What is Long-Period Analysis?

Long-period analysis is a technique for characterizing the periodic structure inside materials and is widely applied to crystalline materials, semi-crystalline polymers, and nanostructured materials at the nanoscale. Since long-period structure (periodicities on the range of tens to hundreds of angstroms) is closely related to the physical properties and functionality of materials, this detailed analysis is extremely important for the development of new materials and performance improvement.

For example, in the polymer materials polypropylene and polyethylene, crystalline lamellae are regularly arranged between amorphous layers. This periodicity has a marked effect on the mechanical strength, flexibility, and heat resistance of the materials.

For long-period analysis, small-angle X-ray scattering (SAXS) is effective because it can measure in the small-angle region (2θ = several degrees). When density fluctuations exist (e.g., when crystalline and amorphous materials are periodically arranged), diffraction due to the difference in electron density is observed in the small-angle region, which is called long-period scattering.

Long-period scattering is the result of interference of diffracted X-rays due to the periodicity in the sample and is the same as the Bragg diffraction condition. Therefore, the periodicity of the structure can be determined by calculating the d-value from the peak positions. Furthermore, it is possible to evaluate the orientation of the structure from the relationship between the sample arrangement and the direction in which the long-period peak is detected, and the disorder of the structure from the peak spread. In addition, long-period scattering and microstructure like lamellar thickness or amorphous content are correlated, and structure can be inferred.

Thus, a detailed understanding of the internal structure of materials through long-period analysis is essential for research to improve material properties and develop new materials.