Magnetic Nanoparticles in Human Health and Medicine. Группа авторов

Magnetic Nanoparticles in Human Health and Medicine - Группа авторов


Скачать книгу
each material time. Only in low and high fields, there are mathematical functions that describe well the magnetization obtained experimentally. Thus, in low magnetic fields (lower than the coercive field of the material [~Hc/10]), magnetization is well described by Rayleigh's law

      (1.22)equation

      In intense magnetic fields, close to saturation, magnetization is well described by the experimentally established Weiss–Forer law:

      (1.23)equation

      where a, b, and c are some coefficients. The last term (χ0H) is determined by the contribution of χ0, independent of the magnetic field H. This term becomes more important when the material is brought to a temperature close to the Curie temperature.

Schematic illustrations of (a) M versus H for (Zn0.15Ni0.85Fe2O4)0.15/(SiO2)0.85 sample. (b) Reduced magnetization curve of the (Zn0.15Ni0.85Fe2O4)0.15/(SiO2)0.85 nanocomposite registered at room temperature and 50 Hz frequency of the magnetization field (H).

      Source: Reprinted from Caizer et al. (2003), with permission of Elsevier;

      (b) Reduced magnetization curve of the (Zn0.15Ni0.85Fe2O4)0.15/(SiO2)0.85 nanocomposite registered at room temperature and 50 Hz frequency of the magnetization field (H).

      Source: Reprinted from Caizer (2008), with permission of Elsevier.

      Magnetization (Figure 1.15.b) in this case follows a Langevin type function as in the case of paramagnetic atoms (Caizer 2004a):

      where (coth α − 1/α) is the Langevin function and

      (1.26)equation

      whereas in high fields close to saturation, the magnetization is described by the following relationship:

      (1.27)equation

      where M is the saturation magnetization (theoretically, in the infinite magnetic field).

Schematic illustrations of (a) M versus H in low fields and (b) M versus 1/H in high fields. (c) magnetic structure in single-domain nanoparticles with uniaxial anisotropy.

      Source:Caizer (2003a). Reprinted by permission of IOP Publishing;

      (c) magnetic structure in single‐domain nanoparticles with uniaxial anisotropy.

      Source: Caizer (2017). Reprinted by permission of Springer Nature.

      In Figure 1.16a and b, these cases are given for Fe3O4 nanoparticles covered with oleic acid and dispersed in kerosene (magnetic ferrofluid with a magnetic packing fraction of 0.024) having an average magnetic diameter of 11.8 nm. Figure 1.16b shows the dependence M = f(1/H), which is a linear function with a negative slope near the magnetic saturation (M).

      This magnetic behavior in the external field, totally different from the bulk magnetic material (ferro‐ or ferrimagnetic), results from the existence of the superparamagnetism phenomenon, evidenced by Nèel and introduced by Bean in the case of nanoparticles. Nèel shows that the magnetic moment of the nanoparticle (mNP) can be reversed at 180° along the easy magnetization axis due to thermal activation (at a temperature), in the absence of the external magnetic field (Figure 1.16c). This behavior is similar to paramagnetic atoms, whose magnetic moments are oriented at a temperature in all directions.

      1.1.7 Magnetic Relaxation in Nanoparticles – Superparamagnetism

      When the size of nanoparticles decreases below the critical diameter (Dc), corresponding to the transition from the state of the structure with magnetic domains to the state with the single‐domain structure, there is another nanoparticle‐specific size, the threshold volume (Vth) (or threshold diameter [Dth]) at


Скачать книгу