Polarization-Modulated SmecticLiquid Crystal Phases

D. A. Coleman,1 J. Fernsler,1 N. Chattham,1 M. Nakata,2

Y. Takanishi,2 E. Korblova,3 D. R. Link,1,2 R.-F. Shao,1 W. G. Jang,1

J. E. Maclennan,1 O. Mondainn-Monval,4,5 C. Boyer,4

W. Weissflog,6 G. Pelzl,6 L.-C. Chien,7 J. Zasadzinski,4

J. Watanabe,2 D. M. Walba,3 H. Takezoe,2 N. A. Clark1*

Any polar-ordered material with a spatially uniform polarization field is inter-nally frustrated: The symmetry-required local preference for polarization is tobe nonuniform, i.e., to be locally bouquet-like or “splayed.” However, it isimpossible to achieve splay of a preferred sign everywhere in space unlessappropriate defects are introduced into the field. Typically, in materials likeferroelectric crystals or liquid crystals, such defects are not thermally stable,so that the local preference is globally frustrated and the polarization fieldremains uniform. Here, we report a class of fluid polar smectic liquid crystalsin which local splay prevails in the form of periodic supermolecular-scalepolarization modulation stripes coupled to layer undulation waves. The polardomains are locally chiral, and organized into patterns of alternating handed-ness and polarity. The fluid-layer undulations enable an extraordinary menag-erie of filament and planar structures that identify such phases.

The discovery that polar order (1) and mac-roscopic chirality (2) appear spontaneously influid smectic liquid crystals (LCs) of achiralbent-core “bow” or “banana-shaped” mole-cules as a result of distinct broken orienta-tional symmetries opened the study of abroad new class of polar condensed phases ofunexpected richness, deriving from the inter-play of polarity and chirality (3). The fourbasic polar chiral smectic banana phases (theSmCPs or B2s) are layered, either with thesame tilt in adjacent two-dimensional (2D)–fluid layers (synclinic, CS) or with oppositetilt in adjacent layers (anticlinic, CA), andeither synpolar (ferroelectric, PF) or antipolar(antiferroelectric, PA), as sketched in Fig. 1A,where chirality (handedness) is indicated bycolor (magenta versus cyan). All four of theseB2 subphases have been found in materials ofbent-core molecular family shown in Fig. 1A:

the SmCSPA (racemic antiferroelectric) andSmCAPA (homochiral antiferroelectric) struc-tures in the prototypical material NOBOW(2, 4); and the SmCAPF (racemic ferroelec-tric) in a material not shown here (5). Severalother materials, including MHOBOW (6, 7),PBCOB (8), H87 (9), and CITRO (10) in Fig.1 exhibit the SmCSPF (homochiral ferroelec-tric) structure, but under heretofore mysteri-ous circumstances: SmCSPF characteristicsappear only if a suitably large electric field isapplied, and then only irreversibly from equi-librium states of unknown structure that areso different from the other B2s that they haveuntil now been grouped as separate phases,the B7 class (11).

Upon cooling from the isotropic, B7 phas-es grow in a wildly variegated morphology ofdomains that are unusually beautiful even byLC standards (see cover), featuring twistedhelical filaments (6, 8, 12–14) (Fig. 2, A andB), high- and low-birefringence focal conicsstriped either parallel or normal to the smec-tic layering (12, 15) (Fig. 2C), banana leaf–shaped domains (15) (Figs. 3E and 4), check-erboard textures (6, 12, 14–16) (Fig. 2C), andfreely suspended filaments (12, 16, 17). Wecombine x-ray diffraction (XRD), freeze frac-ture transmission electron microscopy(FFTEM), and depolarized transmission andreflection light microscopy (DTLM andDRLM) to establish unambiguously the un-derlying structural principle of the B7 phases.In so doing, we find yet another exotic brokensymmetry, the spontaneous periodic modula-tion of the polarization density into splay

domains. We thus establish the existence of anew class of bulk condensed phases, whichjoin the vortex lattice (18), twist grain bound-ary (19), and blue (20) phases as periodicstructures stabilized by a free-energy termlinear in a field gradient.

In polar fluid LCs such as the SmCPs, thepolarization P is free to rotate continuously inthe layer plane in response to surface, elec-tric, and elastic torques (i.e., its orientation isa Goldstone variable, in contrast to solid fer-roelectrics, where P adopts a set of discreteorientations established by a lattice). A con-sequence of this orientational freedom is thepossibility of polarization modulation (PM),an example of which is shown in Fig. 1B.Because of its vectorial symmetry, the localenergy density of the P field contains a termof the form U � (�YP � co)2, where co is aconstant, stabilizing finite splay of P (e.g., co,�YP � 0 in the red example of Fig. 1B) (21).However, filling space such that the volumeaverage ��YP� � 0, requires spatial inhomo-geneity, such as the stripes sketched in Fig.1C, where the regions with �YP � 0 areconfined to less well-ordered defect lines(green). In known ferroelectrics such defectsare too costly in energy, so P reverts to itsuniform state and the tendency for local splayis globally frustrated (22). PM has been pro-posed and observed to date in a variety of LCinterfacial structures, such as freely suspend-ed smectic films (23–30), Langmuir mono-layers (31, 32) and phospholipid tubules (33),and has been proposed to explain undulatedlamellar lipid phases (34) and analog chiralsmectic electro-optic (EO) behavior (35).Here, we demonstrate the existence of bulkphases with polarization modulation stabi-lized by polarization splay.

Based on the results we present below, wewill propose that the B7 is a polarizationmodulated/undulated layer (PM/UL) stripestructure. In a SmCP system, the molecularbananas reorient across splay stripes in fourcombinations of handedness and orientationof P for a given sign of splay, as shown inFig. 1D. The essential feature establishing therelation between the polarization modulationand the layer undulations is illustrated in Fig.1E: Along the PM defect lines, the layers arenecessarily thicker because the disorder inboth P and molecular azimuthal orientation(at the green boundaries in Fig. 1D) willproduce a smaller molecular tilt. In a bulkmaterial, the pitch of the layering along smust be the same everywhere, requiring thethinner layer regions between the defect linesto tilt and effectively thicken along the means, as they do, for example, in the formation ofthe smectic chevron structure (36) and thesmectic undulation instability (37). The result

1Department of Physics and Ferroelectric Liquid Crys-tal Materials Research Center, University of Colorado,Boulder, CO 80309–0390, USA. 2Department of Or-ganic and Polymeric Materials, Tokyo Institute ofTechnology O-okayama, Meguro-ku, Tokyo 152-8552, Japan. 3Department of Chemistry and Biochem-istry and Ferroelectric Liquid Crystal Materials Re-search Center, University of Colorado, Boulder, CO80309–0215, USA. 4Department of Chemical Engi-neering, University of California, Santa Barbara, CA93106, USA. 5Centre de Recherche Paul Pascal–CNRS,Av. A. Schweitzer, 33 600 Pessac, France. 6Institut furPhysikalische Chemie, Martin-Luther-UniversitatD-06108 Halle, Muehlpforte 1, Germany. 7LiquidCrystal Institute, Department of Chemical Physics,Kent State University, Kent, OH 44242, USA.

