Thomas Lafitte

Accurate statistical associating fluid theory for chain molecules formed from Mie segments

A highly accurate equation of state (EOS) for chain molecules formed from spherical segments interacting through Mie potentials (i.e., a generalized Lennard-Jones form with variable repulsive and attractive exponents) is presented. The quality of the theoretical description of the vapour-liquid equilibria (coexistence densities and vapour pressures) and the second-derivative thermophysical properties (heat capacities, isobaric thermal expansivities, and speed of sound) are critically assessed by comparison with molecular simulation and with experimental data of representative real substances. Our new EOS represents a notable improvement with respect to previous versions of the statistical associating fluid theory for variable range interactions (SAFT-VR) of the generic Mie form. The approach makes rigorous use of the Barker and Henderson high-temperature perturbation expansion up to third order in the free energy of the monomer Mie system. The radial distribution function of the reference monomer fluid, which is a prerequisite for the representation of the properties of the fluid of Mie chains within a Wertheim first-order thermodynamic perturbation theory (TPT1), is calculated from a second-order expansion. The resulting SAFT-VR Mie EOS can now be applied to molecular fluids characterized by a broad range of interactions spanning from soft to very repulsive and short-ranged Mie potentials. A good representation of the corresponding molecular-simulation data is achieved for model monomer and chain fluids. When applied to the particular case of the ubiquitous Lennard-Jones potential, our rigorous description of the thermodynamic properties is of equivalent quality to that obtained with the empirical EOSs for LJ monomer (EOS of Johnson et al.) and LJ chain (soft-SAFT) fluids. A key feature of our reformulated SAFT-VR approach is the greatly enhanced accuracy in the near-critical region for chain molecules. This attribute, combined with the accurate modeling of second-derivative properties, allows for a much improved global representation of the thermodynamic properties and fluid-phase equilibria of pure fluids and their mixtures.

Simultaneous estimation of phase behavior and second-derivative properties using the statistical associating fluid theory with variable range approach.

A modified statistical associating fluid theory (SAFT) with variable range version is presented using the family of m-n Mie potentials. The use of this intermolecular potential for modeling repulsion-dispersion interactions between the monomer segments, together with a new method for optimizing the molecular parameters of the equation of state, is found to give a very accurate description of both vapor-liquid equilibria and compressed liquid bulk properties (volumetric and derivative properties) for long-chain n-alkanes. This new equation improves other SAFT-like equations of state which fail to describe derivative properties such as the isothermal compressibility and the speed of sound in the condensed liquid phase. Emphasis is placed on pointing out that the key for modeling the latter properties is the use of a variable repulsive term in the intermolecular potential. In the case of the n-alkanes series, a clear dependence of the characteristic molecular parameters on increasing chain length is obtained, demonstrating their sound physical meaning and the consistency of the new fitting procedure proposed. This systematic method for optimizing the model parameters includes data on the saturation line as well as densities and speed of sound data in the condensed liquid phase, and the results show undoubtedly that the model performance is enhanced and its range of applicability is now widened, keeping in any case a good balance between the accuracy of the different estimated properties.

Group contribution methodology based on the statistical associating fluid theory for heteronuclear molecules formed from Mie segments.

A generalization of the recent version of the statistical associating fluid theory for variable range Mie potentials [Lafitte et al., J. Chem. Phys. 139, 154504 (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 (CH3, CH2, 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.

Simultaneous Application of the Gradient Theory and Monte Carlo Molecular Simulation for the Investigation of Methane/Water Interfacial Properties

This work is dedicated to the simultaneous application of the gradient theory of fluid interfaces and Monte Carlo molecular simulations for the description of the interfacial behavior of the methane/water mixture. Macroscopic (interfacial tension, adsorption) and microscopic (density profiles, interfacial thickness) properties are investigated. The gradient theory is coupled in this work with the SAFT-VR Mie equation of state. The results obtained are compared with Monte Carlo simulations, where the fluid interface is explicitly considered in biphasic simulation boxes at both constant pressure and volume (NPT and NVT ensembles), using reliable united atom molecular models. On one hand, both methods provide very good estimations of the interfacial tension of this mixture over a broad range of thermodynamic conditions. On the other hand, microscopic properties computed with both gradient theory and MC simulations are in very good agreement with each other, which confirms the consistency of both approaches. Interfacial tension minima at high pressure and prewetting transitions in the vicinity of saturation conditions are also investigated.

SAFT-γ Force Field for the Simulation of Molecular Fluids: 2. Coarse-Grained Models of Greenhouse Gases, Refrigerants, and Long Alkanes

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.

Interfacial Properties of Water/CO2: A Comprehensive Description through a Gradient Theory−SAFT-VR Mie Approach

The Gradient Theory of fluid interfaces is for the first time combined with the SAFT-VR Mie EOS to model the interfacial properties of the water/CO(2) mixture. As a preliminary test of the performance of the coupling between both theories, liquid-vapor interfacial properties of pure water have been determined. The complex temperature dependence of the surface tension of water can be accurately reproduced, and the interfacial thickness is in good agreement with experimental data and simulation results. The water/CO(2) mixture presents several types of interfaces as the liquid water may be in contact with gaseous, liquid, or supercritical CO(2). Here, the interfacial tension of the water/CO(2) mixture is modeled accurately by the gradient theory with a unique value of the crossed influence parameter over a broad range of thermodynamic conditions. The interfacial density profiles show a systematic adsorption of CO(2) in the interface. Moreover, when approaching the saturation pressure of CO(2), a prewetting transition is highlighted. The adsorption isotherm of CO(2) is computed as well in the case of a gas/liquid interface and compared with experimental data. The good agreement obtained is an indirect proof of the consistency of interfacial density profiles computed with the gradient theory for this mixture and confirms that the gradient theory is suitable and reliable to describe the microstructure of complex fluid interfaces.

