Persistence length stiff chain polymers

Table 1. Persistence length q and molar mass per unit contour length ML for liquid-crystalline stiff-chain polymers...

RIS theory provides a relatively simle formalism for the evaluation of the persistence vector, a, for a chain that can be represented by a repeating sequence of independent virtual bonds such as polybenzobisoxazole (PBOI and polybenzobisthiazole IPBT). The present study combines RIS theory with long molecular dynamics simulations for small fragments in order to evaluate the limiting length of a for very stiff chains. The approach can be applied to other stiff chain polymers. 

As with flexible chains, most studies of conformational behavior of stiff chains have involved light scattering and intrinsic viscosity studies of dilute polymer solutions. Excluded volume effects are of much diminished significance for stififer chains, so measured persistence lengths usually show only a mild dependence on the nature of the solvent. In fact, Norisuye and Fujita [72] have shown that excluded volume effects become measurable only when chains are very long (L 100 q). Thus, the choice of solvent is normally of less importance in studying the conformation of stiff chains than it is for flexible ones. Temperature, however, frequently has a pronounced impact on the value of q for stiff chain polymers [73]. 

Table 3. Persistence lengths of some stiff chain polymers...

As discussed in the last 3 years, polysaccharides behave in solution under a worm like chain [26] the local stiffness of the chain is characterized by a persistance length (Ip) the larger Ip is, the larger the chain deviates from the gaussian behaviour in the usual molecular weight range of these natural polymers [27], This makes difficult to use the relations given in litterature for synthetic... 

The analysis described above is useful for modelling colligative properties but does not address polyelectrolyte conformations. Polyelectrolyte conformations in dilute solution have been calculated using the worm-like chain model [103,104], Here, the polymer conformation is characterized by a persistence length (a measure of the local chain stiffness) [96]. One consequence of the... 

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. 

N is the number of skeletal bonds in one chain and k is the Boltzmann constant while b is the mean skeletal bond. The mean square end-to-end distance, Nb2, is also referred to as the square of the Gaussian correlation length between the chain ends, o(N) it reflects the effect of linkage of chemical units. The previous relationship between the force f and the extension r is extended to any real chain submitted to a small elongation provided the correlation length, o(N), includes the stiffness property of the polymer o(N)2= A.KNb2 XK is referred to as a persistence length. The related reduction of entropy is expressed as ... 

This result may be compared with Eq. (9.7), from which it follows that the persistence length is equal to half the length of a statistical chain element or Kuhn length ap = i A. This representation of the wormlike chain is of particular importance for the description of stiff polymers. 

The relatively small region of allowable values of tp and j/ in polysaccharides linked between rings makes the wormlike chain model realistic for them. The polymer behaves as a random flight one over contour lengths S Lp, but as a stiff rod if S Lp. Persistence lengths can be fairly large 350 50 A for xanthan gum, 80-100 A for alginate or hyaluronate. ... 

Some important properties of polymer chains in dilute solutions [steric hindrance parameter, characteristic ratio, persistence length, radius of gyration, statistical chain segment length (introduced earlier, in Chapter 11), intrinsic viscosity, and viscosity at small but finite concentrations] will be discussed, and new correlations will be presented for the steric hindrance parameter and the molar stiffness function, in Chapter 12. 

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