An Experimental Study of the State of Hexane in a Confined Geometry
D. MALDONADO, N. TANCHOUX, P. TRENS, F. DI RENZO
and F. FAJULA
Laboratoire de Matériaux Catalytiques et Catalyse en Chimie
Organique, UMR5618, CNRS / ENSCM, Institut Gerhardt FR 1878
8, rue de l'Ecole Normale 34296 Montpellier cedex 3
Abstract
Literature data about hysteresis closure points of sorption isotherms
has been summarized and it was shown that these points are located in
one half of the (1-T/Tc, P/P°) plan. Below the limiting straight line, no
hysteresis can be found. A study of the transition between the
reversible and the irreversible (hysteretic) regime for n-hexane
adsorbed on MCM-41 or similar mesoporous materials has been
carried out. The dependence on pressure, temperature and pore size has
been investigated and confirmed the literature data. Enthalpies of
adsorption have also been derived from the isotherms using the
isosteric method. The enthalpies showed a dependence on pore size:
when the pore size decreases, the adsorptive is stabilised and the
enthalpy of adsorption becomes more negative.
1. Introduction
Although adsorption is of primary interest for catalysis applications,
most studies of this phenomenon have been conducted at very low
temperatures on gases such as N2 and Ar[1,2]. In this study, hexane
adsorption at room temperature has been investigated, extending the
scope of those studies to more realistic catalytic conditions. Moreover,
hysteresis loops usually found for mesoporous materials strongly
suggests that a branch of the isotherm is not at the thermodynamical
equilibrium. In other experimental conditions, small pores or high
temperatures, this hysteresis loop vanishes. The difference between
these two situations in terms of driving force is yet to be completely
understood. Some information can be found by deriving the adsorption
1
enthalpies of hexane in mesoporous materials of different pore sizes,
using the isosteric method.
2. Behaviour of vapours in mesopores
2
CH4
C2H4
1.8
H2
Compressibility Z
1.6
1.4
1.2
1
Ideal Gas
0.8
0.6
0.4
0.2
NH3
0
0
250
500
750
1000
Pressure/ atm
Figure 1. Compressibility dependence on pressure
of selected vapours and gasses.
1
VR = 2
VR = 1
Compressibility Z
0.8
0.6
VR = 0.9
0.4
Nitrogen
Ethylene
0.2
Propane
Methane
0
0
1
2
3
4
5
6
7
pR
Figure 2. Reduced compressibility of selected
vapours and gasses (the reduced volume VR being
fixed as a parameter).
2
At low pressure, gases and vapours can be accurately described by the
model of the ideal gas. As pressure increases, though, this model is no
longer valid and vapours behave very differently from each other, as
shown in figure 1.
0.7
0.6
Benzene
c-alcanes
n-alcanes
i-alcanes
CCl4
0.5
1-TR
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
P/P°
Figure 3. Hysteresis closure points for some
organic vapours.
In order to study the general phenomenon of hysteresis vanishing, and therefore
to compare the properties of various gaseous species, the principle of
corresponding states is used, and we carry out our study with reduced
parameters (pressure, volume and temperature), obtained by dividing the
corresponding parameter by its value at the critical point. Figure 2 shows that in
this system of coordinates, the various gases exhibit the same behaviour.
Adsorption data for various compounds in conditions where they show a
hysteretic behaviour were taken from the literature[3]. The hysteresis closure
points were plotted in a (1-TR, PR) plot (figure 3). It appears that all
representative points are located in a half plan, the other half plan being the
region of reversibility, and the data allows us to determine precisely the limiting
line below which no hysteresis can be found. This existence of two distinct
regimes of adsorption for all gases and vapours is a clear evidence for a general
effect of confinement in porous materials. Nevertheless, the only apparent is
temperature while pore size dependence still remains to be investigated.
