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NMR Studies of Molecular Diffusion
Published in Alexis T. Bell, Alexander Pines, NMR Techniques in Catalysis, 2020
It was demonstrated that nuclear resonant frequencies become functions of position when a spatially dependent magnetic field is applied, and thus the NMR spectrum represents an image of the spatial distribution of the nuclei. Being concerned with the migration of the individual molecules, one has to compare the positions of each molecule at subsequent instants. This measuring principle is realized in the pulsed field gradient (PFG) NMR method [70-73], in which the constant magnetic field is supplemented twice for a short time interval δ by an additional inhomogeneous field (the pulsed field gradients). It is illustrated in Fig. 7 that this procedure may be easily understood on the basis of the semi-classical representation of nuclear magnetism where the individual spins are assumed to rotate about the direction of the constant magnetic field Β with the Larmor frequency ω oc B. Under an appropriate rf pulse (the π/2 pulse), the magnetization is turned into the plane perpendicular to the constant magnetic field, and there the first field gradient pulse effects a dephasing of the vectors of transverse magnetization at different positions and with it a decay of the vector sum.
Microfriction correction factor to the Stokes–Einstein equation for small molecules determined by NMR diffusion measurements and hydrodynamic modelling
Published in Molecular Physics, 2018
Petr Dvořák, Mária Šoltésová, Jan Lang
Due to the great technical progress in the area of pulsed field gradient NMR (PFG NMR) spectroscopy, it is now possible to measure routinely the translational self-diffusion coefficient of molecules in liquid in the absence of a chemical potential gradient. This has given us a tool for the determination of size or weight of molecules or supramolecular assemblies, which is of primary importance in many fields such as supramolecular chemistry, biochemistry, catalysis, material chemistry, polymer chemistry and physics etc. The translational self-diffusion coefficient is related to the molecular size through the well-known Stokes–Einstein relationship (1) [1,2]: where T is the thermodynamic temperature, η is the viscosity of the liquid and kB is the Boltzmann constant. Microfriction correction factor c is equal to 1 according to the original Stokes derivation [3]. Hydrodynamic radius rH can be viewed as a radius of a hypothetical hard sphere, which has the same diffusion coefficient as the studied particle. A lower limit for rH is the van der Waals radius rvdW. The equality rH = rvdW is valid only in the case of a compact molecule without any cavity inlet [4]. The upper bound of the hydrodynamic radius is given by the crystallographic radius rX-Ray, which can be obtained by dividing the volume of the crystallographic unit cell by the number of contained molecules while assuming a spherical shape for the molecule [4].