Neutron scattering experiments on the glass transition of polymers

Physica A 201 (1993) 52-66 North-Holland SDI: 0378-4371(93)E0235-7

Neutron scattering experiments transition of polymers

on the glass

R. Zorna, D. Richter”, B. Frickb and B. Faragob “Forschungszentrum Jiilich, IFF, Postfach 1913, W-51 70 Jiilich, Germany bInstitut Laue-Langevin, BP 156X, F-38042 Grenoble Cedex, France

Neutron scattering experiments have been performed to explore the dynamics of polymers near the glass transition. The experimental data show three distinct types of relaxations: (1) Susceptibility spectra exhibit a contribution in addition to phonons around a temperature independent frequency. (2) Neutron-spin-echo (NSE) experiments show a slow relaxation of the stretched exponential type. Above 220K, the characteristic time of this process strictly follows the Vogel-Fulcher dependence of viscosity data indicating the direct connection between microscopic and macroscopic relaxation. (3) Below 220 K, the temperature dependence of the relaxation observed by NSE changes to an Arrhenius form while the viscosity still follows the Vogel-Fulcher law. Analysis of the Q dependence from IN13 backscattering data reveals a change of mechanism at the crossover. The experimental findings will be discussed emphasizing the comparison with the mode coupling theory. Aspects of agreement as well as deviations will be pointed out in the discussion.

1. Introduction

The glass transition of disordered materials is connected with several anomalies of the dynamics which have been subject of strong experimental and theoretical interest. To name a few, non-Debye relaxations, non-Arrhenius temperature dependencies, and multiple relaxations (a, p, . . .) could be observed. On the theoretic side microscopic descriptions have been developed (especially by the mode coupling theories) in order to explain the dynamical features of disordered materials. Neutron scattering offers the unique possibility to observe the dynamics of disordered materials on a microscopic length scale. This is possible because the wavelength of neutrons matches the characteristic intermolecular distance (some A) and their energy allows the resolution of energy transfers by the slow processes involved (< 1 meV) at the same time. The scattering function S(Q, o), which is basically the probability of scattering dependent on the wave vector Q and the energy transfer fiw, contains the spatial information in the Q 0378-4371/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved

R. Zorn et al. I Neutron scattering from glassforming polymers

53

dependence and the temporal information in the o dependence- both in a Fourier transformed representation of the particle correlation function. By choosing appropriate isotopes, either coherent scattering from the interparticle correlation or incoherent scattering from the particle self-correlation can be observed. Polymers are well suited for the investigation of glass properties because they do not tend to crystallization if their microstructure is sufficiently disordered. In this article we will present neutron scattering experiments on polymers covering different dynamical ranges between some nanoseconds and less than one picosecond. The experiments will be grouped according to the three types of relaxations observed, which can be distinguished by their characteristic times and their temperature dependence.

2. Experiments Most of the experiments have been carried out on deuterated cti-trans-vinyl (47 : 46 : 7) polybutadiene (-CD,-CD = CD-CD,-),. Except for the 7% vinyl content this polymer has no sidegroups which would complicate the dynamical behaviour. It contains randomly distributed C-bond orientations (cis and tram). For this reason crystallization is prevented, and the system is known as a good glass former. The molecular weight was M, = 93 000 with a polydispersity M,lM, = 1.03. The glass transition temperature was determined to 181 K with a width of 2 K by calorimetric measurements. The deuteration of the molecule results in a predominant coherent scattering from two-particle correlations. Diffraction experiments have shown that the static structure fa$or shows a first peak correspon$ing to the interchain (at 160 K) [l]. distance at 1.48 A followed by a minimum at 2.1 A The comparison with dielectric measurements mentioned in section 3.2 had to be done on cis-tram-vinyl (76 : 18 : 6) polyisoprene (-CD,-CD = C(CD,)CD,-), because the methyle group induces the necessary electric dipole moment. The time-of-flight (TOF) measurements were performed at IN6, a timefocusing spectrometer at ILL, Grenoble. The incident wavelength was set to 5.12 A, which makes scattering vectors up to Q = 2.05 A-’ (at zero energy transfer) accessible. The FWHM of the energy resolution was about 90 FeV, but since the resolution function shows strong wings on both sides of the elastic peak, only the range of energy transfers > 100 p,eV could be used. Temperatures between 1.5 and 280 K have been chosen for this experiment. For the backscattering experiments IN13 at ILL, Grenoble, was employed.