*To whom correspondence should be addressed. E-mail: noel.clark@colorado.edu

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is an undulated PM structure having a pitch(distance along s per layer) ds that is largerthan d, the pitch of the flat, defect-free layers,as is observed (Fig. 3D).

B7 layer structure. Synchrotron-basedpowder and single-domain microbeam XRDdata (38, 39) and FFTEM observations pro-vide basic evidence for a generic structure forthe B7 phases. Previous XRD studies of B7phases have found a diffuse peak at highangle, which indicates that the layers are 2Dfluids. Additional small angle peaks indicate

complexity beyond a simple lamellar struc-ture and suggest 2D ordering (12, 15, 40–42).Our powder scans for MHOBOW andPBCOB in Fig. 3, A and B, typical of theblue-labeled B7s in Fig. 1, indeed show 2Dordering, with three distinct features: a seriesof peaks at very small angle, and closelyspaced sets of multiple peaks, previously un-resolved, near scattering vectors q � 0.16Å�1 (Fig. 3A; s 1) and q � 0.33Å�1 (Fig.3B; s 2), where the single-peak lamellarreflections would appear for simple lamellar

SmCP phases (fig. S1). This powder patternis accurately indexed by the rectangular 2Dreciprocal lattice indicated in the inset in Fig.3A, with indices [s,m] on the basis vector set�s s(2/ds) in the mean layer normal di-rection, s, and �m m(2/dm), a muchsmaller fundamental (in-layer) wavevector,with an angle � 90° between s and m. H87,qualitatively identical in its scattering signa-ture, has the largest dm of the B7s studiedhere (fig. S2).

Quantitative analysis of the intensities ofthese peaks follows from assuming the elec-tron density to be that of periodically undu-lated layers, i.e., �(r) n f{z � [nd �un(r)]}, where d is the intrinsic smectic layerthickness, f{z} is the layer electron densityprofile of a single layer, and u(r) j Ajcos( jkmYr) is the periodic local layerdisplacement along s (43). The relativeMHOBOW intensities I(s,m) for s 1 in Fig.3A and s 2 in Fig. 3B can be fit quite wellwith the further assumption that the undula-tion is simply sinusoidal, i.e., with only A1 �0, as indicated in Fig. 3C (44). These and thedata on the other B7s thus indicate a structureof stacked smectic layers, periodically undu-lated with wavelength dm as follows:MHOBOW {d 38.8 Å, A1 11 Å at T 139°C, (274 Å at 139°C) � dm � (349 Å at100°C)} (fig. S1); PBCOB {dm 286 Å atT 110°C}; H87 {(450 Å at 158°C) � dm �(700 Å at 135°C)} (fig. S2); and CITRO{dm 153 Å at T 100°C} (45). Aninteresting feature of the simple undulationmodel is that it predicts zero intensity for s 0, i.e., absence of the zero-order reflectionsshown in Fig. 3B. Thus, these peaks mustoriginate from structural features internal tothe layers, e.g., electron density modulationassociated with the splay defect lines.

X-ray microdiffraction with a 5-�m-diameter beam was carried out on singleCITRO nested cylinder focal conic domains(FCDs) (Fig. 3D) and MHOBOW “bananaleaf ” domains (BLDs) (Figs. 3E and 4),prominent textural features of B7 phases asgrown by cooling from the isotropic with theLC filling the gap of a cell made by spacingtwo plates a few micrometers apart (38). Fig-ure 3E illustrates the BLD experiment withthe beam passing through the BLD within theyellow circle. This experiment revealed theq-space orientation of the BLDs indicated inFig. 3E, with the mean layer normal s parallelto both the glass and to the leaf long axis, andthe undulation wavevector m normal to theglass, and yielded an s 1 q-space structurethat is fully consistent with the powder resultsof Fig. 3C. The I(qm) versus qm scan in Fig.3E is at qs 2/ds (s 1, essentially rockingthe sample about the p axis with qs 2/ds)and shows the s 1, m 0, �1, and �2reflections of the undulation lattice with am-plitude ratios in good agreement with those of

Fig. 1. (A) The B7 materials stud-ied here (blue labels) are homologsof the prototypical SmCP (B2)NOBOW. The SmCP smectic layerstructure has spontaneous polarorder and tilt of the bows, whichmakes the layers chiral, with hand-edness indicated by color (cyan ormagenta), and gives the four pos-sible bilayer phases shown, all ofwhich have been observed. Tees ()indicate the projection of bow-string orientation, with the bar in-dicating the end nearest the read-er. We show here that the B7 tex-tures are a feature only of theSmCSPF. (B) Preferred structure ofa polarization field will be eitherpositive (red) or negative (green)splay. (C) Stripes assuming posi-tive splay can fill space if the re-quired defects (green lines) aresufficiently low in energy. (D) Ele-mental splay stripe varieties, de-pending on handedness and onorientation of P. The absolute signof the polarization splay is un-known at present. For consistencyin the B7 sketches, we draw thepolarization splay with the bent-core vertex splayed out. However,it may be the other way around.The tees indicate tilt of the mole-cule toward the reader. (E) Thebasic undulation-driving mecha-nism is layer expansion at thesplay defect lines. (F and G) Thelayers in the intermediate regionsmust tilt to establish a uniformlayer pitch along s. This organiza-tion of P, chirality, and undulation[yellow (orange) displaced up(down)] is inferred from the opti-cal and x-ray experiments. Thereare two distinct kinds of defectlines: those where handednesschanges (blue), and those where itdoes not (red), making the undu-lation crest curvature differentfrom that of the troughs. (G) Di-rector strain, minimized in theundulated synclinic (CS) localstructure, tends to suppress theundulation in the anticlinic (CA)structure. (H) Layer interdigitationprovides effective molecular pack-ing at the polarization splay de-fects to produce a distinct (B1)family of 2D ordered phases.

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Fig. 3C. Thus, the overall layer structure ofthe BLD, sketched in Fig. 4C, is “bookshelf,”with the layers on-average normal to theplates and the undulation crests and troughsparallel to the glass. Figure 3D shows mi-crobeam scattering from the pictured FCD ofB7 CITRO. With x-rays incident on an FCDgrown by cooling from the isotropic phase(through the red circle and nearly normal tothe glass), the red-shaded scattering is ob-served, the [s 1, m 0, �1] reflections(pink dots) indicating that the undulated lay-ers are oriented as indicated, with both s andm parallel to the glass plates (plane of thepage). The scattering is in arcs here becauseof the large mosaic spread due to the curva-ture of the layers in the nested cylinder struc-ture of the FCD.

