Yamakawa cylinder model

Worm-like chain statistics have been used by Eizner and Pti-tsyn ( ) for a bead model, and by Yamakawa and Fuji (11) for a cylinder model to calculate [Tj] as a function of p, L and the chain diameter d. Their results can be put in the form ([1]] in dl/g). 

For example, estimates for ItiIr given by Yamakawa and Fuji with a wormlike cylinder model and Elzner and Ptitsyn for a wormlike chain of beads are shown in Fig. 4. For a rodlike chain (small d/p) the relation for [r ] can be approximated by the equation... 

Finally, some rather recent devdopments must be noted. Several years ago, Yamakawa and co-workers [25-27] developed the wormlike continuous cylinder model. This approach models the polymer as a continuous cylinder of hydrodynamic diameter d, contour length L, and persistence length q (or Kuhn length / ). The axis of the cylinder conforms to wormlike chain statistics. More recently, Yamakawa and co-workers [28] have developed the helical wormlike chain model. This is a more complicated and detailed model, which requires a total of five chain parameters to be evaluated as compared to only two, q and L, for the wormlike chain model and three for a wormlike cylinder. Conversely, the helical wormlike chain model allows a more rigorous description of properties, and especially of local dynamics of semi-flexible chains. In large part due to the complexity of this model, it has not yet gained widespread use among experimentalists. Yamakawa and co-workers [29-31] have interpreted experimental data for several polymers in terms of this model. 

The Yamakawa-Fujii wormlike cylinder model [25,26] has been widely used for estimation of I (or q) of stiff chain materials from intrinsic viscosities. This approach is based on the equation... 

The most important of recent theoretical studies on semi-flexible polymers is probably the formulation of Yamakawa and Fuji [2,3] for the steady transport coefficients of the wormlike cylinder. This hydrodynamic model, depicted in Figure 5-2, is a smooth cylinder whose centroid obeys the statistics of wormlike chains. In the figure, r denotes the normal radius vector drawn from a contour... 

A wormlike chain is specified by the persistence length A and the contour length Lp. However, it does not have a thickness. We need to give it a diameter b for the chain to have a finite diffusion coefficient. The model is called a wormlike cylinder (Fig. 3.62). The expressions for the center-of-mass diffusion coefficient and the intrinsic viscosity were derived by Yamakawa et al. in the rigid-rod asymptote and the flexible-chain asymptote in a series of h/A and A/A-... 

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