Tilted and Helical Columnar Phases for an Axially Symmetric Discoidal System

We report novel phase behavior for a system of disclike ellipsoidal particles interacting via a pair potential. We identify a structural phase transition between two hexagonal columnar phases, both tilted, induced by spatial ordering of the tilt about the columnar axis and positional correlations between neighboring columns upon cooling. The local minima of the potential energy surface support irregular helical arrangements of the discoids about the columnar axis for the high-temperature hexagonal columnar phase, and a tilted arrangement for both phases. Our study demonstrates that dispersion-repulsion forces corresponding to oblate ellipsoids are sufficient to produce a columnar phase that is tilted and helical.

Figure 1

(a) Evolution of the average second-rank orientational order parameter $⟨P_2⟩$ with temperature $T$. The symbols include circles ($N=500$, $P=50$, MD), squares ($N=500$, $P=75$, MD), diamonds ($N=2048$, $N=50$, MD), and triangles ($N=500$, $P=50$, MC). (b) The columnar distribution function $g_c(r_{\parallel })$ at four different temperatures ($N=2048$, $P=50$). The temperatures correspond to the isotropic phase ($T=2.994$; black curve), the nematic phase ($T=1.895$; red curve), and the two columnar phases ($T=1.845$ and $T=1.649$; blue curve and green curve, respectively). The amplitude of the first peak grows gradually as the temperature falls.

Figure 2

(a) Hexagonal bond order parameter ${\Psi }_6$ as a function of temperature $T$ ($N=2048$, $P=50$). (b) Perpendicular radial distribution function $g_{\perp }(r_{\perp })$ at four different temperatures in the columnar phases ($N=2048$, $P=50$). $T=1.845$ (black curve), $T=1.696$ (red curve), $T=1.649$ (blue curve), and $T=1.395$ (green curve). The amplitude of the first peak grows gradually as the temperature falls.

Figure 3

Snapshots from columnar phases. Typical instantaneous configurations of the (a) $C_{\alpha }$ phase and (b) $C_{\beta }$ phase; (c) an inherent structure of the $C_{\beta }$ phase; two adjacent columns from instantaneous configurations of the (d) $C_{\alpha }$ phase and (e) $C_{\beta }$ phase; a column from an inherent structure of the (f) $C_{\alpha }$ phase and (g) $C_{\beta }$ phase.

Figure 4

(a) Snapshots of typical columns from an inherent structure of the $C_{\alpha }$ phase, displaying only the particle centers to demonstrate helical arrangements around the columnar axis, which is shown for each column. (b) Snapshot of a section through columns from an inherent structure of the $C_{\beta }$ phase, showing typical arrangements of neighboring columns. The dark blue and yellow colored stacks at the back are displaced above, and the orange and purple colored stacks at the front are displaced below, the middle row of stacks (green, red, and light blue) along the columnar axis of the central (red) stack.