Orientation of structural units

Kimura, I., Kagiyama, M., Nomura, S., Kawai, H. General description of optical (Dichroic) orientation factors for relating optical anisotropy of bulk polymers to orientation of structural units. Part II. J. Polymer Sci. A-2, 7, 709 (1969). 

In general it is not meaningful to talk about the orientation of a polymer molecule as a whole it is therefore useful at the outset to refer to the orientation of structural units. Such a unit may be a crystallite, a regular... 

Recent developments in spectroscopic techniques allow for accurate measurement of orientations of structural units in deformed polymeric systems Infrared dichroismCI-R-D) H - N-M.R. spectroscopy, fluorescence polarization (F.P.) are three methods which find increasing use in experimental investigations- The experiments reported in the present paper concern effectively simultaneous measurements of orientation by fluorescence polarization and of stress-strain relationship. It is worth noting that the transition moments of the label involved in fluorescence polarization are not sensitive to their immediate environment. Previous models are briefly reviewed and a new model of orientation of real networks is proposed- Then the fluorescence polarization technique is described and theoretical predictions are compared with measurements on polyisoprene vulcaniza-tes. 

It has been shown previously that the polymerization of unsymmetrical conjugated dienes may give rise to 1,2-, 3,4- and 1,4-units. The 1,2- and 3,4-units may be regarded as arising when the two double bonds in the diene react independently. The diene may then be considered to be a vinyl monomer and the previous observations relating to the orientation of structural units in vinyl polymers may be applied to the 1,2- and 3,4-units in polydienes. In the case of the 1,4-units, however, a somewhat different situation arises. Consecutive 1,4-units may be arranged as follows (for isoprene) ... 

Graphic Representation of the State of Orientation of Structural Units 464... 

There have been several types of graphical illustrations to represent the state of orientation of structural units. Stein has proposed orthogonal equilateral triangle coordinates for the uniaxial symmetric system and Desper has proposed equilateral triangle coordinates for the orthogonally biaxial symmetric system. ... 

The orientation distribution functions for the structural units cannot be directly determined from any experimental sources, except for the crystalline units from X-ray diffraction measurements. Usually the orientations of structural units are obtained as several kinds of averages, i.e. the second and/or fourth orders of the orientation factors from optical measurements such as birefringence and absorption/emission dichroism. 

The Raman measurements provide values directly for P)mn, the coefficients of the Legendre expansion related to coordinates axes chosen with respect to the principal axes of the differential polarizability tensor, hence the superscript r. The coefficients Pimn for the orientation of the units of structure must then be obtained by further calculation from the P)mn. 

This discussion of the structures of diene polymers would be incomplete without reference to the important contributions which have accrued from applications of the ozone degradation method. An important feature of the structure which lies beyond the province of spectral measurements, namely, the orientation of successive units in the chain, is amenable to elucidation by identification of the products of ozone cleavage. The early experiments of Harries on the determination of the structures of natural rubber, gutta-percha, and synthetic diene polymers through the use of this method are classics in polymer structure determination. On hydrolysis of the ozonide of natural rubber, perferably in the presence of hydrogen peroxide, carbon atoms which were doubly bonded prior to formation of the ozonide... 

The quantity N(6, cp, i//) sin ddddcpdi// represents the fraction of structural units oriented in the generalized solid angle sinOdOdtfidij/, with the following... 

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]... 

Finally, as another simple example of description (and symbolic representation) of structures in terms of layer stacking sequence, we now examine structures which can be considered as generated by layer networks containing squares. A typical case will be that of structures containing 44 nets of atoms (Square net S net). The description of the structures will be made in terms of the separation of the different nets, along the direction perpendicular to their plane, and of the origin and orientation of the unit cell. 

Based on the preceding results, we can say that linearly polarized light from the band-gap absorption region can induce either transitory changes or crystallization transformation in amorphous Sbj Sei alloys. These two phenomena critically depend on exposure, show threshold behavior, and seem to arise from apparently different mechanisms defect states or some kind of structural units given preferential orientation under the action of linearly polarized light. 

Another type of structural unit found in many cluster compounds is type III, in which both sulfur atoms of the ligand are bonded to each of two metal atoms. The S—S bond is orientated approximately normal to the metal-metal vector. 

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. 

All methods of deduction of the relative phases for Bragg reflections from a protein crystal depend, at least to some extent, on a Patterson map, commonly designated P(uvw) (46, 47). This map can be used to determine the location of heavy atoms and to compare orientations of structural domains in proteins if there are more than one per asymmetric unit. The Patterson map indicates all the possible relationships (vectors) between atoms in a crystal structure. It is a Fourier synthesis that uses the indices, l, and the square of the structure factor amplitude f(hkl) of each diffracted beam. This map exists in vector space and is described with respect to axes u, v, and w, rather than x,y,z as for electron-density maps. 

FIGURE 11 Soot structure as (a) produced in the laboratory (Sergides et al, 1987), forming (b) basic structural units of 3-4 layers (Heidenreich et al, 1968), (c) randomly oriented basic structural units shown as a 2-dimensional schematic diagram, (d) onion-type particle with several condensation seeds (Heidenreich etal, 1968). 

Crystals containing polyatomic units of structure which are effectively non-spherical usually exhibit some increase in disorder in the mutual orientation of these units when the crystal melts. For such crystal lattices, the total entropy of fusion, Sf, may be written as the sum of two terms Sf = Spos. + 5or.-... 

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