Distribution from sedimentation equilibrium

A New Way of Determining Molecular Weight Distribution, Including Low Molecular Weight, from Equilibrium Sedimentation... 

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. 

The equilibrium sedimentation experiment of sample P was analyzed only by applying the computation-oriented expressions. The resulting f(M) was compared with the previously obtained f(M). From the curve of f(M) the average values were computed and compared with the values computed in the same way from individual distribution curves of fractions A, B, and C. These values were also compared with M values obtained in a conventional way from equilibrium sedimentation by applying Equation 2, and with M values determined from velocity sedimentation experiment, Equation 30 (see Table II). 

Molecular Weight Distributions from Sedimentation Equilibrium Experiments... 

A straightforward determination of is obtained by centrifuging until an equilibrium distribution of the molecules of a protein or other macromolecular material is obtained and by recording the variation in concentration from the center to the periphery of the centrifuge celF 483,i85,i87-i90 ggg Section A,2). Using short cells, this sedimentation equilibrium can be attained in 1-5 hours instead of the 1-2 days needed with older instruments. For a single component system the concentration distribution at equilibrium is given by Eq. 3-12. 

Equilibrium sedimentation studies are mostly used to investigate density differences in different macromolecules. The method has been used, for example, in research on the replication of N-labeled deoxyribonucleic acids. Theoretically, it is also suitable for distinguishing between polymer blends and true copolymers. In such studies, problems usually arise from the considerable back-diffusion and the wide molar mass distribution. The gradient curves are so strongly influenced by these two effects that there is considerable overlap in the curves for substances of differing densities. 

Material may be supplied to the littoral sediment budget by coastal erosion, by feed from offshore or by contributions from rivers. After sediment has been distributed along the coast by longshore drift, it may be deposited in a sediment reservoir and, therefore, lost from the active environment. Sediment reservoirs formed offshore take the form of bars where the material is in a state of dynamic equilibrium, but from which it may easily re-enter the system. Dunes are the commonest types of onshore reservoirs, from which sediment is less likely to re-enter the system. 

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... 

Munk has developed a new algorithm for the analysis of sedimentation equilibrium data from a single experiment to obtain the average molecular weight and its polydispersity, providing that the Schultz-Zimm distribution function and a certain thermodynamic behaviour can be assumed. Simultaneous curve fitting to the equilibrium sedimentation data for three different concentrations facilitated the discovery that filamin monomer and dimers are in equilibrium while the tetrane forms irreversibly. ... 

Table I summarizes some typical distribution coefficients. Sediments become enriched in plutonium with respect to water, usually with a factor of vlO5. Also living organisms enrich plutonium from natural waters, but usually less than sediments a factor of 103 - 101 is common. This indicates that the Kd-value for sediment (and soil) is probably governed by surface sorption phenomena. From the simplest organisms (plankton and plants) to man there is clear evidence of metabolic discrimination against transfer of plutonium. In general, the higher the species is on the trophic level, the smaller is the Kd-value. One may deduce from the Table that the concentration of plutonium accumulated in man in equilibrium with the environment, will not exceed the concentration of plutonium in the ground water, independent of the mode of ingestion.

Molecular weights of polysaccharides in solution can also be measured by osmotic pressure and light scattering. Osmotic pressure yields the number average molecular weight, which can be usefully used with Mw from sedimentation equilibrium as a measure of polydispersity Preston and Wik [28] have done this for example with hyaluronic acid. The ratio Mw/Mn the polydispersity index is often given as a measure of polydispersity, and can be related to the width of a molecular weight distribution via the well-known Herdan [96] relation ... 

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. 

The distribution of Molecular weights can be obtained directly from sedimentation-equilibrium measurements. The solution of an integral equation is involved, however, but the analysis remains a difficult one. 

---