Molecular Weight\nDetermination of Kuhn Monomers from\na Dynamic Property of Polymers

Dynamic rheological responses of polymer solutions exhibit\na range\nof dynamic modes reflecting the hierarchical structures with different\ncharacteristic lengths such as the Kuhn length and mesh size. The\npolymer contribution to the viscoelastic modulus at each dynamic mode\nis proportional to the number density of unit segments at the corresponding\nhierarchical level, allowing for the determination of their molecular\nweight. This paper evaluates the molecular weight of a Kuhn monomer\nfrom the boundary between the Zimm and bending modes, using a worm\nlike micellar solution of cetylpyridinium chloride/sodium salicylate\nas a model system. Employing high-frequency diffusing-wave spectroscopy\nmicrorheology, we determined the molecular weight, which agrees well\nwith that measured by static light scattering. We showed that the\nradius of the Kuhn monomer was also accurately estimated from the\ncharacteristic volume related with the molecular weight. The proposed\nmethod holds potential for application across various dynamic modes\nand polymer solutions.