Tracer diffusion effect

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. 

Bulk path at moderate to high overpotential. Studies of impedance time scales, tracer diffusion profiles, and electrode microstructure suggest that at moderate to high cathodic over potential, LSM becomes sufficiently reduced to open up a parallel bulk transport path near the three-phase boundary (like the perovskite mixed conductors). This effect may explain the complex dependence of electrode performance on electrode geometry and length scale. To date, no quantitative measurements or models have provided a means to determine the degree to which surface and bulk paths contribute under an arbitrary set of conditions. 

Schmitz et al (31) have proposed that the discrepancy between QLS and tracer diffusion measurements can be reconciled by considering the effects of small ions on the dynamics and scattering power of the polyelectrolyte. In this model, the slow mode arises from the formation of "temporal aggregates . These arise as the result of a balance between attractive fluctuating dipole forces coming from the sharing of small ions by several polyions, and repulsive electrostatic and Brownian diffusion forces. This concept is attractive, but needs to be formulated quantitatively before it can be adequately tested. 

The key physics of our model (see Eqs. (9) and (10)) is contained in the nonlocal diffusion kernels which occur after integrating over the atomic processes which produce step fluctuations. We have calculated these kernels for a variety of physically interesting cases (see Appendix C) and have related the parameters in those kernels to atomic energy barriers (see Appendix B). The model used here is close in spirit to the work of Pimpinelli et al. [13], who developed a scaling analysis based on diffusion ideas. The theory of Einstein and co-workers and Bales and Zangwill is based on an equihbrated gas of atoms on each terrace. The concentration of this gas of atoms obeys Laplace s equation just as our probability P does. To make complete contact between the two methods however, we would need to treat the effect of a gas of atoms on the diffusion probabilities we have studied. Actually there are two effects that could be included. (1) The effect of step roughness on P(J) - we checked this numerically and foimd it to be quite small and (2) The effect of atom interactions on the terrace - This leads to the tracer diffusion problem. It is known that in the presence of interactions, Laplace s equation still holds for the calculation of P(t), but there is a concentration... 

Interdiffusion, effective binary diffusion, and multicomponent diffusion may be referred to as chemical diffusion, meaning there are major chemical concentration gradients. Chemical diffusion is defined relative to self diffusion and tracer diffusion, for which there are no major chemical concentration gradients. 

Tracer diffusivities are often determined using the thin-source method. Self-diffusivities are often obtained from the diffusion couple and the sorption methods. Chemical diffusivities (including interdiffusivity, effective binary diffusivity, and multicomponent diffusivity matrix) may be obtained from the diffusion-couple, sorption, desorption, or crystal dissolution method. 

Figure 15-7. Mixed alkali effect tracer diffusion coefficients ), and D(a) from electrical conductivity (D(a ) = (R T/c -ia zfF1)) for (Cs Na, N)20 5 Si02, as a function of N, see [R. Tferai (1971)]. T = 480 °C.

We should mention here that a better way to extract the activation energies for vacancy-mediated diffusion would be to plot the tracer diffusion coefficient of the embedded atoms vs. 1/kT, rather than their jump rate. As we discussed in Section 4, the mean square jump length depends on the proximity of steps, and so does the average jump frequency. This adds non-statistical noise to the two plots in Fig. 12. However, it can be shown easily that these effects on jump length and jump rate cancel in the resulting tracer diffusion coefficient, which thus becomes independent of the distance to steps. In this way, a more accurate value for the activation energy has been obtained for the case of In/Cu(0 0 1) of 717 30meV [23]. 

Here capacitance effects are absent and modifications are due to the different weight of the different charges. If we ignore correlation factors, the general result for the tracer diffusion coefficient is... 

While Dq directly reflects the ionic conductivity measured in a steady state experiment, the relationships are more complex for chemical diffusion and tracer diffusion. For simplicity we assume that the transport is so slow that local relaxation effects occur instantaneously.240... 

Buzzi A, D Isidoro M, Davolio S (2003) A case study of an orographic cyclone south of the Alps during the MAP SOP. Q J R Meteor Soc 129 1795-1818 DTsidoro M, Maurizi A, Tampieri F, Tiesi A, Villani MG (2005) Assessment of the numerical diffusion effect in the advection of passive tracer in BOLCHEM. Nuovo Cimento C 28 151-158... 

The in situ precipitation technique and transmission electron microscopy have been used to investigate the effect of DMSO on percutaneous absorption in the mouse barrier [27] and human SC [46]. Sharata and Burnette examined ultrastructural changes in mouse stratum comeum by determining the distribution of sulfide precipitates of topically applied, water-soluble tracers (Hg and Ni ) after application of enhancer [27]. For skin pretreated with DMSO, mercury and nickel precipitates were found within swollen basal stratum comeum cells as well as intercellularly and associated with the cell envelopes, but not below the stratum comeum-stratum granulosum interface. It was concluded that treatment with DMSO, as well as with other dipolar aprotic solvents such as DMF and DMA, alters the passive intercellular diffusion pathway by expanding the size of the basal stratum comeum cells, resulting in an increased free volume for tracer diffusion. 

The Effect of Ionic Atmosphere on the Tracer Diffusion of Miceiles Toshihiro Tominaga and Masayuki Nishinaka... 

In the two-component system gas + zeolite, in parallel with a general two-component system, one may consider 5 diffusion coefficients Dab (interdiffusion coefficient of sorbate and zeolite) Da, Db (intrinsic diffusion coefficients, respectively, of sorbate and zeolite) and Da, Db (tracer diffusion coefficients, respectively, of sorbate and zeolite). However, because Db and Db are effectively zero, as for a nonswelling crystal. 

In the second part of Eq. (10.22) the fact has been used that, if correlation effects can be neglected, the tracer diffusion coefficient, D, is equal to the self-diffusion coefficient, It is important to note once again that Eq. (10.18) is valid in the limit of small Po -gradients only. Since both D and kg for a given material are a function of its specific defect chemistry, in general, will be a function of process parameters Pq and temperature. 

J. Maier, Mass transport in the presence of internal defect reactions-concept of conservative ensembles I, Chemical diffusion in pure compounds. /. Am. Ceram. Soc., 76(5) (1993) 1212-1217 II, Evaluation of electrochemical transport measurements, ibid., 1218-1222 III, Trapping effect of dopants on chemical diffusion, ibid., 1223-1227 IV, Tracer diffusion and intercorrelation with chemical diffusion and ion conductivity, ibid., 1228-1232. 

For ionic solids, measurement of the ionic conductivity, <7 , has long provided a method for studying their atomic diffusion [25, 209, 225, 226] (see also Chapter 3). The measurements are usually made with an alternating current (AC) bridge operating at a fixed frequency, f (typically >1 kHz), to avoid polarization effects. The early studies were restricted to measurements on single crystals, and in this case (7i and the tracer diffusion coefficient were seen to be related by the Nernst-Einstein equation [25] ... 

In many cases, the NMR method of measuring D is superior to tracer diffusion studies. For liquids, at least, the diffusion coefficient of the tracer does not correspond to that of the major chemical species except for very small tracer concentrations (Ahn, et al., 1972). Furthermore, the NMR techniques do not contaminate the sample, the measured value of D is not disturbed by isotope effects, and the method is not limited to the availability of suitable isotopes, although it is, of course, limited to suitable NMR nuclei and the existence of Hahn echoes. 

Jones, J.D. and K. Luby-Phelps, Tracer diffusion through F-actin Effect of filament length and cross-linking. Biophysical Journal, 1996, 71, 2742-2750. 

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