Magnetic nanoparticles capped with proper surfactants are dispersed well in the aqueous solution. Solution of magnetic nanoparticles called ferrofluid shows the well-known interesting morphological behaviors under magnetic field.
1Magnetic nanoparticles of relatively low concentration agglomerate by magnetic field.2,3 Agglomeration of magnetite nanoparticles under low magnetic field (<100 T/m) is used in the protein purification or the separation of magnetic impurities for water purification. 3,4 Magnetic weight of magnetic nanoparticle, which appears by magnetization of nanoparticle, can be measured with a conventional electronic balance. 5,6 When the magnetic field from a small disc magnet is applied to the superparamagnetic magnetite solution, the magnetic weight of the sample jumps instantaneously (<<1 s) by the Neel and Brown mechanism. Thereafter the magnetic weight increases slowly as the nanoparticles agglomerate at the bottom of the sample holder where the magnetic field gradient is the greatest.Figure 1(a) shows the slow growth of magnetic weight of magnetite solution with a fitting curve. The 1 mL aqueous solution contains 0.7 wt % magnetite nanoparticles. The fitting curve of Figure 1(a) is a stretched exponential as followingwhere the exponent β is 0 < β < 1 and τ is the relaxation time. The initial magnetic weight, M(0), is 8.008 g, which includes the weight of the cuvette and the sample before applying magnetic field, 7.363 g. Increase of the magnetic weight by the Neel and Brown mechanism is 0.645 g. The equation of magnetic force, F = mg = VMrB suggests that the magnetic weight of the sample by the magnetic field gradient at the bottom of the cuvette, 31 T/m is 2.23 g. The saturation magnetization of magnetite (M) is known 4 as 4.7 × 10 5 A/m and the volume of the sample (V) is estimated as 1.5 × 10 −9 m 3 from the concentration of solution and the density of magnetite. If the magnetite sample is thoroughly magnetized, the magnetic weight would be 9.593 g, which is much greater than the final magnetic weight of the fitting curve M(∞), 8.257 g. There is a large difference between the structures of the agglomerate and the crystalline magnetite. The agglomerate can be seen as a polycrystal with very fine, loosely combined domains. Therefore, the magnetic weight of the agglomerate in solution cannot be close to that of solid magnetite. In addition to the structural differences of the agglomerate and the crystalline solid, the error in the estimation of the sample concentration and the magnetic field gradient as well as the inaccuracy of the fitting parameters is attributed to the discrepancy of the final magnetic weights.The stretched exponential growth of the magnetic weight indicates that the energy barrier for agglomeration is not a single value but has some distribution. 7,8 There is a relation of the inverse Laplace transform between the distribution function of the energy barrier and the temporal response function of the dynamics. The distribution function with an asymmetric bell shape can be d...