Freeze fracture was carried out byquenching the LC, sandwiched between 2mm by 2 mm Cu planchettes, from varioustemperatures in the B7 range to 77 K by rapidimmersion in liquid nitrogen or propane, andfracturing cold in a vacuum. FFTEM of Pt-Cfracture face replicas revealed topographieshaving the global structure of single- andmultiple-layer steps familiar from the studyof fluid thermotropic and lyotropic smectics(46, 47). However, the layers that wouldappear flat and smooth for such materialswere, in MHOBOW, distinctly marked by a1D periodic pattern of layer undulations (rip-ples) of supermolecular wavelength dm

[dm � 500 Å in the example of Fig. 5A,quenched from T 120°C (45)]. The single-layer step shown in Fig. 5A reveals directlythe undulation, and the multiple-step “cliffs”in Fig. 5, A and B, show it to propagatethrough many layers unchanged in structure.This structure is qualitatively consistent withthat extracted from the x-ray results, and,given the typical uncertainty in FFTEMscales, the dm’s are in reasonable agreementwith the x-ray values. The ripples in Fig. 5appear to be mirror symmetric about theplanes of layer displacement maxima andminima, justifying the cosine expansion ofu(r). However, they exhibit distinct texturaldomains (Fig. 5B) that indicate (i) a lack ofglide symmetry of the undulation for half-period displacement along m, the direction ofthe undulation wavevector and reflectionabout the plane of zero-layer displacement(i.e., the crests are rounded while the valleysare sharp, or vice versa, Fig. 5B); and (ii) anorthogonal lattice structure because the meanlayer orientation is the same in the two do-mains. Such a layer structure is on averagepolar (along the layer normal, s) (48, 49).

Visualizing the polarization modula-tion. The chemical stability of NOBOW andits B7 analogs in Fig. 1A is limited because ofthe susceptibility of these molecules to hy-drolysis, which splits them in two at theirSchiff’s-base (CHN) linkages. This effect

Fig. 2. Typical textures ofMHOBOW in the B7 phaseviewed in DTLM, showing(A) helical filaments grownin from the isotropic phaseand trapped on the surfaceto form2D FCDs; (B) surfacetrapped filament folding onthe surface as it grows toform a 2D FCD; (C) a check-erboard texture in a 4-�m-thick cell and an FCD (inset)in a 6-�m-thick cell; and (D)growth upon cooling of aMHOBOW filament teth-ered to the surface. Thespontaneously undulatedfil-ament packs into local ar-rangements that can becheckerboard or stripe-like.Scales: (A), 100 �m; (B), 100 �m; (C), 80 �m (inset, 100 �m); and (D) circular domain, 50 �m in diameter.

Fig. 3. (A and B) Powder x-ray struc-ture factor I(q) of B7 MHOBOW atT 131°C and the fit to a set ofpeaks (black line) constrained in po-sition by the 2D rectangular latticein the inset of (A). The PBOCB B7data (T 110°C) can be similarly fit.(C) Relative integrated intensitiesI(s,m) of the MHOBOW peaks of (A)and (B) with I(s, 2) scaled to 1 (opencircles), and predictions of the layerundulation model with undulationamplitude A1 as a parameter (solidlines). The model, quite sensitive toA1, fits best for A1 11 Å forMHOBOW. (D) Area detector imageof x-ray scattering intensity I(qm,qs)with the microbeam illuminationwithin the circled area of a CITROFCD at T 100°C, before (red) andafter (green) electric field applica-tion (imaged area 150 �m2). Beforethe field the s 1, m �1 reflec-tions with ds 36.3 Å and dm 153 Å appear (red), showing that inthe FCD s and m are parallel to theglass plates, as sketched. Field appli-cation yields an I(qm,qs) having asingle lamellar reflection (green) at alarger qs, evidence for the layer flat-tening and contraction produced bythe field elimination of the PM andits undulation. Under this conditionbrush rotation, characteristic of thechiral ferroelectric SmCSPF, is ob-served (green). The shift in qs indi-cates that the maximum undulationslope is 14.5°, which gives A1 6.0Å in CITRO. (E) DTLM image of a200-�m-long MHOBOW bananaleaf domain (BLD), along with x-rayscattered intensity I(qm) at qs 2/ds (s 1) from microbeam illu-mination through a 5-�m-diameterarea (inside yellow circle) of aMHOBOW BLD. I(qs,qm) shows thats is parallel to the BLD long axis andthat m is normal to the plates, assketched. The peak positions (givingdm 330 Å) and intensities agreewell with the powder data and un-dulation model predictions in (C).

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produces a decrease of the isotropic-B7 tran-sition temperatures with x-ray exposure andaging at temperature and, as found in theXRD and FFTEM experiments, an increaseof undulation wavelength with aging, with dm

growing to at least 600 Å in bulk MHOBOW.This effect, although a nuisance, permits di-rect optical microscopic observation of themolecular orientation/polarization modula-tion patterns, because dm was found to in-crease with aging well into the micrometerrange in freely suspended films ofMHOBOW (50), and both thermally and withaging in freely suspended films ofmOAM5AMOm (51) (m 8, 12, 14, 16)(52). Films that were 2 to 10 layers thick (i.e.,with s normal to the film plane) were freelysuspended in air (53) by drawing them in theB7 phase over a 5-mm-diameter hole in aglass cover slip (54) and then imaged withDRLM (55). Freshly made MHOBOW filmsexhibited a 2D focal conic (FC) texture oforientation of the in-plane optic-axis projec-tion (Fig. 6A), which remained unchangedwith application of small in-plane field (E �100 V/cm). Upon aging over several days atT 144°C, a gradually coarsening stripepattern (indicating increasing dm) appearedon the FCs (Fig. 6B), which finally evolvedto distinct defect lines (Fig. 6C) where thebend (splay) deformation of the in-plane ori-entation of the tilted optic axis (of the polar-ization) abruptly changes sign. This texture islocally SmCSPF, responding as a tilted chiralsmectic to an applied in-plane field (53) and,like NOBOW, has a larger in-plane refractiveindex for optical polarization along p (Fig.2A). Because s must be normal to the image-film-layer plane, the initial 2D FC is directevidence that the texture of (m,p) is 1Dsmectic-like, i.e., stripes in the layer planewith a pitch too small to resolve optically,mapping onto the 2D FC as shown in Fig. 6A.DRLM of the FCs shows in-plane opticalanisotropy with higher refractive index forpolarization parallel to these stripes and thusto the polarization direction p, as expected forthe PM structures sketched in Fig. 1C, con-firming the mapping of (m, p). Identical 2Dfocal conic textures and coarsening with ag-ing were found in B7 films of themOAM5AMOm series, with the key addi-tional observation that in this system coars-ening to the splay stripe textures could alsobe induced immediately simply by cooling tothe low end of the B7 phase (Fig. 6F). These2D FC textures in the films are similar to, andhave the same sign of optical anisotropy as,the low-birefringence FC domains grownfrom the isotropic in the glass cells (Fig. 6D),indicating that the latter domains have thesame geometry—i.e., are homeotropic—withs normal to the glass/image plane. The orien-tation pattern in Fig. 6C, identical to thatfound in polarization-modulated SmC films

(30), is mapped in Fig. 6E, showing the splayof P(r) and the line defects that enable it. PMstates found to date in films are bistripe, i.e.,we have not observed the four-stripe bulkMHOBOW structure (Figs. 1F and 4C) inlarge-period film PM. These film observa-tions likely explain the periodic free surfaceundulations found by atomic force microsco-py of B7 preparations (56).