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R. Zorn et al. I Neutron scattering from glassforming polymers

With an FWHM of the energy resolution of 8 PeV this instrument can resolve the broadening of the elastic line also at lower temperatures. Due to its low incident wavelength (2.23 A) it covers a large range of scattering vectors (1.19-4.83 A-‘). Of course this feature can only be achieved at the expense of intensity. So only a few temperatures could be chosen, and the data presented here had to be restricted on incoherent scattering from a protonated sample. Highest energy resolution can be realized by the neutron-spin-echo (NSE) technique on IN11 at ILL, Grenoble. As described elsewhere (see, e.g. [2]), NSE measures directly the normalized intermediate scattering function S( Q, t) / S(Q) in contrast to the aforementioned methods which give the Fourier transform S(Q, w). The time window extends from 3 ps up to 3 ns, which corresponds to an energy resolution of about 0.2 FeV. At present, NSE instruments are only capable to observe one wavevector at a time.rSo most of the experiments were carried out at fixed values Q = 1.48 8, and Q = 1.88 A-l, i.e. at the peak and the first minimum of the static structure factor.

3. Experimental results

3.1. P,,s*relaxation Fig. la shows the scattering

function

s(Q, o) obtained

from the TOF

spectrometer IN6 for the wave vector Q = 1.48 A-‘. The increase of nonelastic intensity with temperature is clearly visible. In order to test whether this increase can be explained by phononic scattering with a constant density of states, the scattering functions have been resealed a Bose factor, [l - exp(tiwl ksT)]-‘, and a Debye-Waller factor, exp(-+ (ri)Q*) (derived in [3] for polybutadiene), to the same reference temperature after subtraction of the elastic line. From fig. lb one can see that this scaling is successful for T s 120 K but for higher temperatures only in the energy range tiw > 3.5 meV. For higher temperatures an additional component arises in the scattering at low energies and increases with temperature stronger than the phononic part. This feature has to be regarded specific for disordered materials as it can be found in many different glass formers (e.g. low-molecular [6], ionic [7], proteins [S]). By the same Bose- and Debye-Waller scaling factors the scattering function at 120 K has been transformed into the phononic part of the scattering function at higher temperatures. The remainder after substraction of this part, ascribed to relaxational processes, is shown in fig. lc as the imaginary part of the susceptibility x’;, 0~wS( Q, 0). The stability of the subtraction procedure was tested against three possible

R. Zorn et al. I Neutron scattering from glassforming polymers

55

.Ol I

-1

0

1

2

3

4 Rd

6

6

7

2

9

10

[mev]

“& 50 ?45 40

-g

‘

35

&g

30

y

25

2

20

m

15 10 5 0 -1

0

1

2

3

4 hd

5

6

7

2

9

10

[meV]

E ImeVl Fig. 1. (a) TOF spectra S(Q, o) for the wave vector Q = 1.48 A-’ coherent scattering from polybutadiene at the temperatures 1 K (instrumental resolution), 100, 120, 160, 180, 200, 240 K (bottom to top curve). (b) Same spectra as in the previous figure after subtraction of elastic line and scaling with the Bose- and Debye-Waller factor. (c) Double logarithmic plot of the relaxatiynal susceptibility of polybutadiene for temperatures 200-280K at the wave vector Q = 1.48 A The line indicates the maximal slope a = 0.395 consistent with MClh which should describe the asymptotic slope of the susceptibility as well as the shift of the minimum in a log/log plot.

