Article pubs.acs.org/IECR
Statistical Refinement and Fitting of Experimental Viscosity-toTemperature Data in Ionic Liquids Juan de Riva, Victor R. Ferro,* Lourdes del Olmo, Elia Ruiz, Rafael Lopez, and Jose Palomar Departamento Química Física Aplicada, Universidad Autónoma de Madrid, 28049 Madrid, Spain S Supporting Information *
ABSTRACT: The viscosity-to-temperature experimental data available in the open literature sources for 134 ionic liquids (ILs) was refined using a statistical procedure based on the confidence bands formalism. 1860 data points of 143 different references, among more than 2600 raw data points found in literature, were processed. As a result, 21% of the data set was rejected. The refined viscosity-to-temperature experimental data were successfully fitted to the η = f(T) Arrhenius-type equation with an R2 correlation coefficient higher than 0.99 in all cases. Parameters A and B of the Arrhenius function for 134 ILs were given for the accurate estimation of viscosity in potential uses and compared to A and B parameters for 134 organic solvents. It was found that the obtained A and B values correlate linearly for the wide sample of 134 ionic liquids. As a consequence, it is concluded that ionic liquids having high viscosities at relatively low temperatures also exhibit an abrupt decay of the viscosity with the temperature. This A−B Arrhenius’ parameter relationship was also found in organic solvents, obtaining a regression line with a nearly identical slope but different intercept than that in the case of ILs. It indicated similar temperature dependence in the viscosity of ILs and organic compounds, but a differential higher viscosity of ionic fluids. In addition, it is observed that, for temperatures over 330−373 K, the viscosities of most ILs studied here are moderate, providing a potential range to manage this kind of solvent in practical applications with less transport property limitations.
■
INTRODUCTION Room temperature ionic liquids (ILs) are liquid salts with melting points below or near 100 °C. They are usually composed of large asymmetric organic cations and inorganic or organic anions. Due to this peculiar chemical structure, they exhibit very interesting properties like, for example, low volatilities (negligible vapor pressures) which make ILs attractive candidates for replacing conventional organic solvents in different practical applications including separation processes,1 catalysis,2,3 electrochemistry,45and analytical chemistry.6,7 However, some drawbacks limit the extensive and definitive application of ILs in the corresponding industrial processes. Probably, their high viscosity is one of the most significant practical disadvantages of the ILs. Common organic solvents typically have room temperature viscosities ranging from 0.2 to 10 cP,8 whereas ILs display a broad range of room temperature viscosities, from 10 to more than 105 cP9 (for more bibliographic details see also the Supporting Information (SI)). However, as also occur in conventional organic solvents, the viscosity of ILs strongly depends on the temperature, showing a characteristic exponential decay for temperatures in the range frequently used in common industrial applications. Additionally, ILs have found other important applications where the control of the viscosity plays an outstanding role: as lubricants and additives10,11−, in absorption refrigeration cycles,12−14 and CO2 capture.15−17 Consistently with the significance of the theme, several research groups have measured the viscosity of the ILs (see references in the SI) under different conditions and using different experimental procedures. As a result, massive viscosity measurements have been carried out and a broad database is being constructed. On the basis of these experimental data, © 2014 American Chemical Society
different studies on the viscosity behavior of the ILs and its determining factors have been performed.18,19 Two different classes of public literature sources on the ionic liquid viscosity can be distinguished: (i) works in which, when dealing with ionic liquids from a general point of view, or for different specific applications than the study of the viscosity itself, single point measurement of viscosity vs temperature are reported (usually at 298.15 K), and (ii) works in which the viscosity is determined at different temperatures, i.e., the viscosity is evaluated systematically as a function of temperature. This kind of work usually offers more reliable values of the viscosity because the temperature-dependence itself acts as a validation criterion of the individual values. However, in some cases, the experimental viscosity data show an undesirable variability, i.e., the viscosities of the ILs presented in the literature show clear inconsistences and important dispersion is observed. The 1-butyl-3-methylimidazolium tetrafluoroborate (bmimBF4) IL provides a good example of this variability as their literature-reported viscosities at 298.15 K are ranged from 43 to 219 cP (see below). This variability of the experimental viscosities severely limits the further application of these data in research activity and process development based on ILs. Therefore, experimental data on viscosity of the ILs cannot be used without an appropriate analysis and re-elaboration. A similar situation has been described for other IL properties as the heat capacity,20 density,21 and so forth. Paulechka,20 for example, has addressed Received: Revised: Accepted: Published: 10475
April 7, 2014 May 27, 2014 May 30, 2014 May 30, 2014 dx.doi.org/10.1021/ie5014426 | Ind. Eng. Chem. Res. 2014, 53, 10475−10484
Industrial & Engineering Chemistry Research
Article
Scheme 1. Decision Algorithm Used in This Work Both for Refining the Experimental Viscosity-to-Temperature Database Collected from Literature and for Fitting the Refined Data to the Two-Parameters Arrhenius-Type Equation of η = f(T)
