Diffusion in Molecular Sieves: A Review of Recent Developments

27 Diffusion in Molecular Sieves: A Review of Recent Developments DOUGLAS M. RUTHVEN

Downloaded by UNIV OF PITTSBURGH on May 4, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0040.ch027

Department of Chemical Engineering, University of New Brunswick, Fredericton, N.B., Canada

ABSTRACT Recent information concerning the diffusion of a range of non-polar molecules in representative types of molecular sieve is reviewed. The general relationships between the pore structure of the sieve, the dimensions of the sorbate molecule and the diffusion behaviour are emphasized. Results of sorption and NMR diffusion measurements are compared. Introduction The structural regularity of zeolite frameworks makes possible detailed studies of the relationship between pore geometry and transport properties and this feature has attracted much research. A general review of the information available to 1970 was presented at the Worcester Conference by Barrer(lj and i t i s the purpose of the present paper to summarize only the more recent developments. The systems selected for discussion are mainly those which we have studied at the University of New Brunswick but these systems are i n a general way representative of the systems of industrial interest. The bidisperse nature of commercial molecular sieve pellets is considered i n some detail elsewhere in this conference!2>3). The present paper deals only with intracrystalline (micropore) diffusion since this i s where the relationships between structure and transport properties are observed. Nevertheless i t must be emphasized that the rate of sorption in a molecular sieve i s not always controlled by intracrystalline diffusion. Sorption and Chromatographic Measurements Refinements of the standard gravimetric method(_l) for determining d i f f u s i v i t i e s from transient sorption measurements include the introduction of a correction factor to account for crystal size distribution and the use of small d i f f e r e n t i a l steps

320 In Molecular Sieves—II; Katzer, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


27.

Diffusion in Molecular Sieves

RUTHVEN

321

to study systems i n which the d i f f u s i v i t y i s c o n c e n t r a t i o n de pendent (JO. Of the p r e c a u t i o n s necessary t o o b t a i n r e l i a b l e r e s u l t s the most important i s v a r i a t i o n o f the sample s i z e or bed c o n f i g u r a t i o n , since t h i s provides a d i a g n o s t i c t e s t both f o r macro d i f f u s i o n a l r e s i s t a n c e o f the bed and thermal effects(.5). Chromatographic methods have a l s o been a p p l i e d t o z e o l i t i c systems. The spread o f the response peak i s determined by the com bined e f f e c t s o f mass t r a n s f e r r e s i s t a n c e and a x i a l d i s p e r s i o n . In order t o determine micropore d i f f u s i v i t i e s the e f f e c t s of macropore and f i l m r e s i s t a n c e as w e l l as a x i a l d i s p e r s i o n must e i t h e r be e l i m i n a t e d o r allowed f o r i n the a n a l y s i s . The method o f Eberly(_6.) depends on the van Deemter equation (χ) r e l a t i n g p l a t e height (HETP) t o gas v e l o c i t y : HETP = A + B/u + Cu

(1)

The constant C which may be determined from the l i m i t i n g slope o f a p l o t o f HETP v s u, i s r e l a t e d t o the macropore and micropore d i f f u s i o n a l time constants. The i n d i v i d u a l time constants may be separated by u s i n g e i t h e r p a r t i c l e s o f d i f f e r e n t s i z e or d i f f e r e n t c a r r i e r eases The method o f moments has a l s o been w i d e l y When 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 a l r e s i s t a n c e i s s i g n i f i c a n t the peaks show pronounced t a i l i n g making accurate e v a l u a t i o n o f the second moment d i f f i c u l t . This d i f f i c u l t y may be avoided by c a l c u l a t i n g the model parameters ( i n p a r t i c u l a r the time constant f o r 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 /D) by matching e i t h e r the Laplace or F o u r i e r transforms (12-15). I t i s g e n e r a l l y assumed t h a t the b a s i c assumptions o f the chromatographic method ( l i n e a r isotherm, constant d i f f u s i v i t y ) w i l l be f u l f i l l e d provided t h a t the sorbate p u l s e i s s u f f i c i e n t l y s m a l l . However, f o r c e r t a i n systems, i n c l u d i n g those s t u d i e d chromatographically by Eberly(jO (Ar-5A, Kr-5A, SFg-13X), g r a v i metric s t u d i e s have shown t h a t even w i t h i n the Henry s Law r e g i o n the d i f f u s i v i t y i s s t r o n g l y dependent on connentration(l6>17): 2

1

D

= D /c ; D O = D * e ?

0

f

E / R T

( )

0

2

1

W i t h i n the Henry s Law r e g i o n c = Kp and Κ v a r i e s w i t h temperature according t o a vant Hoff equation ( K = KQ exp(q /RT)) so t h a t : 0

D =

(DVKQP)

exp[ -(E+q )/RT] Q

(3)

