Radius of gyration

For structural studies of soft matter, the radius of gyration (also radius of gyration or partially gyration called ) is an important parameter for characterizing the spatial extent of irregularly shaped particles. The more compact an object, the smaller its radius of gyration. It can be determined by scattering experiments.

The definition of the radius of gyration is similar to the moment of inertia. The particles consist of N identical blocks with position vectors, so the square of the radius of gyration is defined as the mean square distance between the blocks ( for example, the monomers of a polymer chain) to the focus of the particle:

If the mass distribution in the particle is given by a mass density, we obtain for the radius of gyration:

Where M is the mass of the particle.

In the extreme case of a homogeneous sphere of radius R gives:

The radius of gyration can be determined by scattering experiments on a dilute suspension or solution of the particles: for small scattering vectors the structure can be approximated by the function S

Then thus depends only on the number N of blocks and the radius of gyration. This relationship is known as the Guinier law.

To measure the radius of gyration of the suspended colloids or dissolved polymers often is the light scattering. To characterize the spatial extent of the entangled chain molecules in a polymer melt, the small-angle neutron scattering offers; to obtain a scattering contrast, while the melt is a small proportion of deuterated polymer added.