Phase behavior of binary mixtures of hard convex polyhedra

Abstract

Shape anisotropy of colloidal nanoparticles has emerged as an important design variable for engineering assemblies with targeted structure and properties. In particular, a number of polyhedral nanoparticles have been shown to exhibit a rich phase behavior [Agarwal et al., Nature Materials, 2011, 10, 230]. Since real synthesized particles have polydispersity not only in size but also in shape, we explore here the phase behavior of binary mixtures of hard convex polyhedra having similar sizes but different shapes. Choosing representative particle shapes from those readily synthesizable, we study in particular four mixtures: (i) cubes and spheres (with spheres providing a non-polyhedral reference case), (ii) cubes and truncated octahedra, (iii) cubes and cuboctahedra, and (iv) cuboctahedra and truncated octahedra. The phase behavior of such mixtures is dependent on the interplay of mixing and packing entropy, which can give rise to miscible or phase-separated states. The extent of mixing of two such particle types is expected to depend on the degree of shape similarity, relative sizes, composition, and compatibility of the crystal structures formed by the pure components. While expectedly the binary systems studied exhibit phase separation at high pressures due to the incompatible pure-component crystal structures, our study shows that the essential qualitative trends in miscibility and phase separation can be correlated to properties of the pure components, such as the relative values of the order-disorder transition pressure (ODP) of each component. Specifically, if for a mixture A+B we have that ODP B <ODP A and ∆ ODP = ODP A -ODP B , then at any particular pressure where phase separation occurs, the larger the ∆ ODP the lower the solubility of A in the B-rich ordered phase and the higher the solubility of B in the A-rich ordered phase.

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

“…We observed that the extent of miscibility as inferred from all metrics decreased f or systems L and S relative to system O. Further, in a previous study [21] where the size ratio was 63 % the ODP-matching value, no MRM formed for a wide range of compositions.…”

“…An earlier study [21] on the miscibility trends of binary polyhedra mixtures revealed the importance of the relative size ratio of the components and of similarity in their mesophase behavior [10]. One of our aims is to identify shapes and sizes that favor the formation of entropic rotator mixtures.…”

“…A recent study [21] suggested that the solid miscibility in a binary mixture of polyhedra can be linked to the relative values of the order-disorder transition pressure or ODP. In that study [21], however, the components' ODPs were always substantially different and very limited solid miscibility was observed; hence, the questions of what happens when the ODPs matched and whether that provides optimized mesophase compatibility were left open. For the present simulations, we set the relative particle size ratios such that their ODPs are approximately equal, which coincidentally entail near- * fe13@cornell.edu equal circumradii; namely the ratios of circumradii are CO:TO = 1:1 for COTO, TC4:TO = 1.01:1 for TC4TO and TC4:CO = 1.01:1 for TC4CO (for TC4 we use the largest circumscribing radius).…”

“…For the present simulations, we set the relative particle size ratios such that their ODPs are approximately equal, which coincidentally entail near- * fe13@cornell.edu equal circumradii; namely the ratios of circumradii are CO:TO = 1:1 for COTO, TC4:TO = 1.01:1 for TC4TO and TC4:CO = 1.01:1 for TC4CO (for TC4 we use the largest circumscribing radius). While equal circumradii is an equivalent criterion to ∆ODP=0 for the main mixtures considered here, we will also use a fourth mixture of spheres and cubes to show that ∆ODP=0 optimizes the overall miscibility even when equal circumradii does not.For the main mixtures, we probed the phase behavior as a function of pressure using hard-particle Monte Carlo simulations in the isothermal-isobaric ensemble, including swap moves between the position of particles of different species [21]. We used interfacial runs to test the relative stability of the phases near a phase transition.…”

“…For the main mixtures, we probed the phase behavior as a function of pressure using hard-particle Monte Carlo simulations in the isothermal-isobaric ensemble, including swap moves between the position of particles of different species [21]. We used interfacial runs to test the relative stability of the phases near a phase transition.…”