Thermodynamics of Imidazolium-Based Ionic ... - ACS Publications

Article pubs.acs.org/JPCB

Thermodynamics of Imidazolium-Based Ionic Liquids Containing PF6 Anions Dzmitry H. Zaitsau,*,† Andrei V. Yermalayeu,† Vladimir N. Emel’yanenko,†,§ Simon Butler,∥ Thomas Schubert,⊥ and Sergey P. Verevkin† †

Department of Physical Chemistry and Department of Science and Technology of Life, Light and Matter, University of Rostock, D-18059 Rostock, Germany § Department of Physical Chemistry, Kazan Federal University, Kremlevskaya str. 18, 420008 Kazan, Russia ∥ Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 4, 64287 Darmstadt, Germany ⊥ IoLiTec Ionic Liquids Technologies GmbH, Salzstrasse 184, D-74076 Heilbronn, Germany S Supporting Information *

ABSTRACT: Imidazolium-based ionic liquids (ILs) with PF6− anions are considered as low-cost solvents for separation processes, but they exhibit restricted thermal stabilities. Reliable measurements of vaporization thermodynamics by conventional methods have failed. In this work, we applied a quartz-crystal microbalance method to determine for the first time the absolute vapor pressures for the [Cnmim][PF6] family, with n = 2, 4, 6, 8, and 10, in the temperature range 403−461 K. An absence of decomposition of ILs in experimental conditions was determined by the attenuated total reflection-infrared spectroscopy. The consistency of the experimental results within the homologous series was established through enthalpy and entropy analyses of the liquid and gas phases as well as by molecular dynamics simulations. sensitized solar cells.4 ILs were successfully used for the generation of nanocomposite materials using the discharge plasmas in contact with the liquids.5 In analytical applications, gas chromatography columns based on ILs combine a wide liquid range with the thermal stabilities of dicationic and polycationic bis(trifluoromethylsulfonyl)imide ILs, yielding columns with extended temperature ranges and longer column lifetimes. The focus of the current study is on imidazolium-based ILs containing hexafluorophosphate (PF6−) anions (see Figure 1). They belong to the second generation of ILs, with “neutral” weakly coordinating anions, reported by Wilkes and Zaworotko6,7 in 1992. Unlike first-generation chloroaluminate ILs, the

1. INTRODUCTION Ionic liquids (ILs) have been accepted as a new prospective material for a wide range of industrial applications. This new group of chemicals has the capability of reducing the industrial use of hazardous and polluting organic solvents due to their unique properties, as well as serves as media for various new syntheses. Different terms, such as room-temperature ionic liquid, nonaqueous IL, molten salt, liquid organic salt, and fused salt, are commonly applied to define salts, which are liquids over a wide temperature range.1 The vapor pressures of ILs at ambient temperatures are very low and render the direct determination of the vapor pressures and enthalpies of vaporization of ILs a challenging task, whereas measurements at high temperatures can be accompanied by a possible thermal decomposition. Accurate vapor pressures and enthalpies of vaporization of ILs are required for validation of force-field models, applied in several simulation techniques (molecular mechanics, molecular dynamics (MD), and Monte Carlo calculations) as well as to anchor p−V−T parameters in equations of state and other semiempirical models. Besides academic interest, vapor pressure and enthalpy of vaporization are thermophysical properties important for practical applications. ILs were proposed as heat-transfer fluids2 and liquid thermal storage media in solar thermal power applications.3 ILs applied as electrolytes may improve the performance of dye© 2016 American Chemical Society

Figure 1. Structure of the [Cnmim][PF6] family of imidazolium-based ILs, with n = 2, 4, 6, 8, and 10, studied in this work. Received: June 16, 2016 Revised: July 26, 2016 Published: July 27, 2016 7949

DOI: 10.1021/acs.jpcb.6b06081 J. Phys. Chem. B 2016, 120, 7949−7957

Article

The Journal of Physical Chemistry B

where SC is the surface of the crystal, C is a constant, and f = 6 MHz, with Δf ≪ f . Using the frequency change rate, df/dt, measured by the QCM, the molar enthalpy of vaporization, Δgl Hom(T0), is obtained by the following equation22

second generation of ILs is water insensitive and readily used for extraction of benzene derivatives,8 short-chain aliphatic carboxylic acids,9 phenol and phenol derivatives,10−12 amino acids,13,14 antibiotics,15 azo and acid dyes,16,17 and tetrahydrofuran18 from aqueous systems. However, it has turned out that ILs containing PF6− and BF4− anions exhibit very moderate thermal stabilities, and they easily release HF as one of their decomposition products, with a low activation energy of EA = 68 kJ mol−1.19 For this reason, reliable experimental studies of ILs containing PF6− and BF4− at elevated temperatures are scarce.19−21 In the presented work, we have determined the vapor pressures and enthalpies of vaporization for imidazolium-based ILs with [PF6]− anions, presented in Figure 1. Measurements have been performed using the quartz-crystal microbalance (QCM) method at possibly low temperatures to avoid decomposition of the IL under experimental conditions. However, it turned out that thermal stability of the [Cnmim][PF6] family was sufficient for reliable studies, and the absence of decomposition was carefully controlled by an attenuated total reflection infrared (ATR-IR) analysis. Moreover, the consistency of the measured QCM thermodynamic parameters of vaporization was additionally established with the help of experimental results from adiabatic and solution calorimetric techniques. Finally, MD simulations were carried out for mutual validation of the experimental vaporization enthalpies.

