Back hopping rate

Finally it should be noted that due to the asymmetry in the free energy changes of the two ET steps (Fig.l) the contribution of the back-hopping rate to the exchange interaction J is small (less than 15 % at 300K) and will be neglected in the following treatment of J. 

Ti is a time related to the initial site relaxation rate T2, while p = x x can be expressed in terms of the ratio of the initial back-hopping rate (1/x ) and the initial site-relaxation rate (I/X2) in accordance with the jump-relaxation model (see Sections 6.4 and 6.5). 

The initial equation 6.23 for 1/x is obtained as ITa(O) = 1 and 8back(0 = 8. The rate of back-hopping is regulated by the temporal dependence of 8back(0- K there is no site-relaxation, 8back(f) = 8 for every t and the integration of equation 6.23 yields equation 6.25 ... 

Another example of alternating line width effect was found in the spectra of durosemiquinone (6),9,10 where the effect is due to alkali metal ions hopping back and forth from one oxygen atom to the other. The rates depend on the alkali metal as shown in Table 5.3. 

The Impedance Z can Increase to very high values. If this happens, the oscillator prefers to oscillate In resonance with an anharmonic frequency. Sometimes this condition Is met for only a short time and the oscillator oscillation jumps back and forth between a basic and an anharmonic oscillation or It remains as an anharmonic oscillation. This phenomenon Is well known as "mode hopping". In addition to the noise of the rate signal created, this may also lead to Incorrect termination of a coating because of the phase jump. It Is Important here that, nevertheless, the controller frequently continues to work under these conditions. Whether this has occurred can only be ascertained by noting that the coating thickness Is... 

Within this general scheme, there is much flexibility in the kind of stationary and mobile phases that may be used, but the basic principles of separation remain the same. Consider a molecule dissolved in the mobile phase flowing over the stationary phase. If the solvent (mobile phase) is moving at a velocity Vs, then the solute molecule will be carried along at the same speed. If, however, the solute molecule partitions into, or binds to, the stationary phase, then for the fraction of the time it spends in the stationary phase - it will remain stationary. Consequently, as the molecule hops back and forth between the two phases, its rate of flow will be reduced depending on how much time it spends in the stationary phase. 

We have performed a QNS study over a wide dynamical range on the H diffusion in amorphous P gQSi20 most prominent result is the discovery of two distinctly separated regimes of jump rates instead of the expected continous distribution. From our model-independent data evaluation we get reasonable H diffusion coefficients and we derived that the fast H motion is spatially restricted to regions of about 10 X diameter. From the temperature dependence of the weight of the broad component we conclude that the fast localized motion is due to thermal activation from a trapped state and not to back-and-forth hopping in extended traps. A satisfactory description of the QNS data is possible in the framework of a two-state-model for amorphous Pdg Si Q in which fast local H diffusion is interrupted frequently by trapping events. 

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