Non-random Hydrogen Bonding Research Articles

Sorption of CO2, CH4 and Their Mixtures in Amorphous Poly(2,6-dimethyl-1,4-phenylene)oxide (PPO).

Sorption of pure CO2 and CH4 and CO2/CH4 binary gas mixtures in amorphous glassy Poly(2,6-dimethyl-1,4-phenylene) oxide (PPO) at 35 °C up to 1000 Torr was investigated. Sorption experiments were carried out using an approach that combines barometry with FTIR spectroscopy in the transmission mode to quantify the sorption of pure and mixed gases in polymers. The pressure range was chosen to prevent any variation of the glassy polymer density. The solubility within the polymer of the CO2 present in the gaseous binary mixtures was practically coincident with the solubility of pure gaseous CO2, up to a total pressure of the gaseous mixtures equal to 1000 Torr and for CO2 mole fractions of ~0.5 mol mol-1 and ~0.3 mol mol-1. The Non-Equilibrium Thermodynamics for Glassy Polymers (NET-GP) modelling approach has been applied to the Non-Random Hydrogen Bonding (NRHB) lattice fluid model to fit the solubility data of pure gases. We have assumed here that no specific interactions were occurring between the matrix and the absorbed gas. The same thermodynamic approach has been then used to predict the solubility of CO2/CH4 mixed gases in PPO, resulting in a deviation lower than 9.5% from the experimental results for CO2 solubility.

On the thermodynamic consistency of non-random hydrogen bonding lattice-fluid model for multicomponent mixtures

Compressible lattice-fluid Equation of State (EoS) models have been widely used to interpret phase equilibria and related properties of pure fluids and their mixtures, including polymer solutions. One of the first models of this family has been proposed by Sanchez and Lacombe (SL), providing useful expressions for EoS and chemical potentials for both pure components and mixtures. The assessment of the thermodynamic consistency of the expressions provided by these models for the chemical potential of each component in a mixture is a relevant issue, to which has seldom been devoted the attention it deserves. In fact, it has been demonstrated in the literature that the equations provided by the SL theory for the equilibrium chemical potential of a component in a mixture exhibits a thermodynamic inconsistency emerging from the adopted mixing rules for the close packed volume. Consequently, these expressions do not converge to the proper form in the limit of ideal gas mixtures. Later, the Non-Random Hydrogen Bonding (NRHB) lattice-fluid model was introduced to overcome some limitations of the SL model, by accounting for possible presence of strong specific intermolecular interactions, such as hydrogen bonding, as well as for non-random distribution of intermolecular contacts. In the present work, using a thermodynamic framework endowed with internal state variables, it is shown that the expressions of the chemical potential provided by the NRHB model for a multicomponent mixture at equilibrium, converge consistently to the correct form in the limit of ideal gas mixtures, thus overcoming the inconsistency implicit in the most common corresponding formulations of the SL model. We demonstrate that this feature is essentially related to the assumption of a constant value of the segmental volume, v*, that takes the same ‘universal’ value (9.75/NA cm3/molecular segment, where NA is the Avogadro number) for all pure fluids as well as for their mixtures. In addition, we have re-examined also the inconsistency issue of the SL model proving that this model recovers the thermodynamic consistency if it is assumed again a constant value of v* or if a particular type of mixing rule is assumed for v*.

Experimental Data of Fluid Phase Equilibria- Correlation and Prediction Models: A Review

