Determining the number-average molecular weight of polyelectrolytes

The molecular weight of polyelectrolytes can be reliably measured using terminal modulus (G) (M_n=c_mRT/G) for polyelectrolytes with a high degree of polymerization, or can be measured using diffusion coefficient (D) from NMR and correlation length (ξ) from X-ray scattering (M_n=c_mRTξ²/6η_sD) for polyelectrolytes with a low degree of polymerization (N < 1000) in the semidilute unentangled regime. Reliable measurement of G = (η - η_s)/τ of polyelectrolyte solutions using rheometry requires relaxation time  τ > 0.01 s in order to have one full decade of shear rate with power law shear thinning. Hence, high molecular weight polyelectrolytes with high viscosity solvents (N > 1000 in ethylene glycol or N > 100 in glycerol) are preferred for evaluating  τ and hence G. Measuring D, on the other hand, is more easily performed on low molecular weight polyelectrolytes with NMR diffusometry because of the decrease of the spin dephasing time (T₂) with increasing molecular weight, which leads to peak broadening and poor signal strength for large N. The dispersity of polyelectrolyte samples can also be determined using signal attenuation plots from NMR diffusometry. Convenient determination of M_n and PDI of polyelectrolytes will greatly accelerate their development for real world applications.