Thermodynamic Properties of Ionic Liquids Thermodynamic Properties of Ionic Liquids

Basic physicochemical properties were discussed at different temperatures for 18 hydropho- bic ionic liquids (ILs) which containing imidazolium and pyridinium as cations, separately. The ILs include 1-ethyl-3-methylimizazolium tris(pentafluoroethyl)trifluorophosphate ([C 2 mim][PF 3 (CF 2 CF 3 ) 3 ]), 1-acetonitrile-3- ethylimimdazolium bis(trifluoromethylsulfonyl) imide ([MCNMIM][NTf 2 ]), 1-(cyanopropyl)-3-methylimidazolium bis[(trifluoromethyl)sulfonyl] imide [PCNMIM][NTf 2 ], 1-ethanol-3-ethylimimdazolium bis(trifluoromethylsulfonyl)imide ([EOHMIM][NTf 2 ]), 1-butylamide-3-ethylimimdazolium bis(trifluoromethylsulfonyl)-imide ([CH 2 CONHBuEIM][NTf N-alkylpyridinium n 2 ( 3, 4, 6)}, N-alkyl-3-methylpyridinium bis(trifluoromethyl-sulfonyl)imide {[C n 3Mpy][NTf 2 ] ( n = 3, 4, 6)}, and N-alkyl-4-methylpyridinium bis(trifluoromethylsulfonyl) imide {[C n 4Mpy][NTf 2 ] ( n = 2, 4, 6)}. The molar volume, standard molar entropy, and lattice energy were estimated by the empirical and semiempirical equations. The dependences of density, dynamic viscosity, and electrical conductivity on temperature are discussed in the measured temperature range. It is found that with the increasing temperature, the density and dynamic viscosity decreased, while the electrical conductivity increases. The influences of microstructures of ILs, such as the introduction of the methylene, methyl, and functional groups on cations, on their basic physicochemical properties are discussed.


Introduction
Ionic liquids (ILs) are salts while can exist as liquid at room temperature or near room temperature, which are completely composed of ions [1][2][3]. Compared with traditional organic solvents, ILs have exhibited outstanding properties, such as negligible vapor pressures, nonflammable, wide electrochemical window, high electrical conductivity, adjustable acidity, high dissolving before and after the measurement of properties. The water mass fractions of the ILs are lower than 300 × 10 −6 and 500 × 10 −6 for before and after the property determination, respectively.

Density
The densities of ILs were measured by a Westphal balance (or an automated SVM3000 Anton Paar rotational Stabinger viscometer-densimeter with a cylinder geometry) in the temperature range of T = (283.15 to 338.15) ± 0.05 K. The density values were recorded at every 5 K. For the Westphal balance method, the sample was placed in a cell with a jacket.

Surface tension
Using the tensiometer (DP-AW type produced by Sang Li Electronic Co.) of the forced bubble method, the surface tension of the ILs was measured with the experimental error that is ± 0.1 mJ⋅m −2 . The temperature was controlled by a thermostat. The uncertainties of the measurement are in the range of ± 0.2 mJ⋅m −2 .

Dynamic viscosity
The dynamic viscosity of the ILs was measured using an Ostwald viscometer (or an automated SVM3000 Anton Paar rotational Stabinger viscometer-densimeter with a cylinder geometry, the principle is based on a modified Couette according to a rapidly rotating outer tube and a relatively slow rotating inner measuring bob). The values were recorded at every 5 K. The uncertainties were estimated to be ± 1%.

Electrical conductivity
The electrical conductivity of the ILs was carried out using a MP522 conductivity instrument with the cell constants of 1 cm −1 (the cell was calibrated with the aqueous KCl solution). The uncertainty was reckoned to less than ± 1%. The temperature was regulated by a thermostat with a precision of ± 0.05 K. The experimental data were reported per 5 K after 30 min thermal equilibrium time.

