Comparison plots: recent applications

MICROPOROUS MATERIALS ELSEVIER

Microporous Materials 6 (1996) 385 394

Comparison plots: recent applications 1 Jifi Rathousk) .,,, GOnter Schulz-Ekloff b, Arno~t Zukal a " 3". Heyrovsk~ Institute of Physical Chemistry of the Academy of Sciences of the Czech Republic, Dolejgkova 3, 18223 Prague 8, Czech Republic b Institute of Applied and Physical Chemistry, University of Bremen, 28334 Bremen, Germany Received 29 January 1996; accepted 6 March 1996

Abstract Comparison plots are an effective method for the determination of some structural properties of adsorbents, supports and catalysts. With respect to their very different and often complicated structures, the choice of the reference adsorbent (isotherm) is of fundamental importance. If a deeper insight into the materials under study is aimed at, the analysis of adsorption data by this method should be supplemented by additional experimental data or model calculations. All examples presented pertain to modern materials with interesting potential applications. They represent typical examples for microporous/mesoporous or purely mesoporous solids. Keywords: Physical adsorption; Comparison plots; Reference adsorbents; Structural characteristics

1. Introduction

2. General principles

Gas adsorption measurements are widely used for the characterization of porous solids. In view of the complexity of physical adsorption, it has been found useful to apply a semi-empirical procedure for isotherm analysis [1]. This approach makes use of adsorption data obtained with suitable reference materials and attempts to interpret the differences in isotherm shapes in terms of variations of the structures between the reference adsorbent and the sample under test.

Let Eqs. 1 and 2 express adsorption isotherms on the solid under investigation and on the reference adsorbent, respectively, a = F(p/po)

( 1)

aref= Fref(p/po)

(2)

where a and aref denote the amount adsorbed per unit mass of adsorbent and P/Po the relative pressure. By eliminating the relative pressures from Eqs. 1 and 2 we obtain a = G(aref)

* Corresponding author. 1Dedicated to Dr. Hellmut G. Karge on the occasion of his 65th birthday. 0927-6513/96/$15.00© 1996ElsevierScienceB.V. All rights reserved PH S0927-6513 (96)00033-8

(3)

The last equation shows the principle of a comparison plot: the amount adsorbed on the solid under investigation is plotted against that adsorbed

386

J. Rathouskj~ et al./Microporous Materials 6 (1996) 385-394

on a reference adsorbent at the same equilibrium pressure. Then, this plot enables one to compare adsorption isotherms of the same adsorptive measured on two different adsorbents at the same temperature and does not impose any limitations on the nature of the reference adsorbent. Comparison plots were originally used for the comparison of adsorption isotherms on two nonporous solids, viz. graphitized and non-graphitized carbon black [2]. For most applications it is advantageous to use a non-porous solid as a reference adsorbent, on whose whole surface multimolecular layers are freely formed. If the adsorbent under investigation contains micropores and/or mesopores, then the comparison plot clearly shows their influence on the shape of the adsorption isotherm and enables an assessment of parameters of its porous structure (see an overview in Ref. [3]). In some applications, a microporous material may be used with advantage as a reference adsorbent [4, 5], or even a model reference isotherm for a twocomponent mixture of different materials [5]. For a given gas, such as nitrogen, adsorbed on a series of non-porous substances differing in their surface areas but not too much with respect to other properties, one might expect the variation in the shape of their adsorption isotherms to be relatively weak. The different isotherms should thus be superimposable by mere adjustment of the scale of the ordinates. Therefore, it should be possible to bring the isotherms on various reference adsorbents into coincidence by expressing the adsorption arcf in Eq. 2 in normalized units. As these units, the statistical thickness t or the normalized adsorption cts are mostly used: (i) The statistical thickness of the adsorbed film t = traref/am,ref, where ~r is the thickness of a single molecular layer and a .... f the monolayer capacity (t-plot) [6]; (ii) The normalized adsorption as =aref/ao.4,ref, where ao.4,ref is the amount adsorbed at P/Po = 0.4 (~s-plot) [7]. With nitrogen, this relative pressure corresponds to the lower closure point of the hysteresis loop, i.e. the micropore filling, multilayer coverage or capillary condensation without hysteresis occur at P/Po < 0.4, whereas the capillary condensation with hysteresis takes place at P/Po > 0.4.

