Strong Heterogeneity

Sparnaay, Surf. ScL, 1968, 9, 100 M. J. Sparnaay, in Clean Surfaces Their preparation and characterization for interfacial studies , ed. G. Goldfinger, Marcel Dekker, New York, 1970, p, 153. 

Inserting (34) in (4) gives an integral which can be computed in closed form  

Temkin isotherm, for intermediate pressures,. full monolayer, for p a p.  

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Ni and Fe are the only d-metals for which capacitance curves displaying a nice diffuse-layer minimum have been obtained.727,743 These minima are in reasonable agreement with values obtained with renewable surfaces.730 However, strongly heterogeneous surfaces are expected for these metals and therefore the behavior of a pc sample can be taken as close to the most open main single-crystal face. 

Velocity Mapping of Strongly Heterogeneous Flow Velocity Fields... 

Another study examined the acidity and basicity of bulk Ga203 by NH3 and SO2 adsorptions microcalorimetry performed at 150°C. As alumina, Ga203 is amphoteric, with heats higher than 100 kJ/mol for both NH3 and SO2 adsorption, respectively [186]. The amphoteric character of bulk gallium oxides and strong heterogeneity of the surface acidic and basic sites were proved also by Petre et al. [179] using microcalorimetry of pyridine adsorption at 150°C and CO2 adsorption at 30°C. 

The morphological parameter C which controls the damaging effect of cracks appears to depend only on the crack density and the crack radius. In the case of cracks, the macroscopic mechanical loading defined by Ii or p is expected to induce a strong heterogeneity of the mechanical affinity, due to the stress/strain concentration in the vicinity of the crack tips. 

The structural information of charred materials can also be obtained from low-resolution II NMR in the solid state.14 Since carbonaceous structures form when materials burned are strongly heterogeneous, they should contain regions of different mobilities and thus a study of the molecular dynamics by ssNMR may provide useful information. 

Threshold relationships will tend to be smoothed when applied to a strongly heterogeneous population the response may depend strongly on e.g. age, gender, genetic constitution and health status. 

Mo-V-Te and Mo-V-Te-Nb mixed-metal oxide catalysts have been characterized by means of C3H8-TPR and NH3 adsorption calorimetry. All samples were strongly heterogeneous, with initial adsorption heats of = 100-80 kJ moT for the Mo-V-Te samples. Introducing an Nb component into the catalysts slightly decreased the initial adsorption heats to = 60 kJ moT but drastically increased the surface density of weak acid sites (<30kJ moT ) [83]. 

Osmium isotopes currently provide the strongest case for mineral-to-mineral disequilibrium, and for mineral-melt disequilibrium available from observations on natural rocks. Thus, both osmium alloys and sulfides from ophiolites and mantle xenoliths have yielded strongly heterogeneous osmium isotope ratios (Alard et al., 2002 Meibom et al., 2002). The most remarkable aspect of these results is that these ophiolites were emplaced in Phanerozoic times, yet they contain osmiumbearing phases that have retained model ages in excess of 2 Ga in some cases. The melts that were extracted from these ophiolitic peridotites contained almost certainly much more radiogenic osmium and could, in any case, not have been in osmium-isotopic equilibrium with all of these isotopically diverse residual phases. 

Tackley P. J. (2002) Strong heterogeneity caused by deep mantle layering. Geochem. Geophys. Geosystems 3(4), 101029/2001GC000167. 

Draupne Sand Turbidite fan Strongly heterogeneous Whole range... 

Middle Tarbert 2 Coastal lagoon, barriers, inlet channels Strongly heterogeneous hut many high permeable intercalations Whole range, medium to coarse sand forms an important component... 

The rectangular distribution is a good approximation in the case of strongly heterogeneous surfaces [2]. And this is just the case of the bivalent metal ion adsorption (Freundlich s plots with — [Pg.401]

Now we face the situation that the same physical function Xj(ej) is represented by two analytical functions (1) and (86). However, we have already known, that in the case of a strongly heterogeneous surface, these functions should affect 0jt in a similar way, if the parameters cj, e] and e]" are suitably chosen. So, we took the integration limits e] and ej" as the best-fit parameters and adjusted cj in Eq. (87) in such a way that at higher surface concentrations the tangent of the Freundlich log-log plot for is equal to... 

It is difficult to recognize in which conditions the isotherm (48) is reduced to the Elovich behaviour. This goal is better accomplished by computing the integral (21) using a uniform distribution function, which is the strong-heterogeneity limit of the distribution function of equilibrium surfaces. In this case Eq. (21) becomes ... 

Since the factor 0(1) becomes o(l) for t close to tu and the correction to the logarithm behaviour vanishes as 0(1)desorption kinetics are expected to be observed on strongly heterogeneous surfaces which in equilibrium conditions obey the Temkin equation. For a simplified demonstration that the Elovich equation is expected to be observed in the desorption from heterogeneous surfaces, see Refs. [22, 52],... 

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