J. Phys. Chem. B 2000, 104, 4285-4287
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On the Nature of Slow β-Process in Simple Glass Formers: A 2H NMR Study M. Vogel and E. Ro1 ssler* Physikalisches Institut, UniVersita¨ t Bayreuth, D 95440 Bayreuth, Germany ReceiVed: December 2, 1999; In Final Form: February 23, 2000
We study the dynamics of the glass formers toluene and glycerol below the glass transition temperature Tg by means of 2H NMR techniques. Whereas for toluene a slow β-process is observed in dielectric spectroscopy, this process is not discernible in glycerol. We demonstrate that standard 1D and 2D NMR experiments cannot resolve the motional process because very small angular amplitudes are involved. However, applying the solid-echo technique and varying the interpulse delay, we detect changes of the spectra for toluene but not for glycerol. Performing simulations, we estimate molecular reorientation of about 6°. We conclude that the β-process in simple organic glasses originates from highly restricted molecular reorientation of essentially all molecules. No indications for “islands of mobility” are found.
Introduction Relaxation processes persisting in the glass (T < Tg) are much less studied and understood than those above Tg. Starting at very low temperatures, say below 5 K, the dynamics is governed by tunneling in asymmetric double-well potentials (ADWPs).1 At higher temperatures thermally activated transitions in ADWPs are considered.1 On the other hand, many low molecular weight glass formers exhibit a slow secondary relaxation process, namely the Johari-Goldstein β-process, which emerges a little above Tg and evolves also below Tg2-5 (cf. Figure 1). Its time constant follows an Arrhenius law. Johari and Goldstein (1970) proposed that the β-process is an intrinsic property of glasses.3 Moreover, they introduced “islands of mobility” 3,5,6 which were thought to be “regions where the structure is relatively loose and molecules can undergo hindered rotations”.7 Thus, a nonuniform glass structure with characteristic defects was suggested. Another model was introduced by Williams and Watts (WW, 1971).4 Here, all molecules participate in the β-process; however, only a fraction of the dielectric polarization is relaxed due to hindered reorientation. Pronounced β-processes are observed in polymers, too.2,3,7-9 Therefore, many authors rejected the idea that the β-process is an intrinsic feature of glasses but rather took it as intramolecular relaxation process. This view was supported by Wu (1991)10 who attributed the β-process to rotations of a molecular subgroup. New interest started with the work of the groups of Donth (1996)8 and Richter (1996).9 The first study dealt with the merging of R- and β-process in polymers above Tg, in the second, the β-process in polybutadiene was identified by neutron scattering (NS) and interpreted as intrachain motion within the WW approach. Indications that NS can probe the β-process were already reported in 199111 and discussed by Ro¨ssler12 and Richter et al.13 Concerning simple glass formers, Ro¨ssler et al. (1993)14 applied the WW approach to describe NMR measurements. Kudlik et al. (1997)15 were able to identify the β-process in rigid glass formers such as toluene. So, it became again obvious that the β-process originates from intermolecular reorientation. However, a comparison of several systems has shown that not all glass formers exhibit a β-process.16-18 Glycerol is the most prominent example where no secondary relaxation process peak is observed. There, the high-frequency
Figure 1. Correlation times for toluene17 (R-process: open circles, β-process: solid circles interpolated by an Arrhenius law, solid line) and glycerol18 (R-process: open squares); correlation time window of NMR line-shape is indicated with corresponding temperature range for which line-shape changes are expected for the R- and β-process, respectively.
