Overall heterogeneous

For the blend uniformity application, the primary concern is overall heterogeneity within the sample. This is directly indicated by the width of the distribution and is quantitatively measured as the percent standard deviation relative to the mean (%SD). The %SD value obtained from the PLS scores distribution from each of the six imaged tablets is noted on the histograms in Figure 8.15(A-F). The value of %STD consistently decreases as the blending quality of the sample improves. 

If the interface reaction rate is extremely small so that mass/heat transfer is rapid enough to transport nutrients to the interface, then interface reaction rate (Equation 4-33) is the overall heterogeneous reaction rate (Figure 1-lla). If the interface reaction is relatively rapid and if the crystal composition is different from the melt composition, the heterogeneous reaction rate may be limited or slowed down by the mass transfer rate because nutrients must be transported to the interface and extra junk must be transported away from the interface (Figures 1-llb and 1-llc). If the crystal composition is the same as the melt composition, then mass transfer is not necessary. When interface reaction rate and mass transfer rate are comparable, both interface reaction and mass transfer would control the overall heterogeneous reaction (Figure 1-lld). 

Many of the anti-neoplastic drugs currently available on the market specifically target the cancerous tumor and do not account for the overall heterogeneity of the disease. It is reasonable to assume that due to the complex make-up of a tumor, combined therapies may be necessary to treat the different cell types involved. One major hurdle to understanding tumor cells at the gene expression level is our limited ability to isolate pure populations of diseased cells. 

In fact, most mesoporous adsorbents possess complex networks of pores of different size. It is therefore unlikely that the condensation-evaporation processes can occur independently in each pore. The complexity of capillary condensation in porous materials is illustrated by the recent Monte Carlo computer simulation studies of Page and Monson (1996) and Gelb and Gubbins (1998). The well-defined hysteresis loops observed in the simulation results of both studies were attributed to the presence of thermodynamically metastable states and not to kinetic effects. However, it appears that the extent of die hysteresis was associated with the overall heterogeneity of the adsorbent structure and not simply due to capillary condensation within individual pores. 

Chemical heterogeneity of the parent and mixed oxides surface contributes significantly to their overall heterogeneity. Because of this, the comparison of the parameters of Eq. (32) and Eq. (50) at 1/ = I was performed. It has been found that the 7 values vary non-linearly with T, while the dependence of ko on T is not described by the Arrhenius equation and, hence, is in contradiction with the dependence of these parameters on T as obtained on the basis of kinetic data for chemisorption on the Si, Ti and A1 oxides surface [80]. 

The equilibrium constant of the overall heterogeneous catalytic reaction can be expressed by the multiplication of the equilibrium constants of the elementary steps, which constitute the overall reaction. In the particular case of ammonia synthesis (eq.7.97), the equilibrium constant is given as... 

The composition of pyrolysates of proteins is still obscure despite the effort of several researchers. This is partly due to the different structures of the amino acids, the different stabilities of the various peptide bonds and the overall heterogeneity of the peptide. 

Example 2.4 Give the mechanism of esterification reaction with certain exchanger catalyst and mathematically model the overall heterogeneous reaction. 

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