Orientation averaging

Figure Cl.5.15. Molecular orientational trajectories of five single molecules. Each step in tire trajectory is separated by 300 ms and is obtained from tire fit to tire dipole emission pattern such as is shown in figure Cl.5.14. The radial component is displayed as sin 0 and tire angular variable as (ji. The lighter dots around tire average orientation represent 1 standard deviation. Reprinted witli pennission from Bartko and Dickson 11481. Copyright 1999 American Chemical Society.

For a removal attempt a molecule is selected irrespective of its orientation. To enhance the efficiency of addition attempts in cases where the system possesses a high degree of orientational order, the orientation of the molecule to be added is selected in a biased way from a distribution function. For a system of linear molecules this distribution, say, g u n ), depends on the unit vector u parallel to the molecule s symmetry axis (the so-called microscopic director [70,71]) and on the macroscopic director h which is a measure of the average orientation in the entire sample [72]. The distribution g can be chosen in various ways, depending on the physical nature of the fluid (see below). However, g u n ) must be normalized to one [73,74]. In other words, an addition is attempted with a preferred orientation of the molecule determined by the macroscopic director n of the entire simulation cell. The position of the center of mass of the molecule is again chosen randomly. According to the principle of detailed balance the probability for a realization of an addition attempt is given by [73]... 

The transition shows up in many other characteristics the fraction of adsorbed monomers (Fig. 5(a)), and the average orientation of bonds. 

The main limitation of birefringence is that it only provides an averaged orientation value without any discrimination between amorphous and crystalline phases, or between the components in polymer blends, copolymers, and... 

The site I adducts are characterized by a near-parallel (within 25°) average orientation of the planar pyrene residue with the planes of the DNA bases, and a relatively strong interaction between the TT-electrons of the pyrene residues and the DNA bases. 

Since the transition moments of the antisymmetric and symmetric CH2 stretching vibrations and the methylene chain axis are mutually perpendicular, the average orientation angle y of the hydrocarbon chain axis around the surface normal is obtained to be 27° by the orthogonal relation... 

Figure 7. Average orientation of the xyz axis system of TEMPAMINE in the fixed (x y z1) axis system of clay.

Fiber orientation uniformity is also affected by small-scale or timewise variations in polymer viscosity, related to breakage of polymer chains during the extrusion process. The degradation occurs as a result of residual moisture that immediately reacts to break chains, and by thermal degradation that occurs more gradually over time. Different residence times and temperature histories within the laminar flow streamlines lead to different viscosities, and hence different average orientation levels in the different fibers. 

Here 6 is the instantaneous angle between a given C-D bond vector and the axis of rotational symmetry of the molecules, i.e., the bilayer normal. The brackets denote an average over the time scale of the experiment 10 s) so that Sen is the time-averaged orientation of the particular C—D bond with respect to the bilayer normal. 

Mesophase formed by a non-chiral compound or by the racemate of a chiral compound in which the spatial distribution of the molecular centers of mass is devoid of long-range positional order and the molecules are, on average, orientationally ordered about a common axis defined as the director and represented by the unit vector n. 

Note 2 The average orientation of the planes of the molecular discs is not necessarily normal to the column axes. 

The orientation and dynamics of dodecyl D-glucopyranoside in phospholipid bilayers were studied by NMR in oriented samples [153,154]. The fully Relabeled glycolipid was embedded in a magnetically orientable membrane system (DMPC-CHAPSO) and examined by NMR. The analysis of the set of data allowed to determine the average orientation of o-glucose with respect to the bUayer the ring is extended from the plane of the bilayer with vector C-2/C-6 approximately... 

Fig. 119. Schematic diagram showing the proposed average orientation in LB film form [457]...

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