this challenge and developed a consistent methodology to filter the experimental data of heat capacity and to provide confident parameters for describing the dependence of this property with the temperature in pure ILs. In this work, a statistical procedure is proposed to appropriately refine the viscosity experimental database as a function of the temperature for pure ILs. The filtered database is finally adjusted to a convenient viscosity-to-temperature equation in order to obtain the corresponding fitting parameters. Furthermore, the fitting parameters (A and B) of the η = f(T) Arrhenius’ equation help to systematically both overview the behavior of the viscosity of ILs in the temperature range frequently used in practical applications and compare the ILs viscosities with those of the conventional organic compounds. Current results contribute to statistically tailoring the viscosity-to-temperature data experimentally reported in literature and to make them reliable and applicable to other potential uses. Concretely, the Arrhenius’ equation data can be exported to a process simulator, as Aspen Plus, in order to find ILs with optimized properties for specific tasks, and the conceptual design of new processes based on ILs14,22,23
273.15 to 353.15 K, have been collected in 22 different literature references. After discarding those systems in which no temperature dependency was found and those which offered less than 4 measurements at different temperatures and after including new systems not found in the database collected by Yu et al.,19 1860 remaining points were treated. The final sample (Table 1) is integrated by 134 different ILs. They comprise imidazolium, pyridinium, pyrrolidinium, ammonium, phosphonium, and sulphonium as primary cation families and chloride (Cl), iodide (I), tetrafluoroborate (BF4), hexafluorophosphate (PF6), bis(trifluoromethylsulfonyl)imide (NTf2), lactate (Lac), acetate (Ac), methylsufate (MeSO4), dicyanamide (DCN), and so forth as principal anion species. The most commonly studied range of temperatures when measuring the IL viscosity ranges from 298.15 to 353.15 K. In summary, 1860 data points of a total of 143 different references are evaluated.
■
STATISTICAL FITTING: MODEL SELECTION Six different models (Table 2) are evaluated as candidates to represent the temperature dependence of the ILs’ viscosity. Their selection is made considering the next two circumstances: (i) to be commonly used with this aim9,24,19,25,26 and (ii) to be selectable in the Aspen Plus process simulator. More information about these equations, their origin and their parameters can be obtained, for example, in the Aspen Plus Documentation file AspenPhysPropModel V7.3. The Andrade’s equation (model 1 in Table 2) is evaluated with either three (A, B, and C) or two (A and B) adjustable parameters. The latter is also identified in the literature as an Arrhenius-type equation.9,19 The Andrade equation is the implicit model for calculating viscosities of pure liquids in the Aspen Plus. In order to select the appropriate model for fitting the viscosity-to-temperature data some criteria are considered (Table 3). Any criterion must (i) be capable to represent a wide range of viscosity (from 10 cP to over 105 cP) for relatively narrow temperature intervals, i.e., the equation should be flexible with respect to the viscosity order of magnitude to
■
EXPERIMENTAL DATABASE The present work is basically supported by the information previously gathered by Yu et al.19 which collect viscosity measurements of 696 pure ILs composed by 220 cations and 125 anions which includes more than 2600 data points. For several of these ILs, only one viscosity value (often at 298.15 K) with no temperature dependence is provided. In this work, only ILs having temperature dependent viscosity data are included. For statistical confidence reasons, at least 4 different viscositytemperature data points are required in order for an individual IL to be selected (Scheme 1). However, for several ILs, more than 20−30 data points at different temperatures proceeding from various literature sources are assessed, e.g., for the 1-butyl3-methylimidazolium tetrafluoroborate IL (IL-14) 102 viscosity measurements at 15 different temperatures in the range from 10476
dx.doi.org/10.1021/ie5014426 | Ind. Eng. Chem. Res. 2014, 53, 10475−10484
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
11
1 2 3 4 5 6 7 8 9 10
IL no.
1-methyl-3-allylimidazolium 1-butyl-3-methylimidazolium 1-hexyl-3-methylimidazolium 1-benzyl-3-methylimidazolium 1-octyl-3-methylimidazolium tributyl-octylphosphonium trihexyl-tetradecylphosphonium 1-propyl-3-methylimidazolium Butyl-bis(3-methylimidazolium) triethylene glycol-bis(3methylimidazolium) tetraethylene glycol-bis(3methylimidazolium) 1-ethyl-3-methylimidazolium 1-isobutenyl-3-methylimidazolium 1-butyl-3-methylimidazolium 1-hexyl-3-methylimidazolium 1-octyl-3-methylimidazolium 1-butyl-2.3-dimethylimidazolium 1-butylpyridinium 1-butyl-2-methylpyridinium 1-butyl-3-methylpyridinium 1-butyl-4-methylpyridinium 1-octylpyridinium 1-octyl-3-methylpyridinium 1-butyl-3-methylimidazolium 1-ethyl-3-methylimidazolium 1-butyl-3-methylimidazolium 1-butyl-3-methylpyridinium 1-butyl-4-methylpyridinium 1-butyl-1-methylpyrrolidinium trimethylsulfonium ethyldimethylsulfonium methyldiethylsulfonium triethylsulfonium methyldipropylsulfonium ethyldipropylsulfonium methyldibutylsulfonium ethyldibutylsulfonium trihexyl-tetradecylphosphonium 1-ethyl-3-methylimidazolium
cation name
tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate tetrafluoroborate thiocyanate dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide dicyanamide tricyanomethanide
iodide
chloride chloride chloride chloride chloride chloride chloride iodide iodide iodide
anion name
30 10 102 21 35 16 54 25 39 41 15 27 7 31 32 15 8 16 5 6 6 6 6 6 6 6 15 21
6
7 7 6 17 7 11 16 9 4 6
no. points
19 0 61 11 20 7 28 0 18 0 0 0 0 10 21 0 0 1 0 0 0 0 0 0 0 0 6 12
0
0 0 2 10 3 0 0 0 0 0
discarded points
25 10 15 15 15 10 15 21 14 6 15 21 6 26 19 10 8 12 5 6 6 6 6 6 6 6 11 18
6
7 7 4 16 4 11 14 8 4 6
no. temp.
