J. Phys. Chem. 1991,95.6322-6329
6322
sorption spectrum of ZnPBR does not change. The formation of the porphyrin radical cation in the presence of persulfate is also observed for ZnP, but to a smaller extent (ca. 30% of the signal observed for ZnPBR). The inset in Figure 8 shows the transient absorption spectrum obtained for ZnPBR in the anionic microemulsion in the presence of protons. The similarity between these transient spectra suggests that, also in the presence of protons, the porphyrin radical cation is formed. Addition of protons to ZnPBR leads to the formation of approximately 10% H42+PBR.30 This species, however, does not absorb at 532 nm (Figure 3), and a control experiment carried out with ZnPB under the same conditions showed no transient formation. Thus, in our system, protons seem to act as electron acceptors with the probable formation of hydrogen. Conclusions Porphyrin-bipyridine-cap d R u 0 2 particles with an average RuO, cluster size of 21 7 and a modified surface have been synthesized. In these systems, the zinc porphyrin or its diacid derivative is covalently attached, through a bipyridine linkage, to a R u 0 2 cluster leading to a diminution of both the porphyrin fluorescence intensity and a triplet-state yield compared to the uncomplexed porphyrin. Intermolecular adsorption of the porphyrin on the Ru0, cluster is excluded at these concentrations by absorption and fluorescence studies with separate porphyrin and dimethylbipyridine-capped R u 0 2 particles. For ZnPBR, the porphyrin singlet-state lifetime is drastically reduced, whereas the
*
!r
triplet-state lifetime is unaffected, suggesting that electron transfer from the first excited singlet state of the porphyrin to R u 0 2 is dominant. A diminished fluorescence intensity of H4,+PBR relative to H42+PBis also observed and from the redox potentials of H42+0EPand ZnTPP,I0 we suggest that this effect may similarily be attributed to hole transfer from the diacid porphyrin to the R u 0 2 moiety. Electrochemical studies of the bipyridinecapped R u 0 2 particles suggest good catalytic activity for the four-electron oxidation of water and moderate catalytic activity for the reduction of water to hydrogen. Flash photolysis studies of ZnPBR in the anionic microemulsion show evidence for photoinduced electron transfer resulting in the formation of the porphyrin radical cation with protons acting as electron acceptors. Acknowledgment. We thank D. J. Kiserow for help with the time-resolved fluorescence measurements, M. Arendt for conducting the XPS measurements, Dr. X.-X. Tang for assistance in the TEM experiments, and Drs. B. A. Gregg, J. Waluk, Y.S. Obeng, and V. Balaji for stimulating discussions. Financial support of the National Science Foundation and the Robert A. Welch Foundation is gratefully acknowledged, as well as fellowship support for U.R. from the Wigner Foundation. The flash photolysis experiments were performed at the Center for Fast Kinetics Research, which is supported jointly by the Biomedical Research Technology Program of the Division of Research Resources of the National Institutes of Health (RR00886) and by the University of Texas at Austin.
Siting of Cu2+ in Zeolites by Electronegativity Equalization Method Calculations Stefaan De Tavemier, Bart Baekelandt, and Robert A. Scboonbeydt* Centrum voor Oppervlaktescheikunde en Katalyse, K. U.Leuven, K. Mercierlaan, 92, 3001 Leuven, Belgium (Received: December 20, 1990)
The external potential of Cu2+at cation sites has been calculated for zeolite A and faujasite with the electronegativityequalization method (EEM). For mordenite both the external potential and the ionic energy of the unit cell have been calculated with EEM for Cu2+ located at all the possible cation sites. Site I in zeolite A, site I’ in faujasite, and site A in mordenite provide minima in the external potential and the ionic energy and are the preferred Cu2+sites in agreement with XRD data. For faujasite this site preference is independent of the Si/AI ratio. For mordenite, A1 in the four-rings gives the lowest ionic energy per unit cell. Cu2+is located asymmetricallyat the various sites of mordenite. The site preference becomes less pronounced with increasing Si/Al ratio.
Introduction The exchangeable cations in zeolites have received a great deal of attention in the scientific literature. Thermal stability, sorptive, and catalytic properties are all determined by the type and number of exchangeable cations and their distribution over the available sites. X-ray diffraction (XRD) has been and is the first-choice technique, as illustrated by Mortier’s compilation of extraframework sites.’ Ozin and co-workers have developed far-infrared (FIR) spectroscopy techniques of vibrations of the exchangeable cations at various sites as a complementary technique for the study of the siting of exchangeable cations.24 The method is quite involved because of the number of different sites and because a cation may (1) Mortier, W. J. Compilation of Extra Framework Sites in Zeolites; Butterworth: Guildford, U.K., 1982. (2) Baker, M. D.; Ozin, A.; Godber, J. Catal. Reo.-Sci. Eng. 1985.27, 591. . . .. (3) Ozin, G. A.; Baker, M. D.; Godber,J.; Gil, C. J. J . Phys. Chem. 1989, 93, 2899. (4) Baker, M. D.; Godber, J.; Ozin, G. A. In Perspecriues in Molecular Sieurs Science; Flank, W. H., Whyte, T. E., Eds.; ACS Symposium Series 368; American Chemical Society: Washington, DC, 1988; p 136.
