Intrinsic viscosity of polymers: From linear chains to dendrimers

We present a simple theory for the intrinsic viscosity of polymers of arbitrary architectures, based on a partially permeable sphere model. The model introduces two phenomenological functions, the drainage function κ(r) and the drag function ξ(r), which are determined by the density profile, as a mean-field description of the multi-body, long-range and accumulated effects of the hydrodynamic interactions. By combining Debye's theory for free draining polymer chains with Einstein's theory for hard spheres, we arrive at a simple expression for the intrinsic viscosity. Results from our theory show broad agreement in all the key features of the intrinsic viscosity with existing experimental results for polymers ranging from linear chain to branched polymers to dendrimers.