o Δgl Hmo(T0) − Δgl Cpm T0 ⎛ 1 ⎛ df ⎞ 1⎞ ln⎜ T ⎟ = K′ − ⎜ − ⎟ ⎝ dt ⎠ R T0 ⎠ ⎝T

+

R

⎛T ⎞ ln⎜ ⎟ ⎝ T0 ⎠

(2)

where K′ includes all empirical parameters of the apparatus and compound under study. T0 appearing in eq 2 is a reference temperature (set to Tav in this study). The value Δgl Copm = Copm(g) − Copm(l) is the molar heat capacity difference between the gas phase, Copm(g), and the liquid phase, Copm(l). The vaporization enthalpy, Δgl Hom(T), obtained from the QCM study is adjusted to any required temperature according to o Δgl Hmo(T ) = Δgl Hmo(T0) + Δgl Cpm (T − T0)

(3)

A typical experiment was carried out in a few consequent series (7−11 temperature points), with increasing and decreasing temperatures. Such an approach allows for distinguishing any side effect due to a possible decomposition or the possible presence of impurities on the measured frequency loss rate (df/ dt). When the enthalpy of vaporization, Δgl Hom (Tav), obtained in the sequential runs agreed within the assessed experimental uncertainty of ±1 kJ mol−1, the study was considered complete. The absence of a possible chemical transformation of the IL under experimental conditions was proven with help of ATR-IR spectroscopy of the residue in the cavity as well as of the deposit collected on the QCM. Primary experimental results of the QCM studies are given in Table S2 of the Supporting Information. 2.3. High-Precision Solution Calorimetry. The molar solution enthalpies of LiPF6 and [C2mim][PF6] were measured with a modified commercial LKB 8700-2 isoperibolic solution calorimeter. A full description of the device and the measuring procedure can be found elsewhere.24 In short, a sample of known mass is loaded into a glass ampoule, which is crushed in a 25 mL calorimetric glass cell filled with 25.00 ± 0.01 g of bidistilled water. The mass of the studied sample is adjusted to provide a final solution molality of 0.02 mol kg−1 or lower. Shortly before and after the solution experiment, electrical calibrations are performed. The temperature jump due to the solution process is corrected for the heat exchange between the calorimetric system and calorimetric bath by integration of cubic splines fitting of the temperature change throughout the experiment. The performance and accuracy of the calorimetric setup were tested by measuring the enthalpy of the KCl solution in water at 298.15 ± 0.01 K. The mean measured value of the enthalpy of solution (17.41 ± 0.04 kJ mol−1) was in excellent agreement with the recommended value25 (17.47 ± 0.07 kJ mol−1). All of the reported uncertainties correspond to the 0.95 confidence level for normal distribution (k ≈ 2), unless stated otherwise. 2.4. Force-Field and MD Methodologies. In the present work, a force field developed by Bhargava et al.26 for the [C4mim] cation and [PF6] anion was applied. The interatomic potential is identical to that used by Lopes et al.,27 with the differences being in the refined site charges and Lennard-Jones parameters. Compatible force fields for the [C2mim]+ and

2. MATERIALS AND METHODS 2.1. Materials. The samples of [Cnmim][PF6] ILs were of commercial origin (IoLiTec GmbH), with an initial purity of 99%. The amount of halogen ions in the samples under study was less than 100 ppm, according to the specification by the manufacturer. Before the experiments, vacuum pretreatment at 333 K and 10−2 mbar for more than 24 h was performed to reduce solvent and moisture traces. The samples used in the vaporization studies were additionally conditioned inside the vacuum chamber at the highest temperature of the experiment for 12 h. This additional purification allowed for removal of residual traces of volatile impurities, as well as for collecting the amount of vaporized ILs required for ATR-IR analysis. The provenance and purity of the ILs used for thermochemical studies in this work are given in Table S1. 2.2. QCM. Recently, we applied the temperature dependence of the change in the quartz-crystal vibrational frequency for determination of the standard molar vaporization enthalpies of ILs.22 This method has been developed for studying compounds exhibiting extremely low vapor pressures at ambient temperatures. The experimental setup and measuring procedure were validated with measurements on the [Cnmim][NTf2] family of aprotic ILs, and the details are given elsewhere.22 In short, an IL sample in an open cavity inside the thermostat metal block is exposed to vacuum (10−5 Pa). Evaporation of the sample occurs from the open surface (Langmuir evaporation). The quartz crystal is fixed directly above the cavity. At a constant temperature, a very small amount of the vaporizing material is deposited on the surface of the quartz crystal, changing the fundamental frequency, f, of it. The change in the vibrational frequency, Δf, is related to the mass of the IL, Δm, deposited on the crystal, according to the Sauerbrey equation23 Δf = −Cf 2 ΔmSC−1

