Diastereomeric liquid crystal domains at the mesoscale

In many technologies used to achieve separation of enantiomers, chiral selectors are designed to display differential affinity for the two enantiomers of a chiral compound. Such complexes are diastereomeric, differing in structure and free energy for the two enantiomers and enabling chiral discrimination. Here we present evidence for strong diastereomeric interaction effects at the mesoscale, manifested in chiral liquid crystal guest materials confined in a chiral, nanoporous network of semi-crystalline helical nanofilaments. The nanoporous host is itself an assembly of achiral, bent-core liquid crystal molecules that phase-separate into a conglomerate of 100 micron-scale, helical nanofilament domains that differ in structure only in the handedness of their homogeneous chirality. With the inclusion of a homochiral guest liquid crystal, these enantiomeric domains become diastereomeric, exhibiting unexpected and markedly different mesoscale structures and orientation transitions producing optical effects in which chirality has a dominant role. Helical nanofilaments—composed of achiral, bent core molecules—have been shown to assemble into left- and right-handed structures. Here, the authors show diastereomeric interactions on the mesocale between chiral liquid crystal guest compounds and helical nanofilament-based pores.

S ince the first demonstration of the handedness of tartaric acid molecules by Pasteur 1 , resolution of enantiomers and dissymmetric induction in synthesis have been important from the perspectives of both science and technology [2][3][4][5] . In recent years, much effort has been expended on researching methods of fabricating nanoscale chiral surfaces, in many cases with the goal of improving enantioselectivity in asymmetric induction 6 , high-performance liquid chromatography 7,8 and high-sensitivity chirality detection 9,10 . Fabrication techniques include cleaving metal surfaces along low-symmetry planes 11 , adsorption of chiral molecules onto metal surfaces [12][13][14] , electrodeposition 15 , molecular imprinting [16][17][18] , glancing-angle deposition 19 and employment of metal-organic frameworks 20 . Liquid crystal (LC) systems have recently emerged as a promising class of materials exhibiting chiral interface effects, since they readily self-assemble into complex chiral structures in response to little more than appropriate sequences of changing temperature 21 . Liquid crystals exhibit a wide variety of chiral structures and responses, in both synthetically chiral systems and those where there is spontaneous reflection symmetry breaking, at lengths ranging from the molecular (in chiral bent-core phases, for example) to the macroscopic (as in the induction of chirality by micron-scale twist of the nematic director in a twisted cell geometry).
During the last decade, spontaneous reflection symmetry breaking has been reported in several fluid LC phases of achiral bent-core molecules, with macroscopic, chiral conglomerate domains and a wide variety of novel structural phenomena involving the interplay of chiral, polar and liquid crystalline order observed in smectic phases of tilted molecules [22][23][24][25][26][27][28][29] . Among the novel phases exhibited by bent-core mesogens, the helical nanofilament (HNF) phase is one of the most fascinating and potentially useful. In this phase, also known as the B4, the bentcore molecules form well-defined smectic layers with in-plane hexatic order, and the combination of macroscopic polarization and molecular tilt makes the layers chiral (Fig. 1a). The layers are intrinsically unstable with respect to local saddle-splay distortion, a result of the internal stretch of the top and bottom halves of each smectic layer in nearly orthogonal directions (Fig. 1b), leading to the spontaneous formation of left-and right-handed helical nanofilaments (Fig. 1c) 30,31 . The preferred local radius of the saddle-splay (RB25-30 nm) 30 is such that only saddlesplayed layers grow in upon cooling, so each filament becomes a chiral, twisted bundle of a few (B8) smectic layers that is arbitrarily long (limited by the size of the cell, for example) but of finite diameter (DB30 nm). Helical nanofilaments are unique among mesogenic structures with respect to their stability, reproducibility, and controllability. The HNF phase is one of the rare liquid crystal phases that preserves its nanoscale LC structure in a room temperature semi-crystalline state 32 . The nanofilaments can be aligned with self-assembled monolayers 33 , shearing 34 , topographic confinement 35 and controlled growth in a unidirectional director field 36 . Potential applications of HNFs utilize electric-field controlled optical activity in nano-segregated 5CB/HNF mixtures 37 , the enhanced optical activity of achiral, rod-like molecules nanosegregated in the HNF structure 38 or the self-assembled hydrophobic surfaces formed by toric focal conics and HNFs 39 . HNF networks can even form organogels that absorb large amounts of solvent at concentrations as low as 2 wt% (refs 40,41).
