Simultaneous Measurement of Speed of Sound, Thermal Diffusivity

Article pubs.acs.org/JPCB

Simultaneous Measurement of Speed of Sound, Thermal Diffusivity, and Bulk Viscosity of 1‑Ethyl-3-methylimidazolium-Based Ionic Liquids Using Laser-Induced Gratings Dimitrii N. Kozlov,† Johannes Kiefer,*,‡,§,⊥ Thomas Seeger,‡,∥ Andreas P. Fröba,‡,# and Alfred Leipertz‡,# †

A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, 119991 Moscow, Russia Erlangen Graduate School in Advanced Optical Technologies (SAOT), D-91058 Erlangen, Germany § Technische Thermodynamik, Universität Bremen, D-28359 Bremen, Germany ∥ Lehrstuhl für Technische Thermodynamik, Universität Siegen, D-57076 Siegen, Germany ⊥ School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, Scotland, United Kingdom # Lehrstuhl für Technische Thermodynamik (LTT), Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany ‡

ABSTRACT: The technique of laser-induced gratings (LIGs) has been applied to the simultaneous determination of speed of sound and thermal diffusivity of four 1-ethyl-3methylimidazolium ([EMIm])-based room temperature ionic liquids (RTILs)[EMIm][N(CN)2], [EMIm][MeSO3], [EMIm][C(CN)3], and [EMIm][NTf2]at ambient pressure (1 bar (0.1 MPa)) and temperature (28 °C (301 K)). Transient laser-induced gratings were created as a result of thermalization of a quasiresonant excitation of highly lying combinational vibrational states of the RTIL molecules and electrostrictive compression of the liquid by radiation of a pulse-repetitive Q-switched Nd:YAG pump laser (1064 nm). The LIGs temporal evolution was recorded using Bragg diffraction of the radiation from a continuous-wave probe laser (532 nm). By fitting the temporal profiles of the LIG signals, the speed of sound and thermal diffusivity were determined, and the isentropic compressibility and thermal conductivity were calculated. Independently, the special experimental arrangement allowed the measurement of the damping of the laser-excited acoustic waves and the derivation of the RTIL bulk viscosity for the first time. techniques.19−26 Of special interest, the interionic interactions in [EMIm]-based RTILs have been intensively studied in recent years. They are characterized by a complex mixture of mechanisms like hydrogen bonding, dispersive forces, and polar interactions. In particular, the hydrogen bonds were found to have major impact on the molecular and macroscopic properties.27−29 General rules and prediction methods, however, are yet to be found and require further research. In this context, techniques facilitating the determination of multiple parameters simultaneously are advantageous for identifying possible correlations. An attractive but not commonly used experimental method to study RTILs is the nonlinear optical technique employing laser-induced gratings (LIGs).30 LIGs are transient spatially periodic modulations of the refractive index. The LIG technique permits noncontact measurements of multiple properties of a medium, like the speed of sound, thermal diffusivity, and acoustic damping rate, in a single measurement. In a LIG experiment, two coherent pump beams from a pulsed laser are overlapped and create an interference pattern in the intersection region. Thermalization of the energy conveyed to

1. INTRODUCTION The past two decades have seen an ever increasing interest in room-temperature ionic liquids (RTILs) because of their beneficial properties for applications as solvents, reaction media, electrolytes, and beyond.1−10 These properties often include extremely low vapor pressure, nonflammability, and high electrical conductivity combined with good thermal and electrical stability. Owing to the countless number of potential combinations of cations and anions composing RTILs, a profound understanding is required to enable tailoring fluids for specific applications in the future. The ultimate aim is to predict the desired properties of a RTIL at a given condition without the need for excessive measurements. A common subclass of RTILs is based on dialkylimidazolium cations. Variations of both the alkyl chain lengths and the counterion give rise to a huge number of possible pairs of ions that can be combined in order to obtain the desired properties. In the present work, we focus on four RTILs with a common 1ethyl-3-methylimidazolium ([EMIm]) cation. To understand the fundamental properties and their relationships with the molecular structure and interactions, many approaches, both theoretical and experimental ones, have been and are being employed. The list of analytical methods contains density functional theory11−14 and molecular dynamics simulations 15−18 as well as a large variety of experimental © 2014 American Chemical Society

Received: October 9, 2014 Revised: November 19, 2014 Published: November 21, 2014 14493

