Size, Shape, and Molecular Weight Determinations

if diffusion starts at f 0, the integration constant obtained from integration of Eq. (10.10) is zero. Thus, we have 

But the mean-square displacement is proportional to the time 2t with the proportionality constant equal to the diffusion coefficient D  

Kirkwood derived an equation to correlate the diffusion coefficient D with the size of polymer molecule Ry) in the form 

If a particle of a suspension (here, we mean a macromolecule) is spherical, then the following equation provides the relationship between the diffusion coefficient D and the radius of the sphere r  

Perrin in 1936 derived equations that relate frictional coefficients to the shape of macromolecules formed as ellipsoids of revolution. The frictional coefficients (/) of prolate and oblate ellipsoids (see Chapter 8) are both greater than the frictional coefficients of spheres (/( or /o) of equal volume. The difference depends on the ratio of the major to the minor axis. Let p = b/a be the axial ratio, where b is the equatorial radius and a is the semiaxis of revolution. For prolate ellipsoids or elongated ellipsoids a/b 1), we have 

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