J. Phys. Chem. B 2007, 111, 7291-7302
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Solvation and Rotational Dynamics of Coumarin 153 in Ionic Liquids: Comparisons to Conventional Solvents Hui Jin,† Gary A. Baker,‡ Sergei Arzhantsev,† Jing Dong,† and Mark Maroncelli*,† Department of Chemistry, The PennsylVania State UniVersity, 104 Chemistry Building, UniVersity Park, PennsylVania 16802, and Chemical Sciences DiVision, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6110 ReceiVed: February 2, 2007; In Final Form: April 3, 2007
Steady-state and time-resolved emission spectroscopy with 25 ps resolution are used to measure equilibrium and dynamic aspects of the solvation of coumarin 153 (C153) in a diverse collection of 21 room-temperature ionic liquids. The ionic liquids studied here include several phosphonium and imidazolium liquids previously reported as well as 12 new ionic liquids that incorporate two homologous series of ammonium and pyrrolidinium cations. Steady-state absorption and emission spectra are used to extract solvation free energies and reorganization energies associated with the S0 T S1 transition of C153. These quantities, especially the solvation free energy, vary relatively little in ionic liquids compared to conventional solvents. Some correlation is found between these quantities and the mean separation between ions (or molar volume). Time-resolved anisotropies are used to observe solute rotation. Rotation times measured in ionic liquids correlate with solvent viscosity in much the same way that they do in conventional polar solvents. No special frictional coupling between the C153 and the ionic liquid solvents is indicated by these times. But, in contrast to what is observed in most low-viscosity conventional solvents, rotational correlation functions in ionic liquids are nonexponential. Time-resolved Stokes shift measurements are used to characterize solvation dynamics. The solvation response functions in ionic liquids are also nonexponential and can be reasonably represented by stretched-exponential functions of time. The solvation times observed are correlated with the solvent viscosity, and the much slower solvation in ionic liquids compared to dipolar solvents can be attributed to their much larger viscosities. Solvation times of the majority of ionic liquids studied appear to follow a single correlation with solvent viscosity. Only liquids incorporating the largest phosphonium cation appear to follow a distinctly different correlation.
1. Introduction Research exploring the uses of room-temperature ionic liquids is growing at an exponential pace. A recent news article lists solvents for nucleoside chemistry and biosensing, liquid rocket propellants, high-temperature lubricants, and index matching fluids as just some of the newest applications of ionic liquids.1 In parallel with the these developing applications, much recent work has focused on characterizing the physical properties of ionic liquids and how they differ from those of conventional organic solvents.2-5 One important aspect of the latter work involves attempts to understand the unique features of solvation in ionic liquids, using both thermodynamic6-11 and spectroscopic methods.8,11-13 In addition to equilibrium aspects of solvation, a number of groups have applied various techniques to measure dynamical aspects of solvation such as translational14-16 and rotational17-29 diffusion of solutes and measurements of solvation dynamics, the time-dependent response to a solute perturbation.30,31 Study of the latter dynamics has been especially popular,18-22,26-29,32-45 and several papers have just been published reviewing the status of this area.38,46,47 In the present paper we add to the growing literature on solvation in ionic liquids through spectroscopic measurements * Author to whom correspondence should be addressed. E-mail:
[email protected]. † The Pennsylvania State University. ‡ Oak Ridge National Laboratory.
