New Experimental Data and Modeling of Glymes: Toward the

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New experimental data and modeling of glymes: towards the development of a predictive model for Polyethers Pablo Navarro, Emanuel Almeida Crespo, João Costa, Felix Llovell, JULIAN GARCIA, Francisco Rodríguez, Pedro Jorge Carvalho, Lourdes F. Vega, and Joao A.P. Coutinho Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 15 Jun 2017 Downloaded from http://pubs.acs.org on June 15, 2017

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Industrial & Engineering Chemistry Research

New experimental data and modeling of glymes: towards the development of a predictive model for polyethers Pablo Navarro†,‡,┴, Emanuel A. Crespo†,┴, João M. L. Costa†, Fèlix Llovell§, , Julián García‡, Francisco Rodríguez‡, Pedro J. Carvalho†,*, Lourdes F. Vega¥ and João A. P. Coutinho† †

CICECO – Aveiro Institute of Materials, Department of Chemistry, University of Aveiro, 3810-193 Aveiro, Portugal ‡ Department of Chemical Engineering, Faculty of Chemical Sciences, Complutense University of Madrid, 28040, Madrid, Spain § Department of Chemical Engineering and Materials Science, IQS School of Engineering, Universitat Ramon Llull, Via Augusta, 390, 08017 Barcelona, Spain ¥ Gas Research Center and Chemical Engineering Department. Khalifa University of Science and Technology – The Petroleum Institute, P.O. Box 2533. Abu Dhabi. United Arab Emirates

Corresponding author E-mail address: [email protected] (P.J. Carvalho). ┴

P.N. and E.A.C contributed equally

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Abstract

The design and optimization of industrial processes relies on the availability of robust and accurate models and equations of state (EoSs). Aiming at further advancing the use of softSAFT EoS, towards its implementation on industrial processes, a methodology to determine the molecular model and transferable molecular parameters of glymes is here discussed. In addition to the commonly used vapor pressure and saturated liquid densities, the description of the temperature and pressure effect is improved by including one additional density– pressure and one isothermal compressibility isotherm (both at 323 K) for the molecular parameters optimization. Guiding the selection and optimization of the soft-SAFT EoS molecular model and parameters, new high pressure density data (pρT) and derived properties, such as isothermal compressibility and isobaric thermal expansion, of 8 glymes (glycol ethers) have been determined in a wide range of temperatures (283–363) K and pressures (0.1–95) MPa. The selected molecular model (considering that only the hydroxyl end-groups are able to establish associative interactions) and its parameters provide an excellent description of the experimental data, being able to predict the characteristic crossover point observed for the isobaric thermal expansivities. The robustness and enhanced physical meaning of the molecular model and molecular parameters allow the use of correlations with the molecular weight. The transferability of the proposed molecular parameters are further used to predict the liquid densities for PEGDME250 (a blend of dialkyl ethers similar to the Selexol solvent).


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1. Introduction Aiming at the development of thermodynamic models capable of describing complex thermodynamic behaviors, most of the activity coefficient models and traditional cubic equations of state are being phased out due to their known limitations in dealing with complex polar and associating molecules. Furthermore, recent developments on statistical thermodynamics and on advanced molecular based EoSs, capable of describing more complex systems with parameters having a greater physical meaning, have raised further interest on this type of approaches. This was first applied to the EoS developed by Chapman and coworkers,1–5 based on Wertheim’s first-order thermodynamic perturbation theory,6–9 named the Statistical Associating Fluid Theory (SAFT), where a hard sphere reference fluid is perturbed by different contributions accounting for different effects, such as the molecular shape, dispersive interactions and molecular association in the fluids thermodynamic behavior. SAFT provides a physical interpretation of the system, as the molecular structure is built into the equation from its inception. Moreover, the theory underlying the equation makes possible its systematic improvement and extensions in a sound manner, allowing to introduce dipolar, quadrupolar or coulombic contributions,10–12 as well as calculations of other properties, by coupling it to other theories with the same level of approximation. This includes the calculation of interfacial properties by incorporating, for instance, the Density Gradient Theory (DGT) of van der Waals,13 and transport properties, by coupling the Free Volume Theory (FVT).14,15 Among several modifications to the original SAFT, soft-SAFT16 stands out as one of the most accurate versions. Soft-SAFT ability to successfully describe the thermodynamic behavior of a wide variety of compounds, such as n-alkanes,17 water,18 glycols,19 alkan-1ols,20 nitriles,21 perfluoroalkanes,22 ionic liquids,23,24 refrigerants25 and polymers26,27 is well known, staging soft-SAFT amongst the best choices to tackle the abovementioned challenge. As in any molecular based EoS, soft-SAFT performance relies on the adequate selection of a molecular model capable of correctly mimicking the compounds physical nature. The developments on SAFT-type EoSs have emphasized the importance to adjust the purecomponent parameters to different properties aiming at obtaining a realistic balance between the different interactions with a limited set of experimental data.28 Although the discussion about the most reliable properties for the optimization procedure is still open, the simultaneous description of density and derivative properties appears as one of the most appropriate approaches.28 Nonetheless, not only the fitting procedure of the pure-component 3 ACS Paragon Plus Environment


