Cross enhancement factors

Table XIV. Cross Enhancement Factors for Carbamate Pesticides...

The results of a study of carbofuran treatment intensity on the cross enhancement factors for carbaryl, cloethocarb and oxamyl are... 

C Linewidth (Hz), Nuclear Overhauser Enhancement Factor (p), and T- (s), for Linear PS and 1% Cross-Linked PS in Chloroform and Dimethylformamide. 

The terms pc and py correspond to 1/Tic and 1/Tih, respectively, and CTCH is the cross-relaxation rate. It should be stressed that the simplicity of the above equation is a consequence of the rareness of the I spins and of the dominant strength of the dipolar interaction between directly bonded nuclei. The situation for homonuclear proton spin systems is often more complicated, since the protons usually constitute a much larger spin system, and a separation into distinct two-spin systems may be not valid in this case. The broadband irradiation of the protons yields, in a steady state, Mhz = 0 and M z = Mj (1 rj). The factor 1 + 77 is called, as introduced above, the nuclear Overhauser enhancement factor. The NOE factor is related in a simple way to the equilibrium magnetizations of the I- and S-spins (which are proportional to the magnetogyric ratios 71 and 7s), the cross-relaxation rate and the relaxation rate of the I-spin ... 

In conclusion, for most of the molecules discussed here and for others reported in the hterature (and for which full spectral characterization is available), the cross section of multi-branched chromophores is either found to scale linearly with the munber of branches or exhibit a small enhancement when the molecular size is increased (or the evidence for the enhancement depends on the choice of normahzation factors). The enhancement factor can be larger if cross sections at the same wavelength are compared, instead of the 3max values, if there is a change in the band shape or position. These factors could be relevant for applications that have limitations on the operational excitation wavelength. 

The problem now reduces to finding how ra is related to the experimental parameters. The gas supply functions for different tip geometry have already been discussed in Section 2.1.2 and they are given by eqs (2.9), (2.11) and (2.12). zs is the total gas supply function Z multiplied by sa/A where sA is the cross-section of a surface atom in capturing an incoming gas atom, and A is the total area of the gas supply function. For a large field enhancement factor, = aF2/2kT, zs can be approximated by... 

Meijers JC, Middeldorp S, Tekelenburg W, van den Ende AE, Tans G, Prins MH, Rosing J, Buller HR, Bouma BN. Increased fibrinolytic activity during use of oral contraceptives is counteracted by an enhanced factor Xl-independent down regulation of fibrinolysis a randomized cross-over study of two low-dose oral contraceptives. Thromb Haemost 2000 84(1) 9-14. 

Since most biomolecules normally exhibit medium or low Raman cross sections, an enhancement of the signal intensity for the ability to characterize even low concentrations would be preferable. Besides the application of resonance Raman spectroscopy, surface-enhanced Raman spectroscopy (SERS) is a promising alternative. In doing so the vicinity of molecules to rough noble metal surfaces leads to Raman enhancement factors of 106-108 and even up to 1014 leading to a single molecule detection limit [9]. 

Figure 10.1. Comparison of normal (top) and surface-enhanced (bottom) Raman scattering. The top panel shows the conversion of incident laser light of intensity /(vl) into Stokes scattered light /NRS, which is proportional to the Raman cross section and the number of target molecules N in the probed volume. In the bottom panel

The size of the enhancement factor or the effective SERS cross section is a key question for the application of SERS as a tool for ultrasensitive detection. The effective cross section must be high enough to provide a detectable Raman signal from a few molecules. In the early SERS experiments, Van... 

M in concentration. This is in the range required for single-molecule detection. These sensitivity levels have been obtained on colloidal clusters at near-infrared excitation. Figure 10.3 is a schematic representation of a single-molecule experiment performed in a gold or silver colloidal solution. The analyte is provided as a solution at concentrations smaller than 10-11 M, Table 10.1 lists the anti-Stokes/Stokes intensity ratios for crystal violet (CY) at 1174 cm-1 using 830-nm near-infrared radiation well away from the resonance absorption of CY with a power of 106 W/cm2 [34]. CV is attached to various colloidal clusters as indicated in the table. Raman cross sections of 10-16 cm2/molecule or an enhancement factor of 1014 can be inferred from the data. 

FIG. I. Spin-lattice relaxation time of Li in 3-9 M LiClin HiOasafunctionofinverse absolute temperature. Circles experimental relaxation time. 7 ," crosses dipolar contribution, obtained from T,"" and the nuclear Overhauser enhancement factor t). The linear least-squaresfit for the latter yields an activation energy of 3-6kcalmol (16)... 

Since the HRS scattering cross section is so small, enhancement of the signal intensity is indispensable for a practical use of the HRS technique in the field of molecular science. As already mentioned, one of the methods for signal enhancement is to use plasmonic resonances of metal nanostructures [20, 21, 25]. This enhancement technique is called surface-enhanced hyper-Raman scattering (SEHRS) because it is similar to that of surface-enhanced Raman scattering (SERS). In SERS or SEHRS, both excitation absorption and scattered emission benefit from plasmonic field enhancement. Therefore, the plasmonic enhancement factor M is described as... 

Le Ru et al. demonstrated that a careful consideration of the minimum signal required for detection, the Raman cross section of the molecules involved, and the characteristics of the hot spot were required to determine the minimum enhancement factor necessary for single-molecule detection using SERS [95]. Through this process they concluded that a minimum enhancement factor of 2 x 10 was required for detection of single molecules with bare Raman cross sections of 10 cm sr This is 10 times smaller than the 10 " initially claimed to be essential for single-molecule SERS. The bare Raman cross section of many... 

As shown in Fig. 12, another regime of relaxation is reached at very low temperature (7 <8 K), where a behavior l/T, oc Tis recovered [51, 69, 70, 144]. The low temperature regime looks like a Korringa law with an enhancement factor of the order 10 with respect to the regime r>30 K. It has been first proposed that this change in behavior for the enhancement originates in the dimensionality cross-over of one-particle coherence and the restoration of a Fermi liquid component in two directions. It is still an open problem to decide whether the Fermi liquid properties recovered below 8 K are those of a 2-D or 3-D electron gas. Furthermore the intermediate temperature regime 8 K ... 

To examine the role of the LDOS modification near a metal nanobody and to look for a rationale for single molecule detection by means of SERS, Raman scattering cross-sections have been calculated for a hypothetical molecule with polarizability 10 placed in a close vicinity near a silver prolate spheroid with the length of 80 nm and diameter of 50 nm and near a silver spherical particle with the same volume. Polarization of incident light has been chosen so as the electric field vector is parallel to the axis connecting a molecule and the center of the silver particle. Maximal enhancement has been found to occur for molecule dipole moment oriented along electric field vector of Incident light. The position of maximal values of Raman cross-section is approximately by the position of maximal absolute value of nanoparticle s polarizability. For selected silver nanoparticles it corresponds to 83.5 nm and 347.8 nm for spheroid, and 354.9 nm for sphere. To account for local incident field enhancement factor the approach described by M. Stockman in [4] has been applied. To account for the local density of states enhancement factor, the approach used for calculation of a radiative decay rate of an excited atom near a metal body [9] was used. We... 

Figure 1. Raman scattering cross-section enhancement factor due to local incident field enhancement as a function of spectral shift.

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