o Δgl Cpm

(1) 7950


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The Journal of Physical Chemistry B Table 1. Molar Enthalpies of Vaporization for the [Cnmim][PF6] Family, Derived from QCM Results IL

T-range (K)

Tav (K)

1

2

3

[C2mim][PF6] [C4mim][PF6] [C6mim][PF6] [C8mim][PF6] [C10mim][PF6]

414−457 403−450 408−455 410−458 413−461

435.2 425.7 430.7 433.7 436.3

Δgl Hom (Tav) (kJ mol−1)

Δgl Gom (Tav)a (kJ mol−1)

4 129.9 137.1 140.0 143.4 148.5

± ± ± ± ±

Δgl Cop,mb (kJ mol−1)

5 0.5 0.6 0.7 0.8 0.6

78.2 78.6 78.7 80.2 81.7

± ± ± ± ±

6 −74 −74 −81 −85 −93

1.5 1.4 1.5 1.5 1.5

Δgl Hom (298.15 K)c (kJ mol−1) 7 140.0 146.5 150.8 154.9 161.4

± ± ± ± ±

2.8 2.6 2.7 2.8 2.8

a

The standard Gibbs energies of vaporization were evaluated using calibration coefficient K′ from Table S6. bCalculated from the experimental and evaluated volumetric properties using eqs 5 and 6. cAdjusted to 298.15 K using Δgl Cop,m values from column 6; the final uncertainties of vaporization enthalpy are expanded, taking into account the uncertainty of heat capacity difference Δgl Cop,m, assigned to be ±20 J K−1 mol−1.

[C6mim]+ cations are easily obtained following the scheme in the latter. For [C2mim]+, this means adjusting the charge of the terminal ethyl carbon atom to −0.037e, so as to keep the total ion charge at +0.8e. For [C6mim], the terminal carbon of the hexyl chain has a charge of −0.093e, according to the same procedure. The net charge of the missing/additional CH2 groups is thus compensated. Robustness checks were performed by distributing the charge throughout the hexyl chain instead: these checks demonstrated that the calculated enthalpy of vaporization is reasonably insensitive to the exact charge distribution, with a deviation of only ±0.1 kJ mol−1 observed. The vaporization enthalpy for the studied compounds was computed as the difference between the calculated molar energies of the vapor and liquid phases Δgl Hmo(T ) = ⟨U g⟩(T ) − ⟨U l⟩(T ) + RT

at the B3LYP/6-31+G(d,p) level of theory. Corresponding calculations have been performed for the [Cnmim][PF6] ionic pairs at the HF/3-21G*, HF/6-31G(d,p) level and fully optimized at the B3LYP/6-31+G(d,p) level. Finally, energetics of structures of ionic pairs optimized with the DFT methods, were calculated with the G3MP2 method. The H298 values of the ion pairs were computed using the well-established procedures of statistical thermodynamics.31

3. RESULTS AND DISCUSSION 3.1. Enthalpies of Vaporization of [Cnmim][PF6]. Results of the QCM studies of the [Cnmim][PF6] series are presented in Table 1. The standard molar enthalpies of vaporization, Δgl Hom(Tav), referenced to the average temperature, Tav, of the range under study have to be adjusted with eq 3 to the reference temperature, T = 298.15 K, to be comparable to the values measured by other methods. The values of Δgl Cop,m are required for this adjustment. In our recent works,32−34 we applied a simple equation to assess Δgl Cop,m values

(4)

where ⟨Ug⟩ and ⟨Ul⟩ are the ensemble mean internal energies of an ion pair in the gas and liquid phases, respectively. Simulations were performed using the GROMACS simulation package.28 Nonbonded interactions were cutoff at a distance of 1.2 nm. The Berendsen method was applied for temperature and pressure control. The thermostat and barostat relaxation times were set to 1.0 and 2.0 ps, respectively. The pressure was set to 1 atm. The simulations employed a time step of 2 fs. Equilibration of liquid-phase configurations containing 216 ion pairs each was performed for 30 ns, and production runs were then performed for a further 10 ns. Gas-phase configurations were generated by extracting contact ion pairs from the final liquid configuration. An individual cation was selected at random, for which all anions within half the PF6 radius were identified as contact pairings, thereby ensuring that a representative selection of cation ion orientations was sampled. Thirty such configurations were generated in each case and then run for a further 10 ns under NVT conditions, with no periodic boundary conditions and electrostatic interactions calculated via the Coulomb method, with a 1.2 nm cutoff distance. The ensemble average gas-phase energy in eq 4 is thus determined as the gas-phase energy measured across all 30 ionpair simulations. 2.5. Quantum-Chemical Calculations. Calculations were carried out using the Gaussian 09 program package.29 The general calculation procedure has been described elsewhere.30 Conformers of the [Cnmim] cation were studied at the RHF/321G* level at 0 K. Rotation of the alkyl groups around N−C and C−C bonds of the alkyl group (CCCN and CCNC dihedrals) around 360°, with a 10° step, was used to locate the molecular structures and calculate the relative energies of all observed conformations of the cation. The energies and vibrational normal modes were computed for stable conformers

