Cation partitioning among sub-lattices in zeolites

Cation partitioning among sub-lattices in zeolites R. M.

Barrer

Physical Chemistry Laboratories, Imperial College, London S.W.7 (Received 10 May 1984) A zeolite normally provides a number of cation-bearing sub-lattices with more sites than the number of cations required to neutralize the anionic charge on the aluminosilicate framework. Partition equilibria therefore arise among sub-lattices involving one or more cations and the cation vacancies• Two situations have been considered quantitatively for aluminous zeolites. In the first the fraction ei of total cationic charge associated with any sub-lattice i is constant at constant temperature. In the second the ei vary with cationic composition. The e~ may also vary with temperature. Thermodynamic and equilibrium aspects of all these features have been developed and have been considered in relation to cation distributions in anhydrous homoionic forms of faujasite and zeolite A. Keywords: Zeolites; cations; sub-lattices;partitioning

1. I N T R O D U C T I O N In tectosilicates (zeolites, felspathoids, felspars) in which A1 or other trivalent elements replace some Si atoms in the framework one negative charge is acquired by the framework for each trivalent substituent atom. The A1m is buried in a tetrahedron of oxygens and the negative charge as 'seen' by the exchangeable counter ions of Na ÷, K +, Ca 2+ etc may be considered to be distributed fractionally among the framework oxygens to which they are attracted. Thus in the most aluminous tectosilicates with alternating A1 and Si on tetrahedral sites the effective anionic charge per oxygen averages -0.25e. This situation, describable as a more or less uniform distribution of anionic charge, is to be contrasted with that which arises in organic polymer exchangers with ionized pendant groups such as - S O 2 0 - or - C O 0 - , carrying integral negative charges neutralised by direct one to one contact with ions such as Na +, or two to one contact with Ca 2+. As the tectosilicates become richer and richer in Si the average negative charge per framework oxygen declines toward zero which is the limit for crystalline silicas having the topology of the original tectosilicate. Also the AI h~ centres which create the negative charge become on average further and further apart, and the assumption of a uniform distribution of nett anionic charge among the oxygens will become less and less satisfactory. Instead in high silica zeolites like ZSM-5 there will be localized pockets of negative charge averaging -0.25e for each of the four oxygens surrounding an AI llI. Potential sites for cations arise on various sub-lattices as a result of the framework structure but the numbers of these which are occupied on a given sub-lattice will in turn be determined by their proximity to pockets of negative charge. For zeolites there are often many more potential sites than the number of cations required to neutralize the framework charge and so cations and vacancies are distributed among sub-lattices according to the

numbers of sites provided by each sub-lattice and to site preferences. In high silica zeolites (ZSM-5, zeolite ~, ZSM-11 and the like) crystallographically possible cation sites on a particular sub-lattice may be some distance from any centre of anionic charge and so will not have a probability of occupancy. Only sites on the sub-lattices adjacent to centres of negative charge will be likely to be occupied by cations. For the most aluminous zeolites on the other hand, where AI:Si = 1:1, all sites on a given sub-lattice will be equally near to centres of anionic charge since each framework oxygen may be considered to carry the same effective negative charge. All cation sub-lattices must then be considered and all sites on each sub-lattice. However, differences in binding energy on sites in different sub-lattices may mean that cation partitioning is usually limited to a rather small number of sub-lattices. In this paper some theoretical aspects of cation partitioning will be considered in terms of the above picture, with more aluminous zeolites in mind. The results will then be considered in relation to homoionic, dehydrated exchange forms of zeolite A and faujasite. 2. P A R T I T I O N I N G OF T W O C A T I O N S The two cations A z~ and Bz~ are distributed at equilibrium among n sub-lattices and are also at equilibrium with an external solution. The overall exchange reaction is zsA~÷ + zAB~.~ ~ zsA~~"+ ZAB:~'

(1)

where subscripts 's' and 'z' refer to solution and crystals respectively and ZA and zs are stoichiometric • • numbers for the reaction. In soluuon A 72 and Bz%are m association with a common anion and in the zeolite they are in association with their equivalents of anionic framework. For exchange between solution

0144-2449/84/040361-08503.00

~) Butterworth & Co. (Publishers) Ltd.

