Time-resolved laser spectroscopy of nonreactive processes in ionic liquids and their binary mixtures with organic solvents and CO2

Journal of Molecular Liquids 192 (2014) 87–93

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Time-resolved laser spectroscopy of nonreactive processes in ionic liquids and their binary mixtures with organic solvents and CO2 N.P. Ernsting a,⁎, T. Lenzer b,⁎, K. Oum b,⁎ a b

Humboldt-Universität zu Berlin, Institut für Chemie, Physikalische Chemie, Brook-Taylor-Str. 2, 12489 Berlin, Germany Universität Siegen, Physikalische Chemie, Adolf-Reichwein-Str. 2, 57076 Siegen, Germany

a r t i c l e

i n f o

Available online 3 September 2013 Keywords: Ionic liquids Time-resolved laser spectroscopy Solvation dynamics Polarity

a b s t r a c t Nonreactive dynamics of molecules in ionic liquids (ILs) have been investigated in various environments, such as in neat aprotic and protic ILs, as well as in binary mixtures of ILs with polar organic solvents and CO2. Transient broadband absorption and fluorescence spectroscopic techniques on timescales from femtoseconds to milliseconds have been applied to elucidate the importance of different types of solute–solvent interactions in these media. Molecular probes such a 12′-apo-β-carotenoic-12′-acid and Coumarin C153 have been used as reporter molecules for ionic liquid solvation dynamics, micropolarity, hydrogen-bonding and collisional relaxation. With Coumarin C153 in ILs, the relationship between the complete solvation response and microwave-terahertz absorption measurements of the neat liquid was explored quantitatively. A reduced value for the conductivity plays a key role in such solvation experiments. Aprotic ILs exhibit a micropolarity larger than expected from their static dielectric constants, whereas the local polarity of protic alkylammonium formate ILs appears to be similar to that of alcohols having comparable dielectric constants. In IL mixtures with organic solvents or CO2, there is no indication for differences in the bulk composition and the local composition around the molecular probe. Collisional relaxation processes in ILs take place on similar timescales as in dipolar organic solvents. © 2013 Elsevier B.V. All rights reserved.

1. Introduction

2. Experimental

Ionic liquids (ILs) have emerged as unique solvent media with applications in a wide range of fields [1–4]. Over the recent years, considerable information regarding the structural complexity and molecular motions of ILs has been gathered by various techniques such as dielectric relaxation spectroscopy (DRS), optical Kerr effect spectroscopy (OKE), THz, ESR, NMR, neutron and X-ray scattering techniques, as well as transient absorption of solvated electrons [5,6]. Nonreactive and reactive processes crucially depend on the interactions of the embedded solute molecule(s) with the constituent ions of the IL. Therefore detailed information on Coulomb, dipolar, hydrogen-bonding and dispersion contributions to the solute–IL interaction is required. Sensitive spectroscopic techniques following the response of photoexcited molecular probes, which cover the timescale from the subpicosecond to the nanosecond regime, have allowed us to investigate the solvent properties of ILs, such as solvation dynamics of molecular probes in ILs, solvent polarity, collisional energy transfer, and charge transfer processes in ILs. In the following, we highlight selected results on these issues.

2.1. Steady-state absorption / fluorescence experiments

⁎ Corresponding authors. E-mail addresses: [email protected] (N.P. Ernsting), [email protected] (T. Lenzer), [email protected] (K. Oum). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.08.010

Steady-state absorption spectra of the dyes in different solvents were measured on Varian Cary 5000 (Siegen) and 300 (Berlin) spectrometers with baseline correction. Fluorescence spectra were recorded using a Horiba Jobin-Yvon Spex Fluorolog-2 (Berlin) spectrometer. Samples were excited at or close to the absorption maximum. The fluorescence raw data were corrected for the instrument response function by comparison with a secondary standard lamp.

2.2. Ultrafast transient absorption experiments Ultrafast broadband transient absorption spectroscopy based on the pump-supercontinuum probe (PSCP) method [7] was employed. In the current projects the spectral range 340−770 nm was covered with a time resolution down to 50 fs [8–10]. In addition, single-wavelength visible pump-near IR probe spectroscopy has been applied and proved itself to be particularly useful for elucidating the dynamics of carotenoid systems [11–13]. Ionic liquid samples were studied in a temperatureregulated stainless steel cell with adjustable path length (1 or 2 mm) [11].

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2.3. Broadband fluorescence upconversion spectroscopy (FLUPS) Broadband fluorescence upconversion was based on the experimental setup which is described in ref. [14], operating at 1 kHz repetition rate. Briefly, the fluorescence is excited with 400 nm, 0.2 μJ pulses. Gate pulses at 1.3 μm (60 μJ) have their pulse front tilted for optimal overlap in the nonlinear optical crystal. Sum frequency is formed in a BBO crystal, cut at 40° for a type II process. For 80 fs time resolution (fwhm) the crystal must be 0.1 mm thick. Phasematching over a 10000 cm−1 wide spectral fluorescence window is achieved, with relatively flat response, by predispersion of the fluorescence in a thin calcite wedge which is placed in an intermediate focus. The IL to be measured was flown slowly through a cuvette with 0.4 mm internal path length. In addition, the cuvette was oscillated perpendicular to the optical axis. Coumarin C153 was dissolved in the liquid such that the optical density was b0.4 at the peak of the first absorption band. In almost all ILs the water content was kept below 200 ppm, as determined by Karl Fischer titration afterwards.

