Predicting the phase behavior of ABAC tetrablock terpolymers: Sensitivity to Flory–Huggins interaction parameters

Self-consistent field theory (SCFT) is a powerful tool for discovering new nanostructures in self-assembling block polymers. However, the reliability of the resulting predictions depend strongly on the Flory-Huggins interaction parameters χ_ij used to quantify the excess free energy of mixing of different blocks i and j arising from segment-segment interactions. The problem is especially significant for multiblock polymers, owing to the multitude of χ_ij parameters and the sensitivity of the resulting phase behavior when the χ_ij do not differ substantially for different block pairs. To illuminate this issue, we examine how the SCFT-predicted phase behavior of a poly(styrene)-b-poly(isoprene)-b-poly(styrene)’-b-poly(ethylene oxide) (SIS'O) tetrablock terpolymer changes depending on the method used to estimate the trio of χ_ij parameters for this chemistry. SIS'O is an ideal model system for our purposes, as it exhibits a large number of poly(ethylene oxide) sphere-forming phases, emerging from the segregation of the poly(ethylene oxide) block due to the relatively high values of χ_SO and χ_IO, accompanied by subtle matrix segregation effects arising due to the smaller χ_IS between poly(isoprene) and poly(styrene). We first use χ_IS, χ_IO, and χ_SO available in the literature that were estimated using mean-field theory order–disorder transitions of the relevant diblock polymers. As this method is expected to lead to significant errors in χ_ij that propagate into the SCFT predictions, we also consider two fluctuation-corrected approaches to extract χ_ij from diblock polymer data, namely (i) fitting the order-disorder transition temperature to that predicted by molecular dynamics simulations and (ii) renormalized one-loop theory predictions for the structure factor of the disordered state. While even the fluctuation-corrected χ parameters do not lead to SCFT phase behavior that exactly matches experiments, the SCFT calculations using the molecular dynamics-fitted χ parameters correctly predict stable Frank–Kasper A15 and σ phases. The results presented here highlight the challenges in predictively modeling the phase behavior of multiblock polymers using SCFT, a critical task for the discovery of new multiblock polymer materials.