tail of the R-process degenerates to a power-law susceptibility at T < Tg with an exponent close to zero. Thus, a kind of 1/f noise is the dominant contribution in these glasses.17,18 Hence, Kudlik et al.17 distinguished type A glass formers which do not exhibit a discernible β-relaxation peak and type B systems which do. Yet, the nature of β-process and the reasons for its presence are not understood. NMR experiments were applied to characterize the β-process, particularly in polymers.19,20 However, for simple glass formers, experimental data is spare. Mostly spin-lattice relaxation studies were carried out which are difficult to interpret.14,21,22 Here, we want to present the first results of 2H NMR line-shape (1D) and two-dimensional exchange (2D) studies on toluene-d5 (type B, Tg = 117 K) and glycerol-d5 (type A, Tg = 188 K) which clearly prove that the dynamics at T < Tg is significantly different in these two systems. Results From experiments in the glass,14,21,22 i.e., at temperatures where the R-process can be ignored, one has drawn the
10.1021/jp9942466 CCC: $19.00 © 2000 American Chemical Society Published on Web 04/14/2000
4286 J. Phys. Chem. B, Vol. 104, No. 18, 2000
Letters
Figure 3. 2H NMR solid-echo spectra for several interpulse delays tp: (a) glycerol-d5, (b) toluene-d5, (c) simulations assuming small angle reorientation (cf. text).
Figure 2. 2H NMR solid-echo spectra with interpulse delay tp ) 20 µs for (a) glycerol-d5 (type A glass former) reflecting changes due to the R-process and (b) toluene-d5 (type B system) at temperatures where changes due to the β-process are expected. Time constants of R- and β-process are indicated (cf. Figure 1).
conclusion that the NMR spectrum is determined by its rigid limit coupling constant; in the case of 2H NMR a Pake spectrum is found. Apparently, similar results are observed when toluened5 and glycerol-d5 are investigated. In Figure 2 the 2H NMR spectra are displayed for temperatures where changes due to the (a) R- and (b) β-process are expected (cf. Figure 1 for the correlation times of both processes17,18 and the time window of the chosen NMR technique). In the case of glycerol, the NMR line-shape reflects a transition from a Lorentzian line at high temperature to a Pake spectrum at low temperature, i.e., a transition from fast to slow isotropic reorientation as it is expected for the R-process. We note that the 2H NMR frequency in organic molecules is determined by the orientation of the C-2H bond with respect to the magnetic field.20 Any reorientation of the bond on the time scale of 1D NMR is probed. On the other hand, the line-shape of the toluene spectra does not change at temperatures where the β-process is expected to show up. Instead, a Pake spectrum is always observed. The R-process of toluene cannot be monitored because of the high tendency to crystallize. To explain the absence of spectral changes in Figure 2b, one may speculate that the distribution of correlation times is partially outside the NMR time window and/or that the molecular reorientation is too small in angle to affect the line shape. To check the first possibility we measured 2D spectra. The spectra obtained for mixing times up to 100 ms exhibit no discernible off-diagonal intensity, whereas for longer times indications for an onset of spin-diffusion mediated by dipolar coupling are observed. We conclude that the motional process related to the β-process is essentially characterized by smallangle reorientation. Next, we took advantage of the possibility to apply multipulse sequences in NMR. Monitoring broad 2H NMR absorption lines, a two-pulse solid-echo sequence has to be applied.20 Actually, this was also done recording the spectra in Figure 2. There, a short interpulse distance tp ) 20 µs was chosen. However, enlarging the pulse delay tp allows one to increase the sensitivity on the motional mechanism significantly.20,23 The longer the tp
Figure 4. 2H NMR solid-echo spectra of toluene-d5: (a) interpulse delay tp ) 300 µs at T ) 116 K, (b) tp ) 200 µs at various temperatures.
