Polymers of Different Geometry

The aa-component of the preaveraged Oseen tensor for the star polymer is given by Zimm and Kiib as follows  

No attempt has been made to treat excluded volume for branched polymers. 

Ring Polymers. The translational friction coefficient and the intrinsic viscosity for ring polymers were calculated by Fukatsu and Kurata (50-52) and by Tanaka and Yamakawa (53). These calculations treat the excluded volume effect in the form of perturbation. Those of Fukatsu and Kurata give results for twisted or multiple rings in addition to those for single rings. 

A theory for the dynamic properties of ring polymers was proposed by Bloomfield and Zimm (54). This theory is another application of the method of the original Zimm theory (29) to a different geometry. Therefore, Eq. (2.1)—(2.10) are used again with a slight modification. Suppose the ring model consists of (N +1) beads. The (1, l)-element 

Since Eq. (2.34) gives a radius of gyration in conflict with the result of the perturbation theory for e 0, Yu and Fujita (55) solved the problem with an expression for R different from that of Eq. (2.34). However, their expression for R is not well-defined as revealed very recently (53). 

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