Loss penetration depths

A factor closely related to the catalyst loading is the efficiency or utilization of the electrode. This tells how much of the electrode is actually being used for electrochemical reaction and can also be seen as a kind of penetration depth. To examine ohmic and mass-transfer effects, sometimes an effectiveness factor, E, is used. This is defined as the actual rate of reaction divided by the rate of reaction without any transport (ionic or reactant) losses. With this introduction of the parameters and equations, the various modeling approaches can be discussed. 

For ideal solutions, the partial pressure of a component is directly proportional to the mole fraction of that component in solution and depends on the temperature and the vapor pressure of the pure component. The situation with group III-V systems is somewhat more complicated because of polymerization reactions in the gas phase (e.g., the formation of P2 or P4). Maximum evaporation rates can become comparable with deposition rates (0.01-0.1 xm/min) when the partial pressure is in the order of 0.01-1.0 Pa, a situation sometimes encountered in LPE. This problem is analogous to the problem of solute loss during bakeout, and the concentration variation in the melt is given by equation 1, with l replaced by the distance below the gas-liquid interface and z taken from equation 19. The concentration variation will penetrate the liquid solution from the top surface to a depth that is nearly independent of zlDx and comparable with the penetration depth produced by film growth. As result of solute loss at each boundary, the variation in solute concentration will show a maximum located in the melt. The density will show an extremum, and the system could be unstable with respect to natural convection. 

The values of e and e" of a food material play a critical role in determining the interaction of the microwave electric field with the material. A discussion of these interactions follows. A "map" of foods plotted against their dielectric parameters was introduced by Bengtsson and Risman (1971). Table 1 gives values for the dielectric constant, loss factor and penetration depth, and Figure 1 shows a "map" of these values for common foods. 

The more absorptive a material, i.e., the higher the loss factor e", the less deep microwave energy will penetrate into that material. A parameter, penetration depth, dp, has been defined which measurers this penetration, dp is a function of both e and e" and serves as a guideline to the heating effectivity of a material. 

The penetration depth of a material depends on both the dielectric constant, e and loss factor e" of the material. An approximate formula which holds to better than 5% for foods is ... 

Another important factor in dielectric heating is the depth of penetration of the radiation because an even field distribution in a material is essential for the imiform heating. The properties that most strongly influence the penetration depth are the dielectric properties of the material. These may vary with the free space wavelength and frequency of the propagating wave. For low loss dielectrics such as plastics (e" l) the penetration depth is given approximately by ... 

The penetration depth increases linearly with respeet to the wavelength, and also inereases as the loss factor decreases. Despite this, however, penetration is not influenced signifieantly when increasing frequencies are used beeause the loss faetor also drops away maintaining a reasonable balance in the above equation. 

As the material is heated, its moisture content deereases leading to a deerease in the loss factor. It can be seen from equation (8) that the decrease in loss factor causes in the penetration depth of radiation. 

Fig. 12. Mean penetration depth (Rp) and fluctuations (<7) in the energy loss associated with He+ implanting into Si as a function of the collision energy of He . (Ref. 64). Theoretical data are from Ref. 65.

The above considerations show that only the electrons which have escaped from the host material without energy loss contribute to the Auger peak. This contribution is made in an exponentially decreasing manner ) for successive deeper layers ) with a characteristic distance d ). Thus the extent to which such measurements are specific to the surface region depends on the ejection depth d of the Auger electrons and not on the penetration depth of the exciting particle into the specimen. 

The electronic structure of a nanodiamond sample may be examined by various spectroscopic techniques. Depending on the choice of method, the information obtained from doing so corresponds to different depths of the lattice. The Auger spectroscopy, for instance, has a low penetration depth, so it may serve to determine the situation of n-electrons on the surface. In the Cls-loss spectrum, on the other hand (Section 5.4.1.3), no 7i-transitions are observed as this method chiefly yields information on the second to seventh layer of atoms below the surface. 

Mirin is a condiment with almost 40%-50% sugar and is widely used in Japanese cuisine. Dielectric loss factor of mirin is affected by both the dipolar loss component and the ionic conductivity. Ionic conductivity is lower at higher microwave frequencies. The combined effect of temperature, microwave frequency, and sugar content is complex and hard to describe. Nevertheless, the e" increases with frequency and temperature. The penetration depth decreases as the processing temperature increases. The effect of temperature on the is significant at lower processing frequencies at higher frequencies, temperature has only moderate effect on the d. Tanaka et al. (2005) reported similar results for soy sauce. It was noted by Liao et al. (2003) that this trend is distinctive for thick or complex solutions. 

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