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Adsorption

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European Master Adsorption Modeling of physisorption in porous materials Part 2 Bogdan Kuchta Laboratoire MADIREL Universit Aix-Marseille ... – PowerPoint PPT presentation

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Title: Adsorption


1
European Master
Adsorption Modeling of physisorption in porous
materials Part 2
Bogdan Kuchta Laboratoire MADIREL Université
Aix-Marseille
2
Typical hysteresis of adsorption-desorption cycle
Hysteresis loops H1 and H2, are characteristic
for isotherms of type IV (nanoporous materials).
Loop of hysteresis H1 shows nearly vertical and
parallel branches of the loop  it indicates a
very narrow distribution of pore sizes. Loop of
hysteresis H2 is observed if there are many
interconnections between the pores.
3
Typical hysteresis of adsorption-desorption cycle
Loops of hysteresis H3 et H4, appear on isotherms
of type II where there is no saturation. They are
not always reproducible. Loop of hysteresis H3,
is observed in porous materials formed from
agregats, where the capillary condensation
happens in a non-rigid framework and porosity not
definitly defined. Loop of hysteresis H4 are
often observed in structures built from planes
that are not rigidly
4
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7
Theories of adsorption
Frundlich model Langmuir model BET
8
Theory of adsorption by Freundlich x/m ? c1/n
x adsorbed mass m mass of adsorbent c
concentration ?, n experimental constants
x/m
lg(x/m)
c
Conclusion adsorption is better at higher
pressure
lg(c)
9
Langmuir theory
- 1 one type of  adsorption sites" - No lateral
interactions - 1 site of adsorption allows 1
particle to be there adsorption is limited to
one layer N s number of adsorption sites N a
number of adsorbed molecules ? fraction of
the surface covered
10
Langmuir theory
  • Isotherm of Chemisorption
  • at low pressure bp ltlt 1, so
  • Henrys law
  • at high pressure, bp gtgt 1, si

11
Langmuir isotherm influence of the coefficient
b
12
Variations on Langmuir and Henry
Henry Freundlich Langmuir Sips
(Langmuir-Freundlich) Toth Jensen Seaton
13
Variations of Langmuir and Henry
14

Methode  BET 
15
Théorie de Brunauer Emmett et Teller (BET)
  • Hypothèses
  • Starting from the second layer E1?EL energy of
    molecules in liquid state


- 1 one type of  adsorption sites" - No lateral
interactions
E1energy of adsorption of the first layer
16
Basic hypothesis of the BET theory
q
EL
B
1
E1
Energy of adsorption
Relative pressure p/p
  • E1 Energy of adsorption for the first layer
  • El Energy of liquid state

17
Basic hypothesis of the BET theory
  • surface so covered with 0 adsorbed layers
  • ... s1 ... 1
  • ... ... ...
  • ... si ... i
  • Accessible surface A so s1 si ...

18
Derivation of the BET formula
ki si-1 p k-i si
19
Derivation of the BET formula
ki si-1 p k-i si
Total surface of adsorbent
Total quantity of adsorbed gas
Asuming, that the layer properties are all the
same
C1(T)exp(-E1/kT) Ci(T)exp(-EL/kT)
20
Derivation of the BET formula
21
Theory of Brunauer Emmett and Teller (BET)
  • Equations
  • N number of layersx p/p0 relative
    equilibrium
  • pressure
  • if N ? ?
  • Transformed equation BET

22
Influence of number of layers N on the shape of
isotherms of adsorption (BET)
N 7
N 25 à ?
N 6
N 5
N 4
23
Influence of the constant C on the shape of
isotherms of adsorption (BET)
24
Application for calculation of the adsorption
surfaceexample alumin NPL / N2 / 77 K
Pente Ordonnée
25
Verifications of BET results example alumin
NPL / N2 / 77 K
26
Lateral interactions
Normal interactions
27
Simulation of adsorption
  1. Calculation of energy of adsorption
  2. Simulation of isothermes (with different strength
    of interaction)
  3. Analyse the results
  1. Simulation Monte Carlo grand canonique (GCMC)
  2. Tool program GCMC (Fortran)