have, depending on the symmetry, more than one IR active vibration. It is advisable to have a reliable basis for the interpretation. Even then, problems may arise. For instance, according to the interpretation of Ozin et al.) residual Na+ in NH,Na+Y with large x do not occupy site I, whereas XRD data and statistical thermodynamic calculations are indicative for a preferential occupation of site I by Na+.5 At very low exchange levels transition-metal ions (TMI), especially Cu2+,have been used as site probes. Electron spin resonance (ESR) spectroscopy and diffuse reflectance spectroscopy (DRS) in combination with a theoretical analysis of the spectra in the frame of the ligand field (LF) or angular overlap model (AOM) theories have been a p lied by Schoonheydt et ai.” Kevan and co-workers studied C$+ by electron spin echo envelope J ~ are dismodulation (ESEEM) or similar t e c h n i q ~ e s . ~ There (5) Van Dun, J. J.; Dhaeze, K.; Mortier, W. J. J . Phys. Chem. 1988, 92, 6747. (6) Packet, D.; Schoonheydt, R. A. In Perspectfues In Molecular Sieves Science; Flank, W. H., Whyte, T. E., Eds.; ACS Symposium Series 368; American Chemical Society: Washington, DC, 1988; p 203. (7) Schoonheydt, R. A. J . Phys. Chem. Solids, 1989, 50, 523. (8) De Tawnier, S.; Schoonheydt, R. A. Zeolites, in press.
0022-365419 112095-6322$02.50/0 0 1991 American Chemical Society
Siting of Cu2' in Zeolites by EEM Calculations
The Journal of Physical Chemistry, Vol. 95, No. 16, 1991 6323
TABLE I: Space Groups, Site Midtiplicities, and Coordinate Tramformatioiis (KT) for Zeolite A Fm3c E. F i f k F23 !EL F222 K X a 2 2
a
T 01.2 03 1 I1 Ill
96 96 192 64
96 96 96
24
24 96
96
KT 1 KT2 KT3 KT4
48 48 48 16
32
-% .P, 2 x, 2. y 2, x, y
24 48
16 16 16 16 24 16
8 8 8 8 8 8
+ '12
'IZ?09 'I2
crepancies in the interpretation of the data between these two groups, but they can to a large extent be traced back to differences in sample preparation. In any case, the Cu2+distribution at these small loadings is different from the XRD distribution."J2 Thus, if site preference is reflected in the site occupancy, then in faujasites I' is the preferred site according to XRD (= high loadings), while at the low loadings of the ESR-DRS experiments it is site IL6*' The advantage of a L F or AOM analysis of the ESR and DRS spectra is that one obtains (1) the ligand field stabilization energy (LFSE), (2) an idea about the nature of the bonding between the TMI and the lattice oxygen, and ( 3 ) the geometry of the surface complex, including distortion from ideal symmetry by a Jahn-Teller effect. However the LFSE is only a minor component of the total stabilization energy of Cu2+on a particular site. The major part is due to the spherically symmetric, electrostatic (Madelung) interaction. The calculation of the Madelung potentials in faujasites by Dempsey is the first, and one of the best attempts that have been published on this subject so far.I3J4 Dempsey used a fully ionic model. This was also done by Preuss et al.I5 in combination with Monte Carlo statistics for the Si, A1 distribution. Other research groups took into account the polarization and dispersive and repulsive interactions. Covalency was introduced via Sanderson's electronegativity equalization principle or via the average of an ionic energy and a covalent energy.Iblg Sanders and CatlowZ0 included lattice energy minimization, Le. fixed framework atoms and adjustment of the cation coordinates until an energy minimum was found. The electronegativity equalization method (EEM) allows the calculation of both the partial charges on the lattice atoms and the external potential at any point.21J2 For a given geometry (e.& a given location of Cu2+) EEM provides the charge distribution corresponding to minimum total energy. In this paper we present the results of our EEM calculation on Cu2' in zeolite A, in faujasites, and in mordenites. (9) Kevan, L.; Narayana, M. In Intrazeolife Chemistry; Stucky, G. D., Dwyer, F. G., Eds.; ACS S y m p i u m Stria 218; American Chemical Society: Washington, DC, 1983; p 283. (IO) Anderson, M. W.; Kevan, L. In Perspectives in Molecular Sieves Science; Flank, W. H., Whyte, T. E., Eds.; ACS Symposium Series; 368; American Chemical Society: Washington, DC, 1988; p 150. ( I I ) Maxwell, 1. E.; de Boer, J. J. J . Phys. Chem. 1975, 79, 1874. (12) Gallezot, P.; Ben Taarit, Y.; Imelik, B. J. Catal. 1972, 26, 295. (13) Dempey, E. J . Phys. Chem. 1969, 73. 3660. (14) Dempscy. E. In Molecular Sieves; Barrer, R. M., Ed.; Society of Chemical Industries: London, 1968; p 293. (15) Preuss, E.; Linden, G.;Peuckert, M. J. Phys. Chem. 1985,89,2955. (16) Ogawa, K.; Nitta, M.; Aomura, K. J . Phys. Chem. 1978,82, 1655. (17) Nitta, M.; Ogawa, K.; Aomura. K. In Proceedings of the 5th International Zeolite Conference; Rea, L. V., Ed.;Heyden: London, 1980 p 291. (18) No, K. T.; Chon, H.; Ree, T.; Jhon, M. S. J . Phys. Chem. 1981,85, 206s. (19) Koh, K. 0.; Chon, H.; Jhon, M. S. J . Carol. 1986, 98, 126. (20) Sanders, M. J.; Catlow, C. R. A. In Proceedings ofthe 6th Interna-
tional Zeolite ConJerence; Olson, D., Bisio, A., Eds.;Butterworth: Guildford, U.K., 1984; p 131. (21) Mortier, W. J.; Gosh, S. K.; Shankar, S. J . Am. Chem. SOC.1986, 108,4315. (22) Van Genechten, K.A,; Mortier, W. J.; Gcerlings, P. J . Chem. Phys. 1981, 86, 5063.
