Birefringence uniaxial orientation

The uniaxial orientation parameter related to the orientation of polymer chains gains particular importance, because it can also be determined by measurement of birefringence [250,252],... 

Biaxial orientation of crystalline plastics generally improves clarity of films. This occurs because stretching breaks up large crystalline structures into smaller than the wavelength of visible light. With uniaxial orientation, the result is an anisotropic refractive index and thus birefringence, especially in crystalline plastics. 

LFnder the influence of a static electric field liquid crystalline solutions of PBLG become uniaxially oriented and show both linear and circular birefringence and linear and circular dichroism. Accordingly, the measured CD shows a dependence of the microscopic angle, a, that the fast optical axis of the oriented solution makes with respect to the plane of polarization of the polarizer in the CD instrument. When the film is reasonably thin (0.01-0.1 mm thick) or/and only partially oriented (less than 5% orientation), the apparent CD of oriented film of deoxyribonucleic acid is expressed by the equation (50) ... 

The fibers spun from nematic phase systems and solvent composition 25.0/75.0 exhibited twice the tenacity and modulus of those extruded from the system of the solvent composition 29.3/70.7. The two fiber types showed significant differences in birefringence, and in the appearance of their external surfaces and fracture surfaces. The comparable moduli of the fiber spun from a nematic solution with those of Fortisan may result from high uniaxial orientation of cellulose molecules in the former fiber. 

It will be shown that the level of uniaxial orientation and the variation of local mechanical properties generated by controlling the injection temperature can be conveniently characterized by microhardness measurement in combination with the measurement of optical birefringence An and DSC. In Section 2.7 we saw that microhardness is a very useful mechanical property, which can provide direct information about the anisotropy developed within highly oriented polymers. 

Galay, J. M. and Cakmak, M., Real time sensing of birefringence development in uniaxially oriented PEN and PEN/PEI films using a fast dual wavelength optical technique, in Proceedings of the 55th SPE ANTEC 97... 

A specially oriented (hypothetical) sample of a polymer has one half of its structural units oriented with their axes parallel to the draw direction and the other half oriented with their axes uniformly distributed in the plane normal to the draw direction. If the birefringence of this sample is 0.02, calculate the birefringence of a fully uniaxially oriented sample. 

A particular sample of a semicrystalline pol5mer with the simplest form of uniaxial orientation is found to have a birefringence of 0.042. Density measurements show that it has a volume crystallinity of 0.45 and X-ray measurements show that P2icosff)) for the crystalline phase is 0.91. Assuming that An ax is 0.050 for the crystalline phase and 0.045 for the amorphous phase, estimate (P2(cos 0)) for the amorphous phase. 

A uniaxially oriented fibre of a certain polymer has a birefringence of 0.03 and the birefringence for a fully oriented fibre of the polymer is 0.05. Assuming that, to a good approximation, all the polymer chains in the partially oriented fibre make the same angle 6 with the fibre axis and that the simplest theory of birefringence applies, calculate 6. 

A particular sample of a uniaxially oriented polymer is composed of structural units each of which is transversely isotropic with respect to an axis Oz within the unit. The value of (cos 0) is 0.65, where 6 is the angle between the Oz axis of a typical unit and the draw direction. There are 4.2 x 10 structural units per m in the polymer and the polarisabilities of an individual unit for light polarised parallel and perpendicular to Oz are 2.6 x 10 and 1.9 x 10 F m, respectively. Calculate the polarisabilities of the sample for light polarised parallel and perpendicular to the draw direction and hence the birefringence of the sample. 

The birefringence An for a uniaxially oriented sample with draw ratio X = 3.5 was found to be 8.1 x 10 . Assuming that the orientation of the polymer molecules is adequately described by equation (11.6) using only the first term on the RHS, deduce An for a similarly drawn sample with X = 2.0. 

Deduce whether the affine rubber or the pseudo-affine aggregate model better describes these data. Given that the birefringence observed for a very highly uniaxially oriented sample of the polymer is 0.078, deduce what numerical information you can about a sample with draw ratio 3.0. 

Uchi5rama, A., and Yatabe, T. (2003). Analysis of extraordinary birefringence dispersion of uniaxially oriented poly(2,6-dimethyl 1,4-phenylene oxide)/atactic pol5rstyrene blend films. Ion. I. Add/. Phvs.. 42, 3503-3507. 

Fig. 4. CorO for the unique axes of fluorescent VPBO molecules dispersed in uniaxially oriented tapes of polyethylene terephthalate plotted against the birefringence — of the tapes. O, samples drawn at S(PC to draw ratios between 1 and 6 . samples drawn to draw ratio 2 7 at temperatures between 65° and 90°C. (Reproduced by permission from Ref. 18. Copyright I PC Business Press Ltd.)...

