Crystalline orientation averages

Amorphous orientation average Crystalline orientation average Nuclear spin number Scattered intensity Scattered intensity Transmitted intensity... 

It has been demonstrated that there is a direct relationship between the fiber mechanical properties and the molecular orientation (Figure 1). A similar relationship exists between the processing conditions, molecular orientation and mechanical properties. It has been shown that a combination of optical birefringence and the infrared spectroscopy techniques can be used for the measurement of molecular orientation. The results show that for a set of fiber samples, the 841 cm" infrared peak can be confidently used for the estimation of crystalline orientation averages. The 973 cm" peak can be separated using curve fitting procedures into 972 and 974 cm" components and the latter component can be used to estimate the amorphous orientation averages. 

Another way to divide the overall orientation is to recognise the distinction between crystalline material which is all in the trans conformation, and amorphous material which is both trans and gauche. By combining infra-red and X-ray orientation data, together with the determination of the proportion of crystalline material, the amorphous orientation average fa = gauche = 0. which is seen from the above results to be very reasonable,... 

When measuring absorption spectra, one records a signal that is related to the wavelength-dependent probability of making a spectroscopic transition. From the molecular point of view, this probability is proportional to the dot product jl p where (L is the molecular transition moment and p is the photon polarization direction. When the orientational distribution of the molecules is isotropic (not crystalline, liquid crystalline, or bound to a surface), its absorption spectrum represents the orientationally averaged probability of making a spectroscopic transition and the measured spectrum is independent of polarization direction. When the orientational distribution of the molecules is anisotropic, the probability of making a spectroscopic transition depends on the polarization direction, and that dependence can be exploited to deduce the direction of the transition moment relative to the laboratory frame. Because transition moments are often trivially related to the orientation of the molecule, structural information can be deduced from polarized absorption measurements on anisotropic samples. 

In one study. X-ray diffraction, Fourier transform infrared (FTIR) spectroscopy and refractive index measurements were utilized to characterize the state of molecular orientation in one-way and two-way (bi-axially) drawn isotactic polypropylene (iPP) films [6]. It was shown that the use of all three techniques leads to much greater confidence in the orientation averages deduced than can be obtained by using any two of the techniques. It was observed that, with one-way drawing, the chain axes of both crystalline and amorphous regions orient towards the direction of drawing. The crystalline chains are more highly oriented than the amorphous chains and tend to orient towards the plane of the... 

Average-orientation, amorphous-orientation, and crystalline-orientation functions are required to describe the oriented state completely (3,36). This description permits the calculation of amorphous-phase orientation, which is required to relate and predict physical properties. The determination of crystalline orientation requires the more advanced analytical techniques of X-ray diffraction or dichroic ratios from polarized infrared spectroscopy. Average or total orientation functions are measured by birefringence. Amorphous and crystalline orientation functions are separated by measuring the sonic modulus and assuming a molecular model for the semicrystalline polymer (3). 

Random crystalline-amorphous copolymers have the tendency to aggregate in rod-like structures exhibiting a density modulation along the rod (see Sect. 5.1). The form factor appropriate for an ensemble of isotropically oriented cylinders is given by the orientational average of A(Q,R,L,a), the Fourier transform of a cylinder with a as the angle between its axis of symmetry and the scattering vector Q [55] ... 

Figure 2 The lamellar substructure of a fibril. (a) Reciprocal positions of crystalline lamellae as a result of fiber annealing. (b) The situation after relaxation of stress affecting TTM. ai.2 - average angle of orientation of TTM CL - crystalline lamellae CB - crystalline blocks (crystallites) mF -border of microfibrils and F - fibril. In order to simplify it was assumed that (1) there are the taut tie molecules (TTM) only in the separating layers, (2) the axis of the fibril is parallel to the fiber axis.

The low electrical conductivity of PET fibers depends essentially on their chemical constituency, but also to the same extent on the fiber s fine structure. In one study [58], an attempt was made to elucidate the influence of some basic fine structure parameters on the electrical resistivity of PET fibers. The influence of crystallinity (jc) the average lateral crystallite size (A), the mean long period (L), and the overall orientation function (fo) have been considered. The results obtained are presented in the form of plots in Figs. 9-12. 

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