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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Femtosecond Raman-Induced Kerr Effect Study of Temperature-Dependent Intermolecular Dynamics in Molten Bis(Trifluoromethylsulfonyl)Amide Salts: Effects of Cation Species Shohei Kakinuma, and Hideaki Shirota J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b03302 • Publication Date (Web): 10 May 2018 Downloaded from http://pubs.acs.org on May 15, 2018

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The Journal of Physical Chemistry

Femtosecond Raman-Induced Kerr Effect Study of Temperature-Dependent Intermolecular Dynamics in Molten Bis(Trifluoromethylsulfonyl)amide Salts: Effects of Cation Species

Shohei Kakinuma† and Hideaki Shirota†‡*

†

Department of Nanomaterial Science and ‡Department of Chemistry, Chiba University, 1-33 Yayoi, Inage-ku, Chiba 263-8522, Japan

[email protected]

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ABSTRACT In this study, we have investigated the effects of cation structures on the temperature dependence of the intermolecular vibrational dynamics of ionic liquids using femtosecond Raman-induced Kerr

effect

spectroscopy.

The

ionic

liquids

used

in

this

study

are

bis(trifluoromethylsulfonyl)amide [NTf2]− salts of the cations 1-butyl-3-methylimidazolium [C4MIm]+,

[Pyrr14]+,

1-butyl-1-methylpyrrolidinium [N1224]+,

butyldiethylmethylammonium triethyloctylphosphonium [P2228]+.

1-butylpyridinium

triethyloctylammonium

[N2228]+,

[C4Py]+, and

All the ionic liquids show temperature-dependent

low-frequency spectra. A difference in the temperature dependence between the spectra of the aromatic and nonaromatic cation based ionic liquids is especially significant. In the case of the aromatic cation based ionic liquids [C4MIm][NTf2] and [C4Py][NTf2], the spectral intensities in the low-frequency region below ca. 50 cm−1 increase and the high-frequency components at ca. 80 cm−1 shift to lower-frequencies with rising temperature. In contrast, the ionic liquids based on nonaromatic cations only exhibit an increase in the low-frequency region below ca. 50 cm-1 with increasing temperature, while the high-frequency region of the spectra above ca. 50 cm-1 shows little change with variation of the temperature. These results suggest that the presence or absence of aromatic rings is the main factor in determining the temperature-dependent spectral features, particularly in the high-frequency region. We also found that the alkyl chain length and central atoms of the nonaromatic quaternary cations do not have much influence on the temperature-dependent spectral features. The first moments of the aromatic cation based ionic liquids are a little more sensitive to temperature than those of the nonaromatic cation based ionic liquids. The temperature-dependent viscosities and fragilities of the ionic liquids have also been examined.


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1. INTRODUCTION Molecular motions such as intermolecular vibrations and orientational dynamics in liquids and solutions appear in the low-frequency region of ca. 1–150 cm−1 (or the terahertz region of ca. 0.03 – 4.5 THz). These motions have been investigated extensively because of their importance in understanding the elementary processes of chemical reactions in solution.1 Femtosecond Raman-induced Kerr effect spectroscopy (fs-RIKES) is a third-order nonlinear spectroscopic technique that has been utilized to study the liquid and solution dynamics in the low-frequency region.2-8 The fs-RIKES has been used to study not only simple molecular liquids9 but also complex systems,10 such as hydrogen-bonding molecular systems,11,12 solvents confined in nanoporous glasses,13-15 polymer solutions,16-20 microemulsions,20-22 biomolecular systems,23-27 and ionic liquids (ILs), which are the subject of this study.28-30 Room temperature ILs are salts that remain in the liquid state at room temperature.31,32 ILs are generally composed of asymmetric organic cations and inorganic or organic anions. Because some physical properties of ILs, such as their low melting points and low volatility at ambient temperature and pressure, are unique, they have been actively investigated.33-35 The representative cations of ILs can be broadly classified into two groups: aromatic cations and nonaromatic cations. The physical and chemical properties of aromatic and nonaromatic cation based ILs differ in several ways. For example, the viscosities of aromatic cation based ILs are generally lower than those of nonaromatic cation based ILs with similar cations’ formula weights and the same anions.33 Although the electric conductivities of aromatic cation based ILs are higher than those of nonaromatic cation based ILs, the electrochemical potential windows of nonaromatic cation based ILs are larger than those of aromatic cation based ILs.36 The microscopic structures



of aromatic cation based ILs also exhibit greater spatial inhomogeneity than nonaromatic cation based ILs.37 In addition to their physical properties, aromatic and nonaromatic cation based ILs also present differences in their intermolecular vibrations.38,39 The low-frequency Kerr spectra of aromatic cation based ILs are generally broader than those of nonaromatic cation based ILs.38 This can be explained by the librational motions of the aromatic ring, which create additional components in the high-frequency region at about 100 cm−1. In addition, the relationships between the low-frequency spectra and bulk properties of aromatic and nonaromatic cation based ILs are different.38 Linear correlations between the first moment of the intermolecular vibration band and the square root of the surface tension divided by the density have been found in ILs, as well as in aprotic molecular liquids.9 However, the first moments of aromatic cation based ILs are more insensitive to changes in the bulk properties than those of nonaromatic cation based ILs, although aromatic and nonaromatic molecular liquids do not exhibit such a difference. This is attributed to the microheterogeneity of ILs. That is, aromatic cation based ILs are more segregated at the molecular level than the respective nonaromatic cation based ILs,37 and thus the information from the ionic region is more reflected in the low-frequency Kerr spectra than nonaromatic cation based ILs, which causes the differences in the correlations between the low-frequency Kerr spectra and the bulk properties. We also studied the low-frequency spectra of a series of systematically different ILs with charged and/or neutral aromatic rings in their cations.40 Both charged and neutral aromatic rings contribute to the high-frequency components, while the charged aromatic rings appear at higher frequency than the neutral ones. To elucidate the complex intermolecular vibrational spectra of liquids and solutions, it is essential to study their temperature dependence. The temperature-dependent low-frequency 4 ACS Paragon Plus Environment

