Adapting SAFT-γ Perturbation Theory to Site-Based Molecular Dynamics Simulation: An Application to Homogeneous and Inhomogeneous Systems

Molecular simulation has become an indispensable tool in developing theories to describe fluid properties. Ideally, atomistic detail applied in the simulation is sufficient to characterize the properties of interest and theories are refined until they are consistent with the details of the simulations. Currently, the leading theory in the prediction of fluid properties is Statistical Associating Fluid Theory (SAFT). Equations of states (EOSs) based on SAFT, which benefit from Wertheim's first order Thermodynamic Perturbation Theory (TPT1), reproduce molecular simulation results and provide an analytical equation that facilitates interpolation and extrapolation of fluid properties on much shorter time scales than full potential molecular simulation.

In its original form, and most subsequent forms, SAFT assumed that polyatomic species were composed of tangent sphere segments. Although this form was shown to agree reasonably well with simulations of tangent hard sphere chains, significant discrepancies arise when compared to simulations of more realistic molecular models such as fused soft-sphere chains. One particular implementation of SAFT that ostensibly includes atomistic detail in fused chain description of molecules is the SAFT-γ EOS (Lymperiadis, J. Chem. Phys. 127, 234903 (2007)). The SAFT-γ model assigns an interaction site to each site-type in a united-atom characterization of the molecule. This level of description is consistent with molecular simulations based on transferable force fields such as the TraPPE-UA model. However, characteristic repulsive and attractive adjustable parameters of SAFT-γ EOS are fitted to experimental bulk fluid properties. Therefore, an agreement at the atomistic level with molecular simulation is not guaranteed. In fact, we demonstrate that there will be significant deviations between simulation and theory when reference and perturbation contributions of EOS are lumped together and fitted to experimental data.

In this context, we seek to develop a form of SAFT-γ EOS such that molecular simulations - based on transferable and united atom force fields - can be checked for consistency with SAFT-γ predictions. While our objective is a theory of interfacial properties, we find it necessary to first elucidate the details of the SAFT-γ approach in terms of site-based simulations for homogeneous fluids. Once these details are well-defined at the bulk level, we adopt classical density functional theory (DFT) to address the interfacial properties. DFT involves estimating the Helmholtz energy at intermediate densities between the vapor and the liquid, in other words, at thermodynamically unstable points inside the binodal. This step requires that the EOS be accurate in order for extrapolation inside the binodal to provide meaningful results. We aim to establish that accuracy based on homogeneous (bulk) fluids, then to test the extrapolations based on molecular simulations of inhomogeneous fluids.

We apply the rapidly convergent Weeks-Chandler-Andersen (WCA) perturbation theory to investigate the properties of softly repulsive reference fluids for realistic and fused models of polyatomic molecules. The SAFT-γ methodology plays an important role in developing a master curve for each reference fluid that can be applied to multiple temperatures and multiple values of the well-depth parameter (ε). Once the reference fluid is characterized, we turn our attention to the perturbation contributions. In particular, we compute perturbation terms for multiple chain lengths rather than simply extrapolating corresponding contributions of spherical molecules, finding that such extrapolations are not entirely reliable. Consistent with recent work by Jackson and coworkers (Avendano, J. Phys. Chem. B 2013, 117, 2717-2733), we find that inclusion of the third order term substantially improves accuracy in the critical region, noting that this accuracy is important for interfacial properties.

The resulting EOS takes force field parameters (σ and ε) as input variables and has no binary interaction parameter for united-atom site-site interactions. Finally, we validate our adaptation of SAFT-γ with extensive comparisons to site-based molecular simulations of the full potential force fields such as TraPPE-UA, OPLS and NERD. The results show satisfactory agreement between EOS and simulation for the entire phase diagram including the critical point region. For example, the deviation of predicted liquid density and vapor pressure of n-alkanes from methane to n-dodecane compared to those of TraPPE-UA force field is less than 1% and 6%, respectively. The same level of agreement is also obtained for mixtures and derivative properties such as heat capacity. Furthermore, the density profile of monomers and mixtures of fused soft chain molecules against a hard wall as well as in confined systems are predicted by SAFT-γ + DFT EOS and compared to atomistic molecular simulation of real molecules. Excellent agreement with simulation is achieved not only for center of mass density profiles but also for each united-atom site type comprising the molecular structure of studied compounds. Surface tension, adsorption isotherms, and atomistic density profiles of real substances and their mixtures at planar vapor-liquid interfaces are also predicted and compared to molecular simulation with reasonable agreement.

In summary, we can show that a robust comparison between theory and simulation at the development stage can lead to an EOS that is consistent with molecular simulation of transferable united-atom force fields for both homogeneous and inhomogeneous systems. The resulting EOS would inherit many advantages of molecular simulation while facilitates engineering applications with imposing very short time scales for calculation process. Also, the direct correspondence between EOS and simulation can be recognized as a valuable tool to further optimize force field parameters efficiently for the system of interest.