LITURGIA DE LA PALABRA Primera Lectura: Sabiduría 7,7-11
11 Feria o Memoria Libre: Santa Soledad Torres Acosta, Virgen y San Juan XXIII, Papa
When ferromagnetic nanoparticles and superparamagnetic nanoparticles are subjected to external AMF, they have different magnetization behaviors, as shown in Figure 2.26174. For ferromagnetic nanoparticles, due to their high anisotropy energy (single domain nanoparticles) or the movement of domain walls (multi-domain nanoparticles), there is a delay of magnetization, which demonstrates as hysteresis in the M-H curve (cf. Figure 2.26(a)). For the superparamagnetic nanoparticles, as their anisotropy energy is very small, they flip fast and change simultaneously with applied AMF, they demonstrate a sigmoidal M-H curve during magnetization (cf. Figure 2.26(b)).
Generally, the heat generation of MNP upon AMF is based on three mechanisms: (1) hysteresis (the magnitude represented by the area inside the hysteresis loop, cf. Figure 2.26(a)), (2) Néel relaxation (rotation of the magnetic moment within the particle), and (3) Brownian relaxation (physical rotation of the whole particle within the dispersing medium)174, 175. Due to the different magnetization behavior, the dominating mechanism of magneto-heating is also different for ferromagnetic and superparamagnetic nanoparticles. While the main source for heat generation of ferromagnetic nanoparticles is hysteresis loss, for superparamagnetic nanoparticles it is relaxation losses176, 177.
Figure 2.26. Typical M-H curves for
nanoparticles during magnetization.
marked with red stripes), represents the amount of magnetization cycle. The superparamagnetic nanoparticles
curve, but show no hysteresis
coercivity, Mr is remanence magnetization and M
The heating efficiency of magnetic nanoparticles can be estimated theoretically according to the heating mechanisms and measured experimentally by calorimetry.
Theoretically, the heat dissipation of ferromagnetic nanoparticle determined by integrating the area of hysteresis loop
generation per unit volume) of such particle the area of hysteresis loop178:
Where µ0 is the permeability of free space, f is the frequency of alternating magnetic
the magnetic field amplitude and M is the induced magnetization of MNP. Experimentally, as there is no dependence between frequency and area (integral of Equation 2.4) for ferromagnetic nanoparticle
Theory and literature review
H curves for (a) ferromagnetic nanoparticles and (b) superparamagnetic during magnetization. The hysteresis loop of ferromagnetic nanoparticles
represents the amount of energy dissipation of the material during one superparamagnetic nanoparticles respond to an external field
no hysteresis. Here H is applied external magnetic field, M is magnetization, H is remanence magnetization and Ms is saturation magnetization
of magnetic nanoparticles can be estimated theoretically according to the heating mechanisms and measured experimentally by calorimetry.
, the heat dissipation of ferromagnetic nanoparticle (FM) by hysteresis loss can be ating the area of hysteresis loop (Figure 2.26(a)). Loss power density (h
of such particle can be calculated by multiplying the frequency with
P
= μ
f ∮ H dM
is the permeability of free space, f is the frequency of alternating magnetic and M is the induced magnetization of MNP.
there is no dependence between frequency and area
or ferromagnetic nanoparticle, the power dissipation can be easily Theory and literature review
44 (a) ferromagnetic nanoparticles and (b) superparamagnetic
nanoparticles in (a) (the area energy dissipation of the material during one
to an external field with a sigmoidal external magnetic field, M is magnetization, Hc is
is saturation magnetization174.
of magnetic nanoparticles can be estimated theoretically according to the
by hysteresis loss can be Loss power density (heat can be calculated by multiplying the frequency with
(2.4)
is the permeability of free space, f is the frequency of alternating magnetic field, H is
there is no dependence between frequency and area of hysteresis loop the power dissipation can be easily
Theory and literature review
45 determined from quasi-static measurement of hysteresis by Vibrating Sample Magnetometer (VSM) or Superconducting Quantum Interference Device (SQUID) magnetometer178.
