Hydrogen self-diffusion coefficients

Fig. 12. Evolution of the ratio of lithium and hydrogen self-diffusion coefficients as a function of either the nature or the amount of the added salt to P15-TFSI at 25°C.

C4 hydrocarbons, presence of water in NaX, self-diffusion coefficients, 39 391-393 Chymotrypsin, 20 344, 356, 386, 387 Cl, see Configuration interaction Cirmarttaldehyde, hydrogenation of, 42 490... 

Examples of Ihe deterniinalioii of self-diffusion coefficients in solids are Ihe diffusion of hydrogen ions and water molecules (labelled with T and O, respectively) in alums, of Cl (labelled with Cl) in AgCl, and of 1 (labelled with l) in Agl. Besides self-diffusion, many other diffusion coefficients of trace elements in metals, oxides, silicates and other substances have been determined by application of radio-tracers. Investigation of the migration of trace elements from solutions into glass revealed fast diffusion of relatively small monovalent ions such as Ag+. 

In addition, a model has been formulated to predict the self-diffusion coefficient of diffusing species, which are hydrogen and aluminum ions. The interdiffusion coefficient value for the coupled transport of these two ions is also determined for the two types of membranes. 

Experiments were carried out with Ionac MC 3470 to determine the self-diffusion coefficient values for H+ and Al + in the coupled transport. Data points were used from the experiment involving 2N acid sweep solution in Figure 34.24b, presented later. These values formed the basis for aluminum transport rate or flux (7ai) calculation at different time intervals. The equilibrium data generated in Figure 34.20b were used in conjunction with Equation 34.25 to determine the interdiffusion coefficient values. Local equilibrium was assumed at the membrane-water interface. Eigure 34.24a shows computed Dai,h values for this membrane. When compared with Dai,h values for Nafion 117, it was noticed that the drop in interdiffusion coefficient values was not so steep, indicative of slow kinetics. The model discussed earlier was applied to determine the self-diffusion coefficient values of aluminum and hydrogen ions in Ionac MC 3470 membrane. A notable point was that the osmosis effect was not taken into account in this case, as no significant osmosis was observed in a separate experiment. 

Even for lonac MC 3470, it was the H" " ion that was the trace species. A comparison of the diffusion coefficient values for the two membranes is presented in Table 34.3. From this table, it can be observed that the self-diffusion coefficient values for aluminum and hydrogen ions are similarly lowered as the experimental interdiffusion coefficient value. This lowering is about one order for both the cases. Explanation for low Dai,h values in the heterogeneous membrane is desired, as it explains the slow transport kinetics in heterogeneous membrane. 

It was seen that in the experiments performed hydrogen ion was the trace species. Therefore, for coupled Al -H transport, the interdiffusion coefficient approached the self-diffusion coefficient of the faster-diffusing ions. This conclusion appears counterintuitive, but explains the good kinetics of the process. 

An attempt has been made to correlate some of the above results in hydrogen with the self-diffusion coefficient D following a suggestion by Zwanzig. The partial success of this attempt (a near-linear variation of Ti with D at a given temperature) can be understood by writing out the self-diffusion coefficient in terms of the velocity autocorrelation function... 

To address the question of hydrogen bonding and ion-pairing in ionic liquids, an obvious approach is to study the self-diffusion coefficients of the individual ions. 

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. Andrec et al. used a Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data. Sturz and Dolle examined the reorientational motion of toluene in neat liquid by using relaxation measurements. The relaxation rates were analyzed by rotational diffusion models. Chen et al measured self-diffusion coefficients for fluid hydrogen and fluid deuterium at pressures up to 200 MPa and in the temperature range 171-372 K by the spin echo method. The diffusion coefficients D were described by the rough sphere (RHS) model invoking the rotation translational coupling parameter A = 1. 

The distribution of these impurities or minor alloy constituents near lattice discontinuities is known to affect the chemical and mechanical properties of the contaminated materials for example the presence of sulfur on a metal surface can promote ) or retard - o) corrosion, modify the surface energy ) or cause considerable increase in the surface self-diffusion coefficient ). Sulfur accumulation along grain boundaries may induce intergranular weakness and render otherwise ductile materials brittle ), either by formation of precipitates " ) or by enhancement of hydrogen adsorption >227)... 

Two unusual features can be observed in these plots (and, at least for the self-diffusion coefficient, this behaviour is common to all hydrogen-bonded liquids). This ratio is a function of temperature. At constant temperature and pressure, rotation and translation reveal the same isotope effect. From simple sphere dynamics one would expect the rotation to scale as the square root of the ratio of the moments of inertia (=1.38) while for translational mobility the square root of the ratio of the molecular masses ( = 1.05) should be found. This is clearly not the case, indicating that the dynamics of liquid water are really the dynamics of the hydrogen-bond network. The hydrogen bonds in D2O are stronger than those in H2O and thus the mobility in the D2O network decreases more rapidly as the temperature decreases. 

These values are to be considered tentative since there is some drift in the values with concentration, and it is likely that the above equilibria do not completely define the system. Self-diffusion coefficients of the zirconium-EDTA complex in slightly acidic solution also indicate a considerable degree of polymerization [417) as do the hydrogen ion dependence data of Ermakov [172). In the direct analytical titration of zirconium with EDTA, polymeric species must be depolymerized. This may be accomplished by boiling the solution with 5 N sulfuric acid [430). 

The diffusivity of hydrogen molecules is mostly studied for hexagonal ice and sll clathrate structure. Strauss [23] showed by neutron inelastic scattering that the diffusion coefficient of H2 in deuterated ice at 25-60 K is rather high and comparable with the self-diffusion coefficient in liquid hydrogen. About 272 K, hydrogen solubility in hexagonal ice is comparable with that in liquid water at atmospheric pressure and differs by two times at 100 MPa [24]. 

The same water model, SPC/E at 25 °C was used by other authors too. Chowd-huri and Chandra (2001) employed 256 water molecules per ion, as well as lower ratios at increasing concentrations, and reported the average residence times of water molecules near ions in ps Na+ 18.5, K+ 7.9, and Cl 10.0. Guardia et al. (2006) also reported residence times in ps of the water molecules in the first hydration shells of ions Li+ 101, Na+ 25.0, K+ 8.2, Cs+ 6.9, F 35.5, Cl 14.0, and I 8.5, compared with 10 1 for water molecules in the bulk. These values, resulting from detailed considerations of the hydrogen bond dynamics in water and near the ions, can be compared with experimental values derived from NMR. According to Bakker (2008) these are Li+ 39, Na+ 27, K+ 15, Cl 15 (by definition the same as for K+), Br 10, and 5 ps, and for water molecules in the bulk 17 ps, calculated from the self diffusion coefficient. 

Their calculated mean square displacement P t) and the self-diffusion coefficient D for the carbon and hydrogen atoms defined in Section 3.3.1 [Eqs. (24) and (25)] show that PAc chains undergo diffusional motion mainly along their axial (c)... 

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