Phase diagram of octapod-shaped nanocrystals in a quasi-two-dimensional planar geometry

Abstract

Recently, we reported the formation of crystalline monolayers consisting of octapod-shaped nanocrystals (so-called octapods) that had arranged in a square-lattice geometry through drop deposition and fast evaporation on a substrate [W. Qi, J. de Graaf, F. Qiao, S. Marras, L. Manna, and M. Dijkstra, Nano Lett. 12, 5299 (2012)]. In this paper we give a more in-depth exposition on the Monte Carlo simulations in a quasi-two-dimensional (quasi-2D) geometry, by which we modelled the experimentally observed crystal structure formation. Using a simulation model for the octapods consisting of four hard interpenetrating spherocylinders, we considered the effect of the pod length-to-diameter ratio on the phase behavior and we constructed the full phase diagram. The methods we applied to establish the nature of the phase transitions between the various phases are discussed in detail. We also considered the possible existence of a Kosterlitz-Thouless-type phase transition between the isotropic liquid and hexagonal rotator phase for certain pod lengthto-diameter ratios. Our methods may prove instrumental in guiding future simulation studies of similar anisotropic nanoparticles in confined geometries and monolayers.

Phase diagram of two-dimensional hard ellipses

“…These applications have encouraged several experimental and simulation studies on the behavior of 2D-confined nanocrystals of different shapes 8 . For instance, experiments and simulations have shown that needles, squares, octapods, and ellipsoidal anisotropic particles produce a rich mesophase behavior when confined to a quasi-2D plane [8][9][10][11][12][13][14] . For designing such arrangements, it is important to take into account the directional nature of entropic forces acting on anisotropic particles 15,16 , i. e. the effective forces that result from a system's statistical tendency to increase its entropy.…”

Accelerated discovery of nanomaterials using computer simulation

“…The challenge with this approach is to realize the obtained interaction in experiment. Another route is to propose the candidate phases (often crystalline phases) and then perform free energy calculations to find the thermodynamically most stable structure [19][20][21]. Alternatively, molecular simulation is employed with the physical models of the building blocks interacting based on van der Waals and Coulombic interactions.…”

“…For instance, the bilayer sheets assembled by polymer-tethered nanorods transition into the honeycomb grid upon lengthening the rod segments, and vice versa ( Figure 2H) [73]. Higher-order assemblies, such as terminal clusters [81] and unusual complex crystals and quasicrystals [20,70,82,83], are predicted to form by patchy particles, Janus particles and faceted polyhedra. MD simulation also predicted that a dodecagonal quasicrystal approximant could form in a mixture of spherical and elongated micelles ( Figure 2I) [74], which is to be realized in experiment.…”

Packing, entropic patchiness, and self-assembly of non-convex colloidal particles: A simulation perspective

“…The first step of the process involves the formation of linear chains driven by the interlocking of a particles as shown in Figure 3(a), followed by the arrangements of the chains themselves to form a three-dimensional ordered porous superlattice (see Figure 3(b)). Further control of the structures formed by particles with different arm lengths can be achieved by confining the particles in monolayers 38,46,92 . This type of confinement is readily realized when a liquid droplet containing the octapods is placed on a substrate and allowed to rapidly evaporate.…”