Handedness characteristics

Films of pure CNLCs have a unique transmission behavior as CP light with the same sense of circular polarization as the CNLC is filtered out by reflection, while CP light of the opposite handedness as the CNLC film is transmitted. This selective optical transmission characteristic is referred to as a one-dimensional photonic stop-band or a selective reflection band. The stop-band is centered at a certain wavelength Ac, which is dependent on the pitch length p and the average refractive index n of the CNLC ... 

As another example of the effects of shape and molecular handedness, look at the substance called carvone. Left-handed carvone occurs in mint plants and has the characteristic odor of spearmint, while right-handed carvone occurs in several herbs and has the odor of caraway seeds. Again, the two structures are the same except for their shapes, yet they have entirely different odors. 

Twisting a nematic structure around an axis perpendicular to the average orientation of the preferred molecular axes, one arrives at the molecular arrangement commonly called cholesteric (Kelker and Hatz, 1980). The twisted nematic phase is optically uniaxial, however with the axis perpendicular to the (rotating) director. Such a mesophase combines the basic properties of nematics with the implications of chirality The structure itself is chiral and as a consequence, a non-identical mirror image exists as it is shown schematically in Fig. 4.6-7. Besides the order parameters mentioned before, the essential characteristics of a cholesteric mesophase are the pitch, i.e., the period of the helical structure as measured along the twist axis, and its handedness, i.e., whether the phase is twisted clockwise or anticlockwise. 

Figure 5.12 Examples of the characteristic graphs of the crossing patterns of three orthogonal views of the chain molecule backbone of the A.-Cro Repressor protein. The chain is oriented from the N-terminal to the C-terminal and the vertices of the graphs are labeled according to the handedness of the crossing - for left handed crossings, + for right handed crossings, 0 for the two terminals of the chain (no crossing).

In a suitably chosen mixed solvent system, such as acetic acid and 1-propanol (21), a sharp reversible transition between Form I and Form II can be achieved with a small change in solvent composition. Measurements of optical activity provide a convenient way to follow the transition in dilute solution. There are large changes in optical activity because Forms I and II are helices of opposite handedness. The left panel in Figure 3 depicts the reversible transition that is detected by circular dichroism measurements in mixtures of trifluoroethanol and 1-propanol. Form II is the only conformation present in trifluorethanol. A solution of poly(L-proline) in 35 65 trifluoroethanol 1-propanol exhibits the same circular dichroism pattern as does a solution where the solvent is pure trifluoroethanol. However, further addition of 1-propanol produces a dramatic change in the circular dichroism. At 20 80 trifluoroethanol 1-propanol the circular dichroism pattern is that characteristic of Form I. Data in Figure 3 do not extend beyond 10 90 trifluoroethanol 1-propanol because of the low solubility of poly(L-proline) in 1-propanol. 

One other feature is worth noting at this poiit, and it concerns the case where the synergistic pair has a fixed mutual crientation, even if the pair itself rotates freely. While the local symmetry of each of the absorbers A and B determines the selection rules for the transitions they undergo, the symmetry of their relative juxtaposition also plays a role in determining the polarization characteristics of their synergistic photoabsoiption. This is principally manifest in the occurrence of two-photon circular dichroism where the A—B pair has definite handedness, as will be demonstrated in Section IX. Thus it transpires that not only the local symmetry, but also the global symmetry... 

For aspects of performance, percent normal scores are computed by expressing subject Y s availability of performance resource fc[J Aj.(Y)] as a fraction of the mean availability of that resource in a specified reference population (pop)]- Ideally, the reference population is selected to match the characteristics of the individual as closely as possible (e.g., age range, gender, handedness, etc.). 

Figure 13.21 presents the picture of the dielectric ellipsoid orientation within each unit cell that is at the nanometer scale. The weak molecular chirality results in additional weak twisting of all structures with characteristic pitch of about Po 0.1-1 pm. An example of a such twisted structure is shown in Fig. 13.22 it is an antiferroelectric double-layer cell describing two geared helices upon rotation about z-axis. The helices are shifted in phase by (p = 7t and have the same handedness. On the molecular scale, due to molecular chirality, the c-director turns from layer to layer by a small angle 5cp = 2nllPo, therefore, for / Inm,... 

The fact that a low concentration of a chiral compound governs the molecular arrangement of the whole solution and that the conse-quent high order induces a pronounced effect in the characteristic physical parameters such as pitch and handedness, points out the possibility of "amplifying" a small dissymmetric characteristic of the solute. 

Rather than having a situation where a unit cell consists of one or more molecules, as in small molecule crystals, the situation is reversed a single molecule participates in many unit cells. This has significant ramifications for the correlations, both structural and dynamical, between unit cells. Second, the periodicity of the crystal lattice usually implies a periodicity for the conformation of the polymer chain itself. This condition places a severe restriction on the conformation space available to the chain in a crystalline solid. Polymer chains in crystals are more appropriately described as helices rather than coils. A helix conformation consists of a regular repetition of the torsion angles characteristic of a small subsection of the chain, the helix repeat unit [4,5]. Each helix has an axis and a handedness of rotation (the direction in which the chain backbone winds around the helix axis). The helix itself is characterized by the translational displacement parallel to the helix axis, d, and the angle of rotation about the helix axis, a, executed by a single helix repeat unit. The coordinates of Eq. (1) may be expressed in terms of these helical parameters as follows ... 

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