YIELDING PROCESS - Fractal Mechanics of Polymers - page 62

The Gibbs function of suprasegmental (cluster) structure self-assembly
at temperature T = T g - D T was calculated as follows [45]:



, (4.20)

i G

D =D D ST

where D S is entropy change in this process course, which can be estimated
as follows [47]:

D S = (3 ÷ 5)× k × f g ×ln f g. (4.21)

In the Eq. (4.21), the coefficient (3 ÷ 5) takes into account conforma-
tional molecular changes contribution to D S , k is Boltzmann constant, f g is a
polymer relative fluctuation free volume.
Let us consider now the results of the concept [44, 45] application to
polymers yielding process description. The yielding can be considered as
polymer structure loss of its stability in the mechanical stresses field and
the yield strain e Y is measure of this process resistance. In Ref. [44], it is
indicated that specific lifetime of suprasegmental structures t im is connected
with D  as follows:

im

( )

-D 

t

im

~ exp G

im

RT

(4.22)

where R is the universal gas constant.
Assuming, that t im ~ t Y ( t Y is time, necessary for yield stress is Y achieve-
ment) and taking into account, that e Y ~ t Y , it can be written [43]:

( )

-D 

im

e ~ exp G RT

(4.23)

Y

Let us note, that the Eq. (4.23) correctness in reference to polymers
means, that yielding process in them is controlled by supra segmental struc-
tures thermodynamical stability.
In Fig. 4.10 , the dependence of e Y on

( )

-D  , corresponding to
the Eq. (4.23), for all groups of the considered in Ref. [43] polymers. De-
spite definite (and expected) data scattering it is obvious, that all data break
down into two branches, the one of which is approximated by a straight line.
Such division reasons are quite obvious: the data with negative value of
im

im

exp G RT

D  cover one (right) branch and with positive ones − the other (left) one.
The last group consists of semicrystalline polymers with devitrificated at
testing temperature loosely packed matrix (polytetrafluoroethylene, polyeth-
ylenes, polypropylene). The cluster model [18, 24] postulates thermofluctua-
tion character of clusters formation and their decay at T > T g . Therefore, such