The application of the universal nitrogen isotherm is only the first approximation in the analysis of adsorption isotherms under test. From a consideration of the nature of the forces bringing about physical adsorption, it is evident that the detailed course of the isotherm on a particular solid must depend on the nature of both the gas and the solid. For this reason it was proposed to characterize the intensity of interaction between the gas and surface of the solid by the constant CBET of the BET equation [8]. Consequently, a set of experimental reference isotherms, corresponding to definite ranges of the CBEr constant value between 20 and 3000 was chosen. The much debated question about differences between various plots described above has been addressed in the literature, an overview being given in Ref. [3]. According to this reference the knowledge of the numerical thickness is irrelevant for the purpose of testing for conformity to the standard isotherm. Since the object is merely to compare the shape of the isotherm under test with that of the reference isotherm, it is not necessary to involve the monolayer capacity itself. It is sufficient to introduce as normalizing factor the value of adsorption ao.4.

3. Application of comparison plots There are many applications of t- and ~s-plots published in the literature. In this overview only one example for an ~s-plot will be shown. The other examples presented here are non-standard, based on own experimental data, and the general method of comparison plots has been used. Important contributions of other authors obtained on analogous materials are also cited. The adsorption isotherms were measured with an Accusorb 2100 E instrument (Micromeritics, USA). Nitrogen (at 77 K) is the recommended adsorptive for determining the surface area and mesopore size distribution [1]. For this reason, this adsorptive is mostly used here. However, in some cases the investigation of the adsorption of organic vapours at, or near ambient temperature can be convenient. This is especially advantageous in case of zeolites, for which the isotherms of these

J. Rathousk~ et al./Microporous Materials 6 (1996) 385-394

adsorptives, such as cyclopentane, are not so steep as those of nitrogen. It enables one to obtain adsorption isotherms in the low-pressure region with better accuracy. The results presented here have been chosen from a large body of experimental data to show materials of various structure types. As our efforts are aimed at a deeper insight into the materials studied, the analysis of adsorption data by the method of comparison plots is put into a broader context and supplemented by additional aspects. All samples presented belong to modern materials with interesting application possibilities. As examples for microporous/mesoporous solids an activated charcoal cloth, a zeolite with embedded metal dispersion and aluminophosphates with embedded dye molecules have been chosen. A precursor of a nickel catalyst represents a polydispersed mesoporous material. Finally, MCM-41 materials are the first truly mesoporous molecular sieves. 3.1. Structural characteristics of activated charcoal cloth In case of an activated charcoal cloth the as-method can be used with advantage (e.g., [9,10]). Fig. 1 shows the nitrogen isotherm for a typical example of this adsorbent (manufactured by Charcoal Cloth, UK). This isotherm is characterized by a small hysteresis loop and a small

387

volume of mesopores with diameters larger than ca. 4 nm (0.040 cm3/g). Fig. 2 shows the corresponding cq-plot. Standard data of nitrogen adsorption for the ~s-plot have been taken from Ref. [11]. These data were measured down to the region of small ~s (corresponding to P/Po > 0.00005 and 0q > 0.06), which is especially important in case of microporous carbons, such as activated carbon fibers. The micropore volume is filled by nitrogen molecules at extremely low equilibrium pressures (P/Po < 0.00005). As the corresponding reference data are not available, the extra-low pressure part of the ~s-plot could not be drawn. The linear region in the ~,-plot corresponds to an adsorption process similar to the multilayer coverage of the fiat surface. This process occurs on the surface of all pores excluding micropores, being restricted by their size at ~ > 0 . 8 . For the linear region of the ~-plot, Eq. 4a holds: a = A + B ~ = 4.858 + 9.422~

(4a)

The intercept of this straight line determines the micropore volume of Avm=4.858vm=O.169 cm3/g (Vm is the molar volume of liquid nitrogen). The slope B, is proportional to the surface area of all pores with the exception of micropores which have been filled before ~, attained 0.06. If we denote the surface areas of the solid under test and the reference adsorbent as S and Sref, respectively, we obtain [3]: S = B=Sref/ao.4.ref

(5a)

1515

1312

~

11 ¸

~

9

"~ "6 E E

t~

9

6

0.2

0.4

0.6

0.8

p/po

0

0

012

014

016

018

i

alpha s Fig. 1. Adsorption isotherm of nitrogen on charcoal cloth at 77.2 K.

