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Characterisation of microporous materials by adsorption microcalorimetry
Recent Advances in Gas Separation by Microporous Ceramic Membranes N.K. Kanellopoulos (Editor) 2000 Elsevier Science B.V. All rights reserved.
213
Characterisation of microporous materials by adsorption microcalorimetry Philip Llewellyn Centre of Thermodynamics and Microcalorimetry- CNRS, 26 rue du 1416meRIA, 13331 Marseille cedex 3, France Calorimetry, or the study of heat, traces its origins back to Lavoisier and Laplace in 1783. Although the use of calorimetry for the study of adsorption phenomena dates back to around Favre in 1854, it remains a rarely used technique. This is mainly due to the strict experimental conditions required to obtain good results. Under these conditions, adsorption microcalorimetry is both a powerful and sensitive tool for the study of adsorption phenomena. The energetic information thus obtained provides supplementary resolution with respect to adsorption manometry and is complementary to other structural and/or diffusion studies. The present chapter aims to give an introduction to current calorimetric methods available for the study of adsorption phenomena. This is followed by a hypothetical breakdown of the adsorbate - adsorbent interactions, which is the basis of a classification of different calorimetric curves. Finally, several experimental results are highlighted for various microporous adsorbents. 1. DIFFERENT CALORIMETRIC METHODS AVAILABLE FOR THE STUDY OF
ADSORPTION PHENOMENA
There are a number of conditions under which calorimetric measurements can be carried out [1]. Adiabatic calorimetry, that is when the surrounding temperature is made to follow that of the sample, is quite interesting for the determination of the heat capacity of a system. Isoperibol calorimeters, where no special connection is made between the sample temperature and that of the surroundings were the first to be used to measure adsorption phenomena. However, there are a number of drawbacks which make gas adsorption studies uncertain. Finally, diathermal calorimetry, where the sample temperature follows that of the surroundings is that most suited to the following of gas adsorption phenomena. Thus the isothermal conditions of adsorption manometry can be reproduced to be able to measure the actual heat effects that occur during adsorption. The examples given later in this chapter are obtained under these diathermal or quasi-isothermal conditions. An example of a diathermal calorimeter used for adsorption studies is given in Figure 1. This apparatus is formed of three main parts : the dosing apparatus, the sample cell and the calorimeter. The dosing apparatus, consisting of a reference volume (A), pressure gauge (B) as well a vacuum line (C) and gas inlet (D) is connected to the sample cell (E). This cell is placed in the calorimeter. A detailed explanation of this Tian-Calvet calorimeter are elsewhere [2, 3]. The calorimeter itself is placed in a liquid nitrogen (or agron) cryostat (F). Two thermopiles (G) are mounted in electrical opposition. A resistance (H) is placed into the reference thermopile allowing calibration via the Joule effect. ~t
email, [email protected], fr
214
A
C
0
H
0
~-"G 0
J Figure 1 : Schematic representation of a calorimetric set-up used for adsorption experiments. There are however, two different methods of adsorbate introduction. The first, and most common, is to inject discrete quantities of adsorptive to the adsorbent. A peak in the curve of energy with time is obtained which has to be integrated to give an integral molar enthalpy of adsorption for each dose. This method is explained in section 1.2. Alternatively, it is possible to introduce the adsorptive to the adsorbent in a continuous manner whilst ensuring that the adsorbate - adsorbent equilibrium is maintained. This leads to a high-resolution curve that is necessary for the observation of subtle adsorption phenomena such as phase transitions. This second method is described in section 2.2. However, beforehand, it is worth describing an indirect manner to obtain energetic information directly from two or more adsorption isotherms using the isosteric method. 1.1 The isosteric method
If one has the possibility to carry out two or more isotherms at various different temperatures, it is possible to calculate the differential enthalpy of adsorption using the isosteric method. From these isotherms, a plot of log pressure, In p, for a given amount adsorbed n a as a function of reciprocal temperature, 1/T, can thus be drawn. It is then possible to make use of the Claussius-Clapeyron equation for a single gas-liquid system. One has to assume that there is no variation of enthalpy or entropy with temperature. The equation used is thus :
/aln~]
'] A aa,/~,o : R 0(l/r) ),,o
{Eq. 1}
Where Aaa~/~ is the differential enthalpy of adsorption and R the gas constant. Often however, one can measure two isotherms measured at around 1OK apart; for example in liquid
215 nitrogen (77 K) and liquid argon (87 K). It is thus possible to relate the equilibrium pressures
pl and p2 at corresponding temperatures T1 and T2 for a given quantity adsorbed: A,d~/~= - RT~T2 In P__L
{Eq. 2}
It can be seen that the precision of this calculation depends greatly on the measurement of the pressure. This can be a problem at low pressures. Not due to the precision of the pressure reading itself, as modem pressure gauges are more than sufficient, but to the exactness of the adsorbate-adsorbent equilibrium itself. This is especially the case for micropore filling in poor conducting materials, such as silica. A small deviation from this equilibrium, due to molecular diffusion or thermal transfer, can lead to a relatively large variation in pressure. This would explain some of the disparity in results obtained using the isosteric method and direct calorimetric measurements. However, as we shall see later, the calculation of the enthalpy of adsorption using the direct calorimetric procedure becomes less precise at higher pressures. This makes both methods quite complementary.
1.2 Discontinuous procedure of adsorptive introduction The discontinuous (or point by point) procedure of adsorptive introduction is the one most widely used for the determination of adsorption isotherms via manometry experiments. The same procedure can be used for the determination of differential enthalpies of adsorption using an apparatus such as that shown in Figure 1. The introduction of each dose of adsorptive to the adsorbent gives rise to a thermal effect until equilibrium is attained. This results in a peak in the curve of heat flow with time. Integration of this peak gives the overall heat effect due to adsorption. The calorimetric cell (including the relevant amounts of adsorbent and adsorptive) is considered as an open system. In this procedure, as well as in the quasi-equilibrium procedure of adsorptive introduction (section 1.3) it is important to consider the adsorptive introduced reversibly. However, to calculate the differential enthalpy of adsorption via the discontinuous procedure, one must introduce quantities dn small enough for a given pressure increase dp. Under these conditions it is possible to determine the differential enthalpy of adsorption Aaa,/~, via the following expression :
Aads~ : l dQr;v~ .~ Vc( d~Pa~
{Eq. 3}
dn Jr t,.dn Jr Here, dQrev is the heat reversibly exchanged with the surroundings at temperature T, that is
to say the heat measured by the calorimeter. 8n a is the amount adsorbed after introduction of the adsorptive dose, dp is the increase in pressure and Vc is the dead space volume of the sample cell within the calorimeter itself (thermopile). If the conditions of reversible adsorption and small doses are not fulfilled, then the quantity calculated using Eq. 3 should be more properly be termed "pseudo-differential enthalpies".
1.3 Quasi-equilibrium introduction of adsorptive For the observation of subtle adsorption phenomena such as phase changes, an increased resolution in both isotherm and differential enthalpy curves is requires. It would be possible to introduce very small doses of adsorptive to increase the number of points taken. This is both
216 time consuming and may lead to a number of errors. However, a continuous introduction of adsorptive leads to an infinite resolution in both curves.
Figure 2 9Comparison of the results obtained using either the discontinuous (rectangles) or continuous (full line) procedure of adsorptive introduction. Figure 2 highlights how this resolution can be interesting. The peak in the full line would be indicative of an adsorbate phase change which would go unnoticed using the discontinuous procedure of adsorptive introduction. In what has been termed the "continuous flow" procedure, the adsorbate is introduced to the system at a defined rate, slow enough that the adsorbate- adsorbent system can be considered to be essentially at equilibrium at all times [4,5]. As we shall see later, different tests easily allow verification as to whether the experiment indeed proceeds at quasiequilibrium. In this "quasi-equilibrium" state, the quantity of adsorbate admitted to the system An can be replaced in adsorption calculations by the rate of adsorptive flow dn/dt. The calorimeter, under these conditions, thus measures a heat flow, ~. Under certain experimental conditions, it is possible to render constant the adsorptive flow to the sample, f = dn/dt. A rate of adsorption, f~, can therefore be calculated using the following expression"
f<,
dn <' I ( V a Vc)dp : - - - - ~ : f - R ~,Ta --Tcc --~
{Eq. 4}
Here, Vd and Vc are the volumes of the dosing system and that "accessible" to the calorimeter at temperatures Td and To. The corresponding heat flow, ~b,can be given by 9
dQ,~,, dQ,e,, dna ~= dt - d n " at
= f<'fdQ-~r~ i
Can )~
{Eq. 5}
Introducing Eq. 4 into Eq. 5 leads to 9
an 9
+ Vc = +V tan ) 7 7 c at dn~
f--W ~b+Vc --~
{Eq. 67 {Eq. 7}
217 Blank experiments can lead to an estimation of Vc(dp/dt). This term is large at horizontal parts of the isotherm. The error in the estimation of the differential enthalpy thus becomes large. However, it is just in this region of the isotherm that the estimation of the differential enthalpy via the isosteric method is most exact. This highlights how both methods are complementary. In the present case however, where the adsorption on microporous materials is under examination, the term Vc(dp/dt) is minimal. Effectively, the increase in pressure with time is small during micropore filling. Furthermore, during micropore filling, all of the flow of adsorptive to the sample is adsorbed making f = f . In such cases, Eq. 7 can be simplified to :
A ~,,a.h ,~ s f
{Eq. 8}
Thus if the rate of adsorptive flow, f is constant, a direct measurement of A,d,/;~ with the amount adsorbed is recorded. An example of the results that can be obtained using combined adsorption manometry / calorimetry is given in Figure 3. This figure represents the direct signals of pressure and heat flow as a function of time, recorded during the adsorption of nitrogen onto a well-organised graphite sample [6].
