Helix Self-Assembly from Anisotropic Molecules

We explore the potential energy landscape for clusters composed of disklike ellipsoidal particles interacting via an anisotropic potential based on the elliptic contact function. Over a wide range of parameter space we find global potential energy minima consisting of helices composed of one or more strands. Characterizing the potential energy surface in the region of helical global minima reveals a topology associated with “structure-seeking” systems. This result indicates that the helices will self-assemble over a wide range of temperature.

Figure 1

The effect of ${\sigma }_0$ on the shape of the PY potential, for equal attractive and repulsive semiaxes. $V$ is the potential energy and $d_r$ is the directional distance for two ellipsoids, which vanishes whenever the two ellipsoids touch. The shapes of the repulsive ellipsoidal cores for the roundest and flattest particles considered are shown in the inset.

Figure 2

Global minimum for a cluster containing 13 discoids interacting via the PY potential. (a) A double helical structure is preferred for a face-to-face/side-by-side strength ratio of 0.2 ($a_{11}=0.15$, $a_{21}=0.06$). (b) The same structure as in (a), but showing the double helical arrangement of the centers of the discoids.

Figure 3

(a) Probability distribution for the potential energy of local minima for a 20-particle cluster composed of particles with $a_{11}=0.05$, $a_{21}=0.4$, and ${\sigma }_0=18$. This distribution corresponds to the minima visited during 100 basin-hopping steps. Inset: helical structure of the global minimum for this system. (b) Face-to-face (blue curve) and side-by-side (red curve) interaction profiles as a function of the intercenter distance. (c) Disconnectivity graph for the same system, showing the organization of the landscape for the lowest 100 minima. Four of the minima are also illustrated.

Figure 4

Global minimum for a cluster assembled from 55 discoids with $a_{11}=0.15$, $a_{21}=0.4$, and ${\sigma }_0=30$. Each strand is colored differently. In this structure there are eight ellipsoids that cannot be assigned to any helical strand (colored in black): two in the middle of the cluster and three at both ends of the helices.