Heterogeneity of the surface

All gases below their critical temperature tend to adsorb as a result of general van der Waals interactions with the solid surface. In this case of physical adsorption, as it is called, interest centers on the size and nature of adsorbent-adsorbate interactions and on those between adsorbate molecules. There is concern about the degree of heterogeneity of the surface and with the extent to which adsorbed molecules possess translational and internal degrees of freedom. 

Surface Area. Surface area is the available area of fillers, be it on the surface or in cracks, crevices, and pores. The values obtained from different methods for measuring the surface area of a filler may vary significandy. These variations are because of the nature of the methods and in many instances yield information related to the heterogeneity of the surface. Understanding the surface area is important because many processing factors are dependent on the surface area, eg, ease of filler dispersion, rheology, and optimum filler loading. 

The impedance spectroscopy of steel corrosion in concentrated HC1, with and without inhibitors, exhibit relatively straightforward electrochemical phenomenology and can be represented by simple equivalent circuits involving primarily passive electrical elements. Analysis of these circuits for steel corroding in HC1 per se reveals that the heterogeneity of the surface is established rapidly and can be simulated with a simple electrical circuit model. 

Through such chemisorption studies, the values of >, have been determined not only by geometric accessibility, but also by the chemical heterogeneity of the surface. This can result in abnormal values of D, and demonstrates the scale effect on the kinetics and selectivity of catalytic reactions. For such studies, Farin and Anvir [213] derived the equations that can be applied for characterization of supported catalysts ... 

Nevertheless, surfactant sorption isotherms on natural surfaces (sediments and biota) are generally non-linear, even at very low concentrations. Their behaviour may be explained by a Freundlich isotherm, which is adequate for anionic [3,8,14,20,30], cationic [7] and non-ionic surfactants [2,4,15,17] sorbed onto solids with heterogeneous surfaces. Recently, the virial-electrostatic isotherm has been proposed to explain anionic surfactant sorption this is of special interest since it can be interpreted on a mechanistic basis [20]. The virial equation is similar to a linear isotherm with an exponential factor, i.e. with a correction for the deviation caused by the heterogeneity of the surface or the energy of sorption. 

It is a perfect straight line relationship. This is very important from the standpoint of the heterogeneity of the surface. If the decrease... 

Heterogeneity of the surface may also be produced by impurities. In case of metals, such impurities—however small—if expressed as percentages of total weight may cover a large part of the surface,... 

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. 

In Section 6.8.10 we saw that the Temkin isotherm is based on the Langmuir isotherm. One advantage of the Temkin isotherm is that it considers the heterogeneity of the surface. However, like the Langmuir isotherm, it does not take into account lateral interactions between the adsorbates. 

In order to introduce the heterogeneity of the surface, these ion and water interaction energies can be divided into two groups. One of them corresponds to the energy involved when the ion gets rid of its hydration sheet, the breaking of the bond between the n water molecules and the metal that the ion needs to displace to get adsorbed, and finally, the part of the ion-metal interaction (bond) that arises from the ion s orbitals, i.e., AG and. AG° W (see Fig. 6.90). 

The second part includes the metal side of the ion-metal and water-metal bonds at the jth site. This term depends on the heterogeneity of the surface and is given by Uj i and Uj w. Therefore the chemical term AGch is written as... 

This partial isotherm was constructed by considering a heterogeneous surface built by patches of different energy Up and the equation is then applicable only in the/th patch. This partial isotherm can be rearranged by grouping on the left the terms that are related to the heterogeneity of the surface, i.e., 0y and Up... 

In the previous section we developed an isotherm, Eq. (6.246), which was intended to represent the adsorption process of ions on metallic surfaces. It included conditions such as the heterogeneity of the surface, displacement of solvent molecules, transfer of charge, lateral interactions, and size of the ions some of the main parameters involved in this isotherm were shown in Tables 6.11 and 6.12 for three adsorbing ions. 

What information can be obtained from A/ ds One important parameter involved in the enthalpy of the reaction is the ion-metal bond. However, A7 ds includes all the different interactions involved in the adsorption process, e.g., the breaking of the hydration sheet of the electrode and the ion, lateral interactions, and heterogeneity of the surface. One can subtract all these energy terms from AH ds and obtain in this way the energy (or strength) of the ion-metal bond. For the example of the adsorption of bisulfate ions onpolycrystalline platinum (Fig. 6.105), the ion-metal bond was found to be -214 60 kJ mol-1. 

However, adsorption is a complex process that cannot be described by only one parameter. Thus we developed an isotherm for adsorption of ions that included most of the parameters already described (Section 6.8.13). It included heterogeneity of the surface, displacement of solvent molecules from the electrode, transfer of charge, deformation of the adsorbing ions, ion size, lateral interactions, etc. 

The adsorption process should also be greatly influenced by the heterogeneity of the surface, as discussed in Section 6.8.3, and by the lateral interactions among the adsorbed species (Section 6.8.2.3). Thus, from Eq. (6.266) it follows that... 

The drop in heat of adsorption, and therefore in strength of the bond, will cause an induced heterogeneity. Boudart suggests that the presence of active centers is not necessarily due to an a priori heterogeneity of the surface, but may arise from this induction effect only a small fraction of the surface will be active at any one time although the whole surface will be involved in catalysis. 

Exceptions to such a correlation can easily occur, however, because of the heterogeneity of the surface. Indeed, it is found that the bond strength often depends on the degree of coverage. Another factor is the special geometry at the active site of the catalyst. Finally, it may be remarked that a concerted mechanism can occur in which the Me—O bond strengths are only relevant in close connection with the complex to be oxidized. 

The contradiction in Equation (1) concerning the homogeneity and heterogeneity of the surface is eliminated by accepting the theory of quasi-homogeneous surfaces developed in some detail by the author (22). A quasi-homogeneous surface is one, the two different active centers of which are characterized by a constant ratio... 

---