Self-Consistent Field Theory Study of Heterogeneous Polymer Nanostructures in Thin Film Confinement

Abstract

Block copolymers (BCPs) are macromolecules with distinct polymer blocks cova- lently bonded within a single chain, allowing them to self-assemble into periodic nanostructures. This self-assembly is driven by the chemical incompatibility be- tween blocks and is governed by parameters such as the Flory-Huggins interaction parameter (χ), the degree of polymerization (N), and the volume fraction of spe- cific blocks. The resulting morphologies, including lamellae, cylinders, spheres, and gyroids, are periodic on the nanoscale and exhibit exceptional versatility in material design. BCP thin films, formed by techniques such as spin coating and annealing, are particularly promising for applications in nanolithography, filtration, and energy storage, as their tunable patterns enable the precise control of nanostructures. Star-shaped BCPs represent a unique subclass of BCPs, where multiple arms radiate from a central core, imposing geometric constraints that significantly alter their self- assembly behavior compared to linear BCPs. As the number of arms increases, the inner blocks tend to localize near the core, resulting in hierarchical and asymmetric phase diagrams. These properties enable star-shaped BCPs to form complex nanos- tructures, such as hexagonally arranged tubular morphologies, which are challenging to achieve with linear BCPs. Thin films of star-shaped BCPs provide further opportunities to explore novel mor- phologies under confinement. Film thickness, substrate interactions, and surface affinity play critical roles in directing the alignment and stability of nanostructures. For example, specific substrates such as graphene-coated surfaces can promote di- rectional ordering, while confined trench geometries guide the formation of lamellae and nanotubes. These confined systems highlight the interplay between molecular architecture, surface chemistry, and external constraints in determining the nanos- tructures. This thesis investigates the self-assembly of star-shaped BCPs in bulk, thin film, and trench-confined environments using self-consistent field theory (SCFT). Through a detailed analysis of phase behavior and morphology, the study provides insights into the mechanisms governing self-assembly and the conditions necessary to achieve desired nanostructures. These findings contribute to the understanding of linear and star-shaped BCPs as a platform for designing advanced materials with hierarchical and complex architectures.