Biodegradable Ionic Liquids: Effects of Temperature, Alkyl Side-Chain

Article pubs.acs.org/IECR

Biodegradable Ionic Liquids: Effects of Temperature, Alkyl Side-Chain Length, and Anion on the Thermodynamic Properties and Interaction Energies As Determined by Molecular Dynamics Simulations Coupled with ab Initio Calculations Mostafa Fakhraee and Mohammad Reza Gholami* Department of Chemistry, Sharif University of Technology, Tehran, 11365-11155 Iran S Supporting Information *

ABSTRACT: The effects of incorporating the ester functional group (COO) into the side chain of the 1-alkyl-3methylimidazolium cation ([C1COOCnC1im]+, n = 1, 2, 4) paired with [Br]−, [NO3]−, [BF4]−, [PF6]−, [TfO]−, and [Tf2N]− anions on the various thermodynamic properties and interaction energies of these biodegradable ionic liquids (ILs) were investigated by means of molecular dynamics (MD) simulations combined with ab initio calculations in the temperature range of 298−550 K. Excluding the simulated density, the highest values of the volumetric properties such as molar volume, isobaric expansion coefficient, and isothermal compressibility coefficient can be attributed to the largest cation incorporated with the weakest coordinating anion, [Tf2N]−, and the minimum of the corresponding properties correspond to the smallest cation, especially when combined with the smaller anions, including [NO3]− and [Br]−. In addition, ion-pair, cationic, and anionic volumes were computed using MD simulations as well as ab initio calculations. The results revelaed an increasing trend in the molar enthalpy of vaporization. The reverse trends of the volumetric properties were observed for the cohesive energy density, Hildebrand solubility parameter, surface tension, surface excess enthalpy, lattice energy, thermal pressure, internal pressure, binding energy, and interaction energy. On the basis of the optimized structures, we believed that a reduction in the strength of the hydrogen bonds due to the larger charge distribution and steric hindrance of bulkier ions is responsible for the observed trends. These results were also confirmed by calculating the critical and boiling temperatures (by two different empirical equation), surface excess enthalpies, parachors, and standard molar entropies. The other derivatives of the thermodynamic properties such as the isobaric and isochoric heat capacities, isothermal bulk moduli, and speeds of sound in the ILs were computed as functions of temperature. Interestingly, a direct relationship was found between the simulated results for the surface tension and the computed values of the bulk modulus. Furthermore, it was found that sound waves are transmitted faster in a compact IL than in a compressible IL. In addition, for each IL, the molar refraction, refractive index, dielectric constant, and mean static polarizability were approximated at room temperature. The smallest values of these properties were observed for ILs composed of the spherically symmetric anions [PF6]− and [BF4]−. In addition, the formation of multiple intramolecular hydrogen bonds between the O atoms of the ester functional group and the hydrogen atoms of the cation was also observed for all optimized conformations. Finally, the obtained results demonstrate that the introduction of an ester group significantly increases the interionic interactions and, subsequently, the packing efficiency of these ILs in comparison with those of conventional imidazolium-based ILs. and experimental investigations.10,17−24 It has been reported that ILs containing hydroxyl and amine functional groups on the alkyl side chain of the imidazolium cation exhibit a significant enhancement in their ability to absorb greenhouse gases, especially carbon dioxide (CO2).25−32 As a result, such ILs can be preferably used as recyclable alternatives to traditional alkanolamine solvents.25,31 Recently, a novel family of functionalized ILs with an ester functional group (COO) in one of the alkyl side chains of the imidazolium cation (such as the target ILs in the present study) were synthesized, and the

1. INTRODUCTION Ionic liquids (ILs) are a novel class of salts having liquid form below 100 °C.1,2 Because of their unique features, especially including negligible vapor pressure, nonflammability, very wide electrochemical window, and outstanding thermal and chemical stabilities, ILs have attracted considerable attention from scientists in academic and industrial investigations.2−8 Furthermore, because of their ability to dissolve various organic and inorganic compounds, ILs have been widely used as suitable replacements for toxic and volatile conventional organic solvents.1,2,9,10 Taking advantage of these significant and beneficial properties, ILs have been utilized in sustainable processes for organic synthesis, catalysis, extraction, and separation.11−16 Among the well-known families of ILs, imidazolium-based ILs have recently attracted most attention in both computational © 2015 American Chemical Society

Received: Revised: Accepted: Published: 11678

August 30, 2015 October 14, 2015 November 3, 2015 November 16, 2015 DOI: 10.1021/acs.iecr.5b03199 Ind. Eng. Chem. Res. 2015, 54, 11678−11700

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Industrial & Engineering Chemistry Research angles

bonds

biodegradability characteristics of these ILs were experimentally studied.33−35 The obtained results indicate that the introduction of the ester functional group particularly improves the biodegradability of this class of ILs.33 Moreover, the effects of the ester group on the physicochemical properties,28 gas solubility,28,36 and antimicrobial activity37 of this class of ILs have been investigated. It was reported that the presence of the ester group in these ILs decreases their thermal stability but greatly increases their biological activity in comparison with the properties of common imidazolium-based ILs with the same hydrocarbon chain length.37 Costa Gomes and co-workers published a theoretical study of the influence of ester functional groups on the solvation of gases. Interestingly, their results indicate that the incorporation of the ester functional group does not markedly affect carbon dioxide (CO2) solvation.36 A few experimental data on the fundamental thermodynamic properties of ester-functionalized ILs were previously reported owing to the sensitivity of these properties to even a small amount of impurities.26,29 Indeed, classical molecular dynamics (MD) simulations have already proved to be a powerful tool for predicting the thermodynamic properties of neat ILs with microscopic knowledge.22,25,26,29 Taking into account these advantages, this work was undertaken to predict various thermodynamic properties and interaction energies of ester-functionalized ILs, including 3-methyl-1-(methoxycarbonylmethyl)imidazolium ([C1COOC1C1im]+), 3-methyl-1-(ethoxycarbonylmethyl) imidazolium ([C1COOC2C1im]+), and 3-methyl1-(buthoxycarbonylmethyl)imidazolium ([C1COOC4C1im]+) cations incorporated with [Br]−, [NO3]−, [BF4]−, [PF6]−, [TfO]−, and [Tf2N]− anions by means of MD simulations coupled with ab initio calculations. To the authors’ knowledge, no systematic MD simulations of the thermodynamic properties and interaction energies of ester-functionalized ILs have previously been reported. Ball-and-stick models of the selected ILs are shown as Figure 1.

Utot =

∑

kr , ij(rij − r0, ij)2 +

ij

+

kθ , ijk(θijk − θ0, ijk)2

ijk dihedrals

+

∑

4

∑ ∑ Vm, ijkl[1 + (−1)m cos(mφijkl)] ijkl

m=1

improper

4

∑ ∑ Vm, ijkl[1 + (−1)m cos(mφijkl)] ijkl

m=1

⎧ ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ ⎫ σij ⎥ ⎪ ⎢ σij 1 qiqj ⎪ ⎜ ⎟ ⎜ ⎟ ⎬ ⎨ ∑ 4εij⎢⎜ ⎟ − ⎜ ⎟ ⎥ + rij ⎠ rij ⎠ 4πε0 rij ⎪ ⎝ ⎝ j>1 ⎪ ⎦ ⎭ ⎩ ⎣

N−1 N

+

∑ i=1

(1)

It might be obvious that the right-hand side of eq 1 includes both intra- and intermolecular potentials. Actually, intramolecular contributions to the potential are provided by covalent bonds and valence angles, which are treated using harmonic potential functions. Likewise, a cosine potential function is implemented to take into account the improper dihedral and torsion dihedral angle terms. Obviously, intermolecular potential terms includes repulsive−dispersive [i.e., van der Waals (vdWs)] and electrostatic interactions. The cross-term parameters for the vdW interactions between unlike atoms were obtained by using the geometrical-means combining rules.38,39 It is worth noting that the intermolecular contribution takes into account not only the interactions between molecules, but also the interactions between atoms of a molecule that are separated by more than three bonds. vdW and electrostatic interactions of the dihedral angle potentials were precisely considered by using a scaling factor 0.5.38,39 The details of the method employed to calculate the point charges on each atom of the cations and their force field parameters are summarized in Tables S1−S4 of the Supporting Information. All MD simulations in the present study were correctly performed using the DL_POLY 2.18 program package.40 Additional details of the simulations in this study are exactly the same as in our previous work.29 2.2. Ab Initio Calculations. Additional details of cation− anion interionic interactions were obtained by optimizing the structures of isolated ion pairs using the Gaussian suite of programs.41 In addition, to understand the order of magnitude of cation−anion binding and the interaction energy of each ion pair, these values were calculated at the B3LYP/6-311++G(d,p) theoretical level. Afterward, the results for the interaction energies obtained from the ab initio calculations were compared with the corresponding values calculated from the MD simulations. Finally, the findings obtained in this section were utilized to interpret the MD results.

3. RESULTS AND DISCUSSION 3.1. Density, Molar Volume, and Molecular Volume. Density is the common precise source of experimental data that can be used as a criterion for evaluating the accuracy of the applied force field and performed simulations. Therefore, the density (ρ) and molar volume (Vm) of the target ILs were investigated. The simulated densities of the ester-functionalized ILs as functions of temperature are summarized in Table 1. It must be emphasized that the standard deviations of thermodynamic properties are generally determined using the law of the propagation of errors. The simulated density of [C1COOC2C1im][Tf2N] at 223 K was computed as 1.609 g cm−3

Figure 1. Ball-and-stick models of the ester-functionalized ILs investigated in this study.