The PM/UL state. Simple theoreticalconsiderations impose additional constraintson the layer organization of a PM state: (i)Stripe domains in SmCP layers come in thefour varieties of Fig. 2C, depending on therelative orientation of P and the handednessof the molecular tilt. However, in the PM/ULstructure these must be such that the tilt issynclinic (CS), as in Fig. 1G, with the tilt

plane orientation compensating the undula-tion to reduce elastic strain in each layer. AsFig. 1G shows, anticlinic (CA) layering leadsto large elastic deformation in alternate layersthat suppresses the modulation. (ii) PM willnot be observed in any antiferroelectricSmCP, because alternation in sign of thepolarization splay from layer to layer re-moves the basic driving force for global splayof P. Thus, strong evidence that polarizationsplay drives PM is provided by our key ob-servation that among known SmCPs, the PM/UL state is a feature of only the SmCSPF

variety of Fig. 1A (57). Next, we consider theoverall arrangement of the P-splay stripes,which may depend on the material and mayeven be different in a different domain of agiven material. Thus, antiferroelectric order-

Fig. 4. Transmission polarized light micrographs of a 4-�m-thick MHOBOW B7 BLD showing theoptical effects of oblique incidence obtained by tilting the sample. The orientation of the s-m-ptriad is inferred from the microbeam x-ray of Fig. 3E. (A) At normal incidence (sample flat), the leafis birefringent and achiral, extinguishing between crossed polarizer (blue)/analyzer oriented parallelor normal to the long axis, and transmitting otherwise. Tilting around the BLD short axis (p)produces no change in this. Scale bar, 50 �m. (B) Remarkably, upon tilting around the BLD long axis(s) the domain becomes optically chiral, extinguishing the exiting light (white arrow), with polarizerand analyzer uncrossed as indicated. The angle of the optical polarization rotation, �, is propor-tional to the sample tilt. (C) Structure of a MHOBOW BLD [along with photo of Fig. 4B inperspective] as inferred from the x-ray, freeze fracture, and optical data. The structure shows thePM stripe undulation, alternation of polarity and chirality, and two distinct types of PM defect lines(red, blue). (D and E) Top and side views of the PM structure, with green (orange) arrows indicatingincident light with the cell tilted about p,s as in (A) and (B), respectively. Inspection shows that atnormal incidence stripes of opposite chirality have identical response, giving overall achiral optics.This is also the case in (D), for sample tilt around p, where, although orange and gray-green shadedregions become optically nondegenerate upon tilt, each is independently on-average achiral.However, in (E), for sample tilt around s, the pink and gray shaded stripes become opticallynondegenerate and are of opposite chirality, leading to the optical rotation shown in (B).

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ing accounts for the absence of second-harmonic generation in the as-grown steadystates of MHOBOW and CITRO (10), andthe antiferroelectric racemic arrangement ofP-splay domains (monostripe alternation inP, bistripe alternation in handedness), shownin Fig. 1, E to G, uniquely accounts for theoptical properties of banana leaf domains, asdiscussed below. Further evidence for thispicture is found in chiral MHOBOW: In achiral material (Fig. 1), the neighboring (op-posite handedness) undulation periods are nolonger enantiomeric and thus should havedifferent mean layer spacings, resulting in aweak distortion to an oblique lattice. The(S)-MHOBOW lattice is indeed found to beidentical in dimension to that of racemicMHOBOW but slightly oblique (fig. S3),with an angle of � 88.2° � 0.2° between�s and �m at T 131°C (43).

Electric-field expulsion of the polariza-tion modulation. Further evidence for thePM state comes from features of the responseof the B7s to an applied electric field E, withthe LC as the dielectric in indium oxide–on–glass transparent capacitors: (i) For lowfields, the coupled polarization and molecularorientation are constrained by the modulationstructure, and only a weak electro-optical(EO) response is expected or found. (ii) Non-zero E raises the internal energy of the PM,which is then expelled in favor of a state ofuniform P for E above a threshold Eth, i.e., aB7-to-SmCSPF transition is induced. A sim-ple (over)estimate of Eth can be obtained byequating the electric energy density with theelastic energy density of the PM: PEth �K/dm

2, where K � 9 pN is the elastic constantfor tilt plane reorientation (58), predictingEth � 30 V/�m for a typical B2, with P 300 nC/cm2 and dm 30 nm. This field-induced B7-to-SmCSPF phase change wasobserved as an irreversible, first-order transi-tion (59) in all B7s studied, with Eth in therange 1 V/�m � Eth � 20 V/�m. Abovethreshold, the complex maze of as-grown B7focal conic, banana leaf, homeotropic, andcheckerboard domains gives way to a homo-geneous texture of simple tilted smectic ho-mochiral ferroelectric SmCSPF focal conics,with their unmistakable chiral EO response,described in detail for MHOBOW in (6). Thethreshold for the field-induced B7-SmCSPF

transition in H87 has been found to decreaseas the temperature TB7CP of the thermal B7-SmCP transition is approached (9). Becausedm increases from 450 to 700Å through theB7 range as T approaches TB7CP, the predict-ed inverse relation between Eth and dm isqualitatively confirmed.

Combined EO and XRD evidence thatE-induced elimination of the PM also ex-pels the layer undulation is presented inFig. 3D, which shows optical micrographsand microbeam scattering from FCDs of

Fig. 5. (A and B) FFTEM images of a Pt-C replica shadowing the topography of a surface of aMHOBOW sample quenched from the B7 phase (T 115°C) and fractured. Surface topographyis such that darker areas would be shadowed with oblique illumination coming in the directionof the yellow arrows. The smectic fracture surfaces exhibit the usual single-layer steps, but alsoexhibit an atypical bulk coherent periodic undulation of wavelength dm � 500 Å. The lineswhere the undulation abruptly changes direction are suggestive of FCDs in their 1D periodicorder. (B) The undulation troughs and crests are not mirror symmetric, as evidenced by domainwalls (blue arrows), which separate domains of opposite net polarity along s. The coplanarity ofthe layers in these two domains is indicative of a rectangular lattice. A detailed sketch of theundulated structure in shown in Fig. 4C.

