J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solidr 111 Studies in Surface Scicnce and Catalysis, Vol. 87 1994 Elsevicr Scicnce B.V.

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IN-CRY STAL OXYGEN POLARIZABILITY FOR POROUS AND NON-POROUS MATERIALS

R J-M Pellenq and D, Nicholson

Department of Chemisttyy, Imperial College of Science Technology and Medicine, LONDON S W 7 2A Y , UK

ABSTRACT

Anionic dipole polarizabilities in porous in zeolitic solids can be found from a knowledge of atomic relaxations associated with the redistribution of electron density around the cation target after the ejection of two electrons in the Auger process. A method is given based on the comparison between two compounds to eliminate unknown quantities by using a reference compound. The polarizability of the oxygen anion in a wide range of porous materials is calculated. An analysis of data for zeolites with high and low Si/AI ratios leads to the conclusion that local effects are the major factor in determining Auger parameters, and that conversely polarizabilities can be found for the different oxygen locations in porous zeolites. The results have significant consequences for the heterogeneity of porous zeolitic adsorbents.

INTRODUCTION

Although polarizability plays a key role in determining intermolecular potentials there are few accepted values for in-crystal species. A notable exception being the values found for ionic species using high quality quantum mechanical calculations [ I ] . This problem can be highlighted by considering the use of gas adsorption in the characterisation of porous zeolitic structures. The availability of reliable potential functions as input to simulations is of crucial importance in the interpretation of experimental data for physisorption as we have demonstrated elsewhere [2]. For example the potential function representing the interaction of a simple gas such as argon or krypton with an adsorbent is essentially a summation of attractive and repulsive parts in which the former are dominated by dispersion interactions. The interaction function, including the dispersion terms can, in principle be found from full scale quantum mechanical calculations (including correlation interaction), but in practice a map out of the full potential surface of an adsorbate in a zeolite cavity would require gigantic computing resources, and it is necessary to resort to methods based on a perturbation expansion and atom atom summation as the only feasible procedure. Many of the several contributions from the perturbation expansion to the dispersion interactions depend on a knowledge of the dipole-dipole polarizability of the interacting species.

In this paper we give a brief description of how Auger data can be used to obtain this quantity, and describe some results relating to aluminosilicate framework structures which have been determined in this way. A fuller account of the underlying method appears elsewhere [3], here we lay particular stress on the distinction between polarizabilities of oxygen anions at different sites within the porous structure.

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METHOD

The method depends on a simple electrostatic model developed by Moretti [4] in which the relaxation of a cation target (eg Si in Si compounds), consequent on the ejection of two electrons in the Auger process is identified with the polarization energy of the neighbouring anionic environment.

The generalised Auger parameter is defined as

where E ( i j , k ) is the kinetic energy of an Auger electron emitted in an ( i , j , k ) transition between core levels i , j and k , and E(i) is the binding energy in level i relative to the Fermi level. The variation of the generalised Auger parameter between two compounds AC can be identified with the difference in the extra atomic relaxation energy between the two compounds [3]:

A t ( i j j ) = 2 A R F ( J ) (2)

Here the two final state holes have the same principal quantum number and angular momentum, and AR,'"(j) is the difference in extra atomic energy of a single isolated hole between the two compounds. The only assumption necessary to derive this result is that the interaction between two holes in the final state of the Auger process is the same in both compounds [3]. For cations without 3d electrons such as Si and Al which are of primary interest here the extra atomic relaxation energy is dominated by local mechanisms [4] and can be identified with the polarization energy of the species which are nearest neighbours to the target cation. The dipoles induced in the ligands i j are directed towards the cation target and connected by the vectors R$ Assuming the environment of a central cation to be symmetric R,=ZRcosO,, where 0, is the angle between the induced dipole directed along the ligand and the vector R,, and R is the distance of the ligand atom from the cation target.

