Enhancement factor, calculation

Fig. 9 SEFS enhancement factor calculated for a polystyrene film doped with oxazine 720 on arrays of nanoholes (150 nm diameter) of different periodicities...

Recently, Sun et al. [60] proposed to fabricate Ag nanostructures by electrochemical deposition of Ag in anodic aluminum oxide templates with each pore diameter of 100 nm. The morphology of Ag substrates was characterized by EESEM. The length of the Ag nanowires is estimated to be about 2 pm from the EESEM images. In addition, the SERS enhancement factor calculated for Ag nano wires SERS substrates is approximately 10 in magnitude. The Ag nano wire arrays are expected to have important applications in the development of high sensitivity SERS-based substrates. 

Figure 4-16. Stratospheric enhancement factor calculated by Meier et al.(1982) for different values of the albedo.

Values of the enhancement factor calculated for the ten possible RO single-particle transitions in the model... 

The enhancement factor calculated theoretically is obtained experimentally only when an ideal laser source is used. The enhancement factor is strongly affected by the beam quality of the laser. Thus, a laser with a single transverse mode must be used to obtain an enhancement factor close to the theoretical one. A CW laser, such as an argon ion laser, is usually operated in the single mode and is preferred in thermal lensing spectrometry. A pulsed laser, such as a dye laser pumped by an excimer laser, provides rather poor beam quality, unless the beam shape is specially controlled by using a pinhole followed by amplification. The enhancement factor obtained experimentally in pulsed thermal lens spectrometry is usually small in comparison with the theoretical value. Aberration of the focusing lens may also affect the... 

FIGURE 2.12 (a) Hydrogen uptake enhancement factor calculated as a function of the promoter coverage (in ML), for three different values of the hydrogen adsorption oveipotential, t) used in text, (b) Maximum rate enhancement at the critical value of as a function of the hydrogen overpotential. Reproduced with permission from Taylor et al. [159]. Electrochemical Society. 

Correlations for chemical mass transfer coefficients, and were not regarded as necessary as they differ for different chemical systems and reactions employed. On the other hand, correlations for k a and k can be adapted to other physical systems by just making a diffusivity correction. Mass transfer coefficients assessed with absorption and chemical reaction can then be estimated using Equations (18) and (19) together with the enhancement factor calculated specifically for the chemical system of interest. 

Pettinger et al. observed a TERS spectrum of monolayer-thick brilliant cresyl blue (BCB) adsorbed on a smooth Au film surface by using a Ag tip, while no STM image of the adsorbed surface was shovm [23]. The Raman intensity increased when the tip was in the tunneling position, meaning that the tip-surface distance was around 1 nm. They calculated the field enhancement factor by the method described by... 

The perimeter ib, representing the turbulent intensity at the bubble layer-core interface, is calculated as the product of the single-phase turbulent intensity at the bubble-layer edge and a two-phase enhancement factor. The resulting expression is... 

Calculations for TE polarized light give similar results42, but the maximum induced 8/Vell in the PWEF waveguide is about three times smaller than for the TM mode. This difference is largely due to the absence of the surface field enhancement factor of (9.5), since the electric field of the TE mode is parallel to the waveguide surface and hence there is no electric field discontinuity. 

Here, Kx and Kz are the X and Z components of the absorption coefficient, and mx and mz are those of the intensity enhancement factor in the RA measurements due to the presence of the Ag film. The second term in the denominator of the right hand side of Eq. (1) was added to take into account the slight contribution of the electric field parallel to the film surface in the RA measurements. After a simple calculation under the condition of the uniaxial orientation, we have... 

The enhancement factors mz and mx can be calculated exactly by Hansen s formulas for optics of thin multilayer film [10]. The results of the calculation for our experimental systems are shown in Figure 9 as a function of wavenumber. Three lines for the mz values and those for the mx values refer to the refractive indices of the LB film, 1.4, 1.5, and 1.6. The mx values are very small and about one percent of the mz values. This means that the electric field generated by the RA measurements is practically perpendicular to the film surface, as was mentioned above. 

The equations (23) to (27) can only be solved numerically. However such a numerical solution gives less insight in the factors governing the transport and conversion processes. Therefore we consider another approach. In this approach, the transport and conversion of component A are calculated under the assumption that no reaction of ozone with component B takes place. The enhancement factor for mass transfer of ozone, EA, can now be given by the equation ... 

