Local structures in ionic liquids probed and characterized by microscopic thermal
diffusion monitored with picosecond time-resolved Raman spectroscopy
Kyousuke Yoshida, Koichi Iwata, Yoshio Nishiyama, Yoshifumi Kimura, and Hiro-o Hamaguchi
Citation: The Journal of Chemical Physics 136, 104504 (2012); doi: 10.1063/1.3691839
View online: http://dx.doi.org/10.1063/1.3691839
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/136/10?ver=pdfcov Published by the AIP Publishing
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Local structures in ionic liquids probed and characterized
by microscopic thermal diffusion monitored with picosecond
time-resolved Raman spectroscopy
Kyousuke Yoshida,1Koichi Iwata,2,a)Yoshio Nishiyama,3,b) Yoshifumi Kimura,3
and Hiro-o Hamaguchi1,4,a)
1Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,
Tokyo 113-0033, Japan
2Department of Chemistry, Faculty of Science, Gakushuin University, Mejiro 1-5-1, Toshima-ku,
Tokyo 171-8588, Japan
3Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
4Institute of Molecular Science and Department of Applied Chemistry, National Chiao Tung University, 1001
Ta Hsueh Road, Hsinchu 300, Taiwan
(Received 8 December 2011; accepted 10 February 2012; published online 8 March 2012)
Vibrational cooling rate of the first excited singlet (S1) state of trans-stilbene and bulk thermal
diffu-sivity are measured for seven room temperature ionic liquids, C2mimTf2N, C4mimTf2N, C4mimPF6,
C5mimTf2N, C6mimTf2N, C8mimTf2N, and bmpyTf2N. Vibrational cooling rate measured with
picosecond time-resolved Raman spectroscopy reflects solute-solvent and solvent-solvent energy transfer in a microscopic solvent environment. Thermal diffusivity measured with the transient grat-ing method indicates macroscopic heat conduction capability. Vibrational coolgrat-ing rate of S1
trans-stilbene is known to have a good correlation with bulk thermal diffusivity in ordinary molecular liquids. In the seven ionic liquids studied, however, vibrational cooling rate shows no correlation with thermal diffusivity; the observed rates are similar (0.082 to 0.12 ps−1in the seven ionic liquids and 0.08 to 0.14 ps−1in molecular liquids) despite large differences in thermal diffusivity (5.4–7.5 × 10−8 m2 s−1 in ionic liquids and 8.0–10 × 10−8 m2 s−1 in molecular liquids). This finding is
consistent with our working hypothesis that there are local structures characteristically formed in ionic liquids. Vibrational cooling rate is determined by energy transfer among solvent ions in a lo-cal structure, while macroscopic thermal diffusion is controlled by heat transfer over boundaries of local structures. By using “local” thermal diffusivity, we are able to simulate the vibrational cooling kinetics observed in ionic liquids with a model assuming thermal diffusion in continuous media. The lower limit of the size of local structure is estimated with vibrational cooling process observed with and without the excess energy. A quantitative discussion with a numerical simulation shows that the diameter of local structure is larger than 10 nm. If we combine this lower limit, 10 nm, with the upper limit, 100 nm, which is estimated from the transparency (no light scattering) of ionic liquids, an order of magnitude estimate of local structure is obtained as 10 nm < L < 100 nm, where L is the length or the diameter of the domain of local structure. © 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3691839]
I. INTRODUCTION
It is gradually being accepted that room temperature of ionic liquids tend to form specific local structures that are not common in ordinary molecular liquids.1This tendency is
con-sistent with the fact that ionic liquids are composed solely of ions and that long range Coulombic interaction is domi-nantly working between ions. Information on these possible local structures in ionic liquids has been collected by Raman spectroscopy,1x ray diffraction,2–5 neutron scattering,6,7
dif-fusion measurement,8,9 acoustic velocity measurement,10 or
molecular dynamics simulation.11–15 If there are local
struc-a)Authors to whom correspondence should be addressed. Electronic addresses: koichi.iwata@gaskushuin.ac.jp and hhama@chem.s.u-tokyo. ac.jp.