The polarization energy can be expressed in terms of the electrostatic interaction E experienced by each ligand and a term y which depends on the specific geometry of the cation site and the dipole polarizability a of the ligand anion [ 5 ] , and is given by:

( 3 ) ~ - 1 1 + coszej

D =c D a 4ns0 j = l 8 c0s3ej

y = I+-

in which N is the number of ligands. Since E can also be expressed in terms of a it follows that the difference in generalised Auger parameter between two compounds 1 and 2 for the same cation target, can be written in terms of a,D,N and R for each compound:

where A6 is in eV, R in 8, and a in A'. Thus the dipole polarizability of a ligand in a given compound can be calculated provided the generalised Auger parameter is available, and the relevant information is known for a reference compound. In this work hypothetical

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unpolarizable compounds were used for reference. It was shown by Riviere and coworkers [16,17] that 5 is a linear function of (n’-l)ln2 where n is the refractive index (or the square root of the dielectric constant). The intercept of this plot for a set of compounds with a common cation therefore yields the Auger parameter of the hypothetical unpolarized compound. Equation (4) can now be rearranged as an expression for the mean dipole polarizability of the anion adjacent to a cation j in a given compound:

colnpowul - A t R49, 14.4Nj - Dj R , A t a o / j - (5 )

In quartz for example, a is the polarizability of the oxygen and j is Si. In aluminosilicates, the oxygens surrounding a target cation may not be equivalent and 01 in equation (5) will be a mean polarizability. Thus equation (5) enables the polarizability to be found from a knowledge of the generalised Auger parameter and the environment of the oxygen anion. In porous aluminosilicates the T-atoms are in tetrahedral sites for which D is 1 . 1 5 ; the S i - 0 and AI-0 distances were taken as 1.60w and 1.74w respectively [3]. The method outlined above was validated by applying it to MgO for which good quality experimental and ab initio polarizabilities are available [1,3]. A summary of the definitions of the different polarizabilities used in this paper is given in the Appendix.

POROUS AND NON-POROUS COMPOUNDS

The data for several porous and non-porous materials are summarised in Tables 1 and 2 and 3. Oxygen polarizabilities for non porous solids have been reported previously [3], it was found that in most examples they were higher than those in porous solids. In siliceous solids this can occur because cations such as Mg and Ca tend to make the oxygens more ionic which increases their polarizability. Other factors such as the presence of octahedral sites and the greater ionicity of the AI-0 bond can increase oxygen polarizabilities in non- porous Al compounds.

Table I : Classical A uger parameter [8], generalized A uger parameters [I31 and refractive index /I41 for several silicon compounds.

~

Compound N 2 s ) (ev) 5 (ev) n in2- 1 )/n’

quartz 1762 9 -28 65 1 547 0 578

(FeMg),SiO4 1763.5 -28.10 1.635 0.626

Si,N, 1765.0 -26.40 2.045 0.76 1

Si 1767.0 -24.30 3.449 0.916

Data for four Si containing solids [3] plotted in Figure 1 fall on a good straight line and a yield a value of 6 of -36.6(10.2)eV. Similarly data for several A1 compounds gives excellent correlation with (nz-I) /n2 and an intercept of -33,6(+.2)eV. Porous solids, shown as stars on the graphs, exhibit apparently anomalous behaviour.

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Table 2: Classical A ugerparameier [8] ([lo] f o r mordenite), genemlized A uger paranicier [I31 and refractive index f o r several aluminium compounds [14].

Compound n (n2-l)/n2 W P ) (ev) 5 (ev)

aAl,O, 1.765 0.679 1462.1 -25.1

Muscovite 1.60 0.609 1461.3 -26.0

Albite 1.54 0.578 1460.8 -26.5

rAl,O, 1.70 0.654 1461.5 -25.7

Sapphire 1.763 0.678 1462.0 -25.2

Natrolite I .47 0.537 1460.8 -26.5

Mordenite 1.365 0.463 1459.8 -27.5 Si/A1=90

There are two possible reasons for this: ( i ) Porous zeolites may retain template material or other adsorbate which could modify the Auger process. (ii) Al in these materials is not evenly distributed, being more concentrated in the surface regions [6]. The Auger process, which probes these regions only, therefore corresponds to an Al concentration which is not the same as that giving rise to the refractive index, which is a bulk averaged property.

-20

81

I 0.5 0.8 0.7 0.e

-N 0.4

Figirre I . A uger parameter scaling line f o r non porous silicon compounds. compounds (0) and porous compo14nds (*).

Figure 2. A s figure I f o r afum iniutii

Table 4 summarises the values of the oxygen polarizabilities in porous solids according to the cation to which they are attached [3].

