Rods, scattering from

D Streak Analysis. The rod scattering from the equatorial streak, Ir (s), is extracted from the scattering pattern [200] and projected... 

Zhou, W., Islam, M.F., Wang, H., Ho, D.L., Yodh, A.G., Winey, K.I., and Fischer, J.E. (2004) Small angle neutron scattering from single-wall carbon nanotube suspensions Evidence for isolated rigid rods and rod networks. Chem. Phys. Lett. 384, 185-189. 

For a viscoelastic material both K and G are complex quantities. When the material sample has finite dimensions other modes of wave propagation may occur as a result of multiple scattering from the material boundaries. Mode conversion from longitudinal wave to shear wave, and vice versa, occurs on reflection at a solid boundary. For material samples in the form of thin rods or plates the modes of wave propagation are extenional waves (with speed determined by the Young s modulus, or the plate modulus), and flexural (bending) waves [8]. 

However, the SALS pattern (Figure 10) of a film sheared at 270 °C between microscope slides resembles a streak. The direction of the streak Is perpendicular to the shear direction. This result Is consistent with Rhodes and Stein s (42) expression for scattering from an assemblage of highly ordered rods. An optical micrograph... 

The intensity variation along the rod (i.e. as a function of or /) is solely contained in the structure factor it is thus related to the z-co-ordinates of the atoms within the unit-cell of this quasi-two dimensional crystal. In general, the rod modulation period gives the thickness of the distorted layer and the modulation amplitude is related to the magnitude of the normal atomic displacements. This is the case of a reconstructed surface, for which rods are found for fractional order values of h and k, i.e. outside scattering from the bulk. 

Angular dependence of light scattered from concentrated solutions of the bovine enzyme is characteristic of scattering from a rod-shaped polymer (58,102). Studies of the small-angle X-ray diffraction (106) and viscosity (107) of enzyme solutions as a function of protein concentration have also shown that the enzyme aggregates to form linear polymers. 

In this section some general considerations about S(q, t) are given, then in Sections 8.7 and 8.8 dynamic models for scattering from rigid rods and Gaussian coils are discussed. 

Relative integrated intensities of light scattered from optically isotropic rigid rods. S is the total relative integrated intensity, So the intensity of the pure translational part, Si the first non-zero term whose spectral width contains the rotational diffusion coefficient, and Si, the sum of intensities of all other terms. 

A detailed experimental study of the isotropic component of light scattered from dilute solutions of tobacco mosaic virus (a rod-like molecule with L = 3000 A and cross section diameter = 180 A) has been perfomed by Cummins et al. (1969) using spectrum analysis techniques. These authors found that the measured spectrum fit the theory described above rather well. Wada et al. (1971) repeated these experiments using an autocorrelator with similar results. 

In Section 8.7 a calculation was presented for a very stiff rod-like molecule. Although this model is adequate to describe light scattering from many real systems, most molecules have some degree of flexibility. When the intramolecular motions have large configurational changes associated with them, relaxation times for these motions will be... 

Maeda and Saito (1973) have calculated the spectrum of light scattered from optically anisotropic rigid rods whose length is >q J. This calculation is even more complex than that for the integrated intensity (zero-time scattered-field correlation function) for the same model given in Appendix 8.B, and will, therefore, not be given here. The interested reader should consult the article by Maeda and Saito. 

Substituting Eq. (8.B.4) into Eqs. (8.9.5) and (8.9.6) and using the result obtained in Section 8.2 for the scattering from optically isotropic rigid rods, we obtain... 

In Section 5.2.2 it was shown that at large q the intensity I(q) of scattering from a sphere decays as q A, from a thin disk as q 2, and from a thin rod as q l. The power-law exponent at large q is therefore seen to be related to the dimensionality of the scattering object. There are, however, many cases in which the intensity varies as an unexpected or even fractional power of q. In the case of a Gaussian model of a polymer chain, the intensity was seen to decrease as q 2 even though a chain obviously is a three-dimensional object. The inverse power-law exponents that differ from 1, 2, or 4 can be explained in terms of the concept of a fractal. 

We have calculated the scattering from an object of known shape like a sphere for which measurements of the angular dependence of intensity permits a determination of its radius. Similar calculations are possible for other shapes like rods or ellipsoids leading to measures of their size. For a polymer coil, the shape and size is not fixed, so a statistical description is necessary. In addition, chain branching will affect the shape and size of the polymer coil. 

The X-ray scattering from dilute systems of particles follows the discussion in Section 3.3.2. For spherical particles or rods, eqns. (40) and (45) of that section apply. A general form has been obtained by expanding the (sin hr/hr) term of eqn. (66) of Section 3.3.2 in a power series to give... 

The theory of the scattering from rods has been generalised to include the case of anisotropic rods by Rhodes and Stein who give, for example, for the Hy scattering intensity from a thin rod of length L lying in a plane perpendicular to the incident beam and tilted at an angle a with respect to the vertical direction (Fig. 45) ... 

Rod scattering patterns differ from spherulitic patterns in that the scattering is a maximum at 0 = 0 and decreases with increasing scattering angle. Hence, the size of the rod cannot be simply obtained from the position of a scattering maximum as in the case of spherulitic scattering, but must be determined from a quantitative measure of the rate of fall-off of intensity with 0. 

Recent discussion and application of rod scattering theory to the scattering from hydroxypropyl cellulose has been given by Samuels and from collagen by Chang and Chien and Wilkes. ... 

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