Hierarchical parallel orientation

Mechanical Properties. Although wool has a compHcated hierarchical stmcture (see Fig. 1), the mechanical properties of the fiber are largely understood in terms of a two-phase composite model (27—29). In these models, water-impenetrable crystalline regions (generally associated with the intermediate filaments) oriented parallel to the fiber axis are embedded in a water-sensitive matrix to form a semicrystalline biopolymer. The parallel arrangement of these filaments produces a fiber that is highly anisotropic. Whereas the longitudinal modulus of the fiber decreases by a factor of 3 from dry to wet, the torsional modulus, a measure of the matrix stiffness, decreases by a factor of 10 (30). 

Figure 4.9 Model for the hierarchical selforganization of A-l. (a) E forms tapes comprising two covalently linked single parallel P-sheet domains with opposite orientation, (b) F-l aggregate into more flexible and less stable single antiparallel P-sheet tapes, (c) Tapes obtained by parallel P-sheet formation from A-D are polar...

Fig. 1 Hierarchical assembly of nanofibrillar hydrogels. Individual molecules organize into nanofibrils, which subsequently associate and/or entangle to form a 3D water-swollen network. Biopolymer molecules are often oriented parallel to the long axis of the nanofibril, whereas synthetic polymer chains are oriented perpendicularly to the main axis. Gelation can be triggered by changes in temperature and pH, an increase in polymer concentration, or an increase in ionic strength of the polymer solution, to name a few...

To form helicoids, each individual nano-fibril is arranged parallel to another one in stacked planes. From plane to plane, the orientation of the fibrils changes by a few degrees to obtain the helicoidal structure. While in many instances the dimensions of such helicoidal structures are not on the right length-scale to produce structural colour, there are many examples where such hierarchical structures provide a vivid and strong iridescent colouration. 

Fig. 9.16. Hierarchical structure of adult human bone. Tropocollagen molecules are arranged in a so-called quarter-stagger structure, with platelets of hydroxy apatite in between. The fibres formed by this structure unite to fibre bundles which in turn form lamellae. The major part of the bone consists of osteons made of ring-shaped lamellae. Near the bone s surface, the lamellae are parallel to the surface. The orientation of the fibre bundles within the lamellae depends on the mechanical loads on the bone in tensile regions, they are ahgned in the loading direction as shown in the figure, in compressive regions, the fibre bundles of some lamellae are perpendicular to the loading direction...

In conclusion, the hierarchical structures in the swollen pellicles are composed of (1) the dendritic network (Figure 12 (b-1)) composed of the percolated bundles with mass fractal dimension of Dm = 2.5 and the upper and lower cutoff lengths of Ls4 30pm and Ls3 2pm, respectively (2) the bundles in turn are composed of the ribbons with Dm =1.0 and the upper and lower cutoff lengths of 1 3 2 pm and Ls2 600nm, respectively (3) the ribbons are further composed of the mass fractally arranged MFs oriented parallel to the ribbon axis with the lateral mass fractal dimension Dmj.= 1.35 and the upper and lower cutoff lengths of Ls2 600 nm and Lsi 6 nm, respectively. 

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