We have built a simple apparatus for measuring the magnetic weight of magnetic materials, that is, the magnetic force that the magnetic materials experience under the magnetic field gradient as in the Gouy balance. The magnetic force is measured with a conventional electronic balance connected with a computer in the field gradient range of 23~34 T m-1. The magnetic weights of the superparamagnetic solutions of magnetite nanoparticles are recorded every minute in order to observe the agglomeration dynamics. As soon as the sample solution is placed on a magnet, the magnetic weight of the sample jumps by the Neel and Brown relaxation, and then grows slowly following the stretched exponential function with the agglomeration of nanoparticles as shown in the attached Figure. The magnetizations of the magnetite nanoparticles are calculated from the magnetic weights and compared with the Langevin function for magnetization, which shows that the magnetizations of the nanoparticles are close to the saturation magnetization in the experimental range of the magnetic field gradient. The saturation magnetization of the nanoparticles is estimated to be ~60% of that of the bulk magnetite by the comparison. The fitting parameters of the stretched exponential function hardly change in our experimental conditions. The stretched exponential indicates that the energy barrier for the agglomeration of nanoparticles is not a single value but distributed. The energy barrier distribution function can be determined by the inverse Laplace transformation of the temporal change of the magnetic weight. When the Arrhenius rate equation is employed with the A factor evaluated based on the doublet formation, the energy barrier distribution function has the maximum of ~51 kJ mol-1 and the width of ~2 kJ mol-1.

Agglomeration dynamics of magnetic nanoparticles at low magnetic field gradient studied by monitoring temporal changes of magnetic weight

256th National Meeting (2018)

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