Phase transitions in block copolymer thin films: from self-consistent field theory to field theoretic simulation

Abstract

The phase behavior and order-to-disorder transition (ODT) of block copolymers (BCPs) is a fundamentally important subject, and the design of long-range ordered structure is also important for the industrial application. Unlike the phase transitions in the bulk BCPs, ODT of the film is influenced by the interfacial interactions. There have been various experimental and theoretical reports on this subject, but it is still an unsettled issue and we have seen quite a few contradictory claims on the direction of the ODT change. In this study, we utilize two theoretical tools to investigate the formation of heterogeneous nanostructures in thin film and the effect of fluctuation. The first one is the discrete chain self-consistent field theory (DCSCFT) which provides the mean field theory of discrete bead model. Nowadays, BCPs with low molecular weight and high χ parameter are promising materials to create short period nanostructure, and polymers with finite number of segments can be an alternative model in SCFT. DCSCFT can also naturally adopt finite-range interactions between segments. In this work, we investigated the effect of preferential and/or neutral interfaces on the shift of ODT temperature, and the theoretical results are compared with experiments. The second one is the Langevin field theoretic simulation (L-FTS). Unlike the Complex Langevin FTS which makes sampling in full complex plane, saddle point approximation is adopted in L-FTS for the pressure field, but the exchange field is sampled by the Langevin equation. Unfortunately, as the simulation grid size reduces to zero, the FTS calculation suffers the so-called ultraviolet divergence and we chose a renormalization method proposed by Vorselaars and Matsen to remove this divergence. We could successfully perform L-FTS at experimentally relevant invariant polymerization index, and it shows that (χN)ODT increases at decreasing film thickness for the cylinder-forming film confined by neutral interfaces.