Solid-state materials, particularly those performing useful functions (e.g. zeolites), often form frameworks or cellular structures on the nanoscale1. These frameworks are usually rigid. Liquid crystals (LC), on the other hand, have a capacity to change shape and respond to external stimuli, such as pH or temperature, and offer the prospect of forming responsive cellular structures. T-shaped block molecules bearing three types of mutually incompatible groups (triphilic) were found to self-assemble into just such honeycomb-type structures. The rigid rod-like cores of the molecules lie normal to the honeycomb channel and form the cell walls, while the flexible side chains fill the cell interior. 1 In a recent report in Science researchers from the Universities of Sheffield (UK) and Halle (Germany) describe how a relatively simple modification, i.e. addition of a second side-chain incompatible with the first (an X-shaped tetraphilic molecule), substantially broadens the range of new cellular LC morphologies, and introduces the concept of multicolour tiling2 in LC design. Here “colour” refers to the chemical composition which can differ from cell to cell. The work shows how promotion of geometric frustration can bring about 2D nanopatterns of large periodicity and unprecedented complexity. It also illustrates the analogy between the LC phase transitions and critical phenomena in ferro- and antiferromagnets, highlighting the universality of physical concepts across widely different types of condensed matter.
The X-shaped tetraphilic molecules (Fig. 1A) used in this work have a rigid aromatic rod-like core with “sticky” hydrogen-bonding ends, and with a carbosilane RSi (green) and a fluorinated RF chain (black) attached at either side. With relatively short side-chains a triangular honeycomb is expected (Fig. 1B), while larger polygons (“tiles”), such as square or hexagonal, are expected for compounds with longer chains (Figs. 1C,D). Here we describe the actual experimental results on three selected compounds with different side-chain lengths relative to the length of the rod-like core. They will be referred to as short-chain, medium-chain, and long-chain compound, respectively. The short-chain compound was indeed found to form honeycombs with triangular cells. Are the chains separated into RF and RSi cells? The answer is yes, at lower temperatures (low-T) – see the electron density map in Figure 2I. However, on increasing T a second-order (i.e. continuous) phase transition occurs, so that above the critical temperature Tc the long-range order of colours is lost and all cells appear the same, having an averaged electron density – Fig. 2H).
Figure 1: (A) Schematic representation of the X-shaped molecules studied: grey = rod-like aromatic core, blue = glycerol terminal groups, black and green = fluorinated (RF) and carbosilane (RSi) side-chains. (B,C) sections through the two-colour triangular and square honeycombs. (D) The two-colour frustrated structure of the low-T hexagonal phase of the long-chain compound. Arrows point in the direction of RSi (green) chain; double-arrowed lines indicate that the molecules spend 50% of their time facing one or the other direction. Copyright American Association for Advancement of Science (AAAS), 2011.
Turning to the compound with the longest chains, it was indeed found to form hexagonal honeycombs. However, here we encounter a problem: how can RF and RSi chains, which prefer to keep apart, separate cleanly each in their own cell? That there is a problem is illustrated at the top of Fig. 1D, which makes it plain that clean separation is impossible. Powder small-angle X-ray scattering (SAXS) experiments as a function of T (Fig. 2A), show again that there is a low-T and a high-T phase, the two being separated by a second order transition at 59°C. We note that the unit cell area of the low-T phase is 3 times that of the high-T phase. The electron density maps, reconstructed from SAXS data in Figure 2A, are shown in Figure 2F &,G. As in the short-chain compound, in the high-T phase all cells are equal, i.e. the RF and RSi chains are apparently mixed, with a small preference for the high-density RF segments to occupy the centre of the cell (Fig. 2G). But what about the low-T phase? The electron density map in Figure 2F gives the answer: a compromise “two-colour” solution is adopted, with one hexagon containing nearly pure RSi chains (orange in Fig. 2F, dark green in Fig. 1D) being surrounded by six mixed cells (blue-green in Fig. 2F, light green in Fig. 1D). A mixed cell contains, on average, 4.5 RF and 1.5 RSi chains. This situation is confirmed also by neutron scattering experiments carried out at ILL, and by atomic force microscopy (AFM), as shown in Figs. 2D, & 2E. Here the bright patches are the harder fluorine-rich regions.
Figure 2: Two-colour (low-T) to single-colour (high-T) tiling transition in hexagonal (A-G, long-chain compound) and triangular LC honeycombs (H, I, short-chain compound). (A) SAXS curves of bulk LC as a function of temperature (recorded at I22, Diamond Light Source). (B, C) GISAXS patterns of an aligned film of the long-chain compound on Si surface (B) above and (C) below the transition temperature Tc = 59°C (recorded at beamline I16, Diamond Light Source) (D, E) AFM phase images of the long-chain compound recorded respectively at 85 and 55 °C (Fourier filtered). (F,G) Electron density maps of the low-T and high-T triangular honeycomb phases of the long-chain compound. (H) Electron density map of the high-T and (I) the low-T phase of the short-chain compound. The maps refer to the colour scale on the right. Copyright AAAS, 2011.
