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Diffusion in A, X, and Y Zeolites DOUGLAS M . RUTHVEN University of New Brunswick, Department of Chemical Engineering, Fredericton, N.B., Canada

Diffusion of hydrocarbons and other simple molecules in A, X and Y zeolites has been studied by a range of experimental methods including direct sorption rate measurements, chromatography and NMR. The advantages and limitations of these techniques are considered and results of recent experimental studies are reviewed with emphasis on the detailed microdynamic information obtainable by NMR. E a r l i e r studies of i n t r a c r y s t a l l i n e d i f f u s i o n i n z e o l i t e s were c a r r i e d out almost e x c l u s i v e l y by d i r e c t measurement of s o r p t i o n r a t e s but the l i m i t a t i o n s imposed by the i n t r u s i o n of heat t r a n s f e r and e x t r a - c r y s t a l l i n e mass t r a n s f e r r e s i s t a n c e s were not always f u l l y r e c o g n i z e d . As a r e s u l t the reported d i f f u s i v i t i e s showed many obvious i n c o n s i s t e n c i e s such as d i f f e r e n c e s in d i f f u s i v i t y between adsorption and desorption measurements(1~3) d i f f u s i v i t i e s which vary with f r a c t i o n a l uptake(4) and large d i s crepancies between the values measured i n d i f f e r e n t l a b o r a t o r i e s for apparently s i m i l a r systems. More r e c e n t l y other experimental techniques have been a p p l i e d , i n c l u d i n g chromatography and NMR methods. The l a t t e r have proved e s p e c i a l l y u s e f u l and have allowed the microdynamic behaviour of a number of important systems to be e l u c i d a t e d i n considerable d e t a i l . In t h i s paper the a d vantages and l i m i t a t i o n s of some of the common experimental techniques are considered and the r e s u l t s of studies of d i f f u s i o n i n A , X and Y z e o l i t e s , which have been the subject of several d e t a i l e d i n v e s t i g a t i o n s , are b r i e f l y reviewed. 9

Sorption Rate Measurements Measurement of the t r a n s i e n t adsorption or desorption curve for a sample of z e o l i t e c r y s t a l s exposed to a step change i n ambient sorbate concentration (pressure) p r o v i d e s , i n p r i n c i p l e , a simple and d i r e c t method of measuring the i n t r a c r y s t a l l i n e d i f f u s i v i t y (D). Such measurements are conveniently c a r r i e d out by g r a v i m e t r i c , volumetric or piezometric methods. The

0097-6156/83/0218-0345$06.50/0 © 1983 American Chemical Society Stucky and Dwyer; Intrazeolite Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

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diffusional time constant (D/r2) is determined by matching the experimental uptake curve to the appropriate transient solution of the diffusion equation, which, for the simplest case of a set of uniform spherical crystals subjected to a step change in con centration at time zero, is given by: mt/moo ~ 1 - ( 6 / ϊ Τ )

?

2

n-1

— n

2

. exp (-n 7T D t / r ) 2

2

(1)

2

This methods depends on the implicit assumption that the up take rate is controlled entirely by intracrystalline diffusion in an isothermal system, with all other resistances to either mass or heat transfer negligible. This is a valid approximation i f d i f fusion is sufficiently slow or i f the zeolite crystals are sufficiently large but the dominance of intracrystalline d i f f u sional resistance should not be assumed without experimental v e r i f i c a t i o n . In many practical systems, particularly with small commercial zeolite crystals, the external heat and mass transfer resistances are in fact dominant. A detailed discussion of such effects has been given by Lee and Ruthven(5-7), In order to minimize external (bed) diffusion resistance and maximize the heat transfer rate it is desirable to use a very small adsorbent sample with the crystals spread as thinly as possible over the balance pan or within the containing vessel. To minimize the effect of non-linearities, such as the strong con centration dependence of the d i f f u s i v i t y , measurements should be made d i f f e r e n t i a l l y over small concentration changes. Variation of the step size and comparison of adsorption and desorption curves provide simple tests for linearity of the system. The large differences between adsorption and desorption d i f f u s i v i t i e s , reported in some of the earlier work, have been shown to be due to the concentration dependence of the d i f f u s i v i t y ( 8 ) and in d i f ferential measurements under similar conditions no such anomaly was observed. Variation of the crystal size and/or the adsorbent sample bed configuration provide simple and direct experimental tests for intracrystalline diffusion control. As an example diffusional time constants for CO2 in several different size fractions of 4A crystals (9)