Density
A straight line can be obtained according to plot lnρ against T/K. And the lnρ against T/K can be fitted by the following empirical equation: lnρ / g · cm -3 = b-αT / K (1) where b is an empirical constant and α is the thermal expansion coefficient.
At 298.15 K, the molecular volume, V, standard molar entropy, S 0 , and lattice energy, U POT , of the ILs can be obtained from the experimental density by the following equations: S 0 = 1246.5 · ( V ) + 29.5 U POT = 1981.2 · ( ρ / M ) 1/3 + 103.8 (4) where M is molar mass, ρ is the density, and N is the Avogadro's constant.

Surface tension
The surface tension, γ, has the relationship with the temperature in terms of the Eötvös equation: where V is the molar volume of the liquid, T c , is the critical temperature, and k, is an empirical constant.
The molar enthalpy of vaporization, Δ l g H m 0 , was estimated by the following equation: where V is molar volume, γ is surface tension, and N is Avogadro's constant.
At 298.15 K, according to the literature studies [6,7], the interstice volume, v, can be estimated by interstice model theory: v = 0.6791 ( k b T / γ ) 3/2 (8) herein, k b is the Boltzmann constant, T is thermodynamic temperature, and γ is the surface tension of ILs.
According to Yang et al., the molar volume of ILs is composed of the volume of inherent and interstices; herein, the molar volume of the interstice is, ∑ν = 2Nν, the molar volume of the ILs can be calculated by the following equation: (9) herein, V is the molar volume, V i is the inherent volume, and 2Nv is the interstice volume.
At 298.15 K, Yang et al. pointed out that the expansion volume of ILs only results from the interstices expansion following the temperature increase. Then, the thermal expansion coefficient, α, can be estimated by the interstice model theory by the following equation:

Dynamic viscosity
The temperature dependence of the dynamic viscosity for ILs can be fitted using the Vogel-Fulcher-Tammann (VFT) equation: where η is the dynamic viscosity; η 0 , B, and T 0 are the fitting parameters.
Usually, the Arrhenius equation was used to fit the dynamic viscosity and the equation is: where E a is the activation energy for dynamic viscosity, η ∞ is the maximum dynamic viscosity, and k B is the Boltzmann constant.
According to Vila et al. [12], the VFT equation for dynamic viscosity was related to the Arrhenius equation, η 0 = η ∞ and B = E η /k B . The activation energy of dynamic viscosity was introduced in the final version VFT equation. The final version of the VFT equation can be expressed as follows:

Electrical conductivity
Usually, the VFT is also used for the fitting of temperature dependence on electrical conductivity. Herein, the temperature dependence of electrical conductivity of the ILs was also fitted according to the following VFT equation: here σ is the electrical conductivity; σ 0 , B, and T 0 are fitting parameters.
Sometimes, the Arrhenius equation is also used to fit the electrical conductivity: where E σ is the activation energy, which indicates the energy needed for the ion to hop into a free hole, σ ∞ is the maximum electrical conductivity, and k B is the Boltzmann constant.
According to the discussion, Vila et al. [8] have introduced the activation energy of electrical conductivity in the VFT equation by establishing the fitting parameters of the VFT equation with the Arrhenius equation: σ 0 = σ ∞ and B = E σ /k B . The final version of the VFT equation can be expressed as follows:

Walden rule
The classical Walden rule was usually used for the assessing of the ionicity of ILs [9,10]. The ionic mobilities (represented by the equivalent conductivity Λ = FΣμ i Z i ) and the fluidity φ (φ = η −1 ) of the medium can be related to the Walden rule through the ions move. On the basis of this fact, the relationship of the molar electrical conductivity and dynamic viscosity for ILs can be described by the following equation: where Λ is the molar electrical conductivity, η is the dynamic viscosity, and k is a temperature dependent constant. The Walden's product (in [S·cm 2 ·mol −1 ][mP·s]) can be calculated at 298.15 K.

