Bulk orientation parameter

Basic to this review is the intent to bring together methods and the basic principles of their application by which specific or average orientational parameters) may be obtained and interpreted and to point out some new technological and theoretical advances made that can be usefiilly applied in reaching a better understanding of molecular behavior of polymers in the bulk state. 

As shown in Figure 14.15, the orientation parameters and of the PLC domains in the composites increase more slowly with increasing 2 than the bulk PLC. However, as Vf increases, the curve for the composite moves closer to that of the PLC. At high draw ratio (2 = 15), the composites with Vf > 0.55 have essentially the same P and P values as the PLC, but the composites with Vf < 0.3 have a significantly lower degree of chain orientation. 

In describing a particular surface, the first important parameter is the Miller index that corresponds to the orientation of the sample. Miller indices are used to describe directions with respect to the tluee-dimensional bulk unit cell [2]. The Miller index indicating a particular surface orientation is the one that points m the direction of the surface nonual. For example, a Ni crystal cut perpendicular to the [100] direction would be labelled Ni(lOO). 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

It is interesting to note that the simple Morse potential model, when employed with appropriate values for the parameters a and D (a = 2.3 x 1010 m 1, D = 5.6 x 10 19 J as derived from spectroscopic and thermochemical data), gives fb = 6.4 nN and eb = 20%, which are quite comparable to the results obtained with the more sophisticated theoretical techniques [89]. The best experimental data determined on highly oriented UHMWPE fibers give values which are significantly lower than the theoretical estimates (fb 2 nN, b = 4%), the differences are generally explained by the presence of faults in the bulk sample [72, 90] or by the phonon concept of thermomechanical strength [15]. 

Molecules adsorbed at interfaces are in constant motion, both from the point of view of their orientation and of the dynamic exchange with the bulk solution. The distribution of orientation angle is characterized by the parameter D, see Eq. (13), or the angle of orientation Q. Complete randomness for the angle 0, the angle of rotation around the principal... 

If we were to have an isolated polymer chain with a single nuclear spin attached to each segment (the marked chain) crosslinked into an unmarked network, the second moment of the NMR line of that spin species would carry information relating to the separation of chain segments, and to their relative orientation with respect to the field direction. If the network were to be subjected to a bulk deformation, these geometrical parameters would be altered, and hence we would expect a corresponding change in the value of the experimentally measured... 

Choice of an appropriate steric reference reaction can be tricky problems can arise from the nonspheroidal shape of groups and the relative orientation of the sterically bulky groups vis-a-vis the steric probe. Thus, it is important to ensure the transferability of steric parameters. Fortunately, such a system is available for studying the relative steric bulk of ring annelations. 

There are several interesting observations that can be made about (12.32). Integrated absorption is independent of the damping constant y the only bulk parameter that affects it is the plasma frequency. If the particles are in air, then integrated absorption is independent of the shape this is true not only for a single oriented ellipsoid but also for a collection of randomly oriented ellipsoids. It is instructive to rewrite (12.32) using (12.29) ... 

We used the dielectric function e of bulk MgO calculated from oscillator parameters determined by Jasperse et al. (1966), together with the dielectric function em of the KBr matrix given by Stephens et al. (1953) (corrected by June, 1972), to calculate the absorption spectrum (12.37) of a dilute suspension of randomly oriented MgO cubes. These theoretical calculations are compared with measurements on well-dispersed MgO smoke in Fig. 12.16c. Superimposed on a more or less uniform background between about 400 and 700 cm-1, similar to the CDE spectrum, are two peaks near 500 and 530 cm- , the frequencies of the two strongest cube modes. It appears that for the first time these two modes have been resolved experimentally. If this is indeed so we conclude that the widths of individual cube modes are not much greater than the width of the dominant bulk absorption band. Genzel and Martin (1972)... 

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