Sedimentation and electrophoresis of interacting substances, II. Asymptotic boundary shape for two substances interacting reversibly

Abstract

When a solution is analyzed by means of electrophoresis, or sedimentation in the ultracentrifuge, the schlieren pattern, which is related in a simple way to the gradients of concentration at the junction of solution with solvent, generally gives a direct measure of the concentrations of the various species of macromolecule present. This is no longer true if reversible interaction occurs between the primary molecules in the solution, and the present paper endeavours to show how interaction modifies the schlieren pattern. A reversible reaction A + B = C is treated, and equations for the schlieren pattern are deduced which cover all possible values of the concentrations of A and B, for a given equilibrium constant, and all values of the velocity of C relative to that of A and B. It has not been possible to include the effects of diffusion, and finite rate of reaction, but, instead, the asymptotic shape of the schlieren pattern, which would be approached with time, has been found. Examples of typical patterns are given, and cases are also illustrated in which boundaries are present which tend to become sharper through interaction, instead of spreading continually. Published experiments on the electrophoresis of interacting systems in which two components appear to be present in one boundary system and three in the conjugate boundary system find an explanation in these patterns of the model system.