Viscosity measurements of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (EMIM OTf) at high pressures using the vibrating wire technique

Journal Pre-proof Viscosity measurements of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (EMIM OTf) at high pressures using the vibrating wire technique Maria C.M. Sequeira, Helena M.N.T. Avelino, Fernando J.P. Caetano, João M.N.A. Fareleira PII:

S0378-3812(19)30415-7

DOI:

https://doi.org/10.1016/j.fluid.2019.112354

Reference:

FLUID 112354

To appear in:

Fluid Phase Equilibria

Received Date: 18 July 2019 Revised Date:

16 September 2019

Accepted Date: 6 October 2019

Please cite this article as: M.C.M. Sequeira, H.M.N.T. Avelino, F.J.P. Caetano, Joã.M.N.A. Fareleira, Viscosity measurements of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (EMIM OTf) at high pressures using the vibrating wire technique, Fluid Phase Equilibria (2019), doi: https://doi.org/10.1016/ j.fluid.2019.112354. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

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Viscosity measurements of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (EMIM OTf) at high pressures using the vibrating wire technique

3 4 5

Maria C. M. Sequeira1, Helena M. N. T. Avelino1,2, Fernando J. P. Caetano1,3, João M. N. A. Fareleira1

6 1

7 8

Centro de Química Estrutural, Instituto Superior Técnico, Universidade de Lisboa. Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal

2

9 10

Área Departamental de Engenharia Química, Instituto Superior de Engenharia de Lisboa, Instituto Politécnico Lisboa, R. Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal

11 12

3

Departamento de Ciências e Tecnologia, Universidade Aberta, Rua da Escola Politécnica, 141, Lisboa, Portugal

13 14 15 16 17 18 19 20 21 22 23 24 25

Keywords: ionic liquid; viscosity; high pressure; EMIM OTf; vibrating wire

1

1

Abstract

2 3

The goal of the present work is to contribute to the characterization of ionic liquids by

4

measuring their viscosity at high pressures. As 1-ethyl-3-methylimidazolium

5

trifluoromethanesulfonate (EMIM OTf ) has been used as a solvent in CO2 capture processes,

6

the temperature and pressure ranges of the measurements cover the intervals used in those

7

processes.

8

Measurements of the viscosity of EMIM OTf along five isotherms in the range (298-358) K

9

and at pressures up to 50 MPa, have been performed using the vibrating wire technique in the

10

forced mode of operation. As far as the authors are aware, these are the first measurements of

11

this ionic liquid at pressures higher than 0.1 MPa, to be published. The viscosity results were

12

correlated with the molar volume, using a modified hard-spheres model. The root mean

13

square (σ) deviation of the data from the correlation is less than 0.5% The expanded

14

uncertainty of the present viscosity data is estimated as ±2.0% at a 95% confidence level. As a

15

complement, the pressure-viscosity coefficient has been calculated within the temperature

16

range of the present results.

17

Previous studies of the influence of the electric conductivity of ionic liquids, including EMIM

18

OTf, in the vibrating wire method, have been taken into account for the present work.

19

Complementary measurements of the density have been performed along seven isotherms in

20

the temperature range from (298 to 363) K and pressures from (0.1 to 70) MPa. The density

21

measurements were carried out with an Anton Paar vibrating U-tube densimeter and the raw

22

data were corrected for viscosity effects. The density results were correlated with the

23

temperature and pressure using a modified Tait equation. The expanded uncertainty of the

24

present density data is estimated as ±0.2% at a 95% confidence level.

25 26 27

1. Introduction

28

The capture of CO2 emissions has become a worldwide concern. As a consequence, the

29

conversion of captured CO2 into other chemical species has become the center of intense

30

research. Special attention has recently been paid to the electrochemical reduction of CO2 at

31

high pressure, using ionic liquids as electrolytes [1,2]. In particular, Pardal et al. [1] have used

2

1

1-ethyl-3-methylimidazolium trifluoromethanesulfonate (EMIM OTf) mixed with water as

2

the electrolyte to successfully reduce CO2 at high pressure.

3

The use of ionic liquids in industrial processes require their thermophysical properties, in

4

particular, the viscosity and the thermal conductivity. However, transport properties are scarce

5

due to the difficulty of the measurements, particularly at pressures higher than the

6

atmospheric pressure. The scarcity of experimental data naturally hinders the development of

7

reliable estimation and correlation techniques.

8

As a result of, not only, the difficulties associated to with the measurement itself, but also to

9

some of the characteristics of ionic liquids, large discrepancies between thermophysical

10

properties of ionic liquids have been found along the time. Diogo et al.[3] have remarked the

11

appearance of large discrepancies between values for the viscosity of ionic liquids, in a period

12

of time when the need for properties to enable applications for that new class of substance

13

was becoming more demanding. Castro [4] pointed out that huge discrepancies could be

14

found in the literature. Even in attempts to define new standard fluids for viscosity, large

15

differences were reported by that author [4]. De Castro et al. [5] have recommended the

16

utilization of quasi-primary methods for purposes requiring a high accuracy level, like the

17

establishment of standard reference fluids.

18 19

Our group has developed a programme of measurements aiming at obtaining rigorous results

20

for the viscosity of ionic liquids using the vibrating wire method. This technique, although

21

very accurate for molecular, non-conducting liquids, could have some difficulties with ionic

22

liquids due to their electrical conductivity. Therefore, we have carried out studies involving

23

the measurement of the viscosity of electrically conducting liquids [3,6,7] and at the same

24

time we developed an instrumentation to measure the electrolytic conductivity of several ionic

25

liquids as a function of the frequency of the driving current [8]. The latter study was

26

motivated by the use of the vibrating wire method in the steady-state or forced mode of

27

oscillation, whereby a wire immersed in a liquid sample and subject to a magnetic field

28

undergoes transverse oscillations driven by an electric alternate current. The method requires

29

the acquisition of the frequency response of the wire in a range of frequencies containing the

30

velocity resonance for the transverse oscillations of the wire. Ref [6] in particular, describes a

31

set of experimental tests in order to assess the capability of the vibrating wire method in the

32

forced mode of oscillation to measure electrically conducting liquids.

