- Email: [email protected]
A Brillouin scattering study of an extremely ‘fragile’ molecular glass former
Journal of Non-Crystalline Solids 131-133 (1991) 139-143 North-Holland
139
A Brillouin scattering study of an extremely 'fragile' molecular glass former L. B~Srjesson, M. Elmroth and L.M. Torell Department of Physics, Chalmers University of Technology, S-412 96 Gothenburg, Sweden
BriUouin scattering results on the structural relaxation in fragile glass-forming propylene carbonate are presented. A new analyzing technique has been employed in which the full shape of the Brillouin spectrum was compared with a general hydrodynamic theory that has been modified to include non-exponential relaxation. The relaxation is found to be considerably stretched and time-temperature scaling is obeyed. This is by contrast with the reported crossover towards exponentially decay at high frequencies/high temperatures which has been observed previously with Brillouin scattering in other fragile systems such as glass-forming ionic liquids and ionic aqueous solutions. Such a crossover is also expected at sufficiently high temperatures both in mode-coupling and recent geometric phase-space percolation theories. It is concluded that there is no simple relation between the non-exponentiality of the relaxation and the degree of fragility as has been suggested.
1. Introduction
Most liquids can be supercooled below their equilibrium melting points and solidified to a glass provided that the cooling-rate is fast enough to avoid crystallization. It has been suggested that the viscosity and structural relaxation of glass-forming liquids show universal behaviour independent of the specific molecular interactions in the liquid. Universal features are departure from the Arrhenius behaviour of the relaxation time, nonexponential time decay often expressed in terms of the Williams-Watts (WW) relaxation function [1] q~(t) = %exp[ - (t/~') t~wW] and a cooling-rate dependent glass-transition temperature, Tg. Further, it has been proposed that time-temperature superposition (or scaling) of the relaxation function is obeyed in the transition region. The claimed time-temperature superposition principle is of considerable interest since in most theories it is either predicted or assumed. For example the mode-coupling theory [2] predicts scaling of the relaxation process at least around a critical temperature, Tc, located some 30 K above Tg. There are however several experimental results that show strong temperature dependences of flww and thus question the validity of the time-temper-
ature superposition principle [3-12]. Convincing results are reported from a 13 decades of frequency investigation of the dielectric relaxation in six molecular glass-forming liquids which show a continuous approach towards exponential relaxation at high frequencies/high temperatures [12]. Further, we have previously demonstrated that mechanical relaxation tends towards exponential relaxation at high temperatures for ionic glass formers and supercooled aqueous solutions by use of Brillouin scattering data combined with reported ultrasonic results [6,7]. Similar findings have been reported by other groups [8-11]. In the present work we have investigated a molecular glass former, propylene carbonate (PC), of extreme fragility with Brillouin scattering. The aim is, in a comparison with the previously studied ionic glass formers [6], to determine differences and similarities in the high-frequency relaxation properties between fragile glass-forming liquids [3] of different microscopic interactions. In order to obtain a complete view of the structural relaxation in PC, we apply other spectroscopic techniques (e.g. neutron scattering, photon correlation, Raman and dielectric measurements), preliminary neutron scattering results of which also appear in this volume [13].
