Magnetic particle‐loaded polymer brushes induced by external magnetic field: A Monte Carlo simulation

Abstract

The effects of applied magnetic field on the system composed of polymer brushes and magnetic particles are studied by means of Monte Carlo simulation. The direction of the applied magnetic field is chosen to be perpendicular to the substrate plane. Polymer brushes and magnetic particles are attracted to each other. The average heights of polymer brushes depend not only on the strength of applied magnetic field (H) but also on the brush grafting density (r) and the chain length (N). The applied magnetic field influences the arrangement of magnetic particles, and in turn, the arrangement of magnetic particles affects the spatial distribution of polymer brush monomers. When the strength of the magnetic field is increased, the average height of polymer brushes will be increased accordingly. The reason is that the orientations of the magnetic moments of particles must be along the mag-netic field direction, and this leads polymer brushes to rearrange along the magnetic field direction. At the same time, the chain length and the grafting density of polymer brushes have also effects on the properties of the magnetic particles, such as the magnetic particles distribution, magnetic susceptibility, and pair correlation functions. Comparisons with the experimental ones are also made, and this investigation can provide some insights into statistical properties of magnetic particle-loaded brushes induced by external magnetic field.

Magnetic‐induced coil‐globule transition for polyelectrolytes

“…Our work introduces a model system to study the effects of the applied magnetic field on the conformational properties of charged PEs polymers. Additionally, our previous works22 has provided some good results consistent with the related experiment 23. Although the logical and meaningful results have been obtained, it would be more reasonable if the long‐range property of electrostatic interaction can be seriously considered.…”

“…Meanwhile, the values of E PP , E NN , and E PN remain unchanged, indicating the structures of aggregates are relatively stable. The sum of E PP and E NN can be used to show whether the string‐like structures22 are stable or not in energy. Similarly, the sum of E NN , E PN , E PP , and E D reveals the stability of aggregates to some extent.…”

“…Pair correlation function g ( r ) is often used to investigate the distribution of particles. In view of the anisotropy resulting from the magnetic field, g xy ( r ) and g z ( r ) are considered, respectively, which are defined as22 and where V denotes the system volume, N z is the number of pairs whose distance is r along the z ‐axis, and N xy the number of pairs whose distance is r in the xy ‐plane. As g xy ( r ) shown in Figure 7(a), in the absence of the magnetic field ( H = 0), the probabilities of finding particles separated from each other for different distances r do not differ much.…”

“…As is known, the electrostatic interaction is inversely proportional to the distance r , which indicates the long‐range interaction. Here, the cutoff distance of $r_C = \sqrt{5}$ is selected instead of $r_C = \sqrt 2$ used in the previous work,22 which would make the results more precise. Here, we aim at studying the effects induced by the magnetic field.…”

“…The cutoff distance of $r_C = \sqrt 5$ in the calculations of magnetic dipole–dipole interactions does not affect the relation between the applied magnetic field and the statistical properties of system. More detailed discussions about the interactions are included in the Ref 22…”