Tilting

Becker et al. (11) have performed extensive experiments on surface-breaking cracks, tilting both the cracks or the back-side. The cracks are like a half ellipse, but could presumably be reasonably approximated by a strip-like crack. Figure 3 shows a comparison between the experiments and UTDefect for a 2.54 mm crack with varying tilt. The thickness of the plate with the crack is 15.24 ram. The probe is a circular 45 SV probe with frequency 2.25 MHz and diameter 12.7 mm. The experiments are calibrated with a notch but this is presently not... 

Fig. 3 Maximum. signal response as a function of craek tilt for a surfaee-breaking erack of width...

In this case, we can conclude that the small sensor is lightly tilted with an angle of 0,25 degrees. We have concluded, during experimentations, that the measurement of the magnetic field is very sensitive to the angle of inclinaison of the sensor. In this way, we validate the computation of the incident field E (r). We can also expect some difficulties for the validation of the forward problem by experimental data. 

The refractograp of figure 4 shows highly oriented micro cracks of a polystyrene sample. The orientation of the cracks is perpendicular to the mechanical strain direction. The X-ray refracted intensitiy can be interpreted as crack density, i.e. the inner surfaces within a unit volume. Changing the tilt angle (of polystyrene and polystyrene blend samples) with respect to the primary beam leads to significantly different distributions of crack orientation (Fig. 5). 

The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

This region has been divided into two subphases, L and S. The L phase differs from the L2 phase in the direction of tilt. Molecules tilt toward their nearest neighbors in L2 and toward next nearest neighbors in L (a smectic F phase). The S phase comprises the higher-ir and lower-T part of L2. This phase is characterized by smectic H or a tilted herringbone structure and there are two molecules (of different orientation) in the unit cell. Another phase having a different tilt direction, L, can appear between the L2 and L 2 phases. A new phase has been identified in the L 2 domain. It is probably a smectic L structure of different azimuthal tilt than L2 [185]. 

LS. In the LS phase the molecules are oriented normal to the surface in a hexagonal unit cell. It is identified with the hexatic smectic BH phase. Chains can rotate and have axial symmetry due to their lack of tilt. Cai and Rice developed a density functional model for the tilting transition between the L2 and LS phases [202]. Calculations with this model show that amphiphile-surface interactions play an important role in determining the tilt their conclusions support the lack of tilt found in fluorinated amphiphiles [203]. 

Grazing incidence excitation of a fluorescent probe in a phospholipid monolayer can also be used to indicate order. The collective tilt of the molecules in a domain inferred from such measurements is indicative of long-range orientational order [222]. 

Figure Bl.5.11 Tilt angle 0 between the moleeular axis of sodium-dodeeylnaphtalene-sulphonate (SDNS) and the surfaee nonnal as a fiinetion of the surfaee pressure ti at the air/water interfaee. (From [77].)...

Figure Bl.22.3. RAIRS data in the C-H stretching region from two different self-assembled monolayers, namely, from a monolayer of dioctadecyldisulfide (ODS) on gold (bottom), and from a monolayer of octadecyltrichlorosilane (OTS) on silicon (top). Although the RAIRS surface selection rules for non-metallic substrates are more complex than those which apply to metals, they can still be used to detemiine adsorption geometries. The spectra shown here were, in fact, analysed to yield the tilt (a) and twist (p) angles of the molecular chains in each case with respect to the surface plane (the resulting values are also given in the figure) [40].

Figure Bl.22.8. Sum-frequency generation (SFG) spectra in the C N stretching region from the air/aqueous acetonitrile interfaces of two solutions with different concentrations. The solid curve is the IR transmission spectrum of neat bulk CH CN, provided here for reference. The polar acetonitrile molecules adopt a specific orientation in the air/water interface with a tilt angle that changes with changing concentration, from 40° from the surface nonnal in dilute solutions (molar fractions less than 0.07) to 70° at higher concentrations. This change is manifested here by the shift in the C N stretching frequency seen by SFG [ ]. SFG is one of the very few teclnhques capable of probing liquid/gas, liquid/liquid, and even liquid/solid interfaces.

Figure Bl.22.10. Carbon K-edge near-edge x-ray absorption (NEXAFS) speetra as a fiinotion of photon ineidenee angle from a submonolayer of vinyl moieties adsorbed on Ni(lOO) (prepared by dosing 0.2 1 of ethylene on that surfaee at 180 K). Several eleetronie transitions are identified in these speetra, to both the pi (284 and 286 eV) and the sigma (>292 eV) imoeeupied levels of the moleeule. The relative variations in the intensities of those peaks with ineidenee angle ean be easily eonverted into adsorption geometry data the vinyl plane was found in this ease to be at a tilt angle of about 65° from the surfaee [71], Similar geometrieal detenninations using NEXAFS have been earried out for a number of simple adsorbate systems over the past few deeades.

Figure Bl.24.1. Schematic diagram of the target chamber and detectors used in ion beam analysis. The backscattering detector is mounted close to the incident beam and the forward scattering detector is mounted so that, when the target is tilted, hydrogen recoils can be detected at angles of about 30° from the beam direction. The x-ray detector faces the sample and receives x-rays emitted from the sample.

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