2. COMPUTATIONAL METHODS 2.1. Molecular Dynamics Simulations. Extensive MD simulations and ab initio calculations of ester-functionalized ILs were carried out in the temperature range of 298−550 K. The applied force field parameters in the present study are in OPLS-AA/AMBER framework.38,39 The general potential function used in the current work is given by 11679

DOI: 10.1021/acs.iecr.5b03199 Ind. Eng. Chem. Res. 2015, 54, 11678−11700

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Industrial & Engineering Chemistry Research Table 1. Densities (ρ, g cm−3) of Selected ILs as Functions of Temperature Simulated by Means of MD Simulations T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550

[C1COOC1C1im][Br] 1.468 1.459 1.452 1.443 1.433 1.413 1.390 1.362

± ± ± ± ± ± ± ±

0.004 0.004 0.004 0.005 0.005 0.006 0.006 0.007

[C1COOC2C1im][Br] 1.397 1.385 1.375 1.365 1.357 1.329 1.297 1.268

± ± ± ± ± ± ± ±

0.005 0.005 0.005 0.006 0.006 0.007 0.008 0.008

[C1COOC4C1im][Br] 1.311 1.300 1.286 1.275 1.260 1.232 1.196 1.164

± ± ± ± ± ± ± ±

0.005 0.005 0.006 0.006 0.007 0.008 0.008 0.009

[C1COOC1C1im][NO3] [C1COOC1C1im][BF4] [C1COOC1C1im][PF6] 1.358 1.349 1.338 1.328 1.313 1.292 1.262 1.233

± ± ± ± ± ± ± ±

0.004 0.004 0.004 0.005 0.005 0.006 0.006 0.007

1.323 1.313 1.301 1.289 1.276 1.251 1.222 1.192

± ± ± ± ± ± ± ±

0.004 0.004 0.005 0.005 0.005 0.006 0.007 0.007

1.467 1.454 1.444 1.434 1.419 1.392 1.360 1.327

± ± ± ± ± ± ± ±

0.005 0.005 0.005 0.006 0.006 0.007 0.008 0.009


± ± ± ± ± ± ± ±

0.005 0.005 0.005 0.006 0.006 0.007 0.008 0.008

1.292 1.280 1.263 1.249 1.230 1.196 1.163 1.129

± ± ± ± ± ± ± ±

0.005 0.005 0.006 0.006 0.007 0.007 0.008 0.009

1.430 1.419 1.403 1.386 1.366 1.333 1.295 1.254

± ± ± ± ± ± ± ±

0.005 0.006 0.006 0.006 0.007 0.008 0.009 0.010


± ± ± ± ± ± ± ±

0.005 0.005 0.006 0.006 0.007 0.008 0.008 0.010

1.214 1.201 1.186 1.168 1.155 1.121 1.085 1.051

± ± ± ± ± ± ± ±

0.005 0.006 0.006 0.007 0.007 0.008 0.009 0.010

1.351 1.336 1.320 1.300 1.278 1.244 1.204 1.167

± ± ± ± ± ± ± ±

0.006 0.006 0.007 0.007 0.008 0.009 0.009 0.011

[C1COOC1C1im][TfO] [C1COOC1C1im][Tf2N] 1.477 1.467 1.455 1.444 1.429 1.401 1.371 1.342

± ± ± ± ± ± ± ±

0.004 0.004 0.005 0.005 0.005 0.006 0.007 0.008

1.602 1.590 1.578 1.561 1.542 1.506 1.466 1.426

± ± ± ± ± ± ± ±

0.005 0.006 0.006 0.007 0.007 0.008 0.009 0.011


± ± ± ± ± ± ± ±

0.005 0.005 0.006 0.006 0.006 0.007 0.008 0.009

1.566 1.548 1.529 1.509 1.488 1.441 1.399 1.354

± ± ± ± ± ± ± ±

0.007 0.007 0.008 0.009 0.009 0.010 0.011 0.012


± ± ± ± ± ± ± ±

0.005 0.006 0.006 0.007 0.007 0.008 0.009 0.010

1.495 1.476 1.452 1.438 1.412 1.365 1.322 1.280

± ± ± ± ± ± ± ±

0.006 0.007 0.008 0.008 0.008 0.010 0.011 0.012

a different combinations of anions: [Tf2N]− > [TfO]− ≥ [PF6]− > [BF4]− > [NO3]− > [Br]−. It should be noted that the IL containing [C1COOC4C1im]+ cation with [PF6]− anion has a higher molar volume than [C1COOC4C1im][TfO]. These results are in good agreement with those reported for traditional imidazolium-based ILs composed of similar anions.45 The molecular volume (V) of an IL is the sum of the cation and anion volumes, which were approximated by two different methods in this study. In the first approach, these volumes were computed using MD simulations as17,29,46−54

in this study, which is in good agreement with the previously reported simulated and experimental values of 1.568 and 1.594 g cm−3, respectively.39 As expected, a decreasing trend was observed for variations in the calculated density with temperature. Additionally, the densities of selected ILs decreased with increasing alkyl side-chain length of the cation. This might be be caused by a significant enhancement in the dispersion of the positive charge, after which electrostatic interactions would dissipate and a considerable reduction in the density would be observed. Moreover, the higher steric hindrance of larger alkyl side chains could cause a significant reduction of the packing efficiency of ILs, which could directly decrease the overall density. The predicted densities of these ILs with different combinations of anions are in the following order: [Tf2N]− > [TfO]− > [PF6]− > [Br]− > [NO3]− > [BF4]−. To be more precise, the IL consisting of the [C1COOC1C1im]+ cation paired with the [Br]− anion has a slightly larger density than [C1COOC1C1im][PF6]. Although bulkier anions exhibit greater charge diffusion and larger steric hindrance, their higher molecular weights are believed to be responsible for the observed trend in the simulated densities. The introduction of the ester group in the alkyl side chain of the imidazolium cation significantly enhances the interionic interactions and improves the packing efficiency of these ILs. Generally, the density values of ester-functionalized ILs are higher than those reported for conventional imidazoliumbased ILs.17,22,38,42−44 The variations in the molar volumes of these ILs with respect to temperature are shown in Figure 2. The highest values of molar volume belong to the bulkier cations associated with voluminous anions, as expected. The following trend was obtained for the molar volume of ester-functionalized ILs with

V=

V M = m Nρ N

(2)

where M is the molar mass, Vm is the molar volume, and N is Avogadro’s constant. A similar trend in molar volumes was exactly observed for the molecular volumes. As can be comprehended from Figure 2, the mean contribution to the molecular volume per methylene (CH2−) group is 0.026 nm3, which is slightly lower than previously reported values of 0.0268 nm3 for [Cnmim][OAc] (n = 2, 3, 4, 5, 6),50 0.0275 nm3 for [Cnmim][BF4] (n = 2, 4, 6, 8, 10) and [Cnmim][Tf2N] (n = 1, 2, 4, 6, 8, 10, 12),5 0.0278 nm3 for [Cnmim][Ala] (n = 2, 3, 4, 5, 6),54 and 0.0280 nm3 for imidazolium-based ILs [Cnmmim][Tf2N] (n = 2, 4).47 Numerical values of Vm and V are listed in Tables S5 and S6, respectively, of the Supporting Information. In the second method, molecular volumes were estimated by ab initio calculations. In this case, the molecular volumes of isolated ion pairs were computed at the B3LYP/6-311+ +G(d,p) level of theory. The molecular volumes obtained by 11680


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Figure 2. Computed molar (Vm) and molecular (V) volumes of the investigated ILs in the temperature range of 298−550 K.

the ab initio method vary in the following order: [Tf2N]− > [PF6]− ≈ [TfO]− > [BF4]− > [NO3]− > [Br]−. The molecular volumes predicted from the ab initio calculations follow nearly the same trend as the corresponding results obtained by MD simulations with a significant underestimation. Given that the molecular volumes of many common anions have already been determined,46−48,51−53 the molecular volumes of unknown cations (V+) can easily be derived from the equation46,52

V V+ = cell − V − N

3.2. Enthalpy of Vaporization, Cohesive Energy Density, and Hildebrand Solubility Parameter. To calculate the enthalpy of vaporization (ΔHvap m ), gas-phase simulations were conducted in the NVT ensemble with a long time period of 40 ns.55 The enthalpy of vaporization can be expressed as ΔHmvap(T ) = Um,gas − Um,liquid + P(Vm,gas − Vm,liquid) = ΔUmvap(T ) + RT

(4)

where Um,gas and Um,liquid are the molar configuration energies of the gas and liquid phases, respectively. Figure 3 displays the simulated values of ΔHvap m at the desired temperatures. The results reveal a decreasing trend of ΔHvap m with increasing temperature, which might be related to a weakening of interionic interactions in the liquid phase. As a result, the differences between the internal energies of the gas and liquid phases decrease, resulting in a decrease in the simulated values of ΔHvap m , whereas elongation of alkyl side chain leads to opposite effects. A considerable enhancement of the vdW interactions in the condensed phase and the lack of such interactions in the gas phase are perceived to be responsible for this trend. These results are consistent with those of previous studies of traditional imidazolium-based ILs.3,10,17,24,43,44,55−60 The following trend can be seen for the ΔHvap m values of ILs containing the [C1COOC1C1im]+ cation combined with different anions: [PF6]− > [NO3]− > [Br]− > [TfO]− > [BF4]− > [Tf2N]−. A similar trend holds for the [C1COOC2C1im]+ cation, with [C1COOC2C1im][PF6] having the highest ΔHmvap value, followed by [C1COOC2C1im][NO3] and then [C1COOC2C1im][Tf2N]. The ΔHvap m results for ILs containing the [C1COOC4C1im]+ cation paired with the different anions follow the order [TfO]− > [NO3]− > [PF6]− > [Br]− > [BF4]− > [Tf2N]−. The computed results for the ΔHvap m values of ester-functionalized ILs are distinctly larger than those reported for common imidazolium-based ILs.3,10,17,24,43,44,55−60 In addition, the other derivatives of the heat of vaporization, such as the cohesive energy density (CED) and Hildebrand solubility parameter (δH), were computed to predict the solubility trends of these ILs. CED is defined as the energy required to

(3)

where V+ is the cation volume, V− is the anion volume, Vcell is the volume of the simulation box, and N is the number of ion pairs. Good accuracy for the cation volume can be obtained by taking the average volume using different reference anions.46,52,53 The mean values of V+ were found to be 0.220, 0.245, and 0.300 nm3 for [C1COOC1C1im]+, [C1COOC2C1im]+, and [C1COOC4C1im]+, respectively (see Table 2). The average volume of a methylene group in the cationic volume of the selected ILs was found to be 0.026 nm3. This value is larger than the 0.023 nm3 volume46 and smaller than the 0.028 nm3 volume48 found for conventional imidazolium-based cations paired with [BF4]− and [Tf2N]−, respectively. Furthermore, it is possible to estimate the volume of analogous series of cations (cations with the different alkyl side-chain lengths) based on the average volume variation upon the addition or subtraction of a CH2− group.46 Ab initio calculations of an isolated cation are another procedure for estimating the mean volume contribution of a methylene group to the cationic volume. For this reason, each selected cation was optimized at the B3LYP/6-311++G(d,p) theoretical level. Subsequently, the optimized geometries were utilized to calculate the volumes of cations. The values of V+ obtained from ab initio results were 0.212, 0.222, and 0.260 nm3 for [C1COOC1C1im]+, [C1COOC2C1im]+, and [C1COOC4C1im]+, respectively. Therefore, 0.015 nm3 can be regarded as the average contribution to V+ of one CH2− group. This value is significantly lower than that (0.026 nm3) predicted from MD simulations. 11681


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Table 2. Room-Temperature Molecular Volumes of Cations (V+), Anions (V−), and Isolated Ion Pairs (V) Calculated by Means of MD Simulations and ab Initio Caculations method MD simulation V− (nm3)

IL

V+ (nm3)

MD simulation V− (nm3)

V+ (nm3)

ab initio V− (nm3)

V+ (nm3)

V (nm3)

0.068 0.069 0.071 0.080 0.118 0.218

0.172 0.185 0.217 0.267 0.217 0.201

0.240 0.254 0.288 0.347 0.335 0.419

0.068 0.069 0.071 0.080 0.118 0.218

0.178 0.195 0.237 0.261 0.213 0.221

0.246 0.264 0.308 0.341 0.331 0.439

0.068 0.069 0.071 0.080 0.118 0.218

0.215 0.250 0.284 0.277 0.250 0.274

0.283 0.319 0.355 0.357 0.368 0.492

+

a

[C1COOC1C1im][Br] [C1COOC1C1im][NO3] [C1COOC1C1im][BF4] [C1COOC1C1im][PF6] [C1COOC1C1im][TfO] [C1COOC1C1im][Tf2N]

− 0.064a 0.073a,b,c 0.107a 0.129a 0.230a

− 0.202 0.231 0.233 0.213 0.221


− 0.064a 0.073a,b,c 0.107a 0.129a 0.230a

− 0.230 0.256 0.258 0.236 0.246


− 0.064a 0.073a,b,c 0.107a 0.129a 0.230a

− 0.288 0.315 0.317 0.280 0.300

[C1COOCn=1C1im] Cation − − − − 0.078d 0.226 0.109b,d,e 0.231 0.131b,e 0.211 0.232b,c,e 0.219 [C1COOCn=2C1im]+ Cation − − − − 0.078d 0.251 0.109b,d,e 0.256 0.131b,e 0.234 0.232b,c,e 0.244 [C1COOCn=4C1im]+ Cation − − − − 0.078d 0.310 0.109b,d,e 0.312 0.131b,e 0.278 0.232b,c,e 0.298

Reference 48. bReference 52. cReference 53. dReference 51. eReference 46.