on the solvatochromic probe coumarin 153 (C153; Scheme 1) in a diverse collection of 21 ionic liquids. This work collects data previously reported by our group on a number of imidazolium19,21 and phosphonium20 ionic liquids together with new data on two homologous series of ammonium and pyrrolidinium ionic liquids. In addition to summarizing the ionic liquid results, a focus of the present work is to compare the solvation of C153 in ionic liquids and conventional dipolar solvents. We use steady-state absorption and emission data to measure solvent contributions to the free energy difference and reorganization energy associated with the S0 T S1 transition of C153. In conventional dipolar solvents these equilibrium solvation quantities are well described by dielectric continuum models of solvation. On the basis of the data currently available on the dielectric constants of ionic liquids,48-50 it appears that the same models are not useful for predicting the energetics in these solvents. Reasonable correlations are, however, observed for these energies with ion size. Time-resolved anisotropy measurements made with the time-correlated single photon counting (TCSPC) method are used to measure the reorientation of C153. In both conventional solvents and in ionic liquids the rotation times follow simple hydrodynamic predictions to a reasonable degree of accuracy. We find no evidence for the frictional coupling between this dipolar solute and its environment being qualitatively different in ionic liquids compared to conventional dipolar solvents. Finally, TCSPC measurements of the dynamic
10.1021/jp070923h CCC: $37.00 © 2007 American Chemical Society Published on Web 05/27/2007
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SCHEME 1
Stokes shift of C153 are used to quantify solvation dynamics in ionic liquids. It has been recognized for some time18 that, despite the fact that slow dynamics are often observed, a substantial fraction of the solvation response is missed in such experiments, which are limited in our case by a 25 ps instrument response time. Fortunately, recent work with higher time resolution38 indicates that the integral solvation times measured with TCSPC provide good estimates of the noninertial portions of the dynamics. Comparisons of these times measured in ionic liquids with the equivalent times in dipolar solvents reveals a single overall correlation between solvation time and solvent viscosity, albeit a very crude one. In ionic liquids, the connection between viscosity and solvation time appears to be much closer, especially if some account is made for ion size. 2. Materials and Experimental Methods The 21 ionic liquids surveyed in this work are listed in Table 1. Structural formulas of the ions involved and the designations that we employ for them are described in Figure 1. 1-Butyl-3-methylimidazolium chloride [Im41+][Cl-], 1-butyl-3-methylimidazolium hexafluorophosphate [Im41+][PF6-], 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [Im41+][Tf2N-], 1-butyl-3-methylimidazolium tris(trifluoromethylsulfonyl)methide [Im41+][ Tf3C-], and 1-propyl-2,3dimethylimidazolium bis(trifluoromethylsulfonyl)imide [mIm31+][Tf2N-] were obtained from Covalent Associates (electrochemical grade, >99.5%, 50 ns) and with higher signal-to-noise, threeor even four-exponential representations may be needed to fit anisotropy data. For this reason we do not ascribe any meaning to the stretched-exponential function or its parameters here. Instead we use it as a convenient way to approximately represent the data. Table 3 contains a summary of the parameters τ0r and βrot from stretched-exponential fits as well as rotational correlation times 〈τrot〉 (the integral of r(t)/r0) determined by averaging values obtained from both stretched-exponential and biexponential fits. The uncertainties listed in 〈τrot〉 partially reflect the differences in the times obtained by these two fitting methods. In general, the values of βrot observed here indicate a significantly nonexponential character to the reorientational correlation functions. This nonexponentiality is somewhat unusual in the sense that hydrodynamic modeling76 predicts exponential anisotropies. At least in low-viscosity solvents, C153 does rotate exponentially. However, studies in conventional solvents have shown that reorientational correlation functions of C153 are often nonexponential in slowly relaxing solvents such as the normal alcohols.76,77 We conjectured previously that such nonexponential dynamics reflect the non-Markovian character of rotational friction in slowly relaxing solvents.76 Such an explanation is also plausible in ionic liquids, but dynamic heterogeneity might also be the source of this behavior, at least in some instances.
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TABLE 3: Summary of Dynamical Quantitiesa rotation
solvation
no.