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
140
L. Bi~rjesson et aL / An extremely "fragile" glass former
2. Experimental
In this paper, we report on a state-of-the-art Brillouin scattering investigation of the dynamics around the glass transition. A wide frequency window in combination with a new analyzing procedure makes it possible to stuc]y the relaxation characteristics over a relatively large temperature/ frequency range. For the frequency resolution, we have taken advantage of a Sandercock tandem F a b r y - P e r o t interferometer that provides a unique combination of a wide frequency window and a high resolution [14] and is thus ideal for Brillouin studies of the liquid-glass transition. Brillouin spectra were recorded in the temperature interval 140-345 K. Due to the tandem arrangement the obtained spectra are well resolved, are of highstatistical accuracy and are undistorted by neighbouring interference orders. Thus, the spectra are of such high quality that they can be used for a detailed comparison with theories. A new analyzing procedure has been employed in which we fit a general linearized hydrodynamic theory including non-exponential relaxation to the complete spectra. We have used the dynamic structure factor, S(Q, to), of the linearized hydrodynamic theory of ref. [15] for the analysis of the spectra. However, we have modified S(Q, to) to allow for non-exponential relaxation. In the analysis we have used the Cole-Davidson (CD) relaxation function rather than the commonly discussed WilliamsWatts function. This is because the CD form is more easily processable in the computing and its shape in frequency space is very similar to that of the Williams-Watts function [16]. The ColeDavidson relaxation function was introduced via Moo - M * ( i t o ) -
Mr
(1 + itoT) acD'
performed in this treatment [15,17]. Such a simple decomposition is not possible in the case of a non-exponential relaxation and, further, it involves a series of approximations whose validity is questionable for supercooled liquids. In the fitting procedure, the limiting low- and high-frequency sound velocities, c o and coo, the relaxation time, T, the non-exponentiality parameter, flCD, and an arbitrary intensity scaling variable were free parameters. Details of the experiment and the analysis can be found elsewhere [18].
3. Results
In fig. 1 we present typical experimental spectra, which have been deconvoluted from the instrumental resolution function using a modified Van Cittert [19] method, together with the corresponding best fits of S(Q, to). The spectra are obtained in the three ranges tot << 1, tot -- 1, and tot >> 1, respectively. The fits of S(Q, to) were at every temperature in excellent agreement with the experimental spectra. The analysis gave realistic values of all the fitting parameters only when the relaxation was allowed to be non-exponential, which then motivates the extra parameter flCD introduced via the Cole-Davidson function.
(1)
where 0 < flCD < 1, M * is the complex longitudinal modulus, M r = Moo- M0, and Moo and M 0 are the limiting high- and low-frequency values, respectively. Note, that the common decomposition of S(Q, to) into four components, representing the two longitudinal Brillouin modes, a Mountain mode and a Rayleigh mode, is not
-16.00
-8.00
0.00
8.00
16.00
Frequency Shift (GHz) Fig. 1. Brillouin spectra of propylene carbonate taken at temperatures corresponding to to~">> 1 (180 K), tot ~ 1 (255 K), and a~- << (330 K). The dots represent experimental data and the solid lines represent fits of general linearized hydrodynamic theory (see text).
L. BSrjesson et al. / An extremely "fragile"glass former
In fig. 2 we present the measured real and imaginary parts of the reduced complex longitudinal modulus, N ' = ( M ' - M o ) / M r and N " = M " / M r, in a masterplot representation. The values of N ' and N'" are derived directly from the parameters obtained from the fits of S ( Q , ¢o) for different temperatures [17] and t~ is taken from the frequency shift of the Brillouin peaks. Note that each point in fig. 2 represents a specific temperature. The relaxation is considerably stretched; the width of the loss peak is - 2 . 2 decades compared with 1.14 for exponential relaxation. The solid line in fig. 2 represents a frequency domain fit to the Williams-Watts relaxation function with flww = 0.6. The observed form of N " for propylene carbonate is significantly different from those reported previously for Ca0.4K0.6(NO3)l. 4 (CKN)
1.0
0.8-
N'
•
N" o Oo
o
o O
o
°,6
2
"O
~ 0.4" iI
0.2
0.0
-2.0
==
•
,
-1.0
'
1,0-
O--O
O---
0.8~w
Wo.. 6' xw
.K
w
x
X~
0.4
0.2
.0
112
14
116
6
T/Tg Fig. 3. Stretching parameter, flww, as a function of temperature for: ×, propylene carbonate; El, Cao.4Ko.6(NO3)l.4; O, Ca(NO3) 2 + 8H20. Solid lines are guides for the eye.
