Viscosity, Density, Heat Capacity, Speed of Sound and Other Derived

Article pubs.acs.org/jced

Viscosity, Density, Heat Capacity, Speed of Sound and Other Derived Properties of 1‑Butyl-3-Methylimidazolium tris(Pentafluoroethyl) Trifluorophosphate over a Wide Range of Temperature and at Atmospheric Pressure Javid Safarov,†,‡ Felix Lesch,† Khagani Suleymanli,‡ Abilgani Aliyev,‡ Astan Shahverdiyev,‡ Egon Hassel,† and Ilmutdin Abdulagatov*,§ †

Lehrstuhl für Technische Thermodynamik, Universität Rostock, 18051 Rostock, Germany Department of Heat Energy, Azerbaijan Technical University, Baku AZ 1073, Azerbaijan § Department of Physical and Organic Chemistry, Dagestan State University, Makhachkala 367008, Russian Federation ‡

ABSTRACT: New experimental data on the viscosity, η(T), heat capacity CP(T), speed of sound c(T), and density ρ(T) of 1-butyl-3-methylimidazolium tris(pentafluoroethyl) trifluorophosphate [BMIM][FAP] are reported that allow the development of wide range reference correlation. The measurements have been made at atmospheric pressure over a temperature range from (263 to 414) K for the viscosity (η), from 273 to 413 K for the heat capacity (CP), from 273 to 413 K for the density (ρ), and from 283 to 343 K for the speed of sound (c) using various types of commercial instruments. The combined expanded uncertainty of the viscosity, heat capacity, speed of sound, density, and temperature measurements at the 0.95 confidence level with a coverage factor of k = 2 is estimated to be 0.35% and 1.0% (for two different instruments), 1.5%, ± 0.5 m·s−1, (0.05 to 0.3) kg· m−3, and 0.05 K, respectively. These new experimental data were used to develop a wide range correlation for the viscosity based on theoretically confirmed Vogel−Tamman−Fulcher (VTF) model. The value of the glass temperature (Tg) for the IL was estimated using the VTF parameters derived from the present viscosity measurements. Measured values of density, heat capacity, and speed of sound were used to calculate other very important thermodynamic properties, kS, kT,aP, γV, ΔH, CV,

( ∂∂HP )T , and ( ∂∂UV )T .

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INTRODUCTION Accurate thermophysical properties data for the ionic liquids (ILs) are very important for various technological applications.1 For example, for the effective utilization of solar energy, a precise thermodynamic and transport property data of working fluids are required. ILs are claimed to be useful as heat-transfer fluids in solar heating and absorption refrigerating systems.2−4 The present work is the continuation of our previous study of the volumetric, calorimetric, and transport properties of pure ILs ([EMIM][EtSO 4 ],[EMIM][MeSO 3 ], [C6mim][NTf2], [C4mim][NTf2], 1-ethyl-3-methylimidazolium methanesulfonate), [BMIM][FAP],5−10 and IL containing binary mixtures (ethanol+[BMIM][BF4], methanol+[BMIM][BF4], methanol +[BMIM][PF6], methanol+[BMIM+][OcSO 4̅ ])11−19 at high temperature and high pressures. The main objective of the present work is to provide accurate and reliable experimental density, heat capacity, speed of sound, and viscosity data for ILs [BMIM][FAP] at high temperatures from 263 to 414 K and at atmospheric pressure. The present results are considerably expanding the temperature range in which viscosity data for [BMIM][FAP] are available and providing new heat capacity and speed of sound data. For example, in the present work we first © 2017 American Chemical Society

reported new high-accuracy viscosity data for [BMIM][FAP] at temperatures above 373 K and below 293 K, and first reported the heat capacity and the speed of sound data for [BMIM][FAP]. The high-pressure (up to 140 MPa) and high-temperature (from 273 to 413 K) density (PVT properties) data for this IL were reported in our previous publication.19 Brief Review of the Reported Heat Capacity, Speed of Sound, and Viscosity Data for the IL ([BMIM][FAP]) at Atmospheric Pressure. Reported density data for [BMIM][FAP] at atmospheric pressure and at high pressures were detailed critically and analyzed in our recent publication19 (see also ref 20). In total six data sources20−25 for the viscosity and density of [BMIM][FAP] were found in the literature. Only one data source21 for the viscosity of [BMIM][FAP] was found in the NIST/TRC archive (Version 9.1. TDE search). Table 1 summarizes the measurements20−25 of the viscosity, density, and other thermophysical properties of [BMIM][FAP] at atmospheric pressure reported in the literature based on Received: July 11, 2017 Accepted: September 13, 2017 Published: September 25, 2017 3620

DOI: 10.1021/acs.jced.7b00618 J. Chem. Eng. Data 2017, 62, 3620−3631

Journal of Chemical & Engineering Data

Article

Table 1. Summary of Reported Viscosity and Density Data of 1-Butyl-3-methylimidazolium tris(Pentafluoroethyl) Trifluorophosphate [BMIM][FAP]a first author

year

properties

method

P/MPa

T/ K

uncertainty

number of data points

purity w.f.

source

Dutt24 Almantariotis21 Vraneš22 Liu21 Součkova20 Xiao25 this work

2010 2012 2014 2010 2012 2012 2017

T, ρ, η T, ρ, η T, ρ ρ,T ρ, T, σ T, ρ, η ρ, T, c, CP

PMCR 101 APR AMVn VTD VTD HW NA RMCR 302

0.101 0.101 0.101 0.101 0.101 0.101 0.101

298 to 348 293 to 373 293 to 323 298.15 279 to 354 293 262 to 414

NA 1.5% 2 × 10−2 2 × 10−2 3 × 10−4ρ NA 1.5%

9 8 7 1 16 1 417

0.99 0.995 0.99 0.997 0.99 0.98 0.99

Merck Merck Merck Merck Merck Merck Merck

T, temperature; P, pressure; ρ, density; η, viscosity; σ, surface tension; c, speed of sound; APR, AMVn-Anton Paar AMVn rolling ball viscosimeter; RMCR, 302-Rheometer MCR 302; PMCR, 101-Physica MCR Rheometer; VTD, vibrating tube densimeter; HW, hydrostatic weighing; w.f., weight fraction. a

Table 2. Ionic Liquid Sample 1-Butyl-3-methylimidazolium tris(Pentafluoroethyl) Trifluorophosphate (Chemical Formula: C14H15F18N2P) Description Studied in This Work sample

M (g·mol−1)

CAS#

source

purity (wt.f.)

