Figure 2 - uploaded by Theodora Spyriouni
Content may be subject to copyright.
Experimental data26 (points) and EoS correlation (lines) for the saturated liquid density of (a) alcohols and water, and (b) ketones.
Source publication
Polar forces have a considerable effect on the thermodynamic and phase equilibrium properties of pure and mixture fluids. In this work, the statistical associating fluid theory (SAFT) and perturbed chain–SAFT (PC-SAFT) are extended to explicitly account for dipole–dipole interactions. A recently proposed perturbation theory for pure dipolar fluids...
Context in source publication
Citations
... It should be noted that often the electrostatic interactions are not taken into account explicitly, assuming that they can be effectively accounted for in the dispersion term [29]. However, several models were developed [30,31,32] and the authors concluded that the addition of dipole-dipole interactions improve the results. Recently, it was demonstrated [27] that usage of water dipole moment as an adjustable parameter in PCP-SAFT-based cDFT leads to better quantitative agreement with experimental data on surface tension as well as binodal. ...
Theoretical modeling of water adsorption in micro- and mesoporous materials remains a challenging problem for physical chemistry and chemical engineering despite its great importance for industrial applications. Here, we present the theoretical study of bulk and inhomogeneous water within the classical density functional theory. Our model includes all important intermolecular interactions, such as dispersion, association, and dipole-dipole. We validated the model via comparison with existing literature experimental and computer simulation data. Among the others, the following water properties were compared: liquid-vapor binodal (T - ρ), surface tension, latent heat of vaporization, wetting contact angle, and adsorption isotherms on nonporous silica and alumina. Our computational results demonstrate good agreement with the experimental literature data and show similar trends compared to the several commonly used water models (SPC/E, TIP4P, TIP4P/2005). Because the presented model can accurately describe the thermodynamic and interfacial properties of water then it can be of interest to the adsorption community. Also, the model may serve as a starting point for further works regarding porous adsorbents characterization employing classical density functional theory.
... Their study also showed that the addition of dipole term had a significant effect on the phase equilibrium of methanol and ethanol, but it had little effect on higher 1-alkanols. Karakatsani et al. [6] developed SAFT and PC-SAFT equations of state by adding a dipole term to the PSAFT and PC-PSAFT equations of state, respectively. They obtained vapor pressure, vapor, and saturated liquid density for alcohols, ketones, water, and other polar materials based on the new equation of state for pure, binary, and ternary systems. ...
By combining a dipole expression with an Soave–Redlich–Kister, SRK, equation of state, a new SRK equation of state is developed. a0, ci\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_{i}$$\end{document}, b and bp, the parameters of this equation, were optimized for pure compounds by using experimental data of vapor pressure and saturated liquid density. Examining the modeling results for the dipolar compounds shows that this equation correlates well with their behavior. The physical properties of pure compounds, including the heat capacity, speed of sound, Joule–Thomson coefficient and enthalpy of evaporation were calculated using this equation of state, and were in good agreement with the experimental results. By combining a dipole expression with the SRK equation, a good improvement in the prediction of the Joule–Thomson coefficient of the liquid phase was made. Also, vapor–liquid equilibrium calculations were performed for four binary systems by using this SRK equation, which shows that the prediction of the system behavior by the revised SRK equation was improved.
... Based on the original PC-SAFT (perturbed-chain statistical associating fluid theory) EOS, 81 Karakatsani et al. proposed the tPC-PSAFT EOS model, which can describe mixed systems of dipolar and quadrupolar molecular fluids as well as gas-IL systems. 82 In this model, the residual Helmholtz energy consists of distinct contributions: ...
Predictive molecular thermodynamic models can bridge the gap between the microscopic molecular level and macroscopic system scale. Over the past few decades, ionic liquids (ILs), as a class of green solvents and functional materials, have received widespread research interest in the field of chemical processing owing to their unique physicochemical merits. This review aims to provide an easy‐to‐read and exhaustive reference regarding state‐of‐the‐art predictive thermodynamic models for ILs, with more focuses on UNIFAC‐ and COSMO‐based models and various applications involving phase equilibrium prediction, guidance for IL screening and design, and building equilibrium stage models for separation processes. This review provides a theoretical perspective on the structure–property relationships between molecular structures and phase behaviors for the systems and the constituted components covering a multi‐scale viewpoint from molecular level to industrial scale. Moreover, the predictive capacities of different thermodynamic models are comprehensively compared.
... The pure PhG PC-SAFT parameters (Table S3) were fitted from vapor pressure data available in the literature [51]. The PC-SAFT parameters of the other compounds (Table S3) used in this study (water, EG, 1,3-PD, Gly) were retrieved from the literature [34,[52][53][54][55]. ...
