Abstract
The extent to which the ‘splay ’, ‘bend’ and ‘twist’ constants (
K
1, 2, 3
) of a nematic liquid crystal differ from one another and the way in which they depend upon the degree of alignment (as characterized by the nematic order parameter
S
2
) are determined by the interaction responsible for alignment,
V
ij
. Priest (1973) has already shown that if
V
ij
is expanded in products of spherical harmonic functions such as
Y
l
i
,m
Y
l
j
,m
the contributions made to
K
1
,
K
2
and
K
3
by successive terms in the expansion are additive, and he has discussed the relative magnitude of these contributions for
l
i
=
l
j
= 2 and
l
i
= 2,
l
j
= 4. Priest’s results in the limit
S
2
= 1 are here confirmed, and they are extended to the case
l
i
=
l
j
= 4. To obtain results for the range 0.7 >
S
2
> 0.4 which is of interest experimentally, however, Priest invoked the mean field approximation, and his conclusion that the contributions he considered are proportional to
S
2
2
and
S
2
S
4
respectively is invalid for that reason. Methods of analysis developed in previous papers of this series are here used to show that Priest’s
S
2
2
should be replaced over the range of interest by say
AS
n
2
, where both
A
(≈ 1) and
n
(≈ 1.35) depend in principle on
m
and on whether it is
K
1
,
K
2
, or
K
3
that interests us, though the variations are not great in practice. The same expression (
AS
n
2
with
A
≈ 1) may be used to describe the order-dependence of (
l
i
= 2,
l
j
= 4)- and (
l
i
= 4,
l
j
, = 4)-contributions to
K
1, 2, 3
, with
n
≈ 3.25 ( ± 0.25 say) and
n
≈ 4.2 ( ± 0.4 say) respectively. The revised results can be fitted to recent data for nematic 5CB, but it would be premature to draw firm conclusions about the nature of
V
ij
in this substance, because several approximations are still present in the theory. A conjecture made in earlier papers in the series concerning <
P
4
(cos
β
ij
)> (alias σ
4
) is here confirmed.
Cited by
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