cos 2θ al ¼
1
λ
¼
6 S
β 4 þ 2S À S
2
À
Á , 1 þ
3 À U
ð
ÞS À US
2
þ 2US
3
D e
2
À 1
!
λ
2
¼ 0
(47)
where for simplicity, the equality 18η = ς is used to relate translational (η) and
rotational (ς) viscosities (see for example Eq. 30 of Rey 2010). Figure 14a shows the
computed scalar order parameter S and the alignment angle as a function of De for
steady shear of an isotropic solution, for β = 0.95 and several values of U; the shapes
Fig. 12 Scaled dimensionless storage (G
0 /M 1 ) and loss (G
00 /M 2 ) moduli as a function of the
dimensionless frequency ω for Psi4, AZA9, DDA9, PBLG 17%, PPTA 8.8%, and PBLG 12%
1000000
100000
10000
1000
100
10
1
0.1
0.0001
0.001
0.01
1/2
0.1
1,2,3,5
1) PSi4
2) AZA9
3) DDA9
5) PBLG 17% in m-cresol
6) PPTA 8.8% in SO 4 D 2
7) PBLG 12% in m-cresol
7,6
2
1
10
100
1000
~
SCALED DIMENSIONLESS STORAGE MODULUS (G'/M 1 )
~
SCALED DIMENSIONLESS LOSS MODULUS (G"/M
2 )
Fig. 13 Scaled loss tangent tanδ/M as a function of the dimensionless frequency ω for Psi4, AZA9,
DDA9, PBLG 17%, PPTA 8.8%, and PBLG 12%
302
A. D. Rey et al.