Flowing and stationary adsorption experiment. Chromatographic determination of adsorption isotherm parameters Waldemar Nowicki, Grażyna Nowicka Department of Physical Chemistry Faculty of Chemistry UAM, Poznań

The overlapping of the electrical fields of colloidal particles causes the shift of the adsorption equilibrium of ionic species and changes their equilibrium concentration in the bulk

Supernatant-sediment separation method Constant potential Overestimation

Supernatant-sediment separation method Constant charge Equilibrium ? Underestimation

 Is there any possibility to retrieve the adsorption isotherm parameters from the chromatographic data?  Does the analytical relationship exist between the adsorption isotherm and the chromatographic outlet profile parametes?

Inverse problem of chromatography (IPC) – calculation of the adsorption isotherm from the profiles of bands. Frontal analysis (FA) – the determination of the amount adsorbed as a function of the mobile phase concentration Perturbation on a plateau technique (PPT) – the determination of the slope of the isotherm as a function of the mobile phase concentration Perturbation on a plateau technique (PPT) – the determination of the slope of the isotherm as a function of the mobile phase concentration

Inverse problem of chromatography (IPC) – calculation of the adsorption isotherm from the profiles of bands. Frontal analysis by characteristic point (FACP), elution by characteristic point (ECP) – the analysis of the diffuse rear boundary Inverse numerical procedure (INP) – calculation of the adsorption isotherm from the profiles of overloaded bands by minimizing the differences between overloaded profiles and the profiles calculated by solving the mass balance equation (EDM)

Flow Elemental plate

Henry (linear) isotherm Langmuir isotherm Generalized Freundlich isotherm Langmuir-Freundlich isotherm Toth isotherm Frumkin-Fowler- Guggenheim isotherm

Jovanovic isotherm Extended Jovanovic isotherm Fowler­–Guggenheim/Jovanovic-Freundlich isotherm

Simulation of the adsorbate percolation through the column Parameters of the simulation shown on the program interface Rectangular inlet profile, Langmuir model Sinusoidal inlet profile, Langmuir model Sinusoidal inlet profile, Henry model Sinusoidal inlet profile, FFG model

Simulation results: No adsorption – diffusion only

Simulation results: Henry isotherm

Simulation results: Langmuir isotherm

Simulation results: Generalized Freundlich isotherm

Simulation results: Langmuir-Freundlich isotherm

Simulation results: Toth isotherm

Simulation results: Frumkin –Fowler-Guggenheim isotherm

Simulation results: Jovanovic isotherm

Simulation results: Extended Jovanovic isotherm

The result generalization:  The adsorption isotherm parameters (q, b,,  ) are correlated to the outlet profile parameters (the time of retention, the peak asymmetry)  There is the explicit analytical relationship between the retention time and some isotherm parameters  The outlet profile can be approximately described by the two parameter equation

Equation of the uotlet profile (extension of the Henry model): Retention coefficient from differential mass balans equation: Assumption:

Retention coefficients calculated in the different way (Lamgmuir isotherm)

The dependence 1/(κ-1)=f(C 0 ) for Langmuir isotherm

The dependence 1/(κ-1)=f(C 0 ) for Toth isotherm

The dependence 1/(κ-1)=f(C 0 ) for Langmuir-Freundlich isotherm

The dependence 1/(κ-1)=f(C 0 ) for Frumkin-Fowler-Guggenheim isotherm (only two parameters can be retrieved)

For the small adsorbate concentration FFG model for α=1  Henry model FFG model for α=0  Langmuir model

Conclusions:  Some two or three parameter isotherms can be retrieved from the chromatograhic data  The correct relationship between the retention coefficient and the adsorbate concentration for any isotherm is found  In the case of the Langmuir isotherm the relationship between initial adsorbate concentration and the time of retention can be written in the rectilinear form (L model)  Isotherms with heterogeneity parameters can be retrieved using the nonlinear least square method from the retension time vs. initial adsorbate concentration dependencies (T model )  The adsorbate-adsorbate interaction parameter can be obtained on the basis of the elution profile asymmetry analysis (FFG model)