adsorption and intrusion methods for the characterization of ......adsorption and intrusion methods...
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matériaux avancés pour
la catalyse et la santé
F. Di Renzo1*, A. Galarneau1, F. Quignard1,
S. Valange2, Z. Gabelica3, J.-P. Bellat4
direnzo@enscm.fr
1Institut Charles Gerhardt Montpellier, UMR 5253 CNRS-UM2-ENSCM-UM1, Matériaux Avancés pour la Catalyse et la Santé,
ENSCM, 8 rue Ecole Normale, 34296 Montpellier, France
2Laboratoire de Catalyse en Chimie Organique, Université de Poitiers, Poitiers, France
3LPI-GSEC, ENSCMu, Université de Haute Alsace, Mulhouse, France
4Institut Carnot de Bourgogne, UFR ST, Université de Bourgogne, Dijon, France
Adsorption and Intrusion Methods for the
Characterization of Mesoporous Materials
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
matériaux avancés pour
la catalyse et la santé
Adsorption and Intrusion Methods for the
Characterization of Mesoporous Materials
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
Nitrogen adsorption and mercury intrusion in
mesoporous silicas with different pore connectivities
A. Galarneau1, B. Lefèvre1, H. Cambon1,
S. Valange2, Z. Gabelica3, J.P. Bellat4,
F. Di Renzo1
1Laboratoire de Matér iaux Catalytiques et Catalyse en Chimie Organique,
UMR 5618 ENSCM-CNRS-UM1 Institut Gerhardt FR 1878
ENSCM, 8 rue de l'Ecole Normale, 34296 Montpellier Cedex 5, France
galarne@enscm.fr2Laboratoire de Catalyse en Chimie Organique, Universit é de Poitiers, France3Université de Haute Alsace, Mulhouse, France4Laboratoire de Recherches sur la Réactivité des Solides, Université de Bourgogne, Dijon, France
● an inventory of superposed phenomena
● surface tension, liquid-solid interfaces and capillarity
● new standard materials allow a new look at old models
● shape effects and the limits of capillarity
● non-wetting fluids and still more shape effects
N2 adsorption-desorption isotherms at 77 K for
mesoporous silicas prepared by different methods
MCM-41 structured by CTMA swollen by TMB
SBA-15 structured by PEO-PPO-PEO triblock copolymer
Sylopol commercial precipitated silica
0
200
400
600
800
1000
1200
1400
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 g
-1 S
TP
the relative pressure of the
capillary condensation step
indicates the pore size
9.5
nm10.3
nm
21
nm
2 cm3 g-1
1.5 cm3 g-1
1.2 cm3 g-1
ad
so
rbe
d g
as v
olu
me
280 m2 g-1490 m2 g-1
840 m2 g-1
the amount adsorbed at
the top of the first
adsorption step indicates
the surface area
the amount of nitrogen
adsorbed at the top of
the condensation step
indicates the pore
volume
N2 inside the pores is a
dense phase and presents
nearly the density of liquid N2
for N2, ρliq/ρgas = 647
Isotherm interpretation : separation of superposed phenomena
(which, happily, do not depend on pressure in the same way)
Contributions of capillary condensation and multilayer adsorption can be easily
separated if mesopores present a narrow pore size distribution
Layer adsorption : spread over the whole pressure field according to a known law
p
pc
p
p
p
pc
n
n
m )1(11
BET equation
(multilayer Langmuir)n adsorbed amount
nm monolayer capacity
p/p° relative pressurec parameter related to the difference of
adsorption heat between monolayer and
following layers
Condensation : occurs at pressure values which depend on the pore size
RTr
V
p
p m2ln
0
Kelvin equationγ surface tension R gas constant T temperature
Vm molar volume r mesopore core radius
0
100
200
300
400
500
600
0 50 100 150 200 250
cm3 (STP) g
-1 (aerosil reference)
cm
3 (
ST
P)
g-1
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
monolayer
adsorption
multilayer
adsorptionmesopore
filling
multilayer
mesopore
emptying
slope proportional to
the total surface area
slope proportional to
the outer surface area
0
100
200
300
400
500
600
0 50 100 150 200 250
cm3 (STP) g
-1 (aerosil reference)
cm
3 (
ST
P)
