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Topological and Stereochemical Characteristics of Zeolite Frameworks
Topological and Stereochemical Characteristics of Zeolite Frameworks
M. Sat0 Department of Chemistry, Gunma University Kiryu, Gunma 376, Japan ABSTRACT A new approach for the characterization of zeolite frameworks has been tried by applying the concept of topological and stereochemical compatibility to consecutive concentric clusters (CCL). Topological compatibility means the topological consistency between a kernel and peripheral clusters, while the stereochemical one imposes chirality and steric compatibility in threedimensional space. This method is successfully applied to the characterization of 12 distinct zeolite frameworks: AFT, AEI, CHA, EMT, FAU, GIs, GME, KFI, MER, PAU,PHI, and RHO. I NTRODUCT ION Zeolite frameworks can be topologically characterized in terms of the secondary building units (SBU) criterion [l] or the CCL one [ 2 ] . The SBU is a simple and effective geometrical means of characterizing the zeolite frameworks, but inferior because it lacks a mathematical foundation. In contrast, the CCL is based on the graph theory and can be applied widely to existing and non-existing frameworks. Any kind of zeolite framework can be completely covered with CCLs by extending the topological distance from 0 to infinity, and the characteristics of zeolite frameworks are realized on those of the CCLs. However, it is also true that the CCL representation becomes very complicated with increase of topological distance and it is not always realistic as a framework characterization. In this paper, a new topological and stereochemical approach to characterize zeolite frameworks has been tried on the complicated CCLs.
93
94
M. Sato
TOPOLOGICAL COMPATIBILITY An nth CCL is defined as a set of all the points ranging from topological distance 0 to n , and all the lines responsible for the connection between them. Fig.1 shows some examples of consecutive CCLs up to the 3rd step. Both 0th and 1st CCLs are common to any kind of frameworks, but 2nd and 3rd CCLs are not. As can be seen, FAU (faujasite) can be topologically differentiated from both ANA (analcime) and LAU (laumontite) in the 2nd step, because they contain different kinds of 2nd CCLs. Also LEV (levynite) containing two kinds of CCLs is obviously differentiated from all the others in the 2nd step. ANA is differentiated from LAU in the 3rd step. These are topological criteria for characterizing zeolite frameworks. In these consecutive CCLs, it must be noted that an (n+l)th CCL is formed on the basis of nth CCLs, all of the same kind or of several kinds. Strictly speaking, an (n+l)th CCL is constructed on the basis of five nth CCLs, one central CCLs (kernel CCL) and four surrounding ones (peripheral CCLs). This can be mathematically expressed as, C(n+l,O)= C(n,O) + C(n,l) + C(n,2) + C(n.3)
+ C(n,4)
in which C(n+l,O) and C(n.0) denote the (n+l)th and nth kernel C(n,p) (p=1,2,3,4) CCLs having its origin at site 0, while denote the nth peripheral CCLs having their origins at the sites 1,2,3, and 4. Sites 1,2,3,4 are those next to site 0. The symbol + indicates coupling the clusters. Fig. 2 shows their connective FAU in Fig. 1. In this construcrelations which is realized on tion, a topological compatibility between the kernel and the peripheral clusters is required to form a new large CCL. Two CCLs are completely compatible when they overlap each other perfectly. This is the case when the same kind of CCLs have a common origin. However, if their origins are in different sites, they can overlap partially. Two different kinds of CCLs can overlap partially or hardly. Fig. 1 shows that the 2nd CCLs of FAU and ANA are partially compatible to form the 3rd CCL of LEV, but those of LTA and FAU are not.
Topological and Stereochem~calCharacteristics
0th
3rd
2nd
1st
ANA
LAU
a-
+
f
i
/
\ LEV
&
FAU
LTA
Fig. 1 Consecutive CCLs (concentric clusters) and corresponding zeolite species. ANA: analcime, LAU: laumontite, LEV: levynite, FAU: faujasite, LTA: Linde type A.