ZEOLITES, 1984, Vol 4, October 361

Cation partitioning among zeolite sub-lattices: R. M. Barrer

and the cations on sub-lattice i the exchange reaction is zaA~÷ + zAB~~--* zBA~"¢+ zAB~~

(2)

RT

A6e = -

RT AG O = - ~ In Ki

(3)

The fraction of the total cationic charge which is on sub-lattice i is Ei where ZACiA + zBCiB

I?.i =

(4) i=l

(ZACIA + zBCiB )

where also

Kii = Kj/Ki

=

(12)

Equations 2 and 3 assume the Ei independent of Cia, Cm. The Ci.\ and Cm are the number densities of ions A "s and W", i.e. the numbers of these ions per unit volume o.fcrystal. The cation eqt, ivalent fi'action, El, of ions A ~' on sub-lattice i is (6)

with a similar expression EiB for the other cation present on i. It follows that

,,,',c e

(13)

i=l

(5)

i=l

zaCiA EiA = ZACi A + zBCiB

In Kij

ZAZB

A¢ 1

RT

AG o = -

Since the overall reaction is the sum of its parts

and

e~ =

(11)

ZAZB

and between any pair of sub-lattices i and j it is zsA~ + ZAB~~-* z.Aj'x + zAB("

In Ka

ZAZB

and K.=

f i K~'

(14)

i=l

In the equations 11-14 K,, is the overall thermodynamic equilibrium constant, Ki is that for equilibrium between the ions in solution and those on.sub-lattice i and Kii is that for equilibrium between the ions on sub-lattices i and j. When equilibrium between solution and each sub-lattice is considered one thus obtains the following set of relations

EiA + EiB = 1

a~h Finally the cation equivalent fraction overall for ions A zz is EA =

i=l

zACiA

(zACiA + zBCia)

(7)

with a like expression for EB, giving

(8)

EA + Ea = 1 It is also seen from the above expressions that EA = ~ eiEiA; EB = ~ eiEis i=l

i=l

(9)

and that

i=l

(EiEiA + eiEis) = 1

(10)

We have now to recognize two different physical situations. In the first of these the ei do not change with cationic composition of the crystal or with temperature; and in the second they do.

2.1 Partitioning w h e n the el are fixed This situation has received attention previously 1-3 and only the results need be referred to here. The equilibrium constants and standard free energies for reactions 1, 2 and 3 are respectively, per equivalent of reaction

362

ZEOLITE& 1984, Vol 4, October

~,~

- K.

a~' a~"

-

K j

( ¢ I B C I B ) z"

(qS,AC,a)""

(l~iBCiB) za (•nBCnB) z'x = Ki ((~)iACiA)Za -- ... = K,, (¢,,AC.A)'" (15)

The a in equation 15 are activities of ions A 7x and B ~' in solution (subscripts 'sA' and 'sB') and in the crystals (subscripts 'A' and 'B'). The dPi:xand qbiB are non-ideality factors for the two ions on sub-lattice i where i = 1 to n. They allow for non-ideal mixing of the ions on the sub-lattice and are the equivalent for sub-lattice i of the overall activity coefficients of the ions in the crystal 4. For convenience and brevity we write IJPiACiA = aiA and (DiBCiB = am. The separate equations embodied in equation 15 can be combined to give a~i' K,, a~"

i=l

Ki am ~--~

(16)

aiA

so that from equations 14 and 16 one finds how the ZA ZB ratio aB/aA for the whole crystal is related to the ratios for each sub-lattice: a~" -

l-I

\ai~

(17)

Explicit expressions for the equilibrium constants of the set of relations in equation 15 can be derived using statistical thermodynamic procedures 5.

