Counter diffusion coefficients

The tlrermodynamic activity of nickel in the nickel oxide layer varies from unity in contact with tire metal phase, to 10 in contact with the gaseous atmosphere at 950 K. The sulphur partial pressure as S2(g) is of the order of 10 ° in the gas phase, and about 10 in nickel sulphide in contact with nickel. It therefore appears that the process involves tire uphill pumping of sulphur across this potential gradient. This cannot occur by the counter-migration of oxygen and sulphur since the mobile species in tire oxide is the nickel ion, and the diffusion coefficient aird solubility of sulphur in the oxide are both vety low. 

The term in the square bracket is an effective diffusion coefficient DAB. In principle, this may be used together with a material balance to predict changes in concentration within a pellet. Algebraic solutions are more easily obtained when the effective diffusivity is constant. The conservation of counter-ions diffusing into a sphere may be expressed in terms of resin phase concentration Csr, which is a function of radius and time. 

The Hl value is reduced by an increase in the viscosity of the solvent or by a decrease in the temperature. Longitudinal diffusion can thus be reduced by decreasing the diffusion coefficient and increasing the flow rate however, these two actions are counter-effective in liquid chromatography because of the mass transport term. 

The diffusion coefficients for the two carbon species are almost certainly different but each may be assumed to be constant in a given melt. Because CO2 is a linear molecule (long cylinder with about 1.4 A radius, and 3 A half-length) with a small radius on the base (only slightly larger than the radius of H2O molecule), whereas COf is a relatively large anion (thin disk with about 1.4 A half-thickness, and 3 A radius), and because diffusion of anions requires counter motion of other ions, it is expected that the diffusivity of CO2 is much larger than that of COf-. 

Finally, intraparticle diffusion appears to be an important factor in adsorption kinetics for many types of systems. In the past it has been customary to define such mass transfer quantitatively in terms of an effective diffusivity. However, even in gas-solid systems more than one process can be involved for porous particles. Thus, two-dimensional migration on the pore surface, surface diffusion, is a potential contribution. Liquid systems appear to be more complex, and, with electrolytes, it has been shown that the electric potential induced by counter-diffusing ions should be taken into account. A realistic description of intraparticle mass transfer in such cases requires more than a single rate coefficient for a binary system. 

The diffusion behaviour of Shirakawa polyacetylene is complicated by its fibrillar morphology and high surface area, so that weight changes depend on pore transport and surface adsorption, as well as on diffusion into the fibrils. Chien 6) has reviewed earlier studies of the diffusion of dopant counter-ions in Shirakawa polymer and has emphasised the wide range of values of diffusion coefficient which are reported and which depend a great deal upon the morphological model chosen to interpret experimental data. 

Table 3. Diffusion coefficients for dopant counter ions...

Kaneto et al.523) have made measurements on the diffusion of lead perchlorate in polythiophene by following the colour change. They found a diffusion coefficient which varied from 10-1° to I0-12 cm2 s 1, depending upon the applied potential. The complexities introduced by morphological heterogeneity, counter-ion motion and solvent effects mean that further studies will be required to determine the relative importance of factors affecting diffusion in these materials. 

If a membrane separates two solutions with mixtures of counterions — in which each counter-ion is present only on one side of the membrane — and the same co-ion, we meet with a so-called multi-ionic system. These are also treated by F. Helfferich (53, 55) (ref. 55, page 327). An explicit solution of the flux equations in this case is obtained if the flow of co-ions is neglected and if all the counter-ions possess the same valency. Gradients of activity coefficients in the membrane and convection are also neglected. Diffusion coefficients and concentration of active groups are considered to be constant. It is assumed that there is equilibrium between the salt solution and the membrane surface on either side of the membrane. 

Strictly the mathematical expression to be used for the diffusion process should take account of these constraints however, this kind of counter-diffusion involving two reactants and two products in proportions determined by the stoichiometry of the process is of a complexity which has not yet been considered theoretically. In the absence of such a theoretical treatment, Equation (3) was applied using diffusion coefficients reported in the literature for each of the components for diffusion at room temperature. A small correction for the effect of the temperature gradient in the boundary layer on the diffusion coefficient was made in a manner discussed later. 

