Helical Nanofilament Phases

See allHide authors and affiliations

Science  24 Jul 2009:
Vol. 325, Issue 5939, pp. 456-460
DOI: 10.1126/science.1170027

Packing Bananas and Boomerangs

Assembling achiral molecules typically generates achiral domains. However, odd things can happen when the molecules are banana-or boomerang-shaped—their cores can twist out of plain to form left- or right-handed helices, which can then pack into chiral domains that will polarize light (see the Perspective by Amabilino). Hough et al. (p. 452) show that if you make the situation even more complex by frustrating the packing of adjacent layers, you can create a material that appears to be macroscopically isotropic with only very local positional and orientational ordering of the molecules but still shows an overall chirality. In a second paper, Hough et al. (p. 456) also show that if you change the chemistry of the molecules to allow for better overall packing, you can create a situation where helical filaments form that also tend to pack in layered structures. However, the frustration between the two types of packing leads to macroscopically chiral and mesoporous structures.


In the formation of chiral crystals, the tendency for twist in the orientation of neighboring molecules is incompatible with ordering into a lattice: Twist is expelled from planar layers at the expense of local strain. We report the ordered state of a neat material in which a local chiral structure is expressed as twisted layers, a state made possible by spatial limitation of layering to a periodic array of nanoscale filaments. Although made of achiral molecules, the layers in these filaments are twisted and rigorously homochiral—a broken symmetry. The precise structural definition achieved in filament self-assembly enables collective organization into arrays in which an additional broken symmetry—the appearance of macroscopic coherence of the filament twist—produces a liquid crystal phase of helically precessing layers.

The principal ordering motif of materials at low temperature is crystallization, the organization of atoms or molecules into layers. However, some species—for example, pear-shaped molecules with mutually adhesive stems—prefer to assemble into aggregates that do not pack very well into layers. With such frustration, crystallization can take place at the expense of local strain or may be suppressed entirely. In addition to these homogeneous possibilities, ordering into inhomogeneous states can occur in which the local preference is manifest only in some places, leading to order that is spatially modulated on the mesoscopic scale. Interesting and useful phenomena result, including vortex lattice (1) and magnetic stripe phases (2), lipid bilayer ripples (3), and polarization splay modulation (4).

A particularly noteworthy instance of competition between local preference and global ordering is that between chirality and layering, present in all chiral crystals and layered chiral liquid crystals. The chiral packing of molecules induces local molecular twist, but macroscopic ordering into layers expels twist, leaving the local organization strained. In fluid layered (smectic) liquid crystals of rod-shaped molecules, this competition produces inhomogeneous phases in which molecular and layer twist coexist, the latter enabled by periodic arrays of (twist) grain boundaries (5, 6) or melted sheets (7). Here, we studied a system of simple bent-core molecules in which a particularly strong coupling between chirality and layering originates in the requirement to accommodate the size and shape of molecular subfragments in the presence of a robust tendency for layering. The bent-core molecules are achiral, but spontaneous polar order and chirality appear as broken symmetries, coupling to drive local Gaussian curvature (saddle splay deformation) of the layers—a local solution that cannot fill space. This frustration leads to a spectacular hierarchical structure in which layering can appear only if twisted, doing so in the form of nanofilaments of twisted layers. The nanofilaments in turn collectively organize into a homochiral liquid crystalline array with coherent twist. Such macroscopic nanoporous assemblies of helically precessing layers are unanticipated solutions to the problem of obtaining coexisting layering and twist in a condensed phase, and may be useful in applications requiring chiral nanoporous media.