... The pure PhG PC-SAFT parameters (Table S3) were fitted to experimental vapor pressure data available in the literature [51]. The PC-SAFT parameters of the other compounds (Table S3) used in this study (water, EG, 1,3-PD, Gly) were retrieved from the literature [44,[52][53][54][55]. As depicted in Figure S14, the hydrogen bonds formed between HBD/water have a maximum that depends on the amount of water in the mixture, which leads to aggregation with the solute [75]. ...
Phlorotannins are highly bioactive phenolic compounds mainly found in brown algae. Phloroglucinol is the basic unit from which phlorotannins polymerize. Deep eutectic solvents (DES) are potentially beneficial for increasing phenolics solubility, therefore good solvent candidates for phlorotannins extraction processes. Solubility measurements were performed for phloroglucinol in pure water and aqueous mixtures of DES or their constituents, i.e., different hydrogen bond donors (HBD) and choline chloride (ChCl). The stable crystal form of the phenolic in equilibrium was phloroglucinol dihydrate within the studied temperature range (293.15-313.15 K) and water weight fractions (≥ 0.25). The water + ChCl + HBD mixtures yielded higher solubility for phloroglucinol dihydrate than the corresponding water + HBD or water + ChCl mixtures. Solubility predicted with PC-SAFT was in quantitative agreement with the experimental data. The solubility behavior of phloroglucinol dihydrate in the different mixtures was related to the hydrogen bonds formed using molecular dynamics and PC-SAFT.
... In the present contribution, choline chloride and methanol (MOH) are represented by the 2B scheme [35,55]. In contrast, to assess the association capability of hydrogen bond donors, ethylene glycol (EG) and glycerol (G) are modelled with 2B and 4C schemes [55][56][57]. The association among compounds forming the DESs and methanol is represented in Fig. 1, and the purecompound parameters are summarised in Table 1. ...
The search for new solvents which fulfil the needs of modern times has put the Deep eutectic solvents (DESs) in a leading role given their wide range of applications, versatility, low cost, and minimal environmental impact. For the above reason, it is critical to achieving predictive capabilities and the accurate description of their properties, both macroscopic and microscopic. In this work, DESs based on choline chloride as the hydrogen bond acceptor plus ethylene glycol and glycerol as hydrogen bond donors have been analysed in a mixture with methanol. Densities, excess volume and viscosity were determined by molecular dynamics and predicted by the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). Radial distribution functions and the number of hydrogen bonds derived from molecular simulations confirmed an anticipated bonding network within the liquid, with significant ordering interactions. When methanol is added to the eutectic solvent become incorporated into this structure as a second hydrogen bond donor. Methanol reduces the viscosity, but the eutectic solvents retain their characteristics because of methanol. The analysis performed in this work could be a valuable feature of the new theory in developing more realistic models of the hydrogen-bonding interaction in deep eutectic solvents.
... For investigating the effect of polar interactions on the thermodynamic behavior of fluid systems within the framework of SAFT-based EoSs, the inclusion of an additional perturbation term (multipolar term) to explicitly account for the effect of these polar interactions is a necessity for accurate and representative models of polar fluids. 31,32 The framework of SAFT-based models has been extended to the explicit modeling of polar interactions, such as polar PC-SAFT, 2,33-35 PCP-SAFT, 36,37 truncated PC-SAFT, [38][39][40] sPC-SAFT, 41 GC-SAFT, 42,43 SAFT-VR + D/Q, 44,45 SAFT-VR Mie, 46,47 and polar soft-SAFT. 48 These different models, in some cases validated with molecular simulation data, have been applied to describe the thermodynamic behavior of a variety of experimental pure fluids and multicomponent mixtures. ...
In this work, polar soft-Statistical Associating Fluid Theory (SAFT) was used in a systematic manner to quantify the influence of polar interactions on the phase equilibria, interfacial, and excess properties of binary mixtures. The theory was first validated with available molecular simulation data and then used to isolate the effect of polar interactions on the thermodynamic behavior of the mixtures by fixing the polar moment of one component while changing the polar moment of the second component from non-polar to either highly dipolar or quadrupolar, examining 15 different binary mixtures. It was determined that the type and magnitude of polar interactions have direct implications on the vapor-liquid equilibria (VLE), resulting in azeotropy for systems of either dipolar or quadrupolar fluids when mixed with non-polar or low polar strength fluids, while increasing the polar strength of one component shifts the VLE to be more ideal. Additionally, excess properties and interfacial properties such as interfacial tension, density profiles, and relative adsorption at the interface were also examined, establishing distinct enrichment in the case of mixtures with highly quadrupolar fluids. Finally, polar soft-SAFT was applied to describe the thermodynamic behavior of binary mixtures of experimental systems exhibiting various intermolecular interactions (non-polar and polar), not only demonstrating high accuracy and robustness through agreement with experimental data but also providing insights into the effect of polarity on the interfacial properties of the studied mixtures. This work proves the value of having an accurate theory for isolating the effect of polarity, especially for the design of ad hoc polar solvents.
