The Persistence Length

The characteristic ratio as well as the hindrance parameter is a measure for the rigidity of the polymer chain. However, both values are not suitable to compare the rigidity of different chain types, since Eqs. (8.15) and (8.18) both need an additional 

Polyethylene chain Amylosic chain Cellulosic chain Gutta-percha (trans polydiene) Natural rubber (cfs polydiene) Polypeptide 

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If the persistence length Ip is much larger than the mean chain diameter, d, Yamakawa and Fujii gave limiting values for ai = - ln(d/2Ip) and = 0.1382. Freire and Garcia de la Torre [122] have considered further these coefficients. The factor 2Ip appears rather than Ip simply because 2Ip is equivalent to the statistical Kuhn segment length... 

The worm like chain behaviour of the pectins is developped allowing to predict the dimensions of the chain as soon as the persistence length is known. The experimental data are compared with the theoretical prediction obtained from conformational analysis. 

From disaccharide analysis, few authors predict the conformation of the poly a-D galacturonan as well as the role of the charge density [35,36] they determine the persistence length Ip that will allow us to explain the behaviour in solution. 

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

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-... 

With the aim to establish an [rj]-M relation (Equation (36)) for universal calibration and for the determination of the persistence length, intrinsic viscosities were measured with an Ubbelohde capillary viscometer. The respective data are also included in Table 3. 

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

Geometrical and flexibility data pertaining to the same polymers are also given in Table 1, namely the persistence length and the average chain-to-chain interaxial distance D. The first five polymers in Table 1 have D values smaller than 6 A, unlike all the following polymers (i.e., no. 6 to 19 in Table 1, Class II). This is a consequence of the relatively bulky substituents carried by Class II polymer chains. For some of the polymers in Table 1 the C0o and P literature values are widely scattered or unavailable. In those cases lower-limit values of P from experimentally determined geometrical parameters, are predicted from our model by suitable interpolation and reported within parentheses. 

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. 

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

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