Two crossover regions in the dynamics of glass forming ... - Fisica

2440 J. Chem. Phys., Vol. 117, No. 5, 1 August 2002 Corezzi et al.
TABLE I. Havriliak–Negami fit parameters for the relaxation of PPGE and DGEBA at several temperatures. When a shape parameter was undergoing
additional constraints as explained in the text, the respective error is not reported.
T K
PPGE
HN s m n T K HN s m n However, the significant uncertainty of HCS parameters restrains
us from going into a deeper comparison.
The dielectric relaxation times max obtained from the
fitting procedure, together with the calorimetric characteristic
times max obtained from the location of the peak in the
isochronal or isothermal c p spectra, are reported in the
Arrhenius plot of Figs. 6 and 7 and compared with the viscosity
data. The trace of calorimetry and dielectrics coincide
within the experimental uncertainty, and their temperature
dependence closely parallels that of . Figure 8 shows a
convincing check of the relation max in our samples, up
to 332 K in PPGE and 343 K in DGEBA. It displays that a
linear fit of log max vs log has slope 0.990.02 and 0.98
0.02 in PPGE and DGEBA, respectively. According to
max, the viscosity data are rescaled up to the highest temperatures
measured, and shown as solid lines in the Arrhenius
plot of Figs. 6a and 7a. We notice that the proportionality
of max to in supercooled liquids has a physical basis
in the -scale universality predicted by the mode coupling
theory and verified in different systems e.g., see Ref. 40,
but it is possible that at sufficiently high temperatures a
max/T regime ensues, as predicted by the hydrodynamic
Debye model and recently observed in low-molecular-weight
organic compounds. 13 However, the possible differences in
Figs. 6 and 7 due to a maxT rescaling of the viscosity
data for temperatures higher than those represented in Fig. 8
have no significant effect on the analysis and discussion reported
in the following.
Together with the secondary relaxation times, Figs. 6a
and 7a give the complete relaxation map of our samples in
the supercooled and glassy state, as revealed by dielectric
spectroscopy, HCS, and viscosity measurements. As known,
the glass transition phenomenon is commonly described as
an ergodic- to nonergodic-state transition and T g is defined as
the temperature at which the ergodicity is broken on the ex-
DGEBA
331.8 (7.63)109 0.63 0.41 2.70.6 343 (9.52.3)1010 10.03 0.42 0.60.3
327.9 (1.040.06)108 0.63 0.40 3.10.6 333 (2.40.5)109 10.03 0.42 1.30.2
323.1 (1.800.05)108 0.64 0.40 3.20.3 323 (5.00.5)109 10.04 0.42 2.00.3
317.9 (3.60.2)108 0.63 0.40 3.40.4 313 (1.250.08)108 0.950.03 0.41 2.70.2
313.0 (6.60.2)108 0.63 0.40 3.80.3 303 (4.480.13)108 0.880.02 0.41 3.50.4
308.0 (1.450.06)107 0.63 0.39 4.10.4 298 (1.080.05)107 0.870.02 0.41 3.90.5
303.1 (3.80.2)107 0.610.02 0.390.02 4.40.2 293 (3.210.08)107 0.880.02 0.39 4.20.3
298.3 (1.070.03)106 0.620.02 0.390.02 4.70.3 288 (8.90.4)107 0.860.03 0.400.05 4.70.3
293.1 (4.130.06)106 0.640.015 0.390.02 4.90.2 283 (3.750.12)106 0.860.03 0.400.04 5.10.3
287.5 (2.1900.013)105 0.630.02 0.390.02 5.390.15 278 (2.210.06)105 0.830.02 0.390.02 5.710.03
283.9 (7.80.3)105 0.640.02 0.400.02 5.60.2 273 (2.120.08)104 0.850.01 0.400.01 6.210.03
278.9 (5.70.2)104 0.650.01 0.400.01 5.90.2 268 (3.390.09)103 0.850.01 0.400.01 6.830.05
274.4 (4.820.13)103 0.650.01 0.400.01 6.380.05 263 (7.10.3)102 0.820.02 0.430.02 7.370.05
270.1 (5.220.17)102 0.650.01 0.390.01 6.80.2 261 (3.20.2)101 0.820.02 0.430.02 7.730.08
266.3 (5.70.1)101 0.650.02 0.400.01 7.20.2 259 (1.650.04)1 0 0.830.02 0.400.01 7.80.2
262.1 (1.020.08)10 1 0.670.03 0.400.01 7.50.2 256 (2.250.06)10 1 0.820.04 0.400.01 8.00.2
FIG. 6. a Arrhenius plot for PPGE. The temperature dependence of the
dynamic glass transition is reconstructed via the trace of max(2f max) 1
from open circles and c p solid triangles, and via the viscosity data
the solid line shows experimental data of log( 1 ), with log 8.3 and
in Pa s. The dielectric and relaxation times are reported with diamond
and squares, respectively. The dash line is an Arrhenius fit to the TT g
relaxation data log 0s14.70.2, E a6.670.15 kcal/mol; its extrapolation
above T g is drawn with dot line. The dash-dotted line is an
Arrhenius fit to the -relaxation data log 0 s14.60.3, E a11.3
0.2 kcal/mol. The- and -crossover regions are indicated by arrows.
b Temperature dependence of the dielectric strengths of PPGE. The inset
shows, in an enlarged scale, circles and down triangles above
T g , and the calorimetric intensity c p up triangles, in units J kg 1 K 1 .
The solid line is a linear fit to , extrapolated to the onset temperature
T on . The dashed line is not a fit, but only a guide to the eyes, drawn to
demonstrate the compatibility of the c p trend with the dielectric onset.
Error bars smaller than the symbol size are omitted.
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