Dynamics of Wormlike Chains

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- 

Problem 3.29 Use the general formula, Eq. 3.55, to calculate the hydrodynamic radius of a rodlike molecule with length L and diameter b. The average between two beads at x and y on the rod measured from one of the ends is calculated only for jc - y 6. 

This rough method gives the same result as Eq. 3.256 to the leading order. 

Problem 330 The Legendre polynomial P z) satisfies the following differential equation  

Solution 3.30 Using the integral by parts leads to d(P,(cos0)) 

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This book offers a detailed explanation on conformation and dynamics of wormlike chains and helical wormhke chains by an expert of the model. 

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