Particle isotropic shape

The polarizability of cylindrically symmetric particles (rod-shaped or ellipsoidal particles) can be characterized by isotropic (a) and anisotropic (P) parts of the polarizability tensors ... 

Depolarized Scattering and Rotational Diffusion Most flexible and semiflexible polymers are isotropic and hence do not depolarize incident polarized light. For particles with shape anisotropy there will be a tensor polarizability and the scattered fight will have depolarized components. Depolarized scattering principles and nomenclature are covered in Sections 8.1,8.2.4, and 8.4. 

Figure 4.6 Change in POM images across the transition from well-oriented hex to bcc that was then followed by the reverse transition from bcc to hex. Since cylindrical particles exhibit form birefringence, the prominent POM image is ascribed to a grain structure of oriented cylinders spreading from 10 pm to 0.3 mm. Note here that spherical microdomains have no form birefringence due to their isotropic shape. (Reproduced from K. Kimishima el al. (2000) Macromolecules 33 968-977, Copyright (2000) with permission from the American Chemical Society.)...

This species has been used as precursor of nanogold particles by electrodeposition. When the electrodeposition is induced from the isotropic state at 117 °C, the nanoparticles obtained are nanodots aggregated in a spherical-like shape. In contrast, the morphology of the nano particles prepared from the SmA mesophase at 111 °C consist of leaf-like forms interlocked in rosettes. 

If mixtures and assemblies of different kinds of particles are studied, a shape reconstruction is no longer possible from a study of isotropic SAXS in solution [188],... 

For a cube of side /, Eq. (4-50) gives the resistance as 12.70/, compared with experimental values of 12.58/ (P6), 12.63/ (H4), and 12.71/ (Cl). To the accuracy of the determinations, the resistance can be taken as 4ti / (DI). It is noteworthy that Eqs. (4-26) and (4-27) predict that a spherically isotropic cylinder with aspect ratio 0.812 should have a drag ratio of 1.050, while Eq. (4-50) gives Ag = 1.054. Agreement is so favorable that Eq. (4-50) may be useful for spherically isotropic particles other than the simple shapes for which it was developed. 

Further experimental evidence of shape effects in absorption spectra of SiC particles is found in the data of Pultz and Herd (1966), who investigated infrared absorption by SiC fibers with and without Si02 coatings. Although these measurements were not mass-normalized, they show a strong absorption band at 795 cm-1 and a weaker band at 941 cm-1. If the fibers are approximated as ellipsoids with L2 = L3 = and Lx = 0 (i.e., a cylinder), then the ellipsoid equation (12.27) predicts absorption peaks for particles in air at frequencies where c = -1 and c = — oo. This corresponds to absorption bands at 797 and 945 cm-1 for the dielectric function of isotropic SiC, in excellent agreement with the experimental peak positions for the fibers. 

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