Figure 3 : Plot of the signals of heat flow and pressure obtained during the adsorption of nitrogen on graphite at 77. 4 K. (adapted from [6]). This diagram highlights several points relative to the measurement of differential enthalpies of adsorption using the continuous procedure of adsorptive introduction. It can be seen that the initial introduction of gas, up to 1.5 hours, leads to only a slight increase in the pressure signal. This corresponds to a relatively strong signal in the heat flow curve that is the result of monolayer adsorption on a highly organised homogeneous surface. The point "P" corresponds to a small step in the pressure signal and a large peak in the heat flow signal. This phase transition corresponds to the completion of the monolayer in epitaxy with the highly organised substrate [6]. At point "s" however, the flow of adsorptive is stopped in order to check equilibrium. It can be seen that the pressure signal does not change and the heat flow
218 signal decreases to the baseline within the response time of the calorimeter. These two points allow the conclusion of a quasi-equilibrium state. At point "s'", the vacuum line is opened to desorb the nitrogen and check the reversibility of the system. Note that this is one of the requirements for the above-mentioned calculations. It can be seen that at "P'", an effect similar to that produced on adsorption occurs. This and the fact that the two hatched areas are equivalent show the reversibility of this system. 2. CLASSIFICATION OF CALORIMETRIC CURVES As shown above, the differential enthalpy curves obtained using such adsorption microcalorimetric experiments is a global effect that includes both adsorbate- adsorbent as well as adsorbate- adsorbate interactions. Various adsorbate filling mechanisms and phase transitions can be highlighted as well as any structural changes of the adsorbent. Interaction Energy
Relative Coverage 0
Figure 4 9Hypothetical breakdown of calorimetric curves due to various interactions in play during the adsorption of simple gases at low temperature 9(a) adsorbate- adsorbate interaction, (b) interactions of an adsorbate with an energetically h_omogeneous adsorbent, (c) interactions of an adsorbate with an energetically heterogeneous adsorbent In general though, the calorimetric curve highlights three different types of behaviour as schematised in Figure 4. As the amount of adsorbate increases on a sample, then the interactions between the adsorbate molecules increase (a). Concerning the a d s o r b a t e adsorbent interactions themselves. The interaction of an adsorbate molecule with an energetically homogeneous surface will give rise to a constant signal (b). Finally, in most cases, the adsorbent is energetically heterogeneous due to a pore size distribution and/or a varying surface chemistry (defects, cations ..). One would expect relatively strong interactions between the adsorbing molecules and the surface initially which decrease as these specific sites are occupied. Thus, for energetically heterogeneous adsorbents, a gradual decrease in the calorimetric signal is observed (c). However, each differential enthalpy curve varies and is a composite of varying percentages of each type of interaction. Both Kiselev [7] and Sing [8] have put forward classifications of differential enthalpy curves. Figure 5 shows hypothetical differential enthalpy of adsorption curves which would correspond to the IUPAC [4] classification of adsorption isotherms. For non-porous and macrporous (dp > 50 nm) solids which give rise to Type II isotherms, the differential enthalpy curve invariably decreases rapidly to the enthalpy of vaporisation (AvapH) of the adsorptive. In several cases where there exist many specific sites on these
219 materials, this decrease in the curve is less marked. These differences would seem to correspond to different C values derived from the BET equation. Mesoporous materials (2 < dp < 50 nm) which normally give rise to Type IV isotherms also give rise to differential enthalpy curves which decrease to the enthalpy of vaporisation (AvapH) of the adsorptive under investigation. For solids with a very narrow pore size distribution (MCM-41 type materials, for example) a slight increase in calorimetric signal of around 2 kJ-mol "l is observed during the capillary condensation step [8]. II high CBET
I
l
B
f
~O=WCBET %~
aads ~1
,AvapH
III
IV
AvapH i
VI ~Av_ae.l-I "
..f
_._."'_..
,
J B <-
na/m s
J
IV
III
v
_s f
vl
j
: p/pO
Figure 5 : Hypothetical differential enthalpy of adsorption curves (7eft) corresponding to the IUPAC classification [4] of adsorption isotherms (righO. Systems that give rise to Type III or Type IV isotherms are indicative of very weak adsorbate - adsorbent interactions. For these systems, the differential enthalpy of adsorption is initially below that of the enthalpy of vaporisation of the adsorptive. In such cases, it would seem that entropy effects drive the adsorption process. Type VI isotherms are typical for very homogeneous two-dimensional solids such as graphite. Each step corresponds to the edification of a different adsorbate layer. The differential enthalpy curve is relatively constant for the initial monolayer coverage. The completion of this monolayer results in a distinct peak in the differential enthalpy curve which corresponds to the epitaxal formation (see above, Figure 3). It is noteworthy that this 2dimensional disorder - order transition was first observed by microcalorimetry [5] before being characterised by neutron diffraction methods. Finally, the filling of micropores (dp < 2 nm) is characterised by Type I isotherms. The initial uptake is characterised by a very small increase in pressure and is the result of enhanced interactions. Such cases are ideal for microcalorimetric studies as the technique is at its most sensitive. The differential enthalpy of adsorption curves are typically elevated
220
throughout the pore filling process. The examples given later in this chapter all give rise to primary micropore filling process [10]. The secondary micropore filling process gives rise to a slightly weaker signal. 3. VARIOUS RESULTS OBTAINED WITH MICROPOROUS ADSORBENTS 3.1 Carbons Carbons are one of the most widely used industrial adsorbents. They can be prepared with surprising high surface areas and in certain cases, with a relatively narrow pore size distribution. Their hydrophobic properties make them quite interesting for the separation of organics from water. However, their applications are far wider. The adsorption of simple gases onto microporous active carbons generally lead to calorimetric curves containing three different regions during the filling of the micropores. An example is given in Figure 6 for the adsorption of nitrogen and argon onto an activated carbon at 77.4 K. The three regions are clearly shown : the first region, AB, decreases before a second, more horizontal region, BC. The third region, CD, again shows a marked decrease towards the enthalpy of liquefaction of the gas under consideration.
~ 0
o
10
E E
a
t-
6
E
--j
15
r
13
9
IA,~pH~I _
0
005
0.1
p / pO
0.15
02
0
_ IAvapHN,I,
0.'2
04
,
- -
016
0.'8
i
Relative Coverage (0)
Figure 6 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen and argon adsorbed onto an activated carbon [11].
A number of authors have noted and discussed such phenomena with varying interpretations [1, 12]. It would seem that the following conclusions are generally given : 9 Region AB is characteristic of interactions between the adsorbate and an energetically heterogeneous adsorbent (Figure 4). If one considers that the 2-dimensional graphite surface is energetically homogeneous, as explanation of the observed heterogeneity has to be found. Such heterogeneity can arise from defect, impurities as well as from a large distribution in micropore size. Although the first two solutions can be eliminated in some cases, the nature of the preparation and activation of such materials make a certain pore size distribution inevitable. One can therefore assume the filling of the smallest micropores (or ultramicropores) in this initial region AB. 9Region BC however, corresponds to a more homogeneous phenomenon than the latter. It is also noteworthy to remark that this region corresponds to an enthalpy of adsorption not far
221 from that for the adsorption on a perfect 2-dimensional surface (~ 14 kJ'moll). Furthermore, simulation studies [ 13] have shown that for the adsorption of nitrogen in larger micropores (or supermicropores), above 0.7 nm in diameter, a two step process may occur. The first step would seem to correspond to the coverage of the pore walls whereas the second to the filling of the void space. It would thus seem possible that the region BC corresponds to the coverage of the pore walls. The fact that this step is not completely horizontal in comparison to the adsorption on a 2-dimensional graphite surface may be due to curvature effects within the micropores. 9 Taking into account the above-mentioned hypothesis, it would seem that the region CD corresponds to the completion of the filling of the larger micropores. The adsorption of simple gases onto carbon nanotubes leads to slightly different results. An example here is given in Figure 7 [14]. Here, two main regions can be distinguished. It is well known that such nanotubes are closed at each end so blocking any inherent microporosity. Moreover, these nanotubes arrange themselves into bundles with a porosity of around 0.3 nm between the fibres. This latter porosity should thus be inaccessible. 2119
S... o E --, v'
A
B
08
17
06
15
r-
13
<] '
11
%. 0.4 t:).
c
D 02
9 7
o o
1
2
3
4
5
n a / m m o l . g "~
Figure 7 : Enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for methane on carbon nanotubes [14]. The first step (AB, Figure 7) may be explained by the filling of a small percentage of unblocked nanotubes. According to the preparation mode, the quantity of unblocked pores can be in the region of 20%. The second region, BC, would thus seem to be the formation of a monolayer on the external surface of these nanotubes.
3.2 Clays Clay materials form a vast family of inexpensive and readily available adsorbents. They can be used for their intra-sec properties as well as binders for other active materials such as zeolites. Due to the sheet-like nature of the majority of clays, no microporous properties are observed. Nevertheless, it is worth dwelling on the example of the adsorption of nitrogen and argon on kaolinite (Figure 8). This example shows a possibility, via microcalorimetry, to estimate the ratio of different mineral facets.
