Are Room Temperature Ionic Liquids Dilute Electrolytes?
AAre Room Temperature Ionic Liquids Dilute Electrolytes?
Alpha A Lee, Dominic Vella, Susan Perkin, and Alain Goriely Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom Department of Chemistry, University of Oxford, Oxford, OX1 3QZ, United Kingdom
An important question in understanding the structure of ionic liquids is whetherions are truly “free” and mobile which would correspond to a concentrated ionicmelt, or are rather “bound” in ion pairs, that is a liquid of ion pairs with a smallconcentration of free ions. Recent surface force balance experiments from differentgroups have given conflicting answers to this question. We propose a simple modelfor the thermodynamics and kinetics of ion pairing in ionic liquids. Our modeltakes into account screened ion-ion, dipole-dipole and dipole-ion interactions in themean field limit. The results of this model suggest that almost two thirds of theions are free at any instant, and ion pairs have a short lifetime comparable to thecharacteristic timescale for diffusion. These results suggest that there is no particularthermodynamic or kinetic preference for ions residing in pairs. We therefore concludethat ionic liquids are concentrated, rather than dilute, electrolytes.
Keywords: Ion Pairs, Associating Liquids, Electrolyte Solutions, McMilan-Mayer model,Poisson-Boltzmann theory
Room temperature ionic liquids are salts that are in the liquid state under ambientconditions. They are important in diverse chemical and physical applications [1], fromsolvents in organic synthesis [2, 3] to applications in field effect transistors [4]. Naively, anionic liquid appears to be a fluid of free ions. However, the presence of strong and long-rangedCoulomb interactions complicates the picture. Recent surface force balance experiments onionic liquids confined between charged surfaces led to the conclusion [5] that ionic liquidsbehave as dilute electrolytes: the majority of ions in solution are bound as cation-anion pairsthat behave effectively as dipoles. The authors concluded that these dipoles behave as asolvent containing a relatively low concentration of truly free ions. This conclusion followedfrom fitting measured double layer forces to the linear Debye-H¨uckel theory: a very largeDebye screening length, of O (10nm), was found from this fit, corresponding to a very low a r X i v : . [ c ond - m a t . s o f t ] D ec concentration of free charges.This description of ionic liquids triggered an intense discussion in the literature [6, 7]. Akey argument for the dilute electrolyte picture is the apparently large dissociation constant.The equilibrium constant for dissociation was estimated as [5] K = exp (cid:18) − ∆ E d (cid:15)k B T (cid:19) (1)with dissociation energy of the ion pair ∆ E d = 315 .
26 kJmol − (taken from quantum elec-tronic structure calculations of an ion pair in vacuum [8]), and (cid:15) = 11 .
6, the low frequencydielectric constant (measured using dielectric spectroscopy) [9]. However, it is importantto recall that in arriving at this estimate, several assumptions have been made. First, thevalue of ∆ E d used is the theoretical gas phase dissociation energy, which is likely to bean overestimate because it neglects the electrostatic screening by other free ions [10]. Fur-ther, dividing the interaction energy by the dielectric constant, as measured from dielectricspectroscopy, is unlikely to account correctly for the electrostatic interaction between ions[10, 11]. Therefore, Equation (1) only holds when the concentration of free charges is low,since it implicitly assumes that the typical interaction energy between a bound ion and aneighbouring free charge is significantly less than the thermal energy [12].In this Letter, we attempt to remove some of these implicit