Fig. 2. as-plotfor charcoal cloth.

1.2

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J. Rathousk~ et al./Microporous Materials 6 (1996) 385-394

With our sample the surface area corresponding to the slope B~ = 9.422 mmol/g is 462 m2/g. If instead of a s the adsorption arcf on the reference adsorbent is used, i.e. a comparison plot is used instead of an ~s-plot, a dependence is obtained which is quite similar to that in Fig. 2. For its linear region, Eq. 4b holds a= A+

Ba,refaref

(4b)

Then the surface area of the solid under test equals S = B a,rofSref

(5b)

The es-plot is especially suitable for carbonaceous adsorbents, where the application of the universal reference isotherm is - unlike other materials, such as oxidic ones with all sorts of chemical composition - legitimate. In the case of carbonaceous materials relatively well defined graphitized carbons have been used as reference adsorbents. The isotherm under test is thus compared with that on the basal plane of graphite. Consequently, the adsorption on the reference adsorbent depends only on its surface area, which is eliminated by the normalization with the variable e~

3.2. Effect of an embedded platinum dispersion on the structure of the faujasite host Zeolite-hosted metal particles, which exceed by far the supercage size, have been found to be accommodated exclusively within the faujasite matrix [12], which has led to suggestions of zeolite lattice destruction during the particle growth process [13]. Although the existence of the abovementioned changes was confirmed by X-ray diffraction and transition electron microscopy [ 14], the extent of the destruction of the zeolite lattice can be determined with sufficient accuracy only by physical adsorption. In this overview the results obtained on faujasites X with platinum dispersions differing in the metal content (1.9, 4.3 and 17.0 platinum atoms per unit cell) and particle size (achieved by varying the decomposition/reduction procedures of the tetraammine platinum complex [15]), are presented. The samples PtX/F and PtX/C contain Pt particles of mean diameters of 1 to 2 nm and 4 to 5 nm, respectively (Table I).

Table 1 Volumes Va<4 and the spacing between platinum particles in faujasite crystals

Sample

V d< 4

n

l

l/d

0.435 a 0.396 0.407 0.262 0.409 0.432 0.274

_ 61.6 27.2 6.9 1663.2 734.9 185.9

_ 9.9 7.5 4.8 29.6 22.6 14.3

_ 6.6 5.0 3.2 6.6 5.0 3.2

(cma/cm3)

NaX PtX/F/1.9 PtX/F/4.3 PtX/F/17.0 PtX/C/1.9 PtX/C/4.3 PtX/C/17.0

(nm)

• Obtainedfrom the adsorptioncorrespondingto the pressure of the lower closure point of the hysteresisloop. Fig. 3 shows adsorption isotherms of cyclopentane on the parent NaX and samples PtX/F/4.3 and PtX/C/4.3. For the sake of clarity points corresponding to the adsorption at low equilibrium pressures are not shown in this figure but separately in Fig. 4. Because of the Pt content, the molecular weights of PtX/F/4.3 and PtX/C/4.3 are higher than that of NaX. To make the adsorption isotherms on all samples comparable, the amount adsorbed on all these materials has been expressed in millimoles of cyclopentane adsorbed in 1 cm 3 of zeolite. The isotherms for Pt loaded samples are characterized by a hysteresis loop, which indicates the presence of mesopores with diameters larger than ca. 4 nm [3]. With all samples their volume was

5.0 i

4.5

2

o

-~ a

4.0

3.5

3.0 0

0.2

0.4

0.6

0.8

p/po Fig. 3. Adsorptionisothermsof cyclopentaneat 293.2 K on ( 1) NaX, (2) PtX/F/4.3, (3) PtX/C/4.3.