3
3. Experimental Study
3.1. ADSORPTION ISOTHERM. DETERMINATION APPARATUS
The apparatus (figure 4) is based on volumetric measurements and the
adsorption is followed by two pressure gauges. The sample cell can be
disconnected from the system to undergo a thermal treatment (up to 250°C)
0-10 torr
0-1000 torr
p1
p2
V1
V4
Vacuum
V3
V2
Filter
Secondary
Valve
Valve
Climatic Chamber
adsorptive adsorbent
Figure 4. Scheme of the Adsorption Isotherm
Determination Apparatus (AIDA).
A primary pump coupled with a turbo molecular pump (PT 50, supplied by
Leybold) is linked to the apparatus through two different inlets allowing rough
or fine control of the depression rate in the system, protecting it from any solid
contamination. Three thermal Pt 100 probes (provided by Serv'Instrumentation)
are placed on the cell, the adsorptive cell and the main connecting pipe, used as
calibrated reservoir, to record the temperature of the system and check the
thermal stability of the whole system.
The apparatus is placed in a climatic chamber (VT200, provided by Vötsch)
allowing a thermal stability better than 0.1 K from 250 K up to 350 K. The
whole system (electromagnetic valves, climatic chamber, pressure gauges and
thermal probes) is interfaced to a computer and controlled by a programme
especially designed for it. The different volumes were calibrated by weighing
the sample cell filled with mercury and then by expanding hexanes from this
volume into the rest of the apparatus, monitoring pressure. The system was
tested for the adsorption of n-hexane on 3.6 nm pore size MCM-41 material and
the isotherm was found to be consistent with data available from the literature[4].
4
3.2. TEMPERATURE DEPENDENCE OF THE ISOTHERMS
Sorption isotherms of n-hexane on a 3.6 nm pore size material were determined
for temperatures ranging from 1°C to 60°C. Figure 5 shows the adsorbed
amount as an equivalent volume for standard pressure and temperature against
relative pressure i.e. the pressure divided by saturated vapour pressure.
Adsorbed Amount /cm 3.g-1 (STP)
120
100
80
60
1°C
30°C
40°C
50°C
60°C
40
20
0
0
0.2
0.4
0.6
0.8
1
p/p°
Figure 5. n-Hexane sorption isotherms for a
3.6 nm pore size MCM-41 material (Filled
symbols and crosses stand for adsorption, hollow
symbols and underscores for Desorption).
All of the isotherms are reversible in this temperature range and clear trends
appear as temperature increases. The adsorption step shifts towards high relative
pressure, as can be predicted by the Kelvin equation relating the equilibrium
pressure p to the pore radius for a spherical meniscus (equation 1). The slope of
the step decreases for the same reason (if we consider a given pore size
distribution and differentiate equation 1 with respect to rp, the step width
depends on temperature). Finally, the maximal adsorbed amount decreases, as
density of the fluid increases.
(1)
 2 Vl
ln( p 0 ) 
p
rp  RT
3.3. PORE SIZE DEPENDENCE.
A series of sorption isotherms was then determined for materials with pore sizes
of 4.4 nm and 5.9 nm (figure 6 and 7, respectively) for the same temperature
5
range as before. For each studied pore size, the same trends as before can be
shown. For the intermediate pore size (4.4 nm), an hysteresis loop appears at
low temperature (0°C) and for the larger pore size (5.6 nm), hysteretic
behaviour occurs up to 50°C, which is the highest temperature studied for this
material. These results show that pore size and temperature play a role in the
transition between hysteretic and reversible regime, and a complete study of this
transition would requires not a (PR,TR) plot for the closure point but a three
dimensional (PR, TR, pore size (Ф)) plot, and the determination of a limiting
surface between the two observed regimes.