Polymers may exhibit a biaxial orientation. The segmental orientation function is in this case a function of two angular variables, i.e. /(, v), as shown in Figure 10.7. The in-plane orientation is different in the zx and zy planes (Figure 10.7). There are several methods commonly used to determine chain orientation in-plane birefringence, wide angle X-ray diffraction, small angle X-ray diffraction, infrared spectroscopy and sonic modulus measurements. In the case of uniaxial orientation there is only... 

It is possible to assess the Hermans orientation function by birefringence measurements. X-ray diffraction and infrared spectroscopy. The full description of uniaxial orientation fief) cannot thus be attained by a single birefringence measurement. 

Fischer e.a. [117] proposed an entirely new origin for the band structures. They felt that it was due to buckling of uniaxially oriented birefringent entities. They observed self-extension phenomena which provide the axial compression which produces the buckling. In addition they observed a novel related rheological phenomenon a spontaneous stress build-up upon cessation of shear. 

In systems with uniaxial orientation, the optical axis is coincident with the direction of principal orientation (Xin Fig. 54b). The system will exhibit two polarizabilities / , and and two principal refractive indices n, and T2 /, parallel and perpendicular to X respectively. The birefringence A is designated as being positive if n, > ni and negative if n, <( ni and its m nitude is given by... 

If uniaxial orientation is imperfect (see Fig. 57), the birefringence of the system is a measure for its average orientation. We shall briefly discuss how this average orientation can be rationally expressed in one single figure, designated as the orientation factor... 

The meaning of can be explained thus. Let us imagine a case of imperfect uniaxial orientation of rodlets, thereby characterized that all the rodlets lie at the same angle a with respect to the optical axis of the system. (Fig. 60). Now, if we set the condition that the birefringence of this system shall be equal to that of the actual system under consideration, then the angle a shall be equal to am. For the... 

With the aid of equations (33) and (34) the orientation factor and the average angle of orientation of uniaxially oriented cellulose objects can be computed, if their birefringence is measured. This may be of some use in botanical work and in fibre research. It is necessary, however, to use the correct values of % and n jj. For practical purposes it will be sufficient to discriminate between native cellulose and regenerated cellulose. Further, the moisture content must be taken into account. The figures of % and n y for the usual density of 1.555 in native and 1.520 in regenerated fibres, adjusted to the usual regain at 65 % rel. humidity which the fibres attain if first swollen in water and then conditioned in air of this humidity, arc listed in Table 9. 

Firstly, one can measure the principal refractive indices of the object separately, using the immersion method of Becke or that of Schroder van der Kolk. In the case of uniaxial orientation the birefringence is equal to the difference of the two principal refractive indices. 

The theoretical descriptions of biaxial orientation and the relationships to physical properties are not as well developed as those of uniaxial orientation. In amorphous polymers, birefringence can measure total molecular orientation and can be used to predict properties. For semicrystalline polymers, a more... 

Fig. 5.87 Incomplete extinction in uniaxially oriented TLCP fibers, ribbons and films gives a salt and pepper texture which is seen as individual domains less than 0.5/xm across. The similar polarization colors in polarized light suggest the domains are within the same order, and thus have similar birefringence. 

The more formal approach, involving values of , has been used by Purvis et al. [7] to study uniaxially oriented specimens of poly(ethylene tereph-thalate). These measurements were part of a wider study involving birefringence and Raman studies, and the results are more conveniently considered in the following section. 

On this model, the birefringence Att of a uniaxially oriented polymer is given by... 

A more comprehensive investigation on uniaxially oriented sheets of polymethylmethacrylate and polystyrene was undertaken by Wright et al. [94] using ultrasonic measurements. The results are summarised in Figure 8.29 (a) and (b), where the stiffness constants are shown as a function of the birefringence. Rawson and Rider [95] have also reported ultrasonic data for oriented polyvinyl chloride and observed a similar degree of anisotropy to that seen in Table 8.8 from Hennig s work. 

The parameters average values (amplitudes). Note that is the Hermans orientation function. The full description of uniaxial orientation /(0) cannot thus be attained by a single measurement of birefringence. The Hermans orientation function can be given a simple interpretation. A sample with orientation f may be considered to consist of perfectly aligned molecules of the mass fraction / and randomly oriented molecules of the mass fraction 1 — /. Liquid-crystalline polymers are often characterized by their order parameter, denoted S (Chapter 6). This quantity is equivalent to the Hermans orientation function. 

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