Scattering curve ellipsoid

Analysis of low angle X-ray scattering data gives a value for the radius of gyration at infinite dilution of 18.3 A (254)- The scattering curve can best be explained on the basis of a cylinder or prolate ellipsoid... 

Scattering curves for prolate and oblate ellipsoids can be calculated. For an ellipsoid of revolution of axes 2a la Iva [6] ... 

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. 

Fig. 3 Small angle neutron (squares) and X-ray (triangles) scattering curves given as I q)/cm versus The symbols correspond to the experimental data and the solid lines represent fits with a form factor model for monodisperse oblate ellipsoids...

Suau et al. studied the conformation of chromatin as a function of ionic strength and Braddock et al. fitted model calculations for the nucleosome core particle in solution to these experimental scattering curves. The best fit to the data was found for a model in which there were 1.7 0.1 turns of DNA wrapped around a hydrophobic core. Models in which this core was cylindrical or wedge-shaped were compatible with the measured scattering curves. However, spherical or ellipsoidal core models were incompatible and had to be rejected. 

It should be noted that the polydispersed spheres give similar scattering curves as those for monodispersed ellipsoids [5, 6]. So, the observed scattering curves may be explained by polydispersed spheres, although we did not... 

Thus, if the particle has no permanent dipole moment, the rise and decay signals of the birefringence are symmetrical [cf Eqs. (13) and (14)]. The rotational diffusion coefficient 9 is usually obtained directly from the decay curve, Eq. (14) and Eq. (11), together with the apparent hydrodynamic radius Vf, determined in light scattering experiments, can be used to obtain information about the size and eccentricity alb of the rotating ellipsoid. 

Fig. 20. Experimental results on 183 Mev electron scattering for several nuclei. The differential cross-section is divided by cos ( /2)/sin (d/2) in order to display the diffraction structure. The data are plotted versus. 4 sin( /2). The dashed vertical lines indicate approximately the location of the first, second, and third diffraction minimum. The curves are shifted vertically for convenience of comparison. The nuclei labeled b are believed to have an ellipsoidal shape. [Figure from Hahn et al. Phys. Rev. 101, 1127 (1956).]...

We also made a check of all the samples to see if there were any deviations from the dependence in the linewidth. For spheres, the decay time of the autocorrelation function is DK. However, for rods and ellipsoids of revolution, there are additional terms. Figure 5 shows a plot of the decay time F (from histogram fits) versus K, the square of the scattering vector. The linear behavior predicted for spheres is very precisely obeyed and the intercept is zero. All the samples we studied had similar curves leading us to conclude that in all of them, the dispersed phase droplets were spherical in shape. 

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