Rod-shaped particles

Since the Stokes diameter for the rod-shaped particle will obviously differ from the rod diameter, this difference represents added information concerning particle shape. The ratio or the diameters measured by two different techniques is called a shape factor. 

The lowermost curve in Fig. 45 represents P(0) plotted against according to Eq. (31) for random coil molecules. The results of similar calculations for spherical and for rod-shaped particles of uniform density are shown also. The curve for the former of these is not very different from that for randomly coiled polymers at corresponding values of the abscissas the factor P(0) for rods differs appreciably, however. 

Fig. 3.12 Model of an agglomerate consisting of many small interstellar dust particles. Each of the rod-shaped particles consists of a silicate nucleus surrounded by yellowish organic material. A further coating consists of ice formed from condensed gases, such as water, ammonia, methanol, carbon dioxide and carbon monoxide. Photograph Gisela Kruger, University of Bremen...

Table 6.2 Theoretical multiplication factors for anisometric particles with an aspect ratio r 1. (Note For a disc-shaped particle the aspect ratio is the ratio of disc diameter disk thickness and for a rod-shaped particle it is the ratio of rod length rod diameter). (Source R. Bown, Physical and Chemical Aspects of the Use of Fillers in Paper , in Paper Chemistry , ed. J.C. Roberts, Blackie, Glasgow, 1992, pp. 162-196).

The ratio (a/b), called the axial ratio of the ellipsoid, is frequently used as a measure of the deviation from sphericity of a particle. It plays an important role, for example, in our discussions of sedimentation and viscosity in Chapters 2 and 4, respectively. In the event that a > b, the prolate ellipsoid approximates a cylinder and, as such, is often used to describe rod-shaped particles such as the tobacco mosaic virus particles shown in Figure 1.12a. Likewise, if a < b, the oblate ellipsoid approaches the shape of a disk. Thus, even the irregular clay platelets of Figure 1.12b may be approximated as oblate ellipsoids. 

In brief, the extrusion process involved emulsification of orange peel oil into a melt of the ingredients described above. The molten products were then extruded under pressure through a die template into a chilled isopropyl alcohol bath. Subsequently, the products were broken into small, rod-shaped particles and dried to remove the alcohol. 

Figure 7-8 (A) Electron micrograph of the rod-shaped particles of tobacco mosaic virus. Omikron, Photo Researchers. See also Butler and Klug.42 (B) A stereoscopic computer graphics image of a segment of the 300 nm long tobacco mosaic virus. The diameter of the rod is 18 nm, the pitch of the helix is 2.3 nm, and there are 16 1 3 subunits per turn. The coat is formed from 2140 identical 17.5-kDa subunits. The 6395-nucleotide genomic RNA is represented by the dark chain exposed at the top of the segment. The resolution is 0.4 nm. From Namba, Caspar, and Stubbs.47 (C) A MolScript ribbon drawing of two stacked subunits. From Wang and Stubbs.46...

Rigid rodcrystallisation, 706 Rod climbing effect, 526 Rod-like molecules, 252 Rod-like polymer molecules, 274 Rod-shaped particle, 276 Rubber elasticity, 401 Rubbery plateau, 400 Rudin equations, 272 Rudin-Strathdee equation, 602 Rules of thumb for substituting an H-atom by a group X, 182... 

Generally commercial products are used as test samples. If a product is composed of rod-shaped particle, it can not be put into a steel tube it must be divided into smaller pieces. 

Consider for a moment a rod-shaped particle of unit length. The orientation of the rod, u, can be specified by a unit vector u directed along its axis with spherical polar coordinates, D - id, random walk along the surface of the unit sphere. Debye [16] in 1929 developed a model for the reorientation process based on the assumption that collisions are so fiiequent that a particle can rotate throu only a very small angle before having another reorienting collision (i.e., small step diffusion). Debye began with the diffusion equation... 

If the particle-size distribution of a powder composed of hard, smooth s eres is measured by any of the techniques, the measured values should be identical. However, there are many different size distributions that can be defined for any powder made up of nonspheri-cal particles. For example, if a rod-shaped particle is placed on a sieve, its diameter, not its length, determines the size of aperture through which it will pass. If, however, the particle is allowed to settle in a viscous fluid, the calculated diameter of a sphere of the same substance that would have the same falling speed in the same fluid (i.e., the Stokes diameter) is taken as the appropriate size parameter of the particle. 

There are two major theoretical approaches to the understanding of orientational ordering of extended chain polymers one is a model wherein rod-shaped particles are confined to a lattice under the restriction that segments may not overlap with one another the other utilizes a virial expansion that accounts for mutual orientational correlations and interactions of pairs, triplets, etc. of elongated particles at varied concentrations. 

The response therefore, is not proportional to the volume of the particle, but is modified by the a/A term. For rod-shaped particles whose length is smaller than the aperture length, this leads to an oversizing of about 6% in... 

Figure 7-8 (A) Electron micrograph of the rod-shaped particles of tobacco mosaic virus. Omikron, Photo Researchers. See also Butler and Klug. ...

Victorian coals contain significant quantities of cylindrical rod-shaped particles, 1 xm in diameter and 6-8 xm long, which are high in carbon and hydrogen. 

These phenomena can be interpreted in terms of molecular orientation by the velocity gradient in the flowing liquid, opposed by the rotary Brownian movement which produces disorientation and a tendency toward a purely random distribution. The intensity of this Brownian movement is charaterized by the rotary diffusion constants, 0, discussed in the preceding section. The fundamental treatment of this problem, for very thin rod-shaped particles, was given by Boeder (5) the treatment has been generalized, and extended to rigid ellipsoids of revolution of any axial ratio, by Peterlin and STUARTi 56), [98), (99) and by Snell-MAN and Bj5knstAhl (J9J). The main features of their treatment are as follows 1 ... 

Figure 1. SEM micrographs of the pure oriented M0O3 (left) having undergone the "mechanical mixture procedure, and the mechanical mixture of tne two - BiP04 corresponds to the small white rod-shaped particles (right).

Samples of each formation were etched briefly in weak HCl and examined with the scanning electron microscope (SEM). Rod-shaped particles of possible nannobacteria (see Folk, 1993) or biofilms of microbially formed polymers (see Westall Rince, 1994) occur entombed in calcite cement in both Pliocene units and in the upper part of the Mamoso-arenacea Formation. The role played by microbes is uncertain, but the possibility of microbially mediated precipitation of calcite must be considered even at the depths at which these rocks were cemented (Folk, 1993). 

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