Chemistry Reference
In-Depth Information
sition temperature
T
g
for amorphous glassy polymers and melting tempera-
ture
T
m
- for semicristalline ones. The necessary for calculation parameters
and final values κ
1
and κ
2
are adduced in Table 7.1.
TABLE 7.1
The Local Overloading Coefficients (κ
1
and κ
2
) and Necessary For Their
Calculation Parameters [5]
Conventional
sign
E
,
GPa
κ
1
T
g
(
T
m
),
K
a×
10
5
,
K
-1
s
o
,
MPa
Polymer
κ
2
Polytetrafluoroethylene
PTFE
2.56
0.27
0.38
293
600
0.20
Poly(ethylene terephta-
late)
PET
1.98
1.26
0.98
905
520
0.25
Polypropylene
PP
1.70
0.50
1.11
629
440
0.67
Polyethylene
PE
2.29
0.29
0.47
553
380
0.93
Polyamide-6
PA-6
2.38
1.64
0.86
651
500
0.20
Poly(vinyl chloride)
PVC
2.57
0.47
0.52
844
360
1.04
Polycarbonate
PC
2.35
1.29
0.79
833
425
0.44
Polystyrene
PS
1.96
1.44
1.08
725
373
0.44
Poly(methyl methacry-
late)
PMMA
2.33
1.94
0.77
756
375
0.38
Polysulfone
PSF
1.56
1.70
1.50
909
465
0.25
Alexander and Orbach [8] showed that vibrational excitations on frac-
tal were localized in virtue of medium fractal geometry and named such
localized excitations fractons. It has been shown experimentally that for
polymers the fracton regime is realized within the linear sizes scale from
several Ångströms up to several tens Ångströms [12, 13] and the last value
corresponds excellently with distances between clusters
R
cl
range for the in-
dicated above polymers (Table 7.1). Let us remind, that chains parts between
clusters breaking represents itself polymers fracture on molecular level. A
localization of excited states (phonons) within the indicated above scales
range means, that phonon cannot be moved over distances larger than inter-
atomic ones, in other words, L ≈
a
and κ ≈ 1 according to the Eq. (7.1). This
condition is fulfilled in virtue of chain part between its topological fixation
points fractality [14, 15]. The transition to phonons usual behavior, that is,
