Conductivity and Solvation Dynamics in Ionic Liquids - American

Letter pubs.acs.org/JPCL

Conductivity and Solvation Dynamics in Ionic Liquids Xin-Xing Zhang,†,‡ Min Liang,§ Nikolaus P. Ernsting,‡ and Mark Maroncelli*,§ †

Department of Physics, Nankai University, Tianjin, China Department of Chemistry, Humboldt Universität zu Berlin, Germany § Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania, United States ‡

S Supporting Information *

ABSTRACT: It was shown recently that a simple dielectric continuum model predicts the integral solvation time of a dipolar solute ⟨τsolv⟩ to be inversely proportional to the electrical conductivity σ0 of an ionic solvent or solution. In this Letter, we provide a more general derivation of this connection and show that available data on coumarin 153 (C153) in ionic liquids generally support this prediction. The relationship between solvation time and conductivity can be expressed by ln(⟨τsolv⟩/ps) = 4.37 − 0.92 ln (σ0/S m−1) in 34 common ionic liquids.

SECTION: Liquids; Chemical and Dynamical Processes in Solution oom-temperature ionic liquids are finding application in virtually every area of chemistry.1−6 Particularly active areas include use of ionic liquids as alternatives to conventional organic solvents for separations and chemical synthesis5,7 and as nonvolatile liquid electrolytes for various energy transduction and storage applications.8−10 These uses, as well as the intrinsic interest in this new class of materials, have spawned a good deal of research into fundamental aspects of solvation and electrical conductivity in ionic liquids. With respect to conductivity, of most interest is how ion−ion interactions lead to higher viscosities and more limited conductivities than might be optimal for device applications.11−14 In the case of solvation, key questions concern what distinctive features arise in a purely ionic solvent compared to conventional dipolar solvents and how one can begin to predict the energies and time scales of solvation in these media. In contrast to dipolar solvents, where dielectric constants enable reasonable first estimates of solvation energies via Born/Onsager-type models, the presence of mobile charges overwhelms the effect of dipolar contributions (see below) and renders the dielectric constant of little predictive value.15,16 Instead, empirical studies indicate that it is ion concentration or charge density that dictates relative (electrostatic) solvation energies in different ionic liquids.17−21 Solvation dynamics, the response of a medium to changes in (electrical) solute−solvent interactions, is also quite different in ionic liquids compared to most conventional solvents. Not only is full relaxation of the solvation energy much slower as a result of the high viscosities of ionic liquids, but it is also temporally dispersive, including important contributions stretching from subpicosecond to nanosecond times.20,22−26 This dispersive response gives rise to distributed kinetics in room-temperature

R

© XXXX American Chemical Society

ionic liquids, similar to what is found in supercooled conventional solvents.27−29 A number of workers have sought to understand solvation dynamics in ionic liquids in terms of computer simulations30−33 and analytical theories.34−36 The simplest theoretical description, the dielectric continuum model, connects the molecularlevel phenomenon of solvation with the macroscopic dielectric response of the neat solvent as obtained through frequencydependent dielectric measurements. It has been known for some time that such a description works surprisingly well for predicting solvation times in typical dipolar solvents.37−40 Very recently, the availability of femtosecond-resolution solvation data and dielectric data extending to terahertz frequencies has enabled us to test the applicability of the dielectric continuum model for predicting solvation time scales in ionic liquids.20,36 We found that, with the proper inclusion of conductivity contributions, dielectric continuum calculations provide a good representation of the dispersive nature of solvation in ionic liquids. However, in contrast to the case of dipolar liquids, where observed solvation times agree with continuum predictions, in ionic liquids, the predicted dynamics are too fast by at least a factor of 2−4. The present Letter represents an extension of the aforementioned studies.20,36 When analyzing additional data, some of the authors discovered that dielectric continuum theory predicts a simple connection between the integral time of solvation and the electrical conductivity of the solvent Received: February 17, 2013 Accepted: March 19, 2013

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dx.doi.org/10.1021/jz400359r | J. Phys. Chem. Lett. 2013, 4, 1205−1210

