Molecular diffusion on a time scale between nano- and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions: Application to polymer melts

Abstract

A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed. The intermolecular spin-lattice relaxation contribution can be determined with the aid of isotopic dilution, that is, mixtures of undeuterated and deuterated molecules. Experiments have been performed with melts of polyethyleneoxide and polybutadiene. The mean-squared segment displacements have been evaluated as a function of time over five decades. The data can be described by a power law. The extrapolation to the much longer time scale of ordinary field-gradient NMR diffusometry gives good coincidence with literature data. The total time range thus covers nine decades.

Proton spin dynamics in polymer melts: New perspectives for experimental investigations of polymer dynamics

“…Indeed, as anticipated above, it has been shown that the intermolecular contribution to R 1 (ω) must not be ignored suggesting that the exponent α might also be influenced by the intermolecular relaxation [13,16,17,25]. Moreover, the intermolecular relaxation is an important source of information regarding translational dynamics in polymer melts.…”

“…The next step of analysis of (8) is the approximation of the propagator by a Gaussian distribution [16,21]: …”

“…The dynamics of the investigated systems is mainly reflected through characteristic features of nuclear spin relaxations. Important findings of recent years [7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], affecting the understanding of the proton spin dynamics in polymer melts are the subject of discussion of this paper.…”

Comment on “Neutron scattering study of the dynamics of the polymer melt under nanoscopic confinement” [J. Chem. Phys. 131, 174901 (2009)]

“…It may be noteworthy in the present context that coherent neutron scattering which probes displacements of different scattering centers relative to each other has also an NMR analogue in a sense: evaluating the intermolecular dipolar interaction contribution to spin-lattice relaxation permits one to study relative diffusive displacements as demonstrated in Ref. 20. Thus, both the "self" and "pair" correlation functions of incoherent and coherent neutron scattering, respectively, have NMR counterparts which should be considered in any study of translational fluctuations.…”

Characterization of Structure and Self-Diffusion of Elastomers by NMR Method

“…Numerous experimental NMR data on linear exible polymers (rubbers and thermoplastics) show that, in the amorphous state at T > T g (T g is the glass transition temperature), the FID is exponential for short chains with a average molecular weight M w < 10 4 and not exponential for longer chains M w > 10 4 [4]. And, irrespective of chemical structure of the polymer, the experimental dependence of the spin-spin relaxation time T 2 on the molecular weight M w and temperature shows that T 2 decreases with an increase in M w and at high temperature region has two clearly pronounced breaks [4].…”