W
(111 Figure 1. Structures of (top) zeolite A, (center) faujasite, and (bottom) mordenite with indication of the exchangeable cation positions. TABLE 11: Space Groups, Site Multiplicities, and Coordinate Transformations (KT) for Faujasite Structures Fd3m LE!, F d 3 E I U F 2 3 & F222 Q C222 origin 3, I 23 222 222
T
192
0
I
96 16
96 96 16
48 48 16
1' 11
32 32
32 32
16 16
16 16 16 16 16
8 8 8 8 8
Structures and Methods
Three zeolites were investigated: zeolite A, faujasite-type zeolites, and mordenite. Zeolite A. The pseudosymmetry (pure Si02composition) is Pm3m. The strict alternation of A1 and Si doubles the unit cell parameter and the space group is F m k . The multiplicity of the Si sites and the AI sites is 96. The multiplicity of the cation sites does not allow a neutralization of the negative charges by divalent cations in F m k , and subgroups have to be found. In Table I we give the subgroups used, the multiplicity of lattice sites and of the exchangeable cation sites, and the coordinate transformations
6324 The Journal of Physical Chemistry, Vol. 95, No. 16, 1991
TABLE III: Space Groups, Site Multiplicities, and Coordinate Transformations (KT) of Mordenite CmCm E!, Pbcn E&P2/c !S$ PT 16 8 4 2 8 8 4 2 16 8 4 2 8 8 4 2 8 8 4 2 8 8 4 2 4 4 2 2
TI-2 T3-4 01-3 04-6 07
08 09-10 A
4
B D
4 4 8
E KT 1 KT2 KT3
’ 1 2 , ‘127 ’ 1 2 - x,
4
0
‘I2-y, x, Y , I 1 2 - z
1 2 2 2
De Tavernier et al. and z b = Nbo are the numbers of electrons on the isolated atoms a and b, respectively. Rabis the interatomic distance. xa* and qa* are expansion coefficients of the intraatomic contribution of the energy, namely the electronegativity and hardness coefficients of atom u, respectively. They have to be calibrated and are transferable from one molecule to another.2’,22 For every atom an equation of the type of ( 1 ) can be written, and together with the condition that C q a = const a
we have n + 1 equations in n + 1 unknowns ( x and the charges qa), which are exactly solvable. The last term on the right side of eq 1 is the extemal potential, from which the ionic energy per unit cell is calculated as N
’I2 + z
to go from one group to the other. For each space group the atomic coordinates and unit cell parameters were calculated with DLS,” starting from the crystallographic coordinates given by Pluth and Smith.23 The coordinates are given in Table 1A (Supplementary Material). The ideal bond lengths in the DLS program were taken as 0.162 nm and 0.175 nm for the S i 4 and A 1 4 bond lengths, respectively. The structure with the nomenclature of the cation sites is shown in Figure 1. Faujasite. The space group of faujasite with Si02 composition is Fd3m with the origin on h.For Si/Al = 1 the space group is Fd3. The subgroups necessary for higher Si/AI ratios can be found from Fd3, when the origin is shifted to (I/*,, I,/&. In Table I1 we summarize the space groups, site multiplicities, and coordinate transformations for the space groups allowing Si/AI ratios of 1 , 2, 3, and 5 . For each space group the atomic coordinates and unit cell parameters were calculated with DLS, starting from the crystallographic coordinates of De Boer and Maxwell.” The Si, A1 distribution has a minor effect on the electrostatic field around the exchangeable cations.I3J4Therefore an arbitrary distribution was adopted taking into account Loewenstein’s rule. The coordinates are given in Table 2A (Supplementary Material). The structure is shown in Figure 1 , which also shows the sites and their nomenclature. Mordenite. The structure of mordenite, its sites, and their nomenclature are drawn in Figure 1. The space groups of mordenite that allow the study of the effects of the Si/AI ratio and the Si, AI and exchangeable cation distributions are shown in Table 111. For Si/AI = 5 , A1 was placed in the tetrahedra forming the walls of the 12-membered-ringchannels. The space group is Pbcn or P2/c, depending on the location of Cu2+. AI was also placed in the tetrahedra forming the four-membered rings (two per four-ring). The space group used is P i . For %/A1 = 7 and 1 1 , the space group is Pi with A1 in the four-ring tetrahedra.25 For each space group the coordinates of the atoms and the unit cell parameters were determined with the ORFFE and DLS prog r a m ~ . ~They ~ , ~are ~ given in Table 3A (Supplementary Material). EEM Calculations. The fundamental EEM equation is qb x = xa* + 2qa*qa + E (1) b+aRab x is the average electronegativity of the material under study; qa and qb are the charges on the atoms, defined respectively as Za - Na qa = Nao - Na and z b - Nb = 46 = Nbo - Nb. za= Nao (23) Pluth, J. J.; Smith, V. J. J . Am. Chem. Soc. 1980, 102, 4704. (24) Baerlocher, Ch.: Hepp, A.; Meier, W. M.DLS-76 A frogrumfor the Sfmulation of Crystal Structures; ETH: Zurich, 1978. (25) Mortier, W. J.; Pluth, J. J.; Smith, J. V. Mater. Res. Bull. 1975, I O , 1037. (26) Busing, W.R.; Martin, K. 0.;Levy, H. A. Program ORFFE; Oak
Ridge National Laboratory: Oak Ridge, Tennessee, 1964. The program has been adapted by W. J. Mortier, Laboratorium vmr Oppcrvlaktechemie, K. Mercierlaan, 92, 3001 Leuven, Belgium.
