Modeling of the branching influence on liquid-liquid equilibrium of binary and ternary polymer solutions by lattice-cluster theory

► Liquid-liquid equilibrium (LLE) is calculated with the lattice-cluster theory (LCT). ► Equations of the LCT are reduced to only three geometrical parameters. ► Branching influence on the LLE is modeled for binary and ternary polymer solutions. ► Branched and linear solvents and polymers are compared in their influence on LLE. ► Solutions of branched polymers in branched solvents show the best miscibility.