Fig. 6. Optical pho-tomicrographs of B7preparations havingthe smectic layersparallel to the planeof the image (with snormal to the imageplane), from (A toC) an 8-layer-thickMHOBOW freely sus-pended film; (D) a4-�m-thick homeo-tropic of MHOBOWsample between be-tween glass; and(F) a �10-layer-thick10OAM5AMO10 film.The fresh films (A) andbulk (D) of MHOBOWshow a low birefrin-gence 2D focal conictexture [dark samplearea surrounded bybright outline in (D)],evidence for the smec-tic-like organization ofthe PM, each stripe[white line in (A)] be-having as a 1D layer inthe 2D smectic planes.In the film, the PMperiod increases withtime until, after 1 day,it is visible optically (B), and after several days increases to reveal the polarization modulation stripes(C). (E) Mapping of p in the PM defect loop in (C). Identical structures have been observed in other PMfilm and interfacial systems (30). (D) B7 drop surrounded by isotropic (black area), showing alow-birefringence interior with s normal to the page and a bright outline with s parallel to the glass, bulk3D smectic focal conic as in Fig. 3D. Scale bars: (A) to (C) and (F), 100 �m; (D), 60 �m. (F)10OAM5AMO10 in a temperature gradient (cooler on the right) showing the increase of dm and themelting of the PM lattice with decreasing T.

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CITRO at T 100°C in the B7 phase,as-grown (red scattering, discussed above)and E-modified (green scattering). Below athreshold field, neither the optical nor thex-ray data are modified by the field, but forE � 20 V/�m, the domain begins to exhibitthe chiral extinction brush rotation shown,a signature of the transition to the PM-freeSmCSPF state (6 ), and the accompanyingtransition from the red- to green-shaded scatter-ing is observed with x-ray illumination throughthe same region (in the red/green circles). Thegreen scattering is a single peak centered atqm 0 and shifted out relative to the red to thepoint indicated by E on the qs axis, indicativeof simple planar layers with a spacing d that issmaller than the pitch ds along s with the un-dulation present. Thus, the elimination of thePM defects enables the layers to become thin-ner at the crests and troughs. The consequentreduction of the undulation amplitude requiresthe layering pitch along s to become equallythinner at the regions of maximum slope, ap-proaching the PM-free layer thickness d as theslope is reduced to zero. The peak positionsshow that in CITRO, the maximum slope in theundulation is �max 14.5°, and thus the frac-tional layer expansion �d/d at the crests andtroughs is �d/d [cos(�max)]�1 3.3%. Afascinating aspect of the field experiments isthat even though the SmCSPF layering is onaverage racemic in the PM stripes of Figs. 2 and4, the macroscopic SmCSPF state that resultsupon undoing the PM is homochiral (6, 10, 40).

Achiral/chiral optics of the banana leafdomains. The orientation of the s-m-p lat-tice obtained from the x-ray data on BLDsenables a definitive interpretation of theiroptical properties and detailed insight into thenature of the PM in MHOBOW. The keytransmission polarized light microscopic ob-servations are shown in Fig. 4, A and B, andinterpreted in Fig. 1, D to F, and Fig. 4, C toE. With normal incidence, the banana leafappears achiral and birefringent with opticaxes along s and p, and remains so if thesample is tilted about p, the BLD short axis.Remarkably, chiral optical rotation of ampli-tude linear in the tilt angle � appears fortilting the sample about s (the off-diagonaldielectric tensor element εsp � i�). Theseobservations put strict constraints on the pos-sible internal organization of BLD polarity,chirality, and undulation symmetry. Becauseoptical rotation disappears at normal inci-dence, the overall structure must be on aver-age achiral, i.e., with left- and right-handedstripes related by glide reflections. Becausetilting about p renders only the regions ofdiffering sign of undulation slope inequiva-lent (Fig. 4D), the absence of optical rotationupon p-tilt implies that the regions of eachsign of slope must be independently on aver-age achiral. This indicates that s-m is theglide plane, requiring then that the overall

structure be antiferroelectric with a period oftwo undulation wavelengths. It then remainsonly to choose between two possibilities forthe alternation in handedness in the stripes(flipping at either the blue or red defect lines).Of these, only the choice in Fig. 1, D to F,and Fig. 4, C to E, yields the s-tilt opticalrotation. Its most interesting feature is theexistence of two distinct types of PM defects:those where the handedness changes and theclinicity remains the same (drawn at thecrests), and those where the handedness re-mains the same and the clinicity changes(drawn at the troughs). Because these defectsare distinct structures, the crests and troughsof the undulation must be inequivalent, assketched in Figs. 1, 4, and 5 and observed inthe freeze-fracture experiments.

Filaments and textures. Figure 7, A toD, presents MHOBOW photomicrograph,freeze-fracture, and x-ray data that reveal thefollowing general characteristics of the fila-ments, both freely suspended and grown infrom the isotropic, that can be readily formedfrom PM phases: (i) Filaments have s normal ornearly normal to the filament long axis, i.e., alocal structure of nested cylindrical surfaces (ofcircular or racetrack-shaped cross section), con-sistent with the layering structure proposed byJakli et al. (13). (ii) Filaments exhibit PM layerundulation similar to that of the bulk, with mmaking an angle �(�) (Fig. 7C) with the local

filament axis, where � is the distance from thefilament center (60).

Observation (ii), coupled with the ease withwhich PM phases form filaments relative tonon–PM phases (e.g., B2), provides strong ev-idence that the PM is the essential elementstabilizing filament structure. PM coupled withthe smectic layering forms a 2D-ordered struc-ture analogous to that of the 2D-ordered fluidcolumnar phases, which are known to formfreely suspended filaments (61, 62). However,the extreme anisotropy of its 2D orderingmakes the PM case much more interesting, asevidenced, on the one hand, by the spectacularrange of possibilities (Fig. 7A), and, on theother hand, by the rigor with which a chosenstructure is maintained (Figs. 2 and 7A). Thelatter suggests that in a growing filament, �,once chosen, is fixed. The anisotropic soft-ness, as evidenced by the low threshold forE-field–induced PM suppression (63), en-ables the PM ordering to accommodate thelayer curvature at the filament surface and,importantly, reduces the energy cost of heli-cal winding of the PM undulations aroundand along the filament (� � 75°, evident inFig. 7C). The helical winding of the PMwithin the filament, with � established by anucleation event and remaining fixed duringgrowth (64), provides a natural explanationof the twist deformation of filaments. Notethat with this mechanism for filament helix-

Fig. 7. Filaments and fibers. (A)Transmission polarized light im-ages of different MHOBOWfilaments growing within a 500-�m-by-500-�m area upon cool-ing a 6-�m-thick cell from theisotropic phase (scale bar, 50�m). The twist structures arehighly diverse but rigorouslymaintained once established, ev-idence of a topologically deter-mined internal organization (64).(B and C) FFTEM images ofMHOBOW filaments, showingthe nested cylinder smectic layerorganization: (B) 1-�m diameterwith angle � � 0° between thefilament axis and the modulationwavevector m, and (C) 3.4-�mdiameter with � � 80°. The fil-ament helical twist is likely dueto this internal helical PM wind-ing. (D) X-ray scattering from asingle �30-�m-diameter freelysuspended MHOBOW filament(T 130°C), formed in situ byslow pulling of a pin from a1-mm-diameter cup of LC. Thex-ray beam illuminates a 0.2-mm-long segment of the fila-ment, and the figure shows in-tensity contours of scans in qh asa 1.4-mm length of the filament is translated through the beam parallel to its axis (x). The [s 1,m 0], [s 1, m 1], and [s 1, m 2] lattice points pass successively through the Ewald plane,indicative of a slightly helixed PM lattice with � � 0, twisting at a rate of � 10°/mm along thefilament, consistent with the forcing of m normal to the filament axis by the drawing process. �increases to �90° as the filament thins (60).