3

1

Those previous works included the study of the difficulties associated to with the

2

measurement of the viscosity of ionic liquids in general and, in particular, using the vibrating

3

wire technique [3]. The measurements of the electrolytic conductivity of four ionic liquids,

4

including EMIM OTf [8], involved the analysis of the conductance of the ionic liquid samples

5

as a function of the applied frequency, and, most important, they also implied the

6

measurement of new experimental data for both the viscosity and the density for four ionic

7

liquids [3,6,7]. Taking into account all those previous studies [3,6–8], it may be expected

8

that no significant effects of the electrical conductivity will affect the present measurements.

9

Considering the importance of finding efficient processes to reduce CO2, we have carried out

10

viscosity measurements of EMIM OTf, covering the temperature and pressure ranges used by

11

Pardal et al. in their work [1]. The present measurements are the continuation of the efforts to

12

study volumetric and related properties as well as the viscosity of ionic liquids and their

13

mixtures with sustainable solvents that have been carried out in Centro de Química Estrutural

14

[9–11].

15 16

2. Experimental Section

17

2.1. Materials and reagents

18

1-ethyl-3-methyl-imidazolium trifluoromethane sulfonate (triflate), was used as received. This

19

ionic liquid is often known by several acronyms, v.g., EMIM OTf, [C2mim][OTf], [C2mim]

20

[CF3SO3] and C1C2Im OTf. Before the measurements, the water content has been

21

determined using a Karl–Fischer 831 KF Coulometer from Metrohm. Table 1 shows the

22

characterization of the EMIM OTf samples used in this work.

23 24 25

Table 1 - Characterization of the liquids used in this work. Water content EMIM OTf

1-ethyl-3-methylimidazolium triflate

CAS number Supplier

145022-44-2

IoLitec

(mg⋅kg-1)

308.1

Purity (Fraction mass) 99%

Lot number

P00271

26 27 4

1 2 3 4

2.2. Experimental Procedure

5 6

2.2.1 Density measurements

7

Density of the EMIM OTf was measured in the temperature range (298.15 to 363.15) K and

8

pressures up to 70 MPa, using an Anton Paar DMA HP densimeter, using a DMA 5000

9

instrument as reading unit. The experimental procedure has been previously described by

10

Brito e Abreu et al. [12].

11

The influence of the viscosity on the raw density data as read by the densimeter was

12

evaluated. For this purpose, the viscosity correction was estimated following the procedure

13

described by Diogo et al. [13]. The viscosity correction amounts to a maximum of about

14

0.05%, which is smaller than the measurements uncertainty but is greater than their

15

repeatability.

16

Along each isotherm about half of the measurements have been performed in a sequence of

17

increasing pressures and the other half in a sequence of decreasing pressures. The datum at

18

atmospheric pressure has always been repeated in each isotherm.

19

The repeatability of the present density measurements is better than ±0.1 kg⋅m−3. The overall

20

uncertainty of the present density measurements is estimated to be within ±0.2%, at a 95%

21

confidence level. This estimate is based on previous sensitivity studies [12]

22 23

2.2.2 Viscosity measurements

24

Viscosity of EMIM OTf was measured in the temperature range (298 to 358) K and pressures

25

up to 50 MPa, using a vibrating wire viscometer. The instrument was built in-home and is

26

described elsewhere [14]. The vibrating wire sensor used in the viscosity measurements of

27

EMIM OTf is the same that has been used to measure DBA [15], TOTM [14,16], and n-

28

tetradecane [17,18]. An axially tensioned tungsten wire, immersed in the liquid sample, is

29

subject to a permanent magnetic field. A driving alternate electric current is passed along the

30

wire and as a result of the electromagnetic interaction it develops transverse oscillations that

31

give rise to an emf at the wire ends. In the present work, the vibrating wire sensor was

32

operated in the forced mode of oscillations. The raw data to calculate the viscosity of the 5

1

sample, consists primarily in the acquisition of the frequency response of the sensor in a range

2

of frequencies of the driving current, containing the velocity resonance for horizontal

3

oscillations of the wire [3,7,14]. The working equations and the procedure used to determine

4

the viscosity of EMIM OTf, have been described previously [3,7].

5

The repeatability, at a 95% confidence level, of the present vibrating wire viscosity

6

measurements is better than ±0.3%. The expanded uncertainty of the present vibrating-wire

7

measurements, at a 95% confidence level, is estimated to be less than ±2%. This estimate is

8

based on previous sensitivity studies [3,6,7,14].

9 10 11

2.2.3. Statistical parameters

12

The statistical parameters used to characterize the quality of the fittings in the present work

13

are defined by Eqs. (1) and (2), namely, the relative root mean square deviation, hereby

14

designated as σ and the bias.

15

1 σ = N 

 X exp,i  ∑i  X − 1  calc,i  N

2

   

1

2

(1)

16

 1 N  X exp,i  − 1 ∑  N i  X calc,i 

17

bias =

18

where N is the total number of experimental data points, the subscripts (exp,i and calc,i) stand

19

for the ith experimental and calculated data points, respectively, and X stands either for the

20

density or the viscosity.

(2)

21 22 23 24 25

6

1 2 3

3. Results and discussion

4

3.1. Density

5

3.1.1. Density results

6

The experimental density values for EMIM OTf performed at pressures up to 70 MPa, and at

7

seven temperatures from (298 to 363) K are presented in Table 2, with and without correction

8

for viscosity effects. The latter values are plotted in Fig. 1 as a function of pressure.

9 10

Fig. 1 Experimental viscosity results for EMIM OTf as a function of pressure, at

11

temperatures:

12

obtained in the present work.

