Chemistry Reference
In-Depth Information
Figure 2.13. Critical volume fraction
vs.
ratio of persistence length to molecular diam-
eter (
l/D
): comparisons of the Onsager and Flory theories with experimental data.
(Modified from Ciferri, 1991. Reproduced by permission of John Wiley & Sons, Inc.)
poly(n-hexyl isocyanate) (PHIC) (
D
=10
.
3 A)/1-CN (Bianchi
et al
.,
1987);
PHIC/toluene (Krigbaum
et al
., 1985);
acetoxypropylcellulose (APC)/DCM (Conio
et al
., 1984);
APC (
D
=12
.
0 A)/DMPh (Laivins & Gray, 1986);
HPC/DCAc (Aden
et al
., 1984);
cellulose acetate (CA) (
D
=8
.
1 A)/DMAc (Bianchi
et al
., 1986);
cellulose (
D
=5
.
8 A)/DMAc (McCormick
et al
., 1985).
Most experimental data fall between the two theoretical expectations
with the Flory model representing the upper limit and the Onsager limit
representing the lower limit. The two theories are in reasonable agreement
with experimental data if the uncertainty of the molecular diameter
D
and
Kuhn length
l
is taken into account.
A comparison of the theoretical expectations of worm-like liquid crys-
talline polymers and experimental data is made in Figure 2.14. The abscissa
is the ratio of total length to persistence length
L/l
; the ordinate is the
critical volume fraction in the unit of the ratio of molecular diameter to
persistence length. The theoretical expectation is taken from Khokhlov
et al
.'s theory (Khokhlov & Semenov, 1982; Odijk, 1986) on the worm-like
chains.