Figure 3. Simulated values of the molar enthalpy of vaporization (ΔHvap m ) and surface tension (σ) as functions of temperature for all selected ILs.

completely overcome intermolecular attractive forces between neighbors and reference molecules and finally release a reference molecule from its nearest neighbors to infinite distance. CED can be computed as18 CED =

Um,gas − Um,liquid Vm,liquid

=

ΔUmvap(T ) Vm,liquid

The variations of estimated CED values as functions of temperature are shown in Figure 4. A decreasing trend of CED values with increasing cation side-chain length can be seen. The simulated values of CED for these ILs have the following trend: [NO3]− > [Br]− > [BF4]− > [PF6]− > [TfO]− > [Tf2N]−. The trend in the CED values of ester-functionalized ILs composed of the largest cation ([C1COOC4C1im]+) is [NO3]− > [Br]− > [TfO]− > [BF4]− > [PF6]− > [Tf2N]−. The localized negative

(5) 11682


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Figure 4. Cohesive energy density (CED) and Hildebrand solubility parameter (δH) estimated from MD simulations for selected ILs.

the intramolecular contributions to the configuration energy.61 Consequently, the heat capacity values that are directly computed from MD simulations (using eq 7) probably have large errors.61 Therefore, the estimation of the heat capacity can be improved using MD simulations combined with ab initio calculations. In this regard, the enthalpy is separated to ideal contribution (Hid) and residual (Hres) terms, where the ideal enthalpy is given by Hid = Uint + K + NkT and the residual enthalpy can be defined as Hres = UNB + PV − NkT. Accordingly, in the present study, the residual contribution of isobaric heat capacity was obtained using the equation22,61−63

charge and lower steric hindrance of the smaller anions enable them to get close to the cation efficiently. Thus, smaller anions increase the interionic interactions. These results are in good agreement with those reported earlier for conventional imidazolium-based ILs.17,43,60 The first insight into the solubility behavior of solvents and the degree of interactions between their ions can be obtained by computing Hildebrand solubility parameters (δH). Solvents with similar solubility parameters are probably miscible in one another. The solubility parameter can be easily derived from the square root of the CED as18,29,47 1/2

δ H = (CED)

⎛ ∂⟨U NB⟩ ⎞ ⎛ ∂⟨H res⟩ ⎞ ⎛ ∂⟨V ⟩ ⎞ ⎟ − NkB ⎟ =⎜ C Pres(T , P) = ⎜ ⎟ + P⎜ ⎝ ∂T ⎠ P ⎝ ∂T ⎠P ⎝ ∂T ⎠ P

⎛ ΔU vap ⎞1/2 ⎡ ΔH vap(T ) − RT ⎤1/2 m ⎟ m ⎥ = ⎜⎜ ⎟ = ⎢⎢ V Vm,liquid ⎥⎦ ⎣ ⎝ m,liquid ⎠

(8)

(6)

In addition, the ideal contributions to the heat capacities were computed using ab initio calculations at the B3LYP/ 6-311++G(d,p) level of theory. The simulated results for CP are collected in Table 3. The temperature has an increasing effect on CP as a result of the activation of more vibrational degrees of freedom. Lengthening of the alkyl side chain of the cation brings about a marked enhancement of the computed values of the isobaric heat capacity. This can be related to the increase in the vibrational degrees of freedom. For the same reason, ester-functionalized ILs incorporating bulkier anions such as [Tf2N]−, [TfO]−, and [PF6]− demonstrate the highest values of CP. The average contribution to the isobaric heat capacity per CH2− group is 50.1 J mol−1 K−1. The residual contribution of the isobaric heat capacity can also be computed using the statistical fluctuation formula as22,63

The same trend as for CED was observed for the Hildebrand solubility parameter (see Figure 4). The miscibility of ILs composed of the same cation paired with [Br]− and [NO3]− can be inferred from the results obtained for δH at the target temperatures. In addition, ILs containing [BF4]− and [PF6]− anions with the same cation can be dissolved in each other owing to their similar solubility parameters. The predicted values of δH for the ester-functionalized ILs in this study are significantly higher than those for traditional imidazolium-based ILs containing the same anions.47 Numerical results for ΔHvap m , CED, and δH are given in Tables S7−S9, respectively, of the Supporting Information. 3.3. Isobaric Heat Capacity. The isobaric heat capacity (CP) can be estimated using the following fluctuation formula (⟨H2⟩ − ⟨H ⟩2 )NpT ⎛ ∂⟨H ⟩ ⎞ δH2 ⎟ = = C P(T , P) = ⎜ ⎝ ∂T ⎠ P NkBT 2 NkBT 2

C Pres(T , P) = (7)

+

where H is the enthalpy, defined as H = UNB + Uint + K + PV, in which UNB and Uint are the intra- and intermolecular energies, respectively, and K is the kinetic energy. As already pointed out by Maginn et al., classical force fields do not correctly provide

1 (⟨U NBĤ ⟩ − ⟨U NB⟩⟨Ĥ ⟩) kBT 2

1 (⟨VĤ ⟩ − ⟨V ⟩⟨Ĥ ⟩) − NkB kBT 2

(9)

where Ĥ is the configuration enthalpy, which is defined as Ĥ = UNB + Uint + PV. It must be stressed that estimating the 11683


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Industrial & Engineering Chemistry Research Table 3. Molar Heat Capacities (CP, J mol−1 K−1) of Selected ILs as Functions of Temperature Calculated Using MD Simulations Combined with ab Initio Calculations T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550 T (K)

[C1COOC1C1im][Br] 295.1 308.0 320.0 331.9 343.5 365.8 386.4 405.3

± ± ± ± ± ± ± ±

1.5 1.5 1.6 1.7 1.7 1.8 1.9 2.0

[C1COOC2C1im][Br] 337.3 352.1 365.9 379.5 392.8 418.3 441.9 463.6

± ± ± ± ± ± ± ±

1.9 2.0 2.1 2.2 2.2 2.4 2.5 2.7

[C1COOC4C1im][Br]

298 325 350 375 400 450 500 550

400.6 419.1 436.2 453.2 469.8 501.6 531.1 558.1

± ± ± ± ± ± ± ±

2.6 2.8 2.9 3.0 3.1 3.3 3.5 3.7


± ± ± ± ± ± ± ±

1.9 2.0 2.0 2.1 2.2 2.3 2.4 2.6

391.3 407.6 422.5 436.9 450.9 477.1 501.0 522.5

± ± ± ± ± ± ± ±

1.6 1.6 1.7 1.8 1.8 1.9 2.0 2.1

424.0 442.5 458.9 474.7 489.7 517.5 542.4 564.7

409.2 426.3 442.1 457.7 472.9 501.9 528.7 553.1

± ± ± ± ± ± ± ±

2.2 2.2 2.3 2.4 2.5 2.6 2.8 2.9

432.8 450.9 467.5 483.7 499.3 528.8 555.6 579.9

± ± ± ± ± ± ± ±

1.9 1.9 2.0 2.1 2.2 2.3 2.4 2.5

468.7 488.9 507.1 524.6 541.3 572.3 600.2 625.2

± ± ± ± ± ± ± ±

2.7 2.8 2.9 3.0 3.1 3.3 3.5 3.6


± ± ± ± ± ± ± ±

2.8 2.9 3.0 3.1 3.2 3.5 3.6 3.8

491.2 513.1 533.0 552.5 571.5 607.4 640.3 670.2

± ± ± ± ± ± ± ±

2.5 2.6 2.7 2.8 2.9 3.0 3.2 3.4

505.1 529.1 550.6 571.4 591.4 628.8 662.6 693.0

⎛ ∂ ln ρ ⎞ 1 ⎛ ∂⟨V ⟩ ⎞ 1 ⎛ ∂ρ ⎞ ⎟ ⎜ ⎟ = − ⎜ ⎟ = −⎜ ⎝ ∂T ⎠ P ⟨V ⟩ ⎝ ∂T ⎠ P ρ ⎝ ∂T ⎠ P

1 (⟨VĤ ⟩ − ⟨V ⟩⟨Ĥ ⟩) ⟨V ⟩kBT 2

± ± ± ± ± ± ± ±

2.5 2.6 2.7 2.8 2.9 3.1 3.3 3.5


± ± ± ± ± ± ± ±

2.0 2.1 2.1 2.2 2.3 2.4 2.5 2.6

602.7 626.3 647.4 667.7 687.0 723.0 755.1 783.8

± ± ± ± ± ± ± ±

3.2 3.4 3.5 3.6 3.7 3.9 4.0 4.2


± ± ± ± ± ± ± ±

1.9 2.0 2.1 2.1 2.2 2.3 2.4 2.5

653.1 678.5 701.3 723.3 744.4 783.5 818.6 849.9

± ± ± ± ± ± ± ±

3.7 3.9 4.0 4.1 4.2 4.5 4.7 4.8


± ± ± ± ± ± ± ±

2.8 2.9 3.0 3.1 3.3 3.4 3.6 3.8

699.2 728.3 754.5 779.8 804.1 849.7 890.9 927.9

± ± ± ± ± ± ± ±

3.5 3.6 3.8 3.9 4.0 4.2 4.4 4.6

[Tf2N]− > [PF6]− > [BF4]− > [TfO]− ≥ [NO3]− > [Br]−. Compared to imidazolium-based ILs bearing the same hydrocarbon chain, ester-functionalized ILs have slightly lower values of thermal expansion.17,22,47,64−72 This might be caused by incorporating an ester functional group that promotes interionic interactions and subsequently improves the packing efficiency of these ILs. 3.5. Isothermal Compressibility Coefficient. For further information about the compressibility of the selected ILs, the isothermal compressibility coefficient (βT) was estimated during NPT simulations over the wide range of temperatures from 298 to 550 K using the equation10,62,63,72

(10)

where the subscript P on the derivatives refers to constant pressure. In another approach, αP can be estimated using the fluctuation formula as follows62,63 αP =

