POLYMERS AS NATURAL COMPOSITES: STRUCTURE AND PROPERTIES - Fractal Mechanics of Polymers - page 295

M

3

a =

, (15.2)

r Np

A

where M is repeated link molar mass, r is polymer density, N A is Avogadro
number, p is atoms number in a repeated link.
For PC M = 264 g/mole, ρ = 1200 kg/m 3 and p = 37. Then a 3 = 9.54 Å 3
and the value N at can be estimated according to the following simple equa-
tion [17]:

l Sn ⋅⋅

st cl

N =

. (15.3)

at

3

a

For PC N at = 193 atoms per one nanocluster (for n cl = 20) is obtained. It is
obvious that the indicated value N at corresponds well to the adduced above
nanoparticle definition criterion ( N at = 10 3 ÷10 4 ) [9, 17].
Let us consider synergetics of nanoclusters formation in PC and PAr. Us-
ing in the Eq. (9.3) as governing parameter critical magnitudes n cl values at
testing temperature T consecutive change and the indicated above the table
of the determined by gold proportion law values A m , m and ∆ i , the depen-
dence ∆( T ) can be obtained, which is adduced i n Fig 15.3 . As it follows
from this figure data, the nanoclusters stability within the temperature range
of 313 ÷ 393K is approximately constant and small (∆ i ≈ 0.232 at minimum
value ∆ i ≈ 0.213) and at T > 393K fast growth ∆ i (nanoclusters stability en-
hancement) begins for both considered polymers.
This plot can be explained within the frameworks of a cluster model
[3-5]. In Fig 15.3 glass transition temperatures of loosely packed matrix T ′
, which are approximately 50 K lower than polymer macroscopic glass tran-
sition temperature T g , are indicated by vertical shaded lines. At T ′ instable
nanoclusters, that is, having small n cl decay occurs. At the same time stable
and, hence, more steady nanoclusters remain as a structural element, that
results to ∆ i growth [14].