The Journal of Physical Chemistry Letters

Letter

(eq 9 below).41 In ref 41, it was assumed that the dielectric dispersion of the solvent could be described by a sum of up to three Debye terms. Herein, we provide an alternative derivation not limited by any particular form of the dielectric dispersion, and we assess the accuracy of this relationship using the body of solvation data previously collected with the probe coumarin 153 (C153). The link to conductivity also resolves an apparent anomaly reported for solvation in ionic liquids containing the large trihexyltetradecylphosphonium cation. The dielectric continuum model employed here represents the solute as a polarizable point dipole centered within a spherical cavity of radius a and the solvent as a featureless continuum with generalized dielectric dispersion η̂(ω). This generalized function differs from the function ε̂(ω) used to describe dielectric behavior in nonconductive media due to the presence of additional contributions from ion translational dynamics. In the presence of ionic mobility, η̂(ω) diverges as ω → 0. For convenience in experimental work, it is usual to separate this diverging portion from the nondiverging part of η̂(ω) and report results as 4πσ0 ηĉ (ω) = η (̂ ω) − i ω

can be related to the extension of eq 2 to nonzero frequencies,44,49 R⃗ (ω) ∝ χ̂(ω)μ⃗(ω), with the susceptibility given by χ ̂ (ω) =

2 ⎛ εc + 1 ⎞⎛ ε0 − 1 ⎞ ⎜ ⎟⎜ ⎟μ ⃗ a3 ⎝ 3 ⎠⎝ 2ε0 + εc ⎠

S(t ) =

ΔAel (t ) − ΔAel (∞) ν(t ) − ν(∞) = ΔAel (0) − ΔAel (∞) ν(0) − ν(∞)

Lp−1{[χ ̂ (p) − χ ̂ (0)]/p} χ ̂ (∞) − χ ̂ (0)

(5)

where L−1 p denotes an inverse Laplace transform with respect to the variable p = iω. The desired relationship between the integral solvation time ⟨τsolv⟩ and the static conductivity σ0 is derived by noting that the Laplace transform of S(t) from eq 5 is s (̃ p) ≡ Lp{S(t )} =

(1)

∫0

∞

exp(−pt )S(t ) dt

1 χ ̂ (p) − χ ̂ (0) p χ ̂ (∞) − χ ̂ (0)

=

(6)

and that ⟨τsolv⟩ ≡

∫0

∞

S(t ) dt = s (̃ p = 0)

(7)

Thus, ⟨τsolv⟩ can be found from ⟨τsolv⟩ =

⎧1 ⎫ 1 lim ⎨ (χ ̂ (p) − χ ̂ (0))⎬ χ ̂ (∞) − χ ̂ (0) p → 0⎩ p ⎭

(8)

In the presence of nonzero conductivity, η̂(p → 0) = 4πσ0/p. Defining ε∞ = η̂(p → ∞), one easily finds χ̂(∞) − χ̂(0) = −(εc + 2)/2(2ε∞ + εc) and {χ̂(p) − χ̂(0)}/p → −(εc + 2)/ 16πσ0 as p → 0, which may be combined to provide

(2)

and the electrostatic solvation free energy is given by Ael = −1/2R⃗ ·μ⃗. In this expression, ε0 = ε̂(ω = 0) is the static dielectric constant, and εc is a cavity dielectric constant used to represent the solute polarizability α via α/a3 = (εc − 1)/(εc + 2). In a conducting medium, the equivalent of ε0 is η0 = η̂(ω = 0) = 4πiσ0/ω, which is infinite. We adopt the perspective that a continuum treatment of an ionic liquid is no different from the ε0 → ∞ limit of the dipolar fluid.45 Thus, the solvation energy becomes simply Ael = −(εc + 1)μ2/6a3. In contrast to the dipolar case, Ael is independent of solvent properties, and the dependence of solvation energies on ion density in ionic liquids must be rationalized by interpreting the effective solute cavity size a to be a function of the sizes of solvent ions.33,46 Solvation dynamics experiments monitor the time evolution of the difference in solvation energies between two solute electronic states. In the present model, one assumes that the electronic states differ solely in dipole moment and that the dipole moment undergoes a step function change at t = 0. (The effect of solute rotation,44,47,48 which may be important in ionic liquids,33 is not considered here.) If the medium response is linear, the normalized solvation response function S( t ) =

(4)

(Because S(t) is normalized, only the frequency-dependent terms in eq 2 need be retained in χ̂(ω).) The time domain solvation energy ΔAel(t) and thus S(t) are related to χ̂(ω) by50,51

where σ0 is the static electrical conductivity, σ0 = σ̂(ω = 0). It should be noted that although this “corrected” dielectric function is typically labeled ε̂(ω) and fit to the same functions used for purely dipolar liquids, subtracting the σ0 divergence in this manner does not provide a rigorous separation of ion translational motions. Such motions still contribute to η̂c(ω) at all nonzero frequencies.31,42 Solvation dynamics can be described in terms of a solvent reaction field R⃗ (t) interacting with the solute’s dipole moment μ⃗ (t). For a dipolar solvent in equilibrium43,44 the reaction field is given by R⃗ =