H2O content

[BMIM][FAP]

584.23

917762-91-5

Merck Co. LLC

>0.99 (NMR)

120 ppm

temperature from 273 to 413 K were measured using four different Anton Paar instruments: DMA 5000M, DMA HPM, SVM 3000, and DSA 5000 M vibration tube densimeters (VTD) with an uncertainty of ± 0.05 to 0.3 kg·m−3 or less than 0.08%. Details of the method, uncertainty assessment, and corrections related with influence of the viscosity and other details of the consistence of the density measurements with reported data were published in our recent work.19 Heat Capacity Measurements. The isobaric heat capacity,CP(T), of [BMIM][FAP] was measured at atmospheric pressure as a function of temperature between 273 and 413 K using the Pyris 1 DSC Differential Scanning Calorimeter (DSC). DSC measures the amount of energy (heat) absorbed or released by a sample as it is heated, cooled, or held at constant (isothermal) temperature. DSC is one of the very reliable and sensitive instruments for calorimetric (heat capacity, enthalpy) measurements, especially near the various type phase transition temperatures (glass transition, crystallization, melting, mesomorphic transition, etc.), see, for example ref 26. These data are very useful as a reference values to calculate high-pressure caloric properties (CP,CV) from equation of state (see, for example, our previous publication19).The combined expanded uncertainty of heat capacity measurements at 95% confidence level with a coverage factor of k = 2 is estimated to be 1.5%. Speed of Sound Measurements. The speed of sound, c(T), of [BMIM][FAP] at atmospheric pressure over the temperature range from 273to 343 K were studied using the Anton Paar DSA 5000 M VTD and sound velocity meter with a combined expanded uncertainty at 0.95 confidence level with a coverage factor of k = 2 of ±0.5 m·s−1. This instrument was previously successfully used in our laboratory for speed of sound measurements of ionic liquids,8 natural, and geothermal waters.27,28 The details of the method and uncertainty assessments were described in past works.27,28 Viscosity Measurements. Measurements of the dynamic viscosity, η(T), of [BMIM][FAP] were performed with a stresscontrolled Rheometer MCR 302 (Anton Paar, Germany) equipped with a cone-and-plate geometry. The cone angle was 1°, and the cone diameter was 50 mm with a gap of 0.099 mm. The IL sample was placed on the plate using disposable pipettes, and excess sample was removed before viscosity measurements were made. The rheometer MCR 302 able to detect torque

NIST/TRC and own search results. Detailed critical analysis of the reported density data for the [BMIM][FAP] was done in our previous work.19 Only three sources21,24,25 are representing very restricted viscosity data (in total 18 data points) for [BMIM][FAP] at atmospheric pressure in the limited temperature range from 293 to 373 K. A literature survey revealed that no viscosity data are available in the literature for [BMIM][FAP] under pressure and at atmospheric pressure above the temperature of 373 K and below 293 K. As will be shown below (see Viscosity Correlation Model for the ILs[BMIM][FAP] Section), relative large scatter and inconsistence, up to 5%, between the various reported viscosity data, were found for [BMIM][FAP]. Unfortunately, we could not find any reported in the literature heat capacity and speed of sound data for [BMIM][FAP]. Such kinds of data were first reported in the present work. The present work is considerably expanding the available viscosity, heat capacity, and speed of sound database for the [BMIM][FAP] to high (to 414 K) and low (to 263 K) temperatures. We reported accurate viscosity data (more than 417 data points) for the [BMIM][FAP] over the temperature range of 263 to 414 K at atmospheric pressure using Anton Paar SVM 3000 Stabinger viscometer and Rheometer MCR 302. New heat capacity and speed of sound data were first reported over the temperature range of 273 to 413 K for heat capacity and from 278 to 343 K, respectively.

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EXPERIMENTAL SECTION Material. The ILs sample 1-butyl-3-methylimidazolium tris(pentafluoroethyl) trifluorophosphate [BMIM][FAP] (chemical formula C14H15F18N2P; CAS # 917762-91-5, product number 4.91232.0100, MIL = 584.2315 g·mol−1) used in this work was supplied by Merck Co. LLC (Germany). The supplier furnished its purity assay (NMR)>0.99 weight fraction. Before use, the ILs sample was degassed under vacuum and dried at about 423 K for a minimum time period of 48 h. Water contents were determined before and after measurements using Karl Fischer titration (a Metrohm 831 KF Coulometer in Canberra and a KEM MKC-510 in Sendai) and found to be less than 120 ppm. Table 2 lists the commercial sources, purities, water content, and analysis method of the samples used. Density Measurements. The density, ρ(T), of the ILs [BMIM][FAP] at atmospheric pressure as a function of 3621



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values down to ∼0.1 μNm. Rheometers are able to take measurements in both oscillation and rotation mode, consequently giving them a wide range of measuring capability. The details regarding the operational system can be found elsewhere5,17,18 (visit also Anton-paar.com). The combined expanded uncertainty of the viscosity (η) and temperature (T) measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 1.0% and 0.05 K, respectively. The Anton Paar Rheometer MCR 302 equipment used in this work for the determination of viscosity of ILs was validated in recent publication.17 In this method the viscosity is defined as τ η(Pa·s) = γṡ where γ̇ (s−1) is the shear rate and τs (N · m−2) is

