Calibration of the Flory-Huggins Interaction Parameter in Field-Theoretic Simulations

Abstract

Field-theoretic simulations (FTS) offer a versatile method of dealing with complicated block copolymer systems, but unfortunately they struggle to cope with the level of fluctuations typical of experiments. Although the main obstacle, an ultraviolet (UV) divergence, can be removed by renormalizing the Flory-Huggins chi parameter, this only works for unrealistically large invariant polymerization indexes, N. Here, we circumvent the problem by applying the Morse calibration, where a nonlinear relationship between the bare chi_b used in FTS and the effective chi corresponding to the standard Gaussian-chain model (GCM) is obtained by matching the disordered-state structure function, S(k), of symmetric diblock copolymers to renormalized one-loop (ROL) predictions. This calibration brings the order-disorder transition (ODT) obtained from FTS into agreement with the universal results of particle-based simulations for values of N characteristic of experiment. In the limit of weak interactions, the calibration reduces to a linear approximation, chi ~ z chi_b, consistent with the previous renormalization of chi for large N.