g-1
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
monolayer
adsorption
multilayer
adsorptionmesopore
filling
multilayer
mesopore
emptying
slope proportional to
the total surface area
slope proportional to
the outer surface area
an isotherm of mesoporous solid and its comparison plot
N2 adsorption at 77 K on Lichrosphere 60
chromatographic silica comparison plots are useful to
evidence different mechanisms in
the adsorption isotherm
in a comparison plot, for each pressure
value the adsorbed amount on the
examined sample is compared with the
adsorbed amount on the reference sample
reference adsorbent SBET 187 m2 g-1
slope of the comparison plot 3.9
Scomparison plot = 187 x 3.9 = 730 m2 g-1
in good agreement with SBET 740 m2 g-1
0
100
200
300
400
500
600
0 50 100 150 200 250
cm3 (STP) g
-1 (aerosil reference)
cm
3 (
ST
P)
g-1
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
monolayer
adsorption
multilayer
adsorptionmesopore
filling
multilayer
mesopore
emptying
slope proportional to
the total surface area
slope proportional to
the outer surface area
0
100
200
300
400
500
600
0 50 100 150 200 250
cm3 (STP) g
-1 (aerosil reference)
cm
3 (
ST
P)
g-1
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
monolayer
adsorption
multilayer
adsorptionmesopore
filling
multilayer
mesopore
emptying
slope proportional to
the total surface area
slope proportional to
the outer surface area
experimental
isotherm
P
Y
0
100
200
300
400
500
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
reference
isotherm
aerosil 200
fumed silica
PX
0
100
200
300
400
500
600
0 50 100 150 200 250
cm3 (STP) g
-1 (aerosil reference)
cm
3 (
ST
P)
g-1
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
monolayer
adsorption
multilayer
adsorptionmesopore
filling
multilayer
mesopore
emptying
slope proportional to
the total surface area
slope proportional to
the outer surface area
0
100
200
300
400
500
600
0 50 100 150 200 250
cm3 (STP) g
-1 (aerosil reference)
cm
3 (
ST
P)
g-1
0
100
200
300
400
500
600
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
monolayer
adsorption
multilayer
adsorptionmesopore
filling
multilayer
mesopore
emptying
slope proportional to
the total surface area
slope proportional to
the outer surface area
comparison
plotY
X
t-plot and αS-plot: two types of comparison plots
0
100
200
300
400
500
600
0 1 2 3 4
alpha S (aerosil reference)cm
3 (
ST
P)
g-1
slope proportional to
the total surface area
slope proportional to
the outer surface area
0
100
200
300
400
500
600
0 5 10 15 20
t / Å (aerosil reference)
cm
3 (
ST
P)
g-1
slope proportional to
the outer surface area
slope proportional to
the total surface area
0
100
200
300
400
500
600
0 1 2 3 4
alpha S (aerosil reference)cm
3 (
ST
P)
g-1
slope proportional to
the total surface area
slope proportional to
the outer surface area
0
100
200
300
400
500
600
0 5 10 15 20
t / Å (aerosil reference)
cm
3 (
ST
P)
g-1
slope proportional to
the outer surface area
slope proportional to
the total surface area
a positive deviation of the comparison plot indicates that a more effective
mechanism of adsorption is superposed to the growth of the adsorbed layer
t-plot: reference adsorbed amount expressed as average thickness of the monolayer
(assumption of constant density of the condensed phase)
thickness t = 1Å = 0.345 µmol m-2
= 15.4 cm3
(STP) m-2
αS-plot: the unit of the abscissae is the reference adsorbed amount at p/p° 0.4, an isotherm
region expected to be often rid of condensation phenomena
http://citt.ufl.edu/Marcela/Sepulveda/html
If cohesive forces of the liquid
are stronger than the adhesive
forces at the interface, the sum
of forces at the surface is
directed towards the interior of
the liquid.
This induces a pressure rise
inside the liquid. The force
balance inside a liquid droplet
allows to correlate this pressure
to the droplet size through the
surface tension.
