Effects of a Concentration Dependence of the Sedimentation Coefficient in Velocity Ultracentrifugation

Abstract

The Lamm differential equation for the sedimentation process in the ultracentrifuge is solved in closed form for the case in which the sedimentation coefficient, s, decreases linearly with the concentration, C, by employing the assumption which was adopted originally by Faxén who considered a similar problem with s independent of C. It is shown that, with increasing concentration dependence of s, the concentration gradient curve is markedly sharpened, and the whole curve is also noticeably shifted towards the solvent side, but symmetry of the curve is practically maintained except at the edges. A simple and approximate equation which predicts the position of the maximum of a given boundary curve as a function of time for a given set of the parameters is derived. It is shown that this equation is useful for evaluating the sedimentation coefficient at a given concentration. An equation which also predicts the maximum height of the boundary curve as functions of time and related parameters with a satisfactory degree of approximation is obtained. Using this equation, reliable values of the diffusion coefficient may be obtained from sedimentation experiments when s depends linearly on C.