Modified interfacial statistical associating fluid theory: application to tethered polymer chains

Modified interfacial statistical associating fluid theory density functional theory is extended to tethered polymer chains in the absence or presence of free polymer chains. The structures of the "dry" and "wet" polymer brushes have been calculated and compared with simulation results available in the literature. The comparisons show that the theory accurately predicts the structure of the tethered polymer brush. The average brush heights calculated from the theory agree with well-established scaling theories for tethered polymers. However, these scaling theories cannot predict the detailed structure, accurately. The effects of the segment-segment interactions of the tethered polymer and the free polymer have been effectively captured by the theory.     

Modeling thermodynamic properties of natural gas mixtures using perturbed-chain statistical associating fluid theory

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was employed for predicting thermodynamic properties of natural gas mixture. Thermodynamic properties like density, isobaric and isochoric heat capacity, enthalpy, entropy, and internal energy were calculated with the PC-SAFT. Results are validated against experimental data for natural gas and mixtures similar to natural gas. The validation show that the Average Absolute Deviation (AAD) for density is 1.10% for binary mixture and 1.08% for mixtures similar to natural gas. Also AAD value for enthalpy is 1.42%, for internal energy, 0.77, for entropy, 0.43, for isochoric heat capacity, 1.26%, and for isobaric heat capacity, 2.66%. Results show PC-SAFT to be able to predict all the thermodynamics properties of natural gas and mixtures similar to natural gas with high accuracy in a wide range of temperature and pressure.     

Thermodynamic regularities for associating fluids from statistical associating fluid theory equation of state

In this work, we used a statistical associating fluid theory to analyze two important thermodynamic regularities for some associating fluids, including water, methanol and ethanol. The studied regularities included: (i) the common bulk modulus point on the isotherms of the reduced bulk modulus versus reduced density, (ii) near linearity of the reduced isothermal bulk modulus as a function of reduced pressure. In this work, we also reported the influence of the molecular size and interaction strength on the bulk modulus point.     

Modified interfacial statistical associating fluid theory: a perturbation density functional theory for inhomogeneous complex fluids

A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.     

A study of square-well statistical associating fluid theory approximations

Six square-well (SW) statistical associating fluid theory (SAFT) models, fitted to the experimental saturated liquid volume and saturated vapor pressure for pure n-alkanes, are analyzed for predicting the coexisting densities, second virial coefficients, and binary phase equilibria. The models that result in low values of the segment energy and weak molecular weight dependence of the parameters are found to be more accurate for real fluids. The inclusion of the dimer structure in the SW chain term seems to produce no significant benefit for representing real substances.     

Predicting adsorption isotherms using a two-dimensional statistical associating fluid theory

A molecular thermodynamics approach is developed in order to describe the adsorption of fluids on solid surfaces. The new theory is based on the statistical associating fluid theory for potentials of variable range [A. Gil-Villegas et al., J. Chem. Phys. 106, 4168 (1997)] and uses a quasi-two-dimensional approximation to describe the properties of adsorbed fluids. The theory is tested against Gibbs ensemble Monte Carlo simulations and excellent agreement with the theoretical predictions is achieved. Additionally the authors use the new approach to describe the adsorption isotherms for nitrogen and methane on dry activated carbon.     

Investigation of the surface tension of methane and n-alkane mixtures by perturbed-chain statistical associating fluid theory combined with density-gradient theory

The perturbed-chain statistical associating fluid theory (PC-SAFT) and density-gradient theory are used to construct an equation of state to describe the phase behavior of binary methane–n-alkane mixtures. With the molecular parameters and influence parameters regressed from bulk properties and surface tensions of pure fluids, respectively as input, both the bulk and interfacial properties are investigated. The surface tension of the binary systems methane–propane, methane–pentane, methane–heptane and methane–decane are predicted, and the results are satisfactory compared with the experimental data. Our results show that PC-SAFT combined with density-gradient theory is able to describe the interfacial properties of binary methane–n-alkane mixtures in wide temperature and pressure ranges, and illustrate the influence of the equilibrium bulk properties and chain length of n-alkane molecule on the interfacial properties.     

Modeling of density of aqueous solutions of amino acids with the statistical associating fluid theory

The density of aqueous solutions of amino acids has been modeled with the statistical associating fluid theory (SAFT) equation of state. The modeling is accomplished by extending the previously developed new method to determine the SAFT parameters for amino acids. The modeled systems include α-alanine/H₂O, β-alanine/H₂O, proline/H₂O, l-asparagine/H₂O, l-glutamine/H₂O, l-histidine/H₂O, serine/H₂O, glycine/H₂O, alanine/H₂O/sucrose, dl-valine/H₂O/sucrose, arginine/H₂O/sucrose, serine/H₂O/ethylene glycol, and glycine/H₂O/ethylene glycol. The density of binary solutions of amino acids has been correlated or predicted with a high precision. And then the density of multicomponent aqueous solutions of amino acids has been modeled based on the modeling results of binary systems, and a high accuracy of density calculations has been obtained. Finally, the water activities of dl-valine/H₂O, glycine/H₂O, and proline/H₂O have been predicted without using binary interaction parameters, and good results have been obtained.     