The p r e c i s e value o f the i n t e g r a l d i f f u s i v i t y determined i n a chromatographic experiment w i l l depend on the p u l s e s i z e but i t i s c l e a r from eqn. 3 t h a t i f the pulse s i z e i s kept constant and the temperature v a r i e d the apparent energy o f a c t i v a t i o n ( E ) w i l l be g i v e n by E = E+q . As may be seen from Table 1, E b e r l e y s chromatographic values o f Ea agree w e l l w i t h the values o f Ε + q from the g r a v i m e t r i c s t u d i e s , i n d i c a t i n g t h a t the discrepancy a r i s e s from the assumption o f a constant d i f f u s i v i t y i n the a n a l y s i s o f the chromatographic data. The d i f f u s i o n of Ar i n kA sieve was s t u d i e d chromatograph i c a l l y by Sarma and Haynes For t h i s system the assumptions a

f

a

0

Q

In Molecular Sieves—II; Katzer, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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of a l i n e a r isotherm and constant d i f f u s i v i t y are v a l i d and the chromatographic data agree w e l l w i t h the e x t r a p o l a t e d s o r p t i o n data of Eagan and Anderson(l8) and Ruthven and Derrah(l6). These c o n d i t i o n s should a l s o "be f u l f i l l e d f o r the d i f f u s i o n of n-butane i n 5A sieve at low concentrations but the chromatographic d i f fus i v i t i es of Hashimoto and S m i t h ( l l ) are s e v e r a l orders of magnitude l a r g e r than the g r a v i m e t r i c values (19). The discrepancy may be r e l a t e d t o the d i f f i c u l t y of e v a l u a t i n g the second moments of the chromatographic peaks. This problem i s compounded by the need t o e x t r a p o l a t e the second moment values i n order to e l i m i n a t e the l a r g e c o n t r i b u t i o n s from macropore r e s i s t a n c e . TABLE I - Comparison of Values of Ε + q^ w i t h Apparent A c t i v a t i o n Energies from Chromatographic Data q* S y S t e m

Et (kcal)

o

(kcal)

Ar-5A Kr-5A SFg-13X

Ε + q (kcal)

a

(kcal)

3.h

«1 2.0 2.8

3.3 3.6 5.0

E t

0

5.6 7.8

3.5 5.9 7.5

* Values of q from E b e r l y ^ at high temperatures. t Value of Ε c a l c u l a t e d according t o eqn. 2 from g r a v i m e t r i c data. t Apparent a c t i v a t i o n energy from chromatographic measurements (6). Q

The advantage of the chromatographic method l i e s i n the s i m p l i c i t y of the apparatus and the r a p i d i t y w i t h which measure ments can be made. Macropore d i f f u s i v i t i e s can be determined with accuracy since v a r i a t i o n of p a r t i c l e s i z e and c a r r i e r gas provide a simple means of v a r y i n g macropore r e s i s t a n c e but the determina t i o n of 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 i e s i s more d i f f i c u l t . Corrected D i f f u s i v i t i e s and Tracer

Diffusivities

From simple thermodynamic c o n s i d e r a t i o n s i t may be shown that the r e l a t i o n s h i p between the F i c k i a n d i f f u s i v i t y (D) and the c o r r e c t e d d i f f u s i v i t y (D ) d e f i n e d i n terms of a chemical p o t e n t i a l gradient d r i v i n g f o r c e , i s given by: 0

D = D (dlna/dlnc) = D (dlnp/dlnc) 0

0

(U)

The second of these equations i n v o l v e s the a d d i t i o n a l assumption of an i d e a l vapour phase. For l i q u i d phase systems i t has been c l e a r l y shown that the chemical p o t e n t i a l g r a d i e n t , r a t h e r than the c o n c e n t r a t i o n g r a d i e n t , i s the t r u e d r i v i n g f o r c e f o r d i f f u s i v e transport(20,21). p o l i t i c systems the e q u i l i b r i u m i s o therms are, i n g e n e r a l , h i g h l y n o n - l i n e a r so t h a t the c o r r e c t i o n f a c t o r dlna/dlnc i s o f t e n l a r g e . When c o n s i d e r i n g the v a r i a t i o n of d i f f u s i v i t y w i t h the p h y s i c a l p r o p e r t i e s of the sorbate or sieve i t i s t h e r e f o r e e s s e n t i a l t o examine the behaviour of D . Although D i s i n p r i n c i p l e a f u n c t i o n of c o n c e n t r a t i o n , the o r

z e

0

0


27.


RUTHVEN

323

c o n c e n t r a t i o n dependence w i l l g e n e r a l l y be l e s s pronounced than that o f D. From the p r i n c i p l e s o f i r r e v e r s i b l e thermodynamics i t has been shown by Ash and Barrer(22) t h a t the d i f f e r e n t i a l d i f f u s i v i t y measured i n a s o r p t i o n experiment (D) i s r e l a t e d t o the t r a c e r s e l f d i f f u s i v i t y {V) by the expression: D

=

2

.dlna

(

)

( 1-CALA*A/ A* AA )