2.5 2.6 2.7 2.8 2.9 3.1 3.2 3.4

[C1COOC2C1im][NO3] [C1COOC2C1im][BF4] [C1COOC2C1im][PF6]

isobaric heat capacity using the fluctuation formula (eq 9) leads to values having high uncertainties.22 3.4. Isobaric Thermal Expansion Coefficient. The coefficient of thermal expansion (αP) basically measures the change in the volume of a substance in response to a change in temperature. Therefore, αP is given by22 αP =

± ± ± ± ± ± ± ±

βT = − (11)

As stated earlier, computing αP from the fluctuation formula results in a high statistical uncertainty. Consequently, in the present work, αP was calculated by using eq 9. The simulated values of αP versus temperature are reported in Table 4. A slight decreasing trend of αP with increasing temperature was found. Furthermore, as the alkyl side chain of the cation was lengthened, an enhancement in the estimated values of αP was observed. The highest value of αP is attributed to the cation with the longest alkyl side chain incorporating bulky anions. This can be justified by the reduction in the packing efficiency of these ILs owing to the higher charge delocalization accompanied by the considerable steric hindrance of voluminous ions. Thus, the αP values of ester-functionalized ILs composed of the same cation exhibit the following trend:

1 ⎛ ∂⟨V ⟩ ⎞ 1 ⎜ ⎟ = (⟨V 2⟩ − ⟨V ⟩2 ) ⟨V ⟩ ⎝ ∂P ⎠T ⟨V ⟩kBT

(12)

Table 5 reports the values of βT obtained as a function of temperature. As already emphasized, computing βT by means of the fluctuation formula results in values with very large uncertainties. An increasing trend was observed for the compressibility variations of these ILs versus temperature. As the alkyl chain of the ester-functionalized cation was lengthened, the simulated values of βT were enhanced. The highest values of βT are ascribed to ILs containing [Tf2N]−, followed by [PF6]−, and the minimum values are attributed to ILs incorporating [Br]− and [NO3]−. This might be due to a larger free volume resulting from a lower packing efficiency of voluminous ions. The results obtained βT show that ester-functionalized ILs are less compressible than common imidazolium-based ILs with alkyl side chains of the same length.65,67,68,73,74 This might be 11684


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Table 4. Isothermal Expansion Coefficients (αP, 10−4 K−1) of Selected Ester-Functionalized ILs as Functions of Temperature Computed Using MD Simulations T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550

[C1COOC1C1im][Br] 3.03 3.02 3.00 2.98 2.96 2.92 2.87 2.82

± ± ± ± ± ± ± ±

0.15 0.15 0.15 0.15 0.15 0.14 0.14 0.14

[C1COOC2C1im][Br] 4.04 4.00 3.97 3.94 3.92 3.84 3.75 3.66

± ± ± ± ± ± ± ±

0.21 0.20 0.20 0.20 0.20 0.20 0.19 0.19

[C1COOC4C1im][Br] 5.03 4.99 4.93 4.89 4.83 4.73 4.59 4.47

± ± ± ± ± ± ± ±

0.21 0.21 0.21 0.21 0.20 0.20 0.20 0.19


± ± ± ± ± ± ± ±

0.17 0.17 0.17 0.17 0.17 0.16 0.16 0.16

4.36 4.33 4.29 4.25 4.21 4.13 4.03 3.93

± ± ± ± ± ± ± ±

0.16 0.16 0.16 0.16 0.16 0.15 0.15 0.15

4.17 4.14 4.11 4.08 4.04 3.96 3.87 3.77

± ± ± ± ± ± ± ±


± ± ± ± ± ± ± ±

0.21 0.21 0.21 0.21 0.21 0.20 0.20 0.19

5.82 5.76 5.69 5.62 5.54 5.38 5.24 5.08

± ± ± ± ± ± ± ±

0.16 0.16 0.16 0.16 0.16 0.15 0.15 0.15

5.62 5.58 5.51 5.45 5.37 5.24 5.09 4.93

± ± ± ± ± ± ± ±

± ± ± ± ± ± ± ±

0.24 0.24 0.24 0.23 0.23 0.22 0.22 0.21

6.20 6.14 6.06 5.97 5.90 5.73 5.54 5.37

± ± ± ± ± ± ± ±

0.20 0.20 0.20 0.19 0.19 0.19 0.18 0.18

6.37 6.30 6.22 6.13 6.02 5.86 5.67 5.50

± ± ± ± ± ± ± ±

0.14 0.14 0.14 0.14 0.13 0.13 0.13 0.13

4.98 4.94 4.90 4.85 4.79 4.68 4.55 4.43

± ± ± ± ± ± ± ±

0.22 0.22 0.22 0.22 0.22 0.21 0.21 0.20


± ± ± ± ± ± ± ±

0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

6.27 6.20 6.12 6.04 5.96 5.77 5.60 5.42

± ± ± ± ± ± ± ±

0.19 0.19 0.19 0.19 0.19 0.18 0.18 0.17

[C1COOC4C1im][TfO] [C1COOC4C1im][Tf2N]

0.17 0.17 0.17 0.17 0.17 0.16 0.16 0.16

6.09 6.01 5.94 5.86 5.77 5.60 5.45 5.28

± ± ± ± ± ± ± ±

0.14 0.14 0.14 0.14 0.14 0.13 0.13 0.13

6.75 6.67 6.56 6.49 6.38 6.17 5.97 5.78

± ± ± ± ± ± ± ±

0.18 0.18 0.18 0.18 0.18 0.17 0.17 0.16

considerable reduction in the cohesive electrostatic interactions due to the higher charge dispersion of bulkier ions. These trends are comparable to those reported for conventional imidazolium ILs.17,56,75−82 Unfortunately, the lack of experimental data does not allow any validation. The temperature dependence of the surface tension can be utilized to estimate the critical temperature (Tc) of an IL by means of the Eötvos79 (eq 14) and Guggenheim80 (eq 15) equations as follows

related to the stronger interionic interactions of these ILs in the presence of the ester functional group. 3.6. Other Derivatives of Thermodynamic Properties. Additional structure−property correlations of these ILs can be identified by estimating the other derivatives of their thermodynamic properties. Numerical values of these properties are presented in Tables S10−S20 of the Supporting Information. 3.6.1. Surface Tension and Critical Temperature. This section continues the analysis by calculating the surface tension (σ) using the empirical equation of Zaitsau et al.45,47,56 ΔHmvap = A(σVm 2/3NA1/3) + B

± ± ± ± ± ± ± ±

4.04 4.01 3.98 3.95 3.91 3.83 3.75 3.67

0.22 0.22 0.21 0.21 0.21 0.21 0.20 0.19



0.19 0.19 0.19 0.19 0.19 0.18 0.18 0.18

(13)

where the first term is associated with the dispersive interactions in which the constant A is equal to 0.01121, Vm is the molar volume, and NA is Avogadro’s number. Nondispersive forces (dipole−dipole, electrostatic, etc.) in eq 13 are considered through the constant B = 2.4 kJ mol−1.45,46,56 The large uncertainties in the ΔHvap m values prevent a linear relation between surface tensions and enthalpies of vaporization. Given that the attractive forces among molecules are responsible for the surface tension of liquids, the obtained results for the corresponding properties can be used as a criterion for the cohesive interactions. The maximum value of surface tension is attributed to ester-functionalized ILs containing the smallest cation ([C1COOC1C1im]+) coupled with [NO3]−, followed by [Br]−, and the minimum of the corresponding property is ascribed to ILs consisting of the largest cation ([C1COOC4C1im]+) paired with bulkier anions, especially [Tf2N]− (see Figure 3). This might be due to a

⎛ M ⎞2/3 σ ⎜ ⎟ = K (Tc − T ) ⎝ρ⎠

(14)

11/9 ⎛ T⎞ σ = K ′⎜1 − ⎟ Tc ⎠ ⎝

(15)

where M is the molecular weight, T is the temperature, σ is the surface tension, ρ is the density, and K and K′ are the empirical constants. Both equations indicate that σ becomes null at Tc. Figure 5 shows the values calculated for the critical temperature using the two mentioned equations. More details on the computed results are provided in Table 6. In general, the values of Tc predicted by the Eötvos equation are higher than those predicted by the Guggenheim equation. The critical temperature is predicted to decrease when the length of the alkyl side chain of the cation is increased. Excluding the ILs containing [PF6]−, the maximum values of Tc are generally related to the ILs containing [NO3]− and [Br]−, followed by [BF4]− and [TfO]−, and the lowest values are associated with the ILs 11685


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Table 5. Isothermal Compressibility Coefficients (βT, 10−6 bar−1) of All Selected ILs in This Study as Functions of Temperature Calculated Using MD Simulations T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550

[C1COOC1C1im][Br] 10.49 11.39 12.16 12.90 15.28 17.55 19.88 24.48

± ± ± ± ± ± ± ±

0.03 0.03 0.04 0.04 0.05 0.07 0.09 0.12

[C1COOC2C1im][Br] 16.46 18.56 19.72 21.37 23.47 28.23 34.30 37.59

± ± ± ± ± ± ± ±

0.05 0.07 0.08 0.09 0.10 0.14 0.20 0.24

[C1COOC4C1im][Br] 21.16 21.21 25.40 27.32 32.78 43.31 50.25 60.88

± ± ± ± ± ± ± ±

0.08 0.08 0.11 0.13 0.17 0.27 0.36 0.49


± ± ± ± ± ± ± ±

0.03 0.04 0.04 0.04 0.06 0.09 0.12 0.14

14.98 15.45 17.18 18.85 21.52 24.71 31.41 36.28

± ± ± ± ± ± ± ±

0.05 0.05 0.06 0.07 0.09 0.12 0.17 0.22

15.92 16.88 17.62 19.32 21.89 25.18 32.40 37.23

± ± ± ± ± ± ± ±


± ± ± ± ± ± ± ±

0.06 0.07 0.08 0.10 0.13 0.17 0.23 0.26

20.36 21.27 23.83 25.96 33.41 37.54 46.59 56.65

± ± ± ± ± ± ± ±

0.08 0.09 0.10 0.12 0.18 0.23 0.33 0.45

21.66 22.82 25.02 28.74 35.13 38.03 47.18 58.62

± ± ± ± ± ± ± ±

± ± ± ± ± ± ± ±

0.09 0.10 0.14 0.16 0.20 0.27 0.39 0.58

25.88 29.27 36.68 39.89 41.97 55.14 59.28 74.62

± ± ± ± ± ± ± ±

0.11 0.14 0.20 0.23 0.26 0.41 0.47 0.68

28.61 31.09 38.07 41.69 44.71 56.26 62.32 81.52

± ± ± ± ± ± ± ±

10.77 12.03 12.93 14.17 16.22 22.00 25.87 29.37

± ± ± ± ± ± ± ±

0.03 0.04 0.04 0.05 0.06 0.10 0.13 0.17

17.18 19.75 21.39 25.15 26.22 30.32 41.72 54.44

± ± ± ± ± ± ± ±

0.06 0.07 0.08 0.11 0.12 0.16 0.26 0.40


0.08 0.09 0.11 0.13 0.19 0.22 0.32 0.45



0.05 0.06 0.07 0.08 0.10 0.12 0.19 0.24

17.41 18.73 21.74 23.76 26.43 31.35 35.68 45.85

± ± ± ± ± ± ± ±

0.06 0.07 0.09 0.10 0.12 0.16 0.21 0.31

25.26 28.78 32.12 38.63 42.03 49.84 59.06 68.51

± ± ± ± ± ± ± ±

0.11 0.13 0.16 0.22 0.26 0.34 0.46 0.60


0.12 0.15 0.20 0.24 0.27 0.40 0.49 0.75

22.28 22.71 28.63 32.89 35.88 44.65 52.79 64.71

± ± ± ± ± ± ± ±

0.09 0.09 0.13 0.17 0.20 0.29 0.38 0.54

27.83 33.84 41.11 42.66 45.15 59.06 69.73 87.00

± ± ± ± ± ± ± ±

0.12 0.16 0.22 0.24 0.27 0.42 0.56 0.80

The computed Tb value for each selected IL is also presented in Table 6. The effects of anion and cation substitution on the boiling temperature values can be easily observed in Figure 5. As expected, the same trend as observed for Tc also applies to Tb. The critical temperatures and, consequently, the boiling temperatures of the investigated ILs were found to be higher than those of the conventional imidazolium-based ILs.47,75,82 3.6.2. Surface Thermodynamic Functions and Parachor. The slope of a plot of surface tension versus temperature, (∂σ/∂T)P, can be used to measure surface thermodynamic functions, such as surface excess entropy (Sσ) and surface excess enthalpy (Hσ) using the equations47,75

Figure 5. Values of the critical (Tc) and boiling (Tb) temperatures computed using two different empirical equations: (right) Eötvos (eq 14) and (left) Guggenheim (eq 15).