and Ca(NO3) 2 + 8H20
(CNH). For the latter systems the N " plots show much more asymmetric shapes, i.e. a broad wing for t0~-> 1 (low temperatures) and an approach towards single relaxation time for ¢a~"< 1 (high temperature) [6]. The different forms imply a stretching parameter flww which is temperatureindependent in the case of PC and strongly temperature-dependent for C K N and CNH. An important advantage of the present analysis
o
141
,
0.0
110
2J0
Log (c0) Fig. 2. Masterplot representation of the real, N', and imagin-
ary N ' , parts of the reduced longitudinal modulus of propylene carbonate obtained in the temperature interval 175-345 K. Solid lines represent a KWW relaxation function with flww = 0.6.
is that the relaxation characteristics, i.e. the relaxation time, ~'CD,and degree of non-exponentiality, fleD, are obtained independently for each temperature investigated. The so-obtained flCO values can be approximately converted to flww by use of the approach described in ref. [16]. In fig. 3 we present the resulting flww as a function of temperature. The value of flww ( - 0.5) is, within the experimental accuracy, observed to be temperature-independent, in accordance with the result of the masterplot analysis above. Thus, the timetemperature superposition principle is obeyed over the entire range from near Tg to more than 2Tg. It is notable that the stretching stays constant even at the high temperatures of 2Tg since one expects a crossover to exponential relaxation (flww = 1) somewhere in the high temperature region where the system becomes a 'normal' liquid. A stretched relaxation has, as far as we know, not previously been reported for any simple glass-forming liquid at the high frequencies/short relaxation times probed by Brillouin scattering. In fig. 3 we compare the present Brillouin results for flww with those obtained previously for C K N and C N H using a variety of different techniques [6,20-22]. It is evident from fig. 3 that the temperature dependence of the non-exponentiality of the relaxation function is completely different for the molecular liquid PC compared with the ionic liquid C K N and the aqueous solution CNH. This is especially
142
L. BSrjesson et al. / An extremely "fragile" glass former
n o t a b l e since these liquids are of similar degree of fragility. It has since long been suggested that for the structural r e l a x a t i o n o f a glass-forming liquid the degree of n o n - e x p o n e n t i a l i t y is i n t i m a t e l y linked with the d e p a r t u r e f r o m A r r h e n i u s behaviour, i.e. fragility [3,24]. F u r t h e r , previous exp e r i m e n t s have i n d i c a t e d that systems of increasing fragility show the stronger t e m p e r a t u r e d e p e n dence of fl a n d a crossover t o w a r d s e x p o n e n t i a l d e c a y at shorter r e l a x a t i o n times [7]. T h e p r e s e n t results then d e m o n s t r a t e that there is no such s i m p l e relation b e t w e e n n o n - A r r h e n i u s a n d n o n e x p o n e n t i a l b e h a v i o u r (see fig. 3). W e therefore question a n y universality related to the t e m p e r a ture d e p e n d e n c e of the stretching a n d in p a r t i c u l a r the t i m e - t e m p e r a t u r e s u p e r p o s i t i o n principle.
4. Conclusions T h e m o d e - c o u p l i n g theory p r e d i c t s scaling, however, o n l y in a limited range a b o v e its critical t e m p e r a t u r e , Tc [2]. A t high e n o u g h temperatures, n o r m a l h y d r o d y n a m i c s will b e o b e y e d a n d a crossover to e x p o n e n t i a l r e l a x a t i o n is therefore expected. Since there is no p r e d i c t i o n for the t e m p e r a t u r e at which this crossover will occur, it is difficult to m a k e a conclusive c o m p a r i s o n with the present results. T h e p e r c o l a t i o n p h a s e - s p a c e m o d e l predicts a crossover t o w a r d s e x p o n e n t i a l relaxation, in this case d e f i n e d b y the high t e m p e r a t u r e at which the system changes f r o m a fractallike r a m i f i e d p e r c o l a t i n g structure to a c o m p a c t structure [23]. It is r e m a r k a b l e that no sign of such a crossover occurs d e s p i t e the fact that the o b servations were carried o u t in the very s h o r t - t i m e range (10-12 s) a n d h i g h - t e m p e r a t u r e range where one w o u l d expect at least a c o n s i d e r a b l e n a r r o w ing of the r e l a x a t i o n width. This work was carried out with the s u p p o r t of the Swedish N a t u r a l Science R e s e a r c h Council. T h e a u t h o r s gratefully a c k n o w l e d g e p a r t i a l financial s u p p o r t from the Carl T r y g g e r F o u n d a t i o n .