ionic liquid
T (K)
η (cP)
τ0r (ns)
βrot
〈τrot〉 (ns)
Crot
1 2 3 3 3 3 3 3 4 5 5 5 5 6 7 7 7 7 7 8 8 8 9 10 11 12 13 14 15 15 16 17 17 18 19 19 20 21 21 21
[Im41+][Cl-] [Im41+][BF4-] [Im41+][PF6-]b [Im41+][PF6-]b [Im41+][PF6-]b [Im41+][PF6-] [Im41+][PF6-] [Im41+][PF6-]b [Im41+][Tf2N-]c [Im41+][Tf3C-] [Im41+][Tf3C-] [Im41+][Tf3C-] [Im41+][Tf3C-] [Im61+][Cl-] [mIm31+][Tf2N-]c [mIm31+][Tf2N-]c [mIm31+][Tf2N-]c [mIm31+][Tf2N-]c [mIm31+][Tf2N-]c [Pr31+][Tf2N-] [Pr31+][Tf2N-] [Pr31+][Tf2N-] [Pr41+][Tf2N-] [Pr61+][Tf2N-] [Pr10,1+][Tf2N-] [Nip311+][Tf2N-] [Nip411+][Tf2N-] [Nip611+][Tf2N-] [Nip10,11+][Tf2N-] [Nip10,11+][Tf2N-] [N4441+][Tf2N-]c [P14,666+][Cl-]d [P14,666+][Cl-]d [P14,666+][Br-]d [P14,666+][BF4-]d [P14,666+][BF4-]d [P14,666+][N(CN)2-]d [P14,666+][Tf2N-]d [P14,666+][Tf2N-]d [P14,666+][Tf2N-]d
333 298 283 293 298 298 318 343 298 293 298 313 333 298 263 273 283 298 323 298 313 333 298 298 298 298 298 298 298 313 298 331 343 343 318 343 343 298 318 343
300 75 492 251 187 187 71 29 42 370 267 112 47 664 760 340 180 80 31 53 43 17 70 93 145 105 130 139 155 73 520 230 133 116 251 87 31 277 102 39
10.2 4.1
0.69 0.76
13 ( 3 4.3 ( 0.6
0.46 0.56
9.3 10.7 4.6 0.81 2.1
0.69 0.73 0.75 0.75 0.77
12.0 ( 2.4 12.0 ( 2.4 5.8 ( 0.9 0.99 ( 0.15 2.6 ( 0.4
0.63 0.62 0.85 0.38 0.61
15.2 5.3 1.5 43
0.65 0.65 0.67 0.46
20 ( 5 5.3 ( 1.6 1.8 ( 0.3 70 ( 30
0.73 0.49 0.42 1.0
11.0 3.6 1.10 2.4 1.25 0.58 3.1 4.0 5.8 4.6 6.0 5.4 7.1 4.0 17 1.3 1.3 1.10 4.2 1.5 0.91 7.5 2.8 1.00
0.66 0.74 0.77 0.75 0.74 0.77 0.71 0.68 0.61 0.72 0.67 0.63 0.73 0.79 0.41 0.36 0.43 0.40 0.42 0.48 0.54 0.46 0.50 0.56
15 ( 3 4.3 ( 0.6 1.30 ( 0.20 2.6 ( 0.4 1.41 ( 0.21 0.65 ( 0.10 3.4 ( 0.5 5.7 ( 0.9 9.0 ( 1.3 4.4 ( 1.1 7.9 ( 1.2 7.8 ( 1.2 9.2 ( 1.4 5.0 ( 0.7 51 ( 25 6.0 ( 0.9 3.9 ( 0.6 3.5 ( 0.5 12 ( 2 3.1 ( 0.5 1.60 ( 0.24 18 ( 4 5.5 ( 0.8 1.7 ( 0.3
0.77 0.52 0.44 0.47 0.33 0.41 0.47 0.61 0.60 0.41 0.60 0.55 0.58 0.70 1.0 0.28 0.33 0.34 0.50 0.40 0.58 0.63 0.56 0.49
∆ν (103 cm-1)
fobs
τ0s (ns)
βsolv
〈τsolv〉 (ns)
1.00 0.99 1.42 1.50 1.37 1.26 1.05 0.93 0.94 1.51
0.45 0.40 0.73 0.75 0.68 0.62 0.49 0.45 0.54 0.73
0.61 0.34 1.2 0.64 0.50 0.71 0.30 0.11 0.23 1.08
0.54 0.72 0.44 0.44 0.49 0.69 0.73 0.73 0.74 0.55
1.1 ( 0.3 0.42 ( 0.06 3.0 ( 0.6 1.7 ( 0.3 1.03 ( 0.10 1.00 ( 0.15 0.36 ( 0.05 0.14 ( 0.02 0.28 ( 0.04 1.9 ( 0.6
