Soft-SAFT Transferable Molecular Models for the Description of Gas

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Soft-SAFT Transferable Molecular Models for the Description of Gas Solubility in Eutectic Ammonium Salt-Based Solvents R. M. Ojeda† and F. Llovell*,† †

Department of Chemical Engineering and Materials Science, IQS School of Engineering, Universitat Ramon Llull, Via Augusta 390, 08017, Barcelona, Spain S Supporting Information *

ABSTRACT: Research on new sustainable technologies focused on carbon capture is a priority in most industrial processes, particularly in the combustion of fossil fuels. One challenging option is the replacement of corrosive, volatile, and nonbiodegradable amine-based solvents by the more tunable, greener, and less expensive deep eutectic solvents (DESs). However, the large amount of eutectic mixture combinations requires an intense experimental characterization. The implementation of semipredictive theoretical models to describe the physicochemical properties is a useful tool to reduce the amount of experimental work. In this contribution, the well-established soft-SAFT equation of state is applied to develop consistent molecular models of different eutectic ammonium chloride and bromide saltbased DESs with ethylene glycol and levulinic acid to describe their density and the solubility of CO2 and SO2 in them. In all cases, DESs are modeled as a mixture of two independent entities, overcoming the limitations of the onecompound approach. The choice of the number of association sites is assessed combining previous experience with the analysis of the molecules charge density using the COSMO-RS software. The results obtained show an accurate description of the density and gas solubility, while presenting a set of transferable molecular parameters that can be used to screen new DESs mixtures.

1. INTRODUCTION One of the most difficult challenges in the coming years is supplying enough energy to maintain the elevated standards of living, while satisfying water and food demand of a population that is estimated to increase further to 9.7 billion in 20501 without harming the environment. Even if there is an effort to find other natural resources, this increasing energetic demand is still primarily dependent on the combustion of fossil-fuels such as coal, oil, and natural gas.2 Among the several environmental concerns associated with these processes, the release of flue gases containing carbon dioxide (CO2) is one of the most urgent issues to solve, due to its impact on global warming. According to the latest emissions report of the European Comission, 35.8 Gton of CO2 were emitted during 2016 in the world.3 All experts agree that the effects of excessive CO2 originated from anthropological sources have destabilized the natural carbon cycle and, at this point, are causing changes in the weather patterns, having as a consequence the appearance of phenomena such as the sea level rise, droughts and floods, affecting food production.4 To address this global problem and comply with the policies’ roadmaps, such as cutting by at least 80% CO2 emissions in the European Union (EU) for 2050,5 multiple approaches are listed and compared to find adequate solutions.6 Among them, carbon capture and storage (CCS) techniques represent an excellent strategy to capture large amounts of intensive CO2 emitters. If one focuses on the separation stage of these © XXXX American Chemical Society

processes, absorption techniques stand out for their high efficiency and maturity in their deployment. In this approach, the sorbent is typically an alkanolamine, or a blend of different amines, with monoethanolamine (MEA) and diethanolamine (DEA) being the most commonly used. However, there is constant research in the improvement of the capture process due to the volatility and corrosiveness of these sorbents, which is translated into an energy intensive regeneration stage unit, significantly increasing the operational costs. 7−9 Additionally, when CO 2 is produced from combustion, other gases such as sulfur dioxide (SO2) are emitted and must be separated because of their impact on air quality and their transformation to other pollutants, such as sulfur oxides (SOx), that have a harmful impact on human health and the environment.10 For this reason, when new solvents are studied for CCS techniques, it is important to determine the solubility of this gas and the separation selectivity with respect to CO2. One of the directions of these studies takes into account the possibility of using ionic liquids (ILs) and/or deep eutectic solvents (DESs). These compounds have claimed the attention of the industry because of the possibility of tuning Special Issue: Emerging Investigators Received: December 22, 2017 Accepted: January 23, 2018

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DOI: 10.1021/acs.jced.7b01103 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Finally, Haghbakhsh and Raeissi27 studied the density and CO2 solubility in a total of 15 DESs, including those presented in the present work, with the CPA EoS. They described the DESs considering them as one-compound systems and then established a model with and without CO2 solvation, also including a temperature-dependent binary parameter. In a subsequent publication, the same authors extended this work to model a total of 27 DESs with CPA and PC-SAFT, coupling the friction theory to describe their viscosity.25 These are some of the few examples where a molecular-based EoS, explicitly accounting for hydrogen bonding interactions, has been used to study this type of systems. An additional computational tool to provide new insight on understanding the behavior of these solvents is the use of quantum chemistry-based techniques, such as COSMO-RS. This software has claimed recent attention in this field due to its potential to determine the charge density on the surface of the molecule and their mixtures and to predict relevant properties for DESs screening, such as activity coefficients.28 Some interesting applications include the study of acid gas removal using ILs29 and, more recently, of different DESs such as ChCl/urea for natural gas dehydration30,31 and tetrabutylammonium chloride ([TBA][Cl]) with levulinic acid (LevA) for liquid−liquid extraction.32,33 Moreover, COSMORS has also demonstrated to be very useful in the extractive denitrification of liquid fuels34,35 and the removal of benzene from cyclohexane.36 In all these works, it is possible to infer the number and type of bonding interactions of the molecules forming the eutectic by studying the polarity at the different regions of the charge density σ-profiles, as it is carried out in this work. In the current contribution, it is intended to provide additional knowledge of deep eutectic solvents by applying the molecular-based soft-SAFT EoS to accurately describe the physicochemical properties of different tetralkylammonium bromide- and chloride-based DESs, with particular emphasis on the development of transferable molecular models, keeping a set of parameters with physical sense. The soft-SAFT EoS37 provides a physically grounded theoretical framework that explicitly accounts for hydrogen-bonding effects using a term derived from Wertheim’s first-order perturbation theory38−41 and also uses a Lennard-Jones term37 to consider van der Waals interactions. Within this framework, it is possible to describe the thermophysical properties and phase behavior of complex molecules and their mixtures with excellent agreement with experimental data, as it has been demonstrated for ILs42−49 and their mixtures in aqueous systems.50−56 Additionally, COSMO-RS is used to support the molecular models developed within the soft-SAFT framework by checking the charge density profiles of these molecules, facilitating the assessment related to the choice of the number of associating sites. A relationship between the molecular parameters of the different individual components is developed to transfer the parameter sets to new components of similar DESs. The new modeled compounds are then used to describe the solubility of CO2 and SO2 using a semipredictive method, comparing the results with the available experimental information and predicting the feasibility this compounds to carry out for these particular gases separation. The paper is structured as follows: first, a brief introduction to the theoretical approaches employed in this work is given,

