Sedimentation-diffusion equilibrium method

An alternative analytical method, based upon a detailed analysis of phase relatkmships, is still in an early stage of development. Being an absolute procedure it cotdd be useful for supporting other absolute ta, e.g. those obtained from the sedimentation-diffusion equilibrium in the ultracentrifr e. 

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. 

The amino acid analysis (Table I) strongly supports the value of 31,000 for the molecular weight of DNase I. This value has been accepted in Stockholm (34) and in New York 35), making all previously reported values obsolete [see reviews (10, 26, 27, 30) ]. The values obtained (Table II) by ultracentrifugation methods sedimentation diffusion and approach to equilibrium closely agree with the value of 31,000 based on N-terminal determination. 

This standard method of density gradient centrifugation, however, has a serious disadvantage. Because of the sedimentation and diffusion equilibrium formation of the density profile the time needed for orie experiment amounts to more than 15 hours. 

In the sedimentation-equilibrium method a lower centrifugal field is applied and the processes of sedimentation and diffusion are brought to equilibrium [13]. In this case the governing equation contains sedimentation equilibrium concentrations of species at different positions from the axis of rotation, but one does not need to know D. It should be pointed out that sedimentation and diffusion are more complicated when the species are electrically charged. This is because the smaller counterions sediment at a slower rate than do the colloidal-sized species. This creates an electric potential gradient that tends to speed up the counter-ions and to drag the colloidal species. The reverse effect occurs for diffusion. 

Values kindly determined by Mr. D. M. Brown and Prof. E. L. Smith on a sample prepared in this laboratory. The values have been obtained, respectively, by the Archibald method of sedimentation equilibrium and by sedimentation-diffusion, assuming a partial specific volume of 0.721 for the protein. 

A summary of degrees of polymerization reported for hardwood xylans and the methods used for their determination, together with isolation procedures, yields, and viscosity data, is presented in Table V. The methods used include osmometry, light-scattering, sedimentation equilibrium, and sedimentation-diffusion (not listed). Recourse has also frequently been had to chemical methods for determining chain length. These methods are, however, far less reliable than physical techniques, and they will not be... 

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. 

Table XV shows that the two methods used (equilibrium/ultracentrifugation and sedimentation/diffusion) give comparable results. The sodium taurocholate micelle is swollen appreciably by the presence of even small amounts of potassium oleate. As the weight ratio increases the micelle increases in size. It is not possible to say whether there are two different species of micelle present, although this seems unlikely since the schlieren sedimentation curve was symmetrical and showed no shoulders or second bumps that would suggest polydispersity. It is probable that sodium taurocholate and potassium oleate form a mixed micelle that increases in size as more oleate is added. Since both these compounds are soluble amphiphiles (42) they will be present in both the micelle and as monomers. At present it is impossible to know how the species are partitioned. If one assumes that the micelle composition is similar to that of the whole solution (a valid assumption at high micelle concentrations) then the number of molecules of each...

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... 

The sedimentation equilibrium method, in which diffusion plays an equally important role. This is done at a relatively low speed, for example, 12,000 rpm. 

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 first method (sedimentation velocity) requires an independent determination of the diffusion coefficient, which is avoided in the second method. Thus, in the second method (sedimentation equilibrium) we do not need to know the shape/solvation of particles. Molecules as small as sugars have been studied with the sedimentation equilibrium method. The disadvantage of the second method is that the establishment of equilibrium may take as long as several days. 

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. 

An analytical ultracentrifugation method for determining the molecular mass, diffusion coefficient, and/or state of oligomerization of a macromolecule by conducting sedimentation conditions to establish an equilibrium distribution of the macromolecule from the meniscus to the bottom of the observation cell. 

In this method, usually a density profile is formed in the ultracentrifugation cell by centrifuging solutions for instance of sucrose or Metrizamide in water or methanol until the equilibrium state between sedimentation and diffusion of the dissolved molecules has been established. Figure 1 shows schematically two of such equilibrium density profiles (dotted lines). 

CR, cryoscopic method DV, diffusion constant and intrinsic viscosity EB, ebullioscopic method EG, end-group titration IV, intrinsic viscosity-molecular weight relationship in other solvents LS, light scattering MV, melt viscosity-molecular weight relationship OS, osmotic pressure PR, analysis of polymerization rate SD, sedimentation and diffusion constants SE, sedimentation equilibrium (Archibald s method) SV, sedimentation constant and intrinsic viscosity [see Eq. (72)]. 

Understanding of sediment diagenesis and benthic fluxes has evolved with advances in both experimental methods and modeling. Measurements of chemical concentrations in sediments, their associated pore waters and fluxes at the sediment-water interface have been used to identify the most important reactions. Because transport in pore waters is usually by molecular diffusion, this medium is conducive to interpretation by models of heterogeneous chemical equilibrium and kinetics. Large chemical changes... 

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

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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