Quasielastic neutron scattering and microscopic dynamics of liquid ethylene glycol

Chemical Physics 334 (2007) 36–44 www.elsevier.com/locate/chemphys

Quasielastic neutron scattering and microscopic dynamics of liquid ethylene glycol O. Sobolev a

a,*

, A. Novikov b, J. Pieper

c

Laboratoire de Ge´ophysique Interne et Tectonophysique, BP 53, Maison des Ge´osciences – Domaine Universitaire, 38041 Grenoble, Cedex 9, France b Institute for Physics and Power Engineering, Bondarenko Sq. 1, Obninsk, Kaluga Reg. 249033, Russian Federation c Technische Universita¨t Berlin, Straße des 17, Juni 135, D-10623 Berlin, Germany Received 14 May 2006; accepted 7 February 2007 Available online 12 February 2007

Abstract Quasielastic neutron scattering (QENS) by liquid ethylene glycol was analyzed using different model approaches. It was found that approximation of the QENS spectra by a set of Lorentzian functions corresponding to the translational and rotational motions produce physically unrealistic results. At the same time, the Fourier transform of the stretched-exponential function exp((t/s)b) fits the experimental data well, and results of the fit are in good agreement with those obtained earlier for other systems. The stretching parameter b was found Q independent and shows weak temperature dependence. The mean relaxation time as a function of Q departs strongly from the simple diffusion low and can be approximated by a power law hswi = s0Qc with the exponent parameter c = 2.4.  2007 Elsevier B.V. All rights reserved. Keywords: Quasielastic neutron scattering; Ethylene glycol; Diffusion

1. Introduction Ethylene glycol (HO–CH2–CH2–OH, EG) is the simplest diatomic alcohol, which is used mainly as an antifreeze and for organic syntheses. Besides its technological importance, it is of interest for the liquid state physics. Two hydroxyl groups and two oxygen atoms of the molecule can act correspondingly as proton donors and proton acceptors in hydrogen bound (HB). The EG molecule can have therefore four HB, and a three-dimensional network of hydrogen-bonded molecules is formed in the liquid state. In this regard EG may be viewed as being similar to water. EG can be also interesting as a low molecular weight glass forming liquid. The microscopic properties of EG were studied by different methods [1–11]. The most of the experimental results suggest that the EG molecule in the gas and liquid phase *

Corresponding author. Tel.: +33 (0)4 7682 8009; fax: +33 (0)4 7682 8101. E-mail address: [email protected] (O. Sobolev). 0301-0104/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2007.02.008

adopt mainly a gauche conformation and can form intramolecular hydrogen bound. The liquid structure of EG was examined by X-ray and neutron diffraction [5]. It was found that the most probable local structure of molecules in liquid EG is realized by three nearest neighbors forming three intermolecular hydrogen bounds. The structure of liquid EG was also investigated by molecular dynamics (MD) simulation with several force fields, which had the same intermolecular parameters, but supposed different flexibility of the molecule [6]. It was established that the structure is dominated by three-dimensional networks of hydrogen-bonded molecules with a mean number of hydrogen bonds per molecule slightly lower than four, independently of the potential model used. On the other hand, the self-diffusion coefficients obtained for the distinct models are quite different. This was interpreted as a result of a coupling between intramolecular motions and self-diffusion. Hence, the comparison with experimental dynamical data for liquid EG seems crucial in discriminating amongst the different models in order to select the most realistic one [6]. The neutron scattering is

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

37

the most suitable experimental method for such a comparison, because it provides information about microscopic dynamics in the same time scale as the MD method, and corresponding scattering functions can by easily calculated from the MD data. Our previous attempts to analyze the microscopic dynamics of liquid EG by neutron scattering are presented in Ref. [10,11]. In work [11] we tried to analyze quasielastic neutron scattering (QENS) on liquid EG in terms of the simplest models for the diffusion and reorientation motions, which were successfully applied earlier in the study of diffusive molecular motions in water [12–15]. On the other hand, the authors of [8] shown that QENS spectra of liquid EG can be interpreted in terms of the a-relaxation dynamics, which is traditionally attributed to supercooled liquids. The aim of this work is to study QENS on liquid EG in more detail using different model approaches.