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Table 3: Generalized Auger parameter f o r silicates. n are taken from references [IS] and (1 41. Classical A uger p a r m eters are from reference (81

Compound n (nz- 1 )In2 5 (ev) ~ 3 1 5 (ev> (this work)

Hemimorphite 1.62 0.619 -28.4 -28.2

Pyrophyllite 1.59 0.605 -28.3 -28.5

Muscovite 1.60 0.609 -28.6 -28.6

Almandine --- --- -28.2 -28.2

Anorthite 1.58 0.560 -28.7 -28.5

Mi crol ine 1.515 0.564 -29.1 -28.7

Beryl _ _ _ --- -29.0 -28.9

Albite 1.54 0.578 -28.8 -28.7

Natrolite 1.47 0.537 -28.7 -28.6

Soda1 i te 1.483 0.545 -28.7 -28.3

Table 4: A irger parameters, polarizabilities and mean lattice polarizabilities f o r several zeolites, R ratio silicon to aluminium in brackets (na=not available).

Ref Compound ~ V i S , %/A1 A

PI Natrolite(2.5) 8.1 7.1 1.24 1.49 1.4

P I ZSM-5(90) 7.9 4.2 1.19 0.80 1 .O

[lo1 Mordenite(90) na 6.0 na 1.21

[ I l l H-zeolon(5) 7.7 6.6 1.16 1.36 1.2

[ 121 H-Mordenite(8.5) 7.6 5.3 1.16 1.03 1 .o

[ I l l HZSM5( 14) 7.7 5 .1 1.17 0.98 1 .o

[ill HZSMll( 1 I ) 7.4 4.7 1.10 0.90 0.8

[ I l l H-Norton(5) 7.6 4.6 1.16 0.88 I .o

t i 11 “2) 7.4 6.7 1.10 1.38 1.2

I1 11 NaY ( 2 . 5 ) 7.4 6.3 1.10 1.29 1.2

(h..05)/A3 (&.05)/A3 (h.04)/A3

PI Sodalite 7.9 na 1.21 na

[I11 NaA( 1) 7.7 6.7 1.16 1.40 1.3

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OXYGENS ON SPECIFIC SITES IN POROUS SOLIDS

A number of different oxygen environments can be identified within a zeolite which contains A1 depending on the adjoining atoms; we designate these as O( 1) etc as follows:

Ht Nat \ / \ / \ I - / \ - /

1 \ / \ / \ / \ -S i -0-S i- -S i-0-Al- -S i -0 -Al - -S i - 0 - A l -

O ( 1 ) O ( 2 ) 0 (H) 0 (Na) It is important to note that these are not actual spatial arrangements; in particular the location of counter ions with respect to 0 is different in O(H) and O(Na), and these in turn differ from O(2). Lewis acid forms are not considered since they only occur after treatment at rather high temperatures. Because of Loewenstein's rule, an Al will always be found in the grouping AI(OSi), with the single negative charge balanced by an associated counterion charge (we only consider Na' and H' counter ions here). On average therefore the 4 oxygens in this grouping will comprise 3 O(2) and one O(X) (X=Na,H).

We now consider specifically NaA. This has a Si/AI ratio of one, and the T-atoms alternate strictly between Al and Si. These atoms each give rise to a single Auger parameter (see Table 4) which implies: (i) that the relaxation around each separate type of T-atom is the same, (ii) that the polarizability response of the oxygens surrounding Si differs from that of the oxygens surrounding Al. The second observation suggests that the local relaxation is in fact primarily due to bond rather than atom polarizability. Indeed this would be anticipated from the partly covalent nature of the zeolitic bonds with the consequence that the most polarizable part of the electron distribution is in the interatomic region. In atom-atom calculations of the potential energy, it is the resultant atom polarizability which is required. We assume here that all polarizabilities are isotropic so that a resultant atom polarizability is the simple mean of the adjoining bond polarizabilities.

Now consider a more general porous aluminosilicate structure containing 2N oxygens in a unit cell of which n are of type O(X), it then follows that there will be n Al atoms, N-n silicons, (2N-4n) oxygens of type O( I ) and 3n of type O(2) . The ratio of Si to Al will be R=(N-n)h We designate the polarizability of a bond between an oxygen of type O(i) and a T-atom as a[O(i)-TI, and the mean polarizability associated with the relaxation around a T-atom as a,,,T (cf eq. ( 5 ) ) , it then follows that:

ao,Al = 0.75 a[0(2) - All + 0.25 a[O(X) - All (6)

- 3 a [ 0 ( 2 ) - Si] + a[O(X) -Si] + 2(R- 1) a[0(1) - Si] (7) ao/si - 2(R+ 1)

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In terms of the resultant atom polarizabilities these equations may be written:

For NaA, as expected from the above discussion, the term in O(1) vanishes, for convenience the left hand side of this equation will be denoted by A . It is apparent from the data listed in table 4, that each structure gives rise to a single Auger parameter for Si and for Al respectively, thus any non local relaxations occur only as averaged effects; we assume that they are also of second order. We can test this hypothesis by calculating A on the left hand side of equation (8) for various zeolites using a,,,,=1.19A3 [ 3 ] .