o o o Δgl Cp,m = −2R − (Cpm − Cvm )l

(5)

The contribution (Copm − Covm)l in eq 5 can be estimated with help of the volumetric properties, according to the equation32 o (Cpm

−

o Cvm )l

=

αp2 κT

VmT

(6)

where αp is the thermal expansion coefficient, K−1; κT is the isothermal compressibility, Pa−1; Vm is the molar volume, m3 mol−1, and T is the temperature, K. Data on the density, speed of sound, and heat capacity for the [Cnmim][PF6] family available in the literature were collected and evaluated in Table S3. Values of Δgl Cop,m calculated according to eqs 5 and 6, given in Table 1, column 6, were used to adjust experimental results to T = 298.15 K. The only experimental enthalpy of vaporization of [C8mim][PF6] available for comparison (147.4 ± 4.0 kJ mol−1) at 530 K was measured using the TPD-LOSMS method.21 We adjusted this result to the reference temperature in the same way as that for our own vaporization enthalpies, and the value ΔlgHmo (298.15 K) = 167.1 ± 6.1 kJ mol−1 is in poor but still acceptable agreement (within the combined uncertainties) with our result. Also, the empirical predictive model developed by Licence and Jones 35 (in which Δ lg H mo (298.15 K) is decomposed into a Coulombic component and a van der Waals component from the anion and cation) significantly overestimates (see Table S4) the vaporization enthalpies for all representatives of the [Cnmim][PF6] family. 7951


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Table 2. Results of MD Calculations of Enthalpies of Vaporization for the [Cnmim][PF6] Family in Comparison with the Results from QCM Studies (in kJ mol−1) IL

Tav/K

Ul

Δgl Hom (Tav)a

Ug

Δgl Hom (298.15 K)b

Δgl Hom (298.15 K)c

1

2

3

4

5

6

7

[C2mim][PF6] [C4mim][PF6] [C6mim][PF6]

435.2 425.7 430.7

−177.3 −148.7 −136.5

−50.6 −17.6 0.0

130.4 134.7 140.1

140.5d 144.5e 150.8

140.0 ± 2.8 146.5 ± 2.6 150.8 ± 2.7

Calculated by the MD method at the Tav of the QCM experiments. bAdjusted from Tav to the reference temperature, T = 298.15 K, with Δgl Cop,m values from Table 1, column 6. cExperimental results from the QCM study from Table 1. dFor comparison, Δgl Hom (298.15 K) = 173.3 ± 0.7 kJ mol−1, calculated from MD simulations.37 eFor comparison, Δgl Hom (298.15 K) = 150.6 kJ mol−1, calculated from MD simulations that employed many-body polarizable force fields.36 a

measured in this work (see eq 7) leads to Som (425.7 K, g) = 788 ± 6 J K−1 mol−1. This experimental value is in agreement with the results of the statistic thermodynamics calculation, 795 ± 8 J K−1 mol−1, within their combined uncertainties. Such a good agreement can be considered as evidence for the consistency of the thermodynamic data in the condensed and ideal gas states, as well as for the reliability of the QCM data and the absence of decomposition of ILs under experimental conditions. 3.3. Vapor Pressures of Extremely Low Volatility Compounds from QCM Measurements. The very high sensitivity of the QCM allows reducing the average temperature in the vaporization studies by approximately 100 K in comparison to that in other conventional techniques.21,38 As a consequence, reliable vaporization enthalpies have been measured even for very thermally unstable ILs, like [Cnmim][PF6]. To derive the absolute vapor pressures from the QCM measurements, extended additional experiments for careful calibration of our setup have been performed in this work. The value directly measurable with the QCM is the frequency change rate, df/dt. It is proportional to the mass uptake rate and the corresponding vaporization rate, dmvap/dt, of the lowvolatility sample under study

