Length scales hierarchical

IPEC or hydrogen-bonded complexes may form not only between mutually interacting polymer blocks but also between a polymer block and low-MW molecules. Complexes between surfactants and block copolymers have been investigated for the formation of micelles. As illustrated by the work of Ikkala and coworkers [313], one of the major interests of these systems is that they combine two different-length scales of supramolecular organizations, i.e., the nanometer-scale organization of the (liquid) crystalline surfactant molecules and the ten-nanometer scale relative to block copolymers. This gives rise to the so-called hierarchical systems. The field of (block)... 

In terms of cyclic plasticity, Shenoy et al. [139, 140], Wang et al. [137], and McDowell [141] performed hierarchical multiscale modeling of Ni-based superalloys employing internal state variable theory. Fan et al. [142] performed a hierarchical multiscale modeling strategy for three length scales. 

The earliest works of trying to model different length scales of damage in composites were probably those of Halpin [235, 236] and Hahn and Tsai [237]. In these models, they tried to deal with polymer cracking, fiber breakage, and interface debonding between the fiber and polymer matrix, and delamination between ply layers. Each of these different failure modes was represented by a length scale failure criterion formulated within a continuum. As such, this was an early form of a hierarchical multiscale method. Later, Halpin and Kardos [238] described the relations of the Halpin-Tsai equations with that of self-consistent methods and the micromechanics of Hill [29],... 

Bones are highly complex biomaterials with multi-hierarchical levels of structure of different length scales ranging from 1 nm to > 1 mm. Solid-state NMR is well suited to characterize the most fundamental structural... 

Figure 3.5.13 (A) Equilibrium times for diffusion on macroscopic (1 mm) and nanoscopic (10 nm) length scales. (B) Illustration of ionic and electronic wiring, with hierarchical porosity as Li+ distribution network and a carbon second-phase e- distribution network. Reprinted from [58] with permission, copyright 2007 John Wiley Sons.

So far, we have discussed various self-assembly and templating mechanisms geared towards the synthesis of porous, ordered materials at different length scales. As was mentioned previously, hierarchically ordered materials that simultaneously exhibit order over all length scales are very attractive novel additions whose synthesis usually requires a combination of all of the techniques mentioned previously. Patterning of mesopores and macropores simultaneously achieves structures with order on several length scales. 

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