Cation partitioning among zeolite sub-lattices: R. M. Barrer

2.2. P a r t i t i o n i n g w h e n t h e ei are f u n c t i o n s o f cationic composition The standard free energy of exchange, is the free energy change on going from the standard states of B-zeolite and of solution containing ions A ~¢ to the standard state of A-zeolite and solution containing ions B eB reversibly and isothermally through the equilibrium state. The standard state of the B-zeolite is its homoionic form in equilibrium with infinitely dilute solution containing ions B e" and an analogous definition holds for A-zeolite. For the aqueous solutions the usual definitions apply 2. Then the first of equations 11 applies whether or not the ei are functions ofcationic composition. However, we can no longer use equation 13 (2kG° = Z~=l eiAGi°) when the el vary with the composition, even though the complete exchange reaction remains the sum of its parts. Let ei0A be the value of el for the homoionic A-zeolite and ei°B be this value for the homoionic B-zeolite, where eiaA ~ ei0B, but where

i=l

eiO~ =

the 24 sites of type 1 and the water molecules occupy the 16 sites o f t y p e 28. When Na + is exchanged by K or Cs + to give leucite or pollucite respectively the K + or Cs + removes the water molecules from sites of type 2 on a 1:1 basis and in the homoionic forms these ions occupy all 16 type 2 sites per unit cell 9'1°. The resultant leucite and pollucite have the same framework topology as analcime. In section 3, when catiori partitioning in homoionic forms of zeolite A and of faujasite is considered, we will see how far and for what cations the ~ may be regarded as constant and for what cations the ei change with composition. If the ei do change with composition one may consider an exchanger such as analcime that provides two cation sub-lattices, and express the change in ei for the first of these sub-lattices as a polynomial in EA, the equivalent cation fraction of ion A ' . Then since el + e2 = 1 (equation 5) el = a + b E A + CE2A+ ... e 2 = 1 - a - b E A - cE~x- ...

1 J

(20)

(18)

~ ei0B = l l'=l

In homoionic A-zeolite where EA = 1

Then equation 13 is replaced by

AGO=

el = e ° A = a + b + c + e 2 = e0A= 1 -- a - - b -

e0, i=l

ZA

i= I

-

g0A)/ZA

ZA

-

(21)

( 19)

where kt°a and gOA are standard chemical potentials of ions B z" and A " in solution and G~m and G~iAare the standard state contributions per g. ion of the cations B e" and A "2 on the i th sub-lattice to the standard free energy of the whole crystal. It is emphasised, in view of past confusion, that neither in equations 11-17 nor in equation 19 are fictitious and non-existent chemical potentials of ions on each sub-lattice involved in formulating thermodynamic equilibrium relationships. It has been pointed out that ascribing chemical potentials to ions on sub-lattices can lead to incorrect conclusions 7. Ions A ~¢ and B ~" on a sub-lattice do not constitute independently variable components of the system as required in the definition of chemical potential 4'3'7. The contribution to AG o from that part of the overall exchange involving sub-lattice i is 0 0 eiA(GiA

} J

In homoionic B-zeolite where EA = 0

0

ZB

...

ZB

I'tsA

+

... c-

~o (~0 ~ i a , - i a

-

g0B)/ZB

This means, per equivalent of total cations in the zeolite, that rio\ equivalents of A "¢ displace ~i° equivalents of B z" from sub-lattice i where ei0A~ eia. The disbalance on sub-lattice i on going from one homoionic state (B-zeolite) to the other (A-zeolite) is 0 and eja O for compensated by the unequal values of ejA A " and B"" on other sub-lattices such as j. An extreme example of a zeolite in which ei0A ~ ei0~ is found in analcime. In this zeolite there are two cation sub-lattices, one providing 24 possible sites per unit cell (type 1) and the other p.roviding 16 (type 2). In an analcime having unit cell composition Na16[AIj6Si32096]16H20 the Na + ions occupy 16 of

el = et°a = a ~ 2 = e°13 = (1 - a)

} J

(22)

Equation 19, on substituting for e~,.x, E?B, E20A, E2B, 0 becomes AGO = (a + b + c + ...)GOA/ZA + (1 -- a -- b - c -