0
0.01
0.02
0.03
0 0.5 1 1.5 2
droplet size (mm)
pre
ssu
re (
atm
)
water surface tension at 20 °C = 0.0728 N m-1
Young-Laplace law
Өcontact
angle
in the presence of a solid, the contact angle depends
on the sum of the surface tensions at the triple point
σvapour-liquid cos Ө + σliquid-solid = σvapour-solid
wetting non-wetting
liquid solid contact
angle
water
glass 0°
silver 90°
wax 107°
mercury glass 135°
2σcos(Ө)
capillary rise
Surface tension around the
perimeter of the tube results in a
force with a vertical component
that drives water upwards.
The movement continues until the
force due to surface tension
equals the weight of the water
column. h capillary rise
σ surface tension
Ө contact angle
r capillary radius
ρ liquid density
g gravity acceleration
mechanical equilibrium
(Young-Laplace)
dpliq-dpvap = d(2σ/rm)
physicochemical equilibrium
(Gibbs-Duhem at constant T)
dμliq = dμvap
Vliqdpliq = Vvapdpvap
d(2σ/rm) = dpvap (Vliq-Vvap) / Vliq
Vliq negligible compared to Vvap
vapour as perfect gas
d(2σ/rm) = - RTdpvap / (Vliq Pvap)
integrating between (rm, p) and (∞, p°)
ln (p/p°) = - 2σVliq / (RT rm)
Kelvin equation
the driving force of capillary
condensation and drop coalescence
is the decrease of the liquid-vapour
interface area
William ThomsonLord Kelvin (1824-1907)
Kelvin equation
surface = high energy state
RTr
V
p
p m2ln
0
2σVm
Schematic representation of adsorbed layer and capillary meniscus in
cylindrical (lefthand) and slit-shaped (rigthhand) pores
ln (p/p°) = - 2 σ VL / (R T rm)
rp = rm + t
Kelvin equation
the correlation between curvature of the meniscus
and pore size depends on the shape of the pore
wp = rm + 2t
Did the availability of new reference
materials modify our understanding of the
adsorption phenomena?
MCM-41, J.S. Beck et al., JACS 114 (1992) 10834
MCM-48
V. Alfredsson and M.W. Anderson,
Chem. Mater. 8 (1996) 1141
SBA-15, Z. Liu et al., ChemPhysChem (2001) 229
t
t
t = 0.5 nm
t = 1.0 nm
t = 2.0 nm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 2 4 6 8 10
a ( nm)
Sg (
m2.g
-1)
t = 0.5 nm
t = 1.0 nm
t = 2.0 nm
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 2 4 6 8 10
a ( nm)
Sg (
m2.g
-1)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 2 4 6 8 10
a (nm)
vf (c
m3.g
-1)
t = 2.0 nm
t = 1.0 nm
t = 0.5 nm
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 2 4 6 8 10
a (nm)
vf (c
m3.g
-1)
t = 2.0 nm
t = 1.0 nm
t = 0.5 nm
Correlations between cell size, pore size,
wall thickness, surface area and
mesoporous volume for MCM-41-like silicas
r = (a - t)/2
Deq = 1.05 (a - t)
radius of inscribed circle
diameter of circle with the
same area as the hexagon
A. Galarneau et al., Micropor. Mesopor. Mater., 27 (1999) 297; Stud. Surface Sci. Catal., 142 (2002) 1057.
Correlations between cell size, pore size,
wall thickness, surface area and
mesoporous volume for MCM-48 silicas
B. Coasne et al., Langmuir, 22 (2006) 11097
A. Galarneau et al.,
Microp. Mesop. Mater.,
83 (2005) 172
L. Jelinek, E.s. Kovats, Langmuir 10 (1994) 4225
Cross-sectional areas of nitrogen molecule:
16.2 Å2
over silylated silica (value usually used in syrface area calculations)
13.5 Å2
over rehydroxylated silica
0
100
200
300
400
500
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
0
100
200
300
0 1 2 3
alpha S (aerosil reference)
cm
3 (
ST
P)
g-1
Reference isotherm of N2 adsorption at
77 K on Aerosil fumed silica
some mesoporosity in a reference
solid assumed as non-porous
αS-plot for a Ca-alginate aerogel
negative deviation
of the αS-plot of a
solid with less
mesopores than
the reference
Ca-alginate aerogelF. Quignard, M. Robitzer, F. Di Renzo
New J. Chem. 32 (2008) 1300
0
200
400
600
800
0 0.2 0.4 0.6 0.8 1
p/p°
cm
3 (
ST
P)
g-1
0
200
400
600
800
0 1 2 3
alpha S (aerosil reference)
cm
3 (
ST
P)
g-1
N2 adsorption-desorption isotherms at 77 K (lefthand) and corresponding
αS-plot (righthand) for a non-microporous SBA-15 silica (filled symbols)
and a sample functionalized with C16 hydrocarbon chains (void symbols)
effect of the nature of the surface on the comparison plots
0
20
40
60
80
100
120
140
160
180
200
0.0 0.2 0.4 0.6 0.8 1.0
alpha-S (Aerosil)
cm
3 (
ST
P)
g-1
0
20
40
60
80
100
120
140
160
180
200
0.0 0.2 0.4 0.6 0.8 1.0
alpha-S (Aerosil)
cm
3 (
ST
P)
g-1
Comparison plots of the adsorption of N2 at 77 K
on (filled triangles) chitosan and (void triangles)
chitin aerogels. The lines represent best-fit linear
correlations extrapolated to αS = 0.