A

B

3. Results and discussion 3.1. Exploring solvatochromism and ultrafast dynamics in neat ILs and in binary mixtures of ILs, organic solvents and CO2 by carotenoid probes 3.1.1. Dynamics in aprotic ILs Terminally carbonyl-substituted polyenes have served as unique reporter molecules for exploring a range of microscopic properties of ILs and IL-based mixtures [8,9,11–13]. In the following, we would like to highlight several examples, where the terminally carbonyl-substituted carotenoid 12′-apo-β-carotenoic-12′-acid (12′CA) acts as a molecular probe, see the inset in Fig. 1(A) for its structure. In a typical experiment, 12′CA is excited to the S2 state by an ultrafast pump pulse in the visible range and then internally converts to the first electronically excited state on a 100–200 fs timescale. This state possesses unique intramolecular charge transfer (ICT) character and is therefore typically denoted as “S1/ICT” [11,15–19]. Most importantly, its stabilization relative to the ground electronic state S0 is sensitive to the local solvent environment. Intermolecular solute–solvent interactions modulate the S1/ICT–S0 energy gap, which results in characteristic changes in the lifetime τ1 for internal conversion (IC) to S0. The dynamics is conveniently probed by broadband PSCP spectroscopy or by single-wavelength detection in the near IR around 850 nm, where the 12′CA probe exhibits characteristic stimulated emission (SE) [19]. Extracted lifetimes τ1 from our previous measurements are plotted in Fig. 1 as a function of the polarity parameter Δf = (ε − 1)/(ε + 2) − (n2 − 1)/(n2 + 2). Here, Δf values have been determined from known static dielectric constants measured by dielectric relaxation spectroscopy (DRS) [20,21]. Lifetimes in organic solvents show a smooth correlation with Δf (black crosses), with a marked reduction of τ1 at higher polarities [11]. In the next step, values of τ1 obtained in other solvents, such as ILs or IL / organic solvent mixtures, can be taken as a measure to determine, what “effective local polarity” the 12′CA probe experiences in this particular environment. Results for a range of aprotic ILs are shown in Fig. 1 as green open circles. The lifetime of 12′CA in aprotic ILs is comparable to that in short-chain alcohols [11,15–17]. Thus, the probe senses a much more polar local environment in aprotic ILs than suggested by DRS [20–30]. Such a “departure from dielectric continuum behavior” is actually consistent with dynamic Stokes shift measurements of probes such as DCS [31] and theoretical models [32–34]. Clearly, the lifetimes in aprotic ILs do not follow the correlation for organic solvents, but appear to be fairly scattered, see Fig. 1. A systematic analysis of the lifetimes of [Tf2N]−-based ILs shows that a reasonable correlation is obtained when the lifetime is plotted against the inverse cation radius. This suggests that the S1/ICT state of 12′CA is considerably stabilized by Coulombtype interactions between the probe's carbonyl function and the IL

Fig. 1. S1/ICT→S0 internal conversion time constants τ1 of 12′CA as a function of the solvent dipolarity parameter Δf. (Black crosses) Organic solvents reported in ref [11]. (Open green circles, expanded view in panel (B)) Aprotic ILs from ref [11]. (Half-filled blue circles) [C6mim]+[Tf2N]−/acetonitrile mixtures from ref [12]. (Red crosses) PILs from ref [13]. (Open red circles) PIL/H2O mixtures from ref [13].

cation, resulting in a better stabilization for IL cations having larger charge density [11]. In addition, using PSCP experiments we recorded the dynamics of different carotenoid probes over a wide spectral range (typically 340–770 nm) with cross-correlation times down to 50 fs [8,9]. Several important points have emerged from these studies: For aprotic ILs, a polarity comparable to short-chain alcohols can be deduced from the characteristic solvent-dependent changes of the S1/ICT transient absorption band shape [8]. This is entirely consistent with the aforementioned findings for the S1/ICT lifetime. In addition, we found evidence for solvation dynamics of the S1/ICT state which results in characteristic blue-shifts of the respective transient excited state absorption bands [8,9]. This adds another dimension to the sensitivity of these carotenoid reporter molecules, because they can be used for tracking not only micropolarity (via S1/ICT lifetime and band shape) but also the relaxation of solvent molecules around the newly formed S1/ICT dipole. The detailed characterization of such solvation dynamics in ILs using other molecular probes (such as Coumarin C153) and the simulation of the spectral relaxation function based on continuum theory is the central issue in Section 3.2. We also note that these findings regarding solvation dynamics at the same time solved a puzzling “mystery” in the photophysics of carbonyl carotenoids [9], where such “extra dynamics” have previously been assigned either to complex intramolecular relaxation pathways or equilibria involving additional electronic states [35,36]. Another interesting question concerns the term “hydrogen-bonding” in the context of aprotic ILs. In our experiments we have observed a substantial transient shift of the S1/ICT→Sn absorption band for our probes 12′CA and 12′-apo-β-caroten-12′-al in imidazolium-based ILs. It was only slightly smaller than in methanol [8]. Such shifts are commonly interpreted in terms of changes in the H-bond network of the

