Langevin Field-Theoretic Simulations of Order-to-Disorder Transition in Block Copolymer Blends Incorporated with Well-Tempered Metadynamics

Abstract

Controlling the phase behavior of block copolymer (BCP) melts is crucial for leveraging their microphase separation in advanced applications. BCP melts can self-assemble into a variety of ordered microstructures, with the specific morphology dictated by parameters such as the Flory–Huggins interaction parameter χN. One common strategy to tune this behavior is blending homopolymers (HPs) or random copolymers (RCPs) with BCPs. Self-consistent field theory (SCFT) has been widely used to explore the phase behavior of these systems; however, its mean-field nature neglects fluctuations that can destabilize ordered structures. To address this limitation, Langevin field-theoretic simulation (L-FTS) incorporates fluctuations by sampling polymer fields that evolve according to the Langevin equation. A major challenge in using L-FTS to determine phase boundaries is hysteresis; metastable phases persist near transitions, complicating precise boundary identification. To mitigate this, we incorporate well-tempered metadynamics (WTMD), which gradually adds biasing potentials to discourage revisiting previously sampled states, thereby enabling a more accurate mapping of the phase boundary. In this study, we combine L-FTS with WTMD to investigate the effects of fluctuations on the order-to-disorder transition (ODT) in BCP melts blended with HPs or RCPs. Specifically, we quantify how variations in the invariant degree of polymerization shift the ODT, providing deeper insights into fluctuation-driven phase behavior.