η (̂ ω) − 1 2η (̂ ω) + εc

⟨τsolv

1 ε∞ + 2 εc) ( ⟩=

4πσ0

(dipole solvation, σ0 ≠ 0)

(9)

Equation 9, which relates the integral solvation time to the static conductivity, is the central result of this work. The present derivation generalizes our previous treatment in which η̂c(ω) was assumed to be represented by a sum of three Debye terms.41 Note that eq 9 is expressed here in electrostatic units. For σ0 expressed in SI units, the equivalent relation is ⟨τsolv⟩ = (ε∞ + 1/2 εc)εf/σ0, where εf = 8.854 × 10−12 s S m−1 is the permittivity of free space. The existence of such a simple relationship between the integral solvation time of a dipolar solute and the static electrical conductivity of an ionic solvent might initially seem surprising. In dipolar solvents, solvation dynamics is associated with the full frequency-dependent dielectric response, a complicated function requiring sophisticated instrumentation for measurement. In contrast, eq 9 says that the integral solvation time in ionic solvents only depends upon a single and much more easily measured quantity, σ0. We digress to consider this apparent distinction. First, we note that the frequency-dependent extension of σ0, σ̂(ω), is simply related to the dielectric dispersion by σ̂(ω) = iωη̂(ω)/4π . Therefore, σ̂(ω) and η̂(ω) contain identical information.52 How the static conductivity relates to solvation

(3) 1206



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Figure 1 shows C153 solvation times plotted versus ionic liquid resistivities, 1/σ0. The data represented here include 38

is most directly seen in the case of charge solvation. In this case, the solvation free energy is Ael = −(1/2)(1 − 1/η0)q2/a, and the relevant susceptibility function associated with a solute charge perturbation is χ̂(ω) = 1 − 1/η̂(ω). The time dependence of the response to such a perturbation is thus dictated by the function 1/ η̂(ω) = M̂ (ω), termed the electric modulus. The time domain analogue of this function, M(t) describes the response of a capacitor to a step function change in applied charge (rather than to change in potential, to which η̂ pertains).53 Repeating the previous derivation with χ̂(ω) = 1 − 1/η̂(ω) provides the relation ⟨τsolv⟩ =

ε∞ 4πσ0

(ion solvation, σ0 ≠ 0)

(10)

This solvation time is identical to the integral time for relaxation of the electric modulus, ⟨τM⟩ = ∫ ∞ 0 M(t) dt, when mobile charges are present.53 The same connection between ⟨τsolv⟩ and ⟨τM⟩ also pertains in the absence of conductivity. When σ0 = 0, one finds (see Supporting Information) ε ⟨τsolv⟩ = ⟨τM⟩ = ∞ ⟨τε⟩ (ion solvation, σ0 = 0) ε0 (11)

Figure 1. Integral solvation times of C153 plotted versus the ionic liquid resistivity 1/σ0. Large symbols denote data from ref 20 recorded with high time resolution, and small symbols represent data from ref 19. The legend indicates the cation type as Im+ = 1-alkyl-3methylimidazolium, Pr+ = 1-alkyl-1-methylpyrrolidinium, N+ = tetraalkylammonium, and P+ = trihexyltetradecylphosphonium. Tf2N− denotes the bis(trifluoromethylsulfonyl)imide anion.

where ⟨τε⟩ is defined by eq 8 with χ̂(ω) replaced by ε̂(ω). This modulus response time is what has often been called the “longitudinal” relaxation time.54 A similar relation also holds for a dipolar solute perturbation 1 ε∞ + 2 εc) ( ⟨τsolv⟩ = ⟨τε⟩ (ε0 + 12 εc)

(dipole solvation, σ0 = 0)

measurements on 34 different ionic liquids near to room temperature. Liquids incorporating a variety of cations, including series of dialkylimidazolium, dialkylpyrrolidinium, and tetraalkylammonium cations, combined with the bis(trifluoromethylsulfonyl)imide (Tf2N−) and other assorted anions are included in this data set. A compilation of all data is provide as Table S1 of the Supporting Information. It is clear from Figure 1 that the integral solvation times are strongly correlated to σ−1 0 , as predicted by eq 9. The data collected here can be approximately represented by the power law

(12)

