Multi-Layer Multi-Component Adsorption Isotherm Model:Theoretical and Experimental Validation

Multi-layer multi-component adsorption isotherm model: Theoretical and experimental validation

Ju Weon Lee¹ Andreas Seidel-Morgenstern^{1, 2}

 

¹ Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

² Institute of Process Engineering, Otto von Guericke University, Magdeburg, Germany

In liquid chromatography, one of many isotherm models introduced based on theoretical and heuristic backgrounds is selected to analyze and describe the retention behaviors of adsorbates [1, 2]. However, most conventional isotherm models are not suitable in cases that adsorbate mixture shows ununiformed behaviors, e.g. in a certain range isotherm shape is changed from Langmuir-like to anti-Langmuir and vice versa, or some components shows different behaviors. Recently, several researchers introduced multi-layer isotherm models for a single component to express theoretical clues for the mixed isotherm behaviors [3-5].

In this work, a novel multi-layer multi-component (MLMC) adsorption isotherm model developed on a theoretical basis was introduced to explain the retention behaviors that the conventional theoretical isotherm models cannot explain. The following equation shows the structure of the MLMC model.

 

where M and N are the number of components and adsorption layers, respectively.

Case Study: Mixed binary system (  )

For mixed binary systems (one component obeys a Langmuir-like isotherm, and the other obeys an anti-Langmuir isotherm), a generalized Langmuir isotherm model (concentration terms in the denominator can be assigned to positive or negative) was introduced in a heuristic manner [6]. Figure 1 shows the simulated elution profiles with the MLMC model.

 

Figure 1. Simulated concentration profiles of the binary mixtures with the MLMC model.
a) , b)

References

[1]   T.L. Hill, “An Introduction to Statistical Thermodynamics” (1960) Dover Publications Inc.

[2]   G. Guiochon, S.G. Shirazi, A.M. Katti, “Fundamentals of Preparative and Nonlinear Chromatography” (1994) Academic Press.

[3]   C.-H. Wang, B.J. Hwang, Chem. Eng. Sci. 55 (2000) 4311.

[4]   F. Gritti, W. Piatkowski, G. Guiochon, J. Chromatogr. A 978 (2002) 81.

[5]   P. Vajda, A. Felinger, J. Chromatogr. A 1324 (2014) 121.

[6]   M. Mazzotti, J. Chromatogr. A 1126 (2006) 311.