Polymer concentration regimes from fractional microrheology

In this work, a framework for deriving theoretical equations for mean squared displacement (MSD) and fractional Fokker–Planck is developed for any arbitrary rheological model. The obtained general results are then specified for different fractional rheological models. To test the novel equations extracted from our framework and bridge the gap between microrheology and fractional rheological models, microrheology of polystyrene in tetrahydrofuran solutions at several polymer concentrations is measured. By comparing the experimental and theoretical MSDs, we find the fractional rheological parameters and demonstrate for the first time that the polymer concentration regimes can be distinguished using the fractional exponent and relaxation time data because of the existence of a distinct behavior in each regime. We suggest simple approximations for the critical overlap concentration and the shear viscosity of viscoelastic liquidlike solutions. This work provides a more sensitive approach for distinguishing different polymer concentration regimes and measuring the critical overlap concentration and shear viscosity of polymeric solutions, which is useful when conventional rheological characterization methods are unreliable due to the volatility and low viscosity of the samples.