95
96
M. Sat0
C(n+l,O)
Fig. 2
Topological compatibility between a kernel and four peripheral CCLs to form a new large CCL
STEREOCHEMICAL COMPATIBILITY In addition to topological compatibility, stereochemical compatibility must be taken into consideration in the formation of real zeolite frameworks. For example, the 2nd CCL of FAU cannot be in a plane configuration, but is in two kinds of stereochemical configuration, i.e. left and right-handed. In this case, a given kernel CCL can be combined with a peripheral one ta satisfy its chirality consistency. Steric hindrance is a more important factor for the combination of CCLs, not only between kernel and peripheral CCLs, but also between two or more peripherals CCLs. Stereochemical compatibility is essential for the characterization of real frameworks. One example is shown on frameworks such as AEI (ALP04-18). AFT (ALP04-52). CHA (chabazite), EMT (hexagonal faujasite), FAU (faujasite), GIS (gismondine), GME (gmelinite), KFI (ZK-5), MER (merlinoite), PAU (paulingite), PHI (phillipsite) and RHO (rho).
Topological and Stereochemical Characteristics
97
All of these differ in framework topology [ 3 ] . However, it is noteworthy that they constitute only one kind of 2nd CCL of FAU, in which three four-membered rings are arranged to share their edges. Stereochemically, they can be characterized in two forms, L (left-handed) and R (right-handed), as shown in Fig. 3.
Fig. 3 Left- and right-handed CCLs allowed in the 2nd CCL of FAU The compatibility between a central cluster and the neighboring clusters can be realized by two symmetry operations, i.e., reflection and rotation. A rotation operation relates a central left-handed cluster with a left-handed one in the first neighbor, while a reflection operation relates a left-handed one with a right-handed one. Fig 4 shows their compatible relation at site 1. As already shown, a given kernel cluster has 4 distinct sites to combined with neighboring clusters. Thus, an L-handed kernel as well as an R-handed one has total 16 stereochemically distinct combinations of clusters. However, the steric hindrance between a kernel and peripheral clusters reduces the number to 9 (Table 1). In them, the arrangements LRLR, LRRR, RRLR are converted to those RLRL, RLRR, RRRL respectively by a symmetry
98
M . Sato
operation of rotation. Thus, only 6 combinations are allowed to form 3rd CCLs. All of them based on the L handed kernel are shown in Fig. 5. 3
I--
2
4
3
1 3
1
2
4
4
2
T I
.......... . Fig.4
Chirality compatibility between a kernel CCL (solid) and a peripheral one (dotted) in terms of rotation (L) and reflection (R)
Table 1
Stereochemically distinct combinations for both L and R kernels. The symbol + means the combinations allowed to appear as the 3rd CCL.
Topological and Stereochemical Characteristics
Fig.5
LLRR
LRLR
LRRR
RRLL
RRLR
RRRR
Six types of 3rd clusters allowed for L-handed kernel
CHARACTERIZATION OF FAUJASITE SERIES FRAMEWORKS Now, it is possible to characterize the above faujasite series frameworks in terms of the 3rd cluster types. Visual examination is very difficult to perform, because all the framework nodes should be examined as centers of the CCLs. A computer program which serves to identify cluster type has been developed for this. The result is shown in Table 2. GIS and MOR as well as FAU and AEI cannot be differentiated in the 3rd CCL, wh.ile others can be clearly differentiated. The absence of the arrangement LLRR in this table suggests that the configuration of the cluster LLRR is closed and cannot be developed further.
99
CONCLUSION The concept presented here can be widely utilized not only for the characterization of various kinds of zeolite frameworks, but also for the generation of existing and non existing zeolite frameworks. A large number of clusters may be topologically compatible, but the numbers is reduced by stereochemical compatibility. This may be the main reason why the number of real frameworks is restricted. A computer program for framework generation based on this concept is now in progress.
REFERENCES 1
2 3
W.M.Meier, Molecular Sieves, Soc.Chem.Ind.London UK, (1968), p.10. M.Sato, J.Phys.Chem.91,(1987),4675. W.M.Meier and D.H.Olson ed. Atlas of zeolite structure types, Zeolites 12,(1992),No.5.