It is to be hoped that future calculations will attempt to predict the diffusion coefficients of solutes in narrow pores. Measurements in such systems are extremely difficult to carry out and recent experiments in an admittedly broad pore (a 2 mm diameter capillary) are therefore of particular interest. Liukkonen and co-workers [61] found that the diffusion coefficient of NaCl in a dilute aqueous solution was 75% greater at the walls of this capillary than in the bulk solution, a result in line with the phenomenon of "surface conductivity [62]. Yet this finding clearly runs counter to the trend in the self-diffusion calculations in much narrower pores. It rather looks at this stage as if electrolytes near polar walls behave quite differently from non-electrolytes. 

As already mentioned the tracer experiment (which can also be conceived as a counter motion of the isotopes) delivers the tracer diffusion coefficient. In the case of oxides ideally the natural oxygen gas phase is instantaneously replaced by a gas phase with the same oxygen partial pressure but exhibiting a different isotope ratio (or an oxide is contacted with the same oxide in which a cation isotope is... 

In an instantaneous-pulse experiment, the electrode material is radioactive and hence detectable by a Geiger counter. As the pulse is realized with an electronic device generating a current of 10 A on a 0.1 -cm electrode for 0.1 s, with a Geiger counter placed 1 cm from the electrode, register the trace of the radioactive univalent ion at 450. 5 after the pulse. Calculate the limiting sensitivity of the instrument. Suppose the diffusion coefficient of the ion is the typical value of 10" m s . (Xu)... 

In the experiment described in Exercise 6 it was found that at a certain time the Geiger counter registered a maximum ion flux, i.e., the intensity of the radiation has a maximum with respect to time. It was also found that by placing the Geiger counter farther away from the electrode, the time at which the maximum occurs becomes longer, and the peak intensity of the maximum decreases rapidly. Justify this observation and evaluate its usefulness in experimentally measuring diffusion coefficients of ions. (Xu)... 

Sato, K., Yonemoto, T., and Tadaki, T. The determination of diffusion coefficients of counter-ion in the ion-exchange membrane by means of a batchwise Donnan dialytic experiments. J. Membr. Sci., 53, 215-227, 1990. 

Due to the small volumes and feature sizes, reaction rates are found to be quite different in the microbiosensor system in comparison to their macro counter part. Most of this is due to the fact that diffusion is not the limiting factor in a reaction any longer. For example, the diffusion time of a particle with a diffusion coefficient = 10 m s is 15 min to travel a distance of 1 mm, but only 10 s to travel 100 /rm and only 0.1 s to travel 10/rm [37]. Therefore, DNA hybridization reactions, antibody-antigen binding events, and enzyme—substrate catalytic reactions take place in a fraction of the time required earlier. DNA hybridization can be accomplished in a matter of seconds in a microchannel system, while it takes in the order of an hour when employing standard Northern or Southern Blotting techniques with a piece of nylon membrane soaking in several milliliters of hybridization solution. 

The characteristic feature of flow FFF is the superimposition of a second stream of liquid perpendicular to the axis of separation. This cross-flow drives the injected sample plug toward a semipermeable membrane that acts as the accumulation wall. The cross-flow liquid permeates across the membrane and exits the channel, whereas the sample is retained inside the channel in the vicinity of the membrane surface. Sample displacement by the cross-flow is countered by diffusion away from the membrane wall. At equilibrium, the net flux is zero and sample clouds of various thicknesses are formed for different sample species. As with other FFF techniques, a larger diffusion coefficient D leads to a thicker equilibrium sample cloud that, on average, occupies a faster streamline of the parabolic flow profile and subsequently elutes at a shorter retention time t,. For well-retained samples analyzed by flow FFF, t, can be related to D and the hydrodynamic diameter d by... 

Importantly, any process that results in lateral coverage gradients of either the additive or metal adatom will be countered by surface diffusion. Such surface transport is known to be strongly influenced by both potential and electrolyte composition through associated impact on the structure and composition of the surface. For example, anions are known to lead to substantial enhancement of metal adatom transport with diffusion coefficients ranging from 2 1CT16 up to 8 10-13 cm2 s 1 [137, 138],... 

The counter-exchange diffusion coefficient, Di 2, was derived from the equation suggested by Krishna [60] based on the generalization of Vignes [61] relationship for diffusion in bulk liquid mixtures ... 

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