Structure and thermodynamics of a ferrofluid monolayer

We model a disordered planar monolayer of paramagnetic spherical particles, or ferrofluid, as a two-dimensional fluid of hard spheres with embedded th ree-dimensional magnetic point dipoles, This model, in which the orientatio nal degrees of freedom are three dimensional while particle positions are c onfined to a plane, can be taken as a crude representation of a colloidal s uspension 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 describin g the structure of this highly inhomogeneous fluid. including the effects o f an external magnetic field. The method hinges on the use of specially tai lored orthogonal polynomials whose Height function is precisely the one-par ticle distribution function that describes the surface- and held-induced an isotropy. The results obtained for various particle densities and external fields are compared with, Monte Carlo simulations, illustrating the capabil ity of the inhomogeneous Ornstein-Zernike equation and the proposed solutio n scheme to yield a detailed and accurate description of the spatial and or ientational structure for this class of systems. For comparison, results fr om density-functional theory in the modified mean-field approximation are a lso presented; this latter approach turns out to yield at least qualitative ly correct results.