Accurate Universal Predictions for Block Copolymer Melts Using Field-Theoretic Simulations
M. W. Matsen, James D. Willis, T. M. Beardsley
Abstract
Langevin field-theoretic simulations (L-FTSs) have recently evaluated complete phase diagrams for diblock copolymer melts [Matsen et al., Phys. Rev. Lett. 2023, 130, 248101], but they involve a partial saddle-point approximation (PSPA). Although previous complex-Langevin field-theoretic simulations (CL-FTSs) calculated complete phase diagrams without the PSPA [Delaney and Fredrickson, J. Phys. Chem. B 2016, 120, 7615], the diagrams disagree with experiments. We find evidence attributing this to nonuniversal behavior resulting from long-range interactions used to remove an ultraviolet divergence. Therefore, we perform CL-FTSs on symmetric diblocks with contact interactions and use the renormalization procedure employed in the L-FTSs. This successfully removes the divergence and restores the universality, but, without the long-range interactions, the fields have a tendency to form intense delta-like “hot spots”, causing the CL-FTSs to fail. Nevertheless, we find good agreement between the CL-FTSs and L-FTSs over the parameter space where the CL-FTSs are sufficiently well behaved. This implies that the renormalization compensates for the inaccuracy of the PSPA, thereby imparting L-FTSs with the ability to provide accurate universal predictions for block copolymer melts of high molecular weight.