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ing neither relies on, nor is indicative of, netSmCP layer chirality, as is assumed in cur-rent models (13). Variation of filament pro-file (e.g., cylinder or racetrack shaped), �(�),PM and smectic elasticity, filament diameter,and filament surface energies should providethe broad parameter space necessary to ac-count for a diverse filament morphology.

The helical filaments play a key role in theformation of the striking B7 domains ob-served in few-micrometer-thick cells (com-pare Fig. 2B and cover). The basic growthscenario is illustrated in the DTLM images ofFig. 2, which shows helical filaments in thebulk being trapped on the surface for part oftheir length to form focal elements. Suchtrapped filaments organize as folded lattices(Fig. 2B) to form birefringent 2D FCDs (Fig.2C). A mechanism for generation of morecomplex textures, such as the checkerboardin Fig 2C, is shown in the parallel polarizerDTLM images in Fig. 2D, in which a fila-ment, tethered to the surface and to the greendots (left), grows upon cooling by addingmolecules all along its length (center). Itspontaneously undulates, perhaps because ofcompressive stress due to its linear expan-sion, and the undulations form a 2D pattern(right) that is checkerboard or stripe-like, de-pending on the phase of the undulation inneighboring filaments. Such arrays internallyreorganize and anneal into remarkably homo-geneous periodic, quasi-periodic, or maze-like structures.

Other phases. If PM produces the struc-ture proposed here for B7, then it may also leadto other bent-core LC phases with B7 properties.For example, the orientation frustration atthe splay defect planes, instead of produc-ing the B7 layer expansion, may be relievedby interdigitation (half-layer displacement)of the layers, which, as shown in Fig. 1H,accommodates in a natural way the oppositeorientation of the bent molecules on oppo-site sides of a defect line. This arrangementleads directly to the 2D rectangular latticein Fig. 1H, which is, in fact, the latticestructure of the B1 phase (3, 51, 65–67 ),identified as the “frustrated” intermediatebetween the B7 and the B6 phases, the latterbeing the lamellar structure having the“half-layer” repeat of the defect regions inFig. 1H. The “half-layer” structure is pre-ferred with short tails, i.e., the layering isweaker, as is the case for calamitic smecticswith shorter tails (68). Thus, the B7-B1-B6sequence found versus decreasing taillength in, for example, the mOAM5AMOmhomologous series of bent-core dimers (51)may well be understood on the basis of PM.Another important example is the materialW1044 (Fig. 1A), which exhibits the spec-tacular textures of the B7 family (13), buthas an interdigitated 2D lattice of a phase ofthe B1 family (3, 69).

An additional possible response to theexcess layer thickness is to form layer twistgrain boundaries (TGBs) at the polarizationsplay defect planes. Then, in the case that thesplay stripes are homochiral, the twist in mo-lecular orientation across the stripes, evidentin Fig. 1H, leads to the “polarization-splayedsmectic slab” TGB structure (70). This maybe the origin of the low-birefringence opti-cally active (dark conglomerate) texturesfound in MHOBOW (10), H87 (9), and otherB7 materials (71, 72).

Conclusion. We have presented exten-sive evidence that several key mysteries offluid smectic bent-core LCs can be under-stood on the basis of new phases in which thelocal spontaneous polar/chiral ordering drivesa larger scale periodic structure of polariza-tion splay defects. The globally 2D rectangu-lar antiferroelectric, racemic phase with splaystripes, exhibiting a striking out-of-phase al-ternation of polarization and chirality, is thedominant structure found in MHOBOW,the most-studied material. A basic questionthat remains is the extent to which thisparticular structure is adopted in other ma-terials, and, for that matter, in MHOBOW,because the twist of the filaments and thevarying strength of chiral response found indomains taken through the field-inducedPM-uniform transition (6 ) are suggestive ofnet handedness. However, such observa-tions need to be carefully interpreted be-cause, for example, other filament-formingsystems of achiral molecules exhibit mac-roscopic chirality as the result of a sponta-neous symmetry breaking (73, 74 ).

These findings raise a host of theoreticalquestions, highlighting the need for a theoryof PM formation in 3D smectic phases that (i)includes the correct treatment of the smecticlayer elasticity and expansion, (ii) predictsthe organization of polarity and chirality, (iii)describes the PM/UL-SmCP phase transitionand the effect of electric field, and (iv) en-ables a mechanistic understanding of the pre-ferred splay, which is likely to be due to stericpacking polarity. The organization of helicalPM in the filaments with the possibility ofPM TGBs (60) is also a fascinating defectproblem, which must be attacked to developan understanding of the filaments’ diversetwisting structures. The results reveal a classof condensed phases in which polarizationmodulation is a dominant effect, a class basedon a molecular-design theme that enablesmany possibilities for substitution and varia-tion in molecular structure.

References and Notes1. T. Niori, T. Sekine, J. Watanabe, T. Furukawa, H.Takezoe, J. Mater. Chem. 6, 1231 (1996).

2. D. R. Link et al., Science 278, 1924 (1997).3. G. Pelzl, S. Diele, W. Weissflog, Adv. Mater. 11, 707(1999).

4. T. Akutagawa, Y. Matsunaga, K. Yasuhara, Liq. Cryst.17, 659 (1994).

5. M. Nakata et al., Liq. Cryst. 28, 1301 (2001).6. D. M. Walba et al., Science 288, 2181 (2000).7. MHOBOW is a chiral molecule and is studied, unlessexplicitly indicated, as the racemate [(R)/(S)-MHOBOW], which behaves as if it were achiral.

8. C.-K. Lee, L.-C. Chien, Liq. Cryst. 26, 609 (1999).9. A. Eremin, S. Diele, G. Pelzl, H Nadasi, W. Weissflog,

Phys. Rev. E 67, 021702 (2003).10. M. Nakata, unpublished data.11. These materials exhibit the following B7 phase-

transition temperatures (in °C) upon cooling:MHOBOW [I 139 B7 90 B4], PBCOB [I 130 B7 80 X],H87 [I 160 B7 132 B2], CITRO [I 110 B7 85 X], and10OAM5AMO10 [I 121 B7 99 X].