56

R. Zorn et al. I Neutron scattering from glassforming polymers

sources of errors: (1) an error in the assumed Debye-Waller factors, (2) a wrong choice of the temperature from which the phononic part is taken, (3) an overall intensity difference between the two spectra to be subtracted. These changes led to no larger deviations than ?lO% in the absolute values of the resulting difference. As can be seen from fig. lc the relaxational susceptibility has its maximum at 1 meV (-0.2THz) for all temperatures. The maximum is followed by a minimum towards lower energy transfers which is deeper at lower temperatures and shifts slightly on the energy scale. The slope leading to the maximum never exceeds one in the log-log plot, so the extra susceptibility is still quasi-elastic, although recent findings of Frick on polyisobutylene show that this is not a general rule in polymers [4]. At the lower end of the accessible energy range the ascent towards the elastic line becomes visible. This could indicate its broadening but as well be a residual wing of the resolution function. This qualitative o dependence applies to all observed wave vectors and also to incoherent scattering from particle self-correlation [5]. This fast relaxational process cannot be explained by side-group motions. Rather it has to be seen as a general phenomenon connected with the glass transition. It cannot be related to the “/3 branches” in relaxation maps from dielectric susceptibility measurements which occur at much lower frequencies (“1 GHz) -for this reason we have introduced the term &. 3.2. (Y relaxation Fig. 2a shows the two-particle correlation function S(Q, t)/S(Q) measured by NSEi at a wave vector near the peak of the static structure factor Q = 1.48 8, [9]. The observed relaxation function has a pronounced Kohlrausch with an exponent /3 = 0.45 + 0.02. From this raw behaviour, fexp[-(t/r)‘], data one can immediately see the strong slowing down of the relaxation when the temperature is decreased. Furthermore, it has to be noted that the correlation functions do not start at the value 1 for small times despite their normalization. This is a consequence of the Pfast relaxation which is not directly observable in the time range of NSE. Spectra of different temperatures can be resealed to a single master-curve using the macroscopic viscosity data. Here, the Vogel-Fulcher expression for the monomeric friction coefficient (which is proportional to the viscosity) 5 = Coexp]l/a(T - TJI, with &,= 1.26 x lo-” dyne s/cm, Z’, = 128 K, and (Y= 7.12 x 10e4 K-l, given by Berry et al. [lo], has been applied. Fig. 2b presents the result of resealing the time to t/T with T = 7,J(T)/T where 7,, is a prefactor common to all temperatures. For more than 7 orders of magnitude in the

R. Zorn et al. I Neutron scattering from glassforming polymers

_‘J

tb’

0

-10

-5

0

57

\1

41 (t/T)

Fig. 2. (a) Neutron spin echo spectra obtained at Q = 1.48 A-’ for temperatures 200-280 K. The solid curves are the result of a combined fit to the Kohlrausch law. (b) Data from (a) with the time resealed to the macroscopic viscosity scale.

resealed time the NSE data follow a Kohlrausch law. This means that the dynamics on the level of interchain distance scales directly to the time scale of the macroscopic viscosity, i.e. microscopic and macroscopic relaxation are directly related. This so-called LYrelaxation universality can be shown in polyisoprene also including data from dielectric spectroscopy [ll]. Both the results of NSE at two wave vectors and dielectric measurements of two modes of the (Ytype#’ [12,13] are presented in fig. 3 as an activation plot of the mean relaxation times (7). One immediately notices the non-Arrhenius character of all relaxation times. In addition, the curves differ only by constant factors, xl The electric dipole moment of the monomeric unit has to the chain contour. Only the perpendicular component contribution dependent on the motion of the individual parallel component sums up over the chain and causes the the end-to-end vector.

components perpendicular and parallel gives rise to a dielectric susceptibility segments, the segmental mode. The normal mode, reflecting the motion of

58

R. Zom et al.

I Neutron scattering from glassforming polymers

I

-iI

,',

+

Scatter

I

++

+

X

xx

X xxx

23

.10-s

I 3.0

I

I 1000K/T

3.5 4.0 1000K/T

Fig. 3.