Table 3. Measured Values of Density (ρ) and Temperature (T) of the IL [BMIM][FAP] Using Different Anton-Paar VTD Instruments at Atmospheric Pressure (101 kPa)a VTD DMA 5000M

shear stress. The shear rate was constant at γ̇ = 6 s−1. The shear stress τs is varied between 0.0327 and 3.85 N·m−2. The rotational speed was ω = 0.506 min−1, while moment of force during the measurements was between 1.07 and 126 μN·m. The combined expanded uncertainty of the viscosity measurements at the 0.95 confidence level with a coverage factor of k = 2 is estimated to be 1.0%, The same ILs sample has been also measured using AntonPaar SVM 3000 Stabinger viscometer with an combined expanded uncertainty at 0.95 confidence level with a coverage factor of k = 2 of 0.35%. These instruments were recently5,17,18 used for the measurements of viscosity of the other ILs. The calibration of the Anton Paar instruments (VTD apparatus, sound velocity meter, and stress-controlled Rheometer MCR 302) and Pyris 1 DSC Differential Scanning Calorimeter were performed with a minimum of two reference fluids, such as water, air, nitrogen, methanol, ethanol, benzene, and toluene, whose thermodynamic and transport properties are well-known (NIST/REFPROP, IAPWS formulation for water). In the present work we used thermodynamic and transport properties of pure water (international accepted standard properties of water, IAPWS) to calibrate the instruments. The other reference fluids (air, nitrogen, methanol, ethanol, benzene, and toluene) were used to confirm the reliability of the calibrations. The accuracy of the methods of thermodynamic and transport property measurements is limited by the calibration procedure and depends on the uncertainty of the properties of calibrating fluid and should be performed very carefully. The final uncertainties of the measured thermodynamic and transport properties (see below Tables 3, 4, 5, 6, and 7) of the IL are including the correction on calibration procedure. Also, the uncertainties of the all measured properties included the impurity corrections.

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T/K

ρ/kg·m−3

273.15 283.15 293.15 298.15 313.15 333.15 353.15

1652.10 1642.74 1630.39 1623.73 1607.76 1584.24 1562.08 VTD DMA HPM

273.16 283.15 293.15 298.15 313.16 333.15 353.15 373.15 393.15 413.15

1652.07 1642.71 1629.96 1623.70 1606.73 1584.22 1561.78 1539.47 1517.22 1495.07 VTD SVM 3000

T/K

ρ/kg·m−3

278.15 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

1649.60 1643.40 1631.20 1619.30 1607.90 1596.60 1585.05 1574.06 1562.10 1553.50 1542.70 VTD DSA5000M

RESULTS AND DISCUSSION

Density, Heat Capacity, Speed of Sound, and Viscosity Measurements. The present measured density data for [BMIM][FAP] using four different Anton Paar Instruments (DMA 5000M, DMA HPM,SVM 3000, and DSA 5000M) are given in Table 3 and depicted in Figure 1. Detailed analyses of the accuracy and consistency assessment of the measured densities of [BMIM][FAP] were performed in our recent work19 where we provided detailed comparison with reported data. In general our density measurements are in good consistence with the most accurate reported data20−23 (see Figure 1). The agreement between the present results and other reported density data sets20−23 is within 0.03 to 0.12%. Acceptable agreement within 0.12% was found with the data reported by Almantariotis et al.21 Excellent agreements within 0.03 and 0.04% were found with the data reported by Vraneš et al.22 and Součkova et al.,20 respectively. Single data point (this is predicting value, not

T/K

ρ/kg·m−3

283.15 293.15 303.15 313.16 323.16 333.15 343.16 343.15 333.15 323.15 313.15 303.15 293.15 283.15 278.15 278.15 283.15 293.15 303.15 313.16

1643.16 1631.68 1620.30 1607.99 1597.06 1585.06 1575.53 1574.07 1586.15 1597.29 1607.81 1619.80 1631.19 1642.69 1648.46 1648.60 1642.84 1631.37 1619.97 1607.98

a

Standard uncertainties u are u(T) = 0.025 K; u(P) = 1 kPa; ur(ρ) = 0.0014 (including impurity correction).

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[BMIM][FAP] in the distinct temperature ranges are depicted in Figure 5. Figure 6 shows the comparison of the present viscosity data for [BMIM][FAP] with the values reported by other authors.21,24,25 Figure 5 demonstrates detailed view of the temperature behavior of viscosity, η − T, in distinct temperature ranges and consistence of the measured values of viscosity reported by various authors. As one can see from Figure 4, the measured values of the viscosity of [BMIM][FAP] decrease rapidly as the temperature initially increases above 263 K (in the range of 263 to 320 K). The rate of viscosity changes, (∂η/∂T), strongly depends on temperature range. The viscosity of [BMIM][FAP] changes (decreases) from 797 mPa·s (at 263 K) to 4.6 mPa·s (at temperature of 414 K), i.e., decreases by about 173 times. At high temperatures, (above approximately 350 K), the viscosity asymptotically approaches a hightemperature limit, i.e., the rate of the viscosity changes with temperature increases becomes very small, (∂η/∂T) almost constant (0.01 mPa·s·K−1). In general, the same temperature behavior of the viscosity was found for all fluids in our previous studies. The qualitative temperature behavior, details of the temperature dependence of the viscosity in the distinct temperature ranges, can be studied using the temperature coefficient of viscosity, (∂lnη/∂T), which is directly related with temperature derivative, (∂η/∂T), of viscosity (rate of viscosity changes). As Figure 7 shows, the temperature rate (left), (∂η/ ∂T), of the viscosity of the ILs decreases with temperature until η asymptotically approaches a constant value at high temperatures (approximately above 350 K). The rate, (∂η/∂T), of viscosity decreases for [BMIM][FAP] sample changes from −103.3 to −0.01 mPa·s·K−1 with increasing temperature from 263 to 414 K. At high temperatures (above 350 K), the rate, (∂η/∂T), is nearly constant at −0.024 mPa·s·K−1. The values of the temperature coefficient of the viscosity, βT = (∂lnη/∂T), calculated from the present viscosity measurements are depicted in Figure 7 (right). The temperature coefficient of the viscosity, βT, for the present ILs sample changes from −0.098 to −0.008 K−1 (decreases almost by 10 times) in the whole experimental temperature range. Reasonable agreement within AAD = 3.4% was found between the present data and the data reported by Almantariotis et al.21 Good agreement within 0.3 to 2% was observed at low temperatures (below 333 K), while at high temperatures (above 333 K) the discrepancy is reaching to 5% and more. Acceptable agreement of 3.06% was found between the present viscosity data for [BMIM][FAP] and the data reported by Dutt et al.24 The single data point (η = 93.0 mPa·s) at 293 K reported by Xioa et al.25 agrees with the present result (η = 99.54 mPa·s) within 7%. The same deviation of 7.5% was found with the data by Almantariotis.21 Viscosity Correlation Model for the ILs[BMIM][FAP]. Various empirical and semiempirical models have been proposed by different authors to represent the viscosity of liquids and liquid mixtures. Messaâdi et al.29 summarized the most frequent using forms of temperature dependence of the viscosity proposed by different authors. They modified linear Arrhenius-type equation by introducing third parameter (Arrhenius temperature TA) (see also ref 30). Messaâdi et al.29 tried to give some physical meaning of the proposed equation parameters. They found correlation between the Arrhenius parameters. The present measured viscosity data of the ILs [BMIM][FAP] were used to develop correlations based on the Vogel−Tammann−Fulcher model.31−33