To gain more confidence in the experimental vaporization enthalpies measured in this study with the QCM, we additionally calculated vaporization enthalpies for three representatives of the [Cnmim][PF6] series (see Table 2) by MD simulations. For the MD simulations, we have deliberately chosen the average temperatures, Tav, of the QCM experiment for each IL from Table 2 to avoid any ambiguity due to the long method of adjustment to T = 298.15 K. As can be seen from the comparison presented in Table 2, the experimental and MD simulation results are practically indistinguishable, yielding confidence in both the experimental and theoretical values. In contrast, the vaporization enthalpy of 150.6 kJ mol−1 for [C4mim][PF6] at 298.15 K, which was derived from MD simulations that employed a validated many-body polarizable force field,36 deviates significantly from our experimental result, Δgl Hom (298.15 K) = 146.5 ± 2.6 kJ mol−1 (see Table 1). Also, the most recent MD results reported by Č ervinka et al.37 for [C2mim][PF6], Δgl Hom (298.15 K) = 173.3 ± 0.7 kJ mol−1, and [C8mim][PF6], Δgl Hom (298.15 K) = 207.8 ± 0.6 kJ mol−1, were considerably overestimated in comparison to our experimental results (see Table 1). 3.2. Vaporization Entropy of [C4mim][PF6] for Validation of QCM Experimental Results. An additional test for the reliability of the experimental QCM results has been performed using the vaporization entropy, Δgl Som, which is obtained from the experimental vapor pressure temperature dependence according to eq 7 (e.g., for [C4mim][PF6])

dm vap /dt = K df /dt

The experimental constant, K, comprises the parameters of the quartz crystal, the thermophysical (density and viscosity) properties of the deposited IL sample, the configuration of the vacuum chamber, and the distance between the sample and the QCM. A possible influence from temperature variation of the thermophysical properties of the deposited sample on the sensor IL was more convenient to study using the thermally very stable IL [C10mim][NTf2]. This additional study was performed at four temperatures of the QCM, between 303 and 343 K. These different conditions were chosen to obtain a significant change in the recorded signal due to variation in the density and viscosity of the material deposited on the QCM sensor. Experimental results of this study are given in Table S5 and are also shown in Figure S1. As can be seen from the results presented in Figure S1, the density and viscosity changes under the significantly different experimental conditions have no systematic influence on the signal recorded with the QCM sensor. This finding has allowed setting the K value given in eq 8 as a robust constant for the arrangement of our experimental setup in the wide range of temperatures maintained in the QCM sensor. This finding was also important to convert the df/dt values directly measured with the QCM to vapor pressure p. Indeed, a combination of eq 8 with the Knudsen equation leads to the calculation of vapor pressure p

Δgl Smo([C4 mim][PF6]) = Δgl Hmo/T − Δgl Gmo /T = 137 ± 4 J K−1 mol−1

(8)

(7)

where the vaporization enthalpy, ΔlgHmo, and Gibbs free enthalpy of vaporization, Δgl Gom, are listed in Table 1, and they are referenced to the average temperature of the QCM study, Tav = 425.7 K. On the other hand, the vaporization entropy, Δgl Som, can be calculated as the difference between the ideal gas phase entropy, Som(g), and the liquid-phase entropy, Som(liq). The latter value is usually derived from the heat capacity temperature dependence measured by cryogenic adiabatic calorimetry. The ideal gas phase entropy, Som(g), is usually calculated by the statistical thermodynamics approach. The thermodynamic properties of [C4mim][PF6] in the condensed phase and the ideal gas state are available in the literature.20,38 We fitted these heat capacities of [C4mim][PF6] with the second-order polynomial equation to obtain entropies at Tav = 425.7 K (the average temperature of the QCM study): Som(425.7 K, liq) = 651 ± 4 J K−1 mol−1 and Som (425.7 K, g) = 795 ± 8 J K−1 mol−1 for comparison with the results from the QCM study. Indeed, the sum of the experimental entropy of [C4mim][PF6], Som (425.7 K, liq), and the vaporization entropy 7952


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The Journal of Physical Chemistry B p=

K df /dt αSK C

2πRT M

It was interesting to compare the absolute vapor pressures of two parent IL families, [Cnmim][PF6] and [Cnmim][NTf2]. This comparison is given in Figure 2.

(9)

where α is the condensation coefficient, S is the surface of the sample, KC is the Clausing factor for the cavity, R = 8.314462 J K−1 mol−1, T is the temperature of the sample in K, and M is the molar mass of the species in the vapor phase. In the cases in which association or dissociation of the sample in the gas phase can occur, the molar mass should be calculated taking into account the equilibrium composition of the gas phase. Equation 9 can be rearranged in the following manner p=

df K 2πR αSK C dt

df T = K′ M dt

T M

(10)

where K′ now encompasses all constants presented in the Knudsen and Sauerbrey equations as well as the configuration of the experimental setup. The K′ value was specific for the experimental setup used in this study. To reveal whether the K′ value depends on the type of IL, a series of additional QCM experiments with different ILs, [Cnmim][NTf2], [CnPy][NTf2], and [CnCnim][NTf2] (see Table S6), have been performed. Reliable data on the absolute vapor pressures and vaporization enthalpies of these ILs are available in the literature.34,39−43 The experimental vapor pressures available in the literature for each individual IL were combined and fit with the Clarke and Glew equation44 Δgl Gmo(θ ) ⎛1 1⎞ + Δgl Hmo(θ )⎜ − ⎟ ⎝ θ θ T⎠ ⎛θ ⎛ T ⎞⎞ o + Δgl Cp,m (θ )⎜ − 1 + ln⎜ ⎟⎟ ⎝ θ ⎠⎠ ⎝T

