Molecular Sieve Zeolites-II

42 Intracrystalline Diffusion R. M . B A R R E R

Downloaded by LOUISIANA STATE UNIV on September 3, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch042

Physical Chemistry Laboratories, Chemistry Department, Imperial College, L o n d o n , S . W . 7, E n g l a n d

The rate of intracrystalline nificant

for molecule

migration

sis. In view of this, an account aspects of diffusion related

diffusion

integral,

and tracer

cataly-

has been given of

various

Ways

dependence

single crystals and powders.

Examples

line channel valence, foreign

J

-

dimensions,

temperature, molecules

Heterogeneous A

anisotropy

of measuring include

molecules,

and

and

the

using penecomplex

intracrystal-

ions of different

concentration,

have also been

these

various

and effects of

exchange

inter-

differential,

are considered,

trants, such as water, small nonpolar Diffusion

Three

can be measured:

coefficients.

is sig-

sieve

in porous aluminosilicates.

coefficients

and their concentration

molecules.

of molecules

sieving and for molecular

size

and

presence

of

discussed.

catalysts are u s u a l l y h i g h - a r e a porous materials w h i c h

m a y b e a m o r p h o u s or c r y s t a l l i n e . A n i m p o r t a n t aspect of a l l s u c h

materials is t h e r a p i d i t y w i t h w h i c h reactant m o l e c u l e s r e a c h active sites a n d p r o d u c t s leave these sites.

A p a r t f r o m flow i n gas o r l i q u i d phase,

there m a y b e surface m i g r a t i o n i n t o a n d f r o m m i c r o p o r e s , w h e t h e r i n a m o r p h o u s catalysts o r i n c r y s t a l l i n e ones, s u c h as t h e zeolites.

It is s t i l l

a n o p e n q u e s t i o n h o w i m p o r t a n t s u c h m i g r a t i o n processes are as ratec o n t r o l l i n g steps.

H o w e v e r , i t seems l i k e l y that active sites d e e p i n a

p o r o u s c r y s t a l w i l l b e less i m p o r t a n t t h a n sites near t h e surface because m a n y m o r e u n i t d i f f u s i o n steps w i l l b e n e e d e d to transport m o l e c u l e s to a n d f r o m d e e p l y b u r i e d sites. A s corollaries, o n e w o u l d expect that o n l y a l i m i t e d v o l u m e f r a c t i o n of a c r y s t a l of a zeolite s u c h as sieve Y is c a t a l y t i c a l l y effective,

a n d that

f o r best p e r f o r m a n c e

crystals

i n the

catalyst s u p p o r t s h o u l d b e w e l l exposed a n d as s m a l l as possible, i n o r d e r to p r o v i d e the largest s u r f a c e - t o - v o l u m e ratio. 1

In Molecular Sieve Zeolites-II; Flanigen, E., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

2

M O L E C U L A R SIEVE ZEOLITES

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 c a n delineate factors

II

limiting

t r a n s p o r t w i t h i n crystals a n d h e n c e w i l l a i d u n d e r s t a n d i n g of m o l e c u l e s i e v i n g a n d site a c c e s s i b i l i t y i n catalysis. basic

d i f f u s i o n studies

O n e m a y h o p e to l e a r n f r o m

h o w d i f f u s i o n coefficients

within

zeolites are


related t o : 1.

Intracrystalline channel geometry a n d dimensions.

2.

S h a p e , size, a n d p o l a r i t y o f p e n e t r a n t molecules.

3.

C a t i o n d i s p o s i t i o n s , size, charge, a n d n u m b e r s .

4.

L a t t i c e defects, s u c h as s t a c k i n g faults.

5.

Presence of " i m p u r i t y " m o l e c u l e s i n channels.

6.

S t r u c t u r a l changes b r o u g h t a b o u t b y penetrants.

7.

S t r u c t u r a l d a m a g e associated w i t h p h y s i c a l a n d c h e m i c a l treatments.

8.

C o n c e n t r a t i o n of p e n e t r a n t w i t h i n t h e crystals.

