Spin diffusion constant, estimation

To obtain a value of b, the domain size, the spin diffusion constant D is estimated fix>m the equation... 

Most approaches to describe spin diffusion are based on a perturbation treatment [11]. Abragam [4] applied Fermi s Golden Rule while Suter and Ernst [12] used the perturbation theory in the rotating frame to obtain an estimate for the rate constant. Henrichs and Linder [13] and Kubo and McDowell [14] used the memory-function theory to model the system. The model of fluctuating local fields can also be applied in a Liouville-space description [15],... 

Self-Diffusion. The self-diffusion coefficient D of liquid PH3 and PD3 in sealed tubes was determined by spin echo measurements of the nuclei H, h, and ip from 139 K to ambient temperature. Numerical values for both phosphanes are given by D(cm2/s) = 5.18x10" exp(-413/T) at temperatures up to 200 K. Above this temperature, D rises faster with temperature to reach 1.5x10 cm /s at 293 K. Attempts to correlate D and the viscosity t failed except at the lowest temperatures [11]. The self-diffusion constant of plastic crystalline PH3 was estimated for a vacancy diffusion mechanism on the basis of the spin-lattice relaxation time. The increase from D = 2x10" to 1x10" cm /s between 103 and 138 K is typical for a plastic crystal. A diffusion activation energy of 19 kJ/mol was estimated [12]. 

Optimal diffusion constants for overall anisotropic rigid body reorientation of enkephalin were computed by least-squares fitting of the observed spin-lattice relaxation times of proton-bearing carbons (Somorjal and Deslaurlers, 1976). Correlation times for Internal motion about Individual C-C bonds In side chains were estimated according to methods described by Deslaurlers and Somorjal (1976). 

On closer inspection, the combination rate constants are about 1/4 of the estimated diffusion-controlled rate constant. For acetonitrile, for example, fcjj - 2.9 X 10 L mol" s from the von Smoluchowski equation wiA a diffusion coefficient from a modified version of the Stokes-Einstein relation, D - fcT/4jiT r. Owing to the restriction to singlet state recombination, an experimental rate constant 1 /4 of is quite reasonable. On the other hand, for these heavy metals, the spin restriction may not apply, in which case one would argue that the geometrical and orientational requirements of these large species could well give recombination rates somewhat below the theoretical maximum. 

This assumes that a chemical species is penetrating into a static film over a time period of t with a diffusiv-ity in the liquid of D. If it is assumed that the exposure time constant t in the equation is equal to the residence time of the liquid on a spinning disk surface, given by Eq. (6), then the liquid-side mass transfer coefficient LG for diffusion into the film can be estimated as... 

The direct NMR method for determining translational difiFusion constants in liquid crystals was described previously. The indirect NMR methods involve measurements of spin-lattice relaxation times (Ti,Ti ),Tip) [7.45]. Prom their temperature and frequency dependences, it is hoped to gain information on the self-diflPusion. In favorable cases, where detailed theories of spin relaxation exist, difiFusion constants may be calculated. Such theories, in principle, can be developed [7.16] for translational difiFusion. However, until recently, only a relaxation theory of translational difiFusion in isotropic hquids or cubic solids was available [7.66-7.68]. This has been used to obtain the difiFusion correlation times in nematic and smectic phases [7.69-7.71]. Further, an average translational difiFusion constant may be estimated if the mean square displacement is known. However, accurate determination of the difiFusion correlation times is possible in liquid crystals provided that a proper theory of translational difiFusion is available for liquid crystals, and the contribution of this difiFusion to the overall relaxation rate is known. In practice, all of the other relaxation mechanisms must first be identified and their contributions subtracted from the observed spin relaxation rate so as to isolate the contribution from translational difiFusion. This often requires careful measurements of proton Ti over a very wide frequency range [7.72]. For spin - nuclei, dipolar interactions may be modulated by intramolecular (e.g., collective motion, reorientation) and/or intermolecular (e.g., self-diffusion) processes. Because the intramolecular (Ti ) and intermolecular... 

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