...) G~2A/ZA

- aG~tB/ZB -- (1 -- a)G~zB/ZB 0 0 + ~l,sB/Z B -- gsA/ZA

(23)

When el and e2 are independent of EA the coefficients b, c, ... are all zero and so equation 19 becomes A G O = aG01A/ZA + (l -- a)G~2A/ZA -

aG~lB/zn

-

(1

-

a)GOB/zB

+ ~ts0B/ZB -- ~,sA/ZA 0

(24)

Accordingly the difference of the two free energies for ZAZ~ equivalents of exchange (equation 1) is ZAZaSGO = zB(b + C + ...)(GOA - G~A)

(25)

2.3. P a r t i t i o n i n g w h e n t h e ei are f u n c t i o n s o f temperature In many crystals such as spinels, garnets and various silicates all sites on cation sub-lattices are occupied so that for mono-cationic phases, or when

ZEOLITES, 1984, Vol 4, October

363

Cation partitioning among zeolite sub-lattices: R. M. Barrer

ZA = Za the ei cannot change with temperature. However in zeolites where cation vacancies arise on sub-lattices there may be redistributions of cations among these sub-lattices as the temperature changes which modify the thermodynamic and other properties. From equation 19 one may obtain the effect of temperature on the standard entropy, enthalpy and heat capacity changes per equivalent of exchange respectively:

neutrality condition imposes the further requirement that

i=l

(aE?A/aT)r = 0

and Y,, (0eioB/0T)p = 0.

i=l A:

=

aZA_ ,.,:,._ Za

i=l L.

+ \aTlp

When the eiaA and SlOBdo not depend either on temperature or on cationic composition ei0A= ei0B= el and the equations 26-28 reduce to

\ aT ]p zA

+ A~(T)

(26) AgO=

z~iB B) + AS°(T)

i=li Ei \zA(S~iA

(31)

A/_/s = ~ [elaA H~iA_ e~a /-~ia _ T (aeiaA~ G~\ i=l , ZA ZB \ aT ]p Z A i=~ \ Za

(aeieB'/ GliB] +

A/-/~(T)

zs

(32)

(27)

+ T \ a T ] v Za_l

AC~p= ,=,~]e'('Z~--~AA Z~'~BB)+ AC~(T) A C~p = ~ i=l

e~\

"'ZA

ei~a

+ 2T

ZB

"" \ a T / p ZA

while equation 19 reduces to AGO

(aei°a'~ ~B 2T \ a T / p zs

T

(33)

=

Ei

i= I

(:A

__

:.) ZB /

\ ZA

_.[..

~sB

°

~0\

ZB

ZA

(34)

\ a T ' } I, ZA n

which is identical with equation 13 because ~i=tel = 1 and + T \'-~]p

za 3 + AC~s(T) (28) ZB

Ge,

In these expressions the S~i, H~i and C~i all refer to one g. ion of A "s or B~'. AS~, A/-/~ and A C~ are respectively the differences in standard state entropy, enthalpy and heat capacity per equivalent of each exchange ion in solution. If Q~" denotes in turn ~ , and C~ per g. ion and corresponds with AS~, A/-/~ or AC~ per equivalent then =

Q B/zB

--

0

(29)

Q~A/ZA

The el, Gi°, S~i, H~i and C~i may all change in part as a result of loss of zeolite water with rising temperature. If Cw is the number of water molecules per unit volume o4" zeolite crystal the combined effect on a quantity x = x (T, P, Cw) of change in temperature and change in Cw is given by

:/ p =

., i "[" C~

/.rp\

(30)

aT /l,

at constant total pressure, P. Constant Cw represents the behaviour along the sorption isostere for water in the zeolite. The total pressure, P, can be maintained constant along the isostere by means ofan inert piston gas. When x = ei°,\ or rob in equation 30 the electrical

364 ZEOLITES, 1984, Vol 4, October

\ ZB

zA /

Finally, re-distribution of cations among sublattices may result from heating the anhydrous zeolite. If the exchange can be effected by heating together water-free zeolite powder and anhydrous salts of the exchanging cations it could be convenient to choose in place of the standard states of section 2.2 the anhydrous homoionic forms, A-zeolite and B-zeolite, and the pure crystalline salts of the cations A z' and Bz". With this choice the meanings of the thermodynamic quantities change appropriately but the equations developed in this section remain valid.