C

L

The expression d e r i v e d by Karger (23) i s s l i g h t l y d i f f e r e n t due t o a d i f f e r e n c e i n the d e f i n i t i o n o f D. In the low c o n c e n t r a t i o n l i m i t dlna/dine 1, ο and the t r a c e r d i f f u s i v i t y approaches the l i m i t i n g d i f f u s i v i t y D . For many z e o l i t i c systems the cross c o e f f i c i e n t L A ^ A appears t o be small even at higher c o n c e n t r a t i o n so t h a t eqn. 5 reduces simply t o Darken s equation(§M. There are only a few systems f o r which both t r a c e r and s e l f d i f f u s i v i t i e s have been determined under comparable c o n d i t i o n s . For the d i f f u s i o n of water i n s e v e r a l n a t u r a l z e o l i t e s Barrer and Fender (25) showed t h a t the concentration dependence o f D could be l a r g e l y accounted f o r by the a c t i v i t y c o r r e c t i o n term and D % V. Barrer l a t e r (1) showed t h a t there i s evidence o f a s m a l l a d d i t i o n a l c o n c e n t r a t i o n dependence a r i s i n g from the term Ο Α ^ Α Κ Α ^ Α Κ ^ Α Α ^ the denominator o f eqn. 5. Tracer d i f f u s i v i t i e s {Ό) f o r CO2 i n UA and 5A sieves(26,27) are i n order of magnitude agreement w i t h values o f D determined i n t h i s l a b o r a t o r y . However, f o r t h i s system the c o r r e c t e d d i f f u s i v i t y i s s t r o n g l y c o n c e n t r a t i o n de pendent so d e t a i l e d comparisons are not p o s s i b l e without more extensive data. The recent t r a c e r data o f Quig and Rees (28) f o r C5-C9 alkanes i n p a r t i a l l y C a exchanged kA sieve are discussed below. D i f f u s i o n i n Small Port Z e o l i t e s Q

1

Q

N

0

+ +

Two d i s t i n c t p a t t e r n s o f d i f f u s i o n a l behaviour have been ob served depending on the r e l a t i v e s i z e s o f the d i f f u s i n g molecule and sieve window. When the c r i t i c a l molecular diameter i s com parable w i t h (or g r e a t e r than) the f r e e aperture o f the sieve window the F i c k i a n d i f f u s i v i t i e s show a monotonie increase w i t h sorbate c o n c e n t r a t i o n , i n accordance w i t h equation 1+ and the c o r r e c t e d d i f f u s i v i t i e s are e s s e n t i a l l y independent o f c o n c e n t r a t i o n . The temperature dependence o f D f o l l o w s the u s u a l E y r i n g equation: D = D* exp(-E/RT) (6) Q

Q

The a c t i v a t i o n e n e r g i e s , f o r a given s i e v e , show a d i r e c t c o r r e l a t i o n w i t h the c r i t i c a l diameters o f the sorbates and the orders of magnitude o f the pre-exponential f a c t o r s are c o n s i s t e n t w i t h the p r e d i c t i o n s o f t r a n s i t i o n s t a t e theory. Such behaviour i s ob served f o r the d i f f u s i o n of monatomic and diatomic gases i n kA z e o l i t e (16) and f o r l i g h t hydrocarbons and CF1+ i n hA and 5A sieves


324

MOLECULAR

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Table I I Systems i n which C r i t i c a l M o l e c u l a r Diameter i s Greater than or Equal t o Window Aperture: Parameters Ε and D* g i v i n g Temperature Dependence o f L i m i t i n g D i f f u s i v i t y D n

σ


System

(1)

Ar-UA 0 -UA Kr-UA

3.U

2

N -UA 2

C K^-kA C H^-5A 0 Η^-ΕΓΪοη. CH^-UA 2

2

2

C H -1+A C H -5A C Hg-Erion. C H -5A 1-CUH8-5A tr-2-C^H8-5A C3H8-UA C H -5A *C H -Chab. nC^H-LQ-UA nC H -5A nC^H -Chab. 2

6

6

2

2

3

6

3

8

3

8

i+

10

10

5 12~ 5 12~ * nC^H -Chabz. nC H -5A n C

H

n C

H

5 A

E r i o n

12

T

l6

CVCI0-C3H6-5A

CF -5A cis-2-Ci H8-5A U

l

3.5 3.6 3.7 It.08 h.08 k.08 k.08 k.08 h.36 k.36 h.36 k.95 h.95 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.1 5.2 5M 5.58

Ε (kcal)

5.8 h.53 8.1 6.1 8.5 2.75 2.3^ 7.U

2.98 6.2k 1.28 U.3 3.U6 3.kh 3Λ6 8.7 3.5 U.OU

8.5 k.O k.l6 U.6 5.0 k.95 7.5 h.3h 9.15 9.2

Experimental χ 10 (cmS.sec ''" ) 8

-

122 660 9.7 96 61 0.198 0.36 5.8 7.2 5.66 3.02 6.6 0.25 0.18 0.26 1.2U 0.82

-

0.U2 0.73

-

0.63 0.09

-

15.0 1.06 250 151

T h e o r e t i c a l Values rotating non-rot. D*xl0 - (cm^. secTî 8

132

-

266 3550 132 830 (172) 172

-

332 1100 96 1660 750 (90) 90

-

(57) 57

103 2.k 13 7.0 5.0 0.2k 1.26 (6.22) 6.22

-

1.01 3.1 0.008 0.062 0.028 (0.01U) 0.01U

-

(0.0021) 0.0021

1000

-

-

0.0025 0.015 0.03k

25 192

-

-

The data are c o r r e l a t e d a c c o r d i n g t o equation k and 6 ( D i n d e pendent o f c ) . The c r i t i c a l diameter σ i s d e f i n e d as the r a d i u s of the s m a l l e s t c y l i n d e r which can c i r c u m s c r i b e the molecule i n i t s most f a v o u r a b l e e q u i l i b r i u m conformation. Window aperatures are about 3.kl f o r kA s i e v e and k.3A f o r 5A. Values f o r hA 5A and e r i o n i t e are from data o b t a i n e d i n these l a b o r a t o r i e s (16,29-33) Values f o r H-chabazite are from B a r r e r and Davies(.2-O The c a l c u l a t i o n o f the t h e o r e t i c a l values o f D^ f o r City and CF^ i s d i s c u s s e d i n d e t a i l by Ruthven and Derrah ( 2 9 ) . Q

9

e


27.