12. G. Pelzl et al., Liq. Cryst. 26, 135 (1999).13. A. Jakli, C. Lischka, W. Weissflog, G. Pelzl, A. Saupe,

Liq. Cryst. 27, 1405 (2000).14. N. Clark, paper presented at the 17th International

Liquid Crystal Conference of the International LiquidCrystal Society, Strasbourg, France, 19 to 24 July,1998.

15. J. P. Bedel et al., Liq. Cryst. 27, 1411 (2000).16. D. R. Link, N. Chattham, N. A. Clark, E. Korblova, D. M.

Walba, Bull. Am. Phys. Soc. 44, 1043 (1999).17. A. Jakli, D. Kreurke, G.G. Nair, Phys. Rev. E 67, 051702

(2003).18. G. Blatter et al., Rev. Mod. Phys. 66, 1125 (1994).19. S. Renn, T. Lubensky, Phys. Rev. A 38, 2132 (1988).20. P. P. Crooker, in Chirality in Liquid Crystals, H. S.

Kitzerow, C. Bahr, Eds. (Springer-Verlag, New York,2001).

21. M. A. Handschy, N. A. Clark, S. T. Lagerwall, Phys. Rev.Lett. 51, 471 (1983).

22. R. Kamien, J. V. Selinger, J. Phys. Condens. Mat. 13,R1 (2001).

23. R. B. Meyer, P. S. Pershan, Solid State Commun. 13,989 (1973).

24. J. V. Selinger, Z.-G. Wang, R. F. Bruinsma, C. M.Knobler, Phys. Rev. Lett. 70, 1139 (1993).

25. J. Pang, N. A. Clark, Phys. Rev. Lett. 73, 2332 (1994).26. G. A. Hinshaw, R. G. Petschek, R. A. Pelcovits, Phys.

Rev. Lett. 60, 1864 (1988).27. G. A. Hinshaw Jr. R. G. Petschek, Phys. Rev. A 39, 5914

(1989).28. S. A. Langer, J. P. Sethna, Phys. Rev. A 34, 5035

(1986).29. I. Kraus, R. B. Meyer, Phys. Rev. Lett. 82, 3815 (1999).30. J. Pang, thesis, University of Colorado (1995); Disser-

tation Abstracts no. 9620652.31. Y. Tabe, N. Shen, E. Mazur, H. Yokoyama, Phys. Rev.

Lett. 82, 759 (1999).32. J. V. Selinger, R. L. B. Selinger, Phys. Rev. E 51, R860

(1995).33. J. V. Selinger, J. M. Schnur, Phys. Rev. Lett. 71, 4091 (1993).34. C.-M. Chen, T. C. Lubensky, F. C. MacKintosh, Phys.

Rev. E 51, 504 (1995).35. R. B. Meyer, R. A. Pelcovits, Phys. Rev. E 65, 061704

(2002).36. T. P. Rieker et al., Phys. Rev. Lett. 59, 2658 (1987).37. N. A. Clark, R. B. Meyer, Appl. Phys. Lett. 22, 493

(1973).38. XRD experiments on powder and freely suspended

filament samples were carried out on the Huberfour-circle goniometer on beamline X10A of the Na-tional Sychrotron Light Source at Brookhaven Na-tional Laboratory. This beamline uses a doublebounce Si monochromater and a Ge 111 analyzer toobtain wavevector resolution �q � 0.0005 Å�1 fullwidth at half maximum. Powder samples were in1-mm-diameter glass capillaries in a temperature-controlled chamber. Single-domain x-ray microbeamexperiments were carried out on Microprobe Beam-line BL-4A of the Photon Factory, Tsukuba, Japan,with 5-�m-thick LC samples contained between 80-�m-thick indium–tin oxide–coated glass plates. Themicrobeam x-ray experiment is detailed in (39).

39. Y. Takanishi et al., J. Mater. Chem. 9, 2771 (1999).40. C.-K. Lee et al., Liq. Cryst. 28, 1293 (2001).41. D. S. Shankar Rao et al., Liq. Cryst. 28, 1239 (2001).42. R. Amaranatha Reddy, B. K. Sadashiva, Liq. Cryst. 29,

1365 (2002).43. D. Coleman, thesis, University of Colorado (2003).44. Note that in the Fourier transform of �(r) used to

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obtain the scattered intensity I(q), the displacementu(r) appears in the argument of an exponential andthus enters I(q) in a nonlinear way. Thus, with sinu-soidal undulation, even though u(r) has only thesingle (fundamental) harmonic, multiple diffractionorders appear versus m for s 1, 2.

45. The dm values quoted here are for fresh samples incapillaries. dm was found to increase in time with x-rayexposure and aging at B7 temperatures (up to dm �600 Å in MHOBOW). This effect was particularlynoticeable in freely suspended film and freeze frac-ture experiments, where there is more exposure to airduring observation and preparation, respectively.

46. J. A. Zasadzinski, J. Phys. 51, 747 (1990).47. T. Gulik-Krzywicki, M. J. Costello, J. Microsc. 112, 103

(1997).48. Several recent papers use evidence for polarization

along the layer normal in B7 phases to argue thatthey are simply lamellar with triclinic local layersymmetry (9, 49). However, the phases in questionare shown here to be undulated and polarizationmodulated so that the claim of triclinic behavior in alamellar smectic may not be justified. In fact, a PMphase is triclinic essentially everywhere (whereverthere is nonzero layer curvature). It may be that localtriclinic symmetry actually drives the PM, but there isno evidence for this at present.

49. A. Jakli, D. Kruerke, H. Sawade, G. Heppke, Phys. Rev.Lett. 86, 5715 (2001).

50. It is not understod why dm is larger in films than inbulk, but this may be due either to surface tension,which provides an additional elastic resistance toundulation, or due to the high surface-to-volumeratio of the films, which enhances hydrolysis andimpurity buildup.

51. S. W. Choi et al., Mol. Cryst. Liq. Cryst. 328, 185(1999).

52. M. Nakata, N. Chattham, N. A. Clark, H. Takezoe,unpublished data.

53. C. Y. Young, R. Pindak, N. A. Clark, R. B. Meyer, Phys.Rev. Lett. 40, 773 (1978).

54. The B7 materials strongly favor formation of freelysuspended filaments (12, 16) rather than films, aconsequence of their 2D lattice structure, but it waspossible to obtain 1- to 10-layer-thick MHOBOWand 10OAM5AMO10 films at high T in the B7 phaseby either pulling the film very slowly (�20 �m/s) orby applying an ac field (�5 V/mm) parallel to thefilm plane during the pulling. An initially thin spot willexpand in area over a large fraction of the film afterseveral hours.