where the sign  denotes the convolution operation, Str(Q, x) and Srqel(Q, x) are Fourier transforms of Itr(Q, t) and Irqel(Q, t) correspondingly. EISF(Q) = Ir(Q, 1) is elastic incoherent structure factor. It characterizes the geometry of the rotation [16,17]. The simplest models for the diffusion motion predict exponential form for the translation diffusion function:

2. Models and methods

CðQÞ ¼ DQ2

The neutron scattering law measured in a neutron scattering experiment is the Fourier transform of the intermediate scattering function I(Q, t): Z 1 ~ ~ tÞ expðixtÞdt; SðQ; xÞ ¼ IðQ; ð1Þ 2p ~ ¼~ where Q ki  ~ k f and gx = Ei  Ef are wave vector and energy transfers correspondingly. Since the incoherent cross section of hydrogen is much larger than those of other atoms contained in EG molecule, we mainly observe the incoherent scattering from protons. In incoherent approximation I(Q, t) describe individual dynamics of the scattering particles: ~rj ð0ÞÞ expði~ IðQ; tÞ ¼ hexpðiQ~ Q~ rj ðtÞÞi;

ð2Þ

where angular brackets denote ensemble average and r(0) and r(t) are, respectively, the coordinate of a proton at time 0 and the coordinate of the same proton at time t. It is generally assumed that different kinds of motions are uncorrelated and the incoherent intermediate scattering function in the long time limit corresponding to quasielastic scattering has the form: I qel ðQ; tÞ ¼ I tr ðQ; tÞI r ðQ; tÞ expð2W Þ;

ð3Þ

where the exponent is Debye–Waller factor, Itr(Q, t) and Ir(Q, t) represent the contributions from the translational and the low-frequency rotational motions respectively. This supposition is not always true, nevertheless, it is widely used in order to have a tractable analytical model for the data analysis. Itr(Q, t) tends to zero at Q ! 0, whereas the reorientation function Ir(Q, t) can split into its asymptotic value in the long-time limit Ir(Q, 1) and the time-dependent part Irqel(Q, t) according to I r ðQ; tÞ ¼ I r ðQ; 1Þ þ I rqel ðQ; tÞ

and the quasielastic scattering law can be expressed [16,17]: S qel ðQ; xÞ ¼ ðEISFðQÞS tr ðQ; xÞ þ S tr ðQ; xÞ  S rqel ðQ; xÞÞ expð2W Þ;

I tr ðQ; tÞ ¼ expðCðQÞtÞ;

ð4Þ

ð5Þ

where C(Q) is the half-width at half maximum of the quasielastic peak. At low Q values C(Q) tends to the limit, which corresponds to the simple diffusion (Fick’s law): ð6Þ

At higher Q different models [16,17] predict deviation from dependence (6) and suppose jumping mechanism of diffusion. The models for rotation motion describe generally Irqel(Q, t) by the infinite series of exponential functions, but in practice, depending on Q range, one–three first terms of the expansion are quite enough for the data analysis. The characteristic times of these exponents, in contrast to Itr(Q, t), do not depend on Q [16,17]. Thus in the framework of the ‘‘traditional’’ approach the quasielastic spectra are approximated usually by a sum of a few Lorentzians corresponding to the translational and rotational motions. The Lorentzian shape of the quasielastic components S(Q, x) is defined by the simple exponential decay of the corresponding I(Q, t) functions. It was found, however, for supercooled liquids, glasses, polymers, proteins and some other substances that diffusive and reorientational relaxation processes in these systems deviate from the exponential form and can be described by the stretched exponent (Kohlrausch–Williams–Watt function, KWW) [18–28]: KWWðtÞ ¼ expððt=sw Þb Þ

ð7Þ

The reasons for such a behavior can be different for different systems. Two limiting scenarios are invoked to explain KWW functional form: ‘‘homogeneous’’ and ‘‘heterogeneous’’ scenarios [19,21]. According to ‘‘heterogonous’’ scenario the KWW function is a superposition of different simple exponential relaxations weighted by a broad distribution of relaxation times. ‘‘Homogeneous’’ scenario supposes that all of the particles in the system relax non-exponential. In case of ‘‘homogeneous’’ nonexponential behavior the shape parameter b is considered as an indicator of the degree of correlation or cooperativity of the relaxation process.