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parameters, but also the association scheme assigned for the different species, stands vital for a good performance of the equation. Nevertheless, very few works have used, up to now, SAFT-type equations for the calculation of derivative properties. Kiselev and co-workers29 used the original SAFT EoS to obtain the isochoric and isobaric specific heats, speed of sound and other properties of pure propan-1-ol with excellent agreement with experimental data but, no further extension to other compounds has been reported with this approach. Colina et al.30 used the soft-SAFT EoS to predict the Joule-Thomson inversion curves for carbon dioxide and the n-alkane series, including heavy n-alkanes up to octatetracontane. Comparisons with available experimental and correlation data, for carbon dioxide and the lighter n-alkanes, showed good quantitative agreement. A strong dependence of the inversion curve on the set of molecular parameters used in the calculations was observed, especially near the inversion point and in the high-temperature region. Later, Lafitte et al.31 evaluated the performance of different SAFT versions for the determination of derivative properties of n-alkanes. Nonetheless, since derived properties were not used in the optimization procedure, only vapor-liquid equilibria (VLE) data, poor agreement was achieved. On the same year, Llovell et al.32 reported the use of soft-SAFT EoS to calculate the derivative properties of nalkanes and alkan-1-ols, using molecular parameters obtained from VLE data alone, as well as mixtures of n-alkanes/n-alkanes and n-alkanes/alkan-1-ols.33 As stated by the authors,32 the singular behavior of the compounds properties is well described by soft-SAFT but, if one is searching for quantitative descriptions of both phase equilibria and derivative properties, additional experimental data should be considered in the optimization of the pure-component parameters. The same was recently highlighted by Oliveira et al.28 in a publication focusing on the role of derivative properties in the development of new procedures for enhancing the transferability of SAFT molecular parameters. The use of a coupling factor to the soft-SAFT fitting procedure, to change the weight of one set of properties comprising VLE data over another containing one derivative property, was proposed. It was shown that only VLE data is needed for simple fluids, such as regular n-alkanes; however, the inclusion of one derivative property in the fitting procedure, in addition to VLE data, clearly enhanced the predictions of the behavior of associating compounds such as alkan-1-ols and water. In this work, aiming at guiding the selection and optimization of the soft-SAFT EoS molecular model and parameters for glymes, new high pressure density data (pρT) of 8 glymes were measured in a wide range of temperatures (283–363) K and pressures (0.1–95) MPa, and the corresponding isothermal compressibility and isobaric thermal expansion 4 ACS Paragon Plus Environment

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derived from them were also calculated. The studied compounds and experimental conditions allow to infer on the combined effects of pressure, number of ethoxy groups and the effect of losing the capability to establish hydrogen bonds, through the replacement of the hydroxyl end-groups by a methyl or ethyl group, on densities and derivative properties. Ultimately, the robustness of the proposed molecular model and molecular parameters was tested against density data available in the literature for PEGDME250, a blend of di-alkyl ethers similar to the Selexol solvent. The proposed molecular parameters were further correlated with the glymes molecular weight, as commonly performed for homologous series, and compared to the parameters obtained for other well-established families, allowing a discussion on their physical meaning and the reliability of the applied model. This work highlights the importance of paying attention to one of the strongest features of SAFT-type equations, such as the physical meaning of the parameters, allowing predicting properties of compounds not included in the original fitting procedure.

2. Experimental section 2.1. Materials. High pressure densities were measured for eight glymes, namely ethylene glycol ethylether (EGEE), diethylene glycol ethylether (DEGEE), diethylene glycol methylether (DEGME), diethylene glycol diethylether (DEGDEE), diethylene glycol dimethylether (DEGDME), triethylene glycol dimethylether (TriEGDME), tetraethylene glycol dimethylether (TeEGDME), and tetraetylene glycol methylether (TeEGME), on the (283–363) K temperature and (0.1–95) MPa pressure range. Prior to the measurements, water and other volatile compounds were removed by drying the compounds at moderate temperatures (≈ 323 K), under vacuum conditions (≈ 0.1 Pa) and under continuous stirring for at least 48 h. 1H and

13

C NMR were used to determine the

compounds’ purity. The final water content was determined by a Metrohm 831 Karl Fischer (using the Hydranal – Coulomat AG from Riedel-de Haën as analyte). The full name, chemical structure, CAS number, molecular weight, water mass fraction content, mass fraction purity and supplier of each glyme are reported in Table 1.