RUTHVEN

325

(29-32) ^ erionite(33) and chabazite(3M. Data for some repre sentative systems are summarized i n table II and figure 2. Data for the lighter molecules are consistent with the assumption of a non-rotating transition state while for the larger molecules, which have high moments of i n e r t i a , the contribution from rotation or rocking vibrations to the partition function of the transition state becomes increasingly important. The large difference i n activation energies between h A and 5A sieves and the smaller d i f ferences between the activation energies for C 2 H 6 and i n 5A and erionite are consistent with the differences in the shapes of the windows and the geometry of the sorbate molecules. However the increase i n activation energy for the series ΟβΗβ, nC]|Hj_0, n ^5H12> 7 l 6 5A shows that c r i t i c a l molecular diameter i s not the only important factor. Diffusion i n p a r t i a l l y C a exchanged UA-5A sieves has also been investigated(28,35 >36). For less than 25$ C a exchange the d i f f u s i v i t y i s essentially the same as for the pure sodium form (hA). There i s a rapid increase i n d i f f u s i v i t y at about 30% C a exchange corresponding to the composition at which the obstructing Na ions are removed from one third of the windows so that each c e l l has, on average, two unobstructed windows. When more than two thirds of the Na ions are replaced a l l windows are open and the diffusional properties become essentially the same as for the C a form (5A). The change i n molecular sieve properties thus occurs almost entirely over the range 26-67$ exchange. A simple theoretical model, based on a random distribution of 'open and closed windows, has been found to provide a very satisfactory correlation of the experimental datai36). This i s i l l u s t r a t e d i n figure The theoretical curve for nC^Ri^ i s calculated on the assumption that D = Ό using approximate (extrapolated) values of D for the extreme hA and 5A forms ( l O " ^ and 10~ cm .sec" ). It i s evident that the theory f i t s the tracer d i f f u s i v i t y data of Quig and Rees(j^) well suggesting that the assumption D % Ρ i s at least approximately correct. This is contrary to the con clusions of Quig and Rees but they used values of D estimated from integral d i f f u s i v i t y measurements by the method of Barrer and Clarke (37). When the d i f f e r e n t i a l d i f f u s i v i t y i s strongly concentration dependent, as with these systems, the method of Barrer and Clarke can lead to large errors in the calculated d i f ferential d i f f u s i v i t i e s . A more detailed analysis requires accurate values of D » determined from d i f f e r e n t i a l measurements at low concentration, as well as tracer data for the extreme hA and 5A forms.


C2HI4.

n C

H

i n

+ +

+ +

+ +

+

+

+ +

1

1

1

1.

Q

1

12

2

1

0

0

Q

Q

Diffusion i n Large Port Zeolites For systems i n which the c r i t i c a l molecular diameter i s s i g nificantly smaller than the window aperture the pattern of d i f fusional behaviour i s entirely different. At low concentrations within the Henry*s Law region, the d i f f u s i v i t y decreases rapidly


326

MOLECULAR SIEVES—II

-

CH -143K(D) 4


-

n C H - 3 7 3 K (Do) 4

-

I 0

^

ο

^ V y ^ n C

^ 4

H

w

- 3 2 3 Κ ( Do)

-

- J — I

1

oi

03

I 04

I

I

% CcT Figure 1. Variation of corrected diffusivities, tracer self diffusivities, and NMR self diffusivities with degree of Ca** exchange in the Na-Ca A zeolites. Theoretical lines are calculated according to the model described in Kef. 36. D values for nC U are from Ruthven (36), D values for CH are from Carο et al. (47), D values for nC H are from Quig and Rees (28). 0

k

k

10

6

1!t


27.

RUTHVEN


327

w i t h i n c r e a s i n g sorbate c o n c e n t r a t i o n , p a s s i n g through a minimum and i n c r e a s i n g again as the s a t u r a t i o n l i m i t i s approached. Cor r e c t e d d i f f u s i v i t i e s c a l c u l a t e d according t o equation h show an inverse dependence on c o n c e n t r a t i o n which may be approximately represented by eqn. 2. Such behaviour i s shown by s m a l l monatomic and diatomic molecules i n the 5A sieve (16) and a l s o by l a r g e r hydrocarbon molecules i n 13x(38). TABLE I I I - Parameters Ε and D * (eqn. 2) f o r Systems i n which C r i t i c a l Molecular Diameters i s Smaller than Window Aperture Downloaded by UNIV OF PITTSBURGH on May 4, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0040.ch027

f

System Ar-5A Kr-5A Xe-5A 0 -5A N -5A SF6-13X nC H!6-13X 2

2

T

C6H -13X 1 2

C6H6-13X C6H5CH3-I3X

(1) 3Λ

3.6 U.O 3.5 3.7 6.1 5.1 6.5 6.5 6.5

Ε (kcal) «1.0 2.0 3.0 1.0 1.5 2.77 6.2 U.96 h.9

6.6

D \ x 10' (molecule. cm^/cavity. sec. ) 0.01 0.077 0.15 0.026 0.052 2.98 22 10.2 h.9

