Search results
Results from the WOW.Com Content Network
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.,
The squared radius of gyration is the sum of the principal moments: ... e.g., when the particles are distributed uniformly on a regular prism. ...
The radius of this circle, , can be determined by equating the magnitude of the Lorentz force to the centripetal force as = | |. Rearranging, the gyroradius can be expressed as = | |. Thus, the gyroradius is directly proportional to the particle mass and perpendicular velocity, while it is inversely proportional to the particle electric charge ...
Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration R g. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient, A 2 , can be calculated.
The given formula is for the plane passing through the center of mass, which coincides with the geometric center of the cylinder. If the xy plane is at the base of the cylinder, i.e. offset by =, then by the parallel axis theorem the following formula applies:
The quadratic mean of the end-to-end distance can be related to the quadratic mean of the radius of gyration of a polymer by the relation: [1] r 2 = 6 s 2 {\displaystyle \left\langle r^{2}\right\rangle =6\left\langle s^{2}\right\rangle }
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 ...
Regular polygons; Description Figure Second moment of area Comment A filled regular (equiliteral) triangle with a side length of a = = [6] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.