The helical nanofilament (HNF) phase, heretofore known as the B4 phase, was one of the first new phases to be observed once the directed exploration of thermotropic smectics of bent-core molecules commenced (810). However, its structure and origin have remained obscure and controversial despite extensive study (1113). The observation of strong optical activity (14) (fig. S11), indicating twist of molecular orientation, as well as x-ray diffraction (XRD) evidence for smectic layering (9, 15) led to the proposal that the B4 phase was some kind of smectic phase with twisted layers (9). However, both the presence of in-plane two-dimensional (2D) positional ordering (15) and XRD evidence showing that the layer ordering in the B4 phase was only short-range (Fig. 1C) were inconsistent with the available models of twisted smectics of chiral molecules—long-range ordered smectic blocks separated by twist grain boundaries (TGBs) (16). Here, we present the structure and origin of a quite distinct way of accommodating twist and layering, which suggests the existence of alternative modes of accommodation of tendencies for local and long-range ordering in a variety of modulated materials systems.

Fig. 1

(A) The structure and phase sequence upon cooling of the four B4 phase–forming compounds studied. (B) DTLM images of a 12-μm layer of the B4 phase of P12OPIMB between glass plates at T = 25°C. Scale bar, 100 μm. These materials are fluid at higher T in the B4 range and have become glassy at T = 25°C. With crossed polarizer (P) and analyzer (A), the sample transmits only weakly because of its low birefringence. Uncrossing the analyzer by 5° reveals areas of uniform but opposite optical activity, several hundred micrometers in width, indicating the formation of chiral conglomerate domains. (C) High-resolution powder x-ray diffraction of P9OPIMB shows that the resolution-limited peaks of the high-T fluid smectic B2 phase give way at the B2-B4 transition to a diffuse reflection indicating short-range local layering only in the B4 phase. At the same time, the broad wide-angle peak indicative of liquid-like in-plane order of the B2 phase is replaced by several diffuse peaks, indicating hexatic in-plane order within the layers in the B4 phase.

We studied the B4 phase of bent-core compounds in the phenylene bis(alkoxyphenylimiinomethyl) benzoate (PnOPIMB) series (9) with the use of atomic force microscopy (AFM), freeze-fracture transmission electron microscopy (FFTEM), x-ray and electron diffraction (XRD, ED), and depolarized transmission light microscopy (DTLM) (Fig. 1A) (16). The B4 phase appears upon cooling from the isotropic phase or from the B2 or B3 phases, smectics in which the achiral bent-core molecules have spontaneously developed polar order and tilt to form chiral planar layers with long-range lamellar order (17, 18). The transition to the B4 phase is marked by the in-plane hexatic positional ordering of the layers (15, 16) (Fig. 1C and fig. S4), as might be expected for a lower-temperature phase. Surprisingly, the B4 layering x-ray reflections appear as diffuse peaks (Fig. 1C and fig. S6), indicating the loss of long-range lamellar smectic order of the B2, and giving layer ordering over scales of only <40 nm (~8 layers). Nonetheless, this B4 local layering, although only short-range, is robust, yielding several harmonic reflections (fig. S5).

FFTEM (n = 9, 12) and AFM (n = 12) were used to reveal details of the B4 local layer structure, resulting in images of the layer organization of the B4 phase (Fig. 2, Fig. 3, and figs. S1, S7, and S8). The key evidence revealing the essential structural basis of the B4 phase came from FFTEM of samples that were cooled into the B4 phase from the higher-temperature phase to near room temperature, either rapidly cooled neat samples or slowly cooled samples diluted by isotropic solvent (16). The resulting images (Fig. 2, D to F, and fig. S1, D and F) reveal independently growing nanofilaments of twisted layers (Fig. 2C) similar to structures observed in the self-assembly of chiral biomolecules (19, 20) and organic gelation (21). The nested smectic layers within each nanofilament exhibit strong saddle splay curvature with a radius comparable to only a few layers (e.g., Fig. 2, Fig. 3, and fig. S1). The FFTEM images show that the filaments are characterized by features at three distinct length scales, which we can identify as the smectic layer spacing d, the filament width w, and the half-pitch h of the layer twist in the filament. In regions of the images where the layers intersect the fracture plane at right angles, they appear as distinct periodic lines of spacing d ≈ 5 nm (e.g., Fig. 2D), consistent with the x-ray spacing (Fig. 1C). An intermediate length scale is the width w of individual NFs, which we measured on isolated NFs to be 25 nm < w < 30 nm (Fig. 2, Fig. 3, and fig. S1). At longer length scale is the NF half-pitch, h ≈ 100 nm, the distance over which the layer normal z makes a π rotation about the filament axis (Fig. 3, A to D). These lengths, although independently established in individually grown NFs, are highly uniform over scales of many micrometers (Fig. 2, D to G, and fig. S1), indicating that they are an inherent property of the local NF structure and formation. Each individual NF is clearly chiral in structure (Fig. 2, D to F), a spontaneously broken symmetry because the molecules are achiral; in addition, the filament assemblies are homogeneously chiral, with all filaments in each FFTEM image found to have the same handedness over micrometer length scales (Fig. 1B, Fig. 2, D to G, Fig. 3, and fig. S1) to form macroscopic (~100 μm) chiral conglomerate domains (Fig. 1B) (22). Because the filaments appear to grow independently, this macroscopic chirality indicates the presence of some effective chiral interaction between them, such as occurs in the homochiralization of stirred solutions (23), as otherwise they would appear locally in both left- and right-handed variants.

