Vaporization Thermodynamics of Pyrrolidinium, Pyridinium, and Imidazolium-Based Ionic Liquids Bearing the Bis(fluorosulfonyl)imide [FSI] and the Bis(trifluoromethylsulfonyl)imide [NTf2] Anions

New experimental vapor pressures in the range 407 K to 460 K and vaporization enthalpy of the ionic liquids (IL) N-alkyl-N-methyl-pyrrolidinium bis(fluorosulfonyl)imide ionic liquids have been measured using quartz crystal microbalance. The absolute vapor pressures and vaporization enthalpies were compared with analogous pyrrolidinium-based ILs with the bis(trifluoromethanesulfonyl)imide anion. The evaluated difference in vaporization enthalpy of ILs with bis(fluorosulfonyl)imide and bis(trifluoromethanesulfonyl)imide anions allowed for estimation of corresponding property for a wide set of ILs with bis(fluorosulfonyl)imide anion. The results are relevant to chemical engineering calculations of processes involving ILs as reaction and separation media.


Introduction
The irreversible trend of modern technologies towards renewable energies requires safe storage and delivery of the generated energy. Lithium-ion batteries are among the most effective technical solutions today. They are widely used in portable This article is part of the Special Issue in Memory of Professor Talgat Khasanshin.

C 1 Pyrr][FSI])
1-butyl-1-methylpyrrolidinium bis(fluorosulfonyl)imide ([C 4 C 1 Pyrr][FSI]) used in this work were of commercial origin (see Table S1). Prior to the experiments, samples were subjected to vacuum evaporation at 413 K and 10 -5 Pa for more than 24 h to reduce possible traces of solvents and moisture. Samples were additionally conditioned inside of the vacuum chamber at the highest temperature of the vaporization experiment within 12 h. This additional purification allowed for removing of residual traces of water and volatile impurities as well as for collecting the amount of the vaporized IL required for the FTIR analysis.

Measurements of Vaporization Enthalpies by the Quartz Crystal Microbalance (QCM)
Absolute vapor pressures and the standard molar enthalpies of vaporization of the [C n C 1 Pyrr] [FSI] were determined using the QCM method [4]. In the QCM method [C3C1Pyrr] [C4C1Pyrr] [FSI]

Fig. 1
Structures of N-alkyl-N-methyl-pyrrolidinium bis(fluorosulfonyl)imide ionic liquids studied in this work a sample of an IL is placed in an open chamber (Langmuir evaporation) inside of the isothermal stainless steel cylinder and exposed to high vacuum  with the whole open surface of the loaded compound. Directly above the measuring cavity containing the sample the QCM sensor is placed. Liquid sample fully covers the bottom of cavity and due to low mass loss during the study the surface area of liquid sample is left constant. Throughout the vaporization into vacuum, a certain amount of sample is deposited on the quartz crystal surface. The change of the vibrational frequency ∆f is directly related to the mass deposition ∆m on the crystal according to the Sauerbrey's equation [5] for the case ∆f << f: here f is the fundamental frequency of the crystal (6 MHz), S C is the surface of the crystal, and C is a constant [6]. The resolution of acquisition device is at level of 0.01 Hz, at the same time preliminary studies had shown the long-term stability of recorded frequency at level of 0.5 Hz. Therefore, during each isotherm the time of vacuum exposure was controlled to achieve the frequency change at level of 100 Hz.
The measured frequency change rates (df/dt) can be used for calculation of absolute vapor pressures p sat according to equation: where the K′ = (9.5 ± 1.1) × 10 −6 Pa·s·kg 1/2 ·Hz −1 ·K −1/2 ·mol −1/2 is the empirical constant containing all parameters of the Sauerbrey equation as well as parameters specific for the geometry of the experimental setup [6]. The K′-value for our apparatus was evaluated with the help of reliable vapor pressure data on imidazolium and pyridinium-based ILs compiled in reference [6]. Using the frequency change rate df/ dt measured by the QCM and the K′-values the standard molar enthalpy of vaporization, Δ where T av is the average temperature of the temperature range of the QCM study. In order to detect and avoid any possible effect of impurities on the measured frequency loss rate (df/dt), a typical experiment was performed in a few consequent series with increasing and decreasing temperature steps. Every series consisted of 9 to 10 temperature points of mass loss rate determination. Several runs have been performed to test the reproducibility of the results. The study was finished when the enthalpy of vaporization, Δ g l H o m (298 K) , obtained in the sequential runs by adjusting Eqs. 3 and 4 to the temperature dependent rates (df/dt) agreed within the assessed experimental uncertainty of about ± 1 kJ·mol −1 . In order to confirm the absence of decomposition of IL under the experimental conditions, the residual IL in the crucible and the IL-deposit on QCM were analyzed by ATR-IR spectroscopy. Primary experimental results of the QCM study is given in Table S1 in the Supporting Information.