⎛ ∂σ ⎞ S σ = −⎜ ⎟ ⎝ ∂T ⎠ P

(16)

⎛ ∂σ ⎞ H σ = σ − T⎜ ⎟ ⎝ ∂T ⎠ P

(17)

As can be seen in Figure 6, surface excess enthalpies decreased with increasing cation alkyl side-chain length. Weakening electrostatic interactions between ions due to greater delocalization of the positive charge and a decrease in the packing efficiency of the lengthened cations appear to be responsible for this reduction. This indicates a significant decrease of the strength of hydrogen bonding and the degree of surface ordering. The surface excess entropy follows a similar trend (see Table 7). This trend is in agreement with the results previously reported for traditional imidazolium-based ILs.47,75 The surface thermodynamic functions are also affected by different types of anions.

containing the largest anions such as [Tf2N]−. The reduction in the strength of the hydrogen bonding between bulkier ions is proposed to be responsible for this behavior. These trends were exactly confirmed earlier by the results obtained for ΔUvap m and CED. The boiling temperature (Tb) can be approximated using the following equation developed by Rebelo et al.,78,83 for ILs: Tb ≈ 0.6Tc. 11686


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Table 6. Critical Temperatures (Tc) and Boiling Temperatures (Tb) of All Selected ILs in This Study Computed by Means of Both the Eötvos and Guggenheim Equations Eötvos IL

K (10−7 J mol−2/3 K−1)

R2

Guggenheim Tc (K)

Tb (K)

K′ (mJ m−2)

R2

Tc (K)

Tb (K)

94.53 95.15 87.79 81.66 84.71 67.95

0.9814 0.9954 0.9657 0.9976 0.9810 0.9817

2464 2450 1767 2396 1867 1591

1478.4 1470.0 1060.2 1437.6 1120.2 954.6

91.74 89.45 86.52 78.80 82.66 67.47

0.9791 0.9882 0.9917 0.9899 0.9943 0.9918

2002 2298 1807 2231 1740 1481

1201.2 1378.8 1084.2 1338.6 1044.0 888.6

85.72 93.80 81.83 77.70 88.38 63.92

0.9928 0.9900 0.9927 0.9957 0.9940 0.9753

1857 1745 1588 1803 1480 1476

1114.2 1047.0 952.8 1081.8 888.0 885.6

+


0.9192 0.7965 1.3353 0.8184 1.3190 1.4857


1.1679 0.7678 1.1587 0.7480 1.3467 1.5584


1.2402 1.4001 1.4829 1.1447 1.8715 1.5326

[C1COOCn=1C1im] Cation 0.9743 2854 1712.4 0.9940 3295 1977.0 0.9410 1986 1191.6 0.9925 3238 1942.8 0.9697 2107 1264.2 0.9666 1783 1069.8 [C1COOCn=2C1im]+ Cation 0.9698 2338 1402.8 0.9599 3388 2032.8 0.9826 2331 1398.6 0.9489 3507 2104.2 0.9887 2801 1680.6 0.9804 1727 1036.2 [C1COOCn=4C1im]+ Cation 0.9893 2275 1365.0 0.9836 2187 1312.2 0.9851 1921 1152.6 0.9877 2456 1473.6 0.9878 1708 1024.8 0.9423 1775 1065.0

Figure 6. Computed values of the surface excess enthalpy (Hσ) and parachor (Pa) in the temperature range of 298−550 K.

In general, ILs with larger anions have higher Sσ values. Moreover, for a given cation, the surface excess enthalpy of the target ILs decreased in the order [NO3]− > [Br]− > [PF6]− > [BF4]− ≠ [TfO]− > [Tf2N]−. This trend can be attributed to the higher interionic interactions of ILs containing smaller anions, especially [NO3]− and [Br]−. This order is close to the findings obtained for CED in this study. The parachor (Pa) is an additive quantity in that, for an IL, it can be approximately expressed as the sum of the cationic (Pa,+) and anionic (Pa,−) parachor contributions.49,50 It can be utilized

to predict the surface tension of a fluid from its density and vice versa through the relation N

Pa =

⎛ M ⎞ 1/4 ⎟σ ⎝ρ⎠

∑ Pa,i = Pa,+ + Pa,− = ⎜ i=1

(18)

where σ is the surface tension, ρ is the density, and M is the molar mass. Regarding the direct relationship between Pa and Vm and the negligible contribution of σ, the same trends of molar volume are approximately viewed for the parachor (see Figure 6). Regarding the additivity principle, values 11687


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Table 7. Surface Excess Entropies (Sσ) and Standard Molar Entropies (S0) of the Investigated ILs at 298 K Calculated by Means of MD Simulations and Room-Temperature Cationic (Pa,+) and Anionic (Pa,−) Parachor Contributions of the Same ILs Estimated by Means of MD Simulations and ab Initio Calculations method MD simulation IL

Sσ (10−5 J m−2 K−1)


4.50 4.55 5.73 3.99 5.24 4.87


5.32 4.55 5.52 4.12 5.45 5.16


5.33 6.18 5.88 4.92 6.76 4.90

MD simulation

S0 (J mol−1 K−1) [C1COOCn=1C1im]+ Cation 361.1 361.1 408.4 453.3 455.8 591.7 [C1COOCn=2C1im]+ Cation 398.5 396.0 439.6 484.5 484.5 622.8 [C1COOCn=4C1im]+ Cation 467.0 468.3 513.1 554.3 539.3 690.1

determined for V+ and V− can be used to calculate the ionic contributions to the parachor using the extra-thermodynamic assumption49,50 ⎡ V+(IL) ⎤ ⎡ Pa, +(IL) ⎤ V+(crystal) ⎥ ⎥=⎢ =⎢ V −(crystal) ⎣ V − V+(IL) ⎦ ⎣⎢ Pa − Pa, +(IL) ⎥⎦

Pa,−

Pa,+

Pa,−

− 364.0 400.1 404.7 367.8 358.0

− 115.3 126.5 185.8 222.7 372.6

343.4 349.1 396.8 454.4 382.5 350.5

135.7 130.2 129.8 136.1 208.0 380.1

− 407.3 443.8 442.8 404.9 397.4

− 113.3 126.6 183.6 221.3 371.5

379.2 384.5 438.9 479.4 403.0 387.1

144.8 136.1 131.5 147.0 223.2 381.8

− 508.0 534.5 531.0 483.2 478.6

− 112.9 123.9 179.2 222.6 366.9

462.4 486.6 526.7 551.1 479.5 470.9

146.2 134.3 131.7 159.1 226.3 374.6

The lattice energy (Upot) of a crystalline solid is expressed as the energy of formation of the crystal from infinitely separated ions in an exothermic process. Experimental investigations do not determine the lattice energy precisely, owing to the impossibility of preparing a sufficient amount of gaseous ions and computing the energy released during their condensation to form the solid crystalline. Therefore, the value of the lattice energy can be estimated by means of theoretical methods. The lattice energy of an IL can be computed from the equation5,49,50,54

(19)

where V+(crystal) and V−(crystal) are the cationic and anionic volumes, respectively, derived from crystal structures; V+(IL) is the ionic volume of the corresponding cation in an IL, Pa,+(IL) is the cationic parachor, and Pa is the parachor for the IL. The value of Pa,+ computed using eq 19 can be used to estimate Pa,− according to eq 18. The ionic parachor contributions obtained by MD simulations and ab initio calculations are summarized in Table 7. The ionic parachor contributions estimated by MD simulations mainly correlate well with the results obtained from ab initio calculations. As can be observed in Table 7, the cations have higher parachor contributions than their anions, which is close to the trend of ionic parachors observed for imidazolium-based ILs.50,54 3.6.3. Standard Molar Entropy and Lattice Energy. The standard molar entropy (S0) for an IL can be expressed as49,50 S 0(298 K) = 1246.5(V /nm 3) + 29.5

ab initio

Pa,+

⎛ ρ ⎞1/3 Upot = 1981.2⎜ ⎟ + 103.8 ⎝M⎠

(21)

where ρ is the density and M is the molar mass. It can easily be seen from Figure 7 that the values predicted for the lattice energies are much lower than those predicted for fused salts;49,50 for example, Upot = 613 kJ mol−1 for fused CsI, which is the minimum value of Upot among alkali halides.50 This is the main reason for forming an IL at room temperature.50 The lattice energy decreases almost linearly with increasing temperature. Cations substituted with longer alkyl side chains results in linear diminish in Upot values, which can be ascribed to the particular reduction of electrostatic interactions. This finding is comparable to the prior results for Upot for traditional imidazolium-based ILs.5,49,50,54 For the same alkyl side-chain length, the Upot values decrease in the order [NO3]− ≈ [Br]− > [BF4]− > [PF6]− ≥ [TfO]− > [Tf2N]−. The localized negative charges and lower steric hindrance of smaller anions bring about significant enhancements in interionic interactions and better interion arrangements. As a result, the possibility of hydrogen-bond formation increases. The observed trends in the lattice energies of the selected ILs are highly consistent with

(20)

where V is the molecular volume. As can be observed, a trend similar to that observed for molecular volume holds for the standard molar entropy at room temperature because of the direct dependence of S0 on molecular volume. This might be related to the fact that ILs containing cations with longer alkyl side chains paired with voluminous anions exhibit lower packing efficiency and bulk organization. The S0 values obtained for these ILs are smaller than those reported earlier for imidazolium-based ILs,5,49,50,54 which might be related to the presence of the ester group as a polar domain. 11688


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Figure 7. Simulated results for the lattice energy (Upot) and isothermal bulk modulus (kT) as functions of temperature.

