Heuristic Rule for Binary Superlattice Coassembly: Mixed Plastic Mesophases of Hard Polyhedral Nanoparticles

Sought-after ordered structures of mixtures of hard anisotropic nanoparticles can often be thermodynamically unfavorable due to the components’ geometric incompatibility to densely pack into regular lattices. A simple compatibilization rule is identified wherein the particle sizes are chosen such that the order-disorder transition pressures of the pure components match (and the entropies of the ordered phases are similar). Using this rule with representative polyhedra from the truncated-cube family that form pure-component plastic crystals, Monte Carlo simulations show the formation of plastic-solid solutions for all compositions and for a wide range of volume fractions.

Figure 1

Pressure ($P^{*}$) versus composition ($x_B$) phase diagram for the three main mixtures. ${\mathrm{DSC}}_C$ and ${\mathrm{DSC}}_T$ are distorted simple cubic structures of COs and TC4s, respectively [12, 14]. $x_B$ represents fraction of COs in the COTO and TC4CO mixtures, and the fraction of TOs in the TC4TO mixture. Each diagram is accompanied by a snapshot of the mixed rotator mesophase (MRM) for $x_B=0.5$ (at $P^{*}=11.2$, 9.6, and 9.6 for COTO, TC4TO, and TC4CO, respectively), its orientational correlation plot, and diffraction pattern.

Figure 2

Plots showing the effect of changing the mesophase composition in the COTO mixture (solid part of each curve represents the stable MRM region). (a) Variation of $P_4$ as a function of pressure $P^{*}$. (b) Pressure dependence of the enrichment factor.

Figure 3

Pressure-composition phase diagrams for spheres (diameter $\sigma$) and cubes (side edge $d$) with different size ratios. Top: $\sigma /d=1.0$ (equal inradius). Center: $\sigma /d=1.23$ (equal ODPs). Bottom: $\sigma /d=1.732$ (equal circumradius). $S=\text{sphere}$ rich solid, $C=\text{cube}$ rich solid, $I=\text{isotropic}$ phase. $P^{*}=P{d}^3/\epsilon$. Data for $\sigma /d=1.23$ are from Ref. [31]. Orientation correlation plots are shown for the cubes in the three phases occurring at the eutectic pressure.