Understanding The Kinetics And Thermodynamics Of Self Assembly Of Faceted Polyhedral Particles Using Computer Simulations

Abstract

The growing ability to synthesize polyhedral particles has fueled the interest in understanding their assembly into ordered structures. The assembly of these particles can be performed with (directed) or without the influence of an external field. A relevant example of directed assembly involves the use of fluid-fluid interfaces. Since the disorder-to-order transitions observed in the bulk self-assembly of polyhedral particles are rare events, they cannot be studied using conventional brute force simulations. We use the combination of advanced sampling methods, namely, Forward Flux Sampling (FFS) and Umbrella Sampling to study the nucleation kinetics of structural order in polyhedral particle suspensions at different degrees of supersaturation (DoSS) in Chapter 1. The estimation of DoSS depends on the precise estimation of thermodynamic quantities at coexistence, which can be obtained by interfacial pinning method described in Chapter 2. We focused first on polyhedral shapes, namely, cuboctahedra, truncated octahedra, and rhombic dodecahedra. They all form a translationally ordered, orientationally disordered phase called a "rotator" or "plastic" solid. While one would have expected these polyhedra to exhibit similar ii nucleation kinetics as hard spheres, we find that the kinetics is orders of magnitude faster. Counterintuitively, it is the coupling between localized orientational and translational order that facilitates the growth of translationally ordered nuclei. We have further extended our analysis to octahedron-like particles in Chapter 5 for which we observe again small transition free-energy barriers for the nucleation of rotator phases. In contrast, for perfect octahedra (which do not form a rotator phase), we find that its crystal nucleation has a larger free energy barrier than that for hard spheres; this is due to the entropic cost of opposing complete face-to-face contacts to allow packing in the (Minkowski) lattice. We also used Monte Carlo simulations to study the thermodynamics of directed selfassembly of polyhedral particles confined to a fluid-fluid interface in Chapter 3. We considered the case of freely rotating hard particles whose centers of mass are pinned to a flat interface. Our results show diversity in the type of mesophases and crystalline phases that different shapes form. As an initial extension to more realistic fluid-fluid interfaces, we studied the role of particle-surface enthalpic interactions in determining the particle orientation behavior. We also describe our efforts to use the FFS framework to simultaneously obtain free energy barriers and rates, and to use alternative rare-event methods to identify optimized reaction coordinates in Chapter 4. Such methods are expected to be especially useful to resolve the transition kinetics of high-asphericity particle shapes (like cubes), binary particle mixtures in the bulk.