Orientation Hermans

Kejcwords amorphous orientation, crystalline orientation, Herman s orientation factor, infrared spectroscopy (IR), IR band assignment, optical birefringence, orientation, structure-property relationships in fibers, X-ray diffraction... 

Calculate the chain orientation (Hermans orientation function) of the schematic molecules shown in Fig. 9.22. 

When fitting two structures, the aim is to find the relative orientations of the two molecules in which the RMSD is a minimum. Many methods have been devised to perform this seemingly irmocuous calculation. Some algorithms, such as that described by Ferro and Hermans [Ferro and Hermans 1977] use an iterative procedure in which the one molecule is moved relative to the other, gradually reducing the RMSD. Other methods locate the best fit directly, such as Kabsch s algorithm [Kabsch 1978]. 

The values of the amorphous orientation index in the form of Hermans function of orientation if a), determined by the authors for PET fibers are listed in Table 6. The differences in the values of fa quoted in Table 6 and referring to particular investigation methods can result from the fact that in some methods the orientation of the amorphous and mesophase are considered jointly. Consequently, in such a case the values of fa will be overrated. 

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 ... 

The factor having the strongest effect is the elongation imparted in the process of production stretching. Second, the overall orientation is affected by the stretching rate. For the same draw ratio, the overall orientation grows with an increase in the stretching rate. The effect of the draw ratio on the value of Hermans function of orientation is illustrated by the values of/o, established by the authors and depicted in Table 7. 

Herman, D.M., E.E. Baird, and P.B. Dervan. Stereochemical control of the DNA binding affinity sequence specificity, and orientation preference of chiral hairpin polyamides in the minor groove. J. Am. Chem. Soc. 1998, 120, 1382-1391. 

Uniaxial orientation parameter (Hermans orientation function) Scattering data evaluation program by A. Hammersley (ESRF) Free Electron Laser Hamburg Full width at half-maximum... 

Figure 9.4. The orientation of structural entities (rods) in space with respect to the (vertical) principal axis and the values of for, the uniaxial orientation parameter (Hermans orientation function) for (a) fiber orientation, (b) isotropy, (c) film orientation...

PH Hermans and D Heikens, Orientation in cellulose fibers as derived from measurements of dichroism of dyed fibers, Reel. Trav. Chim. Pays-Bas, 71 49-55, 1952. 

Prior to 1940 there was little or no education directed toward polymer chemistry. With the contributions of Carothers and others that transformed the practice of polymers into a science, and with the leadership of Herman Mark and others (informal graduate and postgraduate), polymer education took root but rapid expansion and general acceptance by more traditionally oriented academic institutions was slowed by many barriers. Only since 1974 has there been a concerted effort to include education in the basic concepts of polymer chemistry into the undergraduate curriculum. 

It can be assumed that the orientation of the amorphous regions is a result of the deformation of a rubber-elastic network. Therefore, it can be expected that crystallization during spinning occurs at the neck, where the deformation is maximal. The amorphous phase develops into a load-bearing factor which is related to its orientation, as expressed by Hermans orientation factor. 

The problem of calculating the degree of orientation and size from a scattering pattern has been widely addressed in the scientific literature [86, 88]. In the study of regenerated tissues a two-dimensional analog of the Hermans orientation index [89, 90], previously used to specify the orientation of a polymer from X-ray scattering data, was adapted [81, 91]. 

In order to compare orientation in related samples, Hermans suggested the following equation to calculate a degree of orientation [3,19] ... 

Nematic phases are characterized by an unordered statistical distribution of the centers of gravity of molecules and the long range orientational order of the anisotropically shaped molecules. This orientational order can be described by the Hermans orientation function 44>, introduced for l.c. s as order parameter S by Maier and Saupe 12),... 

In favorable situations, segmental orientation in polymer blends can be followed using the technique of IR dichroism. The results can be expressed in terms of the Hermans orientation function shown in Equation 1. 

If Eq. (13.165) is substituted in the Hermans function Eq. (13.151) we obtain a general relationship between the birefringence and the compliance of well-oriented fibres ... 

Nematic phases are characterised by a uniaxial symmetry of the molecular orientation distribution function f(6), describing the probability density of finding a rod with its orientation between 6 and 6 + d0 around a preferred direction, called the director n (see Fig. 15.49). An important characteristic of the nematic phase is the order parameter (P2), also called the Hermans orientation function (see also the discussion of oriented fibres in Sect. 13.6) ... 

---