database description B 5694.4 6538.5 9045.2 7871.4 9083.5 7656.0 6301.6 5648.2 6795.6 2084.3 2895.5 1879.9 5048.9 4118.7 5017.7 4279.5 3055.1 5131.1 5676.3 5403.8 5583.2 4659.9 6214.9 3478.0 1078.9 3232.1 3578.0 3204.0 3183.7 2766.5 2668.6 2539.6 2546.5 3008.1 2964.2 3586.4 3605.8 4564.1 2518.1
A −12.1 −13.6 −20.6 −18.3 −20.6 −17.3 −13.5 −12.2 −16.6 0.013 −2.8 −2.7 −12.2 −9.1 −11.7 −8.8 −4.6 −12.1 −13.1 −12.9 −13.4 −10.1 −14.6 −7.7 −0.6 −7.4 −8.4 −7.2 7.0 −5.9 −5.8 −5.5 −5.6 −6.8 −6.6 −8.0 −8.2 −9.4 5.7
fitting results
0.9999 1.0000 0.9999 0.9998 0.9998 0.9994 1.0000 0.9994 1.0000 0.9996 0.9997 0.9999 0.9999 0.9998 0.9999 0.9995 0.9999 0.9983 0.9986 0.9996 0.9996 0.9996 0.9993 0.9995 0.9995 0.9991 1.0000 0.9997
1.0000
0.9975 0.9992 0.9998 0.9997 0.9999 0.9999 0.9993 0.9994 1.0000 1.0000
R
2
36.8 113.8 111.5 168.9 258.1 283.4 165.6 379.3 185.8 205.6 252.0 515.4 52.7 20.5 31.2 36.6 34.7 39.55 29.3 23.3 20.4 18.9 26.8 28.3 56.2 49.1 368.0 15.44
1003.8
1095.7 4147.4 16945.4 3297.1 19268.1 4351.8 2070.8 849.1 489.1 1086.6
η, cP (298.15 K)
10.4 3.8 6.9 5.7 14.4 36.1 5.2 8.3 4.9 4.8 10.9 7.8 5.1 9.9 3.5 3.3 4.0 4.62 4.5 3.9 3.7 3.4 3.5 3.8 5.0 4.3 17.0 2.83
142.5
23.6 50.5 38.1 16.4 42.2 25.0 29.6 18.9 5.0 266.6
η, cP (373.15 K)
viscosity, cP SI references
8, 17−26 27 3, 5, 6, 8, 17, 20, 22− 24. 28−43 8, 32, 35, 44−47 8, 32, 35, 42, 48 28, 33, 43, 49 50−52 52, 53 51, 52, 54−56 51, 52 50 52, 57 58, 59 17, 39, 60−65 3, 60, 63, 66, 67 52, 68 42 60, 66, 69, 70 71, 72 71 71 71 71 71 71 71 10, 11, 73−75 13, 64, 65, 76, 77
16
1, 2 1, 3 4−6 7 4, 5, 8 9 10−12 13−15 16 16
Table 1. ILs Sample Selected in the Current Work and Results of the Statistical Refining and Fitting of Experimental Viscosity-to-Temperature Data for ILsa
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10478
1-octyl-3-methylpyridinium
1-hexyl-4-(dimethylamino)pyridinium
1-octyl-4-cyanopyridinium
1-hexyl-2-ethyl-3.5-dimethylpyridinium
1-hexyl-3-methyl-4-(dimethylamino) pyridinium
61
62
63
64
1-butyl-4-cyanopyridinium
54
60
1-butyl-3-cyanopyridinium
53
1-hexyl-3.5-dimethylpyridinium
1-butyl-3-methylpyridinium
52
59
1-ethyl-4-cyanopyridinium
51
1-hexyl-3-methylpyridinium
1-ethyl-2-cyanopyridinium
50
58
1-hexyl-2.3-dimethylimidazolium
49
1-ethyl-4-(trifluoromethyl)pyridinium
1-butyl-2.3-dimethylimidazolium
48
57
1.2-dimethyl-3-propylimidazolium
47
1-ethyl-3-(trifluoromethyl)pyridinium
1-decyl-3-methylimidazolium
46
56
1-hexyl-3-methylimidazolium
45
1-hexylpyridinium
1-butyl-3-methylimidazolium
44
55
1-butyl-3-methylimidazolium 1-propyl-1-methylpyrrolidinium 1-butyl-1-methylpyrrolidinium 1-ethyl-3-methylimidazolium
cation name
40 41 42 43
IL no.
