The statistical properties of systems composed of polymer brushes and magnetic nanoparticles placed in a magnetic field are studied by means of Monte Carlo simulation.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

chain length and magnetic nanoparticle concentration.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

because orientations of the magnetic moments of nanoparticles must be along the magnetic field direction.At the same time

the chain length

the grafting density of polymer brushes and the nanoparticle concentration also have an effect on the properties of the magnetic nanoparticles

such as the magnetic nanoparticles distribution

magnetic susceptibility and pair correlation functions.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.