Modeling the Thermodynamic Properties of Saturated Lactones in Nonideal Mixtures with the SAFT-γ Mie Approach.

The prediction of the thermodynamic properties of lactones is an important challenge in the flavor, fragrance, and pharmaceutical industries. Here, we develop a predictive model of the phase behavior of binary mixtures of lactones with hydrocarbons, alcohols, ketones, esters, aromatic compounds, water, and carbon dioxide. We extend the group-parameter matrix of the statistical associating fluid theory SAFT-γ Mie group-contribution method by defining a new cyclic ester group, denoted cCOO. The group is composed of two spherical Mie segments and two association electron-donating sites of type e1 that can interact with association electron-accepting sites of type H in other molecules. The model parameters of the new cCOO group interactions (1 like interaction and 17 unlike interactions) are characterized to represent target experimental data of physical properties of pure fluids (vapor pressure, single-phase density, and vaporization enthalpy) and mixtures (vapor-liquid equilibria, liquid-liquid equilibria, solid-liquid equilibria, density, and excess enthalpy). The robustness of the model is assessed by comparing theoretical predictions with experimental data, mainly for oxolan-2-one, 5-methyloxolan-2-one, and oxepan-2-one (also referred to as γ-butyrolactone, γ-valerolactone, and ε-caprolactone, respectively). The calculations are found to be in very good quantitative agreement with experiments. The proposed model allows for accurate predictions of the thermodynamic properties and highly nonideal phase behavior of the systems of interest, such as azeotrope compositions. It can be used to support the development of novel molecules and manufacturing processes.

The Contribution of the Ion-Ion and Ion-Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions.

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye-Hückel (DH) theory to account for ion-ion interactions and, often, the Born theory of solvation for ion-solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion-ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion-ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion-solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state.

A methodology for obtaining molecular parameters of a modified statistical associating fluid theory for variable-range interactions of Mie form (SAFT-VR Mie) equation of state (EoS) from ab initio calculations is proposed for non-associative species that can be modeled as single spherical segments. The methodology provides a strategy to map interatomic or intermolecular potentials obtained from ab initio quantum-chemistry calculations to the corresponding Mie potentials that can be used within the SAFT-VR Mie EoS. The inclusion of corrections for quantum and many-body effects allows for an excellent, fully predictive description of the vapor-liquid envelope and other bulk thermodynamic properties of noble gases; this description is of similar or superior quality to that obtained using SAFT-VR Mie with parameters regressed in the traditional way using experimental thermodynamic-property data. The methodology is extended to an anisotropic species, methane, where similar levels of accuracy are obtained. The efficacy of using less-accurate quantum-chemistry methods in this methodology is explored, showing that these methods do not provide satisfactory results, although we note that the description is nevertheless substantially better than those obtained using the conductor-like screening model for describing real solvents (COSMO-RS), the only other fully predictive ab initio method currently available. Overall, the reliance on thermophysical data is completely dispensed with, providing the first extensible, wholly predictive SAFT-type EoSs.

Continuum-scale modelling of polymer blends using the Cahn-Hilliard equation: transport and thermodynamics.

The Cahn-Hilliard equation is commonly used to study multi-component soft systems such as polymer blends at continuum scales. We first systematically explore various features of the equation system, which give rise to a deep connection between transport and thermodynamics-specifically that the Gibbs free energy of mixing function is central to formulating a well-posed model. Accordingly, we explore how thermodynamic models from three broad classes of approach (lattice-based, activity-based and perturbation methods) can be incorporated within the Cahn-Hilliard equation and examine how they impact the numerical solution for two model polymer blends, noting that although the analysis presented here is focused on binary mixtures, it is readily extensible to multi-component mixtures. It is observed that, although the predicted liquid-liquid interfacial tension is quite strongly affected, the choice of thermodynamic model has little influence on the development of the morphology.

An investigation of free-energy-averaged (coarse-grained) potentials for fluid adsorption on heterogeneous solid surfaces.

