Crystal surfaces models

The difference in formaldehyde equilibrium concentration between homogeneous and heterogeneous polymerization is large enough to indicate a difference in the physical state of cationic chain ends in the dissolved and in the crystalline polymer. Thus, Model B is ruled out. In the homopolymerization of trioxane and in the heterogeneous copolymerization with small amounts of dioxolane the active centers of chains which have precipitated from the solution predominantly are directly on the crystal surface (Model A). According to Wunderlich (20, 21), this is the first case in addition polymerization where Model A—simultaneous polymerization and crystallization—has been proved experimentally. 

Fig. 9.9. (a) FBZ for four regular layers of nickel atoms (a crystal surface model) (b) the band structure for this qrstem. We see... 

Fig. 9.8. (a) FBZ for four regular layers of nickel atoms (a crystal surface model) (b) the band structure for this system. We see that we cannot understand much just a horrible irregular mess of lines. All the band structures look equally clumsy. Despite this, from such a plot we may determine the electrical and optical properties of the nickel slab. We will see later on why the bands have such a mysterious form. R. Hoffmann, Solids and Surfaces. A Chemist s View of Bonding in Extended Smtcntres , VCH Publishers, New York, 1988 VCH Publishers. Reprinted with permission of John Wiley Sons, Inc. 

Of these, the most extensive use is to identify adsorbed molecules and molecular intermediates on metal single-crystal surfaces. On these well-defined surfaces, a wealth of information can be gained about adlayers, including the nature of the surface chemical bond, molecular structural determination and geometrical orientation, evidence for surface-site specificity, and lateral (adsorbate-adsorbate) interactions. Adsorption and reaction processes in model studies relevant to heterogeneous catalysis, materials science, electrochemistry, and microelectronics device failure and fabrication have been studied by this technique. 

Growth theories of surfaces have received considerable attention over the last sixty years as summarized by Laudise et al. [53] and Jackson [54]. The well-known model of the crystal surface incorporating adatoms, ledges and kinks was first introduced by Kossel [55] and Stranski [56]. Becker and Doring [57] calculated the rates of nucleation of new layers of atoms, and Papapetrou [58] investigated dendritic crystallization. 

A drastic departure from nucleation theory was made by Sadler [44] who proposed that the crystal surface was thermodynamically rough and a barrier term arises from the possible paths a polymer may take before crystallizing in a favourable configuration. His simulation and models have shown that this would give results consistent with experiments. The two-dimensional row model is not far removed from Point s initial nucleation barrier, and is practically identical to a model investigated by Dupire [35]. Further comparison between the two theories would be beneficial. 

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

The effect of alkali presence on the adsorption of oxygen on metal surfaces has been extensively studied in the literature, as alkali promoters are used in catalytic reactions of technological interest where oxygen participates either directly as a reactant (e.g. ethylene epoxidation on silver) or as an intermediate (e.g. NO+CO reaction in automotive exhaust catalytic converters). A large number of model studies has addressed the oxygen interaction with alkali modified single crystal surfaces of Ag, Cu, Pt, Pd, Ni, Ru, Fe, Mo, W and Au.6... 

Stelzer et al. [109] have studied the case of a nematic phase in the vicinity of a smooth solid wall. A distance-dependent potential was applied to favour alignment along the surface normal near the interface that is, a homeotropic anchoring force was applied. The liquid crystal was modelled with the GB(3.0, 5.0, 2, 1) potential and the simulations were run at temperatures and densities corresponding to the nematic phase. Away from the walls the molecules behave just as in the bulk. However, as the wall is approached, oscillations appear in the density profile indicating that a layered structure is induced by the interface, as we can see from the snapshot in Fig. 19. These layers are... 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

The (001) face has the highest density of Mo atoms depending on the lattice fracture plane, unsaturated Mo and Oji can appear. In the a direction two types of bonds arise Mo-On (1.73A) and Mo-On (2.25A) several crystal surfaces can then be envisaged (model 4), viz. (Mo6024), (M06O23) (Mo602i) and MofiOig. 