assumptions. The key ques-tions that we would like to answer are: Are ion pairs abundant in solution? If so, are theylong-lived species, or merely transient intermediates? To estimate the abundance and thelifetime of ion pairs in ionic liquids, we develop a simple theory of ion pairing that accountsfor both screened electrostatic interactions and a dielectric constant that is self-consistentlycalculated with the concentration of ion pair dipoles.We note that the notions of association equilibrium and “ion-pairs” are somewhat artifi-cial: in reality, the liquid is a sea of ions interacting via a Coulomb potential. Nonethelessthe idea of ion pairing is an extremely useful concept as it provides a direct chemical andphysical analogy with dilute/concentrated electrolytes.The picture we suggest is as follows: in an ionic liquid, ions interact with one anotherscreened by other free ions and a background dielectric medium that consists of dipolar ionpairs. At the same time, dipoles (ion pairs) interact with one another, an interaction thatis screened by the presence of free ions and other dipoles (see Fig. 1 for a schematic of thesystem). Related ideas of ion association have been employed in [13–16] to study criticality FIG. 1: An ionic liquid is modelled as a mixture of free ions (coloured spheres) and bounded ionpair dipoles (dumbbells). The free ions provide a characteristic Debye screening length κ − whilethe dipoles provide a background dielectric constant (cid:15) . and the gas-liquid transition in Coulomb fluids.To determine the fraction of free ions, α , we consider a “chemical” equilibrium betweenfree ions and ion pairs, which we define as ions being held at closest approachcation + anion (cid:42)(cid:41) cation − anion . (2)The law of mass action gives the equilibrium constant K = ρ d ρ + ρ − = 2 1 − αρα , (3)where ρ d , ρ + and ρ − are the densities of dipoles, cations and anions, respectively, and ρ isthe total density. Determining α is the central goal of our analysis; ionic liquids would bedilute electrolytes if α (cid:28)
1. To relate K to the interaction potential between ions, v ( r ), wefollow the McMillan-Mayer theory of associating liquids [14, 17, 18], which yields K = 4 π (cid:90) ∞ a d r (cid:2) r ( e − βv ( r ) − (cid:3) . (4)A simple model for charge-charge interaction is the linearised Poisson-Boltzmann ap-proach. Assuming that ions are hard spheres of diameter a that create an exclusion sphereof radius a , the interaction potential v ( r ) between two monovalent ions with opposite charges ± e , can be obtained by solving the linearised Poisson-Boltzmann equation with a uniformcharge density on the surface of the exclusion sphere [13]. This yields βv ( r ) = − l B r e κ ( a − r ) κa + 1 . (5)Equation (5) includes two key lengthscales, the thermal Bjerrum length l B = q e π(cid:15)(cid:15) k B T , (6)which is the typical distance over which electrostatic interactions between two charges in adielectric medium is comparable to the thermal energy k B T , and the inverse Debye screeninglength κ = (cid:112) πl B ( ρ + + ρ − ) = (cid:112) πl B αρ, (7)which describes the physics of electric field screening by free ions.By mass balance and electroneutrality, ρ + = ρ − = αρ/
2, while the ion pair density ρ d = (1 − α ) ρ/
2. To account for the polarisability of ions, we scale charge and take q = 1 / √ (cid:15) ∞ for a monovalent ionic liquid [19, 20], where (cid:15) ∞ is the optical (high frequency) dielectricconstant. Such charge-scaling is shown by simulation to give distribution functions that areexcellent approximations to the full electrostatic problem with polarisability [21] .Definition (6) involves (cid:15) , the static (low frequency) dielectric constant. An ionic liquidis a pure substance and so there is no true “background” dielectric. Instead it is the ionpair dipoles that provides the effective dielectric constant. We treat the sea of ion pairs as adipolar fluid consisting of polarisable spheres with dipole moment µ whose interactions arescreened by free ions. Classic results [22] show that in such a system (cid:15) satisfies( (cid:15) − (cid:15) ∞ )[(2 (cid:15) + (cid:15) ∞ )(1 + κa d ) + (cid:15) ( κa d ) ] (cid:15) ( (cid:15) ∞ + 2) (1 + κa d + ( κa d ) /
