On the Concentration Dependence of the Rates of Sedimentation and Diffusion of Macromolecules in Solution. Preliminary

Abstract

The concentration dependence of the osmotic pressure, rate of diffusion, and sedimentation velocity for solutions of high molecular weight solutes, on the basis of certain assumptions, have been shown to be interrelated. Experimental confirmation, however, has been lacking. Preliminary data are given in this article which satisfy these interrelationships, with fractions of cellulose acetate in acetone; however, more cooperative osmotic pressure, diffusion, and sedimentation experiments on a variety of well-defined systems are necessary to confirm the hypothesis. If and when this additional confirmation is produced, the assumptions involved in the hypothesis may be considered correct; these are: (1) that the frictional coefficient in diffusion is the same (barring special cases of orientation during transport) as the frictional coefficient in sedimentation; and (2) that the driving force of diffusion is the gradient of the free energy of dilution of the system. For solutions with no heat of mixing, the slight dependence of the diffusion constant on concentration has its molecular basis in the fact that the size and shape of the molecules affect the thermodynamic and hydrodynamic contributions to the variation of the diffusion rate to a comparable extent, and these contributions partially cancel one another. This is quantitatively so in the simple case of rigid spheres in an athermal solution.