222 Kaolinite has a 1:1 sheet structure with a layer repeat distance of 0.72 nm. This is approximately the distance of the sheets themselves which means hat there is insufficient space to accommodate intercalated molecules such as water. The isotherms obtained for such materials are of Type-II which are typical for non-porous or macroporous materials. 25-
o E
--j "" .,c:
Ar 15
IAv,~H,,I 5
0
0~2
IAvapHN, I 9-
o', o~8 o18 Relative Coverage (0)
;
1.2
Figure 8 9Enthalpies of adsorption with respect to relative coverage at 77. 4 K for nitrogen and argon on kaolinite. (after [15]).
The differential enthalpy curve for argon and nitrogen (Figure 8) [15] shows two main regions. The first, AB, corresponds to the adsorption on defect sites and the adsorption on lateral facets of the materials. These high energy domains provoke an enhanced interaction with the nitrogen quadrupole. The second region, CD, corresponds to the adsorption on more energetically homogeneous basal planes. Such calorimetric measurements are thus a simple means to estimate the proportion of lateral and basal planes of such materials as well as the effect of grinding. It is possible to create microporosity in these layered clays materials via the replacement of exchangeable ions with more bulky ions. The more bulky ions can then be stabilised by an appropriate thermal treatment. However, some clays do have intra-sec micropores. The palygorskites are fibrous clay minerals. Attapulgite and sepiolite are two members of this family which both contain structural micropores. Their structures comprise of talc-like layers arranged quincuncially, forming microporous channels of rectangular cross-section parallel to the longitudinal axis of the crystals [15]. Whilst attapulgite has a pore section of 0.37 x 0.64 nm 2, the section of sepiolite is of 0.67 x 1.34 nm 2. The pores contain Mg(OH2)2 groups situated in the structural micropore walls. The differential enthalpy curves obtained for the adsorption of nitrogen on sepiolite and attapulgite at 77.4 K are shown in Figure 9 [17, 18]. Two separate domains can be observed for each of these curves. The first, domain, AB (Figure 9), is quasi-horizontal which is characteristic of adsorption in highly homogeneous regions. This would seem to correspond to the adsorption within the intrafibrous micropores containing the Mg(OH2)2 groups.
223
ca)
- (4)
--5 a~
15
t-
<,
IAvapHN21 o
o12
oi~
oi~
o~
relative coverage (0)
Figure 9 "Enthalpies of adsorption with respect to relative coverage at 77. 4 K for nitrogen on attapulgite (a) and sepiolite (b). The second domain in corresponds to the end of any micropore filling in the adsorption isotherms. The differential enthalpy curves in this region, CD (Figure 9), correspond to a decrease towards the enthalpy of liquefaction. This is characteristic of more energetically heterogeneous regions. It would seem that such regions are found between the fibres. Thus this would seem to correspond to adsorption in these interfibrous micropores. 3.3 A m o r p h o u s
Silica's
There are three main classes of amorphous silica's 9pyrogenic silica' s, precipitated silica's and silica gels. Pyrogrenic silica's and precipitated silica's are essentially not microporous. An exception is made for those silica's prepared by the St6ber process. These silica's would seem to be ultramicroporous with pores too small to allow nitrogen molecules to penetrate the porosity. However, the pores are large enough to allow the adsorption of water within the porosity at ambient temperatures. Silica gels can be prepared to contain micropores. A large number of physisorption studies have been carried out on silica gels. A certain number of these are described in Ref. [1]. Although initial synthesis of silica gels resulted in relatively ill-defined samples, it is currently possible to control both the synthesis and drying to form microporous Aerogels and Xerogels.
224 N2
Ar
10,
o E E
%
,.
. ,
'-N2
?
a.
6,
<-
4,
. . . . .
[AvapHArl
o;
o os
0"4 p /
pO
,
,,
9
o is
,|,
o2
5
o
,
03
0"4
,
o'6
IAvapHN=[ 0"8
Relative Coverage (0)
Figure 10 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen and argon adsorbed onto a microporous amorphous silica gel (Davison 950) [11]. An example of the adsorption behaviour on microporous silica gels is given in Figure 10. This figure shows the isotherms and differential enthalpy curves for the adsorption argon and nitrogen on a microporous silica gel (Davison 950). Both the differential enthalpy curves obtained with argon and nitrogen decrease continually with relative coverage. This is characteristic of large electrical homogeneity. This is probably due to both the surface chemistry and pore size distribution. Often the comparison between the results obtained with argon and nitrogen can give an idea of the relative importance of the inhomogeneity due to the pore size distribution and surface chemistry. Indeed, argon being a spherical and non-polar molecule interacts only weakly with surface chemical species such as hydroxyls. The behaviour thus observed is essentially due to the textural properties (pore geometry, pore size distribution ...). Nitrogen however, has a permanent quadrupole which is able to interact with any specific surface groups. The behaviour thus observed corresponds to any specific interactions with the surface as well as any interaction due to the textural nature of the sample. The difference in differential enthalpies of argon and nitrogen can be taken as an indication of the extent of the interactions due to the surface chemistry of the adsorbent under investigation. This for silica' s and other adsorbents. 3.4 Zeolites
From the applications point of view, particularly in membrane science, zeolites and related materials (aluminophosphates, gallophosphates ...) are interesting materials. ~1he synthesis of such materials can be adjusted to give a wide range of crystal structures and an almost infinite variety of chemical compositions giving the possibility to tailor-make samples for specific applications. From a fundamental point of view, the regular pore systems can be indexed by X-ray diffraction and the structure can be elucidated using Riedvield refinement-type methods for example. The zeolite family of materials are thus ideal for the understanding of adsorption phenomena. It is the knowledge gained by such studies, using thermodynamic methods (manometry, calorimetry ...) complemented by structural methods (neutron diffraction, X-ray
225
scattering ...) which permit, by analogy, the interpretation of adsorption phenomena in more disordered systems. Simulation studies are essential to complete the fundamental understanding. Three of the most widely used zeolites today are silicalite, Linde A and faujasite. Probably the most widely studied aluminophosphate is A1PO4-5. All four of these structures give rise to unusual adsorption phenomena during micropore filling. Several examples are highlighted in the following section. 3.4.1. Silicalite Silicalite is the pure silica end analogue of ZSM-5 (structure type MFI [19]). The pore network consists of straight elliptical pores of 0.51 x 0.57 nm 2 in section which intersect (0.8 nm in diameter) with sinusoidal, quasi-circular pores of 0.54 x 0.56 nm 2 in section. As the framework is purely silicic, there are no compensation cations. Figure 11, Figure 12 and Figure 13 highlight the three types of adsorption behaviour that can be observed with silicalite at 77 K for various adsorptives. The adsorption of methane (Figure 11) gives rise to a type I isotherm and a differential enthalpy of adsorption curve which is strictly horizontal during micropore filling. The adsorption of argon (Figure 12) and krypton both give rise to isotherms with a second step (or sub-step), noted [~ in Figure 12. This step in the isotherm corresponds to a distinct variation in the differential enthalpy curve. Finally, for gases such as nitrogen (Figure 13) and carbon monoxide two steps (ct and 13) in the isotherm can be observed. These steps also correspond to distinct variations in the differential enthalpy curve.
r
0,025
..-b, 0,02 16 0
E
0,015
14
12 10
6,, 0
%
0,01
IAv.~HcH,,I
0,005
i
__/ 1
na / mmol.g 1
Figure 11 " Enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for methane on silicalite-I [20].
The behaviour shown during the adsorption methane on silicalite at 77.4 K (Figure 11) can be considered almost model. The quasi-horizontal calorimetric signal, corresponding to the entire micropore filling region would seem to be purely the result of adsorbent - adsorbate interactions. One would expect a certain contribution due to a d s o r b e n t - adsorbent interactions, however this would seem to be minimal.
226
0,002 9
17
0,2
17 ,1,
15
o
..~
T._ 0
13
E
%.
13 0,12
.-j
o
r
t,--
~,
0,16
E
0,0012 11
,i,l
15
0,0016 9
,0,08
0,0008
~,
9
9 ,0,04
0,0004
7
5 0
1
2
3
4
5
6
n" / mmol.g -1
Figure 12 : Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for argon on Silicalite [20].
f 0
1
: .
2
3
4
.... ,5
6
0
na / mol.uc 1
Figure 13 : Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for nitrogen on Silicalite [21].