b)Present address: Department of Photo-Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan.
tures formed in ionic liquids, resultant inhomogeneity is likely to cause discord between microscopic properties determined within a local structure and macroscopic properties measured as a bulk material. In fact, microscopic viscosity determined by the photoisomerization rate of S1 trans-stilbene does not
accord with macroscopic shear viscosity in ionic liquids, al-though these two quantities show clear linear relationship in molecular liquids.16 This observation was one of the
earli-est alerts concerning the discord between microscopic and macroscopic properties in ionic liquids.
Thermal diffusion may also be significantly affected by local structure formation. It is controlled by thermal conduc-tivity and heat capacity of a matter, both of which depend on local as well as bulk structures in different fashions. Macro-scopic thermal diffusion can be precisely observed by the transient grating (TG) method.17 In this method, two pulsed laser beams crossing at a sample liquid containing a probe
0021-9606/2012/136(10)/104504/8/$30.00 136, 104504-1 © 2012 American Institute of Physics
104504-2 Yoshidaet al. J. Chem. Phys. 136, 104504 (2012)
dye form a periodic interference pattern. The light energy absorbed by the dye molecules is eventually converted to heat. It increases the temperature of the sample liquid, or changes its refractive index, according to the formed interference pat-tern of the two laser beams. The periodic patpat-tern of the in-dex functions as a temporarily evolving grating as the gen-erated heat dissipates. It is therefore possible to observe the heat diffusion process by monitoring the time dependence of the probe light intensity diffracted by the grating. Spacing of the interference pattern used by the transient grating method is on the order of laser wavelength or longer. The heat diffu-sion measured by the transient grating method thus represents thermal diffusion of the sample liquid for a micrometer re-gion or larger. Microscopic energy transfer within the range of a few or a few tens of nanometers can be observed by the vibrational cooling process of the S1(the first excited singlet)
state of trans-stilbene with picosecond time-resolved Raman spectroscopy.18,19 When trans-stilbene is photo-excited with an excess energy, hot S1trans-stilbene is formed and it starts
cooling down immediately. The cooling process, proceeding in approximately 10 ps, is observed with the peak position of the 1570-cm−1 Raman band of S1trans-stilbene. It has been
shown by us that the position of the 1570-cm−1band is a lin-ear function of temperature. We use this band as a “picosec-ond Raman thermometer”. The vibrational cooling rate of S1
trans-stilbene thus observed by picosecond time-resolved Ra-man spectroscopy shows a good correlation with bulk thermal diffusivity for ten molecular liquids. In these liquids, the vi-brational cooling rate of S1 trans-stilbene, which represents
microscopic solvation environments, is well accounted for by bulk thermal diffusivity.
In this article, we report on the observation of vibrational cooling process of S1trans-stilbene in seven ionic liquids. We
compare the observed cooling rates with thermal diffusivi-ties determined by the transient grating method. The results from two different experiments are explained if and only if we assume the presence of local structures in ionic liquids. We compare the observed cooling kinetics and a numerical model simulation with the diffusion equation of heat to esti-mate the size of local structure. A preliminary result for two ionic liquids has already been reported in a letter.20
II. EXPERIMENTAL SETUP
We use a picosecond time-resolved Raman spectrom-eter with two independently tunable light sources for the pump and probe pulses.20,21 The output from a
femtosec-ond mode-locked Ti:sapphire oscillator (Coherent, Vitesse, wavelength 800 nm, repetition rate 80 MHz, pulse dura-tion 120 fs, average power 250 mW) was amplified by a Ti:sapphire regenerative-multipass amplifier (Quantronix In-tegra 2.5, wavelength 800 nm, repetition rate 1 kHz, pulse duration 2 ps, pulse energy 2.0 mJ). A half of the ampli-fied pulse was separated and delivered to a β-barium bo-rate crystal. The frequency-doubled output from the crystal pumped an optical parametric amplifier (OPA) (Light Con-version, TOPAS 4/400) to generate Raman probe pulses of 592 nm. The residual of the 800 nm amplified pulse pumped another OPA (Light Conversion, TOPAS 4/800), which gen-erated the pump pulse of 296 nm or 325 nm. For determining
precise Raman band positions in excess energy dependence measurements, we constructed a 4-f band pass filter that im-proved spectral resolution. The configuration of the 4-f band pass filter and its performance will be reported elsewhere.22 Spectral and time resolution were set to 8 cm−1and 4.0 ps, re-spectively, with the band pass filter. Wavelength of the pump pulse was set to 296 and 325 nm, corresponding to the excess energy of 2500 and 0 cm−1, respectively.