In binary mixtures of an HNF-forming bent-core host with many different mesogenic guest compounds, there is strong phase separation, with nanofilaments forming a nanoporous network and the guest material expelled from the HNFs to occupy the interstitial volumes between them 42,43 . In mixtures, the HNFs appear via a first-order phase transition, nucleating randomly at very dilute sites in a typical LC cell 44  determines the handedness of the HNFs, which grow radially outwards from the nucleation site to form a spherulitic domain (Fig. 1f) that is completely homochiral, that is, every HNF grown in a given domain has the same handedness 45,46 . In each chiral domain, the guest material is nanoconfined to the pores of the HNF network, which has a large surface-area-to-volume ratio (B100 m 2 cm À 3 , comparable to aerogel) 40,41 . This geometry suggests that HNF networks might be useful in chiral separations or catalysis 47 , if the appropriate chemical distinctions can be exhibited by the HNF surface. In a typical preparation, there is a patchwork of left-and right-handed HNFs with roughly equal areas, distinguished generally by their optical rotation (OR) or birefringence colour, as in Fig. 1f. In a variety of applications, it would be desirable to engineer HNF networks that have the same chirality everywhere. Induction of globally homochiral, bent-core LC domains has been demonstrated by several methods, including controlled growth in a twisted director field 48 , using biomolecular adsorbates 49 and by mixing chiral dopants into the fluid B2 phase 50 . Homochiral samples can also be achieved by using structurally chiral bent-core mesogens 51,52 . To this end, we investigated in our experiments the properties of left-and right-HNF domains in binary mixtures of the prototypical achiral, HNF-forming bentcore mesogen NOBOW 53 mixed with a variety of chiral dopants. We found, with few exceptions, that the chosen chiral dopants, which include calamitic mesogens and cholesterol derivatives, had no observable effect on the proportion of left-and righthanded domains nucleated in the cell. These mixtures did, however, present an exciting new family of diastereomeric systems to explore, in which nanoporous networks with identical structure but opposite handedness host a chiral LC guest. The failure of the guests to cause chiral induction is likely a consequence of both the high temperature at which the HNFs form in the melt, with the transition into the HNF phase occurring when the guests are isotropic, and of the extremely low solubility of the guests in the HNFs, making the guest-HNF interaction weak at high temperature. As the temperature is reduced, however, the chiral guest acquires local and then macroscopic orientational and positional liquid crystal order within the confines of the left-or right-handed domains of the HNF network 54,55 . This guest-host coupling then becomes significantly enhanced, with the guest increasingly influenced by the difference between the diastereomeric domains as manifested in distinctive thermo-optical orientation effects.

Results
Nanoconfinement of guest molecules in NOBOW HNF networks. Binary mixtures of NOBOW with a variety of guest materials (chiral, racemic and achiral) were prepared and studied. The chemical structures and phase sequences of neat NOBOW and the principally studied guest materials 8S5 (ref. 56) and 7O.5* (ref. 57) are shown in Fig. 2, with the rest of the guests studied shown in Supplementary Figs 1-5 and Supplementary Table 1. The notation '*' indicates that a molecule and its phases (Iso*, N*, Sm* and so on) are chemically, and therefore structurally, chiral. The 8S5 and 70.5* mixtures with NOBOW, prepared with the guest material concentration, c, in the range 30 wt%oco50 wt%, show similar global phase behaviour, indicated schematically in Supplementary Fig. 6 and described as follows. Above the HNF melting temperature, where the guests and NOBOW are isotropic as neat materials, the mixtures form a single, homogeneous isotropic (Iso) phase. On cooling, the NOBOW HNF phase appears first and strongly phase-separates from the isotropic solution. The HNF phase nucleates as internally homochiral, spherulitic