Langevin Field Theoretic Simulation on the Order to disorder Transition of Frank Kasper Phases

Abstract

Frank-Kasper (FK) phases are spherical phases with low symmetry, and their formation is experimentally reported for conformationally asymmetric diblock copolymers. Several theoretical works using self-consistent field theory (SCFT) also predict the emergence of FK phases. However, SCFT does not consider the effect of the compositional fluctuation, which is known to change the nature of the order-to-disorder transition (ODT). Because of this, direct transition from disordered phase to FK phases has not been theoretically predicted, even though it is commonly observed in experiments. In order to understand the nature of ODTs, we perform Langevin field theoretic simulation (L-FTS), which samples the ensemble of polymers so that the effect of compositional fluctuation can be accounted for after enough time steps of simulation. Until now, this method was not feasible to study FK phases due to the large unit cell size and high computational cost. With recently developed L-FTS library accelerated by deep learning, we examine the ODT positions of σ, A15, C15 and C14 phases at various parameter values. We find that direct ODT from disordered phase to some FK phases are possible at high enough fluctuation level, which was reported in recent experiments.