Structure, Function, and Self-Assembly of Single Network Gyroid (I4132) Photonic Crystals in Butterfly Wing Scales

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Birgit Hausmann

Reference

V. Saranathan et. al. "Structure, Function, and Self-Assembly of Single Network Gyroid (I4<math>_1</math>32) Photonic Crystals in Butterfly Wing Scales" Proc. Nat. Acad. Sci., 107, 11676-11681 (2010)

Keywords

biological meta-materials, organismal color, biomimetics, biological cubic mesophases


Overview

Small angle X-ray scattering (SAXS) was used to identify the 3D photonic nanostructures (made of chitin and air) of five butterfly species from two families (Papilionidae, Lycaenidae) as single network gyroid (<math>I4_132</math>) photonic crystals. Photonic band-gap modeling was also performed. Butterflies first develop thermodynamically favored double gyroid precursors and transform these into a single gyroid network which is optically more efficient.

Results and Discussion

A periodic variation in the refractive index on the order of visible wavelengths gives butterflies its structural colors. Pinhole synchrotron small angle X-ray scattering (SAXS) has been used to investigate natural photonic materials with mesoscale (150–350 nm) scattering features (Fig. 2). The order of the lattice constant in these cases require small scattering angles and advanced X-ray optics. Five butterflies species were tested: Parides sesostris, Teinopalpus imperialis, (Papilionidae); Callophrys (formerly Mitoura) gryneus, Callophrys dumetorum, and Cyanophrys herodotus (Lycaenidae) (Fig. 1).

Fig. 1 Anatomy of the structural color-producing nanostructure in lycaenid and papilionid butterflies. (A) Optical micrograph of the ventral wing cover scales of Callophrys gryneus (Lycaenidae). The opalescent highlights are produced by randomly oriented crystallite domains. (Scale bar: 100 μm.) (B) SEM image of the dorsal surface of a C. gryneus scale. (Inset) Simulated SEM (111) projection from a thick slab of a level set single gyroid nanostructure. (Scale bar: 2.5 μm.) (C) TEM image of the C. gryneus nanostructure showing a distinctive motif, uniquely characteristic of the (310) plane of the gyroid morphology. (Inset) A matching simulated (310) TEM section of a level set single gyroid model. (Scale bar: 200 nm.) (D) Optical micrograph of the dorsal wing cover scales of the Parides sesostris (Papilionidae). (Scale bar: 100 μm.) (E) SEM image of the lateral surface of the wing scale nanostructure of P. sesostris showing fused polycrystalline domains beneath columnar windows created by a network of ridges and spaced cross-ribs. The fractured face features a square lattice of air holes in chitin. (Inset) Simulated SEM (100) projection from a thick slab of a level set single gyroid nanostructure. (Scale bar: 2 μm.) (F) TEM image of the P. sesostris nanostructure showing a distinctive motif, uniquely characteristic of the (211) plane of the gyroid morphology. (Inset) A matching simulated (211) TEM section of a level set single gyroid model. (Scale bar: 2 μm.) c, chitin; a, air void.

Figure 2 shows SAXS patterns of these species which predict distinctly oriented crystallite domains that have also been indicated with SEM (Fig. 1 B and E). These results are consistent with the size of the X-ray beam (15 × 15 μm). The unit cell lattice constant of the butterfly scale photonic nanostructures was estimated as a > 300nm which is consistent with EM-estimated lattice parameters assuming a single gyroid space group, rather than a simple primitive or a single diamond symmetry. Higher-order reflections in T. imperialis, C. gryneus, and C. herodotus (Figs. 2 and 3) proves a high degree of order within the nanostructure.

Fig. 2 Representative 2D SAXS patterns (original image 1340 × 1300 pixels) for (A) Teinopalpus imperialis, (B) Parides sesostris, (C) Callophrys (Mitoura) gryneus, and (D) Cyanophrys herodotus. The false color scale corresponds to the logarithm of the X-ray scattering intensity. The radii of the concentric circles are given by the peak scattering wave vector (qmax) times the moduli of the assigned hkl indices, where h, k, and l are integers allowed by the single gyroid (I4132) symmetry space group (IUCr International Tables for Crystallography).
Fig. 3 Normalized azimuthally averaged X-ray scattering profiles (Intensity I∕Imax vs. scattering wave vector q∕qmax) calculated from the respective 2D SAXS patterns for Teinopalpus imperialis, Parides sesostris, Callophrys (Mitoura) gryneus, Callophrys dumetorum, and Cyanophrys herodotus. The vertical lines correspond to the expected Bragg peak positional ratios for the single gyroid crystallographic space group (I4132). The numbers above the lines are squares of the moduli of the Miller indices (hkl) for the allowed reflections. The calculated, normalized structure factors for a single gyroid (I4132) level set model for C. herodotus, with 29% dielectric volume fraction and a lattice constant of 331 nm, is also shown alongside for comparison (yellow diamonds).