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spectra of molecular liquids have been extensively investigated.41-48 For example, Fourkas and coworkers studied the intermolecular dynamics of a series of aromatic liquids44,45 and tetrahydrofuran and its related molecular liquids49 as a function of temperature. They reported that the low-frequency side of the broad spectra shifts to lower-frequency and the high-frequency side shifts to higher-frequency with decreasing temperature. In contrast to molecular liquids, fewer reports on the temperature dependence of the intermolecular vibrational dynamics of ILs have been published. Quitevis and coworkers reported the temperature dependence of the low-frequency spectra of 1-methyl-3-pentylimidazolium ([C5MIm]+) based ILs with bis(trifluoromethylsulfonyl)amide ([NTf2]−),50 hexafluorophosphate ([PF6]−), and bromide anions.51

The renormalized spectra of [C5MIm][NTf2] were

temperature-dependent, however, those of [C5MIm][PF6] and [C5MIm]Br were insensitive to temperature. Wynne and coworkers compared the temperature-dependent low-frequency Kerr spectra and dielectric spectra of some imidazolium and ammonium based ILs.30,52 They discussed the differences in the temperature sensitivities of the spectral components of the α-relaxation process and intermolecular vibration. We studied the temperature-dependent low-frequency spectra of imidazolium monocations and dications with the [NTf2]− anion.53 The spectra of both the monocationic and dicationic ILs showed similar temperature dependence, which could be reasonably explained in terms of imidazolium ring motions.

We also investigated the

temperature-dependent low-frequency spectra of imidazolium cation based ILs with ten different anions, and found that their temperature dependence was largely dominated by the imidazolium ring libration.54 In addition, we also found that the temperature dependences of the first moment of the low-frequency spectra of most of these ILs are similar, but some ILs with smaller and less symmetric anions, such as dicyanamide and thiocyanate, display different temperature dependence.



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Very recently, we investigated the effects of aromaticity in the cation moiety of ILs on the temperature-dependence of their low-frequency spectra.55 1-cyclohexylmethyl-1-methylpyrrolidinium

The low-frequency spectra of

bis(trifluoromethylsulfonyl)amide

only

show

temperature dependence at frequencies less than 50 cm−1, while those of the other ILs with aromatic rings in their cation moieties are temperature-dependent in both the low-frequency region below 50 cm−1 and in the high-frequency region above 80 cm−1. We concluded that the spectral change in the low-frequency region could be explained in terms of both the cation and anion, while that in the high-frequency region was due to the librational motions of aromatic cations. In this study, we further investigate the temperature dependence of the low-frequency spectra of standard ILs with representative cation structures using fs-RIKES. We employ [NTf2]− salts of 1-butyl-3-methylimidazolium ([C4MIm]+), 1-butyl-1-methylpyrrolidinium ([Pyrr14]+), 1-butylpyridinium ([C4Py]+), butyldiethylmethylammonium ([N1224]+), triethyloctylammonium ([N2228]+), and triethyloctylphosphonium ([P2228]+) cations, as shown in Figure 1. The main purpose of this study is to clarify how the differences in the structure of the cations of the ILs affect the temperature-dependent features of their low-frequency spectra.

In the previous study

mentioned above,55 we aimed to reveal the different temperature dependence of charged and neutral aromatic rings, i.e., to study a specific case. In this study, however, we use ILs that are based on more standard and popular cations with linear alkyl side groups, and focus on the effects of the fundamental structures of the cations on the temperature dependence of the low-frequency spectra. The universal and structurally-dependent features of the temperature dependence of the low-frequency spectra are investigated based on comparisons between (i) (aromatic) imidazolium and (nonaromatic) pyrrolidinium cations, (ii) imidazolium and pyridinium cations, (iii) (cyclic) pyrrolidinium and (branched) ammonium cations, (iv) ammonium cations with different alkyl


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groups of different lengths, and (v) ammonium and phosphonium cations. We have further searched the temperature-dependent low-frequency spectra of the molecular liquids 1-methylimidazole, pyridine, 1-methylpyrrolidine, and butyldiethylamine, which are neutral analogues of the cations of the studied ILs. In addition, we have estimated the fragility parameters of the ILs based on measured temperature dependent viscosities.

2. EXPERIMENTAL METHODS [C4MIm][NTf2] was purchased from Kanto Chemical and used as received. [C4Py][NTf2], [N2228][NTf2], and [P2228][NTf2] were the same as previously used.56,57 [Pyrr14][NTf2] and [N1224][NTf2] were synthesized according to the similar procedure.56,57 The synthesized ILs were confirmed by 1H NMR and elemental analysis measurements. Detailed synthetic procedures and assignments for these ILs are described in the Supporting Information. The water contents of the ILs were measured using a Karl Fischer titration coulometer (Hiranuma, AQ-300). The water contents of the [C4MIm][NTf2], [Pyrr14][NTf2], [C4Py][NTf2], [N1224][NTf2], [N2228][NTf2], and [P2228][NTf2] were 16.5, 58.5, 19.6, 27.4, 41.4, and 29.9 ppm, respectively. The sample ILs were dried in vacuo for more than 36 hours prior to measurements. A reciprocating electromagnetic piston viscometer (Cambridge Viscosity, ViscoLab 4100) equipped with a circulating water bath (Yamato, BB300) was used for viscosity measurements at the target temperatures.

1-Methylimidazole (Aldrich) and pyridine (Wako) were used as received.

1-Methylpyrrolidine (TCI) and butyldiethylamine (Aldrich) were used after distillation. Details of the fs-RIKES setup used in this study have been reported elsewhere.9,58,59 The light source for the most current fs-RIKES setup in our laboratory was a titanium sapphire laser 7 ACS Paragon Plus Environment


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(KMLabs, Griffin).59 The output power was approximately 400 mW. The sample liquids were injected into a 3 mm optical-path-length quartz cell (Tosoh Quartz) via a 0.2- or 0.02-µm pore size Anotop filter (Whatman). The temperature of the sample was controlled using a laboratory-built temperature controller based on a Peltier temperature controller set (VICS, VPE35-5-20TS). The scans were performed with a high time resolution of 4096 points at 0.5 µm/step (3.34 fs/point) for a time window of 13.7 ps. Pure heterodyne signals were obtained by recording scans for both plus and minus ~1.5° rotations of the input polarizer and combining these signals to eliminate the residual homodyne signal. Three scans were averaged for each polarization measurement.