the smaller changes in molecular orientation can be detected by the solid-echo technique. In Figure 3a and 3b we present the solid-echo spectra of glycerol-d5 and toluene-d5 for the same reduced temperature T/Tg ) 0.83 and various tp. Pronounced changes are now observed for toluene but not for glycerol. Starting with a Pake spectrum for short tp, the intensity in the middle of the spectrum declines for toluene when increasing tp. As discussed, glycerol does not show a β-process but rather a kind of 1/f noise which is obviously not probed by the spectra. Unlike this, the strong β-process of toluene is reflected provided the solid-echo technique is systematically applied. We conclude that below Tg type B glass formers (toluene) exhibit significantly different molecular reorientation as compared to type A systems (glycerol). The question arises whether all molecules are involved in the β-process. Assuming that not all molecules take part, independent of tp, a Pake spectrum is expected for the rigid fraction and, consequently, intensity in the middle of the spectrum is retained. However, inspecting Figure 4a, where for T ) 116 K and tp ) 300 µs the intensity at ν ≈ 0 almost disappears, we conclude that essentially all toluene molecules participate in the β-process. No indications for “islands of mobility” are found, but all molecules perform small-angle rotational jumps. Of course, for glasses we expect that both angle and time constant are governed by a broad distribution. For example, a small fraction of molecules undergoing less hindered reorientation cannot be completely ruled out. In Figure 4b we show the temperature dependence of the solid-echo spectrum with a fixed interpulse distance tp ) 200 µs. Cooling the glass leads qualitatively to the same effect as shortening tp: the changes as compared to the Pake spectrum become smaller the lower the temperature. This is expected because on lowering temperature the distribution of correlation times of the β-process shifts to longer time constants and, accordingly, fewer and fewer molecules change their orientation on the time scale of 1D NMR. Moreover, knowing from 2D
Letters NMR experiments on toluene-d5 that the spin diffusion rate is invariant in the chosen temperature range, the observation of a temperature-dependent line shape excludes spectral changes due to spin diffusion. To simulate the solid-echo spectra of toluene we assumed that the molecular axis jumps on the edge of a cone with a full opening angle γ. We chose eight equally separated positions on the cone among which the molecular axis exchanges by nextneighbor jumps. In a computer simulation the corresponding trajectories were produced. Knowing them, the NMR spectra can be calculated.23 With this simple model we can already reproduce the salient features of the measured spectra. This is demonstrated in Figure 3c where simulated spectra for γ ) 6° and a time constant τβ ) 1 ms are displayed. In a forthcoming publication, we will demonstrate that introducing a distribution of correlation times and of angles γ as well as using more positions on the cone, i.e., assuming a gradual reorientation, a quantitative description of the spectra is achieved. In the case of glycerol, where the solid-echo spectra are not affected by molecular dynamics, we estimate that on the time scale of 1D NMR hardly any rotational jump involves angles γ > 1°. Altogether, analyzing the solid-echo spectra for large pulse delays tp allows one to estimate the spatial extent of highly hindered reorientation, which is difficult when measuring 1D and 2D NMR spectra in the usual way. We add that secondary processes in polymers can be investigated by recording 2D NMR spectra.19 For poly(methyl methacrylate), significant off-diagonal intensity was found and the secondary process was identified as large-angle reorientation of the side group. Discussion Generalizing our results, we conclude that the β-process in simple organic glasses originates from some kind of highly restricted molecular reorientation