References [1] G. Williams and D.C. Watts, Trans. Faraday Soc. 66 (1970) 80. [2] L. Sjrgren and W. Gi~tze, in: Dynamics of Disordered Materials, eds. D. Richter, A.J. Dianoux, W. Petry and J. Texeira (Springer, Berlin 1989) p. 18. [3] C.A. Angell, in: Relaxation in Complex System, eds. K.L. Ngai and G.B. Wright (Office of Naval Research, Washington, DC, 1984). [4] K.L. Ngai and V. Strom, Phys. Rev. B27 (1983) 6031. [5] P.K. Dixon and S.R. Nagel, Phys. Rev. Lett. 61 (1988) 341. [6] L.M. Torell, L. Chem. Phys. 76 (1982) 3467; C.A. Angell and L.M. Torell, J. Chem. Phys. 78 (1983) 937; L.M. Torell D.C. Ziegler and C.A. Angell, J. Chem. Phys. 81 (1984) 5053; M. Elmroth, L. B~rjesson and L.M. Torell, in: Static and Dynamic Properties of Liquids, eds. M. Davidovic and A.K. Soper, Proc. in Physics 40 (Springer, Berlin, 1989) p. 118. [7] M. Grimsditch, R. Bhadra and L.M. Torell, Phys. Rev. Lett. 62 (1989) 2616; M. Grimsditch and L.M. Torell, in: Dynamics of Disordered Materials, eds. D. Richter, A.J. Dianoux, W. Pretry and J. Teixeira (Springer, Berlin, 1989) p. 196. [8] H.E.G. Knape, J. Chem. Phys. 80 (1984) 4788. [9] G.J. Gruber and T.A. Litovitz, J. Chem. Phys. 40 (1964) 13. [10] P. Macedo and T.A. Litovitz, Phys. Chem. Glasses 6 (1965) 69; W. Capps, P.B. Macedo, B. O'Meara and T.A. Litovitz. J. Chem. Phys. 45 (1966) 3431; J.A. Bucaro, H.D. Dardy R.D. Corsaro, J. Appl. Phys. 46 (1975) 741. [11] M. Soltwisch, J. Sukmanowski and D. Quitman, J. Chem. Phys. 86 (1987) 3207. [12] Paul K. Dixon, Lei Wu, S. Nagel, B.D. Williams and J.P. Carini, Phys. Rev. Lett. 65 (1990) 1108. [13] L. Bi)rjesson and W.S. Howells, these Proceedings, p. 53. [14] R. Mock, B. Hillebrands and R. Sandercock, J. Phys. E20 (1986) 656. [15] R.D. Mountain, J. Res. Nat. Bur. Stand. 70A (1966) 207; B.J. Berne and R. Pecora, Dynamic Light Scattering (Wiley-Interscience, New York, 1977). [16] C.P. Lindsay and G.D. Patterson, J. Chem. Phys. 73 (1980) 3348. [17] R.D. Mountain, Rev. Mod. Phys. 38 (1966) 205. [18] L. BSrjesson, M. Elmroth and L.M. Torell, Chem. Phys. 149 (1990) 209. [19] P.H. Van Cittert, Z. Phys. 69 (1931) 298.
L, B6rjesson et al. / An extremely 'fragile' glass former [20] J.H. Ambrus, H. Dardy and L.T. Moynihan, J. Phys. Chem. 76 3495 (1972). [21] R.W¢iler, R.A. Bose and P.B. Macedo, J. Chem. Phys 53 (1970) 1258. [22] D.L. Sidebottomand C.M. Sorensen, J. Chem. Phys. 91 (1989) 7153.
143
[23] I.A. Campbell, J.-M. Flessdles, R. Jullien and R. Botet, Phys. Rev. B37 (1988) 3825. [24] G. McDuffieand T.A. Lito~tz, J. Chem. Phys. 37 (1962) 1699.