3. DATA ANALYSIS Prior to discussing the temperature dependence of the spectra, we briefly describe the procedures used to analyze the data. The data analysis is based on the procedure established largely by McMorrow and Lotshaw.60,61 The experimentally obtained Kerr transient includes both an instantaneous electronic hyperpolarizability contribution σ(t) and a sum of the nuclear responses ri(t), and is given by = + ∑

(1)

In reality, femtosecond laser pulses are not instantaneous, and thus the measured signal T(τ) consists of a convolution of the true molecular nonlinear response with the second-order autocorrelation function of the laser pulse, G2(t):

= −


(2)

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A Fourier transform deconvolution analysis is carried out on T(τ) to remove the contribution of

σ(t). Essentially, we are interested in the imaginary part. The Fourier transform spectrum is obtained using the expression Im = Im{ / }

(3)

where F denotes the Fourier transform of a function in the time domain. In the present fs-RIKES setup (anisotropy polarization conditions), the obtained Fourier transform spectrum, Im[R(ω)], corresponds to the depolarized Raman spectrum multiplied by the Bose-Einstein thermal occupation factor.62,63 Figure 2a shows the normalized Kerr transient for [N1224][NTf2] at 293 K, as an example. The Kerr transient was normalized at t = 0. The strong intensity near t = 0 is due to the electronic response and subsequently the nuclear responses, the inter- and intra-molecular vibrations and the reorientational dynamics, appear. The Kerr transients after 3 ps were fitted by a biexponential function: + exp $− % + exp $− %

(4)

where a0 is the offset parameter, a1 and a2 are the amplitudes, and τ1 and τ2 are the relaxation time constants for the respective components. It should be noted that ILs show nanosecond-order relaxation processes.30,52,64-67 In this study, we measured the transients of the ILs for a time window of only 13.7 ps, and thus we did not capture the complete reorientational process. Nonetheless, we can adequately discuss the temperature dependence in terms of the low-frequency spectra which originate mainly from the intermolecular vibrations, as was confirmed in our previous study.53 Figure 2b shows the imaginary part of the Fourier transform of the Kerr 9 ACS Paragon Plus Environment


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transient. In this figure, we show the entire spectrum, the contribution of the slow relaxation component, and the difference spectrum obtained by subtracting the slow relaxation component from the entire spectrum. The intermolecular vibrational band in liquids and solutions, which typically appears in the region below ca. 150 cm−1, generally shows a complex spectral line shape. Because we focus on the intermolecular vibration in this study, the difference spectrum in which the slow relaxation component has been subtracted from the entire spectrum is further analyzed and discussed. Details of the line shape analysis have been described in previous reports.29,68 Briefly, we used the sum of an Ohmic function69 &' ω = ' exp −/'

(5)

where aO and ωO are the amplitude and characteristic frequency, respectively, and antisymmetrized Gaussian functions70 &*, =

∑4 5

,*, exp -

−2/ − *, 0 Δ*,

2 − *, exp -

−2/ + *, 0 Δ*,

23

(6)

where aG, ωG, and ∆ωG are the amplitude, characteristic frequency, and width parameter, respectively. The Ohmic function was used to describe depolarized Rayleigh scattering spectra of simple liquids, and was included in the fits because it is assumed to represent collision-induced motions.69 The antisymmetrized Gaussian function is assumed to model an inhomogeneously broadened intermolecular vibrational mode.70 If a clear intramolecular vibrational mode appears in the low-frequency region, a Lorentzian function


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&6 =

6

− 6 + Δ6

(7)

where aG, ωG, and ∆ωG are the amplitude, characteristic frequency, and width parameter, respectively, was used to fit it. These model functions are empirical, but can fit the low-frequency Kerr spectra of not only simple molecular liquids but also complex systems including ILs sufficiently.9,29 The results of the line shape analyses for [C4Py][NTf2] and [N1224][NTf2] are shown in Figure 3 as examples. Reasonable fits were achieved when three antisymmetrized Gaussian components were used for [C4MIm][NTf2] and [C4Py][NTf2], while one or two antisymmetrized Gaussian components were sufficient for the other ILs. On the basis of these analyses, we estimated the first moments M1, which are the characteristic frequencies of the intermolecular vibrational bands, from the low-frequency spectra from which clear intramolecular vibrational modes and picosecond overdamped relaxation components were removed from the entire spectra, defined as 7 = &/ &

(8)

where I(ω) is the frequency-dependent intensity of the spectrum from which the contributions from picosecond overdamped relaxation and clear intramolecular vibrations were subtracted.

4. RESULTS AND DISCUSSION 4.1. Temperature Dependent Low-Frequency Spectra. Figure 4 shows the Kerr transients of the ILs at 293, 308, 323, 338, and 353 K. They are the first reports of the temperature-dependent Kerr transients (and, of course, the Kerr spectra, vide 11 ACS Paragon Plus Environment


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infra) for the present ILs, except for [C4MIm][NTf2] that was previously reported by us.54 Figure 4 shows that the Kerr transients for all the present ILs are clearly temperature dependent. Namely, the amplitude of the picosecond overdamped relaxation process increases with increasing temperature, while the valleys in the early time region (faster than 1 ps), which are due to the underdamped intramolecular and intermolecular vibrational modes, become shallower with rising temperature. As mentioned in the Data Analysis section, the picosecond overdamped decays were analyzed using a biexponential function. The biexponential fit parameters are summarized in Table 1. The time constants were almost independent of temperature within the experimental errors and the fitting standard deviations, while the amplitudes for all the components increased with rising temperature. The Fourier transform Kerr spectra of the ILs, resolved up to 600 cm−1, are shown in Figure 5. Note that the contributions of the overdamped relaxation (the slower component and the offset of the biexponential fits) have been subtracted from the spectra in order to focus on the intermolecular vibrations. The spectra obtained at 293 K are similar to previously reported ones.56,57,71,72 The vibrational bands in the range of 250–370 cm−1 were assigned to the rocking of CF3 and the twisting/wagging/rocking motions of the SO2 groups of [NTf2]−.73

A close

examination of Figure 4 reveals some differences between [C4MIm][NTf2], [P2228][NTf2], and the other ILs. We will discuss this in Section 4.1.7. Figure 6 displays the magnifications of the Fourier transform Kerr spectra of the ILs in the frequency range of 0–200 cm−1. The broad band in this low-frequency region for each IL was attributed mainly to intermolecular vibration, although clear intramolecular vibrational bands are observed at ca. 121 and 168 cm−1.

