Aprotic Ionic Liquids: A Framework for Predicting Vaporization Thermodynamics

Ionic liquids (ILs) are recognized as an environmentally friendly alternative to replacing volatile molecular solvents. Knowledge of vaporization thermodynamics is crucial for practical applications. The vaporization thermodynamics of five ionic liquids containing a pyridinium cation and the [NTf2] anion were studied using a quartz crystal microbalance. Vapor pressure-temperature dependences were used to derive the enthalpies of vaporization of these ionic liquids. Vaporization enthalpies of the pyridinium-based ionic liquids available in the literature were collected and uniformly adjusted to the reference temperature T = 298.15 K. The consistent sets of evaluated vaporization enthalpies were used to develop the “centerpiece”-based group-additivity method for predicting enthalpies of vaporization of ionic compounds. The general transferability of the contributions to the enthalpy of vaporization from the molecular liquids to the ionic liquids was established. A small, but not negligible correction term was supposed to reconcile the estimated results with the experiment. The corrected “centerpiece” approach was recommended to predict the vaporization enthalpies of ILs.


Introduction
Volatile molecular solvents are widely used in the chemical industry for extraction, recrystallization or as a reaction medium. The separation of solvents from chemicals is usually performed by evaporation or distillation [1][2][3][4][5][6][7]. It is inevitable that a significant amount of volatile solvents will be lost into the atmosphere and pollute nature. The extremely low-volatility ionic solvents, on the other hand, do not have this disadvantage and are considered to be a substitute for molecular solvents in many technical applications. Chemical processes are usually carried out at elevated temperatures where vapor pressures cannot be considered negligible. Therefore, a reliable knowledge of the vaporization thermodynamics is essential to avoid material losses or to reveal the limits of thermal stability [8][9][10].
Obtaining the proper vapor measurements of ionic liquids (ILs) are a challenging task because, at low temperatures, the vapor pressure is too low to be measured, but at high temperatures the decomposition processes can occur and falsify the result. For this reason, the experimental results for the vaporization thermodynamics of ionic liquids should be validated before they can be considered as reliable. [8][9][10] It is evident that a better understanding of transition enthalpies also helps to elucidate macroscopic fluid phenomena, and thus promote industrial applications.
Structure-property relationships are a very useful diagnostic tool to establish the internal consistency of available experimental data. They are suitable for predicting at least The main idea of this work is demonstrated in Figure 2. As a matter of fact, in our previous work, we showed that the general regularities revealed for molecular liquids can be transferred to ionic liquids [13].   The main idea of this work is demonstrated in Figure 2. As a matter of fact, in our previous work, we showed that the general regularities revealed for molecular liquids can be transferred to ionic liquids [13]. the level of the property being measured when the data is known for similarly shaped molecules [11]. Unfortunately, only very few vapor pressures and vaporization enthalpies are available for ionic liquids [12]. This work contributes with six new datasets on the vaporization thermodynamics of pyridinium-based ionic liquids with bis(trifluoromethylsulfonyl)imide anion (see Figure 1) and the investigation of the interplay of structure-property relationships in ionic liquids, and leads to the development of a new general approach to predict vaporization enthalpies of ionic liquids using the available knowledge on the vaporization thermodynamics of molecular liquids. In our previous studies, we found that ionic liquids containing the [NTf2] anion are best suited for vapor pressure measurements because of their remarkable thermal stability. The pyridinium-based ionic liquids are used as the first part to understand structure-property relationships in ionic liquids. The similar study of the imidazolium ILs is ongoing. The main idea of this work is demonstrated in Figure 2. As a matter of fact, in our previous work, we showed that the general regularities revealed for molecular liquids can be transferred to ionic liquids [13].  Indeed, the vaporization enthalpies of, e.g., pyridine derivatives, can be reliably predicted with the help of a simple contribution, ∆ m o (H→R1), representing the replacement of an H atom in pyridine with any substituents (see Figure 2a). It was found that, for pyridinium-based ionic liquids, the same numerical values for the contributions  Indeed, the vaporization enthalpies of, e.g., pyridine derivatives, can be reliably predicted with the help of a simple contribution, ∆ g l H o m (H→R 1 ), representing the replacement of an H atom in pyridine with any substituents (see Figure 2a). It was found that, for pyridinium-based ionic liquids, the same numerical values for the contributions ∆ In this work, we ascertain and generalize this finding based on the available data on vaporization enthalpies of pyridinium ionic liquids with the help of complementary measurements of six new ionic liquids.

