Chemistry Reference
In-Depth Information
where h
o
is viscosity of medium, in which particle is moved.
The friction stress
0
fri
s
for cluster from
n
cl
particles (in the considered
case-statistical segments) can be expressed as follows [24]:
0
1/
d
sξ
=
cn
,
(6.8)
fric
0
cl
where
d
is cluster dimension,
c
is coefficient, determined according to the
equation [24]:
1
c
=
,
(6.9)
1/
d
a
r
where r is the polymer density.
Substitution of the Eqs. (6.7) and (6.9) into the Eq. (6.8) gives the follow-
ing relationship [19]:
1/
d
n
,
(6.10)
0
s
=
6
ph
cl
fric
0
r
That is, molecular friction value is independent on the size of particles,
forming a cluster (in the considered case - macromolecule cross-sectional
area).
For determination of cold flow (forced high-elasticity) macroscopic
stress, it is necessary to multiply
0
fri
s
by cluster number, performing mo-
tion in viscous medium. The clusters number
N
cl
per polymer volume unit
can be determined according to the relationship [23]:
n
cl
N
=
,
(6.11)
cl
n
cl
where n
cl
is macromolecular entanglements cluster network density, as the
first approximation equal to a number of segments in clusters per polymer
volume unit.
As estimations according to the Eq. (6.11) with the data of Ref. [23] by
the temperature dependences of n
cl
and
n
cl
drawing have shown, the value
N
cl
is practically independent on
T
. Since is
p
is calculated per cross-sectional
area of sample and
N
cl
is accepted per volume unit, then it is obvious, that