The adsorption of argon on silicalite at 77 K (Figure 12) shows similar behaviour to that of methane during the initial micropore filling process. This would seem to indicate the interaction of the adsorbate with an energetically homogeneous surface. However, the sudden substep at around p/p0 = 0.0002 corresponds to a distinct change in the differential enthalpy curve. Note that the substep in the isotherm was searched for after the change in the calorimetric curve was first observed. This substep, 13, was then characterised by neutron diffraction [20] giving rise to an explanation of a phase change in the adsorbed phase from a fluid state to a more dense "solid-like" state. The picture is certainly more complex with a probable transition of the silicalite structure itself. The adsorption of nitrogen on silicalite at 77 K (Figure 13) gives rise to an isotherm with two substeps ot and 13. It is interesting to note however, that the initial pore filling results in a differential curve which is not completely horizontal. An initial decrease would seem to indicate an enhanced interaction, maybe with defect site. This curve then increases again which would seem to be characteristic of increasing adsorbate- adsorbate interactions. The substeps in the isotherm correspond to marked differences in the differential enthalpy curves. Although this second substep 13, was observed in the isotherm prior to any microcalorimetic measurements [22, 23], the first substep a, was initially observed in the calorimetric curve [21 ]. Again, a complementary study by neutron diffraction was carded out on this system. This study [21 ] concluded that the first substep a, is due to an ordering of the adsorbate from a fluid phase to a network fluid. The second substep 13, would seem to correspond to an adsorbate phase transition similar to that observed for argon (Figure 12), that is to say from a network fluid to a "solid-like" adsorbate phase. These particularities in the behaviour of the adsorbate phase are influenced by the quality of the substrate. The introduction of compensation cations with the introduction of aluminium into the framework (ZSM-5) influences the marked nature of these variations in behaviour of the adsorpbate. Indeed these variations become less marked. This is especially the case for the substep ct which disappears from the isotherm as soon as the quality of the pore network
227 degrades due to the presence of compensation cations, preadsorbed species or even after grinding. These examples however, show the interest of such microcalorimetric measurements with the high resolution, continuous procedure of adsorptive introduction. Such subtle adsorption phenomena allow, not only the quality of crystals to be verified, but also an increased understanding of the influence of the substrate on the adsorption of simple probe molecules. 3.4.2. 5,4 and 13X The study of relatively simple solid / gas systems such as those in sections 3.4.1 and 3.4.3, allow a better understanding of more complex systems such as industrially prepared zeolites with cationic sites. The two most widely used zeolites are 5A and 13X. The 5A zeolites, with LTA structure [19] consist of regularly spaced spherical cages of 1.14 nm in diameter. These cages are linked to each other by six circular windows of around 0.42 nm in diameter. The negatively charged silico-aluminate framework requires compensation cations. In the case of zeolite 5A, these exchangeable cations are generally a mixture of calcium and sodium. The 13X zeolite, or faujasite of FAU structure [19] has very similar primary building blocks to the 5A zeolites. For 13X however, the spherical cages are of 1.4 nm in diameter, which are linked to each other by four circular windows of around 0.74 nm in diameter. The exchangeable cations are generally sodium (NaX). 25-
5A 20 ,1_ o E ,-j
13 X
15
10
IAvapHN, I 5
o
;
i
~
8
n a / m m o l . g -~
Figure 14 9Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for nitrogen on 5A and 13X [24].
A prior study of the adsorption of nitrogen at 77 K on 5A and 13X zeolites using quasiequilibrium, isothermal, adsorption microcalorimetry experiments at 77K [24] detected a step in the differential enthalpies of adsorption, towards the end of micropore filling (Figure 14). At the time, this was interpreted as a consequence of specific adsorbate - adsorbate interactions. Recently however, in the light of other microcalorimetry studies this change in signal has been interpreted as a possible phase change within the cavities [25]. This latter study detected the same phenomenon for a number of other probe molecules including, argon and methane as well as for carbon monoxide. An independent study showed that this latter
228 step corresponds to the delocalised adsorption of mobile molecules as the main cages (or orcages) become almost full [26]. 3.4.3. AIPOr Recently, much research has been made into the synthesis of zeolite-like materials with framework species other than silica and alumina. The first family of materials that resulted from this research were the aluminophosphate molecular sieves. Thus A1PO4-5 [27] with an AFI-type structure [19] has a unidirectional pore system consisting of parallel circular channels of 0.73 nm in diameter. AIPO4-5 has a framework which, like silicalite-I, theoretically is globally electrically neutral, although the pore openings is slightly larger than those of the MFI-type zeolites. These characteristics make AIPO4-5 a fine structure for fundamental adsorption studies. For ALP04-5 the adsorption isotherms of argon and nitrogen traced up to a relative pressure of 0.2 are indistinguishable (Figure 15). This is not the case for methane which adsorbs significantly less, suggesting a different pore filling mechanism. The differential enthaply curves for argon and nitrogen vary. For argon, a slight increase in the differential enthalpy curve occurs due to the increase in adsorbate- adsorbate interactions during the filling of the micropores. For the adsorption of nitrogen, the differential enthalpy curve initially decreases as a result of decreasing adsorbate - adsorbent interactions. The curve then increases due to the adsorbate- adsorbate interactions that increase as the micropore filling process procedes. 3
~
N2
CH4
2.5
14
Ar, N 2
2 .=,: O [::15
E
o E
13
-~9
12
e-
11
1
10 0.5
0
0 05
0.1
p/p0
0.15
0
0.2
0.4
0.6
0 8
Relative Coverage (0)
Figure 15 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen, argon and methane adsorbed on ALP04-5 [28]. For the adsorption of methane however, an exothermic peak (noted ~ in Figure 15) is observed in the differential enthalpy curve for methane, which would seem to correspond to an energetic term ~ RT. This would seem to indicate both a variation of mobility and a variation of the adsorbed methane phase. A complementary neutron diffraction study [29] indicates that an unusual behaviour of the methane adsorbed phase occurs. It would seem that the methane undergoes a transition between two solid-like phases. The first "solid-like" phase
229 corresponds to the adsorption of 4 molecules per unit cell whilst the second phase corresponds to a jump in the quantity adsorbed to 6 molecules per unit cell. This would seem to be a result of a favourable dimensional compatibility between the methane molecule and A1PO4-5 micropore, permitting, from a volumic point of view, the apparition of two relatively dense phases. This hypothesis is supported by simulation studies [30]. 4. CONCLUDING REMARKS The aim of this chapter is to highlight the interest of adsorption microcalorimetry, not only to characterise various adsorption phenomena on well defined adsorbents but also for the characterisation of less well defined microporous adsorbents. Indeed, it is the information gained from fundamental studies on these energetically homogeneous adsorbents that allow, by analogy, the pinpoint of different phenomena that arise in more heterogeneous adsorbents. Microcalorimetric measurements allow the easy detection of adsorption phenomena that are difficult to observe in the adsorption isotherm alone. Direct calorimetric measurements are quite complementary to calculations via the isosteric method. However, direct measurements are far more sensitive for the adsorption of molecules within micropores. Such calorimetric measurements can be completed by structural studies (e.g. neutron diffraction) and finally by computer simulation. 5. LIST OF SYMBOLS C BET constant
dp pore diameter frate of gas flow f ' rate of adsorption n amount of substance n a amount adsorbed nammonolayer capacity p pressure p0 saturation pressure p/pO relative pressure
Qrevheat reversibly exchanged with the surroundings R gas constant T absolute temperature Vvolume (Vc volume of sample cell "accessible" to the calorimeter) AvapHenthalpy of vapourisation Aads/~ differential enthalpy of adsorption r heat flow 0relative coverage (i.e. na/nam)
6. REFERENCES
1. 2. 3. 4. 5. 6. 7.
F. Rouquerol, J. Rouquerol and K. Sing, "Adsorption by Powders and Porous Solids", Acad. Press, London, 1999. J. Rouquerol, In "Thermochimie", Colloques Intemationaux du CNRS, No.201, CNRS Ed., Paris 1972, p.537. Y. Grillet, J. Rouqu6rol and F. Rouqu~rol, J. Chim. Phys., 2 (1977) 179. K . S . W . Sing, D. H. Everett, R. A. W. Haul, L. Moscou, R. A. Pierotti, J. Rouquerol and T. Siemieniewska, Pure Appl. Chem., 57 (1985) 603. C. Letoquart, F. Rouquerol & J. Rouquerol, J. Chim. Phys. 70(3) (1973) 559. J. Rouquerol, S. Partyka and F. Roquerol, J. Chem. Soc. Faraday Trans. 1, 73 (1977) 306. A.V. Kiselev, Doklady Nauk USSR, 233 (1977) 1122.
