Helical buckling in columnar assemblies of soft discotic mesogens

We investigate the emergence of chiral meso-structures in one-dimensional fluids consisting of stacked discotic particles and demonstrate that helical undulations are generated spontaneously from internal elastic stresses. The stability of these helical conformations arises from an interplay between long-ranged soft repulsions and nanopore confinement which is naturally present in columnar liquid crystals. Using a simple mean-field theory based on microscopic considerations we identify generic scaling expressions for the typical buckling radius and helical pitch as a function of the density and interaction potential of the constituent particles.

Figure 1

A columnar fluid of stacked parallel soft disks (in red) confined in a cylindrical parabolic trap with potential $V_c\left(r\right)$. The backbone of the stacks may adopt a linear (left) or buckled (right) configuration. The typical interaction range between adjacent disks is quantified by a (Debye) screening length ${\kappa }^{-1}$.

Figure 2

Renormalized buckling radius and associated deformation free energy (on a log scale) for a linear stack of soft discotic particles as a function of the optimal pitch values $q^{*}\ell$. The energetically most favorable mode is $q^{*}\ell \approx 9.132$, with corresponding radius $R^{*}\approx 0.333{(\rho u_0/v_0)}^{1/3}$. Higher order pitch “harmonics” correspond to increasingly weaker buckling radii $R^{*}$ and free energy reductions.