, 298K;

, 313 K;

, 323 K;

, 333 K;

, 343 K;

, 353 K; , 363 K,

7

Table 2 Density data for EMIM OTf obtained with an Anton Paar DMA HP densimeter, either corrected, ρ, and uncorrected, ρHP, for viscosity effects, and viscosity, η, calculated for T and p using Eqs.(6)-(8). T /K 298.15

p/MPa 0.10 0.10 0.62 1.09 1.58 2.08 3.06 5.02 7.00 9.93 14.88 19.76 24.66 29.55 34.49 39.36 44.31 49.18 54.10 59.02 63.92 68.81

ρHP/ (kg⋅m-3) 1378.1 1378.1 1378.4 1378.7 1379.0 1379.2 1379.8 1380.8 1381.9 1383.5 1386.2 1388.7 1391.2 1393.6 1396.1 1398.4 1400.8 1403.0 1405.2 1407.3 1409.5 1411.6

η /(mPa⋅s) 43.4 43.4 43.6 43.8 44.0 44.2 44.6 45.4 46.2 47.5 49.7 51.8 54.1 56.4 58.9 61.3 63.9 66.4 69.1* 71.8* 74.6* 77.5*

ρ /(kg⋅m-3) 1377.5 1377.5 1377.8 1378.1 1378.4 1378.6 1379.2 1380.2 1381.3 1382.9 1385.5 1388.0 1390.6 1393.0 1395.4 1397.7 1400.1 1402.3 1404.5 1406.7 1408.8 1410.9

T /K 333.15

343.15

p/MPa 14.89 19.81 24.68 29.60 39.35 44.30 49.17 54.11 58.97 63.86 68.76 0.10 0.10 0.62 1.15 1.56 2.17 3.07 5.09 7.02 9.95 14.88

ρHP/ (kg⋅m-3) 1357.9 1360.7 1363.5 1366.2 1371.5 1374.0 1376.5 1378.9 1381.2 1383.5 1385.7 1340.6 1340.5 1341.0 1341.3 1341.6 1341.9 1342.5 1343.8 1345.1 1346.9 1350.0

η /(mPa⋅s) 16.9 17.5 18.1 18.7 20.0 20.6 21.3 21.9 22.6 23.3 24.0 12.0 12.0 12.1 12.1 12.1 12.2 12.3 12.5 12.6 12.9 13.3

ρ /(kg⋅m-3) 1357.4 1360.2 1363.1 1365.7 1371.0 1373.6 1376.0 1378.4 1380.7 1383.0 1385.2 1340.2 1340.1 1340.5 1340.8 1341.1 1341.5 1342.1 1343.4 1344.7 1346.5 1349.6 8

313.15

323.15

0.10 0.10 0.64 1.09 1.58 2.13 3.06 5.04 6.99 9.97 14.87 19.77 24.66 29.60 34.48 39.39 44.24 49.18 54.08 59.01 63.84 68.83 0.10 0.10 0.66 1.13 1.60 2.12 3.04 5.06

1365.5 1365.5 1365.8 1366.1 1366.3 1366.7 1367.2 1368.3 1369.5 1371.2 1373.9 1376.6 1379.2 1381.8 1384.3 1386.7 1389.2 1391.5 1393.8 1396.0 1398.2 1400.3 1357.0 1357.0 1357.4 1357.6 1357.9 1358.2 1358.8 1360.0

26.2 26.2 26.3 26.4 26.5 26.7 26.9 27.3 27.7 28.4 29.6 30.7 31.9 33.2 34.4 35.7 37.0 38.4 39.8 41.2 42.6 44.1 19.7 19.7 19.7 19.8 19.9 20.0 20.1 20.4

1364.9 1364.9 1365.3 1365.5 1365.8 1366.1 1366.7 1367.8 1368.9 1370.6 1373.4 1376.0 1378.7 1381.2 1383.8 1386.2 1388.6 1390.9 1393.2 1395.4 1397.6 1399.7 1356.5 1356.5 1356.9 1357.1 1357.5 1357.7 1358.3 1359.5

353.15

19.78 24.70 29.61 34.47 39.42 44.32 49.21 54.11 59.00 63.91 68.75 0.10 0.10 0.68 1.13 1.58 2.14 3.00 5.02 7.00 9.99 14.87 19.80 24.67 29.61 34.47 39.38 44.27 49.22 54.05

1352.9 1355.9 1358.7 1361.4 1364.1 1366.7 1369.2 1371.7 1374.1 1376.4 1378.6 1332.4 1332.5 1332.9 1333.2 1333.5 1333.9 1334.4 1335.8 1337.1 1339.0 1342.2 1345.3 1348.3 1351.2 1354.0 1356.8 1359.5 1362.1 1364.6

13.8 14.2 14.7 15.2 15.6 16.1 16.6 17.1 17.6 18.1 18.6 9.7 9.7 9.7 9.7 9.8 9.8 9.9 10.0 10.2 10.4 10.7 11.1 11.4 11.8 12.1 12.5 12.9 13.2 13.6

1352.5 1355.4 1358.2 1361.0 1363.6 1366.3 1368.7 1371.3 1373.6 1376.0 1378.2 1332.0 1332.1 1332.5 1332.8 1333.1 1333.5 1334.0 1335.4 1336.7 1338.6 1341.8 1344.9 1347.9 1350.8 1353.6 1356.3 1359.0 1361.6 1364.2 9

7.03 9.99 14.81 19.80 24.69 29.58 34.49 39.40 44.31 49.20 54.10 59.00 63.91 68.79 0.10 0.10 0.66 1.13 1.59 2.12 3.11 5.11 7.04 9.99 14.89

1361.2 1362.9 1365.8 1368.5 1371.3 1373.9 1376.5 1379.0 1381.5 1383.9 1386.3 1388.5 1390.8 1392.9 1348.7 1348.7 1349.1 1349.4 1349.7 1350.0 1350.6 1351.9 1353.1 1354.9 1357.9

20.7 1360.7 21.2 1362.4 22.0 1365.3 22.8 1368.0 23.7 1370.8 24.5 1373.4 25.4 1376.0 26.2 1378.5 27.1 1381.0 28.1 1383.3 29.0 1385.7 30.0 1388.0 30.9 1390.2 31.9 1392.4 333.15 15.2 1348.3 15.2 1348.3 15.3 1348.7 15.3 1349.0 15.4 1349.2 15.4 1349.6 15.5 1350.2 15.8 1351.4 16.0 1352.6 16.3 1354.4 16.9 1357.4 Expanded uncertainties: U(T) = 0.05 K; U(p) = 0.08 MPa; U(ρ) = 0.2%.

