Structure and thermodynamics of a ferrofluid monolayer

Abstract

We model a disordered planar monolayer of paramagnetic spherical particles, or ferrofluid, as a two-dimensional fluid of hard spheres with embedded three-dimensional magnetic point dipoles. This model, in which the orientational degrees of freedom are three dimensional while particle positions are confined to a plane, can be taken as a crude representation of a colloidal suspension of superparamagnetic particles confined in a water/air interface, a system that has recently been studied experimentally. In this paper, we propose an Ornstein-Zernike integral equation approach capable of describing the structure of this highly inhomogeneous fluid, including the effects of an external magnetic field. The method hinges on the use of specially tailored orthogonal polynomials whose weight function is precisely the one-particle distribution function that describes the surface- and field-induced anisotropy. The results obtained for various particle densities and external fields are compared with Monte Carlo simulations, illustrating the capability of the inhomogeneous Ornstein-Zernike equation and the proposed solution scheme to yield a detailed and accurate description of the spatial and orientational structure for this class of systems. For comparison, results from density-functional theory in the modified mean-field approximation are also presented; this latter approach turns out to yield at least qualitatively correct results.

Reference hypernetted chain theory for ferrofluid bilayer: Distribution functions compared with Monte Carlo

“…6 Theoretical angular distribution functions and projections of the pair distribution functions on the standard rotational invariants agree with Monte Carlo (MC) simulations.…”

“…The functions f(cos θ ), g bb (12), and g bt (12) represent the list of the quantities to be found from the integral equations. To determine them we follow the work of Lomba, Lado et al 6 and generalize the theory to the bilayer case. The first Kirkwood-Born-Green-Yvon (KBGY) equation,…”

“…Note that in case of monolayer systems the pair functions are symmetric with respect to the inversion of the connecting vector r ij . 6 This leads to the selection rule for the coefficients in (21): they are non-zero only if m 1 − m 2 is an even number. 6 However, when we turn to the …”

“…II, we describe the bilayer model and extend the integral equations of Ref. 6 to the bilayer case. In Sec.…”

Diffusion process and formation of super-spin-glass state in soft magnetic Fe∕Pt system

“…Numerous experimental and theoretical studies have been performed for various two-and three-dimensional arrangements of magnetic nanostructures having different degrees of structural and magnetic disorder. [1][2][3] For example, grains with in the nanoscale thin films can act as a dense nanomagnet and their random orientation can dictate their magnetic behavior. Since grains with the thin films are randomly oriented they can become soft ferromagnetic despite the presence of some hard ferromagnetic phases.…”