88 E. G. P I C K E L S 



In the derivation of equations (12), (14), and (15) it was assumed 

 that the frictional coefficients in sedimentation and diffusion were 

 equal. For the equihbrium case, this condition is essentially fulfilled, 

 since the two phenomena are counteracting each other under the same 

 experimental conditions. For the same reason, it was the early prac- 

 tice to determine the diffusion constant from the progressive spread 

 of the sedimenting boundary in the ultracentrifuge. This method 

 proved inadequate for several reasons. First, since sedimentation 

 rate generally increases with increasing dilution, there is a sharpening 

 of the sedimentation boundary as the particles in the trailing edge of 

 the boundary continually tend to overtake the slower moving parti- 

 cles in the plateau region. (Boundary sharpening can also be caused 

 by slight convective disturbances.) Secondly, a small percentage of 

 variation in sedimentation rate, as will be caused by slight inhomo- 

 geneity or aggregation, can produce sufficient spread or distortion of 

 the boundary's distribution curve to produce a very large error in 

 any determination of the diffusion constant. Determination of the 

 diffusion constant is now generally made by separate experiments with 

 a regular diffusion cell {87,88). Obviously, a great deal of uncer- 

 tainty regarding the equality of the frictional ratios is removed if 

 the ultracentrifugation and diffusion studies are done at nearly the 

 same temperature, in the same medium, and with the same concen- 

 trations. Another question that immediately presents itself is 

 whether there might be a preferential orientation of asymmetrical 

 particles during sedimentation. There are good theoretical argu- 

 ments (high thermal compared to centrifugally generated energy) 

 against this for particles in the macromolecular range. Furthermore, 

 the effect can be tested by centrifuging at different speeds, but no ex- 

 perimental evidence of orientation has been presented. 



Still another factor that may affect the frictional coefficient and 

 has a direct bearing on the value of p to be used in the equations of 

 Section C is the increase in p and a due to hydrostatic compression 

 in the cell. In the case of aqueous solutions in the ordinary ultra- 

 centrifuge at 60,000 r.p.m., the average increase in the density of the 

 fluid column amounts to about 0.8% (86). If the sedimenting par- 

 ticle suffers no contraction in size at all, its average rate ^vill be de- 

 creased by about 2.5% (assuming V = 0.75) because of the increased 

 buoyancy of the medium. However, if the compressibility ratio of 

 the particle is the same as that of the medium, the rate will increase 

 slightly because of the reduced particle size. It appears logical that 