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two electronic states involved in the transition [37,38]. One would then expect that methylation at the C-2 position of the imidazolium ring should largely suppress H-bonding and reduce these shifts, however we observed essentially the same band shift for the C2-methylated analogue. We conclude that hydrogen-bonding between imidazoliumbased ILs and the carotenoid molecular probes appears to be rather weak. The substantial spectral shift observed for both types of imidazolium species therefore likely arises from Coulomb-type interactions between the carbonyl terminus of the probe (carrying a negative partial charge) and the imidazolium cation. The same type of interaction is also responsible for the aforementioned pronounced reduction of the lifetime τ1 of the 12′CA probe upon interaction with dipolar solvents [8,11]. 3.1.2. Protic ILs Protic ionic liquids (PILs) represent a special class of ILs, which result from combining Brønsted acids and bases. They form a strong hydrogen-bond network and are promising solvents especially for biological applications [39]. Knowledge of their polarity is critical for judging their feasibility for particular reactions, e.g. with respect to the solubility and reactivity of reactants, such as peptides or proteins. Employing the 12′CA probe, we explored the local polarity of the alkylammonium formate (AAF) PILs methylammonium formate (MAF), ethylammonium formate (EAF), and n-butylammonium formate (BAF) by recording the lifetime of the S1/ICT state [13]. Results are plotted in Fig. 1(A) as red crosses. The polarity of MAF, EAF and BAF is similar to the alcohols methanol, ethanol and n-butanol, respectively. In fact, MAF and BAF have been the most and least polar ILs studied so far by the 12′CA probe. Moreover, in contrast to aprotic ILs, the AAFs nicely follow the master curve found for organic solvents. It is suggested that the stronger dipolar character of the PILs makes them more similar to dipolar organic solvents, and that Coulomb-type interactions play a smaller role than in aprotic ILs. Interestingly, [C2mim]+[EtOSO3]−, the aprotic IL with the largest dielectric constant in Fig. 1 (labeled as “3”), which possesses a dipolar anion, is actually also the aprotic IL closest to the master curve, which supports our interpretation. 3.1.3. Binary mixtures of ILs and polar solvents One drawback of ILs is their relatively large viscosity giving rise to rather small diffusion coefficients, which slows down the kinetics of e.g. bimolecular reactions considerably. One way to overcome this problem is adding a well-defined amount of a low-viscosity solvent. At the same time, this changes the polarity of the system. It is therefore required to study systematically the polarity change for such mixtures using adequate molecular probes. We employed 12′CA as reporter for a case study of the polarity of [C6mim]+[Tf2N]−/acetonitrile mixtures. Ultrafast single wavelength visible pump-near IR probe absorption spectroscopy was used together with dielectric spectroscopy as a complementary technique, the latter one carried out in the Buchner group [12]. A systematic study of the S0→S2 absorption spectrum of 12′CA as a function of mixture composition (not shown) provides a linear dependence of the position of the absorption maximum on polarizability. This is a clear indication that the local composition around the probe is quite similar to the bulk value, so preferential solvation can be safely neglected. The lifetimes τ1 of the S1/ICT state of 12′CA in these mixtures are included in Fig. 1(A) as half-filled blue circles (decreasing IL content from left to right). Values change rather uniformly from [C6mim]+[Tf2N]− (94 ps) to acetonitrile (42 ps), and mixtures with high molar fraction of IL are further away from the master curve. A more detailed analysis shows that the lifetime of 12′CA at small IL mole fractions (b 0.1) is — surprisingly — slightly shorter than in pure acetonitrile [12]. Interestingly, DRS finds a corresponding maximum of the static dielectric constant in this mole fraction region. The finding can be most likely explained by the presence of discrete ion pairs of the IL. Another ultrafast lifetime component in the transients can be assigned to a fast

89

solvation component (see also Section 3.2). The ultrafast solvation of acetonitrile (ca. 0.5 ps) is strongly affected by addition of even small amounts of IL. This is found both by the transient absorption and DRS techniques. Most likely this is due to disruption of the acetonitrile network and the viscosity increase [12]. In addition, EAF/water mixtures were investigated [13]. Lifetimes of the 12′CA probe for mole fractions x(H2O) = 0.20, 0.38, 0.58 are included in Fig. 1(A) as red open circles (from left to right). They also follow the master curve quite closely. Neither the ultrafast transient absorption experiments nor the steady-state spectra of the probe provide any indications for differences between the local and bulk composition in EAF/water mixtures.