Ei
= 1/2C qaqb/Rab
(3)
a b+a
where N is the number of atoms in the unit cell. Equation 3 or the potential V in eq 1 are slowly converging series, which are calculated with the method of B e r t a ~ t . ~ ’ The summation is truncated as soon as the charges qa do not change upon addition of terms. That is for AV = 5 X In the calculations the positions of the lattice atoms are fixed and the exchangeable cations are positioned at different sites. Thus, those l / R a b terms due to the lattice atoms are constant. It is then advantageous to write va
= Cqc/Rac +
C qb/Rab
b#a
(4)
where c runs over the exchangeable cations and b over the lattice atoms. From (1) and (4) we have qa = ( X - Xa* -
b#a
qb/Rab - Cqc/Rac)/(2?0*)
(5)
C
Thus the charges qa are expressed as qa = flqc, 46, x ) The charge shift on atom u due to the presence of exchangeable cations with charge qc is then
With the aid of ( 5 ) the derivatives are given by
and (6) becomes
or m
n
Index j runs over the m exchangeable cations per unit cell, and i over the n lattice atoms per unit cell.
uror2 =
arakl 1 /Rrakl + 1 /Rr,kl’ + 1 /Rp,kl” + ... + l / R r g i + l / R r 8 T + ... for r2 # a
-
urd, = l / R r g l t+ l/Rrgl,,
+ ...
(27) Bertaut, F. J . Phys. Radium 1952. 13, 499.
for r l = a
The Journal of Physical Chemistry, Vol. 95, No. 16, 1991 6325
Siting of Cu2+in Zeolites by EEM Calculations
0.00
i
-0.50
-1.00
: cubooctahedron
p a
I/ 0.40
supercage
0.20
0.20
0.00
0.40
Dirtancdom) of Cu from centre of 8-ring
Figure 3. External potential of Cu2+ in the eight-ring of zeolite A. Vertical bars indicate the closest approach of Cu2+to the lattice oxygens. Fractional coordinate ( ~ 1 0 0 0 )of Cu along diagonal a x i s (x-y=z)
Figure 2. External potential of Cu2+on the trigonal axis of zeolite A: (0)CsCuNaA; (A) NaCuA.
The primes denote different unit cells. Equation 8 together with the condition that the sum of the charge shifts on the lattice atoms is zero EAqa = 0 constitutes a set of n 1 equations in n 1 unknowns. Note that we have assumed no charge shift of the exchangeable cations: Aqc = 0. They are taken with their full ionic charge. The reason for this choice is that the expansion coefficients xa* and qa* are unknown for the exchangeable cations studied in this paper. The coefficients ur#, are constant for every exchangeable cation distribution and have to be calculated only once by putting the charges a t the crystallographic positions equal to 1, and to zero elsewhere. The charges on the lattice atoms are given by = q r + Aqr where qr. and qr are the lattice atom charges in the presence and absence of exchangeable cations, respectively. The external potential is then
+
qb/Rab bza
r+o
+
&r/Rar
+ xqk/Rok + k
r#a
qr/Rar
and the last term on the right side is constant. Results
Zeolite A. A CuNaA zeolite with 2 X 16 Cu2+on sites I and 2 X 16 Na+ on sites 1 in space group F'222 was used for the external potential calculation. From the two possible configurations to fill up the four sets of sites I, that configuration is chosen with ORFFE that allows the maximum separation between the Cu2+. Cu2+is placed on the trigonal axis and the potential is calculated for several positions on both sides of the six-rings. Each time the charges on the lattice atoms are recalculated. The results are grapically represented in Figure 2. A minimum of -0.901 au ( 1 atomic unit = 27.17 eV) is found in the supercage close to the plane of the six-ring. The Cu-O bond distance is in agreement with the sum of the ionic radii2*and the angle between the Cu-O bond and the trigonal axis is 107O, to be compared with the value of 107.8O calculated from spectroscopic data.6*29 In the case of CuNaCsA the space group C222 had to be chosen, and according to the X R D data Cs+ prefers the eightrings.'O We sited 3 X 8 Cs+ in the eight-ring at sites 11; 4 X 8 (28) Shannon, R. D. Acta Crysta/logr., 1976, A32, 751. (29) Packet, D.;Schoonheydt, R. A. In Structure and Reactivity of Modved Zeo/ites;Jacob, P.A,, Jim, P..Jaeger, N.,Schulz-Ekloff, G.,Eds.; Studlea in SurfaceScience and Catalysis 18; Elsevier: Amsterdam, 1984; p 41.
(30) Vancc, T. 8.; Seff, K.J . fhys. Chem. 1975,79, 2163.
TABLE I V Potential and Coordinates of Cu2+in Faujasite site V,au X Y Z
a
I
-0,851
1'
-0.706
11
-0).902b -0.881
0.165 0.1651
0.165 0.1651
0.165 0.1651'
0.140 0.131
0.360 0.369
0.140 0.131"
Reference 1 1. *Space group C222;see text.