dx.doi.org/10.1021/jp510186x | J. Phys. Chem. B 2014, 118, 14493−14501

The Journal of Physical Chemistry B

Article

the absorbing species of the medium by the pump radiation, as well as electrostriction result in transient density, and thus refractive index spatial modulations. A third, continuous-wave probe laser beam, adjusted to cross the intersection region is Bragg diffracted by the LIG. The power of the diffracted radiation, detected with high temporal resolution (the LIG signal), characterizes the evolution of the transient grating. Finally, from this signal information about the local thermophysical properties of the medium is extracted. Fundamentals of the technique are described in the book of Eichler, Günter, and Pohl.30 Only a few studies employing the LIG technique to investigate thermophysical properties of RTILs have been reported to date. In most of the past studies, small amounts of absorbing molecules were dissolved in the RTIL under investigation in order to facilitate the creation of LIGs due to energy release. Frez et al.31 studied the effect of anion and cation on the thermal diffusivity, thermal conductivity, and speed of sound in RTILs with systematically varied cations and anions. In detail, they studied the cation 1-butyl-3-methylimidazolium ([BMIm]) combined with different anions and combinations of the anion bis(trifluoromethylsulfonyl)imide ([NTf2]) with different cations. For this purpose, inert ferroin dye was admixed to the liquids and excited with 532 nm pump radiation. Fukuda et al.32 investigated the photothermalization process of malachite green oxalate dye in three imidazoliumbased RTILs ([BMIm][NTf2], [BMIm][PF6], and [BMMIm][BF4]) and conducted measurements of the speed of sound. Excitation of the dye was achieved using ultraviolet subpicosecond pulses at 390 nm. In another work of the same group, the same dye was again added to [BMIm][NTf2] and [BMIm][PF6] to use LIGs for studying the speed of sound dispersion.33 Demizu et al.34 admixed diphenylcyclopropenone to systems of CO2 and [BMIm][PF6] for determining the thermal diffusivity and speed of sound employing LIGs. The third harmonic of a Nd:YAG laser at 355 nm was used as a pump radiation source. However, adding an absorber is not necessary when the experiment is arranged in such a way that the molecules of interest absorb the pump radiation themselves. Recently, our group35 accomplished the generation of LIGs by direct optical excitation of molecules of [EMIm][EtSO4] and the organic solvent acetone, (CH3)2CO, in both pure liquids and their binary mixtures. For this purpose, the fundamental, near-infrared output of a Nd:YAG laser at 1064 nm was employed as the pump source. In the present work, we study the effects of the anion on the properties of [EMIm]-based ionic liquids. Four different anions have been selected: dicyanamide [N(CN)2], methanesulfonate [MeSO 3 ], tricyanomethanide [C(CN) 3 ], and bis(trifluoromethylsulfonyl)imide [NTf2]. The molecular structures of the [EMIm] cation and the [N(CN)2], [MeSO3], [C(CN)3], and [NTf2] anions are shown in Figure 1. The RTILs under study attract particular interest since they are among the first that have been synthesized at technical scale and are commercially available from almost all major chemical suppliers. As in our previous work,35 we make use of the weak absorption of the [EMIm] cation in the near-infrared region around 1 μm and accomplish excitation of LIGs by employing the 1064 nm output of a pulsed Nd:YAG laser. This approach was shown to be appropriate for the measurements of speed of sound and thermal diffusivity. Beyond this, in the present work the feasibility to derive the bulk viscosity is demonstrated for

Figure 1. Molecular structures of the [EMIm] cation (a) and the [N(CN)2] (b), [MeSO3] (c), [C(CN)3] (d), and [NTf2] (e) anions.

the first time to our knowledge. The values obtained using LIGs are compared with those available in the literature.

2. EXPERIMENTAL SECTION 2.1. Experimental Setup. The experimental setup used here was similar to that one employed in our previous work.35 Two short-pulse pump beams were provided by a linearly polarized, Q-switched pulse-repetitive Nd:YAG laser (7 ns, 10 Hz, λp = 1064 nm). Their pulse energies were adjusted to be about 10 mJ. The CW probe beam was emitted by a frequencydoubled diode-pumped Nd:YAG laser (λ = 532 nm, 320 mW). Neutral density filters were installed to reduce the beam power down to about 7 mW. The main difference to the experimental arrangement of ref 35 was the way in which the probe volume was formed. Previously,35 the collinear pump and probe beams were focused by a f = 1000 mm spherical lens into the cylindershaped probe volume (about 0.4 mm in diameter). In contrast, here the beams were made to cross at the appropriate small angles in a 3D forward-scattering geometry after passing a cylindrical lens telescope with f = 530 mm. The telescope focused the beams in the vertical direction and by that formed laser sheets of about 5 mm in width. Hence, the probe volume was slab-shaped, and the vertical interference fringes of the pump radiation were spaced along the wide side of its transverse cross section. The crossing angle of the pump beams was θp ≈ 1.8°, resulting in the fringe spacing Λ = λp/2 sin(θp/2) ≈ 33.0 μm. The angle of incidence of the probe beam satisfied the Bragg condition (first-order Bragg diffraction). Quartz glass cuvettes of 10 mm thickness filled with the liquid samples were placed into the intersection area of the beams. The diffracted probe radiation was recollimated by the second cylindrical lens telescope. The time-resolved recording of the diffracted light power variation, with the temporal resolution of the order of 1 ns, was accomplished using a photomultiplier and a 3 GHz bandwidth digital oscilloscope connected to a computer. 2.2. Sample Preparation and Spectroscopic Characterization. In the present work, samples of [EMIm]-based room temperature ionic liquids were investigated: [EMIm][N(CN)2], [EMIm][MeSO3], [EMIm][C(CN)3], and [EMIm][NTf2]. Details of RTIL synthesis and the sample preparation procedure can be found in refs 36 and 37. The liquids were poured into the cuvettes in an argon atmosphere. The measurements were carried out at ambient conditions: 1 bar 14494



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(0.1 MPa) and 28 °C (301 ± 0.5 K). The temperature was monitored using a thermocouple, but no special efforts for sample temperature control were undertaken. The absorption spectra of the samples in the visible and nearinfrared regions were recorded between 400 and 1100 nm using a PerkinElmer Lambda 40 UV/vis spectrophotometer with a resolution of 2 nm. Quartz glass cuvettes with 10 mm absorption path lengths were used to obtain the spectra in the spectral range around the pump wavelength λp = 1064 nm.