M. Sat0 Department of Chemistry, Gunma University Kiryu, Gunma 376, Japan ABSTRACT A new approach for the characterization of zeolite frameworks has been tried by applying the concept of topological and stereochemical compatibility to consecutive concentric clusters (CCL). Topological compatibility means the topological consistency between a kernel and peripheral clusters, while the stereochemical one imposes chirality and steric compatibility in threedimensional space. This method is successfully applied to the characterization of 12 distinct zeolite frameworks: AFT, AEI, CHA, EMT, FAU, GIs, GME, KFI, MER, PAU,PHI, and RHO. I NTRODUCT ION Zeolite frameworks can be topologically characterized in terms of the secondary building units (SBU) criterion [l] or the CCL one [ 2 ] . The SBU is a simple and effective geometrical means of characterizing the zeolite frameworks, but inferior because it lacks a mathematical foundation. In contrast, the CCL is based on the graph theory and can be applied widely to existing and non-existing frameworks. Any kind of zeolite framework can be completely covered with CCLs by extending the topological distance from 0 to infinity, and the characteristics of zeolite frameworks are realized on those of the CCLs. However, it is also true that the CCL representation becomes very complicated with increase of topological distance and it is not always realistic as a framework characterization. In this paper, a new topological and stereochemical approach to characterize zeolite frameworks has been tried on the complicated CCLs.
93
94
M. Sato
TOPOLOGICAL COMPATIBILITY An nth CCL is defined as a set of all the points ranging from topological distance 0 to n , and all the lines responsible for the connection between them. Fig.1 shows some examples of consecutive CCLs up to the 3rd step. Both 0th and 1st CCLs are common to any kind of frameworks, but 2nd and 3rd CCLs are not. As can be seen, FAU (faujasite) can be topologically differentiated from both ANA (analcime) and LAU (laumontite) in the 2nd step, because they contain different kinds of 2nd CCLs. Also LEV (levynite) containing two kinds of CCLs is obviously differentiated from all the others in the 2nd step. ANA is differentiated from LAU in the 3rd step. These are topological criteria for characterizing zeolite frameworks. In these consecutive CCLs, it must be noted that an (n+l)th CCL is formed on the basis of nth CCLs, all of the same kind or of several kinds. Strictly speaking, an (n+l)th CCL is constructed on the basis of five nth CCLs, one central CCLs (kernel CCL) and four surrounding ones (peripheral CCLs). This can be mathematically expressed as, C(n+l,O)= C(n,O) + C(n,l) + C(n,2) + C(n.3)
+ C(n,4)
in which C(n+l,O) and C(n.0) denote the (n+l)th and nth kernel C(n,p) (p=1,2,3,4) CCLs having its origin at site 0, while denote the nth peripheral CCLs having their origins at the sites 1,2,3, and 4. Sites 1,2,3,4 are those next to site 0. The symbol + indicates coupling the clusters. Fig. 2 shows their connective FAU in Fig. 1. In this construcrelations which is realized on tion, a topological compatibility between the kernel and the peripheral clusters is required to form a new large CCL. Two CCLs are completely compatible when they overlap each other perfectly. This is the case when the same kind of CCLs have a common origin. However, if their origins are in different sites, they can overlap partially. Two different kinds of CCLs can overlap partially or hardly. Fig. 1 shows that the 2nd CCLs of FAU and ANA are partially compatible to form the 3rd CCL of LEV, but those of LTA and FAU are not.
Topological and Stereochem~calCharacteristics
0th
3rd
2nd
1st
ANA
LAU
a-
+
f
i
/
\ LEV
&
FAU
LTA
Fig. 1 Consecutive CCLs (concentric clusters) and corresponding zeolite species. ANA: analcime, LAU: laumontite, LEV: levynite, FAU: faujasite, LTA: Linde type A.
