Nanopolyhedra form a versatile toolbox to investigate the effect of particle shape on self-assembly. Here we consider rod-like triangular prisms to gauge the effect of the cross section of the rods on liquid crystal phase behavior. We also take this opportunity to implement and test a previously proposed version of fundamental measure density functional theory (0D-FMT). Additionally, we perform Monte Carlo computer simulations and we employ a simpler Onsager theory with a Parsons-Lee correction. Surprisingly and disappointingly, 0D-FMT does not perform better than the Tarazona and Rosenfeld’s version of fundamental measure theory (TR-FMT). Both versions of FMT perform somewhat better than the Parsons-Lee theory. In addition, we find that the stability regime of the smectic phase is larger for triangular prisms than for spherocylinders and square prisms.
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The term “mixed” comes from integral geometry, see Ref. 32 for the connection.
Nevertheless, the scaling of all z-coordinates in the whole system (both positions and the particles themselves) by a factor D/L used in Ref. 58 to study the system for will also lead to strongly aligned normal vectors for any type of rod-like particle with a typical diameter D and length L in the limit . For this reason, we abandoned an approach that scaled the system to that of less elongated polyhedra. We thought initially that such an approach would allow us to use the simpler edFMT that already works well for mildly non-spherical particles, but clearly the scaling had exactly the opposite effect that we required a much more complicated theory with high truncation orders.
Note that for the triangular prisms considered here, the calculation could have been optimized somewhat by taking advantage of the rectangular side faces.