Scaling of nanoparticle retardation in semi-dilute polymer solutions

We analyze the scaling law for the polymer-induced retardation a nanoparticle experiences as it moves through a semi-dilute polymer solution. The translational friction is calculated from a modified Stokes flow using a local viscosity near the nanosphere. The results rationalize a general retardation factor, R = exp(Ka^μc^ν) [T. Odijk, Biophys. J., 2000, 79, 2314], revealing scaling exponents μ = 0.77 and ν = 1, which are in agreement with experiment. We find that rotational motion also has a self-similar behavior and R can be described too by a stretched exponential with slightly different exponents.