1.43 1.30 1.55 1.62 1.43 1.02 0.99 0.80 1.28 1.19 1.14 1.24 1.44 1.44 1.26 1.39 1.43 1.81 1.58 1.55 1.76 1.50 1.59 1.57 1.37 1.42 1.60 1.54 1.43
0.71 0.65 0.70 0.84 0.76 0.57 0.56 0.46 0.57 0.56 0.52 0.68 0.78 0.77 0.57 0.65 0.68 0.92 0.83 0.97 0.97 0.93 0.99 1.03 0.95 0.93 1.06 1.03 0.97
0.36 0.17 2.49 2.10 0.98 0.69 0.32 0.14 0.20 0.17 0.07 0.26 0.35 0.73 0.35 0.38 0.64 1.4 1.2 1.30 2.4 1.9 1.3 3.5 1.01 0.36 3.7 1.3 0.44
0.66 0.67 0.54 0.37 0.44 0.57 0.63 0.80 0.65 0.64 0.66 0.61 0.56 0.54 0.62 0.56 0.61 0.62 0.66 0.39 0.43 0.46 0.38 0.41 0.51 0.48 0.42 0.44 0.47
0.50 ( 0.10 0.22 ( 0.03 4.4 ( 0.7 9.1 ( 2.0 2.6 ( 0.6 1.10 ( 0.20 0.45 ( 0.05 0.16 ( 0.03 0.28 ( 0.04 0.23 ( 0.05 0.094 ( 0.014 0.38 ( 0.06 0.59 ( 0.09 1.3 ( 0.3 0.51 ( 0.07 0.64 ( 0.09 0.97 ( 0.15 2.0 ( 1.0 1.6 ( 0.5 4.5 ( 1.5 6.7 ( 1.7 4.5 ( 0.3 5.1 ( 0.4 11.3 ( 0.8 1.98 ( 0.11 0.78 ( 0.05 10.6 ( 0.6 3.52 ( 0.23 0.99 ( 0.06
a Viscosities η were calculated from parametrizations of temperature-dependent data reported in ref 54 or in the earlier references cited. τ and 0r βrot are from stretched-exponential fits of anisotropy data (eq 3.3); 〈τrot〉 is the rotational correlation time determined as an average of the results from both stretched-exponential and biexponential fits. Crot is the rotational coupling factor defined by eq 3.5. ∆ν, τ0s, and βsolv are the parameters of eq 3.6 averaged over ν(t) measured using both the peak and the first-moment measures of frequency. The integral solvation time 〈τsolv〉 is related to these values by 〈τ〉 ) τ0Γ(β-1)/β where Γ is the gamma function. fobs ((0.1) is the fraction of the expected solvation shift actually observed, fobs ) {ν(0) - ν(∞)}/{νest(0) - ν(∞)}. bData from ref 21. c Data from ref 19. d Data from ref 20.
TABLE 4: Dynamic Characteristics Averaged over Cation Classesa Im+ Pr+ N+ P+
no.
βrot
Cobs
βsolv
fobs
12/18 6/6 5/6 9/9
0.71 ( 0.05 0.71 ( 0.06 0.71 ( 0.06 0.46 ( 0.07
0.58 ( 0.15 0.48 ( 0.11 0.57 ( 0.10 0.46 ( 0.12
0.60 ( 0.13 0.61 ( 0.05 0.58 ( 0.10 0.44 ( 0.04
0.62 ( 0.13 0.65 ( 0.11 0.77 ( 0.16 0.98 ( 0.05
a No. is the number of data sets (rotation/solvation) used in the averages. Values are the average over the cation class ( the standard deviation of each set. In computing the rotational averages data from liquids 6 and 16 have been omitted because of their much larger uncertainties.
