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

J. Chem. Phys., Vol. 117, No. 5, 1 August 2002 Two crossover regions in the dynamics of epoxy resins
FIG. 7. a Arrhenius plot for DGEBA. 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 8.4 and
in Pa s, also including data from Ref. 36. The dielectric - and -relaxation
times are reported with diamond and squares, respectively. The dashed line
is an Arrhenius fit to the TT g relaxation data log 0 s14.35
0.13, E a6.60.1 kcal/mol; its extrapolation above T g is drawn with a
dotted line. The dash-dotted line is an Arrhenius fit to the relaxation
data log 0 s14.780.09, E a11.380.08 kcal/mol. The - and
-crossover regions are indicated by arrows. b Temperature dependence of
the dielectric strengths of DGEBA. The inset shows 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 drawn as a guide to
the eyes. Error bars smaller than the symbol size are omitted.
perimental time scale. The characteristic time (T g) may
strongly depend on the experimental probe used and on the
cooling rate; in particular, in a typical dielectric experiment
the out-of-equilibrium state occurs when the structural relaxation
time approximately exceeds 10 2 s. The dielectric value
of T g calculated in our samples by following this criterion is
given in the second column of Table II, where good agreement
with the calorimetric value from conventional DSC can
be noticed. Also included in Table II is the steepness index
md(log )/d(T g /T) TTg , which quantifies the fragility of
the system in terms of its temperature behavior at T g .
At lower temperatures the system is in the nonequilibrium
glassy state. There, two secondary processes and
process coexist, both showing Arrhenius behavior. The corresponding
fitting parameters are listed in Table III. The dotted
segment in Figs. 6a and 7a shows that at temperatures
higher than T g the trace deviates significantly from the
extrapolation of the behavior below T g . In particular, it first
becomes flatter i.e., lower apparent activation energy and
then goes on with increasing slope i.e., increasing apparent
activation energy, which becomes comparable to that found
below T g . Different approaches for analyzing relaxation
functions in the case of the overlap of the two processes are
debated in literature, 41–47 and their repercussions are especially
expected in the Arrhenius diagram in the region where
2441
FIG. 8. Main frame: dielectric relaxation time max vs viscosity in a
log–log representation, where the relation max corresponds to a linear
behavior with slope 1. a The solid line slope 0.990.02 is a linear fit to
the data of PPGE over six decades, in the temperature range 276–332 K. b
The straight line slope 0.980.02 is a linear fit to the data of DGEBA over
ten decades, in the temperature range 256–343 K. Inset: Conductivity vs
reciprocal viscosity 1 in a log–log representation. The straight lines are
fits of the relation n const. a The fitting line corresponds to n0.77
0.03 in the lower-temperature range solid line and n0.940.03 in the
higher-temperature range dashed line for PPGE, and b to n1.02
0.03 in the temperature range 300–378 K for DGEBA. Data corresponding
to characteristic temperatures are indicated for the meaning of T and
T on see text.
the processes tend to merge. Then we cannot completely rule
out the possibility of some influence of the analysis method
on the higher temperature values. However, such an influence
does not affect the data for the relaxation in the
region where the separation from the process is two decades
at least, since under this condition an analysis of the
separation using the additive ansatz is always
justified. 43,44,46 In particular, we notice that a deviation from
the extrapolated Arrhenius behavior of the trace occurs just
above T g where the separation of the and time scales is
nearly ten decades, and this is actually confirmed by deconvoluting
the and processes according to alternative fitting
procedures 48,49 based on the Williams ansatz. 41–47 Moreover,
the effect of different fitting approaches on the relaxation
time values at higher temperatures has been proven 48 not to
affect qualitatively the trend of (T), and we have no reason
to think also the higher-temperature bending of the
trace to be an artifact of the evaluation method.
Also the dc conductivity, , can be used as an efficient
probe of the dynamics of supercooled systems. It should be
noted that different samples of the same material might show
different absolute values, since this is proportional to the
amount of impurities in the sample typically chlorine, in
epoxy compounds. However, the temperature dependence of
Downloaded 14 Nov 2002 to 194.95.63.241. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp