Estimate of the Enhancement Factor

There is no clear definition of what magnitude of enhancement entitles a system to be classified as a SERS-active system. In this review we will arbitrarily set the demarcation line for SERS at a 100-fold enhancement level. Any enhancement higher than that will be considered as SERS, while lower enhancements will be ignored. The reason for this limit is that it is within simple surface coverage effects (roughness factor) and trivial enhancements resulting from reflectivity of metal surfaces and possible orientation effects.  

The estimate of the degree of enhancement in every one of our experiments is of prime importance for understanding SERS. First, the enhancement factors vary from system to system and that may reflect different contributions of the various possible mechanisms. Second, the sensitivity of the Raman systems has improved thus, detection of a signal does not necessarily mean that an enhancement of four to six orders of magnitude occurs. Nowadays one can detect signals which are enhanced by a factor of only 100 to 1000 or less. The Raman scattering of dyes adsorbed on surfaces can be detected even without any enhancement at all. 

There are four main problems which arise when enhancement factors are evaluated. The first problem is that we generally do not know the amount of material on the surface, especially in electrochemical, colloid, and thin-film studies conducted in the ambient or in solution. There are only a few studies which have used radiochemical techniques for electrodes or colloids. A few studies attempted to measure surface coverages from the 

A fourth, trivial, problem in the determination of enhancements, results from changes in relative band intensities of the adsorbed molecules. Generally, one compares the strongest bands. However, due to the (sometimes large) changes in relative intensities, the real meaning of such an estimate is not altogether clear. This consideration may add to the uncertainty another factor 

A potential difficulty is how to distinguish the signals from the surface and from the bulk in contact with it. It turns out that it is not a problem at all in most cases. The following criteria can be used, in part, or sometimes in full, to distinguish a surface spectrum from a bulk signal  

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For first-order NMR spectra of product c, this is the quantity needed for estimates of the enhancement factors (8). Otherwise follovtrs from (14) and... 

In the case for a bivalent interaction, Lees proposed an extension of this model by assuming that the bivalent association constant can be expressed as three related association constants K, K2, and K-iP Each equilibrium constant is derived on the basis of certain approximations such as the number of possible permutations assumed in receptor-ligand site association, monovalent binding (each monomer of the bivalent ligand is capable of binding to one receptor), and effective concentration of bound divalent ligand. An overall divalent association constant, which provides an estimate of the enhancement factor of divalent association, is obtained as a product of the three equilibrium constants as shown in (5). The refinement in p that is afforded from Lees treatment is shown in (6). 

The estimate of the enhancement factor due to the first term in Eq. (5.45) is often performed by invoking the optical reciprocity theorem (ORT) [75]. It states that the interaction of a dipole fi placed in position 0 with an EM field 62 created by a dipole fi2 in position M... 

Practicable isotopic enrichment has the following prerequisites adequately short time for the enrichment process, acceptable asymptotic enrichment factor, and adequate accuracy for the estimation of the enrichment factor. (When total activity, rather than specific activity, is limiting, one must also pay attention to losses during enrichment.) For the argon and carbon enrichments referred to above, enrichment factors of about 100 and 500 were obtained within a week and a few hours, respectively and enrichment factors were deduced from direct observations of adjacent, stable isotopes. The 14C enrichment process provided extra dividends for AMS measurement the sample was implanted in an ideal form for the accelerator ion source, and it was spatially localized (depth) which gave added signal-to-noise enhancement. 

The chemical method used to estimate the interfacial area is based on the theory of the enhancement factor for gas absorption accompanied with a chemical reaction. It is clear from Equations 6.22-6.24 that, in the range where y > 5, the gas absorption rate per unit area of gas-liquid interface becomes independent of the liquid phase mass transfer coefficient /cp, and is given by Equation 6.24. Such criteria can be met in the case of absorption with... 

In the Raman experiments, an excitation wavelength of 785 nm (intensity 1.8 105 W/cm2) was used. The sample, i.e. a drop of Au nanoparticle suspension with soluble pollen content was placed under a (60x) water immersion objective. Raman spectra were recorded with 1 s acquisition time. The control preparations (pollen supernatant with water) did not yield any spectral features. A spectrum of rye pollen supernatant with Au nanoparticles is shown in Fig. 4.9, together with a normal Raman spectrum of a rye pollen grain. The difference in spectral information that can be obtained by both approaches is evident from a comparison of these two spectra. Although an estimate of an enhancement factor is not possible from this experiment, it is clear that... 