the physicochemical properties by a modification of the cation−anion pair of the salt. This versatility makes them an attractive alternative for a wide range of applications.11−16 However, ILs present some disadvantages that can lag their industrial application, such as a toxicity (mostly depending on the alkyl chain length of the cation) similar to other organic solvents, a difficult and expensive synthesis and low biodegradability. Luckily, DESs cope better with these problems, as they are commonly given by a mixture of two or more substances resulting in a nontoxic, cheap, biodegradable mixture with a lower melting point than that of the individual constituents.17,18 This phenomenon is caused by the strong association interactions between one of the compounds, the hydrogen bonding acceptor (HBA), which is normally formed by a halide salt, and the other compound, the hydrogen bonding donor (HBD), which is a neutral complexing agent. Consequently, the thermodynamic behavior of DESs is strongly affected by this type of interaction. The complexity of the hydrogen bonding networks originated in certain DESs is still under investigation due to the vast number of structures that these solvents can present. In this regard, molecular modeling techniques have provided accurate information on some of these compounds and have contributed to describe the physicochemical properties of some DESs departing from the understanding of the physical interactions occurring in these systems.19−21 Unfortunately, the literature related to the understanding and modeling of this type of solvents is not abundant and the use of computational-aided tools to screen the physicochemical behavior of different combinations of HBAs and HBDs is at a premature stage. Most of these studies have focused on understanding the complex interactions between choline chloride (ChCl) (HBA) and urea (HBD), identifying different association structures between both compounds and comparing the most energetically favorable.19 This information is crucial when applying a molecular-based equation of state (EoS) to describe the properties of DESs, as it is done in some recent contributions with the perturbed-chain statistical associating fluid theory (PC-SAFT),22−25 soft-SAFT,26 and cubic-plus-association (CPA) EoSs.25,27 Held and co-workers22,23 have used the PC-SAFT EoS to model different tetraalkylammonium chloride ([TXA][Cl]) with lactic acid (LA) and fatty acids (FA) at different ratios. With LA,22 they compared a model considering the DES as a single compound with a model where the DES was treated as a mixture and each compound had its own molecular model, obtaining better results with the second approach. In collaboration with other authors, they have recently extended the calculation of DESs to solid−liquid equilibria.24 Lloret et al.26 extended the study of these salts with lactic acid to other HBDs, such as ethylene glycol (EG) and triethylene glycol (TEG), and to other properties, such as surface tensions and viscosities, by using an extended version of the soft-SAFT EoS. They also made a comparison between a pseudopure component approach and the two-compounds approach. In both cases, excellent results were achieved when comparing to experimental data, although the second one provided a higher predictive degree, as it was composition independent. Both studies showed how the use of these type of EoSs can theoretically describe the physical interaction and the physicochemical and thermodynamic properties of these complex compounds with excellent agreement with experimental data. B



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distribution function between LJ molecules, being consistent with the reference term. The chain term introduces a parameter related to the number of segments joined, called the chain length, m. Additionally, the association contribution defines each association site with a characteristic volume, kHB, and energy, εHB, of association. The extension of the chain and association terms to mixtures is straightforward, as they were originally written for mixtures. The only particular feature is the evaluation of the crossed molecular parameters of association when dealing with associating mixtures.37,58 In this work, the geometric and arithmetic combining rules for the associating energy and volume, respectively, are used, as done in previous contributions.53−56

starting by the core of the modeling presented here, the softSAFT EoS, as well as some information about COSMO-RS, which is used to decide on the most appropriate molecular model. On the basis of the theory, the molecular models developed for the different DESs are described and justified in detail. Then, the results section displays the performance of these models to describe the density of these DESs at different conditions, highlighting the transferability of the molecular parameters. Additionally, the solubility, absorption energy, and selectivity of CO2 and SO2 in these DESs is also assessed. Finally, the conclusions of this work are depicted in the last section.

2. THEORY 2.1. The Soft-SAFT Equation of State. The soft-SAFT EoS37,57 is one of the most popular versions of the original SAFT58,59 used to accurately describe the behavior of mixtures with hydrogen-bonding interactions characterized by the strength of the short-range directional forces. As any SAFT-type equation, soft-SAFT is based on Wertheim’s first-order thermodynamic perturbation theory (TPT1),38−41 and is expressed in terms of the residual Helmholtz energy, Ares, considering it as the difference between the molar Helmholtz energy of the fluid, A, and that of an ideal gas at the same temperature and molar density, Aid. This residual energy can be assumed to be the sum of different major contributions to a given molecule: the repulsion−dispersion term of an individual segment, Aref, the chain formation term joining these segments, Achain, and the association term between molecules due to hydrogen bonding and other short-range directional forces, Aassoc. Furthermore, for molecules exhibiting polarity, a polar term is added, Apolar. Ares = A − Aid = Aref + Achain + Aassoc + Apolar

