Diffusion coefficients tracer

Figure 23.35 Polymer tracer diffusion in SWCNT/PS nanocomposites measured using ERD. (a) 140kd-PS distribution in 1.60vol.% SWCNT/480k PS nanocomposites as prepared and after annealing at 150°C for different times. The solid lines are fits of the diffusion equation to obtain the diffusion coefficients. Tracer diffusion in these nanocomposites is independent of annealing time (b) d-PS tracer diffusion coefficients in SWCNT/480k PS nanocomposites as a function of SWCNT...

Multicomponent Mixtures No simple, practical estimation methods have been developed for predicting multicomponent hquid-diffusion coefficients. Several theories have been developed, but the necessity for extensive activity data, pure component and mixture volumes, mixture viscosity data, and tracer and binaiy diffusion coefficients have significantly limited the utihty of the theories (see Reid et al.). 

The advantage of the simulations compared to the experiments is that the correspondence between the tracer diffusion coefficient and the internal states of the chains can be investigated without additional assumptions. In order to perform a more complete analysis of the data one has to look at the quench-rate and chain-length dependence of the glass transition temperature for a given density [43]. A detailed discussion of these effects is far beyond the scope of this review. Here we just want to discuss a characteristic quantity which one can analyze in this context. 

Diffusion has often been measured in metals by the use of radioactive tracers. The resulting parameter, DT, is related to the self-diffusion coefficient by a correlation factor/that is dependent upon the details of the crystal structure and jump geometry. The relation between DT and the self-diffusion coefficient Dsclf is thus simply... 

The high sensitivity and selectivity of the EPR response enables diamagnetic systems to be doped with very low concentrations of paramagnetic ions, the fate of which can be followed during the progress of a reaction. The criteria [347] for the use of such tracer ions are that they should give a distinct EPR spectrum, occupy a single coordination site and have the same valency as, and a similar diffusion coefficient to, the host matrix ion. Kinetic data are usually obtained by comparison with standard materials. 

If species 1 is a tracer for species 2, D,2 is termed the tracer diffusion (or self-diffusion) coefficient of species 2,D. Thus, for three ionic species the tracer diffusion coefficients can be obtained from consideration of a three-component (four-species) system in which one species is a tracer for another. 

In the data compiled by Janz and Bansal, various methods for measuring diffusion coefficients in molten salts are mentioned. The methods may be broadly classified as electrochemical and analytical. However, some other methods have occasionally been employed. Various electrochemical methods were reviewed by Lesko. Tracer diffusion in molten salts was reviewed by Spedding in 1971, where some other methods were also mentioned. 

An important result of this study is the conclusion of a particle-size-dependent COads surface mobility. The value obtained for large Ft particles is significantly smaller than Deo at a solid/gas interface. However, Kobayashi and co-workers, using solid state NMR, performed measurements of the tracer diffusion coefficient Deo at the solid/electrolyte interface and for Ft-black particles (about 5nm grain... 

It should be mentioned here that a different definition of the diffusion coefficient is often used in chemical engineering problems, which is more appropriate for the description of reactant or tracer transport. It takes into account the fact that the total fluid contained in a porous substance of porosity e is reduced by this factor relative to the bulk, so that an effective diffusion coefficient D of the reactants is defined such that... 

A similar situation occurs in tracer diffusion. This type of diffusion occurs for different abundances of an isotope in a component of the electrolyte at various sites in the solution, although the overall concentration of the electrolyte is identical at all points. Since the labelled and the original ions have the same diffusion coefficient, diffusion of the individual isotopes proceeds without formation of the diffusion potential gradient, so that the diffusion can again be described by the simple form of Fick s law. 

In considering axial dispersion as a diffusive flow, we assume that Fick s first law applies, with the diffusion or effective diffusion coefficient (equation 8.5-4) replaced by an axial dispersion coefficient, D,. Thus, for unsteady-state behavior with respect to a species A (e.g., a tracer), the molar flux (NA) of A at an axial position x is... 

Diffusion is followed by tracking the movements of tracer species through the solid to obtain the tracer diffusion coefficient, written as D when the tracer is identical to one of the components of the crystal, and D% when an impurity or foreign atom A is the tracer. Earlier studies made extensive use of radioactive isotopes because the progress... 

A plot of In cx versus x2 will have a gradient of [ —1/(4D t) (See also Supplementary Material S5.) A measurement of the gradient gives a value for the tracer diffusion coefficient at the temperature at which the diffusion couple was heated. 

The vacancy will follow a random-walk diffusion route, while the diffusion of the tracer by a vacancy diffusion mechanism will be constrained. When these processes are considered over many jumps, the mean square displacement of the tracer will be less than that of the vacancy, even though both have taken the same number of jumps. Therefore, it is expected that the observed diffusion coefficient of the tracer will be less than that of the vacancy. In these circumstances, the random-walk diffusion equations need to be modified for the tracer. This is done by ascribing a different probability to each of the various jumps that the tracer may make. The result is that the random-walk diffusion expression must be multiplied by a correlation factor, / which takes the diffusion mechanism into account. 

The above sections have focused upon homogeneous systems with a constant composition in which tracer diffusion coefficients give a close approximation to selfdiffusion coefficients. However, a diffusion coefficient can be defined for any transport of material across a solid, whether or not such limitations hold. For example, the diffusion processes taking place when a metal A is in contact with a metal B is usually characterized by the interdiffusion coefficient, which provides a measure of the total mixing that has taken place. The mixing that occurs when two chemical compounds, say oxide AO is in contact with oxide BO, is characterized by the chemical diffusion coefficient (see the Further Reading section for more information). 

Radioactive 22Na was coated onto a glass sample that was made into a diffusion couple (Fig. 5.2) and heated for 4 h at 411°C. The radioactivity perpendicular to the surface is given in the following table. Calculate the tracer diffusion coefficient, D, of 22Na in the glass. 

The radioactive tracer diffusion coefficient of 22Na in glass is given in the following table. Estimate the activation energy for diffusion. 

The correlation factor,/, is defined by the ratio of the tracer diffusion coefficient to the random-walk diffusion coefficient (Section 5.6) ... 

Oxygen Tracer Diffusion Coefficient (D ), Oxygen Surface Exchange Coefficient (Ar) and Oxygen Ionic Conductivity (a, in air) of Doped Lanthanum Cobalt Ferrite-Based Perovskites... 

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