NMR Study of Self-diffusion

General overview of several studies of transport and intermolecular interactions in compressed supercritical fluids is presented. The unique aspects of the instrumentation used in these studies are emphasized. First, the results of NMR studies of self-diffusion in supercritical ethylene and toluene are discussed. These experiments used the fixed field gradient NMR spin-echo technique. Second, the novel NMR technique for the determination of solubility of solids in supercritical fluids is described. 

Callaghan, P.T. and Finder, D.N. (1983). A pulsed field gradient NMR study of self-diffusion in a polydisperse polymer system dextran in water. Macromolecules 16 968. 

P.T. Callaghan and D.N. Pinder, "A Pulsed Field Gradient NMR Study of Self-diffusion in a Polydisperse Polymer System Dextran in Water," Macromolecules. J6, 968-973 (1983). 

In deuteron NMR studies of the diffusion of benzene within zeolites it was found that the pre-exponential factor for the correlation time was inversely proportional to the number of available sites to which a molecule could jump. The pre-exponential factor is the limiting value of the correlation time as temperature tends to infinity. In previous work, the above findings for zeolites have been generalised to so-called "amorphous structures which exhibit the property of self-similarity. It was assumed that the pre-exponential factor for the correlation time was inversely proportional to the number of adsorption sites contained within a limiting length scale, is a parameter of the model determined... 

Garrido, L. Mark, J. E. Ackerman, J. L. Kinsey, R. A., Studies of Self-Diffusion of Poly(dimethylsiloxane) Chains in PDMS Model Networks by Pulsed Field Gradient NMR. J. Polym. Sci., Polym. Phys. Ed. 1988, 26, 2367-2377. 

In the earlier NMR studies the self-diffusivity was derived indirectly from measurements of the spin-lattice relaxation time over a range of temperatures. The correlation time which is roughly equivalent to the average time between successive molecular jumps, may be derived from such information and the self-diffusivity is then estimated from the Einstein relation using an assumed mean square jump length A. For an isotropic cubic lattice... 

Peereboom, P. W. E., Luigjes, H. Prins, K. O. (1989). An NMR spin-echo study of self-diffusion in xenon. Physica, 156A, 260-276. 

Nuclear magnetic resonance (NMR) provides a powerful method for the study of molecular motion. The techniques can distinguish molecular reorientation and translation and have proved particularly valuable for the study of self-diffusion in bulk liquids. The molecular motion of liquids in the confined geometry provided by their containment in porous materials has been of considerable interest for many years. It is of importance both as a fundamental scientific problem and because of its technological importance in such diverse systems as oil recovery from rocks and catalytic agents. The purpose of this paper is to question the reliability of many previous investigations and the validity of their interpretation. Potential sources of error are demonstrated by measurements on mobile liquids adsorbed into porous silicas with different geometrical characteristics. The principles illustrated are equally valid for other porous systems. Preliminary measurements of the diffusion coefficient of n-butane in silica as a fimction of temperature and the effect of pore dimensions are presented. 

Brown, W Stilbs, P Lindstrom, T, Self-Diffusion of Small Molecules in Cellulose Gels using FT-Pulsed Field Gradient NMR, Journal of Applied Polymer Science 29, 823,1984. Brownstein, KR Tarr, CE, Importance of Classical Diffusion in NMR Studies of Water in Biological Cells, Physical Review A 19, 2446, 1979. 

The techniques used for the characterization of the dendrimers Dl, D2, and D3 were H NMR, C NMR, and SEC. Self-diffusion studies were made by pulsed-field spin echo H NMR. The simplicity of the H NMR and C NMR spectra indicates high purity of Dl, D2, and D3. 

Fleisher et al. [12] studied the self-diffusion of oil and water in rape seeds. The selfdiffusion of oil was found to be completely restricted. The experiments could be explained in toms of the model of diffusion within spherical droplets and a Gaussian mass distribution of the droplet radii. At the same time Van den Enden et al. [9] introduced the technique described above. It is a rapid method for the determination of water droplet size distributions in spreads by using low resolution pulsed field gradient NMR. Their method was based on the recognition that a set of echo attenuation values (R) as a function of the field gradient pulsed width, obtained under conditions where R is independent of the time allowed for diffusion, contains all the necessary information on the water droplet size distribution (see above). A log-normal distribution of water droplet sizes was assumed. 

V. Molinier, B. Fenet, J. Fitremann, A. Bouchu, and Y. Queneau, PGFSE-NMR study of the self diffusion of sucrose fatty acid monoesters in water, J. Colloid Interface Sci., 286 (2005) 360-368. 

A more sophisticated method which has found wide application in the study of intracrystalline diffusion in zeolites is the nuclear magnetic resonance (NMR) pulsed field gradient self-diffusion method. The method, which is limited to hydrocarbons and other sorbates with a sufficient density of unpaired nuclear spins, depends on measuring directly the mean square distance traveled by molecules,... 

The self-diffusion of benzene in PIB [36], cyclohexane in BR [37] and toluene in PIB [38-40] has been investigated by PFG NMR. In addition more recently Schlick and co-workers [41] have measured the self-diffusion of benzene and cyclohexane mixtures in polyisoprene. In the first reported study of this kind, Boss and co-workers [36] measured the self-diffusion coefficients of benzene in polyisoprene at 70.4 °C. The increase in Dself with increasing solvent volume fraction could be described by the Fujita-Doolittle theory which states that the rate of self-diffusion scales with the free volume which in turn increases linearly with temperature. At higher solvent volume fractions the rate of selfdiffusion deviates from the Fujita-Doolittle theory, as the entanglement density decreased below the critical value. 

According to Eqs. (4)-(6), the molecular mean square displacements and thus the self-diffusion coefficients may be determined from the slope of a semilogarithmic plot of the PFG NMR signal F versus (Sg) The observation time of self-diffusion is the separation between the two field gradient pulses, t. Owing to their relatively large gyromagnetic ratio and to their natural abundance of 1, protons provide very suitable conditions for NMR self-diffusion studies, but C 44), F 45), and Xe 46-48) resonances have also been used successfully in recent PFG NMR studies of zeolites. 

Table 2 includes as well the results of recent diffusion studies by molecular dynamics (MD) calculations and by quasielastic neutron scattering. Both methods consider the process of self-diffusion and reflect the transport properties over diffusion paths of typically a few nanometers. In view of the satisfactory agreement with the PFG NMR data, there should be no doubt that genuine... 

Figure 22 gives a comparison of the results of NMR tracer desorption studies and self-diffusion measurements on short chain length paraffins in zeolite NaX [48]. For illustration, the complete tracer desorption curves are also given at selected temperatures. Covering the range from — 140 to 200°C and chain lengths from one to six carbon atoms, the intracrystalline mean lifetimes are found to coincide with values of calculated via Eq. (2) from the NMR self-diffusion co-... 

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