The formation of chiral nanopatterns on low-dimensional ionic assemblies via electrostatic interactions

Charged molecular assemblies are interesting for their ability to have long-range periodic patterns and their ability to be dynamically tuned through interactions with the solvent such as pH and Debye length. Charges assembled at an interface is an significant system being that most biological interactions take place on surfaces and not in the bulk. While the configurations of charged planar surfaces have been thoroughly mapped and studied, charged cylindrical surfaces show novel features. In this thesis, the surface patterning of cylindrically confined charges is discussed with emphasis on the role of chiral configurations. The origins of surface patterning due to competing interactions in charged monolayers are summarized along with their associated theoretical models. The electrostatically induced patterns described in this thesis are important in many low-dimensional biological systems such as plasma membrane organization, filamentous virus capsid structure, or microtubule interactions. Beside the ubiquitous presence of electrostatic interactions between filaments in biology, carbon nanotubes hybridized with DNA are proving to be an important system for its separation and materials properties.;Several recent research works focus on nanofibers covered by molecules that self-assemble into chiral helices. While the formation of helical structures has been explained mostly on a case by case basis, the ubiquitous presence of chirality at the nanoscale suggests the existence of a unifying description. A model of lamellar patterns effectively predicting some features of chiral patterns in biological systems is presented, along with the results produced. In particular, the focus is on patterns of chiral helices, achiral rings, or vertical lamellae, with the constraint of global electroneutrality. A study of the dependence of the pattern's size and pitch angle on the radius of the cylinder and salt concentration is contained here. A phase diagram is obtained by using numerical and analytic techniques. Three distinct phases are found: a ring phase for small radii, a chiral helical phase at larger radii and a axial phase for integer commensurate radii. A group theory formulation is presented to formalize the geometry of the patterns predicted. Further, at a critical salt concentration, the characteristic domain size diverges, resulting in an achiral macroscopic phase-segregated structure. A natural extension to the lamellar model are elliptical domains, which add an additional asymmetry in the assemblies of filamentous aggregates.;Finally, a study on how hexagonally arranged ionic lattices can generate asymmetrical structures on the surface of nanoscale fibers is demonstrated. A model consisting of positive and negative charges tiled around a fiber is introduced here. The effect of competing electrostatic and short-range strain interactions is described by a Coulomb potential and lattice strain energies. A determination of the optimal orientation of the ionic lattice with respect to the axis of the cylinder and we compute the effects of the nanofiber curvature is found. Strain energies provide a local interaction that favors achiral lattice for all arrangements, while charged interactions favor chiral arrangements for special families of fiber diameters. The findings of ionic lattice symmetries are shown to be dependent on the stoichiometric ratio. Two ratios 2:1 and 3:1 are considered here.