230 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
K . S . W . Sing, In "Thermochimie", Colloques Intemationaux du CNRS, No.201, CNRS Ed., Paris 1972, p.537. P.L. Llewellyn, Y. Grillet, J. Rouquerol, C. Martin, J-P. Coulomb, Surf Sci., 352-354 (1996) 468. S. J. Gregg and K. S. W. Sing, "Adsorption, Surface Area and Porosity", 2nd Edn., Academic Press, London, 1982. M. Salameh, Ph.D. Thesis, Universit6 d'Aix-Marseille I, 1978. D. Atkinson, P. J. M. Carrott, Y. Grillet, J. Rouquerol and K. S. W. Sing, In "Proc. 2 nd Int. Conf. On Fundamentals of Adsorption" (A. I. Liapis ed.), Eng. Foundation, New York, 1987, p.89. P. Brauer, H._R. Poosch, M. V. Szombathely, M. Heuchel, and M. Jarioniec, In "Proc. 4th Int. Conf. On Fundamentals of Adsorption" (M. Suzuki ed.), Kodansha, Tokyo, 1993, p.67. M. Muds, N. Dufau, M. Bienfait, N. Dupont-Pavlovsky, Y. Grillet and J. P. Palmary, Langmuir, in print, 2000. J. M. Cases, P. Cunin, Y. Grillet, C. Poinsignon and J. Yvon, Clay Minerals, 21 (1986) 55. K. Brauner and A. Preisinger, Tschermarks Miner. Petr. Mitt,. fi (1956) 120. Y. Grillet, J. M. Cases, M. Frangois, J. Rouquerol and J. E. Poirier, Clays and Clay Minerals, 36(3) (1988) 233 J. M. Cases, Y. Grillet, M. Frangois, L. Michot, F. Villieras and J. Yvon, Clays and Clay Minerals, 39(2) (1991) 191 Meier W. M. & Olson D. H., "Atlas of Zeolite Structure Types", Butterworth-Heinemann, London, 1992. P. L. Llewellyn, J.-P. Coulomb, Y. Grillet, J. Patarin, H. Lauter, H. Reichert and J. Rouquerol, Langmuir, 9 (1993) 1846. P. L. Llewellyn, J.-P. Coulomb, Y. Grillet, J. Patarin, G. Andr6 and J. Rouquerol, Langmuir, 9 (1993) 1852. P. J. M. Carrott and K. S. W. Sing, Chem. & Ind., (1986) 786. U. Mtiller and K. K. Unger, Fortschr. Mineral., 64 (1986) 128. F. Rouqurrol, S. Partyka & J. Rouqurrol, in "Thermochimie", CNRS Ed., Paris (1972) p.547. N. Dufau, N. Floquet, J. P. Coulomb, G. Andrr, R. Kahn, P. Llewellyn and Y. Grillet, In "Proc. 5 th Int. Conf. on Characterisation of Porous Solids" K.K. Unger, G. Kreysa, J.P. Baselt eds., Elsevier, Amsterdam, 2000. D. Amad, J. M. Lopez Cuesta, N. P. Nguyen, R. Jerrentrup & J. L. Ginoux, J. Therm. Analysis, 38 (1992) 1005. S. T. Wilson, B. M. Lok, C. A. Messina, T. R. Cannan and E. M. Flanigen, J. Amer. Chem. Soc., 104 (1982) 1146. Y. Grillet, P. L. Llewellyn, N. Tosi-Pellenq et J. Rouquerol, In "Proc. 4th Int. Conf. On Fundamentals of Adsorption ", (M. Suzuki ed.), Kodansha, Tokyo, 1993, p.235. J-P. Coulomb,C. Martin, P. L. Llewellyn, Y. Grillet, In "Progress in Zeolites and Microporous Materials" (H. Chon et al. eds.), Elsevier, Amsterdam, 1997, p.2355. V. Lachet, A. Boutin, R. J. M. Pellenq, D. Nicholson and A. H. Fuchs, J. Phys. Chem., 100 (1996) 9006.
213
Characterisation of microporous materials by adsorption microcalorimetry Philip Llewellyn Centre of Thermodynamics and Microcalorimetry- CNRS, 26 rue du 1416meRIA, 13331 Marseille cedex 3, France Calorimetry, or the study of heat, traces its origins back to Lavoisier and Laplace in 1783. Although the use of calorimetry for the study of adsorption phenomena dates back to around Favre in 1854, it remains a rarely used technique. This is mainly due to the strict experimental conditions required to obtain good results. Under these conditions, adsorption microcalorimetry is both a powerful and sensitive tool for the study of adsorption phenomena. The energetic information thus obtained provides supplementary resolution with respect to adsorption manometry and is complementary to other structural and/or diffusion studies. The present chapter aims to give an introduction to current calorimetric methods available for the study of adsorption phenomena. This is followed by a hypothetical breakdown of the adsorbate - adsorbent interactions, which is the basis of a classification of different calorimetric curves. Finally, several experimental results are highlighted for various microporous adsorbents. 1. DIFFERENT CALORIMETRIC METHODS AVAILABLE FOR THE STUDY OF
ADSORPTION PHENOMENA
There are a number of conditions under which calorimetric measurements can be carried out [1]. Adiabatic calorimetry, that is when the surrounding temperature is made to follow that of the sample, is quite interesting for the determination of the heat capacity of a system. Isoperibol calorimeters, where no special connection is made between the sample temperature and that of the surroundings were the first to be used to measure adsorption phenomena. However, there are a number of drawbacks which make gas adsorption studies uncertain. Finally, diathermal calorimetry, where the sample temperature follows that of the surroundings is that most suited to the following of gas adsorption phenomena. Thus the isothermal conditions of adsorption manometry can be reproduced to be able to measure the actual heat effects that occur during adsorption. The examples given later in this chapter are obtained under these diathermal or quasi-isothermal conditions. An example of a diathermal calorimeter used for adsorption studies is given in Figure 1. This apparatus is formed of three main parts : the dosing apparatus, the sample cell and the calorimeter. The dosing apparatus, consisting of a reference volume (A), pressure gauge (B) as well a vacuum line (C) and gas inlet (D) is connected to the sample cell (E). This cell is placed in the calorimeter. A detailed explanation of this Tian-Calvet calorimeter are elsewhere [2, 3]. The calorimeter itself is placed in a liquid nitrogen (or agron) cryostat (F). Two thermopiles (G) are mounted in electrical opposition. A resistance (H) is placed into the reference thermopile allowing calibration via the Joule effect. ~t
email, [email protected], fr
214
A
C
0
H
0
~-"G 0
J Figure 1 : Schematic representation of a calorimetric set-up used for adsorption experiments. There are however, two different methods of adsorbate introduction. The first, and most common, is to inject discrete quantities of adsorptive to the adsorbent. A peak in the curve of energy with time is obtained which has to be integrated to give an integral molar enthalpy of adsorption for each dose. This method is explained in section 1.2. Alternatively, it is possible to introduce the adsorptive to the adsorbent in a continuous manner whilst ensuring that the adsorbate - adsorbent equilibrium is maintained. This leads to a high-resolution curve that is necessary for the observation of subtle adsorption phenomena such as phase transitions. This second method is described in section 2.2. However, beforehand, it is worth describing an indirect manner to obtain energetic information directly from two or more adsorption isotherms using the isosteric method. 1.1 The isosteric method
If one has the possibility to carry out two or more isotherms at various different temperatures, it is possible to calculate the differential enthalpy of adsorption using the isosteric method. From these isotherms, a plot of log pressure, In p, for a given amount adsorbed n a as a function of reciprocal temperature, 1/T, can thus be drawn. It is then possible to make use of the Claussius-Clapeyron equation for a single gas-liquid system. One has to assume that there is no variation of enthalpy or entropy with temperature. The equation used is thus :
/aln~]
'] A aa,/~,o : R 0(l/r) ),,o
{Eq. 1}
Where Aaa~/~ is the differential enthalpy of adsorption and R the gas constant. Often however, one can measure two isotherms measured at around 1OK apart; for example in liquid
215 nitrogen (77 K) and liquid argon (87 K). It is thus possible to relate the equilibrium pressures
pl and p2 at corresponding temperatures T1 and T2 for a given quantity adsorbed: A,d~/~= - RT~T2 In P__L
{Eq. 2}
It can be seen that the precision of this calculation depends greatly on the measurement of the pressure. This can be a problem at low pressures. Not due to the precision of the pressure reading itself, as modem pressure gauges are more than sufficient, but to the exactness of the adsorbate-adsorbent equilibrium itself. This is especially the case for micropore filling in poor conducting materials, such as silica. A small deviation from this equilibrium, due to molecular diffusion or thermal transfer, can lead to a relatively large variation in pressure. This would explain some of the disparity in results obtained using the isosteric method and direct calorimetric measurements. However, as we shall see later, the calculation of the enthalpy of adsorption using the direct calorimetric procedure becomes less precise at higher pressures. This makes both methods quite complementary.
1.2 Discontinuous procedure of adsorptive introduction The discontinuous (or point by point) procedure of adsorptive introduction is the one most widely used for the determination of adsorption isotherms via manometry experiments. The same procedure can be used for the determination of differential enthalpies of adsorption using an apparatus such as that shown in Figure 1. The introduction of each dose of adsorptive to the adsorbent gives rise to a thermal effect until equilibrium is attained. This results in a peak in the curve of heat flow with time. Integration of this peak gives the overall heat effect due to adsorption. The calorimetric cell (including the relevant amounts of adsorbent and adsorptive) is considered as an open system. In this procedure, as well as in the quasi-equilibrium procedure of adsorptive introduction (section 1.3) it is important to consider the adsorptive introduced reversibly. However, to calculate the differential enthalpy of adsorption via the discontinuous procedure, one must introduce quantities dn small enough for a given pressure increase dp. Under these conditions it is possible to determine the differential enthalpy of adsorption Aaa,/~, via the following expression :
Aads~ : l dQr;v~ .~ Vc( d~Pa~
{Eq. 3}
dn Jr t,.dn Jr Here, dQrev is the heat reversibly exchanged with the surroundings at temperature T, that is
to say the heat measured by the calorimeter. 8n a is the amount adsorbed after introduction of the adsorptive dose, dp is the increase in pressure and Vc is the dead space volume of the sample cell within the calorimeter itself (thermopile). If the conditions of reversible adsorption and small doses are not fulfilled, then the quantity calculated using Eq. 3 should be more properly be termed "pseudo-differential enthalpies".
1.3 Quasi-equilibrium introduction of adsorptive For the observation of subtle adsorption phenomena such as phase changes, an increased resolution in both isotherm and differential enthalpy curves is requires. It would be possible to introduce very small doses of adsorptive to increase the number of points taken. This is both
216 time consuming and may lead to a number of errors. However, a continuous introduction of adsorptive leads to an infinite resolution in both curves.
