Chemistry Reference
In-Depth Information
In the case of the three Fredericks deformations, the correspondent
viscosities are associated with the known viscosities by
η
twist
=
α
3
−
α
2
,
η
twist
)
2
(
η
c
−
η
b
−
η
splay
=
η
twist
−
,
(6.33)
4
η
b
η
twist
)
2
(
η
c
−
η
b
−
η
bend
=
η
twist
−
.
4
η
c
The hydrodynamics of the liquid crystalline polymer is described by the
Ericksen-Leslie theory but liquid crystalline polymers have their polymeric
characteristics, such as the viscosity's dependence on the molecular length.
Doi first proposed the generalized dynamic equations for the concen-
trated solution of rod-like polymers. Such constitutive equations can be
derived from the molecular theory developed by Doi and Edwards (1986).
The basis for the molecular theory is the Smoluchowski equation or Fokker-
Planck equation in thermodynamics with the mean field approximation of
molecular interaction.
The detail of the Doi theory can be refered to in the topic by Doi and
Edwards “The Theory of Polymer Dynamics” (1986) in which the Leslie
coe
cients are related to the order parameter and the isotropic viscosity
η
as follows
2
ηS
2
,
α
2
=
−
2
ηS
(1+2
S
)
(2 +
S
)
α
1
=
−
,
α
3
=
−
2
ηS
(1
−
S
)
,
(2 +
S
)
(6.34)
α
4
=
2
η
(1
−
S
)
,
3
α
5
=2
ηS,
α
6
=0
,
and
η
=
ρk
B
T
2
D
∗
,
(6.35)
where
ρ
is the concentration of liquid crystalline polymers and
D
∗
the
effective rotational diffusion coe
cient of the molecules.
