Homogeneity vs. Heterogeneity

Lansky and Weiss defined [131] the classical dissolution first-order model in terms of the fraction of dose dissolved, ip (t) (equation 5.16 assuming 6=1), 

This measure of heterogeneity generalizes the notion of heterogeneity as a departure from the classical first-order model initially introduced [121] for the specific case of the Weibull function. In addition, the above equation can also be used for comparison between two experimentally obtained dissolution profiles [131]. 

The difference factor fi [137] measures the relative error (as a percentage) between two dissolution curves over all time points  

The similarity factor /2 [137-139] is a logarithmic reciprocal transformation of the sum of squared errors and is a measurement of the similarity in the percentage dissolution between the two curves  

Both factors take values in the range 0-100 assuming that the percentage dissolved values for the two products are not higher than 100%. When no difference between the two curves exist, i.e., at all time points R, = 7 i, then /i = 0 and f2 = 100. On the other hand, when the maximum difference between the two curves exists, i.e., at all time points Ri rl = 100, then /i = 100 and /2 = 0. 

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This article discusses the anodic synthesis of heterocyclic compounds that have appeared during the last decade. The mechanistic aspects involving intramolecular, intermolecular cyclizations and the homogeneous vs heterogeneous anodic oxidations were considered. This review deals with the recent advances in anodic oxidations in which heterocyclic compounds were synthesized through carbon-heteroatom and heteroatom-heteroatom bond formation. 

The packed bed reactors section of this volume presents topics of catalyst deactivation and radial flow reactors, along with numerical techniques for solving the differential mass and energy balances in packed bed reactors. The advantages and limitations of various models (e.g., pseudo-homogeneous vs. heterogeneous) used to describe packed bed reactors are also presented in this section. 

Homogeneous vs. heterogeneous systems. Homogeneous systems are uniform in properties over their entire volume. Otherwise such systems are heterogeneous. 

Table 1. Homogeneous vs. heterogeneous catalysis the advantages and disadvantages...

T Tnder suitably alkaline conditions and with a sufficient volume of water, it is possible to dissolve aluminosilicate gels to form clear liquids free of any residual solids. Such liquids are of interest because from them one may hope to examine the first stages of zeolite crystallization. The question of homogeneous vs. heterogeneous nucleation (7, 8) of zeolite crystals may be studied usefully when clear liquids provide the reaction mixture. For these reasons, we have examined the first solids to appear from such liquids and have followed their subsequent evolution. 

Pd(0) nanopartides (NPs) as catalysts in cross-coupling reactions and the homogeneous vs. heterogeneous debate... 

Homogeneous vs. Heterogeneous Distributions of Functional Groups at Surfaces... 

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