Application of the Perturbed-Chain SAFT equation of state to polar systems

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to pure polar substances as well as to vapor–liquid and liquid–liquid equilibria of binary mixtures containing polar low-molecular substances and polar co-polymers. For these components, the polar version of the PC-SAFT model requires four pure-component parameters as well as the functional-group dipole moment. For each binary system, only one temperature-independent binary interaction k_ij is needed. Simple mixing and combining rules are adopted for mixtures with more than one polar component without using an additional binary interaction parameter. The ability of the model to accurately describe azeotropic and non-azeotropic vapor–liquid equilibria at low and at high pressures, as well as liquid–liquid equilibria is demonstrated for various systems containing polar components. Solvent systems like acetone–alkane mixtures and co-polymer systems like poly(ethylene-co-vinyl acetate)/solvent are discussed. The results for the low-molecular systems also show the predictive capabilities of the extended PC-SAFT model.     

Critical points of hydrocarbon mixtures with the Peng–Robinson,SAFT, and PC-SAFT equations of state

The phase behavior of fluids at high pressures can be rather complex, even for mixtures of relatively simple molecules, such as hydrocarbons. In this work, we use the Hicks and Young algorithm to calculate mixture critical points, comparing five modeling options: Peng–Robinson EOS: (1) original and (2) with parameters fitted from molar volume and vapor pressure data; (3) SAFT EOS; and PC-SAFT EOS: (4) original and (5) with refitted parameters to match pure component critical data. Calculations were carried out for binary hydrocarbon mixtures and 29 multicomponent mixtures. The SAFT EOS provided the worst representation of the systems tested and, interestingly, the conventional cubic EOS provided, in general, the best representation.     

Application of the perturbed chain SAFT equation of state to complex polymer systems using simplified mixing rules

A simplified perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied to polymer systems that include a variety of non-associating (esters, cyclic hydrocarbons), polar (ketones) as well as associating (amines, alcohols) solvents. The solvent pure-component parameters that are not available in the literature are estimated by correlating vapor-pressure and liquid-density data. The performance of the simplified PC-SAFT is compared to the original PC-SAFT equation of state for polymer systems of varying complexity. It is shown that the applied simplification is not at the expense of the accuracy of equation of state, while the computational time and complexity are significantly reduced, especially for associating systems. With no binary interaction parameter, simplified PC-SAFT is successfully able to predict vapor–liquid equilibria of polymers with non-associating solvents. In the case of associating solvents, a small binary interaction parameter k_ij is usually needed for the satisfactory correlation of the experimental data.     

Properties of 1,8-cineole: a thermophysical and theoretical study

This paper reports on an experimental and theoretical study of 1,8-cineole, one of the main components of essential oils in different plants. The pressure-volume-temperature behavior of this fluid was evaluated accurately over wide temperature and pressure ranges and correlated successfully with the empirical TRIDEN equation. From the measured data, the relevant derived coefficients isothermal compressibility, isobaric expansibility, and internal pressure were calculated. The isobaric heat capacities at high pressure were extrapolated from the data measured at atmospheric pressure. The cubic equations of state by Soave, Peng-Robinson, Stryjek-Vera modification of Peng-Robinson, Patel-Teja, Sako-Wu-Prausnitz, and the SAFT and PC-SAFT molecularly based equations of state were used to predict the PVT behavior. The SAFT and PC-SAFT parameters for 1,8-cineole were obtained from correlation of available saturation literature data; the best results were provided by Sako-Wu-Prausnitz and PC-SAFT equations of state, whereas the classical ones were shown to be inadequate. The molecular structure was studied by quantum computations at the B3LYP/6-311++g(d) level and classical molecular dynamics simulations in the NPT ensemble with the OPLS-AA forcefield. On the basis of both macroscopic and microscopic studies, a complex fluid structure was inferred.     

Extremely Low Vapor-Pressure Data as Access to PC-SAFT Parameter Estimation for Ionic Liquids and Modeling of Precursor Solubility in Ionic Liquids

