Free induction decays in entangled polymer melts

Abstract The relaxation of the transverse magnetization components caused by both dipolar interactions between the spins of different polymer chains and the dipolar coupling between CH-protons on an isolated Kuhn segment along a single polymer chain have been calculated. Explicit expressions for the transverse relaxation function are given in terms of the absolute mean squared displacement of the Kuhn segment during melt g r ( t ), the tangent vector dynamical correlation function 〈 b n ( t ) b (0)〉, the segmental relaxation time τ s , the Kuhn segment length b, the bond length a 0 , the internuclear distance d, and the spin number density ρ s . It is shown that the functional dependence of the intramolecular relaxation function on 〈 b n ( t ) b (0)〉 is fairly weak. The time-dependence of the intramolecular contribution to the transverse relaxation function is dominated by the probability density distribution function of the end-to-end vector of the Kuhn segment. The long-time decay of the intramolecular contribution to the transverse relaxation function is found to scale as t − 3/2 for τ s t τ max , where τ max is the maximum relaxation time of polymer chains in melts. For times much less than the spin–spin relaxation time, T 2 ≈ 10 − 3 − 10 − 2 s , we show that the intermolecular contribution to the relaxation function is given by the following expression: exp(− λ 1 ( b , τ s , ρ s ) t 2 / g r 3/2 ( t )). Both the numerical coefficient and the functional dependence of λ 1 on b, τ s and ρ s reproduce the expression obtained from the frequently used second cumulant approximation. For longer times ( T 2 ≤ t τ max ), the intermolecular contribution is determined by the following relation: exp(− λ 2 ( b , τ s , ρ s , t ) g r ( t )). We show that λ 2 increases logarithmically with t. The molecular mass independence of λ 1 and λ 2 shows that, in polymer melts with molecular masses M w far above the critical value M c , the relevant experimental window for the decay of the intermolecular relaxation function is connected with the anomalous diffusion regime. Comparison with the experimental data suggests that the intermolecular contribution plays a significant role in the NMR relaxation process in polymer systems close to the melting point.