In-plane diffraction

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

Bohanon et al. [86] studied heneicosanoic acid (which contains 21 carbon atoms) and Lin et al. [87] studied this material with particular reference to the effect of pH and the presence of divalent cations in the subphase. The former authors made use of in-plane diffraction (method 2 above) and obtained first order and second order diffraction peaks. They were able to show that, at high pressures ( r=35 mN m-1), at low pH (pH = 2) and at temperatures in the region of 0-5 °C, the material packs into a distorted hexagonal structure with the tilt towards the nearest neighbours. However, in the region 5-10°C the tilt is towards the next nearest neighbours. In the latter study [87] in-plane diffraction was studied as a function of pH and the presence of Ca2+ or Cu2+ in... 

Fig. 13a In-plane diffraction intensity for a cardiolipin monolayer on water without and with PDADMAC in the subphase...

Fig. 13b In-plane diffraction intensity versus wave vector transfer Qxy for DNA binding to a DODAB monolayer at high surface pressure...

Figure 16. In-plane diffraction measurements for 1-heneicosanoI as a function of pressure at 21.3°C and 14.6°C. From Barton et al. ...

Mohwald, Als-Nielsen, and their co-workers have performed x-ray studies on DMPA and on OPPC. Their results have been summarized by Mohwald and by Helm et al. In-plane diffraction has been investigated for DMPA, for which 7tc = 10mNm A = 80 A molecule and 71 = 40mNm , A %40 A /molecule. Measurements were carried out at room temperature at pressures from about 12 to 60mNm (Fig. 17). No peak could be detected at the lowest pressure a peak barely above the noise was observed at about 16mNm , which corresponds to a molecular area of about 52 A. ... 

Fig. 14 (a) In-plane diffraction pattern from close-packed hexagonal Tl... 

Adiic and Wang [191] studied the UPD of n on Au(lll) in the presence of Br , which has three potential-dependent, commensurate Tl-Br phases that affect O2 reduction in different ways. The catalytically active (3 x. 3)-2TlBr phase on Au(lll) was monitored by SXS during the course of oxygen reduction by measuring the structure factors for its two low-order in-plane diffractions as a function of potential. The IR voltage drop in the thin-layer cell did not allow drawing definitive conclusions... 

Fig. 5 The in-plane diffraction pattern for the Au(001) surface, (a) The unreconstructed phase (b) the distorted hexagonal phase (c) the rotated, distorted hexagonal phase. In each case, the filled symbols represent the scattering from...

Fig. 18 X-ray diffraction data for Cu/Au(lll) in sulfuric acid solution at the first stage of Cu deposition (a) In-plane diffraction pattern ...

Fig. 1 (a) Definition of parameters (angles, mode numbers, layers, and indices) for a porous silicon (in-plane) diffraction grating and (b) comparison with Bragg gratings... 

In and out-plane X-ray diffraction pattern were recorded on a X-ray diffractometer equipped with a 4-axes goniometer (Rigaku ATX-G). CuKa radiation from copper rotating anode was used for the experiment. Incident angles (oo) for in plane geometry were between 0.14 and 0.36°, those for out of plane were between 0° and 5°. In-plane diffraction pattern is recorded as a result of the periodic structure of the direction perpendicular to the sample surface, out-plane diffraction pattern by structure of the direction parallel to the sample surface. 

Fig. 2.7 Typical diffraction spectra for H2/Pd(lll). Blackline-, apaatam results and red/ine experimental measurements solid line in-plane-diffraction and dashed line out-of-plane diffraction...

An analysis of the complementary channel, molecular scattering, in terms of diffraction probabilities (see Fig. 2.14) reveals that the most populated first order diffraction peaks are not in-plane, but out-of-plane, (01) and (Ol) (see Fig. 2.6), which explains the very low diffraction probability found experimentally [12]. These experiments considered only for in-plane diffraction. 

Fig. 2. Schematic illustration of the in-plane diffraction patterns for (a) an isotopic and (b) an orientationally ordered hexatic smectic liquid crystal.

IN-PLANE DIFFRACTION AND BRAGG ROD DATA FROM ARACHIDIC ACID FILM... 

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