<p> A large focus of this thesis was developing the experimental procedures involved in imaging <i>VO₂</i> during the heating process. In order to study light interactions between an induced dipole and a sample surface to collect various data on its topography, amplitude and phase. Data is collected using a near-eld microscope (s-SNOM) and analyzed using various software that, normalize, lter and display the data in false color image. Specically, research behind this thesis, focuses on the phase transition of Vanadium Dioxide (<i>VO₂</i>) as it goes from an insulating to fully metallic phase. Using a wavelength of &lambda; = 10:7<i>&mu;m</i> to image the resonant behavior of the sample, the nucleation of <i>VO₂</i> was imaged as the temperature increased.</p>

<p> As a class of carbon-based nanomaterials, single-walled carbon nanotubes (SWNT) have many structural variations, called chiralities, each with different properties. Many potential applications of SWNT require the properties of a single chirality, but current synthesis methods can only produce single chiralities at prohibitive costs, or mixtures of chiralities at more affordable prices. Post-synthesis chirality separations provide a solution to this problem, and hydrogel separations are one such method.</p><p> Despite much work in this field, the underlying interactions between SWNT and hydrogel are not fully understood. During separation, large quantities of SWNT are irretrievably lost due to irreversible adsorption to the hydrogel, posing a major problem to separation efficiency, while also offering an interesting scientific problem concerning the interaction of SWNT with hydrogels and surfactants. </p><p> This thesis explores the problem of irreversible adsorption, offering an explanation for the process from a mechanistic viewpoint, opening new ways for improvement in separation. In brief, this work concludes adsorption follows three pathways, two of which lead to irreversible adsorption, both mediated by the presence of surfactants and limited by characteristics of the hydrogel surface. These findings stand to increase the general understanding of hydrogel SWNT separations, leading to improvements in separation, and bringing the research field closer to the many potential applications of single-chirality SWNT.</p><p>