Estimates of Internal Pressure and Molar Refraction of Imidazolium Based Ionic Liquids as a Function...

8/11/2019 Estimates of Internal Pressure and Molar Refraction of Imidazolium Based Ionic Liquids as a Function of Temperature

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J Solution Chem (2008) 37: 203214

DOI 10.1007/s10953-007-9231-5

Estimates of Internal Pressure and Molar Refraction

of Imidazolium Based Ionic Liquids as a Functionof Temperature

Arvind Kumar

Received: 24 May 2007 / Accepted: 29 June 2007 / Published online: 13 December 2007

Springer Science+Business Media, LLC 2007

Abstract Estimates of the internal pressure (U/V )T of the ionic liquids (ILs)

1-butyl-3-methylimidazolium tetrafluoroborate [BMIM][BF4], 1-butyl-3-methylimidazo-

lium hexafluorophosphate [BMIM][PF6], and 1-methyl-3-octylimidazolium tetrafluoro-

borate [OMIM][BF4] were made from experimentally determined densities and speeds of

sound in the temperature range 283.15 to 343.15 K. Values (U/V )Tfor all the ILs stud-

ied are higher than those of water and molecular organic liquids. We also measured the

refractive indices nD in the temperature range 288.15 to 343.15 K and estimated the mo-

lar refraction RM. Refractive indices of ILs were also higher than those of normal organic

liquids but were comparable to those of long hydrocarbon chain organic solvents.

Keywords Ionic liquids Density Speed of sound Refractive index Internal pressure

1 Introduction

Ionic liquids (ILs) [1] are attracting great interest as greener alternatives to conventional

organic solvents because of their wide thermal liquid range and low vapor pressures [2]. ILshave been used as effective solvent media for catalyzing many organic reactions, with their

better kinetics and selectivity [3]. The catalyzing effect of solvent media can be adjudged by

several parameters, such as hydrogen-bonding, solvent polarity, hydrophobic aggregation,

etc. The internal pressure (U/V )T in a liquid, caused by cohesive forces, can be used as

an alternative explanation for describing kinetic rate enhancements in solvent media [47].

To date, the biggest developments in Diels-Alder chemistry have come through reactions

in Li[ClO4] + Et2O, where the high electrolyte concentrations are cited as being benefi-

cial through the high internal pressure of the solvent. It is clear from the cited studies

that extending this concept through to the use of ionic liquid solvents will lead to further

A. Kumar ()

Central Salt and Marine Chemicals Research Institute, Bhavnagar 364002, India

e-mail: [email protected]

A. Kumar

e-mail: [email protected]


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204 J Solution Chem (2008) 37: 203214

extensions in the scope of various organic reactions and eliminate the need for potentially

explosive reaction media.

A liquid undergoing a small, isothermal volume expansion does work against the cohe-

sive forces causing a change in the internal energy, U. The function(U/V )Tis known as

the internal pressure,pi. Hildebrand [8,9] showed thatU /V= nUvap/V, whereUvaprepre-sents the energy of vaporization of the liquid andVis its molar volume. Due to the very low

vapor pressures of ILs, measurement of the enthalpy of vaporization is not convenient under

ambient conditions and thus direct measurements of(U/V )Tand the cohesive energy are

difficult. So far, only a few studies [1013] have been done where cohesive energies or vapor

pressure of room temperature ionic liquids were measured directly, or have been estimated

from the experimental results.

The quantity (U/V )T can alternatively be obtained by using the so-called thermo-

dynamic equation of state, T (p/T )Vp. In liquids, the thermal pressure coefficient

(p/T )V multiplied by the absolute temperature has values of many thousands of at-

mospheres, so that the contribution from atmospheric pressure, p, becomes negligible bycomparison. Measurement of(U/V )Tis thereby reduced to the measurement of the ther-

mal pressure coefficient. The thermal pressure coefficient can be equated to /T, where

is the coefficient of thermal expansion andTis the isothermal compressibility. The quanti-

ties andTcan be estimated using accurate measurements of density and speed of sound

values at constant temperatures.

