Faceting, kinetics

The theory of chemical reactions has many facets iiicliidiiig elaborate qnaritiim mechanical scattering approaches that treat the kinetic energy of atoms by proper wave mechanical methods. These approaches to chemical reaction theory go far beyond the capabilities of a product like HyperChem as many of the ideas arc yet to have wide-spread practical im plemeiitation s. 

One facet of kinetic studies which must be considered is the fact that the observed reaction rate coefficients in first- and higher-order reactions are assumed to be related to the electronic structure of the molecule. However, recent work has shown that this assumption can be highly misleading if, in fact, the observed reaction rate is close to the encounter rate, i.e. reaction occurs at almost every collision and is limited only by the speed with which the reacting entities can diffuse through the medium the reaction is then said to be subject to diffusion control (see Volume 2, Chapter 4). It is apparent that substituent effects derived from reaction rates measured under these conditions may or will be meaningless since the rate of substitution is already at or near the maximum possible. 

The requirement that an enolate have at least one bulky substituent restricts the types of compounds that give highly stereoselective aldol additions via the lithium enolate method. Furthermore, only the enolate formed by kinetic deprotonation is directly available. Whereas ketones with one tertiary alkyl substituent give mainly the Z-enolate, less highly substituted ketones usually give mixtures of E- and Z-enolates.7 (Review the data in Scheme 1.1.) Therefore efforts aimed at increasing the stereoselectivity of aldol additions have been directed at two facets of the problem (1) better control of enolate stereochemistry, and (2) enhancement of the degree of stereoselectivity in the addition step, which is discussed in Section 2.1.2.2. 

Numerous quantum mechanic calculations have been carried out to better understand the bonding of nitrogen oxide on transition metal surfaces. For instance, the group of Sautet et al have reported a comparative density-functional theory (DFT) study of the chemisorption and dissociation of NO molecules on the close-packed (111), the more open (100), and the stepped (511) surfaces of palladium and rhodium to estimate both energetics and kinetics of the reaction pathways [75], The structure sensitivity of the adsorption was found to correlate well with catalytic activity, as estimated from the calculated dissociation rate constants at 300 K. The latter were found to agree with numerous experimental observations, with (111) facets rather inactive towards NO dissociation and stepped surfaces far more active, and to follow the sequence Rh(100) > terraces in Rh(511) > steps in Rh(511) > steps in Pd(511) > Rh(lll) > Pd(100) > terraces in Pd (511) > Pd (111). The effect of the steps on activity was found to be clearly favorable on the Pd(511) surface but unfavorable on the Rh(511) surface, perhaps explaining the difference in activity between the two metals. The influence of... 

The same group has looked into the conversion of NO on palladium particles. The authors in that case started with a simple model involving only one type of reactive site, and used as many experimental parameters as possible [86], That proved sufficient to obtain qualitative agreement with the set of experiments on Pd/MgO discussed above [72], and with the conclusion that the rate-limiting step is NO decomposition at low temperatures and CO adsorption at high temperatures. Both the temperature and pressure dependences of the C02 production rate and the major features of the transient signals were correctly reproduced. In a more detailed simulation that included the contribution of different facets to the kinetics on Pd particles of different sizes, it was shown that the effects of CO and NO desorption are fundamental to the overall behavior... 

Although not all facets of the reactions in which complexes function as catalysts are fully understood, some of the processes are formulated in terms of a sequence of steps that represent well-known reactions. The actual process may not be identical with the collection of proposed steps, but the steps represent chemistry that is well understood. It is interesting to note that developing kinetic models for reactions of substances that are adsorbed on the surface of a solid catalyst leads to rate laws that have exactly the same form as those that describe reactions of substrates bound to enzymes. In a very general way, some of the catalytic processes involving coordination compounds require the reactant(s) to be bound to the metal by coordinate bonds, so there is some similarity in kinetic behavior of all of these processes. Before the catalytic processes are considered, we will describe some of the types of reactions that constitute the individual steps of the reaction sequences. 

It is important to note that, even when the coordination geometry prescribed by the macrocyclic cavity is ideal for the metal ion involved, unusual kinetic and thermodynamic properties may also be observed (relative to the corresponding open-chain ligand complex). For example, very often the macrocyclic complex will exhibit both enhanced thermodynamic and kinetic stabilities (kinetic stability occurs when there is a reluctance for the ligand to dissociate from its metal ion). These increased stabilities are a manifestation of what has been termed the macrocyclic effect - the multi-faceted origins of which will be discussed in detail in subsequent chapters. 

A set of simple physical and chemical principles can be used to understand and predict the surface reconstruction or faceting, which occurs on oxide surfaces.8,9 These include (1) autocompensation of stable surfaces, (2) rehybridization of the dangling bond charge density, (3) formation of an insulating surface, (4) conservation of near-neighbor bond lengths (which minimize the formation of surface strain fields), and (5) surface kinetic factors. We shall briefly discuss all of these factors governing the surface reconstruction of metal oxide. 

On looking over this collection of new findings and insights, I count myself fortunate in having cultivated a modest competence in mathematics, kinetics, thermodynamics and, especially electrochemistry. Without those skills I would not have been able to do what I did. In other words, it was essential for success - and to avoid gross solecisms - to be multi-facetted, and polymer chemistry as usually understood would just not have been enough. 

In this paper we review some of our recent work on the dynamics of step bunching and faceting on vicinal surfaces below the roughening temperature, concentrating on several cases where interesting two dimensional (2D) step patterns form as a result of kinetic processes. We show that they can be understood from a unified point of view based on an approximate but physically motivated extension to 2D of the kind of ID step models studied by a number of workers. For some early examples, see refs. [1-5]. We have tried to make the conceptual and physical foundations of our own approach clear, but have made no attempt to provide a comprehensive review of work in this active area. More general discussions from a similar perspective and a guide to the literature can be found in recent reviews by Williams and Williams and BartelF. 

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