Table 4. Measured Temperatures (T) and Heat Capacities (CP) of [BMIM][FAP] as a Function of Temperature at Atmospheric Pressure (101 kPa)a T/K

CP/kJ·kg−1·K−1

T/K


273.15 283.15 293.15 298.15 313.15

1.137 1.160 1.182 1.193 1.224

333.15 353.15 373.15 393.15 413.15

1.262 1.297 1.329 1.357 1.381

a

Standard uncertainties u are u(T) = 0.025 K; u(P) = 1 kPa; ur(CP) = 0.0075.

Table 5. Measured Temperatures (T) and Speed of Sound (c) of [BMIM][FAP] as a Function of Temperature at Atmospheric Pressure Using Anton-Paar DSA 5000M VTD and Sound Velocity Metera T/K

c/m·s−1

T/K

c/m·s−1

278.15 278.15 283.15 283.15 283.15 293.15 293.15 293.15 303.15

1156.05 1156.10 1143.69 1143.42 1143.69 1119.61 1119.69 1119.07 1096.45

303.15 303.15 313.16 313.15 323.16 333.15 333.15 343.16 343.15

1096.05 1095.76 1073.59 1073.26 1051.73 1030.29 1030.26 1009.68 1009.71

a Standard uncertainties u are u(T) = 0.025 K; u(P) = 1 kPa; u(c) = 0.25 m·s−1.

measured) reported by Liu et al.23 at standard state deviates from the present and other reported values within 0.25%. Measurements of the heat capacity, CP(T), and speed of sound, c(T), were performed at temperatures from 273 to 413 K and from 283 to 343 K, respectively. The measured values of CP(T) and c(T) are given in Tables 4 and 5, respectively and depicted in Figures 2 and 3. As one can see the temperature dependence of the speed of sound for [BMIM][FAP] is almost linear, while the temperature behavior of heat capacity is considerable deviate from the linearity (positively deviate from linearity). Unfortunately, there are no reported heat capacity and speed of sound data for [BMIM][FAP] to compare with the present results and validate the accuracy and reliability of the results. Measurements of the viscosity, η(T), for [BMIM][FAP] as a function of temperature were performed between 263 and 414 K at atmospheric pressure. The measured values of the viscosity of [BMIM][FAP] are presented in Tables 6 and 7 using two different viscometers (Rheometer MCR 302 and Anton-Paar SVM 3000 Stabinger viscometer), respectively. The present study, comprising 417 data points at atmospheric pressure, is the most comprehensive viscosity data set available for BMIM][FAP]. The discrepancy between the two different instruments is AAD = 0.8%. This is confirming the accuracy and consistency of the measurements and the reliability measured values of the viscosity. As one can note from Table 1, the present measurements are considerably extending the available viscosity data for [BMIM][FAP] to high temperatures (to 414 K) and to low temperatures (to 263 K). All measured viscosity data for [BMIM][FAP] are depicted in Figure 4 together with the values calculated from the present and reported correlations. Detailed view of the temperature dependence of the viscosity of 3623



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Table 6. Measured Temperatures (T) and Viscosities (η) of [BMIM][FAP] as a Function of Temperature at Atmospheric Pressure (101 kPa) Using Rheometer MCR 302a Run-1

Run-2

T/K

η/mPa·s

T/K

η/mPa·s

T/K

η/mPa·s

T/K

η/mPa·s

262.57 263.41 264.26 265.11 265.95 266.78 267.62 268.47 269.33 270.18 271.00 271.80 272.59 273.38 274.17 274.96 275.75 276.54 277.34 278.14 278.94 279.73 280.53 281.34 282.14 282.94 283.74 284.54 285.35 286.16 286.95 287.75 288.56 289.36 290.17 290.97 291.78 292.58 293.40 294.23 295.05 295.85 296.65 297.45 298.24 299.03 299.83 300.63 301.43 302.23 303.03 303.84 304.63 305.44 306.23 307.04 307.83 308.64

796.60 744.85 692.89 644.78 601.19 564.21 527.80 492.34 460.31 430.55 404.12 379.90 357.40 336.85 318.36 301.38 284.30 270.37 255.86 243.38 229.81 218.03 207.25 196.67 187.15 178.39 170.06 162.01 154.90 147.79 141.22 134.65 128.53 122.43 116.98 112.21 107.52 103.36 99.541 95.658 91.747 87.899 84.298 80.985 78.291 75.109 72.516 69.807 67.059 64.808 62.425 60.493 58.290 56.805 55.218 53.634 51.676 49.938

339.17 339.98 340.78 341.58 342.38 343.18 343.99 344.79 345.58 346.39 347.20 348.00 348.80 349.60 350.40 351.20 352.01 352.81 353.61 354.41 355.22 356.02 356.82 357.63 358.43 359.24 360.04 360.84 361.65 362.45 363.26 364.06 364.86 365.67 366.47 367.27 368.07 368.88 369.69 370.49 371.29 372.09 372.89 373.69 374.50 375.30 376.09 376.91 377.71 378.51 379.31 380.12 380.92 381.72 382.53 383.33 384.13 384.94

18.728 18.120 17.559 16.949 16.762 16.629 16.180 15.806 15.388 15.292 14.723 14.786 14.198 14.303 14.137 13.886 13.432 13.242 13.173 12.651 12.346 12.020 12.084 11.891 11.673 11.476 11.177 10.985 11.017 10.562 10.354 10.346 10.124 9.994 9.906 9.516 9.374 9.336 9.374 9.228 8.873 8.729 8.624 8.544 8.569 8.319 8.204 8.214 7.887 8.021 7.915 7.477 7.419 7.449 7.306 7.411 7.317 6.962

