Rim-edge model

Daage, M., and Chianelli, R. R., Structure-Function Relations in Molybdenum Sulfide Catalysts The Rim-Edge Model. J. Catal., 1994. 149 pp. 414-427. 

Fig. 7. The rim/edge model. Reprinted from Ref. (89). Copyright 1994, with permission from Elsevier...

Figure 10.6 Rim-Edge Model Showing the Presence of Two Types of Active Sites the Edge Sites Able to Perform Only C-S Bond Rupture Steps and the Rim Sites Able to Perform Both C-S Bond Rupture Steps and Hydrogenation of Benzenic Rings. Adapted from Ref. [144].

The relative proportion of rim and edge sites can then be calculated by using a simple physical model to describe the morphology of the M0S2 particle as illustrated in Fig. 24. This model assumes that the catalyst particles are made of discs n layers thick with a diameter d. In this case, the ratio of rim sites to total sites can be deduced from the expression... 

Optimization of the ratio of rim sites to edge sites in the M0S2 slabs according to the model described by Daage and ChianeUi (137). 

Fig. 10.26. Proposed models for (a) calix[4]arene (lower rim OH) dimers in edge on - with the lower rim pointing towards lower rim -adsorption. (Reprinted from [153], Copyright (2002), with permission from Elsevier) (b) calix[4]arene (lower rim propyl, upper rim COOH) in face up (upright) adsorption. (Reprinted in parts with permission from [154], Copyright 2003 American Chemical Society) (c) C60/ Calix[8]arene OBOCMC8 inclusion complexes again adsorbed upright standing. (Reprinted in parts from [155] with permission of the authors and Wiley, VCH, copyright 2003). All molecules imaged at the solution interface to the (111) facets of Au-beads.

In addition, we employed slightly shorter (20 A), edge-functionalized (5, 5) and (6, 6) SWCNT models, denoted Short-OX , to investigate the dependence of the capping process on the presence of different oxygen-containing functionalities on their rim. These systems will be discussed later in greater detail. 

Fig. 20 Experimental evidence for elevations Qess folded states) at the edge of the crystalline domains and for the rim-hole patterns related to the predictions of the simulation model. The left part shows the formation of high elevations at edges and rim-hole patterns in short chain PEO-2k crystals after long relaxation times at room temperature (RT). In the right part, analogous morphologies are obtained by annealing two-dimensional PS-PEO(3-3) crystals. Basicidly, the copolymer shows the same properties as the homopolymer. However, the non-crystallizable polystyrene block affects the ordering process of PEO chains in the crystal and therefore influences both the entropic barrier and the melting enthalpy (expressed by the effective temperature T in the simulations)...

The tensile stresses go to infinity at the rim of the contact, but the total stress integrated over the whole contact area remains finite. Outside the contact area, the vertical stress is zero since the JKR model assumes that no surface forces act outside the contact area. The infinite stresses at the edge of the contact are physically not possible. Obviously, the description of that region down to molecular scales by a continuum model as the JKR theory carmot be realistic. As soon as one assumes realistic interaction potentials between the molecules at the rim of the contact, these singularities will disappear. However, such detailed models will usually be too complicated to allow their routine use in contact mechanics. 

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