Universal Scaling of Linear and Nonlinear Rheological Properties of Semidilute and Concentrated Polymer Solutions
2008-11-25T00:00:00Z (GMT) by
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/ce, where ce is the entanglement concentration, we show that for each value of c/ce below 2.0 rheological functions are successfully superimposed using de Gennes “blob” scaling laws for the concentration-dependent plateau modulus GN0, and the equilibration time τe,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” ϕs, 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 ϕs 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 ϕs 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.