Table 1. continued
tricyanomethanide bis(fluorosulfonyl)imide bis(fluorosulfonyl)imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide
anion name
8
8
8
8
8
8
8
7
7
10
8
8
10
5
8
8
10
18
7
65
41
18 11 7 34
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
0
44
18
0 0 0 19
discarded points
8
8
8
8
8
8
8
7
7
10
8
8
10
5
8
8
10
18
5
35
17
18 8 7 19
no. temp.
database description no. points
4580.6 4906.4 5138.5 4297.2
−10.6 −10.3 −11.7 −9.7
4643.4
−9.8
4384.6
5313.8
−11.0
−10.0
3643.8
−8.1
4239.4
4638.3
−9.6
−9.5
5176.4
−11.1
4009.8
4297.6
−9.5
−9.0
3146.2
−6.1
3904.3
2478.9
−3.9
−8.5
3253.1
−6.1
4306.1
3532.1
−7.6
−9.4
3205.0
−6.9
4412.4
3263.7 2438.7 2696.5 2826.4
−7.6 −4.5 −5.0 −6.0
−10.4
B
A
fitting results
0.9998
0.9999
0.9994
0.9999
0.9992
0.9999
0.9998
0.9997
0.9997
0.9982
0.9993
0.9999
0.9997
1.0000
0.9994
0.9998
1.0000
0.9997
1.0000
0.9999
0.9999
0.9991 0.9992 1.0000 0.9999
R
2
111.4
253.3
471.6
117.1
110.6
112.1
85.5
99.0
154.9
81.4
321.8
918.3
61.6
386.4
524.1
136.2
85.8
82.6
122.8
69.9
47.0
28.4 39.6 57.1 32.5
6.1
7.9
17.3
5.3
5.8
6.4
5.7
7.1
8.5
4.2
14.1
25.5
5.3
16.9
16.0
7.5
10.3
15.5
13.7
6.5
5.4
3.1 7.7 9.3 4.8
η, cP (373.15 K)
viscosity, cP η, cP (298.15 K) SI references
54
54
99
54
54
54
54
99
99
44, 54
99
99
54, 55
99
99
54
33
18, 24, 19
66, 86, 92, 98
5, 6, 17, 23, 28−30, 33, 38, 39, 55, 66, 84, 86, 87, 91−93 44, 45, 54, 66, 93−97
78 79−83 83 17, 19, 23, 39, 54, 61, 66, 81, 82, 84−90
Industrial & Engineering Chemistry Research Article
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N-hexylisoquinolinium
N-hexylquinolinium
dimethylpropargylsulfonium
72
73
74
10479
N,N,N-trimethyl-N-hexylammonium
acetylcholine
N,N,N-trimethyl-N-(3-chloro-2hydroxypropyl) ammonium N,N,N-tributyl-N-methylammonium
N,N,N-tributyl-N-hexylammonium
N,N,N-trioctyl-N-methylammonium
trihexyl-tetradecylphosphonium
[bis(dihexyl)]dimethylguanidinium
1.3-dimethylimidazolium 1-butyl-3-methylimidazolium 1-benzyl-3-methylimidazolium
79
80
81
82
83
84
85
86
87 88 89
N,N,N-trimethyl-N-butylammonium
N-butylisoquinolinium
71
78
1-propyl-1-methylpiperidinium
70
77
1-(ethoxyethyl)-1-methylpyrrolidinium
69
(ethoxycarbonylmethyl) dimethylsulfonium N,N,N-trimethyl-N-propylammonium
1-butyl-1-methylpyrrolidinium
68
76
1-propyl-1-methylpyrrolidinium
67
triethylsulfonium
1-hexyl-2-propyl-3.5-diethylpyridinium
66
75
1-butyl-nicotinic acid butyl ester
cation name
65
IL no.