38

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

"

3. Experiment

DEtr þ ð1  EISFðQÞÞ DE2tr þ e2 # DEtr þ DErot   RðeÞ; ðDEtr þ DErot Þ2 þ e2

S qel ðQ; eÞ ¼ EISFðQÞ

We discovered previously that QENS on EG has a complex structure and probably reflects different dynamical process with very different characteristic times [11]. This means that in order to explore QENS in more details we needed to perform our measurements with different experimental resolutions, which is equivalent to different observation times: with higher resolution we can observe slower dynamical processes, whereas the faster processes are more visible at lower resolution. A correct model must fit the high and low resolution data with the same values of adjustable parameters. The measurements were performed with the time-offlight spectrometer NEAT at Berlin Neutron Scattering Center, Hahn–Meitner-Institute, Berlin. The parameters of the experiment are listed in Table 1. The resolution function, which is very well described by a Gaussian function, was measured by using a standard vanadium sample. The resolution is slightly angular dependent because of the sample orientation angle of 135 with respect to the incident neutron beam direction. 4. Data analysis After normalization by vanadium and background subtraction raw time-of-flight data was transformed in scattering law S(Q, x) at constant Q. The obtained spectra were fitted with the following expression: SðQ; xÞ ¼ S qel ðQ; xÞ þ S ms ðQ; xÞ þ Binel ðQÞ;

ð8Þ

where Sqel(Q, x) is a model quasielastic scattering law. Binel(Q) represents the inelastic scattering contribution, which is rather small in comparison with the quasielastic component and can be roughly approximated by a flat background. Sms(Q, x) represents the multiple scattering, which was recalculated between fitting sessions using model Sqel(Q, x) with adjusted parameters. FISC program was used for multiple scattering calculations [14,29]. First we tried to analyze our data in the framework of the ‘‘traditional’’ approach, in terms of the simplest models for the diffusion and reorientation motions. In the first stage the QENS spectra were approximated by the following expression:

where Q and e are the neutron wave vector and energy transfer correspondingly. EISF(Q) is the elastic incoherent structure factor [16,17]. The first term in the brackets represents the translation diffusion motions of the molecule; the second one approximates the contribution of the rotation motions of the hydrogen atoms. R(e) is a resolution function, and  denotes the convolution operation. It was found that the ‘‘rotation’’ component is broad (FWHM = 2D Er  0.5–0.8 meV), and its width DEr is almost independent on Q and temperature. The obtained EISF demonstrates strong temperature dependence (Fig. 1). An interpretation of the observed temperature dependence of EISF in the framework of the models for reorientation motion is difficult: this dependence could mean that the radius of reorientation increasing with temperature, but this assumption looks dubious in our case. Another difficulty of model (9) is that there is a significant difference in the adjustable parameters obtained from fitting of the model to the experimental data measured with different experimental resolutions (Fig. 2). One can imagine that the observed difficulties can be caused by another dynamical process, which is not resolved at lower temperatures and lower resolution, but become more visible at higher temperatures and higher resolution, and gives a contribution into the broad component. In our previous work we exploited the model supposed that, in addition to the translational component, QENS contains two reorientation components. One of them was supposed to be connected with the rotations of protons of C–H groups, and another one attributed to the reorientations of the whole molecule [11]. We tried to

Table 1 Parameters of neutron scattering experiment Sample

Temperatures (K)

Incident energy (meV)

Resolution (FWHM) (leV)

Q Range ˚ 1) (A

Flat sample of 0.2 mm thickness (transmission of about 92%)

296, 323, 348, 373 and 393

1.936

90–100

0.3–1.63

296, 323, 348

1.278

30–40

0.24–1.33

ð9Þ

Fig. 1. Experimental EISF (model (9)) at different temperatures.

