Shape persistence length

For worm-shaped entities we will not determine the extension, but only the persistence length of the entities (cf. p. 165). 

Since Robinson [1] discovered cholesteric liquid-crystal phases in concentrated a-helical polypeptide solutions, lyotropic liquid crystallinity has been reported for such polymers as aromatic polyamides, heterocyclic polymers, DNA, cellulose and its derivatives, and some helical polysaccharides. These polymers have a structural feature in common, which is elongated (or asymmetric) shape or chain stiffness characterized by a relatively large persistence length. The minimum persistence length required for lyotropic liquid crystallinity is several nanometers1. 

The most comprehensive studies on shape-persistent Hekates have been performed on stilbenoid star-shaped molecules. Structures and mesomorphic properties are collected in Table 1. Core building blocks with only one repeating unit per arm and one flexible chain 26a,b, 28a-d, 30a did not show any liquid crystal properties [56-58]. In the series of two chain derivatives 28e, 30b,c the formation of meso-phases depend on the core [57-59]. The electron deficient triazine and the dicyanopyridine building block induced obviously columnar mesophases. The pyridine derivative 30b showed only a crystalline phase [58]. In the series of nine chain stars 26c-g [60-62] and 28f-n [57], the compounds formed columnar phases depending on the chain length of the peripheral chains. Propyloxy chains are too short but hexyloxy and dodecyloxy chains are sufficient for the formation of liquid crystal phases by nanosegregation [60-62]. This can be rationalised by a dense... 

As expected, the amount of shape-persistent macrocycle in the crude reaction product depends strongly on the length of the covalent tether (Scheme 6.15)... 

Although pure aliphatic compounds with a high persistent length are known, as for example [njstaffanes, shape-persistent macrocyclic compounds are dominated by structures with an aromatic backbone. 

Jones (1996) recommended a holistic approach to fat replacement, whereby the spherical shape of a fat droplet as well as the properties of a fat are mimicked by using hydrophobic compounds. Accordingly, the least amphiphilic saccharides with the shortest persistence lengths, e.g., pectin and the cellulose derivatives (Lapasin and Pricl, 1995), are suitable models. By their nature, the intermediate DP saccharides fulfil the requirement. 

Another striking experimental feature is that the attractions do not appear to lead to macroscopic phase separation. In this sense, the counterion-mediated attraction between the chains appears to have a different character from ordinary attractions that lead simply to phase separation at sufficiently high concentrations. Instead, the chains tend to form dense bundles of a fairly well-defined thickness [8,11]. The precise morphology of the bundles appears to depend sensitively on the persistence length of the polyelectrolyte, the chain length, and the concentration. In the case of dilute DNA, the bundles tend to be toroidal or rod-shaped. Other stiff polyelectrolytes tend to form rodlike bundles or networks of bundles. In each case, however, there is a well-defined cross-sectional thickness for the bundles. We will concentrate on the question of why there is a characteristic cross-sectional bundle diameter, rather than on the specific morphology of the bundles. 

Structural descriptors at the secondary level (mesoscale) are topology and domain size of polymeric aggregates (persistence lengths and radius), effective length and density of charged polymer sidechains on the surface, properties of the solution phase (percolation thresholds and critical exponents, water structure, proton distribution, proton mobility and water transport parameters). Moreover, -point correlation fimctions could be defined that statistically describe the structme, containing information about surface areas of interfaces, orientations, sizes, shapes and spatial distributions of the phase domains and their connectivity [65]. These properties could be... 

---