In this work we studied the isothermal expansion coefficient , isothermal compression

coefficient T, and estimated internal pressure (U/V )Tof imidazolium based ionic liq-

uids. Besides measuring densities and speeds of sound, we also measured the refractive

index nD and estimated the molar refraction RM over a temperature range. The natures of

the anion, cation and side-chain length of the cation change the physical properties of ionicliquids significantly. Thus, we selected three ILs based on combinations of a common cation

with different anions and a common anion with cations having different alkyl chains.

2 Experimental Section

2.1 Materials

The air- and moisture-stable ILs, 1-butyl-3-methylimidazolium tetrafluoroborate [BMIM]

[BF4], 1-butyl-3-methylimidazolium hexafluorophosphate [BMIM][PF6], and 1-methyl-3-

octylimidazolium tetrafluoroborate [OMIM][BF4], with stated purities >98% mass fraction,

were purchased from Merck. Since the trace amounts of water in ILs can have a dramatic

effect on their physical properties [14, 15], all of the ILs were dried and degassed under

vacuum at 60 C for several days to remove water. Karl-Fisher analysis of the dried samples

indicated that the water content in each liquid was reduced to


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J Solution Chem (2008) 37: 203214 205

Table 1 Comparison of densities (), speeds of sound (u), and refractive indices (nD) for different ILs at

298.15 K with literature values

Compound (Ref.) u u(Ref.) nD nD (Ref.)

(gcm3) (gcm3) (ms1) (ms1)

[BMIM][BF4] 1.2141 1.204362 [17] 1565.1 1564 8 [22] 1.4197 1.410 [23]

1.21119 [18] (296.85 K)

[BMIM][PF6] 1.3679 1.366657 [24] 1442.2 1442.41 [24] 1.4089 1.409 [28]

1.36612 [25] 1441 4 [22]

1.36730 [26] (296.85 K)

1.36543 [18]

[OMIM][BF4] 1.1030 1.10368 [29] 1482.2 1491 [30] 1.4319 1.43422 [30]

1.10530 [30]

sound in water as a reference, and the error was estimated to be less than 0.1 ms1 [31].

Measurements were carried out in a specially designed low-volume sample jar. This sample

jar was provided with an air-tight Teflon covering to keep the samples moisture free dur-

ing measurements. Dried and degassed samples kept in desiccators were directly injected

through a syringe into the sample jar, avoiding contact with atmospheric air. To check the

reproducibility of the results, not less than three experiments were performed for each sam-

ple over the whole temperature range. At each temperature the sample was equilibrated for

about 30 minutes.

2.3 Density Measurements

The densities of the liquids were measured with an Anton Paar (Model DMA 4500)

vibrating-tube densimeter with a resolution of 5 105 gcm3. The temperature of the

apparatus was controlled to within 0.03 K by a built-in Peltier device. The densimeter was

calibrated with doubly distilled and degassed water, with dry air at atmospheric pressure,

and also against the densities of NaCl(aq) [32].

2.4 Refractive Index Measurements

Refractive indices were measured using a Mettler-Toledo (Model RE-40 D) refractometer

with a high-resolution optical sensor. Measurements were made with a resolution and error

limit of1 104. The temperature of the apparatus was controlled to within 0.1 K by a

built-in Peltier device. Dried and degassed samples kept in desiccators were directly injected

through a syringe into the measuring cell. The reproducibility of the results was determined

by performing at least three experiments for each sample over the whole temperature range.

3 Results and Discussion

3.1 Density and Speed of Sound

Experimental values of the densities, speeds of sound and other derived properties for vari-

ous ILs:, s, T and(U/V )Tas a function of temperature, are reported in Table2. The


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Table 2 Experimental densities (), speeds of sound (u), and estimated values of ,s,T and(U/V )Tof different ILs in the temperature range 283.15 to 343.15 K

T/K u 104 1012 s 1012 T (U/V )T

(gcm3) (ms1) (K1) (Pa1) (Pa1) (atm.)