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

39

Fig. 2. Results of fitting model (9) to the experimental QENS spectra measured at T = 323 K with the resolution Dres = 30–40 leV (black circles) and Dres = 90–100 leV (open circles): (a) EISF; (b) full width at half maximum of the ‘‘translational’’ component.

approximate our data with this model and with some other models supposing the presence of three quasielastic components of the Lorentzian shape. However, all these models applied to our data produced physically unrealistic results as well and failed to fit experimental data measured with different resolutions with the same values of adjustable parameters. It is not possible to illustrate all our unsuccessful attempts to fit the data using the above models. We just give an example of the fitting results for the model described in [11] (Eqs. (2) and (3)) at T = 296 K and different resolutions (Fig. 3). The width of the translational diffusion component and two rotation diffusion coefficients DR1 and DR2 were obtained using the values of the ˚ and R2 = 1.1 A ˚ found in our prerotation radii R1 = 1.6 A vious work [11]. DR1 was found equal zero for this temperature, and it is not shown in Fig. 3. The quality of the fit was worse than for model (9) but still acceptable. The values of the parameters obtained with different instrumental resolutions are also in satisfactory agreement in this particular case. The obtained results however are meaningless from the point of view of the used model: the rotation diffusion coefficient shows strong Q dependence, whereas theoretically it must be constant. The translational diffusion width DEr is larger than predicted by the simple diffusion

law, which is also not foreseen by the traditionally used models. The reverse of the data analysis described above suggests an idea about non-Lorentzian shape of QENS spectrum or its particular components. The authors of [8,9] showed that QENS spectra of liquid EG can be interpreted in terms of the a-relaxation dynamics, and experimental data in the frequency domain can be fitted with the Havriliak–Negami (HN) function, which is in some way equivalent to the Fourier transform of the KWW function: HNðxÞ ¼ ðxÞ1 Im½1 þ ðixsHN Þa c

ð10Þ

The correspondence between the HN and the KWW functions, however, is not univocal and takes place only in the restricted interval of the parameters a and c [30]. We therefore chose other method for data analysis, and the QENS data were fitted in the energy domain by expression (8), with Sqel(Q, x) calculated numerically by the Fourier transform of KWW function corrected for the instrumental resolution (Gaussian with dispersion rres): Z 1 1 KWWðtÞ expðr2res t2 =2Þ cosðxtÞdt S qel ðQ; xÞ ¼ p 0 ð11Þ

Fig. 3. Fitting results for the model described in [11] (Eqs. (2) and (3)) at T = 296 K with the resolution Dres = 30–40 leV (black circles) and Dres = 90– 100 leV (open circles): (a) full width at half maximum of the ‘‘translational’’ component; (b) rotation diffusion coefficients DR2. For details see text and [11].

40

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

Fig. 4. Experimental QENS spectra measured at different Q, T, and instrument resolutions, and fit with expression (8) using model (11) (solid line). Dashed line represents resolution function.

The results of the fitting procedure are shown in Fig. 4. The stretching parameter b was found Q-independent (Fig. 5), and its temperature dependence is also weak (Fig. 6). The mean relaxation time hswi is defined as Z 1 sw dtKWWðtÞ ¼ Cðb1 Þ ð12Þ hsw i ¼ b 0 It can be approximated by the power law hsw i ¼ s0 Qc

ð13Þ

with the exponent parameter found equal for the all temperatures c = 2.4 (Fig. 7). In order to check the accuracy and to estimate the applicability limits of the method, we performed the Fourier transforms of the experimental spectra into I(Q, t) and compared with the model KWW curves corrected for the resolution using parameters found by the fitting of Eq. (11) to the experimental spectra in the energy domain. The high resolution (30–40 leV) allows to follow the behavior of I(Q, t) up to time tmax  80 ps (Fig. 8), whereas the low resolution (90–100 leV) put the time observation

limit tmax  20 ps (Fig. 9). Our model curves describe experimental I(Q, t) very well at times shorter than resolution observation limits tmax and larger than tmin = 2 ps, below tmin value the model curves deviate from the experimental points due to the inelastic scattering effects. At the same time the experimental I(Q, t) suffer from truncation effect because of the fact, that we have to integrate the experimental S(Q, x) over a limited interval of x. This introduces spurious oscillations clearly seen in Fig. 9. That is why we preferred to fit experimental spectra in the energy domain performing the Fourier transformation of the model I(Q, t). The model I(Q, t) function can be calculated for any value of variable t and, therefore, it can be integrated over a time interval large enough to avoid the truncation effects. 5. Discussion The analysis presented in the previous section is basically phenomenological, and the results can be interpreted in different ways. Although fitting the data with model (11)

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

41

Fig. 7. Mean relaxation time hswi (symbols) and power-low fit hswi = s0Qc (solid lines). The simple diffusion law s = D1Q2 is shown for room temperature (D = 0.09 · 105 cm2 s1 [4], dashed line).