In this respect, the effect of Fe cations on bofh the oxidation rate and complete mineralization rate of phenol and alike aromatic compounds was considered. Optimum conditions were reviewed to use Fe cations as reaction enhancers (henceforth PC reactions involving optimum Fe concentrations are called Fe-assisted PC reactions). This also involved the assessment of effect and mechanism of Fe ions on fhe PC reaction of phenol and other selected aromatic species. A systematic comparison between the kinetic reaction schemes for both unpromoted PC and Fe-assisted PC reactions for the selected model pollutants was also a primary emphasis. Last, the estimation of the enhancement through efficiency factor calculations was described. 

In the literature there is often some confusion over the precise definition of the enhancement factor as measured experimentally and indeed there are several complications, and frequently assumptions, inherent in the estimation of enhancement factors. This is discussed in depth in a very useful article by Le Ru et al. [37]. 

The appearance of these peaks is a purely dynamical effect not captured by QTST, and a simple estimate for the enhancement factor gives (for the simulation parameters considered here) 3r =4 from the... 

Bringing this discussion to an end, we can summarize our conclusions by stating that again the most clearcut conditions can be obtained for NMR in a magnetized sphere, because then there are no more wall signals and the variation of the enhancement factor with the external field strength for the domain nuclei can be estimated using... 

It is important to note that even if the experimental dEldc dependence is used in Eqs (11), (21)-(24), the estimated diffusion coefficient will still be the chemical diffusion coefficient. However, Levi and Aurbach [1999] have shown that analysis of experimental dEldX (where X is degree of occupation of intercalation sites) allows one to obtain a concentration-independent diffusion coefficient through calculation of the enhancement factor explicitly, as shown below... 

As it turns out eiqierimentally (Figure 13.14) and can be explained theoretically, one can estimate or predict the order of magnitude of the absolute value of the enhancement factor A for any given reaction, catalyst, and catalyst/solid electrolyte interface from ... 

This same sensitivity can, however, be misleading. Even minor radical routes to a particular reaction product could give rise to intense polarized n.m.r. signals which could obscure the normal monotonic increase of the signal due to product formed by a non-radical route. This problem can be overcome in some cases by estimation of the spectral enhancement factor. Again, it is not possible to justify a firm, threshold value, but as a useful rule of thumb when enhancements fall below about 100 then the possibility of an important alternative non-radical route to the same product should be carefully investigated. 

Target attractiveness An estimate of the value of a target to an adversary based on the factors shown below. Experience has shown that, particularly for terrorist attacks, certain targets better accomplish the objectives of the adversaries than do others. Since the SVA is a risk-based analytical approach, consideration must be given to these factors in defining the threat and in determining the need for any enhanced countermeasures. 

Estimates of the relative concentations of selected elements in fine particles collected upstream from the FGD system are listed in Table II. The values listed are some of the highest concentrations yet reported in the literature for fine coal- derived aerosols, especially those of V, Cr, and 2n, which lie in the tenth-percent range. Additional enhancements in the concentration of these elements resulting from FGD were about a factor of 2 for V, U, W, and As, a factor of 4 for Cr and Mn, and a factor of 15 for Se. If, as predicted by vapor-deposition models, the mass of there constituents resides in 0.02-ym-thick surface layers (10), then the surface concentration would be yet another 5 times greater, yielding concentrations of V, Zn, Cr, and Se in the range of 1 to 5%. 

Therefore, the estimation of rate constants for the PAH (including for anthracene) is now uncertain. For substituted PAH, we can estimate approximately the enhancement of the rate constant over that for the parent PAH by using the correlation between the rate constant and Xa+ discussed above for the monocyclic aromatic compounds (Atkinson, 1987), with the enhancement factor being e134 o+. This approach also may work for heteroatom-containing aromatic compounds, such as pyridines and triazines. 

The shortage of reliable estimates of the contribution of anthropogenic factors to formation of today s climate highlights just how difficult it is to understand the dynamical laws of the climate system, let alone evaluation of possible climate changes in future. At the same time, nobody rejects anthropogenically induced enhancement... 

Duyne and co-workers estimated enhancement factors on the order of 105 to 106 for pyridine on rough silver electrodes. The value was obtained from a comparison between surface-enhanced and normal bulk Raman signals from pyridine by taking into account the different number of molecules on the electrode and in solution. The size of the enhancement was found to correlate with the electrode roughness, indicating that enhancement occurs via a strong electromagnetic field. On the other hand, the dependence of the... 

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