[BMIM][BF4]

283.15 1.2252 1604.5 6.04 317.04 371.87 4539

288.15 1.2215 1591.1 6.05 323.38 379.23 4533

293.15 1.2179 1578.0 6.06 329.78 386.84 4532

298.15 1.2141 1565.1 6.05 336.23 394.03 4518

303.15 1.2105 1552.6 6.03 342.73 401.08 4498

308.15 1.2068 1540.3 6.01 349.28 408.15 4478

313.15 1.2032 1528.3 5.98 355.85 415.05 4453

318.15 1.1996 1516.5 5.94 362.46 421.76 4422

323.15 1.1960 1505.1 5.93 369.09 429.08 4408328.15 1.1925 1493.9 5.91 375.75 436.21 4388

333.15 1.1890 1483.0 5.90 382.42 443.56 4373

338.15 1.1855 1472.0 5.89 389.10 450.90 4359

343.15 1.1820 1462.1 5.87 395.79 458.04 4340

[BMIM][PF6]

283.15 1.3807 1479.8 6.13 330.74 386.46 4433

288.15 1.3764 1467.3 6.18 337.45 395.04 4449

293.15 1.3721 1454.8 6.20 344.36 403.29 4448

298.15 1.3679 1442.2 6.22 351.47 411.75 4446

303.15 1.3636 1429.7 6.25 358.78 420.22 4436

308.15 1.3593 1417.2 6.24 366.30 428.92 4424

313.15 1.3551 1404.6 6.22 374.03 437.22 4397

318.15 1.3509 1392.1 6.19 381.99 445.53 4362

323.15 1.3467 1379.6 6.17 390.17 454.25 4332

328.15 1.3425 1367.0 6.16 398.58 463.40 4305

333.15 1.3384 1354.5 6.14 407.25 472.59 4272

338.15 1.3343 1342.0 6.14 416.17 482.45 4247

343.15 1.3302 1329.4 6.15 425.37 492.81 4226

[OMIM][BF4]

283.15 1.1134 1522.5a 6.21 389.51 442.74 3972

288.15 1.1099 1509.5a 6.22 397.52 451.75 3967

293.15 1.1064 1495.6 6.23 405.77 461.41 3958

298.15 1.1030 1482.2 6.24 414.06 471.01 3944

303.15 1.0995 1468.7 6.26 422.96 481.15 3928

308.15 1.0961 1454.4 6.27 431.94 491.86 3903

313.15 1.0926 1441.3 6.25 441.18 501.50 3880

318.15 1.0892 1428.3 6.24 450.68 511.60 3853

323.15 1.0858 1414.2 6.23 460.47 522.62 3827

328.15 1.0824 1401.2 6.22 470.54 533.28 3797

333.15 1.0791 1388.2 6.20 480.90 544.02 3797

338.15 1.0757 1375.1 6.19 491.61 555.31 3769

343.15 1.0724 1361.1 6.18 502.62 567.62 3736

aExtrapolated values to linear fits of experimental measurements


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Table 3 Correlations for the densities (), speeds of sound (u), and refractive indices (nD)of different ILs

as a function of temperature between 283.15 and 343.15 K

Compound /gcm3 s.d.

[BMIM][BF4] 1.429 0.0007 (T/K) 0.0002

[BMIM][PF6] 1.619 0.0008 (T/K) 0.0001

[OMIM][BF4] 1.307 0.0007 (T/K) 0.0001

u/m s1

[BMIM][BF4] 2771.41 5.56 (T/K)+ 0.005 (T/K)2 0.18

[BMIM][PF6] 2189.52 2.51 (T/K) 0.01

[OMIM][BF4] 2283.99 2.69 (T/K) 0.47

nD

[BMIM][BF4] 1.569 0.0007 (T/K) 0.0004

[BMIM][PF6] 1.606 0.001 (T/K) 0.0005

[OMIM][BF4] 1.654 0.001 (T/K) 0.0003

temperature dependences of density, speed of sound and refractive index were correlated by

means of a polynomial-type equation:

F(Q) =

ni=1

Ai Ti1 (1)

where Q represents a measured property (density, speed of sound or refractive index) and

T represents the temperature. Correlation parameters of the density and speed of sound

as a function of temperature, along with their standard deviations, are given in Table 3.

