Persistence length estimation

The persistence length of pectins, in condition of charge screening (O.IM NaCl) were estimated from data as in Figure 6. 

The crystalline lamellar thickness Dc obtained by StrobPs method is initially 1.4 nm and grows to about 2.0 nm, which is roughly equal to the crystallite size in the chain direction of 2.8 nm estimated from the wide-angle X-ray diffraction (WAXD) [7]. Interestingly, the persistence length /p = 1.45 nm just before crystallization measured by SANS (also see Fig. 11) [9,10] is almost equal to the crystal thickness. 

C. Bouchiat, M.D. Wang, J.-F. Allemand, T. Strick, S.M. Block, and V. Croquette Estimating the Persistence Length of a Worm-Like Chain Molecule from Force-Extension Measurements. Biophys. J. 76, 409 (1999). 

Equilibrium rigidity is conventionally expressed in terms of the persistence length q based on the wormlike chain model (Fig. 37). Three methods for estimating q have been adopted 67). 

Table 14. Persistence length of stiff and flexible polymers estimated by various methods67 ...

Theoretical calculations of dimensions of the chains of para-aromatic polyamides were made by Birshtein Persistence length was estimated within the limits of... 

Lower values were obtained when the presistence length was estimated by the beginning of a sharp kink on theqsp/c vs. c plot (c is the concentration). This kink indicates the overlapping of the rotation spheres of asymmetric particles. The persistence length for PBA was found to be equal to 180-240 A, and for PPTA, 150-180 A %... 

Valenti et al. noted a transition to the mesophase under the effect of the applied external field for those semirigid-chain polymers which do not exhibit the liquid crystalline transition under normal conditions. A moderately concentrated solution of polyterephthalamide of p-aminobenzylhydrazide (X-500) in dimethyl sulphoxide does not exhibit the transition into the liquid crystalline state, which can be explained by a relatively low axial ratio for the macromolecules. The persistence length for this polymer is estimated being equal to 50 A. At the same time, according to the data from the literature, high-modulus fibres have been obtained from the solutions of this polymer, which can be connected only with the appearance of the liquid crystalline state in the process of fibre formation. The authors of believe that this... 

Problem 2.4 Suppose a worm-like chain with diameter = 1.5 nm, persistence length kp = 100 nm, and length L = 20 nm is dissolved in a solvent. Estimate 02, the minimum volume fraction"of polymer needed to form a wholly nematic phase, it L is increased to 500 nm, and d and kp are kept the same, what is 02 ... 

Figure 11.2 Chemical structures of some well-studied LCPs. The top four structures are usually used as lyotropic polymers, and the bottom two are thermotropes. Estimates of the persistence lengths (Xp) and effective diameters (d) of these molecules are (Xp, d) = (12,1.04) nm for HPC, (90, 1.5) nm for PBLG. 129.0.6) nm for PPTA. (20.0.6) nm for PBZT. (12.0.6) nm for Vectra A. and (6.0.5) nm for OQO(phenylsulfonyl)10. These values, listed in Baek et al. (1994), Brelsford and Krigbaum (1991), and Farmer et al. (1993), are both solvent- and temperature-dependent, and thus should be used with caution. (From Donald and Windle 1992, with permission from Cambridge University Press.)...

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