extent, of band shapes and positions. Despite the weak absorption, a small amount of absorbed and rapidly thermalized laser energy is sufficient for generating a reasonably strong LIG signal. At the probe radiation wavelength λ = 532 nm the absorption of the samples does not exceed 5.4% for [EMIm][N(CN)2], [EMIm][MeSO3], and [EMIm][NTf2]. On the other hand, the [EMIm][C(CN)3] sample absorbs 95.3% of the probe radiation at the edge of the strong electronic absorption band of the [C(CN)3] anion. Consequently, the diffracted radiation, i.e. the signal, is also significantly absorbed. However, even this high level of attenuation is manageable, and the LIG signals could be recorded with a good signal-to-noise ratio. 3.2. LIG Signals. 3.2.1. Excitation of Laser-Induced Gratings and Formation of LIG Signals. Before recording the LIG signals in the RTIL samples, calibration LIG measurements were carried out in a series of molecular liquids: water, ethanol, acetone, n-pentane, n-hexane, and n-decane. These liquids also weakly absorb the pump radiation at λp = 1064 nm within overtone-combinational vibrational bands of the OH or CH bonds and hence allow generation of LIG signals. The thermophysical properties of these liquids are wellknown and can be found in the literature and the common databases (see e.g. refs 40−44). Hence, the results of the signal temporal profile analysis can be employed for calibration of the fringe spacing Λ and the acoustic transit time (see below) as well as for validation of the thermal conductivity κ measurements. Figure 3 presents an example of a LIG signal, accumulated over 200 laser shots, recorded in n-pentane (representing a liquid with low speed of sound and low kinematic viscosity) at delay times up to 2 and 1000 μs. The signal profiles are characterized by slowly damped high-frequency oscillations at delay times up to 2 μs and by an exponential decay at large delay times. Figure 4 gives an example of a similar LIG signal recorded in [EMIm][MeSO3] (characterized by high speed of sound and kinematic viscosity) at delay times up to 1 and 500 μs. In this case, the signal oscillations at the small-delay time scale have higher frequency and are damped more quickly, while the exponential decay at a large-delay scale occurs at a comparable rate. In both cases, the oscillations last significantly longer than in the signals presented in our previous work.35 This discrepancy results from the different dimensions of the excitation volume and will be discussed later. The diffraction efficiency of LIGs is proportional to the square of the refractive index variation. Thus, the evolution of this value determines the temporal profile of a LIG signal. The characteristic transients in Figures 3 and 4 indicate that the quasi-resonant nanosecond-pulse vibrational excitation of molecular species by spatially periodic 1064 nm radiation is followed by an extremely rapid energy exchange between the excited species and the medium. The energy exchange results in local temperature variations and hence in modulations of the liquid density. These modulations are a superposition of two acoustic waves (counterpropagating in opposite directions perpendicular to the planes of the fringes) and a slowly decaying stationary density grating. The acoustic waves have wavelengths equal to the fringe spacing Λ and similar amplitudes, thus representing a standing acoustic wave with the oscillation period Ta = Λ/υs. Here, υs is the adiabatic speed of sound within the probe volume. The modulation of the refractive index induced by both oscillatory and stationary density variations resulting from the energy exchange is referred

3. RESULTS AND DISCUSSION 3.1. Absorption Spectra. The absorption spectra of the four [EMIm]-based RTILs in the visible-to-NIR range (400− 1100 nm) are displayed in Figure 2. The region from 500 to

Figure 2. Absorption spectra of the investigated [EMIm]-based RTILs, 1, [EMIm][N(CN)2]; 2, [EMIm][MeSO3], 3, [EMIm][C(CN)3]; 4, [EMIm][NTf2], in the visible-to-NIR range (400−1100 nm): the general view (dashed lines) and the 20-fold enhanced part in the range of 500−1100 nm (solid lines); the absorption path length is 10 mm. The wavelengths of the pump and probe radiations are marked by the dashed vertical lines.

1100 nm has been enlarged by a factor of 20 to show the weak absorption lines. In the range of 800−1100 nm the absorption band shapes of all the samples look rather similar. This is a consequence of the fact that all the major absorption features are related to vibrations in CH3 and CH2 groups of the [EMIm] cation (see Figure 1). A detailed discussion of the [EMIm] vibrational structure can be found in Dhumal et al.38,39 In particular, the weak absorption bands peaked at about 900 and 1005 nm can tentatively be assigned to the third overtone of the CH bond stretching vibrations and to the overtonecombinational vibrational states containing 3 quanta of these vibrations, respectively. The growing absorption at 1080−1100 nm is likely to be provided by the wing of the stronger band corresponding to their second overtone. The enhancement of the intensities of the absorption bands at 900 nm and around 1005 nm in [EMIm][MeSO3] can be attributed to the additional CH bonds in the [MeSO3] anion. The pump radiation at λp = 1064 nm is weakly absorbed by the samples in the dip between the band at 1005 nm, with its characteristic shoulder at about 1030 nm, and the lowfrequency slope of the stronger absorption band above 1100 nm. The absorption level differs about 6-fold: between 0.3% in [EMIm][C(CN)3] and 1.7% in [EMIm][MeSO3], corresponding to the absorption coefficients α ≈ 0.003 and 0.017 cm−1, respectively. The difference can be explained by the observable variations of the absorption band strengths and, to a certain 14495



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Figure 3. An example of a LIG signal recorded in n-pentane: (a) initial part, 0−2 μs; (b) large delay part, 0−1000 μs. The slowly damped high-frequency oscillations at small delays and an exponential decay at large ones are clearly observed in the signal profile. The result of modeling and the difference between the experimental and calculated values are shown.

