Rotational anisotropy

As an illustration, we consider the case of SFIG from the (111) surface of a cubic material (3m. syimnetry). More general treatments of rotational anisotropy in centrosymmetric crystals may be found in the literature [62. 63 and M]- For the case at hand, we may detennine the anisotropy of the radiated SFl field from equation Bl.5.32 in conjunction with the fonn of -)from table Bl.5.1. We fmd, for example, for the p-in/p-out and s-... 

Figure Bl.5.7 displays results of a measurement of the rotational anisotropy for an oxidized Si(l 11) surface [65]. For the case shown in the top panel, the results confonn to the predictions of equation Bl.5.42 (with/...

Figure Bl.5.7 Rotational anisotropy of the SH intensity from oxidized Si(l 11) surfaees. The samples have either ideal orientation or small offset angles of 3° and 5° toward tire [Hi] direetion. Top panel illustrates the step stnieture. The points eorrespond to experimental data and tlie fiill lines to the predietion of a symmetry analysis. (From [65].)...

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

In principle, pulsed excitation measurements can provide direct observation of time-resolved polarization decays and permit the single-exponential or multiexponential nature of the decay curves to be measured. In practice, however, accurate quantification of a multiexponential curve often requires that the emission decay be measured down to low intensity values, where obtaining a satisfactory signal -to-noise ratio can be a time-consuming process. In addition, the accuracy of rotational rate measurements close to a nanosecond or less are severely limited by tbe pulse width of the flash lamps. As a result, pulsed-excitation polarization measurements are not commonly used for short rotational periods or for careful measurements of rotational anisotropy. 

Under some circumstances the rotationally anisotropy may be even further simplified for T-R energy transfer of polar molecules like HF (41). To explore this quantitatively we performed additional rigid-rotator calculations in which we retained only the spherically symmetric and dipole-dipole terms of the AD potential, which yields M = 3 (see Figures 1, 3, and 4). These calculations converge more rapidly with increasing N and usually yield even less rotationally inelastic scattering. For example Table 2 compares the converged inelastic transition probabilities... 

Deslouis C, Maurin G, Pebere N, Tribollet B (1988) Investigation of tellurium electrocrystal-Uzation by EHD impedance technique. J Appl Electrochem 18 745-750 Yagi I, Nakabayashi S, Uosaki K (1998) In situ optical second harmonic rotational anisotropy measurements of an Au(l 11) electrode during electrochemical deposition of tellurium. J Phys Chem B 102 2677-2683... 

SHG has been used to study electrode surface symmetry and order using an approach known as SH rotational anisotropy. A single-crystal electrode is rotated about its surface normal and the modulation of the SH intensity is measured as the angle (9) between the plane of incidence and a given crystal axis or direction. Figure 27.34 shows in situ SHG results for an Au(ll 1) electrode in 0.1 M NaC104 + 0.002 M NaBr, using a p-polarized beam. The results indicate the presence of two distinct onefold... 

Another very informative nonlinear experiment involves a typical pump-probe technique, but with varying laser polarization. These experiments, again for isolated chromophores, measure the rotational anisotropy TCF [122]... 

It is worth mentioning that parameter p is insensitive, to first order approximation, to modulation of the residue-specific 15N chemical shift anisotropy tensor and/or dipolar interaction, as the (d2 + c2) term in the R) / R ratio is canceled out. The noncollinearity of the CSA and dipolar tensors will require corrections to Eqs. (10) and (12) for high degrees of rotational anisotropy (D /D > 1.5), as described in detail in Ref. [22]. 

Fig. 12.3 Demonstration of the accuracy of Eq. (10) for a wide range of rotational anisotropies,...

In the absence of accurate structural information, the analysis based on anisotropic diffusion as discussed above cannot be applied. The use of the isotropic overall model is still possible (see below) because it does not require any structural knowledge. However, the isotropic model has to be validated, i.e. the degree of the overall rotational anisotropy has to be determined prior to such an analysis. 