The pump and probe pulses, traveling a common light path after a dichroic mirror, were focused onto the sample solution, which was held in a rotating quartz cell or was cir-culated through a dye laser jet nozzle. The pump and probe pulse energies at the sample point were 0.50 and 0.25 μJ, respectively. Rayleigh scattering and fluorescence in the ul-traviolet region were eliminated by an optical narrow band-rejection filter (Kaiser Optical Systems, Notch filter) and an optical color filter. Scattered light was dispersed by a single imaging spectrograph (Horiba Jobin Yvon, Triax-320) and detected by a liquid-nitrogen cooled CCD detector (Prince-ton Instruments, Spec 10:400B/LN). Time resolution of this apparatus estimated by the rise time of Sn-S1 absorption of
trans-stilbene was 2.2 ps. The spectral resolution with a slit width of 100 μm was 13 cm−1.
Sample of trans-stilbene was purchased from Wako Chemicals (special grade) and was recrystallized from eth-anol. C4mimTf2N (1-butyl-3-methylimidazolium
bis(trifluo-romethylsulfonyl)amide, lot number 609041) was purchased from Kanto Chemical Co., Inc. BmpyTf2N
(1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide) and C4mimPF6 (1-butyl-3-methylimidazolium
hexafluoropho-sphate) were purchased from Fluka and used without further purification. C2mimTf2N
(1-ethyl-3-methylimidazo-lium bis(trifluoromethylsulfonyl)amide), C5mimTf2N
(1-pen-tyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide), C6mimTf2N (1-hexyl-3-methylimidazolium
bis(trifluoro-methylsulfonyl)amide), and C8mimTf2N
(1-octyl-3-methy-limidazolium bis(trifluoromethylsulfonyl)amide) were syn-thesized by previously reported method.23 The ionic liquid
samples were evacuated by a diffusion pump for 2 h or longer for removing water before Raman measurements. Concentration of trans-stilbene was 5.0× 10−3mol dm−3.
The experimental setup for the TG method has been de-scribed in Ref. 24. As the photo-absorbing solute molecule, we used malachite green. The 532 nm second harmonic of a Nd:YAG laser (Spectra-physics GCR-170-10) was used as the excitation pulse. This excitation pulse was split by a beam splitter and crossed into a sample solution with a fixed angle. At the same time, a diode laser beam (780 nm) was brought into the sample solution with an angle which satisfied the Bragg condition. The diffracted probe beam (TG signal) was detected by a photomultiplier tube (Hamamatsu R928) and averaged by a digital oscilloscope (Tektronix TDS-5054).
III. RESULTS AND DISCUSSION
A. Vibrational cooling process and ultrafast solute-solvent energy transfer
Time-resolved Raman spectra of S1 trans-stilbene were
FIG. 1. Transient Raman spectrum of S1trans-stilbene in C5mimTf2N at 10 ps (solid line) and Lorentz function best fitted to the 1570-cm−1band (open
circle). Raman probe and pump wavelengths are 592 and 296 nm, respectively.
