European Master
Adsorption
Modeling of physisorption in porous materials
Part 1
Bogdan Kuchta
Laboratoire MADIREL
Université Aix-Marseille
Notion of Interface
Interface: Separation between two (volume)
phases.
Although words ‘interface’ and ‘surface’ mean
practically the same, the word "interface" is often used
when 2 condensed phases are in contact or when two
phase are explicitly considered.
ex : interface solid/liquid; interface solid/gaz.
The word "surface" is used to describe interface of solid
(when it is (or not) in a contact with different phase)
Adsorption
• Phenomenon of adsorption
When a fluid is in the vicinity of solid surface, its concentration
increases close to the interface.
• Definition
Adsorption is a process that occurs when a gas or liquid solute
accumulates on the surface of a solid or, more rarely, a liquid
(adsorbent), forming a molecular or atomic film (adsorbate).
Word "adsorption" is also used to describe the transition of a
fluid when it transforms into an adsorbed phase.
What is adsorption ?
[c]
Concentration of
the adsorbed phase
Concentration of
the gas phase
z
Adsorption
Adsorption – a phenomenon general which involves the preferential
partitioning of substances from the gaseous or liquid phase onto the
surface of a solid substrate
Gaz phase
Adsorbate
Adsorbed phase
Adsorbent
Physical adsorption is caused mainly by van der Waals forces and electrostatic
forces between adsorbate molecules and the atoms which compose the adsorbent
surface.
Thus adsorbents are characterized first by surface properties such as surface
area, structure (roughness) and polarity.
Adsorption
Chemical (chemisorption) versus physical (physisorption) adsorption.
In chemisorption there is an exchange
of electrons between the surface and
the adsorbed molecules .
Energie
Energie d’activation
n / ms
Adsorption
physique
Adsorption
chimique
Adsorption physique
Adsorption chimique
The energy of
chemisorption is stronger.
P = const.
Tadsorption
How do we represent the adsorbed quantity?
(a) interface layer
Surface : A
Solide :
c
Adsorbed quantity na
vs
Adsorbed quantity: va

n  A  c .dz
a
0
Gas : vg
0

z
How do we represent the adsorbed quantity ?
(b) GIBBS representation
c
Surface of Gibbs
Solide : vs
dn
dv
Excess adsorbed
quantity: n
Excess quantity on
surface n
Volume (total) : vg,0

n  n n
cg
g
i
na = n + cg.va
cg.va
z
T : na  n
g
f
Representations of adsorption equilibrium
Interface layer
Gibbs representation
couche
adsorbée
solide
gaz
solide
Surface
V
S
gaz
c
GDS
V
a
V
g
V S,0
V g,0
(imaginary surface)
c = dn/dV
c = dn/dV
I
II
I
III
II
gas in volumeVg,0
(measured with He)
gas in
volume Vg
(unknown)
c gF
c gF
CS = 0

0
Adsorbed quantity
n a:

z
n  A  c .dz
a
0
CS = 0
0
z
Excess quantity on surface n

g
g
i
f
n  n n
Equilibre d'adsorption
An equilibrium of adsorption , at temperature T, is
characterized par quantity  that depends on
pressure of gas , p :
•
 = n /A
• n  est la quantité d'excès en surface
• A est l'étendue de l'interface
• a est l'aire spécifique (= A /m s)
n
.a  s  f ( p ). g (T )
m
Isotherm of argon at 77.4 K
n
s
m
5
4
3