2.4. F o r m stants

of

partitioning

equilibrium

con-

We consider a mixed (A,B)-zeolite. At distribution equilibrium of ions A "^ between any two sub-lattices i andj the rate at which ions A~¢leave sites they occupy on i and occupy available vacant sites onj must equal the rate at which these ions leave sites onj and occupy available vacant sites on i. In the simplest situation all vacant sites on i or onj are freely and equally available and detailed balancing gives for ions A z'

Cation partitioning a m o n g zeolite sub-lattices: R. M. Barrer kijA~iACiA(Cj

-- q A

-- CjB)

(36)

= kjIACjACjA(C i -- CiA -- CiB )

In equation 36 the kijAand kjiAare rate constants for the forward (i to j) and reverse (j to i) cation jumps. Ci and Cj are the total numbers of sites on sub-lattices i and j respectively per unit volume of crystals. The equilibrium constant for partitioning is then k!jA

= qbiAC,iA(Ci

-

-

CiA -- CiB )

qbjA0iA(1 -- 0iA -- 0iB ) qbiA0ia(1 - 0ja -- 0js)

(37)

The 0 are the degrees of occupation of sites by cations (e.g. 0iA = CiA/Ci). Similarly for ions B':" the equilibrium constant for partitioning can be given by replacing each subscript 'A' by 'B'. The 0 and hence the KijA or KijB are determined by the requirement that at equilibrium their values must be such that the free energy of the whole crystal is minimised and that electrical neutrality is maintained overall. The simplest partition equilibrium quotient expressed in equation 37 may need modification in some real systems where sites on one sub-lattice are so close to those on another that if a site on one of these sub-lattices is occupied those adjacent to this site on the other have little or no probability of being occupied. Such a situation arises in zeolite A and in faujasite and is considered in Section 3.

3. PARTITIONING IN HOMOIONIC DEHYDRATED FORMS OF ZEOLITE A AND FAUJASITE Zeolite A and faujasite (variants X and Y) have been the subjects of many structural studies in which cation distributions have been investigated. Only homoionic dehydrated forms will be considered because here there is least ambiguity in the results. The important sub-lattices for cations are given in Table 1, together

with the number of sites per pseudo-cell with ~ 12.3/k for zeolite A and per unit cell with ~24.7~, for faujasite. In the nomenclature used by Mortier 12 the number following the roman numeral gives the narrowest window (6-, 8- or 12-ring) which limits access to the site. Table 2 gives some reported distributions in zeolite A for homoionic dehydrated Na-, K-, Tl-, Zn-, Cd-, Eu-, Ca- and Sr-forms. It is apparent that few of the results are suitable for evaluating partition coefficients because they are usually rounded numbers corresponding with saturation of sites $2 (or $2") and sites S1, with a minor spill over into sites $3. As the best values so far available we take the Na populations in the last row of the results for Na-A, and the average of the last two rows for K-A. If the ratios of the non-ideality coefficients ~ are taken as unity equation 37 (with 0iB = 0 and 0jB = 0) gives as values of partition coefficients (Ks3,S2)Na = 5 . 0 × 102

