page_title: Polymer scattering
section_title: Small-angle polymer scattering
hierarchical_section_title: Polymer scattering / Small-angle polymer scattering
caption_attribution_description: English: A guinier plot taken using small-angle X-ray scattering.The different curves correspond to different concentrations of the polymer. The slope corresponds to the radius of gyration. O. Glatter &amp; O. Krateky ed., "Small Angle X-ray Scattering", Academic Press (1982).
context_page_description: Polymer scattering experiments are one of the main scientific methods used in chemistry, physics and other sciences to study the characteristics of polymeric systems: solutions, gels, compounds and more. As in most scattering experiments, it involves subjecting a polymeric sample to incident particles, and studying the characteristics of the scattered particles: angular distribution, intensity polarization and so on. This method is quite simple and straightforward, and does not require special manipulations of the samples which may alter their properties, and hence compromise exact results.
  As opposed to crystallographic scattering experiments, where the scatterer or "target" has very distinct order, which leads to well defined patterns, the stochastic nature of polymer configurations and deformations, gives rise to quite different results.
context_section_description: The calculation of the structure factor for cases differing from ideal polymer chains can be quite cumbersome, and sometimes impossible to complete analytically. However, when the small-angle scattering condition is met, , the sinc term can be expanded so one gets:
  and by utilising the definition of the radius of gyration:
  where the final transition utilises once again the small-angle approximation.
  We can thus approximate the scattering intensity in the small-angle regime as:
  and by plotting  vs.  , a so-called "Guinier plot", we may determine the radius of gyration from the slope of this linear curve. This measure is one of many examples of how scattering experiments of polymers can reveal basic properties of those polymer chains.
caption: A Guinier plot made with X-ray scattering in the small-angle regime. The slopes of these linear curves correspond to the radius of gyration of the polymers in the solution, while different curves correspond to different concentrations.
exif: {}