Fig. 4.

3.5

4.0

3.0

4.5

4.5

Fig. 3. Activation plot: Mean relaxation time (T) = (~I~)T(~I~)T,,, vs 100 K/_?; for the dielectric normal mode (+), the dielectric segmental mode (x), NSE at Q = 1.44A (0) and 1.92 A-’ (0). Fig. 4. Plot of (T) divided by the rheological shift factor aT vs 100 KIT. Symbols are the same as in fig. 3.

(T,,,, p)

: (q,,

p)

: (T,,,,)

: (~,,,,)

= 1: 6 : 25 : 2.5 x lo6 .

To show this more clearly, the relaxation times have been resealed by a common shift factor derived from rheological measurements which is given by a Vogel-Fulcher law with T, = 176 K and (Y= 2.0 x 1O-3 K-i [14] in fig. 4. Taking into account the seven decades of total span, the deviations among the scaled values do not contradict scaling. Concerning the Kohlrausch exponent /3 one finds a good agreement between NSE between (/31,48~-1 = 0.38, p1,92~-1 = 0.45) and segmental model (&_,, = 0.39) but a significant deviation for the normal mode (p,,,, = 0.54-0.60, depending on the temperature). Thus, for the segmental model the universality extends not only to the temperature dependence but also to the functional form of the relaxation and the order of magnitude of the characteristic times. relaxation 3.3. Pslow

The preceding NSE experiment could not detect any relaxation for temperatures T s 200 K because the time constants become too large to perform a reliable evaluation from the data in the NSE time window. If one changes to a wave vector corresponding to the first minimum of the static structure factor [15], Q = 1.88 A-’ (fig. 5a), preconditions are better for observations at low

R. Zom et al. I Neutron scattering from glassforming polymers

59

0.6

a 00.6 z 20.4 ;;

Fig. 5. (a) Selected neutron spin echo spectra obtained at Q = 1.88 A-’ for temperatures MO250 K. The solid curves are the result of fits to the Kohlrausch law with the experiment p = 0.37. (b) Data from (a) with the time resealed to the macroscopic viscosity scale. (+) 280 K; (0) 260 K; (A) 250 K; (0) 240 K; (X) 230 K; (0) 205 K; (v) 190 K; (0) 180 K. The solid curve represents the master function obtained for the spectra with T 3 220 K. The dashed curves are the results of individual fits keeping p = 0.37 fixed.

temperatures, because the characteristic times are smaller by an overall factor of about 10 at this wave vector. Here, it becomes clear that relaxation persists down to 180 K in the NSE time window. Inclusion of relaxation curves at temperatures below 220 K into a master-plot as described above leads to the result that scaling is not any more fulfilled in the low temperature regime (fig. 5b). An increase in the amplitude f as well as a deviation of T(T) from the macroscopic viscosity scale can be reported. The latter fact becomes manifest in an activation plot of the characteristic times (fig. 6): while for temperatures above 220 K, r(T) follows the Vogel-Fulcher line of viscosity data, the temperature dependence crosses over to an Arrhenius one below#*. The crossover takes place at a temperature significantly higher than the conventional glass temperature 181 K. Obviously, the simple picture of directly coupled microscopic and macroscopic relaxation does not work any more in the low temperature range. Although a final interpretation of the decoupling is far from being clear we want to point out the similarity of the temperature dependence T(T) as well as the absolute value of r at the crossover to the branch p branch in dielectric measurements on other polymers. Another signature of the anomaly far above Tg = 181 K can be found in the strength of the slolw relaxation, f(T), obtained from the NSE data at a wave [17]. Here, this value f(T) is defined either as the prevector of 1.88 A “Recent rheological measurements [16] have supported the validity of the Vogel-F&her expression down to 190 K. Below, the temperature dependence of viscosity seems even stronger making the discrepancy to NSE times larger.

R. Zorn et al. I Neutron scattering from glassforming polymers

60

t I

l

34

3.5

40

45 WQfT

50

55

Fig. 6.