3) = (1 − α ) ρµ (cid:15) k B T , (8)where a d is the effective diameter of the dipole. (Note that in the limit of no free ions, κ = 0,and (8) reduces to the celebrated Onsager formula [23].) For simplicity we assume that theion pair is a sphere with the same volume as the sum of the constituent ions, i.e. a d = 2 / a and µ = ea d / ea/ / .Substituting (4) and (5) into the LHS of (3), and using the change of variable r → r/a ,we obtain an implicit equation for α , the fraction of ions that are dissociated1 − αα = 2 πρa (cid:90) ∞ r (cid:20) exp (cid:18) l B ar e κa (1 − r ) κa + 1 (cid:19) − (cid:21) d r, (9)with α implicit in the RHS via (6)-(8), noting that (cid:15) is a function of α .Equation (9) is the main result of our model and contains no fitting parameters. The onlyexperimental measurements needed are the density ρ , ion diameter a , and high frequencydielectric constant (cid:15) ∞ . The ion diameter a is difficult to assess experimentally, not leastbecause cations and anions are seldom truly spherical let alone the same size. However, thekey dimensionless parameter is κa , which can be written in terms of another dimensionlessparameter l B /a via κa = (cid:112) ηαl B /a , where η = ( π/ ρa is the packing fraction. Ithas been shown that η is roughly constant for ionic liquids [24], and we take η = 0 . a directly.The high frequency dielectric constant (cid:15) ∞ accounts for high-frequency mode for dielectricrelaxation [26, 27]. Experimentally measured values of (cid:15) ∞ vary somewhat, see e.g. [28, 29],and we will take (cid:15) ∞ = 3 . a . Increasingthe effective ionic radius decreases the density of dipoles and hence decreases the dielectricconstant. We note that this picture only holds for ionic liquids with short pendant alkylchains, and is not valid for ionic liquids with longer side chains and polymerised ionic liq-uids, where locally heterogeneous environments emerge [30–32] [48]. Numerical solution of(9) shows that α is relatively insensitive to the ion radius, but it increases as the polaris-ability, hence (cid:15) ∞ , increases since Coulomb interactions are better screened (see Fig. 2).To understand this trend, we note that in the limit κa (cid:29)
1, the transcendental equation(9) can be solved asymptotically, yielding α ≈ /
3, which agrees well with numerical results(inset of Fig. 2). Physically this result suggests equidistribution between cations, anions andion pairs, as might be expected from entropy maximisation. The leading order expansion of(8) yields (cid:15) ≈ η ( (cid:15) ∞ + 2) l (0) B a , (10)where l (0) B is the vacuum Bjerrum length ( (cid:15) = 1 in (6)). We see that the dielectric constantscales inversely with the ionic radius, in agreement with numerical results (Fig 2).Our main results are that α ≈ / i.e. almost 2 / not bound in ion pairs ina typical ionic liquid at any instant, and that κa (cid:29)
1, that is, the Debye length is small,contrary to previous results [5]. Although Coulomb interactions in free space are strong
FIG. 2: The main panel shows the dielectric constant as a function of ion diameter plotted fordifferent high frequency dielectric constants (cid:15) ∞ . The datapoints show the experimentally obtainedvalues taken from [33] ([C MIm][BF ]), [34] ([C MIm][NTf ]), and [35] ([C MIm][NTf ]). The iondiameter is calculated from the density of the ionic liquids taken from [36], assuming the packingfraction η = 0 .