... Modified PC-SAFT expressions have also been introduced to account for long-range forces related to electrostatic effects due to dipole and quadrupole (and induced) moments or to the presence of charges. PC-SAFT was in fact improved by adding polar and quadrupolar contributions and extending PC-SAFT to electrolytes [111][112][113][114][115][116][117][118][119][120][121][122][123][124], with the obvious introduction of additional parameters. As already underlined, in the case of binary mixtures no mixing rules are required for the chain and association terms. ...
Knowledge of the thermodynamics of sorption of low molecular weight compounds in rubbery and glassy polymers is of great relevance to understanding the physics and dynamics of polymer foaming and for the technological implementation of foaming processes. This chapter is devoted to the illustration of the recent advances in statistical thermodynamics approaches toward the elaboration of a theoretical framework aimed at the description of sorption thermodynamics of small molecules in polymers, addressing also systems that involve specific intra- and intermolecular interactions.
In particular, the attention is focused on sorption models rooted on Equation of State theories. Notably, the models discussed here are structured to specifically account for nonrandom distribution of molecular species and for dealing with several kinds of specific interactions, addressing both for the case of rubbery polymers and of out-of-equilibrium glassy polymers. Moreover, a description of the experimental approaches devoted to the measurement of sorption isotherms is provided.
Several kinds of experimental methodologies aimed at the description of sorption in polymers are described with attention also to the molecular-level characterization of the polymer-penetrant systems provided by vibrational spectroscopy (FTIR, Raman), which allows for the development of in situ, time-resolved measurements.
Sorption thermodynamics in polymers is examined here considering the contact of polymer with a penetrant in a state of a subcritical vapor, of a supercritical fluid, or of a gas.
... In their paper [33], Muller and Gubbins conclude that these interactions are more important than it was previously thought and this would also fully agree with the results shown in Table 1. An extension of Equation (33) by including explicitly the dipoledipole contribution was considered by Karakatsani et al. [81] to deal with strongly dipolar fluids and recently also by Ahem et al. [82]. An extension along the same path was made by Liu et al. [83] who, in addition to incorporating the dipole-dipole interaction, employed the hard-core Yukawa for the monomer-monomer interaction instead of the LJ. ...
... Besides the original SAFT with hard sphere monomers, SAFT-HS, two other main versions are SAFT-VR (variable range) [87,88] and PC-SAFT (perturbed chain) [49]. Furthermore, there is also a group contribution version, SAFT-γ [89], SAFT-RPM [90][91][92] dealing with electrolytes, and SAFT-VR-D [81,93] for dipolar and dipolar and associating fluids. The most recent development includes SAFT-µ [80,94] whose monomer units interact via a Mie-type potential with adjustable exponents. ...
With the exception of purely empirical equations of state, the remaining equations can bear the tag “molecular based.” Depending on their derivation, their molecular basis varies from those having only some traits of ideas/results of molecular considerations to equations obtained truly by application of statistical mechanics. Starting from formulations of statistical mechanics of liquids, a general scheme for derivation of truly perturbed equations is formulated. Two approaches, Bottom-Up and Top-Down, are identified, and the individual steps are discussed in detail along with several rules that reflect the essentials of the physics of fluids, which should be observed. Approximations and simplifications used in the implementation of the scheme are then analyzed in light of these rules, and a classification of equations of state is introduced. To exemplify these approaches in detail, theoretical and SAFT routes toward an equation of state are considered for water along with a potential way of merging these two approaches to obtain a reliable equation with a potential to predict the behavior of real fluids and not only to correlate them.
... Within the SAFT framework, the most suitable association scheme selection for ammonia is still questionnaire and was the subject for several researchers. Most of previous studies have parameterized the ammonia parameters using the 2B [13], 3B [6,9] or 4B [7,8] or 4C [11,16] or 4D [5,10,12,15] association scheme. All of these schemes describe well the PVT properties of pure ammonia, unfortunately, almost failed to correctly describe the phase equilibria of binary mixtures studied in this work. ...
