(673h) Mesophase Behavior of Binary Mixtures of Hard Disks and Squares

In the context of a fundamental understanding of crystalline and mesophase ordering in 2D systems, the assembly of micro- and nanoparticles on hexagonal and square-lattice arrays is well established and has been widely studied; however, much less is known about whether and how a system can be designed to continuously bridge these two types of ubiquitous lattice symmetries. In this work, we tackle this question by studying the entropy-driven assembly of binary mixtures of hard disks with squares using Monte Carlo simulations, where the components have size ratios that optimize their co-assembly into compositionally disordered solids. For this purpose, we adopted the exchange free-energy method [Escobedo, F. A. J. Chem. Phys. 146, 134508 (2017)] to predict the size ratio values of the components in the mixture which tend to maximize the range of compositions and densities where the substitutionally disordered solid solutions occur. For mixture compositions close to the equimolar conditions, we observed a novel mosaic (M) phase sandwiched between the isotropic (I) and two-solid coexistence phases. The M phase has interspersed tetratic, hexatic, and rhombic-like locally ordered clusters, which seamlessly bridges the regions of hexatic mesophase of disks and of tetratic mesophase of squares. As the equimolar mixture transitions from the I to the two-solid phase-separated state through the intermediate M phase, we observed the coarsening in the correlation length of the ordered domains, which goes from being very short ranged (I phase), to mesoscopic (M phase) to macroscopic (two-phase state). We posit that this unique M mesophase behavior engenders when, at a suitable range of compositions and densities, the two competing entropic forces, namely, packing entropy favoring like-particle contacts and mixing entropy favoring random contacts, are in such a close balance that are able to coexist by attaining a “compromise” state exhibiting both segregated like-particle domains and random mixing of those domains. The unique dual crystalline structural characteristics observed in the M phase could be leveraged for potential applications in nanophotonics, sensors and switches. We also study the effect of nonrandom mixing on the demixing transition using a simple lattice-gas model that incorporates a nearest neighbor entropic attraction of the like-particles. The methods used and principles unveiled in our study are general and can be extended to understand the phase behavior of many other mixtures.