THE INTERCOMMUNICATION OF FRACTAL ANALYSIS AND POLYMERIC CLUSTER MEDIUM MODEL - Fractal Mechanics of Polymers - page 3

FIGURE 1.1 The dependence of clusters relative fraction j cl on absolute value of specific
Gibbs function of nonequilibrium phase transition |

D  | for amorphous glassy polymers -

im

polycarbonate (1) and polyarylate (2) [3].

Polymeric medium's structure fractality within the indicated above scale
limits assumes the dependence of their density ρ on dimensional parameter
L (see Fig. 1.2 ) as follows [1]:

dd - ,

r ~ L

(1.2)

f

where d is dimension of Euclidean space, into which a fractal is introduced.
In Fig. 1.3 a morphous polymers nanostructure cluster model is present-
ed. As one can see, within the limits of the indicated above dimensional
periodicity scales Fig. 1.2 and 1.3 correspond each other, that is, the cluster
model assumes ρ reduction as far as possible from the cluster center. Let us
note that well-known Flory “felt” model [20] does not satisfy this criterion,
since for it ρ ≈ const. Since, as it was noted above, polymeric mediums struc-
ture fractality was confirmed experimentally repeatedly [14-16], then it is
obvious, that cluster model reflects real solid-phase polymers structure quite
plausibly, whereas “felt” model is far from reality. It is also obvious, that
opposite intercommunication is true - for density ρ finite values change of
the latter within the definite limits means obligatory availability of structure
periodicity.