3.1.4. Binary mixtures of ILs and CO2 Adding CO2 is another way of reducing the viscosity of ILs, with the added benefit that CO2 can be easily removed by simple depressurization. Local properties of this special class of gas-expanded liquids can be conveniently probed by the 12′CA reporter molecule. In Fig. 2(A) we present shifts of the S0→S2 steady-state absorption spectrum of 12′CA as a function of the CO2 pressure for [C6mim]+[Tf2N]−/CO2. Measurements were performed in a home-built temperature-stabilized stainless steel high-pressure cell with 1 mm path length and sapphire windows. Upon addition of CO2 there is a clear spectral blue-shift. For 12′CA and other carotenoids, it is well known that these shifts are predominantly polarizability-induced [11]. Thus the effect must be due to a polarizability reduction of the mixture caused by CO2. As a second effect, the absorbance decreases with pressure. The volume expands upon CO2 addition, and thus the effective concentration of 12′CA in the observation volume is reduced. Mole fraction dependent spectral shifts relative to the neat solvent are shown in Fig. 2(B) for [C6mim]+[Tf2N]−/ CO2 in blue and are compared with our experiments for acetonitrile/ CO2 in red. The shift for the IL/CO2 mixture is much weaker than for acetonitrile/CO2, because of the much larger molar mass, and thus larger

A

B

Fig. 2. (A) Steady-state absorption spectra of 12′CA in binary mixtures of CO2 with [C6mim]+[Tf2N]− over the pressure range 11–54 bar in a high-pressure cell with a path length of 1 mm. Spectral maxima are marked by red crosses. (B) Comparison of absorption maxima of 12′CA in binary mixtures of CO2 with acetonitrile and with [C6mim]+[Tf2N]−.

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polarizability of the IL. Thus, even at large molar ratios of CO2, the probe interacts much more often with the atoms of the larger bulky IL ions than with the atoms of the small CO2 molecules. Refractive indices for [C6mim]+[Tf2N]−/CO2 mixture have not yet been reported, but a simple estimate based on a linear mixing rule approach results in a linear dependence of the spectral shift on the Lorenz–Lorentz function R(n), suggesting similar local and bulk compositions. In future studies, it will be interesting to see, to what extent the ultrafast dynamics of the 12′CA probe changes in IL/CO2 mixtures with increasing mole fraction x(CO2). 3.1.5. Collisional energy transfer processes in ILs The efficiency of intermolecular collisional energy transfer of large highly vibrationally excited molecules was identified as one important quantity which must be characterized, if one would like to evaluate the performance of ILs e.g. as solvent media for chemical reactions. Collisional energy transfer is crucial for the activation of reactants and the stabilization of “vibrationally hot” products. In the course of our investigations of carotenoid probes of ILs we discovered a way to use carbonyl carotenoids for studying vibrational energy transfer to the IL. Specifically, we have employed high pump laser energies to produce a “hot” 12′CA•+ carotenoid radical cation via two-photon ionization, which has a long lifetime on the order of microseconds [9]. It can be identified by a characteristic transient absorption band in the range 700−770 nm, which originates from its ground electronic state (Fig. 3). Most importantly, there is a characteristic spectral development in terms of a band narrowing and slight blue- shift on the picosecond timescale, which can be unambiguously assigned to vibrational energy transfer from the radical cation to the solvent. Interestingly, relaxation time constants found in methanol and [C6mim]+[Tf2N]− are virtually identical (ca. 6 ps, see the inset in Fig. 3). This timescale is similar to that of hot neutral molecules relaxing in polar organic solvents [40]. This is per se an interesting finding and not expected a priori, because the intermolecular potential between the charged radical cation and the charged IL constituents should be different from that of a neutral solute relaxing in a neutral surrounding. The different thermal diffusivities of methanol and [C6mim]+[Tf2N]−

(κ = 0.9996 · 10−7 m2 s−1 and 0.606 · 10−7 m2 s−1, respectively) would suggest a faster relaxation of the probe in methanol [41,42], yet the applicability of such a simple heat conduction model has been questioned [40]. Further studies are currently pursued to measure such relaxation time constants for a larger range of probes, ILs and IL mixtures. 3.2. Solvation dynamics of Coumarin C153 in ILs: treatment of an underdamped solvation mode In dipolar liquids, the fluorescence Stokes shift of C153 (and of other polarity probes) has long been related to the dielectric properties of the liquid. Not only does the fluorescence peak frequency ν(t = ∞) depend on the static dielectric constant ε0 in a series of liquids (here t = ∞ is used to indicate the quasi-stationary for the fluorescing molecule and its environment). But also when femtosecond pulses are used to excite the probe suddenly, the relaxation ν(t) of the instantaneous peak frequency to ν(t = ∞) reflects the behavior of ε(ω) between its static limit ε0 and the high-frequency limit ε∞ = n2NIR. One usually discusses the normalized spectral relaxation function SðtÞ ¼

