Orientation biaxial distribution

The important information that can be provided by IR spectra is the molecular orientation in/on polymer films, which include SAMs as the specific case (Section 3.11). In the case of self-supporting anisotropic films, the linear dichro-ism is usually calculated from normal-incidence transmission spectra measured at two mutually perpendicular positions of the polarizer [684], Obviously, this approach is insensitive to the modes perpendicular to the film surface. This problem is circumvented by using a combination of the normal-incidence transmission with metallic IRRAS [727], since these methods have complimentary selection rules — the modes whose TDMs are parallel or perpendicular to the surface are active in transmission or IRRAS, respectively. This technique was used to study the MO in ultrathin n-aUcylacrylamide LB films [727, 728]. A strong biaxial distribution was found in these LB films in which the carbon-hydrogen chains are inclined in the dipping direction [727]. 

However, case (ii) above, where there is biaxial symmetry of the distribution function, but no preferred orientation of the structural units about their Ox3 axes is a feasible proposition. Kashiwagi et al.10) and later Cunningham et al. n) have given expressions for the second moment... 

The mathematical expression of N(6, q>, i//) is complex but, fortunately, it can be simplified for systems displaying some symmetry. Two levels of symmetry have to be considered. The first is relative to the statistical distribution of structural units orientation. For example, if the distribution is centrosymmetric, all the D(mn coefficients are equal to 0 for odd ( values. Since this is almost always the case, only u(mn coefficients with even t will be considered herein. In addition, if the (X, Y), (Y, Z), and (X, Z) planes are all statistical symmetry elements, m should also be even otherwise = 0 [1]. In this chapter, biaxial and uniaxial statistical symmetries are more specifically considered. The second type of symmetry is inherent to the structural unit itself. For example, the structural units may have an orthorhombic symmetry (point group symmetry D2) which requires that n is even otherwise <>tmn = 0 [1], In this theoretical section, we will detail the equations of orientation for structural units that exhibit a cylindrical symmetry (cigar-like or rod-like), i.e., with no preferred orientation around the Oz-axis. In this case, the ODF is independent of t/z, leading to n — 0. More complex cases have been treated elsewhere [1,4]... 

Problems related to the use of a guest dye can be reduced if the polymer contains a fluorescent chemical group. Gohil and Salem [70] took advantage of such intrinsic fluorescence to characterize the in-plane distribution of orientation in biaxially drawn PET films. In these experiments, the chain-intrinsic fluorescent label is due to the formation of dimers by two terephthalic moieties, exclusively within the noncrystalline regions. A comparison between sequential and simultaneous drawing along the MD and TD directions was undertaken for a fixed MD draw ratio of 3.5 and various TD draw ratios. The orientational order was characterized by two "orientation ratios" Rmd and RTD such that... 

Other PET grades are manufactured for packaging films, as well as for the production of video and audio tapes. These PET types are often standard grades with an IV of 0.64 dL/g. To reduce the sticking tendency of the final product, solid additives such as Si02 or china clay with specific particle sizes and particle-size distributions are incorporated by master-batch processes. The final product, the so-called BOPET, is a biaxial oriented PET film with high mechanical strength and a thickness between 1 and 180 im. 

In the injection blow molding process, the parison is formed by injection molding of the preshaped parison onto a steel rod, as shown in Fig. 14.18. The rod with the molded thread already completed is moved to the blowing station, where the article is inflated free of scrap. The parison thickness distribution is determined in the injection mold without the need of further control. Some axial orientation is introduced during injection, resulting in an article with partial biaxial orientation. 

The order parameters S for all three molecular axes or alternatively, the combination S plus D describe on the level of the first relevant polynomial term the orientational distribution of a rigid, non-cylindrical molecule in the uniaxial nematic phase. Additional order parameters come into play for biaxial phases (Straley, 1974). A concise overview on the concepts from statistical mechanics relevant to order parameters was given by Zannoni (1979). 

Clearly, situations intermediate between perfect order and random distributions occur in arrays of absorbing chromophores, and a treatment is required that allows expression of the orientational distribution of structural units such as crystallites or segments which may be fluorescent in a bulk sample having uniaxial or biaxial symmetry. A complete mathematical approach using a herical harmonic expansion technique has been developed which expresses the distribution as spherical harmonics of various orders in terms of the Euler angles which specify the orientation of the coordinate system in a fixed structural unit with respect to the coordinate system in the bulk sample This is of use in solid systems, where time dependence is not observed. 

In the case of optically biaxial materials, a magnetic field may alter the distribution of optical orientations at a temperature which is known to be too low to enable molecular reorientation (191. 

The various ID CP NMR spectra of a biaxially drawn industrial PET film are shown in Fig. 14.7. The pronounced sensitivity to the orientation of the sample with respect to the applied magnetic field is also shown [7]. However, the orientation distribution is relatively complicated and, therefore, difficult to quantify from these data. For PET, overlapping resonances from carboxyl and phenylene group carbons are especially troublesome and, consequently, restrict the angular information achievable in ID NMR experiments. 

In biaxial orientation a eylindrically symmetric orientation distribution no longer exists about a reference axis. Therefore, one needs to tilt the sample in order to obtain the orientation function with respect to a second reference axis such as the normal to the plane of a film or the normal to the transverse direction. Knowing two such functions for two orthogonal axes, one can calculate the third function for the third orthogonal axis by use of the direction cosines [Eq. (4)]. 

In the case of PET the (100) and (—105) net planes are of special interest. The normals of the (100) planes are perpendicular to the planes of the benzene rings, while the normals of the (—105) planes are nearly parallel to the chain direction. The corrected pole figures of the two net planes are presented in Fig. 29. From these figures it can be seen immediately, that in the case of the investigated biaxially oriented sample the benzene rings are mostly aligned parallel to the film surface (see Fig. 29 a), while the chains exhibit a relatively broad distribution around the first drawing direction, MD (see Fig. 29 b). 

The absorption correction (correcting for the effects arising from variations in irradiated volume as well as in beam path length within the sample) is important, and one way to ensure its accuracy is to obtain a reference sample having the same constitution and shape as the test sample but known to be isotropic and to make sure that the intensity measured with this reference sample is truly constant after the absorption correction is applied. From the intensity /( ) or /( , ) obtained after the absorption correction, the pole distribution r( ) or t( , d>), for a sample of uniaxial or biaxial orientation, respectively, is evaluated according to... 

For biaxial orientation the pole distribution t(, 4>) may be visualized as a density distribution defined on the surface of a sphere. The method of stereographic projection is then used to transcribe the density distribution from the spherical surface onto a sheet of paper. The contour map thus obtained is called a pole figure. 

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