Ordering properties of anisotropic hard bodies in one-dimensional channels
arXiv:2307.14760 · doi:10.1063/5.0169605
Abstract
The phase behavior and structural properties of hard anisotropic particles (prisms and dumbbells) are examined in one-dimensional channels using the Parsons--Lee (PL) theory, and the transfer-matrix and neighbor-distribution methods. The particles are allowed to move freely along the channel, while their orientations are constrained such that one particle can occupy only two or three different lengths along the channel. In this confinement setting, hard prisms behave as an additive mixture, while hard dumbbells behave as a non-additive one. We prove that all methods provide exact results for the phase properties of hard prisms, while only the neighbor-distribution and transfer-matrix methods are exact for hard dumbbells. This shows that non-additive effects are incorrectly included into the PL theory, which is a successful theory of the isotropic-nematic phase transition of rod-like particles in higher dimensions. In the one-dimensional channel, the orientational ordering develops continuously with increasing density, i.e., the system is isotropic only at zero density, while it becomes perfectly ordered at the close-packing density. We show that there is no orientational correlation in the hard prism system, while the hard dumbbells are orientationally correlated with diverging correlation length at close packing. On the other hand, positional correlations are present for all the systems, the associated correlation length diverging at close packing.
arXiv comment14 pages, 6 figures; v2: minor changes
References in corpus (27)
- From random walk to single-file diffusion
- General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
- Hard-body models of bulk liquid crystals
- Orientational order in dipolar fluids consisting of nonspherical hard particles
- Inhomogeneous hard-sphere mixtures: Manifestations of structural crossover
- The Complete Jamming Landscape of Confined Hard Discs
- Assembly of hard spheres in a cylinder: a computational and experimental study
- 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
- Glass-like behavior of a hard-disk fluid confined to a narrow channel
- Differently Shaped Hard Body Colloids in Confinement: From passive to active particles
- Hard Disks in Narrow Channels
- Exact bulk correlation functions in one-dimensional nonadditive hard-core mixtures
- One-dimensional gas of hard needles
- Correlation lengths in quasi-one-dimensional systems via transfer matrices
- Marginally jammed states of hard disks in a one-dimensional channel
- Universality in the jamming limit for elongated hard particles in one dimension
- Towards understanding the ordering behavior of hard needles: New analytical solutions in one dimension
- Equation of state of hard-disk fluids under single-file confinement
- Comment on "Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system" [Phys. Rev. Research 2, 033351 (2020)]
- Exact solution of a one-dimensional continuum percolation model
- Structural properties of hard-disk fluids under single-file confinement
- One-dimensional fluids with second nearest-neighbor interactions
- Multiple singularities of the equilibrium free energy in a one-dimensional model of soft rods
- Exact Results for Interacting Hard Rigid Rotors on a d-Dimensional Lattice
- Hard-needle elastomer in one spatial dimension