Here we report a two-dimensional amorphous photonic structure (2D APS) discovered in the ligament of bivalve Lutraria maximum, based on scanning electron microscopy and fiber optic spectrometry combined with the image processing technology and pair correlation function analysis. This structure contains 70% in volume of parallel aragonite fibers embedded in a protein matrix. These fibers, in cross section, are hexagonal to polygonal with diameters of 194nm and are packed in short-range order with a nearest-neighbor distance of 202nm. Moreover, experimentally measured reflectance spectrum and theoretical predictions prove that this photonic structure gives rise to a golden structural color with the peak wavelength at about 650nm. We expect this unraveled structure may inspire the design and synthesis of a novel 2D APS.
© 2010 OSA
Biological photonic structures refer to the optical nanostructures evolved in organisms that can often produce structural colors [1,2]. Recently these structures have fascinated scientists for their promising technical applications. For example, they can be directly used as optical gas sensors to fingerprint various volatile substances such as methanol, ethanol and isomers of dichloroethylene . In addition, these structures can serve as templates to make novel photonic materials by the chemical vapor deposition  and sol–gel method , etc.
To date, numerous biological photonic structures have been characterized in a diversity of living species such as insects, birds, and fishes, which have been well reviewed in the literature [1,2,6–8]. They commonly fall into one-, two-, or three-dimensional structures with or without periodicity. Comparatively, the 2D APSs are relatively rare in nature. At my present knowledge, such structures have been only found in some avian and mammalian skins [9–11], which invariably consist of collagen fibers and can produce various structural colors through coherent light scattering.
Here we study a new kind of 2D APS in the bivalve ligament, an elastic material characteristic of bivalve animals of ca. 10,000 species . Previous works have show that the ligament’s structure is similar in different species in that it contains parallel aragonite fibers bonded by a protein matrix [13–15]. So far, the ligament’s functional morphology has attracted much attention [15,16]; however, its optical property has been neglected. We have observed that the ligaments of at least 20 bivalve species display various structural colors [17,18], suggesting the structural colors may be ubiquitous in bivalve ligaments. However, the underlying color-producing photonic structures are not quantitatively characterized. Especially, the spatial degree of order of fibers in the ligament needs examined.
In this work, we used the ligament from the mactrid bivalve Lutraria maximum as our experimental sample, since its nanostructure has not been described before. This ligament is easily fractured into two nearly equal halves with the separation of two shell valves. One half is shown in Fig. 1 , whose shape likes a water drop with the ventral side dilated and dorsal tapered. Commonly, the ligament’s exterior displays gray to brown colors. However, its interior can reflect a golden structural color as shown in Section 3.2.
We aim to quantitatively characterize the nanostructure and structural color found in the interior of L. maximum ligament. We reveal that, in this ligament, a 2D APS is responsible for its structural color.
2.Materials and methods
We obtained specimens of L. maximum from Beibu Gulf of Guangxi in southern China. After removing the soft body, the shells were washed with distilled water and dried in an oven at 40° for 2 days. Then we carefully separated the shell valves and removed the ligament. Next, using a single blade, we broke the ligament in different directions for following experiments.
We took the optical micrographs of the ligament using a stereomicroscope (GL-99, GLO) which is connected to a CCD camera (TK-C921EC, JVC); the experimental setup is shown in Fig. 2 . The reflectance spectra were collected using a fiber optic spectrometer (AvaSpec-2048, Avantes) with its probe perpendicular to the ligament broken surface; a halogen light (AvaLight-HAL, Avantes) was used as the light source and a Teflon white reference tile (WS-2, Avantes) for reflectance calibration.
We examined the ligament’s nanostructure using a scanning electron microscope (SEM) (S-3400N, Hitachi) operated at 30 kV accelerating voltage. Then, the SEM images were processed and analyzed using the Fovea Pro 4.0 plug-in (Reindeer Graphics, Asheville, NC) for Adobe Photoshop CS3(Adobe, San Jose, CA). The Pair correlation function (g(r)) analyses were performed using the spatstat package . Finally, the 2D Fourier predicted reflectance spectra were obtained using Prum and Torres’ Fourier tool .
3.1. Structural characterization
First, we investigate the ligament structure in longitudinal section, which is fractured right to the ventral surface (VS) along the dorsoventral direction [Fig. 3(a) ]. Locally, the fibers are highly aligned as shown in Fig. 3(b)–3(d); but over the entire section, the fibers are slightly misaligned by an angle below 10°. In addition, the fibers are inclined at an angle 25-40° to the outer surface and nearly normal to VS, as indicated by α, the angle between the fiber axis and VS [Fig. 3(b)–3(d)]. In short, the ligament contains approximately unidirectional continuous fibers, whose orientation can be roughly indicated by VS direction.
Next, we investigate the ligament structure in cross section, which is fractured parallel to VS [Fig. 4(a) ]. It shows the aragonite fibers are hexagonal or polygonal and densely packed. As the original image in Fig. 4(a) cannot be directly analyzed quantitatively, we use the software Fovea Pro 4.0 to process it to a binary image [Fig. 4(b)]. Then the fiber’s sizes and coordinates of centroids are extracted by Fovea Pro 4.0 for size and g(r) analysis.
Based on image analysis of Fig. 4(b), we get the aragonite fibers occupy an area fraction (i.e., volume fraction) of 70%. The fiber’s diameter is highly uniform with an average of 194 ± 19nm (n = 611) [Fig. 4(c)]. Figure 4(d) is the g(r) curve of fiber’s centroids, showing a strong first peak at r = 202nm followed by a rapidly decay to unity at larger r values. This suggests that the fibers are packed in short-range order  with a nearest-neighbor distance of d = 202nm. In summary, SEM image analysis proves that the ligament of L. maximum resembles a 2D APS with short range order.