of essentially all molecules. No indications for “islands of mobility” are foundsa conclusion also drawn from spin-lattice relaxation studies.24 Since the β-process is also observed for rigid molecules its origin is intermolecular. Furthermore, because the susceptibility as revealed by DS exhibits a behavior typical of a thermally activated process determined by a broad distribution of activation energies, we think that the β-process is virtually a local process. The β-process exhibits further features which are compiled from DS: (i) a relaxation strength which is constant in the glass but which increases with temperature above Tg.6-9,15,17 This implies that the mean angle of molecular reorientation (γ) is constant in the glass but increases above Tg, i.e., the reorientation becomes less hindered in the supercooled liquid. As will be demonstrated in a forthcoming publication, indication for this change of geometry is found when the solid-echo studies are extended to T > Tg. Furthermore, we will show that indeed γ
J. Phys. Chem. B, Vol. 104, No. 18, 2000 4287 may be taken to be temperature independent in the glass, i.e., at T < Tg. Thus, our measurements do not favor an increase of the numbers of relaxators at T > Tg as expected by the defect model;6 (ii) a mean activation enthalpy proportional to Tg,15,17 and (iii) a merging of R- and β-process at high temperatures.6-10,15,17 These features are difficult to explain if a mere side group reorientation is assumed. As discussed, many polymers show a secondary relaxation process in which a side group reorientation is involved.2,7-9,19,20 We suggest that the secondary relaxation process found in many polymers is in fact a β-process as observed in simple (rigid) glass formers. However, the presence of a side group may possibly lead to an increased relaxation strength. We speculate that the β-process may be taken as self-induced by the specific packing of the molecules in the glass. Due to reasons yet not understood certain molecules pack in a way as to allow for a secondary process and others not. References and Notes (1) Gilroy, K. S.; Phillips, W. A., Philos. Mag. 1981, B43, 735. (2) McCrum, N. G.; Read, B. E.; Williams, G. In Anelastic and Dielectric Effects in Polymer Solids; Wiley: London, 1967. (3) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372. (4) Williams, G.; Watts, D. C. Trans. Faraday Soc. 1971, 67, 1971. (5) Goldstein, M. J. Chem. Phys. 1969, 51, 3728. (6) Johari, G. P. Ann. N. Y. Acad. Sci. 1976, 279, 117. (7) Johari, G. P. J. Chimie 1985, 82, 283. (8) Garwe, F.; Scho¨nhals, A.; Lockwenz, H.; Beiner, M.; Schro¨ter, K.; Donth, E. Macromolecules 1996, 29, 247. (9) Arbe, A.; Richter, D.; Colmenero, J.; Farago, B. Phys. ReV. E 1996, 54, 3853. (10) Wu, L. Phys. ReV. B 1991, 43, 9906. (11) Richter, D.; Zorn, R.; Farago, B.; Frick, B. Phys. ReV. Lett. 1992, 68, 71. (12) Ro¨ssler, E. Phys. ReV. Lett. 1992, 69, 1620. (13) Richter, D.; Zorn, R.; Farago, B.; Frick, B. Phys. ReV. Lett. 1992, 69, 1621. (14) Ro¨ssler, E.; Eiermann, P.; Tauchert, J.; Warschewske, U. P. Physica 1993, A201, 237. (15) Kudlik, A.; Tschirwitz, C.; Benkhof, S.; Blochowicz, T.; Ro¨ssler, E. Europhys. Lett. 1997, 40, 649. (16) Leheny, R. H.; Nagel, S. R. J. Non-Cryst. Solids 1998, 235-237, 278. (17) Kudlik, A.; Benkhof, S.; Blochowicz, T.; Tschirwitz, C.; Ro¨ssler, E. J. Mol. Struct. 1999, 479, 201. (18) Blochowicz, T.; Kudlik, A.; Benkhof, S.; Senker, J.; Ro¨ssler, E. J. Chem. Phys. 1999, 110, 12011. (19) Schmidt-Rohr, K.; Kulik, A. S.; Beckham, H. W.; Ohlemacher, A.; Pawelzik, U.; Boeffel, C.; Spiess, H. W. Macromolecules 1994, 27, 4733. (20) Schmidt-Rohr, K.; Spiess, H. W. Multidimensional Solid-State NMR and Polymers; Academic Press: London. 1994. (21) Schnauss, W.; Fujara, F.; Sillescu, H. J. Chem. Phys. 1992, 97, 1378. (22) Hinze, G.; Sillescu, H. J. Chem. Phys. 1996, 104, 314. (23) Vogel, M.; Ro¨ssler, E. J. Magn. Reson. 1999, submitted. (24) Bo¨hmer, R.; Hinze, G.; Jo¨rg, T.; Qi, F.; Sillescu, H. J. Phys.: Condens. Matter 1999, 11, 1.
