Z-axis alignment

Consider the case of two neutral, linear, dipolar molecules, such as HCN and KCl, in a coordinate system with its origin at the CM of molecule A and the z-axis aligned with the intemiolecular vector r pointing from the CM of A to the CM of B. The relative orientation of the two molecules is uniquely specified by their spherical polar angles 0, 03 and the difierence <]) = - <])3 between their azimuthal angles. The leading temi in the... 

Figure 7-10 Methods of placing the green sheets (a) placed rotated at 90° and, (b) z axis alignment checL...

VF is the protein fixed frame having the z axis aligned with the director of the orienting potential. 

Figure 1. Global co-ordinates of a point, P on the male tooth surface. The axes are chosen so that the tooth surface is normal to the y axis and the origin is in the centre of the coupling with the z axis aligned with the shaft.

The focused aerosol particles are 1 to 5 pm in size and permit microfine conductor structures down to widths of 10 pm and 20 pm spacing. Ink, substrate, and print parameters all have to be closely matched in order to achieve structures as fine as this. On account of the parallel alignment and high exit speed of the aerosol, the contour sharpness of the conductor track geometry remains virtually constant even when the nozzle-to-substrate gap is as wide as 3 mm. Consequently, small irregularities in the substrate surface are easy to print without modification of the print head s z-axis alignment. 

Let us consider the electric field due to a dipole /x aligned along the z axis. The magnitude of the electric field at a point P due to the dipole (see Figure 4.27) is ... 

For oriented systems, the determination of molecular conformation is a complex problem because Raman spectra contain signals inherently due to both molecular conformation and orientation. To extract only the information relative to the conformation, one has to calculate a spectrum that is independent of orientation, in a similar way to the A0 structural absorbance of IR spectroscopy (Section 4). Frisk et al. [57] have shown that for a uniaxial sample aligned along the Z-axis, a spectrum independent of orientation (so-called isotropic spectrum), fso, can be calculated from the following linear combination of four polarized spectra [57]... 

Note that there are other possible ways to impose a time-dependent Bx. The one described in eqn (5.8) corresponds to a circularly polarized field initially aligned along the x-axis and rotating about the z-axis in a counterclockwise direction. The vector product of eqn (5.7) then becomes ... 

Figure 4. First-derivative ESR spectra of a nitroxide spin probe with the x-axis (a), y-axis (b), and z-axis (c) aligned parallel to H. The rigid-limit "powder" spectrum (d) is also shown. The dashed line marks the free electron field position (g = 2.0027). Reproduced from Ref. (jl) with permission of D. Reidel Publishing Co.

Several general observations can be made from the spectra and the calculated ESR parameters. First, the Na+- smectites possess narrower resonance line widths than the Ca +-smectites, with the exception of the saponite. Since Ca +-smectites, unlike Na+ -smectites, do not disperse into individual platelets in aqueous suspension, the Na+-smectite films formed by drying suspensions onto a smooth flat surface have the silicate surfaces more perfectly oriented in the plane of the film. As a result, less angular variation of the z-axis of Cu + relative to the plane of the film would narrow the spectra. One can see evidence of hyperfine splitting in the gj component of the Na+-smectite spectra, but not in the Ca +-smectite spectra. Saponite, unlike the other smectites, has very similar spectral linewidths for the Na+ and Ca + form (Figure 16). Since this Na+-saponite sample does not disperse completely in water (Table II), the alignment of Na+-saponite platelets in the clay film may be no better than that of the Ca +-saponite. 

Orientation b. The molecule is aligned with the dipole vector along the x-axis, and the molecule in the xz-plane. The dipole vector is then rotated about the z-axis in the xy-plane. 

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