Anisotropic particles analysis

In colloidal suspensions of anisotropic particles, the static structure factor plays a prominent role in particle size analysis. We have used transient electric birefringence (TEB) and electron microscopy, in addition to laser light scattering, to correlate our analysis of particle size distributions of bentonite suspensions. The complementary nature of TEB and photon correlation spectroscopy (PCS) in particle size analysis will be discussed. 

In a collection of statistically distributed, mobile dipolar species, the total field-parallel contribution to the polarization is the statistical average over the cos 5 projections on the field vector. For the sake of transparentness we shall confine the further analysis to uniaxial anisotropic particles Bj, i.e., to uniaxial dipole moments m. In this case Eqs. (3.12) and (3.16) read, respectively,... 

Depolarized dynamic light scattering is based on the analysis of time fluctuations in the scattered light intensity due to Brownian motion of optically anisotropic particles suspended in a liquid medium. ... 

As noted earlier, in the 1920s Taylor [38] experimentally verified Jeffery s [37] analysis for the motion of ellipsoids. There were subsequent studies by Taylor in the 1930s [39,40]. In the 1950s Mason and his coworkers [41 to 44] made extensive efforts to visualize anisotropic particle motions in dilute suspensions during flow of rigid rod- and disk-shaped particles. They observed a distribution of orbits. 

If particles have significant anisotropic shapes, such as rods or platelets, then LD significantly overestimates the breadth and can even give bimodal distributions for monodispersed cylinders (Gabas et al. 1994). This is because the diffraction pattern depends on the geometric shadow of the particle with respect to its orientation with the laser beam. If the anisotropic particles are randomly oriented as they go through the analysis zone, then data from all orientations are produced and only if there is a constant form factor (constant thickness for plates or constant diameter for rods) can some information be carefully extracted from LD measurements (Bowen 2002). 

The quantitative analysis of a multiphase topology comprises the formulation of structure models and the fitting of measured data. Fitting is discussed in Chap. 11. In this section the setup of topological models is discussed. The problem arises from the fact that most structural models of particle correlation are anisotropic and the visualization of structure in anisotropic materials by means of the CDF shows that suitable models must be rather complex. Thus a direct fit of anisotropic data would require fitting of a measured 3D or 2D function by a complex model. Both the effort to setup such models, and the computational effort to fit the data are very high. 

Transmission electron microscopy ( ) analysis reveals that these materials crystallize as hexagonal planar particles with marked anisotropic shape,8,37 as shown in Figure 6. When appropriate preparation methods are used, plate-like crystals are obtained with small thickness of about 20-30 nm and an aspect ratio D/h=5-10. Selected area diffraction (SAD) patterns of incident beams perpendicular and parallel to the large hexagonal facet show that they correspond to the crystallographic planes perpendicular to the c axis. The anisotropic shape of the... 

Example. A tailings stream from the hot-water flotation process (oil sands) contains 27 % (mass) solids. Estimate the suspension viscosity. Light-scattering analysis indicates that the particles are finely divided and anisotropic with a 10 Tm major dimension and a 0.5 pm minor dimension. Using Eq. 

The relationship between crystallites and particles with respect to XRD is shown in Figure 2. The morphological "crystal" "c" is composed of anisotropic crystallites with dimensions "a,b". The arrows show the difference in dimension detected by XRD (a,b in two dimensions) and by other methods not requiring coherent scattering methods such as electron microscopy or gas adsorption. It is obvious that there may be little relationship between the particle size determined by microscopy or surface area analysis and the... 

The virial expansion has enjoyed greater appeal, especially as applied to lyotropic systems. Onsager s classic theory rests on analysis of the second virial coefficient for very long rodlike particles. It was the first to show that a solution of hard, asymmetric particles such as long rods should separate into two phases above a threshold concentration that depends on the axial ratio of the particles. One of these phases should be anisotropic (nematic), the other completely isotropic. The former is predicted to be somewhat more concentrated than the latter, but it is the alignment (albeit imperfect) of the solute molecules that is the predominent distinction. The phase separation is a consequence of shape asymmetry alone intervention of intermolecular attractive forces is not required. 

In the previous sections, we discussed the influence of the number of crystals in the sample. The orientations of the crystals were assumed to be random, and obviously, this factor comes into play. Theoretically, quantitative analyses by X-ray diffraction are conducted on samples comprised of a very large number of micrometric crystals without any preferential orientation. This latter condition is sometimes difficult to meet, since it can be sometimes complicated to give the crystals in the sample a random orientation. This effect often occurs when crystals have an anisotropic shape. Clays are an extreme example of this behavior [BRI 80]. Their layered stracture naturally causes a preferential orientation along the (001) planes. Some authors pLO 55, SMI 79, HIL 99] have used atomization methods to produce polycrystalhne particles in which the clay crystals have a random orientation. Another approach consists of quantifying the preferential orientation and to take it into accoimt when calculating the proportions of the phases in the sample. We will not be giving arty details on this method, since it requires considerable skill in the production of pattern and data analysis. It is always better not to have a preferential orientation. 

K. C. Tang and M. Q. Brewster, -Distribution Analysis of Gas Radiation with Non-gray, Emitting, Absorbing, and Anisotropic Scattering Particles, in S. T. Thynell et al. (eds.), Developments in Radiative Heat Transfer, ASME-HTD-vol. 203, pp. 311-320,1992. 

The intrinsic double refraction expresses the essentially anisotropic or internally crystalloidal character of the aligned particles themselves. Since formalin-treated fibers show positive intrinsic double refraction relative to the fiber axis (curve A of Fig. 29) this is probably the normal condition. Because of colloidal variabiUty of native collagen fibers the analysis of form and intrinsic components by means of immersion methods requires prior fixation. 

A nonspherical particle is generally anisotropic with respect to its hydro-dynamic resistance that is, its resistance depends upon its orientation relative to its direction of motion through the fluid. A complete investigation of particle resistance would therefore seem to require experimental data or theoretical analysis for each of the infinitely many relative orientations possible. It turns out, however, at least at small Reynolds numbers, that particle resistance has a tensorial character and, hence, that the resistance of a solid particle of any shape can be represented for all orientations by a few tensors. And the components of these tensors can be determined from either theoretical or experimental knowledge of the resistance of the particle for a finite number of relative orientations. The tensors themselves are intrinsic geometric properties of the particle alone, depending only on its size and shape. These observations and various generalizations thereof furnish most, but not all, of the subject matter of this section. 

Analysis of the slow forward relaxation (12) reveals [63] that the associated Kerr constant follows a power law, i.e., B is proportional to the distance in temperature from Tc as (1 — Tc/Ty", with

static electrical birefringence is in accord with the droplet model [66,67] of critical binary mixtures. The central idea of the droplet model is that the electric field distorts (orients or vectorially amplifies) the spontaneous critical concentration fluctuations. The resulting anisotropic fluctuations then play the role of nonspherical particles in ordinary electrical birefringence. The magnitude of the concentration fluctuations rapidly increases as T,. is approached. 

Using a commercially available finite element analysis program, ABAQUS, models representing SiC particulates in a ZrBa matrix were created. The SiC phase was modeled as a round particle in a two dimension (2D) ZrB matrix. Material properties were assumed to be isotropic for both the ZrB and the SiC after initial modeling efforts indicated only small changes in stress fields as a result of the anisotropic properties of the a-SiC (hexagonal polytype). The material properties used in the models, as well as other key model input variables, are included as Table II. 

---