Densities of various ILs as a function of temperature, along with corresponding literature

values, are compared in Fig. 1. Our density measurements are quite compatible with the

available literature data and the maximum deviations are in the range from 1 to 0.5%,

which can be attributed to the presence of different amounts of water and halide impu-

rities in the ILs used by various authors, and also from the different experimental tech-

niques. The densities decrease linearly with increasing temperature for all the liquids inves-

tigated.Because the temperature dependence of density is linear for the ILs, density val-

ues as a function of temperature were used to calculate the isothermal expansion co-

efficient (reported in Table 2). Estimates of made from experimental densities in-

dicate that the ionic liquids do not expand appreciably between 283.15 and 343.15 K.

All of the investigated ionic liquids show weak temperature dependences for the isother-

mal expansion coefficient, = (5.8 to 6.3 104) K1, which are considerably smaller

than those for molecular organic liquids, but are higher than those of high-temperature

molten salts. ILs with a shorter alkyl chain show less expansion when compared with

an IL having the same anion but with a longer alkyl chain on the cation. The ef-

fect from coiling of the chain may be the reason for the larger expansion coeffi-

cient of the ILs with long alkyl chains. Similarly, the IL with [PF6] as the anion

has a larger expansion coefficient when compared with ILs having [BF4] as the an-

ion.

Speeds of sound, shown in Fig. 2, decrease linearly with increasing temperature for the

investigated liquids. From the measured speeds of sound, isothermal compressibilities were


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Fig. 1 Comparison of measured densities with literature values. [BMIM][BF4]: Q this work; [18]; [21];

[19]; [20]. [BMIM][PF6]: this work; [18]; [27]; + [26]; [19]. [OMIM][BF4]: " this work

Fig. 2 Speeds of sound as a function of temperature: Q [BMIM][BF4]; [BMIM][PF6]; and

" [OMIM][BF4]


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J Solution Chem (2008) 37: 203214 209

estimated using the relation,

T= s + (2T VM)/Cp (2)

where s = 1/u2is the isentropic compressibility, is the coefficient of thermal expansion,

T is temperature,VM is the molar volume and Cp is the heat capacity (heat capacity valuesfor various ionic liquids were taken from [21,33]). The isothermal compressibility increases

linearly with increasing temperature for all of the liquids. ILs studied here are less compress-

ible than organic liquids, as expected due to the strong Coulombic interactions between the

ions. A comparison ofTvalues reveals that an ionic liquid with a larger molar volume is

more compressible. Differences between the compressibilities of ILs with a common cation

and different anions are small due to their comparable sizes, whereas an IL with a longer

cation alkyl chain is more compressible compared with an IL having a small alkyl chain and

the same anion. This may be due to a larger free volume resulting from the large cation-

anion volume ratio in the larger IL. Similar observations were made by Tekin et al. [18]

and Brennecke et al. [28], where isothermal compressibilities of ILs were estimated fromdensity measurements at different pressures.

Estimates of the internal pressure(U/V )Twere made using the calculated and Tvalues, using the relation

(U/V )T= T/T (3)

where all the symbols have their usual meaning. Although the errors in the individual proper-

ties are compounded when their ratio is calculated, the values obtained are extremely useful

because a direct measurement of ( P / T )Vcan not be readily made at or near room tem-

peratures. The overall uncertainties in the derived values are


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investigated liquids are higher than those of water and molecular organic liquids. This may

be due to the higher contribution from electrostatic interactions in the ILs. However, the ILs

have lower (U/V )Tvalues when compared to classical molten salts [34]. This is due to

the fact that in the molten salts, there are purely electrostatic interactions, whereas in the

case of ILs other kinds of molecular interactions such as hydrogen bonding, etc., are alsopresent. The internal pressure decreases with an increase in temperature for all the ILs. This

decrease in(U/V )T is slow at lower temperatures but is more prominent at higher tem-

peratures for all the ILs. Despite the narrow range of structural variation studied, we observe

that (U/V )Tvalues are higher in ILs with a smaller alkyl chain at a given temperature.

For ILs with the same cation, higher values of(U/V )Twere observed for an IL with the

[BF4] anion compared to [PF6] anion at a certain temperature.

