Magnetic Nanoparticle-loaded Brushes Induced By External Magnetic Field: A Monte Carlo Simulation

Recently, Choi et al. investigated the formation of magnetic nanoparticles in polyelectrolyte brushes. It comes to the conclusion that if the brush pattern is exposed to a strong permanent magnet, the height of brushes will increase. The phenomenon is first observed by experimentally, and it is important to have a deeper understanding of the configurations of nanoparticles-loaded brushes and the properties of magnetic nanoparticles in detail. Moreover, among all the simulations and theoretical studies to date, very few studies on magnetic nanoparticle-loaded brushes are discussed. To fill this knowledge gap, here we employ the Monte Carlo simulation method to consider the problem of a polymer brush which has an attractive interaction with nanoparticles which also carry a magnetic moment. Our simulation is not only verify the results of the experiment, but also research statistical behaviors of brushes and the distributions of magnetic nanoparticlesthe physical properties of the brush because of the interaction between nanoparticles and brushes under the applied magnetic field.The effects of applied magnetic field on the system composed of polymer brushes and magnetic nanoparticles are first studied by means of Monte Carlo simulation for the first time. Nanoparticles and polymer brushes are confined between two walls, the brushes graft from the substrate plane. The direction of the magnetic field is perpendicular to the substrate plane. Polymer brushes and magnetic nanoparticles are attractive to each other. The average heights of polymer brushes depend not only on the strength of applied magnetic field, but also on the brush grafting density and chain length. The applied magnetic field influences the arrangement of magnetic nanoparticles, and in turn the permutation of magnetic nanoparticles affects the spatial distribution of brush monomers. When the strength of the magnetic field increases, the average height of polymer brushes increases accordingly, due to orientations of the magnetic moments of nanoparticles must be along the magnetic field direction. At the same time, the chain length and the grafting density of polymer brushes have also an effect on the properties of the magnetic nanoparticles, such as the magnetic nanoparticles distribution, the average length of the strings along Z direction, magnetic susceptibility, and pair correlation functions.1. The brushes of nanoparticle-loaded brushes under magnetic field, the height of the brushes increases roughly linearly with the applied magnetic field H. Afterwards, when the strength is intensive, the average height of the brushes stays roughly constant.2. For different magnetic field, the density profile of magnetic nanoparticles is parabolic. When the applied field increases, the peaks of the profiles decrease, however, the concentration regions for magnetic nanoparticles will broaden. The reason may be that the nanoparticles will arrange sequentially when the applied field increases.3. Under intensive magnetic field, it is observed that the value of l(?)without brushes is much smaller than the value with brushes. The value of l_ with brushes smaller than the value of l(?) with no brush when the magnetic field is weak. Because the brush don't stretch along the Z direction very well, the brush monomer hamper the magnetic particles form the strings along the Z direction4. In the case of different grafting density and brush length, When the magnetic field begins to increase from zero, the value of magnetic susceptibility will increase from a certain value, and then approach a maximum value. When the magnetic field is further increased the value of magnetic susceptibility sharply declines until zero.5. In the case of H=0, the values of the peak for g(?)(r) are fluctuated when the distance r increases. However, in the cases of H=5, and 50, the values of the peak for g(?)(r) decrease abruptly when the distance r increases. In the same time, the higher the strength of the magnetic field, the larger the value of g(?)(r).Our results are in agreement with the experimental ones, and this investigation can provide some insights into statistical properties of magnetic nanoparticle-loaded brushes induced by external magnetic field.