are shown in f igure 1. For the larger crystals the data conf irm intracrystalline control in a near isothermal system since the values of D/r give consistent values of D. For the smallest (7.3ym) crystals, however, analysis of the uptake curves according to eqn. 1 leads to apparent values of D/r which show an unusual concentrât ion dependence and which are only slightly larger than the values for the 21.5μιη crystals. Detailed analysis reveals that in the smallest crystals heat transfer resistance is important. Re-analysis of the uptake curves according to the non-isothermal model of Lee and Ruthven(5) leads to d i f f u s i v i t y values which are entirely consistent with the data for the larger crystals. 2

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Stucky and Dwyer; Intrazeolite Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1983.

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Chromatography In the chromatographic method a pulse or step change i n s o r bate c o n c e n t r a t i o n is introduced i n t o the c a r r i e r stream a t the i n l e t of a packed a d s o r p t i o n column and the d i f f u s i o n a l time con stant is determined from the d i s p e r s i o n of the response s i g n a l a t the column o u t l e t . Since heat t r a n s f e r i n a packed bed is much f a s t e r than i n a c l o s e d system the chromatographic method may, i n p r i n c i p l e , be used to f o l l o w somewhat f a s t e r s o r p t i o n processes. The choice between step or pulse inputs is governed s o l e l y by p r a c t i c a l convenience since the same information may be obtained from e i t h e r measurement. Although most commonly used w i t h an i n e r t c a r r i e r to measure the l i m i t i n g d i f f u s i v i t y a t low sorbate con c e n t r a t i o n s , the method may be extended to the study of d i f f u s i o n a t any c o n c e n t r a t i o n by u s i n g a mixed c a r r i e r s t r e a m ( 1 6 , 2 1 ) . The theory of chromatography depends on the assumption of a l i n e a r system w i t h d i f f u s i v i t y independent of c o n c e n t r a t i o n over the r e l e v a n t range. The v a l i d i t y of t h i s assumption may be con v e n i e n t l y t e s t e d by v a r y i n g the p u l s e (or step) s i z e . The a n a l y s i s of chromatographic data is commonly c a r r i e d out by determining the f i r s t and second moments of the response peak. This method is simple and convenient although somewhat more accurate r e s u l t s may be obtained by more s o p h i s t i c a t e d methods such as F o u r i e r transform or d i r e c t matching of the response curves i n the time d o m a i n ( 1 0 - 1 4 ) . The d e f i n i t i o n s of the moments and t h e i r r e l a t i o n s h i p to the system parameters f o r a biporous (macropore-micropore) adsorbent such as a commercial p e l l e t e d molecular sieve are given by the f o l l o w i n g equations (15,16).

