Particle orientations

Ferefs diameter (Fig. 20-5) is the perpendicular projection, in a fixed direction, of the tangents to the extremities of the particle profile. Martin s diameter is a hne, parallel to a fixed direction, which divides the particle profile into two equal areas. Since the magnitude of these statistical diameters varies with particle orientation, these diameters have meaning only when a sufficient number of measurements are averaged. 

Quite specific effects in the flow of dispersions of long fibers are connected with particles orientation in the flow. Indeed, the state of fibers during the flow changes greatly as compared the initial state, so that the material in a steady-state flow is an anisotropic medium. Therefore the viscosity of such a suspension may become independent of a fiber s length [30], The most strong effects caused by a deformation of anisotropic particles should be expected in transient flows, in particular if the particles themselves are flexible and deformed in the flow. 

To create a useful CFD simulation the model geometry needs to be defined and the proper boundary conditions applied. Defining the geometry for a CFD simulation of a packed tube implies being able to specify the exact position and, for nonspherical particles, orientation of every particle in the bed. This is not an easy task. Our experience with different types of experimental approaches has convinced us that they are all too inaccurate for use with CFD models. This leads to the conclusion that the tube packing must either be computergenerated or be highly structured so that the particle positions can be calculated analytically. 

For small particles supported on thin films of amorphous or microcrystalline materials it is not easy to determine whether there is any consistent correlation between the particle orientation and the orientation of the adjacent locally ordered region of the substrate. For some samples of Pt and Pd on gamma-alumina, for example, nanodiffraction shows that the support films have regions of local ordering of extent 2 to 5 nm. Patterns from the metal particles often contain spots from the alumina which appear to be consistently related to the metal diffraction spots. 

With the exception of the reasons given in Figure 9.22, porosity significantly depends on particle orientation and packing that can be characterized by a coordination number of packing of particles, np, or pores, Zc, which will be discussed in Section 9.6 and Section 9.7. 

It is necessary to disperse the nanomaterials in the best possible manner, especially those layered structures such as graphite, graphene or clays. It is important to obtain very thin (ca. one nanometer) and very wide (ca. 500 nanometers) nanostructures dispersed in the polymer matrices to achieve optimal gas permeability and to improve their mechanical properties without affecting structural quality, using a small amount of the nanomaterial. The particle orientation also has an important effect on the properties of the nanocomposite. Nanoparticles need to be dispersed within the polymer so that are parallel to the material s surface. This condition ensures a maximum tor-... 

One big problem, which arises mainly in crystals with rather large unit cells, is the overlapping of reflections. This prevents an accurate measurement of the local integrated intensities of a large number of reflections. A solution to this problem can be the 2D pattern decomposition method, which is based on the same principles as in X-ray powder diffraction. This method takes into account the dependence of intensities on the particle orientation function and the size of microcrystals. It is therefore necessary to establish the mathematical formalism that describes the dififiaction pattern taking into account these parameters. 

Melting and recrystallisation must be taken into account to interpret the formation of the irregularly shaped Pt Sis particles oriented on various zone axes. The reason may be the decreased melting temperature of small... 

X-rav Diffraction. XRD is the most common method used for coal mineralogy (6.7.8). Its major advantage is the ability to unequivocally identify many minerals. The main disadvantages are 1) reliance on reference minerals, 2) requires careful attention to sample preparation, and 3) low sensitivity to certain minerals (especially many clays) due to poor crystallinity and to particle orientation effects. Many laboratories analyze a separate concentrated clay... 

Phase information was obtained by combining an X-ray structure of the major capsid protein with a cryo-EM reconstruction of the virus. The position and orientation of this model were refined against the experimental data, separately for the two crystal forms, using XPLOR3.1 (Brunger, 1992). An initial estimate of the particle orientation was obtained from a self-rotation fimction. Patterson correlation refinement was performed against 60-15 A resolution data to optimize the orientation. The position and orientation of the particle were then... 

Unlike the sphericity, can be determined from microscopic or photographic observation. Use of is only justified on empirical grounds, but it has the potential advantage of allowing correlation of the dependence of flow behavior on particle orientation. For an axisymmetric particle projected parallel to its axis, is unity. 

For a dilute suspension of identical particles oriented randomly, the mean resistance follows from Eq. (4-6) ... 

Up to this point we have considered only a single ellipsoidal particle oriented so that the electric field of the incident wave is parallel to one of its... 

The presence of fillers in viscous polymer melts not only increases their viscosity but also infiuences their shear rate dependency, especially with non-spherical particles (fibrous or fiake-like) which become oriented in the fiow field. As Fig. 6 shows, particle orientation increases the non-Newtonian behaviour which commences at a lower rate of shear than for unfilled melt. 

In more recent work, talc-filled polystyrene compounds, with various filler volume fractions, have been processed by compression moulding and through a variety of slit, capillary, rectangular and annular dies [37]. Particle orientation has been characterised using wide angle X-ray diffraction, then expressed in the form of pole figures, and by scanning electron microscopy. It was concluded that... 

A more particle-oriented consideration of light shows that light is quantized and is emitted, transmitted, and absorbed in discrete units, so-called photons or quanta. The energy E of a photon or quantum (the unit of light on a molecular level) is given by ... 

The basic structural features of MCM-36 inferred from its X-ray powder pattern are confirmed directly by TEM. The image of a particle oriented with sheets perpendicular to the plane of viewing [see reference 6] shows MCM-22 layers (25 A thick, with a streak of pores possibly forming a continuous line in the middle) spaced at -25 A intervals. The presence of props ( pillars ) keeping the layers apart is not observed directly probably due to insufficient contrast and/or ordering. 

While all vibrational transitions arg allowed by Eq. (1), the intensity of a mode is governed by the (Q c.j term which expresses the component of the neutron momentum transfer along the direction of the atomic displacements. To an extent, this feature can be exploited with substrates such as Grafoil which have some preferred orientation. By aligning Q parallel or perpendicular to the predominant basal plane surfaces, the intensity of the "inplane" and "out-of-plane" modes, respectively, can be enhanced. In practice, while this procedure can be useful in identifying modes (9), the comparison with calculated intensities can be complicated by uncertainties in the particle-orientation distribution function. In this respect, randomly oriented substrates are to be preferred (10). 

Figure 2. Inelastic neutron spectra from 36Ar monolayers adsorbed on Graf oil at 5 K (9). Curves plotted immediately below data are computed spectra for two different particle-orientation distribution functions (a) in-plane configuration with momentum transfer Q parallel to the preferred orientation of the graphite basal planes (b) out-of-plane configuration with Q perpendicular to the preferred basal planes. Curves at the bottom represent the calculated contribution to the observed spectra caused by in-plane scattering from misoriented crystallites.

---