Efficient calculation of χ parameters for polymer interactions from simulation

The χ-parameter is a classic parameter used to describe the thermodynamics of polymeric systems, and its accurate determination is a bottleneck for applying coarse grained theoretical and simulation methods to real chemical systems. Usually, the χ parameter is characterized in the long chain length limit using the Random Phase Approximation, where fluctuations contributions are expected to be small, and much theory has been developed to characterize fluctuation effects associated with finite chain lengths. Unfortunately, to date the chain lengths required to accurately determine the χ parameter are only accessible to experiment and simplified, coarse-grained theoretical models of polymers. As such, there is much active research to develop alternative methods of determining χ in atomistically-detailed models, such as via free energy calculations. In this talk, we present impacts of chain length on estimates of the χ parameter from atomistic simulations. Using insights from the renormalized one-loop theory for diblock copolymers, we demonstrate an approach where we can accurately determine the χ parameter from short-chain simulations, and robustly extrapolate to the long chain limit. We demonstrate our approach an an array of real chemical systems, and compare to experimental and prior computational estimates of the χ-parameter. Our approach greatly reduces the chain lengths and computational cost required to accurately determine χ from simulations, and sets the stage for future, massive computational screening and determination of χ-parameters.