Nonuniform conduction

One would like to be sure that the current is due to uniform conduction, and not to defects or weak places in the films. Some of the earlier data, in our opinion, undoubtedly refer to nonuniform conduction. The Schottky law is still observed in some such cases. It is difficult to compare results from different laboratories because of the variation in conditions under which the oxide was made and the counterelectrodes applied, and because of uncertainties about contact areas, and other details. For example, the oxide will be heated by radiation from the evaporation source, and it is known that a rise of a few 10°C has an appreciable effect on Ta205 films. 

The abihty to accept and hold the electrostatic charge in the darkness. The photoconductive layer should support a surface charge density of approximately 0.5-2 x 10 C/cm. The charge also has to be uniformly distributed along the surface, otherwise nonuniformities can print out as spot defects. The appHed surface potential should be retained on the photoreceptor until the time when the latent electrostatic image is developed and transferred to paper or, if needed, to an intermediate belt or dmm. In other words, the "dark decay" or conductivity in the dark must be very low. The photoconductor materials must be insulators in the dark. 

If the sample is an insulator there are still methods by which it can be studied in the instrument. The simplest approach is to coat it with a thin (10-nm) conducting film of carbon, gold, or some other metal. In following this approach, care must be taken to avoid artifacts and distortions that could be produced by nonuniform coatings or by agglomeration of the coating material. If an X-ray analysis is to be... 

Heterogeneity, nonuniformity and anisotropy are terms which are defined in the volume-average sense. They may be defined at the level of Darcy s law in terms of permeability. Permeability, however, is more sensitive to conductance, mixing and capillary pressure than to porosity. 

Numerous studies of jets supplied into a uniform or nonuniform cross-flow were conducted in application to such areas as air pollution control, burning processes, etc. Detailed discussion of these studies is beyond the current review. However, some results of these studies will be mentioned as needed in the following section. 

The results of the above section show that the significant nonuniformity of the distribution of the filler particles in the thickness of sample is observed during injection moulding of the filled polymers. This nonuniformity must affect the electrical properties of CCM owing to the strong dependence of the CCM conductivity on the filler concentration. Although there are no direct comparisons of the concentration profiles and conductivity in the publications, there is data on the distribution of conductivity over the cross-section of the moulded samples. 

Fig. 28. Wall temperature maps for 1-hole particles (a) without wall conduction (b) with wall conduction, on the same temperature scale as (a) (c) with wall conduction, on a temperature scale chosen to show nonuniform temperature features.

The more recent Thomas model [209] comprises elements of both the Semenov and Frank-Kamenetskii models in that there is a nonuniform temperature distribution in the liquid and a steep temperature gradient at the wall. Case C in Figure 3.20 shows a temperature distribution curve from self-heating for the Thomas model. The appropriate model (Semenov, Frank-Kamenetskii, or Thomas) is determined by the ratio of the heat removal from the vessel and the thermal conductivity in the vessel. This ratio is determined by the Biot number (Nm) which has been described previously as hx/X, in which h is the film heat transfer coefficient to the surroundings (air, cooling mantle, etc.), x is the distance such as the radius of the vessel, and X is the effective thermal conductivity. 

Active centers, nature of, 10 96 Active site, 27 210-221 in catalysts, 17 103-104, 34 1 for olefin chemisorption, 17 108-113 dual-site concept, 27 210 electrical conductivity, 27 216, 217 ESCA, 27 218, 219 ESR, 27 214-216 infrared spectroscopy, 27 213, 214 model, 27 219-221 molybdena catalyst, 27 304-306 Mdssbauer spectroscopy, 27 217, 218 nonuniform distribution, transport-limited pellets, 39 288-291... 

In general, pores swell nonuniformly. As a simplification, fhe random network was assumed to consist of fwo types of pores. In fhis fwo-stafe model, nonswollen or "dry" pores (referred to later as "red" pores) permit only a small residual conductance due to tightly bound surface water, which solvates the charged surface groups. Swollen or "wet" pores (referred to later as "blue" pores) contain extra water in the bulk, allowing them to promote the high bulk-like conductance. Water uptake by the membrane corresponds to the swelling of wef pores and to the increase of their relative fraction. 

The physical mechanism of membrane water balance and the formal structure of modeling approaches are straightforward. Under stationary operation, the inevitable electro-osmotic flux has to be compensated by a back flux of water from cathode to anode, driven by gradients in concentration, activity, or liquid pressure of water. The water distribution in PEMs that is generated in response to these driving forces decreases from cathode to anode. With increasing/o, the water distribution becomes more nonuniform. the water content near the anode falls below the percolation threshold of proton conduction, X < X. This leaves only a small conductivity due to surface transport of water. As a consequence, increases dramatically this can lead to failure of the complete cell. 

Although the matrix may have a well-defined planar surface, there is a complex reaction surface extending throughout the volume of the porous electrode, and the effective active surface may be many times the geometric surface area. Ideally, when a battery produces current, the sites of current production extend uniformly throughout the electrode structure. A nonuniform current distribution introduces an inefficiency and lowers the expected performance from a battery system. In some cases the negative electrode is a metallic element, such as zinc or lithium metal, of sufficient conductivity to require only minimal supporting conductive structures. 

To expand on the last remark, the simulation results from Fuller and Newman are shown in Figure 17. The curves clearly show a nonuniform current distribution that is mainly due to the change in the gas concentrations and the membrane hydration. In the simulation, the initial decrease in the current density is due to the change in the oxygen concentration. However, once enough water is generated to hydrate the membrane, the increased conductivity yields higher local current densities. What... 

A difference of two orders of magnitude has been measured in the DC conductivity of AU55 and Aufj at 100 K [29,30]. From this, and the MES observation [46] that the total electron count in the metal core of Au s may be about 2 less than in AU55, it would appear that there is a very nonuniform distribution of levels, with a much larger energy splitting for the HOMO level of Au j than for AU55. Furthermore, the density of states in these levels must be very low. 

Preliminary residence time distribution studies should be conducted on the reactor to test this assumption. Although in many cases it may be desirable to increase the radial aspect ratio (possibly by crushing the catalyst), this may be difficult with highly exothermic solid-catalyzed reactions that can lead to excessive temperature excursions near the center of the bed. Carberry (1976) recommends reducing the radial aspect ratio to minimize these temperature gradients. If the velocity profile in the reactor is significantly nonuniform, the mathematical model developed here allows predictive equations such as those by Fahien and Stankovic (1979) to be easily incorporated. 

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