domains from point nucleation sites that break achiral symmetry with a random distribution of handedness and grows upon cooling with smooth circular boundaries that advance until neighbouring domains meet (Fig. 1f). The HNFs are typically diluted by guest material and have a helical structure very similar to that of neat NOBOW, as confirmed by freeze-fracture transmission electron microscopy (FFTEM) observations ( Supplementary Fig. 7). Prior X-ray diffraction study 42 indicates the NOBOW/guest phase separation is nearly complete, with guest expelled from the interior and NOBOW similarly insoluble in the guest. FFTEM also shows that the HNFs are completely of a single handedness within each spherulitic domain. The principal optical characterization methods are measurement of optical rotation and birefringence, the former due to the HNF and/or guest chirality, and the latter driven by the local nematiclike orientational ordering of the HNFs in the host network, which is uniaxial about the mean HNF (z) axis, generating an average uniaxial birefringence Dn of the HNF/guest system ( Supplementary Fig. 8). This overall uniaxial symmetry will thus produce orientation distributions of the guest director f(y) that are azimuthally symmetric about z ( Supplementary Fig. 9), with DnphP 2 (cosy)i Q(y), where y is the polar orientation of a local dielectric tensor principal axis, e.g., the guest nematic director n(r), relative to z. The twist sense of the helical nanofilaments in the domains can be determined by combining OR measurements with FFTEM techniques (as explained in Supplementary Discussion 1) which show that, in the high temperature regime where the guests are isotropic, domains of right-handed (lefthanded) HNFs rotate the polarization of visible light clockwise (counter-clockwise). In Figs 3-5, and Supplementary Figs 10, 11, 12 and 16, the notations (Iso), (N), (Sm) and so on indicate the phase of the (bulk) guest in the larger pores of the HNF network host. The phase transition temperatures of the guests in the HNF network are somewhat shifted (by oB10°C) relative to their neat bulk values due to chemical instability of, and impurities in, the NOBOW host.
Even though the HNFs have local uniaxial ordering with preferred orientation along the radial growth direction ( Supplementary Fig. 8), and the NOBOW molecules are strongly optically anisotropic, the spherulitic domains of radial HNFs have only very low, negative, birefringence (|Dn|B|n z -n > |oB0.001) when the HNFs have grown into a guest/NOBOW mixture that is isotropic (the usual case). This suggests that the low Dn is a result of orientational averaging of the local biaxial optical dielectric tensor director field within each HNF ( Fig. 3d and Supplementary Discussion 2), and that around the as-formed HNFs there is little orientation of the confined guest at high T, even at the guest/HNF interfaces. The general structural behaviour of achiral 8S5 and chiral 7O.5* as guests in NOBOW HNF networks is as follows.
8S5 (achiral)/NOBOW mixtures. Because 8S5 is achiral, the leftand right-handed HNF domains in this mixture are enantiomeric, and thus their textures exhibit mirror-symmetric optical rotation as revealed by decrossing of the polarizers (Fig. 3b,c), and are therefore indistinguishable on average when viewed between crossed polarizers. As noted above, Dn of the 8S5/HNF system is very low when 8S5 is in the Iso phase (Fig. 3a,h). However, previous differential scanning calorimetry (DSC) and nuclear magnetic resonance (NMR) study 54,55 shows that the 8S5/ NOBOW and 8CB/NOBOW mixtures exhibit a nematic surface alignment by which the guest forms a several nanometer-thick oriented layer on the HNF surface at lower temperatures in the guest isotropic phase (at TB90°C for 8S5). This surface alignment is referred to as the isotropic surface-aligned state (Iso surf ) and is detectable in 8S5/NOBOW Dn data (Fig. 3h), giving a contribution DnB À 0.001 starting just above the 8S5 Iso-N transition. As the 8S5/NOBOW mixture is further cooled a distinct transition in Dn is observed at T ¼ 77°C (Fig. 3h) where nematic ordering appears in the confined guest (Fig. 3e,f) and the birefringence of domains of both handedness changes sign, becoming positive and growing substantially in magnitude (DnB0.012), but still remaining much smaller than that of aligned monodomain nematic 8S5 (DnB0.12, see Supplementary  Fig. 10). Dn decreases in magnitude at the N-smectic A transition as a result of quasi-cylindrical 8S5 smectic layers growing around the surface of the HNFs (discussed below). Intensity (a.u.)  