Superparamagnetic particles function

The applications of EPR to determine the particle size of the Fe2C>3 clusters distributed in MFI frameworks was illustrated by Ferretti et a/.145-146 By plotting the peak-to-peak line width of the Fe3+ signal as a function of 1/T, the authors explain how an estimate of the dimension of the superparamagnetic particles can be found in this case 30 nm. While only particles with dimensions greater than 10 nm can be analysed by this approach, this work demonstrates the diversity of information that can be extracted from the simple X-band powder spectrum of Fe3+. 

With control of particle size and spacing as per annealing conditions, if one considers Eq. 3 it is possible to extract the critical superparamagnetic particle size. Figure 8 shows a plot of Hc as a function of particle size for FePt/C samples. As expected the coercivity asymptotically approaches a maximum value as the particle size increases. A fit to the data with Eq. 3 reveals that the superparamagnetic particle size for FePt is between 2 and 3 nm [6]. The value of the critical superparamagnetic size can be seen in the figure to be the same, within experimental error, for each of the volume fractions of carbon in the samples. 

Nanosized particles and porous materials play an important role in many technological applications. They have been used widely as biological sensors, integrated electronic devices, catalyst supports, and adsorbents for detoxification of industrial effluents and domestic water, decoloring of processing water, and purification of pharmaceuticals and proteins. In Chapter 3, Xu et al. showed some typical applications of functionalized superparamagnetic particles in biological cell separation and industrial effluent detoxification. Porous media, on the other hand, constitute an... 

If we suppose that monodisperse nano-sized (superparamagnetic) particles are randomly distributed in the polymer network, and the magnetization of individual particles in gel equals the saturation magnetization of the pure and bulk corresponding material, which can be described by the Langevin function (Berkovski and Bashtovoy, 2006 Hadijipanayis and Seigel, 1994 Restorf, 1994) ... 

The a-term comes from the series development of the Langevin function, the b-tsrm is the anisotropy effect, with K the anisotropy constant. /I is a constant that depends only on the material. The fit of the experimental curve with Eq. (13.74) leads to the determination of the fitting parameters and b. On the other hand, the Neel relaxation time for a superparamagnetic particle to respond to the magnetic field is [70] ... 

The height of the energy barrier between the forward and reverse states is the product of the particle volume, V, and the anisotropy constant Kefr (which is, to some extent, a function of particle size). Superparamagnetic relaxation occurs when the thermal energy of the particles exceeds the activation energy barrier between the spin states and so allows rapid, spontaneous fluctuations between these states. The effect of these spin reversals is that the observed magnetic field is reduced or even absent. 

In the majority of cases when one deals with nanosize superparamagnetic grains, polydispersity seems to be an inherent feature. The independent measurement of the size distribution function, such as by electron micrography, is a painstaking and rare opportunity. Besides, even when it is done, from the statistical viewpoint a set of available measurements (103 — 104 grains) for the particle number concentration even as small as 1010 — 1018, that is, 0.01% by volume at the particle size 10 nm, is far from being statistically representative. 

When the superparamagnetic theory is applied for interpretation of any measured susceptibility line, it means that some model function x(V,a>,T) depending on several material parameters, is processed through averaging like such as Eq. (4.121) or (1.122). In our case the basic set of the material parameters comprises magnetization /, anisotropy energy density K, relaxation time To, and the particle volume fraction tp. Obviously, for nanosize-dispersed systems the effective values of /, K, and t0 do not coincide with those for a bulk material. The size/volume averaging itself introduces two independent... 

A consistent study of the linear and lowest nonlinear (quadratic) susceptibilities of a superparamagnetic system subjected to a constant (bias) field is presented. The particles forming the assembly are assumed to be uniaxial and identical. The method of study is mainly the numerical solution (which may be carried out with any given accuracy) of the Fokker-Planck equation for the orientational distribution function of the particle magnetic moment. Besides that, a simple heuristic expression for the quadratic response based on the effective relaxation... 

All the samples measured showed characteristic superparamagnetic behavior with a blocking temperature TB. An independent method of determining the parameters of the particle size distribution g(D) is by means of the analysis of magnetic measurements under equilibrium conditions, i.e. at temperatures above the superparamagnetic blocking temperature Tb- For this purpose we performed magnetization measurements as a function of field M(H) at different temperatures [4,5]. 

The value of K was obtained either from spectra of a series of samples having known average particle sizes at constant temperature or from spectra recorded as a function of temperature of a sample of known particle size. The determination of K was made at the point where half the total area under the spectrum resulted from the Zeeman pattern and the other half from the superparamagnetic fraction. Spectra used for such calculations are exemplified in Fig. 4. These spectra (28) were obtained from microcrystalline a-Fe203 produced by thermal decomposition of ferric nitrate on silica gel and subsequent... 

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