Heterogeneous equivalent

More sophisticated materials have been made by attachment of transition metal complexes to the surface. These materials are designed to enhance the fundamental activity of the metal ion, by providing it with an environment tailored to make it as active as possible, and to aid in its recovery afterwards. The heterogenisation of such (normally homogeneous) complexes has attracted a lot of attention, since the heterogeneous equivalents can be much more easily separated and recycled than the... 

Comparison of the homogeneous polymerizations of transition metal alkyl compounds with their heterogeneous equivalents shows that the higher activity of the latter is due to ... 

For example the heterogeneous equivalent approximation (12), the unequal box size method (13), the orthogonal collocation technique (14) and the aforementioned implicit scheme all will lead to decreased computer time, although a price is usually paid in generality and/or accuracy. 

An example of simplifying assumptions is given by the "heterogeneous equivalent" (HE) method of RuziC and Feldberg (1974), later amended by RuziC (1983) and extended (Ruzid 1985). These authors look at a CE reaction such as... 

Ruzit I, Feldberg S (1974) The heterogeneous equivalent a method for digital simulation of electrochemical systems with compact reaction layers. J Electroanal Chem 50 153. 

Ruzit I (1985) Extension of the improved "heterogeneous equivalent" method to the digital simulation of the slow pseudo-first order homogeneous reactions coupled to the electrode reaction. 

Speiser B (1984) Electroanalytical investigations. Part V. The simulation of fast chemical reactions in cyclic voltammetry by a combination of the orthogonal collocation method and the heterogeneous equivalent approach. J Electroanal Chem 171 95. 

Speiser B (1991) Electroanalytical simulations. Orthogonal collocation simulation of fast second-order chemical reactions coupled to an electron transfer with a heterogeneous equivalent formulation. Anal Chim Acta 243 301-310... 

The equivalent equations for heterogeneous and quasi-heterogeneous systems (tire latter are small vesicles which can practically be handled as homogeneous systems, but which are nevertlieless large enough to possess a macroscopic solid-liquid interface) are dealt witli in section C2.14.7. 

Derivatives of hemicellulose components have properties similar to the ceUulosic equivalents but modified by the effects of thek lower molecular weight, more extensive branching, labile constituents, and more heterogeneous nature. Acetates, ethers, carboxymethylxylan (184), and xylan—poly(sodium acrylate) (185) have been prepared. 

The surface of mercury is homogeneous and all sites (Hg atoms) are equivalent, whereas a solid metal will have a heterogeneous surface with sites that differ in adsorption energies. 

Objective Evaluation of Color. In recent years a method has been devised and internationally adopted (International Commission on Illumination, I.C.I.) that makes possible objective specification of color in terms of equivalent stimuli. It provides a common language for description of the color of an object illuminated by a standard illuminant and viewed by a standard observer (H). Reflectance spectro-photometric curves, such as those described above, provide the necessary data. The results are expressed in one of two systems the tristimulus system in which the equivalent stimulus is a mixture of three standard primaries, or the heterogeneous-homogeneous system in which the equivalent stimulus is a mixture of light from a standard heterogeneous illuminant and a pure spectrum color (dominant wave-length-purity system). These systems provide a means of expressing the objective time-constant spectrophotometric results in numerical form, more suitable for tabulation and correlation studies. In the application to food work, the necessary experimental data have been obtained with spectrophotometers or certain photoelectric colorimeters. 

Presumably the most important kinetie parameter used in the deseription of the kineties of an eleetrode is the exchange current density or the almost equivalent rate constant. It indicates the speed of the heterogeneous process of charging or discharging species at the phase boundary, i.e. the charge transfer process. Its value is influenced by numerous factors of the investigated system. For both applied and fundamental aspects of electrochemical research a list of reported values should be helpful. It concludes this volume. 

Another problem that required solving was the moderate yield obtained in the cyclopropanation reaction when only one equivalent of styrene was used. By increasing the amount of styrene up to its use as the reaction solvent, a noticeable effect on the selectivities was observed when laponite was used as the support [58]. The active role of the clay support was definitely estabhshed when the results in homogeneous and heterogeneous phases were compared (Table 9). These effects involved the reversal of the trans preference in solution to the cis preference with the laponite-supported catalyst in styrene, and also a reversal in the absolute configuration of the major cis enantiomer ob-... 

We can think of a heterogeneous catalyst as a collection of active sites (denoted by ) located at a surface. The total number of sites is constant and equal to N (if there is any chance of confusion with N atoms, we will use the symbol N ). The adsorption of the reactant is formally a reaction with an empty site to give an intermediate I (or more conveniently R if we explicitly want to express that it is the reactant R sitting on an adsorption site). All sites are equivalent and each can be occupied by a single species only. We will use the symbol 6r to indicate the fraction of occupied sites occupied by species R, making N6r the number of occupied sites. Hence, the fraction of unoccupied sites available for reaction will be 1 - 0r The following equations represent the catalytic cycle of Fig. 2.7 ... 

In the case of a heterogeneous polymer comprising molecular species differing in size but otherwise equivalent chemically, substitution of Eq. (12) for ASm gives... 

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