Equations 11 and 12 are generalized versions of equations wellknown in the case of a single Debye-type dielectric response.43,44,55 In all four cases (eqs 9−12), the integral solvation time predicted by dielectric continuum theory is close to the integral time required for relaxation of a bulk fluid after application of a constant charge perturbation, ⟨τM⟩. In dipolar solvents, all components of the dielectric response are represented in ⟨τε⟩ and therefore in ⟨τsolv⟩ ≅ ⟨τM⟩. In contrast, in a conducting solvent, the divergence of η̂(ω → 0) means that the static conductivity, σ0 = σ̂(ω = 0), alone determines ⟨τsolv⟩. Although this difference might suggest that less information about the full system dynamics determines ⟨τsolv⟩ when the solvent is conductive, this is not the case. In the same manner that information about the full ε̂(ω) is distilled into ⟨τε⟩, which is related to the integral of the dipole moment autocorrelation function in dipolar solvents, so too are the full dynamics of an ionic solvent summarized in σ0 by virtue of its being proportional to the integral relaxation time of the solvent current−current autocorrelation function.31,42 We now examine the applicability of eq 9 to solvation in ionic liquids, employing data previously reported on the solvation response of the solute C153. We consider both recently published data recorded with ∼80 fs time resolution20 as well as data on additional ionic liquids from earlier work with ∼25 ps time resolution.19,56,57 In some cases, the 25 ps resolution of the latter experiments is such that only about onehalf of the solvation response is observed. Nevertheless, estimation of the frequency of the “time-zero” spectrum58 and thereby the amplitude of the unobserved component still enables estimates of ⟨τsolv⟩ having sufficient accuracy for the present purposes. (See the Supporting Information.)

ln(⟨τsolv⟩/ps) = 4.37 − 0.92 ln(σ0/S m−1)

(13)

shown as the solid line in Figure 1. The standard error of this logarithmic fit is 0.40, meaning that ⟨τsolv⟩ can be predicted on average to within a factor of 1.5 using this correlation. The dashed line in Figure 1 is the prediction of eq 9 assuming values of εc = 2.0 and ε∞ = 2.1. The latter value is the average over the squared refractive indices of the liquids studied, ε∞ = n2D = 2.07 ± 0.09(1σ). The observed solvation times are on average a factor of 2.4 larger than the values predicted by eq 9. This underprediction of solvation times using the dielectric continuum model is consistent with the more detailed comparisons of the full solvation response made in ref 20. Discussion of why molecular aspects of solvation not captured in the continuum description might lead to slower observed solvation times as well is provided in ref 36. The conductivity correlation shown in Figure 1 helps explain a puzzle concerning solvation dynamics in ionic liquids. Many researchers have reported solvation times to be approximately proportional to viscosity, either within a single ionic liquid as a function of temperature or in a series of related ionic liquids.19,25,56,59−62 Figure 2 uses the solvation data from Figure 1 in an improved 1207



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the dielectric continuum prediction. Thus, conductivity can be used to estimate the time scale of molecular solvation in ionic liquids. Although such estimates are not of high accuracy, given the simplicity of conductivity measurements relative to dynamic Stokes shift or dielectric dispersion measurements, the correlation established here should be of use when considering how the slow solvation characteristic of ionic liquids might impact charge transport and reaction.

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ASSOCIATED CONTENT

* Supporting Information S

Derivation of eqs 11 and 12, compiled data used in constructing Figures 1 and 2, and a version of Figure 1 including ionic liquid + dipolar solvent mixture data. 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].

Figure 2. Integral solvation times plotted versus the ionic liquid viscosity η. Symbols have the same meaning as those in Figure 1. The black line shows the correlation ln(⟨τsolv⟩/ps) = −0.21 + 1.29 ln(η/cP), and the red line is a similar correlation offset by a factor of 9.1.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.L. and M.M. were supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through Grant DE-FG02-12ER16363. X.-X.Z. and N.E. acknowledge support from the Deutsche Forschungsgemeinschaft (priority program “Ionic Liquids”), and X.-X.Z. acknowledges support from the China Scholarship Council.