The examples of phase equilibria in binary systems, solid/liquid (SLE), liquid/liquid (LLE), vapor/liquid (VLE), as well as liquid/liquid equilibria in ternary systems mainly containing ionic liquids (ILs), or the infragrance materials, or pharmaceuticals with molecular organic solvents, such as an alcohol, or water, or hydrocarbons, are presented. The most popular correlation methods of the experimental phase equilibrium data are presented, related to the excess Gibbs free energy models such as Wilson, universal-quasichemical, UNIQUAC and non-random two-liquid model, NRTL as well as several popular theories for the modeling of the phase equilibria and excess molar enthalpy, HE in binary or ternary mixtures are presented: the group contribution method (Mod. UNIFAC) and modified UNIFAC model for pharmaceuticals and lattice theory based on non-random hydrogen bonding (NRHB). The SLE, LLE, or VLE and HE of these systems may be described by the Perturbed-Chain Polar Statistical Associating Fluid Theory (PC-SAFT), or a Conductor-like Screening Model for Real Solvents (COSMO-RS). The examples of the application of ILs as extractants for the separation of aromatic hydrocarbons from alkanes, sulfur compounds from alkanes, alkenes from alkanes, ethylbenzene from styrene, butan-1-ol from water phase, or 2-phenylethanol (PEA) from water are discussed on the basis of previously published data. The first information about the selectivity of extrahent for separation can be obtained from the measurements of the limiting activity coefficient measurements by the gas–liquid chromatography technique. This review outlines the main research work carried out over the last few years on direct measurements of phase equilibria, or HE and limiting activity coefficients, the possibility of thermodynamic modeling with emphasis on recent research achievements and potential for future research.

Water sorption thermodynamics in poly(propylene sebacate)

Water sorption thermodynamics in poly-propylene sebacate, PPSeb, a biodegradable semi-crystalline polyester, has been studied above its glass transition temperature. Experimental results have been obtained by using gravimetric methods to determine water sorption isotherms at several temperatures, as well as by means of in-situ FTIR transmission spectroscopy, to obtain qualitative information and quantitative estimates on the self- and cross-Hydrogen Bonds occurring within the water-polymer mixture. In fact, the water-polymer system has been found to be populated by several water ‘species’, each one characterized by a particular configuration of HB interactions. Different moieties on the polymer backbone are involved in the formation of specific interactions. The experimental results have been interpreted in the light of the Non Random Hydrogen Bonding (NRHB) lattice fluid theory for mixtures, which accounts both for the presence of Hydrogen Bonding (HB) interactions and for non randomness of the lattice contacts. An excellent fitting of experimental water sorption isotherms has been obtained, from which relevant mean-field and HB interactional parameters of the model have been calculated. On that basis, NRHB model has been then used to obtain qualitative and quantitative predictions, at equilibrium, of self and cross HB interactions involving both water molecules and groups present on the macromolecules within the polymer-water mixture, which compare well with the experimental results of FTIR spectroscopy.

Foaming of polymers with supercritical fluids: A thermodynamic investigation

The foaming of polymers using supercritical fluids was investigated, both, from a theoretical and an experimental point of view. Key thermodynamic phenomena that take place during the foaming process were described using the Non Random Hydrogen Bonding (NRHB) equation-of-state, such as the supercritical fluid solubility in the polymer matrix and the plasticization profile of the polymer–supercritical fluid system. Moreover, the NRHB model was combined with the classical nucleation theory in order to describe the energy barrier for nucleation. Subsequently, the foaming of the well-defined polystyrene–CO2 system was experimentally studied. Porous polystyrene structures were prepared using supercritical CO2 as foaming agent at various pressure and temperature conditions that refer to constant amount of dissolved fluid (CO2) inside the polymer matrix, or to constant initial energy barrier for nucleation. The experimental results, which were discussed in the light of the aforementioned theoretical investigation, reveal that at pressure and temperature conditions of constant equilibrium solubility of CO2 inside the polymer matrix, the average pore diameter decreases with increasing foaming temperature, mainly due to the formation of more pores, which is a consequence of the decrease in the energy barrier for nucleation. Furthermore, at conditions that refer to constant initial energy barrier for nucleation, all the produced porous structures presented similar pore diameters and cell population densities, regardless of the foaming temperature. Finally, it is concluded that the energy barrier for nucleation determines the morphology of the final porous structure to a large extent, although other processing parameters, such as the foaming temperature (or pressure) and the amount of the dissolved fluid, may also influence the cell size.