εijHB =

kijHB

As the description of these contributions has been extensively reviewed, the reader is referred to the original works.37,57 Only a few particular details are summarized here. The reference term in soft-SAFT is based on the use of a Lennard-Jones (LJ) intermolecular potential for the reference fluid, where the repulsion and attraction forces are considered in a single term, which is calculated using the Johnson et al. expression.60 The LJ is defined by a characteristic segment diameter, σ, and a certain LJ potential energy, ε, which become two parameters of soft-SAFT. The extension of this term to mixtures is done through the van der Waals one-fluid (vdw-1f) theory.37,61 This theory accounts for the difference in volume and energy of the mixture from the bare sum of their individual contributions. The computation of the vdw-1f theory requires the evaluation of the crossed size and energy LJ parameters. The generalized Lorentz−Berthelot combining rules are used for the segment diameter and the intermolecular energy in eqs 2 and 3, respectively. (2)

εij = ξij(εiiεjj)1/2

(3)

1/3 ⎤3 ⎡ HB1/3 + kjjHB ⎥ kii ⎢ = ⎢ ⎥ 2 ⎣ ⎦

(4)

(5)

The polar contribution to the residual Helmholtz free energy is obtained using a perturbation in terms of a Padé expansion, as proposed by Gubbins and Twu62 and extended to chain molecules by Jog et al.63 The details of the application in softSAFT can be found in a previous contribution.64 As a result of the treatment, the effective quadrupole moment Q and the fraction of segments in the chain containing the effective quadrupole xp are included in the equation. 2.2. COSMO-RS. Quantum-based equilibrium thermodynamic methods have demonstrated to be also a great tool screening alternative new solvents in separation technology. In particular, methods predicting the chemical potential screening charge density, such as conductor-like screening model for realistic solvents (COSMO-RS) have been proven to be very successful.30−36 An extensive explanation of the theoretical background behind the work of Klamt and co-workers can be found in the referred literature.65−67 The idea behind COSMO-RS is to create a virtual conductor embedding the molecule using continuum solvation models to determine the charge distribution of the molecule. Afterward, DFT calculations are used to estimate the chemical potentials, from which other thermodynamic properties, such as the activity coefficients or the solubility, are predicted. In this work, COSMO-RS is used to qualitatively identify the regions in which hydrogen bonding occurs using the charge distribution in the form of σ-profiles. This is done to assess an adequate choice of the number of association sites presented in the studied DESs with soft-SAFT. The σ-profile describes the corresponding polarity of the different areas of the molecule. In these plots, each peak corresponds to the charge density of an atom constituting the molecule. When a constituent-atom presents a positive partial charge, it is screened as a negative charge density and vice versa. To obtain these profiles, the geometry of each salt and the HBD compounds forming the eutectic must be optimized first. The optimization is done using ADF software,67 where the molecules are drawn and preoptimized to reduce the computational effort. Then, the optimization is set under the framework of the Hartree−Fock level and double-ξ (DZ) basis set.68 The choice is based on the accurate results obtained in other contributions.28,36 Once the individual compounds are optimized, a Becke-Perdew66 and a triple-ξ valence potential (TZP) basis set is used to have a better

(1)

⎛ σii + σij ⎞ σij = ηij⎜ ⎟ ⎝ 2 ⎠

εiiHBεjjHB

In eqs 2 and 3, ηij and ξij are the unlike size and energy binary parameters, to account for the differences from the combining rule, as a result of the different nature of the compounds. The chain and association terms are formally identical in all SAFT equations. In soft-SAFT, they depend on the radial C



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3. MOLECULAR MODELS The molecular models used to describe the DESs and the components of the eutectic mixture are a key aspect during the parametrization of the molecular parameters and their future transferability. In several contributions from the literature,25,27,71 the eutectic mixture has been considered as a pseudopure compound with an average molar mass based on the ratio between its constituents, and the self-association between the HBA and the HBD to form a hydrogen bond. Even though this approach has been demonstrated to accurately describe the physicochemical behavior of these solvents, some limitations of this assumption restrict its use. In particular, the transferability of the model becomes more limited, as it involves a composition dependence on the fluid. More importantly, the capability of the model to describe liquid−liquid equilibrium (LLE) in aqueous systems, in which the eutectic can have a different composition in each liquid phase, is limited. Consequently, new approaches to model these solvents from their individual constituents are under development. On the other hand, particular care must be taken if a DES is modeled with their constituents as independent entities, as most of the pure compounds forming it are solid at ambient conditions. Since a SAFT-type EoS is a theory for fluids, it is necessary to apply new approaches to model these compounds.22,26 Hence, two options are possible, either treating the DES as a single compound or as a mixture of two compounds. For the first case, a simple molecular model of a homonuclear chain with two associating sites mimicking the interactions between the two compounds is proposed, following the same assumptions provided in our previous work on the [TXA][Cl]-based DESs.26 The performance of this model is included for completeness in the Supporting Information. For the second more realistic case, an individual molecular model for each salt and for EG, TEG, and LevA is proposed here. The molecular models for [TXA][Cl], EG, and TEG are collected from previous work26,72 for consistency with the published data, while the [TXA][Br] and LevA models are established for the first time here for soft-SAFT. As previously explained, COSMO-RS is used to assess the adequacy of the number of association sites chosen in the soft-SAFT molecular model, helping to identify the charged density points of the molecule, in a similar manner as done in the work of Pereira et al.45 For this purpose, the surface charge distribution and σ-profiles of [TXA][Br] and LevA are plotted in Figure 1 and Figure 2, respectively. The LevA σ-profile, represented in Figure 2a, presents one peak at −0.007 eA−2 and a second smaller one at 0.011 eA−2. The former is a positive charge attributed to the H+ of the carboxylic group, while the latter peak is considered as a negative charge due to the presence of the O− in the ketone group. This can be better appreciated in the reconstructed surface charge distribution, see Figure 1a. On the basis of these facts, a two-site association model within the soft-SAFT framework is proposed for the LevA molecule (also shown in Figure 2a). The family of [TXA][Br] presents identical polarities independently of the alkyl chain length of the cation, as it is observed in the σ-profile of Figure 2b, where two clearly charged peaks, plus a third one apparently without charge, are presented. The identification of these peaks can be determined using Figure 1: the peaks at the range between

characterization of the charge distribution. Once the necessary data are calculated, the software COSMO-RS retrieves the σprofile of the DESs studied. The combination of soft-SAFT with COSMO-RS to define the molecular model enhances the accuracy and transferability of the predicted molecular parameters of each compound. 2.3. Enthalpy and Entropy of Dissolution. Other useful thermodynamic properties to quantitatively determine and describe the absorption of a gas in a solvent are the solution enthalpy and entropy. While the former is useful to infer the strength of the bond between the solvent, in this work the eutectic mixture, and the solute, (i.e., CO2 and SO2), the latter indicates the degree of order when the gas is dissolved in the solvent. Both functions of state can be derived from the Claussius−Clapeyron equation,69 and their value at different constant compositions can be calculated using the data obtained with soft-SAFT EoS. The equations for each case are described as ⎛ ∂ln Pivap ⎞ ΔHdis = R ⎜ ⎟ ⎝ ∂(1/T ) ⎠x

