Polar axis

P = polarizer (axis Hes ia the page) A = analyzer (axis Hes perpeadicular to the page). 

Fig. 5. Interaction between fatty acids and amines to produce an ABAB film having a polar axis.

Pyroelectrics. Pyroelectric ceramics are materials that possess a uoique polar axis and are spontaneously polarized ia the abseace of an electric field. Pyroelectrics are also a subset of piezoelectric materials. Ten of the 20 crystal classes of materials that display the piezoelectric effect also possess a unique polar axis, and thus exhibit pyroelectricity. In addition to the iaduced charge resultiag from the direct pyroelectric effect, a change ia temperature also iaduces a surface charge (polarizatioa) from the piezoelectric aature of the material, and the strain resultiag from thermal expansioa. 

Pol, m. pole (of fabrics) pile, nap. -achse, polar axis, -anziehung, /. polar attraction-... 

When all of the atomic displacement vectors are parallel to a polar axis of the crystal structure, the compound belongs to the one-dimensional category. In this case, linkage manner of octahedrons, MeX6, is of fundamental significance of spontaneous polarization appearance. Typical examples of compounds that belong to the one-dimensional category include perovskites,... 

Compounds that belong to the two-dimensional category undergo polarization reversal due to atomic displacement in a plane that contains a polar axis. The displacement can be imagined as the rotation of atomic groups around an axis that is perpendicular to a reflection plane. Typical examples of two-dimensional compounds include BaMF4 type compounds, where M = Mg, Mn, Fe, Co, Ni, Zn. 

In general terms, the pyroelectric coefficient of a free sample consists of three components. The first, called the real coefficient, depends on the derivative of spontaneous polarization with respect to the temperature. The second is derived from the temperature dilatation and can be calculated based on mechanical parameters. The third coefficient is related to the piezoelectric effect and results from the temperature gradient that exists along the polar axis of the ciystal. 

The Hamiltonian function for this dynamical problem, using polar coordinates with the polar axis in the direction of the lines of force, is... 

In order to find the vertical component of the field we can apply the same approach as before, namely, the integration over the volume of the spheroid, only in this case the polar axis of the spherical system should be directed along the z-axis. However, we solve this problem differently and will proceed from the second equation of the gravitational field. In Cartesian system of coordinates we have... 

US denote by A and C the moments of inertia with respect to the axis, lying in the plane of an equator and the polar axis, respectively. The ratio... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

The dominance of the tt -electron excitations in MNA is demonstrated by the experimental finding that along the polar, axis the second harmonic susceptibility X 2 ) (-2< > < >, m/V is the same as the... 

Figure 3. Projection showing the independent molecular units of the crystallographic unit cell of MNA down the polar axis (2).

In reference to Figure 5 for MNA crystals, the polar axes of the individual molecular sites are aligned with one another along the crystal polar axis. The microscopic co mo nents gx add resulting in the large macroscopic x i i i following equation 7. 

Although we do not have an exact value for the molecular dipole moment, we will consider the implications of dipole moments in the range of 2 to 30D. Taking a 35° as a noncritical estimate of the angle of the dipole with respect to the polar axis, values of L for a series of dipole moment values are shown in Columns 1 and 2 of Table II. In the range of dipoles moments of interest, the limit on L is 0.1 eV. These limits are comparable to the heats of fusion of molecular crystals which makes the limit quite reasonable. 

Obviously, the model is crude and does not take into account many of the factors operating in a real molecular stack. Lack of symmetry with respect to the polar axis and the fact that dipoles may not necessarily be situated in one plane represent additional complications. The angle a could also be field dependent which is ignored in the model. The model also requires that interactions between molecules in adjacent stacks be very weak in order for fields of 10 to 20KV/cm to overcome barriers for field induced reorientation. The cores are then presumably composed of a more or less ordered assembly of stacks with a structure similar to smectic liquid crystals. 

Thus () is an eigenvalue of Lz with eigenvalue The angle-dependent part of the wave equation is seen to contain wave functions which are eigenfunctions of both the total angular momentum as well as the component of angular momentum along the polar axis. 

For this reason, we will restrict our subsequent approach to planar configurations of the two electrons and of the nucleus, with the polarization axis within this plane. This presents the most accurate quantum treatment of the driven three body Coulomb problem to date, valid in the entire nonrelativistic parameter range, without any adjustable parameter, and with no further approximation beyond the confinement of the accessible configuration space to two dimensions. Whilst this latter approximation certainly does restrict the generality of our model, semiclassical scaling arguments suggest that the unperturbed three... 

Molecular chirality, however, proved an extremely powerful tool in the quest for polar LCs. In 1974 Robert Meyer presented to participants of the 5th International Liquid Crystal Conference his now famous observation that a SmC phase composed of an enantiomerically enriched compound (a chiral SmC, denoted SmC ) could possess no reflection symmetry.1 This would leave only the C2 symmetry axis for a SmC a subgroup of C. The SmC phase is therefore necessarily polar, with the polar axis along the twofold rotation axis. 

Figure 8.6 Three-dimensional slice of C2 symmetrical SmC phase, showing tilt cone, polar axis (congruent with twofold symmetry axis), smectic layer planes, tilt plane, and polar plane.

It is now instructive to ask why the achiral calamitic SmC a (or SmC) is not antiferroelectric. Cladis and Brand propose a possible ferroelectric state of such a phase in which the tails on both sides of the core tilt in the same direction, with the cores along the layer normal. Empirically this type of conformational ferroelectric minimum on the free-energy hypersurface does not exist in known calamitic LCs. Another type of ferroelectric structure deriving from the SmCA is indicated in Figure 8.13. Suppose the calamitic molecules in the phase were able to bend in the middle to a collective free-energy minimum structure with C2v symmetry. In this ferroelectric state the polar axis is in the plane of the page. 

One of the key experimental results leading to the elucidation of this overall structural puzzle involved depolarized reflected light microscopy (DRLM) studies on NOBOW freely suspended films in the high-temperature SmCP phase.48 In the freely suspended films it appears that only one phase is observed, which is assumed to be the phase forming the majority domains in the EO cells. The DRLM experiment provides two key results. First, thin films of any layer number have a uniformly tilted optic axis, suggesting all of the layer interfaces are synclinic. Second, films of even-layer number are nonpolar, while films of odd-layer number are polar, with the polar axis oriented normal to the plane of the director tilt (lateral polarization). 

FIGURE 5.5 Polarized PL from a gel-processed, uniaxially drawn film of EHO-OPPE (cf. Figure 5.4) in UHMW-PE. Twisted tapes (drawn to a draw ratio A = 80) are shown under excitation with UV light (365 nm) and the pictures were taken through a linear polarizer with its polarization axis oriented horizontally (a) and vertically (b). (After Weder, C., Sarwa, C., Bastiaansen, C., and Smith, P., Adv. 

---