Cuz+ and 1 X 8 Na+ were sited in sites I. The Cu2+were separated as far as possible. They were moved along the trigonal axis as in the case of CuNaA. The results of the calculations are shown also in Figure 2. The potential minimum is now -1.021 au, but more importantly the minimum is shifted inside the cuboctahedron. This behavior is in agreement with our proposal on the basis of spectroscopy.' Finally, one Cu2+was placed out of center in the eight-ring. This is possible in space group C222. We have then: 1 X 8 Cu2+ in sites 11, 4 X 8 Cu2+ in sites I and 2 X 8 Na+ in sites I. The two empty six-rings were placed next to the occupied eight-rings. The calculations show (Figure 3) that there are no potential minima upon moving Cu2+from the center to the oxygens of the 8-ring. In that case we assume that the Cu-0 distance equals the sum of the ionic radii (vertical lines in Figure 3). The potential is then -0.72 au, far above the value for the six-rings. We conclude that in all cases studied, Cu2+prefers the six-rings to the eight-rings. Faujasite. The external potential at the Cu2+site was calculated for Si/AI = 1 in space group Fd3. In each case one crystallographic position was fully occupied by Cu2+. The remaining positions were occupied either by Cu2+ or by Na+. In the latter case the coordinates of Eulenberger et aL3I were chosen. This leads to the following cation distributions: for Cu2+ on site I, 1 X 16 Cu2+ on sites I and 1 X 32 Cuz+ on sites 11; for Cu2+ on site 1', 1 X 32 Cu2+ on sites I' and 1 X 32 Na+ on sites 11; for Cuz+ on site 11, 1 X 32 Cu2+ on sites I1 and 1 X 32 Na+ on sites 1'. For sites I' and I1 the coordinates of Cu2+ corresponding to the minimum potential were determined and found to agree with those of Maxwell and de Boer." This is shown in Table IV. The external potential follows the order I' > I > 11. In these calculations the repulsion due to simultaneous occupancy of two sites I' at the same hexagonal prism could not be avoided. For a zeolite with only one site I' occupied by Cu2+per hexagonal prism the space group C222 had to be chosen and the remaining negative charge was neutralized by full occupancy of sites I1 with Cuz+. The external potential at site I' decreases then to -0.902 au. Thus sites I' are the most favorable sites, and they will at most be half occupied. This conclusion is in agreement with existing X R D data." (31) Eulenberger, G. R.; 1967, 7/, 1812.
Shoemaker, D.P.; Keil, J. K. J . fhys. Chem.
6326 The Journal of Physical Chemistry, Vol. 95, No. 16, 1991
De Tavernier et al.
TABLE V Space Groups nod Site Occupancies in Mordenite
5O
space group
Si/AI (A1 in six-rings)
Pbcn
no. of cations per unit cell site B site D
site A 4cu2+
Site E
4cu*+
4cuz+ P2/c
56
5< (AI in
four-rings)
PT
4cu2+
2cu2+
2cu2+
4Cu2+(2 sets) 4Cu2+ (2 sets) 7d (AI in four-rings)
4Cu2+(2 sets)
2Nat
2cuz+
Pi
2cu2+ 2Nat
2cu2+
2Nat 2cu2+ 2Na’
2Cu2+(2 sets)
Pi
1l e
2cu2+ 2cu2+
2cu2+
“In Pbcn the multiplicity of sites A, B and D is 4; that of site E is 8. bThe space group P2/c is used to have 4 equivalent sites E, occupied by Cu2+. In P7 the site multiplicity of A is 1, and 2 for the other sites. For Si/AI = 5 , 4Cu2+are necessary to neutralize the framework. We define then two sets of Cu2+on sites B, D and E, while for site A two Cuzt have to be placed additionally on site D. dFor Si/AI = 7, the lattice charge is -6, which is neutralized by 2Cu2+and 2Nat. #ForSi/AI = 11, the charge of the lattice is -4. In PT the site multiplicities are fulfilled with 2CuZt, except for site A where two sets of Cuzt have to be used. In all cases where two sets are introduced, the cations are placed so as to minimize repulsions with
-
ORFFE. -0.10
r
-0*83
[email protected] a
.:a
0
-0.85 -0.30 -0.30
*
k
/
I
/
-0.40
/
‘
0
b 0
a
I
/
-
-0.87
-
A P
A
A
-0.60
I 125
I’ , 175
275
325
A
16
32
48
375
Frretieirl cterdlirtr (11 0 0 0 ) of Cr rlens dirterr1 rxir (x-y-d
Figure 4. External potential along the trigonal axis of faujasite: cations; (-) Cu on site I; (--) Cu on site 1’.
D
-0.89
,II 225
I
-0.91
(-)
no
Cu2+ (and the exchangeable cations in general) creates its own potential: i.e., it perturbs the charges on the lattice atoms so as to attain maximum stability. This is illustrated in Figure 4, where the potential due to the lattice only is shown along the trigonal axis. Cu2+ was placed on sites I and 1’, respectively, and the charges were calculated. Consequently, these charges were used to calculate the potentials without any cations present. The figure shows first of all that I’ is the most favourable cationic site. Second, Cu2+deepens the potential well of site 1’. Third, when Cu2+ is placed in the center of the hexagonal prism (site I), it is unable to create a potential minimum. This is then an unfavorable site for Cu2+. In XRD work a few Cu2+are always placed in the hexagonal prisms.’lJ2 These must probably be located off center to stabilize Cu2+. Different Si/AI ratios were investigated in F222 with one crystallographic position fully occupied by Cu2+ (= 16 Cu2+per unit cell) and the remaining negative charges neutralized by protons. In this way cation-cation repulsions were avoided, as it was shown that protons do not influence the distribution of the cation to any measurable extent.$ In Figure 5 , the external potential for Cu2+ on sites I, 1’, and I1 is plotted against the AI content per unit cell. For sites I’ and I1 the values given are minima (see Figure 4). It was found that the position of these minima was independent of the Si/AI ratio. The trend shown in Figure 5 is that the external potential decreases with increasing AI content. This is of course expected: the higher the negative
64
80
96
AI I U.C.
