Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

Abstract

We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between $\sigma$ and $3\sigma$ ( $\sigma$ is the side length of the square). The exact equation of state and the nearest neighbour distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers and a solid-like structure where the fluid layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e. no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.

References in corpus (15)

• Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media - topical review
• Single-File Diffusion of Atomic and Colloidal Systems: Asymptotic Laws
• From random walk to single-file diffusion
• Phyllotactic description of hard sphere packing in cylindrical channels
• Helical Packings and Phase Transformations of Soft Spheres in Cylinders
• The Complete Jamming Landscape of Confined Hard Discs
• Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
• Static and dynamical properties of a hard-disk fluid confined to a narrow channel
• Structural properties of hard disks in a narrow tube
• Fundamental measure theory for mixtures of parallel hard cubes. II. Phase behavior of the one-component fluid and of the binary mixture
• The Inherent Structure Landscape Connection Between Liquids, Granular materials and the Jamming Phase Diagram
• Hard Disks in Narrow Channels
• Structure of Quasi-One Dimensional Ribbon Colloid Suspensions
• Free Minimization of the Fundamental Measure Theory Functional: Freezing of Parallel Hard Squares and Cubes
• Soft disks in a narrow channel

Cited by in corpus (10)

• Colloidal Hard Spheres: Triumphs, Challenges and Mysteries
• Assembly of hard spheres in a cylinder: a computational and experimental study
• Correlation lengths in quasi-one-dimensional systems via transfer matrices
• Ordering of hard rectangles in strong confinement
• Comment on "Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system" [Phys. Rev. Research 2, 033351 (2020)]
• Analytical canonical partition function of a quasi-one dimensional system of hard disks
• Phase behaviour and correlations of parallel hard squares: From highly confined to bulk systems
• Positional ordering of hard adsorbate particles in tubular nanopores
• Ordering and association of patchy particles in quasi-one-dimensional channel
• Highly confined mixtures of parallel hard squares: A Density Functional Theory study