Corrugation potential

Since the idea that all matters are composed of atoms and molecules is widely accepted, it has been a long intention to understand friction in terms of atomic or molecular interactions. One of the models proposed by Tomlinson in 1929 [12], known as the independent oscillator model, is shown in Fig. 13, in which a spring-oscillator system translates over a corrugating potential. Each oscillator, standing for a surface atom, is connected to the solid substrate via a spring of stiffness k, and the amplitude of the potential corrugation is. ... 

Stability of the atomic system depends on the spring stiffness and the potential corrugation, or more specifically, depends on the ratio of k/. The system would become more stable if the stiffness increases or the potential corrugation decreases, which means less energy loss and lower friction. 

The de Broglie wavelength of thermal He atoms is comparable with the interatomic distances of surfaces and adsorbed layers. Thus, from measurements of the angular positions of the diffraction peaks the size and orientation of the 2D unit cell, i.e. the structure of the outermost layer, can be straightforwardly determined. Analysis of the peak intensities yields the potential corrugation, which usually reflects the geometrical arrangement of the atoms within the 2D unit celP. 

Figures 17b and 17c show the response in the lateral and normal directions to a lateral constant velocity drive for the stick slip regime that occurs at low driving velocities. This behavior is similar for the presently discussed model. The separation between the plates, which is initially Zq at equilibrium, starts growing before slippage occurs and stabilizes at a larger interplate distance as long as the motion continues. Since the static friction is determined by the amplitude of the potential corrugation exp(l — Z/A), it is obvious that the dilatancy leads to a decrease of the static friction compared to the case of a constant distance between plates.

Over a wide range of system parameters the dilatancy is smaller than the characteristic length A. Under this condition the generalized Prandtl Tomlinson model predicts a linear increase of the static friction with the normal load, which is in agreement with Amontons s law. It should be noted that, in contrast to the multi-asperity surfaces discussed in Section VII, here the contact area is independent of the load. The fulfillment of Amontons s law in the present model results from the enhancement of the potential corrugation, a2C7oexp(l — Z/K), experienced by the driven plate with an increase of the normal load. 

Effects of the gas - solid potential corrugation on the behaviour of monolayers formed on the (100) face of an fee crystal at finite temperatures have been recently studied by Patrykiejew et al. [163] with the help of Monte Carlo method. They have considered three-dimensional systems of constant volume and containing fixed number of particles interacting via the Lennard-Jones potential (1). The gas - solid interaction potential has been assumed to be represented by the two-fold Fourier series [88]... 

In the case when the gas solid potential exhibits periodic variations, a competition between the surface potential corrugation and the gas - gas interaction becomes a major factor determining the structure of the film. From the calculations of the heat capacity for... 

F1M has shown unusual forms of diffusion of metal atoms on a surface, including correlated motion between separated atoms (Tsong, 1993). Such diffusion is usually strongly anisotropic, on (110) surfaces for instance it occurs along the close-packed (110) direction which has only a weak potential corrugation compared with the orthogonal direction. 

A relevant property of the coupled equations is the existence of two stable surface separations Zq and Zs, which correspond to the plate being either at rest or in fast motion. At rest the plate feels the lateral corrugation of the potential, 0(Z,Z), and sits at the minima of the potential, while during fast motion there is a decoupling from this potential corrugation. From eqs. 7 and 8, together with 0(X,Z), one obtains the following equation for the maximal dilatancy... 

Patrykiejew et al. [329] have also simulated the behavior of 2D L-J fluids onto the (100) face of a face-centered-cubic crystal. Nevertheless, the Knight and Monson [225] work was not mentioned, so that no comparison of results was performed. To model the gas-surfaee potential, Patrykiejew et al. [329] used the first live terms of Steele s Fourier series [Eq. (14)] for a perpendicular reduced distance less than or equal to 2.5. The results show that at low temperature, the structure of the monolayer film depends strongly on the gas-surface potential corrugation, as well as on the size of the adsorbed atoms. Also, the influence of the corrugation on the melting transition is studied, indicating a different structure of the solid phase. Unfortunately, definitive conclusions about the nature and order of the observed phase transitions were not obtained. 

In this section we study a system with purely repulsive interactions which demonstrates the importance of entropy effects on the stability of phases when the effect of the corrugation potential due to the structured surface is completely neglected. The phase diagrams are determined by finite size scaling methods, in particular the methods of Sec. IV A. 

Of course, the above discussion apphes only to systems exhibiting domain wall structure, i.e., to weakly inhomogeneous phases formed on surfaces with low corrugation of the gas-solid potential and characterized by the presence of more then one type of equivalent sublattices. When this is not the case, i.e., when the dense incommensurate phase can be considered to be... 

Figure 6-12. Model for Ihe Calculation of the van der Waals potential experienced by a single T6 molecule on a Tfi ordered surface. Each molecule is modeled as a chain of 6 polarizable spherical units, and the surface as 8-laycr slab, each layer containing 266 molecules (only pan of the cluster is shown). Tire model is based on X-ray diffraction and dielectric constant experimental data. The two configurations used for evaluating the corrugation of the surface potential are shown. Adapted with permission front Ref. [48].

Another important feature of polymer adsorption is the influence exerted on it by the surface roughness. Ball et al. [22] proposed that if the surface potential is not attractive enough to bind the polymer when flat, then corrugation can aid binding as follows. For a sinusoidal corrugation, one might anticipate that some... 

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