Tetrahedral Interactions in Self-Assembly

Abstract

Tetrahedral geometry is a ubiquitous structural motif in molecular, crystalline, and colloidal materials, where directional interactions and anisotropic particle shape can generate open frameworks, complex superlattices, and hierarchical assemblies. This thesis investigates how tetrahedral interactions and tetrahedral particle morphology can be exploited to control self-assembly across multiple length scales. By combining molecular dynamics, Monte Carlo simulations, enhanced sampling, inverse design, and close comparison with experiments, the work establishes design principles linking microscopic building-block properties to mesoscopic structure and morphology. First, an inverse-design framework is developed for the self-assembly of zeolite-like open crystals using a coarse-grained model of tetrahedral network-forming particles and structure-directing agents. The workflow combines covariance matrix adaptation evolution strategy optimization with seed-pinning molecular dynamics and an environment-similarity order parameter, enabling efficient exploration of a seven-dimensional parameter space while overcoming large nucleation barriers. The method reproduces the self-assembly of previously known Z1 and SGT frameworks, identifies suitable conditions for SOD, CFI, and type-I clathrate formation, and discovers an uncatalogued framework denoted Z5. These results demonstrate that enhanced-sampling inverse design can both target complex porous structures and reveal competing polymorphs that would be difficult to identify through conventional forward screening. Second, the co-assembly of tetrahedral and octahedral nanoparticles is examined as a model space-filling system. Deliberate mismatches in particle size and stoichiometry introduce geometric and crystallization frustration, transforming otherwise high-symmetry packing into a broad range of low-symmetry structures. Simulations and experiments show that size mismatch drives rotational symmetry breaking and the emergence of chiral honeycomb lattices, while stoichiometric mismatch enables periodically ordered vacancies. The same principles also produce three-dimensional homochiral crystals and a heterogeneous epitaxial superstructure formed through lattice-parameter matching. Frustration therefore becomes a programmable design variable rather than an imperfection. Third, the influence of rounding and truncation on tetrahedral nanocrystal assembly is investigated. Small changes in particle morphology redirect assembly among dodecagonal quasicrystals, diamond structures, simple hexagonal, tetragonal, high-pressure lithium, monoclinic, and body-centered-cubic phases. Particle geometry also determines surface architecture: high-index {211} facets arise through surface-roughness minimization, while morphology selects among energetically equivalent surface terminations. Finally, nucleus-size-pinning simulations are used to study the experimentally observed egg-shaped supraparticles formed by rounded tetrahedra. Crystalline nuclei develop statistically significant ellipsoidal shapes in quantitative agreement with experiment. However, similar anisotropy is also found for hard-sphere nuclei, indicating that non-spherical nucleus morphology may be a more general feature of crystallization and that the experimental mechanism remains unresolved. Overall, this thesis shows that interaction anisotropy, particle morphology, and controlled frustration provide complementary routes for engineering complex self-assembled materials.