262.61 263.42 264.25 265.10 265.94 266.77 267.59 268.41 269.23 270.04 270.86 271.67 272.49 273.33 274.17 275.02 275.83 276.63 277.43 278.21 279.00 279.79 280.58 281.37 282.17 282.96 283.76 284.56 285.35 286.15 286.95 287.76 288.56 289.37 290.17 290.98 291.78 292.58 293.38 294.19 294.99 295.80 296.60 297.40 298.20 299.00 299.81 300.61 301.41 302.22 303.02 303.82 304.63 305.43 306.24 307.03 307.83 308.64

784.48 736.48 687.90 640.35 597.92 560.44 524.87 491.20 461.16 432.39 406.50 382.59 359.71 338.00 318.09 299.66 282.81 267.23 252.48 239.23 227.18 215.62 204.96 194.80 185.41 176.46 168.20 160.22 152.83 145.83 139.48 133.33 127.22 121.75 116.45 111.61 107.02 102.57 98.343 94.251 90.586 87.093 83.806 80.551 77.626 74.623 71.880 69.334 66.814 64.496 62.324 60.186 58.079 56.230 54.359 52.509 50.847 49.218

339.16 339.96 340.77 341.58 342.40 343.23 344.05 344.88 345.70 346.52 347.33 348.14 348.94 349.73 350.50 351.28 352.07 352.86 353.65 354.45 355.24 356.03 356.84 357.64 358.44 359.24 360.04 360.85 361.65 362.46 363.26 364.06 364.86 365.67 366.47 367.27 368.07 368.88 369.68 370.48 371.29 372.08 372.88 373.68 374.49 375.28 376.09 376.91 377.70 378.51 379.31 380.12 380.91 381.72 382.53 383.33 384.13 384.94

17.896 17.620 17.488 17.217 16.726 16.334 15.946 15.754 15.602 15.112 14.754 14.420 14.333 14.182 13.731 13.426 13.186 13.169 13.280 12.779 12.650 12.097 11.869 11.753 11.655 11.368 11.082 10.925 10.782 10.775 10.423 10.205 10.117 9.945 9.832 9.629 9.445 9.367 9.261 9.187 8.973 8.787 8.767 8.715 8.555 8.362 8.241 8.155 8.116 8.083 7.850 7.772 7.645 7.474 7.380 7.188 7.113 7.037

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Table 6. continued Run-1

a

Run-2

T/K

η/mPa·s

T/K

η/mPa·s

T/K

η/mPa·s

T/K

η/mPa·s

309.44 310.24 311.05 311.85 312.66 313.46 314.26 315.07 315.87 316.67 317.48 318.28 319.09 319.90 320.68 321.50 322.30 323.10 323.92 324.74 325.58 326.41 327.23 328.03 328.83 329.62 330.40 331.19 331.98 332.77 333.57 334.38 335.18 335.98 336.77 337.57 338.37

48.344 46.899 45.514 44.149 43.012 41.709 40.493 39.290 38.185 37.102 36.301 35.330 34.314 33.147 32.352 31.350 30.452 29.589 28.861 28.591 28.143 26.936 25.762 25.054 24.469 23.894 23.331 22.843 22.456 22.113 21.274 20.714 20.368 19.873 19.412 19.087 18.712

385.74 386.54 387.35 388.15 388.96 389.76 390.56 391.36 392.17 392.96 393.76 394.56 395.37 396.17 396.98 397.78 398.59 399.38 400.19 400.99 401.80 402.60 403.40 404.21 405.01 405.82 406.62 407.42 408.22 409.03 409.83 410.63 411.44 412.25 413.03 413.85 -

6.946 6.889 6.958 6.771 6.787 6.706 6.626 6.547 6.469 6.394 6.240 6.188 5.949 5.920 5.965 5.959 5.899 5.686 5.536 5.509 5.352 5.399 5.241 5.232 5.284 5.347 4.986 4.933 5.010 5.009 4.990 4.843 4.669 4.686 4.675 4.603 -

309.44 310.25 311.05 311.85 312.66 313.46 314.27 315.06 315.87 316.67 317.47 318.28 319.08 319.88 320.69 321.49 322.29 323.10 323.90 324.70 325.51 326.31 327.12 327.92 328.71 329.52 330.32 331.12 331.93 332.73 333.54 334.34 335.14 335.95 336.75 337.55 338.36

47.730 46.227 44.751 43.358 42.169 40.943 39.730 38.504 37.300 36.476 35.384 34.401 33.419 32.478 31.653 30.879 30.440 29.440 28.721 27.939 27.195 26.724 26.110 25.435 24.750 23.775 23.158 22.622 22.200 21.764 21.170 20.617 20.154 19.630 19.425 18.999 18.494

385.74 386.55 387.35 388.15 388.96 389.76 390.56 391.36 392.17 392.96 393.76 394.56 395.37 396.17 396.97 397.78 398.58 399.39 400.19 400.99 401.80 402.61 403.40 404.21 405.01 405.82 406.62 407.41 408.22 409.03 409.83 410.63 411.44 412.24 413.06 413.84 -

6.914 6.907 6.737 6.697 6.708 6.603 6.455 6.361 6.348 6.292 6.204 6.082 6.007 5.981 5.929 5.833 5.753 5.771 5.745 5.640 5.539 5.475 5.471 5.444 5.396 5.258 5.177 5.128 5.149 5.072 4.980 4.926 4.847 4.853 4.810 4.737 -

Standard uncertainties u are u(T) = 0.025 K; u(P) = 1 kPa; ur(η) = 0.01 (including the uncertainty of the calibrating fluid).

⎛b ⎞ b η(T ) = b0exp⎜ 1 ⎟ or ln η(T ) = ln b0 + 1 ⎝T ⎠ T

Table 7. Measured Temperatures (T) and Viscosities (η) of [BMIM][FAP] as a Function of Temperature at Atmospheric Pressure (101 kPa) Using Anton-Paar SVM 3000 Stabinger Viscometera T/K

η/mPa·s

T/K

η/mPa·s

273.15 278.15 283.15 293.15 298.15 303.15 313.15

341.535 238.740 174.760 99.999 78.002 62.135 41.386

323.15 333.15 343.15 353.15 363.15 373.15 -

28.827 21.361 16.371 12.960 10.559 8.6802 -

(1)

where b0 is the viscosity (mPa·s), η = η∞, at the high temperature limit (T → ∞, i.e., viscosity of the system in vapor state); b1 = εa/ R (viscosity Arrhenius energy), and εa = ΔH are the flow activation energy (enthalpy of activation, related with the enthalpy of vaporization), where T is in K. This equation was successfully used previously by many authors to represent temperature dependence of the experimental viscosity data for different type of liquids and liquid mixtures. However, very limited simple pure and binary systems are obeyed to the linear Arrhenius behavior (eq 1) of viscosity. For some liquids and liquid mixtures the experimental curve lnη versus T −1 considerably deviates from the original linear Arrhenius behavior eq 1 at low temperatures. In this case the linear ArrheniusAndrade relation (eq 1) can be slightly modified to extend the temperature range where the equation is valid. Therefore, this equation fails to accurately represent of the experimental viscosity data over the wide temperature range (see also refs

a

Standard uncertainties u are u(T) = 0.025 K; ur(η) = 0.0068 (including the uncertainty of the calibrating fluid); u(P) = 1 kPa.

