Scattering curve hollow sphere

The scattering curve of a sphere descends into a series of minima md maxima as Q increasp- i, with the first minimum at QR = 4.493. Thus the Aq of the sphere can be calculated from the minima as a verification of the Guinier analysis. The curves for full and hollow spheres are very similar at low Q. The intensities of the subsidiary... 

Fig. 7. Scattering curves from models of uniform scattering density, (a) A sphere of radius 6.5 nm and Rq 5.0 nm as used in Fig. 4. (b) A hollow sphere with an outer radius of 6.5 nm as in (a) and a ratio of inner/outer radii of 0.5. (c) A straight, cylindrical rod of length 59 nm and diameter 3.4 nm. (d) The cylindrical rod as in (c) is now bent into a circle of radius 9.4 nm.

This expression is an adaptation of the I(Q) calculation for a sphere and the required integration can be performed numerically. Particles that do not have spherical or near-spherical symmetry do not exhibit the minima and maxima noted above, and the scattering curve I(Q) declines more uniformly as Q increases. Other analytical expressions exist for the calculation of I(Q) for ellipsoids, prisms and cylinders and their hollow equivalents [55]. It should be noted, however, that I(Q) for ellipsoids, prisms and cylinders do not differ greatly. For simple models, a first indication of the macromolecular shape in terms of a triaxial body can be extracted by curve-fitting of the calculated scattering to the experimental curve at low Q. 

To a first approximation, the sizes of isometric viruses can be estimated by comparing the experimental maxima and minima with the theoretical curves calculated for spheres and hollow spheres [492-494,504]. However, viruses are composed of protein shells and nucleic acid cores (with carbohydrate and lipid in more complex viral structures), so a full analysis requires the explicit consideration of non-uniform scattering densities. In addition, the principle of icosahedral symmetry in the assembly of the protein shell means that, at large Q, deviations from spherical symmetry will influence the scattering curve. The separation of the scattering curve... 

Figure 5.7. Unit volume scattering from glass beads in water at scattering angles of IS degrees (solid line with hollow spheres), 45 degrees (solid line), and 90 degrees (dots) for = 633 nm. Each curve is differently scaled.

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