Despite the obvious importance

of d i f f u s i o n studies, i n f o r m a t i o n o n

these t o p i c s is s t i l l l i m i t e d . T h e p o s i t i o n reflects e x p e r i m e n t a l difficulties and,

i n p a r t , a f a i l u r e to r e a l i z e h o w u s e f u l a p r o b e d i f f u s i o n m a y b e .

It is h o p e d that t h e i m p o r t a n c e of d i f f u s i o n w i l l b e c o m e a p p a r e n t f r o m t h e present r e v i e w . Diffusion

Coefficients

I n t h e t w o - c o m p o n e n t system gas + zeolite, i n p a r a l l e l w i t h a g e n e r a l t w o - c o m p o n e n t system, one m a y c o n s i d e r 5 d i f f u s i o n coefficients: ( i n t e r d i f f u s i o n coefficient of sorbate a n d z e o l i t e ) ; D , D A

B

f u s i o n coefficients, r e s p e c t i v e l y , of sorbate a n d z e o l i t e ) ; a n d D ( t r a c e r d i f f u s i o n coefficients, r e s p e c t i v e l y , o f sorbate a n d z e o l i t e ) . ever, because D

B

and D *

D

AB

(intrinsic dif A

*, How

are effectively zero, as f o r a n o n s w e l l i n g

B

crystal, D

=

AB

D

A

It is sometimes a s s u m e d that

= D*

DA

where a

A

=

A

f^i aln

(1)

CA

PA is t h e a c t i v i t y o f sorbate, e q u a l to t h e l o c a l e q u i l i b r i u m

pressure of sorbate, w h e r e t h e c o n c e n t r a t i o n o f A is c . A

H o w e v e r , this r e l a t i o n is n o t correct.

D

A

=

D

A

din aA din CA

T h e t r u e r e l a t i o n ( I ) is

CAL

A

C *L A

A


(2)

42.

BARRER

Here c * A

Intracrystalline

Diffusion

3

is t h e c o n c e n t r a t i o n of i s o t o p i c a l l y l a b e l l e d species at a p o i n t

w h e r e t h e c o n c e n t r a t i o n of u n l a b e l l e d species is c .

L

A

AA

a n d L A * are A

the straight a n d cross p h e n o m e n o l o g i c a l coefficients of t h e i r r e v e r s i b l e t h e r m o d y n a m i c f o r m u l a t i o n of d i f f u s i o n . T h e o r i g i n a l r e l a t i o n , E q u a t i o n 1, assumes a z e r o cross coefficient, w h i c h i n dense i n t r a c r y s t a l l i n e fluids c e r t a i n l y is n o t l i k e l y t o b e true. T h e o n l y i n f o r m a t i o n f o r s o r b a t e - z e o l i t e systems f r o m w h i c h E q u a tion 2 c a n b e discussed was obtained b y Barrer a n d F e n d e r ( 7 ) . T h e y


s t u d i e d i n t r i n s i c a n d tracer d i f f u s i o n of w a t e r i n c h a b a z i t e , h e u l a n d i t e , and gmelinite, using H 0 and D 0 . T h e activity correction: 2

2

din a

A

_ din p

A

din c

din c

A

can

A

b e d e r i v e d f r o m t h e i r w a t e r s o r p t i o n isotherms.

T h e results of a n

analysis o f t h e i r d a t a are p r e s e n t e d i n T a b l e I. T h e r a t i o

c L */c *L A

AA

A

c a n h a v e c o n s i d e r a b l e values, a l t h o u g h t h e c o r r e c t i o n t e r m din a /din A

is d o m i n a n t .

AA

c

A

T h e results i n t h e t a b l e refer to zeolite crystals n e a r l y

s a t u r a t e d w i t h w a t e r , a n d s h o u l d b e e x t e n d e d , f o r v a r i o u s sorbates, o v e r a greater r a n g e of sorbate concentrations. T h e significance of cross coefficients, L *,

has b e e n d e m o n s t r a t e d

AA

also f o r i n t r i n s i c a n d tracer d i f f u s i o n of SO2 i n surface flow t h r o u g h c a r b o n compacts

(I).

