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The fluidity of room temperature ionic liquids
Fluid Phase Equilibria 363 (2014) 66–69
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
The fluidity of room temperature ionic liquids Yizhak Marcus ∗ Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
a r t i c l e
i n f o
Article history: Received 24 July 2013 Received in revised form 31 October 2013 Accepted 11 November 2013 Available online 19 November 2013 Keywords: Room temperature ionic liquids Fluidity Molar volume
a b s t r a c t The fluidities, ˚ = −1 , of room temperature ionic liquids (RTILs) as functions of the temperature can be described in terms of the Hildebrand and Lamoreaux approach. This relates the (temperature dependent) fluidity to the (temperature dependent) molar volume V of the RTIL: ˚ = B[(V − V0 )/V0 ]. The resulting V0 parameters, signifying the absence of free volume, are 99.0 ± 0.5% of the molar volume at 298.15 K. Counter to expectation, the B parameters increase with the interionic attractive forces. It is shown that the volumetric behavior of the RTILs permits the prediction of the temperature dependence of their viscosities, provided that the latter are not larger than ca. 50 mPa s−1 . © 2013 Elsevier B.V. All rights reserved.
1. Introduction
molecules are so closely crowded as to prevent viscous flow while still retaining rotational freedom” [6]. Eq. (3) is re-written as:
The fluidity of a liquid is the reciprocal of its dynamic viscosity: ˚ = −1 and is measured in s mPa−1 . The viscosity, hence the fluidity, of only few room temperature ionic liquids (RTILs) obeys the Arrhenius expression, ˚ = ˚0 exp(E /RT). The fluidities of most RTILs are better described by the Vogel–Tammann–Fulcher (VTF) [1–3] expression: ˚ = ˚0 exp
K
T − T0
(2)
for describing the temperature dependence of the fluidity of RTILs. The present paper explores the application to the RTILs of the expression originally proposed by Hildebrand and Lamoreaux [6,7] for various liquids: ˚=B
V − V 0
V0
(3)
relating the (temperature dependent) fluidity to the (temperature dependent) molar volume V of the liquid. This expression makes the fluidity proportional to the fraction of free volume of the liquid, the parameter V0 denoting that molar volume “at which the
∗ Tel.: +972 2 6585341; fax: +972 2 6585341. E-mail address: [email protected] 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.11.018
B V0
V
(4)
yielding a straight line when ˚ is plotted against V, from the intercept and slope of which the parameters B and V0 are readily obtained.
(1)
with three coefficients, ˚0 , K, and T0 . The VTF expression is in some cases modified by replacement of ˚0 by ˚0 T 1/2 . In the expression proposed by Litovits [4], (T − T0 ) in the denominator of the exponent in Eq. (1) is replaced by T3 . Ghatee et al. [5] proposed the expression: ˚0.3 = a + bT
˚ = −B +
2. Results A large but not exhaustive database of the viscosities of RTILs as functions of the temperature has been assembled and their reciprocals, their fluidities ˚, have been obtained. The corresponding molar volumes V were obtained from the temperature dependent densities, if available in the same publication. Otherwise they were obtained from the temperature dependence of the densities in a recent compilation by the author [8]. Plots of the data according to Eq. (4) yielded straight lines (with a linear correlation coefficient of ≥0.995) only for not highly viscous RTILs. That is, the linear dependence is observed at temperatures well away from their melting temperatures, say above 40 ◦ C, where generally ˚ ≥ 0.02 s mPa−1 , depending on individual cases. With decreasing temperatures the fluidity diminishes below this limit and the lines curve upwards, as shown in Fig. 1 for representative RTILs. The V0 values are not very sensitive (within ±1 cm3 mol−1 ) to where the straight line dependence is cut off, but the B values are not accurate, varying up to 30% according to this place. The resulting coefficients B and V0 are shown in Table 1.
Y. Marcus / Fluid Phase Equilibria 363 (2014) 66–69 Table 1 The coefficients B and V0 obtained from plots of Eq. (4) of the fluidities against the molar volumes of room temperature ionic liquids. RTILa +
−
Memim MeSO4 Etmim+ BF4 − Etmim+ MeSO3 − Etmim+ EtSO3 − Etmim+ N(CN)2 − Etmim+ B(CN)4 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ EtSO4 − Etmim+ OcSO4 − Etmim+ NO3 − Etmim+ CF3 SO3 − Prmim+ NTF2 − Prmim+ NTF2 − Bumim+ MeCO2 − Bumim+ BF4 − Bumim+ BF4 − Bumim+ BF4 − Bumim+ BF4 − Bumim+ N(CN)2 − Bumim+ N(CN)2 − Bumim+ PF6 − Bumim+ PF6 − Bumim+ PF6 − Bumim+ PF6 − Bumim+ NO3 − Bumim+ NO3 − Bumim+ CF3 CO2 − Bumim+ CF3 SO3 − Bumim+ CF3 SO3 − Bumim+ CF3 SO3 − Bumim+ NTF2 − Bumim+ NTF2 − Bumim+ NTF2 − Bumim+ NTF2 − Bumim+ (C2 F5 SO3 )2 N− Pemim+ NTF2 − Hxmim+ BF4 − Hxmim+ N(CN)2 − Hxmim+ CF3 SO3 − Hxmim+ NTF2 − Hxmim+ PF6 − Hxmim+ PF6 − Hxmim+ NO3 − Hxmim+ (C2 F5 )3 PF3 − Ocmim+ BF4 − Ocmim+ BF4 − Ocmim+ BF4 − Ocmim+ PF6 − Dcmim+ BF4 − Bubim+ NTF2 − MePy+ MeSO4 − Me(2Et)Py+ MeSO4 − Me(3Me)Py+ MeSO4 − EtPy+ EtSO4 − Et(2Et)Py+ EtSO4 − Et(4Me)Py+ NTF2 − Et(3Me)Py+ NTF2 − Pr(3Me)Py+ NTF2 − BuPy+ BF4 − BuPy+ BF4 − BuPy+ NTF2 − BuPy+ NTF2 − Bu(3Me)Py+ BF4 − Bu(3Me)Py+ BF4 − Bu(3Me)Py+ N(CN)2 − Bu(3Me)Py+ NTF2 − Bu(3Me)Py+ NTF2 − Bu(4Me)Py+ NTF2 − Bu(3CN)Py+ NTF2 − Hx(3CN)Py+ NTF2 − Hx(4Me)Py+ NTF2 −
Ref.
