(4) In the Cub I phase temperature range, the unit cell
parameter a decreases with increasing temperature, showing a
3
3
negative thermal volume expansion [(1/a )(d(a )/dT) = 24 3
2
2
2
4
21
1
1
0
0
K
]. This trend continues but is greatly reduced (26 3
K21) for temperatures in the Cub II phase range. Bruce
and coworkers reported a similar negative thermal volume
2
3
21
expansion (21.5 3 10
K ) for the Ia3d cubic phase of a
11
silver(i) alkoxystilbazole complex. It seems that negative
thermal volume expansion is characteristic of cubic mesophases
(
fluid nature).
Finally, we comment on two issues. The first relates to the
molecular structure characteristics of ANBC-26. A shorter
alkoxyl homologue, e.g. ANBC-18, shows an Ia3d cubic phase,
and the length of the aliphatic chain is estimated at 2.2 nm in the
extended form, which is about twice the length of the aromatic
core moiety (1.2 nm). For ANBC-26, the aliphatic chain length
is 3.4 nm, about three times larger than the core length (see Fig.
2
). The lengthening of the aliphatic chain unexpectedly
produced two types of cubic phases on heating. Moreover, this
lengthening also much improved the thermal stability among
this series of compounds, as confirmed by thermal gravi-
metry.
Fig. 2 Plots of d-spacing vs. temperature for ANBC-26 on heating. The
molecular structure of ANBC-26 and model structures of the SmC, Cub I
and Cub II phases are shown in the upper and middle part of this figure,
respectively.
Second, paying attention to the location of the methyl end
groups in the two cubic lattices, they form curved interfaces so
as to wrap the jointed rods. These interfaces are alternative sets
of description for cubic phases and are denoted infinite periodic
minimal surfaces (IPMS); three fundamental cubic IPMS have
been reported, the Schwarz P and D and Schöen Gyroid G
surfaces, which correspond to three bicontinuous cubic phases
5
6
the CubD phase of ANBC-16 and 218. On the other hand, the
cubic phase of a 3A-cyano analogue with n = 18 (4A-n-
octadecyloxy-3A-cyanobiphenyl-4-carboxylic acid) was identi-
6
12
fied in space group Im3m, and this phase and the lower-
with symmetries Im3m, Pn3m and Ia3d, respectively. Hyde
temperature Cub I phase are of the same type.
et al. pointed out that three bicontinuous cubic IPMS are
mathematically interrelated to each other by a Bonnet trans-
formation without change in curvature.12 This means that phase
transitions between the three cubic phases should occur without
heat exchange, provided that only the elastic energy of the
system is taken into consideration. This may be a reason why
only one type of cubic phase has been observed to date in a
given thermotropic cubic system; also our observation of a very
ANBC-26 thus shows three liquid-crystalline phases, the
SmC phase with a lamellar structure, and two types of cubic
phases, one with Im3m symmetry and the other with Ia3d
symmetry, on heating. Schematic models for these three
structures are depicted in the middle part of Fig. 2. According to
the models proposed for lyotropic systems by Luzzati and
9
coworkers, both cubic phases are visualized as two sets of
2
1
21
networks of rods, which are interwoven but not connected. For
the Im3m cubic phase, the rods are connected 6-by-6 at right
angles so that they are directed parallel to one of three lattice
axes, while in the Ia3d cubic phase, the rods are connected 3-by-
small entropy change (0.3 J mol
K ) for the Cub I–Cub II
phase transition is consistent with this expectation.
In conclusion, ANBC-26 shows an interesting polymor-
phism, including two cubic mesophases with Im3m and Ia3d
3
, forming two sets of helix-like networks, where each helix is
linked with other four helices. In ANBC-26, the aromatic part
and CO H group form these jointed rods, while the aliphatic
1
symmetries, and a structured liquid I phase. We anticipate that
our finding will lead to a more complete understanding of cubic
molecular organization and its transformation to and from other
types, especially in thermotropic liquid crystalline systems.
2
chain fills out the free space between the rods.
In order to gain insight into the transformation process along
the SmC–Cub I (Im3m)–Cub II (Ia3d) phase sequence, the d-
spacings of diffraction peaks are plotted vs. temperature in the
lower part of Fig. 2. Several interesting points are noted:
Notes and references
1
S. Diele and P. Göring, in Handbook of Liquid Crystals, ed. D. Demus,
J. Goodby, G. W. Gray, H.-W. Spiess and V. Vill, Wiley–VCH,
Weinheim, 1998, vol. 2B, pp. 887-900.
(1) The layer thickness of the SmC phase decreases as the
temperature approaches the SmC–Cub I transition temperature.
When the SmC layer is transformed into the SmA layer, the tilt
angle of the molecular long axis against the layer normal usually
reaches zero and thus the layer thickness increases. Therefore,
the ‘thinning’ of the SmC layers may be characteristic of the
SmC phase that exhibits any cubic phase at the higher
temperature side.
2 G. W. Gray, B. Jones and F. Marson, J. Chem. Soc., 1957, 393.
3 D. Demus, G. Kunicke, J. Neelsen and H. Sackmann, Z. Naturforsch.,
Teil A., 1968, 23, 84; D. Demus, D. Marzotko, N. K. Sharma and A.
Wiegeleben, Kristall. Technol., 1980, 15, 331.
4
S. Kutsumizu, M. Yamada and S. Yano, Liq. Cryst., 1994, 16, 1109; S.
Kutsumizu, R. Kato, M. Yamada and S. Yano, J. Phys. Chem., B, 1997,
1
01, 10 666.
(2) At the SmC to Cub I transition, the SmC layer thickness
5
6
A. Tardieu and J. Billard, J. Phys. Coll., 1976, 37, C3-79.
A. M. Levelut and Y. Fang, Coll. Phys., Coll. 7, 1991, 51, C7-229; A. M.
Levelut and M. Clerc, Liq. Cryst., 1998, 24, 105.
is equal to the (222) interplanar distance of the Cub I phase with
Im3m symmetry. This suggests the existence of the so-called
epitaxial relation10 between the SmC layer planes and the (222)
planes of the Cub I phase. In the Im3m cubic phase with a cell
parameter a, one 6-by-6 connection point is located at (000) and
7 W. Longley and T. J. McIntosh, Nature, 1983, 303, 612.
8 K. Larsson, Nature, 1983, 304, 664.
9
P. Mariani, V. Luzzati and H. Delacroix, J. Mol. Biol., 1988, 204,
1
1
2
1
2
165.
the other at ( ⁄
, while the (222) spacing is given by (√3)a/6. Hence, three
layers should exist between the two connection points.
3) In the Cub I phase, the diffraction of highest intensity is
2
a, ⁄
a, ⁄ a), and the distance between them is (√3)a/
1
1
0 Y. Rançon and J. Charvolin, J. Phys. Chem., 1988, 92, 2646.
1 B. Donnio, B. Heinrich, T. Gulik-Krzywicki, H. Delacroix, D. Guillon
and D. W. Bruce, Chem. Mater., 1997, 9, 2951.
2
(
1
2 S. T. Hyde, S. Andersson, B. Ericsson and K. Larsson, Z. Kristallogr.,
the (321) peak while the (211) diffraction peak is the highest in
the Cub II phase; both spacings, however, show a discontinuity
at the Cub I to Cub II phase transition.
1
984, 168, 213.
Communication 9/02975C
1182
Chem. Commun., 1999, 1181–1182