It is immediately apparent that there is a clear distinction between Na and H forms as noted previously [ 3 ] . Furthermore the average value for A is found to be 1 .26(*0.04)A3 for the Na forms and 0.96(+0.04)A3 for the H forms (excluding H-zeolon). As already mentioned the value of R in the region of the surface (ie. in the few A actually probed by the radiation) may differ from R measured for the bulk crystal [6]. Not all authors take this factor into account; it is possible that such effects could be responsible for the anomalous H-zeolon. Nevertheless the values for A are sufficiently accurate to enable plausible estimates of a,(z) and OoCx) to be made. Thus the value of A=0.96 A3 puts an upper limit on a,(,) of 1 .3A3, also if a,(z) is < l , lp \ ’ then aOwa) would be >1 .7A3. In previous work we found that a for a charged in-lattice oxygen species increases with charge and has a maximum of 1.7A3 for 0’- in MgO. Since it is unreasonable to suppose that O(Na) would carry a charge of this magnitude this sets a0(*) within the range l . l A 3 to 1.3A3. It would appear therefore that aO(’)=l .2(k0.05)A3 is the best estimate; the same as a,(,) within the error limit. This result suggests that the polarizable electronic environment in the vicinity of O(2) is very similar to that at O(1). The values of a,(,) and ctOwa) which follow from this are 0.4A3 and 1.4A3 respectively.

DISCUSSION AND CONCLUSIONS

The use of Auger data to determine polarizability depends on the postulate that local dipole polarizability is the predominant relaxation process in response to the instantaneous electrostatic field created at a cation in the XPS process. The analysis of aluminosilicate zeolites presented here favours this view although with the notable anomaly of zeolon. On balance the evidence of this work argues that particular experimental problems, such as an inhomogeneous distribution of Al through the crystal, rather than failure of the local polarizability postulate, is the most probable explanation of these anomalies. However further work is needed to confirm this suggestion.

The values of specific oxygen polarizabilities obtained here seem to be reasonable in view of what is known of the structure of zeolites. It is perhaps somewhat surprising that O(Na) oxygen should differ in polarizability from O ( 2 ) since these are often portrayed as having exactly symmetrical environments in NaA with respect the position of both T-atoms and the counterion. However the observed values of the Auger parameters taken in the context of the present analysis argue against this symmetry; at the same time it must be said that the difference in polarizability between these species turns out to be only slightly greater than the estimate of uncertainty in the values found. On the other hand the O(H)

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oxygens bonded through lone pairs to H counterions are very much less polarizable than other species. This conclusion seems an inescapable consequence of the lower Auger parameters for H zeolites. Again this deduction is not too surprising if the proton counterion is closely bound to the 0 lone pair. It follows that dispersion interactions at this site are expected to be substantially weaker than at other oxygen sites which in turn would create a wider distribution of adsorption site energies within the zeolitic pore spaces as R is reduced. Certainly the results from adsorption studies on high alumina pentasil zeolites show that adsorption properties change with R in a quite significant way.

Once reliable values of polarizability are available the way is open to calculate the energy distribution inside the pores of these structures and to use these in simulation studies. The results of the present study are sufficiently encouraging to propose that extension to other T-atoms and lattice species within porous structures should be investigated.

ACKNOWLEDGMENTS We thank the EC for a grant (SC*.Ol29.C(JR).

APPENDIX

Polarizability symbols used in the text:

aOIA, average oxygen polarizability around an Al target. a,,,, average oxygen polarizability around a Si target. a,(,) atomic oxygen polarizability in the Si-0-Si environment. ao(,) atomic oxygen polarizability in the Si-0-A1 environment. aO(H) atomic oxygen polarizability in the Si-O(H)-AI environment. C L , ~ , , ~ , atomic oxygen polarizability in the Si-O(Na)-Al environment a[O(i)-TI isotropic bond polarizability for the O(i)-T bond where i = { 1,2,H,Na} and T={Al,Si}

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