Figure 2. Chain-length dependence of absolute vapor pressures for the homologous series [Cnmim][PF6] (◊) and [Cnmim][NTf2] (○) at T = 423.15 K.

R ln(p /po ) = −

It has turned out that the absolute vapor pressures of the [Cnmim][ NTf2] series are 2 orders higher than those for [Cnmim][PF6]. Also, an anomaly in the linear chain-length dependence was observed for [C2mim][PF6] in contrast to that for [C2mim][NTf2]. This difference can be due to a higher structuring of [C2mim][PF6] in the condensed phase, which is also obvious from the comparatively high melting point, Tm = 333 ± 1 K,45,46 of [C2mim][PF6], whereas [C2mim][NTf2] is still a liquid at room temperature. 3.4. Experimental Enthalpy of Formation for [C2mim][PF6]. The standard molar enthalpy of formation, ΔfHom, is an important thermochemical property that is usually applied for assessment of the heat of chemical reactions and for optimization of the energetics of synthesis. In our recent studies of ILs, we used experimental enthalpies of formation in the liquid state, ΔfHmo(liq), combined with vaporization enthalpies to obtain the experimental gas phase enthalpy of formation, ΔfHom(g). Comparison of the experimental ΔfHom(g) value with the theoretical value calculated by high-level quantum-chemical methods has been a valuable test to establish the consistency of the experimental and theoretical data for [C2mim][SCN],47 [C2mim][N(CN)2],30 and imidazoliumbased ILs with the [C(CN)3] anion.48 Most frequently, ΔfHom(liq) values are derived from combustion calorimetry or reaction calorimetry. The vaporization enthalpies of ILs are usually measured by QCM,22 TGA,49 or the Knudsen method.34,39 From our experience, a good agreement between the experimental and theoretical ΔfHmo(g) values can be considered as indirect evidence for the absence of decomposition of the IL sample in the vaporization study. Unfortunately, for ILs with the [PF6] anion, using conventional combustion calorimetry to obtain ΔfHom(liq) is not possible, due to the ill-defined final composition of the combustion

(11)

where p is the vapor pressure at temperature T, po is an arbitrary reference pressure (po = 1 Pa in this work), θ is an arbitrary reference temperature (in this work θ was the average temperature of the experimental range), R is the molar gas constant, Δgl Gom(θ) is the difference in the standard molar Gibbs energy between the gaseous and liquid phases at the selected reference temperature, Δgl Hmo(θ) is the difference in the standard molar enthalpy between the gaseous and liquid phases, and Δgl Cop,m(θ) is the difference in the molar heat capacity at constant pressure between the gaseous and liquid phases. Values of Δgl Cop,m(θ) were taken from our previous studies.32,33 The K′ values for each IL presented in Table S6 were calculated by minimizing the standard deviations of the enthalpies of vaporization according to eq 11. No obvious dependence of K′ values on the type or symmetry of the cation, as well as on the chain length of the alkyl substituent, was detected in this work. Thus, an average value of K′ = (9.5 ± 1.1) 10−6 Pa s kg1/2 Hz−1 K−1/2 mol−1/2 (see Table S6) was calculated and used to convert the experimental rates of frequency change into vapor pressure values. The uncertainty in the calibration coefficient, K′, is represented as twice the standard deviation of the mean, and it statistically corresponds to approximately 10%. However, taking into account the extremely low experimental vapor pressures of the ILs listed in Table S7 and used for calculation of the K′ value, the more realistic uncertainty of absolute vapor pressures derived by the QCM method using the K′ constant has been ascribed to the level of 50%. 7953


