Calibration of Polymer Molecular Weight Using Solution Viscosity in Dilute and Semidilute Solutions

Molecular weight characterization is at the heart of modern polymer science. It relies on size-exclusion chromatography utilizing an extreme dilution of polymer fractions. Here, we present a general framework for obtaining the weight-average molecular weights of linear polymers in a broad concentration range from solution viscosity. In the dilute solution regime (c < c^*), the approach is based on the representation of solution-specific viscosity η_sp as a universal function of chain overlap concentration c* in good and θ-solvents. This approach is extended to the unentangled (Rouse) semidilute solution regime (c ≥ c^*), where we use the linear relationship between specific viscosity and number of correlation blobs per chain, η_sp(c) = N_w/g(c), where N_w is the weight-average degree of polymerization. This analysis defines a set of calibration curves for which the weight-average molecular weight can be determined from a single measurement of specific viscosity without the need for dilution.