Gas-Surface Interaction Potential

1 General Semiclassical Theory of Gas-Surface Scattering 1.1 Gas-Surface Interaction Potential 

Owing to the short-range nature of the interatomic pair potential, the non-stationary part of the atom-surface interaction is 2tssumed to be maunly contributed by the first layer of surface atoms. The instant configuration of this layer is described by the displacement Uk of kth atom from its equihbrium position Rk. It is convenient to express Uk through the amplitudes at of phonon modes I = (q,j) with wave vectors g and polarizations j (the system of units with ft = 1 is used throughout this review)  

Within the linear coupling approximation the interaction potential is 

For long wave phonons and a short-range pairwise potential, the energy of atom-phonon interaction is mainly determined by the displacement u R) of surface point R posed exactly below the gas atom V(r, ufc ) s V (r) — u R)Wt(r), or 

Of course, this does not assume the interaction with a single atom. 

---

Barker J A and Rettner C T 1992 Accurate potential energy surface for Xe/Pt(111) a benchmark gas-surface interaction potential J. Chem. Phys. 97 5844... 

Elastic and inelastic colUsions of atoms and molecules at surfaces are also of importance. The scattering of hydrogen and helium from surfaces leads to diffraction patterns in the same manner as with LEED, but since the atoms penetrate the surface far less deeply than even low-energy electrons, the structures obtained reflect the very surface of the sample. The inelastic surface scattering of molecules can be examined in detail using laser and mass spectromet-ric detection for the scattered molecules. Such measurements can be used to model the form of the gas-surface interaction potential, knowledge of which is a prerequisite for any detailed picture of gas-surface reaction dynamics. 

In analogy to the gas phase, elastic scattering of atoms and molecules from surfaces can provide information about the gas-surface potential. Diffraction intensities and bound-state resonances can be analyzed to provide Fourier coefficients of the interaction potential. Classical mechanical scattering patterns exhibiting "rainbows" and "shadows" may provide additional information about the topography of the potential energy surface. Thus, after a lot of effort, box 1 of Fig. 1 shows promise of providing considerable useful data about gas-surface interaction potentials. 

To date, box 2 has not provided much definitive information about gas-surface interaction potentials. It currently appears feasible to obtain accurate ab initio interaction potentials for physically adsorbed species. Chemically interacting systems will be more difficult. Nevertheless, there is some hopeful progress.Furthermore, information about regions of the potential energy hypersurface that are difficult to probe experimentally can be extremely valuable, even if they are not of high accuracy. 

Of course the real projectile-surface interaction potential is not infinitely hard (cf figure A3,9,2. As E increases, the projectile can penetrate deeper into the surface, so that at its turning point (where it momentarily stops before reversing direction to return to the gas phase), an energetic projectile interacts with fewer surface atoms, thus making the effective cube mass smaller. Thus, we expect bE/E to increase with E (and also with W since the well accelerates the projectile towards the surface). 

The alternate approach to developing interaction potentials is to consider the solid surface as a very large molecule. One can then apply theoretical techniques based on gas-phase reaction ideas. The simulation of real systems, however, often requires that both reactive adsorbed atoms as well as a large number of substrate atoms be explicitly treated, and so these techniques rapidly become computationally infeasible. It is apparent that to simulate the general situation, bonding ideas from both regimes should be used. This breakdown does, however, provide a useful format within which to discuss intermediate-range interaction potentials, and so it will be used to illustrate potentials which are in current use in simulations of gas-surface interactions. 

Cabrera, N., and Goodman, F. O. (1972). Summation of pairwise potentials in gas-surface interaction calculations. J. Chem. Phys. 56, 4899-4902. 

The van der Waals equation describes the critical phenomena of vapour to supercritical gas or fluid. Below critical temperature Tc gas which coexists with the liquid phase is called a vapour. Vapor has own saturated vapour pressure Pq. Then we can use the relative pressure P/Pq for description of adsorption. Fundamentally, physical adsorption is valid for vapours [10]. As the molecule-surface interaction of physical adsorption is weak, a sufficient intermolecular interaction corresponding to heat of vapourization is necessary for predominant physical adsorption. Micropore filling is a physical adsorption enhanced by overlapping of the molecule-surface interaction potentials from opposite pore walls and the adsorptive force is the strongest in physical adsorption. Nevertheless, micropore filling is a predominant process only for vapour. 

The most important step in the simulation is the development of the potentials. The more closely the model potential fits reality, the more reliable the results will be. The ideal potential then would be a potential that is obtained from a quantum electronic calculation. However, such potential energy surfaces are complex and time consuming to calculate, and difficult to use direcdy. In practice, most model potentials take simple mathematical forms with parameters that can be determined either from experimental data or by fitting to results of ab initio calculations. Fortunately, there are many good publications devoted to the development of models for gas-surface interactions in general [11] and specifically for interactions of gases with carbon surfaces (Steele) [12—16] so only a brief description need be given here. 

Surface effects in the photochemistry and photophysics of adsorbed molecules have been the subject of numerous investigations in the last several years. Fundamental studies have examined topics such as the role of surfaces in photochemical reaction dynamics (1) as well as the role of photophysics and photochemistry in affecting gas-surface interactions (2). The photochemistry of organometallics and metal complexes on surfaces has been an important subset of this work (3-11). The driving force behind many of the studies of organometallics and metal complexes on surfaces stems from potential applications in catalysis (3-7) and microelectronics (8-13). 

Several other theoretical models [47-49] have attempted to give a more realistic description than the Langmuir and BET models of the gas-surface interactions that lead to physical adsorption. The variable parameters in these models are the interaction potential, the structure of the adsorbed layer (mobile or localized monolayer of multilayer), and the structure of the surface (homogeneous or heterogeneous, number of nearest neighbors). 

A gas atom or molecule approaching a surface feels an attractive potential. The nature of the gas-surface interaction determines the depth of the potential well (it is deep for chemisorption) and the range of the interaction. We may call the adsorbate-surface interaction weak if it leads to heats of adsorption of less than 10 kcal/mole (42 kJ/mole). This usually means that the adsorbate-adsorbate and adsorbate-substrate interactions are of the same order of magnitude. Therefore, the influence of the substrate atomic surface structure on the adsorption site is considerably weaker in this case than it is for chemisorption and more strongly influenced by coverage (i.e., adsorbate-adsorbate interaction). 

For certain types of gas-surface interactions, it may be useful to view the interaction as between the gas atom and a single surface atom. Weak attractive interaction between a pair of atoms can be due to dispersion forces (London [14, 15]) that represent the interaction of induced fluctuating charge distributions. In addition, molecules that possess permanent dipoles can further polarize each other (Debye [16, 17]) and can have dipole-dipole interactions (Keesom [18, 19]). All these pairwise interaction potentials fall off inversely as the sixth power of the distance. 

Inverse Scattering Problem in Gas-Surface Interaction 15.1 Gas-Cold Surface Interaction Potential Extraction Quasiclassical Approach... 

---