Molecular weight distribution methods sedimentation equilibrium

It is essential that the solution be sufficiently dilute to behave ideally, a condition which is difficult to meet in practice. Ordinarily the dilutions required are beyond those at which the concentration gradient measurement by the refractive index method may be applied with accuracy. Corrections for nonideality are particularly difficult to introduce in a satisfactory manner owing to the fact that nonideality terms depend on the molecular weight distribution, and the molecular weight distribution (as well as the concentration) varies over the length of the cell. Largely as a consequence of this circumstance, the sedimentation equilibrium method has been far less successful in application to random-coil polymers than to the comparatively compact proteins, for which deviations from ideality are much less severe. 

Almost simultaneously with the first attempt to determine molecular weight from equilibrium sedimentation, Rinde tried to widen this method to include determination of the molecular weight distribution (MWD) of a polydisperse system (3). Unfortunately, this attempt proved to be more complicated and did not result in establishment of a reliable routine. Since the appearance of Rinde s dissertation in 1928, many investigators have tried to determine MWD. Most of these efforts, however, did not provide a successful comprehensive technique (4-16). This objective has been accomplished only in a few cases under very limited conditions, such as in case of a Gaussian or near Gaussian MWD, in which only characterizing parameters had to be determined. Scholte (17, 18) determined MWD by performing an experimental procedure based on several equilibrium experiments. 

In the sedimentation equilibrium method, a lower centrifugal field is maintained for a period of time in such a way that sedimentation is balanced by diffusion and M equilibrium distribution of polymer is established in the cell. Although M and Mz are easily determined, the length of time of the experiment is a disadvantage. In contrast to light scattering, this method is not affected by dust particles, and no calibration is needed. The molecular weight distribution may be obtained from the sedimentation velocity data, but not without mathematical difficulties... 

An alternative method of using the ultracentrifuge to measure molecular weights is to allow the distribution of particles to reach equilibrium. As sedimentation occurs in the ultracentrifuge a concentration gradient is established, and this will cause the molecules to diffuse in the opposite direction. Eventually the system reaches a state of equilibrium at which the rate with which the solute is driven outwards by the centrifugal force just equals the rate with which it diffuses inwards under the influence of the concentration gradient. 

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