## 3 Fibrous Structures
### Silk  
Silk is another important fibrous structure of biological origin, the SAXS patterns of which have been investigated in detail. The hierarchical structure of a silk fiber from a silkworm (_B. mori_) is shown in Figure 8a. The basic building block of this structure is a polypeptide chain. As the silkworm extrudes the silk solution from its salivary glands through its spinneret, the shear flow causes the hydrophilic regions to form random coils and \(\alpha\)-helices, while the hydrophobic regions form \(\beta\)-sheets. These alternating amorphous (random coils and \(\alpha\)-helices) and crystalline (\(\beta\)-sheets) phases form \(\sim\)3 nm nanofibrils. Hydrogen bonds between \(\beta\)-sheets and random coils result in a more ordered structure; in earlier models, \(\beta\)-sheets were thought of as cross-linkers connecting neighboring nanofibrils. As multiple nanofibrils combine, they form a 20-100 nm silk fibril, which then bundles into a \(\sim\)10-\(\upmu\)m diameter fibroin filament. Within the molecular chain, nanofibrils, and fibrils, there are globular protrusions that increase the silk's mechanical strength [94]. Figure 7: (**a**) Hierarchical structure of feathers, starting with keratin, the basic structural unit, to the nano- and micro-structures, and finally, the macroscopic feather; reprinted from [PERSON] (2023) [89] with permission from [PERSON]. (**b**) Schematic of the SAXS diffraction patterns from (**i**) rudimentary, (**ii**) channel-type, and (**iii**) sphere-types of feathers. Adapted from [PERSON] et al. (2012) [91]. (**c**) Kratky plot of SAXS feather. Red curve is the azimuthal average of I(\(q\)) to \(q_{\text{max}}\), and the blue curve is fitted to smaller values of \(q\) to reduce scattering from the beam block. The black curve is the optical scattering for \(\theta=10^{\circ}\). Inset is the SAXS diffraction pattern of a feather; reprinted from [PERSON] et al. (2010) [92] with permission from American Physical Society. One example of the SAXS diffraction pattern from dry spider silk is shown in Figure 8b (i). The strong equatorial streak in the pattern (perpendicular to the fiber) arises from fiber surfaces and oriented voids that are invariably present in fibers. However, there is structural information in the equatorial streak related to the lateral organization and orientation of the fibrils [35,96]. The weak, meridional reflections with a spacing of 8.34 nm correspond to the disordered regions (alternating crystalline \(\beta\)-polyalanine and amorphous regions) of the fiber. When hydrated, as the fiber shrinks and the lamellar spacing decreases to 5.86 nm (compression of the crystalline and amorphous regions), a new reflection on the equator appears, corresponding to a new periodic structure (Figure 8b (ii)). The central streak becomes diffuse due to the increased disorder. After drying, as shown in Figure 8b (iii), the strong, equatorial reflection disappears, confirming that water is responsible for the new equatorial reflection. In contrast, when the fiber is hydrated while held stretched, the lamellar peak becomes more prominent without shifting (Figure 8b (iv)). The equatorial streak becomes intense and extends to higher scattering angles as a result of increased tension. Unlike in Figure 8b (ii), the new equatorial reflection is less prominent, suggesting a different structure is present under tension. When a fiber relaxes while wet, Figure 8b (v) shows the equatorial streak broadening, indicating disordering. The lamellar reflections remain unchanged [35]. A second example of silk's SAXS pattern shown in Figure 8c (i) is from bagworm silk, _Eumeta variegate_. A Kratky plot of the data, as shown in Figure 8c (ii), better delineates the peaks in the diffraction scan. The meridional peaks are associated with alternating sections of crystalline and amorphous regions with a periodicity of -40 nm (red, meridional plot).