Effect of Lateral Interactions

We can include surface diffusion by adding to (90), neglecting again the effects of lateral interactions,... 

Figure 7.9. Effect of lateral interactions on the distribution of a single adsorbate species A on the surface. The adsorption energy of each atom A is calculated using Eq. (20) and the interaction energies indicated underthe maps. Negative energies correspond to attraction,...

Figure 7.12. Dissociation of NO N + O in a temperature-programmed desorption and static SIMS experiment, along with Monte Carlo simulations, showing the effect of lateral interactions (see text for explanation). The bottom part shows representative arrangements of NO molecules (grey), and...

Pieniak, A., Densitometric investigation of the effect of lateral interactions exerted on retention and separation of analytes in the non-linear variant of adsorption planar chromatography (in Polish). Ph.D. thesis, The University of Silesia, Katowice (Poland), 2006. 

The previous sections have dealt with equilibrium situations i.e., minima of the (free) energy. For the kinetics we also need to know how lateral interactions affect transition states. There has hardly been any work done on this. ° From a theoretical point of view one can in principle use quantum chemical calculations just as one would for the stable states (see Section 3.4). The kinetic experiments of Section 3.3.3 depend on the activation energies and on the difference between the lateral interactions in the transition state and the initial state of a reaction. The experiments of Sections 3.3.1, 3.3.2 and 3.3.4 do not yield any information on the effect of lateral interactions on transition states. 

The main progress in the theoretical study of the effect of lateral interactions on the kinetics of surface reactions in recent years has been in kMC simulations and in density-functional theory (DFT) calculations of lateral interactions. We deal with the latter in Section 3.4, and with the former in Section 3.1. Section... 

The maximum-entropy principle that we have used above does not include any effects of lateral interactions. We can include them as well if we extend to definition of the entropy in eqn. (19) to that of a free energy... 

Analytical Expressions for Lateral Interactions. To deal with the effects of lateral interactions in a whole adlayer it is necessary to have a concise description of the lateral interactions. This can be done in a number of ways, each corresponding to a different model of the lateral interactions. Such a model needs then further be specified by assigning values to the parameters in the model. This and the following sections discuss some models for the lateral interactions and experimental and theoretical methods to determine values for the interactions parameters. 

We would like to thank all the people who have worked with us on various systems showing the effects of lateral interactions. We are especially grateful for many stimulating discussions with Drs. J.J. Lukkien and M.T.M. Koper, and Profs. R.A. van Santen and J.W. Niemantsverdriet. Our research was financially supported by the National Research School Combination Catalysis (NRSC-C). 

The most general formulas to describe the effect of lateral interaction between adsorbed molecules on the rate constants of various processes on solid surfaces were derived by Zhdanov [103, 104], In particular, the rate constant of the Langmuir-Hinshelwood bimolecular reaction A + B - C is determined by the equations [103]... 

Equations similar to eqns. (5), (6) and (8) were obtained by Zhdanov [104] to describe the monomolecular adsorption and associative desorption and Eley-Rideal s bimolecular reaction. He examined the dependence of the rate constants of these processes on the surface coverages and discussed various approximations applied previously to describe the effect of lateral interaction of adsorbed molecules on the desorption rate constant. He also considered the effect of the lateral interaction on the pre-exponential factor of the rate constants for various processes, and in terms of the "precursor state model, the effect of ordering the adsorbed molecules on the sticking coefficient and the rate constant of monomolecular desorption. 

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. 

The overall proton adsorption from an indifferent electrolyte solution on a heterogeneous surface can simply be described as the sum of the local adsorption contributions. The effect of lateral interactions should be taken into account in the local isotherm. For a patchwise surface with a discrete distribution of intrinsic affinity constants the total... 

The lineshape has been shown in the equations above to be potentially coverage dependent and this is usually due to lateral interactions in the adlaycr which result in attractions or repulsions (increased, or decreased adsorption heat) between the species on the surface. Detailed descriptions of the effects of lateral interactions on desorption have been given elsewhere (King, 1978 Goltze et al., 1981 De Jong and Niemantsverdriet, 1990 Zhdanov, 1991a, b),... 

Fig. 45. The effect of lateral interactions on the energy barrier to surface diffusion. (From Bowker and King [234].)...

Similar results have been obtained using an analytical expression to include the effects of lateral interactions. Making use of the work of... 

By comparing Eqs. (98) and (99) with Eq. (26), we can see that including the effect of lateral interactions affects only the parameters in Temkin s iso-... 

Although kinetics plays such an important role in catalsrsis, its theory has for a long time mainly been restricted to the use of macroscopic deterministic rate equations. These implicitly assume a random distribution of adsorbates on the catalyst s surface. Effects of lateral interactions, reactant segregation, site blocking, and defects have only been described ad hoc. With the advent of Dynamic Monte-Carlo simulations (DMC simulations), also called Kinetic Monte-Carlo simulations, it has become possible to follow reaction systems on an atomic scale, and thus to study these effects properly. 

Reactant or product states of surface reactions are often (de-)stabilized by the presence of other adsorbates. This implies a change in the reaction energy as a function of overlayer composition. The Brpnsted-Evans-Polanyi relation again provides an elegant procedure to estimate the effect of lateral interactions on changes in the activation energies. 

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