256 H. K. SCHACHMAN AND R. C. WILLIAMS 



and if the ions of the electrolyte are of equal size. The primary charge effect, 

 which always causes a reduction of the sedimentation rate of the macro- 

 molecule as compared to an un-ionized molecule of the same size and shape, 

 is attributed to the differential sedimentation of the macro-ions and its 

 counter-ions. In contrast, the secondary charge effect can either enhance or 

 diminish the sedimentation rate of large ions. This depends on the charge of 

 the large ion and the relative sizes of the positive and negative ions of the 

 low molecular weight electrolyte added to the solution. If, for example, the 

 macromolecule is negatively charged and the so-called supporting electro- 

 lyte is cesium chloride, there will be an enhancement of the sedimentation 

 rate. Had the supporting electrolyte been lithium iodide, there woidd be a 

 decrease in sedimentation rate as a consequence of the operation of the 

 secondary charge effect. 



Like many physical chemical properties, the sedimentation coefficient 

 frequently exhibits a marked dependence on concentration with the sedi- 

 mentation becoming more rapid as the solutions are diluted. This can be 

 attributed to three effects which are only partially understood in theoretical 

 terms (Schachman and Kauzmann, 1949). Foremost of these factors is the 

 so-called viscosity effect. As the solutions become more concentrated, the 

 viscosity increases and the frictional resistance experienced by an individual 

 molecule during its migration likewise increases. It is an oversimplification, 

 however, to ascribe the concentration dependence of the sedimentation co- 

 efficient solely to the viscosity of the solution. Since the centers of two solute 

 molecules can approach one another to a distance no less than the sum of 

 their radii (or equivalent dimensions for nonspherical particles) there is, in 

 effect, an exclusion of solute molecules from the immediate vicinity of each 

 individual one. Thus each solute molecule sediments in a medium that has 

 a viscosity somewhat less than the bulk viscosity of the solution. How much 

 less than the over-all viscosity is this effective viscosity remains difficult to 

 ascertain. Second in importance in causing sedimentation coefficients to 

 decrease with an increase in concentration is the so-called backward flow 

 effect. As the molecules plus their solvation mantles migrate toward the 

 closed cell bottom, there is return flow of liquid to make room for the sedi- 

 menting molecules and to fill the space formerly occupied by the molecules 

 in the region above the moving boundary. This backward flow causes a 

 decrease in the rate of sedimentation, which is measured relative to the cell 

 walls, by an amount which might be expected to mcrease with an increase in 

 concentration. For particles that are nearly spherical, the backward flow 

 correction is the predominant one. Finally, the sedimentation rates decrease 

 as the solutions become more concentrated because the density of the medium 

 increases and the buoyant force on the sedimenting unit consequently 

 decreases. Generally this is a small effect. 



