MOLECULAR MOBILITY - Fractal Mechanics of Polymers - page 22

FIGURE 2.3 The dependence of fractal dimension D ch of chain part between entanglements
nodes on testing temperature T for HDPE. The calculation of D ch according to the equations:
1 - (2.8), the model of fixed valent angles, 2 - (2.8), the model with braked internal rotation,
3 - (2.12), 4 - (2.16), 5 - (2.5) [38].
For the observed distinctions explanation it is necessary to point out,
that the Eqs. (2.8) and (2.12) take into consideration only molecular char-
acteristic, namely, macromolecule flexibility, characterized by the value C ∞ .
Although the Eq. (2.12) takes into account additionally topological factor
(traditional macromolecular binary hooking network density n e ), but this
factor is also a function of C ∞ [40, 42]. The Eqs. (2.16) and (2.5) take into
account, besides C ∞ , the structural organization of HDPE noncrystalline re-
gions within the frameworks of cluster model of polymers amorphous state
structure [5] or fractal analysis with the aid of the value d f [22]. Hence,
HDPE noncrystalline regions structure appreciation changes sharply the de-
pendence D ch ( T ).
Let us also note that the chain model choice influences on the value D ch .
As it follows from the data of Fig. 2.3, the model with braked internal rota-
tion ( j = 0 [18]) gives smaller values D ch , than the model with fixed valent
angles. Besides, the first from the indicated models gives better correspon-
dence to calculation according to the Eqs. (2.5) and (2.16), from which it
follows, that it better describes real polymer chains behavior.
The calculation of D ch according to the Eqs. (2.8) and (2.12) as a matter
of fact gives D ch lower and upper boundaries, accordingly, as one can see
from the plots of Fig. 2.3. The small absolute D ch values, received with the