Spin diffusion time constants

Fig. 10.19. Measurement of the interpolymer spin-diffusion time constant for PS/PVME cast from toluene (Bt) and chloroform (Be), respectively. The deviation of the methine/methoxy line intensity of PVME from the equilibrium value obtained for > T, is plotted in arbitrary units vs. T after selective inversion of the aromatic PS line. (Reprinted with permission from Ref. [119]. 1986 American Chemical Society, Washington, DC.)...

Spin diffusion Time constant for all processes that move magnetization between positions in the ESR spectra of two different species... 

Nuclear spin diffusion Time constant for mutual electron spin interchange,... 

Hz) about the magic angle and the mixing time is synchronized with the sample rotation. The rotation speed has to be slower than the fluctuations of the local fields but faster than the spin-diffusion rate constant. Under this condition one can rewrite Equation (4.11) and define an average rate constant... 

Where no decrease in magnetization was observed. Tip was set to infinity. Since the spin diffusion times can be related to the distance between the coupled spins [14], i.e., Tis 1 o<= rj3-6, then these constants are useful for inferring distance... 

Figure 8 Effects of spin diffusion. The NOE between two protons (indicated by the solid line) may be altered by the presence of alternative pathways for the magnetization (dashed lines). The size of the NOE can be calculated for a structure from the experimental mixing time, and the complete relaxation matrix, (Ry), which is a function of all mterproton distances d j and functions describing the motion of the protons, y is the gyromagnetic ratio of the proton, ti is the Planck constant, t is the rotational correlation time, and O) is the Larmor frequency of the proton m the magnetic field. The expression for (Rjj) is an approximation assuming an internally rigid molecule.

It may be concluded that during the contact time in the competing process for the energy in the various spin systems, the carbon atoms are trying to reach thermal equilibrium with the proton polarization, which is in itself decreasing with a time constant, (Tig, H). In fact the protons undergo spin diffusion and can be treated together, whereas the carbon atoms behave individually. Therefore one implication is that we can also expect to obtain a C-13 spin polarization proportional to the proton polarization. 

The essence of the DDIF method is to first establish a spin magnetization modulation that follows the spatial variation of the internal magnetic field within the individual pore. Such modulation is created by allowing spins to precess in the internal magnetic field. Then the diffusion-driven time-evolution (often decay) of such a modulation is monitored through a series of signal measurements at various evolution times tD. The time constant of this decay corresponds to the diffusion time of a molecule (or spin) across the pore and thus is a direct measure of the pore size. 

It should be noted that the decomposition shown in Eq. 3.7.2 is not necessarily a subdivision of separate sets of spins, as all spins in general are subject to both relaxation and diffusion. Rather, it is a classification of different components of the overall decay according to their time constant. In particular cases, the spectrum of amplitudes an represents the populations of a set of pore types, each encoded with a modulation determined by its internal gradient. However, in the case of stronger encoding, the initial magnetization distribution within a single pore type may contain multiple modes (j)n. In this case the interpretation could become more complex [49]. 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

Fig. 15. Effects of small-amplitude reorientation on 2H NMR stimulated-echo experiments, as calculated by means of RW simulations. The C-2H bonds perform rotational random jumps on the surface of a cone with a full opening angle % = 6°, which are governed by a broad logarithmic Gaussian distribution of correlation times G(lgr) (a = 2.3). (a) Correlation functions m tp — 30 is) for the indicated mean logarithmic time constants lgr 1. The calculated data are damped by an exponential decay, exp[—(tm/rso)] with rSD = 1 s, so as to mimic effects due to spin diffusion. The dotted lines are fits with Fcos(tm tp) = (1—C) expHtm/t/l + Qexp[—Om/rso)]- (b) Amplitude of the decays, 1-C,p, for various t resulting from these fits. The dotted line is the value of the integral in Eq. (12) as a function of rm. (Adapted from Ref. 76).

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... 

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