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Table 1. Chemical structure, compound description, CAS number, molecular weight, water mass fraction content, mass fraction purity and supplier of the studied glymes. Compound

Chemical structure

Ethylene glycol ethyl ether (EGEE) CAS: 110-80-5; M = 90.12 g·mol-1; H2O wt = 0.0041; purity = 99 wt %. Acquired from Panreac. Diethylene glycol ethyl ether (DEGEE) CAS: 111-90-0; M = 134.17 g·mol-1; H2O wt = 0.0003; purity = 98 wt %. Acquired from Acros Organic. Diethylene glycol diethyl ether (DEGDEE) CAS: 112-36-7; M = 162.23 g·mol-1; H2O wt = 0.0007; purity = 98 wt %. Aquired from Fluka. Diethylene glycol dimethyl ether (DEGDME) CAS: 111-96-6; M = 134.17 g·mol-1; H2O wt = 0.0160; purity = 99.5 wt %. Acquired from Sigma Aldrich. Triethylene glycol dimethyl ether (TriEGDME) CAS: 112-49-2; M = 178.23 g·mol-1; H2O wt = 0.0002; purity = 99 wt %. Acquired from Fluka. Tetraethylene glycol dimethyl ether (TeEGDME) CAS: 143-24-8; M = 222.28 g·mol-1; H2O wt = 0.0002; purity = 99 wt %. Acquired from Fluka. Diethylene glycol methyl ether (DEGME) CAS: 111-77-3; M = 120.15 g·mol-1; H2O wt = 0.0015; purity = 99 wt %. Acquired from Acos Organic. Tetraethylene glycol methyl ether (TeEGME) CAS: 23783-42-8; M = 208.25 g·mol-1; H2O wt = 0.0015; purity = 99 wt %. Acquired from Sigma Aldrich.

2.2. Density measurements. Density determination was performed in the (283–363) K and (0.1–95) MPa temperature and pressure ranges, respectively, using an Anton Paar high pressure density meter (DMA-HPD) equipment coupled to a mPDS 5 unit. The standard uncertainty on the density was found to be 5 10-4 g·cm-3.19 A Julabo MC circulator was used to thermostatize the measuring cell with a stability of ± 0.01 K and the temperature measurements were determined to present an uncertainty of ± 0.1 K. The pressure was measured by a silicon piezoresistive transducer from Kulite (HEM 375) with accuracy better than 0.2% and placed directly in ¼’’ stainless steel line, between the measuring cell and the


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movable piston to minimize dead volumes. A detailed description of the apparatus and methodology can be found elsewhere.19

3. Model Description The Statistical Associating Fluid Theory (SAFT) was originally proposed by Chapman and co-workers,1–5 based on the Wertheim’s first order thermodynamic perturbation theory,6–9 using a hard-sphere as reference fluid. Afterwards, several modifications to the original model were proposed (being SAFT-VR34, soft-SAFT16 and PCSAFT35 the most popular ones); most of them keeping the chain and association terms from Wertheim’s theory and varying on the choice of the reference fluid. Soft-SAFT, as all other SAFT versions, is written as a sum of different contributions to the residual Helmholtz energy: ‫ܣ‬௥௘௙ is defined as the contribution due to the repulsive and attractive interactions of the monomers constituting the chain; ‫ܣ‬௖௛௔௜௡ considers the chain formation; and ‫ܣ‬௔௦௦௢௖ explicitly takes into account strong, short-range and highly directional attractive interactions (e.g. hydrogen bonding). Ares = Atotal − Aideal = Aref + Achain + Aassoc

(1)

The reference term is given by a Lennard-Jones (LJ) spherical fluid36 (hence, the name “soft”), that takes into account both the repulsive and attractive interactions of the monomers or segments integrating the molecule. This term defines the monomer using two molecular parameters: the diameter of the spherical monomers (ߪ) and the dispersive energy between segments (ߝ). These two molecular parameters and the chain length (݉) are the three pure-component parameters required by soft-SAFT to fully characterize a nonassociating compound. For associating components, two additional parameters, related to the energy (ߝ ு஻ ) and volume (ߢ ு஻ ) of the association sites, are required. A more detailed description of the soft-SAFT EoS and each one of its terms can be found elsewhere.16 The proper selection of a coarse-grained model, capable of capturing the basic physical features of the compounds, and the properties to be used in the fitting procedure of the pure component parameters stand out as crucial for a good performance of the model and its predictive power. Thus, following our previous work where a simplified association scheme was applied to model different glycols,19 glymes are here modeled considering that only the hydroxyl end groups are able to establish associative interactions. Therefore, for 7 ACS Paragon Plus Environment


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each monoalkyl ether, one associating site “A” is assigned, mimicking the hydroxyl endgroup and allowing “A–A” interactions. Conversely, the dialkyl ethers studied in this work were considered as non-associating compounds due to the absence of hydroxyl end groups. A sketch of the proposed molecular models is depicted in Figure 1. The modelling of glycol ethers using SAFT-type equations is rather scarce with results only available for dialkyl ethers, always considered as non-associative species, as in the works of Nannan et al.37 and Polishuk et al.38 The former applied the PC-SAFT EoS35 to model the vapor-liquid equilibria and liquid heat capacities of CH3O[CH2CH2O]nCH3 for n=1 up to 4. The parameters obtained were then applied to describe the entire homologous series up to n = 9 and the thermodynamic properties of two different blends of glymes with satisfactory accuracy. However, no attempt to the simultaneous description of the derivative properties was carried out in their work. Polishuk et al.38 applied the Free Volume Theory (FVT) and the Modified Yarraton-Satyro correlation combined with the SAFT + Cubic EoS39 to successfully model the viscosities of different compounds including the TriEGDME. The EoS parameters proposed for this compound were shown to be able to accurately describe its liquid density, speed of sound and isothermal compressibility, although no description of the vapor pressure was given. Nevertheless, the simultaneous description of densities and derivative properties was only possible due to the higher number of parameters applied within this EoS (5 parameters are required to describe a non-associating molecule). The compounds molecular parameters were obtained in this work by fitting the EoS against the VLE data, one density–pressure and one isothermal compressibility isotherms (both at 323 K). The obtained parameters, together with those proposed previously for glycols,19 allowed to discuss their physical meaning and evaluate the ability of the proposed soft-SAFT model and methodology in dealing with compounds containing ethylene oxide functional groups, as will be shown in the next section.


