Adsorbate mobility

Figure 15.4 Schematic representation of the Langmuir-Hinshelwood reaction between two adsorbates mobile X (black) and immobile Y (white) on a stepped single-crystalline surface (a) and a facetted nanoparticle (b).

One has to be able to image the exact position of each adsorbate to obtain the radial distribution function. This requires a low adsorbate mobility, since a full scan typically takes one minute to do. This method is therefore mainly applied to atoms on low-temperature surfaces. The consequence of keeping the temperature low to suppress surface mobility is that the absolute value of the repulsive interactions that can be determined is also small, typically less than 10 kJ/mol at room temperature. 

This again confirms the reasoning presented above, according to which loosely adsorbed mobile oxygen which does not exchange electrons with the catalyst, or does so in a restricted sort of way, is the essential partner for the surface reaction. 

Another way of decreasing the retention volume of functional macromolecules can be found in raising the column temperature. In this case, it should be borne in mind that a change in temperature causes a number of changes in the chromatographic system, mainly associated with the shift in the equilibrium between the components of the adsorbed mobile phase and water, which results in a change in the eab of the mixture and the adsorbent activity. 

From the Snyder-Soczewinski model (12, 13), the entire adsorbent surface is covered by an adsorbate monolayer that consists of mobile phase. Retention is assumed to occur as a displacement process in which an adsorbing solute molecule X displaces some number n of previously adsorbed mobile-phase molecules S... 

In natural soils which commonly contain illite and smectite, there can be a significant charge imbalance between Si4+ and Al3+ in the structures of these clay minerals. This results in a net negative charge on the clay mineral surfaces, resulting in more adsorption of mobile cations. When an acid front encounters these adsorbed mobile cations, they are very easily displaced by the H ion, which by virtue of its small size is strongly adsorbed to the clay surface. As a result, the measured CEC of such clay-bearing soils is predicted to increase, as we have observed in our experiments. 

Two models have been developed to describe the adsorption process. The first model, known as the competition model, assumes that the entire surface of the stationary phase is covered by mobile phase molecules and that adsorption occurs as a result of competition for the adsorption sites between the solute molecule and the mobile-phase molecules.1 The solvent interaction model, on the other hand, suggests that a bilayer of solvent molecules is formed around the stationary phase particles, which depends on the concentration of polar solvent in the mobile phase. In the latter model, retention results from interaction of the solute molecule with the secondary layer of adsorbed mobile phase molecules.2 Mechanisms of solute retention are illustrated in Figure 2.1.3... 

Proportionality of and t Is often (but not always) an indication of a diffusion-controlled process, but such a proportionality does not have to extend over the entire time domain considered. It may happen that diffusion control is realized but that the computed D, is lower than the corresponding value in the gas phase. One possible explanation for this may be that the supply is followed by a slower surface diffusion process, which Is rate-determining. Surface diffusion coefficients D° tend to be lower than the corresponding bulk values. Such diffusion has been briefly discussed In sec. I.6.5g, under (1). When surface diffusion Is zero, the adsorbate is localized. In that case equilibration between covered and empty parts of the surface can only take place by desorption and readsorption. For D° 0 the adsorbate is mobile it then resembles a two-dimensional gas and we have already given the partition functions for one adsorbed mobile atom in sec. I.3.5d. In sec. 1.5d we shall briefly discuss the transition between localized and mobile adsorption. 

As another approach, one could think in terms of simulations or develop two-dimensional analogues of the semi-emplrlcal equations of state discussed in sec. I.3.9d. Models that fit into the picture of adsorbate mobility ignore variations parallel to the surface, i.e. adopt the mean field approach. Such models have a hierarchy similar to that of the FFG or two-dimensional Van der Waals equations, where any effect that lateral interaction may have on the distribution is also disregarded. 