Non-equilibrium compressible lattice theories accounting for hydrogen bonding interactions: Modelling water sorption thermodynamics in fluorinated polyimides

In this contribution the sorption thermodynamics of water in glassy fluorinated polyimides has been interpreted by using two non-equilibrium lattice models, accounting for hydrogen bond formation, which have been developed by extending, respectively, the Panayiotou–Sanchez (PS) and the Non-Random Hydrogen Bonding (NRHB) equilibrium models to the case of glassy polymers. The procedure used to extend the equilibrium models follows the same line of thought utilized by Doghieri and Sarti in deriving the Non-Equilibrium Thermodynamics for Glassy Polymers (NET-GP) model.The approach has been found to be successful in interpreting experimental water sorption isotherms in two different perfluorinated polyimides, namely 6FDA-ODA and 6FDA-6FpDA. The models have been also found to be capable of supplying a good qualitative and quantitative estimate of the number of water–water and water/polymer hydrogen bonds, as emerged from the comparison of theoretical predictions with experimental data obtained by means of previous IR spectroscopic measurements.

Polymeric hydrogels and supercritical fluids: The mechanism of hydrogel foaming

A novel method, the hydrogel foaming, is used in this work for the production of porous, polymer-based materials by processing with supercritical carbon dioxide (CO 2). This method is applied to crystalline hydrophilic polymers that, practically, exhibit no phase transition (melting or glass transition) below thermal decomposition temperature and, due to their crystallinity, do not absorb CO 2. Such polymers are mainly natural (semi)-crystalline polymers (e.g. chitosan, cellulose, etc.) for which the classical polymer foaming method with supercritical carbon dioxide is not applicable. The hydrogel foaming process (similar to classical polymer foaming) is applied to gelatin, chitosan, and gelatin/chitosan blend hydrogels that are physically crosslinked and may also be chemically crosslinked with glutaraldehyde vapour. After the foaming process, water is removed from the gels by mild freeze-drying leading to porous materials. Pore size control can be achieved by controlling different process parameters. Gelatin exhibits solubility in water up to high concentrations and forms thermoreversible hydrogels, rendering it a suitable choice for the investigation of the process mechanism. The mechanism of hydrogel foaming is explored on the basis of X-ray diffraction, calorimetry, rheology, sorption, Raman spectroscopy measurements and theoretical calculations with the NRHB (Non Random Hydrogen Bonding) equation-of-state model. The sorption and Raman spectroscopy measurements suggest that, besides dissolution in water (of the hydrogel), extensive CO 2 sorption by the polymer also occurs. Based on these results, a critical discussion is made and a mechanism for the hydrogel foaming is proposed.

Simultaneous determination of sorption, heat of sorption, diffusion coefficient and glass transition depression in polymer–CO 2 systems

Polymer–CO 2 interactions dictate the evolution of various phenomena such as sorption of CO 2, polymer swelling, and polymer plasticization. The knowledge of key quantities and parameters such as the amount of absorbed gas, the heat of sorption, or the diffusion coefficient is of great importance for a rational design of related processes. We have designed and constructed an apparatus based on the combination of Calvet calorimetry and pressure drop method. This combination allows for the determination of the amount of absorbed CO 2, the heat of sorption, the diffusion coefficient of CO 2 in the polymer and, finally, the concentration of CO 2 that causes plasticization of the polymer at a specific temperature (below the atmospheric glass transition temperature). We describe and propose a methodology for the simultaneous measurement of the four, above mentioned, parameters. The glass transition depression is determined by a novel approach which, in addition, allows for information about the kinetics of plasticization to be derived. New results at 54.3 °C and at various pressures are presented for the PMMA–CO 2 system, and wherever possible, compared with literature data and modeled with the NRHB (Non Random Hydrogen Bonding) model and the dual sorption model.

Liquid–liquid phase equilibrium of (piperidinium-based ionic liquid + an alcohol) binary systems and modelling with NRHB and PCP-SAFT

The phase diagrams for binary systems of {1-propyl-1-methylpiperidinium bis{(trifluoromethyl)sulfonyl}imide [PMPIP][NTf 2] + an alcohol (butan-1-ol, pentan-1-ol hexan-1-ol, heptan-1-ol, octan-1-ol, decan-1-ol and undecan-1-ol} have been determined at atmospheric pressure using a dynamic method. The influence of an alcohol chain length is discussed for this ionic liquid (IL). A systematic decrease in the solubility is observed with an increase of the alkyl chain length of an alcohol. Liquid + liquid phase equilibrium (LLE) with an upper critical solution temperature was observed. The phase diagrams reported are compared to systems published earlier with the 1-alkyl-1-methylpiperidinium-based ionic liquid. The basic thermal properties of the pure IL, i.e. melting temperature and the enthalpy of fusion, the glass transition temperature and heat capacity at melting temperature have been measured using a differential scanning microcalorimetry technique. The density of [PMPIP][NTf 2] as a function of temperature was measured. The results of the LLE correlation with two models viz. the lattice theory based on non-random hydrogen bonding (NRHB) and the Perturbed-Chain Polar Statistical Associating Fluid Theory (PCP-SAFT) are presented. Both models are capable of describing pure fluid properties of IL (densities and solubility parameters) by using one set of parameters and the LLE in binary systems. This is to our knowledge the first paper presenting the SAFT modelling of binary LLE in ionic liquid systems.