There is a significant difference in the degree of nonexponentiality of the rotational anisotropy decays observed in the phosphonium ionic liquids compared to all of the other liquids studied. The distinction is most obvious in the cation-averaged data shown in Table 4. Here we list βrot values averaged over data for the four different types of cations examined. It is clear from this summary that liquids incorporating the large phos-
phonium cation P14,666+ stand out as being markedly more nonexponential than the remaining types of liquids (see also Figure 4 of ref 20). The values of βrot ≈ 0.7 in the other ionic liquids indicate a degree of nonexponentiality that is roughly comparable to what was found for C153 in normal alcohol solvents.76,77 The fact that we have failed to observe an excitation wavelength dependence for the rotation times of C153 in [Nip311+][Tf2N-] (298 K, βrot ) 0.72 ( 0.01 for λexc ) 410460 nm) suggests that in the majority of the ionic liquids studied here heterogeneity is not the main source of the nonexponential rotations. In the phosphonium liquids, however, rotational motion is highly dispersive (βrot ≈ 0.5) and similar to what is observed near the glass transition of fragile glass-forming liquids when the solute/solvent size ratio is small.27,78,79 We conjecture that in these latter ionic liquids the large size of the cation relative to the solute (VP+/VC153 ≈ 2.6) might produce dynamic heterogeneity similar to that observed in conventional glassforming liquids. Alternatively, the heterogeneity might result from the domain-like structures observed in simulations of ionic
Dynamics of Coumarin 153 in Ionic Liquids
J. Phys. Chem. B, Vol. 111, No. 25, 2007 7297
Figure 6. Rotational correlation times of C153 in 27 dipolar solvents at room temperature (small symbols, data from ref 76) and in ionic liquids (larger symbols with error bars) plotted vs η/T. The solid line shows the best fit of the dipolar liquid data to the proportionality 〈τrot〉 ) A(η/T) with A ) 1.73 × 10-8 s K cP-1. The dashed lines show the predictions of hydrodynamic calculations using slip and stick boundary conditions.
liquids with long alkyl chains.80,81 Whatever the origin, the character of the rotational correlation functions in the phosphonium liquids is decidedly different from those in the other liquids studied. We now turn to the rotational correlation times of C153, 〈τrot〉 ) r0-1 ∫ r(t) dt. Figure 6 displays the results measured in ionic liquids and conventional solvents. Rotation times are plotted versus η/T (viscosity/temperature), the scaling expected from hydrodynamic models. The smaller points in Figure 6 are data in 27 dipolar solvents at room temperature, as taken from ref 76. The solid line in this figure shows that in dipolar solvents, both protic and aprotic and including the n-alcohols, rotation times of C153 conform to the expected proportionality to η/T, albeit with some scatter. The rotation times in ionic liquids show greater scatter but nevertheless also follow essentially the same correlation established by the dipolar solvents. The dashed lines in Figure 6 are the predictions of hydrodynamic models, made by assuming a solute of ellipsoidal shape with semi-axis dimensions of 2.0, 4.8, and 6.1 Å76 and the relation
τ(2) )
Vη fC kBT
(3.4)
where V is the solute volume (246 Å3), f is a shape factor (1.71), and C is a “rotational coupling factor”. For stick boundary conditions C ) 1, and for slip boundary conditions C ) 0.24.76 Virtually all of the rotation times, in both dipolar and ionic liquids, fall between these two limiting predictions. A convenient way to examine deviations from hydrodynamic predictions is to calculate an empirical value of the coupling factor
Crot )
kBT 〈τrot〉 ) (2) Vηf τ
(3.5)
stk
where τ(2) stk is the stick hydrodynamic prediction. In dipolar solvents we find Crot ) 0.57 ( 0.09. Values of this factor in the ionic liquids are listed in Tables 3 and 4 and plotted in Figure 7. Neglecting liquids 6 and 16 whose long rotation times make the data highly uncertain, the average value of Crot is 0.53 ( 0.13, close to the dipolar liquid value. Although there are several cases, for example, [P14,111+][Cl-] and [P14,111+][Br-] (17 and 18), where the deviations of Crot from the dipolar liquid values are greater than the estimated uncertainties, most values
Figure 7. Rotational coupling factors of C153 measured in ionic liquids. The solid and dashed horizontal lines in this figure indicate the average and standard deviation of Crot observed in the sample of dipolar liquids. The error bars here include the estimated uncertainties in both the rotation time and the viscosity (assumed to be (10%). Numbers indicate ionic liquids according to Table 1.
