Phase behaviour and correlations of parallel hard squares: from highly confined to bulk systems Articles uri icon

publication date

  • April 2016

start page

  • 1

end page

  • 15


  • 24(244002)


  • 28

International Standard Serial Number (ISSN)

  • 0953-8984

Electronic International Standard Serial Number (EISSN)

  • 1361-648X


  • We study a fluid of two-dimensional parallel hard squares in bulk and under confinement in channels, with the aim of evaluating the performance of Fundamental-Measure Theory (FMT). To this purpose, we first analyse the phase behaviour of the bulk system using FMT and Percus-Yevick theory, and compare the results with MD and MC simulations. In a second step, we studythe confined system and check the results against those obtained from Transfer Matrix Methodand from our own Monte Carlo simulations. Squares are confined to channels with parallel wallsat angles of 0 or 45 relative to the diagonals of the parallel hard squares, respectively, whichallows for an assessment of the effect of the external-potential symmetry on the fluid structuralproperties. In general FMT overestimates bulk correlations, predicting the existence of a columnarphase (absent in simulations) prior to crystallisation. The equation of state predicted by FMTcompares well with simulations, although the PY approach with the virial route is better in somerange of packing fractions. The FMT is highly accurate for the structure and correlations of theconfined fluid due to the dimensional crossover property fulfilled by the theory. Both density profilesand equations of state of the confined system are accurately predicted by the theory. The highlynon-uniform pair correlations inside the channel are also very well described by FMT.


  • Mathematics


  • parallel hard squares; fundamental measure density functional; transfer matrix method; percus-yevick approximation; highly confined fluid; fundamental measure-theory; density-functional theory; white bear version; equation-of-state; free-energy model; dimensional crossover; sphere mixtures; cubes; fluid; particles; parallel hard squares; fundamental measure density functional; transfer matrix method; percus–yevick approximation; highly confined fluid