Densest-known packings and phase behavior of hard spherical capsids

By mostly using Monte Carlo numerical simulation, this work investigates the densest-known packings and phase behavior of hard spherical capsids, i.e., hard infinitesimally thin spherical caps with a subtended angle larger than the straight angle. The infinitely degenerate densest-known packings are all characterized by hard spherical capsids that interlock and can be subdivided into three families. The first family includes crystalline packings that are constructed by suitably rotating and stacking layers of hexagonally arranged and suitably tilted hard spherical capsids; depending on the successive rotations, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. The second family includes crystalline packings that are characterized by rhombic motifs; they all become the face-centered cubic crystal in the hard-sphere limit. The third family includes crystalline packings that are constructed by suitably shifting and stacking layers in which hard spherical capsids are arranged in tightly packed, straight or zigzag, columns; depending on the successive shifts, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. In the plane number density vs subtended angle, the phase diagram of hard spherical capsids features a hexagonal columnar liquid-crystalline phase, toward the hard-hemispherical-cap limit, and a plastic-crystalline phase, toward the hard-sphere limit, in addition to the isotropic fluid phase and crystalline phases. On departing from the hard-sphere limit, the increasing propensity of hard spherical capsids to interlock progressively disfavors the plastic-crystalline phase while favoring auto-assemblage into mostly dimeric interlocks in the denser isotropic fluid phase so that a purely entropic isotropic-fluid-plastic-crystal-isotropic-fluid re-entrant sequence of phase transitions is observed in systems of hard spherical capsids with a subtended angle intermediate between the straight angle and the complete angle.