64. The inset shows the fraction of free ions, α , as a function of packing fraction η and unscreened electrostatic interaction at closest contact l B /a . The white box in the inset showsthe largest possible parameter space for a reasonable ionic liquid: ion diameter 5˚ A -10˚ A and density ρ = 4 × m − ( ≈ M ). and long-ranged, the presence of other free ions significantly screens these interactions. Theinset of Fig 2 shows that the result α ≈ / α (cid:28)
1, is for small ions at low packing fraction. In this regime, the systemis best described as a dilute gaseous plasma-like system rather than an ionic liquid.We should comment on several key assumptions of our model: ( i ) The mean-field lin-earised Poisson-Boltzmann treatment neglects fluctuation effects, which would renormalisethe screening length and, for large electrolyte densities, induce an oscillatory decay in theelectric potential away from the ion [37]. This subtlety is likely to affect the quantitativepredictions of our theory, but not our qualitative conclusions as we have accounted for strongelectrostatic correlations beyond mean field by considering bound ion pairs. ( ii ) The estimateof the dielectric constant, (8), uses a mean-field treatment of dipole-dipole interactions, andlinearised Poisson-Boltzmann electrostatics (consistent with our treatment of ion-ion interac-tions). ( iii ) The calculation of the equilibrium constant is based on McMillan-Mayer theoryof an associating solution. The physical picture is that we correct the non-ideality of theion mixture by introducing dipolar ion-pairs, and Equation (4) comes from a self-consistentevaluation of the virial coefficients [17]. Various other approaches have been proposed in theliterature [14, 38, 39], with various theories differing in their the thermodynamic definitionof an “ion pair”; these yield qualitatively similar results for our model system. ( iv ) Wehave only considered ions and ion-pairs here. Interactions between higher order multipolesare weaker. Therefore the fact that even ion-pairs are not abundant means that the ef-fects of larger aggregates would be negligible. ( v ) Ionic liquids are typically geometricallyanisotropic and have short ranged directional interactions such as hydrogen bonds. We haveneglected those factors here as they are secondary in the formation of ion pairs.It is important to bear in mind that an ion pair is only a transient species — ions candissociate and form an ion pair with another surrounding ion. Therefore, another naturalmeasure of whether ionic liquids are dilute electrolytes is the lifetime of an ion pair. Assumingrandom packing, the average distance between one ion in an ion pair and another ion ofopposite charge is approximately σ = 2[3 / (4 πρ )] / = a/η / . For an ion pair to ‘break’, oneion must move away from the pair. In doing so, the electrostatic energy increases beforethe ion passes through a “transition state” energy maxima, after which it forms a new ionpair. The energy landscape as the ion moves away from its existing partner and towards anadjacent ion is given by V ( r ) = v ( r ) + v ( σ − r + a ) , (11)where r is the separation between the original ion pair (see Figure 3a) and v ( r ) is given by(5). The lifetime of an ion pair is the mean first passage time through the energy maximaat r = ( σ + a ) /
2, and can be estimated using Kramers-Smoluchowski theory to be [40] τ = 1 D (cid:90) σ ( σ + a ) / d x (cid:90) xa d y (cid:16) yx (cid:17) exp [ V ( x ) − V ( y )] , (12)where D is the self-diffusion coefficient. Table I shows that the estimated lifetimes of the ionpairs in typical ionic liquids are relatively short and comparable to the diffusion timescale τ D = a /D .The short lifetime, together with the fact that cations, anions and ion pairs exist inroughly equal numbers, suggest that an ion pair is not after all a “special” species — theprobability and lifetime of two oppositely charged ions being found within close separation Ionic Liquid Ions D/ m s − a/ ˚ A τ /ps p = τ /τ D [C MIm][BF ] 1.6 [41] 5.4 140 7.7[C MIm][NTf ] 1.2 (est. from [42]) 6.5 71 2.0[C MIm][NTf ] 1.2 [42] 6.7 63 1.7TABLE I: The ion pairs have relatively short lifetimes (as estimated by (12)). D is the diffusioncoefficient, a the ion diameter (estimated from