νðtÞ‐νð∞Þ νð0Þ‐νð∞Þ

ð0Þ

The connection between S(t) and ε(ω) has been established quantitatively for solutions like acetonitrile [43], methanol [37], and water [44]. Given the current precision with which S(t) can be measured (± 0.5%), simple continuum theory (Fig. 4) is sufficient to describe the connection. A typical measurement of dynamic solvation is shown in Fig. 5. In this case C153 was dissolved in 1-butyl-3-methylimidazolium dicyanamide, [Im41][DCA]. The peak frequency ν(0) of the emission band at timezero, i.e. before any solvent relaxation has occurred, can be estimated from stationary spectra in reference solvents [45]. The experimental data points are shown as dots in Fig. 6. With ionic liquids, conductivity σ0 must be included in a generalized permittivity function (s = iω) 2

εðsÞ ¼ δ0

Fig. 3. Transient PSCP spectra of the 12′-apo-β-carotenoic-12′-acid radical cation in methanol upon photoexcitation at 480 nm using “high” pump energy for initial preparation of cations by two-photon ionization. The inset shows the kinetics in methanol (red circles) and [C6mim]+[Tf2N]− (blue circles) at 760 nm.

1 1 1 ω3 þ δ1 þ δ2 þ δ3 2 þ ε∞ sτ0 1 þ sτ1 1 þ sτ2 ω3 þ γ3 s þ s2

ð1Þ

A novel aspect for our work is given by the damped harmonic oscillator mode (DHO, 4th term) whereas the preceding two Debye terms represent strongly overdamped motion, as in previous discussions [46]. Expression (1) is used here as an example of how S(t) can be fitted, varying parameters like σ0, δi, τi, ωk, γk. The case of two Debye modes (N = 2) and one DHO mode is easily extended to larger sets. With eq. (1, N = 3) the red curve in Fig. 6 is obtained as an optimal fit. The description is quantitative for t N 1 ps and qualitatively correct at earlier times. Most notably, the conductivity σ0 = 0.432 S m−1 from the fit is found to be significantly reduced compared to the macroscopic dc value. Indeed, the reduction of σ0 from the macroscopic value seems to be the key for understanding systematic differences between predicted and observed S(t) curves [47–49]. In the following we treat the example of Eq. (1) explicitly. Frequency parameters [ps−1] are assumed to have been ordered τ−1 b τ−1 b 1 2 −1 γ3, ω3. Here δ0 = σ0/εvac, where σ0 is the conductivity [S m or A V− 1 m− 1] and εvac the vacuum permeability [8.8542 A ps V−1 m−1]. τ0 = 1 ps is needed for formal reasons, so that all amplitudes δi are dimensionless. ε∞ describes the contribution from electronic polarisation. In addition to the parameters which occur in Eq. (1) we will need a dielectric constant εc for the cavity in which the probe molecule resides. For the calculations it is convenient to abbreviate δ0/τ0 ≡ ρ0. Altogether the following parameters enter the calculations: ρ0 and ε∞, εc and δ1, δ2, δ3 and τ1, τ2, γ3, ω3. Equations marked * are used in numerical calculations; unmarked equations are needed for the

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dielectric relaxation

91

polar solvation

A

E ( )

( )

perturbing el. field

Polarisation (t)

B

D

Reactionfield (t)

t

t

L-1 -d/dt -d/dt

L

C

( )

1

2

( ) ( )

n2 2 n2

THz-TDS

t

1 1 1 1

Fig. 4. The generalized relative dielectric permittivity function ε * (ω) of an IL between plate capacitor (A) governs the relaxation of bulk polarisation, when an external perturbing field is suddenly switched off (B). Similarly a molecular dipole in a spherical cavity (E) may be switched suddenly, so that the reaction field relaxes (D). Simple continuum theory (lower panels) is used to connect the two processes. L is the Laplace transformation.

conceptual development. The following intermediate parameters are formed:

GðsÞ ¼

2

λ0 ¼ ρ0 ω3   2 3 λ1 ¼ ðδ1 þδ2 þδ3 þε∞ Þ ω3 þρ0 γ3 þ ðτ1 þτ2 Þω2 2

A bridge from dielectric susceptibility to dipolar solvation susceptibility is provided by the Glarum functional: εðsÞ‐1 ε∞ ‐1 ‐ 2εðsÞ þ εc 2ε∞ þ εc

ð5Þ

2

λ2 ¼ ðδ1 þδ 2 þε∞ Þγ3 þ ðδ2 þδ3 þε∞ Þω 3 τ1 þ ðδ1 þδ3 þε∞ Þω3 τ2 2 þ ρ0 1 þ γ3 ðτ1 þτ2 Þþτ1 τ2 ω3 2

λ3 ¼ ðδ1 þδ2 þε∞ Þ þ ðδ2 þε∞ Þγ3 τ1 þ ðδ1 þε∞ Þγ3 τ2 þ ðδ3 þε∞ Þω3 τ1 τ2 þ ρ0 ðτ1 þτ2 þγ3 τ1 τ2 Þ λ4 ¼ ðδ2 þε∞ Þτ1 þ ðδ1 þε∞ Þτ2 þε∞ γ3 τ1 τ2 þρ0 τ1 τ2 λ5 ¼ ε∞ τ1 τ2 ð2⁎Þ and η0 η1 η2 η3 η4 η5

