UC Berkeley

Fabrication of materials through bottom-up, noncovalent self-assembly has the potential to revolutionize many areas of science and engineering that depend upon the precise arrangement and interaction of nanometer-scale particles. Theory and computation provide a useful route to studying self-assembly of these materials due to their ability to study the kinetic and thermodynamic features of simplified systems at a level of detail not possible in experiments. In this thesis we study the self-assembly of two bio-inspired systems using a combination of theory and computation. The first is comprised of archaeal chaperonin proteins that form in-vitro two remarkably different structures: filamentous chains and layers of sheets. Using a quasi-dynamical Monte Carlo algorithm, we show that the binary decision for sheet or string formation can be explained by allowing for conformational changes between a sheet-favoring state and a string-favoring state. Using advanced sampling techniques, we find that the energy gap for this conformational change controls structure formation. The second system is a self assembling cyclic peptide inside a block copolymer matrix. We develop a computationally efficient pseudospectral technique to simulate a Langevin dynamics derived from the block copolymer field-theoretic Hamiltonian and demonstrate two different processes by which nanoparticles may be incorporated into this framework.

In support of the peptide-polymer work, we develop a new algorithm for Metropolis Monte Carlo simulations on high-performance graphics processing units (GPUs) that relies on the local equilibration of non-interacting regions of a lattice system. We show how the technique can better exploit the GPU memory hierarchy resulting in over 100-fold speedups. This technique is well-suited for lattice systems with couplings beyond nearest neighbors and systems with complicated local or dynamical constraints.

Finally, we investigate the implications for excluding volume in a $\phi^4-\phi^2$ field theory, representative of a block copolymer theory. We provide a simplified derivation for the response of a Gaussian liquid to a volume-excluding solute. We apply this technique to a discrete $\phi^4-\phi^2$ theory and show that the effects of volume exclusion act independently of the $\phi^4$ term. Finally, we show using Monte Carlo simulations that the stabilization provided by the $\phi^4$ term may be replaced by a hard constraint on density fluctuations that imparts stability, while making the model's connections to well-studied Gaussian models of liquids more transparent.