6.6

The data are c o r r e l a t e d according t o equations 2 and h. Free aperature o f 5A s i e v e = h.3A and of 13X s i e v e = 7·^Α. Data f o r 5A are from Ruthven and Derrah(l6) a . f o r 13X from Ruthven and an

Representative data are shown i n f i g u r e 2 and 3 and the parameters f o r s e v e r a l systems are g i v e n i n t a b l e I I I . When the s i e v e window i s l a r g e r e l a t i v e t o the d i f f u s i n g molecule the energy b a r r i e r between cages i s s m a l l . Most o f t h e molecules s t r i k i n g a window w i l l pass through and the b a s i c assumption o f t r a n s i t i o n s t a t e theory ( e q u i l i b r i u m between 'reactants' and t r a n s i t i o n s t a t e ) w i l l not be f u l f i l l e d . The i n verse c o n c e n t r a t i o n dependence suggests t h a t , even a t low con c e n t r a t i o n s , the d i f f u s i o n path i s l i m i t e d by c o l l i s i o n s between sorbate molecules. A simple q u a n t i t a t i v e treatment based on t h e assumption t h a t the p r i n c i p a l c o n t r i b u t i o n t o t h e f l u x a r i s e s from the small f r a c t i o n o f molecules t r a v e l l i n g on paths p r e c i s e l y a l i g n e d through the centres o f successive windows and which can t h e r e f o r e t r a v e r s e s e v e r a l cages i n each f l i g h t , can account f o r the order o f magnitude o f the experimental d i f f u s i v i t i e s f o r monatomic and diatomic gases i n 5A sieve (16) and f o r SFg in 13x(il)The behaviour o f the l a r g e r molecules such as benzene and toluene i n 13X i s intermediate between the constant D p a t t e r n observed f o r the small port z e o l i t e s and the r e c i p r o c a l concen t r a t i o n dependence which i s observed when the s i e v e aperture Q


328


MOLECULAR

AlChE Journal

Figure 3. Concentration dependence of corrected diffusivity for hydrocarbons in 13X zeolite. Comparative data for nC H in 5A are also shown. 7

16


SIEVES—II

27.

RUTHVEN


329

i s l a r g e . Such "behaviour suggests t h a t even l a r g e r molecules i n 13X may show the constant D p a t t e r n . 0

Comparison

of NMR

and S o r p t i o n Data

S e v e r a l systems have r e c e n t l y been s t u d i e d by both NMR and s o r p t i o n methods and comparative data are presented i n t a b l e IV. The NMR techniques are of two kinds(39>k0). The r e l a x a t i o n method depends on the d e t e r m i n a t i o n of the c o r r e l a t i o n time f o r molecular motion (τ) and the s e l f d i f f u s i v i t y i s then c a l c u l a t e d u s i n g an assumed mean jump d i s t a n c e (λ): V = λ /6τ = x 2 - E / R T

()

2


e

/6xo

T

I n the more recent p u l s e d f i e l d g r a d i e n t spin-echo method(^2-U7) the s e l f d i f f u s i v i t y i s determined more d i r e c t l y as the measure ments y i e l d the mean square d i s t a n c e t r a v e l l e d i n a known time i n t e r v a l . For those systems which have been s t u d i e d by b o t h methods (nCl^H-jî 0 γ Η ^ , C g H ^ i n 13X) t h e r e i s good agreement when λ i s taken as the l a t t i c e parameter, suggesting t h a t d i f f u s i o n occurs by jumps between neighbouring cages. The NMR s e l f d i f f u s i v i t i e s are however much l a r g e r than v a l u e s of D from sorp t i o n measurements and the a c t i v a t i o n energies are lower b u t , d e s p i t e the l a r g e d i f f e r e n c e i n numerical v a l u e s , both NMR and s o r p t i o n data show s i m i l a r t r e n d s . The r e l a t i v e v a l u e s of d i f f u s i v i t i e s f o r the Cl| hydrocarbons i n 5A z e o l i t e f a l l i n the same sequence and, f o r the 13X systems, Ρ(NMR) and D ( s o r p t i o n ) both show a s i m i l a r i n v e r s e dependence on c o n c e n t r a t i o n . As i l l u s t r a t e d i n f i g u r e 1 the p a t t e r n of v a r i a t i o n of both Ρ(or τ) and D w i t h Ca exchange i n NaCaA z e o l i t e s can a l s o be q u a n t i t a t i v e l y ac counted f o r i n terms of the same t h e o r e t i c a l model. I f the adsorbed phase behaves as a set of l o c a l i z e d E i n s t e i n o s c i l l a t o r s w i t h complete r o t a t i o n a l freedom, as i s suggested by heat c a p a c i t y measurements (50). the v i b r a t i o n frequency (v) may be estimated from the Henry constant: Κ = K exp(q /RT); K Q / C S = (kT/e ) ( 2 τ π η ν 2 ) (8) For the 13X systems the v i b r a t i o n f r e q u e n c i e s are c l o s e to the r e c i p r o c a l NMR c o r r e l a t i o n times whereas f o r the 5A systems the r e c i p r o c a l c o r r e l a t i o n times are much s m a l l e r . This suggests t h a t i n the 13X s i e v e molecular jumps occur predominantly between neighbouring cages whereas i n the 5A s i e v e jumps w i t h i n a c a v i t y are much more frequent as i s to be expected from s t r u c t u r a l con sideration. S i m i l a r l y l a r g e d i s c r e p a n c i e s between d i f f u s i v i t i e s measured by NMR and other methods have been observed f o r molecular solids(51?52) but the e x p l a n a t i o n i s u n c e r t a i n . The p u l s e d f i e l d g r a d i e n t spin-echo method i s f r e e from the obvious o b j e c t t h a t t r a n s l a t i o n a l motion may be too slow t o dominate the r e l a x a t i o n process and s i n c e the r.m.s. d i s t a n c e s measured i n an experiment are much l a r g e r than the l a t t i c e parameter, the c o n c l u s i o n t h a t the technique measures molecular motion between c a v i t i e s seems t o η