C r o s s coefficients

m u s t arise f r o m d i r e c t

interactions

b e t w e e n A a n d A * , a n d s h o u l d b e significant w h e n e v e r sorbate is suffi c i e n t l y c o n c e n t r a t e d f o r s u c h encounters t o b e c o m e

Table I.

Relation Between D

and D *

A

Chabazite B

Heulandite

Gmelinite

T,°

75 65 55 45 35 75 65 55 45 35 55 45 35

C

I n the

for Water in Several Zeolites

A

dln&A

CALAA*

dim A

CA*LAA

5.4 3.8o 2.5

23.0 24.0 25.5 27.0 28.0

0.09I 0.15 0.17 0.21 0.27

3.7 2.U 1.24

3.0 1.9 1.26 0.78 0.46

30.0 32.0 34.0 35.5 37.0

0.39 0.44 0.48 0.51 0.56

7.3 5.0 3.3i

1.9 1.40 0.97

26.5 28.0 29.5

0.15

D * X 10 , Cm Sec~ s

A

Zeolite

frequent.

2

l

46., 31. 21. 14.x 9.0

D X W\ Cm Sec~ A

2

l

IO.65 7.6

8

4

5

0

9.8

0

6.1

6

0

3

5

5


O.O65

0.030

4


d i l u t e H e n r y ' s l a w s o r p t i o n r a n g e , cfln a /dln

c

A

A

=

II

1. S i n c e encounters

of A a n d A * w i l l t h e n b e m u c h less f r e q u e n t , t h e cross coefficient s h o u l d be m i n i m a l a n d D

A

=

B

T h e d i f f u s i o n coefficients D

A

D

->

A

D* A

andD *

r e f e r r e d to a b o v e a r e differ

A

e n t i a l v a l u e s f o r p a r t i c u l a r concentrations c ,

o r else d e t e r m i n e d o n l y

A

over a n a r r o w concentration range.

O v e r a w i d e concentration r a n g e —


e.g., i n m a n y s o r p t i o n rate e x p e r i m e n t s — a m o r e accessible q u a n t i t y is the i n t e g r a l v a l u e , D , w h e r e A

D

A

=

c

A

- f c J l

A

D(c )dc A

Q

A

or, f o r i n t e r v a l e x p e r i m e n t s , c

A

D

A

Measurement

=

of Molecule

X

,

N

Diffusion

/

D(c )dc

in Zeolite

A

A

Crystals

Single Crystals. N a t u r a l l y - o c c u r r i n g zeolites are sometimes f o u n d as l a r g e single crystals. T i s e l i u s (34, 35) u s e d this feature t o s t u d y d i f f u s i o n i n zeolites. D i f f u s i o n of w a t e r i n h e u l a n d i t e crystals w a s f o l l o w e d b y a n

Figure 1. A stage of diffusion in a heulandite single crystal viewed through crossed Nicols ( 3 4 ) . The diferent distances moved by the band in 2 directions show the diffusion anisotropy. The direction of more rapid penetration is normal to 201, and that of less rapid pentration is normal to 001


42.

BARRER

Intracrystalline

5

Diffusion

o p t i c a l p r o c e d u r e i n w h i c h b i r e f r i n g e n c e of a c r y s t a l p l a t e w a s o b s e r v e d u n d e r crossed N i c o l s . B i r e f r i n g e n c e w a s a f u n c t i o n inter alia o f t h e c o n c e n t r a t i o n of sorbate.

A c c o r d i n g l y , u n d e r crossed N i c o l s d a r k

bands

progress i n t o t h e c r y s t a l as d i f f u s i o n proceeds ( F i g u r e 1 ) . A t t i m e t, i f the b a n d has p r o g r e s s e d t h r o u g h distance x, t h e n x

2

=

2D t A

T h e figure shows strong a n i s o t r o p y i n t h e d i f f u s i o n of z e o l i t i c w a t e r , t h e


d a r k b a n d h a v i n g m o v e d f u r t h e r f r o m t h e 201 t h a n f r o m t h e 001 face.

