Dispersion, defined

The authors developed two general concepts for the synthesis of these mono-disperse, defined oligomers. The oligomers can be built up in a stepwise fashion, e.g. via addition of organomelallic species to cyclohexane-1,4-dione followed by aromatization to the oligo(arylene) (e.g. for 25). 

The dispersion, defined as the fraction of all metal atoms that are present at the surface. 

The next question is Where do supported metal catalysts fit into this pattern of co-ordination numbers Most platinum group metal catalysts can be prepared in supported forms in which the dispersion (defined as the % of metal atoms exposed at the surface of the particles) approaches 100%. While there may be good grounds for doubting the accuracy of calculations of dispersions, depending as they do on arbitrary assumptions about particle shapes,14 adsorption ratios, etc., it is certain that dispersions greater than, say, 50% are frequently obtained. Table 1 shows how the dispersion relates to particle diameter and to number of atoms for a simple octahedral structure. From this we see that 50% dispersion corresponds to a particle diameter of... 

As characterized in Fig. 6.7, once a chemical is released into the atmosphere, it is rapidly transported by the average wind and subjected to dispersion, defined as spreading as a result of thermal or density gradients and/or turbulence, and advection, defined as movement as... 

It is noted that there are two types of dispersion model at the discrete scale, both based on idealised calculations. One type considers how dispersion is affected by individual obstacles and their wakes, while the other concentrates more on dispersion defined by groups of obstacles along and above street canyons. Such models have the capability of being combined and extended. Future work should include the special problems of dispersion in particular building complexes and the use of real time data to assess and predict releases whose occurrence is not detected until consequences have become apparent. 

Supports, or carriers, perform many functions, but most imponant is maintenance of high surface area for the active component. This is best illustrated with platinum, an important catalytic metal widely used for catalytic reforming " and automobile exhaust clean-up. For high activity, platinum crystallites must have the highest surface area possible. Figure 2.3 shows the relationship between dispersion, defined as the fraction of platinum atoms on the surface of the spherical crystallite, and diameter of the sphere. Dispersion decreases very rapidly between 1 and 10 nm. Ideally, platinum crystallites should be as smalt as possible, but certainly... 

To compare two or more phase estimators, some measure of the estimation error is needed. Dispersion defined by the relation... 

Linear dispersion defines the extent to which a spectral interval is spread out across the focal field and is expressed in nanometre per millimetre (nm/mm) -(or its inverse, the reciprocal dispersion in mm/nm). Linear dispersion is associated with an instrument s ability to resolve fine spectral detail. It depends of several parameters such as the focal distances and the widths of entrance and exit slits of the instrument. In general the better the dispersion the greater is the physical separation distance between two given wavelengths (Figure 14.11). 

As the ADE applications accumulated, it became apparent that the ADE might not satisfactorily describe some important features of solute transport in soils. Two phenomena were documented that could result from non-Fickian dispersion. First, the dispersivity defined as the ratio DJ tended to increase as the length of soil column or the soil depth increased (Khan Jury, 1990 Beven et al., 1993). Second, breakthrough curves of non-reactive solutes had larger tails that those predicted with the ADE, so that the solute appeared sooner and/or was retained in soil longer than the ADE predicted (Van Genuchten Wierenga, 1976). 

For this simple case, the sdution of the kinetic equation also gives an evaluation of the composition hetetogeiwity of the reactimi products. Because of the stodiastic and independent nature of the siibstitutimi processes A B, the process can be regarded as a Markov chain of the zeroth order. From the general theory of regular Markov chains, it is known that the compositimi distribution is Bemoiillian in this case, with dispersion defined as... 

The typical release profiles shown in Figure 32.4 for reservoir and matrix delivery systems may present variations a burst effect due to the presence of some core material too close to the external device surface for matrix devices, or a delayed time to start diffusion due to the diffusion of the core through the encapsulating layer of the reservoir device. Also, the physical state of the core material (dissolved or dispersed) defines the release kinetics. For example, a reservoir system in which the active core is not dissolved results in zero-order kinetics (constant flow), whereas it results in first-order kinetics (exponentially decreasing flow) if the core is dissolved in the encapsulated material. 

Elsewhere, we have given an alternative, but equivalent, explanation in terms of the interaction of two bundles of eigenvalues, one bundle of magnitude fi, and the other with magnitudes d, and a dispersion defined by the distribution PAr [81.V1]. 

Linear dispersion - defined as the segment across the focal plane on which the spectral interval is spread out (generally expressed in nm/mm). The linear dispersion is given by the formula... 

Scattering techniques allow to measure the structure factor S(Q) as a function of the wave vector Q of colloidal dispersions defined as... 

Cobalt tends to form large crystallites on metal oxide supports. Cobalt dispersion, defined as the fraction of the metal atoms residing at crystallite surfaces, rarely exceeds 0.1, except when using organometallic precursors [5]. These precursor often leave carbonaceous residues and the resulting small crystallites tend to re-oxidize during FT synthesis. 

There are two ways one might think of that could help to reach that goal further increasing the platinum dispersion (defined as the ratio of surface metal atoms to total number of atoms) by making finer platinum particles, if there is no decrease of Pt-specific activity (activity per tmit Pt surface area) or alternatively, increasing the Pt-specific activity. One could also seek a combination of these two approaches. 

Mmim-Obukhov lenpfth A value used in gas dispersion, defined by Equation (2.52). 

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