The Analysis of Small-Angle Scattering Data from Polydisperse Rodlike Particles by Indirect Transform and Maximum-Entropy Methods

Both the indirect transform and maximum-entropy methods are developed for analyzing small-angle scattering data from polydisperse rodlike particles to recover the original length distribution. Simulated small-angle scattering data are used to test the ability of these two methods. Both methods are found to be able to recover accurately the original length distribution of the rodlike particles when the full e-range scattering data are available. However, the maximum-entropy method is not able to recover the original length distribution as accurately as the indirect transform method when the very low Q scattering data are not available. The indirect transform method is successfully applied to the analysis of experimental small-angle scattering data from diheptanoylphosphatidylcholine rodlike micelles. The recovered length distribution of these rodlike micelles agrees well with that predicted by the 'ladder' thermodynamic model for rodlike micellar systems. This study shows that the indirect transform method described in this paper can be successfully used in the analysis of the small-angle scattering data from polydisperse rodlike particles to recover their length distribution. To use the maximum-entropy method for analyzing the small-angle scattering data from polydisperse rodlike particles, scattering data down to the very low Q limit must be measured in order to recover the length distribution accurately.