Figure 2 9Comparison of the results obtained using either the discontinuous (rectangles) or continuous (full line) procedure of adsorptive introduction. Figure 2 highlights how this resolution can be interesting. The peak in the full line would be indicative of an adsorbate phase change which would go unnoticed using the discontinuous procedure of adsorptive introduction. In what has been termed the "continuous flow" procedure, the adsorbate is introduced to the system at a defined rate, slow enough that the adsorbate- adsorbent system can be considered to be essentially at equilibrium at all times [4,5]. As we shall see later, different tests easily allow verification as to whether the experiment indeed proceeds at quasiequilibrium. In this "quasi-equilibrium" state, the quantity of adsorbate admitted to the system An can be replaced in adsorption calculations by the rate of adsorptive flow dn/dt. The calorimeter, under these conditions, thus measures a heat flow, ~. Under certain experimental conditions, it is possible to render constant the adsorptive flow to the sample, f = dn/dt. A rate of adsorption, f~, can therefore be calculated using the following expression"
f<,
dn <' I ( V a Vc)dp : - - - - ~ : f - R ~,Ta --Tcc --~
{Eq. 4}
Here, Vd and Vc are the volumes of the dosing system and that "accessible" to the calorimeter at temperatures Td and To. The corresponding heat flow, ~b,can be given by 9
dQ,~,, dQ,e,, dna ~= dt - d n " at
= f<'fdQ-~r~ i
Can )~
{Eq. 5}
Introducing Eq. 4 into Eq. 5 leads to 9
an 9
+ Vc = +V tan ) 7 7 c at dn~
f--W ~b+Vc --~
{Eq. 67 {Eq. 7}
217 Blank experiments can lead to an estimation of Vc(dp/dt). This term is large at horizontal parts of the isotherm. The error in the estimation of the differential enthalpy thus becomes large. However, it is just in this region of the isotherm that the estimation of the differential enthalpy via the isosteric method is most exact. This highlights how both methods are complementary. In the present case however, where the adsorption on microporous materials is under examination, the term Vc(dp/dt) is minimal. Effectively, the increase in pressure with time is small during micropore filling. Furthermore, during micropore filling, all of the flow of adsorptive to the sample is adsorbed making f = f . In such cases, Eq. 7 can be simplified to :
A ~,,a.h ,~ s f
{Eq. 8}
Thus if the rate of adsorptive flow, f is constant, a direct measurement of A,d,/;~ with the amount adsorbed is recorded. An example of the results that can be obtained using combined adsorption manometry / calorimetry is given in Figure 3. This figure represents the direct signals of pressure and heat flow as a function of time, recorded during the adsorption of nitrogen onto a well-organised graphite sample [6].
Figure 3 : Plot of the signals of heat flow and pressure obtained during the adsorption of nitrogen on graphite at 77. 4 K. (adapted from [6]). This diagram highlights several points relative to the measurement of differential enthalpies of adsorption using the continuous procedure of adsorptive introduction. It can be seen that the initial introduction of gas, up to 1.5 hours, leads to only a slight increase in the pressure signal. This corresponds to a relatively strong signal in the heat flow curve that is the result of monolayer adsorption on a highly organised homogeneous surface. The point "P" corresponds to a small step in the pressure signal and a large peak in the heat flow signal. This phase transition corresponds to the completion of the monolayer in epitaxy with the highly organised substrate [6]. At point "s" however, the flow of adsorptive is stopped in order to check equilibrium. It can be seen that the pressure signal does not change and the heat flow
218 signal decreases to the baseline within the response time of the calorimeter. These two points allow the conclusion of a quasi-equilibrium state. At point "s'", the vacuum line is opened to desorb the nitrogen and check the reversibility of the system. Note that this is one of the requirements for the above-mentioned calculations. It can be seen that at "P'", an effect similar to that produced on adsorption occurs. This and the fact that the two hatched areas are equivalent show the reversibility of this system. 2. CLASSIFICATION OF CALORIMETRIC CURVES As shown above, the differential enthalpy curves obtained using such adsorption microcalorimetric experiments is a global effect that includes both adsorbate- adsorbent as well as adsorbate- adsorbate interactions. Various adsorbate filling mechanisms and phase transitions can be highlighted as well as any structural changes of the adsorbent. Interaction Energy
Relative Coverage 0
Figure 4 9Hypothetical breakdown of calorimetric curves due to various interactions in play during the adsorption of simple gases at low temperature 9(a) adsorbate- adsorbate interaction, (b) interactions of an adsorbate with an energetically h_omogeneous adsorbent, (c) interactions of an adsorbate with an energetically heterogeneous adsorbent In general though, the calorimetric curve highlights three different types of behaviour as schematised in Figure 4. As the amount of adsorbate increases on a sample, then the interactions between the adsorbate molecules increase (a). Concerning the a d s o r b a t e adsorbent interactions themselves. The interaction of an adsorbate molecule with an energetically homogeneous surface will give rise to a constant signal (b). Finally, in most cases, the adsorbent is energetically heterogeneous due to a pore size distribution and/or a varying surface chemistry (defects, cations ..). One would expect relatively strong interactions between the adsorbing molecules and the surface initially which decrease as these specific sites are occupied. Thus, for energetically heterogeneous adsorbents, a gradual decrease in the calorimetric signal is observed (c). However, each differential enthalpy curve varies and is a composite of varying percentages of each type of interaction. Both Kiselev [7] and Sing [8] have put forward classifications of differential enthalpy curves. Figure 5 shows hypothetical differential enthalpy of adsorption curves which would correspond to the IUPAC [4] classification of adsorption isotherms. For non-porous and macrporous (dp > 50 nm) solids which give rise to Type II isotherms, the differential enthalpy curve invariably decreases rapidly to the enthalpy of vaporisation (AvapH) of the adsorptive. In several cases where there exist many specific sites on these
219 materials, this decrease in the curve is less marked. These differences would seem to correspond to different C values derived from the BET equation. Mesoporous materials (2 < dp < 50 nm) which normally give rise to Type IV isotherms also give rise to differential enthalpy curves which decrease to the enthalpy of vaporisation (AvapH) of the adsorptive under investigation. For solids with a very narrow pore size distribution (MCM-41 type materials, for example) a slight increase in calorimetric signal of around 2 kJ-mol "l is observed during the capillary condensation step [8]. II high CBET
I
l
B
f
~O=WCBET %~
aads ~1
,AvapH
III
IV
AvapH i
VI ~Av_ae.l-I "
..f
_._."'_..
,
J B <-
na/m s
J
IV
III
v
_s f
vl
j
: p/pO
Figure 5 : Hypothetical differential enthalpy of adsorption curves (7eft) corresponding to the IUPAC classification [4] of adsorption isotherms (righO. Systems that give rise to Type III or Type IV isotherms are indicative of very weak adsorbate - adsorbent interactions. For these systems, the differential enthalpy of adsorption is initially below that of the enthalpy of vaporisation of the adsorptive. In such cases, it would seem that entropy effects drive the adsorption process. Type VI isotherms are typical for very homogeneous two-dimensional solids such as graphite. Each step corresponds to the edification of a different adsorbate layer. The differential enthalpy curve is relatively constant for the initial monolayer coverage. The completion of this monolayer results in a distinct peak in the differential enthalpy curve which corresponds to the epitaxal formation (see above, Figure 3). It is noteworthy that this 2dimensional disorder - order transition was first observed by microcalorimetry [5] before being characterised by neutron diffraction methods. Finally, the filling of micropores (dp < 2 nm) is characterised by Type I isotherms. The initial uptake is characterised by a very small increase in pressure and is the result of enhanced interactions. Such cases are ideal for microcalorimetric studies as the technique is at its most sensitive. The differential enthalpy of adsorption curves are typically elevated
220
throughout the pore filling process. The examples given later in this chapter all give rise to primary micropore filling process [10]. The secondary micropore filling process gives rise to a slightly weaker signal. 3. VARIOUS RESULTS OBTAINED WITH MICROPOROUS ADSORBENTS 3.1 Carbons Carbons are one of the most widely used industrial adsorbents. They can be prepared with surprising high surface areas and in certain cases, with a relatively narrow pore size distribution. Their hydrophobic properties make them quite interesting for the separation of organics from water. However, their applications are far wider. The adsorption of simple gases onto microporous active carbons generally lead to calorimetric curves containing three different regions during the filling of the micropores. An example is given in Figure 6 for the adsorption of nitrogen and argon onto an activated carbon at 77.4 K. The three regions are clearly shown : the first region, AB, decreases before a second, more horizontal region, BC. The third region, CD, again shows a marked decrease towards the enthalpy of liquefaction of the gas under consideration.
~ 0
o
10
E E
a
t-
6
E
--j
15
r
13
9
IA,~pH~I _
0
005
0.1
p / pO
0.15
02
0
_ IAvapHN,I,
0.'2
04
,
- -
016
0.'8
i
Relative Coverage (0)
Figure 6 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen and argon adsorbed onto an activated carbon [11].
