adsorbed segments in every loop and terminal constituent chains per polymer
chain), the following structure parameters were introduced by Song [8]:
1. For the E-constituent chains:
X 1
k¼1
À À
N 1kE ¼
X
m¼1
À À
N tmE ¼ 1
ð1Þ
a E ¼
4
2
X
k¼1
À À
N 1kE and m E ¼
3
2
X
m¼1
À À
N tmE
ð2Þ
The Eq. (1) is normal condition, the Eq. (2) (a E and m E ) represents the average
constrained dimensional number of loop and terminal E-constituent chains in the
long loop and terminal entanglement spaces per polymer chain (or the degree of
Fig. 1 (a) Schematic illustration of polymer chain in multiple entangled state [8] solid line is the
testing polymer chain, in circle dotted line is the polymer segments of entanglements, in circle
broken line is the tail polymer segments of entanglements (b) schematic illustration of polymer
chain in multiple adsorptions state solid line is the testing polymer chain, in circle dotted line is the
polymer segments for adsorption, in circle broken line is the tail polymer segments of adsorption,
in circle æ is filler particle
Fig. 2 Model of elementary constituent chain by entanglements (a) and adsorptions (b) in the
double networks [8]
164
Y. Chen and C. Xu