Fouad, W. A., Khalifa University of Science and Technology
We present a general relationship for excess chemical potential that enables development of activity coefficient models from free energy perturbation theory. We previously showed that the Flory configurational contribution is a simple ideal gas term. Based on the Polar SAFT equation of state, we explain the approximations necessary in Flory-Huggins theory and present corrections for molecular size and shape as well as multiple polar functional groups, polarizability, and multiple association sites. The result is a general activity coefficient model with realistic molecular interactions. We present detailed equations for each term of the model as a SAFT activity coefficient model (SAFT-AC). Depending on the choice of mixing conditions, a simplified model can be derived. We further present a much simpler, segment based activity coefficient model (SAFT-SAC) in which we choose mixing conditions so that multiple terms cancel in the derivation, resulting in a simplified activity coefficient model. Applications of SAFT-AC and SAFT-SAC are shown for mixtures of non-polar molecules with polar, polarizable, and associating components. Approximations and other issues implicit in previous models are also addressed.
There are several advantages in the new approach to activity coefficient models. The model explicitly includes the effects of multiple polar functional groups, multiple hydrogen bonding sites, and polarity as well as molecular size and shape so that the model is applicable to molecules from solvents to polymers. Further, the model is consistent with bulk equations of state, in this case polar SAFT models, so that there is a smooth transition from activity coefficient approach to fugacity coefficient approach when necessary. The model derivation clearly shows when approximations for the activity coefficient approach are 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 is relatively straightforward.