the packing fraction, as outlined in the main text), τ the ion lifetime and τ D = a /D . (thus by our definition an ion pair) is almost the same as what one would expect from therelative diffusion of ions in the absence of any interactions.Further insights can be obtained by writing (12) in dimensionless form τ /τ D = p (cid:18) al B , κa (cid:19) (13)where p is a cumbersome quadrature that depends on two dimensionless lengthscales. Fig.3b shows that, for fixed ion size, p decreases as the dielectric constant, and thus a/l B ,increases. However, surprisingly, p increases before decreasing as the Debye length decreases.Decreasing the Debye length decreases the magnitude of the electrostatic interactions, butthe energy barrier ∆ E = V (( R + a ) / − V ( a ) is a non-monotonic function of κa . The initialincrease in the energy barrier as κa increases is due to the effect of screening decreasing V ( a ),but to a lesser extent the energy maximum at V (( R + a ) / κa all interactions arestrongly screened and therefore ∆ E decreases. Increasing the ion diameter a whilst keepingthe Debye and Bjerrum lengths fixed leads to a decrease in the lifetime due to the reductionof surface charge density on the ion surface.The simple model developed here captures the essential physics of ion-ion, ion-dipoleand dipole-dipole interaction in determining the abundance of ion pairs in ionic liquids.Despite its simplicity, the theory agrees well with available experimental measurements ofthe dielectric constant. Crucially, our theory predicts that free ions outnumber ion pairsby 2:1 with pairs being short-lived. This prediction suggests that ionic liquids cannot beconsidered as dilute electrolytes.On the experimental front, we note that the good quantitative fit obtained in [5] thatsupported the dilute electrolyte picture may be an artefact of the surface morphology andinterfacial chemistry of gold. It is known that the gold surface is not atomically flat and (a) (b) FIG. 3: a) Schematic cartoon illustrating the energy landscape of the ion pair exchange. b) Thescaling function p = τ /τ D as a function of two dimensionless lengthscales κa and a/l B . surface reconstruction occurs upon contact with ionic liquids [43, 44]. In fact, other surfaceforce balance studies [45, 46] seem to indicate a very high degree of Coulomb correlation.We conclude that, unless new experiments reveal new unexplained behaviour, ionic liquidsshould not be viewed as dilute electrolytes. Acknowledgments
We thank D Frenkel for insightful discussions. We also thank the anonymous reviewersfor insightful suggestions regarding the interpretation of our results. This work is supportedby an EPSRC Research Studentship to AAL. AG is a Wolfson/Royal Society Merit AwardHolder and acknowledges support from a Reintegration Grant under EC Framework VII. [1] Fedorov, M. V., and Kornyshev, A. A. ( ) Ionic Liquids at Electrified Interfaces.
Chem.Rev. 114 , 2978–3036.[2] Welton, T. ( ) Room-temperature ionic liquids. Solvents for synthesis and catalysis.
Chem.Rev. 99 , 2071–2084.[3] Hallett, J. P., and Welton, T. ( ) Room-temperature ionic liquids: solvents for synthesisand catalysis. 2.
Chem. Rev. 111 , 3508–3576. [4] Fujimoto, T., and Awaga, K. ( ) Electric-double-layer field-effect transistors with ionicliquids. Phys. Chem. Chem. Phys. 15 , 8983–9006.[5] Gebbie, M. A., Valtiner, M., Banquy, X., Fox, E. T., Henderson, W. A., and Israelachvili, J. N.( ) Ionic liquids behave as dilute electrolyte solutions.
Proc. Natl. Acad. Sci. U.S.A. 110 ,9674–9679.[6] Perkin, S., Salanne, M., Madden, P., and Lynden-Bell, R. ( ) Is a Stern and diffuse layermodel appropriate to ionic liquids at surfaces?
Proc. Natl. Acad. Sci. U.S.A. 110 , E4121–E4121.[7] Gebbie, M. A., Valtiner, M., Banquy, X., Henderson, W. A., and Israelachvili, J. N. ( )Reply to Perkin et al.: Experimental observations demonstrate that ionic liquids form bothbound (Stern) and diffuse electric double layers.
Proc. Natl. Acad. Sci. U.S.A. 110 , E4122–E4122.[8] Hunt, P. A., Gould, I. R., and Kirchner, B. ( ) The structure of imidazolium-based ionicliquids: Insights from ion-pair interactions.
Aust. J. Chem. 60 , 9–14.[9] Weing¨artner, H. ( ) Understanding ionic liquids at the molecular level: facts, problems,and controversies.