Fig. 2

(A) Hierarchical self-assembly of the nanofilament (NF) phase starts with bent-core mesogenic molecules, which form well-defined smectic layers with in-plane crystal or hexatic order, macroscopic polarization, and tilt of the molecular planes, making them chiral. (B) In this state, the half-molecular tilt directions on either side of the layer midplane are nearly orthogonal. (C to F) The projections onto the layer midplane of the lattices formed by the core arms (yellow and violet) do not match, resulting in a local preference for saddle splay layer curvature and driving the formation of nanofilaments. These nanofilaments grow independently [(E) and (F)] or collectively in packs that order in the bulk into a nanoporous nanofilament structure (F) having macroscopic coherence of the phase of the NF twist. (D) FFTEM image of NFs of P12OPIMB (T = 25°C). The smectic layers are visible, with a spacing d ≈ 5 nm. (E) FFTEM image of NFs of P9OPIMB grown from a mixture with the calamitic LC 8CB (cooled from the isotropic phase and quenched from T = 37°C). (F) FFTEM image of individual NFs obtained by fast cooling of P12OPIMB from the isotropic to T = 25°C (quenched from T = 25°C). (G) FFTEM image of the bulk B4 phase of P9OPIMB at T = 25°C exhibiting large domains of parallel, coherently twisting NFs (quenched from T = 25°C). Note the phase coherence of the NF twist in independently grown but contacting filaments in (E) to (G) [circles in (E) and (F)], indicative of the phase fluidity and lubrication of the filaments enabling sliding along one another into preferred positions. Scale bars, 60 nm (D), 400 nm [(E) and (G)], 370 nm (F).

Fig. 3

(A and C) FFTEM images of P9OPIMB. (D and E) AFM images of P12OPIMB. These images show the three characteristic length scales of the bulk NF phase at T = 25°C [sketched in (B)]: individual layers as the thin dark lines spaced by d ≈ 5 nm, the NF width w ≈ 25 nm, and the NF twist half-pitch h ≈ 100 nm. In (A), (C), and (D), image planes nearly parallel to the helix axis p reveal the distinct saddle structure of the layers. In (E), an AFM image of a plane nearly normal to p exhibits the Bouligand texture (16, 26), showing the macroscopic helical precession of the smectic layers in the NF array, propagated by NFs (white squares) contacting with the layers face-to-face. In this image the NFs anneal at the surface into the “loaf-of-bread” structure, whereas in other images the NF terminations are more prominent (16) (figs. S7 and S8). Scale bars, 100 nm.

