[email protected] flowing and stationary adsorption experiment. chromatographic determination of...
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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
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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
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Supernatant-sediment separation method
Constant potentialConstant potential
Overestimation
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Supernatant-sediment separation method
Constant charge Constant charge
Equilibrium ?
Underestimation
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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?
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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
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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)
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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
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bCq *
bCbC
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
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Jovanovic isotherm
bC exp1
Extended Jovanovic isotherm
bC exp1
Fowler –Guggenheim/Jovanovic-Freundlich isotherm
expexp1 bC
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Retention coefficients calculated in the different way(Lamgmuir isotherm)
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The dependence 1/(κ-1)=f(C0) for Langmuir isotherm
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The dependence 1/(κ-1)=f(C0) for Toth isotherm
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The dependence 1/(κ-1)=f(C0) for Langmuir-Freundlich isotherm
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The dependence 1/(κ-1)=f(C0) for Frumkin-Fowler-Guggenheim
isotherm (only two parameters can be retrieved)
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00 d
/1erferf
21
zzH
zz
Hz
00 d
/1erferf
21
zzH
zz
Hz
12
1D
D 1
21D
D
,,1 qbfD ,,1 qbfD
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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
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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)