Field-Theoretic Study of Complex Systems of Linear Polymer Chains

Abstract

In this thesis, I present studies that employ polymer field theory to investigate complex systems of linear chains, together with random-phase approximation (RPA) calculations for several polymer chain models. For the RPA calculation, order–to- disorder transition (ODT) boundary is examined by comparing χN_ODT and the natural lamellar period L0 for two discrete chain models (the N bond and N − 1 bond models) against a continuous chain model. In the first study, I use self-consistent field theory (SCFT) to investigate the WiFi-like nanostructure observed experimentally in polystyrene-block-polymethylmethacrylate (PS-b-PMMA) block copolymer melts confined in hemispherical anodized aluminum oxide (AAO) nanocavities with half of the surface coated with gold. The calculations reproduce the WiFi-like pattern at the top surface of the cavity show that the resulting morphology depends on the commensurability between the gold layer thickness and the lamellar period. Second, I extend SCFT to complex-valued fields and analyze solutions in A and B homopolymer mixtures and AB block copolymer melts. The results reveal continuous families of complex solutions that share the same free energy as the conventional real solution. I further show that the complex fields exhibit a Hermitian property, confirmed for lamellar, body-centered cubic (BCC), and double gyroid morphologies. This property provides insight into the instabilities observed in complex Langevin field-theoretic simulations (CL-FTS). Third, I apply Langevin field-theoretic simulations (L-FTS) to quantify ODTs in conformationally asymmetric diblock copolymer melts. To test whether stronger fluctuations promote direct ODTs into Frank–Kasper phases, I compare ODT boundaries at different fluctuation levels. The results indicate that increasing fluctuations do not facilitate Frank–Kasper phase formation near the ODT. I then examine dispersity of chain length using binary blends with Ð = 1.125 and Ð ≈ 1.333. Although direct ODTs into Frank–Kasper phases are not observed, increasing dispersity narrows the χN_ODT gap between the Frank–Kasper phases and BCC phases, suggesting a plausible route to enhanced the Frank–Kasper phase stability under realistic experimental conditions.