Determination of polymer morphology from the intensity measurement in the reciprocal space

Reciprocal space techniques based on scattering have been widely used for structure analysis of polymer materials. It would be more useful if the reciprocal methods can determine simultaneously the morphology of the polymer as those in the real space. However, the inverse problem, i.e., determining polymer morphology from the available scattering pattern, is very difficult because of the absence of the relative phase spectrum in the experimental measurements. Therefore, the retrieval of the missing phase spectrum plays a crucial role in this problem. Herein we theoretically propose that this can be accomplished by using phase-spectrum retrieval technique. We combined the Gerchberg–Saxton and hybrid input–output algorithms to determine the morphology of block copolymers from the corresponding scattering patterns in the reciprocal space. Numerical computations have been carried out to demonstrate the concept. It has also been shown that the algorithm is immune to noise. The demonstrated method could provide an extensive methodology for the investigation of polymer behaviors in the micro- and nano-scales by interconnecting real and reciprocal spaces.