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Mono-alkyl glymes: e.g. diethylene glycol methyl ether

Di-alkyl glymes: e.g. diethylene glycol dimethyl ether

Figure 1. Sketch of the proposed molecular models for the monoalkyl ethers and dialkyl ethers.



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4. Results and Discussion 4.1. Pressure-Density-Temperature (pρT) measurements. Densities of eight glymes, namely EGEE, DEGME, DEGEE, DEGDME, DEGDEE, TriEGDME, TeEGME and TeEGDME, were determined in the (283–363) K temperature and (0.1–95) MPa pressure ranges. An exhaustive comparison between the glymes experimental density data at atmospheric pressure, obtained with two different apparatuses and methodologies, was previously reported by us.40 Thus, density data at atmospheric pressure is only measured and included here for comparison against the data already reported, as depicted in Figure 2. The densities here obtained are in good agreement with those obtained at 0.1MPa with EGEE showing the highest deviation, but still with a percentage absolute average relative deviation (%AARD) lower than 0.40%.

Figure 2. Percentage relative deviations (%RD) (left) and density differences (right) between density data, at 0.1 MPa, determined here and those reported in a previous publication. 40 Several authors have reported density data for a wide range of pressures and temperatures for glymes. Comuñas and coworkers41–45 presented density data for EGEE, DEGDME, TriEGDME and TeEGDME within the (293-353) K and (0.1-60) MPa temperature and pressure ranges, respectively. The experimental data reported here shows percentage absolute average deviations (%AARD) of 0.75%, 0.04%, 0.05% and 0.03%, respectively, against their data, as depicted in Figure 3. Lopez et al.46 reported densities for DEGEE and DEGME, as a function of temperature from (283 to 353) K and pressure from (0.1 to 25) MPa, presenting an %AARD of 0.11% and 0.02%, respectively, against our data. Esteve et al.47 published density data for DEGDEE at 1 MPa and the (283–363) K temperature range with a comparative %AARD of 0.11%. The available high pressure densities were compared with the experimental data measured in this work and the 10 ACS Paragon Plus Environment

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percentage relative deviations are also depicted in Figure 3. High pressure densities for TeEGME are here reported for the first time.

Figure 3. Percentage relative deviations between literature 41–47 and experimental pρT data as function of temperature and pressure. The new experimental pρT data obtained is depicted in Figure 4 and the values are detailed in the supporting information. Molar volumes of the different glymes were calculated as a function of temperature and pressure and are depicted in Figure 5 (see details in the supporting information). The molar volumes exhibit small dependencies with temperature and pressure, with a minor molar volume increase with temperature and decrease with pressure. Furthermore, glymes with higher number of ethoxy groups show a slight larger pressure and temperature dependency. This behavior has been previously shown for glycols.19 Furthermore, as reported before19,40 the molar volumes increase with the number of ethoxy groups by 38.8 cm3 mol-1 per group. Moreover, the substitution of a hydrogen on one of the diols hydroxyl groups by an ethyl group for the case of DEGEE and DEGDEE, or by a methyl group for the case of TeEGME and TeEGDME, represents an increase of 42.0 cm3 mol−1 and 23.4 cm3 mol−1, respectively. This corresponds to the summation of the CH3 and CH2 group volumes (ethyl) and that of a CH3 (methyl). These observations confirm the molar volumes characteristic additivity.



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Figure 4. Density as function of pressure and temperature of the studied glymes. The solid lines represent the soft-SAFT EoS density description. 12 ACS Paragon Plus Environment

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Figure 5. Molar volumes as function of temperature, pressure and the studied glymes. 4.2. soft-SAFT EoS modelling results. SAFT-type EoS molecular parameters are generally fitted to VLE data, namely vapor pressure ( p* ), and saturated liquid density ( ρL ). Parameters from this fitting are then used to predict other thermophysical properties, with different degrees of accuracy. The main reason behind this simple approach is the availability of VLE data for most of the substances under consideration. However, there is an open discussion on the most appropriate properties to be used for obtaining robust molecular parameters, provided they are available; several researchers denote the importance of using additional data (e.g. enthalpies of vaporization, monomer fractions and derivative properties) in the parameters optimization.28,48,49 The approach of using additional fitted properties has the advantage to provide molecular parameters that better describe other properties, but at the cost of additional fitted properties. Recently, Oliveira et al.28 pointed out the importance of using derivative properties, in addition to VLE, in order to enhance the performance of SAFT-type EoSs for associating fluids. In the present work, we extend this approach and consider not only the VLE data of the pure compounds (namely vapor pressures and saturated densities), taken from DIPPR50, but also high pressure densities and isothermal 13 ACS Paragon Plus Environment


