Isotropic Orientation

Composites fabricated with the smaller floating catalyst fiber are most likely to be used for applications where near-isotropic orientation is favored. Such isotropic properties would be acceptable in carbon/carbon composites for pistons, brake pads, and heat sink applications, and the low cost of fiber synthesis could permit these price-sensitive apphcations to be developed economically. A random orientation of fibers will give a balance of thermal properties in all axes, which can be important in brake and electronic heat sink applications. 

Liquid crystals, as the name implies, are condensed phases in which molecules are neither isotropically oriented with respect to one another nor packed with as high a degree of order as crystals they can be made to flow like liquids but retain some of the intermolecular and intramolecular order of crystals (i.e., they are mesomorphic). Two basic types of liquid crystals are known lyotropic, which are usually formed by surfactants in the presence of a second component, frequently water, and thermotropic, which are formed by organic molecules. The thermotropic liquid-crystalline phases are emphasized here they exist within well-defined ranges of temperature, pressure, and composition. Outside these bounds, the phase may be isotropic (at higher temperatures), crystalline (at lower temperatures), or another type of liquid crystal. Liquid-crystalline phases may be thermodynamically stable (enantiotropic) or unstable (monotropic). Because of their thermodynamic instability, the period during which monotropic phases retain their mesomorphic properties cannot be predicted accurately. For this reason it is advantageous to perform photochemical reactions in enantiotropic liquid crystals. 

Simulation. In this study, VSFS and molecular dynamics calculations were employed to examine the structure and dynamics of the hydrogen bonding network of water at the hexane/water, heptane/water and octane/water interfaces in detail [66]. The complementary nature of the approaches has allowed a more detailed understanding of the interface. The calculations provide information not available in the spectroscopic studies, namely the interactions between interfacial water molecules that are isotropically oriented. The direct and iterative comparison of experiment with theory allows for the improvement of the models used to describe water-water and water-solute interactions. 

In transient shear flows starting from an isotropic distribution of fiber orientations, considerably higher viscosities will be initially observed, until the fibers become oriented. In Bibbo s experiments, t]r for isotropically oriented fibers is around 3.5 for v = 75. These viscosities can also be predicted reasonably well by semidilute theory and by simulations (Mackaplow and Shaqfeh 1996). Figure 6-25 shows the shear stress as a function of strain for a polyamide 6 melt with 30% by weight glass fibers of various aspect ratios, where the fibers were initially oriented in the flow-gradient direction. Notice the occurrence of a stress overshoot (presumably due to polymer viscoelasticity), followed by a decrease in viscosity, as the fibers are reoriented into the flow direction. 

Line broadening in solid-state NMR arises from spin interactions which can be described in first order by coupling tensors of rank two (cf. Section 3.1) [Hael, Mehl, Schl], The spin interactions are either linear or bilinear in the spin operator. Linear interactions are the Zeeman interaction, the chemical shielding, and the interaction with the rf field. Bilinear interactions are the J coupling, the dipole-dipole coupling, and the quadrupolar interaction. In isotropic materials like powders, glasses, and undrawn polymers, wide lines are observed as a result of an isotropic orientational distribution of coupling tensors. 

Scattering methods for structure determination rely upon the availability of crystalline samples. On the other hand, NMR can make use of samples which have an isotropic orientation distribution and/or amorphous structures. This greater range of sample possibilities not only makes NMR applicable to studies of biomolecular structure with different macroscopic properties but also raises opportunities for different experimental procedures leading to increased amounts of structural information. However, attention must always be paid to the effect sample preparation may have on the conformation of the protein molecules relative to the naturally occurring strncmre. 

The loss of r will result through molecular motion within the excited state fluorescence lifetime (rf) until the photoselected population achieves an isotropic orientation. If the anisotropy decays following a simple, single relaxation mechanism, it will be described by Equation 2.31... 

Equations (6.3.22a - 6.3.22b) can be simplified, for the case of isotropically oriented molecules, unpolarized radiation, and zero external magnetic or electric fields, by summing over M (see Hougen, 1970, p. 39).f The resultant M-independent (f2 J a f]J) direction cosine matrix elements are listed in Table 6.1. Note that the a Ail = Tl matrix elements have opposite signs for P versus R transitions, whereas the az Afl = 0 matrix elements have the same signs for P and R transitions. 

The void area fraction in (21-76) is based on the fractional area in a plane at constant x that is available for diffusion into catalysts with rectangular symmetry. A rather sophisticated treatment of the effect of g 6) on tortuosity is described by Dullien (1992, pp. 311-312). The tortuosity of a porous medium is a fundamental property of the streamlines or lines of flux within the individual capillaries. Tortuosity measures the deviation of the fluid from the macroscopic flow direction at every point in a porous medium. If all pores have the same constant cross-sectional area, then tortuosity is a symmetric second-rank tensor. For isotropic porous media, the trace of the tortuosity tensor is the important quantity that appears in the expression for the effective intrapellet diffusion coefficient. Consequently, Tor 3 represents this average value (i.e., trace of the tortuosity tensor) for isotropically oriented cylindrical pores with constant cross-sectional area. Hence,... 

Domains in the initial film are aligned in such a way that columns of the complex are parallel to the substrate with isotropic orientational distribution parallel to the film plane. During irradiation, there is an in-plane reorientation of domains (columns). 

The molecules of a gas sample in thermal equilibrium will be isotropically oriented in space, as will their angular momentum vectors. 

Figure 11.3 shows the two-dimensional distribution of orientation vectors of solutions of rod-like polymers in a variety of circumstances. Figure 11.3a shows the isotropic orientation distribution expected in an isotropic phase at rest. Figure 11.3b shows that the effect of shear on an isotropic phase is to distort the spherical (circular in two-dimensions) distribution into an elliptical one. The normal stress implication is that the tendency of the distorted distribution to relax back to the spherical shape implies a traction in the shear direction, or, equivalently, a compression orthogonal to it. Elastic normal stresses associated with this situation are invariably positive. The situation for a nematic phase of rod-like polymers is shown in Figure 11.3c. The following three paragraphs are taken verbatim from [68] ...

The scattering from randomly oriented non-spherical inhomogeneities is isotropic. Oriented scatterers, however, result in an anisotropic scattering. Cargill (1972) observed an anisotropy in the small angle X-ray scattering from evaporated amorphous germanium films. From his results he concludes that the amorphous films ( 7 /xm thick) contain 1-2 volume % of rod shaped voids whose dimensions are 22 A X 46 A in the plane of the film and 2200 A normal to the film plane. 

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