Sedimentation velocity method

The methods covered in detail in this manual are mainly those of chromatography and electrophoresis. Although isopycnic centrifugation is covered ( 11.3), sedimentation velocity methods are only touched on ( 11.2). It is intended to cover these in a future manual. The other major omission is the use of cellulose acetate and DEAE-... 

Most ultracentrifuge studies of humic substances have used the sedimentation-velocity method. Flaig et al. (1975) have reviewed this work. In general, the results of this work indicated that all the solutions studied were polydisperse as we have discussed previously, in a polydisperse system, the ordinary sedimentation-velocity equation cannot be applied because each different particle size has a different diffusion coefficient and different sedimentation constant. 

The sedimentation equilibrium method does not require an independent measurement of the diffusion coefficient, in contrast to the sedimentation-velocity method. However, the time required for complete equilibrium to be established is so long that the method is often inconvenient to use, especially if the molecular weight is greater than 50 000. 

Band ultracentrifugation is also a sedimentation velocity method, but here the particles sediment in a mixed solvent system (e.g., a salt solution). First a density gradient is produced by ultracentrifugation of the solvent system alone. Then the solute solution is added at the cell meniscus. The individual components sediment in bands which are no longer contaminated by the other components. The relatively weak density gradient is solely... 

Two approaches are in vogue for determination of molecular weights through centrifugation, the sedimentation velocity method and the sedimentation equilibrium method, the former being more popular. A third method, the approach to equilibrium method is also used. 

The sedimentation velocity method, in which dilfusion is negligible. This is done by setting the rotor at a very high speed, for example, 60,000 rpm (rotations per minutes), which is equivalent to a pressure of 420 bars. 

In the sedimentation velocity method a high ultracentrifugal field (up to about 400 OOOg) is applied and the displacement of the boundary set up by sedimentation of the colloidal particles is measured from lime to time. In the sedimentation equilibrium method, the colloidal solution is subjected to a mueh lower centrifugal field, until sedimentation and diffusion (mixing) tendencies balance one another and an equilibrium distribution of particles throughout the sample is attained. 

The sedimentation velocity method involves rotating the solution cell at... 

The sedimentation velocity method has the advantage of being a much more rapid technique, but is a semi-empirical method which normally... 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

In sedimentation velocity experiments, a dilute solution in high centrifugal field gets separated into a clear pure solvent layer and a solution. The initial clear boundary between the two then spreads because of diffusion. The rate of movement of boundary can be measured by suitable methods. Sedimentation constants is given by... 

Although the sedimentation velocity of particles tends to decrease steadily as the concentration of the suspension is increased, it has been shown by Kaye and Boardman11 that particles in very dilute suspensions may settle at velocities up to 1.5 times the normal terminal falling velocities, due to the formation of clusters of particles which settle in well-defined streams. This effect is important when particle size is determined by a method involving the measurement of the settling velocity of particles in dilute concentration, though is not significant with concentrated suspensions. 

The sedimentation velocity determination is dynamic and can be completed in a short period of time. The sedimentation equilibrium method gives quantitative results, but long periods of time are required for centrifugation at relatively low velocities to establish equilibrium between sedimentation and diffusion. 

Two-Layer Method. A suspension is spread in a thin layer on the surface of a clear, solids-free liquid. The particles then fall through the liquid in order of decreasing sedimentation velocity and reach the measuring plane in succession. 

Gilbert, L. M. and Gilbert, G. A. 1973. Sedimentation velocity measurements of protein association. Methods Enzymol. 27, Part D, 273-296. 

Diffusion coefficients can be related to molecular weight in three ways first by application of the Stokes-Einstein equation, second by combination with sedimentation data, and third by consideration of homologous polymer solutions. In the first method, an equivalent spherical size of the molecules is calculated from Dt, and an approximate molecular weight is found by combining these data with the appropriate density. In the second method, diffusion measurements are coupled with those of sedimentation velocity to give molecular weights, and in the third method, molecular weights may be determined directly from measurements of diffusion coefficients alone once a calibration has been... 

Sedimentation in a centrifugal field has been demonstrated to be a useful tool in the investigation of micellization in block copolymers, as first demonstrated by Tuzar etal. (1974). In this method, the velocity at which a solute species (unimer or micelle) is displaced under the influence of a strong centrifugal force is measured (Brown et al. 1995). For a given centrifugal force, the sedimentation velocity of a solute depends on its molecular weight, its buoyancy and friction... 

Indirect methods for obtaining information on the kinetics of the associa-tion/dissociation equilibrium include sedimentation velocity and GPC experiments. The application of these techniques is based on comparison of sedimentation or GPC elution curves with model curves based on theories for separation of unimers and micelles during a sedimentation velocity (Gilbert 1955) or GPC (Ackers and Thompson 1965 Coll 1971 Prochazka et at. 1988, 1989) experiment. Experiments have been performed that demonstrate several of the qualitative model predictions (Prochazka et at. 1989). The main conclusions were that GPC curves with two well-separated peaks can only result from a slow dynamic molecule micelle equilibrium, and that no simple interpretation of elution curves in terms of relative concentrations of unimer and micelles is possible (Prochazka et at. 1989). Thus no quantitative information on the kinetics of the molecule micelle equilibrium can be obtained from sedimentation velocity or GPC data. 

The most convenient of these methods is viscosity measurement of a liquid in which particles coated with a polymer are dispersed, or measurement of the flow rate of a liquid through a capillary coated with a polymer. Measurement of diffusion coefficients by photon correlation spectroscopy as well as measurement of sedimentation velocity have also been used. Hydrodynamically estimated thicknesses are usually considered to represent the correct thicknesses of the adsorbed polymer layers, but it is worth noting that recent theoretical calculations52, have shown that the hydrodynamic thickness is much greater than the average thickness of loops. 

In the sedimentation equilibrium method, the solution is allowed to come to equilibrium. When this happens, the analysis becomes very similar to that described in the previous section for gravitational fields, with the gravitational work mgdh replaced by mu2rdr, where u is the angular velocity of the centrifuge (in rad sec-1) and r is the distance from the center of the centrifuge. The final result is an equation similar to (12.21)... 

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