B (s mPa−1 )
V0 (cm3 mol−1 )
[9] [10] [11] [12] [12] [13] [10] [12] [14] [15] [16] [17] [11] [18] [18] [14] [19] [20] [21] [18] [22] [23] [15] [22] [24] [25] [21] [18] [18] [26] [21] [15] [21] [18] [21] [27] [14] [28] [21] [14] [18] [15] [15] [15] [29] [18] [18] [29] [30] [18] [22] [18] [18] [11] [31] [31] [31] [16] [33] [31] [15] [15] [10] [32] [10] [28] [16] [22] [22] [15] [16] [33] [34] [34] [34]
2.26 1.70 1.21 1.41 3.16 5.39 0.18 2.17 2.22 2.20 2.81 1.95 0.44 2.18 4.04 2.63 2.49 1.05 1.89 1.57 2.72 2.21 3.40 5.24 0.67 1.23 1.04 1.34 1.07 1.92 2.52 1.83 1.86 2.84 2.36 2.36 2.08 2.61 1.58 2.59 1.20 2.72 1.51 2.02 0.84 0.70 1.07 1.94 1.29 1.07 1.67 0.66 0.88 1.49 1.69 1.06 1.96 2.14 1.19 2.69 2.54 2.49 0.74 2.48 0.31 2.58 1.91 3.12 4.28 2.19 2.45 2.51 1.25 1.10 1.29
156 152 165 188 156 217 256 255 257 255 256 190 291 180 188 293 296 188 188 188 189 188 192 194 207 209 207 206 253 174 207 221 221 222 290 291 290 290 345 309 281 225 256 348 240 335 253 395 258 329 259 377 370 310 151 191 167 189 213 288 289 308 180 185 284 287 204 201 206 325 309 325 303 338 338
67
Table 1 (Continued) RTILa +
−
OcPy BF4 Oc(3CN)Py+ NTF2 − Ocisoquin+ NTF2 − BuMe3 N+ NTF2 − Oc3 MeN+ NTF2 − PrMePyrr+ NTF2 − BuMePyrr+ NTF2 − BuMePyrr+ NTF2 − BuMePyrr+ NTF2 − BuMePyrr+ CF3 SO3 − MeOCH2 MePyrr+ NTF2 − PrMePip+ NTF2 − Bu3 MeP+ MeSO4 − Bu3 EtP+ Et2 PO4 − Bu3 OcP+ Cl− Hx3 TdP+ N(CN)2 − Hx3 TdP+ MeSO3 − Hx3 TdP+ NoCO2 − Hx3 TdP+ NTF2 −
Ref.
B (s mPa−1 )
V0 (cm3 mol−1 )
[32] [34] [36] [28] [12] [14] [14] [15] [28] [15] [37] [14] [35] [35] [35] [38] [38] [38] [38]
1.35 0.94 0.87 1.78 0.48 1.94 1.90 1.82 1.96 1.45 2.60 1.70 0.84 1.21 0.29 1.11 0.71 0.98 1.15
252 373 393 285 616 305 301 302 303 233 277 315 311 382 383 618 633 754 723
a Mim, 3-methylimidazole-1-; bim, 3-butylimidazole-1-; NTF2 , bis(trifluoromethyl-sulfonyl)amide; Py, pyridine, Pyrr, pyrridoline; Pip, piperidine; Td, tetradecyl.
3. Discussion The upwards curvature of the plots of Eq. (4) at low temperatures, demonstrated in Fig. 1 for representative RTILs, means that the Hildebrand concept of fluidity breaks down under such conditions and the ions of the RTIL cannot rotate freely any more. However, above ca. 40 ◦ C the ˚ = f(V) curves are linear as stipulated by this concept. The V0 values recorded in Table 1 are 99.0 ± 0.5% of the molar volume at 25 ◦ C, which may therefore be taken as the molar volume at which the ions are closely crowded, making viscous flow difficult while the ions still retain rotational freedom. Little can be said about the B values shown in Table 1. For a series of cations, say the 1-alkyl-3-methylimidazolium ones, with a given anion the B values tend to diminish as the cation becomes larger and its V0 values increase. The products BV0 are very roughly constant. 350 ± 40 for the tetrafluoroborate salts, 250 ± 20 for the hexafluorophosphate salts and 670 ± 100 for the bis(trifluoromethylsulfonyl)amide salts. When a B value is outside
Fig. 1. Plots of the fluidity against the molar volume at a range of temperatures for Etmim+ B(CN)4 − () with data from [12], Bumim+ NTF2 − () with data from [17], and Et(3Me)Py (䊉) with data from [14]. Filled symbols conform to a straight line with a linear correlation coefficient ≥0.995, empty symbols do not.
