Chemistry Reference
In-Depth Information
FIGURE 4.16
Decomposition of strain vector into two components in a dynamic experiment.
τ
a
is the storage compliance
J
0
(
in-phase strain to the stress amplitude
), and the
ratio of the out-of-phase strain to the stress amplitude is the loss compliance
Jv
(
ω
).
G
0
(
) and
J
0
(
) are associated with the periodic storage and complete release
of energy in the sinusoidal deformation process. The loss parameters
G
ω
ω
ω
v
(
ω
) and
J
v
(
) on the other hand reflect the nonrecoverable use of applied mechanical energy
to cause flow in the specimen. At a specified frequency and temperature, the
dynamic response of a polymer can be summarized by any one of the following
pairs of parameters:
G
0
(
ω
),
J
0
(
ω
) and
G
v
(
ω
ω
) and
J
v
(
ω
), or
τ
a
/
γ
a
(the absolute mod-
ulus
.
An alternative set of terms is best introduced by noting that a complex number
can be represented as in
Fig. 4.17
by a point
P
(with coordinates
x
and
y
)orbya
vector OP in a plane. Since dynamic mechanical behavior can be represented by
a rotating vector in
Fig. 4.15
, this vector and hence the dynamic mechanical
response is equivalent to a single complex quantity such as
G
(complex modu-
lus) or
J
(complex compliance). Thus, in shear deformation,
j
G
j
) and tan
δ
G
ðωÞ 5
G
0
ðωÞ 1
iG
vðωÞ
(4-46)
1
G
ðωÞ
5
1
G
0
ðωÞ 1
J
ðωÞ 5
J
0
ðωÞ 2
vðωÞ
5
iJ
vðωÞ
(4-47)
G
[
Equation (4-47)
can be derived from
Eq. (4-46)
by comparing the expressions
for
z
and
z
2
1
in
Fig. 4.17
.] It will also be apparent that
G
j 5 ½ð
G
0
Þ
2
2
1
=
2
j
1ð
G
vÞ
(4-48)
