Optically active particles

Turner (1973) and McKellar (1976) applied RG theory to ensembles of randomly oriented particles of arbitrary shape the former author included spheres with anisotropic optical constants. Optically active particles have been treated within the framework of the RG approximation by Bohren (1977). 

In this chapter we consider theories of scattering by particles that are either inhomogeneous, anisotropic, or nonspherical. No attempt will be made to be comprehensive our choice of examples is guided solely by personal taste. First we consider a special example of inhomogeneity, a layered sphere. Then we briefly discuss anisotropic spheres, including an exactly soluble problem. Isotropic optically active particles, ones with mirror asymmetry, are then considered. Cylindrical particles are not uncommon in nature—spider webs, viruses, various fibers—and we therefore devote considerable space to scattering by a right circular cylinder. 

In problems involving optically active particles it is usually more convenient to use the amplitude scattering matrix in the circular polarization representation. The transformation from linearly to circularly polarized electric field components is... 

The cross sections for extinction and scattering by an optically active particle are different for incident left-circularly and right-circularly polarized light. For an optically active sphere, the cross sections can be obtained in a manner similar to that for a nonactive sphere (Section 4.4). Therefore, we give only the results and omit the details ... 

It is the off-diagonal elements of (13.7) that give rise to cross polarization (S, = = S22) as well as the nonzero elements S13, S14, S23, and S24 in (13.8). That S3 and S4 should be nonzero for optically active particles follows from elementary physical reasoning optical rotatory power in a homogeneous medium causes the direction of vibration to be rotated upon transmission of linearly polarized light by the medium. However, optical activity of the bulk... 

Bohren, C. F., 1977. Circular dichroism and optical rotatory dispersion spectra of arbitrarily shaped optically active particles, J. Theor. Biol., 65, 755-767. 

This work demonstrated (a) that there are distortions in the CD of particulate systems (this had not previously been appreciated and the distorted spectra had been interpreted in terms of unique conformational features), (b) that the distorted spectra can be calculated and hence corrected, and (c) that there is a measurable differential scatter of left and right circularly polarized light by optically active particles. Thus, in addition to correcting spectra for suspensions of particulate systems that may be interpreted in terms of biomolecular conformation, the third point makes it possible to obtain an optical rotatory dispersion spectrum for the particle surface. In the case of membranes this will allow determination of relative amounts of surface area which are covered by ordered protein. This information coupled with the CD spectrum for the whole membrane will provide considerable information on the structure of membranes. 

Mutual interactions of the nonlinear optically active particles modify the local fields (Ye and Shen 1983). 

The second system studied was the separation of the chiral epoxide enantiomers (la,2,7,7a-tetrahydro-3-methoxynaphth-(2,3b)-oxirane Sandoz Pharma) used as an intermediate in the enantioselective synthesis of optically active drugs. The SMB has been used to carry out this chiral separation [27, 34, 35]. The separation can be performed using microcrystalline cellulose triacetate as stationary phase with an average particle diameter greater than 45 )tm. The eluent used was pure methanol. A... 

Molecular structure and weight Melting point Thermal profile Particle size and shape Hygroscopicity potential Ionization constant Light stability Optical activity pH solubility profile pH stability profile Polymorphism potential Solvate formation... 

Similar downward trends in PMI() have been observed at surface measuring sites in the United States in urban, suburban, and rural areas. Figure 16.44, for example, shows the trends in the annual average PMI() levels in these three types of air environments (Darlington et al., 1997). Reductions of 3-4% per year have been observed. Simultaneously, the annual average gas-phase concentrations of S02 and NOx, precursors to sulfate and nitrate in particles, decreased. Downward trends of —1.6—1-8% per year in the optically active aerosol over the United States has also been reported (e.g., Hofmann, 1993). 

In most experiments and observations we are confronted with a collection of very many particles unless special pains are taken to align the particles, or in the absence of a known alignment mechanism, we may reasonably assume that they are randomly oriented. Under these conditions the quantities of interest are the average cross sections (Cabs) and (Csca), which are independent of the polarization of the incident light provided that the particles are not intrinsically optically active. Let p(Cl) dti be the probability that one of the axes fixed relative to a particle, the x axis, say, lies within a solid angle dSl around the... 

This relation is not restricted to a specific particle for an optically active sphere, however, two of the matrix elements are equal S3c = S4c. 

The maximum amount of information about scattering by any particle or collection of particles is contained in all the elements of the 4x4 scattering matrix (3.16), which will be treated in more generality later in this chapter. Most measurements and calculations, however, are restricted to unpolarized or linearly polarized light incident on a collection of randomly oriented particles with an internal plane of symmetry (no optical activity, for example). In such instances, the relevant matrix elements are those in the upper left-hand 2x2 block of the scattering matrix, which has the symmetry shown below (see, e.g.,... 

This is the form of the scattering matrix for any medium with rotational symmetry even if all the particles are not identical in shape and composition. A collection of optically active spheres is perhaps the simplest example of a particulate medium which is symmetric under all rotations but not under reflection. Mirror asymmetry in a collection of randomly oriented particles can arise either from the shape of the particles (corkscrews, for example) or from optical activity (circular birefringence and circular dichroism). 

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