2
n
.a  s  f ( p)
m
1
p / po
0
0
0.2
0.4
0.6
0.8
1
Isotherme d'adsorption (définition)
Isotherm of adsorption:
is an ensemble of equilibrium states, at temperature T, for all
pressures p between 0 et p° (pressure of saturated vapor of
adsorbate at temperature T ).
p/p° is called « relative equilibrium pressure".
n
ms
5
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
p / po
Adsorption
Special case – materials with large surface:
porous materials: specific surface between 0.1 and 2600 m2g-1
Micropores
<2 nm
 mesopores (nano-pores):
2 – 50 nm in diameter
Macropores
>50 nm
 “nanomaterials” of technological interests
with 1, 2 or 3 dimensions  100 nm
b
c
f
d
a
a : corrugation
b : bottle neck
c : opening
d : interconnection
e : close-ended
f : closed (isolated)
Adsorption
n/ms
Adsorption mechanism:
– localized adsorption
– filling of micropores
– monolayer adsorption
– multilayer adsorption
– capillary condensation
p/p°
Classification of isotherms of physical adsorption :
Fundamental questions :
1. Mechanism of adsorption – influence of the
geometry and pore structure
2. Influence of confined geometry (interaction
with walls) on structural transformations
3. Capillary condensation
4. Hysteresis and metastability
I
II
III
B
n/ms
IV
V
VI
B
p/p0
Different stages of adsorption on heterogeneous
adsorbent
Ultramicropore
Supermicropore
Specific sites
Internal surface
External surface
Mesopores
(nanopores)
Adsorption on purely microporous samples: d  0.4 à 2 nm
d ( pore)
1à5
d ( gaz )
n / ms
Filling of micropores
 ultramicropores
 supermicropores
 cooperative
mechanism
p / p0
Adsorption on purely non-porous sample
 Building statistical monolayer
 Multilayer
Adsorption
n / ms
B
p / p0
Adsorption on purely mesoporous sample : d  2 à 50 nm
 Building statistical monolayer
 Multilayer
Adsorption
 Capillary
condensation
n / ms  Hysteresis
B
d ( pore)
 5 à 125
d ( gaz )
p / p0
Adsorption on heterogeneous sample
n/ms
p/p°
Interpretation of isotherms of physical adsorption
• Generally, adsorption starts at lower
pressure when the interaction
between the surface and the
adsorbed particles is stronger
a
n /m
s
D
• When an adsorbate is in contact
with an adsorbent, adsorption is
first observed (that is, at lowest
relative pressure, domain A) on the
centers of adsorption that are the
most strongly attractive (defaults,
imperfections, etc..)
C
B
A
0
0.2
0.4
0.6
p/p
0
0.8
1
Interpretation of isotherms of physical adsorption
a
n /m
s
The filling of the micropores
happens also at pressures
relatively low (domain B)
D
C
B
A
0
0.2
0.4
0.6
p/p
0.8
1
0
Domain C corresponds to pressures where the adsorption
monomolecular is observed. At the end of this domain , statistically,
the whole surface of solid is totally covered by a monolayer adsorbed
on the surface.
Interpretation of isotherms of physical adsorption
a
n /m
s
When the relative pressure
increases, (domain D), the
surface is covered by multilayer
of increasing thickness:
multilayer adsorption
D
C
B
A
0
0.2
0.4
0.6
p/p
0.8
1
0
Starting at some pressure in the domain D, one can observe a rapid
acceleration of adsorption, due to the phenomenon of capillary
condensation (in nanopores)
Different domains of physical adsorption
n/ms
Capillary condensation
Building of monolayer
Multilayer adsorption
Localised dsorption
Filling of micropores
p/p°
Classification de l'IUPAC des isothermes d'adsorption physique
I
II
III
B
n/ms
IV
V
VI
B
p/p0
T < Tc
Classification (I)
The isotherms of adsorption
of type I are characterized
par horizontal line which
indicates saturation of the
adsorbent. This isotherm is
observed
in
adsorbents
having only micropores that
are filled at low pressures.
Lower pressure of filling,
smaller the size of the pores.
I
II
III
B
n/ms
IV
V
VI
B
p/p0
Classification (II)
The isotherms of adsorption
of type II are characterized
par
increase
of
the
adsorbed quantity, in a
continuous way, as a
function of the equilibrium
pressure. This type of
isotherms is observed in
non-porous adsorbents or in
macropores. It indicates the
multilayer adsorption..
I
II
III
B
n/ms
IV
V
VI
B
p/p0
Classification (III)
Desorption is very often
Isotherms of the type IV have the
nonreversible; one observes
same shape as the type II at
a hysteresis of desorption
lower pressures (approximately,
with respect to adsorption.
below 0.4 of the reduced
pressure). At higher pressures it
I
II
III
is characterized par saturation
which is observed at different
B

s
pressures. This type of isothermsn /m
V
IV
VI
is observed when adsorption
happens
in
nanoporous
B
(mesoporous) materials where
the capillary condensation is
0
p/p
observed.
Classification (IV)
The isotherms of adsorption
of type III and V are less
frequently observed: they
are similar to isotherm of
type II and IV but they differ
at low pressures. This
difference is attributed to
weak interaction between
adsorbent and the adsorbed
molecules. For example, it
is observed for adsorption
of water on hydrophobic
surfaces.
I
II
III
B
n/ms
IV
V
VI
B
p/p0
Classification (V)
Step-wise
isotherms
of
adsorption (type VI) are
observed in adsorption on
homogeneous surfaces where
the layers are formed one
after another.
I
III
B
n/ms
IV
The proposed classification
shows the typical adsorbents.
The real isotherms are very
often composed of different
types discussed above.
II
V
VI
B
p/p0