Demixing and orientational ordering in mixtures of rectangular particles

TL;DR

This paper uses scaled-particle theory to analyze the stability and demixing behavior of binary mixtures of two-dimensional hard particles, focusing on the emergence and destabilization of tetratic and nematic phases in mixtures of rectangles and squares.

Contribution

It provides a theoretical analysis of phase stability and demixing in mixtures of hard rectangles and squares, highlighting the effects of particle shape, aspect ratio, and mixture composition on orientational order.

Findings

Tetratic phase can be stable in pure hard rectangle fluids with low aspect ratios.

Mixing rectangles with other particles destabilizes tetratic order, leading to phase transitions.

Demixing occurs in mixtures of hard squares with large size ratios.

Abstract

Using scaled-particle theory for binary mixtures of two-dimensional hard particles with rotational freedom, we analyse the stability of nematic phases and the demixing phase behaviour of a variety of mixtures, focussing on cases where at least one of the components consists of hard rectangles or hard squares. A pure fluid of hard rectangles may exhibit, aside from the usual uniaxial nematic phase, an additional (tetratic) oriented phase, possessing two directors, which is the analogue of the biaxial or cubatic phases in three- dimensional fluids. There is computer simulation evidence that the tetratic phase might be stable with respect to phases with spatial order for rectangles with low aspect ratios. As hard rectangles are mixed with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilised, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry, dimensions and thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard discs or disco-rectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behaviour, or simply rectangles of different aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic--tetratic or tetratic--tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.