Angular orientation

First of all, one needs to choose the local coordinate frame of a molecule and position it in space. Figure 2a shows the global coordinate frame xyz and the local frame x y z bound with the molecule. The origin of the local frame coincides with the first atom. Its three Cartesian coordinates are included in the whole set and are varied directly by integrators and minimizers, like any other independent variable. The angular orientation of the local frame is determined by a quaternion. The principles of application of quaternions in mechanics are beyond this book they are explained in detail in well-known standard texts... 

For cross-ply laminates, a knee in the load-deformation cun/e occurs after the mechanical and thermal interactions between layers uncouple because of failure (which might be only degradation, not necessarily fracture) of a lamina. The mechanical interactions are caused by Poisson effects and/or shear-extension coupling. The thermal interactions are caused by different coefficients of thermal expansion in different layers because of different angular orientations of the layers (even though the orthotropic materials in each lamina are the same). The interactions are disrupted if the layers in a laminate separate. 

FIGU RE 22.21 The heme structure with a molecule of oxygen attached. Note the angular orientation of the oxygen molecule and that the Fe... 

Figure 3.21 Low-angle grain boundary (a) two misaligned parts of the crystal represented as a series of steps and (b) a tilt boundary consisting of an array of edge dislocations. The angular orientation difference between the two parts is 0, and the Burgers vector of the dislocations is b.

Quintiere, J.G., The effects of angular orientation on flame spread over thin materials, Fire Safety J., 2001, 36(3), 291-312. 

Richardson, the extent of dipolar repulsion (and ease of displacement) was dependent upon (a) the proximity, (b) the angular orientation, and (c) the numbers of permanent dipoles, with the most significant dipolar repulsions occurring when vicinal groups and the developing transitory dipoles in the S/y2 transition state are parallel and aligned (Scheme 42). 

The highest stability of the sensor-analyte complex is achieved when the substrate fits perfectly in the hole within the receptor. The analyte does not have to fit the receptor cavity perfectly efficient binding can be achieved by careful design of the receptor. In the case of metal ion sensors the receptor must contain a proper type and number of donor atoms angular orientation and directionality of lone electron pairs are also of crucial importance [5]. 

The unidimcnsional disorder of graphene stacking has a two-dimensional counterpart in the relative angular orientation of the hexagons within adjacent graphene layers. Figure 7 shows schematically the two... 

Mendes SB, Bradshaw JT et al (2004) Technique for determining the angular orientation of molecules bound to the surface of an arbitrary planar optical waveguide. Appl Opt 43(l) 70-78... 

The results show that values of jiQ vary over a wide range. This is one of the reasons for the very considerable differences in mobilities of these materials. The prefactor mobility is proportional to the intermolecular transfer integral J as fiQ oc j2t For charge transfer between molecules, J depends on the molecular angular orientations, unless the initial and final states are spherically symmetric. Slowik and Chen (1983) have shown that for carbazole molecules, J may vary by orders of magnitude as the molecular planes are rotated. It is likely that differences in the prefactor mobility are largely due to differences in orientation of the donor molecules. Differences in intersite distances may also contribute to differences in prefactor mobilities. 

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