Typical Applications of Small-angle X-ray Scattering Technique in Polymer Characterization

Small-angle X-ray scattering (SAXS) technique is one of the most significant methods for determining the micro-structures of polymeric materials due to its statistical average and nondestructive detecting feature. Usually, a monochromatic parallel beam of X-rays is used for scattering experiments. When passing through a sample, the oscillating electromagnetic field (mostly the electric part) of X-rays interact with electrons, making the electrons secondary sources of X-rays of the same frequency. Those secondary X-rays interfere with each other to form a specific pattern deviating from the primary beam path depending on the actual locations of the electrons in the sample. Mathematically, such interferences can be obtained by a summation of all secondary Xray waves. As the number of the electrons within the sample is very large, an integration is used to represent the summation mentioned above. Because of the wave nature of the X-rays, the amplitude of the scattered X-rays determined by the above integration is just a Fourier transformation of the electron density distribution within the scattering volume. Due to the limitation in detection technique, the complex value of amplitude of scattered Xrays with real and imaginary parts cannot be recorded. It is the intensity rather than the amplitude that is recorded during experiments resulting in a loss of the phase information. Therefore, obtaining exact structural information (electron density distribution) becomes not easy and must be based on specific model fittings. Besides structures, SAXS intensity distribution can be used to investigate sample's gross properties such as fraction of phases or local properties such as fractal dimensions of interfaces between phases. This work began with an introduction of the fundamental theories of the SAXS technique, followed by practical suggestions on performing the experiments and brief summaries of models developed for different structures. The authors wish this review could help the beginners to comprehend the elements of the SAXS technique and serve as an instruction manual for valid data acquisition.