Predicting χ from Concentration Response to Spatially Varying Potentials

The excess free energy of mixing, parameterized by the Flory-Huggins χ parameter, dictates polymer phase behavior. We have developed a “push-pull” simulation method to measure the mixing free energy, first applied to regular solutions of small molecules. The method applies a spatially varying external potential to the molecules; in response, the system adopts a spatially varying concentration such that the total chemical potential is constant. In this work, we extend the push-pull method to polymers. For long polymers in push-pull simulations of manageable size, the square-gradient term in the free energy density contributes significantly to the local chemical potential. We develop a method to measure the coefficient of the square-gradient term, which is a microscopic length of order of the persistence length. We then validate the push-pull method by applying it to both bead-spring and chemically realistic polymer blends and comparing to χ values from our previously developed “morphing” technique. The new push-pull approach has two important advantages: (1) only one simulation is required, and (2) the chains need not be structurally similar, which enables prediction of χ for polymer blends with any chemical structure.