95
96
M. Sat0
C(n+l,O)
Fig. 2
Topological compatibility between a kernel and four peripheral CCLs to form a new large CCL
STEREOCHEMICAL COMPATIBILITY In addition to topological compatibility, stereochemical compatibility must be taken into consideration in the formation of real zeolite frameworks. For example, the 2nd CCL of FAU cannot be in a plane configuration, but is in two kinds of stereochemical configuration, i.e. left and right-handed. In this case, a given kernel CCL can be combined with a peripheral one ta satisfy its chirality consistency. Steric hindrance is a more important factor for the combination of CCLs, not only between kernel and peripheral CCLs, but also between two or more peripherals CCLs. Stereochemical compatibility is essential for the characterization of real frameworks. One example is shown on frameworks such as AEI (ALP04-18). AFT (ALP04-52). CHA (chabazite), EMT (hexagonal faujasite), FAU (faujasite), GIS (gismondine), GME (gmelinite), KFI (ZK-5), MER (merlinoite), PAU (paulingite), PHI (phillipsite) and RHO (rho).
Topological and Stereochemical Characteristics
97
All of these differ in framework topology [ 3 ] . However, it is noteworthy that they constitute only one kind of 2nd CCL of FAU, in which three four-membered rings are arranged to share their edges. Stereochemically, they can be characterized in two forms, L (left-handed) and R (right-handed), as shown in Fig. 3.
Fig. 3 Left- and right-handed CCLs allowed in the 2nd CCL of FAU The compatibility between a central cluster and the neighboring clusters can be realized by two symmetry operations, i.e., reflection and rotation. A rotation operation relates a central left-handed cluster with a left-handed one in the first neighbor, while a reflection operation relates a left-handed one with a right-handed one. Fig 4 shows their compatible relation at site 1. As already shown, a given kernel cluster has 4 distinct sites to combined with neighboring clusters. Thus, an L-handed kernel as well as an R-handed one has total 16 stereochemically distinct combinations of clusters. However, the steric hindrance between a kernel and peripheral clusters reduces the number to 9 (Table 1). In them, the arrangements LRLR, LRRR, RRLR are converted to those RLRL, RLRR, RRRL respectively by a symmetry
98
M . Sato
operation of rotation. Thus, only 6 combinations are allowed to form 3rd CCLs. All of them based on the L handed kernel are shown in Fig. 5. 3
I--
2
4
3
1 3
1
2
4
4
2
T I
.......... . Fig.4
Chirality compatibility between a kernel CCL (solid) and a peripheral one (dotted) in terms of rotation (L) and reflection (R)
Table 1
Stereochemically distinct combinations for both L and R kernels. The symbol + means the combinations allowed to appear as the 3rd CCL.
Topological and Stereochemical Characteristics
Fig.5
LLRR
LRLR
LRRR
RRLL
RRLR
RRRR
Six types of 3rd clusters allowed for L-handed kernel
CHARACTERIZATION OF FAUJASITE SERIES FRAMEWORKS Now, it is possible to characterize the above faujasite series frameworks in terms of the 3rd cluster types. Visual examination is very difficult to perform, because all the framework nodes should be examined as centers of the CCLs. A computer program which serves to identify cluster type has been developed for this. The result is shown in Table 2. GIS and MOR as well as FAU and AEI cannot be differentiated in the 3rd CCL, wh.ile others can be clearly differentiated. The absence of the arrangement LLRR in this table suggests that the configuration of the cluster LLRR is closed and cannot be developed further.
99
CONCLUSION The concept presented here can be widely utilized not only for the characterization of various kinds of zeolite frameworks, but also for the generation of existing and non existing zeolite frameworks. A large number of clusters may be topologically compatible, but the numbers is reduced by stereochemical compatibility. This may be the main reason why the number of real frameworks is restricted. A computer program for framework generation based on this concept is now in progress.
REFERENCES 1
2 3
W.M.Meier, Molecular Sieves, Soc.Chem.Ind.London UK, (1968), p.10. M.Sato, J.Phys.Chem.91,(1987),4675. W.M.Meier and D.H.Olson ed. Atlas of zeolite structure types, Zeolites 12,(1992),No.5.