Other orientations

Other orientational correlation coefficients can be calculated in the same way as tf correlation coefficients that we have discussed already. Thus, the reorientational coiTelatio coefficient of a single rigid molecule indicates the degree to which the orientation of molecule at a time t is related to its orientation at time 0. The angular velocity autocorrelatio function is the rotational equivalent of the velocity correlation function ... 

Traditionally, the electron and proton transport pathways of photosynthetic membranes (33) have been represented as a "Z" rotated 90° to the left with noncycHc electron flow from left to right and PSII on the left-most and PSI on the right-most vertical in that orientation (25,34). Other orientations and more complex graphical representations have been used to depict electron transport (29) or the sequence and redox midpoint potentials of the electron carriers. As elucidation of photosynthetic membrane architecture and electron pathways has progressed, PSI has come to be placed on the left as the "Z" convention is being abandoned. Figure 1 describes the orientation in the thylakoid membrane of the components of PSI and PSII with noncycHc electron flow from right to left. 

In acyclic structures, such effects are averaged by rotation, but in cyclic structures differences in C—H bond strengths based on the different alignments can be recognized. The C—H bonds that are in an anti orientation to the lone pair are weaker than the C—H bonds in other orientations. 

Dichroism is a property of an optical material that causes light of some wave lengths to be absorbed when the incident light has its electric field vector in a particular orientation and not absorbed when the electric field vector has other orientations. 

FIGURE 13.28 Whether a reaction takes place when two species collide in the gas phase depends on their relative orientations. In the reaction between a Cl atom and an HI molecule, for example, only those collisions in which the Cl atom approaches the HI molecule from a direction that lies inside the cone indicated here lead to reaction, even though the energy of collisions in other orientations may exceed the activation energy. 

It is sometimes desirable to draw Haworth formulae with the ring in other orientations (see Chart II), when there are bulky substituents to be represented, or when linkages in oligo- or poly-saccharides are to be shown. If the ring is inverted [as in (g)-(l)], the numbering runs counterclockwise. 

Ferroelasticity is the mechanical analogon to ferroelectricity. A crystal is ferroelastic if it exhibits two (or more) differently oriented states in the absence of mechanical strain, and if one of these states can be shifted to the other one by mechanical strain. CaCl2 offers an example (Fig. 4.1, p. 33). During the phase transition from the rutile type to the CaCl2 type, the octahedra can be rotated in one or the other direction. If either rotation takes place in different regions of the crystal, the crystal will consist of domains having the one or the other orientation. By exerting pressure all domains can be forced to adopt only one orientation. 

Flexagonal Mn203 plates with other orientations were also found, for example those perpendicular to the [320] direction (Fig. 2a). 

The first-order interaction of the two bonding levels should be the controlling interaction. The calculated PMO energies for concerted reactions are 0.61/ for the observed orientation and 0.53y for the other orientation. Calculated energies for biradical reactions are much smaller. 

Are crystalline regions in one orientation commonly associated with regions of some other orientation (e.g. because of the occurrence of twinning or because of a crystal-substrate relationship) ... 

The rate of removal of surface silicon atoms by the electrochemical reactions is orientation dependant, lowest on (111) and higher on other orientations. 

In contrast to porosity, the pore density and the specific surface area are quantities directly related to the actual size of pores and pore walls. The pore density NP is defined as the number of pores per unit area and it usually refers to a plane normal to the pore axis. For (100) oriented substrates this plane is parallel to the electrode surface, but for other orientations or strongly branched pores, there is no preferred plane orientation and NP refers to an average of the pore density of different planes. For arrays of straight pores the pore density can be directly calculated from the array geometry. For cylindrical pores of diameter d orthogonal to the electrode surface, for example, the average pore density NP is given by ... 

No data are available for other orientations, but equations similar to those for bubble formation, taking the appropriate component of the force due to kinetic energy, will be applicable. 

If m = 0, the nanotubes are called zigzag nanotubes, if n = m, the nanotubes are defined as armchair nanotubes, and all other orientations are called chiral . The deviation of Cn from a is expressed by the inclination angle 0 and ranges from 0° ( armchair ) to 30° ( zigzag ) [17]. 

The situation with Mn + center distribution between Ca(I) and Ca(II) positions in the apatite lattice is the opposite to this for REE + in artificially activated apatite the Mn(I) center clearly dominates the fluorescence spectra (Ryan et al. 1970), while in the natural one only Mn(ll) centers have been detected (Tarashchan 1978). In order to clarify the distribution in different Ca positions, luminescence spectra have been measured with different polarizations from one section or from prismatic and basal sections with the same analytical conditions. As was foimd earher (Barbarand and Pagel 2001) the shapes of the spectra are usually the same for both crystallographic orientations, while the major difference in the spectra is their intensity, with the mean intensity for the basal section lower than for the prismatic face. Nevertheless, in certain cases polarization changes lead to different spectra (Fig. 5.46). In this case spectra are composed mainly of the Nd and Mn with relatively weak Eu lines. The polarization change results in an inversion of the relative intensities of the liuninescence bands Mn +(I) emission dominates in one orientation and REE emission is practically not seen, but Mn " (II) in other orientations is much weaker compared to Mn +(I), while the... 

For a nematic LC, the preferred orientation is one in which the director is parallel everywhere. Other orientations have a free-energy distribution that depends on the elastic constants, K /. The orientational elastic constants K, K22 and K33 determine respectively splay, twist and bend deformations. Values of elastic constants in LCs are around 10 N so that free-energy difference between different orientations is of the order of 5 x 10 J m the same order of magnitude as surface energy. A thin layer of LC sandwiched between two aligned surfaces therefore adopts an orientation determined by the surfaces. This fact forms the basis of most electrooptical effects in LCs. Display devices based on LCs are discussed in Chapter 7. 

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