Precursor solubility is a crucial factor in industrial applications, dominating the outcome of reactions and purification steps. The outcome and success of thermodynamic modelling of this industrially important property with equations of states, such as Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), vastly depends on the quality of the pure-component parameters. The pure-component parameters for low-volatile compounds such as ionic liquids (ILs) have been commonly estimated using mixture properties, e. g. the osmotic pressure of aqueous solutions. This leads to parameters that depend on the solvent, and transferability to other mixtures often causes poor modeling results. Mixture-independent experimental properties would be a more suitable basis for the parameter estimation offering a way to universal parameter sets. Model parameters for ILs are available in the literature [10.1016/j.fluid.2012.05.029], but they were estimated using pure-IL density data. The present work focuses on a step towards a more universal estimation strategy that includes new experimental vapor-pressure data of the pure IL. ILs exhibit an almost negligible vapor pressure in magnitude of usually 10⁻⁵ Pa even at elevated temperatures. In this work, such vapor-pressure data of a series of 1-ethyl-3-methyl-imidazolium-based [C₂mim]-ILs with various IL-anions (e. g. tetrafluoroborate [BF₄]⁻, hexafluorophosphate [PF₆]⁻, bis(trifluoromethylsulfonyl)imide [NTf₂]⁻) were experimentally determined and subsequently used for PC-SAFT parameter estimation. The so-determined parameters were used to predict experimental molecular precursor solubility in ILs and infinitely diluted activity coefficients of various solvents in ILs. The parameters were further compared to modeling results using classical parametrization methods (use of liquid-density data only for the molecular PC-SAFT and the ion-based electrolyte PC-SAFT). As a result, the modeled precursor solubilities using the new approach are much more precise than using the classical parametrization methods, and required binary parameters were found to be much smaller (if needed). In sum, including the pure-component vapor-pressure data of ILs opens the door towards parameter estimation that is not biased by mixture data. This procedure might be suitable also for polymers and for all kind of ionic species but needs extension to ion-specific parametrization in the long term.     

Study on Vapor-Liquid Nucleation Rates for n-Alcohols by Density Functional Theory

The statistical associating fluid theory (SAFT) in conjunction with the Weeks‐Chandler‐Anderson (WCA) approximation for intermolecular interaction is employed to construct a non‐uniform equation of state (EOS) for n‐alcohols. The molecular parameters for methanol, ethanol, 1‐propanol, 1‐butanol, 1‐pentanol and 1‐hexanol are obtained by fitting to the experimental data of vapor‐liquid equilibria and then used to predict the nucleation rates under the framework of density functional theory (DFT). The predictions are found to be in quite good agreement with the experimental data. Investigation shows that the combination of DFT and SAFT is a successful approach for vapor‐liquid nucleation rates of n‐alcohols.     

Thermophysical properties of the binary mixtures (1,8-cineole + 1-alkanol) at T = (298.15 and 313.15) K and at atmospheric pressure

This work presents the measurements of the density, speed of sound, refractive index and enthalpy of binary mixtures containing {1,8-cineole + 1-alkanol (ethanol, 1-propanol, 1-butanol, and 1-pentanol)} at two temperatures (298.15 and 313.15) K and atmospheric pressure. The determination of excess molar volume, speed of sound deviation, refractive index deviation, molar refraction, molar refraction deviation, excess isentropic compressibility, and excess molar enthalpy are also given. Redlich–Kister equation was used to fit these derivate properties. The experimental data of the constituent binaries were analysed to discuss the nature and strengths of intermolecular interactions. Eventually some models, SAFT and PC-SAFT for density, Free Length and Collision Factor for speed of sound, Gladstone-Dale Arago-Biot for refractive index, and UNIFAC for excess molar enthalpy, among others, were successfully applied.     

In Situ Direct Measurement of Vapor Pressures and Thermodynamic Parameters of Volatile Organic Materials in the Vapor Phase: Benzoic Acid,Ferrocene, and Naphthalene

We report the direct determination of vapor pressures and optical and thermodynamic parameters of powders of low‐volatile materials in their vapor phase using a commercial UV/Vis spectrometer. This methodology is based on the linear proportionality between the density of the saturated gas of the material and the absorbance of the gas at different temperatures. The vapor pressure values determined for benzoic acid and ferrocene are in good agreement with those reported in the literature with ～2–7 % uncertainty. Thermodynamic parameters of benzoic acid, ferrocene, and naphthalene are determined in situ at temperatures below their melting points. The sublimation enthalpies of the investigated organic molecules are in excellent agreement with the ICTAC recommended values (less than 1 % difference). This method has been used to measure vapor pressures and thermodynamic parameters of organic volatile materials with vapor pressures of ～0.5–355 Pa in the 50–100 °C temperature range.     

