Mobility of adsorbed molecules

Transition metal colloids can also be prevented from agglomeration by polymers or oligomers [27,30,42,43]. The adsorption of these molecules at the surface of the particles provides a protective layer. In the interparticle space, the mobility of adsorbed molecules should be reduced decreasing the entropy and thus increasing the free energy (Fig. 2). 

Since the most active catalytic sites are usually steps, kinks, and surface defects, atomically resolved structural information including atomic distribution and surface structure at low pressure, possible surface restructuring, and the mobility of adsorbate molecules and of the atoms of the catalyst surface at high temperature and high pressure is crucial to understanding catalytic mechanisms on transition metal surfaces. The importance of studying the structural evolution ofboth adsorbates... 

Structure and mobility of adsorbed molecules may exhibit a wide spectrum of features. As a general view it is commonly accepted that layers are formed on increasing abundance. The mobility of molecules in the first layer depends strongly on interactions present in a given case. Local domains of adsorbed molecules may be formed in the case of non-uniform surface. Analysis of deuteron spectra for a series of molecules adsorbed on neutral alumina led to the conclusion that while the exchange of molecules between layers in a given domain is fast, the diffusion rate between domains is slow [5],... 

The rotational mobility of adsorbed molecules is caused by its rotational degree of freedom (resulting from the fact that the molecule is tightly bound to the substrate through the only atom) and by the coupling of molecular vibrations with surface atomic vibrations. The rotational motion intensity is strongly temperature-dependent and affects spectroscopic characteristics. As a result, the rotational mobility of surface hydroxyl groups was reliably detected.200 203... 

Using silica of a different source, Turro [46] again found that the E/C ratios from irradiation of adsorbed alkanophenones 97 (n = 4, 7,10) at room temperature (3.7-3.9) are close to the values obtained from irradiations in t-butyl alcohol (4.2-6). Consistent with the expected reduction in mobility of adsorbed molecules on silica surfaces at lower temperatures, only cyclization products were isolated from irradiations of 97 on silica at — 125°C. At these... 

The same conclusion may be obtained from the study of the behavior of many gases adsorbed on charcoal. We shall discuss the mobility of adsorbed molecules in Sec. VII, but we may mention here one of the results of such studies. Many gases, such as A, N2, 02, CO, CH4, etc., when adsorbed on charcoal, behave as two-dimensional nonideal gases (44)- This behavior can be described by a two-dimensional van der Waals equation, from which a two-dimensional van der Waals constant o2 (comparable with the normal three-dimensional van der Waals a) may be derived. The two-dimensional van der Waals constants can also be calculated from the three-dimensional values of a (45). The experimental results show that the actual a2 constants for gases adsorbed on charcoal or on mercury are always far lower than the theoretical ones and are very often even negative (45). The adsorbed molecules tend to repel each other instead of showing a mutual attraction. This behavior also points to a polarization of the adsorbed molecules by the field of the charcoal or of the mercury (47). 

To compose equations for adsorption of the 02 molecules with an allowance for the slow surface mobility of adsorbed particles along a surface. Compose the similar equations for adsorption of the CO molecules at low temperatures, when the surface mobility of adsorbed molecules needed be taken into account. 

The use of the surface concentration gradient as the driving force for surface diffusion is the most popular approach with which to describe the mobility of adsorbed molecules. When each adsorbed species is assumed to be at adsorption equilibrium and transported along the surface independently of the other species, the molar flux of species i due to surface diffusion can be written as... 

One of the most intriguing aspects of surface diffusion is the strong dependence of the diffusivity on sorbate concentration. The dependence of surface diffusivities on pressure, temperature and composition is much more complicated than those of the molecular and Knudsen diffusivities, because of all the complexities of porous medium geometry, surface structure, adsorption equilibrium, mobility of adsorbed molecules, etc. 

In contrast to localized adsorption, mobile adsorption models assume that molecules can diffuse freely on the surface. One of the most popular equations used to describe mobile adsorption is that proposed by Hill and de Boer [105] as an analogue of the FG isotherm. This equation can be obtained by combining the two-dimensional form of van der Waals equation with the Gibbs adsorption isotherm. Note that the pre-exponential factors for localized and mobile adsorption are different. In the case of localized adsorption, the pre-exponential factor Kq takes into account the vibrations of adsorbing molecules in X, y and z direction, whereas the factor for the mobile adsorption contains only the partition functions for vibration in the z-direction and the transnational partition function describing mobility of adsorbing molecules in the (x,y)-plane. 

The above-mentioned adsorption is similar to that for a Langmuir type monomolecular adsorption where the adsorbed molecules are not mobile. The modification required to take into account the mobility of adsorbed molecules has been discussed by several authors. ... 

Next, we will discuss one of the recent equations introduced by Nitta and his co-workers. This theory based on statistical thermodynamics has some features similar to the Langmuir theory, and it encompasses the Langmuir equation as a special case. Basically it assumes a localised monolayer adsorption with the allowance that one adsorbate molecule can occupy more than one adsorption site. Interaction among adsorbed molecules is also allowed for in their theory. As a special case, when the number of adsorption sites occupied by one adsorbate molecule is one, their theory is reduced to the Fowler-Guggenheim equation, and further if there is no adsorbate-adsorbate interaction this will reduce to the Langmuir equation. Another model of Nitta and co-workers allowing for the mobility of adsorbed molecules is also presented in this chapter. 

Eq. (2.3-24) is known as the Volmer equation, a fundamental equation to describe the adsorption on surfaces where the mobility of adsorbed molecules is allowed, but no interaction is allowed among the adsorbed molecules. 

The first exponential term in the RHS of eq. (2.3-27) describes the mobility of adsorbed molecules, and when this term is removed we will have the case of localised adsorption with lateral interaction among adsorbed molecules, that is ... 

Similarly for the Hill-de Boer equation, we obtain the same isosteric heat of adsorption as that for the case of Fowler-Guggenheim equation. This is so as we have discussed in the section 2.3.3 for the case of Volmer equation that the mobility of adsorbed molecule does not influence the way in which solid interacts with adsorbate. 

The above equation of Nitta et al. deals with mobility of adsorbed molecules and their lateral interaction. When the lateral interaction is zero, eq. (2.5-10) becomes ... 

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