J. Rathousk$, et al./Microporous Materials 6 (1996) 385-394

389

to form the centre of a cube with sides equal to 1

3

l = 2.5n 1/3 (nm)

,9o "5 E t~

0.001

0.002

0.003

0.004

0.005

p/po Fig. 4. Adsorptionisothermsof cyclopentaneat 293.2 K on ( 1) NaX, (2) PtX/F/4.3, (3) PtX/C/4.3 at low equilibrium pressures.

only small and does not surpass 0.05 cm3/g. Table 1 lists the volumes Va<4 of pores whose diameters are smaller than 4 nm. This volume has been calculated from the adsorption at the lower pressure junction point of the hysteresis loop [3]. The changes found in the volume Va<4 of platinum loaded samples and the formation of mesopores with diameters larger than 4 nm clearly show that the growth of platinum particles has caused lattice destruction in the particle surroundings. Unlike the size of platinum particles, the Pt content decisively influences Va<4 (Table 1). This phenomenon can be explained as follows: Let us assume that platinum particles in both fine and coarse dispersions have a spherical shape with a mean diameter of d = 1.5 nm or 4.5 nm, respectively. Under this assumption, the mean number n of zeolite unit cells hosting one metal particle can be calculated. As the volume proper of platinum particles is negligible in comparison with that of the zeolite crystal, Eq. 6 holds n = nNdvt d3/6m

(6)

where N is the number of unit cells per 1 g of zeolite, dvt the density of platinum and m the weight of platinum contained in 1 g of zeolite. If platinum particles are distributed uniformly in the zeolite crystal, each particle could be considered

(7)

l giving the mean spacing between particles. The factor 2.5 (nm) is the length of the side of the cubic unit cell of the faujasite lattice. From Eqs. 6 and 7 it follows that the ratio l/d depends only on the platinum content in the zeolite. This ratio, giving the relative distance between the centres of neighbouring platinum particles, most probably decisively influences the degree of destruction of the faujasite lattice. The values of n, / and l/d are presented in Table 1. The metal content in loaded samples has been chosen in order to obtain a series of samples with approximately constant changes in the ratio l/d. On the other hand, the volume Vd<4 of the same series of samples is practically constant and similar to the parent NaX at low Pt contents, which corresponds to only small changes in the zeolite lattice. However, this volume decreases abruptly at the largest Pt content of 17 atoms per unit cell, which indicates a more substantial destruction of the zeolite lattice probably due to interconnections of destroyed surroundings of the platinum particles. The fundamental question whether the thus damaged zeolite lattice contains intact (identical with the parent NaX) and destroyed regions, or its properties have been changed within the whole crystal can be answered using the method of comparison plots. To this end reversible parts of isotherms have been transformed to comparison plots with zeolite NaX used as the reference adsorbent (Fig. 5). The curves of both samples are similar. On backextrapolation, the linear parts pass through the origin with a slope equal to one. They end at the adsorption corresponding to the filling of ca. 50% of the volume V a<4. Then the adsorption increases with increasing equilibrium pressure more slowly than on NaX. On increasing the equilibrium pressure even further, the adsorption approaches again that on NaX. If a faujasite crystal could be divided into intact regions with adsorption properties identical with those of the parent NaX and destroyed ones, the slope of the linear part should be smaller than one

390

J. Rathouskp et al./Microporous Materials 6 (1996) 385-394

2

1.6

3E

"~

o= 2

E

E

E:

/

1,2

0.8

0.4"~

O 0

a ref [mmol/cm3]

Fig. 5. Comparison plots for (1) PtX/F/4.3, (2) PtX/C/4.3.

corresponding to the proportion of intact regions. However, this is not the case. The presence of Pt embedded in the faujasite lattice causes a change of adsorption properties of the whole crystal, which may be brought about by, e.g. a lower content of Na ÷ cations, or by chemical changes of the lattice during the autoreduction of Pt(NH3) 2+ .

