Orientation and birefringence

Using this model, the birefringence and orientation angle, %, of the principal directions of the refractive index tensor can be determined. If light is propagating along the y axis, we find that... 

Optical measurements often have a greater sensitivity compared with mechanical measurements. Semidilute polymers, for example, may not be sufficiently viscous to permit reliable transient stress measurements or steady state normal stress measurements. Chow and coworkers [113] used two-color flow birefringence to study semidilute solutions of the semirigid biopolymer, collagen, and used the results to test the Doi and Edwards model discussed in section 7.1.6.4. That work concluded that the model could successfully account for the observed birefringence and orientation angles if modifications to the model proposed by Marrucci and Grizzuti [114] that account for polydispersity, were used. 

Fouda, I.M., and Seisa, E.A., Birefringence and Orientation Parameters of Cold-Drawn Viscose Fibers , Journal of Applied Polymer Science, 106, 1768-1776, 2007. 

Anisotropic behaviour is also exhibited in optical properties and orientation effects can be observed and to some extent measured by birefringence methods. In such oriented materials the molecules are in effect frozen in an unstable state and they will normally endeavour to take up a more coiled conformation due to rotation about the single bonds. If an oriented sample is heated up the molecules will start to coil as soon as they possess sufficient energy and the mass will often distort. Because of this oriented materials usually have a lower heat distortion temperature than non-oriented polymers. 

This is the form of the scattering matrix for any medium with rotational symmetry even if all the particles are not identical in shape and composition. A collection of optically active spheres is perhaps the simplest example of a particulate medium which is symmetric under all rotations but not under reflection. Mirror asymmetry in a collection of randomly oriented particles can arise either from the shape of the particles (corkscrews, for example) or from optical activity (circular birefringence and circular dichroism). 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

If orientation is assumed to occur only in one dimension (an oversimplification), birefringence and several related phenomena (infrared dichroism, etc.) measure the quantity , which is the average angle 8 between the molecular chain direction and that of the orienting force, such as the fiber stretch axis. It is convenient to introduce an orientation function [12]... 

Figure 16.8. Relationship between the crystal orientation factor and birefringence and the draw ratio-of BPDA-PFMB fibers. 

C0Pi6 (137) was the first to give an expression for the contribution of the form birefringence to the Maxwell constant. His theory is based on the elastic dumb-bell model, which has been used in early theories on flow birefringence and viscosity and which is identical with the model used in Sections 2.6.1 and 2.6.2. The ratio of Maxwell constant to intrinsic viscosity is probably unaffected by this simplification, when also the viscosity is calculated with the same model, as Copi6 did. For the absence of the form effect, this has strictly been shown in the mentioned Sections. In fact, in the case of small shear rates the situation is rather simple To a first approximation with respect to shear rate, the chain molecules are only oriented, their intramolecular distances which are needed for the calculation of form birefringence, being unaffected. 

It is evident that the contributions due to angular movements are caused by diffusion forces corresponding to the state of orientation, whereas the radial component is a hydrodynamic contribution. The radial force, as exerted by the flowing solvent, is balanced by the rigidity of the rod and has no consequences for the birefringence of orientation. According to eqs. (5.15), one obtains for rigid dumb-bells ... 

The just described compensation method for the parasitic birefringence of windows and polarizing prisms is also useful with respect to the parasitic birefringence created by reflections from the cylinder walls. As has been pointed out, the disturbance caused by the windows is compensated at its maximum. This means, as the test fluid possesses an extinction angle of 45°, that the extinction positions of the window birefringence are oriented parallel and perpendicular to the direction of flow (i.e. the... 

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