Modeling the phase behavior of H2S+n-alkane binary mixtures using the SAFT-VR+D approach

A statistical associating fluid theory for potential of variable range has been recently developed to model dipolar fluids (SAFT-VR+D) [Zhao and McCabe, J. Chem. Phys. 2006, 125, 104504]. The SAFT-VR+D equation explicitly accounts for dipolar interactions and their effect on the thermodynamics and structure of a fluid by using the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. In this work, we apply the SAFT-VR+D approach to real mixtures of dipolar fluids. In particular, we examine the high-pressure phase diagram of hydrogen sulfide+n-alkane binary mixtures. Hydrogen sulfide is modeled as an associating spherical molecule with four off-center sites to mimic hydrogen bonding and an embedded dipole moment (micro) to describe the polarity of H2S. The n-alkane molecules are modeled as spherical segments tangentially bonded together to form chains of length m, as in the original SAFT-VR approach. By using simple Lorentz-Berthelot combining rules, the theoretical predictions from the SAFT-VR+D equation are found to be in excellent overall agreement with experimental data. In particular, the theory is able to accurately describe the different types of phase behavior observed for these mixtures as the molecular weight of the alkane is varied: type III phase behavior, according to the scheme of classification by Scott and Konynenburg, for the H2S+methane system, type IIA (with the presence of azeotropy) for the H2S+ethane and+propane mixtures; and type I phase behavior for mixtures of H2S and longer n-alkanes up to n-decane. The theory is also able to predict in a qualitative manner the solubility of hydrogen sulfide in heavy n-alkanes.     

Equation of state and liquid-vapor equilibria of one- and two-Yukawa hard-sphere chain fluids: theory and simulation

The accuracy of several theories for the thermodynamic properties of the Yukawa hard-sphere chain fluid are studied. In particular, we consider the polymer mean spherical approximation (PMSA), the dimer version of thermodynamic perturbation theory (TPTD), and the statistical associating fluid theory for potentials of variable attractive range (SAFT-VR). Since the original version of SAFT-VR for Yukawa fluids is restricted to the case of one-Yukawa tail, we have extended SAFT-VR to treat chain fluids with two-Yukawa tails. The predictions of these theories are compared with Monte Carlo (MC) simulation data for the pressure and phase behavior of the chain fluid of different length with one- and two-Yukawa tails. We find that overall the PMSA and TPTD give more accurate predictions than SAFT-VR, and that the PMSA is slightly more accurate than TPTD.     

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.     

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.     

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.     

Perturbed chain-statistical associating fluid theory extended to dipolar and quadrupolar molecular fluids

The perturbed chain statistical associating fluid theory (PC-SAFT) is extended to polar molecular fluids, namely dipolar and quadrupolar fluids. The extension is based on the perturbation theory for polar fluids by Stell and co-workers. Appropriate expressions are proposed for dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions. Furthermore, induced dipole interactions are calculated explicitly in the model. The new polar PC-SAFT model is relatively complex; for this purpose, a truncated polar PC-SAFT model is proposed using only the leading term in the polynomial expansion for polar interactions. The new model is used for the calculation of thermodynamic properties of various quadrupolar pure fluids. In all cases, the agreement between experimental data and model predictions is very good.     

Density and chain conformation profiles of square-well chains confined in a slit by density-functional theory

Density and chain conformation profiles of square-well chains between two parallel walls were studied by using density-functional theory. The free energy of square-well chains is separated into two contributions: the hard-sphere repulsion and the attraction. The Heaviside function is used as the weighting function for both of the two parts. The equation of state of Hu et al. is used to calculate the excess free energy of the repulsive part. The equation of state of statistical associating fluid theory for chain molecules with attractive potentials of variable range [A. Gil-Villegas et al. J. Chem. Phys. 106, 4168 (1997)] is used to calculate the excess free energy of the attractive part. Because the wall is inaccessible to a mass center of a longer chain, there exists a sharp fall in the distribution of end-to-end distance near the wall as the chain length increases. When the average density of the system is not too low, the prediction of this work is in good agreement with computer simulation results for the density profiles and the chain conformation over a wide range of chain length, temperature, and attraction strength of the walls. However, when the average density and the temperature are very low, the prediction deviates to a certain degree from the computer simulation results for molecules with long chain length. A more accurate functional approximation is needed.     

基于化学缔合统计理论的链状流体状态方程

基于化学缔合统计理论的链状流体状态方程(EOS)能够反映实际分子的形状、链节成链、缔合等具体信息,在实际流体热力学性质计算中有着广泛应用.一般的链状流体EOS仅考虑相邻链节间的相关性,我们则借助统计力学和计算机模拟结果在模型中纳入了相间链节间的相关性,获得的硬球链流体(HSCF)模型能够更好地预测模型流体的压缩因子和第二维里系数.以HSCF为参考,引入方阱色散微扰项获得了实际方阱链流体(SWCF)EOS;结合根据黏滞球模型导得的缔合项,进一步构建了缔合流体EOS.最近,我们根据微扰理论和积分方程方法又开发了一新的变阱宽方阱链流体(SWCF-VR)模型.SWCF和SWCF-VREOSs可很好地用于计算小分子、聚合物、离子液体等纯流体及混合物的相行为、热焓、表面张力、黏度等热力学及传递性质,显示了模型良好的工程应用价值.本文就本课题组多年来在自由空间范畴内基于化学缔合统计理论开发链状流体EOS及其实际应用作系统的总结.     

