Impacts of topological and molecular mass polydispersity on self-assembled polymeric micelles

Abstract

This thesis investigates how architectural complexity and mass polydispersity influence the self-assembly, structure, and mechanics of polymer systems, using a combination of analytical theory and self-consistent field theory (SCFT) calculations. Across four studies, we extend theoretical frameworks, develop computational tools, and apply them to underexplored polymer architectures with relevance to soft materials design.

The first study extends strong stretching theory to polydisperse linear brushes on curved surfaces in good solvent and melt conditions. Using realistic Schulz-Zimm chain length distributions, we quantify how curvature and polydispersity affect chain end distributions, brush shape, and bending moduli. We identify conditions under which end exclusion zones (EEZs)—regions devoid of chain ends—appear in convex geometries, and show that their location can be tuned via the polymer length distribution, offering a novel route to control brush structure and mechanical response.

In the second study, we develop a SCFT algorithm using real-space methods with adaptive spatial and contour discretization. By refining resolution near surfaces and grafting points, the method captures sharp gradients and reduces numerical instability with minimal cost. Validated on block copolymer films and brushes, it enables accurate and efficient simulations in three dimensions, expanding the tractable range of SCFT applications.

The third study examines micelles formed from polydisperse linear-hyperbranched block copolymers (LHBCs), comparing them to linear-dendritic (LDBC) and linear diblock polymers. Using molecular dynamics to generate realistic LHBC structures, we show via SCFT that LHBC micelles have lower critical micelle concentrations, greater stability, and higher drug loading capacity than LDBC micelles—benefits that increase with polydispersity. LHBCs also exhibit a high number of terminal groups for functionalization, independent of branching heterogeneity.

Lastly, we explore the self-assembly of amphiphilic gradient copolymers with a 1:1 styrene-isoprene composition in a selective solvent. SCFT calculations reveal a transition from spherical to cylindrical to lamellar micelles as the gradient flattens, with near-degenerate free energies. A phase diagram for idealized gradient copolymers shows that solvophobic block size dominates morphology selection, while gradient shape further modulates micelle structure and stability.