363.16

58.98 63.82 68.73 0.10 0.10 0.61 1.14 1.61 2.14 3.04 5.04 6.99 9.97 14.83 19.77 24.64 29.60 34.49 39.38 44.27 49.20 54.08 59.03 63.86 68.79

1367.0 1369.4 1371.7 1324.4 1324.4 1324.8 1325.2 1325.5 1325.9 1326.5 1327.9 1329.2 1331.3 1334.5 1337.7 1340.8 1343.8 1346.8 1349.6 1352.4 1355.0 1357.7 1360.1 1362.6 1364.9

14.0 14.4 14.8 7.9 7.9 7.9 8.0 8.0 8.0 8.1 8.2 8.3 8.5 8.7 9.0 9.3 9.6 9.9 10.2 10.5 10.8 11.1 11.4 11.7 12.0

1366.6 1369.0 1371.3 1324.0 1324.1 1324.5 1324.8 1325.2 1325.5 1326.2 1327.5 1328.9 1330.9 1334.1 1337.3 1340.4 1343.4 1346.4 1349.2 1352.0 1354.6 1357.2 1359.7 1362.1 1364.5

*Extrapolated using Eqs (6)-(8) with parameters of Table 5.

10

1

3.1.2. Density correlation with temperature and pressure

2

The so-called “Tait equation” is widely used in the thermophysical properties community to

3

correlate liquid densities of a large class of real fluids. The density data for EMIM OTf,

4

ρ(T,p), presented in Table 2, were correlated using the modified Tait-type equation [19].

5

  D + p  ρ = ρ 0 1 − C ln    D + p0   

6

In this work, the density, ρ0(T, p0), at a pressure p0= 0.1 MPa, is used as a reference, and is

7

described by the polynomial, Eq (4).

−1

(3)

2

8

ρ0 = ∑biT i

(4)

i =0

9 10

It is assumed that C is temperature independent and the temperature dependence of the parameter D is described by the polynomial, Eq. (5).

11

D = ∑ diT i

3

(5)

i =0

12

The fitting parameters C, bi and di were obtained by fitting Eqs. (3)-(5) to experimental

13

density data corrected for viscosity effects, as shown in Table 2. The fitting of the modified

14

Tait-type equation, to the experimental density results, was made using MatLabTM software

15

with a Nelder−Mead algorithm). The root mean square deviation, σ, of the fitting is about

16

0.003% and the bias is essentially zero. The values of the statistical parameters are listed in

17

Table 3.

18

Fig. 2 shows the deviations of the DMA HP Anton Paar density data (with correction for

19

viscosity effects), ρ, from the correlation Eq. (3), using the parameters shown in Table 3. The

20

maximum relative deviation of all the data is smaller than ±0.008%.

21 22 23 24 11

1 2

Table 3 Fitting parameters of Eqs. (3)-(5) for the density data, ρ, after correction for viscosity effects. b0 / (kg⋅m-3) b1 / (kg⋅m-3⋅K-1) b2 / (kg⋅m-3⋅K-2)

1666.834 -1.0921 4.0804 10-4

d0 / MPa d1 / (MPa⋅K-1) d2 / (MPa⋅K-2) d3 / (MPa⋅K-3)

493.98600 -1.72665 2.57270 10-3 -1.76144 10-6

C

0.066031

σ/% bias / %

0.003 0.00005

3

4 5

Fig. 2 Deviations of the density, ρ, of EMIM OTf obtained in the present work, with an

6

Anton Paar DMA HP densimeter and corrected for viscosity effects, from the correlation Eqs.

7

(3)-(5), as a function of pressure, for the temperatures:

8

333 K;

, 343 K;

, 298K;

, 313 K;

, 323 K;

,

, 353 K; , 363 K.

9 10 12

1

3.1.3 Comparison with literature density data

2

Only two sets of high-pressure density data were found in the literature, including the ionic

3

liquid database (ILThermo) – NIST [20]. Gardas et al. [21] have measured the density of a

4

sample of EMIM OTf in a wide range of temperatures (293 to 393 K) and at pressures from

5

(0.1 to 30) MPa, using an Anton Paar U-tube DMA 512 densimeter. The overall uncertainty

6

claimed by the authors is ±1 kg⋅m-3. It is noteworthy that those data have not been corrected

7

for viscosity effects. The data set reported by Gardas [21] along the isotherms (293 and 363)

8

K and at pressures up to 30 MPa were compared with the present density results, as described

9

by Eqs (3)-(5). The relative deviations of their data from the present results are plotted in Fig.

10

3. The deviations are all negative, ranging between -0.1% and -0.6%, becoming more

11

negative as the temperature increases.

12 13 14 15 16

Fig. 3. Deviations from correlation Eqs. (3) - (5) of the density, ρ, for EMIM OTf, obtained by Gardas et. al. [21], at temperatures: , 303 K; , 313 K; , 323 K; , 333 K; , 353 K; and by Klomfar et al. [22]: +, in the temperature range between (293 and 363) K.