(6)

i

⎛ ∂ ln Pivap ⎞ ΔSdis = −R ⎜ ⎟ ⎝ ∂ ln T ⎠x

i

(7)

where ΔHdis is the molar enthalpy of absorption; ΔSdis is the molar entropy of absorption; R is the universal gas constant (8.3145 J·mol−1·K−1); and Pivap is the vapor pressure of the dissolved gas. 2.4. Henry’s Law Constants and Gas Selectivity. The calculation of the main thermodynamic properties from softSAFT allows the evaluation of one of the most widespread thermodynamic parameters used to describe carbon dioxide capture efficiency in any solvent: the Henry’s law constant.26,45,70,71 This constant is related to the amount of a specific gas dissolved in a liquid at a determined isotherm and can be calculated from predicted data using the following equation: Hi = lim xi → 0

fiL (P , T , ρ) xi

(8)

In this equation, the Hi is the Henry’s law constant, xi is the molar fraction of the gas dissolved in the liquid phase, P is the system pressure, T is the temperature, ρ is the density, and f iL is the fugacity that in the studied case, at atmospheric pressure and moderate range of temperatures, can be approximated to the vapor pressure. The evaluation of this limit can be simplified using l’Hôpital’s rule as the slope of the gas vapor pressure against the molar fraction of the dissolved gas at infinite dilution. Once Henry’s law constants are predicted using the calculated data of the selected gases, it is possible to estimate the gas selectivity of each solvent between both gases considered in this work, SO2 and CO2, respectively. The equation used for this calculation is SSO2 /CO2 =

HDES,CO2 HDES,SO2

(9) D



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the same type (AA, BB interactions) and with different sites (AB interactions). Additionally, a model for CO2 and SO2 molecules is required to estimate their solubility in the [TXA][Br]:LevA studied DESs. As these molecules had been studied in previous publications, their molecular models and parameters are retained here.44,64 CO2 is modeled as a Lennard-Jones (LJ) chain, where quadrupolar interactions are explicitly considered. The fraction of segments in the chain containing quadrupoles xp is fixed to 1/3, while the quadrupolar moment Q was effectively fitted to VLE data and compared with the experimental value, in order to ensure it is of a similar order of magnitude. Contrarily to CO2, SO2 presents weak dipolar interactions. Since these are very slight, and in order to preserve the original model, the molecular model for this gas describes the dipole effect by means of two association sites of different natures (positive and negative, respectively). This approach has been previously used to describe the solubility of SO2 in several ionic liquids with great accuracy between experimental and modeling data in the range of conditions used in this work.44

4. RESULTS Once the molecular models for each molecular have been proposed, the parametrization of the different molecules involved in this work is done. However, as mentioned before, a different strategy from the classical fitting must be used to estimate the properties of a DES as a mixture of two compounds. In Figure 3, the path followed to find an accurate molecular model for each DES, enhancing the transferability among them, is highlighted. This will facilitate the reader the analysis of the results. 4.1. [TXA][Cl] and [TXA][Br] Families with EG and Lev Acid. Following the path summarized in Figure 3, this study departs from the reoptimization of the tetrabutylammonium chloride molecular parameters [TBA][Cl]. The reason behind this refitting is the recent publication of a new modeling study of the glycols family with soft-SAFT, in which a more refined model was used to determine the parameters of the glycols family, using new experimental data.72 As the previous parametrization of [TBA][Cl] was done using a eutectic mixture with TEG, the new parameters of this molecule have an impact on the [TBA][Cl] parametrization. The new optimization, done using [TBA][Cl]:TEG density data at four different ratios, provides similar parameters and the same excellent degree of accuracy (AAD% of 0.067%) than the one obtained before.26 The new parameters are included in Table 1, while the temperature-density diagram for this eutectic mixture is provided in the Supporting Information (Figure S1). Once the [TBA][Cl] parameters have been established, the equivalent ammonium-based salt with bromide, [TBA][Br], is parametrized (Stage 1 in Figure 3). For this purpose, a DES of this compound with EG has been used to find the parameters of the salt. As previously mentioned, the highest degree of transferability is sought in order to have consistent sets of molecular parameters between compounds with similar chemical structures. In this regard, different strategies were used to determine the transferability of the molecular parameters between the [TBA][Br] and the [TBA][Cl] salts, looking for a compromise between simplicity and accuracy. As a working hypothesis, the energy and volume of association of both fluids was kept constant, assuming that

Figure 1. Surface charge density obtained with COSMO-RS and molecular structure indicating with dashed circles the association sites considered in the molecular model in soft-SAFT for (a) LevA, (b) [TEA][Br], (c) [TPA][Br], and (d) [TBA][Br].

