Proton mean jump times

QENS studies on the dynamics in PEMs suggest that water and protons attain microscopic mobilities that are similar to those in bulk water, with mean jump times of protons in the order of 1 ps. The experimental scattering data include two components, which correspond to fasf (At O (1 ps)) and slow (At 0 (100 ps)) motions. Observation of the latter type of motion suggests that hydronium ions exist as long-lived entities in Nation (Perrin et al., 2006). 

In this expression yn is the proton gyromagnetic moment and the dipolar second moment. This latter quantity is determined by the arrangement of the protons in the crystal structure and can be calculated if structural data are available for a given ternary hydride. It is also possible to derive the dipolar second moment from the NMR line shape. For a random walk diffusion process the mean jump time is related to the diffusion constant D via the expression (Cotts, 1972)... 

Fig. 4.16 Time evolution of the mean squared displacement (r ) (empty circle) at 363 K and the non-Gaussian parameter 2 obtained from the simulations at 363 K (filled circle) for the main chain protons of PL The solid vertical arrow indicates the position of the maximum of 2> At times r>r(Qinax)> the crossover time, a2 assumes small values, as in the example shown by the dotted arrows. The corresponding functions (r ) and a2 are deduced from the analysis of the experimental data at 320 K in terms of the jump anomalous diffusion model and are displayed as solid lines for (r )and dashed-dotted lines for a2- (Reprinted with permission from [9]. Copyright 2003 The American Physical Society)...

Deuterium diffusion was studied in VDX, where 0.4 < x < 0.6, by means of 2H NMR measurements.599 1H and 51V spin-lattice relaxation times for TaV2Hx, where x < 0.18, were consistent with two co-existing proton-jump processes.600 3H, 2H and 51V spin-lattice relaxation times were also determined for NbVCrHo.3, NbVCrD0.3g and NbV 14Cro.6Ho.6 in the temperature range 11-424 K.601 A DFT/broken symmetry approach has been used to study exchange... 

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