Figure 5. External potential of CuZt in faujasite as a function of AI content: (0)site 1’, HCuY; (A)site 11, HCuY; (0)site I, HCuY; (m) site 1’, NaCuX; (A)site 11, NaCuX; ( 0 )site I, NaCuX.
charge of the lattice, the stronger the interaction with Cu2+. The dependence is not linear, but this may be due to the distribution of the protons. The latter was not optimized. Mordenite. The situations studied are given in Table V. Space Groups Pbcn and P 2 / c ; Si/AI = 5. Not only the potential but also the ionic energy of the unit cell has been calculated for Cu2+ on the different sites of mordenite. Pbcn only allows a symmetric siting of Cu2+ on the various sites. For site A the coordinates of Cu2+are then (0.0, 0.5,O.S); on sites B and D Cuz+ can be displaced on the two-fold axis, while for site E it can be displaced perpendicular to the plane of the oxygens of site E. The effect of these displacements on the potential and the electrostatic energy is shown in Figure 6. When Cut+ is moved from site 8 to site D (Figure 6a) two minima are found in the potential as well as in the ionic energy, which do not fully coincide. In any case, the minimum is more pronounced for site D than for site B, thus showing that D is a more favorable site than B. The potential of site E has no minimum, but the electrostatic energy has one. The minima are given in Table VI. The external potential follows the order E < D < B < A, while for the ionic energy the order is E < A < D < B. The high potential for the fully occupied site A (Pbcn, 4Cu2+)is due to the short Cu2+-Cu2+ separation of 0.49 nm. This is a very unfavorable situation.
The Journal of Physical Chemistry, V O ~95, . No. 16, 1991 6327
Siting of Cu2+ in Zeolites by EEM Calculations -0.50
-0.84
* Potential
-0.84
-0.50
ti I
V
A
N
I
m
El
d
-0.55
-
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-0.60
1
-0.65
-0.70
-0.75' 0.00
'
' 0.10
'
' 0.20
'
' 0.30
'
'
'
0.40
4.4 . E
-0.86
-0.85
c
F R
-0.86
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-0.86
0
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. I
-0.87 0.50
b -0.75
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5
-
-0.58
g
-0.66
-a-
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a .-
-
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v
-0.83
t
-0.50
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-0.87 0.50
0.40
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-0.84
-I
Plan. or 11t. E
.4.4
-0.85
1
-0.82
I
*
9
i Y
8
N
I
Potential V
-
EnOIlY E
Bl
-0.83
"i
-0.60
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.-a
-0.84
Plane of site E
5 U
E
- -0.85
-0.70
5
4.4
c -0.74
4.4
-0.86
* F
-0.87
-
U
d
m d
i
Bnersl E
n U .-
A
N I
+ POt.nl1.l
0.30
Unit cell coordinate ylb on 2 - f o l d axis -0.82
9
0.20
0.10
Unit cell coordinate ylb on 2-fold axis -0.50
-0.86
-o.82
-0.88
-0.90
0.05
0.00
0.05
0.10
8
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0.15
Distance (nm) of Cu to plans of lite E
Diitance (nm) of Cu to plane of site E
Figure 6. (a, Top) External potential of Cuz+and ionic energy of the unit cell along the two-fold axis through sites B and D in mordenite: AI in the 12-ring;Si/AI = 5; space group Pbcn. (b, Bottom) External potential
Figure 7. (a, Top) External potential of Cu" and ionic energy of the unit cell of mordenite when Cuz+is displaced along the center axis through the eight-ring channel: Si/AI = 5 ; AI in the four-rings; space group PI. (b, Bottom) External potential of Cu2+and ionic energy of the unit cell of mordenite when Cu2+is moved perpendicularly to site E: Si/Al = 5 ; AI in the four-rings; space group Pi.
of Cu2+ and ionic energy of the unit cell of mordenite when Cu2+is displaced perpendicularly to site E: Si/AI = 5 ; space group P2/c.