Materials and Methods
The samples of alkyl-pyridinium-based ionic liquids with the bis(trifluoromethylsulfonyl) imide anion of 99% purity were of commercial origin (see Table S1) and were used as received. Before starting the experiment, however, a sample of an IL was placed in an open cavity of the thermostatted block and subjected to vacuum (10 −5 Pa) for conditioning. The quartz crystal microbalance (QCM) [14] was used for vapor pressure measurements at different temperatures. A sample of an IL was placed in an open cavity (Langmuir evaporation) of the thermostatted block inside the set-up. The standard molar enthalpies of vaporization, ∆ g l H o m , were derived from the temperature dependences of vapor pressures. A concise description of the L-QCM (Langmuir quartz crystal microbalance) method and data treatment is presented in the Supporting Information.

Experimental Vaporization Thermodynamics of Pyridinium Based ILs
The original experimental vapor pressures of Ils at different temperatures are collected in Table S2. They were used to derive the standard molar enthalpies of vaporization ∆ g l H o m (T av ), which are referenced to the average temperatures T av . These results are shown in Table 1 [13]). To investigate the structure-property relationships, we also compiled (see Tables 2 and 3) the vaporiza-tion enthalpies of the pyridinium-based ILs connected to the [NTf 2 ] anion available in the literature.  Table 1 a Method: K-QCM-Knudsen effusion cell combined with a quartz crystal microbalance; L-QCM-Langmuir evaporation from the open surface combined with the quartz crystal microbalance; TPD-temperature-programed desorption line-of-sight mass spectrometry at a ultra-high vacuum. b Vaporization enthalpies measured in the specified temperature range and referenced to the average temperature T av . c The heat capacity differences were derived in our previous work [15] from the experimental volumetric properties. d Vaporization enthalpies   [19].

Comparison of the Vaporization Enthalpies Derived from the Theoretical and Empirical Methods
Taking into account the difficulties of experimental measurements of the extremely low vapor pressures, the vaporization enthalpies should be compared to results obtained from other methods (see Tables 4 and 5).  [24] 143.9 ± 10 143.1 ± 10 145.8 ± 10 --

Molecular Dynamic (MD)
A number of different MD simulation methods were used to calculate the vaporization enthalpies of ionic liquids [20][21][22][23] with varying degrees of success (see Table 4). The General AMBER Force Field (GAFF) [20] failed to predict the enthalpy of the vaporization of [1-C 3 -Py][NTf 2 ] properly. Additionally, the original CL&P FF method [21] heavily overestimates the vaporization enthalpy of [1-C 4 -Py][NTf 2 ]. However, after the refinement of this method [21], an acceptable agreement with the experiment was achieved for [1-C 4 -Py][NTf 2 ] (see Table 4). Borodin [22] used a version of the MD simulation package Lucretius for MD simulations, which includes many-body polarization simulations. His result for the vaporization enthalpy of [1-C 4 -Py][NTf 2 ] is in excellent agreement with the experiment. The empirical force fields are usually parametrized with experimental thermodynamic and structural data. Hence, our new experimental results on vaporization enthalpies for pyridinium-based series can be used for the development, re-parametrization, and validation of modern MD methods [10,28,29].