D

A

is g i v e n i n T a b l e I I ; t h e a c t i v a t i o n energies, E, i n t h e A r r h e n i u s e q u a t i o n D

A

=D

0

e x p — E/RT

are 5400 a n d 9140 c a l / m o l e , r e s p e c t i v e l y , f o r

d i f f u s i o n n o r m a l to 201 a n d 001.

Table II.

T,

°C

20 33.8 46.1 60.0 75.0

Diffusion Anisotropy in Heulandite D

A

X W -L 201 Cm Sec~ 7

2

l

2.7 4.1 4.8 7.6 11.1

D

A

X 10 J_ 001 Cm Sec~ 7

2

l

0.23 0.45 0.66 1.45 2.8

W. Meier, "Molecular Sieves," Society of the Chemical Industry

Figure 2. Sheets of linked tetrahedra present in heulandite ( 2 5 ) . Diffusion across these sheets does not occur. Between the sheets, different intersecting channels run parallel to a and c, respectively, forming twodimensional networks


6


II

H e u l a n d i t e consists of sheets ( F i g u r e 2 ) l i n k e d to other l i k e sheets a n d e n c l o s i n g b e t w e e n e a c h p a i r a t w o - d i m e n s i o n a l c h a n n e l system N o r m a l to the

sheets, T i s e l i u s f o u n d the

d i f f u s i o n coefficient

(25). to

be

n e g l i g i b l e , as w o u l d b e e x p e c t e d f r o m the c o m p a c t n a t u r e of the sheets. B e t w e e n the sheets are channels c i r c u m s c r i b e d b y 10-rings a n d 8-rings:


(a)

P a r a l l e l to a, e l l i p t i c a l 8-rings of free d i a m e t e r 2.4 a n d 6.1 A .

( b ) P a r a l l e l to c, 3.2 a n d 7.8A ( 1 0 - r i n g s ) a n d 3.8 a n d 4 . 5 A ( 8 - r i n g s ) . T h e a n i s o t r o p y f o r different d i r e c t i o n s p a r a l l e l to the sheets is i n a c c o r d w i t h the structure, w h i c h w a s u n k n o w n at the t i m e of T i s e l i u s ' measure ments. T i s e l i u s , a g a i n u s i n g s u i t a b l y c u t plates of h e u l a n d i t e , e s t a b l i s h e d a c t u a l c o n c e n t r a t i o n gradients f r o m b i r e f r i n g e n c e studies as a f u n c t i o n of distance x f r o m the surface. If the c o n c e n t r a t i o n at t = 0 is c t h r o u g h o u t the c r y s t a l , a n d at t i m e t is c at distance x; w h i l e at x = 0, c = c « f o r a l l t > 0, t h e n 0

x

,c=c

T h e concentration-distance

c u r v e at t i m e t serves to give dx/dc

and

xdc Hence, D is o b t a i n e d . T h i s m e t h o d is associated w i t h B o l t z m a n n (14) a n d w a s d e v e l o p e d b y M a t a n o (24). S o m e results are g i v e n i n T a b l e I I I . T h e s a t u r a t i o n w a t e r content, c , was 19.67% b y w e i g h t of w a t e r ; the values of c are g i v e n i n the table. D s h o u l d be, a n d w a s , w i t h i n error, i n d e p e n d e n t of c . T h e v a r i a t i o n of D w i t h c o n c e n t r a t i o n c

=

Cx

x

0

A

0

Table III.

Wt% 10 11 12 13 14 15 16 17 18 19

D J L 201 A

Co

D

= A

A

Plane in Heulandite at 20°C, C m X

8.3% 10

0.04 0.2 0.7 1.3 2.0 2.7 3.0 4.0 4.0 3.3

7

Co

D

= A

X

18.2% W

2.1 2.6 3.5 4.2 4.1 3.5

7

Co

D

= A

X

2

Sec

16.2% 10 7

4.0 4.2 4.1


1

42.

