THE INTERCOMMUNICATION OF FRACTAL ANALYSIS AND POLYMERIC CLUSTER MEDIUM MODEL - Fractal Mechanics of Polymers - page 2

During the last 25 years, fractal analysis methods obtained wide-spread at-
tention in both theoretical physics [1] and material science [2], in particular,
in physics-chemistry of polymers [3-8]. This tendency can be explained by
fractal objects wide distribution in nature.
There are two main physical reasons, which define intercommunication
of fractal essence and local order for solid-phase polymers: the thermody-
namical nonequilibrium and dimensional periodicity of their structure. In
Ref. [9], the simple relationship was obtained between thermodynamical
nonequilibrium characteristic - Gibbs function change at self-assembly
(cluster structure formation of polymers D  − and clusters relative frac-

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tion j cl in the form:

D 

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G ~ φ

(1.1)

cl

This relationship graphic interpretation for amorphous glassy polymers −
polycarbonate (PC) and polyarylate (PAr) - is adduced i n Fig. 1.1 . Since at
T = T g ( T m ) (where T , T g and T m are testing, glass transition and melting tem-
peratures, accordingly)

D  =0 [10, 11], then from the Eq. (1.1) it follows,
that at the indicated temperatures cluster structure full decay (j cl = 0) should
be occurred or transition to thermodynamically equilibrium structure.
As for the intercommunication of parameters, characterizing structure
fractality and medium thermodynamical nonequilibrium, it should exist in-
disputably, since precise nonequilibrium processes formed fractal structures.
Solid bodies' fracture surfaces analysis gives evidence of such rule fulfill-
ment—a large number of experimental papers shows their fractal structure,
irrespective of the analyzed material thermodynamical state [12]. Such phe-
nomenon is due to the fact that the fracture process is a thermodynamically
nonequilibrium one [13]. Polymers structure fractality is due to the same
circumstance. The experimental confirmation can be found in Refs. [14-16].
As for each real (physical) fractal, polymers' structure fractal properties are
limited by the defined linear scales. So, in Refs. [14, 17] these scales were
determined within the range of several Ångströms (from below) up to sever-
al tens Ångströms (from above). The lower limit is connected with medium
structural elements finite size and the upper one − with structure fractal di-
mension d f limiting values [18]. The indicated above scale limits correspond
well to cluster nanostructure specific boundary sizes: the lower - with statis-
tical segment length l st , the upper - with distance between clusters R cl [19].

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