Chemistry Reference
In-Depth Information
Figure 2.3. The pressure
vs.
volume of Onsager rigid rod system. (Modified from
Onsager, 1949.)
When the isotropic-nematic transition occurs the concentration of rods
changes abruptly and the order parameter jumps from zero to a value
S
c
.
The conclusions are dependent on the shape of rigid rods and hence the
second virial coecient. Thus, the concentration difference and the critical
order parameter differ at the nematic — isotropic transition for different
shapes of rods.
For simplicity, Onsager suggested that the orientation distribution
function
f
(Ω) has the form as follows
α
4
π
ch
(
α
cos
θ
)
shα
f
(Ω) =
,
(2.25)
where
α
is the variational parameter. At the phase transition, the osmotic
pressure and chemical potential are equal for the two phases. The results
associated with the phase transition are
(1) The nematic to isotropic transition of rigid rods in solution is of the
first order. If the axial ratio
L/D
is great, the concentration of rods
φ
∼
D/L <<
1, even at the N
−
I transition, meets the condition of
the second virial approximation.