Toward a COSMO equation-of-state model of fluids and their mixtures

The basic objective of this work is the development of an approximate, yet coherent and consistent equation-of-state model of fluids, which will benefit from recent developments in the successful COnductor-like Screening MOdel (COSMO)-type group-contribution models with their quantum-mechanical description of fluids. The development is done within our recent non-random hydrogen-bonding (NRHB) equation-of-state framework. In contrast to NRHB, the new model will not need any new parameters for the strong specific interactions, such as hydrogen bonds, since they will be provided by its COSMO component and the associated quantum-chemistry calculations. The bridge between COSMO and NRHB is the non-randomness factors as calculated by the quasi-chemical treatment of the non-random distribution of molecular entities in the system. Analytical expressions are provided for all basic thermodynamic quantities, including expressions for the cavitation and charging components of the solvation Gibbs energy. The new equation-of-state model is tested against experimental data for vapor pressures, heats of vaporization, and liquid densities of pure fluids and on phase equilibria of mixtures. The strength and perspectives of the new model are critically discussed.

Solvation Thermodynamics and Non-Randomness. Part I: Self-Solvation

The central theme in this series of papers is the development of a coherent and consistent equation-of-state model of fluids in the frame of solvation thermodynamics. Two main ingredients will be used for this purpose: the first will be the successful conductor-like screening model (COSMO) type group-contribution models with their quantum-mechanical description of fluids. and the second, our recent nonrandom hydrogen-bonding (NRHB) equation-of-state framework. The bridge between the two is the quasi-chemical treatment of the nonrandom distribution of molecular entities in the system, a treatment used by Henry Kehiaian in his DISQUAC group-contribution model. In this first part we develop the solvation formalism of NRHB and propose a first approach for turning the COSMO model into an equation-of-state model in a straightforward and consistent manner. Although the formalism is general, the focus is on the self-solvation of fluids. This development permits the calculation of the various components of solvation Gibbs energy. such as the cavitation and charging components or the enthalpic and the entropic ones. It permits, in particular. their study over a broad range of external conditions. The strength of the intermolecular forces and its role on the variation of these components. as well as their interdependence. are critically discussed.

Use of monomer fraction data in the parametrization of association theories

Association theories such as the CPA (cubic-plus-association), NRHB (non-random hydrogen bonding) equations of state and the various variants of SAFT (statistical associating fluid theory) have been extensively applied to phase equilibrium calculations. Such models can also be used for estimating the monomer fraction of hydrogen bonding compounds and their mixtures. Monomer fraction data are obtained from spectroscopic measurements and they are available for a few compounds such as pure water and alcohols as well as for some alcohol–alkane and similar mixtures. These data are useful for an understanding of the capabilities and limitations of association models. The purpose of this work is two-fold: (i) to compare the performance of three models, CPA, NRHB and sPC-SAFT, in predicting the monomer fraction of water, alcohols and mixtures of alcohol-inert compounds and (ii) to investigate whether “improved” model parameters can be obtained if monomer fraction data are included in the parameter estimation together with vapor pressures and liquid densities. The expression “improved” implies parameters which can represent several pure compound properties as well as monomer fraction data for pure compounds and mixtures. The accuracy of experimental monomer fraction data is discussed, as well as the role of monomer fraction data in clarifying which association scheme should be used in these equations of state. The results reveal that the investigated association models (CPA, sPC-SAFT and NRHB) can predict, at least qualitatively correct, monomer fractions of associating compounds and mixtures. Only, small differences are observed between the models. In addition, it has been shown that, using a suitable association scheme, a single set of parameters can describe satisfactorily vapor pressures, liquid densities and monomer fractions of water and alcohols. The 4C scheme is the best choice for water, while for methanol there is small difference between the 2B and 3B association schemes.