Figure 8 illustrates experimental viscosity data for [BMIM][FAP] in the lnη versus T−1 projection. As one can see from Figure 8, lnη − T−1curve is not a straight line as it follows from the original linear Arrhenius-Andrade relation34−41 3625



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Figure 1. Measured densities of the IL [BMIM][FAP] at atmospheric pressure as a function of temperature together with reported data. ●, this work (DSA 5000M); ○, Vraneš et al.;22 □, Součkova et al.;20 △, Almantariotis et al.;21 ■, this work (SVM 3000); ◊, this work (DMA HPM); ▲, this work (DMA-500 M); × , Liu et al.23 Solid line is calculated from the present correlation eq 17. Dashed line is calculated from correlation by Almantariotis et al.21

Figure 3. Measured speed of sound of [BMIM][FAP] as a function of temperature at atmospheric pressure. Solid line is calculated from the correlation eq 19.

Figure 4. Measured viscosities of [BMIM][FAP] as a function of temperature at atmospheric pressure together with the values calculated from various correlations. ●, this work (Run-1); ○, this work (Ru-2). Dashed curve is calculated from VFT eq 4 by Almantariotis et al.21 Solid curve is calculated from Vogel−Tammann−Fulcher model eq 3 (this work).

Figure 2. Measured heat capacities of [BMIM][FAP] as a function of temperature at atmospheric pressure. Solid curve is calculated from the correlation eq 18.

⎛ B ⎞ B η(T ) = η∞exp⎜ ⎟ or ln η(T ) = ln η∞ + − − T T T T0 ⎝ 0⎠

42,43), especially at low temperature where rapid increases of the viscosity are observed. In this case the empirical modification of the original linear Arrhenius-Andrade relation, eq 1, can be used (see also Millat et al.44 and Reid et al.45)

(3)

where optimal values of VTF parameters for [BMIM][FAP] are lnη∞ = −1.500859, B = 727.37 K, and T0 = 174 ± 0.5 K. The accuracy and reliability of the presentation of the measured viscosity data for [BMIM][FAP] with eq 3 were examined statistically in terms of the absolute average deviation (AAD), the bias (Bias), the standard deviation (St. Dev.), the standard error (root-mean-square deviation) (St. Err.), and the maximum percentage deviation (Max. Dev.). Deviation statistics are AAD = 0.59%, Bias = −0.004%, St. Dev. = 0.76%, St. Err. = 0.05, and Max.Dev. = 3.1%, where (1) Absolute average deviation:

⎛b b ⎞ b b η(T ) = b0exp⎜ 1 + 22 ⎟ or ln η(T ) = ln b0 + 1 + 22 ⎝T T T ⎠ T (2)

However, eq 2 also failed to accurately represent measured viscosities of [BMIM][FAP] in the low temperature range (near the melting temperature) where rapid increases of the viscosity are observed. Vogel−Tamman−Fulcher31−33 proposed new modified model of Arrhenius equation to accurately represent low temperature behavior of the viscosity. In the present work we used the Vogel−Tamman−Fulcher (VTF) type equation31−33 for representation of the measured viscosity data for [BMIM][FAP]

100 AAD = N 3626

N

∑ |(Y exp − Y cal)/Y exp|i i=1

(4)



Article

Figure 7. Temperature dependence of the rate of viscosity changes (left), (∂η/∂T), and the temperature coefficient of the viscosity (right), βT = (∂lnη/∂T), calculated from VTF correlation eq 3 for [BMIM][FAP].

Figure 5. Detailed view of the temperature dependence of viscosity of [BMIM][FAP] reported by various authors together with the present results in the distinct temperature ranges (A, low temperature range; B, high temperature range). Symbols and curves are the same as in Figure 4. Dashed curve is calculated from VTF model by Almantariotis et al.21

Figure 8. Measured values of viscosity lnη of [BMIM][FAP] as a function of T−1 at atmospheric pressure. Symbols are the present experimental data. (- - - -), original linear Arrhenius-Andrade type eq 2; (),Vogel−Tammann−Fulcher model eq 3.

(3) Standard deviation: St. Dev. = ⎧ 1 ⎨ ⎩N − 1 ⎪

⎪

N

∑ [100(Y

exp

cal

− Y )/Y

exp

i=1

⎫1/2 − Bias] ⎬ ⎭i 2⎪ ⎪

(6)

(4) Standard error (root-mean-square error): ⎧1 St. Err. = 100⎨ ⎩N ⎪

⎪

⎫1/2 exp cal exp 2 ⎬ Y Y Y [( − )/ ] ∑ ⎭i i=1 N

⎪

⎪

(7) Figure 6. Measured viscosities of [BMIM][FAP] as a function of temperature at atmospheric pressure together with reported data. ●, this work (Run-1); ○, this work (Ru-2); △, Almantariotis et al.;21 × , Dutt et al.;24 (), Vogel−Tammann−Fulcher model eq 3 (this work).

