Persistent worm-like chain model

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... 

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. 

Since the extension of the neck-linker made of 15-amino acids can be obtained from the simulation (contour length L = 5.7 nm, extension x = 3.1 0.8 nm), with a proper range of persistence length for the polypeptide chain (/p = 0.4-1. Onm) [40,41,56] one can estimate the internal tension on the neck-linker as/= 7-15pN by using the force-extension (/- x) relation of the worm-like chain model [44]) ... 

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 ... 

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... 

Nordmeier and Dauwe [282] reported static light scattering experiments on polystyrene sulphonate at 0.005 m c 2 m and analyzed the data by a worm-like chain model. The resulting total apparent persistence length is compared to the data of [210] in Fig. 18. The agreement is quite poor, and the data of [282] do not follow at all the scaling-law (solid line in Fig. 18). 

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... 

In main-chain LCPs, molecular flexibility can be distributed more-or-less uniformly along the chain, as is the case for PBLG, HPC, or Vectra A, or it can be concentrated in flexible spacers, as in OQO(phenylsulfonyl)lU (see Fig. 11-2). The former are called persistently flexible molecules, and are often modeled by the worm-like chain, with a uniform bending modulus, while for the latter, a reasonable model might be the freely jointed chain (see Fig. 11-3 and Section 2.2.3.2). For a recent discussion of the phase behavior and dynamics of worm-like chains, see Sato and Teramoto (1996). 

Flory, P. J., Statistical Mechanics of Chain Molecules, Hanser Publisher, New York (1989). To express the stiffness of a chain, the worm-like chain is a useful model, which is characterized by two parameters the persistence length Ip and the contour length L. In the limit of L/lp —> oo, the Kuhn segment length as defined by Eq. (1.32) is twice the persistence length. 

The worm-like chain has proved to be an appropriate model for studying the conformational characteristics of chitosan. Considering that the persistence length is a parameter that characterizes the stiffness of a worm-like chain, many authors have evaluated it with conflicting results [38, 76, 78], denoting that many factors influence its experimental determination. 

Shape persistence as a basis for controllable function is one of the main features of proteins that serve as mechanical support for cofactors (e.g., chromophores in light harvesting complexes), transmit mechanical force (e.g., in muscles), or function as nanoscopic pumps in active transport of substrates through cell membranes. Transfer of this concept to the realm of functional materials is a rather recent development and the term shape persistence for synthetic macromolecules is often used with the loose meaning of relatively rigid compared to most synthetic polymers. For linear polymers, shape persistence can be quantified by the persistence length Lp if one assumes that residual flexibility conforms to the worm-like chain (WLC) model. This assumption has been rarely tested and for many synthetic polymers Lp is either unknown or known with rather limited precision. 

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