FFTEM and AFM of samples cooled slowly into the B4 phase show that the equilibrium bulk B4 structure is the ordered packing of NFs with little distortion of the filament structure (Fig. 2G, Fig. 3, and fig. S1), also characterized by the length scales d, w, and h. The smectic layering is apparent in both AFM and FFTEM images (Fig. 2, Fig. 3, and fig. S1), giving d ≈ 5 nm. The filament width w, which can be identified in the bulk images as the spacing between the distinct saddle domains (Fig. 3 and fig. S1), is approximately the same in the bulk structure as in the images of individual filaments (25 nm < w < 30 nm). Finally, the apparent periodicity appears as a range of values, h(θ) = h sec(θ) ≥ 100 nm, made longer by oblique cuts at angle θ to the helix axis (16).

The twisted nanofilament growth motif suggests that layer flatness becomes thermodynamically unfavorable in the HNF phase, which we now try to understand in terms of the layer structure. Transmission ED study of ultrathin B4 films, shear-aligned between polished NaCl crystals to have single or few domains of the in-layer ordering, produced a definitive determination of the in-plane structure in both flat layers and the twisted layers of nanofilaments (Fig. 4 and fig. S4). Because each of the four sublayers j [either tail (t) or core arm (ca)] of a given layer (t-ca-ca-t) is composed of parallel rod-like molecular elements tilted from the layer normal by angle βj, the scattering from sublayer j is weak unless the scattering vector q lies within its form-factor sheet (i.e., is in the plane normal to nj) (16) (fig. S4B). As shown by powder x-ray diffraction measurement of d(n), the B4 layer spacing versus carbon number n shows that d varies linearly with n (fig. S2), with a slope that indicates that βt = 24° ± 2°. An extrapolation to n = 0 yields a core (c) dc = 2.47 nm (fig. S2), which, when combined with quantum chemical calculations of the alkoxy O-O separation (LOO, fig. S3), gives βca = 38° ± 2° (16). Thus, the core arms and tails have different tilts, making it possible to orient the layer to obtain substantial ED from only a single sublayer.

Fig. 4

Details of the molecular organization within the layer structure obtainable from the ED patterns of thin films of P9OPIMB. (A and B) Two different patterns, false-colored in red and green, are scattering from flattened layers and twisted layers within a single filament, respectively. The (1,1) peaks are diffuse but strong from the twisted layer sample and appear at larger q than expected on the basis of the (2,0) and (2,1) positions [yellow dots in (B)], indicating that there are two different lattices contributing to the ED of the twisted layers. The (1,1) peaks in (B) are due to the core domains and are rotated relative to the (2,0) and (2,1) peaks from the tail domains as a result of the twist of the layer within a filament. The (1,1) peak lattice is also sheared as a result of the chiral symmetry of polarization p, oriented along one of the square diagonals (cyan arrow). (C) The tilt of the tails relative to the cores is such that both lattices project onto the same centered rectangular herringbone lattice (yellow and purple layers). The rectangular lattices from the two half-layers (top, yellow; bottom, purple) are orthogonal. The two half-layers are covalently linked in the layer midplane (orange). (D) The elastic strain required to join the two half-layers can be partially relieved by layer curvature. (E) In the 3D case, this elastic strain leads to the formation of saddles, with elastic strain determined by the polarization (teal arrow) between the two principal curvature directions and the radius of curvature R. (F) This phase is SHG-active, and thus polar, and so the polarization direction must lie along the helix axis giving the molecular geometry shown. (G and H) The herringbone ordering and polarization create inequivalent sublattices that generate split peaks in the cross-polarization/magic angle spinning 13C nuclear magnetic resonance of the B4 phase (11).

