A group contribution method for associating chain molecules based on the statistical associating fluid theory (SAFT-)

A group contribution method for associating chain molecules based on the statistical associating fluid theory (SAFT-) The Journal of Chemical Physics 127, 234903 (2007) (2013)] is formulated within the framework of a group contribution approach (SAFT-γ Mie). Molecules are represented as comprising distinct functional (chemical) groups based on a fused heteronuclear molecular model, where the interactions between segments are described with the Mie (generalized Lennard-Jonesium) potential of variable attractive and repulsive range. A key feature of the new theory is the accurate description of the monomeric group-group interactions by application of a high-temperature perturbation expansion up to third order. The capabilities of the SAFT-γ Mie approach are exemplified by studying the thermodynamic properties of two chemical families, the n-alkanes and the n-alkyl esters, by developing parameters for the methyl, methylene, and carboxylate functional groups (CH 3 , CH 2 , and COO). The approach is shown to describe accurately the fluid-phase behavior of the compounds considered with absolute average deviations of 1.20% and 0.42% for the vapor pressure and saturated liquid density, respectively, which represents a clear improvement over other existing SAFT-based group contribution approaches. The use of Mie potentials to describe the group-group interaction is shown to allow accurate simultaneous descriptions of the fluid-phase behavior and second-order thermodynamic derivative properties of the pure fluids based on a single set of group parameters. Furthermore, the application of the perturbation expansion to third order for the description of the reference monomeric fluid improves the predictions of the theory for the fluid-phase behavior of pure components in the near-critical region. The predictive capabilities of the approach stem from its formulation within a group-contribution formalism: predictions of the fluid-phase behavior and thermodynamic derivative properties of compounds not included in the development of group parameters are demonstrated. The performance of the theory is also critically assessed with predictions of the fluid-phase behavior (vapor-liquid and liquid-liquid equilibria) and excess thermodynamic properties of a variety of binary mixtures, including polymer solutions, where very good agreement with the experimental data is seen, without the need for adjustable mixture parameters.

An application of the "top-down" concept for the development of accurate coarse-grained intermolecular potentials of complex fluids is presented. With the more common "bottomup" procedure, coarse-grained models are constructed from a suitable simplification of a fulldetailed atomistic representation, and minor adjustments to the intermolecular parameters are made by comparison with limited experimental data where necessary. By contrast in the top-down approach, a molecular-based equation of state is used to obtain an effective coarsegrained intermolecular potential that reproduces the macroscopic experimental thermophysical properties over a wide range of conditions. These coarse-grained intermolecular potentials can then be used in a conventional molecular simulation to obtain properties (such as structure or dynamics) that are not directly accessible from the equation of state or at extreme conditions where the theory is expected to fail. In order to demonstrate our procedure, a coarse-

In the first paper of this series [C. Avendaño, T. Lafitte, A. Galindo, C. S. Adjiman, G. Jackson, and E. A. Müller, J. Phys. Chem. B2011, 115, 11154] we introduced the SAFT-γ force field for molecular simulation of fluids. In our approach, a molecular-based equation of state (EoS) is used to obtain coarse-grained (CG) intermolecular potentials that can then be employed in molecular simulation over a wide range of thermodynamic conditions of the fluid. The macroscopic experimental data for the vapor-liquid equilibria (saturated liquid density and vapor pressure) of a given system are represented with the SAFT-VR Mie EoS and used to estimate effective intermolecular parameters that provide a good description of the thermodynamic properties by exploring a wide parameter space for models based on the Mie (generalized Lennard-Jones) potential. This methodology was first used to develop a simple single-segment CG Mie model of carbon dioxide (CO2) which allows for a reliable representation of the fluid-phase equilibria (for which the model was parametrized), as well as an accurate prediction of other properties such as the enthalpy of vaporization, interfacial tension, supercritical density, and second-derivative thermodynamic properties (thermal expansivity, isothermal compressibility, heat capacity, Joule-Thomson coefficient, and speed of sound). In our current paper, the methodology is further applied and extended to develop effective SAFT-γ CG Mie force fields for some important greenhouse gases including carbon tetrafluoride (CF4) and sulfur hexafluoride (SF6), modeled as simple spherical molecules, and for long linear alkanes including n-decane (n-C10H22) and n-eicosane (n-C20H42), modeled as homonuclear chains of spherical Mie segments. We also apply the SAFT-γ methodology to obtain a CG homonuclear two-segment Mie intermolecular potential for the more challenging polar and asymmetric compound 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf), a novel replacement refrigerant with promising properties. The description of the fluid-phase behavior and the prediction of the other thermophysical properties obtained by molecular simulation using our SAFT-γ CG Mie force fields are found to be of comparable quality (and sometimes superior) to that obtained using the more sophisticated all-atom (AA) and united-atom (UA) models commonly employed in the field. We should emphasize that though the focus of our current work is on simple homonuclear models, the SAFT-γ methodology is based on a group contribution methodology which is naturally suited to the development of more sophisticated heteronuclear models.

reported the phase behavior of monolayers of polymeric Brownian squares platelets. As the density is increased, this system exhibits the formation of two crystal structures not expected for particles with square symmetry, namely, a hexagonal rotator crystal phase and a rhombic crystal phase. Molecular simulations by Wojciechowski and Frenkel [Comp. Met. Sci. Technol., 2004 10, 235] had predicted instead the formation of tetratic and square crystal phases. In this work, we report Monte Carlo simulation results of rounded hard squares of varying degrees of roundness, hence interpolating between disks and perfect squares. Our simulations show that the roundness of the particles gives rise to the phases observed by Zhao et al. and further provide a roadmap for the regions of stability of different ordered phases as a function of particle roundness. In particular, our results suggest that depending on the degree of roundness, the isotropic phase would transition either into a hexagonal rotator phase through a hexatic-like intermediate, into a square phase through a tetratic-like intermediate, or (in a narrow range of crossover values of roundness) into a novel polycrystalline phase containing domains with square order in coexistence with clusters of particles having a weak hexagonal order.

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11154 (2011)] our methodology for the development of accurate coarse-grained (CG) SAFT-force fields for the computer simulation of molecular fluids was introduced with carbon dioxide as a particular case study. The procedure involves the use of a molecular-based equation of state to obtain effective intermolecular parameters (from experimental fluid phase equilibrium data) appropriate for molecular simulation over a wide range of fluid conditions. We now extend the methodology to develop coarse-grained models for benzene (C 6 H 6 ) that can be used in fluid phase simulations. Our SAFT-CG force fields for benzene consist of a simple single-segment spherical model, and a rigid three-segment ring structure of tangent spherical groups interacting via Mie (generalized Lennard-Jones) segment-segment interactions. The description of the fluid phase behaviour of benzene with our simplified CG force fields is found to be comparable to that obtained with the more sophisticated models commonly used in the field; a marked improvement is seen with our SAFTmodels for the vapour pressure, particularly at lower temperatures. These models of benzene together with the previously developed SAFT-three-segment chain model of n-decane are used to develop hetero-group force fields for n-decylbenzene, in the spirit of a group contribution methodology. In our approach, the parameters of the phenyl and n-decyl groups are obtained transferably from the individual models of benzene and n-decane, respectively, and the unlike energetic parameters between the phenyl and decyl segments can be obtained from vapour-liquid equilibria data for n-decylbenzene using the SAFT-equation of state. The resulting CG heterogroup models are found to describe the fluid properties of n-decylbenzene over a wide range of conditions, exemplifying how our approach can be used as a group contribution methodology. This is the first example of the development of hetero-group SAFT-force fields for molecules formed from Mie segments of different size, energy, softness/hardness, and range.

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