Modeling and Analysis of the Electrokinetic Mass Transport and Adsorption Mechanisms of a Charged Adsorbate in Capillary Electrochromatography Systems Employing Charged Nonporous Adsorbent Particles.

Abstract Mass-transfer systems based on electrokinetic phenomena (i.e., capillary electrochromatography (CEC)) have shown practical potential for becoming powerful separation methods for the biotechnology and pharmaceutical industries. A dynamic mathematical model, consisting of the momentum balance and the Poisson equations, as well as the unsteady-state continuity expressions for the cation and anion of the background electrolyte and of a positively charged analyte (adsorbate), is constructed and solved to determine quantitatively the electroosmotic velocity, the electrostatic potential, the concentration profiles of the charged species in the double layer and in the electroneutral core region of the fluid in the interstitial channels for bulk flow in the packed chromatographic column, and the axial current density profiles as the adsorbate adsorbs onto the negatively charged fixed sites on the surface of the nonporous particles packed in the chromatographic column. The frontal analysis mode of operation is simulated in this work. The results obtained from model simulations provide significant physical insight into and understanding of the development and propagation of the dynamic profile of the concentration of the adsorbate (analyte) and indicate that sharp, highly resolved adsorption fronts and large amounts of adsorbate in the adsorbed phase for a given column length can be obtained under the following conditions: (i) The ratio, γ 2, 0 , of the electroosmotic velocity of the mobile liquid phase at the column entrance after the adsorption front has passed the column entrance to the electrophoretic velocity of the anion is very close to −1. The structure of the equations of the model and model simulations indicate that a stable adsorption front cannot develop when γ 2, 0 is less than −1 unless the value of the mobility of the cation is less than the value of the mobility of the analyte, which may be a rare occurrence in practical CEC systems. (ii) The ratio of the mobility of the cation to the mobility of the analyte is less than two orders of magnitude. This effect becomes more significant as the value of the equilibrium adsorption constant, K A, 3 , of the analyte increases. (iii) The concentration of the analyte relative to the concentration of the cation is increased (feed solutions with less dilute concentrations of the analyte are employed). Therefore, to obtain good performance for CEC systems operated in the frontal analysis mode (well-resolved adsorption fronts and high adsorbate amounts in the adsorbed phase), one can choose an electrolyte whose cation has a mobility that is not more than one or two orders of magnitude greater than the mobility of the analyte and whose anion has a mobility such that the value of γ 2, 0 is close to −1; one can then bring the value of γ 2, 0 closer to −1 by decreasing the particle diameter, d p , and/or making the value of the surface charge density, δ 0 , of the particles more negative (in effect, making the value of the zeta potential, ζ p , at the surface of the particles more negative at time t =0) to change the value of the velocity, «υ x »| x=0 , of the electroosmotic flow (EOF) at the column entrance («υ x »| x=0 is determined after the adsorption front has passed the column entrance). This approach could provide conditions in the column that avoid overloading of the adsorbate. One can obtain faster breakthrough times at the sacrifice of resolution and utilization of the adsorptive capacity of the packed bed if one employs a cation whose mobility is very large relative to the mobility of the analyte and/or an anion that provides a value of γ 2, 0 significantly greater than −1. If it is possible, one can increase the concentration of the analyte in the feed stream to avoid sacrificing resolution and adsorptive capacity of the packed bed and still decrease the time at which breakthrough occurs. Also, the dynamic behavior of the axial current density, i x , profiles indicates that the magnitude of i x and/or the change in the value of i x across the adsorption front could serve as a measurement for the rate of propagation of the adsorption front through the column. Furthermore, the effect of the decreased magnitude of the velocity of the EOF in the region of the column where the analyte is present in the adsorbed phase could act to decrease the effect of tailing when CEC systems are operated in the pulse injection mode (analytical electrochromatography) because the higher velocity of the fluid upstream of the migrating adsorption zone may compress the tail of the peak.