Edge-effects

Uniformity of the current density over the whole area of the electrode is important for the interpretation of current-potential data. We recall that the measured quantities are the total current and the potential at a certain point in solution, where the tip of the Luggin capillary is located. From this we can calculate the average current density, but not its local value. As for the potential, we have already noted that, unless the cell is properly designed, the potential measured may be grossly in error, if the reference electrode is located at a point where the local current density deviates significantly from its average value. 

An interesting case to be discussed is the edge effect calculated for the point of contact between an electrode and the insulator in which it is cast. The equation describing the current density as a function of distance d from the point of contact is 

A complete evaluation of the uniformity of current distribution should take into account the finite rate of the charge-transfer reaction that is taking place at the interface. When this is done, the current density becomes more uniform, and it neither declines to zero, nor does it increase to infinity at the edge, as implied above. 

It turns out that both lower exchange-current density for the metal deposition process and lower applied current density enhance the uniformity of the current distribution. 

Maintaining a uniform current distribution is of great importance in the electrochemical industry. In plating it determines the uniformity of the thickness of the deposit in electro-organic synthesis it affects the uniformity of the products. A nonuniform current distribution can lead to the formation of undesired side products and to waste of energy in all areas of the electrolytic industry. 

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HyperChem uses th e ril 31 water m odel for solvation. You can place th e solute in a box of T1P3P water m oleeules an d impose periodic boun dary eon dition s. You may then turn off the boundary conditions for specific geometry optimi/.aiion or molecular dynamics calculations. However, th is produces undesirable edge effects at the solvent-vacuum interface. 

When the cutoff is sharp, discontinuities in the forces and resultant loss of con servation of energy m molecular dynamics calcnla-tionscan result.To minimi/e edge effects of a cu toff, often theciit-off IS implemented with a switching or shifting function to allow the interactions to go smoothly to /ero. 

Use a solvent or water bath to capture the influence of solvent on the solute. Use the fewest shells of water/solvent possible, but no fewer than two, if resources are scarce. Use a formal "box" of water, if possible, to reduce the influence of edge effects. 

Fig. 14. Edge effects produced during development (a) schematic and (b) a microdensitometrie trace across a developed edge resulting from a knife-edge...

A constant is often determined from measurements with a Newtonian oil, particularly when the caUbrations are suppHed by the manufacturer. This constant is vaUd only for Newtonian specimens if used with non-Newtonian fluids, it gives a viscosity based on an inaccurate shear rate. However, for relative measurements this value can be useful. Employment of an instmment constant can save a great deal of time and effort and increase accuracy because end and edge effects, sHppage, turbulent interferences, etc, are included. 

FIG. 5-5 Heating and cooling of a solid of infinite thickness, neglecting edge effects. (This may he used as an approximation in the zone near the surface of a body of finite thickness.)... 

There will be many times when the quantity of sample is limited. While it is best to use the 92.9 cm" (0.1 ft") area leaf in order to minimize edge effects and improve accuracy, when the sample volume is limited it is much better to have several data points with a smaller leaf than onl one or two using the larger leaf. Data from leaves as small as 23.2 cm" (0.025 ft") are reasonably accurate and can be used to scale up to commercially sized units. However, it is usually prudent to employ a more conservative scale-up factor. 

When an isotropic material is subjected to planar shock compression, it experiences a relatively large compressive strain in the direction of the shock propagation, but zero strain in the two lateral directions. Any real planar shock has a limited lateral extent, of course. Nevertheless, the finite lateral dimensions can affect the uniaxial strain nature of a planar shock only after the edge effects have had time to propagate from a lateral boundary to the point in question. Edge effects travel at the speed of sound in the compressed material. Measurements taken before the arrival of edge effects are the same as if the lateral dimensions were infinite, and such early measurements are crucial to shock-compression science. It is the independence of lateral dimensions which so greatly simplifies the translation of planar shock-wave experimental data into fundamental material property information. 

Prompt instrumentation is usually intended to measure quantities while uniaxial strain conditions still prevail, i.e., before the arrival of any lateral edge effects. The quantities of interest are nearly always the shock velocity or stress wave velocity, the material (particle) velocity behind the shock or throughout the wave, and the pressure behind the shock or throughout the wave. Knowledge of any two of these quantities allows one to calculate the pressure-volume-energy path followed by the specimen material during the experimental event, i.e., it provides basic information about the material s equation of state (EOS). Time-resolved temperature measurements can further define the equation-of-state characteristics. 

It should also be noted that in some cases correction factors, Fj, and Fp are applied to the drag and pressure flow terms. They are to allow for edge effects and are solely dependent on the channel width, T, and channel depth, h, in the metering zone. Typical values are illustrated in Fig. 4.11. 

When using air curtains the edge effects are neglected and the flow is treated as two-dimensional. The different parts of a two-dimensional jet are sketched in Fig. 10.63. 

Alternatively to (3), account for certain end and edge effects (e.g., shear-extension coupling) in the data-reduction process. 

R. Byron Pipes and I. M. Daniel, Moir6 Analysis of the Interiaminar Shear Edge Effect in Laminated Composites, Journal of Composite Materials, April 1971, pp. 255-259. 

For a theoretical analysis of SFA experiments it is prudent to start from a somewhat oversimplified model in which a fluid is confined by two parallel substrates in the z direction (see Fig. 1). To eliminate edge effects, the substrates are assumed to extend to infinity in the x and y directions. The system in the thermodynamic sense is taken to be a lamella of the fluid bounded by the substrate surfaces and by segments of the (imaginary) planes x = 0, jc = y = 0, and y = Sy. Since the lamella is only a virtual construct it is convenient to associate with it the computational cell in later practical... 

Somewhat along the same lines are techniques that have been employed to avoid edge effects by having the specimen come into contact only with... 

EC mechanism, 34, 42, 113 E. Coli, 186 Edge effect, 129 Edge orientation, 114 Electrical communication, 178 Electrical double layer, 18, 19 Electrical wiring, 178 Electrocapillary, 22 Electrocatalysis, 121 Electrochemical quartz crystal, microbalance, 52 Electrochemihuiiinescence, 44 Electrodes, 1, 107... 

Liquid flows down an inclined surface as a film. On what variables will the thickness of the liquid film depend Obtain the relevant dimensionless groups. It may be assumed that the surface is sufficiently wide for edge effects to be negligible. 

Edge effects must be considered carefully since there are so many interior edges with a segmented mirror telescope. Again several approaches have been considered. The approach used for the Keck segments was to pohsh the mir-... 

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