C5o3 *	Average	C5#1	C5#2	C5#3	Average
SLP (A) [W/g]	5.41	5.85	4.85	5.37 ± 0.50	8.35	9.54	9.07	8.99 ± 0.60
SLP (B) [W/g]	3.69	4.48	3.95	4.04 ± 0.40	13.26	12.56	13.26	13.03 ± 0.40
QA-SLP [W/g]	3.80	4.52	3.79	4.04 ± 0.42	14.50	12.57	13.17	13.42 ± 0.99
σ(QA-SLP) [W/g]	0.13	0.10	0.28	0.11	0.38	0.28	0.37	0.20
NP	C12#1	C12#2	C12#3	Average	C26#1	C26#2	C26#3	average
SLP (A) [W/g]	12.87	11.33	9.58	11.26 ± 1.65	84.44	75.68	59.19	73.10 ± 12.82
SLP (B) [W/g]	11.16	13.26	14.65	13.03 ± 1.75	96.25	106.01	101.83	101.37 ± 4.90
QA-SLP [W/g]	11.56	13.85	14.50	13.30 ± 1.54	97.50	106.43	104.21	102.71 ± 4.65
σ(QA-SLP) [W/g]	0.77	0.64	0.70	0.41	4.85	0.95	1.88	1.76

* o subscript indicates an octane.

reports the SLP evaluated by means of the three computation methods expressed by Equations (1) and (2) and QA-SLP for three different temperature-time curves. The temperature was recorded on a time interval of 2400 s applying a magnetic field at 177 kHz with a maximum value of 170 Oe. All the curves reach the limit temperature at a steady state. The measurements were repeated three times and the average SLP was computed for each NP sample. The temperature values were normalized to the initial temperature then Figure 6 represents the temperature increment with respect to the initial temperature.

Figure 6 shows an example of a typically normalized temperature increment as a function of the time related to the different nanofluids analyzed at a given frequency and magnetic field intensity. The temperature was acquired up to 2400 s (40 min) and in this acquisition interval, it arrives at a T_max value. At around 100 s, the C26 curve experiments with a modification of the slope in the heating curve, and a small peak is visible. This could be due to the deposition of the fluid in the bottom of the vial. Then only half of the first-time interval, (up to 100–120 s) could be used to evaluate SLP using the slope method. Consequently, for this sample, an interval of 60 s could be adequate to evaluate SLP. This phenomenon was less visible for the C5 and C12 nanofluid samples at around 300–400 s. The observation of the behavior of curves in Figure 6 and the determination of the approximated time constant of the exponential suggested the amplitude of the quasi-adiabatic interval characteristic of each nanofluid. Table 4 reports the SLP evaluated by means of the three computation methods expressed by Equations (1) and (2) and QA-SLP for three different temperature-time curves. The temperature was recorded on a time interval of 2400 s applying a magnetic field at 177 kHz with a maximum value of 170 Oe. All the curves reach the limit temperature at a steady state. The measurements were repeated three times and the average SLP was computed for each NP sample. The temperature values were normalized to the initial temperature then Figure 6 represents the temperature increment with respect to the initial temperature.

The different NP samples show different temperature-time curves. In particular, pure Iron-oxide NPs show a smaller temperature increment with respect to the Mn-Iron-oxide sample. The heating properties of the different samples were evaluated by means of the SLP computed on the mass of NP dispersed in 3 mL of fluid. Then considering a NP powder concentration of 10 mg/mL, the SLP values using the initial slope method and the QA-SLP were computed considering a time interval between 10 and 60 s. In the interval of 10–60 s, the quasi-adiabatic condition is verified considering the criterion described in the Methods paragraph. Data in Figure 6 suggest the length of time analysis depends on the initial temperature rate: the faster the temperature increment, the shorter the analysis window. For instance, the C26 nanofluid has a heating rate of 10 °C in less than 40 s, whereas the other nanofluids show a 10 °C gap in 300 s. The behavior of the time curve in Figure 6 related to sample C26 suggests the presence of two time constants of the heating phenomena related to a first faster slope followed by a slower slope after the peak. This peak that occurs around 200 s represents the time instant at which the nanoparticles were deposed on the vial bottom. In fact, after 1 min the nanoparticles appear deposed on the vial bottom and they are separated by suspension fluid. This way two phases are in the vial: a small volume with all the nanoparticles and the fluid. The first part of the curve represents the heating of the fluid when the nanoparticles were homogeneously distributed in the fluid and the part after the small peak represents the fluid heating by the heating source, the nanoparticles, deposed on the vial bottom. Then, the phase separation that occurs in sample C26 suggests the need to set the time length of the window analysis shorter than the other nanofluids that did not experience the phase separation. For the other sample, a different time window could be considered and a typical length is between 60 and 100 s. From Table 4 it appears that the SLP(B) and QA-SLP methods give equivalent results. The advantage of QA-SLP methods is that the analysis window is not predetermined but is sized according to data.

