gwnow@amu.edu.pl

Flowing and stationary adsorption experiment.

Chromatographic determination of adsorption isotherm

parameters

Flowing and stationary adsorption experiment.

Chromatographic determination of adsorption isotherm

parameters

Waldemar Nowicki, Grażyna NowickaWaldemar 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 potentialConstant potential

Overestimation

Supernatant-sediment separation method

Constant charge 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

Frontal analysis (FA) – the determination of the amount adsorbed as a function of the mobile phase concentration

ads

0DR*

V

CVVq

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

0

*

00ret 11

)(

0

tC

q

VtCt

CC

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

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)

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)

1-sol,isol,i1-sol,isol,i 2nn

dnn 1-sol,isol,i1-sol,isol,i 2

nnd

nn

,,,_,,surf,isol,isurf,isol,i bqtypeisothermNnnfRnn ,,,_,,surf,isol,isurf,isol,i bqtypeisothermNnnfRnn

Flow

Elementalplate

bCq *

bCbC

qq

1

*

bCbC

1

bC

bC

1

/11 bC

bC

exp1

expbCbC

Henry (linear) isotherm

Langmuir isotherm

Generalized Freundlich isotherm

Langmuir-Freundlich isotherm

Toth isotherm

Frumkin-Fowler-Guggenheim isotherm

Jovanovic isotherm

bC exp1

Extended Jovanovic isotherm

bC exp1

Fowler –Guggenheim/Jovanovic-Freundlich isotherm

expexp1 bC

Simulation of the adsorbate percolation through the columnParameters 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:

t/t0

0.8 1.0 1.2 1.4

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

d=0.8d=0.6d=0.4d=0.2d=0.0

t/t0

0.8 1.0 1.2 1.4

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

d=0.8d=0.6d=0.4d=0.2d=0.0

No adsorption – diffusion only No adsorption – diffusion only Column volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000

Precision 1e-9

Simulation results:

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.200b=0.100b=0.050b=0.020b=0.010b=0.005

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.200b=0.100b=0.050b=0.020b=0.010b=0.005

Henry isotherm Henry isotherm Column volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000Dispersion parameter 1.0Heterogeneity coefficient 1.0Precision 1e-9

Simulation results:

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.200b=0.100b=0.050b=0.020b=0.010b=0.005

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.200b=0.100b=0.050b=0.020b=0.010b=0.005

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

Langmuir isotherm Langmuir isotherm Column volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000Dispersion parameter 1.0Heterogeneity coefficient 1.0Precision 1e-9

Simulation results:

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

c/c0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

c/c0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Generalized Freundlich isotherm Generalized Freundlich isotherm Column volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000

Heterogeneity coefficient 1.0Precision 1e-9

Simulation results:

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Langmuir-Freundlich isotherm Langmuir-Freundlich isotherm Column volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000

Heterogeneity coefficient 1.0Precision 1e-9

Simulation results:

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

Thet

a

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1.0 1.2 1.4 1.6 1.8

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

Thet

a

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1.0 1.2 1.4 1.6 1.8

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Toth isotherm Toth isotherm Column volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000

Heterogeneity coefficient 1.0Precision 1e-9

Simulation results:

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

Thet

a

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1.8 2.0 2.2

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.10, =1.0b=0.10, =0.8b=0.10, =0.6b=0.10, =0.4b=0.10, =0.2b=0.10, =0.0b=0.10, =-0.2b=0.10, =-0.4b=0.10, =-0.6

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

Thet

a

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1.8 2.0 2.2

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.10, =1.0b=0.10, =0.8b=0.10, =0.6b=0.10, =0.4b=0.10, =0.2b=0.10, =0.0b=0.10, =-0.2b=0.10, =-0.4b=0.10, =-0.6

Frumkin –Fowler-Guggenheim isothermFrumkin –Fowler-Guggenheim isothermColumn volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000Adsorption constant 0.02

Precision 1e-9

Simulation results:

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.200b=0.100b=0.050b=0.020b=0.010b=0.005

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.200b=0.100b=0.050b=0.020b=0.010b=0.005

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

Jovanovic isotherm Jovanovic isotherm Column volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000Dispersion parameter 1.0Heterogeneity coefficient 1.0Precision 1e-9

Simulation results:

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Equilibrium concentration

0.0 0.2 0.4 0.6 0.8 1.0

The

ta

0.0

0.2

0.4

0.6

0.8

1.0

t/t0

1 2 3

c/c 0

0.0

0.2

0.4

0.6

0.8

1.0

b=0.050, =1.0b=0.050, =0.9b=0.050, =0.8b=0.050, =0.7b=0.020, =1.0b=0.020, =0.9b=0.020, =0.8b=0.020, =0.7b=0.020, =0.6

Extended Jovanovic isothermExtended Jovanovic isothermColumn volume 1Column length 10Maximum adsorption amount 10Solution concentration 1.00Input impuls time 100Concentration profile rectangleElution time 3500Theoretical shell number 1000

Heterogeneity coefficient 1.0Precision 1e-9

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):

NtD

tu

xN

ttND

ttu

xNCtxC

2

0

01

00

02

erf2

erf2

,

Retention coefficient from differential mass balans equation:

u

u0 10

CCCVq

Assumption:

0

0T

uu

CC

u 10

CCCVq

Retention coefficients calculated in the different way(Lamgmuir isotherm)

The dependence 1/(κ-1)=f(C0) for Langmuir isotherm

The dependence 1/(κ-1)=f(C0) for Toth isotherm

The dependence 1/(κ-1)=f(C0) for Langmuir-Freundlich isotherm

The dependence 1/(κ-1)=f(C0) for Frumkin-Fowler-Guggenheim

isotherm (only two parameters can be retrieved)

00 d

/1erferf

21

zzH

zz

Hz

00 d

/1erferf

21

zzH

zz

Hz

12

1D

D 1

21D

D

,,1 qbfD ,,1 qbfD

For the small adsorbate concentration

FFG model for α=1 Henry model

FFG model for α=0 Langmuir model

H2

1 1 DCD

H2

2 1 DCD

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)