Fig. 10)). Such a reduction in Dn requires a guest nematic director that is twisted in the pores, with a small net average orientation parallel to the local HNF axis. There is no observable difference between the left-and right-handed HNF domains between crossed polarizers at any temperature, indicating that they have the same Dn. The scale bar in (a) is 100 mm. (g) Transmitted white light intensity through a c ¼ 30% 8S5/NOBOW cell between crossed polarizer and analyser. Incident light passes through a 30 mm diameter spot selected to be within a spherulite and to have the HNF axes making an average angle of 45°with respect to the polarizer axis. (h) Resulting measured birefringence, Dn. Moving to other positions in either L or R domains with polarizer and analyser crossed produces minor variations in the intensity curves due to the textures being slightly different. When 8S5, which is achiral, transitions from Iso to N, the birefringence of both chiral domains changes from negative to positive, giving a minimum in the transmitted intensity at around 78°C. This change of sign shows that the growth of nematic order can produce ordering of sign different from that due to the surface ordering in the isotropic phase. The magnitude of the birefringence decreases as the 8S5 transitions from the nematic to the SmA phase, consistent with quasi-cylindrical guest smectic layers growing around the surfaces of the HNFs (as in Fig. 7f (Fig. 1f), a result of the essentially complete phase separation of the mixture that reduces the possibility of significant chiral induction by the chiral guest molecules. Upon cooling, isotropic 7O.5* also exhibits an Iso* to Iso* surf transition at which an oriented LC layer on the HNF surfaces appears 54,55 at T E 70°C, as indicated optically by the sign change of Dn of the (R,R) domain and by DSC ( Supplementary Fig. 13). The Iso* surf state for To70°C is also marked optically by an increasingly positive birefringence of the (R,R) domains (Fig. 4j,k, Supplementary Fig. 11), and an increasingly negative birefringence of the (L,R) domains, a clear manifestation of the diastereomeric nature of the 7O.5* nanoconfinement, at the earliest stages of its ordering. Upon further cooling, the 7O.5* undergoes the Iso* surf ÀN* phase transition within the HNF network, also indicated by DSC, and by a strong increase in |Dn|, with Dn remaining positive in the (R,R) domains and negative in the (L,R) domains (Fig. 4b-e, Supplementary Figs 11 and 12). As the N*-smectic A* (Sm*) transition is approached, the Dn of the (R,R) domains begins to significantly decrease, crossing zero to produce a striking extinction at T ¼ 50.8°C, homogeneously within each (R,R) domain, and simultaneously throughout all of the (R,R) domains of the sample (Fig. 4f). This reversal of Dn is due to quasicylindrical 7O.5* smectic layers growing around and enveloping the surface of the HNFs, observable using FFTEM (discussed below). Thus, for To50.8°C the Dn of the (R,R) domains becomes negative, again with the same sign as that of the (L,R) domains (Fig. 4g-i). This results in the (R,R) domains having a range of T with positive Dn, while the (L,R) domains have negative birefringence at all T, a mesoscopic manifestation of their diastereomeric nature.  For example, in Fig. 5, a c ¼ 5% CB15/45% 8S5/50% NOBOW mixture is cooled from the isotropic until HNF domains appear. At high temperature, where the guest material is Iso*, the chiral HNF domains of NOBOW exhibit very weak, negative birefringence and opposite OR, as for achiral 8S5 (Fig. 5a-c). However, the diastereomeric nature of the domains becomes optically very evident in the N* phase, with only one handedness of the HNF domains changing sign of Dn at the transition (as was also observed in the 7O.5*/NOBOW mixtures).
