Planar metallic surfaces

Siepmanna and Sprik used a classical MD method to simulate the ordering of a water film adsorbed on an atomic model of a tip of scanning tunneling microscope (STM) probe approaching a planar metal surface.71 They investigated the structural rearrangements... 

The shape of the metal specimen considered is obviously related to the kind of system to be modelled. For SERS and the others SE phenomena, the presence of curved surfaces, with a curvature radius on the nanometric scale, is fundamental for the enhancement. Thus, spheres, ellipsoids, ensembles of spheres, spheres close to planar metal surfaces and planar metal surfaces with random roughness have been considered. We refer to the review by Metiu [57], which describes most of these analytically solvable models. More recently, the modelling of the electric field acting on the point molecule has moved to more realistic shapes (including fractal metal specimen) [59] which require numerical methods to be tackled. The aim of these approaches is usually to calculate the total electric field around the metal particle, and the molecule does not even appear explicitly in the calculations. Interested readers are referred to some recent reviews on the subject [60] (see also Chapters 2 and 5 of ref. [56]). 

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

These electromagnetic waves are very sensitive to any change in the boundary—for example, to the adsorption of molecules onto the metal surface. SPR has measured the absorption of material onto planar metal surfaces (typically Au, Ag, Cu, Ti, or Cr) or onto metal nanoparticles and is used in many color-based biosensor applications and lab-on-a-chip sensors. To observe SPR, the complex dielectric constants e1 of the metal and s2 of the dielectric (glass or air) must satisfy the conditions Re(ei) < 0 and > e21,... 

If the incoming flow from a nozzle is at 90° to a planar metallic surface, then the flow impinges onto the metal surface and moves radially outward. The flow is redirected from being perpendicular to the planar surface to radial parallel to the surface. Mass transport solutions to this situation have been proposed and in general depend upon the ratio of vertical distance to nozzle diameter Hid) and the radial position on the plate (xld) as shown in Fig. 10. Chin and Tsang (4,17) showed that, for Hid between 0.2 and 6 and xld between 0.1 and 1,... 

Figure 6-1. Left Schematic view of a double-strand oligonucleotide linked to an atomically planar metal surface via an oligo-methylenetluolate linker. The yellow sphere attaching the linker and the oligonucleotide to the surface is a sulfur atom. Right The four nucleobases and their single-base nucleosides and nucleotides.

The transitory stage is followed by a stationary phase with a constant and higher rate of NO conversion. We measured the rate of conversion during this stationary stage. These data give a yield of 2 NO molecules converted per second and adsorption site. This value should be taken as a nominal number rather than an absolute value due to the lack of an independent evaluation method for the number of available adsorption sites. The above number was calculated from the number of copper atoms in a closely packed planar metal surface. 

A useful limiting form of Equation (57a) for the potential of a conducting sphere with charge q at a distance d from a (grounded) planar metal surface is obtained for 2 = 0 and Dj = 00 ... 

In more recent works [75-79], analytical plates from Whatman with flexible backing have been used. In these works, the developed plate could be either scraped to allow recovery of the fraction into solution or cut into small pieces to allow selected fractions to be stuck onto the laser target plate of the Bruker mass spectrometer for direct LD from the silica surface. The advantage of this method was that the intractable, relatively immobile material was dispersed thinly over the silica and was less likely to generate cluster ions as laser fluence increased. Also, these intractable fractions tended to be impossible to recover completely into solution. In addition, Knockenmuss [80] showed that secondary ionic reactions are less likely when ablation is from a structured silica surface rather than from a planar metal surface. 

In Eq. (5.63), kp is the Fermi wavevector. This dielectric constant can be used in the framework of the specular scattering or semiclassical infinite-barrier (SCIB) model for planar metal surface [88]. Within the framework of such approach, the different descriptions of the metal response discussed so far (local dielectrics, hydrod3mamic dielectric function and Lindhard-Mermin dielectric function) can be compared. This has been done in Ref. [89] for the metal-induced non radiative rate of a molecule close to an Ag surface. The results are summarized in Fig. 5.9. 

---