A new map-polynomial fitting extrapolation method of data in the low scattering vector region for dilute polydisperse spherical systems in SAXS

Abstract

Dilute polydisperse system is a common research object in small angle X-ray scattering (SAXS). In SAXS studies, the extrapolation of the scattering data in the low scattering vector region is necessary for many quantitative structural analyses. The classical Guinier extrapolation method is based on the Guinier approximation, which is only applicable to the scattering data with a distinct linear segment on the Guinier plot. In this contribution, a new map-polynomial fitting extrapolation method is proposed. It takes the bilateral data constructed by mapping the measured data as the fitting object, and provides reliable extrapolation results within an explicit fitting range and a specific polynomial order. The new method is superior to the Guinier method in terms of extrapolation effect and applicability range. The feasibility of the proposed method is verified by experimental sample.