Liquid–liquid equilibria (LLE) of polymer solutions are strongly influenced by molecular weight distributions and polymer architecture, yet most theoretical approaches treat polydispersity only at the mean-field level. While Lattice Cluster Theory (LCT) captures short-range correlations and architectural effects, existing formulations assume discrete components and cannot account for polydispersity within the excess Gibbs energy. In this work, a Continuous Lattice Cluster Theory (CLCT) is developed by embedding Continuous Thermodynamics directly into the multicomponent LCT framework. Discrete component sums in both the mean-field and excess Gibbs energy terms are replaced by integrals over continuous polymer distributions, such that polydispersity enters the entropic correction as well as the first- and second-order energy contributions through distribution moments, resulting in closed expressions for cloud-curve conditions and critical points for binary polymer–solvent LLE. Model calculations show that, in contrast to the LCT with continuous mean field approach, CLCT yields systematic shifts of critical points and qualitative changes in binodal topology with increasing polydispersity and branching, reflecting physically meaningful fractionation with respect to size and architecture. Applications to oligodimethylsiloxane–acetone and polystyrene–cyclohexane systems confirm that CLCT captures experimentally observed fractionation effects, particularly for highly polydisperse and branched polymers.
Singer et al. (2026) studied this question.