Density functional theory of fluid-solid phase transition in a two-dimensional system of superparamagnetic colloids in tilted magnetic field

Abstract

We have used density functional theory (DFT) of freezing to investigate the fluid-solid phase transition in a system of super-paramagnetic colloidal particles confined to a two dimensional plane and exposed to an external magnetic field which is tilted from the direction parallel to the plane. Magnetic field induces magnetic moment in the particles which are directed along the field. Because of the tilted induced magnetic moments, particles interact via anisotropic repulsive dipole-dipole interaction potential. We solve the Ornstein-Zernike(OZ)equation within the hypernetted chain (HNC) approximation to obtain the pair-correlation functions (PCF), which are used as structural input in DFT. All the pair functions were expanded in a suitable orthogonal basis and the expansion coefficients were determined by using the method of Fries and Patey [32] which leads to an unphysical negative contact value of radial distribution functions. We have employed a method similar to that of Hansen and Hayter [35], to resolve this issue. The accuracy of the resulting PCFs are tested by performing NVT Monte Carlo simulation. We found that for the tilt angle of the external field in the range 900 to 750, the fluid freezes into triangular solid, beyond which DFT fails to stabilize the solids considered in this work.