Table 1. continued
bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide bis(trifluoromethylsulfonyl) imide methylsulfate methylsulfate methylsulfate
anion name
7 14 17
7
13
15
8
7
10
11
6
4
6
10
12
10
6
8
9
5
7
37
7
8
8
0 0 0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
discarded points
7 9 17
7
9
8
7
7
10
11
4
4
5
10
10
10
6
8
9
4
7
16
4
8
8
no. temp.
database description no. points
4136.2 4826.0 2865.8
−8.8 −10.3 −5.0
4331.1 3362.4 2734.5 6376.8 6065.1 5836.7 2499.6 2362.3 3528.0 4485.6 6927.8
−9.5 −6.2 −3.8 −15.0 −13.8 −13.3 −2.5 −2.1 −7.6 −9.7 −15.2
5063.5
4210.7
−8.8
−12.3
6115.8
−15.6
3751.6
3483.1
−7.7
−8.3
3376.1
−7.0
3593.1
3493.7
−7.7
−7.0
4911.4
−11.1
2618.1
5837.0
−13.3
−5.3
B
A
fitting results
0.9999 0.9997 0.9991
0.9993
0.9973
0.9996
0.9995
0.9992
0.9998
0.9992
0.9997
0.9997
1.0000
0.9998
0.9998
1.0000
1.0000
1.0000
1.0000
0.9997
0.9997
0.9996
0.9997
0.9998
0.9998
R
2
68.9 209.5 3090.1
338.0
359.1
531.9
694.0
594.6
215.2
160.4
152.4
108.1
72.5
156.2
32.5
100.7
360.1
159.6
204.9
136.0
53.6
75.5
55.6
215.5
532.4
6.4 10.2 29.0
68.8
66.6
10.4
11.6
8.1
34.1
16.6
8.2
3.6
5.8
13.9
5.6
14.6
13.9
9.8
12.0
2.2
5.1
7.7
5.3
7.9
10.4
η, cP (373.15 K)
viscosity, cP η, cP (298.15 K) SI references
124 55, 66, 125 7, 9
120, 123
74, 11, 44, 73, 10, 66, 121, 122
61, 92, 98, 114, 120
106, 118, 119
117, 106
33
17, 33
95, 114, 115, 116
114
101, 112, 93, 113
33
72, 33, 111
33
108
110
108, 109
107, 101, 82, 91, 93
23, 33, 30, 55, 100, 101−103, 79, 66, 102−104 105, 106
6, 23, 30, 82, 100−102
54
54
Industrial & Engineering Chemistry Research Article
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cation name
cocosalky pentaethoximethylammonium tributyl-methylphosphonium 1-ethyl-3-methylimidazolium 1-ethylpyridinium 1-ethyl-3-methylpyridinium 1-ethyl-2-cyanopyridinium 1-ethyl-3-cyanopyridinium 1-ethyl-4-cyanopyridinium 1-ethyl-nicotinic acid ethyl ester 1-butyl-3-methylimidazolium 1-butylpyridinium 1-butyl-3-methylimidazolium
1-butyl-3-methylimidazolium tetrabutylammonium 1-butyl-3-methylimidazolium
1-hexyl-3-methylimidazolium 1-octyl-3-methylimidazolium tributyl-ethylphosphonium 1-butyl-1-methylpyrrolidinium
1-butyl-3-methylimidazolium hydroxyethylammonium bis(hydroxyethyl)ammonium bis(2-hydroxyethyl)methylammonium tributyl-(3-amino-propyl)phosphonium hydroxyethylammonium bis(hydroxyethyl)ammonium bis(2-hydroxyethyl)methylammonium tributyl-(3-amino-propyl)phosphonium
tributyl-(3-amino-propyl)phosphonium
1-butyl-3-methylimidazolium tributyl-(3-amino-propyl)phosphonium tributyl-(3-amino-propyl)phosphonium
tributyl-(3-amino-propyl)phosphonium
tributyl-(3-amino-propyl)phosphonium
tributyl-(3-amino-propyl)phosphonium
IL no.
90 91 92 93 94 95 96 97 98 99 100 101
102 103 104
105 106 107 108
109 110 111 112 113 114 115 116 117
118
119 120 121
122
123
124
Table 1. continued
hexafluorophosphate hexafluorophosphate diethylphosphate tris(pentafluoroethyl) trifluorophosphate acetate acetate acetate acetate glycine 2-hydroxypropionate 2-hydroxypropionate 2-hydroxypropionate (S)-2-pyrrolidinecarboxylic acid L-α-amino-3-hydroxypropionic acid trifluoroacetate L-α-aminoisovaleric acid L-α-amino-3-hydroxybutyric acid L-α-amino-3-methylvaleric acid L-α-amino-4-methylvaleric acid L-α-diaminocaproic acid
methylsulfate methylsulfate ethylsulfate ethylsulfate ethylsulfate ethylsulfate ethylsulfate ethylsulfate ethylsulfate trifluoromethanesulfonate trifluoromethanesulfonate 2-(2-methoxy−ethoxy)ethylsulfate octylsulfate docusate hexafluorophosphate
anion name
10480
0
0
6 6
0
1 0 0
0
2 1 1 0 0 1 0 0 0
27 0 0 0
0 0 63
0 0 0 0 0 9 0 0 0 0 0 0
6
11 6 6
6
13 12 12 11 6 12 11 11 6
42 31 12 17
19 6 106
8 11 16 18 17 16 16 16 8 16 20 8
discarded points
6
6
6
10 6 6
6
11 12 12 11 6 12 11 11 6
23 14 11 17
19 6 32
8 11 10 18 17 16 16 16 8 10 18 8
no. temp.
