Elongated particles

Otlier possibilities for observing phase transitions are offered by suspensions of non-spherical particles. Such systems can display liquid crystalline phases, in addition to tire isotropic liquid and crystalline phases (see also section C2.2). First, we consider rod-like particles (see [114, 115], and references tlierein). As shown by Onsager [116, 117], sufficiently elongated particles will display a nematic phase, in which tire particles have a tendency to align parallel to... 

Particle Shape. Whereas the Stokes particle is assumed to be a sphere, very few real soHds are actually spherical. Flat and elongated particles sediment slower than spheres. For maximum sedimentation rate, the particle should be as spherical as possible. 

Equation (1) points to a number of important particle properties. Clearly the particle diameter, by any definition, plays a role in the behavior of the particle. Two other particle properties, density and shape, are of significance. The shape becomes important if particles deviate significantly from sphericity. The majority of pharmaceutical aerosol particles exhibit a high level of rotational symmetry and consequently do not deviate substantially from spherical behavior. The notable exception is that of elongated particles, fibers, or needles, which exhibit shape factors, kp, substantially greater than 1. Density will frequently deviate from unity and must be considered in comparing aerodynamic and equivalent volume diameters. 

Fig. 5.22 (A-D) Scheme of Au nanoparticle growth between bilayers (A) nucleation at bilayer interfaces and bulk-like growth when particle size is smaller than the lamellar d spacing (B) once the transversal particle size is larger than the d spacing, growth is slowed by the bilayers, the transversal Au3+flux being limited, leadingto elongated particles shapes (C) when the constraint exerted by the particles on the bilayers is...

According to gel-filtration experiments conducted by P. Wills and J. Dijk (personal communication), proteins L17, L25, L28, L29, and L30 are compact LI, L4, L5, L6, L13, L16, L19, and L24 are moderately elongated and L2, L3, L9, Lll, L15, L23, L27, L32, and L33 are quite extended. A discrepancy between these results and those mentioned earlier is protein L9 which appears to be globular from hydrodynamic measurements (Giri et al., 1979), but the Stokes radius calculated from gel-filtration experiments was found to be quite large, suggesting an elongated particle. 

A good design for a hard magnetic material is to have small, elongated particles. 

A few particles, such as spores, seem to be rather well approximated by spheroids, and there are many examples of elongated particles which may fairly well be described as infinite cylinders. Our next step toward understanding extinction by nonspherical particles is to consider calculations for these two shapes. To a limited extent this has already been done spheroids small compared with the wavelength in Chapter 5 and normally illuminated cylinders in Chapter 8. We remove these restrictions in this section measurements are presented in the following section. Because calculations for these shapes are more difficult than for spheres, we shall rely heavily on those of others. 

Extinction is easy to measure in principle but may be difficult in practice, especially for large particles where it becomes difficult to discriminate between incident and forward-scattered light. Spheres and ensembles of randomly oriented particles do not linearly polarize unpolarized light upon transmission. But single elongated particles or oriented ensembles of such particles can polarize unpolarized light by differential extinction. 

This critical field called coercivity ff. or switching field Ff., is also equal to FF. If a field is applied in between 0 and 90° the coercivity varies from maximum to zero. In the case of this special example the applied field Ha = Hs = Hc = Hk. Based on the classical theory, Stoner-Wohlfarth (33) considered the rotation unison for noninteracted, randomly oriented, elongated particles. The anisotropic axis can be due to the shape anisotropy (depending on the size and shape of the particle) or to the crystalline anisotropy. In the prolate ellipsoids b is the short axis and a the longest axis. The demagnetizing factors are IV (in the easy direction) and The demagnetizing fields can then be calculated by Hda = — Na Ms, and Hdb = — Nb Ms. The shape anisotropy field is Hd = (Na — Nb)Ms. Then the switching field Hs = Hd = (Na — Nb)Ms. 

---