Angew. Chem. Int. Ed. 47 , 654–670.[10] Lynden-Bell, R. ( ) Screening of pairs of ions dissolved in ionic liquids.
Phys. Chem.Chem. Phys. 12 , 1733–1740.[11] Schr¨oder, C., Hunger, J., Stoppa, A., Buchner, R., and Steinhauser, O. ( ) On the collec-tive network of ionic liquid/water mixtures. II. Decomposition and interpretation of dielectricspectra.
J. Chem. Phys. 129 , 184501.[12] Fowler, R. H., and Guggenheim, E. A.
Statistical Thermodynamics ; Cambridge UniversityPress, .[13] Fisher, M. E., and Levin, Y. ( ) Criticality in ionic fluids: Debye-H¨uckel theory, Bjerrum,and beyond.
Phys. Rev. Lett. 71 , 3826.[14] Levin, Y., and Fisher, M. E. ( ) Criticality in the hard-sphere ionic fluid.
Physica A 225 ,164–220.[15] Weiss, V., and Schr¨oer, W. ( ) Macroscopic theory for equilibrium properties of ionic-dipolar mixtures and application to an ionic model fluid.
J. Chem. Phys. 108 , 7747–7757.[16] Kobrak, M. N. ( ) The Chemical Environment of Ionic Liquids: Links Between LiquidStructure, Dynamics, and Solvation.
Adv. Chem. Phys. 139 , 85–138. [17] Woolley, H. W. ( ) The representation of gas properties in terms of molecular clusters. J.Chem. Phys. 21 , 236–241.[18] McMillan Jr, W. G., and Mayer, J. E. ( ) The statistical thermodynamics of multicom-ponent systems.
J. Chem. Phys. 13 , 276–305.[19] Yu, H., and van Gunsteren, W. F. ( ) Accounting for polarization in molecular simulation.
Comput. Phys. Commun. 172 , 69–85.[20] Leontyev, I., and Stuchebrukhov, A. ( ) Electronic continuum model for molecular dy-namics simulations.
J. Chem. Phys. 130 , 085102.[21] Schr¨oder, C. ( ) Comparing reduced partial charge models with polarizable simulationsof ionic liquids.
Phys. Chem. Chem. Phys. 14 , 3089–3102.[22] Schr¨oer, W. ( ) Generalization of the Kirkwood-Fr¨ohlich theory of dielectric polarizationfor ionic fluids.
J. Mol. Liq. 92 , 67–76.[23] Onsager, L. ( ) Electric moments of molecules in liquids.
J. Am. Chem. Soc. 58 , 1486–1493.[24] Slattery, J. M., Daguenet, C., Dyson, P. J., Schubert, T. J., and Krossing, I. ( ) How toPredict the Physical Properties of Ionic Liquids: A Volume-Based Approach.
Angew. Chem.Int. Ed. 119 , 5480–5484.[25] Song, C., Wang, P., and Makse, H. A. ( ) A phase diagram for jammed matter.
Nature453 , 629–632.[26] Fumino, K., Wulf, A., and Ludwig, R. ( ) The Cation–Anion Interaction in Ionic LiquidsProbed by Far-Infrared Spectroscopy.
Angew. Chem. Int. Ed. 47 , 3830–3834.[27] Weing¨artner, H. ( ) The static dielectric permittivity of ionic liquids.
J. Mol. Liq. 192 ) Dielectric response of imidazolium-based room-temperature ionic liquids.
J. Phys. Chem. B 110 , 12682–12688.[29] Nakamura, K., and Shikata, T. ( ) Systematic Dielectric and NMR Study of the IonicLiquid 1-Alkyl-3-Methyl Imidazolium.
ChemPhysChem 11 , 285–294.[30] Bhargava, B. L., Devane, R., Klein, M. L., and Balasubramanian, S. ( ) Nanoscale orga-nization in room temperature ionic liquids: a coarse grained molecular dynamics simulationstudy.