17

Klomfar et al. [22] have measured the density of a sample of EMIM OTf in the temperature

18

range between (264 and 347) K and at pressures from (1 to 60) MPa, using an isochoric

19

method. The claimed combined uncertainty at a 95% confidence level of their density data is

20

±1 kg⋅m-3. These deviations are always positive and are about 0.6%. 13

1

It is to be remarked that both data sets deviate from the present results by more than their

2

claimed uncertainties. However, their mutual disagreement is even higher, as one of the data

3

sets [21] evidence systematic negative deviations from the present work, while the other [22]

4

shows systematic positive deviations. The sample of EMIM OTf used by Gardas et al. [21] and by

5

Klomfar et al. [22] were obtained from the same supplier and have the same purity, greater than 99%,

6

as the sample used in the present work. The water in our sample (308 mg⋅kg-1) is larger than both that

7

of Klomfar (93 mg⋅kg-1) and Gardas (21 mg⋅kg-1). Therefore, both the water content and the purity of

8

those samples cannot consistently justify the deviations from the present density results

9 10 11 12

3.2 Viscosity

13

3.2.1. Viscosity results

14

The viscosity of EMIM OTf was measured using the vibrating wire method at pressures from

15

(0.1 to 50) MPa, along five isotherms between (298 and 358) K. The results are listed in

16

Table 4 and plotted in Fig. 4 as a function of pressure. The density data needed to compute

17

the vibrating wire viscosity results were obtained from Eqs. (3)-(5) with the parameters listed

18

in Table 3.

14

1 2

Fig. 4 Experimental viscosity results obtained in the present work for EMIM OTf as a

3

function of pressure, at temperatures:

, 298K;

, 313 K;

, 328 K;

, 343 K;

, 358 K.

4

15

1 2 3

Table 4 Viscosity data for EMIM OTf measured with the vibrating wire technique at temperatures from (298 to 358) K and pressures up to 50 MPa. Density values were obtained by Eqs. (3)-(5). T /K T /K T /K ρ /MPa Ρ /(kg⋅m-3) η /(mPa⋅s) ρ /MPa Ρ /(kg⋅m-3) η /(mPa⋅s) ρ /MPa Ρ /(kg⋅m-3) η /(mPa⋅s) 298.22

0.21 0.21 0.21 0.21 0.21 0.22 0.22 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.36 1.37 2.17 2.17 2.17 2.17 2.17 2.17 2.17 2.18

1377.5 1377.5 1377.5 1377.5 1377.5 1377.5 1377.5 1378.2 1378.2 1378.2 1378.2 1378.2 1378.2 1378.2 1378.2 1378.2 1378.2 1378.6 1378.6 1378.6 1378.6 1378.6 1378.6 1378.6 1378.6

43.44 43.16 43.30 43.26 43.42 43.55 43.49 43.85 43.72 43.98 44.01 43.88 43.87 43.50 44.22 44.09 44.14 44.47 44.04 43.95 44.17 44.56 43.92 44.16 44.00

313.23

328.18

30.26 30.25 30.25 30.25 30.25 30.25 30.25 30.25 49.79 49.79 49.79 49.79 49.79 49.79 49.79 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 1.18

1381.5 1381.5 1381.5 1381.5 1381.5 1381.5 1381.5 1381.5 1391.1 1391.1 1391.1 1391.1 1391.1 1391.1 1391.1 1352.4 1352.4 1352.4 1352.4 1352.4 1352.4 1352.4 1352.4 1352.4 1353.1

33.01 33.12 32.98 33.14 33.12 33.11 33.07 32.89 38.45 38.40 38.14 38.72 38.60 38.48 38.62 17.27 17.31 17.40 17.23 17.20 17.30 17.27 17.27 17.22 17.40

343.19

2.12 2.13 2.13 2.13 2.13 2.13 2.13 5.19 5.19 5.19 5.19 5.19 5.19 5.19 5.19 5.19 5.18 10.17 10.17 10.17 10.17 10.17 10.17 10.17 10.17

1341.4 1341.4 1341.4 1341.4 1341.4 1341.4 1341.4 1343.4 1343.4 1343.4 1343.4 1343.4 1343.4 1343.4 1343.4 1343.4 1343.4 1346.6 1346.6 1346.6 1346.6 1346.6 1346.6 1346.6 1346.6

12.20 12.24 12.18 12.19 12.14 12.17 12.18 12.42 12.49 12.48 12.46 12.42 12.44 12.45 12.37 12.42 12.48 12.88 12.87 12.88 12.86 12.85 12.93 12.87 12.86 16

4.84 4.83 4.82 4.80 4.79 4.78 4.75 4.73 4.72 5.27 5.27 5.28 10.49 10.48 10.48 10.48 10.47 10.47 10.47 10.47 20.01 20.01 20.01 20.01 20.00 20.00 20.00 20.00 20.00 20.00

1380.1 1380.1 1380.1 1380.1 1380.1 1380.1 1380.1 1380.0 1380.0 1380.3 1380.3 1380.3 1383.2 1383.2 1383.2 1383.2 1383.2 1383.2 1383.2 1383.2 1388.2 1388.2 1388.2 1388.2 1388.2 1388.2 1388.2 1388.2 1388.2 1388.2

45.09 45.08 45.01 45.12 45.04 44.93 44.94 44.89 44.89 45.34 45.40 45.50 47.55 47.85 47.55 47.61 47.72 48.01 47.62 47.91 51.96 51.53 51.73 52.07 51.81 51.90 51.55 51.80 51.97 51.70

1.20 1.24 1.26 1.27 1.28 1.29 1.29 1.30 2.13 2.13 2.12 2.13 2.13 2.13 2.13 2.13 2.13 5.03 5.03 5.03 5.02 5.02 5.02 5.02 5.02 5.02 5.35 5.35 5.35 5.35

1353.1 1353.1 1353.1 1353.1 1353.1 1353.1 1353.1 1353.1 1353.7 1353.7 1353.6 1353.7 1353.7 1353.7 1353.7 1353.7 1353.7 1355.5 1355.5 1355.5 1355.5 1355.5 1355.5 1355.5 1355.5 1355.5 1355.7 1355.6 1355.7 1355.7

17.42 17.54 17.35 17.56 17.33 17.50 17.41 17.47 17.41 17.46 17.47 17.57 17.57 17.44 17.45 17.55 17.60 17.71 17.80 17.84 17.69 17.74 17.81 17.77 17.70 17.75 17.97 17.88 18.04 17.95