... GC-PPC-SAFT [15] crossover SAFT [6] CP-PC-SAFT [16] SAFT-VR [5] PC-SAFT [11] SAFT-VR-Mie [7] SAFT [8] Soft-SAFT [12] PC-SAFT [9] PC-SAFT (this work) PC-SAFT [13] Soft-SAFT [10] 1300e1585 K [98] 1470e1585 K [38] 1410 K [49] 1550e1630 K [99] 1600 K [39] 1600 K [100] 1645 K [101] 1412e2212 K [102] 1863e2263 K [51] 1460 K [103] 1400e1460 K [42,104] 1400e1600 K [105] 1560 K [106] 1565 K [53] 1812 K [107] Fig. 1. Vapor pressures, liquid density (correlation-left) and heat of vaporization (prediction-right) of ammonia. ...
... Thus, the knowledge of the VLE properties of these mixtures plays an important role for numerous industrial applications [76]. In this section, PC-SAFT molecular parameters of all considered refrigerants were obtained by simply fitting to its vapor pressure and liquid density using the objective function in equation (9). Note that, these compounds are considered as non-polar, non-associative molecules and possess their own molecular parameters ( Table 1). ...
The phase equilibria of ammonia containing systems were investigated using the modified group-contribution PC-SAFT approach. The new proposed parameter set for ammonia with the 2B association scheme shows a better correlation/prediction of the phase behavior of ammonia and its mixtures over other published PC-SAFT parameter sets. The association energy parameter of pure ammonia and its complexes obtained in this work shows a very good agreement with the experimental/simulation data.
The assignment of the association scheme for ammonia was discussed and studied using the PC-SAFT EoS by applying the model to describe the phase equilibria of different mixtures. It was found that, in order to accurately describe the phase behavior of ammonia + aromatic, + unsaturated hydrocarbon or + refrigerant (HFCs/HCFCs) mixtures, a cross-association link was necessary. For almost considered mixtures, good vapor-liquid and liquid-liquid equilibria computation results were obtained including the double azeotropes systems.
... The most widely applied expressions for the multipolar perturbation term accounting for multipolar interactions in chainlike fluids applied to SAFT EoSs are those based on Jog and Chapman (JC), 7, 25 Gross and Varbec (GV), 26,27 and Economou and co-workers (KSE), 28,29 extending original theories by Gubbins and Twu,30,31 Saager and Fischer, 32,33 and Larsen et al., 34 respectively. All of these expressions for multipolar interactions have been successfully applied to the framework of the perturbed-chain SAFT (PC-SAFT) to model dipole-dipole, quadrupole-5 quadrupole and cross-polar interactions (i.e. ...
... dipolar-quadrupolar). These three expressions formed the basis for a number of different polar versions of SAFT EoSs such as polar PC-SAFT, 2,7,35,36 PCP-SAFT, 26,27 truncated PC-SAFT, 28,29,37 sPC-SAFT, 23 GC-SAFT, 38,39 SAFT-VR + D/Q, 40,41 SAFT-VR Mie 42,43 and others. We refer the reader to the works of Al-Saifi et al. 44 and Cripwell et al. 45 on comparing the application of the three expressions for multipolar contribution (i.e. ...
The consideration of polar interactions is of vital importance for the development of predictive and accurate thermodynamic models for polar fluids, as they govern most of their thermodynamic properties, making them highly non-ideal fluids. We present here for the first time the extension of the soft-SAFT equation of state (EoS), named polar soft-SAFT, to explicitly model intermolecular polar interactions (dipolar and quadrupolar), using the approach of Jog and Chapman (P. K. Jog and W. G. Chapman, Mol. Phys. 97(3) 307–319 (1999)). The theory is first validated using molecular simulation data for a wide range of polar model systems including Stockmayer fluids, LJ dimers with dipole, and quadrupolar LJ fluids, for a wide range of thermophysical properties such as liquid density, vapour pressure, surface tension and heat capacities. Excellent agreement between polar soft-SAFT and simulation data has been obtained for all examined fluids and properties for systems exhibiting low to intermediate polar strength, while the agreement deteriorates at very high polar strengths. Once validated with simulations, the equation has been applied to calculate vapour-liquid equilibria (VLE), surface tension and second-order derivative properties of systems such as 2-ketone and methane chloride families as showcases for dipolar fluids and the benzene family for quadrupolar fluids, finding very good agreement with experimental data. In order to preserve the robustness of the model, the experimental value of the dipole or quadrupole was used in these calculations, while the additional parameter for the polar fluids was set a priori rather than included in the fitting procedure. The excellent agreement found with simulations and experiments empowers the soft-SAFT equation with new capabilities for the development of robust and accurate molecular models of polar fluids of industrial relevance.
