Chirality Induction through Nano‐Phase Separation: Alternating Network Gyroid Phase by Thermotropic Self‐Assembly of X‐Shaped Bolapolyphiles

Abstract The single gyroid phase as well as the alternating double network gyroid, composed of two alternating single gyroid networks, hold a significant place in ordered nanoscale morphologies for their potential applications as photonic crystals, metamaterials and templates for porous ceramics and metals. Here, we report the first alternating network cubic liquid crystals. They form through self‐assembly of X‐shaped polyphiles, where glycerol‐capped terphenyl rods lie on the gyroid surface while semiperfluorinated and aliphatic side‐chains fill their respective separate channel networks. This new self‐assembly mode can be considered as a two‐color symmetry‐broken double gyroid morphology, providing a tailored way to fabricate novel chiral structures with sub‐10 nm periodicities using achiral compounds.

New routes to chirality from initially achiral systems are of particular contemporary interest for obtaining chiral templates in asymmetric synthesis and catalysis. [1] This is important for the use in different fields of material-and nanoscience [2] as well as for the understanding of fundamental principles of the emergence of biological homochirality. [3] Creating chirality in liquids and liquid crystals (LCs), having no fixed positions of individual molecules,i se specially challenging. [4,5] Nevertheless,i tw as recently achieved by mirror symmetry breaking through synchronization and locking-in of transient chiral conformations and configuration. [6] Here we report anew approach to spontaneous generation of chirality based on nano-phase segregation. In the reported case,b reaking the inherent mirror symmetry of the double gyroid cubic phase (Ia " 3d,Q230), known from lyotropic [7] and thermotropic liquid crystals (LCs) [8] (Figure 1a), is achieved by self-assembly of X-shaped polyphilic molecules with two different chains at opposite sides of ar od-like molecular core. [8b] Thecores organize along the gyroid minimal surface, forming aw all that separates the two enantiomeric infinite networks involving these chains.N ano-phase separation of the two poorly compatible semiperfluorinated and aliphatic side-chains,i nto their own networks (blue and red in Figure 1b), gives rise to agyroid cubic phase with two chemically non-equal networks (the "single gyroid" I4 1 32, Q214). This structure has broken mirror symmetry and represents the first alternating network gyroid cubic LC,a nd the first LC with chirality solely based on phase separation. Previous attempts to produce asingle gyroid structure were based on replication from butterflyw ings, [9] lithography [10] and templating. [11] The alternatingd ouble network gyroid wasf ound in narrow compositionr anges of multiblock copolymer blends, [11,12] leading to structures in the > 100 nm range in allc ases.T he new concept reportedh erein providesat ailoredw ay to fabricate chiral structures withm uch smaller sub-10 nm periodicities, which are of great potential in nano-templating and as enantiospecific membranes for use in enantiomer separation. To this end, as eries of X-shaped molecules has been specifically designed and synthesized. These molecules are based on a p-terphenyl core terminated by two hydrogenbonded polar glycerol groups,a nd bearing two laterally attached incompatible chains,t hat is,a na liphatic hydrocarbon chain (R H )a nd as emiperfluorinated chain (R F ) containing as hort -(CH 2 ) n -s pacer and al ong perfluorinated end segment -C m F 2m+1 (see Table 1). Ford etails on synthesis and experimental procedures,s ee the Supporting Information. Most compounds form enantiotropic LC phases,except for compound 1c, which only exhibits am onotropic soft crystal phase (see Table 1). Here,compounds 1b, 2 and 3 are of main focus,all forming anovel alternating double network gyroid phase with lattice parameters below 10 nm upon both heating and cooling.
As the length of the perfluorinated side chain is increased, compounds 1a-c exhibit ap hase sequence Col hex /p6mm-Cub/I4 1 32-Cr Lam (Table 1a nd Tables 1, S1). Thel attice parameter corresponds to about three times the molecular length (L mol = 2.3-2.6 nm measured between the two terminal polar groups). Theelectron density map reconstructed based on p6mm symmetry ( Figure S10) shows ap artly segregated two-color tiling composed of al ower-density (alkyl) column and two higher density (mixed) columns. [13] Thea nalysis of the two-color Col hex phase is described in Section 5ofthe Supporting Information.
Thea romatic cores make up the walls between the columns with glycerol groups forming the hydrogen bonding networks at cell edges ( Figure 4g).