Comparison plots of the adsorption of N2 at 77 K
on (filled circles) ionotropic alginate, (void circles)
alginic acid, and (void squares) carrageenan
aerogels. The lines represent best-fit linear
correlations extrapolated to αS = 0.
t-plots for the adsorption of N2 at 77 K
on polysaccharide aerogels
0
20
40
60
80
100
120
140
-10 -5 0 5 10 15 20
intercept at αS = 0 (cm3 STP g
-1)
C (
BE
T)
Correlation between the energetical parameter C of the BET equation and the intercept of the αS
plots of polysaccharide aerogels with different surface groups: acetylated amines (chitin, void
triangles), amines (chitosan, filled triangles), hydroxyls (agar, void lozenges), sulphates
(carrageenan, void squares), carboxylic groups (alginic acid, void circles), and salified carboxylates
(alginate, filled circles). St. Andrews cross for the Aerosil fumed silica used as reference isotherm.
chitin
chitosan
agarose κ-carrageenan
alginic acid
energetical
parameters of the
adsorption of N2
at 77 K on
polysaccharide
aerogels
0
1
2
3
4
0 0.5 1 1.5 2
monolayer fraction V/Vm
kJ m
ol-1
Net molar energy of adsorption of argon on (filled circles) Ca-alginate and
(void triangles) chitin aerogels and (St. Andrews' crosses) fumed silica.
isosteric heats of adsorption of Ar
on polysaccharide aerogels
alginic acid
chitin
am
ou
nt
ad
so
rbe
d,
n
= H1 = H3 = H2
am
ou
nt
ad
so
rbe
d,
n
= H1 = H3 = H2
am
ou
nt
ad
so
rbe
d,
n
= H1 = H3 = H2
Different shapes of hysteresis of type IV isotherms
H4
H1 narrow mesopore size distribution
H2 ink-bottle pores
H3 broad pore size distribution with smaller
pores accessible through the larger ones
H4 similar to H3 in the presence of
microporosity
Schematic representation of the N2 adsorption-desorption isotherms at 77 K
and corresponding pore size distributions for materials with 10 nm cavities and
entrance sizes between 2 and 10 nm
lower limit of the hysteresis loop: catastrophic desorption
adsorption isotherms of N2 at 77 K on (a) SBA-15,
(b) TMB-swollen MCM-41, and (c) MCM-41 silicas
limit of reversible pore filling
-12
-10
-8
-6
-4
-2
0
1 1.5 2 2.5Tc/Trpf
ln(p
rpf/p
c)
reduced temperature and pressure of the limits of reversible pore filling for N2
(void squares), Ar (filled squares), Xe (filled triangles), O2 (void lozenges), CO2
(void triangles), cyclopentane (void circles), benzene (St. Andrews crosses), 2,2-
dimethylbutane (crosses). Tc and pc are the critical conditions.