and extended version of a viscosity correlation previously reported19 for the probe C153. Whereas a wide variety of different ionic liquids follow a single correlation with viscosity, ionic liquids comprised of the large trihexyltetradecylphosphonium cation (P14,666+) stand apart. In the earlier study,19 it was conjectured that the distinctive behavior of the phosphonium ionic liquids might reflect some special feature of solvation resulting from the extensive nonpolar domain structure expected in these liquids.63,64 In light of the single correlation observed here with conductivity, it appears that no special aspects of solvation need be invoked to explain these data. Instead, what is distinctive about P14,666+-based ionic liquids is the fact that their conductivities are much lower than their moderate viscosities would otherwise imply. That is, their ησ products are unusually small compared to other ionic liquids.13,65 The derivation of eq 9 is not restricted to purely ionic solvents, and it might be expected to apply to solutions of ions in dipolar solvents, at least at high ion densities.45 We have recently measured the fs+ps-resolved solvation dynamics of C153 in mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate with acetonitrile and water (unpublished results). In mixtures containing only a small amount of dipolar solvent, solvation times appear to follow the same trend established in neat ionic liquids. However, at mole fractions xIL ≤ 0.5, the trends exhibited by two mixtures deviate from one another and, in the case of the acetonitrile mixture, from the neat ionic liquid correlation (Figure S1, Supporting Information). Moreover, the conductivity of both mixtures goes through a maximum at xIL ≈ 0.1,66,67 whereas solvation times do not. Thus, eq 9 does not apply to dilute ionic solutions. In summary, we have shown that the simple continuum model of solvation predicts the integral solvation time of a dipolar solute to be inversely proportional to the electrical conductivity of a conducting solvent (eq 9). Solvation times of the probe C153 in 34 ionic liquids generally support this prediction. Measured solvation times can be correlated to ionic liquid conductivities via a relation of the form ⟨τsolv⟩ ∝ σ−p, with p≅ 1 and with a proportionality constant ∼2.4 times larger than

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REFERENCES

(1) Torimoto, T.; Tsuda, T.; Okazaki, K.-i.; Kuwabata, S. New Frontiers in Materials Science Opened by Ionic Liquids. Adv. Mater. (Weinheim, Ger.) 2010, 22, 1196−1221. (2) Plechkova, N. V.; Seddon, K. R. Applications of Ionic Liquids in the Chemical Industry. Chem. Soc. Rev. 2008, 37, 123−150. (3) Werner, S.; Haumann, M.; Wasserscheid, P. Ionic Liquids in Chemical Engineering. Annu. Rev. Chem. Biomol. Eng. 2010, 1, 203− 230. (4) Sun, P.; Armstrong, D. W. Ionic Liquids in Analytical Chemistry. Anal. Chim. Acta 2010, 661, 1−16. (5) Hallett, J. P.; Welton, T. Room-Temperature Ionic Liquids: Solvents for Synthesis and Catalysis. 2. Chem. Rev. 2011, 111, 3508− 3576. (6) Ueki, T.; Watanabe, M. Polymers in Ionic Liquids: Dawn of Neoteric Solvents and Innovative Materials. Bull. Chem. Soc. Jpn. 2012, 85, 33−50. (7) Moniruzzaman, M.; Nakashima, K.; Kamiya, N.; Goto, M. Recent Advances of Enzymatic Reactions in Ionic Liquids. Biochem. Eng. J. 2010, 48, 295−314. (8) Wishart, J. F. Energy Applications of Ionic Liquids. Energy Environ. Sci. 2009, 2, 956−961. (9) Armand, M.; Endres, F.; MacFarlane, D. R.; Ohno, H.; Scrosati, B. Ionic-Liquid Materials for the Electrochemical Challenges of the Future. Nat. Mater. 2009, 8, 621−629. (10) Sun, X.; Luo, H.; Dai, S. Ionic Liquids-Based Extraction: A Promising Strategy for the Advanced Nuclear Fuel Cycle. Chem. Rev. 2012, 112, 2100−2128. (11) Harris, K. R. Relations between the Fractional Stokes−Einstein and Nernst−Einstein Equations and Velocity Correlation Coefficients in Ionic Liquids and Molten Salts. J. Phys. Chem. B 2010, 114, 9572− 9577. (12) Tokuda, H.; Tsuzuki, S.; Susan, M. A. B. H.; Hayamizu, K.; Watanabe, M. How Ionic Are Room-Temperature Ionic Liquids? An 1208