−0.003 and −0.006 eA−2 are attributed to the positive charge caused by the N+ of the [TXA]+, while the peaks between 0.016 and 0.017 eA−2 are generated by the presence of the anion [Br]−. Additionally, the smaller polar peaks between 0 and 0.002 eA−2 can be attributed to the interaction of the alkyl-chain with the anion. Therefore, it is plausible to consider a molecular model with two association sites, one representing the positive charge of the N+, and another one for the negative charge of the [Br]−. Besides, the molecular model presented in previous works26 for the [TXA][Cl] family is supported by this work since both salts have a similar structure. In the present work, [TXA][Cl] molecular models are extracted from the above-mentioned work, where two association sites, one for the cation N+ and another for the anion [Cl]−, are considered. The molecular model for TEG and EG and their soft-SAFT molecular parameters are taken from the work of Crespo et al.72 In that work, glycols were considered as LJ chains with one associating site for each hydroxyl end group, having two different association sites per molecule that account for the dual positive−negative nature of the hydroxyl group, allowing the interactions between sites of E



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Figure 2. σ-Profile obtained with COSMO-RS indicating the observed polarization and sketch of the molecular models used with soft-SAFT for the (a) LevA and (b) [TXA][Br] family.

chain length is dependent on the composition (ratio) of the mixture (see Table S1). Luckily, a linear relationship with the averaged molecular weight can be established, allowing the prediction at different compositions:

association contribution due to hydrogen bonding is of the same order in both cases. The energetic differences between the chloride and bromide anions of the salt were accounted in the dispersive energy contribution, ε/kB, considering a higher value for chlorine due to its electronegativity compared to bromide. Additionally, it was assumed that both molecules have a similar size, as they share the same cation. Consequently, the minor size differences were accounted in the chain length parameter, m, while the segment diameter, σ, was kept constant and transferred from the [TBA][Cl] molecule. Consequently, 3 out of the 5 molecular parameters needed to describe [TBA][Br] were taken from its homologous chloride salt, while the two remaining parameters were fitted to a mixture with EG at different ratios. The final set of molecular parameters is included in Table 1. An analysis of the parameters reveals that the chain length is slightly higher for [TBA][Br] compared to [TBA][Cl], as expected due to the higher size of the bromide. Also, an optimal dispersive energy ε/kB = 367.4 K is found for [TBA][Br], which is clearly lower than that of [TBA][Cl] (ε/kB = 420.1 K). The performance of soft-SAFT using the optimized parameters is displayed in Figure 4a. As it can be seen, very good agreement with the experimental data73 is found at all ratios, from (1:2) until (1:5), with some minor deviations for the [TBA][Cl]:EG (1:6), which was not included in the fitting, but predicted with the current set of parameters. The density of pure EG is also included in Figure 4a to highlight that the parameters used for EG perfectly describe this fluid.72 Consequently, there is no reason to think that the model deteriorates at high EG concentrations, even if there is a certain discrepancy with the data of [TBA][Cl]:EG at a (1:6) ratio. These results can be compared with the single-compound approach, where the DES is treated as one molecule. Although an excellent representation of the density is also obtained (see Figure S2 of the Supporting Information), and four out of five soft-SAFT parameters are kept constant, the

m = 0.01860M w + 0.008744

(R2 = 0.9999)

(10)

Coming back to the two-compounds approach, the strategy of parametrization is extended to other members of the ammonium bromide salt (Stage 2 of Figure 3). The availability of experimental data for the tetrapropylammonium bromide [TPA][Br] with EG allows the characterization of this fluid following the same procedure. In this case, the only difference between both fluids is the fact that the quaternary branches of the cation are propyl chains instead of butyl chains. Consequently, there is a higher impact on the size of the molecule than in the energy contributions. For this reason, the dispersive energy and the association parameters were transferred from those of [TBA][Br], while the size parameters defining the volume of the salt, m and σ, were fitted to data of the eutectic mixture with EG at three different ratios. The molecular parameters obtained allow a very accurate description of the density of the DES when compared to experimental data at three different ratios,74 as shown in Figure 4b, with an AAD% of 0.087%. As expected, the chain length and the segment diameter parameters are lower than those of [TBA][Br]. These results can be compared with the results for the one-compound approach, in a similar manner as done for [TBA][Br]. Once again, a good description at all ratios (see Figure S3 in the Supporting Information) can be achieved for [TPA][Br] using four constant parameters, being three of them transferred from [TBA][Br]. The chain length accounts for the differences among the different mixtures following a linear trend: m = 0.01993M w + 0.008673

(R2 = 0.9999)

(11)

With the purpose of extending the characterization of the bromide ammonium salt family to more members, a search F



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Figure 3. Schematic procedure indicating the steps followed to optimize the molecular parameters of the DESs studied in this work, including the CO2 and SO2 solubility in them.

Table 1. Molecular Parameters Optimized with Soft-SAFT for Selected Deep Eutectic Solvents and CO2

a

compound

Mw (g/mol)

m

σ (Å)

ε/kB (K)

εHB/kB (K)

kHB (Å3)

AAD (%)

[TEA][Br] [TPA][Br] [TBA][Br] [TEA][Cl] [TBA][Cl] LevA EG TEG CO2a SO2

210.2 266.3 322.4 165.7 277.9 116.1 62.07 150.2 44.01 64.06

3.272 4.259 5.315 3.227 4.875 2.901 1.951 3.525 1.571 2.444

4.390 4.432 4.532 4.390 4.532 3.782 3.533 3.887 3.184 2.861

367.4 367.4 367.4 420.1 420.1 381.2 325.1 346.2 160.2 228.3

3384 3384 3384 3384 3384 3850 4140 3891

2100 2100 2100 2100 2100 2250 2600 2600

1130

601

0.0230 0.0870 0.3217 0.0680 0.0670 0.0250 ref 72 ref 72 ref 64 ref 44

−40

Additional molecular parameters for the polar contribution: Q = 4.40 × 10 G

2

1

C·m , xp = /3. DOI: 10.1021/acs.jced.7b01103 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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Figure 4. Density−temperature diagram for (a) [TBA][Br]:EG (1:2) (diamonds), [TBA][Br]:EG (1:3) (circles), [TBA][Br]:EG (1:4) (squares), [TBA][Br]:EG (triangles), [TBA][Br]:EG (1:6) (crosses) and pure [EG] (inverse triangles). (b) [TPA][Br]:EG (1:3) (circles), [TPA][Br]:EG (1:4) (squares), and [TPA][Br]:EG (1:5) (triangles). In all panels, symbols are experimental data73,74 while the lines are the soft-SAFT calculations.