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RUTHVEN

In order to determine the i n t r a c r y s t a l l i n e d i f f u s i o n time constant from a chromatographic measurement, it is necessary to ensure that the c o n t r i b u t i o n s from other mass t r a n s f e r r e s i s t a n c e s (external f i l m and macro d i f f u s i o n ) are not important. T h i s can o f t e n be achieved by reducing the s i z e of the adsorbent p a r t i c l e s . V a r i a t i o n of the p a r t i c l e s i z e provides a simple and convenient t e s t f o r the s i g n i f i c a n c e of e x t r a c r y s t a l l i n e r e s i s t a n c e . I t is i n p r i n c i p l e p o s s i b l e to e l i m i n a t e e x t e r n a l mass t r a n s f e r r e s i s tance by packing the column with unaggregated c r y s t a l s rather than with p e l l e t e d m a t e r i a l . In p r a c t i c e it is however d i f f i c u l t to o b t a i n s u f f i c i e n t l y large q u a n t i t i e s of the l a r g e r c r y s t a l s to pack any reasonable length of column. The e l i m i n a t i o n or e s t i m a t i o n of the a x i a l d i s p e r s i o n c o n t r i b u t i o n presents a more d i f f i c u l t problem. E s t a b l i s h e d c o r r e l a t i o n s f o r the a x i a l d i s p e r s i o n c o e f f i c i e n t are n o t o r i o u s l y u n r e l i a b l e f o r small p a r t i c l e s at low Reynolds number(17,18) and it has r e c e n t l y been shown that d i s p e r s i o n i n a column packed with porous p a r t i c l e s may be much greater than f o r i n e r t non-porous p a r t i c l e s under s i m i l a r hydrodynamic c o n d i t i o n s ( 1 9 , 2 0 ) one method which has proved u s e f u l is to make measurements over a range of v e l o c i t i e s and p l o t ( σ 2 / 2 μ ) ( L / v ) vs l / v ^ . I t f o l l o w s from eqn. 6 that i n the low Reynolds number region where D L is e s s e n t i a l l y constant, such a p l o t should be l i n e a r with slope D L and i n t e r c e p t equal to the mass t r a n s f e r r e s i s t a n c e term. R e p r é s e n t a t i v e data f o r s e v e r a l systems are shown p l o t t e d i n t h i s way i n f i g u r e 2(21). CF4 and 1C4H10 molecules are too large to penetrate the 4A z e o l i t e and the intercepts correspond only to the e x t e r n a l f i l m and macropore d i f f u s i o n r e s i s t a n c e which v a r i e s l i t t l e with temperature. For Ν2 which can penetrate the sieve the i n t e r c e p t is much l a r g e r and s t r o n g l y temperature dependent, as a r e s u l t of the dominance of i n t r a c r y s t a l l i n e d i f f u s i o n r e s i s t a n c e . β

2

Several systems have been i n v e s t i g a t e d by both g r a v i m e t r i c and chromatographic methods with c o n s i s t e n t r e s u l t s ( 1 6 , 2 1 ) . Since the e x t r a c r y s t a l l i n e r e s i s t a n c e s to both heat and mass t r a n s f e r are c e r t a i n l y d i f f e r e n t i n the g r a v i m e t r i c and chroma tographic systems such agreement confirms i n essence the v a l i d i t y of both experimental methods. NMR Methods The a p p l i c a t i o n of NMR to the study of d i f f u s i o n i n z e o l i t e s involves the refinement and extension of methods o r i g i n a l l y developed to study s e l f d i f f u s i o n i n l i q u i d s and low melting solids. The method is r e s t r i c t e d to species such as hydrocarbons which contain a s u f f i c i e n t l y high d e n s i t y of atoms such as Η w i t h unpaired nuclear s p i n s . A u t h o r i t a t i v e reviews of the a p p l i c a t i o n of NMR to the study of adsorbed molecules have been given by Pfeifer(22,23) d only a b r i e f o u t l i n e is included h e r e . a n

Relaxation Time Measurements The e a r l i e r NMR measurements depended on determining the c o r r e l a t i o n time f o r molecular r e o r i e n t a t i o n ( T ) which was considered as equal to the average time c


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2


21.