Letter

Indicator of the Physicochemical Properties. J. Phys. Chem. B 2006, 110, 19593−19600. (13) Fraser, K. J.; Izgorodina, E. I.; Forsyth, M.; Scott, J. L.; MacFarlane, D. R. Liquids Intermediate between “Molecular” and “Ionic” Liquids: Liquid Ion Pairs? Chem. Commun. 2007, 3817−3819. (14) Kashyap, H. K.; Annapureddy, H. V. R.; Raineri, F. O.; Margulis, C. J. How Is Charge Transport Different in Ionic Liquids and Electrolyte Solutions? J. Phys. Chem. B 2011, 115, 13212−13221. (15) Weingärtner, H. Understanding Ionic Liquids at the Molecular Level: Facts, Problems, and Controversies. Angew. Chem., Int. Ed. 2008, 47, 654−670. (16) Kobrak, M. N.; Li, H. Electrostatic Interactions in Ionic Liquids: The Dangers of Dipole and Dielectric Descriptions. Phys. Chem. Chem. Phys. 2010, 12, 1922−1932. (17) Fujisawa, T.; Fukuda, M.; Terazima, M.; Kimura, Y. Raman Spectroscopic Study on Solvation of Diphenylcyclopropenone and Phenol Blue in Room Temperature Ionic Liquids. J. Phys. Chem. A 2006, 110, 6164−6172. (18) Kimura, Y.; Hamamoto, T.; Terazima, M. Raman Spectroscopic Study on the Solvation of N,N-Dimethyl-p-nitroaniline in RoomTemperature Ionic Liquids. J. Phys. Chem. A 2007, 111, 7081−7089. (19) Jin, H.; Baker, G. A.; Arzhantsev, S.; Dong, J.; Maroncelli, M. Solvation and Rotational Dynamics of Coumarin 153 in Ionic Liquids: Comparisons to Conventional Solvents. J. Phys. Chem. B 2007, 111, 7291−7302. (20) Zhang, X.-X.; Liang, M.; Ernsting, N. P.; Maroncelli, M. Complete Solvation Response of Coumarin 153 in Ionic Liquids. J. Phys. Chem. B 2012, DOI: 10.1021/jp305430a. (21) Kobrak, M. N. The Relationship between Solvent Polarity and Molar Volume in Room-Temperature Ionic Liquids. Green Chem. 2008, 10, 80−86. (22) Halder, M.; Headley, L. S.; Mukherjee, P.; Song, X.; Petrich, J. W. Experimental and Theoretical Investigations of Solvation Dynamics of Ionic Fluids: Appropriateness of Dielectric Theory and the Role of DC Conductivity. J. Phys. Chem. A 2006, 110, 8623−8626. (23) Lang, B.; Angulo, G.; Vauthey, E. Ultrafast Solvation Dynamics of Coumarin 153 in Imidazolium-Based Ionic Liquids. J. Phys. Chem. A 2006, 110, 7028−7034. (24) Arzhantsev, S.; Jin, H.; Baker, G. A.; Maroncelli, M. Measurements of the Complete Solvation Response in Ionic Liquids. J. Phys. Chem. B 2007, 111, 4978−4989. (25) Kimura, Y.; Fukuda, M.; Suda, K.; Terazima, M. Excited State Intramolecular Proton Transfer Reaction of 4′-N,N-Diethylamino-3hydroxyflavone and Solvation Dynamics in Room Temperature Ionic Liquids Studied by Optical Kerr Gate Fluorescence Measurement. J. Phys. Chem. B 2010, 114, 11847−11858. (26) Muramatsu, M.; Nagasawa, Y.; Miyasaka, H. Ultrafast Solvation Dynamics in Room Temperature Ionic Liquids Observed by ThreePulse Photon Echo Peak Shift Measurements. J. Phys. Chem. A 2011, 115, 3886−3894. (27) Jin, H.; Li, X.; Maroncelli, M. Heterogeneous Solute Dynamics in Room-Temperature Ionic Liquids. J. Phys. Chem. B 2007, 111, 13473−13478. (28) Castner, E. W., Jr.; Margulis, C. J.; Maroncelli, M.; Wishart James, F. Ionic Liquids: Structure and Photochemical Reactivity. Annu. Rev. Phys. Chem. 2011, 62, 85−105. (29) Sahu, K.; Kern, S. J.; Berg, M. A. Heterogeneous Reaction Rates in an Ionic Liquid: Quantitative Results from Two-Dimensional Multiple Population-Period Transient Spectroscopy. J. Phys. Chem. A 2011, 115, 7984−7993. (30) Shim, Y.; Jeong, D.; Manjari, S.; Choi, M. Y.; Kim, H. J. Solvation, Solute Rotation and Vibration Relaxation, and ElectronTransfer Reactions in Room-Temperature Ionic Liquids. Acc. Chem. Res. 2007, 40, 1130−1137. (31) Shim, Y.; Kim, H. J. Dielectric Relaxation, Ion Conductivity, Solvent Rotation, and Solvation Dynamics in a Room-Temperature Ionic Liquid. J. Phys. Chem. B 2008, 112, 11028−11038.