20, 30, 50, 70, and 100 ps. Transient Raman spectrum ob-served at each time delay agreed with the spectra measured in molecular solvents.25–27 The transient Raman spectrum
of S1 trans-stilbene in C5mimTf2N at 10 ps is shown in
Figure1. Shot noise resulting from fluorescence was larger in ionic liquids than in molecular solvents. It was possible, how-ever, to determine the exact peak position of the 1570-cm−1 Raman band, which corresponds to the central C=C stretch vibration of S1 trans-stilbene. The position of this band is
used as “picosecond Raman thermometer” as described in more details later. The observed 1570-cm−1 Raman band in ionic liquids is fitted well by a single Lorentz function, as was the case in molecular liquids. The uncertainty of fitted band position was 0.3 cm−1.
Time dependence of the peak position of the 1570-cm−1 Raman band represents the vibrational cooling process of S1
trans-stilbene after photoexcitation with an excess energy. The peak position determined from the fitting analysis is plotted against time delay in Figure2(a). The peak position changes from 1567 to 1573 cm−1as time delay increases. As already shown, the peak position of the 1570 cm−1 changes linearly with temperature and is used as a thermometer with a picosecond time resolution.18 The time dependence shown
in Figure2(b)indicates that the cooling kinetics of S1
trans-stilbene in C5mimTf2N is very similar to that observed in
molecular liquids; this decay curve is well fitted by a single exponential function with a rate constant of 0.11 ps−1. The single exponential function serves as a simple model function that characterizes the cooling kinetics with a single time con-stant.
B. Comparison of vibrational cooling rate with thermal diffusivity
We compare here the observed vibrational cooling rates with thermal diffusivities of ionic liquids measured by the transient grating method.17 The observed vibrational cooling rates are plotted against thermal diffusivities in Figure3, together with the corresponding results for molecu-lar liquids. The vibrational cooling rates in molecumolecu-lar liquids show a good correlation with thermal diffusivities as reported earlier.18The observed cooling rate in ionic liquids, however,
ranges from 0.082 to 0.12 ps−1and are similar with those ob-served in molecular liquids, although thermal diffusivities of ionic liquids (5.4 × 10−8 to 7.5× 10−8 m2 s−1) are
obvi-ously smaller than those of molecular liquids (8.0× 10−8 to
FIG. 2. Time-resolved Raman spectra of S1trans-stilbene in C5mimTf2N (a), and time dependence of the peak position of the 1570-cm−1Raman band (b).
Raman probe and pump wavelengths are 592 and 296 nm, respectively.
104504-4 Yoshidaet al. J. Chem. Phys. 136, 104504 (2012)
FIG. 3. Vibrational cooling rate vs thermal diffusivity plot for ionic and molecular liquids.
10 × 10−8 m2 s−1). The vibrational cooling rates show no
clear correlation with thermal diffusivities in ionic liquids. It should be noted that the vibrational cooling rates in ionic liq-uids are similar with those in alkane solvents, suggesting that the trans-stilbene molecule is solvated selectively in alkane-rich environments in ionic liquids.
Thermal diffusivity κ is defined in the diffusion equation of heat as follows:
∂θ ∂t =
λ
cρθ= κθ, (1)
where θ is temperature, t is time, λ is thermal conductivity, c is specific heat, ρ is mass density, and is the Lapla-cian (= ∂2/∂x2+ ∂2/∂y2+ ∂2/∂z2). Thermal diffusivity κ represents the rate of temperature change caused by heat conduction, which is characterized by thermal conductivity λ, in a media. We are comparing here the vibrational cooling rate determined by “picosecond Raman thermometer” with thermal diffusivity in Eq. (1). For molecular liquids, we ob-served a good correlation between the two quantities. In ionic liquids, however, there is no obvious correlation observed be-tween them.