Soft Matter 3 , 1395–1400. [31] Triolo, A., Russina, O., Bleif, H.-J., and Di Cola, E. ( ) Nanoscale segregation in roomtemperature ionic liquids. J. Phys. Chem. B 111 , 4641–4644.[32] Xiao, D., Hines Jr, L. G., Li, S., Bartsch, R. A., Quitevis, E. L., Russina, O., and Triolo, A.( ) Effect of cation symmetry and alkyl chain length on the structure and intermolecu-lar dynamics of 1, 3-dialkylimidazolium bis (trifluoromethanesulfonyl) amide ionic liquids.
J.Phys. Chem. B 113 , 6426–6433.[33] Stoppa, A., Buchner, R., and Hefter, G. ( ) How ideal are binary mixtures of room-temperature ionic liquids?
J. Mol. Liq. 153 , 46–51.[34] Huang, M.-M., Jiang, Y., Sasisanker, P., Driver, G. W., and Weinga rtner, H. ( ) StaticRelative Dielectric Permittivities of Ionic Liquids at 25 ◦ C. J. Chem. Eng. Data 56 , 1494–1499.[35] Weingartner, H. ( ) The static dielectric constant of ionic liquids.
Z. Phys. Chem. 220 ,1395–1406.[36] Zhang, S., Lu, X., Zhou, Q., Li, X., Zhang, X., and Li, S.
Ionic Liquids: PhysicochemicalProperties ; Elsevier, .[37] Attard, P. ( ) Electrolytes and the electric double layer.
Adv. Chem. Phys. 92 , 1–160.[38] Holovko, M.
Ionic Soft Matter: Modern Trends in Theory and Applications ; Springer, ;pp 45–81.[39] Schr¨oer, W. ( ) On the chemical and the physical approaches to ion association.
J. Mol.Liq. 164 , 3–10.[40] H¨anggi, P., Talkner, P., and Borkovec, M. ( ) Reaction-rate theory: fifty years afterKramers.
Rev. Mod. Phys. 62 , 251.[41] Noda, A., Hayamizu, K., and Watanabe, M. ( ) Pulsed-gradient spin-echo 1H and 19FNMR ionic diffusion coefficient, viscosity, and ionic conductivity of non-chloroaluminate room-temperature ionic liquids.
J. Phys. Chem. B 105 , 4603–4610.[42] Tokuda, H., Hayamizu, K., Ishii, K., Susan, M. A. B. H., and Watanabe, M. ( ) Physic-ochemical properties and structures of room temperature ionic liquids. 2. Variation of alkylchain length in imidazolium cation.
J. Phys. Chem. B 109 , 6103–6110.[43] Aliaga, C., Santos, C. S., and Baldelli, S. ( ) Surface chemistry of room-temperature ionicliquids.
Phys. Chem. Chem. Phys. 9 , 3683–3700.[44] Uhl, B., Buchner, F., Alwast, D., Wagner, N., and Behm, R. J. ( ) Adsorption of the ionicliquid [BMP][TFSA] on Au (111) and Ag (111): substrate effects on the structure formation investigated by STM. Beilstein J. Nanotechnol. 4 , 903–918.[45] Perkin, S., Albrecht, T., and Klein, J. ( ) Layering and shear properties of an ionic liquid,1-ethyl-3-methylimidazolium ethylsulfate, confined to nano-films between mica surfaces.
Phys.Chem. Chem. Phys, 12 , 1243–1247.[46] Perkin, S., Crowhurst, L., Niedermeyer, H., Welton, T., Smith, A. M., and Gosvami, N. N.( ) Self-assembly in the electrical double layer of ionic liquids.
Chem. Commun. 47 , 6572–6574.[47] Choi, U. H., Mittal, A., Price Jr, T. L., Gibson, H. W., Runt, J., and Colby, R. H. ( )Polymerized ionic liquids with enhanced static dielectric constants.