RUTHVEN

351

between molecular jumps. This quantity may be found from measure ments of the l o n g i t u d i n a l ( s p i n - l a t t i c e ) r e l a x a t i o n time as a f u n c t i o n of temperature. The d i f f u s i v i t y is then estimated from E i n s t e i n ' s equation (D = Χ 2 / 6 τ f o r an i s o t r o p i c cubic l a t t i c e ) using a reasonable estimate f o r the mean square jump length ( λ ? ) . Since the jump length g e n e r a l l y cannot be estimated with confidence t h i s represents a severe l i m i t a t i o n of the method. Pulsed F i e l d Gradient (PFG) S e l f D i f f u s i o n Measurement(24) This method, which was f i r s t developed by S t e j s k a l and TannerC25-26) f o r l i q u i d s , provides a more r e l i a b l e measurement of the s e l f d i f f u s i v i t y since the mean square molecular displacement, i n a known time i n t e r v a l of a few ms, is measured d i r e c t l y . A pulsed magnetic f i e l d gradient is a p p l i e d to a sample p r e pared by a radio frequency pulse of s u i t a b l e i n t e n s i t y and width. This s t a r t s the nuclear spins p r e c e s s i n g with an angular v e l o c i t y determined by the p o s i t i o n of the molecule at time zero. A f t e r a known time i n t e r v a l the gradient pulse is r e v e r s e d . If there were no d i f f u s i o n the second gradient pulse would e x a c t l y counteract the e f f e c t of the f i r s t p u l s e , l e a v i n g all spins i n phase. However, as a r e s u l t of molecular migration the c a n c e l l a t i o n is incomplete and the a t t e n u a t i o n of the s i g n a l provides a d i r e c t measurement of the mean square displacement during the known time i n t e r v a l between gradient p u l s e s . A number of c o n d i t i o n s concerning the duration of the time i n t e r v a l r e l a t i v e to the r e l a x a t i o n time must be f u l f i l l e d and the rms displacement must be l e s s than the c r y s t a l diameter (24,27). χ net r e s u l t of these l i m i t a t i o n s is to r e s t r i c t the method to r e l a t i v e l y r a p i d l y d i f f u s i n g systems (D^lO^cn^.s" ). The v a r i a t i o n i n apparent d i f f u s i v i t y with temperature and c r y s t a l s i z e is of the form i l l u s t r a t e d i n f i g u r e 3. At lower temperatures and i n l a r g e r c r y s t a l s the rms displacement is always smaller than the c r y s t a l diameter and under these c o n d i t i o n s the i n t r a c r y s t a l l i n e d i f f u s i v i t y is measured d i r e c t l y . At higher temperatures and f o r smaller c r y s t a l s the molecule escapes from the c r y s t a l during the time i n t e r v a l of the measurement and the apparent d i f f u s i v i t y corresponds to the long range e f f e c t i v e e x t r a c r y s t a l l i n e or macro d i f f u s i v i t y . In the intermediate r e g i o n there is a p l a t e a u region of r e s t r i c t e d d i f f u s i o n i n which the molecules do not have s u f f i c i e n t energy to escape from the c r y s t a l and are r e f l e c t e d from the s u r f a c e . The d i f f u s i v i t y at the p l a t e a u is simply r e l a t e d to the c r y s t a l s i z e and t h i s provides a d i r e c t check on the consistency of the method. Other simple t e s t s such as b l o c k i n g the i n t e r c r y s t a l l i n e space with CCI4 have a l s o been p e r formed i n order to confirm that the s i g n a l s are associated with i n t r a c r y s t a l l i n e rather than e x t r a c r y s t a l l i n e d i f f u s i o n ( 2 7 ) . Combining the PFG s e l f d i f f u s i o n measurement w i t h a measure ment of the c o r r e l a t i o n time provides a means of determining d i r e c t l y the mean jump d i s t a n c e . η β

1


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CHEMISTRY

Γ

1

^

τ

Figure 3. Variation with temperature of effective d i f f u s i v i t y from NMR PFG experiment for n-hexane in NaX zeolite. r=O.9ym, 0=O.49, O; r=2ym, Θ=O.39, V; r=9ym, 0=O.35, Ο and r=25ym, 0=O.29, o. ( 0 = fractional saturation; saturation capacity 215 mg/g). (Reproduced with permission from Ref. 24. Copyright 1976, Z. Chemie.)


21.


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Fast Tracer Desorption There are many z e o l i t i c systems i n which i n t r a c r y s t a l l i n e d i f f u s i o n is too slow to measure d i r e c t l y by the PFG method. A m o d i f i c a t i o n of t h i s method which makes it p o s s i b l e , under c e r t a i n c o n d i t i o n s , to measure much slower d i f f u s i o n processes has r e c e n t l y been introduced by Karger(28,29). By i n c r e a s i n g the time i n t e r v a l i n a PFG experiment an i n c r e a s i n g f r a c t i o n of the molecules escapes from the c r y s t a l d u r i n g the time i n t e r v a l of the measurement. If there is a s u f f i c i e n t l y large d i f ference between the i n t r a c r y s t a l l i n e and e f f e c t i v e extracrystalline d i f f u s i v i t i e s it becomes p o s s i b l e to determine the f r a c t i o n escaping during the time i n t e r v a l of the measurement from the v a r i a t i o n of the s i g n a l attenuation with the i n t e n s i t y of the gradient p u l s e . By v a r y i n g the time i n t e r v a l it is then p o s s i b l e to determine the desorption curve f o r the s p i n l a b e l l e d molecules under e q u i l i b r i u m c o n d i t i o n s . The d i f f u s i o n a l time constant is found by matching t h i s desorption curve to eqn. 1. Comparison with time constants measured d i r e c t l y by the PFG method provides d i r e c t evidence concerning the s i g n i f i c a n c e of any 'surface b a r r i e r ' to mass t r a n s p o r t . Comparison of NMR and Sorption D i f f u s i v i t i e s The r e l a t i o n s h i p between the transport d i f f u s i v i t y (D), as measured under n o n - e q u i l i b r i u m c o n d i t i o n s i n an uptake experiment and the t r a c e r s e l f d i f f u s i v i t y ( D ) , measured under e q u i l i b r i u m c o n d i t i o n s i n an NMR experiment, has been discussed by Ash and Barrer(30) and Karger (31,32) show that s