Numerical challenge 1. Simulations of
equilibrium between gas and adsorbed phase 2.
Modeling of interaction between pore walls and
adsorbed particles
28
Working case MC simulation of adsorption in a
pore
Problem Fluid adsorption in cylindrical pores.
Grand Canonical Monte Carlo
?VT- constant
External ideal gas pressure P
29
Working case MC simulation of adsorption in a
pore
P1 and T fixed R (radius)
P2 and T fixed R (radius)
30
Working case MC simulation of adsorption in a
pore
T const
p ltNgt ? 0.05 234.7 16.2 0.1 362.8 7.6 0.2 38
5.8 5.8 0.3 401.9 6.9 0.4 421.2 9.7 0.5 448.3 13.2
0.7 558.3 31.6 0.8 691.6 26.7 0.9 1259.1 8.3
31
Directory Run program (compiled) input
files gcmc_H2.dat gcmc_H2_par.dat pos_inp.da
t spline
execute
Results files ene.ini - initial molecular
energies ene.fin - final molecular
energies mc.pos - molecular position after each
bin mc_ene.dat - energies after each bin
(wall and total) mc_ent.dat -
energies pos_inp.res -
analysis of results
Rename pos_inp.res ? pos_inp.dat
OK STOP
NO
32
mc.pos
Nbin N x
y z 1 154
10.886520 -14.887360 9.244424
10.898990 14.983010 21.000650
14.028510 11.913710 2.990251
-14.459990 11.605350 .722188
1.908520 18.285780 22.916110
1.256716 -18.238170 4.253842
13.606980 -12.499060 7.607756
-15.536920 -9.600965 16.492660
-15.764630 -9.760927 24.275380
-4.318254 -17.841070 23.939530
15.933630 -9.115001 17.567660 . ..
Nbin 1 N 154
Nbin 1000 N 258
Nbin 2000 N 615
33
Equilibrium situation
T const
p ltNgt ? 0.05 234.7 16.2 0.1 362.8 7.6 0.2 38
5.8 5.8 0.3 401.9 6.9 0.4 421.2 9.7 0.5 448.3 13.2
0.7 558.3 31.6 0.8 691.6 26.7 0.9 1259.1 8.3
Mean values Variation -337.7 13.5
-1160.2 15.3 -1497.9 10.2 234.7 16.2
34
Experimental results of adsorption
Milestones results
  1. Isotherms
  2. Energy of adsorption
  3. Hysteresis properties

35
Approach thermodynamic energie of adsorption
?? ?g u? pv? -Ts? ug pvg - Tsg u?-Ts? ug
RT - Tsg (v? 0, pvg RT) sgsg,0 R
ln(p/p0) ?adsh u?- ug - RT ? const. ?adss0
s? - sg,0 ? const.
Adsorption is a phenomenon exothermic !!!
36
Approach thermodynamic energie of adsorption
37
Basic types of adsorption energy curves
Curves 3 and 4 correspond delocalized and
localized adsorption on a homogeneous surface,
with lateral interactions between molecules.
Curve 2 appears in homogeneous systems with no
lateral interaction.
Curve 5 shows an existence of well defined
fomains.
Curve 1 is characteristic for heterogeneous
surfaces.
p/p0
38
Examplemesoporous system MCM-41 et 77K
  • CO CH4
  • Typical for heterogeneous surface
  • ? ?adsh (?2 kJ.mol-1) during the capillary
    condensation
  • Kr
  • ? ?adsh (?5 kJ.mol-1) during the capillary
    condensation? solidification ?

CO
Kr
CH4
39
Milestone properties
  • Capillary condensation is accompnied with
    histeresis of variable form

Ar
N2
lichrospher
CPG
40
Milestone properties
  • Hysteresis disappears at some high temperature

Argon / MCM41 (Morishige et al)
41
Milestone properties
  • For each temperature, there is a size of pore
    (and/or equilibrium pressure), that the
    hysteresis disappears below this value.

Llewellyn et al., Micro. Mater. 3 (1994) 345.
42
Adsorption - Desorption Isotherms ? MCM41 à 77K
Ar
N2
CO
Llewellyn et al., Surf. Sci., 352 (1996) 468.
43
Nitrogen / black of de carbon (Carbopack)
M. Kruk, Z. Li, M. Jaroniec, W. B. Betz, Langmuir
15 (1999) 1435-1441.
44
Adsorption on precipitated silica Isotherms
N2 Ar à 77K
P. J. M. Carrott K. S. W. Sing, Ads. Sci.
Tech., 1 (1984) 31.
  • The conditions of the sample preparation are
    very important!!!!
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