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However, we studied the sample [C2mim][PF6] by the QCM method above the melting temperature, Tfus = 332.8 K,45,46 and derived the vaporization enthalpy and not the sublimation enthalpy. The sublimation enthalpy, ΔgcrHom(Tfus) = 155.3 ± 3.7 kJ mol−1, required to calculate the ΔfHom([C2mim][PF6]g) value was obtained as a sum of the vaporization enthalpy, Δgl Hom(332.8 K) = 137.4 ± 3.6 kJ mol−1, and the experimental46 enthalpy of fusion referenced to the melting temperature, ΔfusHom(332.8 K) = 17.86 ± 0.56 kJ mol−1. The Δgl Hom(332.8 K) value was adjusted to temperature Tfus using Δgl Copm = −74 J K−1 mol−1 from Table 1. The enthalpy of sublimation at 298.15 K, ΔgcrHom (298.15 K) = 156.3 ± 3.7 kJ mol−1, was adjusted using the heat-capacity difference,38 ΔgcrCopm = −29 J K−1 mol−1, with an uncertainty of 5 J K−1 mol−1. Finally, the sum of ΔgcrHom(298.15 K) and the enthalpy of formation in the crystal state, ΔfHom([C2mim][PF6]cr) = −2098.9 ± 4.7 kJ mol−1, provided the enthalpy of formation in the gas phase, ΔfHom([C2mim][PF6]g) = −1942.5 ± 6.0 kJ mol−1. This experimental value was important for comparison with the results from quantum-chemical calculations. 3.5. Theoretical Gas-Phase Enthalpies of Formation for [Cnmim][PF6] from Quantum-Chemical Calculations. The composite G3MP2 method has been proven to be reliable for the calculation of gaseous enthalpies of formation of ILs.30,47,48 The H298 enthalpies calculated by the G3MP2 method for conformers of [Cnmim][PF6] were converted to the enthalpies of formation, ΔfHom(g, 298.15 K), using the conventional atomization reaction (e.g., for [C2mim][PF6])

products. Also, using reaction calorimetry, like in the case of ILs with halide anions,50,51 is not possible because of the absence of suitable reactions. In this work, to obtain the ΔfHom(liq) values of the ILs with the [PF 6 ] anion, we used solution calorimetry.24,52 The idea is that under the assumption of full dissociation of the IL in water (under conditions of infinite dilution) the enthalpy of formation of an IL in aqueous solution, ΔfHom(ILaq), can be considered as a sum of appropriate contributions from the cation and anion constituting the IL Δf Hmo(ILaq) = Δf Hmo(cation+aq) + Δf Hmo(anion−aq)

(12)

The enthalpy of reaction 12 is defined as the enthalpy of solution of an IL at infinite dilution, ΔsolH∞ m (IL). The latter value can be precisely measured by solution calorimetry. The enthalpies of formation of aqueous cations and anions of typical inorganic salts are well known from the literature.53 The experimental enthalpies of formation of the aqueous cations and anions specific to the ILs are currently under development.24,54 Thus, for many ILs, the ΔfHom(ILaq) value can be obtained as a sum of ΔfHom(cation+aq) and ΔfHom(anion−aq) contributions, according to eq 12. Combining the aqueous enthalpy of formation of an IL with the calorimetrically measured enthalpy of a solution of the IL in water, the liquidphase enthalpy of formation of an IL can be derived as Δf Hmo(IL, liq) = Δf Hmo(ILaq) − Δsol Hm∞(IL)

(13)

Equations 12 and 13 are also valid for crystal samples of ILs. Thus, the aqueous enthalpy of formation for the [PF6]− anion was determined from the enthalpy of formation of LiPF6, ΔfHom (298.15 K, cr) = −2296 ± 3 kJ mol−1, measured by Gavritchev et al.,55 and the enthalpy of solution of LiPF6, ΔsolH∞ m (LiPF6) = −22.2 ± 1.9 kJ mol−1, measured in this work (see Table S7). Using the ΔfHmo(Liaq+) value available in the literature,53 ΔfHom(Li+aq) = −278.45 ± 0.2 kJ mol−1, the enthalpy of formation for the PF6− anion in aqueous solution was calculated as follows

C6H11F6N2P → 6 × C + 11 × H + 6 × F + 2 × N

Using the enthalpies of [Cnmim][PF6] from reaction 15, calculated by the G3MP2 method, the enthalpies of formation of individual ILs were calculated (see Table 3). However, from Table 3. G3MP2 Enthalpies of Formation for [Cnmim][PF6] in the Ideal Gas Phase at 298.15 K (kJ mol−1)

Δf Hmo(PF−6 aq ) = Δf Hmo(LiPF6 cr ) + Δsol Hm∞(LiPF6) −

Δf Hmo(Li+aq)

−1

= −(2039.8 ± 3.6) kJ mol

(15)

+1×P

(14)