An estimate of the degree of rotational anisotropy can be obtained from the spread of the experimental values of p, assuming that the minimal and maximal observed values of P (Pmin and pmax) correspond to NH vectors oriented parallel (0 = 0) and perpendicular (8 = 90°) to the rotational diffusion axis. We obtain ... 

The isotropic model is justified when the estimated degree of the overall rotational anisotropy is small. A D /D l ratio of less than 1.1-1.2 could probably be considered as a reasonable value for the isotropic model, although an anisotropy as small as 1.17 can be reliably determined from 15N relaxation measurements, as demonstrated in Ref. [15]. 

Additional limitations in the accuracy of the derived dynamic parameters could be related to the limitations in the analytical approaches. For example, neglect of the overall rotational anisotropy could lead to considerable errors in the model-free parameters, as illustrated earlier [46]. As also shown in Ref. [6], the model-free parameters could be in error if the site-specific variations in 15N CSA are not properly taken into account, particularly at higher fields (>600 MHz 111 frequency). 

It should be mentioned that rotational anisotropy of the molecule will result in an increase in the R2 values for NH vectors having particular orientation with respect to the diffusion tensor frame [46]. This increase could be misinterpreted as conformational exchange contributions, and, vice versa, small values of Rex, usually of the order or 1 s 1 or less, could be mistaken for the manifestation of the rotational anisotropy. Therefore, identification of residues subjected to conformational exchange is critical for accurate analysis of relaxation data. Additional approaches are necessary to distinguish between the two effects. As suggested earlier [27] (see also Ref. [26]), a comparison between R2 and the cross-correlation rate r]xy could serve this purpose, as tjxy contains practically the same combination of spec-... 

It has been found [446] that in situ optical second-harmonic rotational anisotropy was significantly changed along with the first UPD of Te, and that bulk Te deposition attenuated the anisotropic character of the overall surface symmetry. 

Fig. 3.2. SH rotational anisotropy from a Si(lll) surface in air. Excitation was with p-polarized 532 nm light from a Q-switched Nd YAG laser incident at 45° from the surface normal. The rotation angle lies between the x axis in the plane of incidence and the [100] projection axis on the surface. (a) S-polarized SH data (solid line) and theoretical fit (dashed line) to Eq. (3-10) (with A = 0). (b) P-polarized SH data and theoretical fit to Eq. (3-10) (with B = -A). From Ref. 67 and also shown in Ref. 68 with a different definition of the angle of rotation.

In similar work, Sipe, Moss and Van Driel [84] determined a functional form of the rotational anisotropy for cubic centrosymmetric media. Their derived expressions for the total reflected p- and s-polarized SH fields from perfectly terminated (111) and (100) crystals under p- and s-polarized excitation take the form... 

As with all surface analytical methods, surface preparation is critical to obtaining reproducible SHG from metallic surfaces and single crystals in particular. For surfaces prepared in UHV and then transferred to an electrochemical cell, sputtering and heating or annealing followed by Auger analysis of impurities should proceed inert transfer. Low energy electron diffraction (LEED) can also be used to check surface order. Metal electrode surfaces, particularly for the rotational anisotropy ex-... 

Fig. 5.3. SH rotational anisotropy from clean Ag(lll) in UHV at 3xl(T10 torr under p-polarized excitation at 1064 nm. The open circles represent the p-polarized (a) and s-polarized (b) SH data. Theoretical fits using Eqs. (3-11) and (3-13) are indicated with the solid line. From Ref. 124.

How this additional field will alter the magnitude of the various tensor elements and the form of the rotational anisotropy has been examined by Koos et al. [122]. X0) has the properties of a fourth-rank tensor such that the third order polarization... 

All of the studies discussed above for silver have been done with an incident beam of 1064 nm. These studies have proven that the anisotropy in the nonlinear polarizability from the silver surface is not purely free-electron-like at these wavelengths, that the anisotropy can be correlated with surface symmetry, and that the SH response measured in situ is nearly identical to that measured in UHV. The issue of the sensitivity of the rotational anisotropy to surface electronic properties has been the topic of very recent work which has been conducted by variation of the incident wavelengths to where optical resonances in the bulk or surface electronic structure can be accessed. 

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