Figure 7 and Figure 8 show the SLP histogram evaluated using QA-SLP and the temperature as a function of the time in the measurement interval between 0 and 160 s for the samples C5 (Figure 7A,B), C12 (Figure 7C,D), and C26 (Figure 8C,D). All the samples were dispersed in water, and they are heated by applying a magnetic field of 227 Oe at 5 kHz. Figure 8A,B refer to sample C26 where the water dispersed when the time-varying magnetic field amplitude is 170 Oe. In particular, the data in panels (C,D) in Figure 8 related to sample C26 show a double slope. After 120 s and 80 s sample experiences, first, faster heating was followed by a temperature decrement and a different slope of the temperature as a function of time. The new temperature slope is lower with respect to the one at the magnetic field turn-on. In fact, in this time interval, NPs deposed on the vial bottom, then the suspension fluid heating is related to a heating source (NPs) more concentrated than by heating the fluid by convection.

The p-values obtained from ANOVA analysis (see

Table 5. p-value related to ANOVA analysis to compare two by two of the SLP evaluated using the three methods, SLP(A), i.e., exponential method, SLP(B), i.e., Initial slope method, and QA-SLP, i.e., Quasi-Adiabatic method, for the data series in Table 4.

	C5o *	C5	C12	C26
SLP (A)-SLP (B)	0.0231	6.37 × 10−4	0.2734	0.0234
SLP (B)-QA-SLP	0.9925	0.5643	0.8459	0.7466
SLP (A)-QA-SLP	0.0241	0.0027	0.1920	0.0198

* o subscript indicates an octane.

) suggest that the QA-SLP and SLP (B) methods provide similar results in terms of SLP values (p-value > 0.05), while SLP (A) provides different results with the exception of sample C12.

Iron oxide NPs (C12 and C5) have SLP histograms that show a symmetric distribution around an average value, whereas the histogram of SLP of C26 NPs shows a non-symmetric distribution. The non-symmetric distribution shows a modification of the SLP during the first second of heating, whereas the symmetric distribution identifies a constant SLP.

3.2.2. Evaluation of the SLP by Selection of Quasi-Adiabatic Heating Interval

Table 6. SLP value and related standard deviation evaluated applying the quasi-adiabatic methods (average value of three series) for different magnetic field intensities at three different frequencies. Linear fit for a right with 0-intercept and its R2 value.

		C5 Octane		C5 Water		C12 Water		C26 Water
f [kHz]	Field [Oe]	SLP [W/gNP]	σ (SLP)	SLP [W/gNP]	σ (SLP)	SLP [W/gNP]	σ (SLP)	SLP [W/gNP]	σ (SLP)
177	113	1.99	0.09	5.19	0.39	3.52	0.12	33.27	0.73
177	170	4.36	0.73	12.85	0.31	12.67	1.01	102.43	1.48
177	227	5.86	0.24	14.92	0.21	31.24	0.59	132.89	6.15
Linear fit		0.066 (R2 = 0.981)		0.025 (R2 = 0.987)		0.104 (R2 = 0.868)		0.551 (R2 = 0.967)
215	113	3.37	0.12	8.62	0.17	5.19	0.18	42.30	3.02
215	132	4.67	0.19	10.6	0.24	8.39	0.44	73.98	0.86
215	263	7.85	0.72	16.82	0.31	46.83	0.24	192.81	3.87
Linear fit		0.068 (R2 = 0.99)		0.031 (R2 = 0.99)		0.141 (R2 = 0.863)		0.657 (R2 = 0.965)
245	56	2.33	0.86	3.22	0.37	1.73	0.12	2.28	0.21
245	113	3.52	0.12	10.62	0.52	5.59	0.16	44.22	0.64
245	170	6.14	0.22	15.38	0.35	17.65	1.05	126.76	2.46
Linear fit		0.089 (R2 = 0.99)		0.035 (R2 = 0.99)		0.088 (R2 = 0.898)		0.595 (R2 = 0.88)

and Figure 9 report the average SLP values (evaluated using three measurements of the same sample), with the standard deviation of the average, computed using the software developed by [45]. The SLP was evaluated on a time range between 10 and 100 s from the start of the temperature recording as in [45]. The temperature curves were recorded for different magnetic field intensity values at three different frequencies.

From the analysis of SLP, it is evident that different types of nanoparticles in the same fluid, water, are able to generate different power densities. Moreover, the generated power is different considering different suspension fluids with different heat capacities.

For each series of data at a given frequency of the magnetic field, the points at different magnetic field intensities were fitted with a right line with 0-intercept (no field—no temperature increment), and the slope coefficient of the right line was reported in

Table 7. Comparison of the advantages and disadvantages of the methods for SLP determination.