A number of authors have noted and discussed such phenomena with varying interpretations [1, 12]. It would seem that the following conclusions are generally given : 9 Region AB is characteristic of interactions between the adsorbate and an energetically heterogeneous adsorbent (Figure 4). If one considers that the 2-dimensional graphite surface is energetically homogeneous, as explanation of the observed heterogeneity has to be found. Such heterogeneity can arise from defect, impurities as well as from a large distribution in micropore size. Although the first two solutions can be eliminated in some cases, the nature of the preparation and activation of such materials make a certain pore size distribution inevitable. One can therefore assume the filling of the smallest micropores (or ultramicropores) in this initial region AB. 9Region BC however, corresponds to a more homogeneous phenomenon than the latter. It is also noteworthy to remark that this region corresponds to an enthalpy of adsorption not far
221 from that for the adsorption on a perfect 2-dimensional surface (~ 14 kJ'moll). Furthermore, simulation studies [ 13] have shown that for the adsorption of nitrogen in larger micropores (or supermicropores), above 0.7 nm in diameter, a two step process may occur. The first step would seem to correspond to the coverage of the pore walls whereas the second to the filling of the void space. It would thus seem possible that the region BC corresponds to the coverage of the pore walls. The fact that this step is not completely horizontal in comparison to the adsorption on a 2-dimensional graphite surface may be due to curvature effects within the micropores. 9 Taking into account the above-mentioned hypothesis, it would seem that the region CD corresponds to the completion of the filling of the larger micropores. The adsorption of simple gases onto carbon nanotubes leads to slightly different results. An example here is given in Figure 7 [14]. Here, two main regions can be distinguished. It is well known that such nanotubes are closed at each end so blocking any inherent microporosity. Moreover, these nanotubes arrange themselves into bundles with a porosity of around 0.3 nm between the fibres. This latter porosity should thus be inaccessible. 2119
S... o E --, v'
A
B
08
17
06
15
r-
13
<] '
11
%. 0.4 t:).
c
D 02
9 7
o o
1
2
3
4
5
n a / m m o l . g "~
Figure 7 : Enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for methane on carbon nanotubes [14]. The first step (AB, Figure 7) may be explained by the filling of a small percentage of unblocked nanotubes. According to the preparation mode, the quantity of unblocked pores can be in the region of 20%. The second region, BC, would thus seem to be the formation of a monolayer on the external surface of these nanotubes.
3.2 Clays Clay materials form a vast family of inexpensive and readily available adsorbents. They can be used for their intra-sec properties as well as binders for other active materials such as zeolites. Due to the sheet-like nature of the majority of clays, no microporous properties are observed. Nevertheless, it is worth dwelling on the example of the adsorption of nitrogen and argon on kaolinite (Figure 8). This example shows a possibility, via microcalorimetry, to estimate the ratio of different mineral facets.
222 Kaolinite has a 1:1 sheet structure with a layer repeat distance of 0.72 nm. This is approximately the distance of the sheets themselves which means hat there is insufficient space to accommodate intercalated molecules such as water. The isotherms obtained for such materials are of Type-II which are typical for non-porous or macroporous materials. 25-
o E
--j "" .,c:
Ar 15
IAv,~H,,I 5
0
0~2
IAvapHN, I 9-
o', o~8 o18 Relative Coverage (0)
;
1.2
Figure 8 9Enthalpies of adsorption with respect to relative coverage at 77. 4 K for nitrogen and argon on kaolinite. (after [15]).
The differential enthalpy curve for argon and nitrogen (Figure 8) [15] shows two main regions. The first, AB, corresponds to the adsorption on defect sites and the adsorption on lateral facets of the materials. These high energy domains provoke an enhanced interaction with the nitrogen quadrupole. The second region, CD, corresponds to the adsorption on more energetically homogeneous basal planes. Such calorimetric measurements are thus a simple means to estimate the proportion of lateral and basal planes of such materials as well as the effect of grinding. It is possible to create microporosity in these layered clays materials via the replacement of exchangeable ions with more bulky ions. The more bulky ions can then be stabilised by an appropriate thermal treatment. However, some clays do have intra-sec micropores. The palygorskites are fibrous clay minerals. Attapulgite and sepiolite are two members of this family which both contain structural micropores. Their structures comprise of talc-like layers arranged quincuncially, forming microporous channels of rectangular cross-section parallel to the longitudinal axis of the crystals [15]. Whilst attapulgite has a pore section of 0.37 x 0.64 nm 2, the section of sepiolite is of 0.67 x 1.34 nm 2. The pores contain Mg(OH2)2 groups situated in the structural micropore walls. The differential enthalpy curves obtained for the adsorption of nitrogen on sepiolite and attapulgite at 77.4 K are shown in Figure 9 [17, 18]. Two separate domains can be observed for each of these curves. The first, domain, AB (Figure 9), is quasi-horizontal which is characteristic of adsorption in highly homogeneous regions. This would seem to correspond to the adsorption within the intrafibrous micropores containing the Mg(OH2)2 groups.
223
ca)
- (4)
--5 a~
15
t-
<,
IAvapHN21 o
o12
oi~
oi~
o~
relative coverage (0)
Figure 9 "Enthalpies of adsorption with respect to relative coverage at 77. 4 K for nitrogen on attapulgite (a) and sepiolite (b). The second domain in corresponds to the end of any micropore filling in the adsorption isotherms. The differential enthalpy curves in this region, CD (Figure 9), correspond to a decrease towards the enthalpy of liquefaction. This is characteristic of more energetically heterogeneous regions. It would seem that such regions are found between the fibres. Thus this would seem to correspond to adsorption in these interfibrous micropores. 3.3 A m o r p h o u s
Silica's
There are three main classes of amorphous silica's 9pyrogenic silica' s, precipitated silica's and silica gels. Pyrogrenic silica's and precipitated silica's are essentially not microporous. An exception is made for those silica's prepared by the St6ber process. These silica's would seem to be ultramicroporous with pores too small to allow nitrogen molecules to penetrate the porosity. However, the pores are large enough to allow the adsorption of water within the porosity at ambient temperatures. Silica gels can be prepared to contain micropores. A large number of physisorption studies have been carried out on silica gels. A certain number of these are described in Ref. [1]. Although initial synthesis of silica gels resulted in relatively ill-defined samples, it is currently possible to control both the synthesis and drying to form microporous Aerogels and Xerogels.
224 N2
Ar
10,
o E E
%
,.
. ,
'-N2
?
a.
6,
<-
4,
. . . . .
[AvapHArl
o;
o os
0"4 p /
pO
,
,,
9
o is
,|,
o2
5
o
,
03
0"4
,
o'6
IAvapHN=[ 0"8
Relative Coverage (0)
Figure 10 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen and argon adsorbed onto a microporous amorphous silica gel (Davison 950) [11]. An example of the adsorption behaviour on microporous silica gels is given in Figure 10. This figure shows the isotherms and differential enthalpy curves for the adsorption argon and nitrogen on a microporous silica gel (Davison 950). Both the differential enthalpy curves obtained with argon and nitrogen decrease continually with relative coverage. This is characteristic of large electrical homogeneity. This is probably due to both the surface chemistry and pore size distribution. Often the comparison between the results obtained with argon and nitrogen can give an idea of the relative importance of the inhomogeneity due to the pore size distribution and surface chemistry. Indeed, argon being a spherical and non-polar molecule interacts only weakly with surface chemical species such as hydroxyls. The behaviour thus observed is essentially due to the textural properties (pore geometry, pore size distribution ...). Nitrogen however, has a permanent quadrupole which is able to interact with any specific surface groups. The behaviour thus observed corresponds to any specific interactions with the surface as well as any interaction due to the textural nature of the sample. The difference in differential enthalpies of argon and nitrogen can be taken as an indication of the extent of the interactions due to the surface chemistry of the adsorbent under investigation. This for silica' s and other adsorbents. 3.4 Zeolites
From the applications point of view, particularly in membrane science, zeolites and related materials (aluminophosphates, gallophosphates ...) are interesting materials. ~1he synthesis of such materials can be adjusted to give a wide range of crystal structures and an almost infinite variety of chemical compositions giving the possibility to tailor-make samples for specific applications. From a fundamental point of view, the regular pore systems can be indexed by X-ray diffraction and the structure can be elucidated using Riedvield refinement-type methods for example. The zeolite family of materials are thus ideal for the understanding of adsorption phenomena. It is the knowledge gained by such studies, using thermodynamic methods (manometry, calorimetry ...) complemented by structural methods (neutron diffraction, X-ray
225
scattering ...) which permit, by analogy, the interpretation of adsorption phenomena in more disordered systems. Simulation studies are essential to complete the fundamental understanding. Three of the most widely used zeolites today are silicalite, Linde A and faujasite. Probably the most widely studied aluminophosphate is A1PO4-5. All four of these structures give rise to unusual adsorption phenomena during micropore filling. Several examples are highlighted in the following section. 3.4.1. Silicalite Silicalite is the pure silica end analogue of ZSM-5 (structure type MFI [19]). The pore network consists of straight elliptical pores of 0.51 x 0.57 nm 2 in section which intersect (0.8 nm in diameter) with sinusoidal, quasi-circular pores of 0.54 x 0.56 nm 2 in section. As the framework is purely silicic, there are no compensation cations. Figure 11, Figure 12 and Figure 13 highlight the three types of adsorption behaviour that can be observed with silicalite at 77 K for various adsorptives. The adsorption of methane (Figure 11) gives rise to a type I isotherm and a differential enthalpy of adsorption curve which is strictly horizontal during micropore filling. The adsorption of argon (Figure 12) and krypton both give rise to isotherms with a second step (or sub-step), noted [~ in Figure 12. This step in the isotherm corresponds to a distinct variation in the differential enthalpy curve. Finally, for gases such as nitrogen (Figure 13) and carbon monoxide two steps (ct and 13) in the isotherm can be observed. These steps also correspond to distinct variations in the differential enthalpy curve.
r
0,025
..-b, 0,02 16 0
E
0,015
14
12 10
6,, 0
%
0,01
IAv.~HcH,,I
0,005
i
__/ 1
na / mmol.g 1
Figure 11 " Enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for methane on silicalite-I [20].
The behaviour shown during the adsorption methane on silicalite at 77.4 K (Figure 11) can be considered almost model. The quasi-horizontal calorimetric signal, corresponding to the entire micropore filling region would seem to be purely the result of adsorbent - adsorbate interactions. One would expect a certain contribution due to a d s o r b e n t - adsorbent interactions, however this would seem to be minimal.