of Crot measured in the ionic liquids fall within the scatter of the dipolar liquid data (denoted by the dashed lines in Figure 7). Overall, these results indicate that there is no obvious difference between the way in which rotation of C153 is coupled to bulk viscosity in ionic liquids and in conventional dipolar solvents. Also, unlike βrot, there is no clear distinction among the values of Crot in the different cation classes (Table 4). Finally it is worth mentioning how the present data compare to other data on rotation in the literature. Although there are few direct comparisons possible,82 we can compare the general trends observed here to the recent data of Castner and coworkers29 who measured rotation times of C153 in two ammonium and two pyrrolidimium ionic liquids at five temperatures between 278 and 353 K. In the two pyrrolidimium liquids these authors observed small-amplitude components with time constants of greater than 100 ns, which we would not be able to detect in the present experiments. If these slow components of uncertain origin are neglected, then the correlation times measured by Castner and co-workers29 fall nicely on the correlation with η/T established here. For their set of 20 data points we find Crot ) 0.46 ( 0.06, just slightly lower than our average ionic liquid value. C. Solvation Dynamics. Representative time-resolved spectra of C153 in [Nip311+][Tf2N-] are shown in Figure 8. Unnormalized spectra in a wavelength representation are plotted in the upper panel. The spectra decrease in overall intensity due to the ∼6 ns lifetime of C153 and simultaneously shift to the red in a manner characteristic of solvation dynamics. In the bottom panel these spectra have been normalized and fit to a log-normal line shape function58 to illustrate the fact that there is little change in spectral width or shape with time. The dashed curve labeled “est. t ) 0” is the estimated time-zero spectrum69 discussed in subsection 3A, and “obs. t ) 0” is what is observed from deconvolution analysis of the time-resolved data. The displacement between these two curves indicates that some portion (∼40%) of the solvation response is missed in these experiments due to the finite response time of the TCSPC experiment (25 ps fwhm). As will be discussed more later, recent experiments having greater time resolution37,38 have shown that this missing portion of the dynamics contains both subpicosecond inertial contributions as well as components relaxing on the 1-10 ps time scale. For now we note that in many of the ionic liquids studied here we can only partially characterize the solvation response with the present approach. Quantitative information about the solvation response is derived from the time dependence of characteristic frequencies
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ν(t) ) ν(∞) + ∆ν exp{-(t/τ0s)βsolv}
Figure 8. Time-resolved spectra of C153 in [Nip311+][Tf2N-] at 298 K. The top panel contains reconstructed spectra at the times indicated. The bottom panel shows fits of these spectra in a frequency representation to log-normal line shape functions (smooth solid curves). The actual data at t ) 0 and 20 ns are shown as filled and open symbols, respectively. The dashed curves labeled “ss” and “est. t ) 0” are the steady-state and estimated “time-zero” spectra. In the bottom panel, spectra at 5 and 10 ns have been omitted for clarity.
