Chemistry Reference
In-Depth Information
α
5
=
1
7
K
(
a
)(3
S
+4
R
)+
S
K
(
a
)
,
α
6
=
1
7
K
(
a
)(3
S
+4
R
)
−
S
K
(
a
)
,
≡
where
K
(
a
) is the function of the axial ratio
a
L/D
.
K
(
a
)=
a
2
1
a
2
+1
.
−
(6.41)
The quantity
K
(
a
) is near unity for the physical range of
a
. The tumbling
parameter,
λ
, in a simple sheering flow is related to the flow alignment, or
Leslie angle
θ
by
tgθ
=
λ
1
λ
+1
.
−
(6.42)
Larson (1995) simplified the above expression for
λ
in terms of
S, R
and
L/D
:
λ
=
K
(
a
)
(15
S
+48
R
+ 42)
105
S
.
(6.43)
Meyer (1982) predicted that as the length of the chain approaches infin-
ity, the Leslie coe
cients
α
1
and
α
2
should tend to
−∞
∞
,
while
α
4
,α
5
and
α
6
are of finite values. The Miesowicz viscosities
η
a
and
η
b
are finite while
η
c
tends to infinity because the velocity is perpendicular
to the director and the shear flow.
Table 6.7 lists expressions of Kuzuu & Doi (1983, 1984) and Lee (1988)
at the infinite long chain limit. Meyer's prediction is listed for comparison.
From Table 6.7 one can estimate the applicability of the theories.
Table 6.7 reveals that Lee's calculation, based on Doi's argument, is in
better agreement with Meyer's predictions.
and
α
3
tends to
Table 6.7. Comparison of theories on viscosities of liquid crystal with infinite long
chain. (From Lee and Meyer, 1991.)
Viscosity
ratio
Reference (Kuzuu & Doi,
1983, 1984) (
Q →∞
Reference (Lee,
1988) (
Q →∞
Meyer's prediction
(1982) (
L →∞
)
)
)
∝Q
2
η
a
/η
b
1
/µ
finite
π/
8
Q
2
π/
8
Q
2
η
a
/η
c
0
1
/Q
4
πµ/
8
Q
2
η
b
/η
c
∝
0
const-const/
Q
2
− π/
2
µQ
2
η
splay
/η
twist
1
finite
1+
π/
2
Q
2
1+
π
(4
− µ
)
/
8
Q
2
η
twist
/η
c
finite
∝
1
/Q
4
πµ/
8
Q
2
η
bend
/η
twist
0