The bias (Bias) deviation is a measure of any systematic deviations of the correlation eq 3 with the viscosity data, while the standard deviation (St. Dev.) is a measure of the scatter of the data about the Bias. Detailed comparisons of the experimental and calculated from VTF model values of viscosity for [BMIM][FAP] are also presented in Figures 4−6 and 8 together with the present and reported data. These figures included also the values of viscosity calculated from the correlation reported by Almantariotis et al.21

(2) Bias deviation: 100 Bias = N

N

∑ [(Y exp − Y cal)/Y exp]i i=1

(5) 3627



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⎛ 1214 ⎞ ⎟ η(T ) = 0.0006T 0.5exp⎜ ⎝ T − 139 ⎠

value of Tg for ILs, see, for example refs 52,56,57. For example, for the ILs [EMIM][MeSO3] DSC gives the values for Tg as 196 K,56 211 K,57 and 210.3 K.52 Unfortunately, we could not find in the literature reported direct DSC experimental data for Tg of [BMIM][FAP] to compare with the present result. Derived Thermodynamic Properties of [BMIM][FAP]. The present measured thermodynamic (density and heat capacity) and acoustic (speed of sound) data were used to accurately calculate other very useful derived properties, such as

(8)

Unfortunately, this equation was developed on the bases of limited experimental data in the very narrow temperature range. Therefore, this equation is failed to represent present viscosity data for [BMIM][FAP] in the whole experimental temperature range. The present VTF model, eq 3, can be recommended to accurately represent the experimental viscosity data of [BMIM][FAP] in the wide temperature range from 263 to 415 K, especially at low temperature range where sharp changes of the viscosity are observed. Figure 9 shows deviation plot between the

( ∂∂HP )T ,( ∂∂UV )T .

k S , k T , a P , γ V , ΔH, C P , C V ,

All of these

thermodynamic properties were calculated using the wellknown thermodynamic relations:58 (1) Isentropic compressibility, kS =

1 c 2ρ

(10) 1

where k S = − V

( ∂∂VP )Shas been directly calculated using

measured densities (ρ) and speed of sound (c) data. (2) Cubic expansion coefficient,

(

Figure 9. Relative percentage deviation, δη = 100

ηcal − ηexp ηexp

), between

αP = −

the present experimental viscosity data and the VFT correlations (eq 3) for the viscosity of [BMIM][FAP] as a function of temperature.○, Run1; ●, Run-2; × , Dutt et al.;24 □, Almantariotis et al.21

T0

=1+

δ 2.303log10(ηg /η)

(11)

has been calculated using measured densities (ρ). (3) Isothermal compressibility,

present and reported21,24 data and the correlation eq 3 as a function of temperature. The average absolute deviation (AAD for the VTF model) over the temperature range of 263 to 414 K is 0.59%, while for original linear Arrhenius-Andrade eq 2 is 2.93%. VTF model, eq 3, was successfully applied in our previous publication46 for pure MEG, DEG, TEG, and their binary mixtures at atmospheric pressure and IL (EMIM][MeSO3]).18 This model was also successfully used by many authors (see, for example refs 47−52) to represent measured viscosities for 1,nalkenediols, 2-alkylamines, polyethers, and IL.53−55 The Angell relation between the VFT parameters, δ = B/T0 = 4.18, and the glass transition temperature, Tg Tg

1 ⎛ ∂ρ ⎞ ⎜ ⎟ ρ ⎝ ∂T ⎠ P

kT =

αP γV

where k T =

(12) 1 −V

∂V ∂P T

( )

and thermal pressure coefficient,

( ∂P )

γV = ∂T . V (4) Isochoric heat capacity, C V = C P/c 2ρk T

(13)

has been calculated using measured densities (ρ), heat capacities (CP), speed of sound (c), and derived values of kT. 5. Enthalpy difference,

(9)

where log10(ηg/η) = 17, allows the estimate the value of Tg = 192.58 ± 5 K. Usually the DSC technique is used to measure the

ΔH = H(T ) − H(T0) =

∫T

T

C P(T )dT

0

(14)

Table 8. Derived, from the Present Experimental Density, Heat Capacity, and Speed of Sound Measurements, Thermodynamic Properties of ILs [BMIM][FAP] as a Function of Temperature at Atmospheric Pressure (101 kPa)a T/K

ρ/kg·m−3

γV/MPa·K−1

aP × 103/K−1

kT × 103/MPa−1

kS × 103/MPa−1

CV/kJ·kg−1·K−1


c/m·s−1

273.15 283.15 293.15 298.15 313.15 333.15 353.15 373.15 393.15 413.15

1653.63 1642.34 1631.06 1625.41 1608.47 1585.88 1563.27 1540.64 1518.01 1495.36

1.3288 1.2766 1.2276 1.2038 1.1343 1.0431 0.9538 0.8689 0.7929 0.7308

0.6822 0.6871 0.6921 0.6946 0.7022 0.7126 0.7234 0.7344 0.7458 0.7576

0.5134 0.5382 0.5638 0.5770 0.6191 0.6832 0.7584 0.8453 0.9406 1.0367

0.4429 0.4655 0.4892 0.5014 0.5395 0.5940 0.6527 0.7152 0.7815 0.8509

0.981 1.003 1.026 1.037 1.067 1.097 1.116 1.124 1.127 1.134

1.137 1.160 1.182 1.193 1.224 1.262 1.297 1.329 1.357 1.381

1168.50 1143.66 1119.54 1107.75 1073.47 1030.29 990.010 952.624 918.132 886.536

a

Standard uncertainties u are u(T) = 0.025 K; ur(ρ) = 0.0014; u(P) = 1 kPa; ur(γV) = 0.005; ur(ap) = 0.002; ur(kT) = 0.003; ur(kS) = 0.006; ur(cV) = 0.013; ur(cP) =0.0075; ur(cP) = 0.0005. 3628



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has been calculated using measured CP data.

atmospheric pressure over the temperature range of 273 to 415 K.

■

(6) Partial pressure derivative of enthalpy, ⎛ ∂H ⎞ ⎜ ⎟ = V (1 − Tα ) P ⎝ ∂P ⎠T

(15)

*E-mail: [email protected]. ORCID

(7) Partial derivatives of internal energy (internal pressure),

Ilmutdin Abdulagatov: 0000-0002-6299-5280

⎛ ∂U ⎞ ⎜ ⎟ = − P + Tγ 0 V ⎝ ∂V ⎠T

Notes

(16)

The authors declare no competing financial interest.

