Wave-Surface Interactions

The interactions discussed in this section involve rarefactions as well as shock waves. Provided that strains are small, the release path can be approximated by the Hugoniot in the P-u plane. The following graphical solutions to the interactions are approximate, but in many cases the approximation is very good. 

Example 3 (Shoek Refleetion from a Higher Z Interfaee). If material B is replaeed by material C, with a higher shoek impedanee than A, the same interfaeial boundary eonditions ean be applied. In this ease, however (Fig. 2.18), this resulting state ( 2 ), is at higher pressure than state 1. The wave refleeted baek into material A is a shoek. If the right-hand bloek of material is replaeed by another bloek of material A, there are no refleeted waves, and the transmitted shoek is identieal to the ineident wave. 

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The Newns-Anderson approximation successfully accounts for the main features of bonding when an adsorbate approaches the surface of a metal and its wave functions interact with those of the metal. It can also be used to describe features of the dynamics in the scattering of ions, atoms and molecules on surfaces. In particular the neutralization of ions at surfaces is well understood in this framework. The subject is beyond the scope of this book and the reader is referred to the literature [J.K. N0rskov, J. Vac. Sci. Technol. 18 (1981) 420],... 

When infrared beam incidents upon thin organic films extended over a plain metal surface (Figure 1), there usually occurs a standing wave electric field on the metal surface as a consequence of the interference between the incident and reflected beams. Since the standing wave may interact with, i. e. be absorbed by, molecules in the organic film, the reflectance of the beam from the metal surface is reduced. 

The concentration of a solute or adsorbate may be a nontrivial function of the distance to the surface, a function which contains information about the thermodynamics of the surface interaction. To explore the fluorophore concentration C(z) as a function of distance z from the surface, one can record the observed fluorescent intensity F as the characteristic depth d of the evanescent wave is varied. The mathematics of this is discussed immediately following Eqs. (7.44) and (7.45) above. 

Fig 33, from Ref 17, is a schematic representation of the effects of a nearby surface on pressure pulse shapes at various distances below the water surface. It also shows the expected pulse shapes for acoustic rather than shock waves A shock wave in water will be reflected as a rarefaction wave when it encounters another medium less dense than water, eg, a water/air boundary. The rarefaction wave, generated by the reflection of the primary shock wave from the surface, propagates downward and relieves the pressure behind the primary shock wave. If the shock wave is treated as a weak (acoustic) wave, this interaction instantaneously decreases the pressure in the primary shock wave to a negative value, as shown by the broken line in Fig 33 (Ref 17), Point A. Cavitation occurs in seawater when its pressure decreases to a value somewhat above its vapor pressure. The pressure of the primary shock wave is, therefore, reduced to a value which is usually so close to ambient water pressure that the shock wave pulse appears to have been truncated... 

Incidentally we note that resonances do exist, however, in gas-surface collisions in which, as a consequence of the infinite mass of the solid, J is always zero resonances are indeed one major source of information on the gas-surface interaction (Hoinkes 1980 Barker and Auerbach 1984). Likewise, resonances are prominent features in electron-atom or electron-molecule collisions (Schulz 1973 Domcke 1991) the extremely light mass of the electron implies that only partial waves with very low angular momentum quantum numbers contribute to the cross section. 

Figure 13 plots an example of the processed PIV frame. The turbulent velocity field and its boundaries, solid wall, and liquid-free surface are simultaneously shown in Figure 13. The turbulence structures such as the coherent vortical structure near the bottom wall and its modification after release from the no-slip boundary condition near the free surface of the open-channel flow, and the evolvement of the free-surface wave can be seen in Figure 13. This simultaneous measurement technique for free-surface level and velocity field of the liquid phase using PIV has been successfully applied to the investigation of wave-turbulence interaction of a low-speed plane liquid wall-jet flow (Li et al., 2005d), and the characteristics of a swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall (Li et al., 2006c).

A surface plasmon is a light wave that is bound to the interface of a metal in contact to a dielectric medium. The free electrons of the metal respond collectively by oscillating in resonance with the light wave. The interaction occurs only if the momentum of the incoming photon matches with that of the surface plasmon mode. 

These surface modifications were performed in "pure" micro-wave (2.45 GHz, "single-mode") or in combined microwave/ radio frequency (2.45 GHz/13.56 MHz, "dual-frequency") plasma. Important systematic changes of the surface composition, wettability, and adhesion of thin metal films were observed for different substrate bias values, and for the different gases. The modified surface-chemical structure is correlated with contact angle hysteresis of water drops this helps to identify which surface characteristics are connected with the wettability heterogeneity and with adhesive bonding properties, and how they are influenced by plasma-surface interactions. 

Surface plasmon resonance (SPR) biosensors exploit special electromagnetic waves-surface plasmon-polaritons-to probe interactions between an analyte in solution and a biomolecular recognition element immobilized on the SPR sensor surface. A surface plasmon wave can be described as a light-induced collective oscillation in electron density at the interface between a metal and a dielectric. At SPR, most incident photons are either absorbed or scattered at the metal/dielectric interface and, consequently, reflected light is greatly attenuated. The resonance wavelength and angle of incidence depend upon the permittivity of the metal and dielectric. 

The theoretical treatments of other electrocatalytic reactions are very limited. Even semiquantitative treatments are important since they provide insight as to the role of adsorption sites and surface interactions involving reactants, intermediates, and/or products. Of special interest are theoretical treatments of the energetics of adsorption on various sites using molecular orbital and X- scattered wave calculations in combination with experimentally evaluated adsorption isotherms and in situ spectroscopic measurements on single-crystal electrode surfaces. 

Sum-fretiuencv generation (SI Ci) is a nonlinear optical technique basoil on the interaction of two plu tons at a surface. The result of the wave-mixing interaction is the production of a single photon whose frequency is the sum of the incident frequencies. If the two incident photons are of Ihe same frequency, the technique is called second-harmonic generation because the exiting photon has a frequency Iwice iha of the incident photons. Because this is a weak second-order process, intense lasers must be used. 

Hofer M., Finger N., Kovacs G., Schoberl J., Langer U., and Lerch R., Finite element simulation of bulk- and surface acoustic wave (SAW) interaction in SAW devices, presented at IEEE Ultrasonics Symposium, October 8-11, 2002, Munich, Germany. 

One method that has proven to be particularly useful for the analysis of molecule/surface interactions is the constrained space orbital variation (CSOV) scheme originally proposed by Bagus and Hermann [30,31]. As does the Morokuma scheme, it allows for a decomposition of the total SCF or DFT interaction energy into its different contributions by calculating only energy quantities, and not as do most other decomposition schemes by analyzing electronic densities or wave functions. The CSOV analysis consists of several consecutive steps which can be roughly characterized as follows ... 

This is not the place for a full overview of the wave function based post Hartree-Fock methods currently applied for the calculation of intermolecular interactions and in particular molecule/surface interactions. Table 3 contains a brief characterization of the most widely applied schemes. The two most popular methods are MP2 (second order Moller-Plesset perturbation theory), because it covers large part of electronic correlation at comparably low ex-... 

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