Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 379, Issue 2201, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2020.0111
Keywords
chromonic liquid crystals; bacteriophage virus; toroidal clusters; polyconvex functions; absoltue minimizer; solid-liquid transition
Categories
Funding
- National Science Foundation [DMS-DMREF 1729589, DMS-1816740, DMS-1817156]
- Simmons Foundation
Ask authors/readers for more resources
This article studies equilibrium configurations of hexagonal columnar liquid crystals and their application in protein capsids, revealing the energy composition of liquid crystals and various constraints. The study finds that the concentric, azimuthal, spool-like configuration is the absolute minimizer, and compares toroidal structures formed by DNA in free solution with those occurring in experiments with other types of lyotropic liquid crystals.
We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen-Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives. This article is part of the theme issue 'Topics in mathematical design of complex materials'.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available