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compressibilities at 323.15 K for the fitting procedure, an approach similar to that previously applied for glycols.19 The use of this single isotherm is expected to improve the prediction of the pressure effect and thus to allow a better description of the derivative properties. The following objective function (OF) was used:

OF =

δ 

N  ρ cal − ρ exp 0.80 ∑  ρexp N  i =1 

N  p* − p*    cal exp 0.20 +     + ∑ * p i = 1 exp    

323 Κ 323 Κ  N  p ρT − p ρT exp 1− δ  calc 0.90 ∑  323 Κ M  p ρT exp i =1   

323 Κ  N k T calc − kT  + 0.10 ∑  323 Κ  kT exp i =1   

323 Κ exp

   

(2)

where δ is the coupling factor, and N and M represent the number of experimental phase equilibrium and high pressure points, respectively. In this work, a coupling factor, δ = 0.5 was found to provide the best results as previously suggested by Oliveira et al.28 The weights 0.80 and 0.20 were directly taken from previous contributions17,28 while 0.90 and 0.10 were in this work found to provide the most balanced and optimal results. In addition to the fitting procedure already discussed, a key for the successful implementation of any SAFT EoS is the right choice of the molecular model to describe the system of interest. Pedrosa et al.27 applied the soft-SAFT EoS to model short glycols (up to tetraethylene glycol) considering them as homonuclear chains with one associating site at each hydroxyl end group (one “A” and one “B” site) and allowing only for “AB” interactions. Excellent agreement was achieved for the saturated vapor and liquid densities, vapor pressures and binary VLE data; however, the prediction of the glycols derivative properties was not very accurate. In a previous publication19, aiming at overcoming this limitation, a new set of molecular parameters and a new molecular model were proposed for glycols (extending the series studied by Pedrosa et al.

27

to hexaethylene glycol). Then, a small

change in the association scheme, where the dual positive-negative nature of the hydroxyl group was considered (e.g. like “AA”, “BB” and “AB” sites interactions are allowed), a large improvement on the description of the derived properties was achieved. In the current work, the same approach is applied to glycol ethers (see Figure 1). Here, the compounds molecular parameters were regressed using VLE data, one single isotherm of the experimental pρT data and isothermal compressibilities (both at 323 K), aiming at improving the description of the experimental data, while keeping the soft-SAFT predictive ability for the remaining temperatures. The vapor pressures for EGEE, DEGME, DEGEE, DEGDME, and TriEGDME 14 ACS Paragon Plus Environment

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were taken from DIPPR database,50 while for DEGDEE and TeEGDME the works of Lee et al51 and Chaudhari et al.52 were considered. The saturated liquid densities were extrapolated from the densities measured here at 0.1MPa and used on the fitting procedure. The saturated vapor densities were calculated assuming an ideal gas phase. The vapor pressures for TriEGDME reported on DIPPR50 are a prediction based on Riedel’s equation and, for that reason, they were only assessed in a qualitative manner. To the best of our knowledge, only one value of vapor pressure for TeEGME is available at 557.18 K, reported by Davidson53; therefore, no VLE data was used on the optimization of the pure-component parameters for this compound. As mentioned in the “model description” section, glymes were modelled as homonuclear LJ chains with one square-well site embedded off-center in one of the LJ segments mimicking the hydroxyl end-group whenever present. For the dialkyl ethers studied, although the ethylene oxide groups present a hydrogen bonding acceptor character, the absence of hydroxyl end-groups allows to consider the compounds as non-associating. The optimal soft-SAFT pure-component parameters, obtained for the different glymes, are reported in Table 2. The soft-SAFT results obtained for the saturated densities and vapor pressures of pure glymes using the molecular parameters from Table 2 are represented in Figures 6 and 7. A good description of the glymes VLE is obtained with an overall %AARD for the glymes saturated liquid and vapor densities and vapor pressures of 0.33%, 7.66% and 7.80% respectively. These values are similar to the deviations previously reported for other families such as glycols19 and perfluoroalkanes22. The soft-SAFT description of the high pressure densities measured in this work is depicted in Figure 4 and, as can be observed, the molecular model and assumptions here proposed allowed a very good description of the experimental data with maximum %AARDs of 0.41%, as reported in Table 2.



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Figure 6. Saturated liquid and vapor densities as function of temperature for the studied glymes. The solid lines represent the soft-SAFT EoS description of the experimental data.


