Anisotropic particle

Quite specific effects in the flow of dispersions of long fibers are connected with particles orientation in the flow. Indeed, the state of fibers during the flow changes greatly as compared the initial state, so that the material in a steady-state flow is an anisotropic medium. Therefore the viscosity of such a suspension may become independent of a fiber s length [30], The most strong effects caused by a deformation of anisotropic particles should be expected in transient flows, in particular if the particles themselves are flexible and deformed in the flow. 

This is obvious for the simplest case of nondeformable anisotropic particles. Even if such particles do not change the form, i.e. they are rigid, a new in principle effect in comparison to spherical particles, is their turn upon the flow of dispersion. For suspensions of anisodiametrical particles we can introduce a new characteristic time parameter Dr-1, equal to an inverse value of the coefficient of rotational diffusion and, correspondingly, a dimensionless parameter C = yDr 1. The value of Dr is expressed via the ratio of semiaxes of ellipsoid to the viscosity of a dispersion medium. 

Anisotropic Particle Scattering Varying Intensity Decay in Different Directions. In case of anisotropy the decay of the scattering intensity 7 (s) is a function of the direction chosen. The intensity extending from s = 0 outward in a deliberately chosen direction i is mathematically the deAnition of a slice (cf. Sect. 2.7.1, p. 22). Thus, the Fourier-Slice theorem, Eq. (2.38), turns the particle density function Ap (r) into a projection Ap (r) j (r,) and the scattering intensity is related to structure by... 

The surface area ranges from 360 m2/g for the lower pH hydrothermal synthesis to 200 m2/g for the sample prepared at pH of 5.6. The pH also influences the lengths of the crystal-stacking domain along the long and short axes of the anisotropic particles. 

We have discussed intrinsically anisotropic particles—ones with anisotropy originating in their optical constants rather than their shape—in previous chapters. In Section 5.6 we gave the solution to the problem of scattering by an anisotropic sphere in the Rayleigh approximation. From the results of that section and Section 5.5 it follows that the average cross section (C) (scattering or absorption) of a collection of randomly oriented, sufficiently small, anisotropic spheres is... 

A special anisotropic particle scattering problem has been treated by Roth and Dignam (1973), who considered an isotropic sphere coated with a uniform film with constitutive relations... 

Turner, L., 1973. Raylcigh-Gans-Born light scattering by ensembles of randomly oriented anisotropic particles, Appl. Opt., 12, 1085-1090. 

In semi-crystalline polymers the interaction of the matrix and the tiller changes both the structure and the crystallinity of the interphase. The changes induced by the interaction in bulk properties are reflected by increased nucleation or by the formation of a transcrystalline layer on the surface of anisotropic particles [48]. The structure of the interphase, however, differs drastically from that of the matrix polymer [49,50]. Because of the preferred adsorption of large molecules, the dimensions of crystalline units can change, and usually decrease. Preferential adsorption of large molecules has also been proved by GPC measurements after separation of adsorbed and non-attached molecules of the matrix [49,50]. Decreased mobility of the chains affects also the kinetics of crystallization. Kinetic hindrance leads to the development of small, imperfect crystallites, forming a crystalline phase of low heat of fusion [51]. 

Anisotropic particles align with the flow streamlines to reduce their hydrodynamic cross-section. 

When instead assemblies of helices are taken into account, it is well known that for many aspects DNA duplexes in solution can be treated as a charged anisotropic particle [2]. Accordingly, steric, electrostatic, and Van der Waals interactions, together with the mechanical properties of the helix (bending and torsional rigidity), play a major role in the formation of DNA mesophases. In addition, all these different kinds of interactions combine in a subtle and still poorly understood way to generate other forces relevant for the case of DNA. A notable example is the helix-specific, chiral interaction, whose importance for DNA assemblies will be discussed below. 

Compared to the colligative methods light scattering can yield information on a possible dissymmetry of the aggregates. For anisotropic particles the direction of the electric field associated with the incident light may not coincide with the shift of the electron cloud. The intensity of light scattered at (usually) 90° from anisotropic aggregates is increased over the value predicted on the basis of isotropy by the Cabannes factor. 

Diblock copolymers of NIPA and EO showed somewhat different behavior [45]. The copolymers were synthesized using NIPA monomer and PEO-containing macroinitiator. The copolymers aggregated at high temperature with no collapse of individual macromolecules. The essential feature of the polymers in question consisted in the strong sensitivity of the shape of the particles to the polymer concentration and to the molar ratio of EO to NIPA monomer units. At low polymer concentration, the shape of the aggregates was mainly spherical, as indicated by the low Rg/Rh values (Fig. 12). The Rg/Rh ratio is informative of the shape of particles in solution. Anisotropic particles, such as rods and coils, possess high values of the ratio, while for particles of spheroid form, low values of the ratio are observed (for spher-... 

In the limit of dipole scattering, the zero-angle scattering Jones matrix for a system of anisotropic particles is simply found by extending equation (4.66) to the case were the polarizability is a tensor. In this case,... 

From these expressions, the birefringence from the scattering of oriented, anisotropic particles can be calculated. The dichroism can also be calculated, but in this limit, it is only present if the polarizability has an imaginary component. In other words, only absorbing particles are predicted to be dichroic. 

Thermofluctuational behavior of the magnetic moment in a magnetically anisotropic particle acquires new features in comparison with the isotropic case and, accordingly, extends the set of relaxation times. Let us consider a single-domain particle with the easy-axis anisotropy defined by... 

In our model with the aid of parameter e we continuously pass from a zero bistable potential (magnetically isotropic particle) to a pair of symmetric wells of infinite depth (highly anisotropic particle). For the magnetic case, as for those of Refs. 21 and 22, a crucial circumstance enabling the harmonic suppression is that an antisymmetric contribution (bias) should be present in the potential. On the other hand, the presence of a symmetric contribution turns out to be an... 

In a system of nanoparticles, thermal fluctuations of their magnetic moments severely reduce the anisotropy of the resonance magnetic field, resulting in superparamagnetic spectra narrowing. This reduction is the more pronounced the smaller is the particle size. Therefore, the SPR spectra of macroscopically isotropic nanoparticle systems characterised by a distribution in size usually maintain a distinct shape asymmetry characteristic of powder patterns of randomly oriented anisotropic particles. From an inspection of such spectra, one can conclude that the angular dependence of the resonance magnetic field of individual particles is not completely reduced. 

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