Single chain diffusion process and proton magnetic relaxation in polymer melts

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Abstract
The present work aims at connecting properties of the quantum coherence of proton magnetic moments linked to strongly entangled polymer chains to low frequency dynamical properties of polymeric liquids. Theoretical and experimental results giving evidence for the presence of a residual tensorial spin coupling induced by chain confinement or crosslinks are commented by using a freely jointed chain model where every link is supposed to carry a proton pair. The submolecule concept is applied. Due to chain confinement, every submolecule of contour length Le, is supposed to have a temporary end-to-end vector re, inducing a temporary average orientational order of monomeric units, observed from NMR. The free induction decay G(δt) of the magnetization is given a general connection to polymer properties through the relations : i) δ ∝ ΔG l/L e, for strongly entangled chains; with l, the Kuhn step length and ΔG the second moment of the resonance line observed in the glassy state. The order of magnitude of δ-1 is in good agreement with decay times actually observed on real chains; ii) δ g ∝ q2/3 ΔG/Le 4/3, for polymeric gels; with q, the swelling ratio of the gel; the Le-4/3 dependence upon elementary chain length is shown to be related to the absence of any large amplitude fluctuations of crosslink points. A general expression of G(δg t) including the stretching ratio, λ, of the gel is also given. Effects of a fast disentanglement process on the free induction decay of the magnetization are described by considering that the residual spin coupling, δ, associated with the temporary average orientational order of monomer units is destroyed according to a motional narrowing process. The chain motion is supposed to occur according to a Rouse model. This was chosen for the sake of simplicity, although some viscoelastic properties are known to be described in a righter way from the so-called « reptation » model; however, the Rouse model is well appropriate to the illustration ofNMR properties : it shows how δ-1 might serve as a long reference time scale for investigations of renewal times of chain configurations. A qualitative comparison with results obtained from the model of chain disengagement process proposed by De Gennes, is given