Figure 5. Density−temperature diagram for (a) [TBA][Br]:LevA (1:3) (circles) and [TBA][Cl]:[LevA] (1:3) (triangles) with η = 1.032. (b) [TEA][Br]:LevA (1:3) (circles) and [TEA][Cl]:[LevA] (1:3) (triangles). In all panels, symbols are experimental data,75 while the lines are the soft-SAFT calculations.

At this stage, a further test for the strategy presented here, is the validation of the LevA parameters using [TBA][Cl]:LevA data. As the parameters of both compounds are known, the density mixture can be predicted at the selected ratio (1:3). The results showed qualitative agreement but were slightly underpredicting the density of this DES. To reach quantitative agreement, a small correction was introduced using a binary parameter η = 1.032 to account for the density deviations. The results are also displayed in Figure 5a (red line). The final step of the parametrization of the bromide ammonium salt is done obtaining the parameters of [TEA][Br] using mixture data with LevA. Even if the departing eutectic mixture is not with EG, it is expected that the [TEA][Br] molecular parameters will follow the same characteristic trends than the other optimized members of the series. Hence, the dispersive energy and association parameters were again transferred to this molecule, while the two remaining size parameters were fitted to DES data in order to account for the smaller size of the ethylammonium salt. The results of the parametrization are shown in Table 1. As expected, the chain length and segment diameter are lower than the values obtained for the propyl and butyl ammonium chains. More interestingly, it is possible to establish linear trends for the size parameters with the molecular weight, as shown in Figure 6 and in the following equations:

for experimental data of tetraethylammonium bromide [TEA][Br] was carried out. Unfortunately, to our knowledge, no data with a mixture of EG was found. However, some recent studies from Deng et al.70,75,76 characterized two bromide DESs, [TEA][Br] and [TBA][Br], and two chloride DESs, [TEA][Cl] and [TBA][Cl], with the cellulose derived organic Levulinic Acid (LevA). On the basis of this information, it was possible to determine the molecular parameters of the LevA from [TBA][Br] (Stage 3a in Figure 3), to later obtain those of [TEA][Br] (Stage 3b in Figure 3). First, an eutectic mixture of [TBA][Br]:LevA (1:3)76 is used to find the parameters of LevA. As described in the previous section, a molecular model with two association sites is chosen for this carboxylic acid. In this case, no direct constraints were applied to the parameters of LevA. This results into multiple sets of parameters, being dependent on the initial guesses, and providing good agreement with the experimental data. The parameters degeneracy is a well-known drawback in this type of systems when the fitting data follows a straight line. The discrimination was done by comparing these values with those obtained for 1-pentanol in terms of size.57,77 The dispersive and association energies are higher due to the effect of the carboxylic acid group. The final set of parameters is also included in Table 1, while the temperaturedensity diagram of this DES is depicted in Figure 5a (blue line).

m = 0.01820M w − 0.5671 H

(R2 = 0.9996)

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Figure 6. Soft-SAFT molecular parameters trends: (a) tendency of the number of monomers with the molecular weight for [TXA][Br]. (b) tendency of the volume (as mσ3) with the molecular weight for [TXA][Br].

Figure 7. Solubility of SO2 at 0.1 MPa for (a) [TBA][Br]:LevA (1:3) (squares) with ξSO2‑[TBA][Br] = 0.970 and [TEA][Br]:LevA (1:3) (circles), (b) [TBA][Cl]:LevA (1:3) (squares) with ξSO2‑[TBA][Cl] = 0.880 and [TEA][Cl]:LevA (1:3) (circles) with ξSO2‑[TEA][Cl] = 1.040. A constant binary parameter between SO2 and LevA ξSO2‑LevA = 1.055 is used in all panels. Symbols are experimental data,76 while the lines are the soft-SAFT calculations.

Table 2. Binary Parameter ξij Necessary to Fit SO2 and CO2 Solubility for Selected Deep Eutectic Solvents molecules

[TEA] [Br]

[TBA] [Br]

[TEA] [Cl]

[TBA] [Cl]

levulinic acid

SO2 CO2

1.000 1.075

0.970 1.000

1.040 1.075

0.880 0.947

1.055 0.835

mσ 3 = 1.942M w − 136.4

(R2 = 0.9937)

tetraethylammonium chloride [TEA][Cl]. Even if the parameters for this compound were optimized in a previous contribution,26 it was decided to reoptimize the compound for the same reasons explained for [TBA][Cl]. To be consistent with all the previous assumptions, the segment diameter, σ, and the association parameters were transferred from the same member of the family [TBA][Cl], while the dispersive energy, ε/kB, was taken from [TEA][Br]. Consequently, only the chain length parameter was fitted to a eutectic mixture with LevA. Even with all those constraints, it was possible to find an excellent adjustment to the available experimental data,75 with an AAD% = 0.0680. In addition, the chain length was found to be lower than [TBA][Cl] and also slightly lower than [TEA][Br], as it was expected because of the smaller size of the chloride compared to the bromide atom (see Table 1). A comparison of the soft-SAFT description of the density of [TEA][Br]:LevA and [TEA][Cl]:LevA is depicted in Figure 5b. 4.2. Solubility of CO2 and SO2 in Ammonium-Based Eutectic Solvents. Once the parameters of the different DESs have been established, the model can be used to estimate the capacity of these compounds to dissolve acid gases at different working conditions (Stage 4 in Figure 3). In particular, this work is oriented toward the CO 2/SO2 separation capabilities of these compounds.

