Hermans orientation function birefringence measurement

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. 

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. 

Birefringence measurements are classical. The Hermans orientation function (/) is proportional to the birefringence An) ... 

The parameters average values. Note that fj is the Hermans orientation function. The full description of uniaxial orientation /(0) can thus not be given by a single measurement of birefringence. 

Fortunately, the Herman orientation function, F, can be determined by a number of independent techniques, including X-ray diffraction, birefringence, sonic modulus, and refractive index measurements. These methods, coupled with IR dichroic measurements of absorption, can be used to calculate quantitative values for the transition-moment angles by using Eq. (2.15). A plot of F measured by X-ray diffraction versus (i — )/(/ -f 2) will be linear with a zero intercept. A least-squares evaluation of the data from this line will yield the slope, (/ o + 2)/(Ro — ) When is 0° (parallel to the molecular chain axis) the slope equals 1.0 and when equals 90°, the slope equals —2.0. A quantitative value of the transition-moment angle can then be calculated. Transition-moment angle measurements have been published for isotactic polypropylene and some of the results are as follows [22] ... 

The orientation of the crystalline region is measured by x-ray diffraction techniques. The orientation in the less-ordered amorphous region is determined by x-ray, infrared measurements, sonic modulus technique [183], or by separating the crystalline and amorphous contributions to the fiber birefringence [79]. The average orientation of the crystalline regions is specified by the Hermans Stein orientation functions ... 

The quantitative assessment of the overall orientation of PET fibers is generally made on the basis of fiber optical anisotropy measurements, i.e., measurements of the optical birefringence of the fiber. The determination of the value of optical birefringence makes it possible to determine the value of Hermans function of orientation based on the equation ... 

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