Modelling, heterogeneous surfaces

Figure 5.32. Three types of eontact angles computed for a model-heterogeneous surface with concentric circular bands. (Redrawn from Johnson and Dettre, loc. cit.)...

Drelich J, Wilbur JL, Miller JD, Whitesides GM. (1996) Contact angles for liquid drops at a model heterogeneous surface consisting of alternating and parallel hydropho-bic/hydrophilic strips. Langmuir 12 1913-1922. 

As a simple model of a heterogeneous surface, assume that 20% of it consists of sites of Q= 2.5 kcal/mol 45% of sites Q = 3.5 kcal/mol and the remainder, of sites of Q= 4.5 kcal/mol. Calculate Q(P, T) for nitrogen at 77 K and at 90 K, assuming the adsorption to follow the Langmuir equation with bo given by Eq. XVII-15. Calculate qsi for several 6 values and compare the result with the assumed integral distribution hinction. 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

Both extreme models of surface heterogeneity presented above can be readily used in computer simulation studies. Application of the patch wise model is amazingly simple, if one recalls that adsorption on each patch occurs independently of adsorption on any other patch and that boundary effects are neglected in this model. For simplicity let us assume here the so-called two-dimensional model of adsorption, which is based on the assumption that the adsorbed layer forms an individual thermodynamic phase, being in thermal equilibrium with the bulk uniform gas. In such a case, adsorption on a uniform surface (a single patch) can be represented as... 

The effects due to the finite size of crystallites (in both lateral directions) and the resulting effects due to boundary fields have been studied by Patrykiejew [57], with help of Monte Carlo simulation. A solid surface has been modeled as a collection of finite, two-dimensional, homogeneous regions and each region has been assumed to be a square lattice of the size Lx L (measured in lattice constants). Patches of different size contribute to the total surface with different weights described by a certain size distribution function C L). Following the basic assumption of the patchwise model of surface heterogeneity [6], the patches have been assumed to be independent one of another. 

In ethanol In the absence of tin exhibits an emission maximum at 555 nm upon 366 nm excitation. Figures 3 and 4 show emission spectra of the Sn /flavonol complex on Irregularly shaped glass beads of 10-100 tm diameter, and of BuSn /flavonol accvmulated by Pseudomonas 244 cells respectively. The glass bead study serves as a model of tin adhesion to a small heterogeneous surface from which spectra can be directly obtained only by mlcrospectrofluorometrlc techniques. 

In the recent past much ejperimental and theoretical effort has been undertaken to understand the microsoopic steps of heterogeneous surface reactions. Ihe main problem oonsists of evaluating the total energy of the reacting coponents (including tiie surface atoms ) as a function of all nuclear coordinates at any reaction time. The solution of this problem is extremely difficult. Detailed studies with model systems, however, can shed same light ipon the various steps of the interaction pattern. 

Cuf1101-HC00 The decomposition of formic acid on metal and oxide surfaces is a model heterogeneous reaction. Many studies have since shown that it proceeds via a surface formate species. Thus on Cu 110) adsorbed formic acid is found at low temperature. On heating to 270 K deprotonation occurs, giving rise to the surface formate, which in turn decomposes at 450 K with evolution of H2 and C02- In previous studies, particularly with vibrational spectroscopy, it had been demonstrated that the two C-0 bonds are equivalent and that the symmetry is probably C2v [19]. A NEXAFS study by Puschmann et al. [20] has subsequently shown that the molecular plane is oriented perpendicular to the surface and aligned in the <110> azimuth. 

Adsorption Isotherm Measurements and Site-Selective Thermodynamics. For heterogeneous surfaces like CSPs, the adsorption isotherms are usually composite isotherms and often a Bi-Langmuir model (Equation 1.15) describes reasonably well the adsorption behavior [54]. 

Van Riemsdijk.W.A. Bolt, G.H. Koopal, L.K. Blakemeer, J. (1986) Electrolyte adsorption on heterogeneous surfaces. Adsorption models. 

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