Orientational ordering in a fluid of hard kites: A density-functional-theory study Articles uri icon

publication date

  • November 2020

start page

  • 1

end page

  • 15


  • 5(052128)


  • 102

International Standard Serial Number (ISSN)

  • 1539-3755

Electronic International Standard Serial Number (EISSN)

  • 1550-2376


  • Using density-functional theory we theoretically study the orientational properties of uniform phases of hardkites—two isosceles triangles joined by their common base. Two approximations are used: scaled particle theoryand a new approach that better approximates third virial coefficients of two-dimensional hard particles. Byvarying some of their geometrical parameters, kites can be transformed into squares, rhombuses, triangles, andalso very elongated particles, even reaching the hard-needle limit. Thus, a fluid of hard kites, depending onthe particle shape, can stabilize isotropic, nematic, tetratic, and triatic phases. Different phase diagrams arecalculated, including those of rhombuses, and kites with two of their equal interior angles fixed to 90◦, 60◦,and 75◦. Kites with one of their unequal angles fixed to 72◦, which have been recently studied via Monte Carlosimulations, are also considered. We find that rhombuses and kites with two equal right angles and not too largeanisometry stabilize the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites withtwo equal interior angles fixed to 60◦ stabilize the triatic phase to some extent, although it is very sensitive tochanges in particle geometry. Kites with the two equal interior angles fixed to 75◦ have a phase diagram withboth tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stableat different densities. Finally, the success of the new theory in the description of orientational order in kites isshown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to 72◦.These particles also present a phase diagram with stable tetratic and triatic phases.


  • Materials science and engineering
  • Mathematics


  • density functional theory; hard kites; tetratic phase; triatic phase