Universality of the perturbative definition of the Flory-Huggins parameter

Abstract

The effective Flory-Huggins parameter χe 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 χe depends on the details of an arbitrary coarse-grained polymer model. After defining χe 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 N¯, and the interaction parameter χeN. To parametrize our perturbative expression for χe, 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 χe. Our definition of χe enables straightforward quantitative comparison of models with each other and with experiments, which will facilitate the computational design of multicomponent polymer materials.