Strongly Heterogeneous Surfaces

Strongly Heterogeneous Surfaces.—In this case, qM 9n 1/A for + and p(q) = 0 otherwise. 

Inserting this distribution into integral (38) leads to 

In the time range T f= Tmexp(d/fcBT) and for all temperatures the above expression reduces to 

As the Elovich behaviour is observed both for weakly and strongly heterogeneous surfaces grown under equilibrium conditions, the reasons for 

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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. 

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... 

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],... 

As a result the criterions of models (37) or (36a) depend mostly on the difference of the partial p.z.c. values and on the partial compact-layer capacitances. In particular, for the most interesting case of a strongly heterogeneous surface (i.e. having a significant difference between the partial p.z.c. values) the principal condition relates the characteristic size of the uniform regions, j, and the lengths derived from the values of the partial compact-layer capacitances, e.g., for the model of independent electrodes (Eqs. (34) and (37)) ... 

As it happens, it can be shown that in the case of strongly heterogeneous surfaces characterized by a rectangular adsorption energy distribution, Eq. (10), the effects of the lateral interactions do not change the form of the Elovich equation. 

The Polanyi potential theory successfully represents the temperature dependence of adsorption. It is also the only theory that gives quantitative description of physical adsorption on strongly heterogeneous surfaces, such as those of active carbons and oxide gels. However, the significance of the theory had been limited for a long time because it did not provide an analytical expression for the adsorption isotherm. This problem was solved by Dubinin and coworkers. ... 

Figure 5 Log-log plot of the adsorption isotherms which should be observable on strongly heterogeneous surfaces grown at Tp = 1000 K and frozen to 50 K for different energy spectra (from 0.5 to 4.0 Real mol ). The stars roughly indicate the pressures beyond which the Henry behaviour is no longer observed...

The low silica zeolites represented by zeolites A and X are aluminum-saturated, have the highest cation concentration and give optimum adsorption properties in terms of capacity, pore size and three-dimensional channel systems. They represent highly heterogeneous surfaces with a strongly hydrophilic surface selectivity. The intermediate Si/Al zeolites (Si/Al of 2-5) consist of the natural zeohtes eri-onite, chabazite, clinoptilolite and mordenite, and the synthetic zeolites Y, mordenite, omega and L. These materials are still hydrophilic in this Si/Al range. 

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. 

Fig. 26. 50 50 block copolymer of styrene and methacrylate cast from 0.1 wt % solution in toluene onto a chemically heterogeneous surface with Au/Si02 stripes with 60 nm. Periodicity and the degree of order of the striped pattern revealed strong dependence on the molecular weight a 113,000 g/mol and b 177,000 g/mol. Courtesy of T.P. Russell... 

The kinetic theory of interface processes, including the adsorption one, on heterogeneous surfaces was constructed in Refs. [80,85,89]. An example of an application of the theory taking into account both lateral interactions and surface heterogeneity is the TDS for H2 on Ir(110)-2 x 1 described in Refs. [127,128]. The elementary lattice consists of three sites (Fig. 8.8) one strong (site of the first type) and two weak (sites of the second and third types). The sites of the third type are separated only formally for an easier presentation of the distribution function - the molecular characteristics of these sites are the same as those of the sites of second type. 

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]. 

Deactivate the original heterogeneous surface of the silica surface to avoid matrix effects. As silica has a weak acidic surface basic solutes are strongly adsorbed, which should be minimized by surface modification. 

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