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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.,
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.
Since the gyration tensor is a symmetric 3x3 matrix, ... The squared radius of gyration is the sum of the principal moments: = ...
where is the radius of gyration of the polymer, is the number of bond segments (equal to the degree of polymerization) of the chain and is the Flory exponent. For good solvent, ν ≈ 3 / 5 {\displaystyle \nu \approx 3/5} ; for poor solvent, ν = 1 / 3 {\displaystyle \nu =1/3} .
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 ...
In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula is based on experimental results by J. B. Johnson from around 1900 as an alternative to Euler's critical load formula under low slenderness ratio (the ratio of radius of gyration to ...
This makes experimental determination of important quantities such as the root mean square end-to-end distance or the radius of gyration much simpler. Additionally, the theta condition is also satisfied in the bulk amorphous polymer phase. Thus, the conformations adopted by polymers dissolved in theta solvents are identical to those adopted in ...