139
A Brillouin scattering study of an extremely 'fragile' molecular glass former L. B~Srjesson, M. Elmroth and L.M. Torell Department of Physics, Chalmers University of Technology, S-412 96 Gothenburg, Sweden
BriUouin scattering results on the structural relaxation in fragile glass-forming propylene carbonate are presented. A new analyzing technique has been employed in which the full shape of the Brillouin spectrum was compared with a general hydrodynamic theory that has been modified to include non-exponential relaxation. The relaxation is found to be considerably stretched and time-temperature scaling is obeyed. This is by contrast with the reported crossover towards exponentially decay at high frequencies/high temperatures which has been observed previously with Brillouin scattering in other fragile systems such as glass-forming ionic liquids and ionic aqueous solutions. Such a crossover is also expected at sufficiently high temperatures both in mode-coupling and recent geometric phase-space percolation theories. It is concluded that there is no simple relation between the non-exponentiality of the relaxation and the degree of fragility as has been suggested.
1. Introduction
Most liquids can be supercooled below their equilibrium melting points and solidified to a glass provided that the cooling-rate is fast enough to avoid crystallization. It has been suggested that the viscosity and structural relaxation of glass-forming liquids show universal behaviour independent of the specific molecular interactions in the liquid. Universal features are departure from the Arrhenius behaviour of the relaxation time, nonexponential time decay often expressed in terms of the Williams-Watts (WW) relaxation function [1] q~(t) = %exp[ - (t/~') t~wW] and a cooling-rate dependent glass-transition temperature, Tg. Further, it has been proposed that time-temperature superposition (or scaling) of the relaxation function is obeyed in the transition region. The claimed time-temperature superposition principle is of considerable interest since in most theories it is either predicted or assumed. For example the mode-coupling theory [2] predicts scaling of the relaxation process at least around a critical temperature, Tc, located some 30 K above Tg. There are however several experimental results that show strong temperature dependences of flww and thus question the validity of the time-temper-
ature superposition principle [3-12]. Convincing results are reported from a 13 decades of frequency investigation of the dielectric relaxation in six molecular glass-forming liquids which show a continuous approach towards exponential relaxation at high frequencies/high temperatures [12]. Further, we have previously demonstrated that mechanical relaxation tends towards exponential relaxation at high temperatures for ionic glass formers and supercooled aqueous solutions by use of Brillouin scattering data combined with reported ultrasonic results [6,7]. Similar findings have been reported by other groups [8-11]. In the present work we have investigated a molecular glass former, propylene carbonate (PC), of extreme fragility with Brillouin scattering. The aim is, in a comparison with the previously studied ionic glass formers [6], to determine differences and similarities in the high-frequency relaxation properties between fragile glass-forming liquids [3] of different microscopic interactions. In order to obtain a complete view of the structural relaxation in PC, we apply other spectroscopic techniques (e.g. neutron scattering, photon correlation, Raman and dielectric measurements), preliminary neutron scattering results of which also appear in this volume [13].