database description no. points B 6218.6 5332.9 4155.3 4377.2 4226.2 5684.7 7293.6 7396.2 8016.3 3231.1 4146.6 5961.2 4783.0 7699.3 4382.9 5236.0 5956.8 5350.3 3563.1 5510.8 5331.8 5947.2 4929.8 5355.6 5137.3 5253.1 5021.8 6390.5 6086.8 3829.7 5731.2 6364.4 6125.8 6010.5 5953.3
A −13.0 −11.7 −9.3 −9.8 −9.2 −12.2 −16.0 −16.6 −18.7 −6.5 −9.1 −13.0 −9.6 −16.5 −9.2 −11.3 −13.4 −12.3 −6.6 −12.4 −12.2 −13.7 −11.3 −11.5 −11.8 −12.0 −11.5 −14.0 −13.3 −8.6 −12.5 −13.9 −13.4 −13.1 −12.8
fitting results
0.9999
0.9999
0.9999
0.9996 0.9999 0.9999
0.9999
0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.9999 0.9993 0.9999 0.9997
0.9992 1.0000 0.9998
0.9996 1.0000 0.9991 0.9995 0.9998 0.9997 0.9994 0.9991 0.9996 0.9994 0.9999 0.9996
R
2
1296.6
1163.6
1269.1
69.7 830.9 1713.5
1230.6
438.5 293.8 516.5 187.7 640.8 228.3 275.6 209.2 1692.3
524.1 720.0 282.9 210.8
627.8 11199.0 244.8
2584.5 486.2 103.2 131.8 144.7 959.7 4735.6 3666.4 3593.2 76.5 122.5 1090.0
23.4
20.2
20.4
5.3 17.4 23.5
20.3
10.7 8.1 9.4 6.8 17.3 7.2 8.0 7.1 22.8
15.4 13.0 7.7 19.1
25.0 62.4 12.8
39.1 13.4 6.3 6.9 8.4 20.8 34.7 25.1 16.2 8.7 7.5 19.6
η, cP (373.15 K)
viscosity, cP η, cP (298.15 K)
33, 39, 55, 66, 87 129
66, 126, 127 128 56
SI references
141
141
141
84, 39, 54, 66 141 141
141
54, 55, 66, 137 138, 139 139, 140 139 141 138, 139 139 139 141
66, 130, 131 54 5−8, 17, 27, 33, 37, 28, 30, 38−39, 55, 132, 93, 133−134 45, 5, 8, 44, 17, 46, 132, 93, 135, 134, 136 5, 8, 17, 32, 48, 93, 135, 134, 136 9 18, 66
54 7 61, 54, 54, 99 99 99 54 82, 52, 54
Industrial & Engineering Chemistry Research Article
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Table 2. Mathematical Models Considered in This Work to Represent the Viscosity-to-Temperature Dependence in ILs SI references
number
Andrade
33, 144 145 145 145 145
3
PPDS
4
14.0 9.5 40.1 12.1 10.2
141 40, 142, 143 16.8 1.8
22.6 34.4
19.0
105.8 829.4 2664.4 16481.4 961.2 2999.9 6625.1 6224.7 10700.6 6746.6 −5.4 −15.50 −12.99 −26.18 −15.76 11 8 8 7 7 0 0 0 0 0 a
Literature referenced in this table is collected in the SI.
11 8 8 7 7 1-butyl-3-methylimidazolium 1-hexyl-3-methylimidazolium EcoEng500 1-hexyl-3-methylimidazolium 1-hexyl-3-methylimidazolium 130 131 132 133 134
IK-CAPE 1 exponential IK-CAPE 2 polynomial NIST TDE
model equation
B ln η = A + = C·ln T T B ln η = A + T C ln η = C1 + 2 + C3·ln T + C4·T C T 1/3 C − C4 η = C5·e(C1− C2·y)·y , where y = 3 −1 T − C4 η = C1·eC2/ T + C3
η = C1 = C2·T + C3·T 2 + ··· + C10·T 8 η = C1 + C2/T + C3/T 2 + C4 /T 3
be calculated for similar temperature intervals; (ii) be as simple as possible, i.e., the model should have the least amount of parameters possible in order to simplify not only the statistical fitting but also its implementation in the process simulator and the analysis of the results when trying to generalize behaviors or when trying to evaluate the physical significance of the parameters; (iii) not predict a viscosity lower than 0 at any temperature in any case. Every model should fulfill this criterion, in this work, it was found that some of the models analyzed would lead to negative values of viscosity in some temperature ranges because of the particularly abrupt behavior of the ILs’ viscosity temperature dependence, which lead to irregular and curved fits; (iv) present a continuum decay for all the temperature intervals considered in correspondence to the experimental behavior observed for practically all known fluids. Some of the models evaluated here, because of their particular form, can lead to almost perfect fits in the regions where experimental values are used, but extrapolation yields wrong viscosities even for moderate temperatures; and finally, (v) present correct asymptotic behaviors in limT→0 η = ∞ and limT→∞ η = 0. Table 3 collects the results of applying the above criteria on fitting the selected sample of viscosity-to-temperature data for 134 ILs. Because of its lack of flexibility, the PPDS model was rejected. The number of adjustable parameters to be evaluated is unacceptable in the case of the IK-CAPE 2 model as the number of data points needed to perform the fitting should be significantly larger than the number of adjustable parameters (n > 10). The models IK-CAPE (1 and 2) and NIST-TDE are ruled out because they can give negative viscosities depending on the relative values of the adjustable parameters. Finally, the DIPPR, the IKCAPE 1, the IKCAPE 2, and the NIST-TDE models do not fulfill the limT→∞ η = 0 criterion and the PPDS do not lead to infinity viscosity at T → 0 (Table 3). From the preceding analysis (Table 3), the Andrade’s equation seems to be a good candidate to calculate the viscosity of the ILs as a function of the temperature according to the criteria set established in this work to select the most adequate η = f(T) model. However, when the experimental data are fitted to the three-parameter Andrade’s equation, it may give a curled curve leading to regions in which the viscosity increases with the temperature (Figure 1), which is incompatible with the experience and inconsistent from a physical standpoint. Moreover, in several cases, this viscosity