D. Maldonado et al.
J. Porous Mater. 14
(2007) 279
corresponding state graph for the limit of reversible pore filling
suction head
delivery head
piping head
the suction head of a
pump is limited by the
evaporation of the liquid
TemperatureVapor
Pressure
Maximal
elevation
(oC) (oF) (kN/m2) (m)
0 32 0.6 10.3
10 50 1.2 10.2
20 68 2.3 10.1
30 86 4.3 9.9
40 104 7.7 9.5
50 122 12.5 9.1
60 140 20 8.3
70 158 32.1 7.1
80 176 47.5 5.5
90 194 70 3.2
100 212 101.33 0.0
Suction Head as Affected by Temperature
He = (Patm - Pv) / γ
maximum suction head
Clausius-Clapeyron calculations of
the enthalpies of evaporation at
the limit of reversible pore filling
P. Trens et al., Langmuir 21 (2005) 8560
Adsorption/desorption isotherms of nitrogen at 77 K
MCM-41 3 nm (synthesis with CTAB)
▲ MCM-41 4 nm (synthesis with CTAB, swelled with trimethylbenzene)
MCM-41 5.5 nm (synthesis with CTAB, swelled with dodecylamine)
MCM-41 10 nm (synthesis with CTAB, swelled with trimethylbenzene)
0
200
400
600
800
1000
1200
1400
0 0.2 0.4 0.6 0.8 1
p/p°
Ad
so
rbe
d a
mo
un
t / cm
3.g
-1 (
ST
P)
The pore size can
be tuned by the
synthesis method
Enthalpies of adsorption of n-hexane as a function of coverage as calculated from
(left hand) the adsorption data and (right hand) the desorption data on () MCM-
41 3 nm, (▲) MCM-41 4 nm, (■) MCM-41 5.5 nm, (O) SBA-15 10 nm. Dashed line:
condensation heat of hexane.
-40
-35
-30
0 0.5 1
Fraction of pore filling
Ad
so
rptio
n e
nth
alp
y / k
J m
ol-1
-40
-35
-30
0 0.5 1
Fraction of pore filling
Adsorp
tion e
nth
alp
y /
kJ m
ol-1
D. Maldonado et al.
J. Porous Mater. 14
(2007) 279
30
32
34
36
38
40
42
0 2 4 6 8 10
D (nm)
-ΔH
(k
J m
ol-1
)
Condensation enthalpies of n-hexane as a function of the pore size.
Isosteric data from adsorption () and desorption () results.
Continuous line: calculated condensation enthalpy.
Dotted line: condensation enthalpy on a flat liquid surface.
inti h
N
Nhh
cc
ntcondcc
When the meniscus advances,
the interface between adsorbed
layer and vapour disappears
In small mesopores, the energetical
contribution of the interface affects
the enthalpy of capillary condensation
pore surface
adsorbed layer
core filled by
capillary
condensation
p
ccm
N
NNN int
In the hypothesis of constant density of the
adsorbed phase, the fraction of interface
molecules can be evaluated from the
adsorption isotherm
Nm = monolayer amount by BET equation
capillary rise and capillary depression
wetting fluid
Ө < 90°
non-wetting fluid
Ө > 90°
2σcos(Ө)
h capillary rise
σ surface tension
Ө contact angle
r capillary radius
ρ liquid density
g gravity acceleration
ΔP = (2γ/R) cosθ
Washburn-Laplace law for cylindrical pores
corelation pressure-pore size
depending on contact angle
γ(Hg) 0.485 N m-1
if θ = 140°
R = -743/ΔPR = nm ΔP = MPa
180°
130°
110°
1.8
2
2.2
2.4
2.6
1.5 1.7 1.9 2.1 2.3
Log D (Angstrom)
Lo
g P
(M
Pa)
180°
130°
110°
1.8
2
2.2
2.4
2.6
1.5 1.7 1.9 2.1 2.3
Log D (Angstrom)
Lo
g P
(M
Pa)
rm
θrp
Hgrm
θrp
HgHg
intergranular
porosity
grain
packing
structural
porosity
Mercury porosimetry on SBA-15 sample prepared at 130°C
0.7 µ 7.5 nm20 nm
1.0 ml/g
2.2 ml/g
Pore size calculated for θ = 140°
50 nm 3 nm
field of superposition with the
data from nitrogen adsorption
0
1
2
3
4
5
6
7
0.0010.010.11101001000
Diameter (µm)
cu
mu
lati
ve v
olu
me (
ml/
g)
Porosity of SBA-15s from nitrogen adsorption at 77 K