( ∂∂TP )V , of

■

[BMIM][FAP] required to calculated these properties were taken from our previous publication.19 Due to the experimental temperature differences between the various measured properties (density, heat capacity, and speed of sound), the present measured data were fitted to correlation equation

■

where P0 = 0.101 MPa. The values of thermal pressure coefficient, γV =

ρ(T ) = 1960.4986 − 1.1188T − 0.000017T

AUTHOR INFORMATION

Corresponding Author

2

ACKNOWLEDGMENTS One of the authors (J. Safarov) thanks of the University of Rostock and Azerbaijan Technical University for support of the project.

(1) Ionic Liquids: Theory, properties, new approaches; Kokorin, A., Ed.; Intech Web. Org.: Croatia, 2011; p 738. (2) Wu, B.; Reddy, R. G.; Rogers, R. D. Novel ionic liquid thermal storage for solar thermal electric power systems. Proc. Solar Forum 2001 Solar Energy: The Power to Choose, Washington DC, April 22−35, 2001. (3) Valkenburg, M. E. V.; Vaughn, R. L.; Williams, M.; Wilkes, J. S. Thermochemistry of ionic liquid heat-transfer fluids. Thermochim. Acta 2005, 425, 181−188. (4) Chandra, S. Recent trends in high efficiency photo-electrochemical solar cell using dye-sensitized photo-electrodes and ionic liquid based redox electrolytes. Proc. Natl. Acad. Sci., India, Sect. A 2012, 82, 5−19. (5) Schmidt, H.; Stephan, M.; Safarov, J.; Kul, I.; Nocke, J.; Abdulagatov, I. M.; Hassel, E. Experimental study of the density and viscosity of 1-ethyl-3-methylimidazolium ethyl sulfate. J. Chem. Thermodyn. 2012, 47, 68−75. (6) Safarov, J.; Hamidova, R.; Zepik, S.; Schmidt, H.; Kul, I.; Shahverdiyev, A.; Hassel, E. Thermophysical Properties of 1-hexyl-3methylimidazolium bis(trifluoromethylsulfonyl) imide at high temperatures and pressures. J. Mol. Liq. 2013, 187, 137−156. (7) Hamidova, R.; Kul, I.; Safarov, J.; Shahverdiyev, A.; Hassel, E. Thermophysical properties of 1-butyl-3-methylimidazoliumbis(trifluoromethylsulfonyl)imide at high temperatures and pressures. Braz. J. Chem. Eng. 2015, 32, 303−316. (8) Huseynova, G.; Hamidova, R.; Safarov, J.; Bashirov, M.; Hassel, E. Investigation of the density and speed of sound of ionic liquid 1-ethyl-3methylimidazolium methanesulfonate. Trans. Azerb. Nat. Acad. Sci., Ser. Phys.-Math. &Technol. Sci. 2016, 5, 128−135. (9) Polikhronidi, N. G.; Batyrova, R. G.; Abdulagatov, I. M.; Magee, J. W.; Wu, J. T. Saturated and Compressed Liquid Heat Capacity at Constant Volume for 1-Hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide). Phys. Chem. Liq. 2014, 52, 657−679. (10) Polikhronidi, N. G.; Batyrova, R. G.; Abdulagatov, I. M.; Magee, J. W.; Wu, J. T. Thermodynamic properties at saturation derived from experimental two-phase isochoric heat capacity of 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide. Int. J. Thermophys. 2016, 37, 103−130. (11) Abdulagatov, I. M.; Tekin, A.; Safarov, J.; Shahverdiyev, A.; Hassel, E. Densities, Excess, Apparent, and Partial Molar Volumes of Binary Mixtures of Ethanol+[BMIM][BF4] as a Function of Temperature, Pressure, and Concentration. Int. J. Thermophys. 2008, 29, 505− 533. (12) Abdulagatov, I. M.; Tekin, A.; Safarov, J.; Shahverdiyev, A.; Hassel, E. High-Pressure Densities and Derived Volumetric Properties (Excess, Apparent, and Partial Molar Volumes) of Binary Mixtures of Methanol+[BMIM][PF6]. J. Solution Chem. 2008, 37, 801−833. (13) Abdulagatov, I. M.; Tekin, A.; Safarov, J.; Shahverdiyev, A.; Hassel, E. Experimental study of the volumetric properties (density, apparent, partial, and excess molar volumes) of binary mixtures of Methanol+[BMIM][BF4]. J. Chem. Thermodyn. 2008, 40, 1386−1401.

(17)

C P(T ) = 0.183991 + 0.0046432T − 0.42236 × 10−4T 2 (18)

c(T ) = 2126.9957 − 4.4974T + 0.0036185T 2

REFERENCES

(19)

Derived thermodynamic properties of ILs [BMIM][FAP] calculated using eqs 10 to 16 are given in Table 8. Thus, we have all thermodynamic property data for [BMIM][FAP] at atmospheric pressure as a function of temperature from 273 to 415 K. Unfortunately, there are no direct measured thermodynamic properties data for [BMIM][FAP] to check the accuracy and reliability of the derived properties.

■

CONCLUSIONS 417 new experimental viscosity, 10 heat capacity, 48 density, and 18 speed of sound data points are represented for ILs [BMIM][FAP] over the temperature range of 263 to 414 K at atmospheric pressure. The present results are considerably expanding to high (up to 414 K) and to low (up to 263 K) temperature ranges in which viscosity data for [BMIM][FAP] are available. The measured viscosities were used to develop correlation models based on theoretically confirmed Vogel− Tamman−Fulcher model. It was shown that the measured values of the viscosity of [BMIM][FAP] can be best represented by fitting lnη to a VFT correlation model which is consistent with the theory of rate processes. The best fitting (AAD = 0.59%, standard deviation is 0.76%) values of the VTF parameters for [BMIM][FAP] are lnη∞ = −1.50086, B = 727.37 K, and T0 = 174 ± 0.5 K. Original linear Arrhenius- type model for the viscosity failed to accurately represent measured viscosities for [BMIM][FAP] in the low temperature range (near the melting point) where rapid increases of the viscosity is observed, i.e., the deviation of the present viscosity data for [BMIM][FAP] from linear Arrhenius behavior in the low temperature range was found. The value of the glass temperature Tg = 192.58 ± 5 K derived from the present viscosity study for [BMIM][FAP] using VTF parameters is consistent with the values obtained from DSC experimental results of 196 to 211 K reported by other authors for other ILs. The measured density, heat capacity, and speed of sound data were used for accurate calculations of the derived thermodynamic properties data for ILs [BMIM][FAP] at 3629



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