Site exchange motion

The nine lines, designated as the (5 + 4) lines are assigned to the propagating radical, —CpHp2(Ca )R(CH3). Details about the radical were obtained from the shape of the spectrum, especially the relative intensity of the lines which has been interpreted in terms of various factors such as that there are more than two conformations, there is site exchange motion around the (Cc )—Cp bond, and that there is a distribution of dihedral angles for one conformation. Figure 7.4 shows the temperature and solvent dependency of the intensity ratio of the 9 lines. 

Figure 7.26 shows the temperature dependence of ESR spectra of PE chain end type of propagating radical tethered to a PTFE surface [27]. The radicals were produced by ball-milling of PTFE with a large amount of ethylene monomer. The dotted spectra at 15 and 30 K were calculated using the site exchange rates of 10 and 56 MHz, respectively. The spectrum observed at 95 K could be simulated by the rotation of the chain end about the chain axis along with the site exchange motion. The oscillation amplitude was also estimated from the values of SPLIT A and B, shown in Fig. 7.26. The ESR spectra of the end type of scission radicals produced by the mechanical fracture of PE were also simulated by the site exchange model between the sites 1 and 2 as described in Fig. 7.50 (in Appendix A7.1). The reason...

When a sodium cation jumps between two sites with the same EFG tensor components and the same residence times on both positions, but different orientations, then the two-site exchange process can be described by tensor averaging of the two positions. Depending on the jump angle of the tensor, the motionally averaged principal components, Vxx, Vyy, and Vzz, may eventually have to be redefined in ordering to fulfill the requirement in parenthesis in (4). 

Before continuing with the discussion on the dynamics of SE s in crystals and their kinetic consequences, let us introduce the elementary modes of SE motion. In a periodic lattice, a vacant neighboring site is a necessary condition for transport since it allows the site exchange of individual atomic particles to take place. Rotational motion of molecular groups can also be regarded as an individual motion, but it has no macroscopic transport component. It may, however, promote (translational) diffusion of other SE s [M. Jansen (1991)]. 

Correlation diminishes the effectiveness of atomic jumps in diffusional random motion. For example, when an atom has just moved through site exchange with a vacancy, the probability of reversing this jump is much higher than that of making a further vacancy exchange step in one of the other possible jump directions. Indeed, if z is the coordination number of equivalent atoms in the lattice, the fraction of ineffective jumps is approximately 2/z (for sufficiently diluted vacancies as carriers) [C. A. Sholl (1992)]. 

Results of Bo dependency were applied to the two models 1) Static model We assumed a homogeneous population of Na" " in the intracellular fluid, 2) Exchange model We assumed an exchange between Na+ under the slow-motion condition and the Na+ in the extreme narrowing region. Results obtained in this study can be fitted with the two-site exchange... 

Interpretation of these Al spectra might be affected by a partial averaging of the EFG due to Na exchange between the 6- and 8-coordinated sites and motion of the F ions at temperatures well below the a-p structural transition. Near 25°C, the a MAS-NMR peaks for the 6- and 8-coordinated sites are well-resolved (Fig. 16), separated by about 12 ppm, or Av 1300Hz (vq = 105.8 MHz). With increasing temperature, the peaks... 

When the phenylene ring undergoes the flip motion with a frequency of K between the sites described by 5 = 0 and 5=8, the resonance line I(w) will be given by using the two-site exchange theory [1] as... 

The present design of our MAS probe is clearly amenable to variable temperature operation. Hence, one can study site exchange processes as a function of temperature and possibly separate rotational motion from translational motion of the molecule on the surface. Anisotropic rotational motion can be studied by nmr, e.g. deuterated pyridine and n-butyl amine. The ease of the experiment suggested that nmr with enriched samples would be equally as straightforward. In the near future, the Al, Ag, Rh nmr spectroscopy of the surface acceptor can also be studied. 

Motional averaging, for example, a two-site exchange, will affect both solution and solid state spectra. 

Quadrupole echo lineshapes for the phenylene ring-flip motion (or any jump model) are simulated with an n-site exchange calculation one must also include the exchange-caused relaxation between the pulses (echo distor-... 

It is possible to reveal very low fluctuation motions by MAS two-site exchange analysis. The rate constant for flip-flop motions of Tyr side chain in Leu -enkephalin trihydrate, for instance, was obtained as 1.3 X 10 s at ambient temperature from NMR by means of spectral simulation utilizing the two-site exchange model [160]. The similar... 

An atom on a normal lattice site exchanges its place with a vacant site (Fig. 7.11a). The movement of the atom is opposite to that of the vacancy, so we can track the movement of the atom (i.e., atom diffusion) or, equivalently, the motion of the vacancy (i.e., vacancy diffusion). Whereas the diffusion coefficients of the atoms and the vacancies are related, they are not equal. We can see this as follows. An atom can only jump if a vacancy is located on an adjacent lattice site, but a vacancy can jump to any of the occupied nearest neighbor sites. The number of atomic jumps will therefore be proportional to the fraction of sites occupied by vacancies, Cy. The atomic (or self-) diffusion coefficient Da and the vacancy diffusion coefficient Dy are related by... 

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