Equation-of-state modeling of mixtures with ionic liquids

A non-electrolyte equation-of-state model was used to describe the phase behavior of binary systems containing alkyl-methyimidazolium bis(trifluoromethyl-sulfonyl)imide ionic liquids. A methodology is suggested for modeling this phase behavior by using the Non-Random Hydrogen-Bonding (NRHB) model. According to this methodology, the scaling constants of the ionic liquid are calculated using limited available experimental data on liquid densities and Hansen's solubility parameters, while all electrostatic interactions (polar, hydrogen bonding and ionic) are treated as strong specific interactions. Using the aforementioned methodology, the model is applied to describe the vapor-liquid and the liquid-liquid equilibria in mixtures of ionic liquids with various polar or quadrupolar solvents at low and high pressures. In all cases, one temperature-independent binary interaction parameter was used. Accurate correlations were obtained for the majority of the systems, both, for vapor-liquid and liquid-liquid equilibria.

Evaluation of the Nonrandom Hydrogen Bonding (NRHB) Theory and the Simplified Perturbed-Chain-Statistical Associating Fluid Theory (sPC-SAFT). 2. Liquid−Liquid Equilibria and Prediction of Monomer Fraction in Hydrogen Bonding Systems

ADVERTISEMENT RETURN TO ISSUEPREVAddition/CorrectionORIGINAL ARTICLEThis notice is a correctionEvaluation of the Nonrandom Hydrogen Bonding (NRHB) Theory and the Simplified Perturbed-Chain-Statistical Associating Fluid Theory (sPC-SAFT). 2. Liquid−Liquid Equilibria and Prediction of Monomer Fraction in Hydrogen Bonding SystemsIoannis Tsivintzelis, Andreas Grenner, Ioannis G. Economou, and Georgios M. KontogeorgisCite this: Ind. Eng. Chem. Res. 2009, 48, 16, 7860Publication Date (Web):July 23, 2009Publication History Received6 July 2009Published online23 July 2009Published inissue 19 August 2009https://doi.org/10.1021/ie901084hCopyright © 2009 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views425Altmetric-Citations3LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (53 KB) Get e-AlertsSUBJECTS:Alcohols,Molecules,Monomers,Noncovalent interactions,Theoretical and computational chemistry Get e-Alerts

Modeling the Phase Behavior in Mixtures of Pharmaceuticals with Liquid or Supercritical Solvents

The concept of solubility parameter, which is widely used for the screening of solvents in pharmaceutical applications, is combined with a thermodynamic theory that is able to model systems with large deviations from ideal behavior. The nonrandom hydrogen-bonding (NRHB) theory is applied to model the phase behavior of mixtures of six pharmaceuticals (i.e., ibuprofen, ketoprofen, naproxen, benzoic acid, methyl paraben, and ethyl paraben). The pure fluid parameters of the studied pharmaceuticals were estimated using limited available experimental (or predicted) data on sublimation pressures, liquid densities, and Hansen's solubility parameters. The complex hydrogen-bonding behavior was explicitly accounted for, while the corresponding parameters were adopted from simpler molecules of similar chemical structure or/and fitted to the aforementioned pure fluid properties. In this way, the solubility of the studied pharmaceuticals in liquid solvents was calculated. The average root-mean-square deviation between experimental and calculated solubilities is 0.190 and 0.037 in log(10) units for prediction (calculations without a binary interaction parameter adjustment) and for correlation (calculations using one binary interaction parameter fitted to experimental data), respectively. In addition, using one temperature-independent binary interaction parameter the phase behavior of pharmaceuticals in supercritical CO(2) and ethane was satisfactorily correlated. Finally, preliminary encouraging results are shown concerning two ternary mixtures where the model is able to predict accurately the solubility of pharmaceuticals in mixed solvents based on interaction parameters fitted to corresponding single solvent data.

