Scaling Equation for Viscosity of Polymer Mixtures in Solutions with Application to Diffusion of Molecular Probes

We measured macroscopic viscosity as well as nanoviscosity experienced by molecular probes diffusing in solutions containing two polymer species vastly differing in the molecular weight. On this basis we postulated a scaling equation for viscosity of complex liquids characterized by two distinct length-scales. As an experimental model, we used aqueous solutions of low-polydispersity poly(ethylene glycol) and poly(ethylene oxide) with molecular weight ranging from 6 to 1000 kg/mol, polymer concentrations from 0.25% up to 50%, and viscosity up to 500 mPa·s. The proposed model distinguishes between the contributions to the total viscosity stemming from the mesoscopic structure of the complex liquid and from the magnitude of interactions dictated by the chemical nature of its constituents. It allows to predict diffusion rates of nanoscaled probes in polymer solution mixtures and can be adapted to various multilength-scale complex systems.