BARRER

Intracrystalline

Diffusion

7

m a y b e associated w i t h c h a n g e i n the b i n d i n g e n e r g y of w a t e r as c increases a n d w i t h s m a l l lattice changes associated

w i t h rising

water

content. Synthetic

Powders.

zeolites

a n d n a t u r a l l y o c c u r r i n g zeolites

of

s e d i m e n t a r y o r i g i n n o r m a l l y o c c u r as p o w d e r s . F o r t h e m different m e t h ods m u s t b e e m p l o y e d , w h i c h f a l l i n t o 2 s u b d i v i s i o n s :


( a ) S o r p t i o n o r d e s o r p t i o n is m e a s u r e d , k e e p i n g t h e sorbate pres sure constant. ( b ) S o r p t i o n or d e s o r p t i o n occurs i n a c o n s t a n t - v o l u m e v a r i a b l e pressure vessel. C O N S T A N T - P R E S S U R E S O R P T I O N OR D E S O R P T I O N .

The

boundary

condi

tions f o r a n y crystallite are c =

c

c =

Co t h r o u g h o u t t h e c r y s t a l l i t e at t =

just w i t h i n t h e surface f o r a l l t > 0.

x

0.

w h i l e f o r flow ^ When D

A

=

d i v (DA g r a d c).

is i n d e p e n d e n t of c a n d t h e crystals are a l l of t h e same shape

a n d size, e.g., spheres of r a d i u s r Qt - Qo Q — Qo

,

0

6 A 1 x „= i n

D

n izH 2

A

2

m

F o r larger times, a l l b u t one e x p o n e n t i a l t e r m b e c o m e n e g l i g i b l e , a n d t h e e q u a t i o n reduces to , l

Q- n

Q

6

t

Q ^ Q r

l

n

D

A

V

2

rt 2

~ ^

so that a p l o t of t h e left side against t gives a straight l i n e of slope D 7r A

2

~~2~O n c e D is k n o w n , this c a n b e s u b s t i t u t e d i n t h e f u l l e q u a t i o n , w h i c h t h e n c a n b e tested f o r a l l t. A

F o r s m a l l t, s i m p l e r f o r m s c a n b e o b t a i n e d :

I» -

Qo

Wo / 2

r

0

2

or

Plots of t h e left side against \/Tgive

D /r , A

2

0

a n d so D . A


8


II

F o r r e c t a n g u l a r p a r a l l e l e p i p e d crystallites o f edges a, b, a n d c, t h e l i m i t i n g expressions a r e Q~ - Q

512

t =

Qoo

— Q

Q
— yo

i nFigure 3 ( 7 ) . MQO

Journal of Physics and Chemistry of Solids

Figure 3.

The % deviations from the \/T law as func-

tions of 9°° _ 9* Voo

YO

for particles of different forms (7) M

x

Curve 1: Sphere Curve 2: Cube Curve 3: Rectangular parallelepiped (2:2:1) Curve 4: Plane sheet


42.

BARRER

Intracrystalline

Diffusion

9

T h e c o r r e s p o n d e n c e w i t h t h e \ft l a w is i l l u s t r a t e d i n F i g u r e 4 ( 7 ) f o r the i n t r i n s i c d i f f u s i o n o f w a t e r i n c h a b a z i t e , g m e l i n i t e , a n d h e u l a n d i t e . 10Chobozite

09-

/


07-

/

/

040-3-

o o o

o

o

//

0-2-

•

•

1/

0-1-

r

0

Heulandite

/ / /

/ /

. A

o

o

Gmelinite

I

2

3

4

5

R 60

4

I

50

2

4

6

8

10 12

Journal of Physics and Chemistry of Solids

Figure 4.

Applicability of the \ftlaw for the intrinsic diffusion of water in chabazite, gmelinite, and heulandite (7) Calculated curves: Chabazite: O, 75.4°C; *, 30.8°C Gmelinite: O, 62.5°C; #, 31.7°C Heulandite: O, 77.8°C; *, 37.4°C

C O N S T A N T - V O L U M E VARIABLE-PRESSURE

time t =

S O R P T I O N OR D E S O R P T I O N .