0

0

Q

+ +

ΐ / 2

0

0


3 / 2


6

H

T

H

l 6

6

10

13X

0.9 1.5

_

0.U5 (1*7,30) 0.1 (1*8,1*9,30)

(1*8,1*9,30)

(U6.29)

(U2)

2.2 2.5 3.2 3.0

cm sec -1

6 8 (U3) (1*2,32) 15 (^,1*5,38) 15

(Ul.1T)

Ref

1

6

1x10-5 lxlO-

1.5x10-5 1.2x10-5

cm' sec

298K 2

D at

0.01

0.02

0.09

0.017

5.2 6.7

8.0

1 1

0

(l/x ) J" xlO" -1

5.0

h.O

2.8 5.0 9

3.7xl0~° U.8xl05.9x10-? 5.5x10" ,10

6

3.3x10-5 k.9x10-5

„-l

cnr-

298K

D at

2.9 9 . 7 x l 0 " 3.0 1.05x10-5

2.5 2.2

Ε kcal

NMR r e l a x a t i o n

2

Q

1

0

1 1

12

7.8x1ο8.3x1Ο" 5.3x10-12 7-UxlO- ^ 2.6x10 ^

2.7x10-9

1

Λ

o

lU.5 3.0 6.5 0.2U 0.52

0.51* 0.60

6.2

1 0

K xl0 mol/cage ρ dyne·cm^

T.l 7.5 3.8 11.1» 9.2

5.9 6.T

8.5

vxlO" _ i sec

Equilibrium 1 1

- 0.3 f o r t h e 13X systems.

o f Θ f o r t h e r e l a x a t i o n data i n 5A, Θ = 0.6 - 0 . 7 . For 13X

13X systems and i n c r e a s e s

9.2

3.0 3.0 U.O 3.5 3.5

6.2

2.8

cm -1 sec

298K 12

D at

Sorption E kcal

NMR s e l f d i f f u s i o n data are f o r Θ 0.2 - 0.3. V decreases w i t h Θ f o r f o r CHI* and C H6 i n 5A. V f o r r e l a x a t i o n i s c a l c u l a t e d from equation 8 w i t h λ = 12.3A. Values are SFg, Θ = 0.2; nCl|H o-13X and nC7H g-13X, Θ = 0 . 8 l ; CI4. hydrocarbons systems τ i n c r e a s e s w i t h Θ corresponding t o a decrease i n m o b i l i t y . Sorption values o f D are f o r 1 m o l e c u l e / c a v i t y which i s about Θ = 0.2

5A 1-CUH8 t-2-Cl^He cis-2-Cl|H8

nCuH

2

CH^ C H

n C

6 lU nC H C6 12

SF

System

Ε kcal

NMR s e l f d i f f u s i o n

Comparison o f R e s u l t s o f NMR and S o r p t i o n Studies

Table IV


27.

RUTHVEN


331

be j u s t i f i e d . Nevertheless, neutron s c a t t e r i n g s t u d i e s o f CH3CN and CH3OH i n 3A s i e v e , systems i n which the sorbate molecules a r e almost c e r t a i n l y trapped w i t h i n p a r t i c u l a r cages, y i e l d jump times VLO" sec and i n t r a c a v i t y d i f f u s i v i t i e s ^10"5 cm^.sec" a t room temperature These values are c l o s e t o the NMR d i f f u s i v i t i e s of Karger and Car ο f o r CHI* i n 5A sieve The NMR d i f f u s i v i t i e s f o r 13X z e o l i t e are s i m i l a r t o the values f o r the pure l i q u i d s o r bates whereas the s o r p t i o n values are o f the same order as t h e d i f f u s i v i t i e s o f molecular s o l i d s near the m e l t i n g p o i n t . The l a t t e r s t a t e seems more c o n s i s t e n t w i t h heat c a p a c i t y evidence(50). Both NMR and s o r p t i o n data are s e l f - c o n s i s t e n t and show the ex pected trends w i t h changes i n sorbate and s i e v e . The suggestion that s o r p t i o n r a t e s are c o n t r o l l e d by surface r e s i s t a n c e r a t h e r than by 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 , even under p r o p e r l y s e l e c t e d c o n d i t i o n s , i s i n c o n s i s t e n t w i t h the form o f the uptake curves which show the w e l l known i n i t i a l dependence on v t , r a t h e r than the l i n e a r time dependence c h a r a c t e r i s t i c o f a surface c o n t r o l l e d process. The l i m i t e d d i f f u s i v i t y data obtained from c a t a l y t i c k i n e t i c s under d i f f u s i o n l i m i t e d c o n d i t i o n s (5U.55) are a l s o con s i s t e n t w i t h the d i f f u s i v i t i e s from s o r p t i o n r a t h e r than NMR(33) and the recent thermodynamic study o f Stroud e t a l .


