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Demixing and orientational ordering in mixtures of rectangular particles

D. de las Heras*

Yuri Martínez-Ratón†

Enrique Velasco‡

  • Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain

  • Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911 Leganés, Madrid, Spain

  • Departamento de Física Teórica de la Materia Condensada and Instituto de Ciencia de Materiales Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain

  • *daniel.delasheras@uam.es
  • †yuri@math.uc3m.es
  • ‡enrique.velasco@uam.es
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Phys. Rev. E 76, 031704 – Published 7 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031704

Abstract

Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyze the stability of phases with orientational order and the demixing phase behavior of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilized, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares, in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard disks or discorectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behavior, or simply rectangles of different aspect ratio but with the same particle area, or different particle area but with the same 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.

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Phys. Rev. E 76, 031704– Published 7 September, 2007
  • Received 7 May 2007

© 2007 American Physical Society

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