All the present ILs showed temperature-dependent

low-frequency Kerr spectra. However, their temperature-dependent features were unique. We 12 ACS Paragon Plus Environment

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will discuss the temperature-dependent low-frequency spectral features based on the structures of the cations in the following section. 4.1.1. Imidazolium Cation vs. Pyrrolidinium Cation. As shown in Figure 6a and b, the spectral line shapes of [C4MIm][NTf2] and [Pyrr14][NTf2] at room temperature (293 K) are very different, although both cations are based on five-membered-rings. [C4MIm][NTf2] shows a bimodal spectrum at each temperature, while [Pyrr14][NTf2] exhibits a triangular line shape. This difference can be accounted for by the presence or absence of an aromatic ring, which gives a large contribution in the high-frequency region at ca. 100 cm−1. Such broad (and often trapezoidal) low-frequency spectral line shapes are commonly observed not only in ILs, but also in molecular liquids.9,41,45,58,74-77 Several MD simulations indicated that the aromatic ring librations (reorientational motions) in aromatic cation based ILs78,79 and aromatic molecular liquids80-83 contribute strongly to the whole low-frequency spectra but the contributions of the collision (or interaction) induced motions (translational motions) are only in the lower frequency region. Because the aromatic ring libration is a molecular reorientational vibration, the spectral density is well correlated with the molecular polarizability anisotropy.77 Therefore, the spectral densities of aromatic ILs and molecular liquids in the high frequency region, which exhibit bimodal or trapezoidal spectral line shapes, are mainly due to the aromatic ring librations. Figure 6a and b also shows that the temperature-dependent spectral features of [C4MIm][NTf2] and [Pyrr14][NTf2] differ. In the case of [C4MIm][NTf2], the spectral intensities in the low-frequency region below 50 cm−1 increase with increasing temperature, while those in the high-frequency region at approximately 100 cm−1 decrease or are shifted to lower frequency with



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rising temperature. This type of temperature dependence has been observed for imidazolium cation based ILs with various anions54 and dicationic imidazolium based ILs with the anion [NTf2]−.53 We interpreted this temperature dependent behavior as follows. The spectral change in the low-frequency region is due to the activation of the translational motions of both the cation and anion with increasing temperature, while that in the high-frequency region is mainly due to imidazolium ring librations, which slow with increasing temperature because the free volume of the ILs becomes larger and the intermolecular interactions weaken. Molecular dynamics (MD) simulations of the [C4MIm]+ based IL with the spherical top anion hexafluorophosphate also indicated that the temperature dependent features of the density of state (DOS) spectrum of the cation were in good agreement with the experimental features observed using RIKES, and that the DOS spectrum of the anion showed temperature dependent features only in the low-frequency region.54 Thus, the spectral change in the high frequency region with temperature is due to the temperature sensitivity of the aromatic ring libration, but the change in the low-frequency region includes the contributions of both the anion and cation. On the other hand, in the case of [Pyrr14][NTf2], the spectral intensity in the low-frequency region (below 50 cm−1) increases with rising temperature, while that of the high-frequency region (above 50 cm−1) is nearly insensitive to temperature. As mentioned above, the aromatic ring contributes to the temperature-dependent spectral change in the high-frequency region.

Therefore, the presence or absence of an aromatic ring determines whether

temperature-dependent features are observed in the high frequency region of the low-frequency spectra of the ILs.

As mentioned in the Introduction, the spectra of the ILs

1-cyclohexylmethyl-3-methylimidazolium

bis(trifluoromethylsulfonyl)amide

and

1-cyclohexylmethyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide exhibited the


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temperature dependence similar to that of [C4MIm][NTf2] and [Pyrr14][NTf2], respectively.55 The presence of a cyclohexylmethyl side group rather than a butyl group seemed to have little effect on the temperature-dependent features of the low-frequency spectra. In the frequency region below 50 cm−1, an increase in the spectral density with increasing temperature was observed for both the aromatic cation containing IL [C4MIm][NTf2] and the nonaromatic [Pyrr14][NTf2], as shown in Figure 6a and b. As discussed above, this was attributed to the thermal activation of the translational motions of the ion species. In this study, we determined that this temperature dependent spectral feature is common to both aromatic and nonaromatic ILs with simple linear alkyl groups. 4.1.2. Imidazolium Cation vs. Pyridinium Cation. As seen in Figure 6a and c, the spectral line shapes of [C4MIm][NTf2] and [C4Py][NTf2] are different at all the measured temperatures. The spectral intensity of [C4Py][NTf2] in the high-frequency region at ca. 80–100 cm−1 relative to the low-frequency region at ca. 20 cm-1 is greater than that of [C4MIm][NTf2] at all temperatures. This was attributed to the greater polarizability anisotropy of [C4Py]+ compared to that of [C4MIm]+.29 The temperature-dependent spectral features of both ILs are quite similar. As discussed in section 4.1.1, the librational motion of the imidazolium ring mainly affects the temperature-dependent features of the low-frequency spectra. It is reasonable to assume that the librational motion of the pyridinium ring would also make a large contribution to the temperature dependence of the low-frequency spectra, thus explaining the similar temperature dependence of the low-frequency spectra of the imidazolium and pyridinium based ILs. The spectral change in



the high frequency region at approximately 100 cm-1 with the variation of temperature for imidazolium and pyridinium is thus rather universal. 4.1.3. Pyrrolidinium Cation vs. Ammonium Cation. As shown in Figure 6b and d, the differences between the spectra of [Pyrr14][NTf2] and [N1224][NTf2] are small; however, [N1224][NTf2] shows a somewhat broader spectral line shape than of [Pyrr14][NTf2]. This can be attributed to the difference in their molecular structures: the [Pyrr14]+ cation is cyclic, while the [N1224]+ cation has a branched chain structure. Generally, chain compounds have more conformers than cyclic ones due to the lower structural hindrance, which leads to broadening of their intramolecular vibrational modes. This feature was also observed in the low-frequency spectra of oligo(ethylene glycols) compared to cyclic crown ethers.84 As seen in Figure 6c and d, the temperature-dependent spectral features of [Pyrr14][NTf2] and [N1224][NTf2] are similar, that is, the spectral intensity in the low-frequency region below 50 cm−1 increases with increasing temperature, and the intensity of the high-frequency region is almost temperature independent. The difference between the cyclic and chain structures of the cations does not seem to affect the temperature dependence strongly. Differences among cation structures in nonaromatic cation based ILs may have little effect on the temperature dependence of their low-frequency spectra when their alkyl chain lengths are short. 4.1.4. Alkyl Group Length Dependence. Comparing Figure 6d and e, the spectral line shapes of [N1224][NTf2] and [N2228][NTf2] are quite similar despite their different alkyl group lengths. Previously, we discussed the alkyl group dependence of the low-frequency spectra for aromatic cation based ILs.29 The spectral line