COSMO
The quantum-chemistry-based model, COSMO with modifications COSMOtherm [23] and COSMO-RS [24], was used for the prediction of the thermochemical properties of ILs. However, as shown in Table 4, the ∆ g l H o m (298.15 K) values calculated by the original COSMO-RS [24] are systematically (of about 10 kJ·mol −1 ) higher, compared to the experimental result. In contrast, the result for [1-C 6 -Py][NTf 2 ] predicted by the modified COSMOtherm is in agreement with the experiment (see Table 4).

CRDS Method
Gas-phase electronic absorption spectroscopy was successfully used for studies of 3-Me-1-ethylpyridinium and 1-butyl-3-methylimidazolium cations connected with the [NTf 2 ] anion [27]. The vapor pressures at 400-430 K were derived from the measured absorbance. The vaporization enthalpy determined for [3-Me-C 2 -Py][NTf 2 ] using the CRDS (cavity ring-down laser absorption spectroscopy) method is presented in Table 5 and is evidently too high.

Gas Chromatographic Method (GC)
This method is based on the experimental infinite dilution activity coefficients γ ∞ 1 derived from the retention times of various solutes measured by gas chromatography using the IL as the solute [12]. The necessary details are presented in the Supporting Information. Ban et al. [26] used this method and reported the vaporization enthalpies, ∆  Table 4 and they appear to be reasonable, in comparison to other methods. We used the original data for γ ∞ 1 for [4-Me-1-C 4 -Py][NTf 2 ], measured by Domanska and Marciniak [30], and derived, ∆ g l H o m (298.15 K) = 135.7 ± 3.0 kJ·mol −1 (see Table 5), which meets the level expectation.

Empirical Model
In an empirical approach developed by Licence and Jones [25], the ∆ g l H o m (298.15 K)value is decomposed into the Coulombic and van der Waals contributions from the cation and anion. Unfortunately, a very limited experimental data set on vaporization enthalpies was used for the parameterization of this approach. As can be seen from ], in contrast to the established growth trend of the vaporization enthalpy, with increasing chain-length dependence within the homologous series. Apparently, this method needs further development, but unfortunately no update since 2014 has been found in the literature.

Validation of the Vaporization Enthalpies
The comparison of the experimental enthalpies of vaporization with those derived from theoretical and empirical methods of the previous section was not sufficient to validate the available enthalpies of vaporization of the pyridinium-based ILs. The consistency of the complete data set could be checked using structure-property correlations, e.g., chainlength dependence, or using the correlation between the vaporization enthalpy and surface tension of the ILs.  Table 2) with the number of carbon atoms, n, in the alkyl chain attached to the cation nitrogen atom. The following correlation was obtained (see Table S8): The relatively high correlation coefficient R 2 is evidence of a good consistency of experimental data approximated by Equation (2).
The surface tension σ 298 (surface tension at the reference temperature T = 298.15 K) as a thermophysical property is directly related to the vaporization enthalpy ∆  Table 6. Using this data, a robust linear correlation with the alkyl chain length attached to the N atom of the cation was established according to Equation (3):

Correlation of the Vaporization Enthalpies with the Surface Tension
In this work, we correlated ∆  Table 7, column 2. The results are presented in Table 7, column 4. A good linear correlation has been found to be: for the [1-C n -Py][NTf 2 ] series. As shown in Table 7, the differences between the experimental and estimated values do not exceed 1 kJ·mol −1 , demonstrating the consistency of the data set of the unsubstituted pyridinium-based ILs. Can we also use σ 298 values to prove the consistency of the evaporation data for Me-and CN-substituted pyridinium ILs? To test this, we carefully collected the surface tension data of methyl-substituted (see Table 8) and cyano-substituted (see Table 9) pyridinium-based ILs and correlated these values with the vaporization enthalpies evaluated in Tables 1 and 2.  (5), the assessed expanded uncertainty of ± 2.0 kJ·mol −1 (with k = 2 and confidence level 0.95). c Difference between columns 3 and 4. As shown in Tables 7 and 8, the differences between the experimental and estimated values are mostly below 1 kJ·mol −1 , which also demonstrates the sufficient consistency of the data set of the substituted pyridinium-based ILs evaluated in this work. This dataset can now be used to develop a methodology to predict the enthalpies of ILs, which are difficult to access experimentally.