Figure 4. An example of a LIG signal recorded in [EMIm][MeSO3]: (a) initial part, 0−1 μs; (b) large delay part, 0−500 μs. While the signal oscillations at small delays are damped more quickly than those in n-pentane in Figure 3a, its exponential decay at large delays occurs at a comparable rate (Figure 3b). The result of modeling and the difference between the experimental and calculated values are also shown.

to as a thermal laser-induced grating. Independent of the quasiresonant absorption, the deformation of liquids in an electric field (electrostriction), which is proportional to the square of the electric field strength, produces a spatially periodic adiabatic compression of the medium. As a result, a standing acoustic wave (similar to that provided by the rapid energy exchange, but phase-shifted) is generated. The corresponding modulation of the refractive index is referred to as an electrostrictive laserinduced grating. The rate of the absorbed laser energy redistribution process, characterized by a time τ, defines the temporal evolution of a thermal contribution to a LIG. A standing acoustic wave and a stationary density variation are generated as a result of “instantaneous” or “fast” energy exchange, i.e. when τ < Ta/ 2π. In the case τ ≫ Ta/2π the energy exchange is “slow” and favors the formation of a stationary density variation. The development of the acoustic contribution is suppressed under this condition. Furthermore, in all the reported experiments the pump laser pulse with a duration of τL ≈ 7 ns can be regarded as short because τL < Ta. For example, the LIG signal oscillation period Ta in n-pentane (Figure 3a) is found to be 33 ns, and it is 19 ns in [EMIm][MeSO3] (Figure 4a). As in the case of the pump beams focused by the spherical lens,35 the observed damping time of the standing acoustic wave amplitude in the molecular liquids (e.g., above 2 μs in npentane, see Figure 3a) is determined mainly by the transit of the two counterpropagating acoustic wave packets out of the excitation volume. However, when the crossing beams are

focused by a cylindrical lens, which forms wide laser sheets and provides a larger number of the interference fringes, the oscillation decay time becomes more than 10 times larger. Nevertheless, the dissipation of sound due to viscosity and thermal conductivity of the medium still occurs more slowly. This is not the case in the ionic liquids, which are characterized by much higher viscosities and hence stronger attenuation of acoustic waves. As an example, the kinematic viscosity of [EMIm][MeSO3] is more than 120 and 310 times higher than that of water and n-pentane, respectively. The shortening of the LIG signal oscillation decay time in [EMIm][MeSO3] is clearly observed in Figure 4a. It is due to the combined effect of divergence and dissipation of the acoustic waves. On the other hand, the significantly slower decay of the stationary density modulation (see Figures 3b and 4b) is defined by heat conduction alone. 3.2.2. LIG Signal Evaluation Approach and Derived Parameters. Theoretical Model. In our previous work,35 an approximate relation for the LIG signal strength has been proposed which had been used for description of its temporal evolution and derivation of the characteristic parameters. That relation was based on the assumption that part of the energy absorbed by laser-excited species was dissipated instantaneously (within an infinitesimally short time interval τi ≪ τL), and the rest of the energy was further rapidly redistributed during a small finite time interval τf. In addition, the divergence of the acoustic wave packets out of the small diameter excitation volume, resulting in the decay of the standing acoustic wave, 14496



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Table 1. Parameters of the Molecular Liquids Used for Calibration (301 K) a

water, H2O acetone, (CH3)2CO ethanol, C2H5OH n-pentane, C5H12a n-hexane, C6H14a n-decane, C10H22a

ρ, kg/m3

cP, J/(mol K)

υs, m/s

βS,f GPa−1

μ × 103, Pa·s

κ, W/(m K)

996.3 782.6b 781.1b 618.0 652.2 724.3

75 126a 112a 168 195 314

1504 1156c 1135c 998 1044 1222

0.441 0.964 0.994 1.657 1.366 0.930

0.835 0.301e 1.00e 0.213 0.288 0.814

0.6199 0.1596d 0.1657d 0.1103 0.1252 0.1107

a

The literature values are taken from ref 40. bThe literature value is taken from ref 41. cThe literature value is taken from ref 42. dThe literature value is taken from ref 43. eThe literature value is taken from ref 44. fCalculated using eq 6.

where μ and β are the shear and the bulk viscosity, respectively, and γ = cP/cV is the ratio of the specific heats at constant pressure and volume. Equation 1 was obtained from the linearized hydrodynamic equations for the density and temperature variations with the weak damping of the acoustic waves46 following the results of Hubschmid et al.47 The equation was derived under the assumption that the process of the spatially periodic energy redistribution has two stages, with τf/τa ≪ 1, and the transit decay factor exp(−(t/τtr)2) for the oscillating contribution was introduced. This factor corresponds to the Gaussian profile of the pump beams. Equation 1 is in agreement with the simplified eqs 4 and 5 in ref 31 or eq 1 in ref 34. They were introduced to describe the thermal contribution to a LIG, setting the transit decay factor of the oscillating term to 1 and neglecting the electrostrictive contribution. Calibration Measurements. The characteristic parameters of the LIG signals in the liquids under investigation were derived from the experimental data by nonlinear fitting of the temporal profile with the model curve defined by eq 1. Before analyzing RTIL data, the model was applied to the signals from the molecular liquids with well-known thermophysical properties. Some of these properties at 301 K are presented in Table 1. The acoustic frequency Ωa, the acoustic transit time τtr, and the damping time τth were obtained as a result of the fitting routine. For all the liquids used for calibration, the quality of fitting the experimental data was reasonably good. As an example, the result for n-pentane is plotted in Figure 3, where the difference between the observed and the best-fit LIG signals is also shown. First, the derived values of Ωa were employed for determination of the fringe spacing calculated as Λ = υtab s Ta = tab υtab s (2π/Ωa), using the values of υs , taken from the literature. As a result, the average fringe spacing ⟨Λ⟩ = 32.91 ± 0.28 μm was obtained. Second, using Ωa and ⟨Λ⟩ the speeds of sound were calculated via υs = ⟨Λ⟩Ωa/2π. The comparison with the tabulated values yields ⟨Δυs/υtab s ⟩ = 0.02 ± 0.84%. Then, the values of thermal conductivity κcalc were calculated employing eqs 3 and 4 with the derived values of τth and the tabulated thermophysical parameters. The calculation error can be estimated as ⟨Δκ/κtab⟩ = −7 ± 10% by comparing the results were with the data from the literature. The values of τcalc a calculated using eq 5 and the tabulated values for density, specific heat, shear viscosity, and thermal conductivity. In accordance with Stokes’ hypothesis, the bulk viscosity β was set to zero.45 Since τa ≫ τtr in the employed molecular liquids due to their relatively low viscosity (in particular, τa = 81 μs in npentane), the oscillation decay provided the values of the acoustic transit time τtr. They were found to lie in the range of 0.89−1.25 μs (in n-pentane τtr = 1.22 μs, see Figure 3a). Obviously, τtr ∼ 1/υs, and hence the product τtrυs is a constant

