Bond-orientations

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]). 

Figure C2.2.4. Types of smectic phase. Here tire layer stacking (left) and in-plane ordering (right) are shown for each phase. Bond orientational order is indicated for tire hexB, SmI and SmF phases, i.e. long-range order of lattice vectors. However, tliere is no long-range translational order in tliese phases.

The transition from smectic A to smectic B phase is characterized by tire development of a sixfold modulation of density witliin tire smectic layers ( hexatic ordering), which can be seen from x-ray diffraction experiments where a sixfold symmetry of diffuse scattering appears. This sixfold symmetry reflects tire bond orientational order. An appropriate order parameter to describe tlie SmA-SmB phase transition is tlien [18,19 and 20]... 

Birgeneau R J and Ulster J D 1978 Bond-orientational order model for smeotio B liquid orystals J. Physique Lett. 39 399-402... 

K. J. Strandburg, ed. Bond Orientational Order in Condensed Matter Systems. New York Springer, 1992. 

Transfer matrix calculations of the adsorbate chemical potential have been done for up to four sites (ontop, bridge, hollow, etc.) or four states per unit cell, and for 2-, 3-, and 4-body interactions up to fifth neighbor on primitive lattices. Here the various states can correspond to quite different physical systems. Thus a 3-state, 1-site system may be a two-component adsorbate, e.g., atoms and their diatomic molecules on the surface, for which the occupations on a site are no particles, an atom, or a molecule. On the other hand, the three states could correspond to a molecular species with two bond orientations, perpendicular and tilted, with respect to the surface. An -state system could also be an ( - 1) layer system with ontop stacking. The construction of the transfer matrices and associated numerical procedures are essentially the same for these systems, and such calculations are done routinely [33]. If there are two or more non-reacting (but interacting) species on the surface then the partial coverages depend on the chemical potentials specified for each species. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Since niobates and tantalates belong to the octahedral ferroelectric family, fluorine-oxygen substitution has a particular importance in managing ferroelectric properties. Thus, the variation in the Curie temperature of such compounds with the fluorine-oxygen substitution rate depends strongly on the crystalline network, the ferroelectric type and the mutual orientation of the spontaneous polarization vector, metal displacement direction and covalent bond orientation [47]. Hence, complex tantalum and niobium fluoride compounds seem to have potential also as new materials for modem electronic and optical applications. 

From single-crystal X-ray structural analysis the ground-state conformation of (.S )-2-(4-meth-ylphenylsulfinyl)-2-cyclopentenone was shown to have the sulfoxide bond orientated anti to the carbonyl bond, as expected for minimization of electrostatic interactions13. 

The distribution of the intermolecular vector is also of value in distinguishing between smectic A and smectic B phases with the latter having long range bond orientational order [23, 24]. At the local level we can define a bond orientational order parameter, PeCn) for molecule i at position q by [25]... 

Here the summation is over molecules k in the same smectic layer which are neighbours of i and 0 is the angle between the intermolecular vector (q—r ) projected onto the plane normal to the director and a reference axis. The weighting function w(rjk) is introduced to aid in the selection of the nearest neighbours used in the calculation of PsCq). For example w(rjk) might be unity for separations less than say 1.4 times the molecular width and zero for separations greater than 1.8 times the width with some interpolation between these two. The phase structure is then characterised via the bond orientational correlation function... 

Fig. 8. The distance dependence of the bond orientational correlation function gs (r ) found for the mesogen GB(4.4, 20.0, 1, 1) in the smectic A (.) and the smectic B (—) phases...

Strandberg KJ (1992) In Strandberg KJ (ed) Bond orientational order in condensed matter systems, chap 2. Springer, Berlin Heidelberg New York... 

Monosaccharides can differ in their formulas, their ring sizes, and the spatial orientations of their hydroxyl groups. To analyze the differences between two monosaccharides, begin with structural drawings of the molecules, oriented so the ether linkages are in comparable positions. Then examine the stmctures to locate differences in constituents and bond orientations. 

In order to systematise the literature, the following classification is used with respect to the metal dioxygen bonding orientations found in oxygen carriers. 

P2j Z = 2 D = 1.57 R = 0.048 for 931 intensities. The base exists in the thioxo form, with C-8=S and N-7 protonated. The 8-thio substituent causes the base to assume the syn (—102.6°) orientation. The o-ribosyl group is 2T3 (174.8 °, 44.1 °). The exocyclic, C-4 -C-5 bond orientation is trans (—173.2°). This does not favor intramolecular hydrogen-bonding of 0-5 to N-3 of the syn base. The C=S distance is 166.8 pm. The S atom is involved in a weak, acceptor hydrogen-bond to a water molecule, S H-O(w) = 361 pm. The bases are stacked head-to-tail, with overlap of the C=S bonds and the purine ring, in contrast to the known, related structure l-/ -D-ribofuranosyl-2-thioxo-3ff-benzimidazole,197 where similar head-to-tail stacking of the bases involves overlap of the base rings only. 

P212121 Z — 8 Dx= 1.57 R = 0.085 for 1,743 intensities. The two independent molecules have similar conformations. The glycosyl dispositions are anti (90.1°, 91.2°), and the D-ribosyl groups are 3T4 (24.0°, 34.1° 15.6°, 35.5°). The exocyclic, C-4 -C-5 bond orientations are gauche+ (63.1°, 53.8°). The orientation of the methyl groups in both molecules is such that it is directed away from the imidazole moiety of the base, that is, the 0-6-C-7 bond is trans to the C-5-C-6 bond this arrangement constitutes an obstacle to formation of Watson-Crick hydrogen-bonds to the complementary base cytosine. In molecule A, 0-6 and C-7 are displaced from the purine plane by 79 and 87 pm, and, in molecule B, by 49 and 16 pm. The bases are stacked. 

Raman microscopy provides a spatial resolution slightly better than IR, and no sample preparation is necessary in many cases. It has advantages with special types of substances (e.g., systems containing conjugated double bonds, oriented systems, amorphous and crystalline carbon, oxides). SNOM techniques (with spatial resolution below 1 pm) have been more popular with Raman than with IR, so far, but as yet are not routinely practiced. 

Fig. 36 Three-dimensional map of the local bond orientational order. The bond order is expressed by the density-scale given in the legend to the right... 

We also examined the fold statistics in this Ciooo system. The distribution of the inter-stem vectors connecting stems linked by the loops, and their radial distribution function again indicated that about 60-70% of the folds are short loops connecting the nearest or the second and third nearest stems, though the crystallization did not complete. The presence of local order in the under cooled melt in the present Ciooo system is also examined through the same local order P(r) parameter, the degree of bond orientation as a function of position r, but again we did not detect any appreciable order in the undercooled melt. 

We demonstrate that the spectral function of valence harmonic vibrations of a diatomic group that effects rotational reorientations is broadened by w. The vector of atom C displacements relative to the atom B (see Fig. A2.1) may be represented as x(t)e(t), where x(t) is the change in the length of the valence bond oriented at the time t along the unit vector e(/). Characteristic periods of valence vibrations are much shorter than periods of changes in unit vector orientations. As a consequence, the GF of the displacements defined by Eq. (4.2.1) can be expressed approximately as ... 

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