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Figure 7. Logarithm of the vapor pressure, p*, as function of the inverse of temperature for the studied glymes. The solid lines represent the soft-SAFT EoS description of the experimental data. Table 2. soft-SAFT pure-component parameters for the studied glymes and %AARDs to the pρT data measured in this work and to the estimated derivative properties. Glyme

m

σ (Å)

ε/kB (K)

εHB/kB κHB %AARD|pρT %AARD|kT %AARD |αP (K) (Å3)

EGEE

2.705 3.721 294.87 3450 2600

0.086

5.62

3.90

DEGME

2.995 3.889 330.50 3450 2600

0.13

9.63

2.80

DEGEE

3.165 4.009 331.00 3450 2600

0.16

9.13

5.14

TeEGME 4.481 4.061 353.23 3450 2600

0.17

12.9

5.75

DEGDME 3.300 3.955 308.15

-

-

0.28

17.2

2.60

DEGDEE 3.586 4.165 309.43

-

-

0.35

20.2

6.10

TriEGDME 4.021 4.039 318.12

-

-

0.34

22.3

3.09

TeEGDME 4.696 4.107 322.68

-

-

0.41

28.4

2.95



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As can be inferred from Table 2, low deviations to the experimental pρT data were obtained with an overall %AARD of 0.240%. The very good description of the experimental data shows that the addition of one single isotherm (323 K) of the pρT data and the isothermal compressibility measured in this work to the VLE data on the parameters optimization enables the model to correctly describe the effect of both temperature and pressure in all the temperature (283–363) K and pressure (0.1-95) MPa ranges. Furthermore, it can be observed that these deviations tend to increase both with the chain length of the glyme and with the removal of the hydroxyl-end groups (i.e. from monoalkyl ethers to dialkyl ethers). This increase with the removal of the hydroxyl-end groups shows the importance of the ethoxy groups being neglected, since when a hydroxyl-end group is present and selfassociation of the molecule considered (as for monoalkyl ethers) the interactions involving the ethoxy groups can be masked by the association term. Conversely, in dialkyl ethers, here modelled as non-associating species, the model does not consider the ethylene oxide groups explicitly. Instead, the influence of the ethylene oxide groups is implicitly considered by the different values of the remaining molecular parameters. Moreover, the increase of the chain length also deteriorates the description of the high pressure thermodynamic behavior of glymes as previously observed for glycols.19 A challenging test to any molecular approach would be to check its ability to provide other thermodynamic properties of the studied glymes. As derivative properties usually present some singularities observed experimentally,32 an accurate description of the physical features behind second order derivatives stands as relevant to validate the model here proposed as well as the robustness of the fitted parameters. As previously mentioned, despite the importance of checking the accuracy of EoSs for reliable estimations of these properties, the number of contributions related to the application of SAFT-type equations to derivative properties is still very scarce and, in some cases, a poor agreement with the experimental data were observed, depending on the choice of the SAFT version, the fluid under investigation and the property of interest. It should be taken into account, though, that they were calculated in a purely predictive manner, with parameters only fitted to VLE29–33. For this reason, the molecular parameters obtained for the various glymes were further used to predict the isothermal compressibilities (for temperatures different than 323 K), expansivities,

kT , and isobaric thermal

αP , of the studied glymes. The isothermal compressibility is a measure of the

variation of the glymes volume with pressure and can be described as the change in density 18 ACS Paragon Plus Environment

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with pressure, at constant temperature, while the isobaric thermal expansivity is a measure of the change in density with temperature, at constant pressure:  ∂ ln ρ  kT =    ∂p T

(3)

 ∂ ln ρ  αp =    ∂T  p

(4)

The soft-SAFT predictions for the isothermal compressibility and isobaric thermal expansivity for the glymes are depicted in Figures 8 and 9, respectively, and the deviations to these properties derived from the experimental data (Equations (3) and (4)) in %AARD are reported on Table 2. As can be seen in both figures, a good qualitative (and in some cases, quantitative) agreement with the derived experimental data was obtained with an overall %AARD of 15.7% and 4.04% on the isothermal compressibility and isobaric thermal expansivity, respectively. The low deviations obtained to the experimental isobaric thermal expansivities show that, as expected, the temperature effect is very well captured by softSAFT. However, despite the very good qualitative description, higher deviations are observed for the isothermal compressibility. These deviations generally increase with the glymes molecular weight (i.e. with the increase of the number of ethoxy groups) as previously observed for the pρT data. This deterioration for an increasing chain length can be related to the fact that the main role on the thermodynamic behavior of volumetric derivative properties is played by the chain length, rather than the association (as for energetic properties such as heat capacities), as suggested by some of us in a previous publication.32 As depicted in Figure 9, an increase on the number of ethoxy groups in the glyme leads to a smaller temperature and pressure dependency of the isobaric thermal expansivity, which is well captured by soft-SAFT. Additionally, and similar to what it was observed for glycols,19 the isobaric thermal expansivity presents a cross-over point related to a decrease of the intermolecular interactions, with hydrogen bonds breaking due to the temperature increase. Soft-SAFT EoS is able to correctly describe the isobaric thermal expansivity and predict the occurrence of this crossover. However, within the experimental pressure range, the EoS predicts the cross-over only for the di-alkyl glymes. The cross-over is also predicted for the mono-alkyl glymes but at pressures ranging from 150 MPa, for the TeEGME, to 650 MPa, for the EGEE. Furthermore, soft-SAFT denotes a decrease of the pressure at which the 19 ACS Paragon Plus Environment


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cross-over point appears as the glymes chain length decreases and with the replacement of an hydroxyl end-group by an alkyl group. Thus, given the sensitivity of derivative properties to inaccuracies in the models or equations, the good results evidence the robustness of the proposed model and molecular parameters.