Method	Advantages	Disadvantages
SLP(A)	Use of theoretical heating curve Inaccuracy is larger for short measuring times [85]	Long measurement time (>60 min) Dependence on the thermal insulation (adiabaticity)
SLP(B)	Short measurement time (≈1 min) Easy to compute	Uncertainty on the starting point Possible dependence on the measurement time interval Averages adiabatic and non-adiabatic portions of the T vs. t curve
QA-SLP	Short measurement time (≈1 min) Dependence on the time interval considered More consistent with the definition of SLP which assumes an adiabatic precondition to estimation through calorimetry	Elaborate computation

including the R² coefficient of the goodness of fit.

4. Discussion

4.1. Size Characterization

The magnetic diameters of the NP in the different nanofluids (Figure 3) are dispersed in size as evidenced by the histograms in Figure 3B. The shape is close to a square shape for C26; whereas the other two samples show an irregular shape that could be approximated with a round shape. In sample C12, some big triangular elements or hexagonal elements could be evidenced. The distribution of diameters is not symmetric and normal, but it is an asymmetric distribution that in one case fits with Lognormal distribution since there is a prevalence of smaller particles and big particles are less in number.

The hydrodynamic radius relative to the NPs dispersed in water corresponds to the size of the NP aggregate and any information about the thickness of the non-metallic cover layer can be deducted. Nevertheless, the large hydrodynamic radius confirms the NP organization in macroscopic aggregate when dispersed in water even if they are treated with CTAB.

4.2. Thermal Characterization

From the data in Table 4, it appears that different methods to evaluate the SLP of the same sample can give distinctly different values. The method that uses the initial slope evaluated on the first 60 s of the temperature-time curve, SLP(B), is comparable to the SLP obtained using the QA-SLP that averages the SLP values evaluated by means of slope on different time windows on the time interval (10,100) s. Instead, the method of the fit of the exponential model, SLP(A), shows very different SLP values except for the C12 sample. In general, the SLP value evaluated using the fit of the exponential model [43], SLP(A), shows lower values with respect to the ones obtained with the slope-based methods, except for the sample C5 dispersed in octane for which the SLP(A) is higher with respect to the ones obtained with slope-based methods. From the data in Table 4 it appears that the analysis of the thermal transient using the fit of the exponential model proposed by [43,44] can overestimate or underestimate the NP-SLP, and their values depend on the system in the not-adiabatic segment. The variation of the SLP could be due to the fact that the method, even considering the changes due to loss of adiabatic condition and the thermal exchange with the environment, does not consider the possible structural changes in the sample that may happen in such a long acquisition time. In fact, with sample C26 after a few minutes, the NPs tended to aggregate and deposit at the bottom of the test tube as confirmed by the small peak at 85–130 s (Figure 6) that appears in the temperature curve corresponding to the liquid-solid separation.

This analysis also allowed us to compare operatively, the advantages and disadvantages of the three methods, as summarized in Table 7.

Finally, the available methods to quantify the magnetic material in the fluid sample measure the NPs content in a different way, so the SLP for the same NP could be different in the case of the entire NP content being evaluated, instead only the Fe content or Fe-oxide content are considered. In fact, different authors have determined the magnetic material content in NP fluid in different ways as reported e.g., in [44,50,51,52,53,54,55], depending on the measurement method available.

Considering the water and octane suspensions of the C5 nanoparticle (Table 4), the generated heat is higher in the case of water. This effect can be due to the lower specific heat compared to water (4.18 Jg⁻¹K⁻¹ for water and 2.238 Jg⁻¹K⁻¹ for octane) with a contribution due to the differences in the aggregation of nanoparticles as evidenced by their higher hydrodynamic radius.

When the same nanofluid (30 mL with 10 mg/mL of nanoparticle) is exposed to different magnetic field intensities at three different frequencies, it is evident that the heating generation increases both with the magnetic field strength and the magnetic field frequency as evidenced in Figure 9 and Table 4. Data at magnetic field value, given the field frequency, could be interpolated with a straight line with a 0-intercept.

5. Conclusions

The paper reports the evaluation of the Specific Loss Power, SLP, generated by three different types of magnetic nanoparticles, MNPs, either in octane or water suspension. The nanoparticles were synthetized according to established and reproducible procedures such as coprecipitation and thermal decomposition methods. The NPs were characterized in terms of shape, size, and chemical composition. Finally, the suspension, octane, or water, were characterized in terms of SLP using three different methods. The obtained results in the computation of the SLP were compared, and only those that analyze the initial slope showed similar results. In some cases, the exponential method failed and did not prove suitable, for instance, when secondary thermally induced phenomena such as aggregation or precipitation happen during the measurement. Nevertheless, the behavior of the heating curve is useful to evaluate the amplitude of the interval analysis for the initial slope methods. In particular, this study shows that this analysis interval cannot be fixed at equal for all the nanofluids but has to be determined for each sample.