was assumed to occur much faster than their dissipation due to viscosity and heat conduction. In the case of the wide excitation zone created in the present experiments this relation can be written in a more complete form, which accounts for acoustic wave attenuation: S(t ) ≅ S0{M i[cos Ωat exp(− (t /τtr)2 − (t /τa)) ⎛ k 1 f − exp( −t /τth)] + M f [⎜ sin Ωat + 2 1 + kf 2 ⎝ 1 + kf ⎞ × cos Ωat ⎟ exp(− (t /τtr)2 − (t /τa)) ⎠ −

[exp(−t /τth) − exp(−t /τf )] 1 − exp( −t /τf )] τf (1/τf − 1/τth) 1 + kf 2

+ Me sin Ωat exp(− (t /τtr)2 − (t /τa))}2

(1)

Here, S0 is a LIG signal scaling factor, and Mi, Mf, and Me are dimensionless coefficients, which scale the contributions to LIGs due to instantaneous and finite time (fast) energy redistributions, and electrostriction, respectively. Furthermore, in eq 1 Ωa = 2π/Ta is the acoustic frequency, τf is the characteristic time of the fast energy exchange process, and kf = Ωaτf. The decay of the signal oscillations is determined by two parameters: first, the acoustic transit time τtr, which accounts for the movement of the generated two counterpropagating acoustic wave packets out of the excitation volume and, second, the acoustic damping time τa, which is related to the sound absorption coefficient αs according to τa =

1 αsυs

(2)

The damping time τth of the stationary density modulation is related to the thermal diffusivity χ by τth =

⎛ Λ ⎞ 2 −1 ⎜ ⎟ χ ⎝ 2π ⎠

(3)

The thermal diffusivity is given by κ χ= ρcP

(4)

where κ is the thermal conductivity, ρ is the spatially homogeneous density, and cP is the specific heat at constant pressure. The acoustic damping time τa due to viscosity and thermal conductivity of the medium can be expressed in accordance with eq 2 and ref 45 as −1 ⎛ Λ ⎞2 ⎧ 1 ⎡ 4 κ ⎤⎫ τa = 2⎜ ⎟ ⎨ ⎢ μ + β + (γ − 1) ⎥⎬ ⎝ 2π ⎠ ⎩ ρ ⎣ 3 cP ⎦⎭ ⎪

⎪

⎪

⎪

(5) 14497



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Table 2. Fitted Parameters of the LIG Signals and Calculated Values of Taa Ωa, μs−1 [EMIm][N(CN)2] [EMIm][MeSO3] [EMIm][C(CN)3] [EMIm][NTf2] [EMIm][EtSO4]b

331 327 300 230 380

± ± ± ± ±

1 1 1 1 2

Ta, ns

Mi

19.0 19.2 21.0 27.4 16.5

1.09 0.74 1.42 1.03 0.67

τf, ns

Mf

± ± ± ± ±

−3.32 −2.39 −3.24 −6.58 −3.26

6.0 3.2 3.6 5.9 3.7

0.5 0.2 0.2 0.5 0.2

τth, μs 288 306 305 403 233

± ± ± ± ±

τa, μs

2 2 2 3 2

1.30 0.26 2.07 2.12

± ± ± ±

0.09 0.01 0.15 0.15

a

The errors are estimated from the results of independent measurements. The data obtained previously for [EMIm][EtSO4] are given for comparison. bThe values are taken from ref 35 for Λ = 29.0 μm and 293 K.

Table 3. Parameters of the Investigated Ionic Liquids at 301 Ka ρ, kg/m3 [EMIm][N(CN)2] [EMIm][MeSO3] [EMIm][C(CN)3] [EMIm][NTf2]

b

1107 1240c 1079d 1515b

e

326 329f 361e 525g

βS, GPa−1

υs, m/s

cP, J/(mol K)

m

1230

h

1733 1715m 1619m 1203m

m

0.301 0.274m 0.353m 0.456m

χ × 108, m2/s 9.9k 9.9l 6.0i

9.5m 9.0m 9.6m 6.8m

κ, W/(m K) 0.202d 0.192d 0.121d 0.130j

0.194m 0.178m 0.185m 0.138m

a The literature data for 301 K are calculated by linear interpolation of the tabulated values at 303.15 K and 298.15 or 293.15 K. bThe literature values are taken from ref 49. cThe literature values are taken from ref 50. dThe literature value values are from ref 36. eThe literature values are taken from ref 51. fThe literature values are from ref 52. gThe literature values are taken from ref 53. hThe literature values are taken from ref 54. iThe literature value for 296.85 K is taken from ref 31. jThe literature values are taken from ref 55. kCalculated using data of footnotes a, c, and d. lCalculated using data of footnotes c and d. mThis work.

