The effect of polydispersity on measuring polymer self-diffusion with the n.m.r. pulsed field gradient technique

The echo attenuation in the n.m.r. pulsed field gradient technique for polydisperse samples ($\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}\text{= 1.06, 2.0}$ and 10) was calculated, which, for the smallest polydispersity, is already markedly nonexponential. The echo attenuations of solutions of a polydisperse polystyrene, mixtures of monodisperse polystyrenes and the melt of a commercial polyethylene were measured. In the solutions, depending on the concentration regime, the echo attenuations were considerably less nonexponential than calculated and often exponential within experimental error giving one averaged self-diffusion coefficient. An averaging of the self-diffusion process does exist which is not in accordance with the reptation concept. In the entangled melt the echo attenuation is the sum of the contributions of the different molar masses, where no averaging is present, but, due to the strong dependence of the nuclear relaxation times on molar mass, the smaller molar masses are more strongly weighted and a dependence of the echo attenuation on the diffusion time arises.