Universality of the Perturbative Definition of the Flory-Huggins Parameter

Coarse-grained computer modeling is one of the primary tools for the discovery and optimization of polymeric materials. However, it is very hard to relate the parameters of a coarse-grained model to the experimentally relevant quantities. This correspondence can be potentially built using the so-called universality hypothesis; however, the key unresolved obstacle to applying this approach is obtaining the analytical definition of the effective Flory-Huggins parameter χ_e that yields the universal behavior of all coarse-grained models.

In this work, we show that a perturbative approach to χ_e as a function of parameters of an arbitrary coarse-grained polymer model gives excellent agreement among models. Surprisingly, the only quantity parametrizing this expression is the probability distribution of the effective coordination number in the reference homogeneous system. By performing extensive simulations, we showed that our definition of χ_e is able to yield the universal behavior of all studied coarse-grained models of different two-component polymer systems. As a result, we also provided support for the universality hypothesis itself without a priori assumptions. The simplicity and universality of our definition of χ_e can enable researchers to easily and quantitatively predict experiments using coarse-grained modeling, which will facilitate the computational design of multicomponent polymer materials.