¼0 2 ¼ ω3 2 ¼ γ3 þ ðτ1 þτ2 Þω3 2 ¼ 1 þ ðτ1 þτ2 Þγ3 þτ1 τ2 ω3 ¼ τ1 þτ2 þτ1 τ2 γ3 ¼ τ1 τ2

ð3⁎Þ

With their help, the form (1) is recast into a rational polynomial 2

εðsÞ ¼

3

4

5

λ0 þ λ1 s þ λ2 s þ λ3 s þ λ4 s þ λ5 s η0 þ η1 s þ η2 s2 þ η3 s3 þ η4 s4 þ η5 s5

ð4Þ

The limiting values are seen directly: ε(ρ0 = 0, s → 0) = λ1/η1 = δ1 + δ2 + δ3 + ε∞ ≡ ε0 and ε(s → ∞) = λ5/η5 = ε∞.

Fig. 5. The fluorescence of C153 (below) in [Im41] [DCA] was measured by broadband upconversion. Shown are transient spectra at 0.1, 0.3, 2.5, 25, 100, and 650 ps after excitation.

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order 0 N s1 N s2 N s3 N Re(s4). The partial fraction decomposition of G(s) then reads

GðsÞ ¼

  c1 c c c4 c þ 2 þ 3 þ þ 4 ðs‐s1 Þ ðs‐s2 Þ ðs‐s3 Þ ðs‐s4 Þ ðs‐s4 Þ

ð12Þ

The amplitudes ck of the terms in the response function are determined from the theory of functions:  ck ¼

 NðsÞ D′ ðsÞ s→sk

for k ¼ 1; 5

ð13⁎Þ

Only c1, c2, c3, c4 need to be calculated because the fifth root, c4, is the complex-conjugate of c4. The inverse Laplace transformation G(s) → G(t) is performed next. The first three terms in Eq. (12) are transformed readily; the corresponding rate constants are g1 ¼ ‐s1 ; g2 ¼ ‐s2 ; g3 ¼ ‐s3 Fig. 6. Solvation relaxation function S(t) for C153 in [Im41][DCA]. Experimental points are obtained from transient fluorescence spectra as in Fig. 5. The red line represents a fit by ε * (ω) consisting of Debye modes and one underdamped harmonic oscillator mode. In principle the oscillatory behavior of S(t) at early time can be described in this way, but two oscillator modes are needed.

ð14⁎Þ

Since s1–3 are real and all b0, the rate constants gi are all positive. The term in curly brackets must be treated separately. Let the complex root be s4 ¼ ‐g4 þ iw4

with

g4 ; w4 N 0


remember that 0 N Reðs4 Þ ð15⁎Þ

The corresponding complex coefficient is written The next task consists in pushing ε(s), as of Eq. (4), through Eq. (5). The outcome is cast into the following rational polynomial: GðsÞ ¼

NðsÞ DðsÞ

ð6Þ

For this purpose we calculate the coefficients for the constituent polynomials rk ¼ ð2 þ εc Þ ðλk −ηk ε∞ Þ

for k ¼ 0; 4

ð7⁎Þ

c4 ¼ x4 þ iy4

ð16⁎Þ

Thus, we have now four parameters pertaining to the term in curly brackets: g4 ; w4 and x4 ; y4 : The solvation response becomes GðtÞ ¼ c1 Expð‐g1 tÞ þ c2 Expð‐g2 tÞ þ c3 Expð‐g3 tÞ þ 2 Expð‐g4 tÞ ½x4 Cosðw4 tÞ‐y4 Sinðw4 tÞ

ð17Þ

and qk ¼ ð2ε∞ þ εc Þ 2λk þ ηk εc




for k ¼ 0; 5

ð8⁎Þ

In general, if R(t) is a response function, then the relaxation function is C(t) = ∫∞ t R(t′)dt′. Performing this for each component of Eq. (17) we obtain Eq. (19). The relaxation amplitudes are

ð9⁎Þ

ak ¼ ck =gk for k ¼ 1; 3  2 2 acos ¼ 2ðþg4 x4 ‐w4 y4 Þ= g4 þ w4   2 2 asin ¼ 2ð‐g4 y4 ‐w4 x4 Þ= g4 þ w4

With them one has 2

3

4

N ðsÞ ¼ r 0 þ r 1 s þ r2 s þ r 3 s þ r 4 s 2 3 4 5 DðsÞ ¼ q0 þ q1 s þ q2 s þ q3 s þ q4 s þ q5 s

(Note that coefficients, parameters, etc. on the “solvation side” are represented by Latin characters, while Greek characters are used on the “dielectric relaxation side”. An obvious exception is s.) For numerical treatment N(s) and D(s) should be scaled by a common scaling factor such that the values for r0 and q0 are on the order of one. In the following we assume that N(s) and D(s) have been so scaled. Thereafter we also need ′

2

3

4

D ðsÞ ¼ q1 þ 2q2 s þ 3q3 s þ 4q4 s þ 5q5 s

ð18⁎Þ

and we have finally CðtÞ ¼ a1 Expð‐g1 tÞ þ a2 Expð‐g2 tÞ þ a3 Expð‐g3 tÞ þ Expð‐g4 tÞ ½acos Cosðw4 tÞ þ asin Sinðw4 tÞ

ð19Þ

If ρ0 = 0, calculations can be carried through until Eq. (17) inclusively. We find g1 = 0 in this case; in Eqs. (18⁎,19) the first term should be omitted.

