Gb. Mckenna et al., The tau-effective paradox revisited: an extended analysis of Kovacs' volume recovery data on poly(vinyl acetate), POLYMER, 40(18), 1999, pp. 5183-5205
In 1964 Kovacs (Kovacs, AJ, Transition vitreuse dans les polymeres amorphes
. Etude phenomenologique. Fortschr Hochpolym-Forsch 1964;3:394-507) publish
ed a paper in which he analyzed structural (volume) recovery data in asymme
try of approach experiments. Kovacs used a parameter referred to as tau-eff
ective (tau(eff)) which is defined in terms of the volume departure from eq
uilibrium delta as tau(eff)(-1) = -1/delta d delta/dt. In plots of the log(
1/tau(eff)) vs. delta Kovacs observed an apparent paradox in that the value
s of tau(eff) did not converge to the same point as delta approached zero (
i.e. equilibrium). Hence the equilibrium mobility of the structural recover
y seemed path dependent. Also, the apparent paradox was accompanied by a sp
reading of the curves for tau(eff) in the up-jump experiments which has com
e to be known as the expansion gap. While it is currently accepted that the
paradox itself does not exist because the curves will converge if the meas
urements are made closer to delta = 0 (Kovacs' estimates of tau(eff) were m
ade for values as small as delta approximate to 1.6 x 10(-4)), the existenc
e of the expansion gap is still a subject of dispute. This is particularly
relevant today because recent models of structural recovery have claimed 's
uccess' specifically because the expansion gap was predicted. Here we take
the data Kovacs published in 1964, unpublished data from his notebooks take
n at the same time, as well as more recent data obtained at the Institut Ch
arles Sadron under his tutelage in the late 1960s and early 1980s. We then
examine them using several different statistical analyses to test the follo
wing hypothesis: the value of tau(eff) as \delta\ --> 1.6 x 10(-4) for a te
mperature jump from T-i to T-0 is significantly different from the value ob
tained for the temperature jump from T-j to T-0. The temperatures T-i or T-
j can be either greater or less than T-0. If the hypothesis is rejected, th
e tau(eff)-paradox and expansion gap need to be rethought. If the hypothesi
s is accepted, then the argument that reproduction of the expansion gap is
an important test of structural recovery models is strengthened. Our analys
is leads to the conclusion that the extensive set of data obtained at 40 de
grees C support the existence of an expansion gap, hence an apparently para
doxical value of tau(eff), for values of \delta\ greater than or equal to 1
.6 x 10(-4). However, at smaller values of \delta\ it appears that the valu
es of tau(eff) are no longer statistically different and, in fact, the data
suggest that as \delta\ --> 0 all of the tau(eff) values converge. In addi
tion, data for experiments at 35 degrees C do not have sufficient accuracy
to support the expansion gap for such small values of \delta\ because the d
uration of the experiments is significantly longer than those at 40 degrees
C. Consequently the data readings taken at 35 degrees C were made at longe
r time intervals and this leads to dramatically reduced error correlations.
(C) 1999 Published by Elsevier Science Ltd. All rights reserved.