MOLECULAR MOBILITY - Fractal Mechanics of Polymers - page 27

Within the frameworks of cluster model it is postulated, that fluctuation
free volume is concentrated in loosely packed matrix of polymer structure,
the relative fraction of which can be estimated according to the Eq. (2.4). In
Fig. 2.7 , t he correlation f g (j l.m. ) is adduced, which has an expected character.
The straight line on this Figure is drawn according to the following consid-
eration: f g = 0 at j l.m. = 0 and f g = 0.104 × 0.159 at j l.m. = 1.0. These bound-
ary conditions are obvious: at densely packed structure f g = 0 and clusters
full decay (j l.m. = 1.0 or j l.m. = 0) means polymer devitrification and its free
volume achieves incidentally the indicated value [53]. From the data of Fig.
2.7, a very important key conclusion follows: the value f g in loosely packed
matrix is always equal to the value f g at glass transition temperature and
integral value f g counting per volume of the entire polymer is defined by the
value j l.m. [54]. Nevertheless, loosely packed matrix at T < T ' g is in glassy
state, that is clearly demonstrated by the data of Figs. 2.5 an d 2.6 a nd its
devitrification is due to small (instable) clusters [46]. It is natural, that the
condition f g = const defines constancy of loosely packed matrix contribution
in value E as well.
The dependences E ∞ (n cl ) for PC and PAr, also adduced in Fig. 2.5 and 2.6
differ from the dependences E (n cl ) at T < T ' g by loosely packed matrix zero
contribution only. As a matter of fact, the plot E (n cl ) parallel transference is
observed and this circumstance indicates, that relaxation processes in amor-
phous polymers at T < T ' g are realized completely in loosely packed matrix.
In Fig. 2.8 , the dependences E (n cl ) and E ∞ (n cl ) for HDPE, received in
quasistatic tests, are adduced. The principally different picture in compari-
son with PC and PAr behavior at T < T ' g (Figs. 2.5 and 2.6) is observed. Both
adduced in Fig. 2.8 plots are linear and extrapolate to zero at in cl = 0 and re-
laxation processes occurrence is expressed by the plot E ∞ (n cl ) slope change
in comparison with E (n cl ). If equality to zero of values E and E ∞ at n cl = 0 is
defined by HDPE devitrificated loosely packed matrix small elasticity mod-
ulus, then the slope decrease indicates on structural relaxation mechanism
change, which is now controlled by structure second component-clusters
[47].