The lack of correlation between the vibrational cooling rate and thermal diffusivity is well accounted for if we as-sume a non-uniform structure for ionic liquids. The vibra-tional cooling kinetics is controlled mainly by the solvent-solvent energy transfer process from molecules, or ions, in the first solvation shell toward the bulk. Thermal diffusivity, how-ever, is measured for thermal conduction over a range of mi-crometers or longer. If there is a boundary between adjacent local structures where thermal energy transfer is decelerated, observed thermal diffusivity for bulk solvent will be reduced. The vibrational cooling rate reflects the energy transfer kinet-ics within microscopic solvation environments, while thermal diffusivity represents macroscopic heat conduction capability of bulk solvent.
In previous papers, we proposed that local structures, which preserve at least a part of the ordered structures of crystals, are present in ionic liquids. We also suggested that alkyl chains of cations form a domain structure in ionic liq-uids. These local structures, if they exist, make boundaries between adjacent domains. The rate of heat conduction over a boundary is expected to be much smaller than the heat transfer rate within a domain. The heat conduction rate over a bound-ary controls macroscopic thermal diffusion in ionic liquids and therefore macroscopic thermal diffusion is not a direct extension of microscopic thermal diffusion within a bound-ary. Thermal diffusivity measured for bulk solvent might well show a smaller value than what is expected from the energy transfer rate within microscopic solvation environments.
The vibrational cooling rate, which we observe from pi-cosecond time-resolved Raman experiments, is determined by thermal diffusivity of solvation environments, or “local” ther-mal diffusivity. For molecular solvents with no boundary for thermal diffusion, local thermal diffusivity accords well with bulk thermal diffusivity. In ionic liquids, however, direct cor-relation is lost between local and bulk thermal diffusivities. In the following analysis, we estimate local thermal diffu-sivity in ionic liquids from the observed rate of vibrational cooling.
C. Numerical simulation of thermal diffusion in ionic liquids with local thermal diffusivity
We analyze the observed kinetics of the vibrational cool-ing process in ionic liquids with a simple numerical model. In our previous paper,18the vibrational cooling kinetics of S
1
trans-stilbene in chloroform was very well expressed with a solution of the diffusion equation of heat.28,29 We therefore use the same equation for the following analysis of vibrational cooling kinetics: θ(x, y, z, t)− Tr.t.= (4πκt)−3/2 ∞ −∞ ∞ −∞ ∞ −∞ f(x, y, z) × exp{−[(x − x)2+ (y − y)2 + (z − z)2]/4κt}dxdydz, (2)
where θ (x, y, z, t) is temperature at the position (x, y, z) at time t, Tr.t. is room temperature, and f(x, y, z) is the initial
distribution of temperature change,
f(x, y, z)= θ(x, y, z, 0) − Tr.t.. (3)
It is assumed that the solute molecule and the nearest solvent molecules or ions are in thermal equilibrium imme-diately after photoexcitation. The initial distribution function f(x, y, z) is then represented by a box function
f(x, y, z)= T 0 (|x| < a, |y| < b, |z| < c) (otherwise) , (4) where T is the initial temperature change. By substituting
f(x, y, z) of Eq.(2)with Eq.(4), we obtain θ(x, y, z, t)− Tr.t.
×{erf((b − y)/(4κt)1/2)+ erf((b + y)/(4κt)1/2)}
×{erf((c − z)/(4κt)1/2)+ erf((c + z)/(4κt)1/2)}, (5)
where erf represents an error function defined as erf(x)= √2
π x
−∞exp(−t
2)dt. (6)
The dimensions of the initial heat distribution box are taken as a = α + r0, b= β + r0, and c= γ + r0, where
α, β, and γ are the dimensions of the trans-stilbene molecule (α= 0.65 nm, β = 0.35 nm, and γ = 0.10 nm) (Ref.18) and r0represents the thickness of the solvent layer. Then
temper-ature monitored at (x, y, z)= (0, 0, 0) is given as θ(0, 0, 0, t)− Tr.t.
