Highly confined mixtures of parallel hard squares: A Density Functional Theory study

Abstract

Using the Fundamental-Measure Density Functional Theory, we have studied theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting of two consecutive big squares, or three small squares, in the transverse direction, perpendicular to the walls, are forbidden. We analyzed two different mixtures with edge-lengths of species selected so as to allow or forbid one big plus one small square to fit into the channel. For the first mixture we obtained first-order transitions between symmetric and asymmetric packings of particles: small and big squares are preferentially adsorbed at different walls. Asymmetric configurations are shown to lead to more efficient packing at finite pressures. We argue that the stability region of the asymmetric phase in the pressure-composition plane is bounded so that the symmetric phase is stable at low and very high pressure. For the second mixture, we observe strong demixing between phases which are rich in different species. Demixing occurs in the transverse direction, i.e. the dividing interface is perpendicular to the walls, and phases exhibit symmetric density profiles. The possible experimental realization of this behaviour (which in practical terms is precluded by jamming) in strictly two-dimensional systems is discussed. Finally the phase behavior of a mixture with periodic boundary conditions is analyzed and the differences and similarities between the latter and the confined system are discussed. We claim that, although exact calculations discard the existence of true phase transitions in $1+\epsilon$-dimensional systems, Density Functional Theory is still successful to describe packing properties of large clusters of particles.

arXiv comment13 pages, 15 figures

References in corpus (25)

• Tetratic Order in the Phase Behavior of a Hard-Rectangle System
• Shape and symmetry determine two-dimensional melting transitions of hard regular polygons
• Confinement of two-dimensional rods in slit pores and square cavities
• Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory
• Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
• High-Activity Perturbation Expansion for the Hard Square Lattice Gas
• Phase behavior of hard-core lattice gases: A Fundamental Measure approach
• Bulk inhomogeneous phases of anisotropic particles: A fundamental measure functional study of the restricted orientations model
• Domain walls in two-dimensional nematics confined in a small circular cavity
• Phase Separation in Two-Dimensional Additive Mixture
• Correlation lengths in quasi-one-dimensional systems via transfer matrices
• Liquid-crystal patterns of rectangular particles in a square nanocavity
• Ordering of hard rectangles in strong confinement
• Free Minimization of the Fundamental Measure Theory Functional: Freezing of Parallel Hard Squares and Cubes
• Density-functional study of defects in two-dimensional circular nematic nanocavities
• Single-Speed Molecular Dynamics of Hard Parallel Squares and Cubes
• Viral nematics in confined geometries
• Density functional theory study of the nematic-isotropic transition in an hybrid cell
• Uniform phases in fluids of hard isosceles triangles: one component and binary mixtures
• Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares
• Critical behavior of hard squares in strong confinement
• Phase behaviour and correlations of parallel hard squares: From highly confined to bulk systems
• Dynamical properties of heterogeneous nucleation of parallel hard squares
• Positional ordering of hard adsorbate particles in tubular nanopores
• Entropy of hard square lattice gas with $k$ distinct species of particles: coloring problems and vertex models