Dipolar surfaces

Making the appropriate transformations from surface to beam coordinates, Koos et al. [122] note that xSjki has the same form as the second-order surface tensor x fk as a result of the applied field being parallel to the surface normal. Because the field is localized at the surface, the xn> effect should mimic the dipolar surface response with an effective susceptibility of... 

Polarization of Water near Dipolar Surfaces A Simple Model for Anomalous Dielectric Behavior... 

It was recently shown via molecular dynamics simulations14 that, in the close vicinity of a surface, water molecules exhibit an anomalous dielectric response, in which the local polarization is not proportional to the local electric field. The recent findings are also in agreement with earlier molecular dynamics simulations, which showed that the polarization of water oscillates in the vicinity of a dipolar surface,11,14 leading therefore to a nonmonotonic hydration force.15 Previous models for oscillatory hydration forces, based either on volume-excluded effects,18,19 or on a nonlocal dielectric constant,f4 predicted many oscillations with a periodicity of 2 A, which is inconsistent with these molecular dynamics simulations,11,18,14 in which the polarization exhibits only a few oscillations in the vicinity of the surface, with a larger periodicity. 

Nitzan and Brus developed an analytical formula for the molecular absorption cross section given the model defined above [14]. Figure 9.2 is taken fi"om Ref. [13] and shows the calculated absorption cross section based on the model associated with the photodissociation of I2. (The I2 formed through the absorption process is very short lived.) Photodissociation predicted to be enhanced as the molecule is placed near a silver metal nanoparticle of radius a - 50 nm near the electronic transition resonance position of cat) 22,200 cm . If e eiai(co) is the dielectric fiinction for the metal, a small metal nanoparticle plasmon in air will have its dipolar surface plasmon resonance at frequency <24 such that [1]... 

Although type 1 and 2 surfaces may exist, those of type 3, also referred to as dipolar surfaces, are unstable and can only be stabilized through some mechanism to remove the macroscopic field (i.e., by reconstruction, molecular adsorption, and so on). In the MgO case (see Figure 35), the (100) and (110) surfaces correspond to type 1, whereas the (111) surface is type 3. 

Figure 39 Lateral view of the (100) surface of Li20. On the left unreconstructed dipolar surface. On the right reconstructed zero-dipole surface.

The region of contact of two different materials, generally of differing chemical potentials or work functions will give rise to an interfacial potential and therefore a dipolar surface layer. In the event that one or both of the materials has a high dielectric constant or is perhaps easily dissociated, then the formation of ionic species at this surface dipole layer can occur. 

Type III In this case, atom layers are again not neutral but now all possible cuts yield dipolar surfaces. An example of a type III surface is the (111) plane of MgO illustrated in Figure 42c. 

For the unstable dipolar surfaces of types II and III, the fact that a dipolar surface is formed argues against the surface being present in its perfect form on real crystallites. However, if the dipole can be removed, either by the inclusion of surface defects or by chemical alteration of the surface, the crystal face with these indicies may be observed. 

The localized surface plasmon resonance of individual plasmonic nanoparticles depends heavily on the size and shape of each nanoparticle. For instance, the wavelength of the dipolar surface plasmon red shifts with the increase of particle size. However, for much larger nanoparticles new bands for some multipolar modes will appear in the short-wavelength range, while the dipolar band at long-wavelength will be damped. Typically, the size of Au or Ag nanoparticles synthesized for SERS should be less than 150 nm, and larger than 20 nm. 

According to the superposition principle (Rafii-Tabar etal, 2006), the potential drop j(t) is the sum of the ones related to the thickness of the adsorbed water layer (A< i) andthe drop related to the dipolar surface density (A2) ... 

It should be recognized for the small-sphere model that if the molecule is located at a distance from the surface of the particle, the enhancement would be diminished by the factor (a /r ), and near the dipolar surface plasmon resonance... 

It should be pointed out at this juncture that a given laser excitation frequency fixes ef and thus fixes the value of a/b at which the surface plasmon resonance occurs. Molecules located at spheroids with smaller or larger values of a/b will not be enhanced as much because the dipolar surface plasmon is off resonance. Thus, at a given laser excitation, only spheroids of one aspect ratio will show the maximum enhancement. Since in the actual experimental situation, there are various possible molecular orientations and a distribution of bump sizes on an electrochemically pretreated SERS metal surface and in a colloidal system, only a fraction of the sites will show the maximum enhancement. Furthermore, all molecules will not be located at the tip of the metal particles but will be distributed over the metal surface. It follows that the actual EM enhancement will be an average over the spheroid surface of isolated particles as well as an average over the aspect ratio of the particle distribution. These two effects greatly lower the net EM enhancement. 

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