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glycerol groups (deep blue dots) and the aromatic cores (large
used as in Figure 1). The structure factor amplitudes Fhk and
phase angles fhk are calculated analytically from the models.
A reasonably good match between observed and calculated
(F2hk) intensities is obtained (see Supporting Information,
green regions). The position of some molecules is indicated in
Figure 1c by black chevrons. The alkyl segments of the
semiperfluorinated chains account for the lowest density
(yellow/red) moats surrounding the fluorinated regions.
Figure 1d shows a snapshot of a molecular dynamics simu-
lation of one molecular layer (c = 0.45 nm) after annealing,
with periodic boundaries defined by the experimentally
determined unit cell. The simulation confirms efficient
space-filling and microphase separation.
The structure of the Colhex phase formed by compound 2c
with a tolane-based bent core is fundamentally the same as
that described for 1c, but, owing to the larger aromatic core
(l = 1.5 nm for each arm, compared to l = 1.3nm for 1c), the
hexagonal lattice parameter is enlarged to ahex = 5.12 nm.
For compounds 2a and 2b, with the same tolane-based
core as 2c, but with shorter chains, the lattice parameter (ahex
ꢁ 2.8–2.9 nm) is nearly half that for 2c (ahex = 5.12 nm) and
the number of molecules per unit cell is only three, suggesting
that for these compounds only three molecules form a
cylinder frame (Table 1).[12] As shown in Figure 2c and g,
Tables S7a,b). Using the fhk values thus obtained, together
1=2
hk
with amplitudes I from measured intensities Ihk, “exper-
imental” electron-density maps are calculated (see Figur-
es 2c,g). The match between the models and the real
structures can best be judged by comparing the experimental
maps (Figures 2c,g) with those Fourier-reconstructed from
the models (Figures 2b,f, respectively). For the comparison to
be meaningful, in the reconstructions in Figures 2b,f we used
the same range of h and k, that is, the same number of Fourier
terms, as in the reconstructions in Figures 2c,g.[14]
The above procedure thus confirms the proposed 3-
hexagon structure of the trigonal Colhex/p3m1 honeycomb
phase. At the same time, the results illustrate the usefulness of
the procedure itself. To our knowledge, this is the first
electron-density structure determination of a non-centrosym-
metric liquid crystal, and also the first report of a LC phase
with trigonal symmetry.[15] Note that the Laue symmetry (the
symmetry of the diffraction pattern) of a trigonal structure is
still hexagonal p6mm, hence common X-ray techniques
would fail to detect a trigonal liquid crystal. Again, dynamics
simulations (Figures 2d,h) do not contradict the proposed
structures. The non-centrosymmetric mode of self assembly in
this LC system is of potential interest for nonlinear optics
applications.[16]
Overall, the structures of the LC phases of the bent-core
bolaamphiphiles are governed by the 1208 bend of the
aromatic core, which favors the formation of hexagonal
honeycombs. There are two distinct types of hexagons, 3-
hexagons and 6-hexagons, leading to p3m1 and p6mm lattices,
respectively. Either enlarging the perimeter of the hexagons
by extending the chevron-shaped core, or reducing the
volume of the chains, can lead to the change from 6-hexagons
to 3-hexagons. The defining parameter is the ratio between
the length of the backbone and the volume of the attached
chains, that is, the circumference/area ratio of the polygon. A
similar relation was found for the cylinder phases formed by
linear tectons (T-shaped bolaamphiphiles).[17,18] However, in
the cylindrical arrays of linear compounds, the hydrogen
bonding networks were located at the nodes of the honey-
comb (Figure 3a).[17] In the p3m1 phases of compounds 2a,b
(Figure 3c) only every other node contains H-bonds, whereas
in the p6mm phase of compounds 1c and 2c (Figure 3b) none
of the nodes do. Instead, H-bonds are located within the walls,
Figure 2. Colhex/p3m1 phases viewed along the cylinder long axis: a–
d) compound 2a; e–h) compound 2b; a,e) model electron density
maps; b,f) Fourier-approximated model maps; c,g) maps calculated
from the diffraction data; d,h) snapshots of molecular dynamics
simulations; the color code is the same as used in Figure 1 (see text
for details).
this result is achieved if every other corner of the hexagonal
frame contains glycerol groups, the other corners being the
apexes of the aromatic chevrons.[13] In this structure, the
symmetry is reduced to trigonal (plane group p3m1). Con-
structing an electron-density map for this non-centrosym-
metric structure is rather ambiguous since the phase angle of
most reflections can take up any value, rather than being
limited to 0 and p as in the centrosymmetric group p6mm. For
this reason we resorted to building mesoscale 1(x,y) models of
likely structures using relative 1 values and volume fractions
of the different molecular regions, calculated from molecular
models (see Supporting Information, Table S6). The geo-
metric models of the electron-density maps for compounds 2a
and 2b, respectively, are shown in Figures 2a and e, and
consist of polygons of fixed 1 values (the same colour code is
Figure 3. Comparison of hexagonal honeycombs formed by a) linear
and b,c) bent-core bolaamphiphiles; columns containing the hydrogen
bonding networks are represented by cross-hatched circles.
ꢀ 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2008, 47, 6080 –6083