11

1

(56) provides f u r t h e r i n d i r e c t evidence t h a t , f o r CHI4. i n 5A at low temperatures, 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 i s much smaller than the NMR measurements suggest. Counter D i f f u s i o n Studies The data discussed above r e f e r e x c l u s i v e l y t o the d i f f u s i o n of s i n g l e molecular species e i t h e r w i t h a net f l u x , as i n a sorp t i o n experiment, or w i t h no net f l u x as i n a t r a c e r measurement. Many i n d u s t r i a l processes i n v o l v e a c o u n t e r - d i f f u s i o n s i t u a t i o n i n which one component i s d i f f u s i n g i n t o a c r y s t a l while another component i s simultaneously d i f f u s i n g out. I t has been shown t h a t i n t h i s s i t u a t i o n d i f f u s i v i t i e s may be very much smaller than the d i f f u s i v i t i e s o f the i n d i v i d u a l components(57-59) t ) t i t i s not yet c e r t a i n t o what extent such e f f e c t s a r i s e from the change i n the a c t i v i t y c o r r e c t i o n term (31np/31nc) and to what extent they r e f l e c t a c t u a l changes i n the magnitude o f the i n t r i n s i c d i f f u s i v i t y ( D or Ό). From t h e o r e t i c a l c o n s i d e r a t i o n s one would expect t h a t i n systems i n which the d i f f u s i v i t y i s determined p r i m a r i l y by the c r y s t a l l a t t i c e ( i . e . when the molecular diameter i s l a r g e r i n r e l a t i o n t o the window aperture) D should not be s i g n i f i c a n t l y d i f f e r e n t under counter d i f f u s i o n c o n d i t i o n s . How ever, when the c o l l i s i o n a l d i f f u s i o n mechanism i s dominant a s i g n i f i c a n t d i f f e r e n c e between the i n t r i n s i c d i f f u s i v i t y i n a counter d i f f u s i o n s i t u a t i o n , as compared w i t h a s i n g l e component system, i s p o s s i b l e . These hypotheses have not so f a r been t e s t e d experimentally. U

Q

Q


332

MOLECULAR SIEVES—II

Conclusions


The topics covered by this review include only some of the more recent work i n this area. The kinetic data i n the literature show many apparent anomalies and contradiction but i n many cases this seems to be because the pronounced concentration dependence of zeolitic d i f f u s i v i t i e s and the consequent necessity of making differential rather than integral measurements were not appreciated in much of the earlier work. The more recent data show much great er regularity with a clear correlation between the diffusional behaviour and the relative sizes of sorbate molecule and zeolite window. Notation A,B,C a c c D D s

0

constants i n equation 1 sorbate a c t i v i t y sorbate concentration saturation concentration zeolitic d i f f u s i v i t y corrected d i f f u s i v i t y (equation 5) pre-exponential factor for D (equation 7) defined by equation 2 pre-exponential factor for D (equation 3) self d i f f u s i v i t y diffusional activation energy Henry constant (defined by c = Kp) pre-exponential factor for K(K = IêQ-o/RT) straight and cross coefficients i n the irreversible thermodynamic formulation of diffusion mass of sorbate molecule equilibrium sorbate pressure limiting heat of sorption gas constant crystal radius gas velocity fractional saturation (c/c ) NMR correlation time for molecular jumps pre-exponential factor i n equation 7 jump distance vibration frequency Q

!

D D^ V Ε Κ K L-AA'L-A*A 0

1

0

m ρ qQ R r u Θ τ τ λ ν 0

!

0

s


27. RUTHVEN Diffusion in Molecular Sieves

1. 2. 3. 4. 5.


6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 2k. 25. 26. 27. 28. 29. 30. 31.