differs from the case of the excitation of higher energy electronic states of admixtures:31,34 The former may be characterized by a finite vibrational energy thermalization time, while the latter is accompanied by the instantaneous release of a large amount of the absorbed energy. As an example, the fitting result of the [EMIm][MeSO3] LIG signal and the difference between the observed and the best-fit calculated LIG signals are plotted in Figure 4. Similar good quality of the fitting was obtained for the other RTIL samples. Hence, in all the samples under study both considered mechanisms, i.e., internal energy redistribution and electrostriction, could be regarded as being responsible for LIGs formation. 3.3. Discussion. The fitted values of the parameters Ωa and τth enable the calculation of the speed of sound υs and thermal diffusivity χ of the liquids. The frequencies of the generated acoustic waves were relatively low (in the ultrasound range of 36.6−52.7 MHz) and speed of sound dispersion32 may be neglected. In the zero-frequency limit, the speed of sound is related to the isentropic compressibility βS = (1/ρ)(∂ρ/∂P)S as

of the experimental arrangement, characterizing the width of the excitation volume in the direction across the fringes. Indeed, the average value ⟨τtrυs⟩ was found to be 1.34 ± 0.10 mm. This value was employed later in the calculations of the acoustic transit and damping times, τtr and τa, and the bulk viscosity of the RTIL samples. Application to RTILs. After the values of ⟨Λ⟩ and ⟨τtrυs⟩ had been determined, the modeling based on eq 1 was applied to the RTIL LIG signals, and the main temporal fitting parameters of interest, namely, Ωa, τth, and τa were derived. The values of the acoustic frequency Ωa, defined as a result of the fitting procedure, allowed to calculate the values of the acoustic transit time τtr = 2π⟨τtrυs⟩/(⟨Λ⟩Ωa). The values obtained for the fitted parameters for all four RTILs as well as the calculated values of Ta are summarized in Table 2. For comparison, the values defined previously for [EMIm][EtSO4] at Λ = 29.0 ± 0.6 μm and 293 K35 are also given. The indicated errors are estimated from the spread of the values derived from independent measurements. In the fitting procedure, the coefficients Mi and Mf were normalized to Me, which was set equal to 1. In both molecular and ionic liquids under investigation it appears that the electrostrictive and the instantaneous thermal contributions have the sign opposite to that obtained for the fast thermal contribution, and |Mf| ≈ (2−6)|Mi|. This may correspond to the local absorption of energy from the medium during the thermalization process. The fast energy exchange is characterized by a finite time τf ≈ 3−6 ns (e.g., τf = 4.4 ns for npentane and τf = 3.2 ns for [EMIm][MeSO3]). In this case, when the time scale of the fast energy exchange process is equal to or shorter than the laser pulse duration (τf ≤ τL), the instantaneous (with τi ≪ τL) and the fast processes are not clearly distinguishable. This means that the initial (oscillating) part of the signals may be described, in the zeroth approximation, if only the fast thermal contribution is introduced, with the appropriate effective negative amplitude M̃ f and the effective τ̃f. Note that our case of exciting molecules in a liquid to high overtone-combinational vibrational levels

υs 2 =

1 ρβS

(6)

Consequently, combining the directly obtained values of Ωa and τth with those of density ρ and specific heat cP taken from the literature, one can derive the isentropic compressibility βS and thermal conductivity κ using eqs 6 and 4, respectively. The literature data for ρ and cP at 301 K and the results of our calculations, with Λ set equal to 32.91 μm, are presented in Table 3. The values of βS and κ found in the database48 or in the original papers are also given for comparison. The speed of sound of [EMIm][NTf2] derived from the LIG signals agrees with the literature value within the uncertainty of our measurements (about 2%). The values of υs for the other RTILs have not been measured elsewhere, to the best of our knowledge. The calculated values of βS for the investigated RTILs appeared to be larger than those found previously for [EMIm][EtSO4] (0.262 GPa−1). However, they do generally 14498



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not exceed that of H2O (0.441 GPa−1) and are significantly (3− 4 times) smaller than those of the organic molecular liquids used in the calibration measurements. The uncertainty of the values is mainly determined by the uncertainty of determining the fringe period, which was 1%. As a result, the relative standard deviations of the speed of sound values are estimated to be about 2%, those of the thermal diffusivity about 3%, and those of the compressibility about 4%. For [EMIm][N(CN)2], [EMIm][MeSO3], and [EMIm][C(CN)3], the fitted values of the acoustic damping time τa significantly differed (10−50%) from the corresponding values τacalc calculated using eq 5 with β = 0 and the tabulated values of shear viscosity, density, specific heat, and thermal conductivity. Under the assumption that the difference is ascribed to the contribution of bulk viscosity, the latter can be derived from eq 5 as

a

transferred from the cation to the anion in the [EMIm][NTf2] ion pair via this hydrogen bond after vibrational excitation.29 In our present LIG experiments, we achieve vibrational excitation as well. The main difference from the molecular physics point of view is the excitation mechanism. In their femtosecond CARS study, Namboodiri et al.29 excited the lower frequency fundamental modes through a two-photon Raman process. On the other hand, in the LIG experiment we excite higher frequency overtone-combinational vibrational modes through direct one-photon absorption in the near-infrared. In any case, if a hydrogen bond allows vibrational energy transfer under certain conditions, the time of the fast energy exchange with the molecular surroundings, τf, may be influenced by such a cation−anion interaction. Note that, indeed, the τf values in Table 2 are about a factor of 2 larger for the [N(CN)2] and [NTf2] anions than for [MeSO3] and [C(CN)3]. A faster internal energy redistribution within the ion pair may result in a slower energy exchange with the surroundings and hence manifest itself in a larger time τf. In other words, after the vibration is excited, the vibrational energy is redistributed (inside the molecule) over the vibrational degrees of freedom. In order to establish the equilibrium in the vibrational subsystem, some energy may be taken from the surroundings. When the H-bonding allows an additional redistribution of the vibrational energy, this energy exchange with the surroundings may slow down. Interestingly, the two anions, for which a larger “fast” energy exchange time is observed, have a characteristic central nitrogen atom in common. Therefore, our data suggest that this nitrogen atom may play a key role in the cation−anion vibrational energy redistribution. However, a final conclusion cannot be made here as this would require investigating an extended series of systematically varied anions, which is beyond the scope of the present work.

