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 + ǫ-dimensional systems, Density Functional Theory is still successful to describe packing properties of large clusters of particles.

Densest-Packed Columnar Structures of Hard Spheres: An Investigation of the Structural Dependence of Electrical Conductivity

“…Prominent examples include the application of the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as models for bulk crystal structures of solids [4] and the application of random close packings as models for bulk amorphous structures of liquids [3,6]. In contrast to these examples for bulk systems, the past few decades have seen an uprising interest in the packings of particles in confined settings, such as those of particles confined within a two-dimensional box [7,8], within a parallel strip [9][10][11][12][13][14], within a spherical container [15,16], within a cylindrical container [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], onto a cylindrical surface [37], between parallel plates [38][39][40][41][42][43][44][45][46], within a wedge cell [47,48], or within a flexible conta...…”