Using the Semidilute Unentangled Regime to Measure Number-Average Molecular Weight for Ionic Polymers

We use scaling models to derive four methods to calculate the number density of chains and hence number-average molecular weight M_n, from polyelectrolyte chain dynamics in the semidilute unentangled concentration regime. Each method uses combinations of measurements that yield the number density of chains in ways that are insensitive to solvent quality and the presence of salt. We test these methods using pulsed-field-gradient NMR to measure diffusion coefficient, the shear rate dependence of steady shear viscosity to measure viscosity and relaxation time and the correlation length from small-angle X-ray scattering. We will test these methods by investigating the sodium salt of sulfonated polystyrene (where M_n is already known) and a select group of other ionic polymers for which M_n has been elusive. This group of techniques shows promise for breaking the bottleneck of molecular weight determination for general ionic polymers, thus enabling accelerated development and application of these systems.