ED patterns of single domains of in-plane order showed distinct patterns for the flat and twisted layers, shown respectively in red and green in Fig. 4A. The red lattice is centered rectangular (index 0,1 and 1,0 peaks very weak) with herringbone order [(1,2) peak observed], as shown in fig. S4. The rectangular symmetry of this scattering indicates that the tilt direction of the scattering sublayer must be along either the 01 or 10 lattice symmetry directions. Radial scans through the (1,1), (0,2), and (1,2) peaks [Fig. 4A (red) and fig. S4A] yield an in-plane coherence length for in-plane order of ~6 nm in the flattened layers (16). The green lattice exhibits two distinct lattice spacings: (0,2) and (1,2) reflections that overlap with the red lattice, adding to give yellow in the overlaid image of Fig. 4A; and diffuse (1,1) peaks that are nonoverlapping and thus appear green, shifted out to higher q in the 01 direction, indicative of contributions from a distinct sublayer. Because a core arm tilt that is larger than the tail tilt requires a smaller spacing of the core arms and thus scattering at larger q, we assign the (green) diffuse q(1,1) peaks to be scattering from the cores, with the (0,2) and (1,2) reflections dominated by the tail layer. The resulting reciprocal space structure of each half-layer is sketched in fig. S4B.

Remarkably, the core arm (1,1) scattering is also rotated through ~5° relative to the tail scattering—a situation impossible for scattering from extended in-plane 2D ordering. This provides unambiguous evidence that this scattering is coming from a single tail sublayer and adjacent core arm sublayer within twisted layering of limited extent. This rotation is a consequence of the layer twist along the filaments [180°/(h ≈ 100 nm) ≈ 2°/nm], producing a comparable twist about the local z of a tail sublayer relative to its neighboring core arm layer, ~2 nm away (2°/nm × 2 nm ≈ 4°). An additional key observation is that the core arm lattice is sheared to be slightly oblique, with the lattice diagonals differing in length by ~2%. If the sublayer tilts were coplanar through the molecule, as in the untilted polar hexatic (HexAPF) structure, this lattice of (1,1) core arm peaks would be rotated but at the corners of a square. The shear deformation indicates that the tilts of the upper and lower molecular halves are not coplanar, and because the tail lattice is rectangular, these halves must be in mutually orthogonal planes. In this geometry (Fig. 2B and fig. S4, B and F), connecting the molecular arms across the layer midplane to make complete molecules renders the structure macroscopically polar, with polarization p at 45° from the half-molecular tilt planes, t, singling out one of the (1,1) directions (cyan arrow, Fig. 4, C to H, and fig. S4, F to M). The structure is also chiral because of the tilt of the core planes (Fig. 4F and fig. S4F).

The geometry of the real-space tail and core arm lattices is sketched in fig. S4E, and the projections of the lattices from either side of the layer midplane onto the midplane (yellow and violet) are shown in fig. S4, E and G. Because of the anisotropy of the yellow and violet in-plane lattices (Fig. 4C and fig. S4G), the corresponding molecular halves cannot connect across the layer midplane if the layer is flat. However, they can be made to do so by bending the layers with saddle splay curvature (Fig. 4, D and E, blue arrows) such that the lattices match in the layer midplane; in this case, the molecular midpoints necessarily lie on a centered square lattice (orange, Fig. 4, C to H, and fig. S4M).