Density and surface tension of ionic liquid [C 2 mim][PF 3 (CF 2 CF 3 ) 3 ] and prediction of properties [C n mim][PF 3 (CF 2 CF 3 ) 3 ] (n = 1, 3, 4, 5, 6)
As organic salts, the ionic liquids (ILs) have shown many excellent properties, such as the low melting temperature, good solvation, and nonvolatility. So, the industrial and scientific communities have applied ILs in a broad range as the green organic solvents. In particular, the air-and water-stable hydrophobic ILs have been used in some special fields as the stable ILs. Actually, the most ILs are hydrophilic, so, 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (C n mimNTf 2 ) has attracted serious concern as an air-and water-stable hydrophobic compound. And the properties were reporting in succession when the air-and water-stable hydrophobic compounds were synthesized. As another air-and water-stable hydrophobic type IL 1-ethyl-3-methylimizazolium tris(pentafluoroethyl)trifluorophosphate [C 2 mim][PF 3 (CF 2 CF 3 ) 3 ] was provided by Merck Co. This is also the air-and water-stable hydrophobic IL. So, the study on the properties of this type ILs is significant in many concerned fields.
The structure of [C 2 mim][PF 3 (CF 2 CF 3 ) 3 ] is shown in Figure 1. By plotting ln ρ against (T − 298.15) K, a straight line can be obtained (see Figure 2) according to Eq. (1). According to Eq. (1), the correlation coefficient is R = 0.9999, the standard deviation s = 3.0 × 10 −5 g cm −3 , b = 0.53603, the thermal expansion coefficient of the IL is α = 6.96 × 10 −4 K −1 at 298.15 K, respectively.  The experiment values of γ against (T − 298.15) K can be fitted according to the linear equation (see Figure 3). According to the linear equation, the correlation coefficient and standard deviation can be obtained and the values are 0.998 and 0.04 mJ•m −2 , respectively. In Figure 3, the surface entropy, S a = − (∂γ/∂(T − 298.15)) p , can also be obtained and the value is 33 ) were estimated by using the experimental data of density and surface tension according to Eqs. (1)- (7).
The contribution of the methylene (−CH 2 −) group to the molecular volumes can be obtained according to the literature studies [12,13]  According to the literature [12,13], the contribution per methylene (−CH 2 −) to parachor is 31.1 for [C n mim][AlCl 4 ] and 37.5 for [C n mim][Ala]. An average value of the contribution can be calculated to be 34.3. So, the average value can be used to predict the parachor of the ILs [C n mim][PF 3 (CF 2 CF 3 ) 3 ] (n = 1, 3, 4, 5, 6). According to Eq. (6), the surface tension can be calculated from the predicted density and parachor. The molar enthalpy of vaporization, Δ l g H m 0 , can be obtained from the predicted density and surface tension. The data are listed in Table 2.
According to the predicted values of density and surface tension, the other properties can be predicted and the values are also listed in Table 2.
According to the interstice model and Eqs. (8)-(10) [6,7], the interstice volume, v, the molar volume of ionic liquids, V, consists of the inherent volume, V i , and the volume of the interstices; the molar volume of the interstice, ∑ν = 2Nν, the thermal expansion coefficient, α, can be predicted from the interstice model at 298.15 K. All of the data obtained from estimation and prediction are listed in Table 2. Notes: m measurement value; p data in the column were predicted values; e data in the column were estimated values.

