The effective Flory-Huggins parameter ${\chi }_e$ is one of the most important characteristics of any multicomponent polymer system. This parameter characterizes the free energy of interaction between monomers of different types and controls the phase behavior of polymer mixtures. In this work, we developed a perturbation theory and derived how ${\chi }_e$ depends on the details of an arbitrary coarse-grained polymer model. After defining ${\chi }_e$ in this way, we found that the models of symmetric polymer blends and diblock copolymer melts behaved universally: Their phase transition points, free energies, and mesoscopic invariant structure factors depended solely on the chain architecture, the invariant chain length $\overline{N}$, and the interaction parameter ${\chi }_{e}N$. To parametrize our perturbative expression for ${\chi }_e$, only the effective coordination number distribution in a reference homogeneous system needs to be measured. This distribution, in turn, can be directly mapped onto coarse-grained model parameters set prior to simulation, which clarifies how model construction influences ${\chi }_e$. Our definition of ${\chi }_e$ enables straightforward quantitative comparison of models with each other and with experiments, which will facilitate the computational design of multicomponent polymer materials.

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• Phase behavior
• Phase separation
• Block copolymers
• Polymer blends
• Coarse graining
• Molecular dynamics
• Perturbative methods
• Polymer theory