Effects of diffusion on the electrophoretic behavior of associating systems: the Gilbert-Jenkins theory revisited

The Gilbert-Jenkins theory predicts the asymptotic shape of moving-boundary sedimentation and electrophoretic patterns and broad zone molecular sieve chromatographic elution profiles for the class of interacting systems, A + B in equilibrium C, in which two dissimilar macromolecules react reversibly to form a complex. A particularly provocative case is the one in which the complex has a greater migration velocity than that of either reactant, each of which has a different velocity. Depending upon conditions, this case predicts, for example, that in the asymptotic limit an ascending electrophoretic pattern or a frontal gel chromatographic elution profile can show two hypersharp reaction boundaries separated by a plateau. This prediction is now confirmed by numerical solution of transport equations which retain the second-order diffusional term and extrapolation of the computed patterns to zero diffusion coefficient. For finite diffusion coefficient, however, the two hypersharp reaction boundaries are separated by a weak negative gradient. These calculations are extended to an examination of the transitions between the three types of patterns admitted by the case under consideration in order to gain physical understanding and to define criteria for recognizing the transitions. Studies of this kind not only establish confidence in the Gilbert-Jenkins theory, but, in addition, they provide new insights which make for more effective application of the theory to real systems.