Estimating the parameters of competitive Langmuir adsorption isotherms from measured responses to rectangular pulse injections exploiting equilibrium theory

Abstract

Knowledge of adsorption isotherms is essential for the design and optimization of chromatographic separation processes. Since the experimental determination of these thermodynamic functions is a complicated and time consuming task, there is a need to develop methods which are fast and easy to apply. An attractive group of methods is based on neglecting in the analysis of measured dynamic elution profiles all kinetic effects. These methods assume the validity of an isotherm model equation and exploit the possibility to solve analytically the column mass balance equations of the equilibrium model. If just the dispersive part of an elution profile is, the method is known as “elution by characteristic point” (ECP). The ECP method has been applied successfully to analyse column effluent profiles of single component dissolved in a mobile phase. This work extends the ECP method to analyse just the shapes of elution profiles recorded after injecting samples that contain two key components to be separated. The extended ECP method requires recording only one overloaded elution profile for the two-component mixture and offers a fast and efficient way to estimate isotherm model parameters. The method is in particular attractive if there is limited access to the pure components, as for example in cases of enantiomers. The underlying theory is presented and applied for the case that the adsorption equilibria can be described satisfactorily by the classical competitive Langmuir model. Core of the theory are the available analytical equations describing the outlet concentration profiles of the two solutes for the equilibrium controlled case the. Considering a case study, it is shown that the extended ECP method can be applied successfully for columns characterized by 2500 or more theoretical plates. However, the method can be useful also for columns with lower efficiency. It provides then a rough estimation regarding the isotherm courses.