Adsorption equilibrium, analyte behavior

HPLC analytes involved in adsorption equilibrium processes could also participate in other types of processes, such as ionization, tautomerization, solvation, and so on. The analyte behavior in adsorption equilibrium is certainly affected by the presence of secondary equilibrium, and if it could be considered as an independent process based on the time and position of the analyte within the column, this equilibrium could be incorporated in the solution of mass-balance equation. 

A chromatographic system consisting of the binary eluent (e.g., acetonitrile-water) with liophilic salt added in low concentration (not more than lOOmM), along with basic analyte, is considered here. Adsorption behavior of acetonitrile in the column has been discussed in Section 2.12, and we assume that low concentrations of liophilic salt additives and injection of small amount of the analyte does not noticeably disturb its adsorption equilibrium. 

A useful literature relating to polypeptide and protein adsorption kinetics and equilibrium behavior in finite bath systems for both affinity and ion-ex-change HPLC sorbents is now available160,169,171-174,228,234 319 323 402"405 and various mathematical models have been developed, incorporating data on the adsorption behavior of proteins in a finite bath.8,160 167-169 171-174 400 403-405 406 One such model, the so-called combined-batch adsorption model (BAMcomb), initially developed for nonporous particles, takes into account the dynamic adsorption behavior of polypeptides and proteins in a finite bath. Due to the absence of pore diffusion, analytical solutions for nonporous HPLC sorbents can be readily developed using this model and its two simplified cases, and the effects of both surface interaction and film mass transfer can be independently addressed. Based on this knowledge, extension of the BAMcomb approach to porous sorbents in bath systems, and subsequently to packed-, expanded-, and fluidized-bed systems, can then be achieved. 

This behavior is known as hysteresis. Some cases of hysteresis have been ascribed to analytical errors caused by displacement of previously held permanent gases during the adsorption stage other cases may be due to insufficient time to reach equilibrium. Hysteresis has been found, however, even with carbons that were carefully degassed before adsorption and when ample time has been provided to reach equilibrium. 

If the equilibrium isotherm is linear, analytic expressions for the concentration front and the breakthrough curve may, in principle, be derived, however complex the kinetic model, but except when the boundary conditions are simple, the solutions may not be obtainable in closed form. With the widespread availability of fast digital computers the advantages of an analytic solution are less marked than they once were. Nevertheless, analytic solutions generally provide greater insight into the behavior of the system and have played a key role in the development of our understanding of the dynamics of adsorption columns. 

In this equation, rt and q are the adsorbed and the mobile phase concentrations, X is a dimensionless coefficient, and is the equilibrium constant the upper limit of rt is given by N . The linear term describes the interaction of achiral carrier particles with the analyte, while the Langmuir term describes the saturation behavior of the chiral selector. This behavior can be understood by inspection of Fig. 5, which shows in an idealized form the adsorption isotherms of two enantiomers. 

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