TABLE VI: External Potential and Ionic Energy of Cul+ in Mordenita with Space Groups Pbea, P 2/c, and and Si/AI = 5 AI in 12-rings, AI in
Pbcn and P2/c four-rings, PT potential, energy, potential, energy, site au au au au A (center) -0.5332 -86.56 -0.173 3 -86.58 A (displaced; r(Cu-O) = -0,83066 -86.75 0.213 nm) -0.817 26 -0.82956 -87.16 -0.876 16 B (on C2) -0.64039 -85.02 4.645 70 -85.22 B (displaced; r(Cu-O) = -0.152 95 -85.60 0.213 nm) D (on C2) -0.1048 -86.33 -0.685 80 -85.54 D (displaced; r(Cu-O) = -0.81 145 -86.80 0.213 nm) E -0.8600 -81.12 -0.86630 -86.19
Spnce group Pi;Si/AI = 5,7, and 11. For space group Pi AI is in the four-ring tetrahedra. PI also allows a displacement of Cu2+ toward the oxygens such that more realistic Cu-0 bond distances can be realized. This results in a general lowering of the potential and the ionic energy, especially for site A. In Table VI the values are given for the Cu-0 distance of 0.213 nm. For Cu2+ on the C2axis (sites B and D), similar curves as for Pbcn are found but with more pronounced minima (Figure 7a). For site E the ionic energy minimum is less pronounced (Figure 7b). For Si/AI = 5 the potential sequence in the displaced configuration is A < E < D < B, and the energy follows the order A < D
I1 > I, which is in agreement with the occupancy factors determined by XRD.’1J2 Also, when the Cu2+ is allowed to move on the trigonal axis of sites I’ and 11, a minimum of the potential is found at positions that are in very good agreement with Cu2+coordinates. This preference for I’ is only valid when one site I’ is occupied per hexagonal prism. If one allows full occupancy of I’ by Cu2+(32/unit cell and 32 Na+ on I1 for a Si/Al ratio of 1 in the Fd3 space group), then the external potential of Cuz+on I’ is -0,706 au as compared to -0.902 au. The difference is due to 1-1’ repulsion. This repulsion was also recognized by No et a1.‘* Van Dun et aL5included a repulsive energy parameter between cations on sites I and I’ in their statistical mechanical approach of the cation distribution in faujasite-type zeolites. In general, therefore, cations on neighboring sites repel each other. These sites are 1-1’ and 1’-I’ (with an empty site I between). Out of the three sites associated with one hexagonal prism, only one site, either I’ or I, can be occupied. This amounts to 16 cations per unit cell,32at least as long as no other effects, such as an oxygen bridging two cations in the cuboctahedra, come into play. On the basis of our calculations we do agree with Van Dun et al.5 that the cations create to a large extent their own potential. Thus,they prefer the sites where they can make the lowest possible potential. It means that they polarize their environment, and this is taken into account with the EEM calculations, in contrast with most other formalisms in which the (lattice) charges are kept constant . The preference of site I’ is not corroborated by the ESR data, taken a t very small Cu2+ loadings (X0.5 Cu2+/unit ce11),6.7,33-36 or by other theoretical calculations. Thus, the calculations of Dempsey13J4 give site I as the most preferred one for divalent on the basis of ESR and DRS, cations. Packet and S~hoonheydt?~ and Goldfarb and Z ~ k e r m a n on , ~ ~the basis of ESEEM, interpreted their spectra by a preferential occupation of site 11. Ichikawa and K e ~ a n )located ~ . ~ ~ their trace amounts of Cu2+in site I. Thus, our results are the only theoretical ones that are in agreement with XRD data. However, the very low Cu2+content of the ESR samples makes comparison with calculations and with XRD data almost impossible. Mordenite. Three conclusions can be drawn from our calculations on mordenite: (1) The models with A1 in the four-rings give the lowest external potential and lowest electrostatic energies a t the cation sites. This is considered to be the preferential A1 siting. It is in agreement with quantum mechanical calculations.” (2) The cations usually do not occupy the most symmetrical positions with respect to the nearest-neighbor oxygens of the sites; the displaced positions give lower potentials and ionic energies. This is also known from XRD work on e.g. Ca2+siting.23~25*38*39 (32) Morticr, W. J.; Bosmans, H. J.; Uytterhoevcn, J. B. J. Phys. Chem. 1972, 76, 650. (33) Packet, D.; Schoonheydt, R. A. New Developments in Zeolite Science
and Technology. Proceedings of the 7th International Zeolite Confcrcnce; Murakami, Y . , Iijima, A., Ward, J. W., Eds.; Kodansha-Elsevier: Tokyo, 1986; p 385. (34) Ichikawa, T.; Kevan, L. J . Am. Chem. Soc. 1983, 105, 402. (35) Ichikawa, T.; Kevan, L.J . Phys. Chem. 1983,87, 4433. (36) Goldfarb, D.; Zukerman, K. Chem. Phys. Lett. 1990, 171, 167. (37) Derouanc, E. G.; Fripiat, J. Q . Proceedings ofrhe 6th InrernotionaI Zeolite Conference;Olson, D.,Bisio, A,, as.Butterworth: ; Guildford, U.K., 1984; p 717.
J. Phys. Chem. 1991, 95,6329-6336 The interpretation of the ESR and DRS data of Cuz+ on site A is also in better agreement with experiment when Cu2+ is located off-axially.8 (3) The differences in ionic energy or potential of the different sites is small, especially a t Si/Al = 7. It is questionable then, if, in view of the approximations involved in the calculations, a physically meaningful site preference can be derived. In any case, whatever the Si/Al ratio site A has the lowest ionic energy and should be the preferred site. This is in agreement with XRD data2325*38*39 and with the interpretation of ESR and DRS spectraes For the other sites a site preference sequence cannot be established. This means that they have almost equal probability of occupancy. Indeed, their population by Ca2+in dehydrated mordenite is almost equal, although from the temperature dependence of the Caz+ population Mortier concluded that site E was the most preferred site after site A.38 Den Ouden et al.'" performed lattice energy minimization calculations to study the siting of Ni2+ in mordenite. They did not find well-defined sites, but showed that the location of Ni2+ seemed to be related to the presence of Al-O-(Si-O),,-Al sequences. AI in the four-rings creates a cyclic sequence (A1-0Si-O-Al-O-Si-O), which gives the lowest ionic energy to the structure. When Cuz+ is located in sites A, B, C, and D, it has oxygens of the four-rings in its coordination sphere. These sites should then be, according to den Ouden," the preferred sites. This is indeed so for site A. For sites B, C, and D two other factors overrule the hypothesis of den Ouden? (1) simultaneous occupancy of these sites is impossible due to cationic repulsion; (2) cations are very asymmetrically coordinated at these sites and their coordination requirements are difficult to fullfil. (38) Mortier, W. J. J. Phys. Chem. 1977,81, 1334. (39) Elsen, J.; King, G. S. D.; Mortier, W. J. J. Phys. Chem. 1987, 91, 5800. (40)den Oudcn, C. J. J.; Jackson, R. A,; Catlow, C. R. A.; Post, M. F. M.J. Phys. Chem. 1990, 94, 5286.