= Terf{(α + r0)/(4κt)1/2}erf{(β + r0)/(4κt)1/2}
×erf{(γ + r0)/(4κt)1/2}. (7)
We simulate the observed vibrational cooling kinetics us-ing Eq.(7)with the initial temperature increase, T, and the
thickness of the solvent layer, r0, as fitting parameters.
Thermal diffusivity κ in Eq.(7)represents “local” ther-mal diffusivity. We estimate local therther-mal diffusivity from the vibrational cooling rate, by assuming the linear rela-tion between the vibrarela-tional cooling rate and thermal dif-fusivity observed in molecular liquids (Fig. 3). For exam-ple, C5mimTf2N shows vibrational cooling rate constant of
0.11 ps−1, which corresponds to “local” thermal diffusivity of 8.8× 10−8 m2 s−1. The values of estimated local thermal diffusivity for the five ionic liquids are listed in TableI.
Vibrational cooling curves observed in the five ionic liq-uids, C2mimTf2N, C4mimTf2N, C5mimTf2N, C6mimTf2N,
and C8mimTf2N, as well as in three molecular liquids,
hep-tane, decane, and ethanol, have been successfully explained by Eq.(7). The result for C5mimTf2N is shown in Figure4.
The cooling kinetics is very well simulated with optimized parameters of T= 64 K and r0= 1.25 nm. The simulation
also reproduces very well the observed kinetics for the other four ionic liquids and the three molecular liquids. The Tand
r0 values for the other solvents are listed in TableI. There
are no large differences between the Tand r0values in ionic
TABLE I. Thickness of the solvent layer r0, initial temperature increase T,
“local” thermal diffusivity estimated from the numerical model simulation of thermal diffusion.
Thickness of the Initial temperature “Local” thermal nearest solvent layer increase diffusivity
Solvent (nm) (K) (108m2s−1) Heptane 1.26 . . . Decane 1.39 . . . Ethanol 1.11 . . . C2mimTf2N 1.16 59 8.8 C4mimTf2N 1.17 74 8.8 C5mimTf2N 1.25 64 8.8 C6mimTf2N 1.17 71 8.1 C8mimTf2N 1.05 66 8.2
FIG. 4. Time dependence of the peak position of the 1570-cm−1 Raman band which represents the cooling kinetics (open circle) and simulated ki-netics (solid curve) for C5mimTf2N.
liquids and molecular liquids. Solvation structure around S1
trans-stilbene in the five ionic liquids is considered to be sim-ilar to that in molecular liquids.
D. Vibrational cooling kinetics with and without excess energy
Vibrational cooling kinetics of S1trans-stilbene with and
without excess energy were examined for 0–200 ps. Figure5
shows the temporal peak shifts of the 1570-cm−1Raman band of S1 trans-stilbene in C2mimTf2N with pump wavelengths
of 296 nm (2500 cm−1 excess energy) and 325 nm (no ex-cess energy). The peak shifts observed around the time origin, which have been attributed to strong electric field caused by
FIG. 5. Time dependence of the position of the 1570-cm−1 Raman band of S1trans-stilbene in C2mimTf2N for excitation wavelengths of 325 nm
(square) and 296 nm (circle). Raman probe wavelength is 592 nm. The tem-perature increase estimated from the position of the 1570-cm−1Raman band is indicated on the right ordinate.