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Figure 8. Isothermal compressibility, kT, as function of pressure and temperature for the studied glymes. Solid lines represent the soft-SAFT predictions, while the symbols are derived from the experimental data. 21 ACS Paragon Plus Environment


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Figure 9. Isobaric thermal expansion, αP, as function of pressure and temperature for the studied glymes. Solid lines represent the soft-SAFT predictions, while the symbols are derived from the experimental data.


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4.3. Physical trends of soft-SAFT EoS pure-component molecular parameters. One of the main advantages of SAFT-type equations is that their parameters have solid based physical meaning, as stated it in the introduction and model sections. However, in several cases, the SAFT equations are used in almost an empirical manner, with little attention paid to the meaning of these parameters and their possible transferability. A clear example of this limitation is the case of water, for which several molecular models and sets of parameters have been proposed, even with the same SAFT-type equation and same set of experimental data used in the fitting procedure.54 Therefore, when a new molecular model and parameters are proposed, a discussion on their physical meaning and transferability becomes relevant. Since in soft-SAFT compounds are modeled as homonuclear chains, different values of

ε

m, σ

and

ε

are expected for each member of a homologous series. However,

σ

and

should tend to an asymptotic value with an increase of the chain length since the addition

of more groups to already long chains does not significantly modify the molecules structure and the influence of the hydroxyl end groups also decreases. This behavior is depicted in Figure 10 for the different families, n-alkanes17, alkan-1-ols20, glycols19 and the glymes studied in this work. Another interesting result is that these parameters increase linearly with the molecular weight within an homologous series, as showed by Blas and Vega,55 Kraska and Gubbins56 and Vega and collaborators for different chemical families.17,19–24,26,27 These physical trends observed for the pure component parameters of SAFT-type EoS allow the transferability of the parameters to different members within a homologous series, allowing for the prediction of the thermodynamic behavior of higher chain length members for which no VLE data are available and no parameters were fitted.17,19–22,27 These linear trends are also observed in the molecular parameters proposed in this work for glymes. However, since the monoalkyl ethers (glymes m-ether in Figure 10) are considered as associating species and the dialkyl ethers (glymes d-ether in Figure 10) are considered as non-associating species (see Figure 1), significant differences between them are expected, especially in the dispersive energy parameter, as can be observed in Figure 10. Thus, both types of glymes were represented as different families and the linear trends, presented in Table 3, were obtained for each one. Furthermore, the correlations with the molecular weight obtained for the dialkyl ethers were used to predict the liquid densities at atmospheric pressure of the polyethylene glycol dimethyl ether 250 (PEGDME250) reported by Conesa et al.57 The mixture of ethylene glycol dimethyl ethers with different n values (n=3 to 9) was here modelled using a pseudo-pure 23 ACS Paragon Plus Environment


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component approach (n=5.723 and

Page 24 of 35

Mw = 298.21 g/mol) and, as depicted in Figure 11, the

model was able to accurately predict the experimental density data with a %AARD of 0.35%. Note that the data was predicted from the correlation of the molecular parameters. Thus, these results support the model transferability and validate the assumptions therein showing that even for a considerable number of ethylene oxide groups, their influence can be accounted by the effective values of the non-associating molecular parameters, yielding good results also for dialkyl ethers.

Figure 10. Trends of the soft-SAFT pure-component parameters for different families of compounds as a function of their molecular weight.17,19,20 24 ACS Paragon Plus Environment

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Table 3. Behavior of the glymes soft-SAFT molecular parameters with respect to the molecular weight of the compounds. Monoalkyl ethers Dialkyl ethers R 2 = 0.9827

m = 0.01553× Mw +1.191 mσ 3 ( Å 3 ) = 1.368 × M w + 15.90

mε / kB (K) = 6.687×Mw +180.61

m = 0.01633× Mw +1.055

( )

3 3 R 2 = 0.9974 mσ Å = 1.327 × M w + 32.15

R 2 = 0.9963

R 2 = 0.9818

R 2 = 0.9743

mε / kB (K) = 5.864×Mw + 208.59R 2

= 0.9746

Figure 11. Liquid density data for PEGDME250. Symbols represent the experimental data taken from Conesa et al.57 while the solid line depicts the soft-SAFT prediction.



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As mentioned, the differences between the two types of glymes are expected to be more relevant on the energy parameter. Therefore, the values of

m

and σ of both series

seem to be consistent, showing a very similar linear dependency with the molecular weight both on

m and

mσ 3 . However, an outlier is observed (especially on the segment diameter)