For superparamagnetic nanoparticles (SPM), as energy barrier for magnetization reversal is very small, the thermal energy is sufficient to cause magnetization reversal and the particles mainly generate heat by relaxation losses. The calculation for relaxation loss of power of superparamagnetic nanoparticles in AMF is relatively complicated and has been well reviewed by Rosensweig and Hergt177, 179. According to Hergt et al., the loss power density of superparamagnetic nanoparticles can be calculated according to177, 179:
P
= μ π P (f) H
2f
(2.5)Where P (f) is loss component that is related to magnetic loss, µ0 is the permeability of free
space, f is the frequency of alternating magnetic field and H is the magnetic field amplitude. On the other hand, when the mass density of magnetic particles is known, the loss power density P (W m-3) can be related to the specific loss power (SLP) (W g-1), which describes the power achievable per gram of iron in the material and can also be estimated experimentally by calorimetric method.
Since energy dissipation of all MNP will cause the overall temperature elevation of their dispersion, by measuring the elevated temperature of the particle dispersion (e.g. in water), SLP of MNP can be calculated by following equation180:
SLP = c ∙ (m /m ) ∙ (∆T − ∆T )/∆t
(2.6) Where c is the heat capacity of water, ms is the mass of the sample, mFe is the mass of MNP inthe sample, ∆Ts is the temperature increase of the nanoparticle dispersion, ∆Tw is the temperature
increase of water, and ∆t is time duration with AMF on. Here, (∆Ts - ∆Tw)/∆t is the slope of the
heating curve with unspecific heat influence eliminated.
A typical setup of calorimetric measurement is shown in schematic Figure 2.27. The crucial elements include excitation coils to generate adjustable alternating magnetic field, a temperature probe to detect the temperature change of the sample, and the heat insulation layer to ensure adiabatic control and the accuracy of the measurement.
Figure 2.27. Scheme illustrating a typical
The heating efficiency of MNP not only relies
external field conditions. Currently, in most reported studies, the conditions of the tests are not clear or even not mentioned, therefore the heat dissipation of reported MNP is difficult to compare. A standard method or
To summarize, heating performance
materials, structure and mean size, but also on dependence of external magnetic field conditions, including the frequency and field amplitude. A summary of important parameters that affect the magneto-heating efficiency of magnetic
dissipation increases with the size of the particle, and the AMF.
Theory and literature review
Scheme illustrating a typical calorimetry measurement setup for heat generation of MNP181 .
efficiency of MNP not only relies on the properties of particles, but also the external field conditions. Currently, in most reported studies, the conditions of the tests are not even not mentioned, therefore the heat dissipation of reported MNP is difficult to compare. A standard method or criteria to evaluate the heating efficiency
heating performance of MNP is not only intimately entwined with their materials, structure and mean size, but also on dependence of external magnetic field conditions, including the frequency and field amplitude. A summary of important parameters that affect the
iciency of magnetic particles is made in Table 2.2182
with the size of the particle, and the frequency and amplitude of applied Theory and literature review
46 setup for heat generation of
on the properties of particles, but also the external field conditions. Currently, in most reported studies, the conditions of the tests are not even not mentioned, therefore the heat dissipation of reported MNP is difficult to of MNP is needed182. is not only intimately entwined with their materials, structure and mean size, but also on dependence of external magnetic field conditions, including the frequency and field amplitude. A summary of important parameters that affect the
182
. In general, the heat and amplitude of applied
Theory and literature review
47 Table 2.2. Summary of important parameters for magneto-heating182
Nanoparticle Medium Magnetic Field
Saturation magnetization Particle concentration Field amplitude
Magnetic anisotropy Viscosity Field frequency
Magnetic remanence/cocercivity Homogeneity
Size Polydispersity Aggregation Coating
It has been reported that single-domain cubic iron oxide particles can deliver larger heating power, comparing to spherical MNP with similar sizes183. This is because that the anisotropy of cubic particles are corroborated at atomic level, therefore, their heating power is also improved. Moreover, Hergt et al. have done a systematic study of the influence of particle size and distribution on the heating efficiency177. They found bigger particles with narrow size distribution are most efficient for heat generation. For example, bacterial magnetosome with mean core size of 38 nm and mean square deviation of 5 nm, which is relatively big and narrow distributed, has superior magneto-heating efficiency. It has specific power of loss of 960 W/g at field condition of 10 kA/m and 410 kHz184.
There are many applications that utilize the magneto-heating, including hyperthermia therapy to cure cancer, or technical heating processes like hardening of adhesives. Moreover, when MNP are combined with thermo-responsive polymers, the heat generated by MNP can be used to cause thermal effect in thermo-responsive polymeric system by applying a suitable external magnetic field185. This synergistic effect can used to design magneto-responsive hydrogels or membranes for controlled release (cf. section 2.2.3)34, 35, 47, 86, 87, 186 .