Universal Scaling of Linear and Nonlinear Rheological Properties of Semidilute and Concentrated Polymer Solutions

Using oscillatory and steady-shear rheometry on polystyrene (PS) solutions in tricresyl phosphate (TCP) with three nearly monodisperse molecular weights at six values of the reduced concentration c/c_e, where c_e is the entanglement concentration, we show that for each value of c/c_e below 2.0 rheological functions are successfully superimposed using de Gennes “blob” scaling laws for the concentration-dependent plateau modulus G_N⁰, and the equilibration time τ_e,scaling using the literature value of the solvent-quality exponent ν = 0.53 (Solomon, M. J.; Muller, S. J. J. Polym. Sci., Polym. Phys. 1996, 334, 181−192). However, once the polymer volume fraction exceeds the “swelling volume fraction” ϕ_s, above which the polymer takes a random walk configuration on all length scales even in a good solvent, this universal scaling breaks down and the polymer conformation appears to be governed by Colby−Rubinstein’s scaling laws for Θ solutions. We estimate that all polybutadiene solutions in phenyl octane (a good solvent) from Colby et al. (Macromolecules 1991, 24, 3873−3882) are above ϕ_s and can be scaled using Θ solvent scaling laws for concentrations ranging all the way up to the melt, showing that the rheological properties of melts and solutions above ϕ_s follow the same universal behavior. In general, using the “blob” model for semidilute solutions and the Colby−Rubinstein scaling for concentrated solutions collapses linear and nonlinear rheological properties for polymer solutions onto universal curves.