Fig. 5. Stretching parameter b.

Fig. 6. Temperature dependence of the stretching parameter b.

does not consider presence of different components in QENS spectra, we cannot rule out that QENS data can be decomposed by several contributions corresponding to different processes: translation diffusion and reorientation of the molecule, slow intramolecular reorientations of the protons. Our results, however, provide some arguments in favor of the single component approximation. Different components of QENS spectrum, if they exist, must have different Q-dependence: the translation contribution dominates at smaller Q; the reorientation components are well observable at Q P R1 (R is a radius of reorientation). The temperature dependence of the characteristic times for the translation and rotation motions is usually very different as well. If QENS spectrum reflects several distinct dynamical processes, the shape of the QENS peaks should

be Q-dependent and the relaxation times hswi measured at lower and higher Q values should have different temperature dependence. These expectations are not supported by our findings: the shape parameter b is found Q-independent, and the relaxation time hswi measured at different temperatures follows the same power law (13). Moreover, the strong Q-dependence of the relaxation time hswi indicates the diffusive nature of the observed dynamical process. The single component structure of QENS could mean that translational and reorientation motions of the molecules in liquid EG are strongly coupled, so that approximation (3) is not valid. This hypothesis is supported by the results of MD simulation for liquid EG [6] where a coupling between intramolecular motion and self-diffusion was discovered. From the comparison between different molecular models it was found that the model with the fastest diffusion also presents more frequent transitions from one molecular conformation to the other. The QENS results for liquid EG were also published in [9]. In that work the QENS spectra were fitted with HN function (10) and parameters of KWW function were found from the parameters of HN function. However, the published data concern mainly the dynamics of EG confined in porous glass, and the results for bulk EG are described very briefly. The authors of [9] reported the power Q-dependence (13) of the averaged relaxation time hswi with c = 1.35 for bulk EG at T = 12 C. The stretching parameter b was found 0.9 and Q-independent, in contrast to confined EG, where b was found to be Q-dependent and smaller than in the bulk. These contradict the results of current work, though the temperatures in our case are higher, and direct comparison is not possible. For lack of information about bulk EG and data processing published in [9], it is difficult to discuss a possible reason for the difference between our results and the results of [9]. We can just consider Figs. 5 and 6 of [9] where the averaged relaxation times hswi are plotted as a function of Q for confined and bulk EG (for bulk EG only the data

42

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

Fig. 8. Experimental I(Q, t) (circles) and model curves I mod ðQ; tÞ ¼ expðt=sw Þb expðr2res t2 =2Þ obtained with resolution Dres = 30–40 leV, at T = 296 K for different Q values.

Fig. 9. Experimental I(Q, t) (circles) and model curves I mod ðQ; tÞ ¼ ˚ 1 expðt=sw Þb expðr2res t2 =2Þ obtained with Dres = 92 leV, at Q = 1 A for different temperatures.

at T = 12 C are shown). Comparing the data of [9] with our data plotted in Fig. 7 one can see that even for confined

EG, where dynamics is much slower than in the bulk, the hswi values reported in [9] for T = 23 C are significantly smaller than our results and the values predicted by the ˚ 1 and simple diffusion law. Indeed, for Q = 0.5 A T = 23 C the following values are found: hswi  100 ps (confined EG, [9]), hswi  350 ps (bulk EG, our work), hswi = D1Q2 = 444 ps (D = 0.09 · 105 cm2s1 [4]). Moreover, in case of bulk EG at T = 12 C they reported ˚ 1 (Fig. 6, [9]), which is almost hswi  50 ps for Q  0.5 A by order of magnitude smaller than our result for the room temperature. Supposing that the diffusion coefficient D is roughly in inverse proportion to the viscosity g, we can estimate approximately hswi for T = 12 C using the simple diffusion law and the value D = 0.09 · 105 cm2 s1 reported for the room temperature [4]. From the ratio g(T = 12 C)/g(T = 23 C)  6 one can found the value of the averaged relaxation time hswi  444 · 6  2600 ps ˚ 1. Of course, for bulk EG at T = 12 C and Q = 0.5 A this is very rough approximation, and the real hswi deviates