3.3. Encapsulation of methylene blue into aluminophosphate molecular sieves Zeolites and analogous structures can organize organic molecules in their cavities or channels (e.g. [16]). In this overview the results concerning the encapsulation of methylene blue (MB) into some aluminophosphate molecular sieves are presented. Aluminophosphate-hosted MB samples were obtained by addition of the dye to the reaction mixture for the hydrothermal synthesis of A1PO4-5 and AIPO4-11 [17]. Adsorption isotherms for cyclopentane on aluminophosphate hosts, in which incorporated MB had been burnt off, were measured and compared with those on dye-free synthesised samples. This procedure enabled to assess the effect of added MB on the micropore volume and - combined with SEM and XRD on crystal growth or contamination of aluminophosphate molecular sieves. Fig. 6 presents cyclopentane adsorption isotherms on both dye-free and loaded samples of AIPO4-11. The steep increase in the amount

.~r-

~

0.2

~3.~

0.4

2

0.6

0.8

1

p/po Fig. 6. Adsorption isotherms of cyclopentane at 293.2 K on ( 1) A1PO4-11, (2) AIPO4-11/MB.

adsorbed in the low pressure region is connected with the adsorption in the microporous channel system. The hysteresis loop corresponds to the capillary condensation of cyclopentane vapours in mesopores, formed among crystals or particles of this material, i.e. the shape of the hysteresis loop is determined by the crystal morphology. The shapes of adsorption isotherms on both dye-free and loaded samples were compared by the method of comparison plots using the dye-free materials as the reference adsorbents. In Fig. 7, the low pressure parts of the adsorption isotherms (up to p/p, =0.4) from Fig. 6 are transformed into a comparison plot. Since a linear dependence with 1.5

1.2

1

0.9

~

0.6 0.3 0

0

013

016

019

1.2

a ref [retool/g]

Fig. 7. Comparison (2) ALP04-11/MB.

plots

for

( 1)

A1PO4-5/MB,

J. Rathousk~ et al./Microporous Materials 6 (1996) 385-394

a slope equalling one is obtained, the loading of A1PO4-5 with MB does not influence the channel structure of this host. This conclusion is supported by a model calculation. MB molecules can be approximated by a rectangular parallelepiped with dimensions of 1.60x0.7×0.37nm [18]. As the circular channels of the AFI structural type have a crystallographic free diameter of 0.73 nm [19], the MB molecules can be accommodated inside the channels without any interference with the host matrix. The structure of AIPO4-11 is characterised by elliptical channels with dimensions of 0.39 x0.63 nm [19], i.e. the channel dimensions are slightly smaller than that of the MB molecule. As the comparison plot of A1PO: 11/MB is characterised by a linear dependence with the slope equalling 0.47 (Fig. 7), it can be supposed that the solid phase synthesized in the presence of MB contains only ca. 50% of A I P O 4 - 1 1 ; the structure of the other 50% of the material is unknown. The presence of a certain amount of amorphous material also follows from the comparison of X-ray diffractograms of the dye-free and loaded samples. Whether dye molecules are localised in the pores of A1PO:ll or in this amorphous material is unclear.

391

without any interactions arof= Fref(P/Po) = (x 1/ 100) fl (p/po) + (x2/100) fz(p/p0)

(8)

where x~, x2 are the respective percentage of both catalyst components, fl(P/Po),fz(P/Po) the amounts adsorbed on both individual components. Fig. 8 shows isotherms for the pure components (calcined gibbsite and product of the decomposition of N i 6 A l z ( O H ) 1 6 C O 3 "4H20 at 600 K) and the catalyst precursor. All these isotherms are of the IV type [3]. The comparison plot for the nickel catalyst precursor constructed from the adsorption branch (Fig. 9) is very close to a straight line with a slope equalling one which, according to Eq. 8, corresponds to the additive adsorption on both components. Small deviations from linearity are obvious consequences of errors of adsorption measurements because they correspond to a very steep part of the adsorption isotherm. When the comparison plot was constructed from the desorption branch it was practically identical with that from the adsorption one. The thermally treated components of the nickel catalyst precursor are made up of aggregates of non-porous particles. The interstices between these particles form the proper mesoporous (or macroporous, if any) system in aggregates. As follows