temperature was clearly observed for ester-functionalized ILs composed of bulkier cations combined with voluminous anions such as [TfO]− and [Tf2N]−. In contrast, almost a linear decrease in CP − CV values with increasing temperature was seen for ILs containing smaller cations associated with [Br]− and [NO3]−. Briefly, CP − CV values for ester-functionalized ILs composed of larger ions quickly approach the ideal value (8.314 J mol−1 K−1). This might be related to the stronger electrostatic interactions between smaller ions due to their localized charges and lower steric hindrance. 3.6.6. Thermal and Internal Pressure. Internal pressure (πint) is another indication of the order of magnitude of intermolecular interactions. Initially, thermal pressure (γV) should be determined as17

those previously seen for the CED, surface tension, and surface excess enthalpy. 3.6.4. Isothermal Bulk Modulus. The isothermal bulk modulus (kT) is a uniform resistance against compressibility that can be directly measured from knowledge of the isothermal compressibility factor. Accordingly, it can be computed as84 kT =

⎛ ∂P ⎞ 1 = −V ⎜ ⎟ ⎝ ∂V ⎠T βT

(22)

The results for kT are displayed as a function of temperature in Figure 7. The reverse of the trend for βT is observed for kT, as expected. The main source of uncertainty in the calculation of kT is related to the large uncertainty in the βT values. The highest value of kT is attributed to the smallest cation combined with [Br]−, followed by [NO3]−, and the minimum value of the resistance against compressibility corresponds to the IL containing the largest cation paired with [Tf2N]−. This might be due to the higher packing efficiency of the smaller ions. Interestingly, according to the definitions of surface tension and bulk modulus, a direct relationship between the results for these properties can be found. 3.6.5. Isochoric Heat Capacity and Difference between Heat Capacities. Although it is difficult to measure the isochoric heat capacity (CV) for a condensed phase, CV can be calculated from the simulated values of CP by using the equation73,74,85 C V = CP −

T ⟨Vm⟩αP 2 βT

γV =

⎛ ∂P ⎞ αP ⎜ ⎟ = ⎝ ∂T ⎠V βT

(24)

Consequently, πint can be easily estimated according to the expression17 πint =

⎛ ∂U ⎞ ⎛ ∂P ⎞ ⎜ ⎟ = T⎜ ⎟ − P = Tγ − P V ⎝ ∂V ⎠T ⎝ ∂T ⎠V

(25)

The results predicted for γV and πint are plotted in Figure 9. The estimated γV and πint values of these ILs decrease with increasing temperature. This indicates that repulsive interactions are the dominant forces in the bulk of these ILs. Moreover, lengthening the side chain of the cation leads to a reduction of the γV and πint values, which implies a decrease in the dominant repulsive interactions due to the increase in charge diffusion and increasing steric hindrance. Excluding the ILs containing [TfO]−, the maximum values of γV and πint are attributed to the ester-functionalized ILs incorporating [NO3]− and [Br]−, approximately followed by [BF4]− and [PF6]−, and the lowest intermolecular interactions belong to ILs containing the [Tf2N]− anion. In general, a trend similar to that for CED is observed for πint. The lower steric hindrance of smaller ions in an IL enable the ions to approach one another efficiently.

(23)

Figure 8 shows plots of CV against temperature. As expected, a trend similar to that for CP was also found for CV. Furthermore, the difference in heat capacities (CP − CV) was calculated and is presented in Figure 8. Given that CP − CV is equal to 8.314 J mol−1 K−1 for an ideal gas, the value of this quantity can be used as criterion for deviations from ideal behavior. As can be seen in the predicted results for CP − CV in Figure 8, a strong reduction in CP − CV values with increasing 11689


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Figure 8. Computed values for the difference in heat capacities (CP − CV) and the isochoric heat capacity (CV) over a wide range of temperatures.

Figure 9. Estimated results for the thermal (γV) and internal (πint) pressures in the temperature range of 298−550 K.

where the subscript S on the derivative indicates that the entropy is fixed in adiabatic processes. As can be seen in Figure 10, the estimated values of βS are lower than those of βT for each target IL, which is related to the higher values of CP than CV. The speed of sound (u) can be derived from the Newton−Laplace equation17,86,88

As an result, ILs containing smaller ions have more dominant repulsive forces and, consequently, higher internal pressure. In general, ester-functionalized ILs have higher values of πint than imidazolium-based ILs.17,73,86 This might be justified by a higher contribution of electrostatic interactions in these ILs owing to the presence of the polar ester functional group in the alkyl side chain of the cation. 3.6.7. Isentropic Compressibility Coefficient and Speed of Sound. To calculate the speed of sound (u), first, the isentropic compressibility coefficient (βS) should be computed. Accordingly, in adiabatic processes, βS can be calculated as87 βS = −

CV 1 ⎛ ∂⟨V ⟩ ⎞ ⎜ ⎟ = (⟨V 2⟩ − ⟨V ⟩2 ) ⎝ ⎠ ⟨V ⟩ ∂P S C P⟨V ⟩kBT

⎛ ∂P ⎞ 1 u2 = ⎜ ⎟ = ρβS ⎝ ∂ρ ⎠S

(27)

As can be seen in Figure 10, the computed speed of sound decreases as the alkyl side chain of the cation is lengthened. The maximum values of the speed of sound are ascribed to ILs containing [NO3]−, followed by [Br]−, and the lowest values are attributed to the ester-functionalized ILs containing

(26) 11690


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Figure 10. Investigated values of the isentropic compressibility factor (βS) and speed of sound (u) in the temperature range of 298−550 K.

[Tf2N]−. The same trend was also reported for conventional imidazolium-based ILs but with lower values.17,73,86 The greater packing efficiency of ester-functionalized ILs containing smaller ions is suggested to be responsible for the higher speeds of sound in these ILs. As expected, sound waves are transmitted faster in a compact IL than in a compressible IL. 3.6.8. Mean Static Polarizability, Molar Refraction, Refractive Index, and Dielectric Constant. Molar refraction (Rm) is a function of the volume that is actually regarded as a measure of the hard-core molecular volume, which is nearly independent of the temperature.47,49,51,73,86,89 The free volume (f m) is defined as the difference between the molar volume and the molar refraction (Vm − Rm)73,86 and indicates the packing efficiency of these ILs. The Lorentz−Lorenz relationship is used for estimating Rm as47,49,51,73,86 ⎛ n 2 − 1⎞ N ⎟Vm = A ⟨α⟩ R m = ⎜ D2 3ε0 ⎝ nD + 2 ⎠

The anisotropy demonstrates the deviation from spherical symmetry, in that it equals 0 for a spherically symmetric charge diffusion.90 As stated earlier, variations in temperature have a negligible influence on Rm; therefore, only the results obtained at 298 K are reported in Table 8. As can be seen from Table 8, the molar refractions of these ILs increased as the alkyl chain on the cation was lengthened. With the exception of ILs containing [Br]− and [NO3]−, the refractive indexes of the other ILs were enhanced when their cations became larger. The anion of an IL has a marked effect on the predicted values of ⟨α⟩, Rm, and nD. The observed trends in Rm and nD for the same cations combined with different anions are [Tf2N]− > [TfO]− > [Br]− > [NO3]− > [PF6]− > [BF4]− and [Br]− > [NO3]− > [TfO]− > [Tf2N]− > [BF4]− > [PF6]−, respectively. These orders are close to the previous published results for common imidazolium-based ILs.47,49,73,86,89 These findings can be justified by the fact that larger cations combined with bulkier anions such as [Tf2N]− and [TfO]− are easily distorted by the external electric field of neighbor molecules. Furthermore, the charge distribution of an IL composed of spherical anions such as [PF6]− and [BF4]− is less affected by the electric field of the surrounding ions because of the nonpolar nature of these anions and also the residence of an extensive amount of electronic density on the electronegative fluorine atoms. In addition, because of its deviation from spherical symmetry (according to the anisotropy results from Table 8) has a higher polarizability than [PF6]− and [BF4]− with spherical symmetry, even though [Br]− has a spherical charge distribution whose effective nuclear charge is lower than that of the O and F atoms of [NO3]−, [BF4]−, and [PF6]− anions. Therefore, its electronic cloud is more distorted from a spherical shape than those of [NO3]−, [PF6]−, and [BF4]−. As Table 8 demonstrates, the highest values of the free volume are attributed to the largest cations paired with voluminous anions such as [Tf2N]− and [PF6]−, followed by [TfO]− and [BF4]−. Moreover, ILs containing smaller anions such as [Br]− and [NO3]− have lower values of f m. As a result, ILs composed of the bulkier ions are more compressible than

(28)

where nD is the refractive index, Vm is the molar volume, ε0 is the permittivity of free space, and α is the mean static polarizability of the IL. To calculate Rm, the mean static polarizability was approximated by ab initio calculations at the B3LYP/ 6-311++G(d,p) level of theory using the equation90 ⟨α⟩ =

1 (αxx + αyy + αzz) 3

(29)

where αxx, αyy, and αzz are the principal values of the polarizability tensor. Polarizability determines the dynamical response of a compound to external fields and provides insight into the internal structure of a molecule. Also, the anisotropy (κ) is another structural property that is directly correlated to polarizabilities, defined as90 κ=

αxx 2 + αyy 2 + αzz 2 − 3⟨α⟩2 6⟨α⟩2

(30) 11691


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Table 8. Mean Static Polarizabilities (⟨α⟩), Anisotropies (κ), Molar Refractions (Rm), Refractive Indexes (nD), Dielectric Constants (ε), and Free Volumes ( f m) of Selected ILs Computed by Means of MD Simulations Combined with ab Initio Calculations at Room Temperature (298 K) IL

⟨α⟩ (au)

κ

Rm (cm3 mol−1)

nD

ε (10−12 F m−1)

f m (cm3 mol−1)

1.5544 1.5108 1.3951 1.3757 1.4416 1.4384

21.39 20.21 17.23 16.76 18.40 18.32

108.8 112.0 139.0 157.7 151.5 200.4

1.5431 1.5078 1.4060 1.3859 1.4491 1.4397

21.08 20.13 17.50 17.01 18.59 18.35

122.1 124.1 149.5 168.1 161.1 211.3

1.5337 1.4957 1.4105 1.3961 1.4667 1.4520

20.83 19.81 17.62 17.26 19.05 18.67

145.7 150.0 175.9 192.4 178.1 233.2

+


137.439 128.114 117.326 125.516 145.694 191.039

0.004 0.016 0.006 0.011 0.005 0.001


150.383 140.945 130.233 138.028 157.962 202.180

0.017 0.019 0.010 0.004 0.004 0.001


175.700 165.522 155.190 162.866 182.884 230.492

0.010 0.023 0.014 0.011 0.007 0.007

[C1COOCn=1C1im] Cation 51.375 47.889 43.856 46.918 54.461 71.410 [C1COOCn=2C1im]+ Cation 56.213 52.685 48.681 51.595 59.046 75.575 [C1COOCn=4C1im]+ Cation 65.677 61.872 58.010 60.879 68.362 86.158

order: [Tf2N]− < [TfO]− < [PF6]− < [BF4]− < [NO3]− < [Br]−. It is noted that the electrostatic energies of target ILs containing [Br]−, [NO3]−, [BF4]−, [PF6]−, [TfO]−, and [Tf2N]− ions decreased by roughly 7.3, 7.4, 6.7, 6.9, 5.7, and 3.2 kJ mol−1, respectively, upon addition of a methylene group. Electrostatic interactions are the dominant energies in ILs comprising smaller anions such as [Br]−, [NO3]−, [BF4]−, and [PF6]−, whereas vdW energies determine the arrangements of ions around one another in the other ILs. Interaction energies (Eint) were estimated using the equation29

those composed of smaller ions, which have a higher packing efficiency. This order was previously observed for common imidazolium-based ILs.73,86,89 These findings regarding f m are consistent with the results obtained earlier for βT and kT. Finally, the dielectric constant (ε) can be computed using the Clausius−Mossotti equation89 ⎛ ε − ε0 ⎞ ⎛ ε − 1⎞ N ⎜ ⎟Vm = ⎜ r ⎟Vm = A ⟨α⟩ 3ε0 ⎝ εr + 2 ⎠ ⎝ ε + 2ε0 ⎠