Density, dynamic viscosity, and electrical conductivity of imidazoliumtype hydrophobic functional ionic liquids
Ionic liquids (ILs) have exhibited outstanding physicochemical properties, such as good solvation, negligible vapor pressure, good thermal stability, and designability. ILs have been used as the green solvents in industrial and scientific areas. The functional ionic liquids (FILs) have been paid much more attention because of the designability [14][15][16][17][18][19][20][21][22][23][24]. The physicochemical properties can be designed according to the introduction of the functional groups, such as −CN, −OH, and −CH 2 -O-CH 3 .
Egashira et al. [14][15][16] have introduced the cyano group on the imidazolium FILs and quaternary ammonium FILs, respectively. The FILs have been applied in the lithium batteries as electrolyte components. The FILs have showed an improved cycle behavior compared with the electrolyte based on a tetraalkylammonium ionic liquid without a cyano group. The quaternary ammonium-based FILs containing a cyano group showed the better stability of the cathodic than the imidazolium-based FILs. Hardacre et al. [17,18] have also synthesized two series pyridinium type FILs. The effect of electron-withdrawing groups on the properties was discussed according to the presence of the nitrile or trifluoromethyl in this type FILs. The introduction of the two functional groups leads to the increasing of the melting temperature compared the traditional ILs. On the basis of this fact, the authors have observed the liquid charge-transfer complexes form upon contacting electron-rich aromatics with an electron withdrawing group appended 1-alkyl-4-cyanopyridinium ionic liquids. Zhang et al. [19] have studied the solubilities of C 2 H 4 and CO 2 in the cyano-type imidazolium FILs using the gas chromatography. Compared with the 1,3-dialkylimidazolium-type ILs, the cyano-type FILs result in a remarkable decrease of the interactions of hydrocarbons. The cyano-type ILs have exhibited the advanta-geous properties. As the solvent, it can be applied as a suitable reaction media and ligands in catalytic reactions, as an electrolyte in lithium batteries, as a solvent for extraction of metals and dissolution of cellulose.
Although the FILs have been applied in some areas, the physicochemical properties are not enough for the application [20][21][22]. In this chapter, the properties of 1-acetonitrile-3-ethylimim-   In order to compare the influences of methylene and functional group on the properties of ILs, the values of density, dynamic viscosity, and electrical conductivity for ILs are listed in Table 6     As shown in Table 6, the three series ILs have exhibited the same tendency for density after the introduction of methylene on the alkyl side chain. Usually, for dynamic viscosity and electrical conductivity, the introduction of methylene leads to the dynamic viscosity increase and electrical conductivity decrease, such as As indicated in Table 6, the density and dynamic viscosity of the FILs are higher than the nonfunctional ILs, and the electrical conductivity is lower than the nonfunctional ILs after the introduction of the −CN or −CH 2 OH functional group on the imidazolium ring, this result leads to the increasing of Van der Waals force between the cation and the anion relative to the nonfunctional ILs. The order of the effect of the group to the thermodynamic properties is: −CN > −CH 2 OH > −CH 3 .
According to Eqs. (1)-(4), the calculated values of the thermal expansion coefficient molecular volume, standard molar entropy, and lattice energy are calculated and listed in Table 7, respectively.
From Table 7, the contribution of the methylene to the molecular volume is 0.0285 nm 3 Figure 6.
The best fitted values of η 0 , B, T 0 , and the correlation coefficient, R, are listed in Table 8 from the empirical Eq. (11). From  The best fitted values of σ 0 , B, T 0 , and the correlation coefficient, R, are listed in Table 9 from the empirical Eq. (14). From In Figure 9, the 1000/T dependences on ln σ of the  From Figure 9, it can be obviously seen that the measurement points lie far away from the fitted straight lines. According to Eq. (17), the logΛ dependences on logη −1 are illustrated in Figure 10 for Usually, the Walden rule can be used for the presentation of the independent ions of the liquid. If the Walden points close to the ideal line, the liquid can be considered as a relative ideal liquid. The ideal line position was determined according to the aqueous KCl solution at high dilution. As an ideal line, the slop of the ideal line should be unity and not have any interaction of the ions [10,29,30]. In Figure 10

Density, dynamic viscosity, and electrical conductivity of pyridinium-based hydrophobic ionic liquids
Actually, most of the studied ILs are hydrophilic-type ILs. The hydrophobic ILs have been paid much more attention in many fields as a special functional ILs. The bis(trifluoromethylsulfonyl)imide [NTf 2 ] − as an air-and water-stable anion has been applied in many fields [35][36][37]. These types of anion ILs have exhibited a relatively wide liquid range, higher electrical conductivity, and thermal stability than the hydrophilic-type ILs. However, the study of thermodynamic properties of the [NTf 2 ]-type ILs mainly focuses on the imidazolium-type cation ILs [38][39][40]. The study of the pyridinium type cation-based ILs is still not enough [41]. The systematical research on the properties including density, dynamic viscosity, and electrical conductivity is still scarce which can provide the well information of the suitable IL for a specific purpose.
In this section, the basic physicochemical properties of three serious Ils N-alkylpyridinium bis (

Progress and Developments in Ionic Liquids
From Tables 10-13, it can be concluded that the density and electrical conductivity decrease as the alkyl side chain length of the cation increases for the N-alkyl type pyridinium ILs. The dynamic viscosity increases with the extension of the alkyl side chain of the cation for the three series of N-alkyl type pyridinium ILs.

