A hydrothermal synthesis process for preparing crystalline magnetite （Fe₃O₄） nanoparticles was statistically analyzed to control the particle size, using response surface methodology （RSM） based on design of experiments （DOE）. The influence of the experimental parameters （initial ferrous/ferric ion molar ratio, initial concentration of ferrous ions, and heating time） and their interactions on the particle growth was evaluated through the analysis of variance （ANOVA） for the dynamic light scattering diameter. Furthermore, the multiple linear regression analysis （MLRA） was performed, and then the three-dimensional response surface plots were obtained. The particle size was found to be affected by the experimental parameters, in particular, the interaction between the ferrous/ferric ion molar ratio and the concentration of ferrous ions, suggesting that the particle growth mechanism is altered depending on the amount of ferrous ions. The particle size can be successfully controlled to a given target level using the obtained analysis results.

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The interaction between silica particle and mica substrate in highly viscous aqueous polyvinyl alcohol （PVA） solutions of different concentrations was determined by colloidal probe AFM. Since a large hydrodynamic force acts on the colloidal probe in highly viscous solutions, it is difficult to determine the actual interaction between the colloidal probe and the substrate in concentrated polymer solutions. In this study, the hydrodynamic force acting on the colloidal probe in an aqueous solution was determined at a relatively long surface distance ranging from 500 to 900 nm, and the hydrodynamic force acting on the colloidal particle was estimated by Stokes' law. The influence of the polymer concentration on the interaction forces between the silica particle and mica substrate was investigated, where the calculated hydrodynamic force was subtracted from the measured force-distance curve. The attractive force resulting from van der Waals interaction was not observed in PVA solutions. At PVA concentrations below 6 mass％, the repulsive force resulting from the adsorption of PVA on silica particles decreased with increasing PVA concentration. At 9 and 12 mass％ PVA, the repulsive force and the amount of adsorbed PVA showed a sudden increase. It was suggested that the repulsive force is correlated to the amount of adsorbed PVA.

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Brownian diffusion is one of the most important and interesting natures of aerosol particles. It has much effects on aerosols in small-sized space such as aerosol transport through a tube, instruments for aerosol measurements, and fabrication of especially nano-sized aerosols. Numerical simulations of aerosol transport are useful in analysis of aerosol behavior. Aerosol modeling of diffusion has often been carried out using diffusion equation of aerosol. Another way to represent the Brownian diffusion is to solve a Langevin dynamics equation. Due to the rapid advance in computational technology, it is now possible to solve the Langevin dynamics equation. It has been applied to problems that could not be solved by conventional diffusion equations in the previous studies. In this article, we introduced two applications of the Langevin dynamics equation : aerosol diffusion between two parallel walls and aerosol deposition from a laminar flow through a cylindrical tube.

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