Optical, LC ordering and surface anchoring characteristics. This study focuses on HNF/guest systems where the bulk guests have an isotropic-nematic-smectic phase sequence, as summarized in Supplementary Table 1. These systems generally exhibit three transitions between four distinct HNF-confined states of the guest as T is lowered: isotropic (Iso or Iso*)-no measurable guest alignment at the temperatures immediately below that of the HNF network formation; isotropic surface aligned (Iso surf or Iso* surf )-a transition in the Iso phase of the guest to surface-induced alignment of the guest on the HNFs, with the guest contributing Dn guest , of magnitude |Dn guest |B0.001 to the birefringence. This Dn guest can be of either sign, depending on the guest and/or the HNF handedness nematic (N or N*)-the Iso ÀN transition of the bulk guest, marked by a sharp increase in |Dn guest |, up to the |Dn guest |B0.01 range. For achiral guests the sign of Dn may or may not change at the Iso-N transition (the same in both L and R HNF domains of course), whereas for chiral guests at the Iso*-N* transition, Dn guest becomes distinctly different in the two domains with either the (L,R) or (R,R) changing sign at the transition, depending on the guest; smectic (Sm or Sm*)-the N-Sm transition of the bulk guest where the smectic contribution to Dn guest is increasingly negative with decreasing T and as large in magnitude as |Dn guest |B0.02. However, the nanoconfined guest/NOBOW HNF network systems consistently have an overall birefringence that is much smaller than that of the strongly birefringent, oriented bulk phases of the guest and/or NOBOW, in the range of 1 to 10% of the latter 55,56 . Such ratios require subwavelength orientational averaging of the guest LC optical anisotropy in which a significant fraction of the anisotropic molecular components have their high polarizability axes making a substantial angle y with the HNF. This is the case in the fixed helical internal structure of the HNFs, where averaging of the bent-core molecular orientation gives rise to the low Dn HNF (Supplementary Discussion 2). In an analogous manner, the low or negative Dn of the guest LC phases must arise from similarly large y values, in the form of the heliconical director distribution about each HNF shown in Fig. 6c and discussed in Supplementary Fig. 9. Such director distributions require strong anchoring on the HNF surfaces to be maintained, that is, with a surface penetration length, l, (ref. 58) much smaller than the HNF diameter, DB30 nm. Otherwise, if the anchoring were weak (l4D), the HNFs would act as a homogeneous uniaxial orienting force aligning the guest nematic with yB0°, parallel to the HNFs and giving essentially its bulk Dn like a nematic monodomain stabilized by a dilute anisotropic polymer network 59 . Equations 1 and 2 in Supplementary Discussion 2 provide a means of estimating the average birefringence change produced by regions within the network of aligned guest, calculating the contribution to Dn due to a birefringent guest layer of uniform thickness w on the HNF surfaces. Taking the bulk nematic guest optical dielectric anisotropy to be De N ¼ 0.6 and the average guest refractive index to be n b ¼ 1.6, we find the estimated guest contribution to Dn to be Dn guest B0.012 Â w(nm) Â hP 2 (cosy)i, or Dn guest B0.012*hP 2 (cosy)i for a surface film that is about a single molecular monolayer in thickness (wB1 nm).
Isotropic surface aligned. Nanometre-thick films of aligned nematic on solid surfaces in contact with the isotropic phase of a nematic LC are well known [60][61][62] . Applying the estimate of wB1 nm to the isotropic surface-aligned state of 7O.5*, where the contribution of the guest molecules to Dn in the (R,R) and (R,L) domains changes by, respectively, Dn guest(R,R) B þ 0.003 and Dn guest(L,R) B À 0.001, that is, it is both small and diastereomeric, shows that either hP 2 (cosy)i must be small (hP 2 (cosy)iB0.1), due to orientation on the HNFs near y m , or that there is low nematic-like order of the local HNF axes, or that the average HNF surface-oriented film thickness must be substantially less than w ¼ 1 nm, that is, that there can be only partial, perhaps intermittent, coverage of the HNF surfaces. In any case, the manifestation of the diastereomeric nature of the (R,R) and (L,R) domains in so little ordered guest indicates that T =120 °C (Iso*) the earliest stages of ordering of the guest must take place at the HNF surfaces, where the HNF chirality can play a role. This, in turn, suggests the importance in the early stages of guest material confined in the smallest inter-HNF gaps (ranging in size from contact to a few nm).