60

0.7;

’

i 100

I

I

I

I 300

200 T [Kl Fig. 7.

Fig. 6. Arrhenius representation of the relaxation rates obtained by fitting the Kohlrausch law to the NSE data at different temperatures. The three symbol types represent three different sets of experiments carried out in separate runs. The solid line displays the viscosity time scale. The dashed line indicates the Arrhenius behaviour of the &,,, branch. Fig. 7. Temperature dependence of the (Y/&,~ relaxation strength f(Q, T) at Q = 1.88 A-‘. The solid line is the result of a fit with MCTh square-root law. The three symbols display results from three different independent experimental runs.

exponential factor in the Kohlrausch law or as the constant value of S(Q, t)l S(Q) if the relaxation is completely arrested (in the time window of the experiment), fig. 7. While for higher temperatures the constant value 0.77 is assumed, a steep rise of f(T) occurs when the region 210-220 K is crossed towards lower temperatures. This can immediately be recognized from the untreated data (fig. 5b) too: besides the non-scaling on the reduced time axis the data points for T < 220 K fall above the master curve established by the high temperature data. In order to get spatial information about the change of the microscopic mechanism at the crossover, incoherent data from the backscattering instrument IN13 have been fitted by the Fourier transform of the Kohlrausch function convoluted with the resolution function (fig. Sa) [18] for all available wave vectors Q. Under the Gaussian approximation one obtains

S(Q, 4 = exp[-~Q2(r2(t))l for the intermediate incoherent scattering function. Assuming a fractal time law (r*(t)) 0:to (instead of the ordinary diffusion expression (r*(t)) = 6D,t) would

R. Zorn et al. I Neutron scattering from glassforming polymers

d z

‘;; c

t-

10

__\z=\

1 -=y lo* -

0

0

100

61

200

__=

1-x

=-I-=_=

<=1x\

y-L~<~I~ I 1.5

I

1

I

2

3

4

5

0. [A-‘]

tlw [IleVI

Fig. 8. (a) Scattering functions S(Q, w) from the backscattering instrument IN13 (H-polybutadiene at 230K) for the wave vectors Q = 1.19, 1.39, 1.53, 1.79, 1.99, 2.18, 2.37, 2.56, 2.75, 2.93, 3.44, 4.20, and 4.83 A-’ (front to rear). The curves represent fits with the Kohlrausch law with p = 0.3. (b) Double logarithmic plot of Kohlrausch times T(Q) from fitting the IN13 spectra with p = 0.3. The data are from three temperatures (210, 230, and 250 K, top to bottom). The error bars stem from the uncertainty in estimating the sample dependent background. The solid lines represent the relations T(Q) a Q _“.

easily explain the Kohlrausch law, exp{ -[t/r(Q)]‘}, with r(Q) 0~Q-” where np =2 [20]. Fig. 8b shows the Kohlrausch times r from fits for the three temperatures 210, 230, and 250 K #3. The lines indicate the relation T(Q) m Q -“. Indeed, the power law is fulfilled within the range of experimental uncertainties. But the values of PZ(table I) are compatible with np = 2 only in the case T = 210 K. Fits with different p in the allowed range yielded values of n/3 differing not more than 0.1, so we can consider this result as independent of the choice of p. From this we conclude that the hypothesis of Gaussian behaviour with a fractal diffusion cannot be sustained on polybutadiene at least for the small length scale considered here. This is in contrast to the recent result of Colmenero et al. [19,20] for the polymers poly(viny1 methyl ether), poly(viny1 Table I Q dependence exponents of the Kohlrausch times from fits of incoherent spectra with p = 0.3 for different temperatures. Temperature (K)

II

nB

210 230 250

6.0 f 1.6 4.3 f 0.9 4.1 Il.1

1.8020.48 1.30 f 0.27 1.22 2 0.33

‘3 It has to be noted that the determination of the stretching parameter p from the IN13 data alone is difficult because the background (instrumental and due to the fast relaxations) cannot be fixed with certainty. A consideration of the extreme cases of (1) pure instrumental background and (2) maximal subtractable background yields the limits 0.17 s p s 0.40. The results compiled here were obtained with p = 0.3.

