Sedimentation equilibrium of magnetic nanoparticles with strong dipole-dipole interactions

Abstract

Langevin dynamics simulation is used to study the suspension of interacting magnetic nanoparticles (dipolar spheres) in a zero applied magnetic field and in the presence of a gravitational (centrifugal) field. A particular emphasis is placed on the equilibrium vertical distribution of particles in the infinite horizontal slab. An increase in the dipolar coupling constant λ (the ratio of dipole-dipole interaction energy to thermal energy) from zero to seven units causes an increase in the particle segregation coefficient by several orders of magnitude. The effect of anisotropic dipole-dipole interactions on the concentration profile of particles is the same as that of the isotropic van der Waals attraction modeled by the Lennard-Jones potential. In both cases, the area with a high-density gradient separating the area with high and low particle concentration is formed on the profiles. Qualitative difference between two potentials manifests itself only in the fact that in the absence of a gravitational field the dipole-dipole interactions do not lead to the "gas-liquid" phase transition: no separation of the system into weakly and highly concentrated phases is observed. At high particle concentration and at large values of λ, the orientational ordering of magnetic dipoles takes place in the system. Magnetic structure of the system strongly depends on the imposed boundary conditions. Spontaneous magnetization occurs in the infinite horizontal slab (i.e., in the rectangular cell with two-dimensional periodic boundary conditions). Replacement of the infinite slab by the finite-size hard-wall vertical cylinder leads to the formation of azimuthal (vortex-like) order. The critical values of the coupling constant corresponding to the transition into an ordered state are very close for two geometries.

Equilibrium properties of magnetic filament suspensions

“…= 0.67 ensures that at κ = 0 and λ = 0 the system free energy coincides with the free energy of the ensemble of hard spheres with a diameter d [11]. Surely, in a more general case, when λ > 0 or κ > 0, equilibrium properties of filaments will still depend on the particular choice of the steric repulsion potential.…”

“…Simulation algorithm proposed in Ref. [11] was used. Filaments were placed inside the elongated rectangular cavity of the height L z , gravitational field g was acting along the cavity long axis (z-axis).…”

Magnetophoretic Equilibrium of a Polydisperse Ferrofluid

“…where j is the particle flux density. One can find in the literature rather complex expressions for j, which take into account various interparticle interaction effects [19,22]. However, the assumption of noninteracting particles allows us to use the following simplified form:…”

Janus microdimer swimming in an oscillating magnetic field

“…The dipole-dipole interaction energy of particle i provoked by particle j is calculated by [2,[18][19][20][21]]…”