Nematic. Turning to the nematic state of 7O.5*, assuming that the guest volume is now filled (f ¼ 0.5), and again taking De N ¼ 0.6 and n b ¼ 1.6, we find Dn guest B0.1 Â hP 2 (cosy)i from equation 1 of Supplementary Discussion 2. If hP 2 (cosy)iB1, this is also much larger than the measured birefringence, |Dn guest |B0.01. In the nematic ordering of the guest/HNF systems, DSC data, such as Supplementary Fig. 13, indicate that guest nematic order extends over 475% of the available volume. As the nematic order is filling the guest volume, the distribution of pore sizes P(p) in the HNF network, ranging from HNFs in contact to those spaced by hundreds of nanometres 40 , must be taken into account. Filamentary networks typically have lognormal pore size distributions with extended tails for larger pore sizes 63 , visible up to the micron scale in the FFTEM of mixtures 42 . Thus, if the HNF-confined 7O.5* has typical nematic local ordering then its director n(r) must be substantially disordered. Evidence for the nature of this disorder is provided by measurement of the electrooptic response of an 8CB/NOBOW guest/HNF system, as detailed in Supplementary Discussion 3 and Supplementary Fig. 14. Here we find that an applied AC electric field that is large enough to orient the guest only in the largest pores of the HNF network (dimension p4B70 nm) reduces Dn of the spherulitic domains to the DnB0.001 level, comparable to that of the isotropic surface-aligned state. Thus, the nematic director is rendered nearly isotropic by the HNF nanoconfinement in the smaller pores (poB70 nm), where the guest attains a fixed director field conforming to the HNF surface orientation preferences. Strong anchoring on the HNF surfaces combines with their mixed homeotropic and planar aligning faces and the overall orientational averaging due to HNF twist to render the small pores permanently nearly isotropic (Supplementary Discussion 4). By contrast, the guest director n(r) in the larger pores, while also bounded by surfaces with strong anchoring, has enough space to reorder and anneal according to the dictates of its elasticity, inherent chirality and chiral HNF anchoring. Thus, we find that the contrasting (L,R) and (R,R) optical behaviour in the nematic state is a manifestation of the differing molecular organizations of the nematic 7O.5* director n(r) in the largest pores of the left-and right-handed HNF networks, respectively. In both of these domains the guest molecules adopt the righthanded twist direction preferred in the bulk N* phase ( Supplementary Fig. 15), subject to constraints of the twisted boundary orientations imposed by the nearest HNFs, which differ in the (R,R) and (L,R) domains (Fig. 1d). The behaviour of n(r) in the larger pores can be described by the model sketched in Fig. 1d, where the guest is taken to be in a planar slab between walls of HNFs oriented according to the (L,R) or (R,R) chirality, red or blue, respectively. The HNF walls act on the director field of the guest as strongly anchoring, nanotextured sheets, with n(r) disordered on the nanoscale near the HNF sheets but annealing to order out to larger length scales with increasing distance from the HNFs, a scale comparable to the pore dimension in the middle of a pore. This results in an effective orientational anchoring that is much weaker than that on the HNF surface, in the same way that solid substrates having random orientations patterned on the nanoscale produce nearly-degenerate azimuthal alignment of a contacting bulk nematic [64][65][66][67] .
To describe the surface anchoring of 7O.5* on the HNFs we first explore having a preferred orientation of n(r) along the layer edge directions on the HNF surfaces (Figs 1c and 7, Supplementary Fig. 8), which locally make a substantial angle (430°) with the HNF axis. The resulting remnant surface interaction reflecting the surface patterning and thus the chirality of the HNFs is described by a chiral Rapini-Papoular energy on each HNF sheet of the form W(c) ¼ W 0 sin(2c), the lowest order chiral term in a harmonic expansion of W(c). Here c is the angle defined at each pore surface between n(r) and z such that n(r) at the surface is given by n(c) ¼ zcosc þ (z Â s)sinc, where s is the surface normal pointing into the pore (Fig. 6b). In the (R,R) case, The HNF network is approximated as an array of sheets of HNFs separated by pore dimension p. For the case of 7O.5*, the pore is filled by guest mesogens preferring a right-handed twist of director n(r), with a pitch B300 nm. The structure adopted by n(r) in the pore is determined by the strong nanoheterogeneous anchoring on the HNF surfaces, which reflects the HNF chirality, as in (c), but, in the larger pores, anneals to a soft, chiral anchoring potential of the form W As these anchoring potentials are very weak they do not substantially distort the right-handed bulk helix of 7O.5*. Rather, the helix maintains its pitch but simply reorients as a whole as a means of reducing its surface energy, a condition that is generally satisfied if n(c) at both surfaces of a pore (both ends of the guest helix) can simultaneously reorient into a shaded area. The resulting energyminimizing n(r) fields achieving this condition for (L,R) and (R,R) pores of size pBP guest /6 are sketched in Fig. 6b for nematic 7O.5*, along with the sign of the contribution of these orientation fields to Dn.
