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 chi(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 chi(ij) parameters and the sensitivity of the resulting phase behavior when the chi(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) (SISO) tetrablock terpolyrner changes depending on the method used to estimate the trio of chi(ij) parameters for this chemistry. SISO 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 chi(SO) and chi(IO), accompanied by subtle matrix segregation effects arising due to the smaller chi is between poly(isoprene) and poly (styrene). We first use chi(IS), chi(IO), and chi(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 chi(ij) that propagate into the SCFT predictions, we also consider two fluctuation-corrected approaches to extract chi(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 chi parameters do not lead to SCFT phase behavior that exactly matches experiments, the SCFT calculations using the molecular dynamics-fitted chi parameters correctly predict stable Frank-Kasper A15 and sigma 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.