Sedimentation equilibrium

In equilibrium sedimentation, the concentration at every point in the ultracentrifuge cell no longer varies with time, i.e., dc dt = 0. Equation 

9 Determination of Molecular Weight, Molecular-Weight Distribution 

Combining equations (9-110) and (9-102) gives the following for the molecular weight at equilibrium sedimentation  

Equation (9-113) is, strictly speaking, only applicable at infinite dilution. At finite concentrations, it yields an apparent molecular weight (M ) pp, which is extrapolated in the usual manner by plotting 1 /(M )app = / (c) to c 0. 

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Piazza R, Bellini T and Degiorgio V 1993 Equilibrium sedimentation profiles of screened charged colloids a test of the hard-sphere equation of state Rhys. Rev. Lett. 71 4267-70... 

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. 

Analytieal ultraeentrifugation Change in MW (sedimentation equilibrium), sedimentation coefficient ratio of complex to mucin... 

At the top right, the diagram shows the densities and sedimentation coef cients for biomolecules, cell organelles, and viruses. Proteins and protein-rich structures have densities of around 1.3 g cm , while nucleic acids show densities of up to 2 g cm . Equilibrium sedimentation of nucleic acids therefore requires high-density media—e.g., concentrated solutions of cesium chloride (CsCl). To allow comparison of S values measured in different media, they are usually corrected to values for water at 20 °C ( S20W ) ... 

Equilibrium sedimentation technique working with a multi-component solvent forming a density gradient in a centrifugal field... 

Analytical ultracentrifugation s Equilibrium sedimentation at different car-bohydrate protein ratios yields stoichiometry of complex... 

An extreme in sediment volume was usedt as a criterion for the effective cancellation of interparticle attraction by the continuous phase. Nylon-6,6 dispersions consisting of 1.0 g of solid in 10 ml of /2-propanol-thiodiethanol mixtures of various compositions were allowed to settle to sedimentation equilibrium. Listed here are the equilibrium sediment volumes, the volume/volume compositions, and the surface tensions of the media ... 

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

TiTolecular weight determination of a monodisperse macromolecular system from equilibrium sedimentation was devised by Svedberg and Fahraeus in 1925 (I). They applied the following formula... 

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. 

MWD can be expressed by several equivalent formulas derived from the theory of equilibrium sedimentation at ideal conditions. In the following the well-known Fujita formalism (see Equation 2) will be used. This expression related the density of MWD, f(M), to concentrations or concentration gradients, respectively ... 

To substantiate the credibility of the newly developed method, a polydisperse system with f(M) known in advance was subjected to an equilibrium sedimentation experiment. Then the new computation-ori-... 

To perform this verification three narrow fractions of linear polystyrene denoted as A, B, and C were investigated to determine their molecular weights. This task was accomplished by applying velocity as well as equilibrium sedimentation. In addition, these three individual fractions were combined according to a known weight ratio into a new polydisperse sample denoted as P. Sample P was also subjected to equilibrium sedimentation. All samples were investigated in cyclohexane at 35°C (near the 0 temperature) see Table I. 

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). 

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