Determination of Molecular Weights using a Polydisperse Rouse model for Semidilute Unentangled Polyelectrolyte and Neutral Polymer Solutions

The polydisperse Rouse model applies to dynamics of polymer solutions in the semidilute unentangled concentration regime. For neutral polymers, this regime typically spans a factor of ten in concentration, just above the overlap concentration, while for polyelectrolytes with no salt, the semidilute unentangled concentration regime widens as chain length increases, and can easily cover two or three decades of concentration for long chains. We exploit this simple dynamics to provide new methods of determining molecular weight. The polydisperse Rouse model expects the number-average molecular weight M_n to be determined from a combination of self-diffusion coefficient D (from NMR diffusometry) and correlation length ξ (from X-ray scattering), as M_n = ξ²RTc_m /(6η_sD) where R is the gas constant, T is absolute temperature, c_m is mass concentration and η_s is solvent viscosity. We find this relation works nicely, with no adjustable parameters, for various monodisperse cesium polystyrene sulfonate (CsPSS) samples, their binary blends and NaPSS literature data. The polydisperse Rouse model expects the weight-average degree of polymerization N_w to be determined from a combination of specific viscosity η_sp and correlation length ξ as N_w = η_spξ³c where c is the number density of repeat units. For neutral monodisperse polystyrene in the good solvents toluene and tricresyl phosphate we find that has a perfectly linear dependence on N_w but there is a prefactor that requires calibration to determine N_w. For polyelectrolytes we find η_spξ³c ~ N_w^1.1 resulting in N_w = 3.66(η_spξ³c)^0.91 for the CsPSS samples, their binary blends and NaPSS literature data. Finally, we are now in the process of applying these methods to a wide variety of polydisperse polyelectrolytes and neutral polymer solutions in good solvent.