Darken relation

An adsorption kinetic model was developed to evaluate the adsorption rates of five pure gases (Nj, O2, Ar, CO, and CH4) on a Takeda-3A CMS over a wide range of pressures up to ISatm. The kinetic characteristics of adsorption on the CMS were studied by using the adsorption equilibrium of five pure gases measured at three different temperatures and their physical properties. Since the diffiisional time constants of all the components showed much stronger dependence of pressure than those expected by the traditional Darken relation, a structural diffusion model was applied to predict the strong pressure dependence. The proposed model successfully predicted the dif ional time constant up to high pressure on the CMS. 

The exponential increases of the effective difiusional time constant might be explained by the following Darken-relation and this relation was derived under the assumption that the chemical potential gradient is the driving force of the diffusion (Ruthven, 1992). 

If above Darken-relation (Eq. (S)) is combined with the Langmuir, L-F, Toth, and D-R isotherms, the resulted models are as follows ... 

The transport diffusivity and self-diffusivity are related by the Darken relation,... 

This is now known as the Darken relation, and it depends on the equilibrium isotherm between the two phases. It basically states that the surface diffusivity at any loading is equal to the value at zero loading multiplied by a thermodynamic correction factor... 

Let us now turn to the case where both the Langmuir isotherm and surface diffusion are included. We assume that the surface diffusivity takes the following Darken relation form ... 

Caldwell-Babb Darken observed that sohd-state diffusion in metallurgical applications followed a simple relation. His equation related the tracer diffusivities and mole fractious to the mutual diffusivity ... 

The rate of darkening is related to the temperature of the solution and, if warm potassium hydroxide solution is used, the color will de velop somewhat more rapidly. Differences in the rate of darkening do not appear to affect the yield or purity of product. 

Fig. 6.1 Location of the Galapagos Islands in relation to the South American mainland. The darkened island is Albermerle, Isla Isabela, in the Ecuadorian system...

Similarly, five closely related melanocortin receptors that respond to various peptides derived from the POMC precursor have been identified (Fig. 18-7) [24]. As expected, the receptor on adrenal cortical cells responds best to ACTH, which normally stimulates adrenal steroidogenesis, and the receptor on melano cytes responds best to aMSH, which causes skin darkening. However, the pattern of melanocortin receptor expression in the brain is not simply explained by the known patterns of peptide expression in the brain or by the known effects of POMC-derived peptides when applied to various brain regions. With this number of peptide receptors, it is obvious that production of final peptide products must be precisely controlled and that different biosynthetic processing pathways can dramatically affect the biological activity observed (Figs 18-5,18-7). 

It is readily recognized that the conformation in which the lone pair is equatorial corresponds to an anti-arrangement of the carbon lone pair in relation to the adjacent S—C bond (darkened for the sake of clarity) and the axial case a syn orientation. Based on our approach, we would predict that the carbanion with the lone pair equatorial will be the most stable conformation. This is indeed observed experimentally361. ... 

Table 5.51 Energy terms relating standard state chemical potentials of pnre components (p,°o.) to lictive potentials in the host phase (p-Js) in the Will and Powell (1992) application of Darken s Quadratic Formalism to amphiboles. 

The yellow color of urine is due to uro-chromes, which are related to the bile pigments produced by hemoglobin degradation (see p. 194). If urine is left to stand long enough, oxidation of the urochromes may lead to a darkening in color. 

For interdiffusion of neutral metal atoms in alloys, the following relation, referred to as the Darken-Hartley-Crank equation, has been derived (Darken, 1948 Shewmon, 1963 Kirkaldy and Young, 1987) ... 

In irradiated potatoes, especially in some varieties and as a function of cultivating conditions of the raw material, after-cooking darkening may occur. This discoloration is attributed to formation of ferric-phenolic complexes. This phenomenon depends on the iron content, and is related to increased polyphenol formation and reduced citric acid levels, which are influenced by agronomic and climatic factors. Various technological measures have been developed to prevent this after-cooking darkening [23]. 

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