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shapes of 1-alkyl-3-methylimidazolium based ILs with [BF4]− anions showed the alkyl group length dependence. This was partly due to intramolecular bending modes between the alkyl groups and the imidazolium ring, whose frequencies depend on their length and weight. On the other hand, in this study, no apparent differences were observed between butyl ([N1224]+) and octyl ([N2228]+) groups. Upon close examination, the spectra of [N2228][NTf2] were slightly broader than those of [N1224][NTf2], which could be due to the fact that longer alkyl chains have more conformers than shorter ones. A plausible reason for the clearer alkyl group length dependence of the low-frequency spectra of imidazolium cation based ILs compared to ammonium-based ILs is that the intramolecular bending mode between the polarizable imidazolium ring and the alkyl group located in the low-frequency region below 150 cm−1 is relatively stronger than the low-frequency intramolecular vibrational modes of ammonium cations. The temperature-dependent features of these ILs were similar. Thus, increasing the length of the alkyl side chain of the ammonium cation from a butyl to an octyl group had little influence on the temperature-dependent low-frequency spectral features. This may be rather surprising, because many physical properties of ILs, such as the melting point, viscosity, and surface tension, depend strongly on the alkyl group.33 However, the difference between the butyl and octyl groups is probably not great enough to affect the temperature dependence of the intermolecular vibrational band, because the difference in the alkyl group length is not very large. 4.1.5. Ammonium Cations vs. Phosphonium Cations. Figure 6e and f shows a clear difference in the spectral shapes of [N2228][NTf2] and [P2228][NTf2] in the high-frequency region, that is, the spectral intensity in the frequency range of 70–200 cm−1 relative to the peak intensity at ca. 20 cm−1 is greater for [P2228][NTf2] than



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[N2228][NTf2] at all measured temperatures. The spectra of [P2228][NTf2] has been reported to have greater contributions from intramolecular vibrations in the region of 150 cm−1 compared to [N2228][NTf2].57

ILs

based

on

a

different

phosphonium

cation,

(2-ethoxyethoxy)ethyltriethylphosphonium, showed intramolecular vibrational modes of the cation at ca. 140 and 180 cm-1, while these bands were not observed in ILs of an ammonium cation having the same functional groups ((2-ethoxyethoxy)ethyltriethylammonium).57

Thus,

phosphonium cations likely possess lower frequency intramolecular vibrational modes than the corresponding ammonium cations with same functional groups. In terms of the temperature-dependent spectral features, [N2228][NTf2] and [P2228][NTf2] show similar temperature dependence, as do [Pyrr14][NTf2] and [N1224][NTf2]. The effects of the center atoms of the cations on the temperature dependence of the low-frequency spectral shapes seem to be very small. 4.1.6. Molecular Liquids. We also characterized the temperature-dependent low-frequency spectra of molecular liquids that are analogues of the cations of the ILs used in this study in order to determine whether the temperature-dependent spectral features of the ILs are unique to ILs or general for all liquids. Figure 7 shows the temperature-dependent

spectra of 1-methylimidazole, pyridine,

1-methylpyrrolidine, and butyldiethylamine, which are analogues of the imidazolium, pyridinium, pyrrolidinium, and ammonium cations, respectively. Note that the time-domain data of the molecular liquids are summarized in the Supporting Information. Also note that like the IL spectra, the spectra of the molecular liquids do not include the slow overdamped relaxation process. 1-Methylimidazole and pyridine have trapezoidal spectral shapes, while those of the


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1-methylpyrrolidine and butyldiethylamine are monomodal or triangular. As reported previously, aromatic molecular liquids generally show trapezoidal or bimodal spectra due to the librational motions of the aromatic rings, which provide large contributions to the high-frequency region of the low-frequency spectral bands.9,41,45,58,74-77 The spectra of 1-methylimidazole and pyridine show the temperature dependence in both the low- and high-frequency region, similar to [C4MIm][NTf2] and [C4Py][NTf2]. On the other hand, only the low-frequency region below 50 cm−1 is temperature dependent for 1-methylpyrrolidine and butyldiethylamine, similarly to [Pyrr14][NTf2] and [N1224][NTf2] (as well as [N2228][NTf2] and [P2228][NTf2]). This implies that the presence or absence of an aromatic ring is critical in determining the temperature-dependent features of the low-frequency spectra, especially in the high frequency region above 50 cm−1, in both ILs and molecular liquids. 4.1.7. Intramolecular Vibrational Bands. Figure 5 shows evident intramolecular vibrational bands at 250–370 cm−1 for all the present ILs. Figure 8 shows magnifications of the spectra at 293 K to focus on these vibrational modes of the ILs, which originate from the [NTf2]− anion. [NTf2]− has two stable conformers, cisoid and transoid forms, and their conformational changes influence the spectral shapes in this region. The bands numbered 2, 5, 6, and 8 originate purely from the cisoid from, those numbered 3 and 7 originate solely from the transoid form, and 1 and 4 are overlapped cisoid and transoid bands.56,73 It is noteworthy that the relative intensities of these vibrational bands are slightly different among the present ILs. For example, for [P2228][NTf2], the intensity of band 6 is high relative to band 5 and the band 7. In the case of the [Pyrr14][NTf2], the intensity of band 3 is high in relative to band 4. The relative intensities of these bands are not correlated to the intensities of other bands originating from the same conformer. We also note that the intramolecular vibrational 19 ACS Paragon Plus Environment


modes of all the present cations likely occur in the frequency range of 250–370 cm−1, similarly to that of [C4MIm]+.29 Therefore, we conclude that the different relative intensity patterns for the present ILs are not due to different populations of the cisoid and transoid forms of the anion, but caused by the presence of the intramolecular vibrational modes of cations. Figure 9 shows the spectra of the ILs in the frequency range 250–370 cm−1 at various temperatures, which clearly demonstrate that the spectral changes in the frequency range 250–370 cm−1 are similar for all the ILs. The intensities of the bands 3 and 7 decrease, while those of the bands 2 and 6 increase with increasing temperature. The equilibrium between the two conformers changes with temperature, and thus the spectra in the 250–370 cm−1 range are temperature-dependent, as has been discussed previously.53 At higher temperature, the population of the cisoid form increases, while that of transoid form decreases. The temperature sensitivity of the population ratio of the anion conformers seems to be similar among all the present ILs. 4.2. Temperature Dependence of the First Moment. On the basis of the analytical procedure described in Section 3, we performed line shape analysis of the low-frequency spectra and estimated the M1 values of the low-frequency spectra for the ILs. The fit results, fit parameters, and values of M1 for the ILs and molecular liquids are summarized in the Supporting Information.