6329
Conclusions
The EEM method allows the calculation of external potentials and ionic energies of zeolites, taking into account chemical composition and real structures. Optimization of the structures and charge transfer between the exchangeable cation and the lattice can presently not be done. Both the external potential and the ionic energy have welldefined minima at exchangeable cation positions and can be used to study cation distributions and site preferences. The latter is a global property of the material; the former is a local property. The preference of Cu2+for site I in A, site I' in faujasites, and site A (or I) in mordenite, experimentally determined by XRD, has been confirmed. In the latter two cases this preference is independent of the Si/Al ratio. The preference of Cu2+ for site I1 in faujasites, established with ESR at very low loadings, could not be verified because calculations a t these small loadings are prohibitively long. In mordenite, AI in the four-rings gives the lowest external potential and ionic energy. Cu2+is asymmetrically located on the sites, and no other site preference than that of site A could be established. This means that at high %/A1 ratios the energy difference between geometrically different sites diminishes or even disappears. The exchangeable cation distribution may then be determined by the local chemical composition, such as the presence of AI in the four-rings. Acknowledgment. S.D.T. and B.B. acknowledge a Ph.D. grant from the Instituut voor Wetenschappelijk Onderzoek in Nijverheid en Landbouw (IWONL, Belgium). This work was made possible by the financial support of the State Secretary of Scientific Research under Contract G.O.A. 86/91-98. We thank Prof. W. Mortier for valuable discussions. Supplementary Material Available: Tables 1A-3A listing coordinates of atoms for lattices of zeolite A, faujasite, and mordenite, respectively (13 pages). Ordering information is given on any current masthead page.
Uptake of Gas-Phase Alcohol and Organic Acid Molecules by Water Surfaces J. T. Jayne, S. X. Dum, P. Davidovits,* Department of Chemistry, Boston College, Chestnut Hill, Massachusetts 02167
D. R. Wonnop, M. S. Zahniser, and C. E. Kolb Center for Chemical and Environmental Physics, Aerodyne Research, Inc., Billerica, Massachusetts 01821 (Received: January 9, 1991: In Final Form: March 12, 1991) Mass accommodation coefficients (a)have been measured as a function of temperature in the range 260-291 K for methanol, ethanol, 1-propanol, 2-propano1, 2-methyl-2-propano1,ethylene glycol, chloroethanol, bromoethanol, iodoethanol, formic acid, and acetic acid. The experimental method employs a monodispersed train of droplets (1230 pm in diameter) in a low-pressure flow reactor. Droplet-trace gas interaction times are in the range (2-10) X lO-'s. All mass accommodation coefficients show a negative temperature dependence and can be well expressed in terms of an observed Gibbs free energy as a/(1 a) = exp(-PG'&/RT). Of the species studied, iodoethanol has the largest mass accommodation coefficient; for this molecule a ranges from about 0.04 at 290 K to 0.2 at 260 K. 1-Propanol has the smallest a;it ranges from about 0.01 at 290 K to 0.07 at 260 K. The results show systematic trends. Most notably, when AQob is expressed as Aceob = AH& - TASob, it is observed that the magnitudes of both AHoband Lis, correlate and increase in the sequence diols < acids < haloethanols < alkyl alcohols. The results have led to the development of a model for the uptake of gas-phase molecules by liquids. Introduction It is now recognized that many important atmospheric reactions occur inside aqueous droplets of clouds and fogs.1-5 Recognition of the importance of these heterogeneous processes has stimulated ( I ) Graedel, T. E.;Goldberg, K. I. J . Geophys. Res. 1983, 88, 10865. (2) Heikcs, B. G.; Thompson, A. M. J . Geophys. Res. 1983,88, 10883. (3) Chameides. W. L. J. Geophys. Res. 1984.89.4739. (4) Schwartz. S. E. J . Geophys. Res. 1984.89, 11589. (5) Jacob, D.J . Geophys. Res. 1986, 91, 9807.
0022-3654/91/2095-6329$02.50/0
an increasing amount of research in this area and a growing understanding about the nature of heterogeneous processes (see for example refs 6-18). (6) Baldwin, A. C.; Golden, D. M. Science 1979, 205, 562; J . Geophys. Res. 1980, 85, 2882. (7) Lee, J.-H.; Tang, 1. N. Afmos. Elwlron. 1988, 22, 1147. (8) Molina, M. J.; Tso, Tai-ly; Molina, L. T.; Wang, F. C.-P. Science 1987, 238, 1253. (9) Leu, M.-T. Goephys. Res. h t f . 1988, 15, 17.
Q 1991 American Chemical Society