(Ks3,Sl)Na = 4.1 X 10~

(Ksl,S2)Na = 1.22

(Ks3,s2.)K = 6.2 × l02

There is a strong preference for sites in or against 6-rings ($2,$2") and in 8-rings (SI) over sites against 4-rings. The divalent ions are also strongly associated with the 6- and 8-ring sites. The nearness ofsites $2, $2' and $2" to each other, and the cation populations in Table 2, suggest that if one of these sites is occupied by a cation its two near neighbours will have little chance of being occupied. Thus of a total of 24($2 + $2' + $2") sites per pseudo-cell only a maximum of 8 will be occupied. The blocking effect sites of types $2, $2' and $2" exert on one another makes them what may be termed a linked group. In faujasite one expects two linked groups by reason of site proximity. One comprises sites of types II, II' and II* in or adjacent to the single 6-rings. Per unit cell each provides 32 sites but, if total mutual blocking occurs, out of the total of 96 sites not more than 32 will be occupied. Table 3, which gives reported site populations of cations in homoionic dehydrated

Table 1 Examples of sub-lattices in zeolite A and faujasite Site type

(a) Zeolite A In 8-rings In 6-rings In sodalite cage by 6-ring In 26-hedron by 6-ring

Against 4-rings in 26-hedron In centre of Sodalite cage (b) Faujasite In hexagonal prisms In plane of 6-ring of prism In sodalite cage by 6-ring of prism In single 6-ring between sodalite cage & 26-hedron In sodalite cage by single 6-ring In 26-hedron, by single 6-ring Centre of sodalite cage Against 4-rings of 26-hedron At centre of 26-hedron In 12-rings

Number

Naming Barrer 11

Mortier lz

3 (pseudo-cell) 8

$1 $2

8

$2'

III II II

8

$2"

12

$3

1

SU

16 (per unit cell) 32 32 32

32 32 8 48 8 16

I I" I' II I1' I1" U III IV V

II IV V

8 8 6 8 8 6 6

6 6 12

6 12 V 6 IV 12 IV 12 IV 12

ZEOLITES, 1984, Vol 4, October 365

Cation partitioning among zeolite sub-lattices: R. M. Barrer Table 2

Reported cation distributions (numbers per pseudo-cell) in homoionic forms of dehydrated zeolite A

$2

$2"

8Na 8Ne 8Na 7.7sNa 1K

$2'

8K 7.7K 7.74K 7TI 3Ca

1Ca 3Sr 3.0Cd" 3 EuIL 4.0 Zn

$1 4Na 3Na 3Na 2.9oNa 3K 3K 3K 3TI 1Ca 3Sr

1TI 1Ca

1.5Cd n

1.5Cd" 1 Eu" 2.0 Zn

References

$3

13 14 15 16 17 18 18 19 20 20 21 22 23

1Na 1Na 0.78sNa O.4K 0.65K

1 Eu"

Table 3 Unit cell populations reported for some dehydrated homoionic faujasites Distributions on sites Cations per unit cell

Cations located

57 Na 57 Na 58 Na 81 Na 48 K 53 K 55 K 57 K 70 K 87 K 57 Ag 27 Ca 27.Ca, 3 Na

57.5 50.2 52.8 74.8 46.6 53.2 50.3 56.2 54.9 48.4 54.9 28.2 28.6 (as Ca) 24.6 15.6

28 Cu" 19 Lam

I 7.7 7.0 9.3 3.8 6.4 8.6 5.4 12.0 9.4 9.2 16.0 14.2 13.9 1.5 11.5

I"

I'

II

I1'

19.5 13.8 16.7 11.3 14.1 13 18.1 14.2 13.6 13.6 10.6 2.6 4.3

21

11.4

2.8 2.6

II*

III

30.3 29.4 31.3 30.8 26,1 31.6 26.8 30.0 28.9 25.6 28.3 11.4 10.4 3.8

1

1.5, 5.3~ a 1.5b

References 24 25 26 26 27 28 27 24 27 27 24 29 30

3.3

26 31

=The symbol @ here denotes 'an oxygen-bearing species' bPlus 2.9~ at U

lhujasites, confirms that this is so. T h e second linked g r o u p is associated with the h e x a g o n a l p r i s m s and consists ofsites I, I ' a n d I" (Table 1) with 16, 32 and 32 sites per unit cell respectively. M u t u a l blocking will h o w e v e r limit site o c c u p a t i o n again to not m o r e than 32 as the T a b l e confirms with one exception. T h e interference effects a m o n g the linked site groups can be quantified a s s u m i n g total m u t u a l blocking. T h u s for faujasite we will use the notation below:

