Field-cycling NMR relation spectroscopy of molten linear and cross-linked polymers Observation of a T ₁ ∝ ν^0.25 law for semi-global chain fluctuations

Abstract

Melts of polydimethylsiloxane, polyisoprene, polyisobutylene, and polyethylene were studied by the aid of proton relaxation spectroscopy predominantly using the field-cycling technique. Spin-lattice relaxation in the rotating frame (T _1ρ) and transverse relaxation were investigated in addition. With spin-lattice relaxation the total frequency range was 10³ to 3 · 10⁸ Hz. Linear as well as cross-linked polymers with varying molecular weights and mesh lengths, respectively, were studied. Close to or above the critical molecular weight, peculiar frequency dependencies of the spin-lattice relaxation times were found which can be described by power laws ω^1/4 or ω^1/2. Depending on the molecular weight and the temperature, a crossover between these frequency dependences takes place. For low molecular weights and high temperatures the indication of a low-frequency plateau appears. Empirically the dispersion can be described well by the aid of the intensity function $I(\omega ) = \frac{{I(0)}}{{1 + c_1 \omega ^{1/4} + c_2 \omega ^{1/2} }}$. The molecular weight dependences of the low-frequency spin-lattice relaxation times and of the transverse relaxation times suggest that the corresponding fluctuations have partly local and partly global features. The experimental findings are discussed in terms of the three-component scheme of chain fluctuations previously reported.