[C 2 py][NTf 2 ] [C 3 py][NTf 2 ] [C 4 py][NTf 2 ] [C 5 py][NTf 2 ] [C 6 py][NTf 2 ]
298. 15  According to Eq. (5), by plotting the γV m 2/3 against T, straight lines were obtained (see Figure 13). From the plot, the value of empirical constant (k) and critical temperature (T c ) can be obtained according to the fitting equation and the values are listed in Table 16. Rebelo et al. [44] have reported that the normal boiling point, T b , is approximately 0.6T c for ILs. Herein, the normal boiling point, T b , can be calculated and the values are also listed in Table 16. For the majority of organic liquids, k ≈ 2.1 × 10 −7 J•K −1 , but for fused salts, k = 0.4 × 10 −7 J•K −1 for fused NaCl [7]. It indicated that ILs [C n py][NTf 2 ] (n = 2, 4, 5, 6) have the medium polarity between organic liquids and fused salts in terms of the value of the k.    According to Table 12 and Eq. (11), the temperature dependence on dynamic viscosity values of the ILs can also be fitted using the VFT Eq. (11), see Figure 14.
The best fitting parameters of η 0 , B, T 0 , and the corresponding correlation coefficient, R, are listed in Table 17. From  Table 17.
The 1000/T dependences on ln η of the for [C n py][NTf 2 ] (n = 2, 3, 4, 5, 6) were fitted in the temperature range (see Figure 15). The values of the correlation coefficient, R, are 0.9976, 0.9965,    From Figure 15, it can also be obviously seen that the measurement points lie far away from the fitted straight lines. According to Table 13 and Eq. (14), the temperature dependences of electrical conductivity values of the ILs can also be fitted using the VFT Eq. (14), see Figure 16.
In Figure 17,  Table 18). So, the measurement electrical conductivity does not follow the Arrhenius Eq. (15). In Figure 17, it can also be seen that the measurement points lie far away from the fitted straight lines.  Table 18. Fitted values of electrical conductivity of σ 0 , B, E σ , T 0 , and R according to Eqs. (15) and (17).  According to Eq. (17), the logΛ dependence on logη −1 is illustrated in Figure 18 for the [C n py] [NTf 2 ] (n = 2, 3, 4, 5, 6) from 283.15 to 338.15 K.
Usually, the Walden rule can be used for the presentation of the independent ions of the liquid. If the Walden points close to the ideal line, the liquid can be considered as a relative ideal liquid. The ideal line position was determined according to the aqueous KCl solution at high dilution.
As an ideal line, the slop of the ideal line should be unity and not have any interaction of the ions [10,29,30]. In Figure 10, it can be seen that the approximately straight lines can be obtained according to the experimental points.
Like the FILs, the Walden rule can also be used for the presentation of the independent ions of the ILs [C n py][NTf 2 ] (n = 2, 3, 4, 5, 6). From Figure 18, it can be seen that the approximately straight lines can be obtained  [NTf 2 ] (n = 2, 3, 4, 5, 6) can be called "subionic." It means that the ILs [C n py][NTf 2 ] (n = 2, 3, 4, 5, 6) did not yield the expected conductivity from the high fluidities because on average the proton transfer is incomplete. The behavior of the ILs [C n py][NTf 2 ] (n = 2, 3, 4, 5, 6) as if there is only a small population of ions and the "ionicity" of the ILs is therefore reduced [34].
In order to compare the density, dynamic viscosity, and electrical conductivity with the N-alkyl type pyridinium-type ILs at 298.15 K, the values of the three series pyridinium-based ILs are listed in Table 22.  