In the highlighted study the authors also show that the square root of intensity of the (10) X-ray peak (Fig. 2A) is equivalent to sublattice magnetization of an antiferromagnet on the so-called kagome lattice, a classical frustrated system in condensed matter physics. Thus they obtained the critical exponent and other parameters, which were comparable to those in the magnets, illustrating the universality of physical models across condensed matter in spite of the wide difference in the nature of the systems. While in ferro- and antiferromagnets it is the electron spins that flip, in the X-shaped LCs it is the whole molecules that rotate by 180° about their long axis. Grazing incidence small-angle scattering (GISAXS) patterns from thin LC films of the long-chain compound (Figs. 2B,C), illustrate another aspect of the critical behaviour: the sharp (10) Bragg peaks below Tc (Fig. 2C) are replaced by strong but diffuse scattering maxima above Tc (Fig. 2B), indicating strong fluctuations, i.e. numerous small temporary domains of the 2-colour phase in the overall long-range averaged mixed cell phase. These fluctuations and the diffuse scatter disappear at higher T.
Figure 3: The high-temperature honeycomb phase of the medium-chain compound with multicolour tiling. (A) electron density map with overlaid schematic molecules – for colour scale refer to Figure 2. The black rectangle encloses one unit cell. (B) The equivalent pattern of tessellating tiles. (C) GISAXS pattern from a thin film in the high-T phase (recorded at XMaS beamline, BM28, ESRF); the overlaid reciprocal lattices correspond to different orientations of the LC (colour coded). (D) The five types of tiles and their number in a unit cell. Copyright AAAS, 2011.
What about the compound with side-chains of medium length? It turns out that the volume of the side-chains is not quite sufficient to fill a square cell, yet it is too large for triangular cells. Note that the area of a square is 2.3 times that of an equilateral triangle with the same side length. For T-shaped LC molecules with side-chain volume falling between those fitting the triangular and square cells, honeycombs with a relatively simple regular array of squares and triangles have been found.3 However, the tetraphilic medium-chain compound in this work has to fulfil more demanding requirements of both space filling and phase separation between its two incompatible side-chains. This compound has found two compromise solutions, one at lower T, and the other at higher T. Both are honeycombs of considerable complexity. The unit cell of the low-T phase contains four honeycomb cells, of which two are triangles, one is a rhombus and one a square. At higher temperatures this transforms to an even more complex phase. Its structure was determined from the GISAXS pattern in Figure 2C and powder SAXS data. The reconstructed electron density map is shown in Figure 3A, having a very large unit cell (21.3 x 11.1 nm). The map can be understood from the overlaid molecular grid, with the red and green side-arms representing the low-density RSi and the high-density RF chains, respectively. As shown schematically in the tiling pattern in Figure 3, the unit cell contains 18 tiles, or honeycomb cells, of five different shapes and “colours” (compositions). These are described individually in Figure 3D.
Patterns as complex as those in Figure 3 are unprecedented in liquid crystals, and are only approached in complexity by morphologies of some ABC three-arm star block copolymers.1,4 We have learned from examples of metal alloys5 and dendrimeric liquid crystals6 that when superlattice unit cells become too large and too complex, the system can give up on periodicity altogether and opt for a quasiperiodic solution, resulting in quasicrystals. The red ellipses drawn in Figure 3 hint to the possibility that the next step in increasing complexity of such multicolour honeycombs could be a quasicrystal with the “forbidden” 12-fold symmetry.
Zeng, X.B., Kieffer, R., Glettner, B., Nürnberger, C., Liu, F., Pelz, K., Prehm, M., Baumeister, U., Hahn, H., Lang, H., Gehring, G.A., Weber, C.H.M., Hobbs, J.K., Tschierske, C. & Ungar, G. Complex Multicolor Tilings and Critical Phenomena in Tetraphilic Liquid Crystals. Science. 331, 1302-1306 (2011)
- For a recent review see Ungar, G. et al. Self-Assembly at Different Length Scales: Polyphilic Star-Branched Liquid Crystals and Mictoarm Star Copolymers. Adv. Funct. Mater. 21, 1296-1323 (2011).
- Grünbaum, B. & Shephard, G. C. Tilings and patterns. (W.H. Freeman, New York, 1987).
- Chen, B. et al Liquid crystalline networks composed of pentagonal, square, and triangular cylinders. Science. 307, 96-99 (2005).
- Matsushita, Y. et al Hierarchical nanophase-separated structures created by precisely-designed polymers with complexity. Polymer. 50, 2191-2203 (2009).
- Senechal, M. Quasicrystals and geometry. (Cambridge Univ. Press, Cambridge, 1995).
- Zeng, X.B. et al. Supramolecular dendritic liquid quasicrystals. Nature 428, 157-160 (2004).
This work was supported by the ESF Eurocores SONS2 program, project SCALES, funded by EPSRC and DFG.