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

2008-11-25T00:00:00Z (GMT) by Youngsuk Heo Ronald G. Larson
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 <i>c</i>/<i>c</i><sub>e</sub>, where <i>c</i><sub>e</sub> is the entanglement concentration, we show that for each value of <i>c</i>/<i>c</i><sub>e</sub> below 2.0 rheological functions are successfully superimposed using de Gennes “blob” scaling laws for the concentration-dependent plateau modulus <i>G</i><sub><i>N</i></sub><sup>0</sup>, and the equilibration time τ<sub>e,scaling</sub> using the literature value of the solvent-quality exponent ν = 0.53 (Solomon, M. J.; Muller, S. J. <i>J. Polym. Sci., Polym. Phys.</i> <b>1996</b>, <i>334</i>, 181−192). However, once the polymer volume fraction exceeds the “swelling volume fraction” ϕ<sub>s</sub>, 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. (<i>Macromolecules</i> <b>1991</b>, <i>24</i>, 3873−3882) are above ϕ<sub>s</sub> 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<sub>s</sub> 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.