Sedimentation equilibrium, concentration

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. 

Apart from tliese mainstream metliods enabling one to gain a comprehensive and detailed stmctural picture of proteins, which may or may not be in tlieir native state, tliere is a wide variety of otlier metliods capable of yielding detailed infonnation on one particular stmctural aspect, or comprehensive but lower resolution infonnation while keeping tlie protein in its native environment. One of tlie earliest of such metliods, which has recently undergone a notable renaissance, is analytical ultracentrifugation [24], which can yield infonnation on molecular mass and hence subunit composition and their association/dissociation equilibria (via sedimentation equilibrium experiments), and on molecular shape (via sedimentation velocity experiments), albeit only at solution concentrations of at least a few tentlis of a gram per litre. 

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. 

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. 

In a sedimentation equilibrium run, the stationary radial concentration profile, which is established after a few hours for a 1-mm column, is analyzed according to Equation (72) or, in case of polydisperse samples, Equations (74) or (75). Contrary to the sedimentation velocity experiment, the diffusion coefficient D is not required. 

Alternatively, in sedimentation equilibrium experiments, the ultracentrifuge is operated at slow speeds for longer time to permit the solute molecules to attain equilibrium between sedimentation and diffusion. If the sample is monodisperse, its concentrations cb c2 can be measured at 2 positions xh x2 in the cell. 

Z-4A), and zeolite H-ZSM-5. The interlayer distance varied by the intercalation was determined from X-ray diffraction patterns. The interlayer space of the crystalline zeolite is separated by the three-dimensional cage structures. The mean diameters of particles were approximately 1 ym. Such small particles formed very stable suspensions with no sign of sedimentation over the time course of the kinetic measurements. The analytical techniques used to obtain the equilibrium concentration are described elsewhere (10-22). All samples were equilibrated for 24-72 h after preparation. The temperature was controlled at 25 °C. 

Finally, we consider the behavior of a solute in a solution in the cell subjected to the centrifugal field. At a suitable angular velocity, the tendency of the solute to sediment toward the bottom of the cell is countered by its tendency to diffuse backward toward the meniscus, because the concentration increases with increasing r, as indicated in Figure 2. 2 b). At some time, a sedimentation equilibrium is attained. A typical equilibrium concentration distribution is depicted in Figure 2. 2 b). Our aim is to find a quantitative analytical expression for this curve. 

Figure 21.3. Concentration distribution of solute in solution at sedimentation equilibrium. Curve A represents ideal behavior of a monodisperse solute curve B represents nonideality and curve C represents a polydisperse system.

Sorption has been commonly described as an equilibrium process, in which the pesticide molecules are rapidly and readily exchanged between the sediment and aqueous phases. In this approach ( ), the equilibrium water phase concentration, (expressed relative to suspension volume) is related to the sediment phase concentration, (expressed relative to dry weight sediment), through... 

Environmental Protection Agency (22). Figure 1 is a plot of the sediment/aqueous concentration ratio versus time for this system. It is characterized by a rapid sorption process and a much slower sorption process which does not reach equilibrium until about 10 days after initial mixing of the sediment and chlorpyrifos solution. 

Method by which the distribution of the concentration of the solute or dispersed component in a dilute solution or dispersion along the centrifuge cell is measured at sedimentation equilibrium, and the results are interpreted in terms of molar masses or their distribution, or both. 

A large, sealed fish tank - consisting of 20 m of water, 10 m of air, 1 m of sediment, and 0.2 m of fish and other biological organisms - has 100 g of benzene accidentally spilled into it. What will be the eventual (equilibrium) concentrations and mass in each phase The fraction of organic carbon in the sediments has been determined to be 0.01. The density of the sediments has been determined to be 2g/cm. The octanol-water partitioning coefficient for benzene is 138. 

In the sediment, the equilibrium concentration of an organic compound adsorbed to the sediment is dependent on the fraction by weight of organic carbon. 

Round Lake in southwestern Minnesota is down wind from an oil paint factory that has air emissions of solvents. Two of the primary solvents emitted are 1,2-dichloroethylene and heptane, with mean air concentrations over the lake of 2 ppb(v) and 100 ppb(v), respectively. Given the chemical data below, estimate the eventual equilibrium concentration and the mass of these two compounds in the water, suspended particulate, sediments, and the fish of Round Lake. The... 

Itou et al. [60] determined 0II/0C for isotropic solutions of poly(n-hexyl isocyanate) (PHIC) and dichloromethane (DCM) from sedimentation equilibrium data on narrow distribution PHIC samples. Figure 3 shows their results, where the ordinate Mw(0II/0c) represents the osmotic pressure increment on the molar concentration scale. 

In weathering situations, saturation of fluids with SiC relative to any species of pure silica is probably only rarely achieved. In continental and shallow sea deposits, silica is precipitated in some initially amorphous form, opaline or chert when lithified or extracted by living organisms. Authigenically formed silicates are probably not in equilibrium with quartz when they are formed. As compaction increases in sediments, silica concentrations in solution are again above those of quartz saturation (15 ppm) and again it must be assumed that the diagenetic minerals formed are not in equilibrium with a silica polymorph except where amorphous silica is present. It is possible that burial depths of one or two kilometers are necessary to effectively stabilize that quartz form. It must be anticipated that the minerals formed under conditions of silica saturation near the earth s surface will be a minority of the examples found in natural rock systems. 

In principle, the nature of biopolymer interactions in solution can also be determined from sedimentation equilibrium of a single biopolymer component at constant temperature T and angular velocity co. The thermodynamic activity on a weight-concentration basis, z, = yiC/M at radial distance r is related to that at a selected reference radial position (r ) by the following formal expression (Deszczynski et al., 2006) ... 

Nonlinear regression analysis of the dependence of c2(r) upon (r), a transform of the radial distance i leads to evaluation of the reference thermodynamic activity, Mzzz(rf), and the osmotic second virial coefficient, Au/Mi, expressed on a weight basis (litre/g) rather than a molar basis (litre/mol). Furthermore, the values of Miy v/ and ps can be obtained by curve-fitting the sedimentation equilibrium distribution for low biopolymer concentrations (M fr) cf for all r) to the equations (5.36) and (5.37) in order to deduce the quantity [Mj( 1 - v/ps)] from the coefficient of the exponent (Winzor et al., 2001 Deszczynski et al., 2006). 

A preparation of reduced and carboxymethylated Mouse-Elberfeld virus protein particles in water reached sedimentation equilibrium at 25 °C after 40 hr at 12,590 rpm. The following data show the recorder displacement (proportional to concentration) versus r for this protein f... 

The dissociation of SOD observed by gel chromatography in 8 M urea, in contrast with the sedimentation equilibrium data, might be due to differences in the experimental conditions such as concentration effects. 

Figure 3.15. The dissociation of /3-lactoglobulin B at low pH. Idealized curves for the weight-average molecular weight as a function of concentration from sedimentation equilibrium measurements. = pH 2.58, ionic strength 0.15 = pH 2.20, ionic strength 0.15 = pH 2.58, ionic strength 0.10. 40.2 fringes - 10 g/liter. (From Albright and Williams 1968. Reprinted with permission of AVI Publishing Co., Westport, Conn.)...

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