68
Y. Marcus / Fluid Phase Equilibria 363 (2014) 66–69
Fig. 2. The viscosities of methyl-3-methylpyridinium methylsulfate (䊉) from [31] and of N-methoxymethyl-N-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide () from [37] plotted as functions of the ) by Eq. (5). temperature and fitted (
these limits, as e.g. for EtmimBF4 , it is suspected that it is incorrect. For liquid metals [7] and molten salts with melting points above 200 ◦ C [39] the B coefficients increase with the cohesive energy density. This signifies that the more tightly the constituent particles (metal atoms and ions) are bound together, the more does the fluidity increase. This fact, valid also for RTILs, is counter-intuitive and no ready explanation for it could be found. On the positive side, a single determination of the viscosity at one temperature, T1 , provided 1 ≤ 50 mPa s, permits us to predict the temperature dependence of the viscosities of RTILs at T > T1 from just their volumetric behavior. In principle, according to the Hildebrand approach only the isobaric expansibility ˛P of the RTIL [8] is required, with a proper choice of T2 : (T ) =
1 (T1 − T2 )[1 − ˛P (T − T2 )] ∼1 (T − T2 )[1 − ˛P (T1 − T2 )]
T − T 1 2 T − T2
(5)
This choice corresponds to where the molar volume is 99.0 ± 0.5% of that at 298.15 K in view of this being the case for V0 . The approximation on the right-hand side of Eq. (5) results from ˛P T being much smaller than unity for T of a few tens of K at most. Examples of the predicted temperature dependence of the viscosity of RTILs are shown in Fig. 2. The fit is not perfect but the trend is correct. 4. Conclusions The fluidities of RTILs, provided they are not smaller than 0.02 s mPa−1 , can be described by the Hildebrand–Lamoreaux expression in terms of their molar volumes. When the fluidity is smaller than this value there is no free volume in the ionic liquid and the ions have lost their rotational freedom, so that the Hildebrand–Lamoreaux expression cannot any more describe the fluidity. As the temperature is increased and the fluidity increases beyond this limit it is possible to estimate the temperature dependence of the fluidity from the volumetric behavior alone. References [1] H. Vogel, The law of relationship between the viscosity of liquids and the temperature, Z. Phys. 22 (1921) 645–646.
[2] G. Tammann, G. Hesse, Temperature dependence of the viscosity of undercooled liquids, Z. Anorg. Allgem. Chem. 156 (1926) 245–247. [3] G.S. Fulcher, Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8 (1925) 339–355. [4] T.A. Litovits, Temperature dependence of the viscosity of associated liquids, J. Chem. Phys. 20 (1952) 1088–1089. [5] M.H. Ghatee, M. Zare, A.R. Zolghader, F. Moosavi, Temperature dependence of viscosity and relation with the surface tension of ionic liquids, Fluid Phase Equilibr. 291 (2010) 188–194. [6] J.H. Hildebrand, R.H. Lamoreaux, Fluidity: a general theory, Proc Natl. Acad. Sci. U S A 69 (1972) 3428–3431. [7] J.H. Hildebrand, R.H. Lamoreaux, Fluidity viscosity of liquid metals: an interpretation, Proc. Natl. Acad. Sci. U S A 73 (1976) 988–989. [8] Y. Marcus, in: E. Wilhelm, T. Letcher (Eds.), Volume Properties: Liquids, Solutions, and Vapours, Royal Soc. Chem., Cambridge, 2013 (Chapter 19). [9] A.B. Pereiro, F. Santamaria, E. Tojo, A. Rodriguez, J. Tojo, Temperature dependence of physical properties of ionic liquid 1,3-dimethylimidazolium methyl sulfate, J. Chem. Eng. Data 51 (2006) 952–954. [10] A. Noda, K. Hayamizu, M. Watanabe, Pulsed-gradient spin-echo 1 H and 19 F NMR ionic diffusion coefficient, viscosity, and ionic conductivity of nonchloroaluminate room-temperature ionic liquids, J. Phys. Chem. B 105 (2001) 4603–4610. [11] B. Hasse, J. Lehmann, D. Assenbaum, P. Wasserscheid, A. Leipertz, A.P. Fröba, Viscosity, interfacial tension, density, and refractive index of ionic liquids [EMIM][MeSO3 ], [EMIM][MeOHPO2 ], [EMIM][OcSO4 ], and [BBIM][NTF2 ] in dependence on temperature at atmospheric pressure, J. Chem. Eng. Data 54 (2009) 2576–2583. [12] A.P. Fröba, H. Kremer, A. Leipertz, Density, refractive index, interfacial tension, and viscosity of ionic liquids [EMIM][EtSO4 ], [EMIM][NTF2 ], [EMIM][N(CN)2 ], and [OMA][NTF2 ] in dependence on temperature at atmospheric pressure, J. Phys. Chem. B 112 (2008) 12420–12430. [13] T. Koller, M.H. Rauch, P.S. Schulz, M. Berger, P. Wasserscheid, I.G. Economou, A. Leipertz, A.P. Fröba, Viscosity, interfacial tension, self-diffusion coefficient, density and refractive index of the ionic liquid 1-ethyl-3-methylimidazolium tetracyanoborate as a function of temperature at atmospheric pressure, J. Chem. Eng. Data 57 (2012) 828–835. [14] S. Bulut, P. Eiden, W. Beichel, J.M. Slattery, T.F. Beyersdorffr, T.J.S. Schubert, I. Krossing, Temperature dependence of the viscosity and conductivity of mildly functionalized and non-functionalized [Tf2 N]− ionic liquids, ChemPhysChem 12 (2011) 2296–2310. [15] R.G. Seoane, S. Corderi, E. Gomez, N. Calvar, E.J. Gonzalez, E.A. Macedo, A. Dominguez, Temperature dependence and structural influence on the thermophysical properties of eleven commercial ionic liquids, Ind. Eng. Chem. Res. 51 (2012) 2492–2501. [16] J.M. Crosthwaite, M.J. Muldoon, J.K. Dixon, J.L. Anderson, J.F. Brennecke, Phase transition and decomposition temperatures, heat capacities and viscosities of pyridinium ionic liquids, J. Chem. Thermodyn. 