Uniaxial dipole

In a collection of statistically distributed, mobile dipolar species, the total field-parallel contribution to the polarization is the statistical average over the cos 5 projections on the field vector. For the sake of transparentness we shall confine the further analysis to uniaxial anisotropic particles Bj, i.e., to uniaxial dipole moments m. In this case Eqs. (3.12) and (3.16) read, respectively,... 

In order to evaluate quantitatively the orientation of vibrational modes from the dichroic ratio in molecular films, we assume a uniaxial distribution of transition dipole moments in respect to the surface normal, (z-axis in Figure 1). This assumption is reasonable for a crystalline-like, regularly ordered monolayer assembly. An alternative, although more complex model is to assume uniaxial symmetry of transition dipole moments about the molecular axis, which itself is tilted (and uniaxially symmetric) with respect to the z-axis. As monolayers become more liquid-like, this may become a progressively more valid model (8,9). We define < > as the angle between the transition dipole moment M and the surface normal (note that 0° electric field of the evenescent wave (2,10), in the ATR experiment are given by equations 3-5 (8). 

If the absorption dipole is uniaxial (a2 = a3) then the dichroism for a uniaxial deformation along the 3 axis will be... 

Figure 2.31 Electrostatic free energy for a dipole p = 5.65 D in a spherical cavity of radius a=5. 5 A in a uniaxial dielectric, as a function of the dielectric anisotropy Ae. The average permittivity is (a) < e > = 11 and (b) < e > = 9.5. Solid and dashed lines refer to the dipole parallel and perpendicular to the director, respectively.

For comparison, the results obtained using the Maier-Meier theory [4] are also shown this is a generalization of the Onsager model [13] to uniaxial media. The same dipole moment used for the calculations with the molecular shaped cavity was assumed, and the radius a was taken to be 3.9 A, a value derived from the density of the system. Improvement of the predictions, when the sphere is replaced by a molecular shaped... 

In the absence of external fields the suspension under consideration is macroscopically isotropic (W = const). The applied field h (we denote it in the same way as above but imply the electric field and dipoles as well as the magnetic ones), orienting, statically or dynamically, the particles, thus induces a uniaxial anisotropy, which is conventionally characterized by the orientational order parameter tensor (Piin h)) defined by Eq. (4.358). (We remind the reader that for rigid dipolar particles there is no difference between the unit vectors e and .) As in the case of the internal order parameter S2, [see Eq. (4.81)], one may define the set of quantities (Pi(n h)) for an arbitrary l. Of those, the first statistical moment (Pi) is proportional to the polarization (magnetization) of the medium, and the moments with / > 2, although not having meanings of directly observable quantities, determine those via the chain-linked set [see Eq. (4.369)]. 

Liquid crystalline fluorene oligomers can emit polarized fight with proper alignment of their molecular axes and, hence, of their transition dipole moments. For example, linearly polarized emission results from uniaxial alignment of fluorene oligomers. One common way to characterize linearly polarized emission is to measure its emission dichroism, viz. the emission... 

Fig. 10.3.1 [Hepl] F chemical-shift spectra of PTFE. The dipole-dipole interaction has been removed by M V8 multi-pulse excitation, (a) Isotropic molecular orientation, (b) Uniaxially drawn sample. The drawing direction is parallel to the magnetic field.

The tendency to form lamellar structures can be understood as the result of dipole-dipole repulsions between the uniaxially ordered amphiphile molecules theoretical analyses of the pattern formation based on this principle have been carried out. It appears that the lamellar thickness is defined by the equilibrium thermodynamic conditions (Fig. 23) but that the shape and density of the patterns are determined by the dynamics of the process by which they are formed. 

With the purpose of illustrating eqn (4.76) we consider the energy region of a nondegenerate linear polarized dipole-allowed transition in a uniaxial crystal. When neglecting the spatial dispersion, the tensor e j(w) has the following nonzero components (the 2-axis is oriented along the optical axis) ... 

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