ð10⁎Þ 4. Conclusions

We proceed to the solvation response function G(t) which corresponds to G(s). For this purpose the latter is decomposed into partial fractions as follows. First the five roots sk of the denominator are sought DðsÞ ¼ ðs‐s1 Þðs‐s2 Þðs‐s3 Þðs‐s4 Þðs‐s4 Þ

ð11⁎Þ

With physical input data one obtains 0 N Re(sk) for k = 1,4. To match the four s-dependent terms of Eq. (1), we label the roots in the

Transient broadband absorption and fluorescence techniques are powerful tools for elucidating dynamics in ILs and IL mixtures via detection of the optical response of photoexcited “dynamic” molecular probes, such as carotenoids and coumarins. Pronounced differences are found regarding the local polarity and the solvation dynamics of aprotic ILs compared to conventional dipolar organic solvents. Specifically, aprotic ILs feature a micropolarity which is markedly higher than expected

N.P. Ernsting et al. / Journal of Molecular Liquids 192 (2014) 87–93

from extrapolated static dielectric constants extracted from dielectric spectroscopy. A quantitative relationship between the complete solvation response and microwave-terahertz absorption measurements of neat liquids was achieved, with the conductivity playing a key role in solvation experiments. Mixtures of ILs and organic solvents and of ILs and CO2 show no indication of preferential solvation, i.e. the bulk composition and local composition around the probe appear rather similar. The presence of IL ion pairs at low IL concentrations in IL / organic solvent mixtures has been clearly demonstrated by a combination of local molecular probe and dielectric spectroscopy. Acknowledgments The results presented in this paper highlight several important aspects of our works over the 2nd and 3rd funding period within the Priority Programme “Ionic Liquids” of the German Science Foundation (SPP 1191, projects: ER 154/11-2, LE 926/5-1 and -2, OU 58/3-1 and -2). Thanks go to our co-workers involved in these experiments: N. Bartels, F. Ehlers, M. Ekimova, O. Flender, D. Fröhlich, K. Golibrzuch, J.R. Klein, P.W. Lohse, M. Sajadi, M. Scholz and X.-X. Zhang. We would also like to acknowledge the contributions from our external collaborators R. Buchner, M. Liang, R. Lungwitz, M. Maroncelli, J.L. Pérez Lustres, S. Spange and A. Stoppa. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]

P. Wasserscheid, T. Welton, Ionic Liquids in Synthesis, Wiley-VCH, Weinheim, 2007. N.V. Plechkova, K.R. Seddon, Chem. Soc. Rev. 37 (2008) 123. J.F. Wishart, Energy Environ. Sci. 2 (2009) 956. F. Endres, S. Zein El Abedin, Phys. Chem. Chem. Phys. 8 (2006) 2101. E.W. Castner Jr., J.F. Wishart, J. Chem. Phys. 132 (2010) 120901. H. Weingärtner, Angew. Chem. Int. Ed. 47 (2008) 654. A.L. Dobryakov, S.A. Kovalenko, A. Weigel, J.L. Pérez Lustres, J. Lange, A. Müller, N.P. Ernsting, Rev. Sci. Instrum. 81 (2010) 113106. K. Oum, P.W. Lohse, F. Ehlers, M. Scholz, M. Kopczynski, T. Lenzer, Angew. Chem. Int. Ed. 49 (2010) 2230. P.W. Lohse, F. Ehlers, K. Oum, M. Scholz, T. Lenzer, Chem. Phys. 373 (2010) 45. J. Arden-Jacob, K.-H. Drexhage, S.I. Druzhinin, M. Ekimova, O. Flender, T. Lenzer, K. Oum, M. Scholz, Phys. Chem. Chem. Phys. 15 (2013) 1844. P.W. Lohse, R. Bürsing, T. Lenzer, K. Oum, J. Phys. Chem. B 112 (2008) 3048. P.W. Lohse, N. Bartels, A. Stoppa, R. Buchner, T. Lenzer, K. Oum, Phys. Chem. Chem. Phys. 14 (2012) 3596. M. Ekimova, D. Fröhlich, S. Stalke, T. Lenzer, K. Oum, ChemPhysChem 13 (2012) 1854. X.-X. Zhang, C. Würth, L. Zhao, U. Resch-Genger, N.P. Ernsting, M. Sajadi, Rev. Sci. Instrum. 82 (2011) 063108.

