Chapter 8
Influence of Autocatalytic Nucleation on Zeolite Crystallization Processes
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B. Subotić Ruder Bošković Institute, P.O. Box 1016, 41001 Zagreb, Croatia, Yugoslavia
Twenty-eight kinetics of crystallization of different types of zeolites have been analysed using kinetic equation: f = K.tq = K t3 / (1 - K t3) (f is the fraction of zeolite formed at crystallization time t , and Κ , K , K , and q are constants). The analysis showed that the exponent q is a function of the ratio between number N of the particles formed by the growth of nuclei released from the gel during its dissolution (autocatalytic nucleation) and the number N of particles formed by the growth of heteronuclei. Functional dependences between q , Κ , K , K , N , Na , K (growth rate constant) and other factors relevant to zeolite crystallization have been established and the influences of these factors on the characteristics of zeolite crystallizing systems have been discussed. z
c
c
o
o
c
a
c
z
a
a
o
o
a
o
g
There i s a l o t o f e v i d e n c e t h a t t h e c r y s t a l l i z a t i o n o f z e o l i t e s from a l u m i n o s i l i c a t e g e l s i s a solution-mediated transformation process i n which t h e amorphous phase i s a p r e c u r s o r f o r s i l i c a t e , a l u m i n a t e and/or a l u m i n o s i l i c a t e s p e c i e s needed f o r t h e growth o f t h e c r y s t a l l i n e phase (1-9). G e n e r a l l y , i t i s w e l l known t h a t t h e k i n e t i c s o f most g e l - z e o l i t e and z e o l i t e - z e o l i t e t r a n s f o r m a t i o n s can be expressed m a t h e m a t i c a l l y by t h e simple k i n e t i c e q u a t i o n (1,2, 10-12),
f
z
= K-t*
(1)
d u r i n g t h e main p a r t o f the c r y s t a l l i z a t i o n ( t r a n s f o r m a t i o n ) p r o c e s s . Κ and q i n E q u a t i o n (1) a r e c o n s t a n t s f o r g i v e n e x p e r i m e n t a l c o n d i t i o n s . On t h e o t h e r hand, many e x p e r i m e n t a l s t u d i e s o f z e o l i t e c r y s t a l l i z a t i o n have shown t h a t l i n e a r , s i z e -independent c r y s t a l growth d u r i n g the main p a r t o f t h e c r y s t a l l i z a t i o n p r o c e s s i s t y p i c a l f o r most z e o l i t e s y n t h e s e s (2,5,
0097-6156/89/0398-0110$06.00A) o 1989 American Chemical Society
In Zeolite Synthesis; Occelli, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
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8.
SUBOTIC
111
Influence of Autocatalytic Nucleation
6,12-16). I n c o n t r a s t t o more o r l e s s w e l l d e f i n e d k i n e t i c s o f the c r y s t a l growth (5,6,12-16), v a r i o u s n u c l e a t i o n mechanisms have been proposed as z e o l i t e p a r t i c l e s f o r m i n g p r o c e s s e s . Most a u t h o r s e x p l a i n e d t h e f o r m a t i o n o f p r i m a r y z e o l i t e p a r t i c l e s by n u c l e a t i o n i n the l i q u i d phase s u p e r s a t u r a t e d w i t h s o l u b l e s i l i c a t e , a l u m i n a t e and/or a l u m i n o s i l i c a t e s p e c i e s (1,3,5,7,16-22), w i t h homogeneous n u c l e a t i o n (1,5,7,17,22), heterogeneous n u c l e a t i o n (5,24), c e l l w a l l s n u c l e a t i o n (16) and secondary n u c l e a t i o n (5) as dominant p r o c e s s e s o f z e o l i t e p a r t i c l e s f o r m a t i o n , but t h e c o n c e p t s d e a l i n g w i t h the n u c l e a t i o n i n the g e l phase a r e a l s o p r e s e n t e d i n t h e l i t e r a t u r e (2,6,11,12,14,23-25). S i n c e some e f f e c t s , observed d u r i n g t h e c r y s t a l l i z a t i o n o f z e o l i t e s from g e l s , as f o r i n s t a n c e , t h e a u t o c a t a l y t i c n a t u r e o f z e o l i t e n u c l e a t i o n (2,3,12, K a t o v i c , Α.; S u b o t i c , B.; Smit, I . ; D e s p o t o v i c , L j . A. Z e o l i t e s , i n p r e s s ) cannot be r e a d i l y e x p l a i n e d o n l y by t h e c l a s s i c a l approaches t o t h e n u c l e a t i o n p r o c e s s e s i n t h e l i q u i d phase (2,6,10,12), the o b j e c t i v e o f t h i s work i s t o a n a l y s e the c r y s t a l l i z a t i o n k i n e t i c s o f d i f f e r e n t t y p e s o f z e o l i t e s by the k i n e t i c e q u a t i o n d e r i v e d on t h e b a s i s o f Zhdanov's i d e a on a u t o c a t a l y t i c n u c l e a t i o n (2), i n o r d e r t o e x p l a i n t h e i n f l u e n c e o f a u t o c a t a l y t i c n u c l e a t i o n on z e o l i t e c r y s t a l l i z a t i o n p r o c e s s e s . Theoretical
Approach
Our e a r l i e r s t u d i e s o f z e o l i t e - z e o l i t e (10,26) and g e l - z e o l i t e (11, 12) t r a n s f o r m a t i o n s have shown t h a t , under the assumption t h a t the c r y s t a l l i z a t i o n of z e o l i t e i s a solution-mediated transformation p r o c e s s (1-Θ) and t h a t t h e c r y s t a l growth i s s i z e - i n d e p e n d e n t (5,6, 12-16), t h e c r y s t a l l i z a t i o n ( t r a n s f o r m a t i o n ) k i n e t i c s can g e n e r a l l y be e x p r e s s e d a s : f
z
= f ( I ) + f ( I I ) = m (I)/m (t ) + m (II)/m (t ) = 2
2
z
2
e
z
z
e
t c GÇN
0
Kg 4 / m ( t ) + [ G § K ^ / m ( t ) ] z
e
z
e
\ (t - X ) d Ν 3
c
χ
(2)
ο The f i r s t term i n E q u a t i o n (2), i n which G i s t h e g e o m e t r i c a l shape f a c t o r o f z e o l i t e p a r t i c l e s , § i s the s p e c i f i c d e n s i t y o f z e o l i t e formed, N i s t h e number o f n u c l e i ( n u c l e i - I ) p r e s e n t i n t h e l i q u i d phase o f t h e system a t t h e v e r y s t a r t o f t h e c r y s t a l l i z a t i o n ( t r a n s f o r m a t i o n ) p r o c e s s , Kg = d L / d t , i s t h e c o n s t a n t o f t h e l i n e a r growth r a t e (and hence, L = K g t , where L i s t h e c r y s t a l s i z e a t c r y s t a l l i z a t i o n time t ) and m ( t ) i s t h e mass o f z e o l i t e formed a t the end o f t h e c r y s t a l l i z a t i o n p r o c e s s , r e p r e s e n t s t h e change i n t h e f r a c t i o n f ( I ) o f t h e mass o f z e o l i t e ( m ( I ) ) formed by t h e growth o f t h e c o n s t a n t number N o f n u c l e i - I d i s t r i b u t e d through the l i q u i d phase o f t h e c r y s t a l l i z i n g system a t t h e v e r y s t a r t o f the c r y s t a l l i z a t i o n ( t r a n s f o r m a t i o n ) p r o c e s s ( t a* 0). Hence, n u c l e i - I may be h e t e r o n u c l e i formed i n t h e l i q u i d phase by t h e r a p i d heterogeneous n u c l e a t i o n c a t a l y s e d by t h e presence o f t h e a c t i v e c e n t e r s on i m p u r i t y p a r t i c l e s always p r e s e n t i n the l i q u i d phase (27). The second term i n E q u a t i o n (2), i n which dN^is t h e Q
c
c
c
z
e
z
z
Q
In Zeolite Synthesis; Occelli, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
112
ZEOLITE SYNTHESIS
