Sector-shaped ultracentrifuge cell

The evolution with time of the concentration profile x (s> D, r, t) in a sector shaped ultracentrifuge cell is given by the Lamm [45] equation ... 

Because we are considering sedimentation of macromolecules as well as colloidal particles, in analyzing the kinematic wave fronts that will develop in the cell, we must also consider the broadening of these fronts that takes place due to diffusion. The geometry for analysis of a sector-shaped ultracentrifuge cell is shown in Fig. 5.5.2. The solvent-air interface (the meniscus) is located at r , and the bottom of the cell at... 

Because of the extreme importance of the ultracentrifuge, it seems appropriate to describe it in some detail. Although the particulars differ from instrument to instrument, the essential features are present in all ultracentrifuges. The actual sedimentation takes place in a cell mounted within an aluminum or titanium rotor. The cell is sector shaped its side walls converge toward the center along radial lines. Since the radial acceleration is proportional to the distance from the axis of rotation, we see that this quantity varies from top to bottom in the cell. Although this variation is considered explicitly in a section below, it is sufficient for the present to consider the average acceleration at the midpoint of the cell, which is typically located 6.5 10 2 m from the center of the rotor. For speeds of 10,000, 20,000, and 40,000 rpm, accelerations of... 

So far the equations that have been developed are independent of the shape of the cell. In order to make Equation 17 more useful, it is necessary to relate Ci( — 0) to the initial concentration of component i, Coi. To do this one applies conservation of mass, which states that in a closed system (the solution column in the ultracentrifuge cell) the total amount of solute is constant at all times. Since mass equals concentration times volume, it is necessary to know the volume of the centerpiece, and this depends on the shape of the centerpiece. Two types of centerpieces are currently used. One is a sector-shaped centerpiece, and the other is a six-channel, equilibrium [or Yphantis (24)] centerpiece. Top views of both centerpieces are shown in Figure 1. In either centerpiece, one side is reserved for solvent and the other for solution. 

An ultracentrifuge is a high-speed centrifuge equipped with a suitable optical system (usually schlieren or interference optics, the latter being particularly useful when low concentrations are involved) for recording sedimentation behaviour and with facilities for eliminating the disturbing effects of convection currents and vibration. The sample is contained in a sector-shaped cell mounted in a rotor (usually c. 

Figure 4-39. Sector-shaped cells of an analytical ultracentrifuge.

A dilute binary mixture is ultracentrifuged at an angular speed w in a sector-shaped cell. The mixture in the cell is initially uniform with a solute concentration Pp. 

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