The coupling of the electrostatic potential with the transport and adsorption mechanisms in ion-exchange chromatography systems: Theory and experiments

The coupling of the constitutive expression for the electrostatic potential as specified through Poisson's equation together with the constitutive equations for the mechanisms of convection, diffusion, electrophoretic migration, and adsorption provides the necessary set of constitutive expressions to be employed in the material balance equations of ion-exchange chromatography systems to construct macroscopic continuum models that could be used to design and simulate the dynamic behavior of systems involving a single charged adsorbate or multiple charged adsorbates. A physically relevant and consistent macroscopic continuum model that can predict, as has been observed experimentally by UV confocal microscopy (UVCM), the presence or absence of the concentration overshoot phenomenon, based on the pH and ionic strength of the liquid solution, is discussed and expanded to describe the behavior of IEC systems involving competitive adsorption of two or more charged adsorbates. Furthermore, UVCM and confocal scanning laser microscopy (CSLM) experiments and the macroscopic continuum models that could be used to analyze their data are indicated. Results are also presented that have been obtained from molecular dynamics (MD) modeling and simulation studies (microscopic modeling and analysis) employing realistic atomistic models derived from fundamental physics, and indicate the physical mechanisms that are relevant and actively involved in the transport and adsorption of charged adsorbates in IEC systems, as well as their relative importance. The results obtained from the MID simulations show that when a charged macromolecule is adsorbed it is restrained by a strong dominant Coulombic interaction and is trapped by a hydration layer adjacent to the surface and these lead to zero lateral displacement of the adsorbed macromolecule. This finding indicates that surface diffusion could be a physically implausible mechanism in IEC systems involving charged adsorbate macromolecules. Also, the results obtained from the MD simulation studies show that the transport coefficients that characterize the mass transfer of a charged adsorbate in the liquid solution by diffusion and electrophoretic migration have magnitudes along the lateral direction that are different from those along the direction that is normal to the charged surface.