3.2. Optical observation and spectral analysis
The ligament’s exterior commonly displays some kinds of brown colors as shown in Fig. 1. Similarly, its cross section also displays a uniform brown color independent of the viewing or incident angle [Fig. 5(a) ].
In contrast, the ligament’s longitudinal section displays different colors depending on β, the acute angle between the fiber axis and projection of incident beams on the section plane. When β is nearly a right angle (ca. >80°) (i.e., normal incidence), this section reflects a strong golden color with traces of blue to green hues in its inner edge [Fig. 5(b)]. However, when β <80°, this section rapidly changes to reflect a uniform brown color [Fig. 5(c)].
In addition, when β is nearly a right angle, the golden color is independent on incident angel θ (See Fig. 1), suggesting it is a non-iridescent structural color. In summary, we conclude that the brown color results from the pigment, while the golden color from the structure.
In spectrometry of a general structural color investigation, it is common to neglect the polarization effects [9,11,21,22], since color is a visual perception of light by human eyes, which are insensitive to the polarization of light. Further, for a 2D photonic structure, polarizations have little effects on color . Therefore, for simplicity, this work only measured the unpolarized reflectance spectra under normal incidence, which, from most part of the ligament, are characterized by a broad strong peak centered at about 656nm [Fig. 6(a) ], indicating a golden color. This is consistent with above optical observation.
3.3 Theoretical predictions
Here we try to predict the ligament’s optical property. It is worth noting we assume the incident light is normal to the fiber axis and focus on the area of the ligament with a golden structural color.
It has been well established that 2D APS has one isotropic band gap which is governed only by short range order or nearest-neighbor distance of inclusions . When the distance matches the Bragg condition, a strong Bragg scattering resonance occurs that leads to a band gap centered at the wavelength λ max = 2 n avg d , where n avg is the average refractive index and d is the nearest-neighbor distance determined by the first strong peak of g(r). For L. maximum ligament, d = 202nm and n avg can be determined by Gladstone and Dale’s law :27] and f a the fiber volume fraction (70%). n p is the refractive index of proteins and assumed 1.40 based on reference . Hence, according to Eq. (1), n avg = 1.58. Thus, λ max = 2 n avg d = 638 nm.
In comparison, we also use another method, the Prum and Torres’ 2D Fourier tool , to model the ligament’s optical property. This tool is particularly effective in predicting the reflectance spectra of amorphous structures in biology. Its theoretical background has been described in detail elsewhere [9–11]. Briefly, this tool first Fourier transforms the refractive index profile n(x, y) of a structure (indicated by the pixel intensity of the SEM image) into its Fourier components with various amplitudes A i and spatial frequencies k i. Then, the reflectance peaks λ i can be predicted by Bragg’s scattering condition: λ i = 2 n avg / k i with their relative intensities proportional to A i. For L. maximum ligament, given n a = 1.65 and n p = 1.40, we get the predicted reflectance spectrum shown in Fig. 6(b). The predicted λ max is 650nm.
Compared with the measured peak value (656nm), the Bragg predicted λ max (638nm) and Fourer predicted λ max (650nm) show good agreement with an error of 2.7% and 0.9%, respectively. The Bragg predicted λ max is subject to a slightly larger error than Fourier, probably resulting from the Bragg method neglecting the influence of aragonite shapes on λ max. In addition, it is worth noting that the measured reflectance spectrum [Fig. 6(a)] is broader with a full width at half maximum (FWHW) of ca. 440nm than the Fourier predicted [Fig. 6(b)] with a FWHW of ca. 200nm. This is probably due to that the measured surface is the ligament’s broken surface, which is not quite flat and causes some unwanted light to diffuse into spectrometer. In short, although both above methods are subject to error, both accurately predict the color of L. maximum ligament.
As the structural colors in bivalve ligaments are not visible in vivo and can only been seen on ligament’s broken surfaces, this perhaps is the reason why these colors stay unnoticed for a long time. For the first time, we described the nanostructure and structural colors in the ligament of L. maximum. We confirmed that this ligament contains a 2D APS which results a golden structural color by Bragg scattering.
The ligaments are characteristic of bivalve animals of at least 10,000 species . Their common property is that they consist of parallel aragonite fibers embedded in a protein matrix. No exception is the ligament of L. maximum in this work. Despite this similarity, however, the bivalve ligaments are species-specific, especially in their fiber diameters. Up to date, the reported fiber diameters in 24 species range in 65nm-222nm [13,14,17,18]. Among these, the fiber diameter in L. maximum (194nm) is the second largest, only smaller than that in Callista erycina (222nm), while Crassostrea rivularis (65nm) is the smallest. This suggests that the bivalve ligaments may be a natural big repository of 2D APSs that wait to be revealed.
In addition, the bivalve ligaments are easily available in nature since they are a waste product from aquaculture. Moreover, they contain inorganic aragonite crystals, allowing them to have high thermal and structural stability. Therefore, they offer a very cheap but strong template for designing and fabricating 2D APSs. In our team, this work is in progress.
Although this work provides solid evidence that the ligament of L. maximum contains a 2D APS, our understanding of its coloration mechanisms is still at an early stage. Such as, the L. maximum ligament has position-related structural colors, of which the blue to green color in its inner edge needs further works. Additionally, although the simple numerical analysis used is enough to explain our experimental results, more rigorous electromagnetic methods such as FDTD [29,30] and multiple scattering methods  are required to model the ligament optical properties. Further, the bivalve ligament is a dynamic structure which constantly undergoes successive compression-decompression cycles with the movement of two shell valves, but if this mechanical process affects the ligament structural colors is unknown.
We appreciate the financial support of the National Natural Science Foundation of China (Grant No. 40772033).
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