Dividing Planes of Hexagonal H Mesophase - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 92

Here, R n is the radius of the neutral plane, 1/ R 0n is the spontaneous curvature,
A n is the lipid area at the neutral surface, A 0n is the relevant spontaneous area,
and K is the lateral compressibility modulus of the monolayer. Unlike the
pivotal plane, the position of the neutral surface does not depend on the
deformation or on the used experimental technique, so it is impossible to
simply use some variant of the model applied previously for the pivotal plane.
When applying Eq. (3.29) it should be kept in mind that the neutral and pivotal
planes are well defi ned only for small deformations within the limits of validity
of Eq. (3.1). That limitation has to be compatible with the experimental
methods used for obtaining data for the analysis.
Due to the specifi city described above, the neutral plane could be studied
in terms of the deformation of H II phase upon hydration. The fi rst step is to
derive the spontaneous parameters at the pivotal plane—1/ R 0p and k cp . The
spontaneous parameters at the neutral plane—1/ R 0n and k cn — can be calcu-
lated by using the following set of equations (Leikin et al., 1996):

1 1 1

1

+
−

γ
γ

= (3.30)

RR
n 0 0 p

( )

52 /

1
1

− γ

γ

(3.31)

kk
cn

=

cp

( )

32 /

+

k
KR

1

cn

γ≡

(3.32)

2

0 n

Here, is the compression/bending ratio, and it can be estimated only if the

value of K —the lateral compressibility modulus of the monolayer—is known
(from an independent source). In addition,

γ

1
1

−
+

γ
γ

(3.33)

AA
0

≈

n p

11

AA ≈ 1 − γ R RR − (3.34)

n 0 n 0 n

n 0 n

The neutral volume, V n , could be estimated by means of the relation (Leikin
et al., 1996)

1 γ

VVAR

=−

(3.35)

n p 00 n n

− γ

or

1 − φ

l

RA =+ 2 V 2 V (3.36)

nn n l

φ

l