Modeling the vapor–liquid equilibria of polymer–solvent mixtures: Systems with complex hydrogen bonding behavior

The vapor–liquid equilibria of binary polymer–solvent systems was modeled using the Non-Random Hydrogen Bonding (NRHB) model. Mixtures of poly(ethylene glycol), poly(propylene glycol), poly(vinyl alcohol) and poly(vinyl acetate) with various solvents were investigated, while emphasis was put on hydrogen bonding systems, in which functional groups of the polymer chain can self-associate or cross-associate with the solvent molecules. Effort has been made to explicitly account for all hydrogen bonding interactions. The results reveal that the NRHB model offers a flexible approach to account for various self- or cross-associating interactions. In most cases model's predictions (using no binary interaction parameter k ij = 0) and model's correlations (using one temperature independent binary interaction parameter, k ij ≠ 0) are in satisfactory agreement with the experimental data, despite the complexity of the examined systems.

Modeling the solid–liquid equilibrium in pharmaceutical‐solvent mixtures: Systems with complex hydrogen bonding behavior

AbstractA methodology is suggested for modeling the phase equilibria of complex chemical mixtures with an equation of state (EoS) for the case where only limited experimental data exist. The complex hydrogen bonding behavior is explicitly accounted for and the corresponding parameters are adopted from simpler molecules of similar chemical structure and/or are fitted to Hansen's partial solubility parameters. The methodology is applied to modeling the solubility of three pharmaceuticals, namely acetanilide, phenacetin, and paracetamol, using the nonrandom hydrogen bonding (NRHB) EoS. In all cases, accurate correlations were obtained. The prediction ability of the approach was evaluated against predictions from the COSMO‐RS model. A thorough discussion is made for the appropriate modeling of solid solubility considering the effect of the difference of the heat capacities of the solute in liquid and solid state, ΔCp = Cpl − Cps, in the determination of solid chemical potential and, also, of the polymorphism of drugs. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Evaluation of the Nonrandom Hydrogen Bonding (NRHB) Theory and the Simplified Perturbed-Chain−Statistical Associating Fluid Theory (sPC-SAFT). 1. Vapor−Liquid Equilibria

A standard database for the validation of vapor−liquid equilibrium (VLE) models was used to evaluate prediction and correlation accuracy of the nonrandom hydrogen bonding (NRHB) theory and the simp...

Nonrandom Hydrogen-Bonding Model of Fluids and Their Mixtures. 2. Multicomponent Mixtures

Nonrandom hydrogen bonding (NRHB) lattice theory is extended here to multicomponent fluid mixtures rigorously. The model accounts for nonideal thermodynamic behavior of mixtures due to molecular connectivity of nonspherical molecules, weak van der Waals forces between first-neighbor molecular segments, and hydrogen-bonding interactions. The random distribution of molecules in the lattice is calculated using the generalized Staverman theory, while for the nonrandom correction, the Guggenheim quasi-chemical theory is adopted. Finally, the hydrogen-bonding contribution is based on Veytsman statistics as implemented in lattice fluid theory by Panayiotou and Sanchez. The equation of state is coupled with the mass action law due to hydrogen bonding, and both are solved simultaneously. The model is applied for the calculation of vapor−liquid, liquid−liquid, and vapor−liquid−liquid equilibria at low and high pressures of binary mixtures of fluids with large molecular size differences and/or different types of int...

Modeling of fluid phase equilibria with two thermodynamic theories: Non-random hydrogen bonding (NRHB) and statistical associating fluid theory (SAFT)

Two thermodynamic theories, the non-random hydrogen bonding (NRHB) and the statistical associating fluid theory (SAFT) are used to model phase equilibria of pure fluids and mixtures. The scaling parameters for several non-associating as well as self-associating fluids are estimated, for both equations of state, by fitting experimental vapor pressure and saturated liquid density data over a wide temperature range. For the correlation of phase equilibria of mixtures, one binary interaction parameter is calculated for each of the systems examined. Analysis of the results shows that NRHB model is more accurate for the correlation of saturated liquid densities and vapor pressures of most pure fluids. Also, NRHB is clearly more accurate than SAFT for the correlation of phase equilibria of binary mixtures that contain one self-associating fluid, while the accuracy of the two theories is comparable for the case of non-associating mixtures.