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was confi rmed when discotics were found (Boden et al., 1979) with
χ
a
>
0 and
0 in the NaH
x
B - Na
2
SO
4
- DeOH - H
2
O system.
The cause of the diamagnetic anisotropy of micelles has been examined in
detail (Amaral, 1983; Boden et al., 1979, 1981, 1985; Charvolin et al., 1979;
Radley and Reeves, 1975; Radley et al., 1976; Vedenov and Levchenko, 1983).
The orientation of a diamagnetic ellipsoid having the mean susceptibility
calamitics with
χ
a
<
χ
pla
c
ed in a medium having the susceptibility
χ
0
does not depend on the sign
χχ
−
of
0
and is determined unambiguously—the principal axis of the ellipsoid
is established parallel to the fi eld. Therefore cylindrical micelles will orient
with their long axes and discotic micelles with their short axes along the fi eld.
If the difference in energies corresponding to confi gurations in which the
principal axis of the ellipse is parallel or perpendicular to the magnetic fi eld
is
Δ
W
shape
, then we have
V
(
)
(
)
2
(2.3)
∆
W
≅−
H
χχ
−
D
−
D
χ
shape
0
c
a
2
where
V
is the volume of the ellipsoid, and
D
c
and
D
a
are the diamagnetic
factors in the directions of the least and greatest axes of the ellipsoid,
respectively.
The greatest value of
Δ
W
shape
will occur in the case of asymmetric ellipsoids
(
a
≈
1 0
c
). In this case we have
D
a
=
0, while
D
c
=
4
π
for an oblate and 2
π
for
a prolate spheroid. If we assign typical values of
χ
and
χ
0
(see below), then we
fi nd from the condition
1
G
2
cm
3
. Hence, for the usually
employed values of the magnetic fi elds (1 kG), this implies that
V
Δ
W
shape
>
kT
that
H
2
V
∼
1 0
− 6
c m
3
.
This means that only macroscopic diamagnetic particles can be subjected to
orientation due to shape.
As is known (Gelbart et al. 1994; de Gennes, 1993; Kuzma and Saupe, 1997),
orientation owing to the diamagnetic anisotropy of molecules depends on the
sign of
∼
χ
0
. The difference between the energies of micelles corresponding to
confi gurations along the magnetic fi eld and perpendicular to it involves the
number
N
of molecules on the micelle, its volume
V
0
, and the order parameter
S
mol
, which characterizes the ordering of the molecules in the micelle:
WWW
HNV
S
2
0
(2.4)
∆
=− =−
^
χ
mol
mol
a
2
Yet, if the ordering of the principal axes of the micelles in a nematic is
described by the order parameter
S
mic
, then the difference the energies indi-
cated above for a system of
M
micelles will be
HMNV
SS
a
2
0
(2.5)
∆
W
=−
χ
mol
mol
mic
2
One can defi ne the quantity
S
mol
S
mic
S
as the macroscopic parameter. We
shall examine these quantities in greater detail below in Section 2.2. By using
=
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