The ac susceptibility of magnetic markers in solution was studied for biosensor application, where the marker consisted of magnetic nanoparticles and a coating material. From the frequency dependence of the susceptibility caused by the Brownian rotation of the marker, we estimated the distribution of marker size, which is an important parameter for biosensor application. For this purpose, we analyzed the experimental data by the singular value decomposition (SVD) method. Using this method, we can directly estimate the size distribution without assuming any distribution function. The estimated distributions were also compared with those obtained from optical dynamic light scattering (DLS) measurements. It was shown that the size distribution estimated by magnetic measurement (SVD) slightly shifts to a size lower than that estimated by the optical measurement (DLS). It was also shown that the frequency dependence of the susceptibility can be better explained by the size distribution estimated by the SVD method than by the distribution estimated with DLS. The difference between the magnetic and optical measurement results was discussed in terms of aggregation of the markers.
This study investigated the AC susceptibility of magnetic fluids in the nonlinear Brownian relaxation region. The nonlinear properties of the susceptibility in high excitation fields were measured comprehensively, including the decrease in susceptibility, field-dependent Brownian relaxation time, and occurrence of the third harmonic for the susceptibility. These experimental results were compared with numerical simulations based on the Fokker–Planck equation, which describes nonlinear Brownian relaxation. We first performed the numerical simulation by assuming mono-dispersed single-domain nanoparticles. The observed nonlinear properties were shown to be roughly explained by the simulation. To compare the experiment and simulation more accurately, we then considered the size distribution of the magnetic nanoparticles existing in practical samples; this was obtained by analyzing the frequency dependence of the susceptibility in weak fields. Quantitative agreements were obtained between the experiment and simulation for the frequency and field dependences of the nonlinear susceptibility.
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