Mean Square Displacement and Reorientational Correlation Function in Entangled Polymer Melts Revealed by Field Cycling1H and2H NMR Relaxometry

Abstract

Mixtures of protonated and deuterated polybutadiene and polydimethylsiloxane are studied by means of field-cycling (FC) 1H NMR relaxometry in order to analyze the intra- and intermolecular contributions to spin–lattice relaxation. They reflect reorientational and translational dynamics,respectively. Master curves in the susceptibility representation χ″(ωτs) are constructed by employing frequency–temperature superposition with τs denoting the segmental correlation time. The intermolecular contribution is dominating at low frequencies and allows extracting the segmental mean square displacement ⟨R2(t)⟩, which reveals two power-law regimes. The one at short times agrees with t0.5 predicted for the free Rouse regime and at long times a lower exponent is observed in fair agreement with t0.25 expected for the constrained Rouse regime of the tube-reptation model. Concomitantly the reorientational rank-two correlation function C2(t/τs) is obtained from the intramolecular part. Again two power-law regimes t–ε are identified for polybutadiene. The first agrees with t–1 of free Rouse dynamics whereas at long times ε = 0.49 is obtained. The latter is corroborated by the 2H relaxation of deuterated polybutadiene, yet, it does not agree with ε = 0.25 predicted for constrained Rouse dynamics. Thus, the relation C2(t) ∝ ⟨R2(t)⟩–1 as assumed by the tube-reptation model is not confirmed.