Coils persistence length

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

A polymer coil does not only possess a structure on the atomistic scale of a few A, corresponding to the length of covalent bonds and interatomic distances characteristic of macromolecules are coils that more or less, obey Gaussian statistics and have a diameter of the order of hundreds of A (Fig. 1.2) [17]. Structures of intermediate length scales also occur e. g., characterized by the persistence length. For a simulation of a polymer melt, one should consider a box that contains many such chains that interpenetrate each other, i. e., a box with a linear dimension of several hundred A or more, in order to ensure that no artefacts occur attributable to the finite size of the simulation box or the periodic boundary conditions at the surfaces of the box. This ne-... 

Region I here the molecular chains partly assume helical (stiff) conformation from random coils where the persistence length gradually increases. 

The (bending) persistence length of DNA, which is proportional to its bending rigidity, has been extensively studied for well over two decades, usually via its effect on the overall dimensions of the DNA coil. This work... 

Finally, it should be mentioned that an interesting interpretation of the third eq. (5.4) is obtained by introducing the model of the worm-like chain, as developed by Kratky and Porod (153, 154). As is well-known the characteristic quantity of this model is the persistence length, i.e. the projection of the end-to-end distance of an infinitely long coiled worm... 

The potential for novel phase behaviour in rod-coil block copolymers is illustrated by the recent work of Thomas and co-workers on poly(hexyl iso-cyanate)(PHIC)-PS rod-coil diblock copolymers (Chen etal. 1996). PHIC, which adopts a helical conformation in the solid state, has a long persistence length (50-60 A) (Bur and Fetters 1976) and can form lyotropic liquid crystal phases in solution (Aharoni 1980). The polymer studied by Thomas and co-workers has a short PS block attached to a long PHIC block. A number of morphologies were reported—wavy lamellar, zigzag and arrowhead structures—where the rod block is tilted with respect to the layers, and there are different alternations of tilt between domains (Chen et al. 1996) (Fig. 2.37). These structures are analogous to tilted smectic thermotropic liquid crystalline phases (Chen et al. 1996). 

The last relation shows that a long macromolecule rolls up into a coil at high temperatures. The smaller the elasticity coefficient a is, the more it coils up. Another name for the model of flexible thread is the model of persistence length or the Kratky-Porod model. The quantity a/T is called the persistence length (Birshtein and Ptitsyn 1966). 

The anisotropy of the coil has been calculated for other models of the macromolecule. Expressions for the anisotropy coefficient are known in the case where the macromolecule has been represented schematically by a continuous thread (the persistence length model) (Gotlib 1964 Zgaevskii and Pokrovskii 1970) and also in the case where the microstructure of the macromolecules has been specified. In the latter case, the anisotropy coefficient of the macromolecule is expressed in terms of the bond polarisabilities and other microcharacteristics of the macromolecule (Flory 1969). 

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