HAL Id: jpa-00249426
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Submitted on 1 Jan 1995
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Comment on: “Thermally Stimulated Creep: a
Theoretical Understanding of the Compensation Law”, by J. Perez and J.Y. Cavaillé
E. Marchal
To cite this version:
E. Marchal. Comment on: “Thermally Stimulated Creep: a Theoretical Understanding of the Com-
pensation Law”, by J. Perez and J.Y. Cavaillé. Journal de Physique III, EDP Sciences, 1995, 5 (12),
pp.1923-1924. �10.1051/jp3:1995237�. �jpa-00249426�
J. Phi-s. III France 5 (1995) 1923-1924 DECEMBER 1995, PAGE 1923
Classification Physics Abstracts
62.40 65.70 83.20Di
Comment on: "Thermally Stimulated Creep: a Theoretical
Understanding of the Compensation Law", by J. Perez and 3.Y. Cavailld
E. Marchal
CNRS, Institut Charles Sadron, 6
rueBoussingault 67083 Strasbourg Cedex, France (Received 20 September 1995, accepted 23 October 1995)
In a recent paper by Perez and CavaillA [I] (PC), reference is made to a paper by E. Marchal
(E.M.) in which the hypothesis she made has since been modified by her, to be more consistent with experimental findings [2-4]. To summarize her new approach and using P-C's notations, the experimental relaxation time Tap which is equal to the ratio of the relaxation function to its time derivative is a function of time (Ngai's second universal law). E-M- now assumes
that in the glass transition temperature region and above, the four parameters Uo, Too, to and x* are constant, but that the origin of the physical time is itself a function of time and/or temperature. The time parameter to be considered is t~
=t t[ (T, t). From a single thermally stimulated (TS) experiment one cannot distinguish between the two effects on t[. When poling
is done at constant Tp during various times, if the TS response is shifted, one can safely say
that t[ depends on t. This is so when Tp lies in the T-range where the o process appears in the TS diagram [2]. In fact, t[ depends on t and T, since the rate of change of t[(t)
at constant T depends on T. At higher T this is no longer the case and t[ depends on T
only. In practice, there is no need to know a priori whether we deal with t[(t, T) or t[ IT)
when applying this formalism. In short, the non-linearity which forbids to integrate the time derivative of the relaxation function is
nowtaken care of. P-C also overcome this difficulty by assuming the correlation parameter x to be distributed, leading to a distribution of Tap that is T-dependent. They need not, in principk, worry about time effect since it is implicit in the
different Tap-distributions obtained for each fractional creep experiment.
However, the time dependence of Tap does not appear in their expression of rap. As a consequence, the heating rate b is not introduced in their equations; it should, since, at a given T, Tap measured experimentally is b-dependent whenever fl < I, which is the case even for
fractions. Rather,
ii they expand equation (7c) for short times to prove that r~ and rrnoi are related, whereas
long times are concerned in cup, as stated on top of p. 798.
2) they do not say why rap is equal to r~.
3) they neglect can which is the recoverable part of the strain. In TS Depolarization (TSD)
the relaxation corresponding to can is the only one to be considered. In view of the similarity
of TS Creep and TSD behavior and on other grounds, neglecting the can term in the a process
under concern is by far not obvious. The similarity between electrical and mechanical stress
1924 JOURNAL DE PHYSIQUE III N°12
appears, for example, iii the identical values of r~ and T~ obtained by both TS methods in all the available polymers [5]. Also, the parameters deduced from TSD for amorphous PET [6j
are in good agreement with those deduced by PC from dynamic mechanical spectroscopy.
In E.M.'s formalism, T~ appears as the temperature where t'
=
I16 [3j. At T~,
r~
=[btoj~~~~~~Top exp(Up /kTc)
In this equation, using the values of the parameters given in Table I, as well as x*
=
0.3 (or
0.27 for PSI, b
=