358.29

20.19 20.19 20.19 20.19 20.19 20.19 20.19 20.18 20.18 20.18 30.12 30.12 30.12 30.12 30.11 30.11 30.11 30.11 50.10 50.11 50.10 50.11 50.10 50.09 50.09 50.08 10.12 10.11 10.08 10.08

1352.7 1352.7 1352.7 1352.7 1352.7 1352.7 1352.7 1352.7 1352.7 1352.7 1358.5 1358.5 1358.5 1358.5 1358.5 1358.5 1358.5 1358.5 1369.1 1369.1 1369.1 1369.1 1369.1 1369.1 1369.1 1369.1 1334.8 1334.8 1334.8 1334.8

13.84 13.84 13.76 13.75 13.81 13.75 13.79 13.79 13.85 13.82 14.72 14.71 14.71 14.71 14.75 14.78 14.71 14.77 16.68 16.82 16.75 16.82 16.68 16.63 16.63 16.70 9.306 9.290 9.325 9.311 17

313.24

30.24 30.23 30.24 30.24 30.25 30.25 30.25 50.38 50.38 50.36 50.36 50.36 50.35 50.35 50.35 0.22 0.23 0.23 0.24 0.24 0.25 1.16 1.16 1.16 1.16 1.16 1.16 1.16 2.02 2.02

1393.3 1393.3 1393.3 1393.3 1393.3 1393.3 1393.3 1402.8 1402.8 1402.8 1402.8 1402.8 1402.8 1402.8 1402.8 1364.9 1364.9 1364.9 1364.9 1364.9 1364.9 1365.4 1365.4 1365.4 1365.4 1365.4 1365.4 1365.4 1365.9 1365.9

56.59 56.36 56.45 56.41 56.31 56.67 56.56 67.81 67.04 66.93 67.10 66.55 66.83 66.53 66.67 26.34 26.25 26.24 26.30 26.22 26.31 26.32 26.32 26.24 26.27 26.35 26.40 26.41 26.52 26.51

5.35 5.33 5.32 5.33 5.33 5.33 10.07 10.07 10.07 10.07 10.08 20.11 20.11 20.11 20.10 20.10 20.10 20.10 20.10 20.10 20.10 29.91 29.91 29.90 29.91 29.93 29.94 50.08 50.08 50.08

1355.7 1355.6 1355.6 1355.6 1355.6 1355.6 1358.5 1358.5 1358.5 1358.5 1358.5 1364.3 1364.3 1364.3 1364.3 1364.3 1364.3 1364.3 1364.3 1364.3 1364.3 1369.7 1369.7 1369.7 1369.7 1369.7 1369.7 1380.1 1380.1 1380.1

17.98 18.11 17.94 17.91 18.02 18.00 18.47 18.64 18.55 18.54 18.53 19.80 19.73 19.74 19.70 19.65 19.78 19.72 19.80 19.73 19.82 21.44 21.33 21.52 21.43 21.46 21.38 24.52 24.47 24.61

10.10 10.10 10.09 10.10 10.11 20.14 20.14 20.14 20.13 20.14 20.13 20.14 20.15 20.16 30.07 30.07 30.07 30.07 30.08 30.08 49.83 49.84 49.84 49.84 49.84 49.85 49.85 0.22 0.23 0.23

1334.8 1334.8 1334.8 1334.8 1334.8 1341.2 1341.2 1341.2 1341.2 1341.2 1341.2 1341.2 1341.3 1341.3 1347.3 1347.3 1347.3 1347.3 1347.3 1347.3 1358.3 1358.3 1358.3 1358.3 1358.3 1358.3 1358.3 1328.1 1328.1 1328.1

9.299 9.258 9.272 9.305 9.327 9.967 9.945 9.944 9.985 9.978 9.942 9.980 9.916 9.943 10.56 10.55 10.56 10.57 10.60 10.57 11.98 11.96 11.98 12.02 11.95 11.96 11.99 8.76 8.75 8.71 18

2.03 2.03 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 5.02 10.77 10.76 10.76 10.76 10.76 10.76 10.76 10.76 10.76 20.22 20.22 20.22 20.22 20.22 20.23 20.23 20.24 20.24 20.24

1365.9 1365.9 1367.7 1367.7 1367.7 1367.7 1367.7 1367.7 1367.7 1367.7 1367.7 1371.0 1371.0 1371.0 1371.0 1371.0 1371.0 1371.0 1371.0 1371.0 1376.2 1376.2 1376.2 1376.2 1376.2 1376.2 1376.2 1376.2 1376.2 1376.2

26.57 26.52 27.16 27.21 27.35 27.15 27.16 27.14 26.96 27.28 27.14 28.69 28.42 28.55 28.58 28.41 28.49 28.63 28.61 28.54 31.03 31.37 31.05 30.93 30.99 31.02 31.46 30.99 30.43 30.72

343.19

50.07 50.07 50.07 50.07 50.07 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 0.21 1.17 1.17 1.17 1.17 1.18 1.18 1.18 1.19 1.97 1.97 1.97 1.97 1.97 1.97 1.97

1380.0 1380.0 1380.0 1380.0 1380.0 1340.2 1340.2 1340.2 1340.2 1340.2 1340.2 1340.2 1340.2 1340.2 1340.2 1340.8 1340.8 1340.8 1340.8 1340.8 1340.8 1340.8 1340.8 1341.3 1341.3 1341.3 1341.3 1341.3 1341.3 1341.3

24.54 24.50 24.58 24.53 24.57 11.99 11.98 12.02 12.02 12.07 12.02 12.11 12.07 12.04 12.05 12.14 12.12 12.11 12.15 12.08 12.07 12.09 12.12 12.13 12.15 12.12 12.17 12.20 12.15 12.18

0.23 0.24 0.24 0.24 0.24 0.24 1.20 1.21 1.21 1.21 1.21 1.21 1.21 1.21 1.22 1.22 2.21 2.21 2.21 2.21 2.21 2.21 2.21 2.22 5.18 5.18 5.18 5.18 5.18 5.18