At

0, f o r s o r p t i o n , a dose o f gaseous sorbate is i n t r o d u c e d i n t o the

s o r p t i o n v o l u m e a n d left t o d i s t r i b u t e itself b e t w e e n gas phase a n d crys tals.

E x a c t a n a l y t i c a l solutions are a v a i l a b l e , p r o v i d e d s o r p t i o n f o l l o w s

H e n r y ' s l a w (2,27).

T h u s , f o r spheres of r a d i u s r

Qtt -~ Q, Qo _ , - — ^ - 1 -

where r =

a . V ZK(K + D L K i K

0

exp - g ' T

n

w

9

(

J

[

+

1

)

+

a

A

8

j

r

-

^ ~ a n d «„ is the n t h p o s i t i v e root of the r e l a t i o n Tan a r

0

=

3r a 0

3 +

Xr

0

2

a

2

and where K

=

J J L

=

« M _ a=

(Qo)o ~ ( Q - ~ Qo)

I n this last expression, k is t h e H e n r y ' s l a w constant, a n d K denotes t h e


10


e q u i l i b r i u m r a t i o o f gas i n t h e gas phase a n d i n crystals. V

g

v o l u m e s o f gas phase a n d crystals, respectively.

(Qcc)

II

a n d V are 8

a n d (Qo) a r e

g

g

a m o u n t s o f gas finally a n d i n i t i a l l y i n t h e gas phase. F o r s m a l l e n o u g h times, t h e \ / T l a w a g a i n results i n t h e f o r m ( 6 ) Qt ~

Qo

6 (K +

Qco -

Q

r

=

0

0

K

1) \IT52 y

x

6 /(QQ), + Q

\

0

r \(Qo) ~ ( Q - 0

ilD2

Qo)/ r

9


T h e v a l i d i t y o f t h e \ / £ l a w is s h o w n u n d e r c o n s t a n t - v o l u m e

* variable

pressure c o n d i t i o n s w h e n H e n r y ' s l a w is a p p r o x i m a t e l y v a l i d i n F i g u r e 5.

0*8

f

0*6 0-4 0-2

4

Z

4

6

8

.j_

J

fO

/Z

f4

16

Transactions of the Faraday Society

Figure 5. Validity of the V T law in a constant-volume variable-pressure system where the sorption isotherms approach Henry's law (2) Curve 1: Ne in Li-mordenite at —185°C Curve 2: Ne in Ca-mordenite at —185°C Curve 3: Kr in Ba-mordenite at 24°C Curve 4: Kr in Levynite at 0°C O: Experimental points X : Calculated points, using the full solution of the diffusion equation The \ / 1 L a w and Particle Size and Shape Distributions in Powders. A s p e c i a l i m p o r t a n c e o f t h e yfl

l a w s is that, p r o v i d e d t i m e is s m a l l

e n o u g h f o r e a c h p a r t i c l e t o a c t as a semi-infinite m e d i u m , t h e l a w s h o l d w h a t e v e r t h e size a n d shape d i s t r i b u t i o n , w i t h l / r r e p l a c e d b y A / 3 V . 0

Thus, Qt ~ Qco -

Qo _ Qo

Mt_ _ 2A Moo V

(constant pressure)


42.

BARRER

Intracrystalline

Qt ~ Qco

Qo

— Qo

=

Diffusion

11

Mt_

(constant v o l u m e , H e n r y ' s law)

Ma

P r o v i d e d t o t a l surface areas, A, are m e a s u r e d , D

A

c a n be f o u n d . A c a n

b e d e t e r m i n e d i n several w a y s : 1.

B y p r o j e c t e d area ( t r u e area =

2.

B y f l o w [ K o z e n y - C a r m a n (16)

3 X projected area). procedure].

T h e s e g i v e g e o m e t r i c a l or s m o o t h e d areas, not t a k i n g surface

roughness


i n t o account. 3.