104504-6 Yoshidaet al. J. Chem. Phys. 136, 104504 (2012)
an overlap of the probe and pump pulses,30are excluded from the following analysis. There is no large peak shift for 325 nm excitation, while a large shift corresponding to vibrational cooling is observed for 296 nm excitation. No temperature increase is expected for 325 nm excitation that carries no ex-cess energy. The peak position stays constant showing that the temperature of S1trans-stilbene is equal to room temperature
at all time delays. The temperature increase for 296 nm exci-tation estimated from the linear relationship between the peak position and temperature of S1trans-stilbene25is indicated on
the right ordinate in Fig.5. The agreement between the peak shifts with and without excess energy indicates that, even for 296 nm excitation, temperature recovers to the room temper-ature after 30 ps. The excess energy given to S1trans-stilbene
upon photoexcitation fully dissipates to outer bulk solvent ions in a local structure with no detectable temperature increase.
From the observation that the excess energy dissipates completely within a local structure formed in C2mimTf2N, we
are able to estimate the minimum volume of local structure. Slow heat transfer is expected at a boundary of local structure as we discuss for Fig.3. If the volume of local structure is small enough, the excess energy remaining in a local struc-ture causes a temperastruc-ture increase. However, we did not ob-serve such a temperature increase after 30 ps. The local struc-ture in C2mimTf2N should have a volume large enough, for
the excess energy of 2500 cm−1, dissipates fully to make no detectable temperature increase.
E. Numerical simulation of thermal diffusion in local structure of ionic liquids
Here, we analyze the observed vibrational cooling curve of S1trans-stilbene in C2mimTf2N with pump wavelength of
296 nm (2500 cm−1 excess energy) in order to estimate the size of local structure. We use a new numerical model based on the same kinetic model as in Sec.III C. Thermal diffusion within a local structure is modeled with the heat dissipation from a heat source into a finite volume, which is represented by a cube with length L. We assume no heat flow at the bound-ary between local structures and that all excess energy from S1trans-stilbene stays within a local structure. This condition
is modeled mathematically by assuming that heat flow is re-flected back at the edge of the cube and is superposed on the original flow.29The result should reflect the nature of heat
dif-fusion within the volume, although the energy flow across lo-cal structures would surely reduce the amount of heat within a local structure and therefore the estimated size of local struc-ture here may be exaggerated.
If thermal diffusion occurs only in a cube with a length L, the solution of the diffusion equation gives the spatiotemporal profile of temperature θ (x, y, z, t) as29 θ(x, y, z, t)− Tr.t.= T/8 × ∞ n=−∞ {erf((a + x + nL)/(4κt)1/2)+ erf((a − x − nL)/(4κt)1/2)} × ∞ n=−∞ {erf((b + y + nL)/(4κt)1/2)+ erf((b − y − nL)/(4κt)1/2)} × ∞ n=−∞ {erf((c + z + nL)/(4κt)1/2)+ erf((c − z − nL)/(4κt)1/2)}. (8)
The temperature at the coordinate origin (x, y, z)= (0, 0, 0) is therefore θ(0, 0, 0, t)− Tr.t. = T/8 × ∞ n=−∞ {erf((a + nL)/(4κt)1/2)+ erf((a − nL)/(4κt)1/2)} × ∞ n=−∞ {erf((b + nL)/(4κt)1/2)+ erf((b − nL)/(4κt)1/2)} × ∞ n=−∞ {erf((c + nL)/(4κt)1/2)+ erf((c − nL)/(4κt)1/2)}. (9)
As the sum of series for each coordinate converges rapidly with a small number of terms, it is calculated from n= −10 to 10 in the present analysis.
We compare the observed cooling kinetics with the nu-merical simulation with Eq.(9). All the parameters in Eq.(9)
FIG. 6. Time dependence of the temperature increase of S1 trans-stilbene
simulated with the length L of 3.2 (a), 3.5 (b), 4.0 (c), 5.0 (d), 7.0 (e), 10 (f), and 50 nm (g). The observed values are shown with open circles. The dotted line indicates the peak position for room temperature. The initial temperature rise Tis 59 K.
