Molecular Weight Determination of Kuhn Monomers from a Dynamic Property of Polymers

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