In the case of (L,R) or (R,R) domains with 7O.5*, the polar orientation of n(r) is, respectively, larger or smaller than the magic angle y m in Supplementary Fig. 9, giving, respectively, Dno0 or Dn40. In larger pores with p4P guest /4, n(r) will exhibit an integral number of (P guest /4)-thick slabs in each of which there is a p/4 rotation of n(r) and averaging over a similar range of y, which contribute weakly to Dn, plus some remnant length. The surface energy and Dn calculations are then applied only to the remnant tail and the contribution of the pore to the average Dn is correspondingly reduced. In the same way, the larger pores contribute to the enhanced OR in 5CB/NOBOW systems observed by Otani et al. 38 Smectic. At lower temperatures the nematic to smectic transition of the nanoconfined guests takes place, producing changes in both their bulk nematic and surface alignment behaviour, including a substantial increase in the pitch for chiral nematic guests in the larger pores. Smectic layers begin to form in the pores, and in 7O.5* Dn in the (R,R) domains eventually changes sign so that the birefringence in both domains is again negative, implying that in the smectic guest material the highindex axis makes a substantial angle y with the nanofilament axis (Fig. 6c, Supplementary Fig. 9). To further investigate this smectic ordering, we performed FFTEM studies of calamitic guest/ NOBOW mixtures with the guest in the smectic phase. Molecular order near the HNFs is more clearly observed in mixtures where the NOBOW is very dilute. Thus, with c ¼ 95% 7O.5*/NOBOW the HNFs come out of the melt at T ¼ 78°C, well above the bulk isotropic to chiral nematic phase transition of 7O.5* and are wellseparated, enabling observation of the morphology of the guest smectic material near single HNFs. The FFTEM images (Fig. 7c,e) reveal filament structures with a range of diameters larger than the bare HNFs (30 nmoDo55 nm) and very few exposed layer edges, giving an appearance consistent with conformal growth of guest smectic layers on the layer surfaces of the HNFs (Fig. 7c,d), with the guest smectic tending to enhance the characteristic screw-like appearance of the HNFs. Such a cylindrical SmA layer corresponds to the conical distribution of molecular orientations of Supplementary Fig. 9 with y ¼ 90°, clearly contributing negative birefringence to Dn in both the (R,R) and (L,R) domains. We also observe thicker, smoother-coated HNFs that are more cylindrical but have a rope-like surface topography reminiscent of the underlying helical structure (Fig. 7e,f), confirming that the 7O.5* smectic layers coat the HNF surfaces. At higher NOBOW concentrations (c ¼ 50% 7O.5*/NOBOW at T ¼ 45°C in Fig. 7b), the HNFs also show very few of the layer edges seen in neat NOBOW, implying that the nanofilaments are coated by the smectic layers of the guest material over a broad concentration range.
The extinguishing state near T ¼ 50.8°C is imaged at long exposure times in Fig. 7g-i and Supplementary Fig. 12, showing that it is a speckle-like mosaic of micron-scale red (DnB0.002) and blue (DnB À0.002) spots within the (R,R) domains. These spots can be taken as evidence for there being a range dT z of local zero-crossing temperatures for Dn(T). From the minimum birefringence of the spots of |Dn|B0.002, and the slope of Dn(T) near the crossing from Fig. 4k of dDn(T)/dTB0.004/°C we estimate dT z as dT z B0.002/(dDn(T)/dT)B0.5°C, a quite small range, indicating a quite homogeneous intrapore structure and environment throughout the sample, even at the centres of the spherulitic domains.

