Disentangling Nano- and Macroscopic Viscosities of Aqueous Polymer Solutions Using a Fluorescent Molecular Rotor

The macroscopic viscosity of polymer solutions in general differs strongly from the viscosity at the nanometer scale, and the relation between the two can be complicated. To investigate this relation, we use a fluorescent molecular rotor that probes the local viscosity of its molecular environment. For a range of chain lengths and concentrations, the dependence of the fluorescence on the macroscopic viscosity is well described by the classical Förster-Hoffmann (FH) equation, but the value of the FH exponent depends on the polymer chain length. We show that all data can be collapsed onto a master curve by plotting the fluorescence versus polymer concentration, which we explain in terms of the characteristic mesh size of the polymer solution. Using known scaling laws for polymers then allows us to quantitatively explain the relation between the FH exponent and the polymer chain length, allowing us to link the nano- to the macroviscosity.