62

R. Zorn et al. I Neutron scattering from glassforming polymers

chloride), and poly( bisphenol A, 2-hydroxypropylether) where the relation n/3 = 2 is fulfilled well. (Those results are mainly based on IN10 experiments in the wave vector 0.2-2A-1 while our IN13 data cover 1.2-4.8A-*.) Possibly, the discrete nature of the elementary process constituting the cx relaxation becomes visible at the larger wave vectors, i.e. smaller length scale of IN13. Comparing r(Q) for the different temperatures one notices that the data above 220 K are only shifted parallel on the logarithmic scale which means that the same temperature dependence applies to all wave vectors. In contrast to this, the data set at 210 K shows a stronger temperature dependence for low Q. This suggest that motions on a larger spatial scale are suppressed more strongly by cooling down.

4. Discussion and comparison

with mode coupling theory

At least for temperatures above 220 K the basic picture of the mode coupling theory (MCTh) of Gotze et al. (see [21] for a comprehensive presentation of the MCTh) is confirmed by the neutron scattering data: two relaxation processes exist, of which the faster (&,,) process shows essentially no temperature dependence. The slow (a) process is strongly temperature dependent and its time scale is universal on all length scales and for different observation methods in the temperature range 3 220 K. Furthermore the existence of a critical temperature T, in the sense of MCTh can be shown by different approaches. The most convincing result in this respect can be obtained from the temperature dependence of the CYrelaxation strength (fig. 7). The prediction of MCTh,

f( Q, T) = f”( Q)

+

;;4;‘fi+“(‘)

for T < T, , for T > T, ,

where E = (T, - T)/T,, is fulfilled well with T, = 216 k 1 K. This square-root relation can be confirmed for the wave vector at the maximum of s(Q) [9] and for NSE data from polyisoprene [ll] too. Data of the viscosity can also be fitted with the power law dependence resulting from MCTh [22] l(T) = A(T - TJy in the temperature range 250450 K [17]. The fit yields y = 3.2 and T, = 214 k 3 K and describes the data better than the usual Vogel-Fulcher law. Although the choice of the temperature range is somewhat arbitrary this shows at least the compatibility with MCTh. MCTh states that a minimum in x”(o) should occur at the frequency o,~,,

R. Zom et al. I Neutron scattering from glassforming polymers

63

where the (Yrelaxation crosses over to the p relaxation. The minimum position should obey the following power laws asymptotically when T approaches T,:

where E is defined as above and a is a material dependent parameter in the range O
1

1

Y=z+s’

with 3 < A < 1. This system of equations determines all parameters A, u, b, y if only one of them is known and allows the calculation of h from any one of the parameters. Table II shows a comparison of A derived in the different ways. It is clear that the crude determination of a does not give much information but the values from b to y coincide quite well. Finally, we note that the wave vector dependence of the (Y relaxation parameters in coherent scattering qualitatively fulfills the predictions of MCTh: f(Q) has its maximum at the peak of the structure factor while 1/7(Q) goes through a minimum there (fig. 10). The latter fact can also be understood in terms of the De Gennes narrowing: correlations which are preferred by the system, build up the maximum in S(Q) and consequently decay more slowly

PI *

64

R. Zorn

et al. I Neutron

scattering from glassforming polymers

1 ,x3____{ , j

TIKI

1

Q (A-‘)

Fig. 9.

Fig. 9. Temperature dependence for Q = 1.48 A-’ and 2.1 Ai-’

2

Fig. 10. of the square of the minimum in the dynamic susceptibility xLi.

Fig. 10. Q dependence of the (Y relaxation strength f(Q) and the ratio of the relaxation rates T(Q = 1.48A-l)/r(Q). The solid line represents the static structure factor S(Q) at 230K. The different symbols correspond to NSE experiments with different incident wavelengths.