1328.1 1328.1 1328.1 1328.1 1328.1 1328.1 1328.8 1328.8 1328.8 1328.8 1328.8 1328.8 1328.8 1328.8 1328.8 1328.8 1329.5 1329.5 1329.5 1329.5 1329.5 1329.5 1329.5 1329.6 1331.5 1331.5 1331.5 1331.5 1331.5 1331.5

8.77 8.70 8.74 8.73 8.75 8.73 8.85 8.82 8.81 8.80 8.75 8.81 8.75 8.80 8.76 8.86 8.92 8.84 8.86 8.85 8.84 8.88 8.82 8.89 9.07 9.06 9.02 9.07 9.05 9.01 19

1 2

20.22 1376.2 30.82 1.97 1341.3 12.13 20.21 1376.2 30.69 1.97 1341.3 12.21 30.26 1381.5 33.02 1.97 1341.3 12.19 Expanded uncertainties: U(T) = ±0.05 K; U(p) = ±0.08 MPa; U(ρ) =0.2%; U (η) = ±2%

5.16 5.18

1331.5 1331.5

8.99 9.03

20

1

3.2.2. Viscosity correlation with the molar volume

2

The present viscosity results for EMIM OTf were correlated using a semi-empirical method

3

proposed by Li et al. [23] which is a heuristic development of the kinetic theory for dense

4

hard-sphere fluids. The model is based on the hard-spheres theory of dense fluids, developed

5

by Dymond et al. [24]. This method has been previously applied by the authors to several

6

different types of liquids with success [14,17,25–29]. This correlation method defines a

7

dimensionless viscosity, η*, that, using SI units, is written as [24]. 12

8

8

1  η* = 6.035 × 10    MRT 

9

where Vm is the molar volume, R is the gas constant, and M is the molar mass. It is assumed

η (Vm )

23

(6)

10

that the dimensionless viscosity, η*, depends only on the ratio Vm/V0, where V0 is a

11

characteristic molar volume. The dimensionless viscosity results for EMIM OTf were

12

correlated with the ratio, Vm/V0 by Eq (7).

13

4 1 = ∑ ai η * i =0

14

where V0 is a characteristic molar volume whose temperature dependence was described by

15

Eq (8).

16

V0 (T ) = V0,ref + l (T − Tref ) + m (T − Tref

17

The fitting coefficients l and m have been obtained by simultaneous fitting of Eqs. (7) and (8)

18

to the experimental data and are listed in Table 5, together with the relative root mean square

19

deviation, σ, and bias.

20

The calculation of the reference value for V0(Tref) from literature intermolecular pair-potential

21

parameters [30] was assumed to be inadequate for the present substance. As a consequence, a

22

reference value for EMIM OTf has been obtained by fitting Eq (9), to experimental data for

23

the selected reference temperature, where A is an arbitrary constant.

 Vm     V0 

i

(7)

)

2

(8)

24 25

 Vm  V −V  m 0 ,ref

ηcalc = A exp 

  

(9) 21

1

The reference volume, V0(Tref), was obtained by minimization of the objective function, Eq

2

(10), for the isotherm at the reference temperature, Tref = 313.15 K.

3

φ = ∑(ηexp − ηcalc ) N

2

(10)

1=1

4

where N is the total number of experimental data points at 313.15 K. The calculated value for

5

V0,ref was 151.2861 10-6 m3⋅mol-1.

6 7

In Fig. 5 the deviations of the experimental viscosity data for EMIM OTf from the correlation

8

Eqs. (6)-(8) are shown. The rms deviation, σ, from the correlation is 0.48%, and the bias is

9

essentially zero. The absolute values of the deviations are all less than 1.0%.

10

No viscosity data for EMIM OTf at pressures higher than 0.1 MPa could be found in the

11

literature.

12 13 14 15

Table 5

16

Fitting parameters of Eqs. (7) and (8) for the viscosity data, η, obtained with the vibrating

17

wire viscometer. l/ (m3 mol-1 K-1) m / (m3 mol-1 K-2)

-1.68428×10-7 1.70026×10-10

a0

0.490389

a1

-1.525717

a2

1.795105

a3

-0.950462

a4

0.191981

σ/% bias / %

0.48 0.0002

18 19

22

1 2

Fig. 5. Deviations of the viscosity, η, for EMIM OTf obtained in the present work with a

3

vibrating wire viscometer, from correlation Eqs. (6)-(8), at temperatures:

4

K;

, 328 K;

, 343 K;

, 298K;

, 313

, 358 K.

5 6

The Plot in Fig. 4, shows that the effect of a pressure increase on the viscosity, increases as

7

the temperature decreases. This is quantitatively described by the viscosity-pressure

8

coefficient, α, [31] as defined by Eq (10).

9

α=

1  ∂η    η  ∂p T

(10)

10

In order to study the effect of pressure on the viscosity of EMIM OTf, the pressure-viscosity

11

coefficient was calculated from the present results. This parameter, which is especially

12

important to characterize lubricants [31], was calculated by Eq (11), which has been obtained

13

through derivation of Eq. (6).

14

3  + η* 2 

i  Vm   i ai     V0   i =1

15

ρ C α= ρ0 D + p

16

The results obtained for α are listed in Table 6 and plotted in Fig. 6, as a function of pressure

17

for five isotherms.

4

∑

(11)

23

1

Table 6

2

Pressure-viscosity coefficients, α(p), for EMIM OTf p/MPa

T/K 298

313

328 α / GPa 8.1 7.8 7.5 7.2 7.0 6.8

343

358

7.7 7.4 7.0 6.8 6.5 6.3

7.6 7.2 6.8 6.5 6.2 6.0

-1

0.1 10 20 30 40 50

9.7 9.4 9.1 8.8 8.5 8.2

8.7 8.5 8.2 8.0 7.8 7.6

3 4

The local pressure viscosity coefficient, α, decreases when the pressure increases for all

5

temperatures studied. It is also shown that the value of that coefficient increases as the

6

temperature decreases. This general behaviour has been observed for many ionic liquids [32].