37 (2005) 559–568. [17] H. Rodriguez, J.F. Brennecke, Temperature and composition dependence of the density and viscosity of binary mixtures water + ionic liquid, J. Chem. Eng. Data 51 (2006) 2145–2155. [18] K.R. Seddon, A. Stark, M.-J. Torres, Viscosity and density of 1-alkyl-3-methylimidazolium ionic liquids, ACS Symp. Ser. 819 (2002) 34–45. [19] E. Gomez, N. Calvar, E.A. Macedo, A. Dominguez, Effect of temperature on the physical properties of pure 1-propyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and characterization of its binary mixtures with alcohols, J. Chem. Thermodyn. 45 (2012) 9–15. [20] K.G. Bogolitsyn, T.E. Skrebets, T.A. Makhova, Physicochemical properties of 1butyl-3-methylimidazolium acetate, Russ. J. Gen. Chem. 79 (2009) 125–128. [21] H. Tokada, K. Hayamizu, K. Ishii, Md.A.B.H. Susan, M. Watanabe, Physicochemical properties and structures of room temperature ionic liquids. I. Variation of anionic species, J. Phys. Chem. B 108 (2004) 16593–16600. [22] L.G. Sanchez, J.R. Espel, F. Onink, G.W. Meindersma, A.B. de Haan, Density, viscosity, and surface tension of synthesis grade imidazolium, pyridinium, and pyrrolidinium based room temperature ionic liquids, J. Chem. Eng. Data 54 (2009) 2803–2812. [23] K.R. Harris, M. Kanakubo, L.A. Woolf, Temperature and pressure dependence of the viscosity of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate: viscosity and density relationships of ionic liquids, J. Chem. Eng. Data 52 (2007) 2425–2430. [24] A.B. Pereiro, J.L. Legido, A. Rodriguez, Physical properties of ionic liquids based on 1-alkyl-3-methylimidazolium cation and hexafluorophosphate as anion and temperature dependence, J. Chem. Thermodyn. 30 (2007) 1168–1175. [25] K.R. Harris, L.A. Woolf, M. Kanakubo, Temperature and pressure dependence of the viscosity of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate, J. Chem. Eng. Data 50 (2005) 1777–1782. [26] B. Mokhtarani, A. Sharifi, H.R. Mortaheb, M. Mirzaei, M. Mafi, F. Sadeghian, Density and viscosity of 1-butyl-3-methylimidazolium nitrate with ethanol, 1propanol, or 1-butanol at several temperatures, J. Chem. Thermodyn. 41 (2009) 1432–1438. [27] K.R. Harris, M. Kanakubo, L.A. Woolf, Temperature and pressure dependence of the viscosity of the ionic liquids 1-hexyl-3methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, J. Chem. Eng. Data 52 (2007) 1080–1085. [28] H. Tokuda, K. Ishii, M.A.B.H. Susan, S. Tsuzuki, K. Hayamizu, M. Watanabe, Physicochemical properties and structures of room-temperature ionic liquids. 3. Variation of cationic structure, J. Phys. Chem. B 119 (2006) 2833–2839.
Y. Marcus / Fluid Phase Equilibria 363 (2014) 66–69 [29] J.-G. Li, Y.-F. Hu, S. Ling, J.-Z. Zhang, Physicochemical properties of [C6 mim][PF6 ] and [C6 mim][(C2 F5 )3 PF3 ] ionic liquids, J. Chem. Eng. Data 56 (2011) 3068–3072. [30] K.R. Harris, M. Kanakubo, L.A. Woolf, Temperature and pressure dependence of the viscosity of the ionic liquids 1-metyl-3-octylimidazolium hexafluorophosphate and 1-methyl-3-octylimidazolium tetrafluoroborate, J. Chem. Eng. Data 51 (2006) 1161–1167. [31] E. Gomez, N. Calvar, A. Dominguez, E.A. Macedo, Synthesis and temperature dependence of physical properties of four pyridinium-based ionic liquids: influence of the size of the cation, J. Chem. Thermodyn. 42 (2010) 1324–1329. [32] B. Mokhtarani, A. Sharifi, H.R. Mortaheb, M. Mirzaei, M. Mafi, F. Sadeghian, Density and viscosity of pyridinium-based ionic liquids and their binary mixtures with water at several temperatures, J. Chem. Thermodyn. 41 (2009) 323–329. [33] Q.-S. Liu, P.-P. Li, U. Welz-Biermann, X.-X. liu, J. Chen, Density, electrical conductivity, and dynamic viscosity of N-alkyl-4-methylpyridinium bis(trifluoromethyl sulfonyl)imide, J. Chem. Eng. Data 57 (2012) 2999–3004. [34] A.K. Ziyada, C.D. Wilfred, M.A. Bustam, Z. Man, T. Murugesan, Thermophysical properties of 1-propyronitrile-3-alkylimidazolium bromide ionic liquids
[35]
[36]
[37]
[38]
[39]
69
at temperatures from (293.15 to 353.15) K, J. Chem. Eng. Data 55 (2010) 3886–3890. F.J. Deive, M.A. Rivas, A. Rodriguez, Study of thermodynamic and transport properties of phosphonium-based ionic liquids, J. Chem. Thermodyn. 62 (2013) 98–103. U. Domanska, M. Zawaqdzki, A. Lewandrowska, Effect of temperature and composition on the density, viscosity, surface tension, and thermodynamic properties of binary mixtures of N-octylisoquinolinium bis(trifluoromethyl sulfonyl)imide with alcohols, J. Chem. Thermodyn. 48 (2012) 101–111. M. Kanakubo, H. Nanjo, T. Nishida, J. Takano, Density, viscosity, and electrical conductivity of N-methoxymethylpyrrolidinium bis(trifluoromethyl sulfonyl)amide, Fluid Phase Equilibr. 302 (2011) 10–13. C.M.S.S. Neves, P.J. Carvalho, M.G. Freire, J.A.P. Coutinho, Thermophysical properties of pure and water-saturated tetradecyltrihexylphosphonium-based ionic liquids, J. Chem. Thermodyn. 43 (2011) 948–957. Y. Marcus, The fluidity of molten salts, Fluid Phase Equil., submitted November 2013.
