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Open Access Dissertation
Doctor of Philosophy (PhD)
Year Degree Awarded
Month Degree Awarded
Gregory M. Grason
Condensed Matter Physics
In this dissertation we explore the effect of shape, mechanics and geometry in assemblies of tubular filaments by introducing the notion of cohesive contact.
We first study the optimal geometry of cohesive interactions in straight flexible tubes by considering two interaction potentials. We find filaments adopt a locally skewed configuration, associated with a twist angle. The interaction energy decreases with the twist angle and ground states are found to be twisted. For pair-wise interactions, we find a generic behavior in the profile of the cohesive energy where the geometry of close-packed double helices dictates the shape of the assembly. By considering the effect of bending energy we find a critical angle where twisting would be favorable and provide a prediction for carbon nano-tubes. Conversely, in the presence of non pair-wise interactions, we observe metastability for small twist deviations.
Next we explore the packing of curved filaments and their dependence on shape, range of cohesive binding and number of filaments. We study two packing motifs, N−plies and N−packs, where the latter is found to be generically favored as the stable ground state due to its ability to follow a hexagonal arrangement and the larger number of neighbors it can have.
Finally we study the self-assembly of a helical pairs focusing in the orientational dependence of the interactions. We develop a geometric model that describes the energetics of bundle formation, consisting of an optimal inter-filament spacing, a preferred parallel orientation and a preference for a prescribed helical shape. We find the system to be highly frustrated and present a phase diagram with three ground state configurations. We compute threshold values of attraction needed to form bound states and conclude that binding is determined by the shape of the filament. We propose a connection between the nature of interactions and the local geometry of the assembly via coupling constants, which we believe to be the strongest virtue of our model.
Cajamarca Ospina, Luis, "Elasticity and Geometry in Curved-Filament Assemblies" (2015). Doctoral Dissertations. 481.