93

[15] D.A. Wild, K. Winkler, S. Stalke, K. Oum, T. Lenzer, Phys. Chem. Chem. Phys. 8 (2006) 2499. [16] F. Ehlers, D.A. Wild, T. Lenzer, K. Oum, J. Phys. Chem. A 111 (2007) 2257. [17] M. Kopczynski, F. Ehlers, T. Lenzer, K. Oum, J. Phys. Chem. A 111 (2007) 5370. [18] F. Ehlers, T. Lenzer, K. Oum, J. Phys. Chem. B 112 (2008) 16690. [19] S. Stalke, D.A. Wild, T. Lenzer, M. Kopczynski, P.W. Lohse, K. Oum, Phys. Chem. Chem. Phys. 10 (2008) 2180. [20] M.-M. Huang, Y. Jiang, P. Sasisanker, G.W. Driver, H. Weingärtner, J. Chem. Eng. Data 56 (2011) 1494. [21] J. Hunger, A. Stoppa, S. Schrödle, G. Hefter, R. Buchner, ChemPhysChem 10 (2009) 723. [22] C. Wakai, A. Oleinikova, M. Ott, H. Weingärtner, J. Phys. Chem. B 109 (2005) 17028. [23] C. Daguenet, P.J. Dyson, I. Krossing, A. Oleinikova, J.M. Slattery, C. Wakai, H. Weingärtner, J. Phys. Chem. B 110 (2006) 12682. [24] H. Weingärtner, Z. Phys. Chem. 220 (2006) 1395. [25] I. Krossing, J.M. Slattery, C. Daguenet, P.J. Dyson, A. Oleinikova, H. Weingärtner, J. Am. Chem. Soc. 128 (2006) 13427. [26] H. Weingärtner, P. Sasisanker, C. Daguenet, P.J. Dyson, I. Krossing, J.M. Slattery, T. Schubert, J. Phys. Chem. B 111 (2007) 4775. [27] A. Wulf, R. Ludwig, P. Sasisanker, H. Weingärtner, Chem. Phys. Lett. 439 (2007) 323. [28] S. Schrödle, G. Annat, D.R. MacFarlane, M. Forsyth, R. Buchner, G. Hefter, Chem. Commun. (2006) 1748. [29] A. Stoppa, J. Hunger, R. Buchner, G. Hefter, A. Thoman, H. Helm, J. Phys. Chem. B 112 (2008) 4854. [30] D.A. Turton, J. Hunger, A. Stoppa, G. Hefter, A. Thoman, M. Walther, R. Buchner, K. Wynne, J. Am. Chem. Soc. 131 (2009) 11140. [31] S. Arzhantsev, J. Hui, G.A. Baker, M. Maroncelli, J. Phys. Chem. B 111 (2007) 4978. [32] M.N. Kobrak, H. Li, Phys. Chem. Chem. Phys. 10 (2010) 1922. [33] H.K. Kashyap, R. Biswas, J. Phys. Chem. B 115 (2010) 254. [34] X. Song, J. Chem. Phys. 131 (2009) 044503. [35] E. Papagiannakis, M. Vengris, D.S. Larsen, I.H.M. van Stokkum, R.G. Hiller, R. van Grondelle, J. Phys. Chem. B 110 (2006) 512. [36] D. Kosumi, T. Kusumoto, R. Fujii, M. Sugisaki, Y. Iinuma, N. Oka, Y. Takaesu, T. Taira, M. Iha, H.A. Frank, H. Hashimoto, Chem. Phys. Lett. 483 (2009) 95. [37] M. Sajadi, T. Obernhuber, S.A. Kovalenko, M. Mosquera, B. Dick, N.P. Ernsting, J. Phys. Chem. A 113 (2009) 44. [38] E. Krystkowiak, K. Dobek, A. Maciejewski, J. Photochem. Photobiol. A 184 (2006) 250. [39] T.L. Greaves, C.J. Drummond, Chem. Rev. 108 (2008) 206. [40] D. Schwarzer, J. Troe, M. Votsmeier, M. Zerezke, J. Chem. Phys. 105 (1996) 3121. [41] J. Wang, M. Fiebig, Int. J. Thermophys. 16 (1995) 1353. [42] C. Frez, G.J. Diebold, C.D. Tran, S. Yu, J. Chem. Eng. Data 51 (2006) 1250. [43] J. Ruthmann, S.A. Kovalenko, N.P. Ernsting, D. Ouw, J. Chem. Phys. 109 (1998) 5466. [44] J.L. Pérez Lustres, S.A. Kovalenko, M. Mosquera, T. Senyushkina, W. Flasche, N.P. Ernsting, Angew. Chem. Int. Ed. 44 (2005) 5635. [45] R.S. Fee, M. Maroncelli, Chem. Phys. 183 (1994) 235. [46] X.-X. Zhang, C. Schröder, N.P. Ernsting, J. Chem. Phys. 138 (2013) 111102. [47] M. Maroncelli, X.-X. Zhang, M. Liang, D. Roy, N.P. Ernsting, Faraday Discuss. 154 (2012) 409. [48] X.-X. Zhang, M. Liang, N.P. Ernsting, M. Maroncelli, J. Phys. Chem. B 117 (2013) 4291. [49] X.-X. Zhang, M. Liang, N.P. Ernsting, M. Maroncelli, J. Phys. Chem. Lett. 4 (2013) 1205.