(31)

where ε0 is the permittivity of free space, Vm is the molar volume, εr is the relative dielectric constant of a compound, and α is the mean static polarizability. According to the eqs 28 and 31, the relative dielectric constant is equal to the square of the refractive index. The results predicted for the dielectric constant are listed in Table 8. The dielectric constants follow the same trend as nD. 3.7. vdW, Electrostatic, and Interaction Energies. The values of the vdW (EvdW) and electrostatic (Eelect) energies of selected ILs are summarized in Tables 9 and 10, respectively. As expected, the vdW energy is directly related to the number of atoms in a molecule. For a given cation, the vdW energies of thes ILs decreased in the order [Tf2N]− > [TfO]− > [NO3]− ≥ [PF6]− > [BF4]− > [Br]−. Even though [NO3]− has more atoms than [PF6]− and [BF4]−, the stronger dispersive interactions of O atoms (well depth ε ≈ 0.8) compared to F atoms (well depth ε ≈ 0.3) are believed to be responsible for this observation. It was found that the vdW values of the target ILs paired with [Br]−, [NO3]−, [BF4]−, [PF6]−, [TfO]−, and [Tf2N]− increased by nearly 5.2, 3.7, 5.9, 6.1, 5.4, and 5.5 kJ mol−1, respectively, per CH2− group. Large electrostatic contributions characterize ILs composed of smaller ions, which have localized negative charges and lower steric hindrances. Therefore, the cations and anions of these ILs can interact strongly with each other. For a given cation, the electrostatic energy was found to increase in the following

E int = EvdW + Eelect

(32)

A linear decreasing trend of the interaction energies was found with increasing temperature. For a given cation, the structural dependence of the interaction energies of the selected ILs was as follows: [NO3]− ≥ [Br]− > [BF4]− > [PF6]− > [TfO]− > [Tf2N]−. This trend is similar to the observed order for cohesive energy density, surface tension, surface excess enthalpies, lattice energy, thermal pressure, internal pressure, and electrostatic interaction. Numerical values of the calculated interaction energies are collected in Table S21 of the Supporting Information. 3.8. Ab Initio Calculations. To determine the most stable conformers of selected cations, the torsion energy profile of the C5NC6C7 dihedral was obtained by the ab initio method at the B3LYP/6-311++G(d,p) level of theory with a step size of 5°. It can be easily seen in Figure 11 that the global minima of energy are centered at 50° and 310°, which implies strong intramolecular hydrogen bonding between the O8 and H2 sites. Moreover, a local minimum occurs at 0° and 360° that can be related to direct O8H2 intramolecular hydrogen bonding. In addition, the maximum of the energy profile is located at 180°, where O8 forms a direct hydrogen bond with the H5 site. The energy barrier of the C5NC6C7 dihedral barely increased when the length of the alkyl side chain of the cation was increased. 11692


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Table 9. vdW Energies (EvdW, kJ mol−1) of Selected ILs as Functions of Temperature Simulated by Means of MD Simulations T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550

[C1COOC1C1im][Br] −50.4 −49.5 −48.7 −47.8 −46.8 −44.9 −42.7 −40.0

± ± ± ± ± ± ± ±

1.1 1.1 1.2 1.2 1.2 1.3 1.4 1.5

[C1COOC2C1im][Br] −57.1 −55.9 −54.6 −53.5 −52.8 −49.9 −46.5 −43.7

± ± ± ± ± ± ± ±

0.8 0.8 0.9 0.9 1.0 1.1 1.1 1.2

[C1COOC4C1im][Br] −67.2 −65.7 −64.0 −62.6 −60.6 −57.2 −53.0 −49.3

± ± ± ± ± ± ± ±

0.7 0.7 0.8 0.8 0.9 1.0 1.1 1.2

[C1COOC1C1im][NO3] [C1COOC1C1im][BF4] [C1COOC1C1im][PF6] −78.4 −77.1 −75.7 −74.1 −72.2 −69.5 −65.8 −62.2

± ± ± ± ± ± ± ±

1.1 1.2 1.2 1.3 1.3 1.4 1.5 1.6

−65.9 −64.5 −63.0 −61.5 −59.8 −56.8 −53.4 −50.1

± ± ± ± ± ± ± ±

−74.4 −72.8 −71.4 −70.0 −68.4 −65.3 −61.6 −58.0

1.1 1.2 1.2 1.3 1.3 1.4 1.5 1.6

1.2 1.3 1.3 1.4 1.4 1.6 1.6 1.7


± ± ± ± ± ± ± ±

0.9 0.9 1.0 1.0 1.1 1.2 1.2 1.3

−73.9 −72.3 −70.2 −68.4 −66.1 −61.7 −57.8 −53.8

± ± ± ± ± ± ± ±

−82.9 −81.4 −79.2 −77.1 −74.7 −70.5 −66.1 −61.6

0.9 0.9 0.9 1.0 1.1 1.1 1.2 1.3

± ± ± ± ± ± ± ±

0.8 0.9 1.0 0.9 1.0 1.1 1.2 1.3


± ± ± ± ± ± ± ±

0.8 0.8 0.9 0.9 1.1 1.1 1.2 1.3

−82.5 −80.5 −78.2 −75.6 −73.6 −68.6 −63.6 −59.1

± ± ± ± ± ± ± ±

−92.9 −90.5 −88.0 −85.2 −82.0 −77.2 −71.9 −67.0

0.8 0.8 0.9 1.0 1.0 1.1 1.1 1.2

E int = E(B3LYP)CP IP − [E(B3LYP)cat + E(B3LYP)ani ] + Δ(ZPVE) + Δ(TE)

± ± ± ± ± ± ± ±

0.8 0.8 0.9 0.9 1.0 1.0 1.2 1.3

[C1COOC1C1im][TfO] [C1COOC1C1im][Tf2N] −97.6 −95.8 −94.1 −92.4 −90.2 −85.8 −81.3 −77.0

± ± ± ± ± ± ± ±

1.2 1.3 1.4 1.4 1.5 1.6 1.7 1.8

−127.1 −124.9 −122.6 −119.8 −116.6 −110.7 −104.7 −98.8

± ± ± ± ± ± ± ±

1.4 1.5 1.6 1.6 1.7 1.8 1.9 2.1


± ± ± ± ± ± ± ±

0.9 0.9 1.1 1.1 1.1 1.2 1.3 1.4

−135.9 −132.9 −129.1 −125.8 −122.3 −114.7 −107.9 −101.0

± ± ± ± ± ± ± ±

1.2 1.2 1.2 1.4 1.4 1.5 1.6 1.7


± ± ± ± ± ± ± ±

0.9 0.9 1.0 1.0 1.1 1.2 1.3 1.3

−145.8 −142.0 −137.6 −134.8 −130.1 −121.9 −114.3 −107.2

± ± ± ± ± ± ± ±

1.0 1.1 1.1 1.2 1.3 1.4 1.5 1.6

that the anion can have strong interactions with H2, H6, and H10 concurrently. In these configurations, O8H5 intramolecular hydrogen bonding is preferred. Another stable conformation has the anion located at the bottom of the cation (Conf. 2 in Figure 14), where an anion strongly interacts with H5 and H6 at the same time. Subsequently, intramolecular hydrogen bonding is mainly happened between O8H2. It is worth nothing that intramolecular hydrogen bonding between O8H11 can be easily seen for the all examined conformations (Figure 12, Figure 13, and Figures S1−S18 of the Supporting Information). Interestingly, with locating an anion at the bottom conformations (Conf. 2, Conf. 3, and Conf. Four of Figure 14), O8H2 sites intramolecular hydrogen bonding is formed at nearly 2.5 Å, which is in excellent agreement with the matching bond of isolated cation averagely achieved by torsion energy profile at the absolute minimum (Figures S1−S18 of the Supporting Information). Furthermore, in the most stable configuration of [C1COOC4C1im] ILs, butyl side chain of cation is efficiently wrapped to formation of the hydrogen bonding with anion via their hydrogen (H11, H12, H13, and H14). Likewise, Figure S19 (Supporting Information) represents the optimized structures of isolated ion pairs achieved from gas-phase simulations at 298 K, which are in good agreement with those yielded from the ab initio method with slight discrepancies. Notably, wrapping of the butyl linkage of cation and biased interactions of anion-H6 do not observed in MD optimized geometries. Moreover, moving of the [Tf2N] anion to out of ring-plane of associated cation is another partial difference of ab initio and MD optimized conformations. These slight discrepancies can be caused from applying the different approaches in MD method and ab initio calculations.