0022-3093/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
140
L. Bi~rjesson et aL / An extremely "fragile" glass former
2. Experimental
In this paper, we report on a state-of-the-art Brillouin scattering investigation of the dynamics around the glass transition. A wide frequency window in combination with a new analyzing procedure makes it possible to stuc]y the relaxation characteristics over a relatively large temperature/ frequency range. For the frequency resolution, we have taken advantage of a Sandercock tandem F a b r y - P e r o t interferometer that provides a unique combination of a wide frequency window and a high resolution [14] and is thus ideal for Brillouin studies of the liquid-glass transition. Brillouin spectra were recorded in the temperature interval 140-345 K. Due to the tandem arrangement the obtained spectra are well resolved, are of highstatistical accuracy and are undistorted by neighbouring interference orders. Thus, the spectra are of such high quality that they can be used for a detailed comparison with theories. A new analyzing procedure has been employed in which we fit a general linearized hydrodynamic theory including non-exponential relaxation to the complete spectra. We have used the dynamic structure factor, S(Q, to), of the linearized hydrodynamic theory of ref. [15] for the analysis of the spectra. However, we have modified S(Q, to) to allow for non-exponential relaxation. In the analysis we have used the Cole-Davidson (CD) relaxation function rather than the commonly discussed WilliamsWatts function. This is because the CD form is more easily processable in the computing and its shape in frequency space is very similar to that of the Williams-Watts function [16]. The ColeDavidson relaxation function was introduced via Moo - M * ( i t o ) -
Mr
(1 + itoT) acD'
performed in this treatment [15,17]. Such a simple decomposition is not possible in the case of a non-exponential relaxation and, further, it involves a series of approximations whose validity is questionable for supercooled liquids. In the fitting procedure, the limiting low- and high-frequency sound velocities, c o and coo, the relaxation time, T, the non-exponentiality parameter, flCD, and an arbitrary intensity scaling variable were free parameters. Details of the experiment and the analysis can be found elsewhere [18].
3. Results
In fig. 1 we present typical experimental spectra, which have been deconvoluted from the instrumental resolution function using a modified Van Cittert [19] method, together with the corresponding best fits of S(Q, to). The spectra are obtained in the three ranges tot << 1, tot -- 1, and tot >> 1, respectively. The fits of S(Q, to) were at every temperature in excellent agreement with the experimental spectra. The analysis gave realistic values of all the fitting parameters only when the relaxation was allowed to be non-exponential, which then motivates the extra parameter flCD introduced via the Cole-Davidson function.
(1)
where 0 < flCD < 1, M * is the complex longitudinal modulus, M r = Moo- M0, and Moo and M 0 are the limiting high- and low-frequency values, respectively. Note, that the common decomposition of S(Q, to) into four components, representing the two longitudinal Brillouin modes, a Mountain mode and a Rayleigh mode, is not
-16.00
-8.00
0.00
8.00
16.00
Frequency Shift (GHz) Fig. 1. Brillouin spectra of propylene carbonate taken at temperatures corresponding to to~">> 1 (180 K), tot ~ 1 (255 K), and a~- << (330 K). The dots represent experimental data and the solid lines represent fits of general linearized hydrodynamic theory (see text).
L. BSrjesson et al. / An extremely "fragile"glass former
In fig. 2 we present the measured real and imaginary parts of the reduced complex longitudinal modulus, N ' = ( M ' - M o ) / M r and N " = M " / M r, in a masterplot representation. The values of N ' and N'" are derived directly from the parameters obtained from the fits of S ( Q , ¢o) for different temperatures [17] and t~ is taken from the frequency shift of the Brillouin peaks. Note that each point in fig. 2 represents a specific temperature. The relaxation is considerably stretched; the width of the loss peak is - 2 . 2 decades compared with 1.14 for exponential relaxation. The solid line in fig. 2 represents a frequency domain fit to the Williams-Watts relaxation function with flww = 0.6. The observed form of N " for propylene carbonate is significantly different from those reported previously for Ca0.4K0.6(NO3)l. 4 (CKN)
1.0
0.8-
N'
•
N" o Oo
o
o O
o
°,6
2
"O
~ 0.4" iI
0.2
0.0
-2.0
==
•
,
-1.0
'
1,0-
O--O
O---
0.8~w
Wo.. 6' xw
.K
w
x
X~
0.4
0.2
.0
112
14
116
6
T/Tg Fig. 3. Stretching parameter, flww, as a function of temperature for: ×, propylene carbonate; El, Cao.4Ko.6(NO3)l.4; O, Ca(NO3) 2 + 8H20. Solid lines are guides for the eye.
