Characterisation of orientation

Research is proceeding to extend these qualitative observations and provide quantitative links between the mechanical anisotropy and the detailed characterisation of orientation described in this review. 

The discussion of the most general form of biaxial orientation involves fairly complicated mathematics. Further discussion in this section and in the sections on the characterisation of orientation is therefore largely restricted to a special simple type of distribution of orientations of the structural units. This distribution is the simplest type of uniaxial orientation, for which the following conditions apply. 

One method used for studying the orientation of polymers which does not make use of electromagnetic radiation is that of sonic velocity or pulse propagation. This technique is particularly suited to the characterisation of orientation in fibres (or samples having rodlike geometry) and, although the technique suffers somewhat from not having a sound theoretical basis, it is of particular usefulness in instances where an orientation index or parameter is desirable for relative comparisons. 

A number of studies were conducted to elucidate the mechanisms of electron transfer in CNTs, and to determine the physical and chemical features which influence the CNT electrochemistry. In the next sections, we will assess the electrochemistry of CNTs, and demonstrate that the orientation of the CNTs is an important factor affecting the electrochemical performance of these electrodes. Thus, special attention will be paid to the recent trends in the preparation, functionalisation and characterisation of oriented carbon nanotubes, and an extensive review of recent advances in the use of vertically aligned carbon nanotubes (VACNT) electrodes for the establishment of new electroanalytical methods also will be presented. 

We turn now to the orientational correlations which are of particular relevance for liquid crystals that is involving the orientations of the molecules with each other, with the vector joining them and with the director [17, 28]. In principal they can be characterised by a pair distribution function but in view of the large number of orientational coordinates the representation of the multi-dimensional distribution can be rather difficult. An alternative is to use distance dependent orientational correlation coefficients which are related to the coefficients in an expansion of the distribution function in an appropriate basis set [17, 28]. 

Having said this, it was felt therefore that there is a need for a book addressing analysis and characterisation of polymers from the point of view of what we wish to call the primary analytical question. Many excellent textbooks and reference works exist which address one or more individual analytical techniques, see, for example, references [1-10]. These books form the basis of the knowledge of the technique expert. They also contain many excellent and varied examples on successful applications of analytical techniques to polymer analysis and characterisation. There are also books which address the multitude of analytical techniques applied in polymer analysis, see, for example, references [11-24], However, a synthetic chemist may wish to know the constitution of his/her polymer chain, a material scientist may want to find out the reasons why a fabricated sample had failed. What technique is best or optimal to study chain constitution will depend on the situation. Polymer failure may result from morphological features, which needs to be avoided, a contaminant, a surface property degradation, etc. When a sample has been processed, e.g., a film blown, molecular orientation may be the key parameter to be studied. A formulation scientist may wish to know why an additive from a different supplier performs differently. It is from such points of view that polymer analysis and characterisation is addressed in this book. 

The presented derivations of the load rate and the lifetime relationships applying the shear failure criterion are based on a single orientation angle for the characterisation of the orientation distribution. Therefore these relations give only an approximation of the lifetime of polymer fibres. Yet, they demonstrate quite accurately the effect of the intrinsic structural parameters on the time and the temperature dependence of the fibre strength. 

The characterisation of the angular dependence of the interaction of two dipole tensors A1 A2 and B B2 is therefore straightforward, namely it depends on the projection angle of the two bonds between A1 and A2 and between B1 and B2. The orientation and magnitude of the chemical shift anisotropy (CSA) tensor, which also can cause cross-correlated relaxation, is not know a priori and therefore needs to be determined experimentally or... 

Much subsequent work has been carried out on the formation and characterisation of polyimide multilayers ([259-63] and other papers of less relevance to the theme of this book). It has been established that there is substantial orientation of the polymer axes in the direction of dipping, an effect which increased with the length of the polymer chains. Thin films consisting of ten monolayers were far more defect-free than fatty acid films of comparable thickness. Progress has also been made... 

The set of internal variables is usually determined when considering a particular system in more detail. For concentrated solutions and melts of polymers, for example, a set of relaxation equation for internal variables were determined in the previous chapter. One can see that all the internal variables for the entangled systems are tensors of the second rank, while, to describe viscoelasticity of weakly entangled systems, one needs in a set of conformational variables xfk which characterise the deviations of the form and size of macromolecular coils from the equilibrium values. To describe behaviour of strongly entangled systems, one needs both in the set of conformational variables and in the other set of orientational variables w fc which are connected with the mean orientation of the segments of the macromolecules. 

In the model, the uniform contribution (and thus, the doublet splitting) is proportional to the overall average orientation . The interaction parameter u characterises the strength of orientational interactions between segments (0 < u < 1). Thus, for a given deformation ratio X, the spectrum contains one constant splitting and a distribution of additional shifts, which is clearly seen in Figure 15.4. 

It should be emphasised that the micellar structures themselves are still too small to be seen under an optical microscope but they form domains of uniform orientation that can be observed. Other methods for the characterisation of mesophases are scattering methods, e.g. neutron scattering, x-ray diffraction or rheology as pointed out in Section 3.6. For a more detailed description see the literature relevant to this subject [19]. 

X-ray diffraction (in crystalline polymers) Unoriented crystalline polymers show X-ray diffraction patterns, which resemble powder diagrams of low-molecular crystals, characterised by diffraction rings rather than by spots. As a result of orientation the rings contract into arcs and spots. From the azimuthal distribution of the intensity in the arcs the degree of orientation of the crystalline regions can be calculated (Kratky, 1941). 

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) ... 

Solid-state NMR is one of the most powerful spectroscopic techniques for the characterisation of molecular structures and dynamics.1 This is because NMR parameters are highly sensitive to local chemical environments and molecular properties. One advantage of solid-state NMR is that it enables dealing with quadrupolar nuclei, which most of the NMR-accessible nuclei are in the periodic table. Moreover, it provides an opportunity to obtain information regarding the orientation dependence of the fundamental NMR parameters. In principle, such NMR parameters are expressed by second-rank tensors and it is the anisotropy that is capable of yielding more detailed information concerning the molecular properties. 

The interplay of orientation and crystallisation leads to a wide range of super-molecular structures or morphologies. Each different morphology represents to the user a different compromise in physical properties, so that characterisation and control of morphology becomes very important for the efficient application of polymeric materials. 

All systems examined show the same fundamental result found in previous works the critical stress intensity factor, Kc, bears a bi-linear relationship with the factor characterising fibre orientation, with different slopes over different ranges of the orientation factor, suggesting a transition between different fracture mechanisms at a critical angle. 

The integral curvature of a surface is linked to the Euler-Poincare characteristic of that surface (x) by eq. (1.12). This allows the average geometry of orientable surfaces to be related to the number of holes or handles, characterised by the surface genus, g, and the area of the surface. A, by the relation ... 

The Danish labour market system has been through a long period of reforms. The reforms have been characterised by an increased degree of orientation towards labour market needs, decentralisation, the provision of a right and a duty to activation, earlier efforts to mobilise the unemployed persons, and a shortening of benefit periods. 

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