Figure 9. Representative peak frequency data νpk(t) obtained from lognormal fits of time-resolved spectra in the [Prn1+][Tf2N-] and [Nipn11+][Tf2N-] series at 298 K. Points are the actual data, and the smooth curves are stretched-exponential fits (eq 3.6) to these data.
of the time-evolving spectra. Figure 9 shows the time evolution of the peak frequency νpk(t) of the fitted spectra of C153 in the two homologous series [Prn1+][Tf2N-] and [Nipn11+][Tf2N-] with n ) 3, 4, 6, and 10. These plots serve to illustrate the quality of the data recorded here. Assuming that it is reasonable to expect all features of these data to vary systematically with n, the fact that there is some crossover of the curves at long times suggests a precision of roughly (100 cm-1 in νpk(t). Repeated runs on the same liquid suggest similar uncertainties. The curves in Figure 9 are fits of the logarithmically spaced data (symbols) to a stretched-exponential time dependence
(3.6)
As illustrated here, this functional form is able to reproduce the data to well within its anticipated accuracy. Although deviations in some data sets are larger than those shown in Figure 9, we find that such fits adequately capture the dynamics of ν(t) in all of the ionic liquids studied. Multiexponential representations, preferred by most other authors,29,41,46 do fit some data sets more accurately, but they do so only at the expense of introducing additional fitting parameters that we find unnecessary. In Table 3 we summarize all of the solvation dynamics measurements by listing quantities derived mainly from stretchedexponential fits to ν(t) data. ∆ν, τ0s, and βsolv are the values of the parameters in eq 3.6 averaged over fits to ν(t) data using both the peak and the first-moment frequencies of the spectra. The integral solvation time 〈τsolv〉 is related to these values by 〈τ〉 ) τ0Γ(β-1)/β where Γ is the gamma function. fobs is the fraction of the expected solvation shift actually observed, fobs ) ∆ν/{νest(0) - ν(∞)}. Cation-averaged values of β and fobs are also provided in Table 4. The magnitudes of the Stokes shifts ∆ν observed range between approximately 1000 and 2000 cm-1. The fraction of the total solvation response represented by these Stokes shifts varies from about 0.5 to 1 depending on the solvent. As highlighted in Table 4, virtually all of the dynamics are observed in the P14,111+ liquids whereas successively less and less of the response is observed in the ammonium, pyrrolidinium, and imidazolium ionic liquids. Crudely speaking, these trends in fobs are inversely related to the speed of the observed solvation response in the manner expected. Comparing values of βsolv and βrot shows that generally βsolv < βrotsthe observed solvation response functions are usually farther from single-exponential functions than the rotational correlation functions in a given liquid. This observation is consistent with the behavior noted by Ito and Richert in two ionic liquids near their glass transitions.26,27 Table 4 also suggests a significant difference in the degree of nonexponentiality (βsolv) among the different classes of ionic liquids, with the phosphonium liquids again being distinct in their larger departure from exponential time dependence. However, this last observation is probably an artifact related to the insufficient time resolution in the experiments. Values of βsolv are clearly correlated with fobs (the set of all data shows a linear correlation coefficient of 0.75) such that the smaller the fraction of the response observed, the more exponential the response appears to be. (See, for example, the temperature-dependent series in the [mIm31+][Tf2N-] liquid in Table 3.) Data collected with sufficient time resolution to observe the entire solvation response37,38 show that the nonexponentiality of even the noninertial component of the response is systematically underestimated by TCSPC experiments when fobs is significantly less than unity. Thus, values of βsolv reported here are probably best viewed as upper limits to the correct values. Values of τ0s measured by TCSPC were also found to be systematically too large when fobs is much less than unity.38 Luckily, the systematic biases created in βsolv and τ0s as a result of insufficient time resolution work in opposite directions so as to partially cancel when the correlation time 〈τsolv〉 is considered. At least in the set of six ionic liquids fully resolved to date (2-6 and 8), the values of 〈τsolv〉 measured with TCSPC are found to deviate only by an average of 20% from values associated with the noninertial component of the dynamics.38 We therefore focus solely on 〈τsolv〉 in the remaining discussion.