(32) Kobrak, M. N. A Comparative Study of Solvation Dynamics in Room-Temperature Ionic Liquids. J. Chem. Phys. 2007, 127, 184507/ 1−8. (33) Roy, D.; Maroncelli, M. Simulations of Solvation and Solvation Dynamics in an Idealized Ionic Liquid Model. J. Phys. Chem. B 2012, 116, 5951−5970. (34) Daschakraborty, S.; Biswas, R. Ultrafast Solvation Response in Room Temperature Ionic Liquids: Possible Origin and Importance of the Collective and the Nearest Neighbour Solvent Modes. J. Chem. Phys. 2012, 137, 114501/1−114501/11. (35) Song, X. Solvation Dynamics in Ionic Fluids: an Extended Debye−Huckel Dielectric Continuum Model. J. Chem. Phys. 2009, 131, 044503/1−044503/8. (36) Maroncelli, M.; Zhang, X.-X.; Liang, M.; Roy, D.; Ernsting, N. P. Measurements of the Complete Solvation Response of Coumarin 153 in Ionic Liquids and the Accuracy of Aimple Dielectric Continuum Predictions. Faraday Discuss. Chem. Soc. 2012, 154, 409−424. (37) Horng, M. L.; Gardecki, J. A.; Papazyan, A.; Maroncelli, M. SubPicosecond Measurements of Polar Solvation Dynamics: Coumarin 153 Revisited. J. Phys. Chem. 1995, 99, 17311−17337. (38) Song, X.; Chandler, D. Dielectric Solvation Dynamics of Molecules of Arbitrary Shape and Charge Distribution. J. Chem. Phys. 1998, 108, 2594−2600. (39) Ruthmann, J.; Kovalenko, S. A.; Ernsting, N. P.; Ouw, D. Femtosecond Relaxation of 2-Amino-7-nitrofluorene in Acetonitrile: Observation of the Oscillatory Contribution to the Solvent Response. J. Chem. Phys. 1998, 109, 5466−5468. (40) Lustres, J. L. P.; Kovalenko, S. A.; Mosquera, M.; Senyushkina, T.; Flasche, W.; Ernsting, N. P. Ultrafast Solvation of N-Methyl-6quinolone Probes Local IR Spectrum. Angew. Chem., Int. Ed. 2005, 44, 5635−5639. (41) Zhang, X.-X.; Schröder, C.; Ernsting, N. P. Solvation and Dielectric Response in Ionic Liquids  Conductivity Extension of the Continuum Model. J. Chem. Phys. 2013, DOI: 10.1063/1.4796198. (42) Schrö d er, C.; Haberler, M.; Steinhauser, O. On the Computation and Contribution of Conductivity in Molecular Ionic Liquids. J. Chem. Phys. 2008, 128, 134501/1−134501/10. (43) Maroncelli, M.; Fleming, G. R. Picosecond Solvation Dynamics of Coumarin 153: The Importance of Molecular Aspects of Solvation. J. Chem. Phys. 1987, 86, 6221−6239. (44) Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Theory of the Time Development of the Stokes Shift in Polar Media. Chem. Phys. 1984, 86, 257−267. (45) As described in detail in ref 68, derivation of eq 2 assumes that the Laplace equation is valid outside of the solute, that is, it assumes zero charge density in the solvent. Ignoring the fact that the molecules of the solvent are charged simply means that the one course-grains the solvent into regions sufficiently large that the ionic nature of the molecules is irrelevant. We believe such a description to be sensible in the case of a neat ionic liquid. In the case of ionic solutions, once ion concentrations are low enough to produce charge heterogeneity in volumes larger than the volume dictating most of the solvation energy, such a description is less likely to succeed. (46) Lynden-Bell, R. M. Redox Potentials and Screening in Ionic Liquids: Effects of Sizes and Shapes of Solute Ions. J. Chem. Phys. 2008, 129, 204503/1−204503/7. (47) Kumar, P. V.; Maroncelli, M. Polar Solvation Dynamics of Polyatomic Solutes: Simulation Studies in Acetonitrile and Methanol. J. Chem. Phys. 1995, 103, 3038−3060. (48) Sajadi, M.; Weinberger, M.; Wagenknecht, H.-A.; Ernsting, N. P. Polar Solvation Dynamics in Water and Methanol: Search for Molecularity. Phys. Chem. Chem. Phys. 2011, 13, 17768−17774. (49) Wolynes, P. G. Linearized Microscopic Theories of Nonequilibrium Solvation. J. Chem. Phys. 1987, 86, 5133−5136. (50) Rips, I.; Klafter, J.; Jortner, J. Dynamics of Ionic Solvation. J. Chem. Phys. 1988, 88, 3246−3252. (51) We note that eq 5 was incorrectly given in two prior reports.24,36 Calculations were performed with the correct equation; therefore, the results presented therein are correct. 1209



