Jump time

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

The list below shows the last position reached, in units of the jump step a, during a random walk for 100 atoms, each of which makes 200 jumps. If the jump time is 10-3 s and the jump distance, a, is 0.3 nm, estimate the diffusion coefficient (a) in units of a2 s-1 and (b) in units of m2 s-1 ... 

Here is the distance between the two sites and r(E) is the jump time corresponding to an activation energy E ... 

In a mixed-valence system, the isomer shift is able to distinguish the jump time th relative to the time t = 10 s for a MQssbauer nuclear excited state to decay to the ground state. 

The existence of differential reactivity for various sites suggests the possibility that energy absorbed at one site on the chain may be transferred down the chain until it localizes in a site with an unusually high cross section for reaction. Shulman, Gueron, and Eisinger154 claim that energy absorbed in poly dAT at the excited singlet level is transferred to a common excimer between A and T, whence it crosses to a triplet triplet excitons have been observed in poly A with a jump time of 10"8 to 10 10 sec. 

Figure 9.26 Some dynamic features of a liposome membrane (dipalmitoylphos-phatidylcoline, T > Tni). Vertical vibration amplitude 0.3 nm jump time...

Figure 1. System SF6 in zeolite 13X. Base 10 logarithms of intraerystalline lifetime T, experiment time A = (A of text), and relaxation time T2 vs. base 10 logarithms of the diffusion coefficient (lower scale) and jump time (upper scale).

Relaxation times for water filling the pores of an NaX specimen have been fitted to a model with the following assumptions (a) coupling, as above, of molecular diffusion and rotation (b) the median jump time r is governed by a free volume law (allows the curvature in the plots of jump rate, (3r) x vs. 10S/T in Figure 5), and (c) a broad distribution of correlation times (allows a better fit to the data, accounts for an apparent two-phase behavior in T2 (31, 39), and is reasonable in terms of the previous discussion of Pi(f) and r). 

Since the presentation of this model new data have appeared which allow various tests and new conclusions. The diffusion coefficients of Karger (14), together with Equation 1 and the median jump time from the relaxation data at room temperature yield a jump distance of 2.7 A for the zeolitic water as compared with 2.2 A in bulk water (see Table III for a data summary). One might be tempted to explain the jump distance in terms of some geometrical constant of the zeolite structure such as the distance between Sn and Sm ionic sites (40), but with the cages full of... 

Dielectric relaxation measurements for the adsorbed water have been reported by Jansen (44) the dielectric relaxation time is essentially 3r where r is the rotational jump time of the water molecule. From Figure 5 it can be seen that the dielectric and NMR mobility estimates agree rather well. All is not quite in order, however, for Jensen estimates from relaxation strength that he sees only one-third of the water molecules. 

Additional dividends from NMR will most likely continue to lie in the area of diffusion and kinetics. Newer NMR techniques here are the ultra-slow motion (25) and rotating frame relaxation (26) techniques which allow measurements of very long jump times. Application of these techniques to the exchange region has been reported for water on NaX in this region they offer a means of deducing second moments of the tightly bound species (9, 52). The CIDNP technique should be applicable to the study of radical reactions on surfaces and in zeolites (58). 

K. Striking is the broad distribution of jump times of water in cell walls coextending from times of liquid water to ice. We can compare water in cell walls with supercooled water with a broad scale of mobilities. The reduction of the apparent T may be induced by the interaction water/mucopolysaccharid groups. Water in charcoal with mean pore radius of 13 A shows a broader distribution of t but with a... 

Fig. 31. Distribution functions of the jump time (NMR) at 0 °C for liquid water, ice, adsorbed water on a) porous glass AG 39, b) zeolite, c) charcoal and d) bacterial cell walls. (Belfort etal.196))...

Moving from the discrete site to the continuous space representation, and replacing the distance between two nearest-neighbor sites and two consecutive jumps times, which are assumed to be equal to 1, with the earlier expressions for M and K, with a and xu, respectively, we may prove that Eq. (59) yields Eq. (318), with... 

Now, the question is how to get information on the more subtle quantity, the hydration numbers. Some confusion arises here, for in some research papers the coordination number (the average number of ions in the first layer around the ion) is also called the hydration number However, in the physicochemical literature, this latter term is restricted to those water molecules that spend at least one jump time with the ion, so that when its dynamic properties are treated, the effective ionic radius scans to be that of the ion plus one or more waters. A startling difference between co-ordination number and solvation number occurs when the ionic radius exceeds about 0.2 nm (Fig. 2.23a). 

It is important, then, to find out the time that waters stay with the ion. Thus, one can make an order-of-magnitude calculation for the jump time, by a method shown in Section 4.2.17. It comes to approximately 10 s. 

The only characteristic of the carrier motion embodied in this equation is the mean square displacement per unit time, which gives D with a simple numerical factor dependent on the number of degrees of freedom summarized in x. All other detail of the motion is lost, and solutions of the diffusion equation represent the true evolution of p(x) only for times long compared with the jump time. 

Jump frequency of interstitial atoms Frequency of vibration of atoms in a lattice Average jump time (l/pt see pj above)... 

Lithium-doped BPO4, another candidate ceramic electrolyte material for lithium batteries has been studied by Li NMR relaxation and linewidth measurements of samples with Li doping levels up to 20 mol % (Dodd et al. 2000). Comparison of the NMR data with values of the second moment calculated for both random and homogeneous models of Li distribution indicate the existence of Li clusters with an intemuclear distance of 3A, possibly consisting of 1 Li ion fixed at a boron vacancy with additional 2 Li ions in the conduction channels surrounding the vacancy. The atomic jump time, determined from measurements of the Li motional narrowing behaviour, indicate a maximum in the Li ionic mobility at the 10 mol % doping level (Dodd et al. 2000). 

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