333

Literature Cited Barrer, R.M., Adv. in Chem. (1971), 102, 1. Lee, L.K., Yucel, H. and Ruthven, D.M. This conference. Dubinin, M.M. This conference. Loughlin, K.F., Derrah, R.I. and Ruthven, D.M., Can. J. Chem. Eng. (1971),49,66. Ruthven, D.M., Separation and Purification Methods (1976) 5, (2). Eberly, P.E., Ind. Eng. Chem. Fund. (1969), 8, 25. van Deemter, J.J., Zuiderweg, F.J. and Klinkenberg, Α., Chem. Eng.Sci. (1956), 5, 271. MacDonald, W.R. and Habgood, H.W., Can. J. Chem. Eng. (1972), 50, 462. Ma, Y.H. and Mancel, C., Adv. in Chem. (1973), 121, 392. Schneider, P. and Smith, J.M., A.I.Ch.E.Jl. (1968), 14, 762. Hashimoto, N. and Smith, J.M., Ind. Eng. Chem. Fund. (1973), 12, 353. Mixon, F.O., Whitaker, D.R. andOrcutt,J.C,A.I.Ch.E.Jl. (1967), 13, 21. Ostergaard, K. and Michelsen, M.L., Can. J. Chem. Eng. (1969), 47, 107. Sarma, P.N. and Haynes, H.W., Adv. in Chem. (1974), 133, 205. Gangwal, S.K., Ph.D. Thesis, University of Waterloo, Ontario (1976). Ruthven, D.M. and Derrah, R.I., J. Chem. Soc. Faraday Trans I (1975), 71, 2031. Ruthven, D.M. and Doetsch, I.H., Ibid (1976), 72, 1043. Eagan, J.D. and Anderson, R.B., J. Colloid Interface Sci. (1975), 50, 419. Ruthven, D.M. and Loughlin, K.F., Chem. Eng. Sci. (1971), 26, 1145. Haase, R. and Siry, Μ., Z. Phys. Chem. (Frankfurt) (1968), 57, 56. Turner, J.C.R., Chem. Eng. Sci. (1975), 30, 1304. Ash, R. and Barrer, R.M., Surface Sci. (1967), 8, 46l. Karger, J., Ibid. (1973), 36, 797. Darken, L.S., Trans. A.I.M.E. (1948), 175 l84. Barrer, R.M. and Fender, B.E.F., J. Phys. Chem. Solid (1964), 21, 12. Rees, L.V.C. private communication. Sargent, R.W.H. and Whitford, C.J., Adv. in Chem. (1971), 102, 155. Quig, A. and Rees, L.V.C., J. Chem. Soc. Faraday Trans I (1976), 72, 771. Ruthven, D.M. and Derrah, R.I., J. Chem. Soc. Faraday Trans I (1972), 68, 2332. Ruthven, D.M., Derrah, R.I. and Loughlin, K.F., Can. J. Chem. (1973), 51, 3514. Ruthven, D.M., Loughlin, L.F., and Derrah, R.I., Adv. in Chem. (1973), 121, 330. In Molecular Sieves—II; Katzer, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


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32. Doetsch, I.H., Ruthven, D.M. and Loughlin, K.F., Can. J. Chem. (1974), 52, 2717. 33. Ruthven, D.M. and Derrah, R.I., J. Colloid Interface Sci. (1975), 52, 397. 34. Barrer, R.M. and Davies, J.Α., Proc.Roy.Soc. (1971), A322, 1. 35. Wolf, F. and Pilchowski, Κ., Chem. Techn. (1971), 23, 672. Adv. in Chem.(1971), 102, 22936. Ruthven, D.M., Can. J. Chem. (1974), 52, 3523. 37. Barrer, R.M. and Clarke, D.J., J. Chem. Soc. Faraday Trans I (1974), 70, 535. 38. Ruthven, D.M. and Doetsch, I.H., A.I.Ch.E.Jl. (1976), 22, (5). 39. Resing, H.A. and Murday, J.S., Adv. in Chem. (1973), 121, 414. 40. Pfeifer,H., Schirmer,W. and Winkler,H., Ibid.,(1973), 121 430. 41. Thompson, J.K. and Resing, H.A., J. Colloid Interface Sci., (1968), 26, 279. 42. Karger, J., Shdanov, S.P. and Walter, Α., Ζ. Phys. Chem. Leipzig (1975), 256, 319. 43. Karger, J., Bulow, M. and van Phat, Ν., Z. Phys. Chem. Leipzig - in press. 44. Karger, J., Lorenz, P., Pfeifer, H. and Bulow, Μ., Z. Phys. Chem. Leipzig (1976), 257. 45. Nagel, M., Pfeifer, H. and Winkler, Η., Z. Phys. Chem. Leipzig (1974), 255, 283. 46. Karger, J. and Caro, J., J. Colloid Interface Sci. (1975), 52, 623. 47. Caro, J., Karger, J., Finger, G. and Pfeifer, Η., Z. Phys. Chem. Leipzig - in press. 48. Labisch, L., Schollner, R., Michel, D., Rossiger, V. and Pfeifer, Η., Ibid (1974), 255, 58l. 49. Michel, D. and Rossiger, V., Surface Sci. (1976), 54, 463. 50. von Basler, W. and Lechert, Η., Ber .Buns. Ges.Phys .Chem. ( 1974), 78, 667. 51. Chadwick, A.V. and Sherwood, J.N. in "Point Defects in Solids" et J.H. Crawford and L.M. Slifkin, Plenum Press, New York (1975). 52. Sherwood, J.N., Surface and Defect Props, of Solids (1973), 2, 250. 53. Egelstaff, P.A., Downes, J.S. and White, J.W., in "Molecular Sieves", Soc. Chem. Ind., London (1968) p. 306. 54. Miale, J.N., Chen, N.Y., Weisz, P.B., J. Catalysis (1966), 6, 278. 55. Chen, N.Y. and Garwood, W.E., Adv. in Chem. (1973), 121, 330. 56. Stroud, H.J.F., Richards, E., Limcharoen, P. and Parsonage, N., J. Chem. Soc. Faraday Trans. I (1976), 72, 942. 57. Satterfield, C.N., Katzer, J.K. and Vieth, W.R., Ind. Eng. Chem. Fund. (1971), 10, 478. 58. Satterfield, C.N. and Katzer, J.R., Adv. in Chem. (1971), 102, 193. 59. Moore, R.M. and Katzer, J.R., A.I.Ch.E. Jl. (1972), l8, 8l6


Diffusion in Molecular Sieves: A Review of Recent Developments

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