Determining the Molecular Weight of Polyelectrolytes Using the Rouse Scaling Theory for Salt-Free Semidilute Unentangled Solutions

Abstract

Chain dynamics in the semidilute unentangled regime can be used to determine the molecular weight of polyelectrolytes based on the Rouse scaling model. Four methods enable determination of the number density of chains via measurements of correlation length (ξ) by small-angle X-ray scattering, specific viscosity (ηsp) and relaxation time (τ) by rheometry, and diffusion coefficient (D) by NMR. Five narrow dispersity cesium polystyrene sulfonate (CsPSS) solutions without salt are studied in water, anhydrous ethylene glycol, and anhydrous glycerol to test all methods. Combining viscosity and correlation length yields the weight-average molecular weight (Mw) from the Rouse model. Combining diffusion coefficient and correlation length in water provides number-average molecular weight (Mn) reliably for chains with N < 2000 repeat units. Glycerol slows relaxation dynamics, and the shear rate dependence of viscosity yields reliable τ for CsPSS with N > 100, which is governed by the product of z-average and z + 1 average molecular weight (MzMz+1) in the Rouse model. Terminal modulus G = (η – ηs)/τ via rheometry correlates with Mw/MzMz+1.