55. R. Pindak, C. Y. Young, R. B. Meyer, N. A. Clark, Phys.Rev. Lett. 45, 1193 (1980).

56. A. Hauser, A. Schamalfuss, Kresse, Liq. Cryst. 27, 629(2000).

57. Several B7 phases have been previously identified asSmCPA on the basis of antiferroelectric properties,including absence of second-order nonlinear opticalsusceptibility. We contend that the underlying struc-ture is actually SmCSPF and that the antiferroelec-tricity is that of the PM stripe pattern.

58. R. Stannarius, C. Langer, W. Weissflog. Phys. Rev. E66, 031709 (2002).

59. Because the field-induced PM/UL-to-SmCP transitionis an equilibrium energetic effect, the modulationshould in principle return once the field is removed.However, it did not do so spontaneously in any of theexperiments reported here or in (6). This is likely dueto the fact that in order to reach the threshold field,the LC was only 1 to 5 �m thick, and because thelayer structure shrinkage upon PM expulsion waslocked in by the surfaces, an effect similar to theirreversible elimination of the chevron structure inSmCs by field application. The PM/UL-to-SmCP tran-sition in CITRO could be reversed by waveform se-lection (square wave: PM/UL-to-SmCP; triangle wave:SmCP -to- PM/UL) (10).

60. If p is the pitch of a helical winding of m(x) along afilament, then at radius � from the filament core wehave �(�) �(2/p). Thus, if the pitch is indepen-dent of �, then the orientation of m also windshelically versus � at a given x and the PM lattice musthave TGBs.

61. C. R. Safinya, K. S. Liang, W. A. Varady, N. A. Clark, G.Andersson, Phys. Rev. Lett. 53, 1172 (1984).

62. C. R. Safinya, N. A. Clark, K. S. Liang, W. A. Varady,L. Y. Chiang, Mol. Cryst. Liq. Cryst. 123, 205 (1985).

63. The elastic constant C of the PM lattice is comparableto its elastic energy density C � K/dm

2 � 104 J/m3

(see calculation of Eth), about four orders of magni-tude smaller than typical smectic layer compressionmoduli. Thus, the typical fluid smectic focal conicorganization of layers is maintained.

64. The winding of the 2D PM lattice on a filament offixed cross-sectional layer structure is maintainedtopologically by the number of undulation periodsaround the filament. However, the PM lattice musthave dislocations because of the curvature of thesmectic layers (Fig. 7, B and C).

65. J. Szydlowska et al., Phys. Rev. E 67, 031702 (2003).66. The B1 lattice structure shown in Fig. 1H is one of

many possibilities for alternation of polarization andtilt orientation, which also include PM in the absenceof tilt. Thus, the homochiral, synpolar case (e.g., allstripe polarizations toward the reader and in magen-ta) would necessarity have an oblique 2D lattice,which has been found in some B1s, e.g., W1044.

67. The polarization is sketched as uniform in the B1phase in (53) and the B1rev phase in (69), but in factmust be splayed, e.g., as in Fig. 1H.

68. W. L. McMillan, Phys. Rev. A 4, 1238 (1971).69. W1044 has an oblique 2D reciprocal lattice charac-

terized by strong [s, m] [1, 1] and [1, �1] reflec-tions, with complete absence of the s 1, m even

reflections, indicative of an interdigitated real lattice.The real lattice is as in Fig. 1H but oblique, possiblydue to a uniform rather than alternating moleculartilt orientation (43).

70. M. Brunet, L. Navailles, N. A. Clark, Eur. Phys. J. E 7, 5(2002).

71. A. Eremin, S. Diele, G. Pelzl, W. Weissflog, Phys. Rev.E 67, 020702(R) (2003).

72. J. Ortega, C. L. Folcia, J. Etxebarria, N. Gimeno, M. B.Ros, Phys. Rev. E 68, 011707 (2003).

73. B. N. Thomas, N. A. Clark, Phys. Rev. E 59, 3040 (1999).74. S. Pakhomov et al., Proc. Natl. Acad. Sci. U.S.A. 100,

3040 (2003).75. This work was supported by NSF grant DMR-

0072989, NSF Materials Research Science and Engi-neering Centers grants 0213918 (University of Colo-rado) and 0080034 (University of California, SantaBarbara), and NASA grant NAG3-2457. Research wascarried out in part at the National Synchrotron LightSource, supported by U.S. Department of Energy,Divisions of Materials and Chemical Sciences.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/301/5637/1204/DC1Figs. S1 to S3

26 March 2003; accepted 4 August 2003

Major Ecological Transitions inWild Sunflowers Facilitated

by HybridizationLoren H. Rieseberg,1* Olivier Raymond,2 David M. Rosenthal,3

Zhao Lai,1 Kevin Livingstone,1 Takuya Nakazato,1

Jennifer L. Durphy,1 Andrea E. Schwarzbach,4 Lisa A. Donovan,3

Christian Lexer1

Hybridization is frequent in many organismal groups, but its role in adaptationis poorly understood. In sunflowers, species found in the most extreme habitatsare ancient hybrids, and new gene combinations generated by hybridization arespeculated to have contributed to ecological divergence. This possibility wastested through phenotypic and genomic comparisons of ancient and synthetichybrids. Most trait differences in ancient hybrids could be recreated by com-plementary gene action in synthetic hybrids and were favored by selection. Thesame combinations of parental chromosomal segments required to generateextreme phenotypes in synthetic hybrids also occurred in ancient hybrids. Thus,hybridization facilitated ecological divergence in sunflowers.

The role of hybridization in evolution hasbeen debated for more than a century. Twohighly polarized viewpoints have emerged.At one extreme, hybridization is consideredto be a potent evolutionary force that cre-ates opportunities for adaptive evolutionand speciation (1, 2). In this view, theincreased genetic variation and new gene

combinations resulting from hybridizationpromote the development and acquisitionof novel adaptations. The contrasting posi-tion accords little evolutionary impor-tance to hybridization (aside from al-lopolyploidy), viewing it as a primarilylocal phenomenon with only transient ef-fects—a kind of “evolutionary noise” (3–5). Unfortunately, definitive support for ei-ther viewpoint is lacking. Although foot-prints of past hybridization are often detect-ed by molecular phylogenetic studies (6),their presence does not indicate that thehybridization was adaptive. Likewise, thedocumentation of fit hybrids in contempo-rary hybrid zones (2) is not proof of anadaptive role for hybridization, because fit

1Department of Biology, Indiana University, Bloom-ington, IN 47405, USA. 2Laboratoire de Biologie Mo-leculaire et Phytochimie, Universite Claude BernardLyon 1, F-69622 Villeurbanne, France. 3Department ofPlant Biology, University of Georgia, Athens, GA30602, USA. 4Department of Biological Sciences, KentState University, Kent, OH 44242, USA.

*To whom correspondence should be addressed. E-mail: lriesebe@indiana.edu

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