Nonspherical particles crystallization

However, despite this progress, it is highly recommended that both PCS and LD be used simultaneously. It should be kept in mind that both methods are not measuring particle sizes. Rather, they detect light-scattering effects that are used to calculate particle size. For example, uncertainties may result from nonspherical particle shapes and from the assumption of certain parameters that are used to calculate the particle size. Platelet structures commonly occur during lipid crystallization [57] and have also been observed for SLN [11,40,58], The presence of several populations and other colloidal structures adds further difficulties. 

Obscuration is the fraction of light that is obscured by the crystals in a flow cell thus, obscuration is defined as 1 - I/Io where I is the intensity of undiffracted light that passes through the suspension of crystals and 7o is the intensity of the incident light. The obscuration can be accurately measured, and the Beer-Lambert law provides a means by which it can be modelled for comparison with experimental data. As discussed by Witkowski et al. (1990), the obscuration provides a measure of the second moment of the CSD. Preliminary experimental tests indicate that the theorem discussed above relating geometrical cross section to surface area may be helpful in extending the use of obscuration measurement to cases with nonspherical particles. 

In principle, some types of nonspherical particles could be packed more tightly than spheres, although they would start to interact at lower concentrations. In reality, higher viscosities are normally found with nonspherical particles. The concentration law is approximately exponential at low to moderate concentrations, but equations similar to eq. 10.5.1 can still be used as well. The empirical value of 4>m can be much smaller than that for spherical particles (e.g., 0.44 for rough crystals with aspect ratios close to unity Kitano et al., 1981). If fibers are used, this value drops even further, down to 0.18 for an aspect ratio of 27 (see also Metzner, 1985). The decrease with aspect ratio seems to be roughly linear. Homogeneous suspensions of fibers with large aspect ratios are difficult to prepare and handle. As in dilute systems, the type of flow will determine the extent of the shape effect. Extensional flows are discussed below. 

Any study of colloidal crystals requires the preparation of monodisperse colloidal particles that are uniform in size, shape, composition, and surface properties. Monodisperse spherical colloids of various sizes, composition, and surface properties have been prepared via numerous synthetic strategies [67]. However, the direct preparation of crystal phases from spherical particles usually leads to a rather limited set of close-packed structures (hexagonal close packed, face-centered cubic, or body-centered cubic structures). Relatively few studies exist on the preparation of monodisperse nonspherical colloids. In general, direct synthetic methods are restricted to particles with simple shapes such as rods, spheroids, or plates [68]. An alternative route for the preparation of uniform particles with a more complex structure might consist of the formation of discrete uniform aggregates of self-organized spherical particles. The use of colloidal clusters with a given number of particles, with controlled shape and dimension, could lead to colloidal crystals with unusual symmetries [69]. 

Particle shape. Most solid particles tend to be nonspherical, which means that their curvature varies along the surface. This is especially obvious for crystals, where most of the surface is flat while the curvature is very high where two crystal faces meet. This then means that the solubility of the material also varies, and this readily causes local dissolution of material, which is likely to become deposited at sites of small curvature. Table 10.4 shows that for a sucrose crystal a considerable solubility ratio (1.09) is found for r = 10 nm. However, where crystal faces meet, the shape would be cylindrical rather than spherical, leading to a solubility ratio of about 1.045. This is certainly sufficient to cause a crystal edge to become rounded in a saturated solution, and if the crystals are very small, they would likely be almost spherical. Indeed, microscopic evidence shows that many crystals of pm size are roughly spherical and that larger crystals often show rounded edges. 

Polar stratospheric clouds have been classified into two broad types, so-called Type I and Type II (Table 4.1). Type I PSCs have been further subdivided into Type la and Type Ib. Type la PSCs have traditionally been identified as crystals of nitric acid trihydrate, HNO, 3 H2O, denoted NAT, that form once temperatures fall below about 195 K. Type lb PSCs consist of supercooled ternary solutions of HNO3/H2SO4/H2O, also forming at about the same temperature threshold. Type II PSCs are largely frozen water ice, nonspherical crystalline particles, that form at temperatures below the ice frost point. The ice frost point, for example, at 3 X 10 Torr H O is 191 K. Despite the above classification, the composition of PSCs is still uncertain (Toon and Tolbert, 1995). 

Alternatively, nonspherical potentials have also been used, where active spots are located on the particle surface [27], or many body interactions, such as a maximum number of neighbors attracted [28], or combination of both [29], Using these structural or energetic constraints, the formation of a dense phase is hindered, thus impeding crystallization and liquid-liquid crystallization. 

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