Hydrodynamic Radius of a Polymer Chain

2 Hydrodynamic Radius of a Polymer Chain For a linear chain molecule, 

When all of the N monomers in the polymer chain move, each monomer receives a friction from the solvent. The overall friction, however, is not proportional to N but rather is proportional to iW. Because v 1, W The friction of the 

Oseen found that the magnitude of the hydrodynamic interaction between two particles at r and r is proportional to r - r The interaction decays only algebraically with a small exponent of -1 and therefore is long ranged. In a chain molecule, all monomers affect aU other monomers because they are close to each other. 

In Section 3.4.6, we will leant that 1// h of the chain molecule is given as the average of the reciprocal of the distance between two monomers on the chain  

The average is taken with respect to possible positions of the two monomers m and n(m n) and then with respect to m and n that run over aU monomers of the chain. 

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