Surface commensuration between structural

Studies based on the Frenkel-Kontorova model reveal that static friction depends on the strength of interactions and structural commensurability between the surfaces in contact. For surfaces in incommensurate contact, there is a critical strength, b, below which the depinning force becomes zero and static friction disappears, i.e., the chain starts to slide if an infinitely small force F is applied (cf. Section 3). This is understandable from the energetic point of view that the interfacial atoms in an incommensurate system can hardly settle in any potential minimum, or the energy barrier, which prevents the object from moving, can be almost zero. 

Although the structure of the PTCDA/Ag(l 11) interface is dominated by the molecule-substrate interaction (cf. the commensurate interface structure), the interaction between molecules does play an important role for the structural details and the energetics at the interface. On the one hand, there is the attractive electrostatic interaction between molecules. Because of this interaction PTCDA molecules always cluster in two-dimensional islands. However, at surface temperatures below 150 K, these islands do not yet exhibit the familiar herringbone structure [35] since the electrostatic interaction does not exhibit sufficient directional specificity, a considerable degree of structural disorder prevails, in spite of a clear propensity of the molecules to arrange in a T-like... 

As discussed earlier briefly, semicrystalline or amorphous nanotubes can be obtained from 3D compounds and metals by depositing a precursor on a nanotube template intermediately, and subsequently removing the template by calcination. If the template molecules are not removed and they are able to effectively passivate the dangling bonds of the compound, a perfectly crystalline nanotube composite can be obtained. However, after high-temperature calcination, the organic scaffold is removed and the inorganic oxide remains. Because a nanotube is the rolled-up structure of a 2D-molecular sheet, there is no way that all the chemical bonds of the 3D-inorganic compound will be fuUy satisfied on the nanotube inner and outer surfaces. Furthermore, the number of molecules increases with the diameter, and hence a full commensuration between the various molecular layers is not possible. Therefore, nanotubes of 3D... 

The balance between these different types of bonds has a strong bearing on the resulting ordering or disordering of the surface. For adsorbates, the relative strength of adsorbate-substrate and adsorbate-adsorbate interactions is particularly important. Wlien adsorbate-substrate interactions dominate, well ordered overlayer structures are induced that are arranged in a superlattice, i.e. a periodicity which is closely related to that of the substrate lattice one then speaks of commensurate overlayers. This results from the tendency for each adsorbate to seek out the same type of adsorption site on the surface, which means that all adsorbates attempt to bond in the same maimer to substrate atoms. 

Cell membranes consist of two layers of oriented lipid molecules (lipid bilayer membranes). The molecules of these two layers have their hydrocarbon tails toward each other, while the hydrophilic heads are outside (Fig. 30.1a). The mean distance between lipid heads is 5 to 6mn. Various protein molecules having a size commensurate with layer thickness float in the lipid layer. Part of the protein molecules are located on the surface of the lipid layer others thread through the layer (Fig. 30.1fc). Thus, the membrane as a whole is heterogeneous and has a mosaic structure. 

Various phases have been described55 for thiolates adsorbed at Au(lll) surfaces starting from ( /3x /3) i 30° at low coverage and including the 3 x 2 /3, 3x4 and p x 3. All of these are commensurate with the Au(lll) surface. In sharp contrast, with Ag(lll) an incommensurate ( /7x /7) i 19.1° structure forms for carbon chains longer than 2. The deviation from commensurate behaviour is thought to be due to repulsive interactions between the close-packed alkyl chains and the reduction in strength of the Ag-Ag bonds to... 

Lattice Model Carlo simulations of a block copolymer confined between parallel hard walls by Kikuchi and Binder (1993,1994) revealed a complex interplay between film thickness and lamellar period. In the case of commensurate length-scales (f an integral multiple of d), parallel ordering of lamellae was observed. On the other hand, tilted or deformed lamellar structures, or even coexistence of lamellae in different orientations, were found in the case of large incommensurability. Even at temperatures above the bulk ODT, weak order was observed parallel to the surface and the transition from surface-induced order to bulk ordering was found to be gradual. The latter observations are in agreement with the experimental work of Russell and co-workers (Anastasiadis et al. 1989 Menelle et al. 1992) and Foster et al. (1992). 

FIGURE 3.2. (a) Chemical structure of octanethiol. (b) A constant current STM image of octanethiol SAM on Au(l 11). Au reconstruction is lifted and alkanethiols adopt commensurate crystalline lattice characteriized by a c(4 x 2) superlattice of a (a/3 x V3)R30°. (c) Model of commensuration condition between alkanethiol monolayer (large circles) and bulk-terminated Au surface (small circles). Diagonal slash in large circles represents azimuthal orientation of plane defined by all-trans hydrocarbon chain. (Reprint with permission from Ref.25 G. E. Poirier, Chem. Rev., 97, 1117-1127 (1997). Copyright 1997 American Chemical Society.)... 

In layered misfit structures of the type we are discussing, bonds at the layer surfaces (within and between the layers) will be strained periodically along a non-commensurate lattice direction parallel to the layers after a certain number of subcells there is a near match of the layers. Clapp has pointed out that, for a simple case, layer mismatch will cause tension in one layer type and compression in the other. The resulting strain energy may be relieved by the introduction of periodic antiphase boundary (apb) planes so that alternate contraction and extension occurs in all layers (Fig. 22) and hence cancels out (at the price of a small deformation of coordination polyhedra). 

Such forces are also known as hydration forces, structure forces or hydrophobic forces (for hydrophobic surfaces), but we prefer the generic, less specific name. Solvent structure forces certainly play a role in wetting films. According to present insight, such forces decay exponentially with distance, see [5.3.9], exhibiting oscillations if h becomes commensurate with a few times the molecular diameter. For examples see figs. 11.2.2 and 3. In sec. 1.5.4 we discussed such forces between solutes. 

Adsorption processes on crystallographically well-defined substrate surfaces lead to the formation of 2D Meads phases with well-ordered structures denoted as overlayers". Generally, three different types of overlayers, depending on the degree of registry between overlayer and substrate, can be distinguished commensurate, higher-order commensurate or incommensurate overlayers, as illustrated schematically in Fig. 3.14. TTie term superlattice stmcture" is frequently used for commensurate overlayers which can be characterized by either the Wood or the matrix notation [3.271-3.274]. 

The specific adsorption of halide anions has been studied on Au and Ag single crystals [14]. On Au(l 11), these ions form incommensurate hexagonal monolayers that compress as the electrode potential is changed in the positive direction [19]. However, on Ag(lOO), Br adsorption occurs at the hollow site formed by four metal atoms in a square pattern. This type of commensurate monolayer has a c(2 X 2) surface structure. These studies demonstrate the role of atomic surface structure in determining the extent of adsorption. Differences between adsorption on Ag(lOO) and Au(lOO) are explained in terms of differences in the strengths of the metal-halide bonds [14]. 

Alkanethiols form a hexagonal (V3 x V3) R 30° lattice commensurate with the underlying Au(lll) surface. Sulphur atoms in this structure occupy the hollow sites between the gold atoms (Figure 10). The distance between adjacent S atoms in such a structure is 4.97 A4. 

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