0.9999 0.9996 0.9996 0.9992 0.9995
697.6 4.6 5530.0 1408.0 tributyl-(3-amino-propyl)phosphonium 1-ethyl-3-methylimidazolium 128 129
acid alanine hydrofluororide anions (n = 2.3) hexafluoroantimony 2-hydroxypropionate methylsulfate saccharinate acesulfamate
6 7
0 0
6 7
−12.0 −3.2
0.9999 0.9993
1807.6 2839.5 6499.6 6544.8 6 5 tributyl-(3-amino-propyl)phosphonium tributyl-(3-amino-propyl)phosphonium 126 127
butyric acid
acid L-α-aminohydrocinnamic
tributyl-(3-amino-propyl)phosphonium 125
L-α-amino-5-guanidinovaleric
6 L-α-amino-γ-(methylthio)
0
0 0
6
6 5
−14.3 −14.0
0.9999 1.0000
737.2 5427.2 −11.6
R
DIPPR
6
B anion name cation name
Arrhenius type
2
5
A
fitting results
141 141
141
1
1.0000
η, cP (373.15 K)
viscosity, cP
η, cP (298.15 K) 2
no. temp. discarded points
database description
no. points IL no.
Table 1. continued
model name
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Table 3. Criteria Satisfaction Chart of the Mathematical Models Considered in the Current Work to Describe the Viscosity-toTemperature Dependency model
number of parameters
flexibility
continuum decay
η 4 as explained in the prior paragraph) for each IL (all the values provided by all the different sources available are taken in consideration) is fit to the Arrhenius equation. If the R2 of the fit is equal to or greater than 0.99, then the experimental data are assumed to be correct and the parameters A and B are determined. If, alternatively, the first fitting yields R2 < 0.99, then confidence bands for α = 0.05 are built (Figure 2). The points located outside (outliners) the confidence bands above and below the fit curve are rejected. Using the preserved values, a new fit is performed and the procedure is iteratively repeated until the R2 ≥ 0.99 for the corresponding fit. The iterative procedure is applied only when, at least, four experimental points are available in any loop of the computational process.
Figure 2. Examples of the application of the statistical procedure used in this work for refining the η = f(T) experimental data. A: 1-butyl-3methylimidazolium tetrafluoroborate and B: bis(hydroxyethyl)ammonium acetate ionic liquids.
Otherwise, the system is rejected. Comparing Figures 2A and 2B, it is observed that as the number of data points decrease, the separation between the confidence bands and the first linear fit increases. Due to this widening, the refining procedure may be inadequately applied when the number of available data points is lower than 5, since some points that should be rejected may be accepted. After applying the proposed procedure, the 21% of the initial number of data pairs (1860) is discarded (Table 1). No IL with an R2 less than 0.99 is considered. In particular for bmimBF4 IL, 61 from the 102 points taken as initial sample are excluded. The results of the present study (including the values of the parameters A and B of the Arrhenius type equation) are shown in Table 1 for all the 134 ILs included in the study. 10482
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PHYSICAL SIGNIFICANCE OF THE ADJUSTABLE PARAMETERS IN THE ARRHENIUS TYPE η = F(T) EQUATION FOR ILs From the Arrhenius-type equation (Table 2), it is obvious that parameter B characterizes the change of the viscosity with the
both the ILs studied here and the conventional organic compounds (A and B values are taken from ref 8 for the organic compounds), a linear relationship was observed between A and B being the slope of the straight line negative (Figure 3). The B vs A straight line corresponding to the ILs is shifted to (approximately 2000 units) higher values with respect to molecular liquids for the coinciding A values. This reflects that ILs are more viscous than organic compounds at near-to-room temperatures. At the same time, ILs show more negative A values than molecular organic liquids indicating that the viscosity exhibits, as a rule, a more acute decay with the temperature in ILs than in organic compounds. It is relevant that the relationship between A and B for the ILs is displayed in the second and forth quadrants while representing both variables in normalized scales (Figure 4). This means that very viscous ionic liquids at relative low temperatures (large B) also have extremely abrupt decays with the temperature increase (values of A largely negative) (Table 4). On the contrary, those ILs having soft decays of the viscosity with temperature increases have, invariably, low viscosities at relatively low temperatures. This is significant when potential applications of the ILs to industrial processes are evaluated: an adequate selection of the operating temperature ensures in every case relatively low viscosities. For instance, ILs having very different viscosities at 298.15 K exhibit similar viscosities at 373.15 K (Table 4). This fact in a certain sense demystifies the usually accepted idea that IL industrial applications are limited by their high viscosities at least for the cases of operations involving temperatures relatively higher than room temperature.
