Complex tiling patterns in liquid crystals

Abstract

In this account recent progress in enhancing the complexity of liquid crystal self-assembly is highlighted. The discussed superstructures are formed mainly by polyphilic T-shaped and X-shaped molecules composed of a rod-like core, tethered with glycerol units at both ends and flexible non-polar chain(s) in lateral position, but also related inverted molecular structures are considered. A series of honeycomb phases composed of polygonal cylinders ranging from triangular to hexagonal, followed by giant cylinder honeycombs is observed for ternary T-shaped polyphiles on increasing the size of the lateral chain(s). Increasing the chain size further leads to new modes of lamellar organization followed by three-dimensional and two-dimensional structures incorporating branched and non-branched axial rod-bundles. Grafting incompatible chains to opposite sides of the rod-like core leads to quaternary X-shaped polyphiles. These form liquid crystalline honeycombs where different cells are filled with different material. Projected on an Euclidian plane, all honeycomb phases can be described either by uniformly coloured Archimedean and Laves tiling patterns (T-shaped polyphiles) or as multi-colour tiling patterns (X-shaped polyphiles). It is shown that geometric frustration, combined with the tendency to segregate incompatible chains into different compartments and the need to find a periodic tiling pattern, leads to a significant increase in the complexity of soft self-assembly. Mixing of different chains greatly enhances the number of possible 'colours' and in this way, periodic structures comprising up to seven distinct compartments can be generated. Relations to biological self-assembly are discussed shortly.

Temperature-Dependent In-Plane Structure Formation of an X-Shaped Bolapolyphile within Lipid Bilayers

“…11 As shown below, during self-assembly in phospholipid membranes all three distinct units segregate into different domains and, especially the rod-like cores tend to organize in densely packed -stacked nano-domains within the lipid matrix, and therefore we consider compound B12 as a polyphilic (more specifically triphilic) molecule. 12 The properties of other oligo(phenylene ethynylenes) with at least two hydrophilic groups have been reported by various groups, however mostly with lateral hydrophilic groups and without addressing their properties in lipid bilayer membranes. [13][14][15][16][17] The aromatic backbone length of the newly designed molecules is 3.2 nm and is thus in the range of the typical thickness of the lipophilic part of a phospholipid bilayer.…”

Effects of Lateral and Terminal Chains of X-Shaped Bolapolyphiles with Oligo(phenylene ethynylene) Cores on Self-Assembly Behaviour. Part 1: Transition between Amphiphilic and Polyphilic Self-Assembly in the Bulk

“…These flexible lateral chains cause a frustration of the layer-like organization for steric reasons (Figure 1a,b). Moreover, the flexible chains are more or less incompatible with the rigid rod-like cores, thus tending to organize in distinct compartments, and therefore, these molecules are considered as bolapolyphiles [14][15][16][17]. The bulk self-assembly of these compounds is complex, and a huge variety of distinct LC phases can be observed, as shown in Figure 1.…”

“…The bulk self-assembly of these compounds is complex, and a huge variety of distinct LC phases can be observed, as shown in Figure 1. The typical feature of their self-assembly is the formation of polygonal honeycombs where the polar end groups form columns which are interconnected by the rod-like cores, thus forming a network with 2D periodicity in the a-b plane and being expanded into the third dimension c (Figure 1c-k) [14][15][16][17]. Depending on the ratio between chain volume and space available in the prismatic cells (mainly determined by the length of the rod-like units), the cross-sectional shape of the prismatic cells changes.…”

“…Triangular honeycomb morphologies have been observed for flexible star-shaped triblock copolymers [55], as well as for other types of low molecular weight rod-coil polyphiles, namely the facial amphiphiles [56,57]. Highly flexible bolaamphiphilic triblock copolymers (ABA triblocks), such as pluronics, i.e., FEO-PPO-PEO (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)) are known to interact with lipid membranes by polar interactions of the EOs with the polar head groups, and insertion of the PPO blocks into the inner lipophilic part of the bilayers, provided they and the small polygonal honeycombs with triangular and quadrangular shape (c-e), considered here, also larger pentagonal and hexagonal honeycombs (f-h), giant honeycombs formed by end-to-end connected pairs of molecules (i-k), special types of lamellar phases with coplanar rod alignment (l-n), as well as cubic network phases (o) and columnar phases involving coaxial rod-bundles (p) are known [15,17].…”

“…These large molecules with molecular weights between 1 and 2 kg·mol −1 could be considered as triblock rod-coil oligomers with strictly uniform size distribution [16,51]. and the small polygonal honeycombs with triangular and quadrangular shape (c-e), considered here, also larger pentagonal and hexagonal honeycombs (f-h), giant honeycombs formed by end-to-end connected pairs of molecules (i-k), special types of lamellar phases with coplanar rod alignment (l-n), as well as cubic network phases (o) and columnar phases involving coaxial rod-bundles (p) are known [15,17].…”