Group Additivity to Predict the Vaporization Enthalpies of Ionic Liquids Using Contributions from Molecular Liquids
The enthalpy of vaporization is generally a measure of the intensity of intermolecular interactions that hold molecules together in the liquid state. When Van der Waals forces and hydrogen bonding prevail over molecular liquids, the additional strong Coulomb interactions are specific to ionic liquids. This makes the ionic liquids (or molten salts) extremely low volatile, with vaporization enthalpies between 120 and 180 kJ·mol −1 [31]. Group additivity (GA) methods are successfully used to predict vaporization enthalpies of molecular liquids. In conventional GA methods, the vaporization enthalpies of molecules are split up into smallest possible groups in order to obtain well-defined contributions. The prediction is then based on the idea of "LEGO ® bricks", where the energetics of the molecule of interest are collected from the appropriate type and number of bricks. A comprehensive system of group contributions (or increments) covers the major classes of organic compounds [39]. Using the same method for ionic liquids composed of large organic cations and large organic/inorganic anions is impractical, due to too many "bricks" and a very limited amount of available experimental enthalpies of vaporization. To overcome these limitations, we developed a general approach to estimate the vaporization enthalpies based on a so-called "centerpiece" molecule [40,41]. This approach is closely related to the broadly used group additivity (GA) methods [39,42]. The idea of the "centerpiece" approach is to start the prediction with a potentially large "core" molecule that can generally mimic the structure of the molecule of interest, but, at the same time, must has a reliable enthalpy of vaporization. The ionic liquids are predestined for such an approach. The visualization of the "centerpiece" approach for R-substituted [C 2 -Py][NTf 2 ] ionic liquid is presented in Figure 3 as an example.
for [CN-1-Cn-Py][NTf2]: ∆ l m (298.15 K) = −4.16 × σ298(exp) + 284.5 (with R = 0.986) (6) As shown in Tables 7 and 8, the differences between the experimental and estimated values are mostly below 1 kJ·mol −1 , which also demonstrates the sufficient consistency of the data set of the substituted pyridinium-based ILs evaluated in this work. This dataset can now be used to develop a methodology to predict the enthalpies of ILs, which are difficult to access experimentally.

