(148a) Adapting SAFT-? 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.