9

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where f represents a p o s i t i v e f u n c t i o n of the concentrations of marked and unmarked molecules and the s t r a i g h t and c r o s s c o e f f i ents of i r r e v e r s i b l e thermodynamics. It f o l l o w s that the corrected d i f f u s i v i t y (D ) and s e l f d i f f u s i v i t y are r e l a t e d b y : Q

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(6)

s

At low sorbate concentrations f-.o and eqn. 6 reduces to the f a m i l i a r Darken equation(33). i n comparing the r e s u l t s of s o r p t i o n and NMR d i f f u s i v i t y measurements it is l o g i c a l to compare D with D , even though exact agreement can be expected only at low sorbate c o n centrations. At higher concentrations one may expect D ^ D / ( l - f ) . 0

s

Q

s

D i f f u s i o n i n Type A Z e o l i t e s The channels of z e o l i t e A are obstructed by 8-membered oxygen r i n g s of f r e e diameter ^ 4 . 2 A . In the Ca form (5A) the windows are open whereas i n the Na form (4A) or Κ form (3A) the windows are p a r t i a l l y obstructed by Na+ or K i o n s . For all but the smallest +


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molecules, passage through the window is hindered by a s i g n i f i c a n t r e p u l s i v e energy b a r r i e r and d i f f u s i o n a l a c t i v a t i o n energies of s e v e r a l kcal/mole are t y p i c a l . As a consequence of the r e l a t i v e l y high a c t i v a t i o n energy d i f f u s i v i t i e s are g e n e r a l l y l e s s than about 10~8 cm2.s~l at room temperature (except f o r very small molecules i n 5 A ) . D i f f u s i v i t i e s of t h i s magnitude are s u f f i c i e n t l y low to permit r e l i a b l e determination from uptake r a t e measurements, p a r t i c u l a r l y i n the l a r g e r c r y s t a l s (20-50ym) which are e a s i l y synthesized by C h a r n e l l . s method(34). Measurement of d i f f u s i o n of C1-C4 alkanes i n 5A is a l s o p o s s i b l e by NMR methods but d i f f u s i o n i n 4A or of higher hydrocarbons i n 5A is too slow to measure by the PFG method. The behaviour of some r e p r e s e n t a t i v e systems is i l l u s t r a t e d i n f i g u r e s 4-6. The d i f f e r e n t i a l d i f f u s i v i t y g e n e r a l l y shows a strong increase w i t h sorbate concentration but t h i s is due mainly to the n o n - l i n e a r i t y If the r e l a t i o n s h i p between a c t i v i t y and c o n c e n t r a t i o n , as defined by the e q u i l i b r i u m isotherm. Corrected d i f f u s i v i t i e s , c a l c u l a t e d according to eqn. 6, are e s s e n t i a l l y constant w i t h i n the l i m i t s of experimental u n c e r t a i n t y . The d i f f u s i o n a l a c t i v a t i o n energy depends s t r o n g l y on the diameter of the sorbate molecule r e l a t i v e to the sieve window, as is to be expected i f the r e p u l s i v e energy r e q u i r e d to pass through the window is the major energy barrier. In f i g u r e 4 the van der Waals radius is used as a measure of molecular diameter b u t , although the c o r r e l a t i o n is good, it is c l e a r that shape of the molecule is a l s o important since molecules such as 1C4H10 ( σ % 4 . 4 8 Α ) and cyclohexane ( σ ^ 4 . 8 A ) cannot penetrate the 5A l a t t i c e while l i n e a r p a r a f f i n s with much l a r g e r van der Waals r a d i u s can penetrate e a s i l y . The v a r i a t i o n of d i f f u s i v i t y with i o n exchange i n the Na-CaA z e o l i t e s has been shown to be c o n s i s t e n t with a simple model based on a random d i s t r i b u t i o n of open (5A type) and p a r t i a l l y c l o s e d (4A type) windows(36). χ model p r e d i c t s a sharp change i n both d i f f u s i v i t y and a c t i v a t i o n energy at 33% Ca..+ exchange and t h i s is confirmed by the experimental d a t a . Measurements f o r a given sorbate i n s e v e r a l d i f f e r e n t 4A and 5A sieve samples show large d i f f e r e n c e s i n d i f f u s i v i t y but l i t t l e v a r i a t i o n m a c t i v a t i o n energy (9,35,36,41). D i f f u s i o n of n-butane and propane i n large C h a r n e l l 5A c r y s t a l s has been measured by both s o r p t i o n and NMR (PFG) with c o n s i s t e n t r e s u l t s (figure 5)(^1). However, the NMR measurements showed l i t t l e d i f f e r e n c e i n d i f f u s i v i t y between the small Linde c r y s t a l s and the large C h a r n e l l c r y s t a l s whereas the uptake measurements show a very large d i f ference i n d i f f u s i v i t y . T h i s and other s i m i l a r observations l e d to the suggestion that the uptake r a t e i n the small Linde c r y s t a l s may be l i m i t e d by a surface b a r r i e r rather than by a true d i f fusional resistance(27). j apparent support of t h i s hypothesis measurements of uptake r a t e s i n 5A c r y s t a l s showed a large decrease i n apparent d i f f u s i v i t y w i t h c r y s t a l s s i z e ( 4 2 ) . T h i s however appears to have been due to the i n t r u s i o n of heat t r a n s f e r r e s i s t a n c e which becomes s i g n i f i c a n t f o r the smaller c r y s t a l s . A 0

