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A simple theoretical framework for the effect of the eluting salt concentration on the retention factor of proteins in ion-exchange chromatography under conditions of linear elution is described. It is based on the solution of the linearized Poisson-Boltzmann equation for two oppositely charged planar surfaces in contact with a salt solution. The theory predicts a linear relation between the logarithmic retention factor and the reciprocal square root of the ionic strength of the eluent in the salt concentration range used in linear elution chromatography. A large body of retention data obtained in ion-exchange chromatography of proteins over a wide range of experimental conditions was plotted as ln k' vs 1/square root of I, where k' and I are the retention factor and ionic strength, respectively. The plots are linear or nearly so, as predicted for a moderate salt concentration range by the theory. From the slope of such plots the characteristic charges of the proteins were estimated by using only fundamental physicochemical constants. The chromatographically measured protein charges compare well to those obtained from titrimetric experiments at the same pH, although certain deviations are noted. The theoretical approach presented here offers a more realistic treatment of the ion-exchange chromatography of proteins than the stoichiometric displacement model and can serve as a convenient framework for the analysis of retention data.

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Recently, the "slab model" was proposed to describe the interaction between a protein and the charged stationary phase surface in electrostatic interaction chromatography. The model is based on the solution of the linearized Poisson-Boltzmann equation for a system consisting of two charged planar surfaces in contact with an electrolyte solution. In the model it is assumed that the charge densities of both the protein and the stationary phase are constant during the adsorption process. However, as the protein comes close to the oppositely charged stationary phase surface, the protein net charge will change due to the electrical field from the stationary phase. In this paper, the theory for charge regulation is applied to the original slab model, and simple algebraic equations are developed in order to include the effect of charge regulation on the capacity factor. A large body of retention data are reanalyzed with the new model, and it is found that there is good agreement between the chromatographically and titrimetrically obtained protein net charge. An interesting consequence of charge regulation is that it gives a contribution to the retention of proteins with zero net charge and even to proteins with the same sign of charge as the stationary phase.

We have recently proposed a theoretical framework for the effect of the eluting salt ionic strength of the eluent on the retention factor of proteins in ion-exchange chromatography of proteins. It is based on the solution of the linearized Poisson-Boltzmann equation for two oppositely charged planar surfaces in contact with a salt solution and describes the coulombic interaction between the protein and the oppositely charged stationary-phase surface. At sufficiently high salt concentrations in the mobile phase van der Waals interactions between the protein and the stationary phase become important. In this work we consider the effect of salt on the combined coulombic and van der Waals interactions by combining the electrostatic theory with the theory for van der Waals interactions. The combined theory describes the retention of proteins as a function of eluting salt concentration over a wide salt concentration range. The protein molecules are, according to the proposed theory, held in a diffuse layer close to the stationary phase and are not in a distinct layer, which is assumed in the traditional thermodynamic interpretation of the capacity factor. For this reason, we also examine the thermodynamic interpretation of the capacity factor when it is due to distant dependent interactions.