Pair correlations and freezing transitions in a two-dimensional system of tilted axially symmetric quadrupoles

Abstract

We study the pair structure and the transition from the liquid to the solid state in a system of axially symmetric charged particles confined to a two-dimensional plane and characterised by only one non-zero component of the electric quadrupole moment, which we assume to be inclined with respect to the perpendicular to the confining plane. The particles interact via anisotropic repulsive quadrupole–quadrupole interactions. The pair correlation functions (PCF) were calculated by solving the hypernetted chain integral equation (HNC) theory in the range of the tilt angle 75.0 ∘ ≤ 90 ∘ − ϕ ≤ 90 ∘ . NVT Monte Carlo (MC) simulations were also performed to test the accuracy of the PCFs. We find that the PCFs calculated with the HNC theory agree well with those of the MC simulation at smaller tilt angles and show anomalous behaviour with respect to the in-plane angular variation. The PCFs obtained with the HNC theory were used in the Ramakrishnan-Yussouff (RY) density functional theory (DFT) to investigate the transition between liquid and solid freezing. It was found that the RY DFT stabilises the triangular solid only for tilt angles ≥ 80 ∘ . When the tilt angle is decreased compared to the normal orientation of the quadrupoles, the transition density increases.