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
The fluidity of room temperature ionic liquids Yizhak Marcus ∗ Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
a r t i c l e
i n f o
Article history: Received 24 July 2013 Received in revised form 31 October 2013 Accepted 11 November 2013 Available online 19 November 2013 Keywords: Room temperature ionic liquids Fluidity Molar volume
a b s t r a c t The fluidities, ˚ = −1 , of room temperature ionic liquids (RTILs) as functions of the temperature can be described in terms of the Hildebrand and Lamoreaux approach. This relates the (temperature dependent) fluidity to the (temperature dependent) molar volume V of the RTIL: ˚ = B[(V − V0 )/V0 ]. The resulting V0 parameters, signifying the absence of free volume, are 99.0 ± 0.5% of the molar volume at 298.15 K. Counter to expectation, the B parameters increase with the interionic attractive forces. It is shown that the volumetric behavior of the RTILs permits the prediction of the temperature dependence of their viscosities, provided that the latter are not larger than ca. 50 mPa s−1 . © 2013 Elsevier B.V. All rights reserved.
1. Introduction
molecules are so closely crowded as to prevent viscous flow while still retaining rotational freedom” [6]. Eq. (3) is re-written as:
The fluidity of a liquid is the reciprocal of its dynamic viscosity: ˚ = −1 and is measured in s mPa−1 . The viscosity, hence the fluidity, of only few room temperature ionic liquids (RTILs) obeys the Arrhenius expression, ˚ = ˚0 exp(E /RT). The fluidities of most RTILs are better described by the Vogel–Tammann–Fulcher (VTF) [1–3] expression: ˚ = ˚0 exp
K
T − T0
(2)
for describing the temperature dependence of the fluidity of RTILs. The present paper explores the application to the RTILs of the expression originally proposed by Hildebrand and Lamoreaux [6,7] for various liquids: ˚=B
V − V 0
V0
(3)
relating the (temperature dependent) fluidity to the (temperature dependent) molar volume V of the liquid. This expression makes the fluidity proportional to the fraction of free volume of the liquid, the parameter V0 denoting that molar volume “at which the
∗ Tel.: +972 2 6585341; fax: +972 2 6585341. E-mail address: [email protected] 0378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2013.11.018
B V0
V
(4)
yielding a straight line when ˚ is plotted against V, from the intercept and slope of which the parameters B and V0 are readily obtained.
(1)
with three coefficients, ˚0 , K, and T0 . The VTF expression is in some cases modified by replacement of ˚0 by ˚0 T 1/2 . In the expression proposed by Litovits [4], (T − T0 ) in the denominator of the exponent in Eq. (1) is replaced by T3 . Ghatee et al. [5] proposed the expression: ˚0.3 = a + bT
˚ = −B +
2. Results A large but not exhaustive database of the viscosities of RTILs as functions of the temperature has been assembled and their reciprocals, their fluidities ˚, have been obtained. The corresponding molar volumes V were obtained from the temperature dependent densities, if available in the same publication. Otherwise they were obtained from the temperature dependence of the densities in a recent compilation by the author [8]. Plots of the data according to Eq. (4) yielded straight lines (with a linear correlation coefficient of ≥0.995) only for not highly viscous RTILs. That is, the linear dependence is observed at temperatures well away from their melting temperatures, say above 40 ◦ C, where generally ˚ ≥ 0.02 s mPa−1 , depending on individual cases. With decreasing temperatures the fluidity diminishes below this limit and the lines curve upwards, as shown in Fig. 1 for representative RTILs. The V0 values are not very sensitive (within ±1 cm3 mol−1 ) to where the straight line dependence is cut off, but the B values are not accurate, varying up to 30% according to this place. The resulting coefficients B and V0 are shown in Table 1.
Y. Marcus / Fluid Phase Equilibria 363 (2014) 66–69 Table 1 The coefficients B and V0 obtained from plots of Eq. (4) of the fluidities against the molar volumes of room temperature ionic liquids. RTILa +
−
Memim MeSO4 Etmim+ BF4 − Etmim+ MeSO3 − Etmim+ EtSO3 − Etmim+ N(CN)2 − Etmim+ B(CN)4 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ NTF2 − Etmim+ EtSO4 − Etmim+ OcSO4 − Etmim+ NO3 − Etmim+ CF3 SO3 − Prmim+ NTF2 − Prmim+ NTF2 − Bumim+ MeCO2 − Bumim+ BF4 − Bumim+ BF4 − Bumim+ BF4 − Bumim+ BF4 − Bumim+ N(CN)2 − Bumim+ N(CN)2 − Bumim+ PF6 − Bumim+ PF6 − Bumim+ PF6 − Bumim+ PF6 − Bumim+ NO3 − Bumim+ NO3 − Bumim+ CF3 CO2 − Bumim+ CF3 SO3 − Bumim+ CF3 SO3 − Bumim+ CF3 SO3 − Bumim+ NTF2 − Bumim+ NTF2 − Bumim+ NTF2 − Bumim+ NTF2 − Bumim+ (C2 F5 SO3 )2 N− Pemim+ NTF2 − Hxmim+ BF4 − Hxmim+ N(CN)2 − Hxmim+ CF3 SO3 − Hxmim+ NTF2 − Hxmim+ PF6 − Hxmim+ PF6 − Hxmim+ NO3 − Hxmim+ (C2 F5 )3 PF3 − Ocmim+ BF4 − Ocmim+ BF4 − Ocmim+ BF4 − Ocmim+ PF6 − Dcmim+ BF4 − Bubim+ NTF2 − MePy+ MeSO4 − Me(2Et)Py+ MeSO4 − Me(3Me)Py+ MeSO4 − EtPy+ EtSO4 − Et(2Et)Py+ EtSO4 − Et(4Me)Py+ NTF2 − Et(3Me)Py+ NTF2 − Pr(3Me)Py+ NTF2 − BuPy+ BF4 − BuPy+ BF4 − BuPy+ NTF2 − BuPy+ NTF2 − Bu(3Me)Py+ BF4 − Bu(3Me)Py+ BF4 − Bu(3Me)Py+ N(CN)2 − Bu(3Me)Py+ NTF2 − Bu(3Me)Py+ NTF2 − Bu(4Me)Py+ NTF2 − Bu(3CN)Py+ NTF2 − Hx(3CN)Py+ NTF2 − Hx(4Me)Py+ NTF2 −
Ref.
