Simultaneous estimation of the form factor and structure factor for globular particles in small-angle scattering

Small-angle scattering data from non-dilute solutions of particles are often analysed by indirect Fourier transformation using a specific model structure factor to obtain an estimate of the distance distribution function that is free from concentration effects. A new approach is suggested here, whereby the concentration effects are expressed solely through real space functions without the use of an explicit structure factor. This is done by dividing the total distance distribution function for the scattering into three different contributions, as suggested by Kruglov [(2005). J. Appl. Cryst. 38, 716-720]: (i) the single particle distribution which is due to intraparticle effects, (ii) the excluded volume distribution from excluded volume effects which is only dependent upon the geometry of the particles, and (iii) a structure distribution which is due to the remaining interaction between the particles. Only the single particle distribution and the structure distribution are allowed to vary freely (within the restrictions of a smoothness constraint). These two distributions may be separated mainly because they differ in their regions of support in real space. From the estimated distributions the structure factor can be calculated. For deviations of particles from spherical symmetry, the excluded volume distribution may be approximated by that of an ellipsoid of revolution. Excluded volume distributions have been calculated for ellipsoids of revolution of axial ratios between 0.1 and 10 and implemented in the program IFTc, which is described in the appendix. The validity of the approach is demonstrated for globular particles.