Figure 3. Relationship between the parameters A and B in the Arrhenius-type equation for the viscosity-to-temperature dependence of 134 ILs studied in this work and also of 134 conventional organic compounds.
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CONCLUSIONS A statistical procedure based on the use of confidence bands is applied to refine the experimental η = f(T) data available in open literature sources for 134 ionic liquids. Twenty-one percent of the 1860 data points initially considered are finally rejected. Refined data are fitted to the Arrhenius-type equation, and the corresponding A and B parameters are determined. They are accessible for direct applications in process simulations and design tasks carried out with programs integrated, for example, into the Aspen ONE suit. A and B parameters show a linear regression with negative slope, the straight line obtained being limited to the second and fourth quadrants. From this, ILs having high viscosities at near-room temperatures show rapid decays of the viscosity with the temperature for temperatures over 330−373 K, commonly used in industrial processes. Thus, the limitations in the applications of the ILs related to their high viscosities could be overtaken if adequate working temperatures are selected.
Figure 4. Linear relationship between the normalized values of the parameters A and B for all the studied ILs in this work.
temperature while the value of parameter A quantifies the viscosity of the fluid at relative low temperatures: over 10−25 °C for the temperature intervals considered in the present work. Thus, the main features of the η = f(T) dependence could be rationalized in terms of both A and B parameters. Indeed, large negative values of A lead to pronounced changes of the viscosity with temperature, while large values of B indicate also high viscosities at relative low temperatures. For
Table 4. Temperature Dependence of the Viscosity for Two ILs Having Very Different Values of the Parameters A and B in Arrhenius Type Equation for η = f(T)
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(18) Crosthwaite, J. M.; Muldoon, M. J.; Dixon, J. K.; Anderson, J. L.; Brennecke, J. F. Phase transition and decomposition temperatures, heat capacities and viscosities of pyridinium ionic liquids. J. Chem. Thermodyn. 2005, 37, 559−568. (19) Yu, G.; Zhao, D.; Wen, L.; Yang, S.; Chen, X. Viscosity of ionic liquids: Database, observation, and quantitative structure-property relationship analysis. AIChE J. 2012, 58, 2885−2899. (20) Paulechka, Y. U. Heat Capacity of Room-Temperature Ionic Liquids: A Critical Review. J. Phys. Chem. Ref. Data 2010, 39, (3). (21) Valderrama, J. O.; Forero, L. A.; Rojas, R. E. Critical Properties and Normal Boiling Temperature of Ionic Liquids. Update and a New Consistency Test. Ind. Eng. Chem. Res. 2012, 51, 7838−7844. (22) Ferro, V. R.; Ruiz, E.; de Riva, J.; Palomar, J. Introducing process simulation in ionic liquids design/selection for separation processes based on operational and economic criteria through the example of their regeneration. Sep. Purif. Technol. 2012, 97, 195−204. (23) Bedia, J.; Ruiz, E.; de Riva, J.; Ferro, V. R.; Palomar, J.; Rodriguez, J. J. Optimized ionic liquids for toluene absorption. AIChE J. 2013, 59, 1648−1656. (24) Gardas, R. L.; Coutinho, J. A. P. A group contribution method for viscosity estimation of ionic liquids. Fluid Phase Equilib. 2008, 266, 195−201. (25) Domanska, U.; Laskowska, M. Effect of Temperature and Composition on the Density and Viscosity of Binary Mixtures of Ionic Liquid with Alcohols. J. Solution Chem. 2009, 38, 779−799. (26) Khupse, N. D.; Kumar, A. Dramatic Change in Viscosities of Pure Ionic Liquids upon Addition of Molecular Solvents. J. Solution Chem. 2009, 38, 589−600.
ASSOCIATED CONTENT
S Supporting Information *
References of Table 1. This material is available free of charge via the Internet at http://pubs.acs.org/.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to the “Comunidad de Madrid” and to the “Ministerio de Ciencia e Innovación” for financial support throuth Projects P2009/PPQ-1545 and CTQ2011-26758, respectively.
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REFERENCES
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