To understand the quantitative features of the

temperature dependence of the low-frequency spectra, plots of M1 vs. temperature for the ILs and cation analogue molecular liquids are shown in Figure 10. The linear fits, given by M1(T) = aT + M1,0, where T is the absolute temperature, a is the slope, and M1,0 is the intercept of the relation, are also indicated in the figure. These fit parameters are summarized in Table 2. From the figure and the table, the ILs indicate the smaller variation of the slopes than the molecular liquids. However,


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if we closely look at the data of the ILs, [C4MIm][NTf2] and [C4Py][NTf2] show slightly larger slopes than [Pyrr14][NTf2], [N1224][NTf2], and [N2228][NTf2]. The increase in the spectral intensity in the low-frequency region of less than 50 cm−1 with rising temperature makes the larger spectral fraction in the low-frequency region. This provides a reduction of the M1. In addition, the slowing of the librational motions of the aromatic rings reflects the red shifts of the high frequency component of the broad low-frequency spectrum bands, which also lowers M1 as the area ratio of the higher-frequency region decreases.

As a result, the changes of the first moments of

[C4MIm][NTf2] and [C4Py][NTf2] are larger than those of the pyrrolidinium and ammonium based ILs. Of course, the intrinsic first moment M1,0 is larger for the aromatic cation based ILs than the nonaromatic cation based ILs because of the presence of an aromatic ring. Another significant point is that the slope for [P2228][NTf2] was even greater than those of the aromatic cation based ILs, although [P2228]+ is a nonaromatic cation. As discussed in Section 4.1.5, [P2228][NTf2] showed greater intramolecular vibration components in the region of 150 cm−1 than [N2228][NTf2].57 We removed the contributions of the intramolecular vibrations in the estimation of M1 by fitting these components using Lorentzian functions, nonetheless the line shape fits are likely imperfect because of the broadness of these intramolecular vibrational bands and strong overlaps in this frequency region.

On the other hand, we also note that the

intermolecular interactions between the cation and anion are very different for [P2228][NTf2] and [N2228][NTf2].85 It is thus not surprising that they show different temperature dependence in the low-frequency spectral band. At the moment, we cannot clearly conclude the origin of the steeper slope of [P2228][NTf2] compared to the other nonaromatic cation based ILs, because there are two possibilities: the temperature dependence of the purely “intermolecular” vibration for the phosphonium cation based IL and/or the effect of the temperature dependence of the



Page 22 of 55

“intramolecular” vibrational bands of the phosphonium cation. In contrast to the ILs, each molecular liquid shows unique a and M1,0 values whether it is aromatic or nonaromatic.

The results indicate that the temperature sensitivity of the

low-frequency spectrum in the ILs is more affected by the ionic nature (Coulomb interaction) but less influenced by the structure of cation (except for the difference in aromaticity of cation) than that in the neutral molecular liquids. 4.3. Temperature-Dependent Viscosities. The viscosities of ILs are well-known to vary drastically with temperature.86 Thus, it is valuable to discuss the relationship between the temperature dependence of the intermolecular vibrational spectra and the temperature-dependent viscosities of the ILs. Figure 11 shows the temperature dependence of η for the ILs. The values at 293, 308, 323, 338, and 353 K are summarized in Table 1 for a comparison with the fs-RIKES results, and all data are listed in the Supporting Information. The viscosities of ILs generally show a non-Arrhenius dependence on temperature. Instead, the Vogel-Tammann-Fulcher (VTF) equation87-90 is commonly used to fit the temperature dependence of the η values of ILs,86 and is given by 8 = 8 exp 9

:

−

;

(8)

where T is the absolute temperature, η0 is the reference viscosity at which the exponential term approaches unity, D is a fragility related parameter, and T0 is the characteristic temperature at which η diverges. The collected data were fitted using the logarithmic form of eq. 8, ln[η(T)] = ln(η0) + [DT0/(T–T0)], to properly treat the η data spanning several orders of magnitude.91 Each


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data set includes the value of 1×1013 cP at the Tg of the liquid, according to the method of Angell and coworkers,86 in order to estimate the fit parameters more precisely. The Tg values for each IL were taken from previous reports.54,57,92-94 The VTF fitting parameters are summarized in Table 3. The D parameter is a measure of the liquid fragility, which denotes the degree of deviation of the temperature-dependent viscosity from Arrhenius-type behavior.95 Liquids with smaller D values are said to be more fragile, which means that their viscosities increase rapidly near the glass transition, while liquids with larger D values are said to be stronger. Among the studied ILs, the aromatic cation based ILs show smaller D values than the nonaromatic cation based ILs. A similar trend was reported previously: the fragilities of imidazolium, pyridinium, and ammonium cation based ILs were compared, and the pyridinium cation had the largest fragility, although a different type of anion, [BF4]−, was used.86

Among the nonaromatic ILs, the

ammonium cation based ILs showed larger D values than the pyrrolidinium and phosphonium cation based ILs. This might be related to the lower viscosities of the phosphonium-cation based ILs compared to the respective ammonium-cation based ILs.57,96,97 Focusing on the relationship between the temperature dependence of the low-frequency spectra and the D parameters, the ILs with larger a and M1,0 values show smaller D values. Both features can be attributed to the presence of aromatic cations. However, like imidazolium based ILs with a variety of anions,54 it is not confirmed the clear direct correlation between the temperature sensitivity (the slope a in Figure 10) of the M1 and the D parameter for the ILs studied here.

