Phase Behavior of Conjugated Polymer Solutions and Blends: The Flory–Huggins Lattice Model

Abstract

The phase equilibria of binary conjugated polymer/fullerene (or nonfullerene) have been described by the Flory–Huggins model. However, when the interaction parameter χ was used as a fitting function, the chain length was only considered for polymer, indicating the fullerene or nonfullerene small-molecule acceptor (FA or NFA) occupies one cell of the lattice. This method usually results in a large critical parameter, e.g., χ_c > 0.5, in polymer solutions. Hence, in this study, we demonstrate first that the cell size should be determined by the molar volume of the processing solvent. Then the acceptor molecule should be treated as an “oligomer” based on its larger molecular size compared with the solvent, causing one-order smaller χ_c parameter. Second, for χ = a/T + b, the pair-contact energy-relevant term “a” was obtained from the solubility parameter approach, whereas the entropic term “b” could be +0.34 or another fitting variable for polymer blend, leading to a quantitative interpretation of binodal. For this purpose, PM6:Y6, PCDTBT:PC₇₁BM, and others were studied as model systems. This research may provide fundamental insights into improving our understanding of the phase equilibria and microphase separation in the polymer/NFA mixtures for organic photovoltaics.