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.     

Statistical associating Fluid Dimer Theory

Three modified versions of statistical associating fluid theory known as SAFT-D1, SAFT-D2 and SAFT-T for hard sphere chain molecules are used to test the approximation made in the derivation of the statistical associating fluid dimer theory (SAFT-D). The SAFT-D1 model accounts for the chain length independent site–site correlation function at contact, while SAFT-D2 and SAFT-T models account for chain length dependent site–site correlation function at contact. The residual chemical potentials are calculated for hard chain fluids containing chains of length m = 3, 4, 6, 8, 12, 16 and 32?mers and compared with the results obtained by configurational bias Monte Carlo (MC) method at various densities. We find that the approximation used in SAFT-D1 theory leads to an over prediction of residual chemical potential and its magnitude increases with increasing chain length.     

A completely analytic equation of state for the square-well chain fluid of variable well width

A completely analytic perturbation theory equation of state for the freely-jointed square-well chain fluid of variable well width (1 ≤ λ ≤ 2) is developed and tested against Monte Carlo simulation data. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference monomer fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of monomers to form chains. By using a recently developed real function expression for the radial distribution function of hard spheres in perturbation theory, we obtain analytic, closed form expressions for the Helmholtz free energy and the radial distribution function of square-well monomers of any well width. This information is used as the reference fluid in the perturbation theory of Wertheim to obtain an analytic equation of state, without adjustable parameters, that leads to good predictions of the compressibility factors and residual internal energies for 4-mer, 8-mer and 16-mer square-well fluids when compared with the simulation results. Further, very good results are obtained when this equation of state with temperature-independent parameters is used to correlate the vapor pressures and critical points of the linear alkanes from methane to n-decane.     

A cubic perturbed hard-chain equation of state

A cubic equation of state is developed on the basis of perturbation theory. The equation is an association of three segments: the hard-sphere, the hard-chain, and the attraction. The expression for each segment was invoked from approximations of computer simulations of rigorous molecular theories of fluids, but compromised to some extent accuracy and theory for simplicity. This model equation is shown to be potentially capable of describing the PVT behavior of real fluids. As limiting cases, the new equation is reduced to expressions for the hard-sphere and the hard-body fluids. It also represents square-well fluids when the hard-chain contribution is eliminated. The square-well equation was found satisfactory in conforming with the molecular simulation results for square-well fluids and their mixtures.     

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.     

Properties and structure of aromatic ester solvents

This paper reports on an experimental and theoretical study of the aromatic ester solvents family. Several compounds were selected to analyze the different factors that influence their liquid-state properties and structures. The pressure-volume-temperature behavior of these fluids was measured accurately over wide temperature and pressure ranges and correlated successfully with the empirical TRIDEN equation. From the measured data the relevant derived coefficients of isothermal compressibility, isobaric expansibility, and internal pressure were calculated. The statistical associating fluid theory (SAFT) and perturbed chain statistical associating fluid theory (PC-SAFT) molecularly based equations of state were used to predict the PVT behavior with model parameters obtained from the correlation of available saturation literature data; the results provided by PC-SAFT equations of state were clearly superior for all of the studied solvents. The fluid's molecular level structure was studied by quantum computations at the B3LYP/6-311++g** level and classical molecular dynamics simulations in the NPT ensemble with the OPLS-AA forcefield. Molecular parameters, such as torsional barriers or cluster energetics, were analyzed as a function of ester structures. The molecular dynamics study provides, on one hand, theoretical values of thermophysical properties, which are compared with the experimental ones, and, on the other hand, valuable molecular level structural information. On the basis of both macroscopic and microscopic studies complex fluid structures were inferred with important effects arising from the geometries of the studied molecules and from the existence of remarkable intermolecular forces of dominating dipolar nature.     

Calculating thermodynamic properties from perturbation theory: II. An analytic representation for the square-well chain fluid

An analytic representation of thermodynamic properties of the freely jointed square-well chain fluid is developed based on the thermodynamic perturbation theory of Barker–Henderson, Zhang and Weitheim. By using a real function expression for the radial distribution function and incorporating structural information for square-well monomer of TPT1 model, an analytic expression for the Helmholtz energy of square-well chain fluid is expanded from Zhang’s analytic expressions for thermodynamic properties of square-well monomer. The expression leads to good predictions of the compressibility factor, residual internal energy and constant-volume heat capacity for 4-mer, 8-mer and 16-mer square-well fluids when compared with the Monte Carlo (MC) simulation results. The incorporating structural information for square-well dimer of TPT-D model is also calculated. To obtain the constant-volume heat capacity needed, NVT MC simulations were performed.     

An improved renormalization group theory for real fluids

On the basis of White's theory, an improved renormalization group (RG) theory is developed for chain bonding fluids inside the critical region. Outside the critical region, the statistical associating fluid theory based on the first-order mean sphere approximation [Fluid Phase Equilibria 171, 27 (2000)] is adopted and all the microscopic parameters are taken directly from its earlier application of real fluids. Inside the critical region, the RG transformation for long-range density fluctuation is derived in the k space, which illustrates explicitly the contributions from the mean-field term, the local density fluctuation, and the nonlocal density fluctuation. The RG theory is applied to describe physical behavior of ten n alkanes (C1-C10) both near to and far from the critical point. With no additional parameters for chain bonding fluids, good results are obtained for critical specific heat and phase coexistence curves and the resulting critical exponents are in good agreement with the reported nonclassic values.