气相色谱法测定多溴联苯的蒸气压

采用气相色谱法,以二氯二苯三氯乙烷(DDT)为参考化合物,测定了6个多溴联苯(PBBs)在不同温度条件下的蒸气压, 然后使用Slide数理统计软件、以最小二乘法回归计算出Antoine方程的A,B,C参数,从而建立了6个PBBs的蒸气压与温度 的关联式。初步探讨了分子连接性指数与蒸气压的相关性,结果发现一阶拓扑指数与蒸气压表现出很好的线性关系,两者 的相关系数的平方大于0.99,标准偏差小于0.08。     

Vapor liquid equilibrium modeling of alkane systems with Equations of State: “Simplicity versus complexity”

Two types of Equations of State (EoS), which are characterized here as “simple” and “complex” EoS, are evaluated in this study. The “simple” type involves two versions of the Peng–Robinson (PR) EoS: the traditional one that utilizes the experimental critical properties and the acentric factor and the other, referred to as PR-fitted (PR-f), where these parameters are determined by fitting pure compound vapor pressure and saturated liquid volume data. As “complex” EoS in this study are characterized the EoS derived from statistical mechanics considerations and involve the Sanchez–Lacombe (SL) EoS and two versions of the Statistical Associating Fluid Theory (SAFT) EoS, the original and the Perturbed-Chain SAFT (PC-SAFT).

The evaluation of these two types of EoS is carried out with respect to their performance in the prediction and correlation of vapor liquid equilibria in binary and multicomponent mixtures of methane or ethane with alkanes of various degree of asymmetry. It is concluded that for this kind of systems complexity offers no significant advantages over simplicity. Furthermore, the results obtained with the PR-f EoS, especially those for multicomponent systems that are encountered in practice, even with the use of zero binary interaction parameters, indicate that this EoS may become a powerful tool for reservoir fluid phase equilibria modeling.     

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.     

Effect of molecular weight distribution on the liquid-liquid phase separation behavior of polydispersed polyethylene solutions at high temperatures

The phase behaviors of the hexane + polydispersed polyethylene (PE) systems were measured to clarify the effect of the molecular weight distribution (MWD) of PE on liquid-liquid (LL) phase boundaries. The weight fraction for the PE portion of a maximum LL phase separation pressure in the LL phase boundary decreased as the polydispersity of PE increased. Moreover, depression of the phase separation pressure from the maximum phase separation pressure on the higher PE weight fraction side was more drastic as the polydispersity of the PE increased. The LL phase boundaries were correlated using the Sanchez-Lacombe equation of state (S-L EOS). For the correlations, the polydispersed PEs were regarded as mixtures of 16 types of monodispersed PEs with different molecular weights, and the characteristic parameters of the S-L EOS, P*, ρ* and T*, were assigned the same values for all monodispersed PEs even though the molecular weights differed. However, the interaction parameters of the hexane-PE pairs depended on the molecular weight of the PE and the temperature. The correlated results capably reproduced the effect of the MWD of the PE on the LL phase boundaries for the hexane + polydispersed PE systems.     

Evaluating perturbation contributions in SAFT models by comparing to molecular simulation of n-alkanes

SAFT models are generally written as a perturbation series of the Helmholtz energy with reciprocal temperature as the argument. The perturbation coefficients are then functions of density and molecular size. The variation of the perturbation coefficients with molecular size is given primarily by Wertheim's theory [6], [7], [8] and [9], but there may be additional variations as in the PC-SAFT model. In the present work, we compare the characterization of perturbation coefficients inferred from PC-SAFT to those derived from molecular simulations.The molecular simulations are based on Discontinuous Molecular Dynamics (DMD) and second order Thermodynamic Perturbation Theory (TPT). DMD simulation is applied to the repulsive part of the potential model with molecular details like fused hard spheres for the interaction sites and 110° bond angles. The thermodynamic effects of disperse attractions are treated by rigorous application of TPT. The present work re-examines the related work of Elliott and Gray [35] in the low density and critical regions, focusing on n-alkanes with carbon numbers ranging from 3 to 80.We find that SAFT theory overestimates the repulsive contribution (A₀) and underestimates the first order contribution (A₁) of Helmholtz energy relative to simulation. Nevertheless, the correlations are qualitatively reasonable. Significant inconsistencies arise when considering the second order contribution (A₂). For example, the PC-SAFT characterization of A₂ becomes larger than A₁ in the low density, long chain limit, raising concerns about the convergence of the series. Furthermore, fluctuations are underestimated in the critical region and overestimated in the liquid region. In each case, we can suggest improved characterizations. Altogether, these results suggest ways to modify the SAFT formalism to achieve greater consistency between atomistic and coarse-grained models.     

