Assembly Behavior and Thermodynamic Stability of Complex Colloidal Superstructures

Abstract

This thesis present computational studies on the self-assembly and stability of complex colloidal superstructures, including colloidal quasicrystals and polyhedron nanoparticle superlattices. The first work presents a systematic study of the growth of colloidal dodecagonal quasicrystals in systems of hard tetrahedra. Using a pattern recognition algorithm in conjunction with higher-dimensional crystallography, I analyze phason error of growing quasicrystals to follow the evolution of quasiperiodic order. I observe that the colloidal quasicrystals grow via error-and-repair mechanism; quasicrystals first grow with weak phason error and repair the error via structural rearrangements. I also observe transformation from the first order approximant to the quasicrystal via continuous phason strain relaxation. My findings demonstrate that colloidal quasicrystals can be thermodynamically stable and grow with high structural quality – just like their alloy quasicrystals counterpart.

In the second work, I investigate thermodynamic stability of model icosahedral quasicrystals against rational approximants. I construct 6 rational approximants using higher-dimensional projection, and assess the stability of those approximants against the icosahedral quasicrystals. I find in molecular dynamics simulations that 2/1 approximants and 3/2 approximants transform into the icosahedral quasicrystals, which is monitored by evolution of phason strain and diffraction pattern. This result demonstrates that the icosahedral quasicrystals are more stable than the approximants. My finding combined with collaborators' free energy calculations of competing phases demonstrates that the icosahedral quasicrystals are metastable, which is consistent with the majority of experimentally observed icosahedral quasicrystals. Using higher dimensional crystallography, I further show that the transformations of the approximants are manifested as a rotation of hypersurface in six-dimensional space. Phase transformation simulations and higher dimensional crystallography outlined in this work elucidate stability and transformation dynamics of icosahedral quasicrystals.

In the third work, I investigate the assembly behavior of polyhedral nanoparticles coated with flexible DNA ligands. Using a model constructed based on TPT calculations, I find that spatial distribution of DNA ligands on nanoparticle surface plays an important role in stabilizing complex structures of polyhedra. Considering the spatial distributions, I present coarse-grained simulation models that predict assembly behavior of polyhedron nanoparticle superlattices. In molecular dynamics simulations of the models, I observe formation of simple hexagonal, Minkowski, I-43d, and body-centered-cubic phases from DNA-coated octahedra and formation of four complex binary superlattices from binary mixtures of DNA-coated polyhedra that match with self-assembly experiments by collaborators. The assembly of four complex binary superlattices suggests that mixing DNA-coated polyhedra can serve as a powerful approach for preparing complex colloidal superstructures. My simulations and models would be useful for predicting the assembly of complex superlattices from polyhedra coated with flexible DNA.

As a whole, this thesis demonstrates how colloidal interactions originating from geometry or ligand design can have profound impact for the generation of stable complex colloidal superstructures. I anticipate that simulations and computational approaches demonstrated in the thesis offer new paradigms in understanding and predicting assembly of complex colloidal materials.