Towards Understanding the Self-assembly of Complicated Particles via Computation.

Abstract

We develop advanced Monte Carlo sampling schemes and new methods of calculating thermodynamic partition functions that are used to study the self-assembly of complicated ``patchy '' particles. Patchy particles are characterized by their strong anisotropic interactions, which can cause critical slowing down in Monte Carlo simulations of their self-assembly. We prove that detailed balance is maintained for our implementation of Monte Carlo cluster moves that ameliorate critical slowing down and use these simulations to predict the structures self-assembled by patchy tetrominoes. We compare structures predicted from our simulations with those generated by an alternative learning-augmented Monte Carlo approach and show that the learning-augmented approach fails to sample thermodynamic ensembles. We prove one way to maintain detailed balance when parallelizing Monte Carlo using the checkerboard domain decomposition scheme by enumerating the state-to-state transitions for a simple model with general applicability. Our implementation of checkerboard Monte Carlo on graphics processing units enables accelerated sampling of thermodynamic properties and we use it to confirm the fluid-hexatic transition observed at high packing fractions of hard disks. We develop a new method, bottom-up building block assembly, which generates partition functions hierarchically. Bottom-up building block assembly provides a means to answer the question of which structures are favored at a given temperature and allows accelerated prediction of potential energy minimizing structures, which are difficult to determine with Monte Carlo methods. We show how the sequences of clusters generated by bottom-up building block assembly can be used to inform ``assembly pathway engineering'', the design of patchy particles whose assembly propensity is optimized for a target structure. The utility of bottom-up building block assembly is demonstrated for systems of CdTe/CdS tetrahedra, DNA-tethered nanospheres, colloidal analogues of patchy tetrominoes and shape-shifting particles.