POLYMERS AS NATURAL COMPOSITES: STRUCTURE AND PROPERTIES - Fractal Mechanics of Polymers - page 314

And at last, the dimension d surf was calculated with the help of the equa-
tion [20]:

- d d

D

surf

. (15.27)

3 cl

S = 5, 25 × 10

u

2

In Fig. 15.16, the dependence b m ( N u ) for PC is adduced, which is broken
down into two parts similarly to the dependence b m ( f ) ( Fig15.15 ). At T =
293 ÷ 363 K the value b m is independent on N u , since nanocluster - loosely
packed matrix interactions are defined by their friction coefficient. Within
the range of T = 373 ÷ 413 K intercomponent adhesion level enhancement
( b m reduction) at active sites number N u growth is observed, as was to be
expected. Thus, the data of both Figs. 15.16 and 15.15 correspond t o Fig.
15.14 r esults.
With regard to the data of Figs. 15.15 and 15.16 two remarks should be
made. Firstly, the transition from one reinforcement mechanism to another
corresponds to loosely packed matrix glass transition temperature, which is
approximately equal to T g − 50K [11]. Secondly, the extrapolation of Fig.
15.16 plot to b m = 0 gives the value N u ≈ 71, that corresponds approximately
to polymer structure dimension d f = 2.86.

FIGURE 15.16 The dependence of parameter b m on nanocluster surface active
(“nonscreened”) sites number N u for PC [43].