Azimuthal rotations

Fig. 1 Solid-state NMR structure analysis relies on the 19F-labelled peptides being uniformly embedded in a macroscopically oriented membrane sample, (a) The angle (0) of the 19F-labelled group (e.g. a CF3-moiety) on the peptide backbone (shown here as a cylinder) relative to the static magnetic field is directly reflected in the NMR parameter measured (e.g. DD, see Fig. 2c). (b) The value of the experimental NMR parameter varies along the peptide sequence with a periodicity that is characteristic for distinct peptide conformations, (c) From such wave plot the alignment of the peptide with respect to the lipid bilayer normal (n) can then be evaluated in terms of its tilt angle (x) and azimuthal rotation (p). Whole-body wobbling can be described by an order parameter, S rtlo. (d) The combined data from several individual 19F-labelled peptide analogues thus yields a 3D structural model of the peptide and how it is oriented in the lipid bilayer...

The symmetry of the LB films was determined by polarized ultraviolet-visible (UV-Vis) absorption spectroscopy, optical rotation, and second-harmonic generation. All studies showed that the constructed LB films are anisotropic in the plane of the film and that the symmetry of the film is C2 with the twofold rotation axis perpendicular to the film plane. For example, when the SH intensity is plotted as a function of the azimuthal rotation angle (rotation around an axis perpendicular to the plane of the film), the twofold symmetry becomes evident (Figure 9.23). Isotropic films generate an SH signal independent of the azimuthal rotation angle. On the other hand, the LB... 

Figure 9.23 s-Polarized second-harmonic signal detected in transmitted direction as function of the azimuthal rotation angle. Twofold pattern clearly indicates C2 symmetry of sample. 

The adjustable parameters were a, y, and rQ. The best-fit friction factors y for the 43-bp fragment are the same on all four time spans, as shown in Figure 4.9. The best-fit y values are similarly independent of time span for the 69-bp fragment.(109) The hydrodynamic radius a for azimuthal rotation was calculated from the measured friction factor for uniform azimuthal rotation of the entire filament, f = (N+ 1 )y, using the formula of Tirado and Garcia de la Torre,(129)/ii = 3Mlrjna2L(l +<5,), where t is the solvent viscosity, and dM is an end-plate correction, which they tabulate. The same value... 

The friction factor per base pair for azimuthal rotation of a long DNA, for which end-plate corrections are negligible, is calculated from a to be... 

TUt angle of the peptide symmetry axis with respect to the membrane normal Azimuthal rotation angle of the peptide Molecular order parameter of the peptide... 

The peptide alignment is calculated by a / -analysis of the F-NMR chemical shifts as a function of r and p (using Smoi = 1 as there is no wobble), as previously explained [18,19,22,23]. Figure 5A,B shows the allowed regions in the r-p maps for GS-3/3 and GS-l/T, respectively. The overlap of the allowed regions suggests a peptide tilt angle r between 70° and 90°, but the value of the azimuthal rotation p is not well defined. 

Fig. 5 Contour plots showing the alignment of gramicidin S in DMPC membranes at high peptidedipid ratios (>1 40), evaluated in terms of the peptide tilt angle x and its azimuthal rotation p. Feasible solutions from F-NMR of GS-3/3 (A) and GS-1/1 (B) are shown, together with additional N-NMR constraints from GS-3/3 (C) and GS-1/1 (D). A unique overlap is obtained at t 80° and p -45°, as indicated by the shaded dots...

The dimensions of the xylan unit cell are slightly different a = b = 1.340 nm, (fibre axis) = 0.598 nm.) Atkins and Parker T6) were able to interpret such a diffraction pattern in terms of a triple-stranded structure. Three chains, of the same polarity, intertwine about a common axis to form a triple-strand molecular rope. The individual polysaccharide chains trace out a helix with six saccharide units per turn and are related to their neighbours by azimuthal rotations of 2ir/3 and 4ir/3 respectively, with zero relative translation. A similar model for curdlan is illustrated in Figure 6. Examinations of this model shows that each chain repeats at a distance 3 x 0.582 = 1.746 nm. Thus if for any reason the precise symmetrical arrangement between chains (or with their associated water of crystallization) is disrupted, we would expect reflections to occur on layer lines which are orders of 1.746 nm. Indeed such additional reflections have been observed via patterns obtained from specimens at different relative humidity (4) offering confirmation for the triple-stranded model. 

