Abstract
Mössbauer spectroscopy is a well-known technique to study complex magnetic structures, due to its sensitivity to electronic and magnetic interactions of the probed nucleus with its electronic surrounding. It has also been applied to the emerging fields of magnetic hybrid materials as well as to ferrofluids, as information on the magnetic alignment and the velocity of the probed nucleus, i.e. of the particle it is embedded in, can be inferred from the spectra in addition to the above-mentioned quantities. Considering the wide range of preparation methods and sample properties, including fluids, particle powders, sintered pellets, polymer matrices and viscoelastic hydrogels, a considerable advantage of Mössbauer spectroscopy is the usage of γ-photons. This allows measurements on opaque samples, for which optical experiments are usually not feasible, also making the technique relatively independent of specific sample geometries or preparation. Using iron oxide nanoparticles in glycerol solution as an exemplary material here, the variety of system parameters simultaneously accessible via Mössbauer spectroscopy can be demonstrated: Spectra recorded for particles of different sizes provided information on the particles’ Brownian dynamics, including the effect of the shell thickness on their hydrodynamic diameter, the presence (or absence) and ballpark frequency of Néel superspin relaxation as well as the particles’ average magnetic orientation in external magnetic fields. For single-core particles, this resulted in the observation of standard Langevin-type alignment behavior. Mössbauer spectra additionally provide information on the absolute degree of spin alignment, also allowing the determination of the degree of surface spin canting, which limits the maximum magnetization of ferrofluid samples. Analyzing the alignment behavior of agglomerated particles for comparison, we found a completely different trend, in which spin alignment was further hindered by the competition of easy magnetic directions. More complex particle dynamics are observed when going from ferrofluids to hybrid materials, where the particle mobility and alignability depends not only on the particles’ shape and material, but also on the matrices’ inner structure and the acting force-transfer mechanism between particles and the surrounding medium. In ferrohydrogels for example, particle mobility in terms of Mössbauer spectroscopy was probed for different crosslinker concentrations, resulting in widely different mesh-sizes of the polymer network and different degrees of freedom. While a decrease in particle dynamics is clearly visible in Mössbauer spectroscopy upon rising crosslinker density, complementary AC-susceptometry experiments indicated no Brownian motion on the expected timescales. This apparent contradiction could, however, be explained by the different timescales of the experiments, probing either the relatively free Brownian motion on ultrashort timescales or the more bound state preventing extensive particle motion by interaction with the trapping mesh walls in the millisecond regime. However, it should also be considered that the effect of the surroundings on particle rotation in AC-susceptometry may also differ from the variation in translational motion, probed by Mössbauer spectroscopy. Being sensitive mainly to translational motion also results in a wide range of particles to be accessible for studies via Mössbauer spectroscopy, including larger agglomerates embedded in polymers, intended for remote-controlled heating. Despite the agglomerates’ wide distribution in effective diameters, information on particle motion was found to be in good agreement with AC-susceptometry experiments at ultralow frequencies in and above the polymer melting region, while additionally giving insight into Néel relaxation of the individual nanoparticles and their magnetic structure.
On fundamental solutions for 3D singular elliptic equations with a parameter