B (s mPa−1 )
V0 (cm3 mol−1 )
[9] [10] [11] [12] [12] [13] [10] [12] [14] [15] [16] [17] [11] [18] [18] [14] [19] [20] [21] [18] [22] [23] [15] [22] [24] [25] [21] [18] [18] [26] [21] [15] [21] [18] [21] [27] [14] [28] [21] [14] [18] [15] [15] [15] [29] [18] [18] [29] [30] [18] [22] [18] [18] [11] [31] [31] [31] [16] [33] [31] [15] [15] [10] [32] [10] [28] [16] [22] [22] [15] [16] [33] [34] [34] [34]
2.26 1.70 1.21 1.41 3.16 5.39 0.18 2.17 2.22 2.20 2.81 1.95 0.44 2.18 4.04 2.63 2.49 1.05 1.89 1.57 2.72 2.21 3.40 5.24 0.67 1.23 1.04 1.34 1.07 1.92 2.52 1.83 1.86 2.84 2.36 2.36 2.08 2.61 1.58 2.59 1.20 2.72 1.51 2.02 0.84 0.70 1.07 1.94 1.29 1.07 1.67 0.66 0.88 1.49 1.69 1.06 1.96 2.14 1.19 2.69 2.54 2.49 0.74 2.48 0.31 2.58 1.91 3.12 4.28 2.19 2.45 2.51 1.25 1.10 1.29
156 152 165 188 156 217 256 255 257 255 256 190 291 180 188 293 296 188 188 188 189 188 192 194 207 209 207 206 253 174 207 221 221 222 290 291 290 290 345 309 281 225 256 348 240 335 253 395 258 329 259 377 370 310 151 191 167 189 213 288 289 308 180 185 284 287 204 201 206 325 309 325 303 338 338
67
Table 1 (Continued) RTILa +
−
OcPy BF4 Oc(3CN)Py+ NTF2 − Ocisoquin+ NTF2 − BuMe3 N+ NTF2 − Oc3 MeN+ NTF2 − PrMePyrr+ NTF2 − BuMePyrr+ NTF2 − BuMePyrr+ NTF2 − BuMePyrr+ NTF2 − BuMePyrr+ CF3 SO3 − MeOCH2 MePyrr+ NTF2 − PrMePip+ NTF2 − Bu3 MeP+ MeSO4 − Bu3 EtP+ Et2 PO4 − Bu3 OcP+ Cl− Hx3 TdP+ N(CN)2 − Hx3 TdP+ MeSO3 − Hx3 TdP+ NoCO2 − Hx3 TdP+ NTF2 −
Ref.
B (s mPa−1 )
V0 (cm3 mol−1 )
[32] [34] [36] [28] [12] [14] [14] [15] [28] [15] [37] [14] [35] [35] [35] [38] [38] [38] [38]
1.35 0.94 0.87 1.78 0.48 1.94 1.90 1.82 1.96 1.45 2.60 1.70 0.84 1.21 0.29 1.11 0.71 0.98 1.15
252 373 393 285 616 305 301 302 303 233 277 315 311 382 383 618 633 754 723
a Mim, 3-methylimidazole-1-; bim, 3-butylimidazole-1-; NTF2 , bis(trifluoromethyl-sulfonyl)amide; Py, pyridine, Pyrr, pyrridoline; Pip, piperidine; Td, tetradecyl.
3. Discussion The upwards curvature of the plots of Eq. (4) at low temperatures, demonstrated in Fig. 1 for representative RTILs, means that the Hildebrand concept of fluidity breaks down under such conditions and the ions of the RTIL cannot rotate freely any more. However, above ca. 40 ◦ C the ˚ = f(V) curves are linear as stipulated by this concept. The V0 values recorded in Table 1 are 99.0 ± 0.5% of the molar volume at 25 ◦ C, which may therefore be taken as the molar volume at which the ions are closely crowded, making viscous flow difficult while the ions still retain rotational freedom. Little can be said about the B values shown in Table 1. For a series of cations, say the 1-alkyl-3-methylimidazolium ones, with a given anion the B values tend to diminish as the cation becomes larger and its V0 values increase. The products BV0 are very roughly constant. 350 ± 40 for the tetrafluoroborate salts, 250 ± 20 for the hexafluorophosphate salts and 670 ± 100 for the bis(trifluoromethylsulfonyl)amide salts. When a B value is outside
Fig. 1. Plots of the fluidity against the molar volume at a range of temperatures for Etmim+ B(CN)4 − () with data from [12], Bumim+ NTF2 − () with data from [17], and Et(3Me)Py (䊉) with data from [14]. Filled symbols conform to a straight line with a linear correlation coefficient ≥0.995, empty symbols do not.