The internal pressure can be equated with the cohesive energy density by the relation

(U/V )T= nUvap/V. A comparison of our estimated internal pressures and cohesive

energy densities with those estimated by Swiderski and coworkers [10] yields n = 0.459

and 0.494 at 298.15 K for [BMIM][BF4] and [BMIM][PF6], respectively. Due to the lack ofavailability of cohesive energy data, we could not estimate the value ofn for [OMIM][BF4].

The comparatively lower value of n indicates that the ILs investigated in this paper are

moderately polar.

3.2 Refractive Indices

The experimental temperature dependences of refractive indices nD for different ILs are

presented in Table4and are shown in Fig.4. Correlation coefficients ofR1with temperature

are given in Table3. The refractive indices of the studied ionic liquids lie in the range 1.41

to 1.44 near room temperature. Such values are comparable to those for typical long-chain

Fig. 4 Refractive index as a function of temperature: Q [BMIM][BF4]; [BMIM][PF6]; and

" [OMIM][BF4]


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Table 4 Experimental values of the refractive indices (nD), and estimated values of molar refraction (RM),

of ILs at different temperatures

T/K nD RM/(g cm3)

[BMIM][BF4]

288.15 1.4234 47.16

293.15 1.4214 47.11

298.15 1.4197 47.08

303.15 1.4181 47.07

308.15 1.4166 47.06

313.15 1.4155 47.09

318.15 1.4142 47.10

323.15 1.4132 47.14328.15 1.4120 47.16

333.15 1.4109 47.19

338.15 1.4098 47.22

343.15 1.4087 47.25

[BMIM][PF6]

288.15 1.4133 51.52

293.15 1.4110 51.42

298.15 1.4089 51.35

303.15 1.4073 51.34

308.15 1.4057 51.32

313.15 1.4046 51.36

318.15 1.4036 51.40

323.15 1.4025 51.44

328.15 1.4015 51.49

333.15 1.4004 51.52

338.15 1.3994 51.56

343.15 1.3983 51.60

[OMIM][BF4]

288.15 1.4357 66.42

293.15 1.4335 66.34

298.15 1.4319 66.33

303.15 1.4302 66.31

308.15 1.4288 66.33

313.15 1.4277 66.39

318.15 1.4266 66.45

323.15 1.4255 66.51

328.15 1.4245 66.58

333.15 1.4234 66.63

338.15 1.4224 66.70

343.15 1.4213 66.76


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organic solvents such as hexadecane (1.433) and dodecanol (1.441) [35] as a result of the

higher densities of ionic liquids. Values of nD decrease in a curvilinear manner with an

increase in temperature for each IL and follow the order [OMIM][BF4] > [BMIM][BF4] >

[BMIM][PF6]. The temperature derivatives of ILs lie in the range (0.2 to 0.4) 103 K1,

and are somewhat smaller than values found for typical organic solvents. Because molarproperties are more informative, we calculated molar refraction values, RM, for these liquids

using the Lorentz-Lorenz relationship

RM =

M

n2D 1

n2D + 2

(4)

where all the symbols have their usual meaning. Equation4is equivalent to

RM = N /30 (5)

where N is Avogadros number, is mean molecular polarizability ( = 4 0a3, where

a is the spherical radius) and 0 is the permittivity of free space. From Eq. 5, RM can be

interpreted as the hard-core volume, i.e., it is an approximate measure of the total volume

(without free space) of one mole of molecules. RM values are given in Table 4 and follow

the order [OMIM][BF4] > [BMIM][PF6] > [BMIM][BF4].

4 Conclusions

The density, speed of sound and refractive index of the three ILs [OMIM][BF4], [BMIM][PF6] and [BMIM][BF4] were measured as a function of temperature at atmospheric pres-

sure. From the measured properties, estimates were made of the internal pressure and molar

refraction. The internal pressure decreases with increasing temperature for all the ILs. The

internal pressures of the investigated ILs were found to be higher than those of water and

molecular organic liquids. Also, the derived parameters as a function of temperature were

found to vary with the nature of the cation and anion of the ILs.

Acknowledgements The author is thankful to Dr. P.K. Ghosh, Director of the institute, for providing fa-

cilities and interest in this work.

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