Discussion
The striking phase behaviour of enantiomeric or diastereomeric guest/HNF systems has been explored in many mixtures of the HNF-forming bent-core molecule NOBOW with, respectively, nonchiral (achiral, racemic) or chiral guest materials. As a function of temperature, these systems generally exhibit distinguishable isotropic, isotropic surface aligned, nematic and smectic HNF-confined guest states, as manifest optically by the overall birefringence and optical rotation, for example. In a given sample these states are obtained throughout the HNF network and the transitions between them take place homogeneously at distinct transition temperatures. Summarizing the nematic state in the guest/HNF systems, if the guest were in a weakly orienting network Dn would be uniaxial with DnBDn guest /2, reflecting uniform uniaxial alignment of the guest. Measured Dn are B10% of this value, a result that can be achieved only with strong anchoring on the HNFs, enabling the combined disordering effects of the orientation variations in the local HNF axes (Fig. 7b and Supplementary Fig. 8), HNF surface alignment-induced cancellation of Dn in the smaller pores ( Supplementary Fig. 14), and the fractional filling of, and orientational averaging in, the larger pores (Fig. 6b). The homogeneous mesoscopic diastereomeric behaviour implied by the ultra-low network birefringence at temperatures where the guest state changes is a result of the mesoscopic homogeneity of the HNF network and the nematic elastic annealing of the HNF anchoring distortions away from the HNFs in the larger pores. Apart from the isotropic phase, the particular structures of the guest in these various states and the changes observed at the transitions are not universal but, as indicated by Dn, rather appear to depend on the details of the orientational interactions of the guest at the HNF/guest interfaces. Thus, Dn may or may not be the same in the Iso guest and N states, the nematic diastereomeric domains may or may not have opposite sign of Dn, and even the smectic layering can induce positive rather than the negative Dn given by homeotropic orientation in the HNF as discussed above, for example, in cholesterol derivatives such as cholesteryl nonanoate ( Supplementary Figs 16 and 17).
Such features of the polymorphism of the guest/NOBOW mixtures investigated are summarized in Supplementary Table 1. Limited experimentation has also been carried out on guest/ bent-core mixtures using other HNF-forming materials. These bent-core systems, such as W513 (ref. 68), exhibit similar multi-state phenomenology, typified by the 7O.5*/W513 mixture shown in Supplementary Fig. 18. For all mixtures in which the guest material has a chiral nematic phase, the diastereomeric domains are easily distinguished in the microscope.
The experiments reported here detail the structural guest/host behaviour of a class of chiral nanoporous host networks formed by self-assembly and spontaneous symmetry breaking in systems of bent-core liquid crystals. The resulting characterization of guest structure constitutes a general and necessary approach to the development of an understanding of chirality at the nanoscale and its mesoscopic manifestations, particularly if liquid crystal ordering is present or exploited, as a path towards applications in chiral separations and asymmetric synthesis.

Methods
Optical observations were made using a Nikon Eclipse E400 POL microscope with polarizer and analyser equipped with an Olympus Camedia C-5050 Zoom digital camera. Birefringence was measured either using a Zeiss rotary compensator with quartz plates, or by converting intensity measurement as in Figs 3g and 4j to birefringence using the compensator as calibration. Optical rotation (OR) was measured by decrossing the polarizer and analyser. The liquid crystal mixtures were filled into Instec 3.2-mm commercial cells by capillary action at high temperature in the isotropic phase. Temperature was controlled using an Instec STC200D temperature controller. The samples were typically cooled slowly from the isotropic phase (at B À2°C min À 1 ) to avoid any hysteresis effects.
Freeze-fracture transmission electron microscopy experiments were carried out by sandwiching the sample between 2 mm by 3 mm glass planchettes and cooling from the isotropic phase to the desired phase while observing the sample in the microscope. The sample was then rapidly quenched to To À180°C by immersion in liquid propane, and fractured under high vacuum at À140°C. It was subsequently coated with 2 nm of platinum deposited at a 45°angle, followed by B25 nm of carbon deposited at a 90°angle to increase the mechanical rigidity of the replica. After dissolving the liquid crystal, the Pt-C replica was placed on a copper grid and observed in a Philips CM10 100 keV TEM, where the topography of the fracture plane could be observed. Images were taken with a TEM-mounted 1 K Â 1 K Gatan Bioscan digital camera. The surfaces facing the platinum shadowing direction accumulate more platinum and therefore produce darker shadows in the TEM images, revealing height variations in the topography.
Differential scanning calorimetry measurements were carried out using a Mettler Toledo DSC823e/700.