Orientational ordering and close packing properties of quasi-one-dimensional hard Gaussian overlap particles

TL;DR

This study examines how hard Gaussian overlap particles align and pack in a quasi-one-dimensional channel, revealing distinct behaviors for oblate and prolate particles and identifying critical exponents for close-packing.

Contribution

It provides a detailed analysis of orientational ordering and close-packing properties of HGO particles using the transfer operator method, highlighting differences between oblate and prolate particles.

Findings

Oblate particles align along the channel axis with perfect order at high density.

Prolate particles favor planar alignment with partial order even at close packing.

Pressure and orientational fluctuations follow specific divergence exponents, with oblate particles not belonging to the universal class of prolate particles.

Abstract

We investigate the orientational ordering and close-packing behavior of hard Gaussian overlap (HGO) particles, which are confined into a quasi-one-dimensional (q1D) channel. In the channel, particles are allowed to move along the channel and to rotate in three dimensions. Using the transfer operator method, we show that oblate particles align with their short axes along the channel, while prolate particles favor planar alignment perpendicular to the axis of the channel. While perfect orientational ordering develops in the fluid of oblate particles, the ordering is just partial in the fluid of prolate ones even at the close-packing density. The pressure ratio of freely rotating and parallel particles (P / P_parallel), which is an effective marker of structural changes, exhibits a single peak for oblate particles and no peak for prolate ones with increasing density. The close-packing behavior is characterized by exponents for the divergence of pressure (P ~ alpha P_parallel), the decay of orientational fluctuations (<(theta_p - theta)^2> ~ P^beta), and the behavior of the orientational correlation length (xi ~ P^gamma). The obtained values are beta = -1 and gamma = 0 for both oblate and prolate particles, while alpha = 2 for oblate and alpha = 1.5 for prolate particles. Moreover, prolate particles belong to the universality class of hard superellipses, where the combinations alpha + beta = 1/2 and beta + gamma = -1 hold exactly for any k > 1 (S. Mizani et al., Phys. Rev. E 111, 064121 (2025)). However, oblate particles do not belong to this universal class because alpha + beta = 1.