Beyond Flory-Huggins: Activity Coefficients from Perturbation Theory for Polar, Polarizable, and Associating Solvents to Polymers

We present a general relationship for the excess chemical potential that enables the development of activity coefficient models from free energy perturbation theory. We reveal the simple basis and approximations implicit in the Flory-Huggins theory and explain, apparently for the first time, the accuracy of the approach when there is a volume change on mixing. The result has implications in coarse-graining strategies for mesoscale modeling. Further, we present corrections for molecular size and shape as well as multiple association (hydrogen bonding) sites, multiple polar functional groups, and polarizability based on the statistical associating fluid theory (SAFT) equation of state and on the dipolar chain theory. The result is a general activity coefficient model with realistic molecular interactions. We present detailed equations for each chemical potential contribution in a SAFT activity coefficient model (SAFT-AC). Depending on the choice of mixing conditions, multiple terms can be made to cancel in the derivation and a simple activity coefficient model (SAFT-SAC) can be derived. Applications of SAFT-AC and SAFT-SAC are shown for mixtures containing polar, polarizable, and associating components. There are several advantages to the new approach to activity coefficient models. The model is applicable from solvents to polymers, each with multiple polar and hydrogen bonding functional groups. Each contribution from perturbation theory has been validated in comparison with molecular simulation results so that the accuracy of the model is known, and the model should extrapolate accurately beyond the range of fit. Further, the model is consistent with bulk equations of state, in this case, polar SAFT models, so that there is a smooth transition from the activity coefficient approach to the fugacity coefficient approach when necessary. The model derivation clearly defines approximations and conditions when the activity coefficient approach is valid so that a process simulation package can identify when to switch from an activity coefficient approach to a fugacity coefficient approach. Because of the direct connection to statistical mechanics-based theory, improvements of the activity coefficient model and extensions to other systems, including self-assembling systems, can be relatively straightforward. Since parameters in the model are the same as in SAFT models and related to models used in molecular simulations, this approach provides an opportunity to link workflows of activity coefficient models to equations of state and to molecular simulations and mesoscale models.