Dipole transverse

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

Transition dipole moment 88 Transverse relaxation time 31, 32, 33, 44 Twinning 126 Two-phase model 129 Two-term models 149 ----unfolding model 183,185... 

Many of the mesogenic molecules are stericaUy asymmetric, which is determined by the fractures and bending of the molecular core as well as by the presence of the tail chains of different nature, including the branched, biforked or polyphilic moieties (Fig. 2c-f). In terms of the multipole model of molecular asymmetry introduced by Petrov and Derzhanski [34], we can speak about longitudinal or transverse steric dipoles or multipoles (Fig. 3). 

Nuclear spins can be considered as dipoles that interact with each other via dipolar couplings. While this interaction leads to strongly broadened lines in soUd-state NMR spectroscopy, it is averaged out in isotropic solution due to the fast tumbUng of the solute molecules. In Uquid-state NMR spectroscopy, the dipolar interaction can only be observed indirectly by relaxation processes, where they represent the main source of longitudinal and transverse relaxation. 

A series of model nematic liquid crystals (among them oxadiazole derivatives) with transverse dipole moments were used to study the flexoelectric effect in guest-host mixtures with a commercial liquid crystal host <2005CM6354>. 

Vibration Diagram Method. In actuality the last cases above are not described accurately by this dipole array model because actual phases of the electric fields are significantly altered from those of linear waves. (A more realistic, but complex model is to consider amplitude and phase characteristics of the oscillating vertically polarized component of electric field resulting from rotation of a line of transverse dipoles of equal magnitude but rotated relative to each other along the line such that their vertical components at some reference time are depicted by Figure 2.) For this reason and to handle details of focused laser beams one must resort to a more mathematically based description. Fortunately, numerical... 

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

Let us consider a Hn- l 5N spin pair - the transverse relaxation T2 for the 15N spin (and HN as well) is mainly dictated by the dipole-dipole (DD) interaction between the spin pair, and the chemical shift anisotropy (CSA) of... 

The outer angle brackets < > in F t) and C (t) imply an average over the different rods to which the fluorophore is bound. It has been assumed that the motions in the different factors in Eq. (4.24) are statistically independent. Equation (4.24) is expected to be rather generally valid for deformable macromolecules with mean local cylindrical symmetry. Relaxation of the FPA by rotation of the rods around their symmetry axes is contained in C (r). Likewise, relaxation of the FPA by rotation, or end-over-end tumbling, of the rods about their transverse axes is contained in F (t). Motion of the transition dipole with respect to the frame of the rod in which it is attached is contained in / ( ) Further progress requires the evaluation, or estimation, of / (/), F (t), and C (t) for particular models. 

In a microscope, standard polarized epi-illumination cannot distinguish order from disorder in the polar direction (defined as the optical axis) because epi-illumination is polarized transverse to the optical axis and observation is along the optical axis at 180°. However, microscope TIR illumination can be partially polarized in the optical axis direction (the z-direction of Section 7.2) and can thereby detect order in the polar angle direction. Timbs and Thompson(102) used this feature to confirm that the popular lipid probe 3,3 -dioctadecylindocarbocyanine (dil) resides in a supported lipid monolayer with its dipoles parallel to the membrane surface, but labeled antibodies bound to the membrane exhibit totally random orientations. 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

Recapitulating, the SBM theory is based on two fundamental assumptions. The first one is that the electron relaxation (which is a motion in the electron spin space) is uncorrelated with molecular reorientation (which is a spatial motion infiuencing the dipole coupling). The second assumption is that the electron spin system is dominated hy the electronic Zeeman interaction. Other interactions lead to relaxation, which can be described in terms of the longitudinal and transverse relaxation times Tie and T g. This point will be elaborated on later. In this sense, one can call the modified Solomon Bloembergen equations a Zeeman-limit theory. The validity of both the above assumptions is questionable in many cases of practical importance. 

The so-called static dephasing regime (SDR) predicts a linear dependence of I/T2 on the magnetic moment of the particles in solution (22, 25). This regime describes the transverse relaxation of homogeneously distributed static protons in the presence of static, randomly distributed point dipoles. The free induction decay rate, I/T2, is then proportional to the part of the sample magnetization due to the dipoles (p), M = rap, where ra is the concentration... 

The need to include the transverse terms in Eq. (6) is consistent with the water-molecule dipole moments solvating charges and local protein component dipole moments, which may then unlock low frequency modes in the protein structure that, in the absence of a high dielectric medium... 

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