the values of tabulated shear (dynamic and kinematic) and calculated bulk viscosities of the investigated RTILs at 301 K. The bulk viscosity ratio β/μ is given as well. We note that the presented planar beams arrangement provides a sufficiently wide probe volume in order to facilitate measuring the acoustic damping time (sound absorption) using the LIG technique. In turn, this allows us to determine the bulk viscosity utilizing the value of thermal conductivity from the experiment and the value of shear viscosity from the literature. However, it must be kept in mind that such an approach may introduce a significant error since a total damping time is measured, and its value is then subtracted from the larger value defined by the shear viscosity and thermal conductivity only. Another interesting point that can be discussed using the temporal parameters extracted from the experimental LIG signals (cf. Table 2) are the phenomena at the molecular level. In this context, it should be recalled that all RTILs under investigation exhibit the common [EMIm] cation. It possesses a slightly acidic proton at the C2 position of the ring (see Figure 1), while the other ring CH bonds are significantly less polarized. The C2 proton normally represents the predominant site for interionic interactions between the cation and the anion of the same “molecule” (ion pair) or between those of different molecules as it enables the formation of hydrogen bonds.27,28 Very recently, it was shown that vibrational energy can be

4. SUMMARY AND CONCLUSION The nonlinear four-wave mixing technique employing laserinduced gratings was applied to the determination of thermophysical properties of four [EMIm]-based room temperature ionic liquids: [EMIm][N(CN)2], [EMIm][MeSO3], [EMIm][C(CN)3], and [EMIm][NTf2]. The experiments proved the ability of the LIG technique, used without pump radiation absorbing additives, in simultaneous measurements of several characteristics of RTILs. For the first time, to the best of our knowledge, the possibility to derive the RTIL bulk viscosity from a LIG experiment was demonstrated. The speed of sound, thermal diffusivity, and bulk viscosity of the RTIL samples at ambient pressure (1 bar) and temperature (28 °C) were derived from the temporal profiles of the LIG signals. From these values, isentropic compressibility and thermal conductivity were determined. Good agreement between the evaluated values and those provided by alternative methods and taken from the literature was found. This confirms the conclusions of our previous study: the accuracy of the LIG technique is adequate, and the model employed for fitting the LIG signal transients is appropriate. The results obtained further demonstrate the potential of the LIG technique employing 1064 nm radiation of Q-switched Nd:YAG lasers. It can easily be applied to accurate systematic measurements of multiple properties of molecular liquids and gases, which contain CH3−, CH2−, or CH− groups. The technique proves to be a practical instrument to obtain data necessary for modeling the properties of ionic liquids with

⎞ ⎛ Λ ⎞2 ρ ⎛ τ calc − 1⎟⎟ β = 2⎜ ⎟ calc ⎜⎜ a ⎝ 2π ⎠ τ ⎝ τa ⎠ a

(7)

By contrast, in [EMIm][NTf2] the difference between τa and τacalc is only about 0.4%, which is clearly below the estimated error of τa determination (not less than 5%). Table 4 contains Table 4. Shear (Dynamic μ and Kinematic v = μ/ρ) and Calculated Bulk (β) Viscosities and the Bulk Viscosity Ratio β/μ at 301 Ka

[EMIm][N(CN)2] [EMIm][MeSO3] [EMIm][C(CN)3] [EMIm][NTf2]

μ × 103, Pa·s

μ/ρ × 106, m2/s

β, mPa·s

β/μ

16.9b 131.4c 13.7d 29.4b

15.3 106.0 12.7 19.4

22e 86e 10e ≈0e

1.3 0.7 0.8 ≈0

The literature data for 301 K are calculated by linear interpolation of the tabulated values at 303.15 K and 298.15 or 293.15 K. bThe literature values are taken from ref 49. cThe literature values are taken from ref 50. dThe literature values are taken from ref 56. eThis work.

