© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

Reload Adsorption Guide

ADSORPTION: prediction
multicomponent systems
(some ideas)

General Integral Equation / GL (Generalized Langmuir) / All equations (preview)


Adsorption type ( Linear Langmuir plot / Graham plot / Consistency / Henry constant )
Popular isotherms ( Mono-, Multilayer, Experimental, Micro-, Mesoporous )
Data analysis: LSq data fitting / Heterogeneity: Global , σE / Linear plots / φ-function / Pores )
Prediction/Description of Multicomponent adsorption / Wastewater adsorption
Heterogeneity and Molecular Size ( Theory and Prediction / Simple binary isotherm )


General | Prediction | References | Cases | Prediction steps | Examples

Chapter based on:
Unified description of physical adsorption
presented in references and summarized in:
General Integral Equation of Adsorption in multicomponent systems
and Energy correlations

Data analysis - prediction of multi-component adsorption:


Model pictures will be here
Necessary theoretical background and model pictures are given in:
multi-component GIEA and Energy correlations

Examples of analysis/prediction (see the references):
Hand drawing after my paper Ref. 1 above.

Step 1 - single-component adsorption experiment (data from literature, see ref.1 above):
Single-component adsorption of pure benzene and CCl4 vapors on wide porous silica gel KSK and aerosil (experimental data):
Adsorption prediction: pure gases - isotherms
Step 2 - fitting (see ref.1 above):
The isotherms are shown in log-log reduced scale (x=p/ps) (left and top scales). Points are experimental data (raw or transformed), red lines are fitted theoretical GF isotherms (General Freundlich) with LGD (Lopez-Gonzalez-Dietz) multilayer. Lower lines represent calculated monolayer part of adsorption as calculated according to BET (blue) and LGD isotherm (bottom and right scales) - better fitting to LGD is obvious:
Adsorption prediction: pure gases - isotherms (log scale) + monolayer corrections
Table 1. Single-component data fitting: General Freundlich isotherm (GF) with multilayer factor (BET, LGD).
Adsorbent
Temp [K]
Adsorbate i ln Kx,i * mi * am,i **
[mmol/g]
Aerosil
303K
Benzene 1 1.20 0.634 0.600
CCl4 2 0.54 0.769 0.536
KSK silica gel
293K
Benzene 1 1.03 0.613 1.38
CCl4 2 0.08 0.79 1.28

* GF isotherm with multilayer BET correction and LGD (Lopez-Gonzalez-Dietz) correction (see multilayer isotherms). The original adsorption data was reduced to its monolayer part (e.g. for BET, amono = a (1-x), for LGD amono = a (1-x2/2)/(1-x) ); for both multilayer isotherms the pressure, p, in original GF equation was replaced by [x/(1-x)]. The LSQ fitting was performed for log(amono).

** am,i values presented in the table have been obtained as average of 3 values: (1) obtained from GF-LGD fitting, (2) obtained by the B-point method, (3) obtained from adsorption of benzene vapours and corrected with respect to adsorbate molar volume.

Step 3 - prediction, comparison with multicomponent experiment (see ref.1 above):
Experimetal isotherms of binary adsorption in liquid mixtures of benzene(1) + CCl4(2) are compared with predicted/corrected theoretical lines. The heterogeneity parameters have been used as obtained by the prediction method shown above, adsorption capacities are average values as obtained for individual components in adsorption from gas phase. The equilibrium constants are corrected by comparing the experimental data with theoretical lines in log-log plot of GF isotherm:
Adsorption prediction: predicted (corrected) binary isotherms

Table 2. Predicted and corrected parameters of binary liquid adsorption.

Adsorbent Predicted from vapor adsorption of pure components Corrected - fitted to the experimental data
ns * m12 ** ln K12 *** ln K12 ****
Aerosil 0.567 0.938 0.61 1.45
KSK silica gel 1.33 0.89 0.95 1.35

* ns = (am,1 + am,2)/2 (from vapor adsorption)

** m12 are approximated as follows: from individual heterogeneity parameters mi (from vapor adsorption), corresponding energy dispersions σi are calculated. From their positive difference σ12 (corresponds to the distribution of differences of adsorption energy for molecules 1-2 or 2-1, or in other words their competition to the surface sites) the heterogeneity parameter m12 is calculated.

*** ln K12 = ln K1 - ln K2 = ln (K1/K2), corresponds to the difference of average adsorption energies of 1 and 2 (from vapor phase). It original values are properly determined (usually LSQ data fitting is not very sensitive to the K values; the fitted model - energy distribution, multilayer, lateral interactions etc. - may also be an approximation) and at the same time the competition in binary mixture is not altered by the change of state (vapor to liquid) or mixing, then such value may describe adsorption competition from liquid mixture.

**** this value of ln K12 is obtained from fitting the model to the binary liquid adsorption data with ns and m12 fixed to the predicted values.

Conclusions (see references above):
The prediction method worked very well with respect to the heterogeneity effects - the relative differences in adsorption energies of components are well preserved even after change of state of matter. The adsorption equilibrium constants depend to higher degree on the adsorbate state or medium type (gas or liquid, mixing effects in liquid) in which or from which molecules are adsorbed.


Adsorption type ( Linear Langmuir plot / Graham plot / Consistency / Henry constant )
Popular isotherms ( Mono-, Multilayer, Experimental, Micro-, Mesoporous )
Data analysis: LSq data fitting / Heterogeneity: Global , σE / Linear plots / φ-function / Pores )
Prediction/Description of Multicomponent adsorption / Wastewater adsorption
Heterogeneity and Molecular Size ( Theory and Prediction / Simple binary isotherm )


General Integral Equation / GL (Generalized Langmuir) / All equations (preview)

Top
My papers
Search for papers
Main page

E-mail addresses are modified to in order to prevent spamming / mail-abuse:
in e-mail remove spaces, replace " AT@AT " by "@"

Send a message to Adam.Marczewski AT@AT umcs.lublin.pl

Disclaimer