Assembly of hard spheres in a cylinder: a computational and experimental study

Abstract

Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of diameter $\sigma$ within cylinders of diameter $\sigma \le D\le 2.82\sigma$. Although in such a system phase transitions formally do not exist, marked structural crossovers are observed. In simulations, we find that the resulting pressure-diameter structural diagram echoes the densest packing sequence obtained at infinite pressure in this range of $D$. We also observe that the out-of-equilibrium self-assembly depends on the compression rate. Slow compression approximates equilibrium results, while fast compression can skip intermediate structures. Crossovers for which no continuous line-slip exists are found to be dynamically unfavorable, which is the source of this difference. Results from colloidal sedimentation experiments at high Péclet number are found to be consistent with the results of fast compressions, as long as appropriate boundary conditions are used. The similitude between compression and sedimentation results suggests that the assembly pathway does not here sensitively depend on the nature of the out-of-equilibrium dynamics.

11 pages, 8 figures and 63 references

References in corpus (7)

• Perspective: Geometrically-Frustrated Assemblies
• Helical Packings and Phase Transformations of Soft Spheres in Cylinders
• Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
• Phase Transformations in Binary Colloidal Monolayers
• Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares
• Emergent Inter-particle Interactions in Thermal Amorphous Solids
• Emergence of limit-periodic order in tiling models

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• Transverse excitations and zigzag transition in quasi-1D hard-disk system
• 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
• Simulation and observation of line-slip structures in columnar structures of soft spheres
• Theory of rotational columnar structures of soft spheres
• Columnar structures of soft spheres: Metastability and hysteresis
• Inherent Structure Landscape of Hard Spheres Confined to Narrow Cylindrical Channels
• Random sequential adsorption of spheres on a cylinder
• Ordering properties of anisotropic hard bodies in one-dimensional channels
• Exact anisotropic properties of hard spheres in narrow cylindrical confinement
• Positional ordering of hard adsorbate particles in tubular nanopores
• Controlled transitions between phyllotactic states of repulsive particles confined on the surface of a cylinder
• Formation of cylindrical shells via sphere packing from fluidized beds
• Chiral Packings in Cylinders are Ultrasensitive to Confinement Deformation