Thermodynamic properties of Lennard-Jones chain molecules: renormalization-group corrections to a modified statistical associating fluid theory

A modified version of the statistical associating fluid theory (SAFT), the so-called soft-SAFT equation of state (EOS), has been extended by a crossover treatment to take into account the long density fluctuations encountered when the critical region is approached. The procedure, based on White's work from the renormalization group theory [Fluid Phase Equilibria 75, 53 (1992); L. W. Salvino and J. A. White, J. Chem. Phys. 96, 4559 (1992)], is implemented in terms of recursion relations where the density fluctuations are successively incorporated. The crossover soft-SAFT equation provides the correct nonclassical critical exponents when approaching the critical point, and reduces to the original soft-SAFT equation far from the critical region. The accuracy of the global equation is tested by direct comparison with molecular simulation results of Lennard-Jones chains, obtaining very good agreement and clear improvements compared to the original soft-SAFT EOS. Excellent agreement with vapor-liquid equilibrium experimental data inside and outside the critical region for the n-alkane series is also obtained. We provide a set of transferable molecular parameters for this family, unique for the whole range of thermodynamic properties.     

Bulk and interfacial wetting behavior of binary mixtures induced by associating between unlike-pair molecules

The statistical associating fluid theory of Wertheim is applied to describe binary mixtures with associating between unlike-pair molecules. The phase behavior of this binary mixture would fall into five different types (I, II, III, V, and VI) of the classification scheme of van Konynenburg and Scott by varying the associating strength and the energy parameters. Both interfacial wetting behavior and wetting transitions are carefully examined in all the vapor-liquid-liquid (gamma-beta-alpha) three-phase-coexisting regions of the binary mixtures. The global wetting behavior and wetting transitions are delineated by scanning the parameter space. In certain regions, the middle beta phase exhibits interfacial phase transitions sequentially, nonwetting --> partial-wetting --> nonwetting, at the interface separating lower alpha and upper gamma phases along with increasing temperature.     

Thermodynamic modeling of CO2 solubility in ionic liquid with heterosegmented statistical associating fluid theory

Heterosegmented statistical associating fluid theory is used to represent the CO₂ solubility in ionic liquids. As in our previous work, ionic liquid molecule is divided into several groups representing the alkyls, cation head, and anion. The cation of ionic liquid is modeled as a chain molecule that consists of one spherical segment representing the cation head and groups of segments of different types representing different substituents (alkyls). The anion of ionic liquid is modeled as a spherical segment of different type. To account for the electrostatic/polar interaction between the cation and anion, the spherical segments representing cation head and anion each have one association site, which can only cross associate. Carbon dioxide is modeled as a molecule with three association sites, two sites of type O and one site of type C, where sites of the same type do not associate with each other. The parameters of CO₂ are obtained from the fitting of the density and the saturation vapor pressure of CO₂. For the CO₂-ionic liquid systems, cross association between site of type C in CO₂ and another association site in anion is allowed to occur to account for the Lewis acid–base interaction. The parameters for cross association interactions and the binary interaction parameters used to adjust the dispersive interactions between unlike segments are obtained from the fitting of the available CO₂ solubility in ionic liquids. The model is found to well represent the CO₂ solubility in the imidazolium ionic liquids from 283 to 415 K and up to 200 bar.     

Semiclassical approach to model quantum fluids using the statistical associating fluid theory for systems with potentials of variable range

Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.     

Thermodynamic properties of the Mie n-6 fluid: a comparison between statistical associating fluid theory of variable range approach and molecular dynamics results

Molecular dynamics (MD) simulations of direct and derivative thermodynamic properties of the Mie n-6 fluid (n=8, 10, and 12) have been performed for liquid to supercritical states. Using the results, an in depth test of the monomer-monomer interaction estimation of a recently derived statistical associating fluid theory of variable range (SAFT-VR) equation of state [Lafitte et al., J. Chem. Phys., 124, 024509 (2006)] has been carried out based on the Mie n-6 potential. For pure fluids, using an appropriate scaling, MD simulations show that density and isometric heat capacity are nearly independent of n, whereas sound velocity and thermal pressure coefficient tend to increase with n. In addition, the results show that predictions provided by the equation of state are consistent with those coming from MD and catch correctly the trends of each property with n except for the heat capacity. The comparison is next extended to binary mixtures with components differing only in the value of the n parameter and which demonstrate the reliability of the scheme (MX1b) used by Lafitte et al. to deal with this parameter in the SAFT-VR equation of state. In addition, a new empirical one-fluid approximation of the n parameter is proposed thanks to MD simulations, which very favorably compare with the one-fluid model on n previously proposed in the literature. The consistency of this approximation is addressed by making use of it in combination with the SAFT-VR Mie equation of state. It is shown that using such an approach, which is easier to handle than the MX1b one, yields slightly improved results compared to those of the MX1b.     

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.