Adsorption

, Volume 20, Issue 8, pp 987–997 | Cite as

Modeling of high pressure adsorption isotherm using statistical physics approach: lateral interaction of gases adsorption onto metal–organic framework HKUST-1

  • Asma Nakhli
  • Manel Bergaoui
  • Mohamed Khalfaoui
  • Jens Möllmer
  • Andreas Möller
  • Abdelmottaleb Ben Lamine
Article
First Online:
Received:
Revised:
Accepted:

Abstract

A novel theoretical approach for description of high pressure isotherm is developed in the present study. This approach is based on the grand canonical formalism in statistical physics by taking into account the lateral interaction between the adsorbate molecules. This leads to five parameters equation describing the high pressure adsorption equilibrium. This model is applied to experimental adsorption data of hydrogen, nitrogen, methane and carbon dioxide on metal–organic frameworks HKUST-1. There is a good correlation between experimental data and those calculated by the new model at pressure up to 50 MPa. It was found that hydrogen molecules can be considered as a ideal gas over a wide temperature range and even at high pressures. Lateral interactions were found to be necessary to describe the adsorption of N2, CH4 and CO2 at high pressures. The proposed model allows also prediction of some adsorption thermodynamic functions which govern the adsorption mechanism such as the entropy, the Gibbs free enthalpy and the internal energy.

Keywords

Monolayer adsorption Statistical physics model Metal–organic framework Lateral interactions 

List of symbols

a

Cohesion pressure (J mL/mol)

A

Adsorbed molecule (s)

b

Covolume (mL/mol)

C

Adsorbate concentration (mol/mL)

Ea

Total adsorption energy (kJ/mol)

Eint

Internal energy (kJ/mol)

g

Gibbs free enthalpy for one receptor site (kJ/mol)

G

Gibbs free enthalpy (kJ/mol)

J

Grand potential

kB

Boltzmann constant (m2Kg/(s2K))

n

Fraction or the number of adsorbed gas molecule(s) per site

Ni

Occupation site

NM

Receptor sites density (mg/g)

No

Occupation number

Qa

Total number of adsorbed molecules (mg/g)

S

Site

sa

Configurational entropy (J/K)

w

Energetic parameter (J/mol)

w0

Constant

Zgc

Grand canonical partition function

Zgtr

Translation partition function

β

Boltzman constant

\( \varDelta E^{a} \)

Adsorption energy (kJ/mol)

(−ε)

Adsorption energy of a receptor site (kJ/mol)

μ

Chemical potential (KJ/mol)

μp

Chemical potential for ideal gas (kJ/mol)

μa

Chemical potential of adsorbed phase (kJ/mol)

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Asma Nakhli
    • 1
  • Manel Bergaoui
    • 1
  • Mohamed Khalfaoui
    • 1
  • Jens Möllmer
    • 2
  • Andreas Möller
    • 2
  • Abdelmottaleb Ben Lamine
    • 1
  1. 1.Laboratory of Quantum Physics, Faculty of Sciences of MonastirUniversity of MonastirMonastirTunisia
  2. 2.Institut für Nichtklassische Chemie e.VLeipzigGermany

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