Orientational ordering in hard rectangles: The role of three-body correlations

TL;DR

This paper studies how three-body correlations influence phase transitions in two-dimensional hard rectangle fluids, showing that these correlations stabilize certain ordered phases and improve theoretical predictions compared to previous models.

Contribution

It introduces an equation of state incorporating three-body correlations via the third virial coefficient, enhancing the understanding of phase behavior in hard rectangle fluids.

Findings

Three-body correlations increase the stability of the tetratic phase.

The new equation of state predicts transition densities in fair agreement with simulations.

The critical aspect ratio for tetratic phase stability is increased by three-body effects.

Abstract

We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient, $B_3$, is incorporated via an equation of state that recovers scaled particle theory for parallel hard rectangles. This coefficient, a functional of the orientational distribution function, is calculated by Monte Carlo integration, using an accurate parameterized distribution function, for various particle aspect ratios in the range 1-25. A bifurcation analysis of the free energy calculated from the obtained equation of state is applied to find the isotropic (I)-uniaxial nematic (N$_u$) and isotropic-tetratic nematic (N$_t$) spinodals and to study the order of these phase transitions. We find that the relative stability of the N$_t$ phase with respect to the isotropic phase is enhanced by the introduction of $B_3$. Finally, we have calculated the complete phase diagram using a variational procedure and compared the results with those obtained from scaled particle theory and with Monte Carlo simulations carried out for hard rectangles with various aspect ratios. The predictions of our proposed equation of state as regards the transition densities between the isotropic and orientationally ordered phases for small aspect ratios are in fair agreement with simulations. Also, the critical aspect ratio below which the N$_t$ phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation.