Subject sedimentation velocity

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

Diffusion coefficients can also be obtained from sedimentation velocity experiments, but the precision is quite low and subject to some ques-don. Quasi-elastic light scattering is a much more useful technique to obtain diffusion coefficients (see below). 

Let us consider the following mass balance on a tetrahedral element subjected to the velocity field v(x,y,z) of the suspension (as computed from the solution of the flow equations) and a sedimentation velocity, namely ... 

Figure 11. Separation of treated and untreated human erythrocytes by low-electric-field electrophoresis. Human erythrocytes (5 x 107) treated with neuraminidase are mixed with 5 x 107 untreated erythrocytes to a final volume of 5 ml and layered onto a linear gradient of 1.5-cm height. Electrophoresis proceeds for 25 min at 5°C at a constant current of 90 mA. An identical suspension is subjected to velocity sedimentation at unit gravity only. (O) Separation at unit gravity ( ) separation at unit gravity and by electrophoresis. Areas under the migration profile are depicted in shading. Gravity and electric forces act in the same direction (to the right). (Figures 8—11 reproduced with kind permission of the editor of Anal. Biochem.)...

Canavalia urease has been the subject of extensive physical and chemical investigation because of its availability in pure form (see Reithel, 1971 Bailey and Boulter, 1971). Sedimentation velocity investigations reveal six... 

The determination of molecular weight by ultracentrifugal means is of paramount importance in the study of proteins. The subject is treated in great detail in Svedberg s book and we shall go no further than to discuss a few points of general interest. Two methods have been applied in this field, the determination of the sedimentation velocity and the study of the sedimentation equilibrium. In both methods we must distinguish between molecules with a randomly kinked loosely built structure and those which form compact particles, whether spherical or otherwise. This distinction must be made for practical reasons, because the theoretical interpretation of experimental results is much simpler and can be carried out on a safer basis in the case of compact particles than in that of loose structures. 

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. 

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. 

Particle sinking rates are of considerable interest because the fester a particle can make the trip to the seafloor, the shorter the time it is subject to decomposition or dissolution and, hence, the greater its chances for burial in the sediments. The length of the trip is dictated by the depth to the seafloor, the horizontal current velocity, and the particle sinking rates. As shown in Figure 13.5, sedimentation rates decrease with increasing water depth. This relationship reflects the preservation issue and the feet that coastal waters tend to have larger sources of particles to the surfece zone. 

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. 

If a further purification is desired, then the supernatant (above) can be subjected to ammonium sulfate fractionation, gel filtration on Sephadex G-200, and finally on a-aminopropane-agarose affinity column. On polyacrylamide gel electrophoresis in the presence of sodium dodecylsulfate, the final product migrated as a single band with an estimated molecular weight of 113,000. Upon sedimentation equilibrium velocity ultracentrifugation, an estimated molecular weight value of near 117,000 was obtained. 

Early in this chapter it was stated that molecules or particles spinning around an axis are subjected to a centrifugal force, F. Under the influence of this force they sediment toward the bottom of the centrifuge tube at a velocity, v, described by the equation... 

Sedimentation. If particles are subject to sedimentation, this may also lead to enhanced aggregation rate, since particles of different sizes will move with different velocities through the liquid see Section 13.3. This implies that a large particle can overtake a smaller one, and a kind of orthokinetic aggregation occurs. This will be the case if (a) there is a substantial spread in particle size and (b) particle motion over a distance equal to its diameter takes less time by sedimentation than by Brownian motion. The condition for the latter is approximately... 

Acoustic and elastic properties are directly concerned with seismic wave propagation in marine sediments. They encompass P- and S-wave velocity and attenuation and elastic moduli of the sediment frame and wet sediment. The most important parameter which controls size and resolution of sedimentary structures by seismic studies is the frequency content of the source signal. If the dominant frequency and bandwidth are high, fine-scale structures associated with pore space and grain size distribution affect the elastic wave propagation. This is subject of ultrasonic transmission measurements on sediment cores (Sects. 2.4 and 2.5). At lower frequencies larger scale features like interfaces with different physical properties above and below and bed-forms like mud waves, erosion zones and ehatmel levee systems are the dominant structures imaged... 

On the other hand, the particle is subject to the force of resistance from the liquid. The velocity of particle sedimentation is established very quiddy. The characteristic time of this process is estimated by the value a /v equal to the relaxation time of the viscous force. Thus, for values a /v m /s, a 100 (un, this time is equal to 0.02 s. Of greatest interest is the case of small-sized particles, therefore it is possible to assume that their motion is inertialess, taking the expression (8.3)... 

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