Geometrical aspects of soft matter and optical systems

Abstract

Geometrical aspects of several problems in soft matter and optical physics are examined in this dissertation. First, a practical problem in colloidal lithography is reduced to the following question in discrete geometry: What is the set of planar periodic patterns generated by shadows of spheres? To that end, we provide a complete classification and construct a lithographic "phase diagram" of patterns to guide experiments. Motivated by optical metamaterial applications of colloidal lithography, we then consider the influence of particle shape in the scattering of light by subwavelength dielectric particles. We show that upon breaking rotational symmetry in the geometric cross-section of high refractive index nanoparticles, magnetic resonances and directed light scattering can be attained at several frequencies. A model of magnetic modes elucidates the field patterns observed in simulations of silicon nanobars and accounts for their spectrally diverse forward scattering. These results suggest a broader class of nanoparticle geometries than currently used in all-dielectric metamaterials. Finally, we consider whether electrostatic interactions between conducting carbon nanotubes and polyelectrolytes can drive their adsorption in weak salt solutions. Our analytical model and calculations include estimates of the electrostatic and van der Waals contributions, and suggest there exists a critical salt concentration for adsorption to occur. Below this concentration, estimated at $\lesssim$ 2 mM, electrostatic interactions can facilitate double-stranded DNA adsorption onto conducting carbon nanotubes.