From Table 22, the density of the three series of pyridinium-type ILs decreases with the introduction of the methylene group on the alkyl side chain of the pyridinium-type ILs. The result is the same with the imidazolium-type ILs [12,13]. The introduction of the methyl group on the pyridinium-type ILs leads the apparent decrease of the density. However, the degree of decreasing is different on the position 3 and 4 of the pyridinium ring. The introduction of the methyl group on position 4 leads the more decrease than position 3 on the pyridinium ring. The order is as follows: As shown in Table 22, the electrical conductivity of the three series pyridinium-type ILs decreases with the introduction of the methylene group on the alkyl side chain of the pyridinium-type ILs. But, the introduction of the methyl group on the ring leads to the different change tendency for electrical conductivity. For density, the values are decrease with the introduction of the methyl group on positions 3 and 4 of the pyridinium ring. However, the electrical conductivity decreases after the introduction of methyl group on position 3 and increases after the introduction of the methyl group on position 4 of the pyridinium ring. The tendency is just the reverse and the order is as follow:   For the dynamic viscosity, the values of the three series pyridinium-type ILs increase with the introduction of the methylene group on the alkyl side chain of pyridinium-type cation ILs. Like the electrical conductivity, the dynamic viscosity also exhibited the difference tendency with the density after the introduction of the methyl group on the pyridinium ring. However, the tendency is in contrast to the electrical conductivity. For dynamic viscosity, the values increase with the introduction of the methyl group on position 3 of the pyridinium ring and decrease with the introduction of the methyl group on position 4 of the pyridinium ring with the nonsubstituting pyridinium ring. The order is as follows: According to Table 19, the temperature dependence of the density values can be plotted and fitted according to the linear equation (Figure 19).
The thermal expansion coefficient, α, molecular volume, V m , standard molar entropy, S 0 , and lattice energy, U POT , were calculated from experimental density using the empirical Eqs. (1)-(4). The obtained data from the empirical equations are listed in Table 23.
From From Table 20, the temperature dependence on dynamic viscosity can be fitted according to VFT Eq. (11), see Figure 20.
The best-fitting parameters of η 0 , B, T 0 , and the corresponding correlation coefficient, R, are listed in Table 24. From Table 24, the obtained values of the correlation coefficient, R, are higher than 0.9999, which indicates that the VFT equation can be used for fitting the experimental dynamic viscosity.   In Figure 21, the 1000/T dependences on ln η of the  Table 24). So, the measurement dynamic viscosity cannot be well fitted with the Arrhenius Eq. (12). From Figure 21, it can also be obviously obtained that the measurement points lie far away from the straight fitting lines. From Table 21, the temperature dependence on electrical conductivity can be fitted according to VFT Eq. (14), see Figure 22.
The best-fitting parameters of σ 0 , B, T 0 , and the corresponding correlation coefficient, R, are listed in Table 25. From Table 25, the obtained values of the correlation coefficient, R, are higher than 0.9999, which indicates that the VFT equation can be used for fitting the experimental electrical conductivity. The activation energies of electrical conductivity for the two series ILs [C n 3Mpy][NTf 2 ] (n = 3, 4, 6) and [C n 4Mpy][NTf 2 ] (n = 2, 4, 6) were calculated by Eq. (16) and are listed in Table 25.

Conclusion
The density, surface tension, dynamic viscosity, and electrical conductivity of the three series hydrophobic pyridinium-type ILs [C n py][NTf 2 ] (n = 2, 3, 4, 5, 6), [C n 3Mpy][NTf 2 ] (n = 3, 4, 6), and [C n 4Mpy][NTf 2 ] (n = 2, 4, 6) were determined at atmospheric pressure in the temperature range of 278-363 K. The thermal expansion coefficient, molecular volume, standard molar entropy, and lattice energy of the samples were estimated in terms of empirical and semiempirical equations. The density and electrical conductivity decrease with the introduction of the methylene group on the alkyl side chain of the pyridinium type. However, the dynamic viscosity exhibited the inverse tendency. Compared with the methylene group, the introduction of the methyl group on the pyridinium ring exhibited the irregular tendency to the density, dynamic viscosity and electrical conductivity.