5 CONCLUSIONS



In this study, we investigated the temperature dependence of the low-frequency spectra of [NTf2]− salts with a wide variety of cations using fs-RIKES to elucidate the effects of the cation structures on the temperature-dependent spectral features. For the aromatic cation based ILs, the spectral intensities in the frequency region below 20 cm−1 increased with increasing temperature due to the activation of the translational vibrational motions of the ions at higher thermal energies. In addition, the high-frequency components above 80 cm−1 shifted to lower frequency with rising temperature, which was attributed to the slower librational motion of the aromatic ring due to the larger free volume and the weaker intermolecular interaction at higher temperature. On the other hand, in the case of the nonaromatic cation based ILs, the spectral intensities in the frequency region below 50 cm−1 increased with rising temperature; however, the intensities in the frequency region above 50 cm−1 showed little change. Furthermore, molecular liquids with structures similar to the cations of the ILs also showed temperature-dependent spectra, with spectral changes appearing in both the low- and high-frequency regions for 1-methylimidazole and pyridine, while only the low-frequency region below 50 cm−1 was temperature dependent for 1-methylpyrrolidine and butyldiethylamine. Thus, we concluded that the presence or absence of an aromatic ring determined the temperature-dependent features of the intermolecular vibrational spectra in both the ILs and molecular liquids. The M1 values were slightly more sensitive to temperature for the aromatic cation based ILs than the nonaromatic cation based ILs. In contrast, each molecular liquid shows a unique temperature sensitivity to the M1 value. The fragility related parameter D was smaller for the aromatic cation based ILs than for the nonaromatic cation based ILs, which is consistent with previous reports. Thus, the presence or absence of an aromatic ring in the ILs governed both their temperature-dependent spectral features and their liquid properties.


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Supporting Information Details of synthesis procedures of ILs synthesized in this study, line shape analysis results of Kerr spectra of ILs, temperature dependent Kerr transients of molecular liquids, lists of fit parameters for the Kerr transients of molecular liquids, line shape analysis results of the Kerr spectra of ILs and molecular liquids, and temperature-dependent viscosity data of ILs. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENTS This work was partially supported by JSPS KAKENHI (15K05377) and Chiba University (Global Prominent Research Program: Soft Molecular Activation). SK is also supported by JSPS Research Fellowship for Young Scientists (18J12979).



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TABLE 1. Biexponential Fit Parameters for Kerr Transients and Viscosities η of ILs at Various Temperatures. Temperature (K)

a0

293 308 323 338 353

0.0009 0.0010 0.0012 0.0014 0.0015

293 308 323 338 353

0.0004 0.0004 0.0004 0.0006 0.0007

293 308 323 338 353

0.0012 0.0016 0.0020 0.0020 0.0023

293 308 323 338 353

0.0002 0.0003 0.0004 0.0004 0.0005

293 308 323 338 353

0.0002 0.0003 0.0003 0.0003 0.0004

293 308 323 338 353

0.0003 0.0003 0.0004 0.0004 0.0004

a1 τ1 (ps) [C4MIm][NTf2] 0.0103 1.30 0.0134 1.20 0.0121 1.32 0.0120 1.36 0.0144 1.33 [Pyrr14][NTf2] 0.0101 0.93 0.0102 0.95 0.0109 0.94 0.0116 1.00 0.0126 0.94 [C4Py][NTf2] 0.0138 1.26 0.0159 1.26 0.0152 1.37 0.0203 1.22 0.0172 1.38 [N1224][NTf2] 0.0192 0.75 0.0230 0.78 0.0185 0.82 0.0251 0.77 0.0224 0.82 [N2228][NTf2] 0.0079 0.80 0.0106 0.78 0.0141 0.79 0.0137 0.82 0.0145 0.83 [P2228][NTf2] 0.0095 0.78 0.0095 0.80 0.0112 0.77 0.0136 0.71 0.0148 0.72

a2

τ2 (ps)

η (cP)

0.0030 0.0038 0.0045 0.0051 0.0058

8.24 8.17 8.23 8.23 8.29

62.3 32.0 19.2 12.4 8.58

0.0014 0.0017 0.0020 0.0021 0.0025

7.01 6.91 6.98 6.84 6.47

97.1 48.2 27.5 17.4 11.7

0.0044 0.0052 0.0060 0.0077 0.0082

7.18 7.17 7.14 7.30 7.20

73.4 37.0 21.6 13.8 9.50

0.0014 0.0015 0.0019 0.0023 0.0024

6.85 7.57 6.79 6.94 7.21

161 69.1 35.1 20.7 13.2

0.0009 0.0011 0.0012 0.0015 0.0017

7.03 6.92 7.11 7.38 7.21

313 126 58.0 31.3 18.9

0.0010 0.0012 0.0014 0.0018 0.0020

6.52 6.72 5.89 5.27 5.46

146 67.7 35.0 20.9 13.3


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TABLE 2. Linear Fit Parameters for Temperature Dependent First Moments M1 for ILs and Cation Analogue Molecular Liquids. a (cm−1 K−1)

M1,0 (cm−1)

[C4MIm][NTf2]

−0.0495 ± 0.0025

80.7 ± 0.8

[Pyrr14][NTf2]

−0.0381± 0.0028

57.7± 0.9

[C4Py][NTf2]

−0.0493± 0.0008

82.5± 0.3

[N1224][NTf2]

−0.0434± 0.0045

62.6± 1.4

[N2228][NTf2]

−0.0459± 0.0029

63.2± 1.0

[P2228][NTf2]

−0.0513± 0.0020

69.4± 0.6

1-Methylimidazole

−0.0560± 0.0009

85.4± 0.3

Pyridine

−0.0235± 0.0016

68.0± 0.5

1-Methylpyrrolidine

−0.0427± 0.0064

63.8± 2.0

Butyldiethylamine

−0.0603± 0.0061

76.5± 2.0

Sample

39 Environment ACS Paragon Plus


Page 40 of 55

TABLE 3. Glass Transition Temperature Tg and VTF Fit Parameters for ILs IL

Tg (K)

ln(η0) (ln(cP))

D

T0 (K)

[C4MIm][NTf2]

183a

−2.317

5.664

155.7

[Pyrr14][NTf2]

184b

−2.525

6.458

153.5

c

−1.798

4.159

174.2

[N1224][NTf2]

180

d

−4.085

10.26

138.3

[N2228][NTf2]

196e

−3.441

7.715

159.4

[P2228][NTf2]

192e

[C4Py][NTf2]

a

Reference 54.

197

b

Reference 93.

−2.671 c

Reference 94.

6.312 d

Reference 92.


160.5 e

Reference 57.

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Figure Captions.

Figure 1. Structural formulas of cations and anion of ILs used in this study.

