Fig. 4.

Manipulation of entropic bonds, shown via an alluvial diagram, indicating particle shape modification of bonded state structure in $\left(r,{\theta }_1,{\theta }_2\right)$ space for elongated hexagons at $P=\left[16.0,14.9,13.5,12.6,12.1\right]$ for shape parameters $\gamma =\left(\frac{1}{2}.\frac{2}{3},1,\frac{3}{2},2\right)$. Bar sizes correspond to phase space volume associated with each bond type. Gray lines associate “flows” within and between bond types as particle shape changes. Additional bars indicate regions of phase space that change from being associated with bonds to nonbonded or geometrically forbidden states, keeping total phase space volume constant across all shapes. Examples below each shape indicate the same voxel in $\left(r,{\theta }_1,{\theta }_2\right)$ for each shape, and the corresponding bond, demonstrating how the bonds change as a function of particle shape. The most striking observation is the considerable increase in the voxels belonging to the herringbone bond from $\gamma =\frac{1}{2}\to \frac{2}{3}$, followed by the reduction in defect voxels from $\gamma =\frac{3}{2}\to 2$. Observation of the flow between bonding regions as $\gamma$ changes shows that particle shape has a significant impact on entropic bonding regions, suggesting the ability to strategically engineer entropic bonds via shape manipulation. See Fig. 3C and SI Appendix, Figs. S4–S6 for the entropic bonding regions used to compute the alluvial diagram.