Heterogeneity short range

Let us begin our discussion from the model of Cummings and Stell for heterogeneous dimerization a + P ap described in some detail above. In the case of singlet-level equations, HNCl or PYl, the direct correlation function of the bulk fluid c (r) represents the only input necessary to obtain the density profiles from the HNCl and PYl equations see Eqs. (6) and (7) in Sec. II A. It is worth noting that the transformation of a square-well, short-range attraction, see Eq. (36), into a 6-type associative interaction, see Eq. (39), is unnecessary unless one seeks an analytic solution. The 6-type term must be treated analytically while solving the HNCl... 

The work function plays an important role in catalysis. It determines how easily an electron may leave the metal to do something useful for the activation of reacting molecules. However, strictly speaking, the work function is a macroscopic property, whereas chemisorption and catalysis are locally determined phenomena. They need to be described in terms of short-range interactions between adsorbed molecules and one or more atoms at the surface. The point we want to make is that, particularly for heterogeneous surfaces, the concept of a macroscopic work function, which is the average over the entire surface, is not very useful. It is more meaningful to define the work function as a local quantity on a scale with atomic dimensions. 

Various works has pointed out the role of the nanostructure of the catalysts in their design.18-26 There is a general agreement that the nanostructure of the oxide particles is a key to control the reactivity and selectivity. Several papers have discussed the features and properties of nanostructured catalysts and oxides,27-41 but often the concept of nanostructure is not clearly defined. A heterogeneous catalyst should be optimized on a multiscale level, e.g. from the molecular level to the nano, micro- and meso-scale level.42 Therefore, not only the active site itself (molecular level) is relevant, but also the environment around the active site which orients or assist the coordination of the reactants, may induce sterical constrains on the transition state, and affect the short-range transport effects (nano-scale level).42 The catalytic surface process is in series with the transport of the reactants and the back-diffusion of the products which should be concerted with the catalytic transformation. Heat... 

The GE is a source of sampling variation at the local level that is, at the small scale where the sample is actually taken. It is not present in classical SR. The GE is due to (r) the distribution heterogeneity of the material, which is random at the small scale area where we take our sample, (//) the selection of groups of particles, rather than individual particles, and ( //) the segregation of material at the short range where we take the sample. 

Within the frames of the regular solution approach adopted in [4,19,23-29] the dipole-dipole interactions are treated similarly with the short-range ones and for this reason in many cases no distinction between these interactions is made. The dipole-dipole interactions arise from the electric field which is established due to the dipoles of the adsorbed particles. This feature is taken into account here to develop an alternative approach to treat these interactions. The treatment concerns adsorbed layers on energetically homogeneous surfaces. This is a necessary step in formulating an adsorption theory for heterogeneous surfaces, which is presented in section 5. 

The results presented above show that the adsorption characteristics on energetically homogeneous adsorbing surfaces are determined by three main factors. The short-range interactions expressed by the parameter the dipole-dipole interactions, the contribution of which in the simple case of single adsorption is determined by the parameters p = a/ s and B/( a), and the co-adsorption of other adsorbates. On solid surfaces an additional factor should be taken into account. It is the heterogeneity of the adsorbing surface. 

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