YIELDING PROCESS - Fractal Mechanics of Polymers - page 64

D  > 0) is due just to devitrificated amorphous
phase availability, but no crystallinity. At T < T g amorphous phase viscosity,
increases sharply and amorphous chains tightness cannot be exercised its
action, displacing macromolecules parts, owing to that local order formation
has thermofluctuation character. The attention is paid to the obtained plot
community, if to remember, that the values t Y for impact and quasistatic tests
are differed by five orders. This circumstance is explained simply enough,
since the value e Y can be written as follows [43]:

im

tal structures existence (



e = t e

, (4.24)

Y Y

where e  is strain rate and substitution of the Eq. (4.24) in the Eq. (4.23)
shows, that in the right part of the latter the factor e  -1 appears, which for the
considered loading schemes changes by about five orders.
The Gibbs specific function notion for nonequilibrium phase transition
“overcooled liquid → solid body” is connected closely to local order notion
(and, hence, fractality notion, see chapter one), since within the frameworks
of the cluster model the indicated transition is equivalent to cluster forma-
tion start. In Fig. 1.1, the dependence of clusters relative fraction j cl on the
value

D  for PC and PAr is adduced. As one can see, this dependence
is linear, j cl growth at

im

D  = 0 (i.e.,
for the selected standard temperature T = T g ) the cluster structure complete
decay (j cl = 0) occurs.
The adduced above results can give one more, at least partial, explana-
tion of “cell ' s effect.” As it has been shown in Ref. [18], the following ap-
proximate relationship exists between e Y and Grüneisen parameter g L :

D  increasing is observed and at

im im

1

e =

(4.25) Y

2 g

L

Using this relationship and the plots of Fig. 4.10 , it is easy to show, that
the decrease and, hence, j cl reduction results to g L growth, characterizing
intermolecular bonds anharmonicity level. This parameter shows, how
fast intermolecular interaction weakens at external (e.g., mechanical one
[49]) force on polymer and the higher g L the faster intermolecular interac-
tion weakening occurs at other equal conditions. In other words, the greater
im

D  and j cl , the smaller g L and the higher polymer resistance to external
influence. I n Fig. 4.11 , the dependence of g L on mean number of statistical
segments per one cluster n cl , which demonstrates clearly the said above.