Scaling behavior of the fractional Maxwell model parameters for semidilute entangled polymer solutions and its application for predicting linear viscoelastic properties

We report that the parameters of the fractional Maxwell model (FMM) for semidilute entangled polymer solutions can be superimposed onto master curves by applying the scaling rules of the correlation blob theory. The FMM is parametrized by four terms—the quasimoduli parameters V and G and their fractional exponents α and β, where 0 ≤ β < α ≤ 1. To test whether these quasiproperties exhibit a universal behavior, we compiled their values from dynamic shear rheology measurements and literature data for a model system of aqueous poly(ethylene oxide) (PEO) solutions at different concentrations c, and molecular weights M, spanning the concentration range c/ce = 1–16 and molecular weights from M = 300–8000 kDa. The shear rheology data span a broad range of Deborah numbers, capturing both viscous- and elastic-dominated response of the solutions. Here, ce is the solution entanglement concentration. When scaled by the theoretical Rouse modulus GRouse, and plotted against the reduced concentration c/ce, the values of V and G at various c and M, remarkably collapse onto a single curve, supporting the blob theory scaling. Similarly, values of α and β, at these conditions, also superpose onto master scaling curves when plotted versus c/ce. The hitherto unreported possibility to express FMM parameters as universal functions of reduced concentration, consistent with the classical scaling theory, asserts that, despite their fractional units and intermediate nature, they function as real rheological variables than just fitting constants. We then demonstrate that empirical relations derived from the master curves—G/GRouse,V/GRouse,α and β versus c/ce—provide a concise framework for predicting viscoelastic properties of PEO at arbitrary semidilute conditions. The predictions have been validated over different values of c/ce and M from the broad range defined above and have been shown to be credible over a four-decade extrapolated frequency range from 0.01 up to 500 rad/s. The possibility to render parameters of fractional models into scaling relations opens a route for generating rheological look-up charts for polymer solutions, which are elusive using conventional spring-dashpot models due to their larger parameter space.