A one-dimensional model for small-angle X-ray scattering from crystalline block copolymers

Small-angle X-ray scattering patterns (SAXS) are widely used to study polymers. Quantitative treatment of the intensity curves is often realized to obtain the long period and the linear crystallinity of semicrystalline homopolymers presenting a lamellar morphology, mainly using the correlation function. But even in the one-dimensional case, block copolymer systems exhibit more complicated morphologies that cannot be fully interpreted by this standard method. In this work, a model has been developed based on a previous treatment applicable to systems characterized by two different densities. Two additional densities have been considered to model four phase systems that can occur with block copolymers (e.g. two different crystalline domains and amorphous parts). The scattering intensity function was derived as a function of various parameters like the number of stacked lamellar units, the mean values and distributions of widths, and the electron densities.