for DEGDEE. This deviation of the DEGDEE pure-component parameters from the behavior of the remaining glymes can be understood by the larger size of both diethyl end-groups, since DEGDEE was the only diethyl ether amongst the dialkyl ethers evaluated. Moreover, and according to Figure 10, the linear dependency of the segment number (chain length) with the molecular weight seems to be common to the different families, with the exception of the n-alkanes. This general behavior of the chain length parameters shows that the introduction of inner-chain groups, like ethoxy groups, and the removal or addition of similar functional endgroups (e.g. hydroxyl groups) have only a slight effect on the segment number but a higher impact on the segment diameter. Note that the molecular volume is directly related to both by mσ3. As depicted in Figure 10b, the introduction of ethoxy groups in the glyme molecule results in lower segment diameters increments than those observed for the methylene group addition in the n-alkanes and alkan-1-ols, due to the lower volume of the oxygen atoms. Moreover, the alkylation of the end groups also increases the segment diameter (CH3O is bulkier than OH) and thus, the segment diameters proposed in this work are higher than the ones proposed for glycols, as expected. Concerning the dispersive energy parameter, significant differences are observed between the various families. As can be seen in Figure 10c, the dispersive energies proposed in this work for glymes show the following trend when compared to the other families: n -a lk a n e s < g ly m e s d -e th e rs ≅ 1-a lk a n o ls < g ly m e s m -e th e rs < g ly c o ls

The observed trend for dispersive energies denotes that an increase in the associative character of the compound is reflected in an increase in the dispersive energy parameter, since some of the associative behavior of the hydroxyl groups is being incorporated into the dispersive term of soft-SAFT. Moreover, the ethoxy groups are considered in an effective manner with a higher dispersive energy parameter, which explains the similarity of the glymes d-ethers with the alkan-1-ols family. Given the short range and highly directional character of association forces, the association parameters are often kept constant within each family, as these interactions are generally not strongly influenced by the compounds chain length except for the shortest 26 ACS Paragon Plus Environment

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members of the series. The association parameters for alkan-1-ols, glycols and glymes mether are depicted in Figure 12. Both, for glycols and alkan-1-ols, the first member (or first two members) have different association parameters compared to the heavier members showing a much higher energy or volume of association. Note that, in this case, the association is not hindered by steric effects present within the longer molecules. For the glymes m-ethers studied in this work the association energy was transferred from the alkan-1ols, while the association volume was transferred from glycols. This transferability and similarity between the association parameters of these compounds was already expected since the same associative functional groups are being considered (hydroxyl groups) with the differences between the three families being related to the number of hydroxyl end groups (justifying the different association energy values between glycols and glymes), but also due to the influence of the ethoxy groups that can be masked by the association term (this explaining the difference in association volume of alkan-1-ols and glymes).

Figure 12. Soft-SAFT association parameters for different families of compounds. a) Association energy parameter b) Association volume parameter. The robustness of the molecular parameters, describing the expected trends and values, along with the very good descriptions obtained for the VLE, pρT data and derivative properties, both for the glymes evaluated here as for the glycols reported in a previous publication,19 emphasizes the reliability of the simple model adopted here.



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5. Conclusions Aiming at developing a robust molecular approach and propose reliable and transferable molecular parameters, the soft-SAFT EoS was evaluated based on the pρT data measured for the glymes. New experimental pρT data for eight glymes were measured in a wide range of temperatures (283–363) K and pressures (0.1–95) MPa. Additionally, the isobaric thermal expansivity and isothermal compressibility were determined from the experimental data. By modelling the selected glymes as homonuclear LJ chains (with one square-well site embedded off-center in one of the LJ segments, mimicking the hydroxyl end-group in the case of monoalkyl glymes) and using, in addition to VLE data, one single density–pressure and isothermal compressibility isotherms at 323 K, optimized pure-component parameters were proposed. These sets of parameters were then used to describe the pρT data and the second-order derivative properties. It was shown that the adopted procedure allowed very good descriptions of the compounds experimental data, with similar deviations to those reported for other families of compounds using the soft-SAFT EoS. This approach is particularly relevant on the description of the second-order derivative properties, where not only a good qualitative, and in some cases quantitative, description of the experimental data was achieved, but mostly on the model ability to accurately capture the characteristic crossover point of the isobaric thermal expansions. The molecular parameters obtained for glymes and those previously reported for glycols were further analyzed through comparison with other compounds families, such as n-alkanes and alkan-1-ols. The trends shown by the sets of parameters of the studied families are in good agreement with those expected, supporting the robustness and transferability of the proposed molecular approach. Furthermore, these correlations were further used to predict the PEGDME250 densities at atmospheric pressure. The mixture of ethylene glycol dimethylethers was modelled as a pseudo-pure component (n=5.723 and

Mw = 298.21 g/mol)

with the model able to accurately predict the experimental data.

Supporting information The Supporting Information is available free of charge on the ACS Publications website at DOI:


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Acknowledgements This work was supported by PARTEX OIL AND GAS and developed in the scope of the project CICECO - Aveiro Institute of Materials, POCI-01-0145-FEDER-007679 (FCT Ref. UID/CTM/50011/2013), financed by national funds through the FCT/MEC and cofinanced by FEDER under the PT2020 Partnership Agreement. P. J. Carvalho also acknowledges FCT for a contract under the Investigador FCT 2015, contract number IF/00758/2015. Additional support from the Comunidad de Madrid Government (project S2013/MAE-2800) the Catalan Government (project 2014SGR-1582), and the Spanish Government (projects CTQ2014-53987 and CTQ2014-53655-R) is also acknowledged. P. Navarro also thanks Spanish Government for his FPI and mobility grants (BES-2012-052312 and EEBB-I-16-10597).



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