which consists of linked sites I, I ' and I" is e m p t y is then taken as p r o p o r t i o n a l to (32Nc - Ci.~ - CjA Ck.\). Similarly the chance that a g r o u p site which consists of linked sites II, I I ' a n d I I * is e m p t y is a s s u m e d to be p r o p o r t i o n a l to (32N,. - CL.~ - C,,,.~ C,A) p r o p o r t i o n a l to (32N,. - Cia -- C,,,A -- Ck:\). At e q u i l i b r i u m b e t w e e n sites I and I I the rate o f j u m p i n g from I to II equals this rate from II to I. T h u s *

Site types On sub-lattices Concentrations of sites Concentrations of A nt on sites Non ideality Cofficients

= ktiAdolAClA(32Nc - - C i A -- CjA -- CkA )

I i C~

I' j Ci CiA

I" k Ck CkA

II I Ci CIA

I1' m Cm CmA

I1" n Cn CnA

~iA

~)jA

(~)kA

(~IA

(~)mA

~)nA

Ci

F r o m Table 1 it is seen that 2Ci = Cj = Ck = 32N~ a n d that Ct = C m = C , , = 32N,- w h e r e N~ is the n u m b e r of unit cells per unit v o l u m e of crystal. As a simple a p p r o x i m a t i o n we will regard each linked site g r o u p as a single g r o u p site o f which there are 32 of each kind per unit cell. A g r o u p site is considered to be filled by one cation. T h e c h a n c e that a g r o u p site

366

ZEOLITES, 1984, Vol 4, October

kilAdOiACiA(32Nc -- CIA -- CmA -- C,,A) (38)

For the e q u i l i b r i u m c o n s t a n t Kil..~ kilA dplA0~A(2-- 0iA -- 20i..X -- 20kA) • -- kliA -- q~iA0iA(l -- 01:X -- 0,.A -- 0,,A) (39) O n sites of t.vpe i 0i.\ = Ci.\/16N,; [br all other types of site 0 = C / 3 2 N c w h e r e C is the relevant c o n c e n t r a *The k,A and k,A include the fractions of the total numbers of linked sites composing each group site which are of type II and of type I respectively. These fractions are 1/3 for k,A and 1/s for k,A.

Cation partitioning among zeolite sub-lattices: R. M, Barrer

tion. For partition equilibrium between sites I and I I ' or I and II* subscript T in eqn. 39 is replaced by 'm' or 'n' respectively, except for the term in the bracket. I f t h e partition is between I' and II the equilibrium constant is -- (~IA01A (2 - 0iA -- 20iA -- 2 0kA ) KjlA -- 2 (~jA 0jA (1 -- 01A -- 0mA -- 0hA ) (40) while for partition between I' and II' or II* subscript T in equation 40 is again replaced by 'm' or 'n' except for the bottom term in the bracket. One may proceed similarly to obtain partition constants between I" and I I , I I ' or II*. Within a particular linked group one obtains the following equilibrium constants: ~jACiA = 2qbj.\0jA " Kij A = ¢iACiA dt)i.,\0iA ' Kik A

2¢k.,,0kA =

;

(DiA0iA

Kin A -

dl)kA0kA

,l,j,,%

KImA --

(DmA0mA (DIA01A

¢.A0.A (DIA01A

(41)

~nA0nA

'

¢m,,0..A

For several of the faujasites of Table 3 and the preceding modelling of partition equilibria one obtains the selectivity ratios given below: Faujasite unit cell with:

~iA KiiA/~iA (I, I')

~AK,.A/~.A (I, I1")

q~iAKinA/~.a (1'. ll*)