SAFT-γ force field for the simulation of molecular fluids: 3. Coarse-grained models of benzene and hetero-group models of n-decylbenzene

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. B 115, 11154 (2011)] our methodology for the development of accurate coarse-grained (CG) SAFT-γ 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 (C6H6) that can be used in fluid phase simulations. Our SAFT-γ 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 SAFT-γ models for the vapour pressure, particularly at lower temperatures. These models of benzene together with the previously developed SAFT-γ 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-γ equation of state. The resulting CG hetero-group 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-γ force fields for molecules formed from Mie segments of different size, energy, softness/hardness, and range.

Interfacial properties of the Mie n−6 fluid: Molecular simulations and gradient theory results

In a first part, interfacial properties of a pure monoatomic fluid interacting through the Mie n-6 potential (n=8, 10, 12, and 20) have been studied using extensive molecular simulations. Monte Carlo and molecular dynamics simulations have been employed, using, respectively, the test area approach and the mechanic route. In order to yield reference values, simulations have been performed with a cutoff radius equal to 10sigma, which is shown to be sufficient to avoid long range corrections. It is shown that both approaches provide results consistent with each other. Using the molecular simulations results, it is demonstrated that a unique scaling law is able to provide an accurate estimation of the surface tension whatever the repulsive exponent n, even far from the critical point. Furthermore, it is shown that the surface tension of the Mie n-6 fluid is as well accurately described by a unique Parachors law. Density profiles are shown to be well represented by the tanh mean field profile, with slight deviations for the lowest temperatures and the smallest n. In addition, the interfacial width is shown to increase when n decreases (for a given reduced temperature) and to follow the usual scaling behavior for not too low temperature. In a second part, interfacial properties of the Mie n-6 fluid computed by the gradient theory, coupled with an equation of state based on the Barker-Henderson perturbation theory, have been compared with those obtained by molecular simulations. It is demonstrated that, even far from the critical point, the gradient theory is efficient to compute surface tensions and density profiles of this model fluid, provided the equation of state accurately model the phase behavior of the fluid involved (which is not the case for n=8 in this study).

SAFT-γ force field for the simulation of molecular fluids: 4. A single-site coarse-grained model of water applicable over a wide temperature range

In this work, we develop coarse-grained (CG) force fields for water, where the effective CG intermolecular interactions between particles are estimated from an accurate description of the macroscopic experimental vapour–liquid equilibria data by means of a molecular-based equation of state. The statistical associating fluid theory for Mie (generalised Lennard-Jones) potentials of variable range (SAFT-VR Mie) is used to parameterise spherically symmetrical (isotropic) force fields for water. The resulting SAFT-γ CG models are based on the Mie (8-6) form with size and energy parameters that are temperature dependent; the latter dependence is a consequence of the angle averaging of the directional polar interactions present in water. At the simplest level of CG where a water molecule is represented as a single bead, it is well known that an isotropic potential cannot be used to accurately reproduce all of the thermodynamic properties of water simultaneously. In order to address this deficiency, we propose two CG potential models of water based on a faithful description of different target properties over a wide range of temperatures: our CGW1-vle model is parameterised to match the saturated-liquid density and vapour pressure; our other CGW1-ift model is parameterised to match the saturated-liquid density and vapour–liquid interfacial tension. A higher level of CG corresponding to two water molecules per CG bead is also considered: the corresponding CGW2-bio model is developed to reproduce the saturated-liquid density and vapour–liquid interfacial tension in the physiological temperature range, and is particularly suitable for the large-scale simulation of bio-molecular systems. A critical comparison of the phase equilibrium and transport properties of the proposed force fields is made with the more traditional atomistic models.

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

An accurate representation of molecular association is a vital ingredient of advanced equations of state (EOSs), providing a description of thermodynamic properties of complex fluids where hydrogen bonding plays an important role. The combination of the first-order thermodynamic perturbation theory (TPT1) of Wertheim for associating systems with an accurate description of the structural and thermodynamic properties of the monomer fluid forms the basis of the statistical associating fluid theory (SAFT) family of EOSs. The contribution of association to the free energy in SAFT and related EOSs is very sensitive to the nature of intermolecular potential used to describe the monomers and, crucially, to the accuracy of the representation of the thermodynamic and structural properties. Here we develop an accurate description of the association contribution for use within the recently developed SAFT-VR Mie framework for chain molecules formed from segments interacting through a Mie potential [T. Lafitte, A. Apostolakou, C. Avendaño, A, Galindo, C. S. Adjiman, E. A. Müller, and G. Jackson, J. Chem. Phys. 139, 154504 (2013)]. As the Mie interaction represents a soft-core potential model, a method similar to that adopted for the Lennard-Jones potential [E. A. Müller and K. E. Gubbins, Ind. Eng. Chem. Res. 34, 3662 (1995)] is employed to describe the association contribution to the Helmholtz free energy. The radial distribution function (RDF) of the Mie fluid (which is required for the evaluation of the integral at the heart of the association term) is determined for a broad range of thermodynamic conditions (temperatures and densities) using the reference hyper-netted chain (RHNC) integral-equation theory. The numerical data for the association kernel of Mie fluids with different association geometries are then correlated for a range of thermodynamic states to obtain a general expression for the association contribution which can be applied for varying values of the Mie repulsive exponent. The resulting SAFT-VR Mie EOS allows for a much improved description of the vapour-liquid equilibria and single-phase properties of associating fluids such as water, methanol, ammonia, hydrogen sulphide, and their mixtures. A comparison is also made between the theoretical predictions of the degree of association for water and the extent of hydrogen bonding obtained from molecular simulations of the SPC/E and TIP4P/2005 atomistic models.