68
Y. Marcus / Fluid Phase Equilibria 363 (2014) 66–69
Fig. 2. The viscosities of methyl-3-methylpyridinium methylsulfate (䊉) from [31] and of N-methoxymethyl-N-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide () from [37] plotted as functions of the ) by Eq. (5). temperature and fitted (
these limits, as e.g. for EtmimBF4 , it is suspected that it is incorrect. For liquid metals [7] and molten salts with melting points above 200 ◦ C [39] the B coefficients increase with the cohesive energy density. This signifies that the more tightly the constituent particles (metal atoms and ions) are bound together, the more does the fluidity increase. This fact, valid also for RTILs, is counter-intuitive and no ready explanation for it could be found. On the positive side, a single determination of the viscosity at one temperature, T1 , provided 1 ≤ 50 mPa s, permits us to predict the temperature dependence of the viscosities of RTILs at T > T1 from just their volumetric behavior. In principle, according to the Hildebrand approach only the isobaric expansibility ˛P of the RTIL [8] is required, with a proper choice of T2 : (T ) =
1 (T1 − T2 )[1 − ˛P (T − T2 )] ∼1 (T − T2 )[1 − ˛P (T1 − T2 )]
T − T 1 2 T − T2
(5)
This choice corresponds to where the molar volume is 99.0 ± 0.5% of that at 298.15 K in view of this being the case for V0 . The approximation on the right-hand side of Eq. (5) results from ˛P T being much smaller than unity for T of a few tens of K at most. Examples of the predicted temperature dependence of the viscosity of RTILs are shown in Fig. 2. The fit is not perfect but the trend is correct. 4. Conclusions The fluidities of RTILs, provided they are not smaller than 0.02 s mPa−1 , can be described by the Hildebrand–Lamoreaux expression in terms of their molar volumes. When the fluidity is smaller than this value there is no free volume in the ionic liquid and the ions have lost their rotational freedom, so that the Hildebrand–Lamoreaux expression cannot any more describe the fluidity. As the temperature is increased and the fluidity increases beyond this limit it is possible to estimate the temperature dependence of the fluidity from the volumetric behavior alone. References [1] H. Vogel, The law of relationship between the viscosity of liquids and the temperature, Z. Phys. 22 (1921) 645–646.
[2] G. Tammann, G. Hesse, Temperature dependence of the viscosity of undercooled liquids, Z. Anorg. Allgem. Chem. 156 (1926) 245–247. [3] G.S. Fulcher, Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8 (1925) 339–355. [4] T.A. Litovits, Temperature dependence of the viscosity of associated liquids, J. Chem. Phys. 20 (1952) 1088–1089. [5] M.H. Ghatee, M. Zare, A.R. Zolghader, F. Moosavi, Temperature dependence of viscosity and relation with the surface tension of ionic liquids, Fluid Phase Equilibr. 291 (2010) 188–194. [6] J.H. Hildebrand, R.H. Lamoreaux, Fluidity: a general theory, Proc Natl. Acad. Sci. U S A 69 (1972) 3428–3431. [7] J.H. Hildebrand, R.H. Lamoreaux, Fluidity viscosity of liquid metals: an interpretation, Proc. Natl. Acad. Sci. U S A 73 (1976) 988–989. [8] Y. Marcus, in: E. Wilhelm, T. Letcher (Eds.), Volume Properties: Liquids, Solutions, and Vapours, Royal Soc. Chem., Cambridge, 2013 (Chapter 19). [9] A.B. Pereiro, F. Santamaria, E. Tojo, A. Rodriguez, J. Tojo, Temperature dependence of physical properties of ionic liquid 1,3-dimethylimidazolium methyl sulfate, J. Chem. Eng. Data 51 (2006) 952–954. [10] A. Noda, K. Hayamizu, M. Watanabe, Pulsed-gradient spin-echo 1 H and 19 F NMR ionic diffusion coefficient, viscosity, and ionic conductivity of nonchloroaluminate room-temperature ionic liquids, J. Phys. Chem. B 105 (2001) 4603–4610. [11] B. Hasse, J. Lehmann, D. Assenbaum, P. Wasserscheid, A. Leipertz, A.P. Fröba, Viscosity, interfacial tension, density, and refractive index of ionic liquids [EMIM][MeSO3 ], [EMIM][MeOHPO2 ], [EMIM][OcSO4 ], and [BBIM][NTF2 ] in dependence on temperature at atmospheric pressure, J. Chem. Eng. Data 54 (2009) 2576–2583. [12] A.P. Fröba, H. Kremer, A. Leipertz, Density, refractive index, interfacial tension, and viscosity of ionic liquids [EMIM][EtSO4 ], [EMIM][NTF2 ], [EMIM][N(CN)2 ], and [OMA][NTF2 ] in dependence on temperature at atmospheric pressure, J. Phys. Chem. B 112 (2008) 12420–12430. [13] T. Koller, M.H. Rauch, P.S. Schulz, M. Berger, P. Wasserscheid, I.G. Economou, A. Leipertz, A.P. Fröba, Viscosity, interfacial tension, self-diffusion coefficient, density and refractive index of the ionic liquid 1-ethyl-3-methylimidazolium tetracyanoborate as a function of temperature at atmospheric pressure, J. Chem. Eng. Data 57 (2012) 828–835. [14] S. Bulut, P. Eiden, W. Beichel, J.M. Slattery, T.F. Beyersdorffr, T.J.S. Schubert, I. Krossing, Temperature dependence of the viscosity and conductivity of mildly functionalized and non-functionalized [Tf2 N]− ionic liquids, ChemPhysChem 12 (2011) 2296–2310. [15] R.G. Seoane, S. Corderi, E. Gomez, N. Calvar, E.J. Gonzalez, E.A. Macedo, A. Dominguez, Temperature dependence and structural influence on the thermophysical properties of eleven commercial ionic liquids, Ind. Eng. Chem. Res. 51 (2012) 2492–2501. [16] J.M. Crosthwaite, M.J. Muldoon, J.K. Dixon, J.L. Anderson, J.F. Brennecke, Phase transition and decomposition temperatures, heat capacities and viscosities of pyridinium ionic liquids, J. Chem. Thermodyn. 