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Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
It is often useful to give the gyrofrequency a sign with the definition = or express it in units of hertz with =. For electrons, this frequency can be reduced to , = (/).. In cgs-units the gyroradius = | | and the corresponding gyrofrequency = | | include a factor , that is the velocity of light, because the magnetic field is expressed in units [] = / /.
For this case the radius of gyration is approximated using Flory's mean field approach which yields a scaling for the radius of gyration of: R g ∼ N ν {\displaystyle R_{g}\sim N^{\nu }} , where R g {\displaystyle R_{g}} is the radius of gyration of the polymer, N {\displaystyle N} is the number of bond segments (equal to the degree of ...
A quantity frequently used in polymer physics is the radius of gyration: = It is worth noting that the above average end-to-end distance, which in the case of this simple model is also the typical amplitude of the system's fluctuations, becomes negligible compared to the total unfolded length of the polymer N l {\displaystyle N\,l} at the ...
As described above, the radius of gyration, R g, and the second virial coefficient, A 2, are also calculated from this equation. The refractive index increment dn/dc characterizes the change of the refractive index n with the concentration c and can be measured with a differential refractometer.
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. and by utilising the definition of the radius of gyration:
In the orbifold corresponding to the subgroup, a gyration corresponds to a rotation point that does not lie on a mirror, called a gyration point. [1] For example, having a sphere rotating about any point that is not the center of the sphere, the sphere is gyrating. If it was rotating about its center, the rotation would be symmetrical and it ...
It is defined as / where is the effective length of the column and is the least radius of gyration, the latter defined by = / where is the area of the cross-section of the column and is the second moment of area of the cross-section. The effective length is calculated from the actual length of the member considering the rotational and relative ...