Active-area-density effect

Background and Literature, the Active-Area-Density Effect. 124... 

Relatively little attention has been paid to current-density nonuniformity caused by uneven pattern density. This effect has been discussed by Romankiw and coworkers [36-38]. A theoretical investigation of the active-area-density effect was presented by Mehdizadeh et al. [23]. This was followed by an experimental investigation [39, 40]. Some highlights from the above mentioned publications by Mehdizadeh et al. are presented in the next section. Further discussion of the active-area-density effect appears in a recent publication on electroplated thin-film wiring for high-performance packaging [41] and in a paper on the fabrication of flexible circuits [14]. 

Reference [23] describes a treatment of the secondary current distribution on the pattern scale in a case with two adjacent zones with different active-area densities. The development shows that, in the Tafel kinetic regime, the current distribution should depend on the geometry, the Wagner number, and the ratio of the two active-area densities. The Wagner number is based on the length scale of the pattern nonuniformity (for example, the distance from the center of zone (1) to the center of zone (2)) and based on the superficial current density. There is a primary current distribution in the case of Woj = 0, in which /gyp is uniform and i/ is inversely proportional to a. This represents the most extreme case of nonuniformity that pattern effects can produce. Fortunately, differences in active-area densities on patterned workpieces often exist across relatively short distances, and Wa is higher than 1. However, if there is a wide variation of the active-area density from place to place, the pattern-driven nonuniformity can still be severe, even across short distances. 

Working within a similar scheme, DeBecker and West introduced a treatment of feature scale effects on the overall current distribution which they call the hierarchical model [138]. Rather than represent the features as a smoothly varying density of active area, they retain the features, but simplify their representation in the global model. An integral current for each feature is assigned to the geometric center of the feature to provide a simplified boundary condition for the secondary current distribution. This boundary condition captures a part of the ohmic penalty paid when current lines converge onto features. It thus contains more information than the active area approximation but still less than a fully matched current distribution on the two levels. 

The effective diffusivity Dn decreases rapidly as carbon number increases. The readsorption rate constant kr n depends on the intrinsic chemistry of the catalytic site and on experimental conditions but not on chain size. The rest of the equation contains only structural catalyst properties pellet size (L), porosity (e), active site density (0), and pore radius (Rp). High values of the Damkohler number lead to transport-enhanced a-olefin readsorption and chain initiation. The structural parameters in the Damkohler number account for two phenomena that control the extent of an intrapellet secondary reaction the intrapellet residence time of a-olefins and the number of readsorption sites (0) that they encounter as they diffuse through a catalyst particle. For example, high site densities can compensate for low catalyst surface areas, small pellets, and large pores by increasing the probability of readsorption even at short residence times. This is the case, for example, for unsupported Ru, Co, and Fe powders. 

Effective snrface areas generally range from 300 to 1500 mYg, depending on the base material, activation method, density, and so on, althongh some made from petroleum coke exceed 3000 m /g. Larger surface areas are often assnmed to be better, bnt snrface area does not always correlate with capacity. Even when it does, kinetics and other aspects may ontweigh the effect of capacity on overall cost and performance. 

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