3.4. Preparation of a precursor of a nickel catalyst A nickel catalyst precursor was prepared by kneading a physical mixture of two components with water used as a binder [20]. The first component w a s N i 6 A 1 2 ( O H ) 1 6 C O 3 " 4 H 2 0 , the second one gibbsite calcined at 900 K for 10 h. The paste was dried, crushed and calcined at 600 K. Due to calcination the hydroxycarbonate decomposed to a mixture of the respective oxides. The precursor of the nickel catalyst contains 50 wt.-% of the decomposition product of N i 6 A I 2 ( O H ) 1 6 C O 3 ' 4 H 2 0 and 50 wt.-% of calcined gibbsite. With such a mixed material the method of comparison plots can be conveniently used in order to determine the degree of mutual interactions of both components. To this end the reference isotherm (see Eq. 2) has been constructed as a weighted sum of isotherms on pure components

E

0

0.2

0.4

0.6

0.8

p/po Fig. 8. Adsorption isotherms of cyclopentane at 293.2 K on ( 1) the product of the decomposition of Ni6AI2(OH)16CO3.4H20, (2) calcined gibbsite, (3) calcined nickel catalyst precursor. For the sake of clarity isotherms are offset.

392

J. Rathouskj: et al./Microporous Materials 6 (1996) 385-394

2.4'

• "5 E E

1.8" -

1.2-

0.6"

O 0

0.6

~

1.2

a ref

1.8

2.4

3

[retool/g]

Fig. 9. Comparison plots for the calcined nickel catalyst precursor.

from the comparison plot, these components retain in the precursor their individual adsorption properties. Therefore, an intimate contact of both components is not very probable. As the second component, the hydroxycarbonate of magnesium and aluminium Mg6A12(OH)I 6 CO3-4H20 was also used. (The calcination product of this compound is stabilized magnesia which is an excellent support in catalysis [21]). When the nickel catalyst precursor was prepared by mechanical mixing and calcination at 600 K of both hydroxycarbonates, the above-mentioned additive scheme did not hold. From this it follows that both components interact during kneading of the paste mixture of nickel-aluminium and magnesium-aluminium hydroxycarbonates, or during calcination of this mixture.

3.5. MCM-41 mesoporous molecular sieves In 1992, the synthesis of a new family of mesoporous molecular sieves using rod-like micelles of cationic surfactant molecules as templates was reported [22,23], sieves with hexagonally ordered channels being designated as MCM-41. On these molecular sieves capillary phenomena occurring in a system of monodispersed pore channels was firstly observed and analyzed. Shortly after the first studies of a qualitative character [24-29], a version of non-local density functional theory for

the quantitative modelling of nitrogen adsorption on MCM-41 materials was used [30]. In the following the method of comparison plots will be used to estimate the pore structure parameters of MCM-41 mesoporous molecular sieves from nitrogen isotherms. The synthesis of these aluminosilicate materials is described in Ref. [25]. The reference adsorbents were prepared by the thermal destruction of appropriate MCM-41 materials at 1273 K. When the adsorption on reference aluminosilicate adsorbents was related to the unit surface area, all the isotherms were practically identical. The BET surface area of the reference adsorbent used and the constant CBETare shown in Table 2. The BET equation was valid for P/Po from ca. 0.05 to 0.40, less precisely up to about 0.5-0.6. The shape of the adsorption isotherms on three selected samples MCM-41-1, -2 and -3 is typical for this class of materials (Fig. 10). Adsorption isotherms can be approximated by the BET equation from P/Po =ca. 0.05 (with all samples) to an upper limit which increased with the serial number of the sample from ca. 0.20 (MCM-41-1) to ca. 0.45 (MCM-41-3). The surface areas SBETand the CBET constants are summarized in Table 2. Fig. 11 shows the comparison plots obtained by the transformation of the adsorption branches of isotherms up to P/Po =0.8. The low-pressure part of all plots can be approximated by a straight line going through the origin. With MCM-41-1 a sharp knee and a plateau with a small slope follow. By contrast, both MCM-41-2 and -3 are characterized by a steep upward swing passing gradually into a plateau. With MCM-41-2 this steep increase, occurring in the reversible part of isotherm, is the consequence of the capillary condensation without hysteresis in mesopores [24]. With MCM-41-3, on the contrary, it occurs in the hysteresis region. The direct proportionality, which is expressed by Eq. 4b with A=0, indicates that MCM-41 materials do not contain micropores. In the first stages of adsorption the formation of adsorbed layers on MCM-41 is the same as that on a nonporous adsorbent. The slope Ba determines the surface area of the studied solid Stot (see Eq. 5b). The surface areas Stot are very close to the surface areas SB~T (Table 2).