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

usually from the Fick’s law at Q values larger than 0.1– ˚ 1. Nevertheless, it is hard to imagine that the real 0.3 A hswi value can be smaller then the above estimation by factor of 50. Thus the values of hswi reported in [9] seem to be underestimated. This is very possible taking into account the fact that, the energy resolution they used was equal 50 leV, but the QENS width corresponding to the hswi estimated above is less than 1 leV. The Q and T-dependencies of the parameters obtained in the current work are in qualitative agreement with those found for other systems. It was found that the stretching parameter b increases monotonically with increasing temperature. The similar result was obtained earlier for other substances [20]. The Q dependence of hswi measured in our experiment is steeper than predicted by the simple diffusion law Q2 (Fig. 7). This behavior is in contrast with that reported for water and some other liquids, whose QENS data is traditionally described in terms of the models supposing a weaker Q-dependence than Q2 [12–17]. Nevertheless, the power law dependence Qc with c > 2 is not very unusual and was found earlier for glycerol (c = 2.2) [24] and 1-n-butyl-3-methylimidazolium hexafluorophosphate (c = 2.5) [28]. The Qc dependence with c = 2/b is typical for polymers [21–23]. The later also indicates that the atomic displacements can be described in terms of the Gaussian approximation [22]. In our case cGauss = 2/b  2.6–3.2 (with b = 0.62–0.75 obtained in our experiment), which is larger than our experimental result c = 2.4. It should be noted that within the accuracy of our experimental results the parameters c and b are found uncorrelated: c is temperature independent, whereas b shows some temperature dependence. As regards the temperature dependence of hswi, it is hardly possible to decide, whether it is proportional to g/T or to g (Fig. 10), but probably it goes between g/T and g. The same behavior was observed earlier for glycerol [26] and benzene [27]. An interpretation of the observed dynamical phenomena can be qualitatively done employing an idea on cou-

43

pling the diffusive motions to the structural relaxation borrowed from the mode-coupling theory [18,25]. According to this interpretation the non-lorentzian shape of the QENS spectra and deviation of the mean relaxation time hswi from the simple diffusion law indicate that the molecules of the liquid are trapped in a given surrounding and perform quasi-localized motion in a cage formed by neighboring molecules. The trapped particle can escape this cage only though rearrangement of the particles surrounding it. The motion of the particle is highly correlated, because each step out of the cage is followed with high probability by a step back [25]. The simple diffusion law, corresponding to uncorrelated random walk, can be revealed at lower Q values, which correspond to distances (Q1) traveled by the particle long enough to lose a memory of its initial position. In the case of glycerol some indications of a crossover between relaxationlike and diffusionlike motion was ˚ 1 [25]. The stretching parameter b found at Q 6 0.3 A and the Q dependence of the mean relaxation time hswi measured in our experiment do not show any peculiarities (b ! 1 and c ! 2) that could be interpreted as a sign of such a crossover at lower Q. On the other hand, it is seen from Fig. 7 that the measured hswi is very close to the values estimated by the simple diffusion law at Q  0.3– ˚ 1. This means that this transition takes place some0.4 A where in these Q region, which should be explored in more detail with better resolution using back-scattering or spin– echo spectrometers. 6. Conclusion It was established that approximation of the QENS spectra by the set of Lorentzians corresponding to the translational and rotational motions produce physically unrealistic results. At the same time, the Fourier transform of the KWW function fits the experimental data well, and the results of the analysis are in good agreement with those obtained earlier for other systems. The analysis did not reveal the presence of distinct quasielastic components corresponding to different types of the molecular motion. This can be interpreted as an evidence for a strong coupling between reorientation motions and self-diffusion. The stretching parameter b of the KWW function was found Q independent and shows weak temperature dependence. The mean relaxation time as a function of Q departs strongly from the simple diffusion law and can be approximated by power law (13) with the exponent parameter c = 2.4. These results can be qualitatively understood employing an idea on coupling the diffusive motions to the structural relaxation. Acknowledgement

Fig. 10. Temperature dependence of the relaxation time hswi compared with viscosity g [31].

We thank Prof. Margarita Rodnikova, on whose initiative this investigation was started.