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In particular, Figure 6a plots the change of the chain length with the molecular weight, showing an excellent linear regression (R2 = 0.9996). Figure 6b plots the change of volume (calculated as mσ3) versus the molecular weight, showing also good agreement (R2 = 0.9937). These results are particularly challenging because the parametrization of [TEA][Br] was done using a different hydrogen-bonding donor (HBD), compared to [TPA][Br] and [TBA][Br]. However, the final parameters share the same patterns than the other members of the series, clearly showing the transferability of the strategy and the physical principles behind the fitting. In fact, if one uses here a one-compound approach, the change from the glycol to the carboxylic acid would result in a degeneration of the parameters, in terms of following a specific trend, as they would effectively consider the modification of part of the “whole” molecule (seen as a single entity). It is important to remark that the possibility of finding these trends allows the extrapolation to other bromide ammonium salts without the need of experimental data. The study for pure DESs using the two-compounds approach is completed with the parameters optimization of I



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Figure 8. Solubility of CO2 at 303.15 K (circles), 313.15 K (diamonds), 323.15 K (squares), and 333.15 K (triangles) in (a) [TBA][Br]:LevA (1:3), (b) [TBA][Cl]:LevA (1:3) with ξCO2‑[TBA][Cl] = 0.947 and η[TBA][Cl]:LevA = 1.032, (c) [TEA][Br]:LevA (1:3) with ξCO2‑[TEA][Br] = 1.075, and (d) [TEA][Cl]:LevA (1:3) with ξCO2‑[TEA][Cl] = 0.947 transferred from [TEA][Br]:LevA (1:3). A constant binary parameter between CO2 and LevA ξCO2‑LevA = 0.835 is used in all panels. Symbols are experimental data,70 while the lines are the soft-SAFT calculations.

Table 3. Predicted Molar Entalphy (ΔHabs) and Entropy (ΔSabs) of dissolution for CO2 and SO2 in [TXA][Br]:LevA (1:3) and [TXA][Cl]:LevA (1:3) at Fixed CO2 and SO2 Compositions (xCO2 and xSO2) Calculated in the Range of Temperatures 303.15−333.15 K solvent

xCO2

ΔHdis (kJ mol−1)

ΔSdis (J mol−1K−1)

xSO2

ΔHdis (kJ mol−1)

ΔSdis (J mol−1K−1)

[TEA][Br]:LevA (1:3)

0.03 0.04 0.05 0.03 0.04 0.05 0.03 0.04 0.05 0.03 0.04 0.05

−14.00 −13.86 −13.70 −11.55 −11.50 −11.45 −11.72 −11.70 −11.62 −14.49 −14.33 −14.15

−93.75 −125.7 −158.0 −55.05 −73.98 −93.16 −77.46 −104.5 −131.5 −65.31 −87.80 −110.3

0.30 0.40 0.50 0.30 0.40 0.50 0.30 0.40 0.50 0.30 0.40 0.50

−30.16 −28.96 −27.82 −29.83 −28.75 −27.74 −31.74 −29.70 −28.14 −29.04 −27.73 −26.70

−15.71 −26.70 −42.30 −14.31 −23.94 −37.76 −12.96 −22.50 −36.90 −21.56 −35.00 −53.10

[TBA][Br]:LevA (1:3)

[TEA][Cl]:LevA (1:3)

[TBA][Cl]:LevA (1:3)

SO2 and the ammonium salt ξ was fitted to available experimental data.76 This strategy was already followed in a previous contribution in the modeling of DES.26 A summary of the energy binary parameters is given in Table 2. The modeling results are plotted in Figure 7. In Figure 7a, the solubility of SO2 in the ammonium bromide-based DESs at atmospheric pressure is plotted, while Figure 7b depicts the results for the ammonium chloride-based DESs. In both Figures, very good agreement between the available data and the soft-SAFT calculations is achieved for all compounds. Here, it is interesting to note that the binary parameter between the salt and SO2 increases with the increase of the alkyl chain of the cation. This is a common consequence derived from keeping constant the energetic parameters among the members of the same family. Although this is a

First, the solubility of SO2 in [TEA][Br]:LevA, [TBA][Br]:LevA, [TEA][Cl]:LevA and [TBA][Cl]:LevA is studied. Using the two-compounds approach, these systems are treated as a ternary mixture. Consequently, the model has to account for all possible interactions among the three compounds. Hence, cross-association interactions between the two sites assigned to SO2 and the sites of LevA and the ammonium salt are explicitly considered with a calculation using the combining rules shown in eqs 4 and 5, with only positivenegative interactions being allowed. Additionally, the cross dispersive energy between all pairs has been established from eq 3. The energy binary parameter between SO2 and LevA has been fixed to a constant and temperature-independent value of ξSO2‑LevA = 1.055, as it was found to provide good agreement for all mixtures. The binary parameter between J



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absorption capacity of amines. For the case of SO2, also shown in Table 3, the enthalpy is between two and three times higher than for CO2, indicating a higher degree of interaction. The entropies of dissolution of CO2 are also in accordance with the same bibliographic source,70 showing higher values in comparison with the results of this salt with lactic acid,26,71 revealing a higher degree of disorder. For SO2, the entropy is significantly lower, although it is strongly dependent on the composition of the mixture. Finally, the feasibility of these solvents for gas separation has been addressed. The Henry’s constants of CO2 and SO2 for the different [TXA]-based DESs have been predicted using eq 8. The results for both gases are included in Table 4 at four different temperatures ranging from 303 K until 333 K. As it can be noticed, CO2 Henry’s constants are higher for the [TEA]-based DESs than for [TBA]-based solvents and they also increase with the temperature, indicating a decrease in the solubility of CO2. No substantial differences are observed with the change of the anion. These results are in perfect agreement with the bibliography.70 The predictions for SO2 indicate that this gas dissolves better in all DESs, achieving very low Henry’s constants. Consequently, the selectivity between the two gases is quite high. From these results, it is possible to determine the selectivity of these DESs to separate SO2 from CO2. It is important to consider that, as far as SO2 is more soluble than CO2 at the same working conditions, the sulfur gas is the one that will remain in the liquid phase with the DESs in a higher quantity. Using eq 9, the selectivity for the four studied DESs is calculated in the range of working temperatures, achieving in all cases very high values, moving from 75 until 500 (see Table 4). The selectivity decreases with the temperature and with the alkyl chain of the cation, suggesting that small salts and low temperatures are better for this separation. The highest selectivity values are found for [TEA][Cl]:LevA, while the lowest values are obtained for the [TEA][Cl]:LevA. This is an interesting fact because it reveals that the effect of the chain is even stronger than the change of the anion. This selectivity is of the same order than the one obtained using the 1-butyl-3-methyl-imidazolium methylsulfate [C4mim][MeSO4] IL as a solvent.46 However, it is important to remark that the current calculation is neglecting the interaction between both gases, as the Henry’s constants are evaluated from the ternary mixture and not from the quaternary system. In conclusion, the selected DESs do not seem adequate to capture CO2 due to the very low solubility of this gas in them, but they are a good option to separate it from SO2 by absorbing the latter.

