Accuracy of Enskog theory for rotational versus translational motion: A molecular-dynamics study

Two-dimensional system of hard ellipses: a molecular dynamics study

We have simulated the dynamics of a two-dimensional system of hard ellipses by event-oriented molecular dynamics in microcanonical NVE ensemble. Various quantities, namely longitudinal and transverse velocity auto-correlation functions, translational and rotational diffusion mean-squared displacements, pressure, intermediate self-scattering function, radial distribution function, and angular spatial correlation, have been obtained and their dependence on packing fraction is characterized. Despite absence of prominent positional ordering, the orientational degree of freedom behaves nontrivially and exhibits interesting features. Slowing down is observed in the angular part of the motion near isotropic-nematic phase transition. It is shown that above a certain packing fraction the rotational mean-squared displacement exhibits a three-stage temporal regime including a plateau. Comparison to 2D system of hard needles is made and it is shown that from positional viewpoint, the ellipse system is more ordered.

Temporal and structural characteristics of a two-dimensional gas of hard needles

We have simulated the dynamics of a 2D gas of hard needles by event-oriented molecular dynamics. Various quantities namely translational and rotational diffusion constants and intermediate self-scattering function have been explored and their dependence on density is obtained. Despite absence of positional ordering, the rotational degree of freedom behaves nontrivially. Slowing down is observed in the angular part of the motion. It is shown that above a certain density the rotational mean-square displacement exhibits a three-stage regime including a plateau.

The Enskog-type theory of the velocity autocorrelations in the two-dimensional nematic of hard needles

As it was shown from molecular dynamics of two-dimensional hard needles, the uniaxial velocity autocorrelation function (VACF) of this system exhibits a two time scale character. This corresponds to the symmetry of the particles. In this paper we provide a theory of the Enskog type that corroborates the idea that the VACF can be successfully described as a sum of two single decays. From the comparison between molecular dynamics and theoretical results, we show that the Enskog approach is a satisfactory kinetic theory, which functions as well in the nematic as in the isotropic phase. Different properties of VACFs have been investigated, in particular, the dependence on the orientational order, temperature, and particles' inertness.

Velocity correlations of two-dimensional hard needles from molecular dynamics

We present velocity correlations of a two-dimensional system of perfectly smooth hard needles from molecular dynamics. In a nematic phase the autocorrelation velocity function (ACF) clearly separates into two domains with, first, a very quick decay and, then, a long-lasting exponential-like decay that pertains to several characteristic times of the fast decay. The latter one is strongly subjected to the order of the system. We demonstrate that the existence of two time scales corresponds to different relaxations of the transverse and longitudinal components of the ACF.