The deviation from the square planar geometry at the Pd center in complexes 3 can be attributed wholly to steric factors. Calculations have shown that there is a moderate electronic preference favouring the planar coordination amounting to approximately 4.5 kcal/mol. However, steric interactions between the bulky trichlorosilyl ligands with both phenyl substituents of the phosphine and pyrazole ring result in a distortion away from the ideal square planar geometry. We further have found that the framework of the specific chelate backbone positions the pyrazole ring such that these interactions are enhanced. 

Equation (6) links, in a simple way, the thermodynamically important stability constants Kox and /Cred of a complex in different oxidation states with experimentally measurable redox potentials EH and EHa. Therefore it provides an easy way to obtain the ratio of KoxIKted, which is a theoretically useful parameter known as the binding enhancement factor (BEF). We propose that a better description for this ratio would be the reaction coupling efficiency (RCE) since binding by so-called molecular switches may be reduced or enhanced, depending upon the particular system involved. Equation (6) also allows the calculation of Kox if Kted is known or vice versa. 

The surface states observed by field-emission spectroscopy have a direct relation to the process in STM. As we have discussed in the Introduction, field emission is a tunneling phenomenon. The Bardeen theory of tunneling (1960) is also applicable (Penn and Plummer, 1974). Because the outgoing wave is a structureless plane wave, as a direct consequence of the Bardeen theory, the tunneling current is proportional to the density of states near the emitter surface. The observed enhancement factor on W(IOO), W(110), and Mo(IOO) over the free-electron Fermi-gas behavior implies that at those surfaces, near the Fermi level, the LDOS at the surface is dominated by surface states. In other words, most of the surface densities of states are from the surface states rather than from the bulk wavefunctions. This point is further verified by photoemission experiments and first-principles calculations of the electronic structure of these surfaces. 

On surfaces of some d band metals, the 4= states dominated the surface Fermi-level LDOS. Therefore, the corrugation of charge density near the Fermi level is much higher than that of free-electron metals. This fact has been verified by helium-beam diffraction experiments and theoretical calculations (Drakova, Doyen, and Trentini, 1985). If the tip state is also a d state, the corrugation amplitude can be two orders of magnitude greater than the predictions of the 4-wave tip theory, Eq. (1.27) (Tersoff and Hamann, 1985). The maximum enhancement factor, when both the surface and the tip have d- states, can be calculated from the last row of Table 6.2. For Pt(lll), the lattice constant is 2.79 A, and b = 2.60 A . The value of the work function is c() w 4 cV, and k 1.02 A . From Eq. (6.54), y 3.31 A . The enhancement factor is... 

The net enhancement factor for a droplet consisting of pure water can be as much as 1.6 (Madronich, 1987). Calculations by Ruggaber et al. (1997) suggest that the actinic flux inside cloud drops with a typical size distribution and dissolved particulate matter is more than a factor of two greater than in the cloud interstitial air. This effect of enhanced actinic flux inside droplets may be quite important for aqueous-phase photochemistry in fogs and clouds. 

Indeed, these reactions play an important role in the Antarctic ozone hole and they have important implications for control strategies, particularly of the bromi-nated compounds. For example, Danilin et al. (1996) examined the effects of ClO -BrO coupling on the cumulative loss of O-, in the Antarctic ozone hole from August 1 until the time of maximum ozone depletion. Increased bromine increased the rate of ozone loss under the denitrified conditions assumed in the calculations by converting CIO to Cl, primarily via reactions (31b) and (31c) (followed by photolysis of BrCl). Danilin et al. (1996) estimate that the efficiency of ozone destruction per bromine atom (a) is 33-55 times that per chlorine atom (the bromine enhancement factor ) under these conditions in the center of the Antarctic polar vortex, a 60 calculated as a global average over all latitudes, seasons, and altitudes (WMO, 1999). 

Except where noted, adapted from Daniel et al. (1995). Calculations based on a bromine enhancement factor of a = 40 globally (see Chapter 12.D for discussion of a) and assuming phase-out of emissions as scheduled in the Copenhagen amendments to the Montreal Protocol (see Chapter 13.A for a description of these) note that WMO (1999) recommends a = 60. 

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