As the side chain length is increased, the honeycomb is replaced by new mesophases.T he mesophase in compound 1b, having as lightly longer semiperfluorinated chain, grows with ac ompletely dark texture under crossed polarizers ( Figure S2b). This isotropic mesophase has high viscosity, which is typical of ac ubic phase.T he reciprocal d-spacings from the SAXS reflections are in the ratio 2 1/2 :6 1/2 :8 1/2 : 14 1/2 :22 1/2 :26 1/2 :30 1/2 :34 1/2 :36 1/2 :38 1/2 :42 1/2 and could be indexed on ab ody-centered cubic lattice (for Miller indices see Figure 2b). Alternative indexing on ap rimitive Bravais lattice,w ith the first reflection as (100) instead of (110), would have had the a/d of the 4 th reflection equal to 7 1/2 instead of 14 1/2 ,a( h 2 + k 2 + l 2 ) 1/2 value unobtainable for any combination of Miller indices.T hus,aprimitive lattice is excluded. Furthermore,due to the clear absence of the (200) reflection (a/d = 4 1/2 ), only one space group, I4 1 32, satisfies the observed extinction conditions,w hich include the 4 1 screw axis condition 00l: l = 4n. Note that the 9th peak can be indexed as either (600) or (442), hence its presence in powder SAXS does not violate the screw-axis condition. Just to safeguard ourselves against the remote possibility that the absence of (200) is coincidental, we constructed the electron density map using Im " 3m symmetry.However,inthis case we obtain abody centered micellar structure with the fluorinated chains forming the micelles ( Figure S11a);the high curvature of the micelles is unlikely considering the molecular structure, volume fractions and dimensions.A ccordingly,t he mesophase in compound 1b is assigned as ab icontinuous cubic with symmetry I4 1 32 (Figures 2d-g and S11b). Thus,wehave the first documented case of a I4 1 32 cubic phase in liquid crystals,t hermo-or lyotropic. [a] Recorded from first DSC heating at 10 Kmin À1 (see Figure S1) and POM;brackets mean metastable phase (only observed upon heating);transition temperatures T (8 8C) are given in square brackets, associated enthalpy changes DH (kJ mol À1 )a re given in lower lines in italics;[ b] Determined by synchrotronp owder small angle X-ray scattering;[c] Volume fraction of side chains measured using MaterialS tudio. Abbreviations:C r, Cr 1 , Cr 2 = crystalline solid;G= glassy solid;C ol hex /p6mm = Hexagonal columnar phase with p6mm symmetry;C ub/I4 1 32 = alternating double network gyroid cubic phase with I4 1 32 symmetry;C r Lam = lamellar soft crystal phase;I so = isotropicl iquid. *P artial crystallization.
Since the intensities of all remaining reflections are smaller than 1% of the strongest (110) reflection (Tables S2,  S4 and S5), the electron density map is dominated by that reflection, whose phase is either + p/2 or Àp/2 rad. Themap constructed using one of these phases is simply the reverse of that obtained using the other, meaning that the maps are identical except for achange of origin. Different representations of the map are shown in Figure 2d-g, where purple color indicates the regions of high, and red the regions of low electron density.The cyan intermediate density region follows the familiar gyroid surface of minimum curvature.The map is closely related to those of the double gyroid phase,e xcept that in the latter case the color of the regions on both sides of the minimum surface would be the same,asboth networks in the Ia " 3d phase have either lower or higher density than the minimal surface,d epending on the compound. Thus,w ec an conclude that, as in the double gyroid, in our I4 1 32 phase there are two infinite networks with 3-way branched channels separated by the gyroid surface.O nly here one network contains the high-density R F and the other the low-density R H chains (Figure 2d,f,r espectively). In fact, the high-density network is of acore-shell type,with the perfluorinated chain ends in the center of the channels surrounded by the short aliphatic spacers.T he gyroid surface is composed of the glycerol-terminated cores lying within it (Figure 2e,g).
Thedistance between the two 3D networks is a cub 3 1/2 /4 = 4.0 nm, which is the same as the distance between the columns (the prismatic honeycomb cells) of the hexagonal phase of compound 1a,w hich is a hex /3 1/2 = 4.0 nm (Figures S10 and S12). This equivalence is to be expected, as in both cases we have an "inverse" thermotropic LC phase in which columns of flexible chains are surrounded by "walls" of rigid aromaticglycerol rods;inthe columnar case these are the honeycomb cell walls and in the cubic case the wall is the minimal surface of the same constitution.
To confirm our structure assignment in real space, compound 3 was imaged at temperatures of the cubic phase by atomic force microscopy (AFM). Images of two different crystallographic planes,( 110) and (111), are shown in Figure 3a,c.P hase contrast is due to the difference in shear modulus between the stiffer R F chains (dark) and the softer R H chains (light). Ac omparison with the corresponding cuts through the electron density map (Figure 3b,d) confirms the general correspondence in geometry of the ED slices and the AFM images,t he two methods agreeing in spacings and angles within 3%.T he measured distance between the rows of motifs in the (111) plane is 11.2 nm (Figure 3c)w hile the value calculated from SAXS is a ffiffi ffi 6 p =2 ¼10.9 nm, with the rows inclined by exactly 608 8;the measured distance between the rows in the (110) plane of 7.0 nm (Figure 3a)a nd the angle of 758 8 also compares well with the values of 6.8 nm and 738 8 measured from the (110) section through the map in Figures 3b and S14. However,w hile the position of the dark R F spots on the triangular lattice in Figure 3c matches well with those of the centers of the 3-arm stars in Figure 3d,t he star-like feature is absent in the AFM image.Weattribute this discrepancy to surface reconstruction, as broken network segments at the surface coalesce in blobs (white domes in Figure 3e)tominimize their surface energy.