393

J. Rathouskj~ et al./Microporous Materials 6 (1996) 385-394 Table 2 Structure parameters of MCM-41 molecular sieves

Sample

SaEX (m2/g)

CBET

Stot (m2/g)

Sexl (m2/g)

V MCM.41 (cm3/g)

dMCM.41 (nm)

MCM-41-1 MCM-41-2 MCM-41-3 Reference

817.5 1071.7 1015.2 25.5

78.3 76.0 61.3 45.8

876.4 1147.0 1029.4 .

111.9 65.8 (94.8)

0.326 0.743 (0.895) .

1.8 2.9 (3.9)

.

.

z~ (nm) 1.3 1.0 1.2

.

The values in parentheses were calculated using the methods based on the Kelvin equation.

4836

E

The plateau observed in the comparison plots MCM-41-1 and MCM-41-2 at around P/Po= 0.4 formed after the mesopores of MCM-41 structure had been totally filled. The linear part of the plateau corresponds to the formation of adsorbed layers on the surface of all larger pores. If this part is approximated by a straight line (Eq. 4b, Fig. 11) then A gives the volume VMcM-4X of mesopores of the MCM-41 structure proper and Ba the surface area Sext of the larger pores mentioned (Table2). With MCM-41-3 Eq. 4b cannot be applied because of different mechanisms of adsorption on the sample under test (capillary condensation) and on the reference adsorbent (multilayer coverage). By a detailed inspection of the comparison plots small but systematic deviations from the direct proportionality have been found to occur. Therefore, the surfaces of MCM-41 materials and the reference adsorbent are not totally identical with respect to the nature of the adsorbent-adsorbate interactions. This fact is apparent from the variation of the C constant of the BET equation (Table 2), with MCM-41 materials varying between 60 and 80, while with the reference adsorbent it decreases to 45. On the other hand, all these values belong to a single range of CaET as defined in Ref. [8]. For 40 < CBET< 100, a single reference adsorbent can be used. Therefore, the application of the reference adsorbent prepared by the thermal destruction of MCM-41 in this study is fully legitimate, and consequently the values of surface areas Stot and Sext, and the pore volume VMCM-4~ are correct. Based on these values and the lattice constant ao (from XRD), the pore size and pore wall of

60-

24.

0

.

.

.

.

o.e

,

0.4

.

.

0.6

.

.

0.8

p/po Fig. 10. Adsorption isotherm of nitrogen at 77.2 K on (1) MCM-41-1, (2) MCM--41-2, (3) MCM-41-3. For the sake of clarity isotherms are offset.

30-

24-

"6 12

6

0

o:2

o'.4

o'.6

0.8

a ref [mmol/g]

Fig. 11. Comparison plots for (1) MCM-41-1, (2) MCM-41-2, (3) MCM-41-3.

394

J. Rathousk) et al./Microporous Materials 6 (1996) 385-394

thickness were calculated using a geometrical model [31]. The honeycomb structure has been modelled using a system of hexagonally ordered hexagonal channels, which corresponds to a perfect MCM-41 structure. The size of hexagonal pores (Table 2) has been expressed using the diameter of a cylindrical pore of the same volume and length as the hexagonal one according to the formula dMcM-41 = 4.20 VMcM-41/(Stot - Sext)

(9)

The pore wall thickness d (Table 2) was calculated from adsorption and XRD data according to A = ao - 0.95dMcM-41

(10)

The values of the pore size and pore wall thickness calculated (Table 2) are obviously reasonable and typical for well developed MCM-41 materials.

4. Conclusions

Comparison plots are a simple but effective method for the determination of some structural properties of adsorbents, supports and catalysts. With respect to their very different and often complicated structures, the choice of the reference adsorbent (isotherm) is of fundamental importance. In order to attain a deeper insight into the material structure, the results obtained by this method should be supplemented by other experimental data or model calculations.

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