Coarse-grained, two-body fluid-solid potentials provide a simple way to describe the interaction between a fluid molecule and a solid in adsorption theories, and also a means to reduce the computational expense in molecular simulations, compared to those employing full atomistic detail. Here we investigate the applicability of a recently proposed mapping procedure to obtain free-energy-averaged (FEA) fluid-solid interactions for fluids on various heterogeneous surfaces. Methane and graphite are chosen as the fluid and the solid, respectively, and the surface graphene layer is modified to create chemical and geometrical heterogeneities; for the latter surfaces, the FEA mapping is appropriately modified to account for vacancies. Adsorption isotherms and fluid density profiles are obtained by performing grand canonical Monte Carlo (GCMC) simulations for explicit-solid and FEA-potential representations, and are compared to gain insights about the applicability and limitations of the FEA potentials. For solids with homogeneous and chemically heterogeneous surfaces, adsorption isotherms and density profiles obtained using FEA potentials are in good agreement with those obtained using an explicit-solid representation. For surfaces containing vacancies, isotherms and density profiles obtained using the unmodified FEA potential differ significantly from their explicit-surface analogues. When using the FEA potential obtained with the modified mapping procedure some deviations are still seen at very high pressure, however, at low to moderate pressures, agreement is, once again, good.

Structure and Interfacial Tension of a Hard-Rod Fluid in Planar Confinement.

The structural properties and interfacial tension of a fluid of rodlike hard-spherocylinder particles in contact with hard structureless flat walls are studied by means of Monte Carlo simulation. The calculated surface tension between the rod fluid and the substrate is characterized by a nonmonotonic trend as a function of the bulk concentration (density) over the range of isotropic bulk concentrations. As suggested by earlier theoretical studies, a surface-ordering scenario is confirmed by our simulations: the local orientational order close to the wall changes from uniaxial to biaxial nematic when the bulk concentration reaches about 85% of the value at the onset of the isotropic-nematic phase transition. The surface ordering coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension, the adsorption, and the average particle-wall contact distance are reported (over a broad range of densities into the dense nematic region for the first time), which can serve as a useful benchmark for future theoretical and experimental studies on confined rod fluids. The simulation data are supplemented with predictions from second-virial density functional theory, which are in good qualitative agreement with the simulation results.

Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal.

The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

Effective coarse-grained solid-fluid potentials and their application to model adsorption of fluids on heterogeneous surfaces.

The use of effective fluid-surface potentials, in which the full positional dependence is replaced by a dependence only on the distance from the surface of the solid, is common practice as a route to reduce the complexity of evaluating adsorption of fluids on substrates. Conceptually this is equivalent to replacing the detailed description of the discrete molecular nature by a coarse-grained description in which the solid is represented by a continuous (structureless) surface. These effective fluid-surface potentials are essential in the development of theories for surface adsorption, and they provide a means to reduce the computational cost associated with the molecular simulation of the system. The main purpose of the present contribution is to emphasise the necessity of using an adequate averaging procedure to obtain effective fluid-surface potentials. A simple unweighted average of the configurational energy is commonly employed, resulting in effective potentials that are temperature independent. We describe here a procedure to develop free-energy-averaged effective fluid-surface potentials retaining the important temperature dependence of the coarse-grained interaction between the particle and the surface. Although the approach is general in nature, we assess the merits of free-energy-averaged potentials for the adsorption of methane on graphene and graphite, making appropriate comparisons with the description obtained with the more traditional temperature-independent potentials. Additionally, we develop effective fluid-surface potentials for crystalline faces of monolayer and multilayer homogeneous and heterogeneous fcc lattices based on the Lennard-Jones (12-6) pair potential, and compute the corresponding adsorption isotherms of Lennard-Jones fluids on these surfaces using Grand Canonical Monte Carlo (GCMC) simulations. The adequacy of the two different options to obtain effective fluid-surface potentials (a free-energy-based versus a simple unweighted average) is compared critically. It is shown here that the higher the heterogeneity of the surface the less adequate simple unweighted averages are to describe the adsorption behaviour in comparison to free-energy averages.

New methods for calculating the free energy of charged defects in solid electrolytes.

A methodology for calculating the contribution of charged defects to the configurational free energy of an ionic crystal is introduced. The temperature-independent Wang-Landau Monte Carlo technique is applied to a simple model of a solid electrolyte, consisting of charged positive and negative defects on a lattice. The electrostatic energy is computed on lattices with periodic boundary conditions, and used to calculate the density of states and statistical-thermodynamic potentials of this system. The free energy as a function of defect concentration and temperature is accurately described by a regular solution model up to concentrations of 10% of defects, well beyond the range described by the ideal solution theory. The approach, supplemented by short-ranged terms in the energy, is proposed as an alternative to free energy methods that require a number of simulations to be carried out over a range of temperatures.