Isobaric vapor–liquid equilibria for acetone + methanol + lithium nitrate at 100 kPa

Isobaric vapor–liquid equilibria for the ternary system acetone + methanol + lithium nitrate have been measured at 100 kPa using a recirculating still. The addition of lithium nitrate to the solvent mixture produced an important salting-out effect and the azeotrope tended to disappear for small contents of salt. The experimental data sets were fitted with the electrolyte NRTL model and the parameters of the Mock's model were estimated. These parameters were used to predict the ternary vapor–liquid equilibrium which agreed well with the experimental one.     

Statistical associating fluid theory coupled with restrictive primitive model extended to bivalent ions. SAFT2: 2. Brine/seawater properties predicted

Statistical associating fluid theory coupled with restricted primitive model (SAFT2) represents the properties of aqueous multiple-salt solutions, such as brine/seawater. The osmotic coefficients, densities, and vapor pressures are predicted without any additional parameters using the salt hydrated diameters obtained for single-salt solutions. For a given ion composition of brine, the predicted vapor pressure, osmotic coefficient, activity of water, and density are found to agree with the experimental data.     

Thermal behavior of neopentylpolyol esters: Comparison between determination by TGA-DTA and flash point

In the course of an investigation on the properties of neopentylpolyol esters, we examined their behavior at high temperatures using two different methods: thermogravimetry with differential thermal analysis (TGA-DTA) and measurement of flash point (ASTM D-93). Thermal behavior of the neopentylpolyol esters was found to be related to the length of acyl chain (C9 : 0, C12 : 0, C14 : 0, C18 : 1, C22 : 1) and nature of the polyol (PE, TMP, NPGHP).

We also examined the thermal behavior of the partial esters of pentaerythritol in both, helium and air. The TGA-DTA technique appeared to be a suitable replacement for the flash-point methodology (ASTM D-93), especially for studying the thermal behavior of small amounts of the sample.     

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.     

On the properties of methylbenzoate/n-hexane mixed solvents: a theoretical and experimental study

This paper reports on an experimental and theoretical study of methylbenzoate/n-hexane mixed solvents as a function of pressure and temperature in the whole composition range. We have measured the pressure-volume-temperature (PVT) behavior of these fluids over wide temperature and pressure ranges; from the experimental data, relevant derived coefficients required for the fluid's characterization were calculated. The structure of mixed fluids was analyzed from macroscopic data according to excess and mixing properties. The statistical associating fluid theory (SAFT) and perturbed chain (PC)-SAFT molecularly based equations of state were used to predict the PVT behavior with model parameters for pure fluids fitted from correlation of available saturation literature data. The results provided by the PC-SAFT equation of state were clearly superior. Using the fitted PC-SAFT parameters, the global phase behavior of the mixture was predicted, and a type I pattern was inferred according to the van Konynenburg systematic. The molecular level structure was studied through classical molecular dynamics simulations in the NPT ensemble using the optimized potential for liquid simulations (all atom version) (OPLS-AA) force field. Molecular dynamics provides, on one hand, theoretical values of thermophysical properties, which are compared with the experimental ones to check the quality of simulations, and, on the other hand, valuable molecular level structural and dynamic information. Based on both macroscopic and microscopic studies, fluid structure was inferred.     

Application of a new simplified SAFT to VLE study of associating and non-associating fluids

A new equation of state based on the Statistical Associating Fluid Theory (SAFT) is presented to study the phase behavior of associating and non-associating fluids. In the new equation of state, the hard sphere contribution to compressibility factor of the simplified version of the SAFT (SSAFT) is replaced with that proposed by Ghotbi and Vera. The Ghotbi–Vera SSAFT (GV-SSAFT) was also extended to study the phase behavior of associating and non-associating mixtures. The GV-SSAFT like the SSAFT equation of state has three adjustable segment parameters for non-associating fluids and five parameters for associating fluids. The experimental data of liquid densities and vapor pressures for pure fluids studied in this work were used to obtain the best values for the parameters of the GV-SSAFT. The results obtained from the GV-SSAFT for liquid densities and vapor pressures of pure associating and non-associating fluids were compared with those obtained from the SSAFT equation of state. The results showed that the GV-SSAFT similar to the SSAFT can accurately correlate the experimental data of liquid density and vapor pressure for systems studied. On the other hand the results obtained from two SAFT-based equations of state are almost identical. In order to show capability of the GV-SSAFT and SSAFT equations of state, they were used to directly calculate heat of vaporization for a number of pure associating and non-associating fluids. Slightly better results for heat of vaporization comparing to the experimental data were obtained from the GV-SSAFT EOS than those obtained from the SSAFT. The GV-SSAFT was also used to study the VLE phase behavior for a number of binary associating and non-associating mixtures. The results also showed that the GV-SSAFT can be successfully used to study the phase behavior of mixtures studied in this work.