It may be good to note here that various molecular cross-sections have now been considered. In the treatment of adsorption on solid surfaces was introduced. Interpreting this area in terms of lattice models is not a property of the adsorptive molecule but of the adsorbent. It is possible to imagine a situation where greatly exceeds the real molecular cross-section. On the other hand, for mobile monolayers on homogeneous surfaces is the real molecular cross-section or, for that matter, it is the excluded area per molecule. To avoid an undue abundance of symbols we have used the same symbol for both situations, for instance in table 3.3 in sec. 3.4e. It is to be expected that a and a, obtained by compression of monolayers, are more similar to the a s for adsorbed mobile monolayers on homogeneous substrates than to those for localized monolayers. 

Finally, dynamic Monte Carlo simulations are very useful in assessing the overall reactivity of a catalytic surface, which must include the effects of lateral interactions between adsorbates and the mobility of adsorbates on the surface in reaching the active sites. The importance of treating lateral interactions was demonstrated in detailed ab initio-based dynamic Monte Carlo simulations of ethylene hydrogenation on palladium and PdAu alloys. Surface diffusion of CO on PtRu alloy surfaces was shown to be essential to explain the qualititative features of the experimental CO stripping voltammetry. Without adsorbate mobility, these bifunctional surfaces do not show any catalytic enhancement with respect to the pure metals. 

Table 2.1 System of Equations of the Equilibrium-Dispersive Model. Binary Mixture and Pure (or weakly adsorbed) Mobile Phase...

Bhatia [39] studied the transport of adsorbates in microporous random networks in the presence of an arbitrary nonlinear local isotherm. The transport model was developed by means of a correlated random walk theory, assuming pore mouth equilibrium at an intersection in the network and a local chemical potential gradient driving force. The author tested this model with experimental data of CO2 adsorption on Carbolac measured by Carman and Raal [40]. He concluded that the experimental data are best predicted when adsorbate mobility, based on the chemical potential gradient, is taken to have an activation energy equal to the isosteric heat of adsorption at low coverage, obtained from the Henry s law region. He also concluded that the choice of the local isotherm... 

Currently no adequate quantitative theory of the discrete-ion potentials for adsorbed counterions at ionized monolayers exists although work on this problem is in progress. These potentials are more difficult to determine than those for the mercury/electrolyte interface because the non-aqueous phase is a dielectric medium and the distribution of counterions in the monolayer region is more complicated. However the physical nature of discrete-ion potentials for the adsorbed counterions can be described qualitatively. This paper investigates the experimental evidence for the discrete-ion effect at ionized monolayers by testing our model on the results of Mingins and Pethica (9, 10) for SODS. The simultaneous use of the Esin-Markov coefficient (Equation 3) and the surface potential AV as functions of A at the same electrolyte concentration c yields the specific adsorption potentials for both types of adsorbed Na+ ions—bound and mobile. Two parameters which need to be chosen are the density of sites available to the adsorbed mobile Na+ ions and the capacity per unit area of the monolayer region. The present work illustrates the value... 

This is identical with Equation 3 of M.P. (9) if we identify their 4>Na with our (1) — Na(1). Thus, although M.P. did not explicitly introduce the function (1), they allowed for the discrete-ion effect by permitting their specific adsorption energy Na(1) to vary with n. If it is assumed that the adsorbed mobile Na+ ions are uniformly distributed in the "outer zone, so that we use Equations 3 and 14, then in Equation 31... 

If it is assumed that the adsorbed mobile ions are uniformly distributed in the outer-zone, so that we make use of Equations 13 and 14, then Equation 39 is replaced by... 

Elood, E.A. and Huber, M., Thermod3mamic considerations of surface regions, adsorbate pressures, adsorbate mobility and surface tension. Can. J. Chem., 33, 203-214, 1955. 

Models for the interactions of solutes in adsorption chromatography have been discussed extensively in the litera-ture. Only the interactions with silica and alumina will be considered here. However, various modifications to the models for the previous two adsorbents have been applied to modem high-performance columns (e.g., amino-silica and cyano-silica). The interactions in adsorption chromatography can be very complex. The model that has emerged which describes many of the interactions is the displacement model developed by Snyder. " Generally, retention is assumed to occur by a displacement process. For example, an adsorbing solute molecule X displaces n molecules of previously adsorbed mobile-phase molecules M ... 

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