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(8) 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. (9) Olivier-Bourbigou, H.; Magna, L.; Morvan, D. Ionic Liquids and Catalysis: Recent Progress from Knowledge to Applications. Appl. Catal. A 2010, 373, 1−56. (10) Werner, S.; Haumann, M.; Wasserscheid, P. Ionic Liquids in Chemical Engineering. Annu. Rev. Chem. Biomol. Eng. 2010, 1, 203− 230. (11) Köddermann, T.; Wertz, C.; Heintz, A.; Ludwig, R. Ion-Pair Formation in the Ionic Liquid 1-Ethyl-3-Methylimidazolium Bis(triflyl)imide as a Function of Temperature and Concentration. ChemPhysChem 2006, 7, 1944−1949. (12) Katsyuba, S.; Zvereva, E.; Vidis, A.; Dyson, P. Application of Density Functional Theory and Vibrational Spectroscopy toward the Rational Design of Ionic Liquids. J. Phys. Chem. A 2007, 111, 352− 370. (13) Fujii, K.; Seki, S.; Fukuda, S.; Kanzaki, R.; Takamuku, T.; Umebayashi, Y.; Ishiguro, S. Anion Conformation of Low-Viscosity Room-Temperature Ionic Liquid 1-Ethyl-3-Methylimidazolium Bis(fluorosulfonyl) Imide. J. Phys. Chem. B 2007, 111, 12829−12833. (14) Dhumal, N. R.; Kim, H. J.; Kiefer, J. Molecular Interactions in 1Ethyl-3-Methylimidazolium Acetate Ion Pair: A Density Functional Study. J. Phys. Chem. A 2009, 113, 10397−10404. (15) 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. (16) Skarmoutsos, I.; Dellis, D.; Matthews, R. P.; Welton, T.; Hunt, P. A. Hydrogen Bonding in 1-Butyl- and 1-Ethyl-3-Methylimidazolium Chloride Ionic Liquids. J. Phys. Chem. B 2012, 116, 4921−4933. (17) Zahn, S.; Brehm, M.; Brussel, M.; Holloczki, O.; Kohagen, M.; Lehmann, S.; Malberg, F.; Pensado, A. S.; Schoppke, M.; Weber, H.; Kirchner, B. Understanding Ionic Liquids from Theoretical Methods. J. Mol. Liq. 2014, 192, 71−76. (18) Dias, N.; Shimizu, K.; Morgado, P.; Filipe, E. J. M.; Canongia Lopes, J. N.; Chavez, F. V. Charge Templates in Aromatic Plus Ionic Liquid Systems Revisited: NMR Experiments and Molecular Dynamics Simulations. J. Phys. Chem. B 2014, 118, 5772−5780. (19) Gottfried, J. M.; Maier, F.; Rossa, J.; Gerhard, D.; Schulz, P. S.; Wasserscheid, P.; Steinrück, H.-P. Surface Studies on the Ionic Liquid 1-Ethyl-3-Methylimidazolium Ethylsulfate Using X-Ray Photoelectron Spectroscopy (XPS). Z. Phys. Chem. 2006, 220, 1439−1453. (20) Wulf, A.; Ludwig, R.; Sasisanker, P.; Weingartner, H. Molecular Reorientation in Ionic Liquids: A Comparative Dielectric and Magnetic Relaxation Study. Chem. Phys. Lett. 2007, 439, 323−326. (21) Kiefer, J.; Fries, J.; Leipertz, A. Experimental Vibrational Study of Imidazolium-Based Ionic Liquids: Raman and Infrared Spectra of 1Ethyl-3-Methylimidazolium Bis(trifluoromethylsulfonyl)imide and 1Ethyl-3-Methylimidazolium Ethylsulfate. Appl. Spectrosc. 2007, 61, 1306−1311. (22) Fröba, A. P.; Wasserscheid, P.; Gerhard, D.; Kremer, H.; Leipertz, A. Revealing the Influence of the Strength of Coulomb Interactions on the Viscosity and Interfacial Tension of Ionic Liquid Co-Solvent Mixtures. J. Phys. Chem. B 2007, 111, 12817−12822. (23) Grondin, J.; Lassègues, J. C.; Cavagnat, D.; Buffeteau, T.; Johansson, P.; Holomb, R. Revisited Vibrational Assignment of Imidazolium-Based Ionic Liquids. J. Raman Spectrosc. 2011, 42, 733− 743. (24) Vale, V. R.; Will, S.; Schröer, W.; Rathke, B. The General Phase Behavior of Mixtures of 1-Alkyl-3-Methylimidazolium Bis[(trifluoromethyl)sulfonyl]amide Ionic Liquids with N-Alkyl Alcohols. ChemPhysChem 2012, 13, 1860−1867. (25) Sonnleitner, T.; Turton, D. A.; Waselikowski, S.; Hunger, J.; Stoppa, A.; Walther, M.; Wynne, K.; Buchner, R. Dynamics of RTILs: A Comparative Dielectric and OKE Study. J. Mol. Liq. 2014, 192, 19− 25. (26) Allen, J. J.; Bowser, S. R.; Damodaran, K. Molecular Interactions in the Ionic Liquid Emim Acetate and Water Binary Mixtures Probed

arbitrary composition or to screen samples in the process of production of RTILs with specific properties. In addition, since the measurements can be performed using a single laser pulse, the LIG technique can provide data at a definite moment after a single transient event or at high repetition rates during an ongoing process. This is of interest for process diagnostics and control purposes. In addition to the measurement of thermophysical properties, the LIG technique was found to be suitable for identifying and possibly characterizing ultrafast interionic vibrational energy transfer. Our results suggest that the vibrational energy transfer between cation and anion may be facilitated by a directional hydrogen bond formed between the cationic C2proton and a central nitrogen atom in the anion. Those RTILs without such a central nitrogen atom seem to be uninvolved or at least much less involved into the vibrational energy transfer. This hypothesis however needs to be proved in future. Another interesting point will be to perform further tests with liquids that are similar in structure but do not form hydrogen bonds at all. In conclusion, the LIG technique is a versatile experimental tool for studying ionic liquids. It offers noncontact and simultaneous measurements of several thermophysical properties with high spatial and temporal resolution. Moreover, it enables the investigation of interesting physicochemical phenomena. Therefore, the LIG method may become a true alternative to conventional analytical techniques.

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AUTHOR INFORMATION

Corresponding Author

*Phone + 49 (0)421 218-64777; e-mail [email protected] (J.K.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Technical assistance of B. Roshani and J. Lehmann is acknowledged. Part of this work was supported financially by the German Research Foundation (DFG), project SE 804/3-1, and by the Russian Foundation for Basic Research (RFBR), grant No. 08-02-91958. The authors also acknowledge support from the Erlangen Graduate School in Advanced Optical Technologies (SAOT) and the DFG-SPP 1191 priority program, grant FR 1709/9-1.

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REFERENCES

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Simultaneous Measurement of Speed of Sound, Thermal Diffusivity

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