pore size calculated by the method of Broekhoff and de Boer
# T (°C)
synthèse
D (Å)
adsorption
D (Å)
désorption
3439 60 45 48
3440 100 73 75
3806 130 90 96
3441 130 100 105
pore size increases with the
temperature of the second
step of the synthesis
0
100
200
300
400
500
600
700
800
900
0 0.2 0.4 0.6 0.8 1
P/P°
N2
ml/g
ST
P
3439C
3440C
3441C
3806C
A. Galarneau et al., Langmuir 17 (2001) 8328
structural porosity of SBA-15s from mercury intrusion
pore size calculated for contact angle θ = 140°
# T (°C)
synthèse
D (Å)
intrusion
D (Å)
extrusion
3439 60 42 60
3440 100 52 100
3806 130 62 140
3441 130 76 200
hysteresis loop is wider
for larger pores
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.02 0.04 0.06
diameter (micron)
vo
lum
e (
mL
/g)
3439C 3441C 3440C 3806SC
-0,8 -0,4 0,0 0,4 0,8 1,2 1,6-4
-2
0
2
4
6
Intrusion
n = -1
Patm
MTS 10
0C8
MTS 50
C8
MTS
18 C8
MTS
16 C8
ln P
ln RP
-0,8 -0,4 0,0 0,4 0,8 1,2 1,6-4
-2
0
2
4
6
Extrusion
Intrusion
ln Rc1
n ~ - 4
n = -1
Patm
MTS 10
0C8
MTS 50
C8
MTS
18 C8
MTS
16 C8
(•)
ln P
ln RP
Pint RP-1
Pext RP-4
Retraction Propagation
Intrusion of water in MCM-41 grafted with octyldimethylsilane
Intrusion = Propagation
Extrusion depends on cavitation
(nucleation of the vapour phase)
B. Lefèvre et al., J. Colloid Surface A 2004, 241, 265.
p
471.122p4673.9168.366r
empyrical Kloubek-Rigby-Edler
correlation for mercury retraction
Rigby and Edler, J. Colloid Interf. Sci. 2002, 250, 175
0
5
10
15
0 5 10 15
D(BdB) nm
D(W
ash
bu
rn)
nm
comparison of the pore size measured by mercury intrusion
and N2 adsorption for MCM-41 (squares), SBA-15 (triangles)
and porous glass (circles) samples.
mercury porosimetry underevaluates the
pore size for interconnected pore systems
Carbon replica of SBA-15 prepared at 100°C
Liu, Terasaki, Ohsuna, Hiraga, Shin, Ryoo, ChemPhysChem (2001) 229
The carbon rods formed inside the mesopores do not fall apart
when the silica template is dissolved in HF
Carbon replica of SBA-15 prepared at 100°C
Liu, Terasaki, Ohsuna, Hiraga, Shin, Ryoo, ChemPhysChem (2001) 229
Disordered bridges
connecting ordered
parallel mesopores
Connections between pores depend on
the conditions of synthesis
Galarneau, Cambon, Di Renzo, Ryoo, Choi, Fajula, New J. Chem. 27 (2003) 73
SBA-15 prepared at 60 °C
The platinum rods of the
replica do fall apart
(same effect for MCM-41)
SBA-15 prepared at 100 °C
Interconnected pores:
the platinum replica does
not fall apart
50 nmPt-3532CPt-3522C
Pression of intrusion and retraction of mercury
as a function of pore size from nitrogen adsorption
physical impossibility: contact angle higher than 180°
1.8
2
2.2
2.4
2.6
1.5 1.7 1.9 2.1 2.3
Log D(BDB) Angstrom
Lo
g P
/MP
a
intrusion
extrusion 110° 130°
180°
solids with pore
interconnections
Evolution of the contact angle and the radius of the meniscus when mercury
advances in a cylindrical pore with increasing diameter
Kloubek, Powder Technol. 1981, 29, 63; Galarneau et al., J. Phys. Chem. C 2008, 112,12921
Wenzel, J. Phys. Colloid Chem. 1949, 53, 1466
cos θrough = R* cos θflat
a higher pressure is needed to overcome the rim of a pore widening
surface roughness corresponds to an increase of contact angle
R* = ratio of the rough surface area to
its projection on the average plane
Academic Press, 1982 Academic Press, 1999
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