Therefore, according to Eq. (12.57), the molecule feels a LIP AW that de] the orientation of the molecular Z axis relative to the field polarization r azimuthal rotation angle of the molecular frame about the Z axis. 

When all the rotations are possible in the solid state the symmetry increases to hexagonal. This form corresponds to the close packing of spheres or cylinders and the molecule is in a rotational crystalline state, characterized by rigorous order in the arrangement of the center (axes) of the molecules and by disordered azimuthal rotations [118]. If the chain molecules are azimuthally chaotic (they rotate freely around their axes), their average cross sections are circular and, for this reason, they choose hexagonal packing. The ease of rotation of molecules in the crystal depends merely on the molecular shape, as in molecules of an almost spherical shape like methane and ethane derivatives with small substituents, or molecules of a shape close to that of a cylinder (e.g., paraffin-like molecules). 

W21 beamline and diffractometer [33]. A large number, 366 of which 267 were non-equivalent, of in-plane reflections arising from the reconstruction were measured. All peaks were exactly centred at the expected positions to within 0.001° of azimuthal rotation, which showed that the surface reconstruction is perfectly commensurate with the underlying bulk lattice. Their width and Lorentzian shape indicated an exponential decay in correlations with the decay length of -500 A. Several reconstruction diffraction rods were also measured. The absence of symmetry of the rod intensity with respect to =0 showed that the reconstruction has the minimal hexagonal symmetry p3. 

Figure 11.12. Thickness dependence of the FWHMs for (11 l)XPF. Ax and A(p are the tilt and azimuthal rotation angles, respectively, and A0,ot is the FWHM of the deduced rotational misorientation angle [275],...

Fig. 1 Set of experimental NICISS flight time spectra at NiAl(100)-(lxl).

Fig. 2 NICISS pattern for He backscattering at NiAl(l 11). He scattering at a) Ni and b) A1 atoms. -scan the intensity of scattered He is plotted as function of the grazing angle of incidence v /j (0° - 120°) with a constant azimuth rotation (cp [112] for V / = 0°). The inset shows a side view and an on top view of the scattering geometry. Open circles Ni, hatched circles A1 atoms. Head-on scattering situation from first layer atoms (A) and second layer atoms (B) is indicated, (from ref [44]).

Figure 11 shows the C Is diffraction patterns observed in experiments on Ceo monolayers on Cu(lll), Al(lll), Cu(llO), and Al(OOl) surfaces. Figures 11a and b have sixfold symmetry, which shows that a six-carbon ring is facing the Cu(lll) and Al(lll) surfaces. The diffraction patterns between the two are quite similar except for a 30° azimuthal rotation. This shows that the Ceo molecules are rotated by 30°. None of the groups has fivefold symmetry, suggesting that the 5-ring is not... 

The order parameter s finks R to the mosaic distribution of the azimuthal rotation angle about the surface normal (). The former is measured using optical absorption spectroscopy whereas the latter is measured separately for each crystallite types using GIXRD. In this task it has been assumed that the rod-like molecules are always parallel to the (0yz) plane (i.e., perfectly planar alignment) and a two-dimensional order parameter can be given as... 

Almost all the smectic phases, in which the molecules are arranged in layers and are tilted with respect to the layers, have counterpart chiral phases. The most important one of this class is the chiral smectic C phase — Sc phase. In these chiral liquid crystal phases, the molecules are tilted at a constant angle with respect to the layer normal but the tilt azimuthal rotates uniformly along the chiral axis and forms a helical structure. 

In homeotropic cells, however, in-plane rotations of the director are reflected in a net azimuthal rotation of the optical axis (and the light polarization) across the cell which has allowed a detailed exploration of the characteristics of the NR-AR transition. Experiments have shown an excellent agreement with the predictions of generalized Ginzburg-Landau models [36],... 

We examined the effect of coupling between surface plasmon polariton (SPP) modes on the optical activity of metal nanostructures. By measuring the in-plane wave vector dependence on transmission and polarization azimuth rotation, we show that coupling of the SPP modes with orthogonal polarization localized at different interfaces is responsible for the optical activity in metal nanostructures. 

---