Abstract
A numerically solved two-level Stoner-Wohlfarth model with thermal agitation is used to simulate Zero Field Cooling (ZFC)–Field Cooling (FC) curves of monosize and polysize samples and to determine the best method for obtaining a representative blocking temperature TB value of polysize samples. The results confirm a technique based on the T derivative of the difference between ZFC and FC curves proposed by Micha et al. (the good) and demonstrate its relation with two alternative methods: the ZFC maximum (the bad) and the inflection point (the ugly). The derivative method is then applied to experimental data, obtaining the TB distribution of a polysize Fe3O4 nanoparticle sample suspended in hexane with an excellent agreement with TEM characterization.
Highlights
Magnetic nanoparticles (MNPs) are being extensively studied due to their multiple applications in technology1 and biomedicine.2–5 Particles with sizes in the range [5,100] nm (Ref. 6) present a magnetic behaviour determined by its volume, shape and composition, matrix viscosity, and temperature, among other factors
The results confirm a technique based on the T derivative of the difference between Zero Field Cooling (ZFC) and Field Cooling (FC) curves proposed by Micha et al and demonstrate its relation with two alternative methods: the ZFC maximum and the inflection point
A Stoner-Wolfarth model with thermal agitation was developed in order to simulate the Zero Field Cooling-Field Cooling (ZFC-FC) curves of polysize MNPs assemblies
Summary
Magnetic nanoparticles (MNPs) are being extensively studied due to their multiple applications in technology and biomedicine. Particles with sizes in the range [5,100] nm (Ref. 6) present a magnetic behaviour determined by its volume, shape and composition, matrix viscosity, and temperature, among other factors. The resultant mean blocking temperature value hTBi is compared, for several volume distributions, with the commonly used criteria for a representative TB: the inflection point temperature IP and the maximum MAX of the ZFC curve. A SW-like model with thermal agitation and zero width energy minima approximation was developed in order to obtain ZFC-FC curves of fixed MNPs with size dispersion. For a linear temperature variation T(t) 1⁄4 Bt þ T0, the magnetization derivative is dm dm By solving this equation by means of numerical methods, it is possible to simulate a ZFC-FC experiment for a monosize sample. During the warming after zero field cooling (ZFCW for this chapter, usually called just ZFC), the exponential dependence of the inversion frequency with temperature in Equation (3) determines a narrow “blocking region” wherein the MNPs, which were “blocked” at low temperature, begin to respond to the field. A much wider transition region can be seen for the larger dispersion so the different aforementioned criteria would define very separated values for a representative TB
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