and Ca(NO3) 2 + 8H20
(CNH). For the latter systems the N " plots show much more asymmetric shapes, i.e. a broad wing for t0~-> 1 (low temperatures) and an approach towards single relaxation time for ¢a~"< 1 (high temperature) [6]. The different forms imply a stretching parameter flww which is temperatureindependent in the case of PC and strongly temperature-dependent for C K N and CNH. An important advantage of the present analysis
o
141
,
0.0
110
2J0
Log (c0
ary N ' , parts of the reduced longitudinal modulus of propylene carbonate obtained in the temperature interval 175-345 K. Solid lines represent a KWW relaxation function with flww = 0.6.
is that the relaxation characteristics, i.e. the relaxation time, ~'CD,and degree of non-exponentiality, fleD, are obtained independently for each temperature investigated. The so-obtained flCO values can be approximately converted to flww by use of the approach described in ref. [16]. In fig. 3 we present the resulting flww as a function of temperature. The value of flww ( - 0.5) is, within the experimental accuracy, observed to be temperature-independent, in accordance with the result of the masterplot analysis above. Thus, the timetemperature superposition principle is obeyed over the entire range from near Tg to more than 2Tg. It is notable that the stretching stays constant even at the high temperatures of 2Tg since one expects a crossover to exponential relaxation (flww = 1) somewhere in the high temperature region where the system becomes a 'normal' liquid. A stretched relaxation has, as far as we know, not previously been reported for any simple glass-forming liquid at the high frequencies/short relaxation times probed by Brillouin scattering. In fig. 3 we compare the present Brillouin results for flww with those obtained previously for C K N and C N H using a variety of different techniques [6,20-22]. It is evident from fig. 3 that the temperature dependence of the non-exponentiality of the relaxation function is completely different for the molecular liquid PC compared with the ionic liquid C K N and the aqueous solution CNH. This is especially
142
L. BSrjesson et al. / An extremely "fragile" glass former
n o t a b l e since these liquids are of similar degree of fragility. It has since long been suggested that for the structural r e l a x a t i o n o f a glass-forming liquid the degree of n o n - e x p o n e n t i a l i t y is i n t i m a t e l y linked with the d e p a r t u r e f r o m A r r h e n i u s behaviour, i.e. fragility [3,24]. F u r t h e r , previous exp e r i m e n t s have i n d i c a t e d that systems of increasing fragility show the stronger t e m p e r a t u r e d e p e n dence of fl a n d a crossover t o w a r d s e x p o n e n t i a l d e c a y at shorter r e l a x a t i o n times [7]. T h e p r e s e n t results then d e m o n s t r a t e that there is no such s i m p l e relation b e t w e e n n o n - A r r h e n i u s a n d n o n e x p o n e n t i a l b e h a v i o u r (see fig. 3). W e therefore question a n y universality related to the t e m p e r a ture d e p e n d e n c e of the stretching a n d in p a r t i c u l a r the t i m e - t e m p e r a t u r e s u p e r p o s i t i o n principle.
4. Conclusions T h e m o d e - c o u p l i n g theory p r e d i c t s scaling, however, o n l y in a limited range a b o v e its critical t e m p e r a t u r e , Tc [2]. A t high e n o u g h temperatures, n o r m a l h y d r o d y n a m i c s will b e o b e y e d a n d a crossover to e x p o n e n t i a l r e l a x a t i o n is therefore expected. Since there is no p r e d i c t i o n for the t e m p e r a t u r e at which this crossover will occur, it is difficult to m a k e a conclusive c o m p a r i s o n with the present results. T h e p e r c o l a t i o n p h a s e - s p a c e m o d e l predicts a crossover t o w a r d s e x p o n e n t i a l relaxation, in this case d e f i n e d b y the high t e m p e r a t u r e at which the system changes f r o m a fractallike r a m i f i e d p e r c o l a t i n g structure to a c o m p a c t structure [23]. It is r e m a r k a b l e that no sign of such a crossover occurs d e s p i t e the fact that the o b servations were carried o u t in the very s h o r t - t i m e range (10-12 s) a n d h i g h - t e m p e r a t u r e range where one w o u l d expect at least a c o n s i d e r a b l e n a r r o w ing of the r e l a x a t i o n width. This work was carried out with the s u p p o r t of the Swedish N a t u r a l Science R e s e a r c h Council. T h e a u t h o r s gratefully a c k n o w l e d g e p a r t i a l financial s u p p o r t from the Carl T r y g g e r F o u n d a t i o n .