Although these general results are all in favour for the MCTh, a number of discrepancies have also to be noted. First of all, the well-established fact that the critical temperature T, does not coincide with the conventional glass transition temperature Tg but is about 35 K higher is observed in polybutadiene too. This means that below T, the macroscopic viscosity (by which Tg is often defined) still has a finite value. By the neutron scattering experiments reported here, this phenomenon can be tracked down into the microscopic regime: as can be seen from figs. Sa and 5b, relaxation on microscopic length scales persists below T,. The time constants derived from the NSE experiments do not diverge in a (T, - T)-Y fashion, neither do they follow the macroscopic time scale below T,. The minimum in the susceptibility shown in figs. lc and 9 does not drop to zero at T, as it would be expected from MCTh and the scaling law for its position on the energy scale cannot be fulfilled with an a parameter agreeing with the restrictions of MCTh. Table II Comparison of MCTh exponents. Origin

Exponent range

h

/3 slope (Yvon Schweidler fit viscosity power law

a = 0.15-0.61 b = 0.30-0.37

0.50-0.95 0.86-0.90 0.84

y = 3.2

R. Zorn et al. I Neutron scattering from glassforming polymers

65

The reason for these deviations is due to the fact that here- like in most present applications of MCTh - the ideal version of the theory was applied. In this version processes due to thermally assisted hopping over potential barriers created by the neighbouring particles are not taken into account. These processes enable a system to maintain ergodicity also below T,, where the ideal In consequence the glass transition MCTh predicts strict non-ergodicity. becomes “smeared out” or, in other words, the rigorous division into glassy and liquid states cannot be sustained. It can be understood that an approach using non-ideal MCTh would give a qualitative account for the deviations near and below T, mentioned above#4. Nevertheless, the question remains open whether complex phenomena like the branching off of the pslOWprocess from the (Y process can also be explained quantitatively by a non-ideal MCTh. In the sense of the non-ideal MCTh, pslOW and a relaxation are the structural relaxation only differing in the extent to which hopping processes are involved in restoring ergodicity. In this respect the decoupling of time scales of macroscopic and microscopic relaxation is rather surprising. A completely different approach towards the explanation of the Pfast relaxation can be found in the soft-potential model [25-271, which starts from the consideration of eigenmodes in an amorphous solid. This model assumes the occurence of soft-potential modes (i.e., with a dominant fourth-order term in the potential dependence on the normal coordinate of the mode) as a characteristic feature of glassy systems. Indeed, broad low energy excitation bands can be observed in many glassy systems but not in comparable crystalline systems by neutron scattering [28]. In the case of polybutadiene the low energy excitations constitute the maximum at 2 meV, visible in fig. lb, which has been subtracted for the treatment of Pfast relaxation in the framework of MCTh. Under the point of view of the soft-potential model the Pfast contribution is due to an increase of the density of states at low energies when the temperature is raised towards the glass transition”5. So it is not a genuine relaxation and a phenomenon like the inelasticity of the Pfast “relaxation” found in polyisobutylene [4] is not surprising any more. For the time being the soft-potential model proved successful in explaining

“Under this point of view it may even surprise that the square-root singularity in the temperature dependence off is so pronounced. The reason for this lies in the procedure chosen to extract this value: fitting of the Kohlrausch function to the Q relaxation region recovers its true amplitude regardless whether it is totally arrested or not. Would one alternatively chose the value of S(Q, rOla)/S(Q) at a fixed time tala which should separate the two relaxations to define f, one would obtain a smearing out of the singularity. X5Numerical simulations have shown this kind of increase in non-crystalline Lennard-Jones systems [29].

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R. Zorn et al. I Neutron scattering from glassforming polymers

anomalies at temperatures far below Tg (e.g. in the specific heat of anorganic glasses below 2 K). It is still unclear which results an extension to higher temperatures will yield, especially whether finally a connection to the picture of MCTh above T, can be drawn.

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