Sedimentation and electrophoresis of interacting substances. I. Idealized boundary shape for a single substance aggregating reversibly

Abstract

The effect of differential transport on the gradient of concentration across a boundary is calculated for a substance existing in solution as a series of aggregates in mutual equilibrium. General equations are derived which are then used to construct schlieren patterns for a model system in order to illustrate the types of pattern to which aggregation can give rise. It is shown that in electrophoresis experiments the boundary in one limb is diffuse, and in the other hyper-sharp. In sedimentation the boundary is diffuse in general, but may have a hypersharp leading edge if there is a strong dependence o f the sedimentation velocity of the individual species on solute concentration. Although it is not possible for true resolution to occur at the boundary of a system in which equilibrium is maintained, the shapes of the schlieren patterns of the diffuse boundaries can be such as to give the impression that partial resolution is occurring. It means then that aggregates composed of more than two molecules are present and that at least one type of higher aggregate is strongly accentuated.