226
0,002 9
17
0,2
17 ,1,
15
o
..~
T._ 0
13
E
%.
13 0,12
.-j
o
r
t,--
~,
0,16
E
0,0012 11
,i,l
15
0,0016 9
,0,08
0,0008
~,
9
9 ,0,04
0,0004
7
5 0
1
2
3
4
5
6
n" / mmol.g -1
Figure 12 : Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for argon on Silicalite [20].
f 0
1
: .
2
3
4
.... ,5
6
0
na / mol.uc 1
Figure 13 : Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for nitrogen on Silicalite [21].
The adsorption of argon on silicalite at 77 K (Figure 12) shows similar behaviour to that of methane during the initial micropore filling process. This would seem to indicate the interaction of the adsorbate with an energetically homogeneous surface. However, the sudden substep at around p/p0 = 0.0002 corresponds to a distinct change in the differential enthalpy curve. Note that the substep in the isotherm was searched for after the change in the calorimetric curve was first observed. This substep, 13, was then characterised by neutron diffraction [20] giving rise to an explanation of a phase change in the adsorbed phase from a fluid state to a more dense "solid-like" state. The picture is certainly more complex with a probable transition of the silicalite structure itself. The adsorption of nitrogen on silicalite at 77 K (Figure 13) gives rise to an isotherm with two substeps ot and 13. It is interesting to note however, that the initial pore filling results in a differential curve which is not completely horizontal. An initial decrease would seem to indicate an enhanced interaction, maybe with defect site. This curve then increases again which would seem to be characteristic of increasing adsorbate- adsorbate interactions. The substeps in the isotherm correspond to marked differences in the differential enthalpy curves. Although this second substep 13, was observed in the isotherm prior to any microcalorimetic measurements [22, 23], the first substep a, was initially observed in the calorimetric curve [21 ]. Again, a complementary study by neutron diffraction was carded out on this system. This study [21 ] concluded that the first substep a, is due to an ordering of the adsorbate from a fluid phase to a network fluid. The second substep 13, would seem to correspond to an adsorbate phase transition similar to that observed for argon (Figure 12), that is to say from a network fluid to a "solid-like" adsorbate phase. These particularities in the behaviour of the adsorbate phase are influenced by the quality of the substrate. The introduction of compensation cations with the introduction of aluminium into the framework (ZSM-5) influences the marked nature of these variations in behaviour of the adsorpbate. Indeed these variations become less marked. This is especially the case for the substep ct which disappears from the isotherm as soon as the quality of the pore network
227 degrades due to the presence of compensation cations, preadsorbed species or even after grinding. These examples however, show the interest of such microcalorimetric measurements with the high resolution, continuous procedure of adsorptive introduction. Such subtle adsorption phenomena allow, not only the quality of crystals to be verified, but also an increased understanding of the influence of the substrate on the adsorption of simple probe molecules. 3.4.2. 5,4 and 13X The study of relatively simple solid / gas systems such as those in sections 3.4.1 and 3.4.3, allow a better understanding of more complex systems such as industrially prepared zeolites with cationic sites. The two most widely used zeolites are 5A and 13X. The 5A zeolites, with LTA structure [19] consist of regularly spaced spherical cages of 1.14 nm in diameter. These cages are linked to each other by six circular windows of around 0.42 nm in diameter. The negatively charged silico-aluminate framework requires compensation cations. In the case of zeolite 5A, these exchangeable cations are generally a mixture of calcium and sodium. The 13X zeolite, or faujasite of FAU structure [19] has very similar primary building blocks to the 5A zeolites. For 13X however, the spherical cages are of 1.4 nm in diameter, which are linked to each other by four circular windows of around 0.74 nm in diameter. The exchangeable cations are generally sodium (NaX). 25-
5A 20 ,1_ o E ,-j
13 X
15
10
IAvapHN, I 5
o
;
i
~
8
n a / m m o l . g -~
Figure 14 9Differential enthalpies of adsorption and relative pressure as a function of quantity adsorbed at 77. 4 K for nitrogen on 5A and 13X [24].
A prior study of the adsorption of nitrogen at 77 K on 5A and 13X zeolites using quasiequilibrium, isothermal, adsorption microcalorimetry experiments at 77K [24] detected a step in the differential enthalpies of adsorption, towards the end of micropore filling (Figure 14). At the time, this was interpreted as a consequence of specific adsorbate - adsorbate interactions. Recently however, in the light of other microcalorimetry studies this change in signal has been interpreted as a possible phase change within the cavities [25]. This latter study detected the same phenomenon for a number of other probe molecules including, argon and methane as well as for carbon monoxide. An independent study showed that this latter
228 step corresponds to the delocalised adsorption of mobile molecules as the main cages (or orcages) become almost full [26]. 3.4.3. AIPOr Recently, much research has been made into the synthesis of zeolite-like materials with framework species other than silica and alumina. The first family of materials that resulted from this research were the aluminophosphate molecular sieves. Thus A1PO4-5 [27] with an AFI-type structure [19] has a unidirectional pore system consisting of parallel circular channels of 0.73 nm in diameter. AIPO4-5 has a framework which, like silicalite-I, theoretically is globally electrically neutral, although the pore openings is slightly larger than those of the MFI-type zeolites. These characteristics make AIPO4-5 a fine structure for fundamental adsorption studies. For ALP04-5 the adsorption isotherms of argon and nitrogen traced up to a relative pressure of 0.2 are indistinguishable (Figure 15). This is not the case for methane which adsorbs significantly less, suggesting a different pore filling mechanism. The differential enthaply curves for argon and nitrogen vary. For argon, a slight increase in the differential enthalpy curve occurs due to the increase in adsorbate- adsorbate interactions during the filling of the micropores. For the adsorption of nitrogen, the differential enthalpy curve initially decreases as a result of decreasing adsorbate - adsorbent interactions. The curve then increases due to the adsorbate- adsorbate interactions that increase as the micropore filling process procedes. 3
~
N2
CH4
2.5
14
Ar, N 2
2 .=,: O [::15
E
o E
13
-~9
12
e-
11
1
10 0.5
0
0 05
0.1
p/p0
0.15
0
0.2
0.4
0.6
0 8
Relative Coverage (0)
Figure 15 9Isotherms (left) and corresponding differential enthalpies (right) at 77. 4 K for nitrogen, argon and methane adsorbed on ALP04-5 [28]. For the adsorption of methane however, an exothermic peak (noted ~ in Figure 15) is observed in the differential enthalpy curve for methane, which would seem to correspond to an energetic term ~ RT. This would seem to indicate both a variation of mobility and a variation of the adsorbed methane phase. A complementary neutron diffraction study [29] indicates that an unusual behaviour of the methane adsorbed phase occurs. It would seem that the methane undergoes a transition between two solid-like phases. The first "solid-like" phase
229 corresponds to the adsorption of 4 molecules per unit cell whilst the second phase corresponds to a jump in the quantity adsorbed to 6 molecules per unit cell. This would seem to be a result of a favourable dimensional compatibility between the methane molecule and A1PO4-5 micropore, permitting, from a volumic point of view, the apparition of two relatively dense phases. This hypothesis is supported by simulation studies [30]. 4. CONCLUDING REMARKS The aim of this chapter is to highlight the interest of adsorption microcalorimetry, not only to characterise various adsorption phenomena on well defined adsorbents but also for the characterisation of less well defined microporous adsorbents. Indeed, it is the information gained from fundamental studies on these energetically homogeneous adsorbents that allow, by analogy, the pinpoint of different phenomena that arise in more heterogeneous adsorbents. Microcalorimetric measurements allow the easy detection of adsorption phenomena that are difficult to observe in the adsorption isotherm alone. Direct calorimetric measurements are quite complementary to calculations via the isosteric method. However, direct measurements are far more sensitive for the adsorption of molecules within micropores. Such calorimetric measurements can be completed by structural studies (e.g. neutron diffraction) and finally by computer simulation. 5. LIST OF SYMBOLS C BET constant
dp pore diameter frate of gas flow f ' rate of adsorption n amount of substance n a amount adsorbed nammonolayer capacity p pressure p0 saturation pressure p/pO relative pressure
Qrevheat reversibly exchanged with the surroundings R gas constant T absolute temperature Vvolume (Vc volume of sample cell "accessible" to the calorimeter) AvapHenthalpy of vapourisation Aads/~ differential enthalpy of adsorption r heat flow 0relative coverage (i.e. na/nam)
6. REFERENCES
1. 2. 3. 4. 5. 6. 7.
F. Rouquerol, J. Rouquerol and K. Sing, "Adsorption by Powders and Porous Solids", Acad. Press, London, 1999. J. Rouquerol, In "Thermochimie", Colloques Intemationaux du CNRS, No.201, CNRS Ed., Paris 1972, p.537. Y. Grillet, J. Rouqu6rol and F. Rouqu~rol, J. Chim. Phys., 2 (1977) 179. K . S . W . Sing, D. H. Everett, R. A. W. Haul, L. Moscou, R. A. Pierotti, J. Rouquerol and T. Siemieniewska, Pure Appl. Chem., 57 (1985) 603. C. Letoquart, F. Rouquerol & J. Rouquerol, J. Chim. Phys. 70(3) (1973) 559. J. Rouquerol, S. Partyka and F. Roquerol, J. Chem. Soc. Faraday Trans. 1, 73 (1977) 306. A.V. Kiselev, Doklady Nauk USSR, 233 (1977) 1122.
230 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
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