Long-Time Diffusion in Polymer Melts Revealed by 1H NMR Relaxometry

We demonstrate that field-cycling 1 H NMR relaxometry can be used as a straightforward method of determining translational diffusion coefficient D = D ( M ) in polymer systems. The 1 H spin–lattice relaxation dispersion for polybutadiene of different molecular masses M (446 < M /(g mol –1 ) < 9470) is measured at several temperatures (233 < T /K < 408) in a broad frequency range. The diffusion coefficient D ( T ) is determined from the intermolecular contribution to the overall spin–lattice relaxation rate R 1 (ω), which dominates in the low-frequency range and follows a universal dispersion law linear in √ω. The extracted diffusion coefficients are in good agreement with the values obtained previously by field gradient NMR. The molecular mass dependence D = D ( M ) exhibits two power laws: D ∝ M –1.3±0.1 and ∝ M –2.3±0.1 . They show a crossover for M = 2300, a value that is close to the entanglement molecular mass M e of polybutadiene. The corresponding power-law exponents are close to the prediction of the tube-reptation model.