The contribution of the aqueous enthalpy of formation of the cation, ΔfHom(C2mim+aq) = −13.1 ± 3.1 kJ mol−1, was calculated according to eq 13, using the experimental values −1 ΔsolH∞ m ([C2mim][SCN]l) = 8.3 ± 0.7 kJ mol , measured by 54 solution calorimetry in our recent work, and ΔfHom([C2mim]CN]l) = 52.8 ± 2.3 kJ mol−1, measured by combustion calorimetry earlier.47 In the next step, the aqueous enthalpy of formation of the IL, ΔfHom([C2mim][PF6]aq) = −2052.9 ± 4.7 kJ mol−1, was estimated by combining the contributions for the cation and anion according to eq 12. To use eq 13 for estimation of the crystal phase enthalpy of formation of [C2mim][PF6], the enthalpy of solution at infinite dilution, ΔsolH∞ m ([C2mim][PF6]) = 46.0 ± 0.7 kJ mol−1, was measured by solution calorimetry in the present work (see Table S7). The latter value was in a good agreement with the result of 45.1 kJ mol−1, which was indirectly obtained from the solubility measurements of [C2mim][PF6] in water.56 With our result for the solution enthalpy of [C2mim][PF6], the value of ΔfHom([C2mim]F6]cr) = −2098.9 ± 4.7 kJ mol−1 was calculated according to eq 13. It can now be combined with the QCM result to estimate the gas-phase enthalpy of formation for this IL.

IL

ΔfHom G3MP2 (AT)

ΔfHom G3MP2 (AT)corr

[C2mim][PF6] [C3mim][PF6] [C4mim][PF6] [C6mim][PF6] [C8mim][PF6] [C10mim][PF6]

−1909.2 −1934.3 −1958.0 −2007.0a −2055.8a −2104.6a

−1941.3 −1966.4 −1990.1 −2039.1 −2087.9 −2136.7

Calculated according to ΔfHom (g, G3MP2, AT)/kJ mol−1 = −24.4 × NC − 1860.6 (R2 = 0.9997), where NC is the number of C atoms in the alkyl chain of the imidazolium-based cation. a

our experience, the enthalpies of formation of molecular and ionic compounds calculated by the atomization procedure deviate systematically from the experimental values, and they require a simple bias correction.57,58 The value of this correction, Δ = −32.2 kJ mol−1, for the [Cnmim][PF6] family was calculated as the difference between the experimental (ΔfHom([C2mim][PF6]g) = −1942.5 ± 6.0 kJ mol−1, see Section 3.2) and theoretical (−1909.2 kJ mol−1; see Table 3) gaseousphase enthalpies of formation of [C2mim][PF6]. With this bias correction, Δ, the “corrected” enthalpies of formation, ΔfHmo(G3MP2(AT)corr), of the imidazolium-based family, [Cnmim][PF6], were calculated (see Table 3, column 3). We suppose that the bias correction established for the [PF6]7954


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grateful to the Russian Government Program of Competitive Growth of Kazan Federal University for partial financial support of this work.

containing ILs in this work can also be applied to pyrrolidinium-, pyridinium-, and ammonium-based ILs. It has turned out that the high-level G3MP2 method is a very timeconsuming method, and with our available computational capacity, we were able to calculate only the first representatives of this family, with alkyl chain lengths of two, three, and four Catoms (see Table 3). For this reason, we also tested the less time consuming DLPNO-CCSD(T)/CBS methods (see the Supporting Information). Using a number of isodesmic reactions, we calculated ΔfHom([C2mim][PF6]g) = −1915.1 kJ mol−1 (see Table S9), and this value was in the same level as that from the G3MP2 uncorrected atomization procedure (ΔfHom([C2mim][PF6]g) = −1909.2 kJ mol−1; see Table 3). Thus, DLPNO-CCSD(T) methods can also be applied for calculation of the gas-phase enthalpies of formation of [PF6]containing pyrrolidinium-, pyridinium-, and ammonium-based ILs, with a similar correction of Δ = −32.2 kJ mol−1.

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4. CONCLUSIONS The previously elaborated QCM−Langmuir technique was further developed for determination of the absolute vapor pressures and enthalpies of vaporization of thermally unstable ILs. The first reliable experimental determination of the absolute vapor pressures, enthalpies of vaporization, and enthalpies of formation of [Cnmim][PF6] has been reported. The absence of decomposition under the experimental conditions was verified by the ATR-IR spectra of the samples before and after the experiment. The consistency of the experimental data on vaporization enthalpies within the family of homologues has been proven by enthalpic and entropic analyses of the data in the condensed and gaseous phases. A comprehensive set of thermodynamic properties for the [Cnmim][PF6] series, where n = 2, 4, 6, 8, and 10, was established and evaluated. The technique developed in this work for thermally labile ILs introduces a new way to obtain the thermodynamic properties of vaporization of ILs important for practical applications. New data would be reliable for testing MD simulations and quantum-chemical calculations to gain insight into the thermodynamic properties of ILs on a molecular basis.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b06081. Provenance and purity of the studied ILs, primary experimental and computational data, FTIR spectra and optimized geometry (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; dzmitry.zaitsau@uni-rostock. de. Phone: +49-381-498-6508. Fax: +49-381-498-6524. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the German Science Foundation (DFG) in the frame of the priority program SPP 1807 “Control of London Dispersion Interactions in Molecular Chemistry” as well as the priority program SPP 1708 “Material Synthesis Near Room Temperature”. D.H.Z. and V.N.E. are 7955


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