Sec. III C. L is the only adjustable parameter. We limit the time range of simulation to 2–200 ps in order to remove the influence of the artifacts observed in early time delays. The results for L values in the range of 3.2–50 nm are shown in Figure6. It is obvious that the simulated cooling kinetics with an L value of 10 nm or larger reproduces the observed cooling kinetics very well, showing complete recovery to room tem-perature after 30 ps. However, the simulated kinetics stops cooling before reaching room temperature if the L value is 7.0 nm or smaller. For smaller L values, temperature does not cool down to room temperature because heat is not fully dis-sipated, as we have discussed already in Sec.III D. The com-parison between the observed and simulated cooling kinetics shows that the diameter of local structure is most likely to be larger than 10 nm.
F. Local structure in ionic liquids
It has been shown that some of the solvation environ-ments detected by ultrafast spectroscopic methods are not di-rectly correlated with macroscopic properties of bulk ionic liquids. It has been known well that the photoisomerization rate of trans-stilbene correlates well with viscosity of bulk solvent in molecular liquids. The photoisomerization rate ob-served in C4mim[PF6], however, was larger by more than an
order of magnitude than the rate estimated from its viscosity if the relationship between the isomerization rate and viscosity for molecular liquids was assumed.31The rotational diffusion time of a solute molecule often has a linear correlation with solvent viscosity, as indicated by the Debye-Stokes-Einstein theory. In ionic liquids, however, the rotational diffusion time of 2-aminoquiline did not correlate with its viscosity.32
Photo-thermalization rate of malachite green did not show a linear relationship with the solvent viscosity of ionic liquids.33
The lack of correlation between solvation environments and macroscopic properties in ionic liquids is consistent with the presence of local structures discussed by several groups.1–4,8–11,34 Because of the boundary that originates from local structures, microscopic solvation environments cannot be directly extrapolated to macroscopic properties. Considering the fact that ionic liquids are all transparent, the size of local structure must be much smaller than the wave-length of visible light. This fact imposes the upper limit of 100 nm. Combined with the present estimation of the lower limit, 10 nm, an order of magnitude estimate of the size of local structure is obtained as 10 nm < L < 100 nm, where L stands for the length or the diameter of local structure. IV. CONCLUSIONS
The vibrational cooling rate was measured in ionic liq-uids with the peak position of the 1570-cm−1 Raman band of S1 trans-stilbene, or “picosecond Raman thermometer”.
Unlike in molecular liquids, the vibrational cooling rate in ionic liquids showed no correlation with bulk thermal diffu-sivities. The vibrational cooling rate reflects solvent-solvent energy transfer rate within a microscopic region around the solute. The presence of local structure, which has been pro-posed by several researchers, explains well this lack of corre-lation. Macroscopic thermal diffusion is controlled by heat conduction across the boundaries of local structures, while microscopic thermal diffusion is controlled by energy trans-fer within a local structure. We should note that microscopic properties of ionic liquids are not well represented by bulk solvent properties like polarity and viscosity.
It is necessary to characterize microscopic environments in ionic liquids with “local” properties that are defined within a local structure. The idea of local property, such as local ther-mal diffusivity we discuss in this article, will be important to examine in details the microscopic environments in inhomo-geneous media, which includes micelles,35 vesicles, or cell
membranes as well as ionic liquids.
Observation of the vibrational cooling process and its de-pendence on the amount of excess energy is crucial for esti-mating the size of local structure. A model simulation for this observation allows us to estimate the lower limit of the size of local structure in C2mimTf2N as 10 nm.
ACKNOWLEDGMENTS
This work is supported by grant-in-aid for Creative Sci-entific Research (Grant No.11NP0101) from Japan Society for the Promotion of Science (JSPS), and by grant-in-aid for Scientific Research on Priority Areas (Area 452, Grant No. 17073003) and Global COE Program (The University of Tokyo Global COE Chemistry Innovation through Coopera-tion of Science and Engineering) from the Ministry of Educa-tion, Culture, Sports, Science and Technology (MEXT) of the Japanese Government.
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