Rough surface model

A rough surface model in which molecular incorporation is favored at many vacant sites in the nascent lattice layer. In this case the growth rate is... 

The currently useful model for dealing with rough surfaces is that of the selfsimilar or fractal surface (see Sections VII-4C and XVI-2B). This approach has been very useful in dealing with the variation of apparent surface area with the size of adsorbate molecules used and with adsorbent particle size. All adsorbate molecules have access to a plane surface, that is, one of fractal dimension 2. For surfaces of Z> > 2, however, there will be regions accessible to small molecules... 

In particular we would like to treat some essential effects of fluctuations where we assume that, for example, thermal fluctuations exist and are localized in space and time. The effects on large lengths and long times are then of interest where the results are independent of local details of the model assumptions and therefore will have some universal validity. In particular, the development of a rough surface during growth from an initially smooth surface, the so-called effect of kinetic roughening, can be understood on these scales [42,44]. 

As the statistical models for rough surface lubrication and contact are established, a mixed lubrication model can be thus constructed in the following procedure. 

Christensen, H., "Stochastic Models for Hydrodynamic Lubrication of Rough Surfaces, Proc. Inst. Mech. Eng., PartJ J. Eng. Tribol.,Wo. 184,1969-70,p. 1013. 

Kogut, L. and Etsion, I., A Static Eriction Model for Elastic-Plastic Contacting Rough Surfaces," Trans. ASME, J. Tri-bol, Vol. 126,2004, pp. 34- 0. 

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... 

A few additional points have also been raised by specific surface-science work concerning the catalytic reduction of NO. For instance, it has been widely recognized that the reaction is sensitive to the structure of the catalytic surface. It was determined that rough surfaces such as (110), or even (100), planes enhance NO dissociation over flatter (111) surfaces, and also favor N2 desorption instead of N20 production. On the other hand, NO dissociation leads to poisoning by the resulting atomic species, hence the faster reaction rates seen with medium-size vs. larger particles on model rhodium supported catalyst (the opposite appears to be true on palladium). Also, at least in the case of palladium, the formation of an isocyanate (-NCO) intermediate was identified... 

The friction coefficient is expected to depend on the normal pressure which is quite high (of order hundreds of kilobars) surface roughness surface homogeneity and humidity (or other environmental factors). As a result, a is not known, so a quantitative model is not possible, but the expected qualitative behavior is clear. 

The comparison of continuum and atomistic models by Luan and Robbins demonstrates that the atomic details of this contact can have a significant influence on the calculated friction. However, those calculations did not explore atomically rough surfaces, which are most likely found in real engineering contacts. The effect of roughness has been investigated recently by Qi et al. in a study of the friction at the interface between two Ni(100) surfaces.85 Two models were considered in that work. In the first model, both surfaces were atomically flat i.e., the rms roughness was 0.0 A. In the... 

R7.4.1 (2005). Multiscale Modeling of Two Dimensional Rough Surface Contacts. 

Figure 1. Rough surfaces generated by (a) RD model and (b) RDWD model Number of Particles deposited = 4 x 105 on 100x100 square lattice.

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