7

8 9 10

Fig. 6. Local pressure viscosity coefficient, α, as a function of pressure for EMIM OTf at temperatures:

, 298K;

, 313 K;

, 328 K;

, 343 K;

, 358 K.

11 12 24

1

3.2.3 Comparison with literature viscosity data at 0.1 MPa

2

No results for the viscosity of EMIM OTf at pressures higher than 0.1 MPa have been found

3

in the literature. As a consequence, only data at atmospheric pressure could be used for

4

comparison with the present measurements. For this purpose, a small extrapolation of our

5

results is necessary, which is easily accomplished using the correlation Eqs. (6) to (8) with

6

parameters given in Table 5. A characterization of the literature data is shown in Table 7. It is

7

noteworthy that ref [20] – NIST, Ionic Liquids Database - ILThermo (v.2.0) – has been used

8

to identify the original sources of the literature results. In Fig.7 the deviations of the literature

9

data from the correlation of the present results are plotted.

10

25

1 2

Table 7

3

Measurements of the viscosity, η, of ionic liquid EMIM OTf that could be found in the literature. First author

Year

Ref.

Temperature range / K

NP

Method

Purity / %

Water content / (mg/kg)

Nominal

Relative deviations

uncertainty

range/%

Freire

2011

[33]

278-363

18

Stabinger viscometer

99

20

±0.35%

-1.07 to 2.60

Seddon

2002

[34]

283-363

9

Cone and Plate

NA

237

±1.0%

-2.26 to -0.46

Rodriguez

2006

[35]

278-348

8

Cone and Plate

NA

96

±2.0%

-7.12 to 2.27

Yusoff

2013

[36]

303-363

5

Concentric cylinders

98

NA

± 0.05 mPa.s

-0.42 to 25.83

Foo

2015

[37]

313-363

4

Concentric cylinders

98

NA

± 0.04 mPa.s

-0.79 to 25.46

Tsamba

2014

[38]

298-343

5

Concentric cylinders

99.5

100

±1.5%

2.03 to 5.76

Vuksanovic

2013

[39]

288-318

4

Stabinger viscometer

99

130

Morgan

2005

[40]

303

1

Cone and Plate

NA

NA

± 5 mPa.s

23.99

Harris

2016

[41]

268-348

35

Falling body

99.2

1140

±2%

-2.34 to 0.46

Anwar

2018

[42]

298-323

6

Falling ball

98

140

0.2 to 0.8 mPa⋅s

5.23 to 5.58

Aranowski

2016

[43]

298

1

Concentric cylinders

99

13700

NA

3.69

± 0.003 mPa.s

3.48 to 3.96

4 5 6

26

1

2 3

Fig. 7. Deviation of the viscosity, η, for EMIM OTf at atmospheric pressure from the

4

correlation Eqs. (6)-(8), as a function of temperature:

, Freire et al. [33];

5

[34];

, Rodriguez et al. [35];

, Foo et al. [37];

6

[38];

, Vuksanovic et al. [39];

7

al.[42];

, Yusoff et al. [36];

, Morgan et al. [40];

, Seddon et al. , Tsamba et al.

, Harris et al. [41];

, Anwar et

, Aranowski et al. [43].

8 9

The literature data show large inconsistencies among the various sources of data. This

10

illustrates the difficulties associated with thermophysical property measurements on ionic

11

liquids, which have been analysed in previous publications [4,6]. Three data sets evidence an

12

excellent agreement with our correlation, namely the results published by Freire et al. [33],

13

Seddon et al. [34] and Harris et al. [41], whose deviations from our correlation are

14

commensurate with the mutual uncertainty of the measurements. A good agreement is also

15

observed with the data from Vuksanovic et al. [39], which show positive deviations less than

16

4 %. The data by Tsamba at al. [38] also have positive deviations, but increasing slightly with

17

temperature. The data from Anwar et al. [42] deviates positively in a modest range of

18

temperatures. However, some literature data show important systematic deviations from our

19

results, increasing strongly with increasing temperature [36,37], reaching values higher than

20

25 %. The same order of magnitude is attained by the datum from Ref. [40]. 27

1

4. Conclusions

2

The interest of the scientific community on ionic liquids has been raised by several of their

3

characteristics, like the relation between structure and properties and a large number of

4

possible applications. One of the applications that has been considered for ionic liquids

5

consists in the reduction of CO2. One such proposal involves EMIM OTf [1] at moderately

6

high pressures. In the present article, the vibrating wire method is used in the forced mode of

7

oscillation to measure the viscosity of EMIM OTf in the temperature range (298 to 358) K

8

and pressures up to 50 MPa, covering the working temperature and pressure ranges utilized

9

by Pardal et al. [1]. The pressure-viscosity coefficient α has been calculated within the

10

temperature range of the present results.

11

Previous studies of the influence of the electric conductivity of ionic liquids, including EMIM

12

OTf, in the vibrating wire method, have been taken into account for the present work.

13

Complementary measurements of the density have been performed including the same ranges

14

of temperature and pressure that have been used by those authors [1].

15

As far as the present authors are aware, the results for the viscosity of EMIM OTf at pressures

16

higher than 0.1 MPa are the first to be published.

17 18 19

Acknowledgements and Funding

20

This work was supported by the Project UID/QUI/00100/2013 and Project

21

UID/QUI/00100/2019 funded by Fundação para a Ciência e a Tecnologia (FCT), Portugal.

22

The authors are grateful to FCT, Portugal, for its support.

23 24 25

Appendix A. Supplementary Materials

26

In the Supplementary Material, a tool – an Excel™ file – is available to easily interpolate the

27

viscosity and the density in the ranges (0.1 to 50) MPa and (298 to 358) K.

28 29

30 28

1 2

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3 4 5 6 7

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