44

O. Sobolev et al. / Chemical Physics 334 (2007) 36–44

References [1] P. Buckley, P.A. Giguere, Can. J. Chem. 45 (1967) 397. [2] D. Christen, L.H. Coudert, J.A. Larsson, D. Cremer, J. Mol. Spectr. 205 (2001) 185. [3] H. Hayashi, H. Tanaka, K. Nakanishi, J. Chem. Soc., Faraday Trans. 91 (1995) 31. [4] N. Chandrasekhar, P. Krebs, J. Chem. Phys. 112 (2000) 5910. [5] I. Bako, T. Grosz, G. Palinskas, M.C. Bellissent-Funel, J. Chem. Phys. 118 (2003) 3215. [6] L. Saiz, J.A. Padro, E. Guardia, J. Chem. Phys. 114 (2001) 3187. [7] V. Grupi, P. Jannelli, S. Magazu, G. Maisano, D. Majolino, P. Migliardo, D. Sirna, Molecular Phys 84 (1995) 645. [8] V. Crupi, D. Majolino, P. Migliardo, V. Venuti, J. Molecular Struct. 651–653 (2003) 199. [9] V. Crupi, D. Majolino, P. Migliardo, V. Venuti, J. Chem. Phys. 118 (2003) 5971. [10] A. Novikov, M. Rodnikova, O. Sobolev, Appl. Phys. A 74 (2002) S502. [11] A. Novikov, M. Rodnikova, O. Sobolev, Physica B 350 (2004) e363. [12] J. Teixeira, M.C. Bellisent-Funel, S.H. Chen, A.J. Dianoux, Phys. Rev. A. 31 (1985) 1913. [13] J. Teixeira, M.C. Bellisent-Funel, S.H. Chen, J. Mol. Liq. 48 (1991) 123. [14] A. Novikov, M. Rodnikova, J. Barthel, O. Sobolev, J. Mol. Liq. 79 (1999) 203. [15] A. Novikov, M. Rodnikova, V. Savostin, O. Sobolev, J. Mol. Liq. 82 (1999) 83.

[16] M. Bee, Quasielastic Neutron Scattering: Principles and Applications in Solid State Chemistry, Biology and Materials Science, Adam Hilger, Bristol, 1988. [17] M. Bee, Chemical Physics 292 (2003) 121. [18] W. Goetze, J. Sjogren, Rep. Prog. Phys. 55 (1992) 241. [19] H.Z. Cummins, Gen Li, Y.H. Hwang, G.Q. Shen, W.M. Du, J. Hernandez, N.J. Tao, Z. Phys. B 103 (1997) 501. [20] C.A. Angell, K.L. Ngai, G.B. McKenna, P.F. McMillan, S.W. Martin, J. Appl. Phys. 88 (2000) 3113. [21] A. Arbe, J. Colmenero, M. Monkenbusch, D. Richter, Phys. Rev. Lett. 81 (1998) 590. [22] J. Colmenero, A. Arbe, A. Alegria, M. Monkenbusch, D. Richter, J. Phys.: Condens. Matter 11 (1999) A363. [23] A. Arbe, J. Colmenero, F. Alvarez, M. Monkenbusch, D. Richter, B. Farago, B. Frick, Phys. Rev. E 67 (2003) 051802. [24] J. Wuttke, W. Petry, G. Goddens, F. Fujara, Phys. Rev. E 52 (1995) 4026. [25] J. Wuttke, I. Chang, O.G. Randl, F. Fujara, W. Petry, Phys. Rev. E 54 (1996) 5364. [26] J. Wuttke, W. Petry, S. Pouget, J. Chem. Phys. 105 (1996) 5177. [27] S. Wiebel, J. Wuttke, New J. Phys. 4 (2002) 56.1. [28] A. Triolo, O. Russina, V. Arrighi, F. Juranyi, S. Janssen, C.M. Gordon, J. Chem. Phys. 119 (2003) 8549. [29] Yu.V. Lisichkin, A.G. Dovbenko, B.A. Efimenko, et al., Voprosi Atomnoi Nauki i Tehniki. Ser. Yadernie Const. (Russian) 2 (1979) 12. [30] F. Alvarez, A. Alegria, J. Colmenero, Phys. Rev. B 47 (1993) 125. [31] D. Bohne, S. Fischer, E. Obermeier, Ber. Bundesges. Phys. Chem. 88 (1984) 739.