• Typical hysteresis of adsorption-desorption cycle

• Langmuir isotherm :

  influence of the coefficient ‘b’

• Variations on Langmuir and Henry

• Variations of Langmuir and Henry

• Théorie de Brunauer Emmett et Teller (BET)

• Hypothèses

–Starting from the second layer E1»EL energy of molecules in liquid state

• Basic hypothesis of the BET theory

E1 = Energy of adsorption for the first layer

El  = Energy of liquid state

• Basic hypothesis of the BET theory

surface so covered with 0 adsorbed layers

…     s1          …           1

…                  …           …

…     si           …            i

Accessible surface A = so + s1 + … + si + …

• Derivation of the BET formula

• Derivation of the BET formula

• Derivation of the BET formula

• Theory of Brunauer Emmett and Teller (BET)

• Equations

– N= number of layers

x = p/p0 = relative equilibrium

pressure

––if N ® ¥
–Transformed  equation BET

• Influence of number of layers N on the shape of isotherms of adsorption (BET)

• Influence of the constant ‘C’ on the shape of isotherms of adsorption (BET)

• Application for calculation of the adsorption surface

  example : alumin NPL / N2 / 77 K

• Verifications of BET results

  example : alumin NPL / N2 / 77 K

• Approach thermodynamic – energie of adsorption

• Example:

  mesoporous system: MCM-41 et 77K

CO & CH4

Typical for heterogeneous surface

Dadsh (»2 kJ.mol-1) during the capillary condensation

Kr

Dadsh (»5 kJ.mol-1) during the capillary condensationÜ solidification ?

• Milestone properties

• Milestone properties

• Milestone properties

• Nitrogen / black of de carbon (Carbopack)

• Adsorption on precipitated silica

  Isotherms : N2 & Ar à 77K

• The conditions of the sample preparation are very important!!!!

…