Having established the structure of the new cubic LC,itis important to note that I4 1 32 is ac hiral space group,a nd the phase is therefore chiral, even though the compounds forming it are achiral. Thec hirality comes from the fact that the two enantiomorphous networks are chemically different (see Figure 2h,i )w hich breaks the mirror symmetry.I nc ontrast, the achiral double gyroid Ia " 3d phase,having two identical but enantiomorphous networks,p ossesses an umber of glide planes.This is the first case of chirality induction in LCs being exclusively mediated by nano-phase separation [8b,14] of two chemically different molecular segments (the alkyl and perfluoroalky chains) into distinct nano-scale domains (the two networks).
As in other cases of spontaneous mirror symmetry breaking, chirality is likely to be confined to individual cubic domains and, in the absence of an external chiral bias,is likely to be aconglomerate.However, as in the previous case of the chiral triple-network cubic phase of achiral compounds, one chirality tends to win, eventually spreading over the entire sample in av ariant of Ostwald ripening. [6,15] In contrast to the previously reported cases of cubic and other optically isotropic LC phases (refs. [5,6,15]) optical activity or conglomerate formation cannot be observed by chiroptical methods in the I4 1 32 cubic phase reported here. Ther eason is that the chromophore is located on or close to the gyroid minimal surface,which is achiral, whereas the two chiral networks are filled with the alkyl chains and the fluorinated chains,respectively,whose absorption is far away from the spectral range investigated either by polarizing microscopy or by circular dichroism (CD). Hence,o ptical rotation and CD are negligible,leading to optical cryptochir-ality. [16,17] However optical activity and CD are only consequences of the lack of mirror symmetry and are not inevitable,whereas XRD provides adirect proof of chirality, and works irrespective of whether there is only one domain or ac onglomerate.B ecause very strong peaks were observed, that are forbidden in the achiral Ia " 3d lattice,there is no doubt that mirror symmetry is broken.
Further extension of perfluorinated side chains removes the cubic phase and replaces it with amonotropic soft crystal phase in compound 1c having the largest total side chain volume.T his phase appears on cooling and its SAXS Bragg reflections indicate alayer structure with a d = 6.32 nm layer thickness.Asingle sharp peak in the wide-angle region at d = 0.51 nm ( Figure S5) suggests ahexagonal arrangement of the perfluorinated chains lying perpendicular to the layers.T hus, compound 1c exhibits as oft lamellar crystal phase with ABCB stacking of four sublayers,w here A = disordered aliphatic layer, B = disordered aromatic-glycerol layer and C = crystallized fluorinated layer (Figures 4i and S13). The fact that the alkyls are molten while the fluoroalkyls are not can be understood by comparing the melting points of polyethylene and Te flon of ca. 130 8 8Cv s. ca. 300 8 8C, respectively.I nf act, between 30 8 8Ca nd 300 8 8CT eflon forms ah exagonal columnar phase [18] with hexagonally arranged chains with irregular helix reversals. [19] Thep hase sequence Col hex -Cub bi -Lam with increasing side-chain volume is consistent with the established effect of molecular geometry,o nce it is accepted that the present  mesophases are of the "inverse" thermotropic kind. The present molecules could be regarded as having at apered shape,b ut with the chain ends located on average near the narrow end and the rigid rod spanning the wide end of the wedge-see Figure 4a-c. This is the opposite of the usual case of wedge-shaped mesogens,where the aromatic is at the apex and the multiple attached chains fan out at the wide end. [20] Fors uch "normal" wedges it has been shown that ak ey determinant of the adopted phase type is the dV/dr function, describing how volume increases as one moves along r from the apex (r = 0) toward the wide end of the wedge. [21] The same principle can be applied to the present inverse wedges. As af irst approximation, the cross-section area A of the wedge is A(r) / dV/dr / r q .H ere q % 1( slice or triangle shape) suites ac olumnar phase (Figure 4a), q % 0( rectangle, matching aromatic and aliphatic cross-sections) suits alamellar phase (Figure 4c), while 0 < q < 1( shield shape) is most likely to adopt aCub bi phase (Figure 4b). [22] It is worth noting that an etwork of branched columns in aC ub bi phase is an intermediate between straight columns and layers,asdepicted in Figure 4d,e.Amore detailed schematic of the molecular arrangement in the three phase types in the present compounds is given in Figure 4g-i.
In conclusion, we present the first I4 1 32 alternating double network gyroid cubic LC.The work demonstrates anovel way of inducing chirality through phase separation in chemically non-chiral systems.T he network segments reported here are on the scale of only af ew nm between junctions,w hich is of great potential in nano-templating, [12d] for example as enantiomer-specific membranes [8c] for use in enantiomer separation and production and manipulation of circularly polarized light, chirality switching through thermally,c hemically or light-induced mesophase transitions. [23] Moreover,the present study shows how the principle of self-assembled multicolor tiling can be extended from two dimensions (columnar) to three dimensions (cubic), [13,24] providing an ew way to fabricate complex nano-architectures.