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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. [ABSTRACT FROM PUBLISHER]

In this contribution we provide a review and reformulation of perturbation theories (generalised van der Waals approaches) for the description of the fluid phase behaviour and orientational ordering transitions of thermotropic nematic liquid crystals. Free-energy functionals of the basic Onsager form are used as the platform for the development of a general formulation that reduces to the specific forms of the various theories that have found common use. A novel closed analytical description of the thermodynamic properties and degree of nematic order is then obtained by employing the Onsager trial function to represent the orientational distribution function in terms of a single parameter. The latter essentially constitutes an algebraic equation of state for the nematic phase appropriate for use in engineering applications. The description of ordering transitions with scaled-Onsager theories and suitable trial functions has already been illustrated by its application to systems of hard spherocylinders (HSCs), indicating that the approach provides an excellent representation of the orientational order of the hard-core (athermal) system [Mol. Phys. 106, 649 (2008)]. Here, the hard-body model is extended to account for attractive interactions (treated at the van der Waals level) of a general isotropic/anisotropic form (e.g., Lennard-Jonesium (LJ), square-well (SW), Maier-Saupe (MS), etc.). The adequacy of our generalised van der Waals-Onsager theory is exemplified by an analysis of the vapour-liquid, liquid-nematic, and vapour-nematic phase equilibria for hard spherocylinders with attractive square-well interactions (HSC-SW). The effect of the potential range and molecular aspect ratio on the vapour-liquid-nematic equilibria and orientational ordering transitions is examined to investigate the van der Waals limit (corresponding states) of the ordering phase behaviour. In the case of systems with an aspect ratio of ∼5 the corresponding-states limit is reached when the range is about 16 times the molecular diameter. For progressively longer molecules with an attractive range that follows their long dimension, the fluid-nematic equilibrium is enhanced to the point that the vapour-liquid boundary becomes metastable relative to fluid-nematic equilibria. In the case of molecules of very large aspect ratio (∼50), an additional region of nematic-nematic coexistence is exhibited by the system. [ABSTRACT FROM AUTHOR]

The statistical associating fluid theory (SAFT) is now well established as an approach for the description of the thermodynamics and phase equilibria of a wide variety of fluid systems. Numerous SAFT studies of the fluid phase equilibria of pure water and aqueous mixtures have been made with the various incarnations of the theory, yet there is no consensus on what the 'optimal' values of the intermolecular parameters are for water, or what the association scheme should be (two-, three-, or four-site models). We show that the conventional use of vapour-pressure and saturated-liquid-density data on their own leads to a degeneracy in the values of the parameters, particularly in the relative values of the dispersion and hydrogen-bonding energies. A discretized energy-parameter space is examined and a long valley of 'optimal' parameter sets for the vapour-liquid equilibria is found for the various models, ranging from low dispersion (high hydrogen-bonding) to high dispersion (low hydrogen-bonding) energies. Other thermodynamic information such as the heat of vaporization does not allow one to discriminate between the values of the parameters or the association scheme. An examination of the degree of association (hydrogen bonding) allows such a discrimination to be made: the four-site model is found to provide the best overall description of the thermodynamics, fluid phase equilibria, and degree of association. The set of parameters obtained in this way also provides the best description of the fluid-phase equilibria for a mixture of water and methanol. This degeneracy of parameters could also be important when models of water are refined to vapour-liquid equilibria in simulation studies of aqueous systems, and for other systems of associating molecules. [ABSTRACT FROM AUTHOR]