Singlet orientational distribution function and dielectric permittivity of dipolar spherocylinders in the nematic phase

Monte Carlo computer simulation of sedimentation of charged hard spherocylinders

In this article we present a NVT Monte Carlo computer simulation study of sedimentation of an electroneutral mixture of oppositely charged hard spherocylinders (CHSC) with aspect ratio L/σ = 5, where L and σ are the length and diameter of the cylinder and hemispherical caps, respectively, for each particle. This system is an extension of the restricted primitive model for spherical particles, where L/σ = 0, and it is assumed that the ions are immersed in an structureless solvent, i.e., a continuum with dielectric constant D. The system consisted of N = 2000 particles and the Wolf method was implemented to handle the coulombic interactions of the inhomogeneous system. Results are presented for different values of the strength ratio between the gravitational and electrostatic interactions, Γ = (mgσ)/(e(2)/Dσ), where m is the mass per particle, e is the electron's charge and g is the gravitational acceleration value. A semi-infinite simulation cell was used with dimensions Lx ≈ Ly and Lz = 5Lx, where Lx, Ly, and Lz are the box dimensions in Cartesian coordinates, and the gravitational force acts along the z-direction. Sedimentation effects were studied by looking at every layer formed by the CHSC along the gravitational field. By increasing Γ, particles tend to get more packed at each layer and to arrange in local domains with an orientational ordering along two perpendicular axis, a feature not observed in the uncharged system with the same hard-body geometry. This type of arrangement, known as tetratic phase, has been observed in two-dimensional systems of hard-rectangles and rounded hard-squares. In this way, the coupling of gravitational and electric interactions in the CHSC system induces the arrangement of particles in layers, with the formation of quasi-two dimensional tetratic phases near the surface.

Integral equation theory for fluids ordered by an external field: separable interactions

The structural and thermodynamical properties of classical fluids orientationally ordered by an external field are investigated by means of integral equation theories. A general theoretical framework for handling these theories is developed and detailed for the particular case of separable interactions between fluid particles. This approach is then illustrated for the case of two (off lattice) models: the ferromagnetic Heisenberg model and a simple liquid crystal model, for which the numerical solution of integral equations such as the Percus-Yevick, the hypernetted chain, and the reference hypernetted chain closure equations are presented and compared with Monte Carlo simulation results and the analytical solution of the mean spherical approximation. The zero-field case is also examined, and the spontaneous ordering is analyzed in detail, mainly in what concerns the appearance of infinite wavelength singularity in the Ornstein-Zernike equation and the relation with the one-body closure equations and the long range orientational ordering that occurs. In particular, it is shown that the Wertheim one-body closure equation appears as a sum rule compatible with the Ornstein-Zernike equation. The relation between the elastic constant and the long range tail of the pair correlation function is made explicit. In particular, the long range behavior of the various terms in the expansion of the pair correlation function is depicted. The numerical investigation of the two models shows that it is not possible to discriminate between the four integral equations, as to which one would be the most accurate in all cases. The general trends in the thermodynamical and structural properties seem to indicate that the Percus-Yevick approximation is generally better in the strong ordering case, whereas the reference hypernetted chain approximation might be better suited to the study of the isotropic phase and the low ordering regimes.