Kratky worm chain model

From their light-scattering measurements Holtzer, Benoit, and Doty (126) concluded that the short-range interactions control the dimensions of cellulose nitrate chains, and they discussed their results in terms of the worm-like chain model of Kratky and Porod (142), obtaining a persistence length of about 34.7 A. In Fig. 21 these data are shown as a plot of (S yjMw against Mw. The open circles are the experimental points and the broken curve is that calculated from the equations for the worm-like chain model. The theoretical curve is claimed to reproduce the data to within the probable experimental error in all but two cases. 

The worm-like chain model (sometimes called the Kratky-Porod model) is a special case of the freely rotating chain model for very small values of the bond angle. This is a good model for very stiff polymers, such as double-stranded DNA for which the flexibility is due to fluctuations of the contour of the chain from a straight line rather than to trans-gauche bond rotations. For small values of the bond angle ( < 1), the cos 9 in Eq. (2.23) can be expanded about its value of unity at = 0 ... 

As discussed in Chapter 2, xanthan has a structure that is not quite a rigid rod since it has some degree of flexibility. This type of structure was described by Porod and Kratky as the worm-like chain model (Richards, 1980, p. 88). Although this may be visualised intuitively to be rather like a semi-flexible string of plastic pop-in beads, it requires the definition of the persistence length, /p, in order to develop the idea in a more quantitative way. This quantity is defined for an infinite polymer chain as follows ... 

The Kratky-Porod wormlike chain model [20,21] is widely used for describing conformational characteristics of less flexible chains. The polymer is viewed as a semi-flexible string (or worm) of overall contour length L with a continuous curvature. The chain is subdivided into N segments of length AL, which are linked at a supplementary angle r. The persistence length q (Fig. 1) is defined as... 

In 1984, Tricot [266] summarized viscosity results of various vinylic polyacids reported in literature, analyzed the data by the Kratky-Porod worm-like chain model and compared the results with the OSF theory and the theory of Fixman [251] and Le Bret [19]. At low ionic strength, the electrostatic persistence length approximately followed a scaling relation Ip (cf) in complete... 

The Kratky and Porod model is an extension of the freely rotating chain model in which the valence angles between two units are close to 180°. This confers to such chains a certain persistence which prevents them from behaving like a random coil such chains are semi-rigid and are also called worm-like. The persistence length (fl) is defined as... 

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 first model (Kuhn chain) is built up by planar segments of limited conjugation length which are separated by defects, e.g. cis double bonds. The second concept of a worm-like chain (Porod-Kratky chain) visualizes a continuous... 

The wormlike chain of Kratky and Porod [49K1] is characterized by a contour length L and a persistence length a. The latter increases with increasing stiffness, but is (on the basis of the model) independent of L. The relation between the radius of gyration and L for worm-like linear coils without excluded volume is[53Bl] ... 

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