Dynamics of Coumarin 153 in Ionic Liquids
Figure 10. Integral solvation times 〈τsolv〉 in conventional dipolar solvents and in ionic liquids plotted vs solvent viscosity. The dipolar solvent data (small symbols and numerals) are from refs 31 and 67. Numerals n denote normal alcohols CnH2n+1OH. The ionic liquid data (large symbols with error bars) represent observed values of 〈τsolv〉. The upper limits of the error bars are estimated uncertainties whereas the lower limits denote fobs〈τsolv〉 in recognition of the unobserved dynamics in these systems. (If the uncertainty is larger than (1 - fobs)〈τsolv〉, then the uncertainty is plotted instead.) The line shown here is the fit ln(〈τsolv〉/s) ) -26.40 + 1.20 ln(η/cP) (N ) 66, R2 ) 0.91, σfit ) 0.95). The asterisk indicates data in [Nip10,11+][Tf2N-].
In Figure 10 we compare values of 〈τsolv〉 measured in ionic liquids to values previously measured in conventional dipolar solvents at room temperature.31,67 With the exception of the normal alcohols (n in Figure 10 denotes an alcohol with n C atoms) solvation times in most conventional solvents fall in the 1-10 ps range. The times observed in ionic liquids are much longer, typically in the 0.1-10 ns range. These longer solvation times can be partially understood in terms of the much larger viscosities of ionic liquids compared to those of conventional solvents. The solid line in Figure 10 shows a fit of all of the data to 〈τsolv〉 ∝ ηp with p ) 1.2. Clearly, viscosity differences rationalize the >104-fold variations in solvation times of C153, at least in a crude way. But the considerable scatter (10-fold differences for a given value of η) indicates that viscosity is not the only factor involved. Solvation dynamics in conventional dipolar solvents has been studied for many years and is well understood.30,31,83,84 There are two main reasons for the poor correlation between 〈τsolv〉 and η in such solvents. First, in many small-molecule dipolar solvents a substantial fraction of the total response comes from inertial contributions, and these contributions are not expected to be proportional to solvent viscosity. More importantly, dipolar solvation is a collective process whose time scale is determined both by the rate of individual solvent molecule motions, primarily rotation, and by the strength of the solvent-solvent coupling, or “polarity”.30,85 Because polarity is uncorrelated to solvent viscosity, except in homologous series such as the normal alcohols, solvent viscosity alone is unable to account for the variations in solvation times observed. But all of these factors are captured in the dielectric response, (ω), of dipolar solvents, and solvation times of C153 in all of the dipolar solvents included in Figure 10 can be predicted with surprising accuracy from (ω) and simple continuum models of solvation.31,86 Some authors have suggested that these same dielectric approaches might also be used to calculate solvation times in ionic liquids.26,27,43 (ω) data have been recently reported on a few ionic liquids,26,27,49,87-89 and we have been able to make three detailed comparisons to date.38,90 Like the solvation energy-r comparisons in subsection 3A, the few available
J. Phys. Chem. B, Vol. 111, No. 25, 2007 7299 comparisons suggest that if any direct relationship exists between the solvation response and (ω) in ionic liquids, then it is not the same as in dipolar liquids. In the absence of simple models and more dielectric data, we can at present only explore what correlations might exist between 〈τsolv〉 and other properties of these solvents. The viscosity correlation shown in Figure 10 indicates the ionic liquid data fall into two main groupings. The solvation times of the majority (15) of the ionic liquids relate to viscosity in a way that is distinct from the 5 ionic liquids containing the P14,666+ cation. The single liquid [Nip10,11+][Tf2N-] (marked with an asterisk in Figure 10) occupies an ambiguous position between these two groups. We note that this particular solvent exhibited considerably higher background emission than the other liquids studied, and we suspect that these points may be significantly affected by this background, which could not be entirely eliminated. Notwithstanding these errant points, we note that within either of the two main groups of solvents the correlation with viscosity is much better than it is in conventional solvents. For a given viscosity, however, the solvation times in the phosphonium liquids are about a factor of 5 slower than those in the main group of solvents. Another distinguishing feature of the dynamics in the phosphonium liquids is that essentially all of the solvation dynamics are observed (fobs g 93%). In most of the other liquids, even ones in which 〈τsolv〉 is greater than those of many of the phosphonium liquids, fobs is much smaller. Thus, in contrast to most of the other liquids, those liquids containing the P14,666+ cation must lack substantial dynamics on the