57Na c24t 57Na 125~ 57K Iz4~ 57Ag 124~ 27Ca Izgj 27Ca, 3Na qa°~

2.53 1.97 1.1a 0.66 0.18a 0.309

11.1 18.0 7.3 2.5e 0.59 0.48

4.4 9.2 6.1 3.9 3.24 1.5s

As with zeolite A, through lack of highly accurate experimental results, the above results are only semi-quantitative. However, among the examples chosen, which all have comparable exchange capacities, trends are observed. The selectivity ratios between sites I and I' are in the sequence: Na > K > Ag > Ca with I preferred for Ag and Ca and I' for Na and K. The selectivity ratios between I and II* are in the same order and probably so are those between I' and II*. In the latter case sites II* are preferred for all the ions while in the former these sites are preferred for all save Ca. A factor controlling the cation population of a linked group of sites is the amount of negative charge accessible for neutralization by cations on that group. For those faujasites of Table 3 which have like exchange capacities (55 to 58 charges per unit cell) the amounts of positive charge per unit cell on the linked site group I + I' + I", i.e. in or adjacent to hexagonal prisms, are as follows: 27.2 26.0 23.5 26.2 26.6 25.9

(57Na) (58Na) (55K) (57K) (57Ag) = mean

33.6 36.4 31.4 33.5

(27Ca) 42.3 (19La) (27Ca, 3Na) (28Cu ll) = mean

The figures in brackets are the numbers of the named cations per unit cell. Thus on the linked group I + I ' + I" cations A +, A 2+ and A 3+ neutralise respectively about 45, 61, and 74% ofthe total anionic framework charge, leaving about 55, 39 and 26% to be neutralised by cations nearly all on the linked sites associated with single 6-rings, especially on sites II* (Table 3). As the charge on the cation increases the negative charge thus appears to be neutralised increasingly by sites I + I' + I". This may in part be due to polarisation of O ~-. From the above figures and those in Table 3 it is seen, for Na, K and Ag in dehydrated faujasites of similar exchange capacities, that the fractions ~8 of cationic charge associated with the linked groups I + I' + I" and II + II' + II* are rather constant. In dehydrated zeolite A the same is true of the S1 sites associated with the 8-rings and with the linked group $2 + $2' + $2" (Table 2). Thus at least for some pairs of monovalent ions the treatment of exchange of A + and B + between such groups in each of which e is assumed constant is a reasonable approximation. However, when the two ions have difli~rent charges the e° are different and so the e Ibr the (A,B)-zeolite change with cationic composition, as considered in Section 2.2. 4. D I S C U S S I O N

For the examples of dehydrated homoionic forms of faujasite and zeolite A considered in Section 3 the differences between analytically determined cation contents and those found in the X-ray structure measurements are not large. Among hydrated forms of faujasite on the other hand the discrepancy between numbers of cations located and numbers present are usually substantial. An exception is a hydrated Na-faujasite with 81 Na per unit cell 32. In this example the cation populations on the linked site groups I + I' + I" and II + II' + II* were reported respectively as 30.5 and 32. Thus even in this very cation-rich form of faujasite the cation populations still do not exceed the values expected from the theoretical treatment of linked groups given in Section 3. In a limited number of examples comparisons can be made between cation distributions in hydrated and dehydrated homoionic forms of the same zeolite. In TI-A 19 and also for C d - A 23 the distributions reported were the same, although the water contents of the 'hydrated' forms were not given. In C a - A 33 of specified water content all six Ca 2+ ions were on sites associated with 6-rings and in the dehydrated form 2° five of the Ca 2+ were reported to be on these sites. Finally it is seen from a survey of the literature that accuracy in locating extra-framework ions and water molecules in zeolites has often been poor. In order to advance quantitative understanding of cation partitioning among sub-lattices, both in homoionic forms of zeolites and in mixed (A,B)-zeolites, experimental studies must provide accurate cation populations among linked site groups and among sub-lattices for as many cationic forms as possible in a range of different framework topologies. Statistical thermodynamic formulation of the pre-

ZEOLITES, 1984, Vol 4, October 367

Cation partitioning among zeolite sub-lattices: R. M. Barrer

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