37 (2005) 559–568. [17] H. Rodriguez, J.F. Brennecke, Temperature and composition dependence of the density and viscosity of binary mixtures water + ionic liquid, J. Chem. Eng. Data 51 (2006) 2145–2155. [18] K.R. Seddon, A. Stark, M.-J. Torres, Viscosity and density of 1-alkyl-3-methylimidazolium ionic liquids, ACS Symp. Ser. 819 (2002) 34–45. [19] E. Gomez, N. Calvar, E.A. Macedo, A. Dominguez, Effect of temperature on the physical properties of pure 1-propyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and characterization of its binary mixtures with alcohols, J. Chem. Thermodyn. 45 (2012) 9–15. [20] K.G. Bogolitsyn, T.E. Skrebets, T.A. Makhova, Physicochemical properties of 1butyl-3-methylimidazolium acetate, Russ. J. Gen. Chem. 79 (2009) 125–128. [21] H. Tokada, K. Hayamizu, K. Ishii, Md.A.B.H. Susan, M. Watanabe, Physicochemical properties and structures of room temperature ionic liquids. I. Variation of anionic species, J. Phys. Chem. B 108 (2004) 16593–16600. [22] L.G. Sanchez, J.R. Espel, F. Onink, G.W. Meindersma, A.B. de Haan, Density, viscosity, and surface tension of synthesis grade imidazolium, pyridinium, and pyrrolidinium based room temperature ionic liquids, J. Chem. Eng. Data 54 (2009) 2803–2812. [23] K.R. Harris, M. Kanakubo, L.A. Woolf, Temperature and pressure dependence of the viscosity of the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate: viscosity and density relationships of ionic liquids, J. Chem. Eng. Data 52 (2007) 2425–2430. [24] A.B. Pereiro, J.L. Legido, A. Rodriguez, Physical properties of ionic liquids based on 1-alkyl-3-methylimidazolium cation and hexafluorophosphate as anion and temperature dependence, J. Chem. Thermodyn. 30 (2007) 1168–1175. [25] K.R. Harris, L.A. Woolf, M. Kanakubo, Temperature and pressure dependence of the viscosity of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate, J. Chem. Eng. Data 50 (2005) 1777–1782. [26] B. Mokhtarani, A. Sharifi, H.R. Mortaheb, M. Mirzaei, M. Mafi, F. Sadeghian, Density and viscosity of 1-butyl-3-methylimidazolium nitrate with ethanol, 1propanol, or 1-butanol at several temperatures, J. Chem. Thermodyn. 41 (2009) 1432–1438. [27] K.R. Harris, M. Kanakubo, L.A. Woolf, Temperature and pressure dependence of the viscosity of the ionic liquids 1-hexyl-3methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, J. Chem. Eng. Data 52 (2007) 1080–1085. [28] H. Tokuda, K. Ishii, M.A.B.H. Susan, S. Tsuzuki, K. Hayamizu, M. Watanabe, Physicochemical properties and structures of room-temperature ionic liquids. 3. Variation of cationic structure, J. Phys. Chem. B 119 (2006) 2833–2839.
Y. Marcus / Fluid Phase Equilibria 363 (2014) 66–69 [29] J.-G. Li, Y.-F. Hu, S. Ling, J.-Z. Zhang, Physicochemical properties of [C6 mim][PF6 ] and [C6 mim][(C2 F5 )3 PF3 ] ionic liquids, J. Chem. Eng. Data 56 (2011) 3068–3072. [30] K.R. Harris, M. Kanakubo, L.A. Woolf, Temperature and pressure dependence of the viscosity of the ionic liquids 1-metyl-3-octylimidazolium hexafluorophosphate and 1-methyl-3-octylimidazolium tetrafluoroborate, J. Chem. Eng. Data 51 (2006) 1161–1167. [31] E. Gomez, N. Calvar, A. Dominguez, E.A. Macedo, Synthesis and temperature dependence of physical properties of four pyridinium-based ionic liquids: influence of the size of the cation, J. Chem. Thermodyn. 42 (2010) 1324–1329. [32] B. Mokhtarani, A. Sharifi, H.R. Mortaheb, M. Mirzaei, M. Mafi, F. Sadeghian, Density and viscosity of pyridinium-based ionic liquids and their binary mixtures with water at several temperatures, J. Chem. Thermodyn. 41 (2009) 323–329. [33] Q.-S. Liu, P.-P. Li, U. Welz-Biermann, X.-X. liu, J. Chen, Density, electrical conductivity, and dynamic viscosity of N-alkyl-4-methylpyridinium bis(trifluoromethyl sulfonyl)imide, J. Chem. Eng. Data 57 (2012) 2999–3004. [34] A.K. Ziyada, C.D. Wilfred, M.A. Bustam, Z. Man, T. Murugesan, Thermophysical properties of 1-propyronitrile-3-alkylimidazolium bromide ionic liquids
[35]
[36]
[37]
[38]
[39]
69
at temperatures from (293.15 to 353.15) K, J. Chem. Eng. Data 55 (2010) 3886–3890. F.J. Deive, M.A. Rivas, A. Rodriguez, Study of thermodynamic and transport properties of phosphonium-based ionic liquids, J. Chem. Thermodyn. 62 (2013) 98–103. U. Domanska, M. Zawaqdzki, A. Lewandrowska, Effect of temperature and composition on the density, viscosity, surface tension, and thermodynamic properties of binary mixtures of N-octylisoquinolinium bis(trifluoromethyl sulfonyl)imide with alcohols, J. Chem. Thermodyn. 48 (2012) 101–111. M. Kanakubo, H. Nanjo, T. Nishida, J. Takano, Density, viscosity, and electrical conductivity of N-methoxymethylpyrrolidinium bis(trifluoromethyl sulfonyl)amide, Fluid Phase Equilibr. 302 (2011) 10–13. C.M.S.S. Neves, P.J. Carvalho, M.G. Freire, J.A.P. Coutinho, Thermophysical properties of pure and water-saturated tetradecyltrihexylphosphonium-based ionic liquids, J. Chem. Thermodyn. 43 (2011) 948–957. Y. Marcus, The fluidity of molten salts, Fluid Phase Equil., submitted November 2013.