200
160
Adsorbed Amount / cm 3.g-1 (STP)
Adsorbed Amount /cm 3.g-1 (STP)
200
120
80
0°C
30°C
40°C
50°C
40
160
120
80
1°C
30°C
40°C
50°C
40
0
0
0
0.2
0.4
0.6
0.8
1
p/p°
Figure 6. n-Hexane sorption
isotherms for a 4.4 nm pore size
MCM-41 material (Filled symbols
stand for adsorption, hollow symbols
for Desorption)
0
0.2
0.4
0.6
0.8
1
p/p°
Figure
7.
n-Hexane
sorption
isotherms for a 5.9 nm pore size
MCM-41 material (Filled symbols
stand for adsorption, hollow symbols
for Desorption)
4. Hysteresis vanishing
A plot of the closure pressure against temperature when hysteresis is detected
and of the inflexion point against temperature for reversible systems (figure 8)
shows that for a given solid these points are located on a straight line.
Moreover, if we report the literature data already discussed (dotted line), we
find a good correspondence between the three series discussed above and
literature data. The systems corresponding to the line located above the dotted
line are fully reversible for this temperature domain (for instance for a 3.6 nm
pore size), those located below the line are reversible for these temperatures (5.9
nm) and those crossing the line show a transition between the two regimes. This
plot gives us precious hints at how to study the effects of this change on
6
reactivity: using a model reaction, we can vary the pore size of the catalyst in
order to cross the line and monitor a selected property of the reaction such as
conversion or selectivity in order to detect a change between the regimes.
p/p°
0.5
3,6nm
5,9nm
Limit
4,2nm
4,4nm
0.25
0
-20
-10
0
10
20
30
T/ °C
40
50
60
70
80
Figure 8. Hysteresis closure pressure for the adsorption of n-hexane on
MCM-41 type materials of different pore sizes (the dotted line figures
the limit derived from the literature for other organic compounds)
-25
Isosteric Adsorption Enthalpy
/kJ.mol-1
0
0.2
0.4
0.6
0.8
1
1.2
-30
9.9 nm
5.9 nm
3.6 nm
-35
-40
Pore Filling
Figure 9. Isosteric enthalpy of adsorption for n-hexane over
materials of different pore sizes
7
5. Isosteric adsorption enthalpy
Isotherms also convey information about the thermodynamics of adsorption.
Using the isosteric method[5], It was possible to derive adsorption enthalpies and
plot them against pore filling for systems with various pore sizes.
For any given pore size the general trend is the following (figure 9) : at very low
coverage, the adsorptive molecules interact with geometrical defects of the
structure leading to a strong adsorption and therefore to a very negative
adsorption enthalpy. As the pore filling increases, the enthalpy increases
towards a value which is predicted to be the bulk condensation enthalpy by the
Brunauer-Emmett-Teller model and which is indeed attained for the 9.9 nm
pore size material. According to this theory, it should then be constant and equal
to the bulk condensation value during pore condensation.
Our system however, behaves differently. In the first step, the enthalpy raises
during multilayer adsorption to reach a maximum, the value of which depends
on pore size (the smaller the pores, the more negative the maximum) and which
is inferior or equal to bulk condensation enthalpy. The enthalpy then reaches a
plateau during pore condensation. The value at the plateau becomes, again,
more negative as pore size decreases, but it can be noted that even for large
pores such as 9.9 nm, it is more negative than for bulk condensation, indicating
some kind of stabilisation. Of course, at the onset of condensation on the outer
surface of the particles, the enthalpy raises to the bulk condensation value. This
dependence of condensation enthalpy on pore size is another effect of
confinement and hints at a thermodynamic explanation for the existence of two
different regimes for the corresponding isotherms.
6. Conclusion
This work shows that confinement effects arise for pores of sufficiently small
sizes, leading to reversible phase transition and to a stabilisation of adsorbed
molecules. The magnitude of these effects increases as pore size decreases. As
in porous materials, for gaseous bulk reactants, reactions usually occur in a
liquid like state, these aspects are of major interest for catalysis. A precise
cartography of hysteresis loop vanishing in a (T,P,Ф) 3-dimensional space will
allow a catalytic study of reactivity using hexane as gas phase "solvent" and
with a well chosen parameter f(T,P,Ф) varying in order to cross the
reversible/irreversible border. The change of physical properties of hexane
should then result in a change of rate or selectivity of the model reaction. This
aspect is currently investigated in our group.
8
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