Figure 2. (a) Normalized Kerr transient of [N1224][NTf2] at 293 K. Biexponential fit is indicated by blue line. (b) Fourier-transform Kerr spectra of [N1224][NTf2] at 293 K. Black line denotes the entire spectrum, blue line denotes the contribution of the slow relaxation component, and red line denotes the spectrum subtracted the slow relaxation component from the entire spectrum.

Figure 3. Line shape analysis results of the low-frequency spectra of (a) [C4Py][NTf2] at 293 K, (b) [C4Py][NTf2] at 353 K, (c) [N1224][NTf2] at 293 K, and (d) [N1224][NTf2] at 353 K. Black dots denote the experimentally obtained data.

Green, blue, and orange areas denote Ohmic,

antisymmetrized Gaussian, and Lorentzian functions, respectively. Red lines denote the entire fit. Dashed red lines denote the sum of the Ohmic and the antisymmetrized Gaussian functions.

Figure 4.

Log–log plots of Kerr transients for (a) [C4MIm][NTf2], (b) [Pyrr14][NTf2], (c)

[C4Py][NTf2], (d) [N1224][NTf2], (e) [N2228][NTf2], and (f) [P2228][NTf2] at 293 K (black), 308 K (blue), 323 K (green), 338 K (yellow), and 353 K (red).

Figure 5.

Low-frequency Kerr spectra in the frequency range of 0–600 cm−1 for (a)

[C4MIm][NTf2], (b) [Pyrr14][NTf2], (c) [C4Py][NTf2], (d) [N1224][NTf2], (e) [N2228][NTf2], and (f) [P2228][NTf2] at 293 K (black), 308 K (blue), 323 K (green), 338 K (yellow), and 353 K (red).



Figure 6.



Figure 7.


1-methylimidazole, (b) pyridine, (c) 1-methylpyrrolidine, and (d) butyldiethylamine at 293 K (black), 308 K (blue), 323 K (green), 338 K (yellow), and 353 K (red).

Figure 8. Low-frequency Kerr spectra in the frequency range of 250–370 cm−1. From top to bottom, [C4MIm][NTf2], [Pyrr14][NTf2], [C4Py][NTf2], [N1224][NTf2], [N2228][NTf2], and [P2228][NTf2] at 293 K.

Figure 9.



Figure 10.

Plots of first moments vs. temperature for (a) [C4MIm][NTf2] (black circles),

[Pyrr14][NTf2] (green squares), [C4Py][NTf2] (red left-pointing triangles), [N1224][NTf2] (yellow triangles), [N2228][NTf2] (blue crosses) , and [P2228][NTf2] (purple right-pointing triangles) and (b) 1-methylimidazole (black circles), pyridine (red left-pointing triangles), 1-methylpyrrolidine (green squares), and butyldiethylamine (yellow triangles). Solid lines denote linear fits.


Page 42 of 55

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Figure 11.

(a) Temperature-dependent viscosities for [C4MIm][NTf2] (black circles),

[Pyrr14][NTf2] (green squares), [C4Py][NTf2] (red left-pointing triangles), [N1224][NTf2] (yellow triangles), [N2228][NTf2] (blue crosses) , and [P2228][NTf2] (purple right-pointing triangles). (b) VTF fits including the shear viscosity value of 1013 cP at the glass transition temperature are shown.



Figure 1. Structural formulas of cations and anion of ILs used in this study.


Page 44 of 55

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Figure 2. (a) Normalized Kerr transient of [N1224][NTf2] at 293 K. Biexponential fit is indicated by blue line. (b) Fourier-transform Kerr spectra of [N1224][NTf2] at 293 K. Black line denotes the entire spectrum, blue line denotes the contribution of the slow relaxation component, and red line denotes the spectrum subtracted the slow relaxation component from the entire spectrum.



Figure 3. Line shape analysis results of the low-frequency spectra of (a) [C4Py][NTf2] at 293 K, (b) [C4Py][NTf2] at 353 K, (c) [N1224][NTf2] at 293 K, and (d) [N1224][NTf2] at 353 K. Black dots denote the experimentally obtained data.

Green, blue, and orange areas denote Ohmic,

antisymmetrized Gaussian, and Lorentzian functions, respectively. Red lines denote the entire fit. Dashed red lines denote the sum of the Ohmic and the antisymmetrized Gaussian functions.


Page 46 of 55

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Figure 4.

Log–log plots of Kerr transients for (a) [C4MIm][NTf2], (b) [Pyrr14][NTf2], (c)

[C4Py][NTf2], (d) [N1224][NTf2], (e) [N2228][NTf2], and (f) [P2228][NTf2] at 293 K (black), 308 K (blue), 323 K (green), 338 K (yellow), and 353 K (red).



Figure 5.




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Figure 6.





Figure 7.


1-methylimidazole, (b) pyridine, (c) 1-methylpyrrolidine, and (d) butyldiethylamine at 293 K (black), 308 K (blue), 323 K (green), 338 K (yellow), and 353 K (red).


Page 50 of 55

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Figure 8. Low-frequency Kerr spectra in the frequency range of 250–370 cm−1. From top to bottom, [C4MIm][NTf2], [Pyrr14][NTf2], [C4Py][NTf2], [N1224][NTf2], [N2228][NTf2], and [P2228][NTf2] at 293 K.



Figure 9.




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Figure 10.

Plots of first moments vs. temperature for (a) [C4MIm][NTf2] (black circles),

[Pyrr14][NTf2] (green squares), [C4Py][NTf2] (red left-pointing triangles), [N1224][NTf2] (yellow triangles), [N2228][NTf2] (blue crosses) , and [P2228][NTf2] (purple right-pointing triangles) and (b) 1-methylimidazole (black circles), pyridine (red left-pointing triangles), 1-methylpyrrolidine (green squares), and butyldiethylamine (yellow triangles). Solid lines denote linear fits.



Figure 11.

(a) Temperature-dependent viscosities for [C4MIm][NTf2] (black circles),

[Pyrr14][NTf2] (green squares), [C4Py][NTf2] (red left-pointing triangles), [N1224][NTf2] (yellow triangles), [N2228][NTf2] (blue crosses) , and [P2228][NTf2] (purple right-pointing triangles). (b) VTF fits including the shear viscosity value of 1013 cP at the glass transition temperature are shown.


Page 54 of 55

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TOC Graphic. Kakinuma and Shirota.


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