An alternative type of tip-induced nanostructuring has recently been proposed. In this method, a single-crystal surface covered by an underpotential-deposited mono-layer is scanned at a close tip-substrate distance in a certain surface area. This appears to lead to the incorporation of UPD atoms into the substrate lattice, yielding a localized alloy. This procedure works for Cu clusters on Pt(l 11), Pt(lOO), Au(l 11), and for some other systems, but a model for this type of nanostructuring has not been available until now. (Xiao et al., 2003). 

As the crystal surface exposed to the atmosphere is usually not ideal, specific sites exist with even much lower co-ordination numbers. This is shown schematically in Fig. 3.5, which gives a model comprising so-called step, kink and terrace sites (Morrison, 1982). This analysis suggests that even pure metal surfaces contain a wide variety of active sites, which indeed has been confirmed by surface science studies. Nevertheless, catalytic surfaces often behave rather homogeneously. Later it will be discussed why this is the case. In short, the most active sites deactivate easiest and the poorest active sites do not contribute much to the catalytic activity, leaving the average activity sites to play the major role. 

In this chapter, we will focus on some of the recent developments in understanding the influence of solution and electrochemical conditions over model single-crystal surfaces. Specifically, we will review work applying electronic structure methods to probe electrocatalytic mechanisms occurring at this complex interface. 

While experiment and theory have made tremendous advances over the past few decades in elucidating the molecular processes and transformations that occur over ideal single-crystal surfaces, the application to aqueous phase catalytic systems has been quite limited owing to the challenges associated with following the stmcture and dynamics of the solution phase over metal substrates. Even in the case of a submersed ideal single-crystal surface, there are a number of important issues that have obscured our ability to elucidate the important surface intermediates and follow the elementary physicochemical surface processes. The ability to spectroscopically isolate and resolve reaction intermediates at the aqueous/metal interface has made it difficult to experimentally estabhsh the surface chemistry. In addition, theoretical advances and CPU limitations have restricted ab initio efforts to very small and idealized model systems. 

In this chapter, we present a brief background account of recent progress in the application of ab initio methods to elucidating the fundamental physicochemical processes that take place at the electrified aqueous metal interface. Our focus is predominantly on model single-crystal surfaces at lower surface coverages. 

Rainer, D. R., Vesecky, S. M., Koranne, M. et al. (1997) The CO + NO reaction over Pd A combined study using single-crystal, planar-model-supported, and high-surface-area Pd/Al203 catalysts , J. Catal., 167, 234. 

The model was also extended11 to single-crystal surfaces of silver. Although the calculated inner-layer capacitances varied in the right way from one face to another, the values were much too low. The problem was suspected to be due to the importance of the d electrons. What is still needed in this model is a better treatment of the solvent phase, valid at higher charge density, and a better way of deriving the repulsive potential of the solvent on the electrons, perhaps by a direct pseudopotential calculation, as done by Price and Halley.98,99... 

We note here that all the information presently available on high molecular weight polymer crystal structures is compatible with the bundle model. While very nearly all crystalline polymer polymorphs involve all-parallel chain arrangements, even the only known exception, namely y-iPP [104,105], where chains oriented at 80° to each other coexist, is characterized by bilayers of parallel chains with opposite orientation. This structure is thus easily compatible with crystallization mechanisms involving deposition of bundles of 5-10 antiparallel stems on the growing crystal surface. Also the preferred growth... 

Nicholas, J. E., An Atlas of Models of Crystal Surfaces. Gordon Breach, New York, 1965. 

Figure 1,4 The atomic arrangement in the missing row model of the reconstructed iridium (110) crystal surface. From G.A. Somorjai, Chemistry in Two Dimensions, Cornell University Press, London, 1981, p. 146. Used by permission of Cornell University Press.

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