Absolute Vapor Pressures
Absolute vapor pressures and vaporization enthalpies of the [C n C 1 Pyrr][FSI] have been measured for the first time. Ionic liquids are widely applied in the modern catalytic processes like Solid Catalyst with Ionic Liquid Layer (SCILL) [7,8] or Supported Ionic Liquid Phase (SILP) [8,9]. For the catalyst to work stably, it is necessary to know the vapor pressure of an IL at any temperature. The temperatures 373 K and 473 K seem to be a reasonable choice to assess the vapor pressure as a measure of a possible long-term uptake of the IL during catalytic applications. As can be seen from Table 1

Standard Molar Vaporization Enthalpy from Vapor Pressure Measurements
The standard molar enthalpies of vaporization Δ g l H o m (T av ) derived from the temperature dependence of the vapor pressures measured with the QCM (see Table 2, column 4) are referenced to the average temperature T av (see Table 2, column 3), which is the middle of the temperature range under study.
It is commonly recognized that reliable experimental data on enthalpies of vaporization for ILs are very scarce. For this reason, the development of a simple or sophisticated method for predicting or correlating enthalpies of vaporization is highly desirable. An example of the successful structure-property correlation within a homologous series is the chain length dependence of the Δ  Table 4) was measured and evaluated in our recent work [13]. Using this data set and the average contribution   Table 4).
Another suitable example is calculation of the vaporization enthalpies of [C n mim][FSI] (see Table 4 Table S5). These new empirical values could be used to validate theoretical results from the literature. In fact, a careful literature search has shown that experimental studies of the enthalpies of vaporization of ILs with the [FSI] anion are absent in the literature. The few theoretical enthalpies of vaporization that were found for comparison are listed in Table 5.
Results of molecular dynamics (MD) simulations using a polarizable many-body force field have been reported [14] on pyrrolidinium and imidazolium ILs with [FSI] and [NTf 2 ]. As can be seen from  a The standard Gibbs energies of vaporization were evaluated using the calibration coefficient developed in our recent work [6] b Heat capacity differences between liquid and gas phases were calculated according to empirical equation Δ  a Measured in this work (see Table 2) b Enthalpies of vaporization derived from the chain-length dependence of experimental data given in  a Enthalpies of vaporization derived from the chain-length dependence of experimental data given in Table S4 b Enthalpies of vaporization derived from the chain-length dependence of experimental data given in Table S5 c Calculated as the sum of the enthalpy of vaporization given in column 2 and the contribution ∆ from volatile solute (typically an industrially relevant solvent such as benzene, methanol, acetone, denoted with a subscript 1) in an ionic liquid as a solvent (denoted with a subscript 2) are conveniently measured using gas-chromatography [16]. Usually, a set of ∞ 1 -values for 20 to 40 solutes of different polarity is correlated with the solubility parameters of solutes, which leads to the vaporization enthalpy of the solvent (ionic liquid) under study. In our experience, the reliability of the GC method depends crucially on the right choice of solutes [17]. Rabhi  . The significant spread of the correlated data led to a significant overestimation of the ILs vaporisation enthalpies, as shown in Table 5.

Conclusions
The experimentally determined absolute vapor pressures of pyrrolidinium-based ILs with the bis(fluorosulfonyl)imide anion are 10 times lower than that of analogous pyrrolidinium-based ILs with the bis(trifluoromethanesulfonyl)imide anion. Accordingly, the enthalpies of vaporization of the [FSI] containing ILs are higher. Simple additive rule was developed to get reasonable vaporization enthalpies of pyridinium and imidazolium-based ILs bearing the [FSI] anion. The evaluated values are useful for chemical engineering calculations for the processes involving ILs as catalysis, reaction media and separation phase.