0

η β

n



RUTHVEN

3.0

4.0

5J0

355

6.0

l-butene>cisbutene(52). A c t i v a t i o n energies f o r all these species are s i m i l a r and increase somewhat with l o a d i n g . C o r r e l a t i o n times are a l s o s i m i l a r and the d i f f e r e n c e i n d i f f u s i v i t y is due to a d i f f e r e n c e in the rms jump d i s t a n c e , which e v i d e n t l y v a r i e s as a r e s u l t of d i f f e r e n t degrees of s t e r i c hindrance to passage through the 12membered 0 r i n g . Thus f o r every jump between cages, the slowest d i f f u s i n g species (cis-butene) makes, on average, about. 8 jumps w i t h i n a cage compared with only about two i n t r a cage jumps f o r trans-butene. T h i s d i f f e r e n c e is a t t r i b u t e d to the o r i e n t i n g e f f e c t of the small but s i g n i f i c a n t d i p o l e moment of c i s - b u t e n e . P a r t i a l ion exchange of Na+ f o r A g leads to a dramatic r e d u c t i o n i n d i f f u s i v i t y f o r the o l e f i n s (more than two orders of +


INTRAZEOLITE

360

CHEMISTRY

c o n c e n t r a t i o n / m g g"

1

Figure 7. Concentration dependence of s e l f d i f f u s i v i t y f o r i-octane n-heptane 7, η-octane, Φ and n-deeane at 358K. P o i n t s i n parenthesis are f o r f u l l y saturated s i e v e . (Reproduced w i t h permission from Ref. 41. Copyright 1981, J.

Chem.

Soc.)


RUTHVEN


icrV

Ol 0

ι 4

ι ι 8 12 Carbon Number

ι 16

I

20

Figure 8. Comparison of d i f f u s i v i t i e s and d i f f u s i o n a l a c t i v a t i o n energies f o r l i n e a r p a r a f f i n s as f r e e l i q u i d s and a d sorbed on NaX z e o l i t e . (Reproduced with permission from Ref. 47. Copyright 1980, J. Chem. S o c i e t y . )


INTRAZEOLITE

ο

x

n-butane

ο • Δ

n-hexane n - heptane cyclohexane

CHEMISTRY

•

Δ

X Δ

—

X Ο

Δ

a

o

x

-

χ ι

0

ι

20 40

I

60

ι

1

80 100 Loading

I

120

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I

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140 160 180

Δ

Intrazeolite Chemistry - American Chemical Society

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