Molecular dynamics of a model anisotropic system

Abstract

The molecular dynamics method has been used to study a model system of 1000 symmetric top particles placed at the sites of a cubic lattice and interacting with the pair potential U_ij = - ε _ij P ₂(cos β _ij ). Here ε _ij is a positive constant, ε, for neighbouring sites and zero otherwise. The equations of motion are written in the quaternion representation and contact is made with the more familiar Euler parameterization of rotations. In particular, explicit expressions are given for the Wigner rotation matrices in terms of quaternions. The model is known from Monte Carlo simulations to possess an orientational phase transition and this fact is confirmed. Both static and dynamic properties have been calculated for a few selected temperatures. The singlet orientational distribution function has been obtained as a two dimensional histogram and order parameters ⟨P ₂⟩, ⟨P ₄⟩, ⟨P ₆⟩, have been calculated. It is shown that the appropriate way to describe the orientational dynamics in uniaxial systems of cylindrically symmetric particles is through the set of Wigner rotation matrix correlation functions φ _mn ^LL′ (t) = ⟨D_mn ^L (0)*D_mn ^L′ (t)⟩. Results for the φ _mn ^LL′ (t) of ranks L, L′ = 1, 2 are reported for two temperatures in the ordered phase and one in the isotropic phase. It is pointed out that correlation functions such as ⟨P ₁(1(0) · 1(t))⟩ and ⟨P ₂(1(0) · 1(t))⟩ depending solely on the angles between successive positions of the orientation vector 1(t) only afford partial information on the dynamics, in contrast to the behaviour in isotropic systems. Although the model potential studied here is relatively simple the treatment is general and should be of use to future molecular dynamics simulations of anisotropic fluids.