Further information on the estimated thermodynamic properties was obtained by optimizing the geometries of isolated ion pairs and determining their interaction and binding energies at the B3LYP/6-311++G(d,p) theoretical level (Figures 12 and 13). The interaction energies of selected ILs were computed as91

(33)

where E(B3LYP) is the electronic energy; ZPVE is the zeropoint vibrational energy; and TE is the thermal energy, which can be directly obtained from the frequency calculations. The basis-set superposition errors (BSSEs)92 were removed by use of the counterpoise (CP) method.93 The binding energies were calculated according to the equation94 E bin = E(B3LYP)CP IP − [E(B3LYP)cat + E(B3LYP)ani ] + Δ(ZPVE)

± ± ± ± ± ± ± ±

(34)

The optimized geometries of the individual ions were used as the starting points for optimizing the isolated ion pairs. Figure 14 shows four possible locations of the anion around the cation that were weighed to determine the lowest-energy configurations. The optimized structures were verified to be minima by means of frequency calculations. As can be seen in Figures 12 and 13, incorporating the ester functional group into the alkyl side chain enhanced the acidity strength of the H6 site compared to that of the corresponding site in common imidazolium-based ILs. Therefore, in the most stable conformations, anions are located at the top of the cation biased toward the acidic hydrogen H6 site (Conf. 1 in Figure 14), so 11693


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Table 10. Electrostatic Energies (Eelect, kJ mol−1) of Selected ILs at Target Temperatures Calculated by Means of MD Simulations T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550 T (K) 298 325 350 375 400 450 500 550

[C1COOC1C1im][Br] −433.2 −431.9 −430.9 −429.6 −428.3 −425.1 −421.2 −417.1

± ± ± ± ± ± ± ±

0.6 0.6 0.7 0.7 0.8 0.9 1.0 1.1

[C1COOC2C1im][Br] −427.1 −425.4 −424.2 −422.9 −420.9 −417.3 −413.2 −408.7

± ± ± ± ± ± ± ±

0.7 0.7 0.7 0.8 0.8 0.9 1.1 1.1

[C1COOC4C1im][Br] −409.2 −407.6 −406.1 −404.6 −403.3 −399.4 −394.6 −390.1

± ± ± ± ± ± ± ±

0.7 0.8 0.8 0.9 0.9 1.0 1.1 1.3


± ± ± ± ± ± ± ±

0.6 0.7 0.7 0.8 0.8 0.9 1.0 1.1

−383.0 −381.3 −379.8 −378.1 −376.1 −372.5 −368.1 −363.7

± ± ± ± ± ± ± ±

0.6 0.7 0.7 0.7 0.8 0.9 1.0 1.0

−357.4 −356.1 −354.6 −353.3 −351.9 −348.7 −344.2 −339.9

± ± ± ± ± ± ± ±

0.6 0.7 0.7 0.8 0.8 0.9 1.0 1.1


± ± ± ± ± ± ± ±

0.7 0.7 0.7 0.8 0.9 1.0 1.1 1.1

−376.4 −375.0 −373.1 −371.7 −369.4 −365.3 −361.0 −356.9

± ± ± ± ± ± ± ±

0.6 0.7 0.7 0.8 0.8 0.9 1.0 1.1

−350.7 −349.1 −347.8 −346.4 −344.5 −341.0 −336.7 −332.8

± ± ± ± ± ± ± ±

0.6 0.6 0.7 0.7 0.8 0.8 0.9 1.0


± ± ± ± ± ± ± ±

0.8 0.8 0.9 0.9 1.0 1.1 1.2 1.3

−358.7 −356.9 −354.1 −353.1 −350.3 −346.3 −341.7 −337.5

± ± ± ± ± ± ± ±

0.7 0.7 0.9 0.9 0.9 1.0 1.1 1.2

−332.3 −330.8 −329.4 −328.0 −325.9 −322.2 −318.4 −314.2

± ± ± ± ± ± ± ±

0.6 0.7 0.7 0.8 0.8 0.9 1.0 1.1


± ± ± ± ± ± ± ±

0.7 0.8 0.8 0.9 1.0 1.0 1.1 1.2

−123.0 −122.2 −119.8 −118.0 −116.2 −111.4 −106.1 −101.6

± ± ± ± ± ± ± ±

0.9 1.1 1.1 1.1 1.3 1.3 1.4 1.5


± ± ± ± ± ± ± ±

0.7 0.7 0.8 0.9 0.9 1.0 1.0 1.1

−120.5 −117.7 −116.2 −113.3 −111.2 −106.4 −101.9 −97.7

± ± ± ± ± ± ± ±

1.0 1.0 1.1 1.2 1.3 1.3 1.4 1.5


± ± ± ± ± ± ± ±

0.7 0.8 0.9 0.9 1.0 1.1 1.2 1.3

−101.6 −99.9 −98.5 −96.4 −94.1 −89.8 −85.6 −80.9

± ± ± ± ± ± ± ±

1.0 1.1 1.1 1.2 1.2 1.3 1.4 1.6

Figure 11. Torsion energy profiles for the C5NC6C7 dihedral angles of selected cations computed using the ab initio method at the B3LYP/ 6-311++G(d,p) theoretical level. The hydrogen bonds are indicated by dotted lines, and average distances are in angstroms.

It can be understood from the ab initio results that lengthening of the alkyl side chain does not significantly affect the interaction and binding energies of the selected ILs, which

was previously verified by the MD results. Excluding the ILs containing [TfO]−, the interaction and binding energies obtained from the ab initio calculations are in excellent 11694


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Figure 12. Most stable conformations of ILs paired with [Cl]−, [NO3]−, and [BF4]− anions calculated at the B3LYP/6-311++G(d,p) level of theory. The hydrogen bonds are shown by dotted lines, and distances are in angstroms. The interaction energy (in kJ mol−1) of each isolated ion pair corrected by the counterpoise method is written under each configuration.

be attributed to the smallest cation combines with the smaller anions, especially [NO3]− and [Br]−. Furthermore, ion-pair, cationic, and anionic volumes were estimated using both MD simulations and ab initio calculations. The ab initio findings for these volumetric properties follow nearly the same trend as the results obtained by the MD simulations with a significant underestimation. According to the simulation results, the mean contribution to the molecular and cationic volumes per methylene (CH2−) group was predicted to be 0.026 nm3, which is comparable to the values reported for common imidazolium-based ILs. The estimated value 0.015 nm3 can be regarded as the mean contribution to the cationic volume of one CH2− group from ab initio calculations. The simulated results revealed a decreasing trend in the molar enthalpy of vaporization with increasing temperature. This might be related to the elimination of the interionic interactions in the liquid phase. Interestingly, lengthening of the alkyl chain of the cation leads to the opposite effect. This finding can be rationalized by the marked enhancement of the dispersive interactions in the condensed phase. In general, the enthalpies of vaporization computed for ester-functionalized ILs are distinctly larger than those reported for common imidazolium-based ILs. The reverse trends of the volumetric properties (with the exception of density) were observed for cohesive energy density, Hildebrand solubility parameter, surface tension, surface excess enthalpies, lattice energy, thermal pressure, internal pressure,

agreement with the results for the matching property determined from the MD simulations. This might be due to the higher steric hindrance of [TfO]− in the liquid state, that is not observed in the gas phase. Figure 15 compares the interaction energies predicted by both MD simulations and the ab initio method. With the exception of ILs containing [TfO]− and [Tf2N]−, the interaction energies estimated from MD simulation are greater than those obtained from the ab initio calculations. Finally, the ab initio and MD results show that the ester functional group plays a significant role in the arrangement of anions around their cations.

4. SUMMARY AND CONCLUSIONS Systematic molecular dynamics simulations and ab initio calculations on the various thermodynamic properties of esterfunctionalized imidazolium-based ionic liquids (ILs) containing [C1COOCn=1,2,4C1im]+ cations associated with [Br]−, [NO3]−, [BF4]−, [PF6]−, [TfO]−, and [Tf2N]− anions were carried out in the temperature range of 298−550 K. Volumetric properties such as density, molar volume, isobaric expansion coefficient, and isothermal compressibility coefficient were computed at the desired temperatures. Excluding the simulated density, the highest value of the volumetric properties can be attributed to the largest cation incorporating the weakest coordinating anion [Tf2N]−, and the minimum of the corresponding properties can 11695


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Figure 13. Most stable conformations of ILs paired with [PF6]−, [TfO]−, and [Tf2N]− anions, calculated at the B3LYP/6-311++G(d,p) level of theory. The hydrogen bonds are shown by dotted lines, and distances are in angstroms. The interaction energy (in kJ mol−1) of each isolated ion pair corrected by the counterpoise method is written under each configuration.

Figure 14. Four possible locations of the anion around the cation.

binding energy, and interaction energies. The findings obtained for these properties revealed that the maximum values of cation−anion association are attributed to the smallest cation combined with [Br]− and [NO3]− and the minimum values of interionic interactions are ascribed to the bulkiest cation paired with weakly coordinating anions such as [Tf2N]−. The reduction in the strength of the hydrogen bonding due to the greater charge distribution and steric hindrance of bulkier ions is believed to be responsible for the observed trends. These results

Figure 15. Predicted values of the vdW, electrostatic, binding, and interaction energies of selected ILs from MD simulations and ab initio calculations at room temperature. 11696


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Industrial & Engineering Chemistry Research were also confirmed by calculating the critical and boiling temperatures, surface excess entropy, parachor, and standard molar entropy. The ionic parachor contributions were computed by means of MD simulations and ab initio calculations. The ionic parachor contributions estimated from the MD simulations correlate well with the results obtained from the ab initio calculations. The results obtained demonstrate that cations have higher parachor contributions than anions. The other derivatives of the thermodynamic properties such as isobaric and isochoric heat capacities, isothermal bulk modulus, and speed of sound were also computed as functions of temperature. The highest values of the heat capacities are related to the ILs containing voluminous ions. Interestingly, CP − CV values for the ester-functionalized ILs composed of larger ions approached the ideal value (8.314 J mol−1 K−1) more rapidly than ILs with smaller ions. This might be due to the stronger electrostatic interactions between smaller ions resulting from their localized charges and lower steric hindrance. Surprisingly, a direct relationship was found between the simulated results for surface tension and the computed values of isothermal bulk modulus. As expected, in a compact IL, sound waves are transmitted more rapidly than a compressible IL. To estimate the molar refraction, refractive index, free volume, and dielectric constant of selected ILs, the mean static polarizability was approximated by the ab initio method. The maximum values of molar refraction were found to be associated with the bulkiest cations combined with voluminous anions, including [Tf2N]− and [TfO]−, and the lowest values of the corresponding properties are ascribed to the smallest cations paired with spherically symmetric anions such as [PF6]− and [BF4]−. This can be justified by the residence of an extensive amount of the electronic density on the electronegative fluorine atoms. A trend similar to that for the refractive index holds for the dielectric constant. The highest values of the free volume were found for the ILs composed of the largest ions. As a result, the ILs composed of bulkier ions are more compressible than those comprising smaller ions, which have a higher packing efficiency. This finding is in excellent agreement with the results obtained for the volumetric properties. The optimized structures of isolated ion pairs indicated that the anions are located at the top of the cation biased toward the acidic hydrogen of alkyl side chain, which is positioned between the imidazolium ring and the ester functional group. Interestingly, intramolecular hydrogen bonding between the O atoms of the ester group and the H atoms of the imidazolium ring and alkyl side chain was easily observed in all examined conformations. It can be comprehended from the ab initio results that lengthening of the alkyl side chain does not markedly affect the interaction and binding energies of selected ILs, as was previously verified by the MD results. In summary, the introduction of an ester functional group into the alkyl side chain of a cation increases the interionic interactions and consequently improves the packing efficiency of these ILs in comparison with conventional imidazoliumbased ILs.

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Force field parameters for [C1COOCnC1im] cations (Tables S1−S4); numerical values of the thermodynamic properties such as molar volume (Table S5), molecular volume (Table S6), molar enthalpy of vaporization (Table S7), cohesive energy density (Table S8), Hildebrand solubility parameter (Table S9), surface tension (Table S10), surface enthalpy (Table S11), parachor (Table S12), lattice energy (Table 13), isothermal bulk modulus (Table S14), difference between heat capacity (Table S15), isochoric heat capacity (Table S16), thermal pressure coefficient (Table S17), internal pressure (Table S18), isentropic compressibility coefficient (Table S19), speed of sound (Table S20), and interaction energy (Table S21) as functions of temperature; and optimized conformers of isolated ion pairs (Figures S1−S19) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +98 216 616 5314. Fax: +98 216 600 5718. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Our special thanks go to the Department of Chemistry and High Performance Computing Centre (HPCC) of Sharif University of Technology for generously supplying the computer facilities.

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REFERENCES

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b03199. 11697


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