Water diffusion jump time

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... 

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). 

Discussion. We can now propose a coarse description of the paraffinic medium in a lamellar lyotropic mesophase (potassium laurate-water). Fast translational diffusion, with D 10"6 at 90 °C, occurs while the chain conformation changes. The characteristic times of the chain deformations are distributed up to 3.10"6 sec at 90 °C. Presence of the soap-water interface and of neighboring molecules limits the number of conformations accessible to the chains. These findings confirm the concept of the paraffinic medium as an anisotropic liquid. One must also compare the frequencies of the slowest deformation mode (106 Hz) and of the local diffusive jump (109 Hz). When one molecule wants to slip by the side of another, the way has to be free. If the swinging motions of the molecules, or their slowest deformation modes, were uncorrelated, the molecules would have to wait about 10"6 sec between two diffusive jumps. The rapid diffusion could then be understood if the slow motions were collective motions in the lamellae. In this respect, the slow motions could depend on the macroscopic structure (lamellar or cylindrical, for example)... 

Neutron-scattering and dielectric relaxation studies [23] both indicate that the water molecules solvating monovalent exchangeable cations on montmorillonite are a little less mobile, in respect to translational and reorientational motion, than are water molecules in the bulk liquid. For example, as with vermiculite, neutron-scattering data show that no water molecule is stationary on the neutron-scattering time scale. In the one-layer hydrate of Li-montmorillonite, the residence time of a water molecules is about six times longer than in the bulk liquid, with a diffusive jump distance of about 0.35 nm, and a water molecules reorients its dipole axis about half... 

Figure 3.2 and Figure 3.4 (lowest panel) show evidence that water remains mobile in the glass, and diffuses exclusively through jumps. From a stretched exponential fit of the incomplete decay of Fs(k,t) at 220 K, we estimated the characteristic time for water to move one water diameter k = 27t/33 A) to be Tw 1-3 fjis. This renders an estimated water diffusion coefficient... 

The dependence of the inverse of the characteristic times for water translation in 12% water-DP12 at T = 1.4Tg = 475 K (circles) shows the characteristic shape of jump-diffusion mechanism (Equation 3.2) without any contribution from a continuous diffusion mechanism. When the segmental mobility of the oligomer is increased by eliminating the torsional barriers between the monomeric residues, water mobility acquires a continuous diffusion component (circles). The data for water in the monomer at the same reduced temperature T = l-4Tg = 335 K and water content is also shown for comparison (squares). The existence of a continuous component in water diffusion in these low water content mixtures requires a continuous component in the mobility of the sugar. 

Tor of the LIB state actually represents the waiting time before the proton jumps. This molecular picture is supported of the experimental studies by Teixeira et al. [15] in high-quality quasi-elastic incoherent neutron scattering in water. The jump diffusion of the proton across the tetrahedral angle is rather temperature independent. A very useful interpretation of this experiment made recently by Teixeira [16] is reproduced in Appendix I. 

Pulsed field gradient (PFG)-NMR experiments have been employed in the groups of Zawodzinski and Kreuer to measure the self-diffusivity of water in the membrane as a function of the water content. From QENS, the typical time and length scales of the molecular motions can be evaluated. It was observed that water mobility increases with water content up to almost bulk-like values above T 10, where the water content A = nn o/ nsojH is defined as the ratio of the number of moles of water molecules per moles of acid head groups (-SO3H). In Perrin et al., QENS data for hydrated Nation were analyzed with a Gaussian model for localized translational diffusion. Typical sizes of confining domains and diffusion coefficients, as well as characteristic times for the elementary jump processes, were obtained as functions of A the results were discussed with respect to membrane structure and sorption characteristics. ... 

Figure 5. Median jump frequencies (Sr ) 1 for water adsorbed on NaX to saturation, for water on charcoal at saturation, and that expected for bulk water (from NMR relaxation times) dashed curve marked diff diffusion coefficients by magnetic field gradient technique normalized to (Sr) 1 by choice of jump distance of 2.7 A + dielectric relaxation times of Jansen...

The movement of biological stressors have been described as diffusion and/or jump-dispersal processes. Diffusion involves a gradual spread from the site of introduction and is a function primarily of reproductive rates and motility. Jump-dispersal involves erratic spreads over periods of time, usually by means of a vector. The gypsy moth and zebra mussel have spread this way the gypsy moth via egg masses on vehicles and the zebra mussel via boat ballast water. Biological stressors can use both diffusion and jump-dispersal strategies, which makes it difficult to predict dispersal rates. An additional complication is that biological stressors are influenced by their own survival and reproduction. 

It has been possible to describe the short time diffusion (a few picoseconds) of water molecules close to a hydrophilic surface in terms of simple models [70] for all of the studied samples. At short times, the water molecules close to some hydrophilic surface perform very local rotational jumps characterized by D and x, like in bulk water but with a longer residence time Xq on a given site before diffusing to an adjacent site along the surface with a diffusion coefficient equal to locai diffusion is limited to some volume estimated as spherical. For the 25% hydrated sample, the diffusion coefficient measured by NMR appears to be smaller than Dj which is smaller than [71 ]. This is due to the fact that NMR... 

It appears that the short time dynamics of water molecules at or near the hydrophilic model surface and at a soluble protein surface is much slower than that of the bulk water. It is important to note that the more significant slow dynamics of interfacial water is reflected in the long residence time for jump diffusion. This suggests that there may be a common underlying mechanism for the slowing down of the single-particle dynamics of interfacial water. 

The dependence of the inverse of the characteristic times for water translation does not show exclusively the linear behavior of continuous diffusion (Equation 3.1) or exclusively the shape of a simple jump diffusion model (Equation 3.2), but is very well represented (lines) by considering that both mechanisms contribute to the relaxation (Equation 3.3). The symbols correspond to the simulation data at different temperatures 365 K (circles), 335 K (squares), and 310 K (triangles). 

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