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(52) Sangoro, J. R.; Kremer, F. Charge Transport and Glassy Dynamics in Ionic Liquids. Acc. Chem. Res. 2012, 45, 525−532. (53) Richert, R. The Modulus of Dielectric and Conductive Materials and Its Modification by High Electric Fields. J. Non-Cryst. Solids 2002, 305, 29−39. (54) Friedman, H. L. Fast Response of a Dielectric to the Motion of a Charge. J. Chem. Soc., Faraday Trans. II 1983, 79, 1465−1467. (55) Mazurenko, Y. T.; Bakhshiev, N. G. Effect of Orientation Dipole Relaxation on Spectral, Time, and Polarization Characteristics of the Luminescence of Solutions. Opt. Spectrosc. (USSR) 1970, 28, 490−494. (56) Arzhantsev, S.; Ito, N.; Heitz, M.; Maroncelli, M. Solvation Dynamics of Coumarin 153 in Several Classes of Ionic Liquids: Cation Dependence of the Ultrafast Component. Chem. Phys. Lett. 2003, 381, 278−286. (57) Ito, N.; Arzhantsev, S.; Heitz, M.; Maroncelli, M. Solvation Dynamics and Rotation of Coumarin 153 in Alkylphosphonium Ionic Liquids. J. Phys. Chem. B 2004, 108, 5771−5777. (58) Fee, R. S.; Maroncelli, M. Estimating the Time-Zero Spectrum in Time-Resolved Emission Measurements of Solvation Dynamics. Chem. Phys. 1994, 183, 235−247. (59) Samanta, A. Dynamic Stokes Shift and Excitation Wavelength Dependent Fluorescence of Dipolar Molecules in Room Temperature Ionic Liquids. J. Phys. Chem. B 2006, 110, 13704−13716. (60) Sanders Headley, L.; Mukherjee, P.; Anderson, J. L.; Ding, R.; Halder, M.; Armstrong, D. W.; Song, X.; Petrich, J. W. Dynamic Solvation in Imidazolium-Based Ionic Liquids on Short Time Scales. J. Phys. Chem. A 2006, 110, 9549−9554. (61) Nagasawa, Y.; Oishi, A.; Itoh, T.; Yasuda, M.; Muramatsu, M.; Ishibashi, Y.; Ito, S.; Miyasaka, H. Dynamic Stokes Shift of 9,9′Bianthryl in Ionic Liquids: A Temperature Dependence Study. J. Phys. Chem. C 2009, 113, 11868−11876. (62) Kashyap, H. K.; Biswas, R. Stokes Shift Dynamics in Ionic Liquids: Temperature Dependence. J. Phys. Chem. B 2010, 114, 16811−16823. (63) Shimizu, K.; Costa, G. M. F.; Padua, A. A. H.; Rebelo, L. P. N.; Canongia, L. J. N. Three Commentaries on the Nano-Segregated Structure of Ionic Liquids. J. Mol. Struct.: THEOCHEM 2010, 946, 70−76. (64) Kashyap, H. K.; Santos, C. S.; Annapureddy, H. V. R.; Murthy, N. S.; Margulis, C. J.; Castner, E. W., Jr. Temperature-Dependent Structure of Ionic Liquids: X-ray Scattering and Simulations. Faraday Discuss. 2012, 154, 133−143. (65) Note that ησ is not the Walden product used to gauge ion association. The latter is ηΛ, where Λ is the molar conductivity, which differs from ησ by a factor of molar volume. (66) Stoppa, A.; Hunger, J.; Buchner, R. Conductivities of Binary Mixtures of Ionic Liquids with Polar Solvents. J. Chem. Eng. Data 2009, 54, 472−479. (67) Stoppa, A.; Hunger, J.; Hefter, G.; Buchner, R. Structure and Dynamics of 1-N-Alkyl-3-N-methylimidazolium Tetrafluoroborate + Acetonitrile Mixtures. J. Phys. Chem. B 2012, 116, 7509−7521. (68) Böttcher, C. J. F.; van Belle, O. C.; Bordewijk, P.; Rip, A. Theory of Electric Polarization: Dielectrics in Static Fields; Elsevier: Amsterdam, The Netherlands, 1973; Vol. 1.

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Conductivity and Solvation Dynamics in Ionic Liquids - American

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