Computer models of the single gyroid, simple primitive, and single diamond nanostructures were also performed, which produced simulated TEM and SEM projections of appropriate thicknesses and chitin volume fractions, along various lattice directions/cleavage planes, including (110), (111), and (211). SEM and TEM images of all five butterfly show characteristics of the single gyroid space group (Fig. 1 B and E, and Fig. S1 B, E, and H). Figure 4 compares the predicted reflectance from SAXS patterns with measured optical reflectance. The optical and X-ray scattering peaks agree reasonably well (< ∼ 15 nm) with a value of 1.16 for <math>n_{av}</math>, which corresponds to a chitin volume fraction of 0.25 (Fig. 4). Bandgap calculations indicate three closely spaced pseudogaps or partial photonic bandgaps along Γ-N (110), Γ-P (111), and Γ-H (200) directions for the butterfly photonic nanostructures. The Bragg attenuation lengths of the butterfly nanostructures were calculated to be between 3.9–4.4 a (Table S1). When the Bragg condition is met most of the light gets reflected while broader reflectance peaks seem to evolve from multiple scattering.

Fig. 4 Predicted reflectance (black line) from azimuthal average of SAXS patterns versus measured optical reflectance (blue line) for (A) Teinopalpus imperialis, (B) Parides sesostris, (C) Callophrys (Mitoura) gryneus, and (D) Cyanophrys herodotus. The SAXS predicted reflectance follows from Bragg’s law and is given by mapping the X-ray scattering intensity from scattering wave vector to wavelength space by choosing a value of 1.16 for the average refractive index, nav, which corresponds to a chitin volume fraction of 0.25.

Also, a model for the development of the 3D photonic nanostructure in the wing scale cells of lepidopteran pupae is presented. TEM images from developing pupae of C. gryneus (Fig. 5A) seem to indicate that "the cell plasma membrane and the SER membrane interact to form a pair of parallel lipid-bilayer membranes, separated by the cellular cytoplasm. The two parallel lipid-bilayer membranes of the developing scale cell form a pentacontinuous structure with a core-shell double gyroid morphology, similar to those seen in ABC triblock copolymer melts (Fig. 5 A and B)." The lipid-bilayer membranes of developing butterfly photonic scale cells seem also to define "the unique pentacontinuous volumes of a core-shell double gyroid (Ia3d) structure of the form ABCB′A′, in which A is the extracellular space, B is the plasma membrane, C is the cell’s cytoplasmic volume, B′ is the SER membrane, and A′ is the intra-SER space (Fig. 5A and Insets). As in a triblock copolymer system, the proposed ABCB′A′ core-shell double gyroid system in the butterfly scale has the lipid-bilayer membranes (B and B′) together with the intervening cytoplasmic space (C) forming the matrix phase (BCB′) of the system." While developing chitin is deposited and polymerized in the extracellular space (A) that is now within the peripheral outline of the scale cell and forms the core of one of the gyroid networks (Fig. 5C, red), which is enclosed by the plasma membrane (Fig. 5C, black). When the cell dies, the cellular cytoplasm and the membranes (BCB'A' blocks of the core-shell double gyroid) are replaced with air, leaving behind a single gyroid network of chitin (A) in air (Fig. 5C). The TEM section in Fig. 5A (which was taken from reference 11) indicates two different regions through the (110) plane. Initial chitin deposition is also visible in Fig 5A as dark lines in the spaces surrounding the double (right), while chitin rods are visible as dark spots in the center of the double rings (left, yellow square). Although SEM and TEM images are not sufficient to state on the chirality of the considered systems the given SEM images indicate single gyroid networks with both left- and right-handed chiralities (Fig. S8).

Fig. 5 Development of butterfly wing scale photonic nanostructure. (A) TEM cross-section of a ventral wing scale cell from a 9-day-old C. gryneus pupa (from refs. 11 and 21), depicts the complex infolding of the plasma membrane and SER membrane. The developing nanostructure shows the diagnostic motif of two concentric rings roughly in a triangular lattice (compare with Fig.5B). Yellow and red boxes highlight areas revealing different sections through the (110) plane of a polarized (ABCB′A′) pentacontinuous core-shell double gyroid (color insets). (Scale bar: 1 μm.) (Inset) Colored model of a core-shell double gyroid of ABCB′A′ form: A (red) is the extracellular space, B (black) is the plasma membrane, C (white) is the cytoplasmic intracellular space, B' (blue) is the SER membrane, and A' (yellow) is the intra-SER space. [Reprinted with permission from ref. 11.) (B) OsO4-stained (110) TEM section of an ABC triblock copolymer with core-shell double gyroid morphology. (Scale bar: 200 nm.) (Reprinted with permission from ref. 40. Copyright 2005, John Wiley and Sons.) (C) Three-dimensional model of development of photonic butterfly wing scale cell. (I) Unit-cell volume rendering of the core-shell double gyroid model structure of the form ABCB′A′. Color of each component from inset inA. (II) Single gyroid composed of cell plasma membrane (black) surrounding extracellular space (red). (III) As the scale cell dies, the cellular cytoplasm and membranes (BCB′A′ blocks of the core-shell double gyroid) are replaced with air leaving behind a single gyroid core-shell network of chitin (red) in air.