d i f f e r e n t i a l number of nuclei (nuclei-II) formed within a d i f f e r e n t i a l time dT during the c r y s t a l l i z a t i o n process and *r i s the time (0 < X < t ) at which nuclei-II appear and s t a r t to grow ( K g = dL/dT , L = K n ( t - X ) ) , represents the f r a c t i o n f (II) of the mass of z e o l i t e (m (II)) formed by the growth of number Ν·γ of nuclei-II formed by some of the time-consumed nucleation processes during the c r y s t a l l i z a t i o n . Theoretically, at the constant linear growth rate of crystals and at constant nucleation rate ( i . e . , homogeneous nucleation i n the l i q u i d phase at constant supersaturation; dN^ = K dT(28)), the solution of the second term i n Equation (2) i s (1,2,10): z
z
n
f (II) = G § K
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z
where K hence,
n
n
κ| t£/4 m ( t ) = K(II) t£ 2
(3)
e
i s the rate constant of the homogeneous nucleation, and
f
z
= G§N
0
Yi\ t|/m (t ) + G § K 2
e
n
W
κ| t^/4 m ( t ) z
e
The Equation (4) can be correlated by Equation (1) with 3 t ) and 0
Q
z
e
a
Q
z
e
c
e
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β = 6/(q+1)(q+2)(q+3)
(6)
From the set of equations: 3
K 't e /(1 - K 0
m
0
= K -t
3
Q
3
Q
t ) = m e
= 1 - K -t
e
+ m
0
3
and m
a
= 1; K - t | = 1 - K t
Q
0
= 1 - K -t
a
3
a
0
3
= K -t| ,
e
a
a r i s i n g from Equation (5) under the conditions: m ( t ) = m + m = 1 and f = 1 f o r t = t , i t can e a s i l y be calculated that the r a t i o between the mass m of p a r t i c l e s formed by the growth of nuclei-II and the mass m of the p a r t i c l e s formed by the growth of nuclei-I, contained i n the f i n a l product of the c r y s t a l l i z a t i o n process i s : z
z
c
e
Q
Q
e
Q
Q
m
/m
Q
= K /K
0
Q
(7)
Q
Since K /K Q
0
/G g Ν κ | = β Ν / Ν
=
0
α
(8)
0
(see Equation (5)), the combination of Equations (7) and (8) gives: β = N m /N m 0
Q
Q
(9)
0
showing that β i s the r a t i o of average masses of p a r t i c l e s - I and p a r t i c l e s - I I present i n the system at the end of the c r y s t a l l i z a t i o n process. The solution of Equation (6) i n q gives:
q = [3/β + (9/ β
2
- 1/27)
1 / 2
]
1 / 3
+ [*3/fl
- 2 « (6/β )
1 / 3
- (9/ β
2
- 1/27)
1/2
]
-2
and hence, i n accordance with Equation (9),
q κ [ 6 N m /N m J a
0
0
Q
- 2
In Zeolite Synthesis; Occelli, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.
(10)
114
ZEOLITE SYNTHESIS
Equation (10) shows that the value of the exponent q i n Equation (1) i s the function of the r a t i o N - m ( t ) / N · m ( t ) indicating that the numerical value of the exponent q increases with the increasing N /N r a t i o , as evidenced experimentally by the analysis of the k i n e t i c s of c r y s t a l l i z a t i o n of z e o l i t e A from d i f f e r e n t l y aged gels (12). Q
a
0
e
0
Q
e
0
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Results and Discussion Twenty-eight k i n e t i c s of c r y s t a l l i z a t i o n of different types of z e o l i t e s (A (2,12,13,35,36), X (2,6,37), L (38), Ρ (34), ZSM-5 (3941), synthetic mordenite (2,42) and o f f r e t i t e (43)), synthetized by various authors under various experimental conditions, have been analysed by using Equations (1) and (5). The numerical values of the exponent q i n Equation (1) were calculated by the slope of log f versus log t plots, and the intersections of the straight l i n e s with the abscissa represent the numerical values of log K, i . e . , log f = log Κ + q log t . In a l l the kinetics analysed, log f versus log t plots were linear up to f «0.7 - 0.8 (autocatalytic stage of the c r y s t a l l i z a t i o n process; see Figures 1 - 3), with linear correlation c o e f f i c i e n t s not lower than 0.98. The numerical values of the constants K and K i n equation (5) were calculated as average values, 2
c
z
c
z
c
z
Q
Q
n-1 H / Ζ [ i=1 j = i+1
1 / ( t
}
c J
"
1 / (
*ο>ϊ|/[