Group Additivity to Predict the Vaporization Enthalpies of Ionic Liquids Using Contributions from Molecular Liquids
The enthalpy of vaporization is generally a measure of the intensity of intermolecular interactions that hold molecules together in the liquid state. When Van der Waals forces and hydrogen bonding prevail over molecular liquids, the additional strong Coulomb interactions are specific to ionic liquids. This makes the ionic liquids (or molten salts) extremely low volatile, with vaporization enthalpies between 120 and 180 kJ⋅mol −1 [31]. Group additivity (GA) methods are successfully used to predict vaporization enthalpies of molecular liquids. In conventional GA methods, the vaporization enthalpies of molecules are split up into smallest possible groups in order to obtain well-defined contributions. The prediction is then based on the idea of "LEGO ® bricks", where the energetics of the molecule of interest are collected from the appropriate type and number of bricks. A comprehensive system of group contributions (or increments) covers the major classes of organic compounds [39]. Using the same method for ionic liquids composed of large organic cations and large organic/inorganic anions is impractical, due to too many "bricks" and a very limited amount of available experimental enthalpies of vaporization. To overcome these limitations, we developed a general approach to estimate the vaporization enthalpies based on a so-called "centerpiece" molecule [40,41]. This approach is closely related to the broadly used group additivity (GA) methods [39,42]. The idea of the "centerpiece" approach is to start the prediction with a potentially large "core" molecule that can generally mimic the structure of the molecule of interest, but, at the same time, must has a reliable enthalpy of vaporization. The ionic liquids are predestined for such an approach. The visualization of the "centerpiece" approach for R-substituted [C2-Py][NTf2] ionic liquid is presented in Figure 3 as an example.   [15]. It is quite evident that the contributions, ∆ g l H o m (H→R), for the "appending" to the [1-C 2 -Py][NTf 2 ] "centerpiece" are comparatively small and affordable for a reliable assessment. As a matter of fact, in our recent work [13], we have shown that the ∆ g l H o m (H→Me) and ∆ g l H o m (H→CN) contributions derived from the molecular liquids (substituted pyridines and quinolines) are generally transferrable to ionic liquids. The numerical values for these contributions are presented in Table 10. Let us consider the prediction of the vaporization enthalpy for [3-Me-1-C 3 -Py][NTf 2 ] as an example (see Table 11). The  Table 11), where reliable experimental vaporization enthalpies were available.
Even a quick look at the results presented in Table 11 can reveal that the "centerpiece" approach of about 5 kJ·mol −1 systematically overestimates the vaporization enthalpies, if we directly take the ∆  Table 11). One of the plausible explanations for this observation is that the ∆ g l H o m (H→R) contributions are derived from molecular liquids. For vaporizing molecular liquids, all types of interaction need to be overcome for bringing the monomer molecules into the gas phase. This situation is different for ionic liquids, which evaporate as ion pairs. Thus, an attractive cation-anion Coulomb interaction, hydrogen bonding between both ions and, in particular, a dispersion interaction within the ion pair are taken into the gas phase. The overestimation of the vaporization enthalpies in the order of 5 kJ·mol −1 by applying the "centerpiece" is in the order of the derived dispersion energies between the cations and anions in an ion pair [44][45][46][47][48]. Indeed, such a contribution should be more or less constant for all types of ionic liquids, and only marginally dependent on the nature of the cation and anion, as demonstrated in the present paper.
Admittedly, these forces play only a subordinate role in ionic liquids. Thus, a direct transfer of the ∆ g l H o m (H→R) contributions from the molecular to the ionic liquids evidently requires a systematic correction. Considering the common nature of the systematics observed for the ILs in Table 11, we propose the application of the "centerpiece" approach to ILs, along with the correction term ∆ = (−4.9 ± 0.8) kJ·mol −1 (see Table 11), to predict the  Table 5, we collect the results for five ionic liquids of the [Alkyl-1-C 3 -Py][NTf 2 ] series. The ∆ g l H o m (298.15 K) values for this series were of a different quality. Nonetheless, our calculations using the "corrected-centerpiece" approach allows for a reliable estimate of the "expected" level of vaporization enthalpy for each species in Table 5, to detect the "sick" data and help to improve the experimental and theoretical methods. A prime example to support this idea is the calculation for [3-Me-1-C 2 -Py][NTf 2 ] (see Table 5, line 3 and Table S5). The "corrected-centerpiece" result ∆ measured by the CRDS method is definitely an error, even taking into account the extremely significant uncertainties. However, by having such a convenient tool as the "corrected-centerpiece" approach, it might be possible to improve the measuring technique, provided that the level of the "expected" vaporization enthalpy is preliminarily assessed.   Table 9. c Enthalpies of vaporization of the "centerpiece" molecules from Tables 1-3. d Calculated as the sum of columns 2 and 3. e Calculated as the difference of columns 5 and 4. f Weighted mean value (the uncertainty was taken as the weighing factor).

Conclusions
The structure-property correlations have proven to be a useful diagnostic tool for predicting the vaporization enthalpies for ILs. The general transferability of the group contributions derived from molecular liquids to estimate the vaporization enthalpies of ionic liquids was demonstrated. It was shown that, with the "centerpiece" approach, it is possible to estimate the appropriate level of vaporization enthalpy. The further refinement of this approach with the small, but not negligible, correction term has helped brought the estimated results into agreement with the experiment. The corrected "centerpiece" approach was recommended to predict the vaporization enthalpies of ILs. The application of this approach to imidazolium-based ILs will be explored in the upcoming studies.    [14,15,30,35,[49][50][51][52][53][54][55].