B y a d s o r p t i o n , u s i n g either (a) w a t e r - f i l l e d crystals, so that N or K r s o r p t i o n is l i m i t e d to external areas, or (b) s p h e r i c a l sorbate m o l e c u l e s too large to enter the c r y s t a l s — e.g., i s o - C H i or n e o - C , H i for c h a b a z i t e , sieve A , or a n y zeolite less o p e n t h a n these. 2

4

0

r

2

T h e a d s o r p t i o n area i n c l u d e s a l l

fine-scale

roughness a n d h e n c e i n

general w i l l exceed the s m o o t h e d areas f o u n d b y the other T h e t w o areas w i l l l e a d thus to different values of D , A

methods.

a n d it is not clear

w h i c h is best. F o r longer times, t h o u g h p o s s i b l y s t i l l i n the y/T

range,

effects of surface roughness u p o n the d i f f u s i o n w i l l h a v e d i e d out.

In

the first m o m e n t s t h e y w i l l not. It is u s e f u l to d e t e r m i n e b o t h areas, a n d so to g i v e u p p e r a n d l o w e r l i m i t s to D .

T h i s has not a l w a y s b e e n d o n e ,

A

a n d i n c o m p a r i n g values of D

f o u n d b y different authors, the m e t h o d

A

of d e t e r m i n i n g A s h o u l d be t a k e n i n t o account. A s expected f r o m the d i f f u s i o n theory, the larger the particles, the s l o w e r the s o r p t i o n ; A becomes s m a l l e r for constant V . T h i s is i l l u s t r a t e d i n F i g u r e 6 (8)

for s o r p t i o n of p r o p a n e at 2 0 0 ° C i n c h a b a z i t e .

Concentration-Dependent D

A

in Powders. It has b e e n a s s u m e d i n

the p o w d e r t e c h n i q u e s d i s c u s s e d so f a r that D

A

intracrystalline concentration.

does not d e p e n d u p o n

F o r the d i l u t e range of sorptions—e.g.,

w h e r e H e n r y ' s l a w is v a l i d — t h i s is correct.

H o w e v e r , as a l r e a d y c o n

sidered

i n concentration

(Table

III),

over e x t e n d e d ranges

Tiselius's

results f o r w a t e r i n a single c r y s t a l of h e u l a n d i t e s h o w e d strong c o n c e n tration dependence.

F o r p o w d e r s , 2 m e t h o d s m a y be m e n t i o n e d .

INTERVAL METHOD. The quantity Q

0

of sorbate i n i t i a l l y i n the c r y s t a l

c a n be v a r i e d systematically b y steps f r o m zero to near saturation. e a c h v a l u e of Q

0

of D

A

o b t a i n e d c a n be r e g a r d e d as constant over e a c h i n t e r v a l Q

0

Thus D

A

is f o u n d as a f u n c t i o n of Q .

dQ was often c o n s i d e r a b l e , c o m p a r e d w i t h Q . 0

A

-f- dQ.

A n i n t e r v a l m e t h o d w a s u s e d for

{)

several d i f f u s i n g species i n c h a b a z i t e b y B a r r e r a n d B r o o k (4), of D

At

a s m a l l extra a m o u n t , dQ, is t h e n s o r b e d , a n d the v a l u e

w a s o b t a i n e d over the i n t e r v a l Q

0

to Q*.

in which

Thus, an integral value Some results are g i v e n i n

T a b l e YVa, i n w h i c h the areas A w e r e those d e t e r m i n e d b y a flow m e t h o d . D

A

appears to decrease rather s t r o n g l y w i t h i n c r e a s i n g average c o n c e n t r a -


12


II

^Cftrve I: Particlesfa-% inch diametery outdsssed 14hs. dt470'480°C '.Particles 20-30mesh;out&jsscd l4hrs.dt4JD-4S$ Curve 3: Particles -80-IOC mesh; outyHut I4hrs. at470-480*C. Curve4: Partizks

Molecular Sieve Zeolites-II

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