General local-equilibrium chromatographic theory for eluents containing adsorbing buffers

An efficient, general strategy was developed for numerically solving the system of equations that describe a pH gradient under local-equilibrium conditions when the elution buffer contains arbitrary numbers of both adsorbed and unadsorbed buffering species (weak electrolytes) and for a weak- or strong-base ion-exchange column packing. Since the method involves the solution of algebraic equations, instead of partial differential equations, it can be used to rapidly determine the effluent pH profile given the adsorption equilibrium constants for the buffering species. It can also be used iteratively to determine the adsorption equilibrium constants for the buffering species from an experimentally determined effluent pH profile as well as to determine the composition of the elution buffer required to achieve a desired shape for the pH gradient given the adsorption equilibrium constants for the buffering species. The calculation method is verified experimentally and used to illustrate the behavior of chromatographic methods which employ retained pH and ionic strength gradients.