Biocompatible magnetic nanoparticles (MNPs) are increasingly being used in many biomedical applications, such as magnetic resonance imaging, drug delivery, cell and tissue targeting or hyperthermia [
1-
3]. For hyperthermia therapy, nanotechnology offers a powerful tool to the design of nanometre heat-generating sources, which can be activated remotely by the application of an external alternating magnetic field (AMF). The magnetic energy absorption of nanoparticle-containing tissues induces a localized heating that allows a targeted cell death at a critical temperature above 42 to 45°C. This temperature increase can be used to selectively kill cancer cells [
4,
5]. Previous reports show that the effective use of MNPs to induce magnetic heating by application of an external radio-frequency magnetic field depends essentially on several factors related to the size, shape, solvent and magnetic properties of nanoparticles [
6-
9]. Of special interest is the heating power rate that can be attained with MNPs because an increase of the heating rate would imply lower doses of MNPs administered to the patient and lower time of stay in the body of the patient. For this reason, it is necessary to optimize the design of the nanoparticles in order to achieve the required structural and magnetic properties which lead to the maximum heating power.
For single-domain particles, which are below the superparamagnetic (SPM) size limit, no heating due to hysteresis losses occurs. Therefore, the heating power arises from the energy dissipated in the reversible process of relaxation of the magnetic moments to their equilibrium orientation once the magnetic field is removed. This mechanism is characterized by the Néel relaxation process. In addition to this, the rotational motion of the particles within the solvent due to the torque forces on the magnetic moment, Brownian relaxation, constitutes another source of heating, as a consequence of the energy liberated by friction in the reorientation of the particle in the surrounding carrier liquid. The well-known Rosensweig equation [
10] predicts the SAR of a magnetic nanoparticle exposed to a varying magnetic field as SAR =
P/(ρΦ), where
P is the dissipated power heat:
in which the magnetic susceptibility χ" contains the action of both relaxation mechanisms:
Through an effective relaxation time of the two mechanisms working in parallel:
is the Brown relaxation time depending on the solvent viscosity η and the hydrodynamic radius of the NP,

, and
is the Néel relaxation time depending on the magnetic volume of the NP,

and K
an is the magnetic anisotropy energy constant of the magnetic core of the NP.
Therefore, the heat dissipation of a magnetic hyperthermia experiment performed on a ferrofluid will depend on: (1) the applied magnetic field strength and frequency and (2) the physical properties of the ferrofluid: solvent viscosity, magnetic and hydrodynamic radius of the NPs, and the magnetic anisotropy energy constant of the magnetic core of the NP.
Adequately coated iron oxide-based nanoparticles have been the most extensively studied material in hyperthermia experiments because they have very low toxicity, making them suitable for in vivo applications [
11,
12]. In particular, the polyacrylic acid (PAA) coating is an aqueous soluble polymer with a high density of reactive functional groups which make it very attractive in biomedicine due mainly to its capability to form flexible polymer chain-protein complexes trough electrostatic, hydrogen bonding or hydrophobic interactions. Furthermore, the biochemical activity of the protein is maintained in the resulting protein-polymer complexes [
13].
Therefore, the use of biocompatible SPM nanoparticles capable of residing inside the human body for a reasonable time is highly desirable for biomedical applications. The absence of coercive forces and remanence prevents the magnetic interaction between particles and the formation of particle aggregates and small clusters [
1].
Both mechanisms depend on particle size, whereas only the Brownian contribution depends on the viscosity, η, of the carrier solvent. However, although the size dependence of the heating power has been already investigated and indicates the existence of an optimal particle size in which the heating power is maximum [
14], there are no systematic data on the influence of particle concentration or solvent properties in the same magnetic system and in a simultaneous way. As deduced from the Rosensweig equation and under certain experimental conditions, both Néel and Brownian relaxation times are comparable for SPM nanoparticles around 10 nm; therefore, changes in the particle concentration, solvent viscosity or particle surface modification could lead to important differences in the SAR observed. To our best knowledge, no heating properties of PAA-modified high quality magnetite MNPs have been previously reported. Such combination of the chemical features described above makes colloidal PAA-magnetite a promising system in advanced bionanotechnologies. For this reason, data about its heating properties under specific experimental conditions, which could reproduce physiological conditions in an
in-vivo experiment, are highly desired.
Our approach in this research includes the synthesis of different biocompatible and monodisperse high quality single-domain magnetite NPs based ferrofluids and has been focused on the specific absorption rate (SAR) dependence of factors related to the particle concentration and solvent properties, crucial parameters for the biomedical applications in order to provide the patients with an optimal dosage.
To our knowledge, we provide for the first time useful information in order to correctly interpret and design PAA-coated magnetite based biomedical applications in which the target tissues may have different viscosities and different capacity to retain low or high concentrations of NP inside, yielding unexpected results.
Experimental
Iron oxide MNPs were obtained in order to study the effect of some colloidal parameters on their hyperthermia properties. Magnetite MNPs of ≈10 nm were synthesized by chemical co-precipitation of an aqueous solution containing Fe2+ (FeSO4·7H2O, 99%) and Fe3+ (FeCl3·6H2O, 97%) salts in the molar ratio Fe2+/Fe3+ = 0.67 with ammonium hydroxide (NH4OH, 28%). To obtain Fe3O4@PAA MNPs, immediately after magnetite precipitation an excess of PAA (Mn = 1800) was added to the solution. The PAA coating reduces the electrostatic particle interactions and therefore greatly increases the colloidal stability of the dispersion. Finally, the pH of the solution was adjusted to pH = 10 by adding tetramethylammonium hydroxide (TMAOH) 10% in order to improve the stability of the ferrofluid as much as possible.
Specific absorption rate of the samples was measured by means of a home-made magnetic radio-frequency (RF) power generator operating at a fixed frequency of ν = 308 KHz and an induced magnetic field of B = 15 mT. A cylindrical Teflon sample holder was placed in the midpoint of an ethylene glycol cooled hollow coil (maximum of RF magnetic field), inside a thermally isolated cylindrical Dewar glass under high vacuum conditions (10-6 mbar). Measurements were carried out by placing 140 μL of ferrofluid in the sample holder and recording the temperature increase versus time with a fibre-optic thermometer (Neoptix) during approx. 5 min of applied magnetic field.