This lattice mismatch–driven layer curvature was modeled quantitatively, using the process indicated by the red arrows in Fig. 4D. The half-layers were represented by elastic slabs of the unit cell shape (Fig. 4C), taken to be isotropic for simplicity and thus characterized by compressional and shear elastic moduli, M and μ, respectively. The yellow half-layer of Fig. 4C was compressed in the t direction by a factor 1 – β (≈ 7.3/8.4 = 0.87, Fig. 4C), dilated by 1 + β in the ⊥ direction (making it square), and adhered to the violet layer, which had been given the deformation of opposite sign until square. The elastic energy fE(σ′, σ′′) of the resulting laminate of half-layers in a given state of curvature was then calculated to quadratic order in the principal curvatures σ′ and σ′′. The layer elastic energy per volume obtained is fE = K/2 (σ′ + σ′′)2Embedded Image(σ′σ′′) + G(σ′′ – σ′), where K is the Frank elastic constant for mean curvature (σ′ + σ′′), Embedded Image is the Frank constant for Gaussian curvature (–σ′σ′′), and G ∝ β drives curvature in response to the frustrated internal in-plane layer strain β (16). For a minimal surface (σ = σ′ = –σ′′), the free energy is particularly simple: Embedded Image = Embedded Imageσ2 – 2Gσ, making RpEmbedded Image/G the preferred radius of curvature. The energy f = fE(σ′, σ′′) + Δu, where Δu is the Gibbs potential per volume of the in-plane freezing, can be used to predict the structure of a filament, viewed as a set of ribbon-like layers twisted with a half-pitch h ≡ π/q (16). The central layer is a minimal surface of curvature σ = q along its centerline, so that for a very narrow ribbon (w << h), minimizing Embedded Image gives q = G/Embedded Image and therefore h = π/σp = πRp ~ 20 nm. However, as T is lowered into the B4 range, the ribbon can further lower its free energy by growing wider, gaining Δu in a larger volume. Overall energy minimization yields finite-width filaments with the layer ordering suppressed (melted) outside, as the increase in w is ultimately limited by the energy cost of reduced (and thus less favorable) curvature away from the centerline in a wider ribbon. Predicted values of w and h are consistent with Rp ~ 200 nm, about 4 times the estimate from the in-layer structure (16).

The orientation of the in-plane structure within the nanofilaments is shown in Fig. 4, F to H, and fig. S4M. The lattice diagonal (polarization p) must be either along or normal to the NF axis for the saddle splay curvature to give the required NF twist (Fig. 4, E and F). The choice of p to be along the NF axis is clearly indicated by second harmonic generation (SHG) evidence for local C rather than D symmetry of the phase (16, 24). With this orientation, the filament edges are (1,1) rows of molecules (fig. S4M); the result is a crystal face with a low Miller index that resists the addition of new material upon cooling, thereby promoting the highly anisotropic growth of the needle-like filaments.

Upon slow cooling into the B4 phase, the filaments appear via heterogeneous nucleation at dilute sites. Each nucleation site is homochiral; FFTEM and AFM show that once a handedness is chosen, single-handed domains are formed, out to distances of 10 to 100 μm. This leads to the observed strong “sergeants and soldiers” enantioselection of B4 chirality by weak chiral doping (18), chiral surface treatment (25), or nucleation from a chiral phase (14). At higher temperatures the NF phase is fluid, likely a consequence of lubrication of the filaments by the B2 or isotropic phase that is suppressed from hexatic ordering by the requirement for layer curvature. This fluidity enables the filaments to anneal in their orientation and twist phase into the coherent helical structures seen in Fig. 2G, Fig. 3, and fig. S1. Such coherence shows that the filaments must interact, but this interaction is weak in that it does not noticeably influence the structure of contacting filaments (Fig. 2, E and F). The AFM textures like that in Fig. 3E, visualizing the planes nearly normal to p, suggest that this interaction is strongest when layers in adjacent filaments are face-to-face and provide unambiguous evidence for the coherent macroscopic helical twist of the layering.

The B4 or HNF phase appears in a simple bent-core molecular system as a response to the competition between layering and twist inherent in chiral media. The inability of the best local solution to fill space selectively suppresses layering to produce a nanophase segregation of different degrees of order in a structural hierarchy that enables both macroscopic chirality and layering in an exotic liquid crystal phase.

Supporting Online Material

Materials and Methods

SOM Text

Figs. S1 to S8


  • Deceased.

References and Notes

  1. See supporting material on Science Online.
  2. Supported by NSF grant DMR 0606528 (N.A.C.), NSF Materials Research Science and Engineering Center grant DMR 0820579 (N.A.C.), an NSF Graduate Research Fellowship (L.H.), Deutsche Forschungsgemeinschaft grant Sfb 448 (J.P.R.), and NIH grant HL-51177 (J.Z.). Use of the National Synchrotron Light Source was supported by the U.S. Department of Energy, Divisions of Materials and Chemical Sciences.
View Abstract

Navigate This Article