Table 4. Predicted Henry’s Law Constants of CO2 and SO2 and Their Selectivity for the [TXA][Br]:LevA (1:3) and [TXA][Cl]:LevA (1:3) DESs in the Range of Temperature of 303.15−333.15 K solvent [TEA][Br]:LevA (1:3) [TBA][Br]:LevA (1:3) [TEA][Cl]:LevA (1:3) [TBA][Cl]:LevA (1:3) [TEA][Br]:LevA (1:3) [TBA][Br]:LevA (1:3) [TEA][Cl]:LevA (1:3) [TBA][Cl]:LevA (1:3) [TEA][Br]:LevA (1:3) [TBA][Br]:LevA (1:3) [TEA][Cl]:LevA (1:3) [TBA][Cl]:LevA (1:3)

303.15 K

313.15 K

323.15 K

333.15 K

H1,CO2 (MPa) 16.44 20.22

23.87

27.35

12.50

14.70

16.86

18.99

17.67

20.84

23.93

26.94

10.90

13.55

16.12

18.60

H1,SO2 (MPa) 0.05236 0.08088

0.1194

0.1708

0.05651

0.08103

0.1171

0.1639

0.03563

0.05647

0.08588

0.1257

0.08182

0.1257

0.1842

0.2601

313.9

SSO2/CO2 250.0

200.0

160.1

221.2

181.4

143.9

115.8

495.8

369.0

278.6

214.3

133.3

107.8

87.52

71.53

reasonable assumption that simplifies the fitting and facilitates the transferability to other compounds of the same family, the capacity of the salts with shorter alkyl chain lengths to interact with other compounds, such as SO2, will be higher as the apolar region is smaller and it is easier to access to the charged nitrogen atom. Consequently, the cross dispersive energy of [TEA][Br] is higher than that of [TBA][Br] which, in turn, provides a higher binary parameter to correct the mean geometric average. Analogously, the same behavior is observed for [TEA][Cl] and [TBA][Cl]. Finally, the solubility of CO2 is also evaluated using the data provided by Deng et al.70 In this case, several isotherms of experimental data are available for the same DES. The procedure is the same followed for SO2: an energy binary parameter is fixed for the interaction between CO2 and LevA. This value is temperature-independent and common in all DESs. In addition, the cross-dispersive energy of the ammonium salts with CO2 is fitted to an intermediate isotherm at 313 K and used to predict the other isotherms. The results are plotted in Figure 8. As it can be seen, excellent agreement is found at all temperatures and compositions. It is interesting to note that, in this case, it was possible to use the same binary parameter for the [TEA] cations with CO2, independently of the anion. Unfortunately, the same rule could not be applied to the [TBA] cations without losing accuracy in the description of the solubility. On the basis of these modeling results, the enthalpies and entropies of dissolution have been predicted by applying eqs 6 and 7. The results presented in Table 3 for CO2 are in good agreement with the values reported by Deng et al.,70 and reveal low enthalpies of dissolution of similar order of those measured for [TXA][Cl]:Lactic Acid,71 very far from the

5. CONCLUSIONS A transferable molecular model and an accurate parametrization has been presented here to address gas solubility of CO2 and SO2 in tetraalkylammonium bromide and chloride with levulinic acid DESs using the soft-SAFT equation of state. Even if some preliminary calculations treating the DESs as a whole single molecule have provided an accurate description of the density, a specific molecular model for each compound for the eutectic mixture has been preferred in order to avoid the composition dependence of the molecular parameters. To estimate the number of association sites for each molecule, COSMO-RS has been used to determine the charge density of the molecules presented in the DESs. As a K



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result, a set of independent parameters has been found to provide excellent agreement with the available data. An analogy between the members of the two eutectic families ([TXA] with chloride or bromide:LevA) has been provided by transferring as many parameters as possible. Logical trends with the molecular weight have been found in all cases, allowing the prediction of other compounds of the family. The characterization has been completed by modeling the solubility of CO2 and SO2 in these solvents with a minimum amount of binary parameters and experimental data. The results corroborate the possibility of using soft-SAFT to provide an accurate description of these systems, allowing the prediction of other properties, such as the enthalpy and the entropy of dissolution, the Henry’s constants, and the selectivity, facilitating the screening of more DESs for gas separation applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b01103. Density−temperature diagram for the [TBA][Cl]:TEG DES at different ratios treating the DES as a binary mixture; density−temperature diagrams for [TPA][Br]:EG and [TBA][Br]:EG at different ratios using the one-compound approach; molecular parameters optimized with soft-SAFT for selected DESs using the pseudopure compound approach (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

F. Llovell: 0000-0001-7109-6810 Funding

GESPA has been recognized as Consolidated Research Group by the Catalan Government with code 2017-SGR-1016. F. Llovell acknowledges funding from the Universities and Research Secretariat of the Ministry of Business and Knowledge of the Generalitat de Catalunya, under Project 2017-URL-Proj-029. Additional financial support from the Spanish Government (CTQ2014-53987-R) is also acknowledged. Notes

The authors declare no competing financial interest.

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REFERENCES

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