References [1] G. Williams and D.C. Watts, Trans. Faraday Soc. 66 (1970) 80. [2] L. Sjrgren and W. Gi~tze, in: Dynamics of Disordered Materials, eds. D. Richter, A.J. Dianoux, W. Petry and J. Texeira (Springer, Berlin 1989) p. 18. [3] C.A. Angell, in: Relaxation in Complex System, eds. K.L. Ngai and G.B. Wright (Office of Naval Research, Washington, DC, 1984). [4] K.L. Ngai and V. Strom, Phys. Rev. B27 (1983) 6031. [5] P.K. Dixon and S.R. Nagel, Phys. Rev. Lett. 61 (1988) 341. [6] L.M. Torell, L. Chem. Phys. 76 (1982) 3467; C.A. Angell and L.M. Torell, J. Chem. Phys. 78 (1983) 937; L.M. Torell D.C. Ziegler and C.A. Angell, J. Chem. Phys. 81 (1984) 5053; M. Elmroth, L. B~rjesson and L.M. Torell, in: Static and Dynamic Properties of Liquids, eds. M. Davidovic and A.K. Soper, Proc. in Physics 40 (Springer, Berlin, 1989) p. 118. [7] M. Grimsditch, R. Bhadra and L.M. Torell, Phys. Rev. Lett. 62 (1989) 2616; M. Grimsditch and L.M. Torell, in: Dynamics of Disordered Materials, eds. D. Richter, A.J. Dianoux, W. Pretry and J. Teixeira (Springer, Berlin, 1989) p. 196. [8] H.E.G. Knape, J. Chem. Phys. 80 (1984) 4788. [9] G.J. Gruber and T.A. Litovitz, J. Chem. Phys. 40 (1964) 13. [10] P. Macedo and T.A. Litovitz, Phys. Chem. Glasses 6 (1965) 69; W. Capps, P.B. Macedo, B. O'Meara and T.A. Litovitz. J. Chem. Phys. 45 (1966) 3431; J.A. Bucaro, H.D. Dardy R.D. Corsaro, J. Appl. Phys. 46 (1975) 741. [11] M. Soltwisch, J. Sukmanowski and D. Quitman, J. Chem. Phys. 86 (1987) 3207. [12] Paul K. Dixon, Lei Wu, S. Nagel, B.D. Williams and J.P. Carini, Phys. Rev. Lett. 65 (1990) 1108. [13] L. Bi)rjesson and W.S. Howells, these Proceedings, p. 53. [14] R. Mock, B. Hillebrands and R. Sandercock, J. Phys. E20 (1986) 656. [15] R.D. Mountain, J. Res. Nat. Bur. Stand. 70A (1966) 207; B.J. Berne and R. Pecora, Dynamic Light Scattering (Wiley-Interscience, New York, 1977). [16] C.P. Lindsay and G.D. Patterson, J. Chem. Phys. 73 (1980) 3348. [17] R.D. Mountain, Rev. Mod. Phys. 38 (1966) 205. [18] L. BSrjesson, M. Elmroth and L.M. Torell, Chem. Phys. 149 (1990) 209. [19] P.H. Van Cittert, Z. Phys. 69 (1931) 298.
L, B6rjesson et al. / An extremely 'fragile' glass former [20] J.H. Ambrus, H. Dardy and L.T. Moynihan, J. Phys. Chem. 76 3495 (1972). [21] R.W¢iler, R.A. Bose and P.B. Macedo, J. Chem. Phys 53 (1970) 1258. [22] D.L. Sidebottomand C.M. Sorensen, J. Chem. Phys. 91 (1989) 7153.
143
[23] I.A. Campbell, J.-M. Flessdles, R. Jullien and R. Botet, Phys. Rev. B37 (1988) 3825. [24] G. McDuffieand T.A. Lito~tz, J. Chem. Phys. 37 (1962) 1699.