Spin-diffusion constant

Physical parameters Molecular 0.1-1 nm Dipole-dipole interaction Second moment, fourth moment of lineshape Incoherent magnetization transfer characteristic times for cross-polarization and exchange Mesoscopic lnm-0.1 p,m Longitudinal relaxation time Ti Transverse relaxation time T2 Relaxation time Tip in the rotating frame Solid-echo decay time T2e Spin-diffusion constant Microscopic 0.1-lOp.m Molecular self-diffusion constant D Macroscopic 10 p,m and larger Spin density... 

The magnetization-decay curves have been analysed for each position in space. The spin-diffusion constants were obtained from the H linewidths of the broad and the narrow components according to [Demi],... 

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

Figure 7 shows the temperature dependence of the relaxation times of polarons in P30T determined from its dispersion spectrum terms presented in Fig. 4 of the spin diffusion constants Did and D3D and of the conductivity due to polaron mobility along OiD and between Oid polymer chains. ... 

Figure 2.19. Thermal dependence of the spin diffusion constant D n) and normalised d.c. conductivity (

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.

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

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. 

Mechanisms of micellar reactions have been studied by a kinetic study of the state of the proton at the surface of dodecyl sulfate micelles [191]. Surface diffusion constants of Ni(II) on a sodium dodecyl sulfate micelle were studied by electron spin resonance (ESR). The lateral diffusion constant of Ni(II) was found to be three orders of magnitude less than that in ordinary aqueous solutions [192]. Migration and self-diffusion coefficients of divalent counterions in micellar solutions containing monovalent counterions were studied for solutions of Be2+ in lithium dodecyl sulfate and for solutions of Ca2+ in sodium dodecyl sulfate [193]. The structural disposition of the porphyrin complex and the conformation of the surfactant molecules inside the micellar cavity was studied by NMR on aqueous sodium dodecyl sulfate micelles [194]. 

Fig. 4. Schematic representation of transient method employed by Devaux and McConnell9 to measure the rates of lateral diffusion of phospholipids in model membranes. The upper diagram represents a concentrated patch of labels at the beginning of the experiment, time f = 0. At later times f>0, the molecules diffuse laterally, as shown in the lower two drawings. The paramagnetic resonance spectra depend on the spin-label concentration in the plane of the membrane, and an analysis of the time dependence of these spectra yielded the diffusion constant. [Reprinted with permission from P. Devaux and H. M. McConnell, J. Am. Chem. Soc., 94, 4475 (1972). Copyright by American Chemical Society.]...

Devaux et al. have described in some detail the use of the Bloch equations to relate electron spin-spin interactions between spin-labeled lipids to diffusion constants. This method was originally employed by Trauble and Sackmann,50 Scandella et al.,42 Devaux and McConnell,10 and Devaux et al.11 to measure diffusion constants in multibilayer model membranes and in biological membranes. In all cases diffusion constants of the order of those reported previously were obtained. 

A second steady-state method involves the analysis of the broadening of the nuclear magnetic resonance spectra of phospholipids in bilayers containing low concentrations of spin-labeled phospholipids. A theoretical analysis of the relation between this line broadening and diffusion rates has been given by Brulet and McConnell.3 [In this paper (6) is not correct the subsequent equations are nonetheless correct. For an alternative derivation, see Brulet.2] In this paper it is shown that a number of measurements of nuclear relaxation rates T71 of nuclei in phospholipids are consistent with lateral diffusion constants in the range 10 7 to 10 R cm2/s. 

In principle the deviation <5 can be determined by the use of usual analytical chemistry or a highly sensitive thermo-balance. These methods, however, are not suitable for very small deviations. In these cases the following methods are often applied to detect the deviation physico-chemical methods (ionic conductivity, diffusion constant, etc.), electro-chemical methods (coulometric titration, etc.), and physical methods (electric conductivity, nuclear magnetic resonance, electron spin resonance, Mossbauer effect, etc.), some of which will be described in detail. 

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