Vapor Adsorption on Zeolites Considered as ... - ACS Publications

43 Vapor Adsorption on Zeolites Considered as Crystalline Specific Adsorbents

Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch043

Α. V. K I S E L E V Department of Chemistry, M.V. Lomonosov State University of Moscow and Institute of Physical Chemistry, U S S R Academy of Sciences, Moscow

Adsorption

on zeolites is discussed

a general theory of molecular porous

adsorbents,

relating of

a system

and

taking

in deriving

chemical

constants

vestigation

of

constants

on the

molecule;

(4)

different surements; librium

the

from the

structure

within

the

the

these

zeolite

and

field

zeolite

and

the

with the

(5) molecular—statistical the

of

the

(3)

in

adsorbate of

the

interactions

energy

for

possible

use

adsorption

calculations particular

these

physico-

physicochemical

and

potential

cavity,

data in conjunction

use data

these interactions; of

of the of

equations

adsorbate-adsorbent

experimental

dependence

of and

characteristics

(2) the

and the molecule-molecule

between

molecular

selection

interactions;

calculation

points

spectroscopic

of

characterizing

the

molecule-zeolite

(1)

thermodynamic

into account

adsorbate-adsorbate

equations

The

the

the framework on nonporous

considering:

in a general way

within

adsorption

of the

of

mea equi

molecules.

w i t h i n the zeolite cavities, e s p e c i a l l y near

the

-•• c a v i t y w a l l s , is heterogeneous, b u t the d i s t r i b u t i o n of the field p o t e n t i a l , w h i c h is d e t e r m i n e d b y the c r y s t a l l i n e structure of the z e o l i t e , is r e g u l a r t h r o u g h o u t the s a m p l e ( a l l cages are almost i d e n t i c a l ) . to the r e g u l a r d i s t r i b u t i o n of the

field

Owing

p o t e n t i a l , the m a i n features of

a d s o r p t i o n o n porous zeolites are s i m i l a r to those o n n o n p o r o u s crystals. F o r e x a m p l e , f o r b o t h n o n p o r o u s adsorbents

a n d p o r o u s zeolites,

the

heat of a d s o r p t i o n o f t e n increases w i t h the a d s o r p t i o n l e v e l because of adsorbate-adsorbate

interaction.

Sometimes, o w i n g to the sequence of

increase a n d decrease of this i n t e r a c t i o n , the heat of a d s o r p t i o n c u r v e acquires a w a v e - s h a p e d p a t t e r n ( F i g u r e 1 ) a n d the a d s o r p t i o n isotherms pass t h r o u g h i n f l e c t i o n points ( F i g u r e 2).

T h i s s i m i l a r i t y shows that i t

37

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


38

M O L E C U L A R SIEVE ZEOLITES

5 Q , / J mole/m

10

10 a, m mole/gram

2

Figure

1.

II

Heat of adsorption, Q , at different values of adsorption level a a. Isobutyl alcohol on graphitized carbon black (6) b. Water (4) on zeolite KX L = heat of condensation of the vapor

10

10 20 30 40 50 60 o,ju moles /gram

0.02 .04 .06 .08 0.1 /?mm Hg Figure 2.

100

200 300 tf,mg/gram

400

10 /^mm Hg

Adsorption of CCl on graphitized carbon black (34) a. Heats of adsorption (15) b. Adsorption isotherms (34) Adsorption of phosphorus vapor on zeolite NaX (13) c. Heats of adsorption d. Adsorption isotherms h


43.

KISELEV

Vapor Adsorption

On

Zeolites

39

is possible to a p p l y the m o l e c u l a r t h e o r y of a d s o r p t i o n (28,

35, 38)

to

p o r o u s zeolites. S u c h a n a p p r o a c h makes it unnecessary to assign to the adsorbate i n s i d e the m i c r o p o r e s the p r o p e r t i e s of c o n t i n u o u s c o m p r e s s e d l i q u i d , w h i c h u s u a l l y is d o n e i n the case of a d s o r p t i o n b y m i c r o p o r o u s adsorbents. T h e d e v e l o p m e n t of the m o l e c u l a r t h e o r y of a d s o r p t i o n s h o u l d c o n


sist of the f o l l o w i n g aspects: ( 1 ) E q u a t i o n s s h o u l d b e selected or a n e w m o r e g e n e r a l e q u a t i o n d e v e l o p e d w h i c h h a v e a m o l e c u l a r - s t a t i s t i c a l basis a n d d e s c r i b e the r e l a t i o n s h i p s b e t w e e n the a m o u n t of a d s o r p t i o n , the heat of a d s o r p t i o n , the heat c a p a c i t y of the system, the pressure, a n d the t e m p e r a t u r e . V a r i ous constants i n these equations m u s t h a v e a clear p h y s i c a l m e a n i n g . T h e s e equations m u s t d e s c r i b e the exact shape of the isotherms ( F i g u r e 2 ) a n d m u s t r e d u c e to the H e n r y e q u a t i o n at l o w coverage. ( 2 ) T h e d e v e l o p e d equations s h o u l d b e u s e d f o r a n a l y z i n g e x p e r i m e n t a l t h e r m o d y n a m i c d a t a to o b t a i n p h y s i c o c h e m i c a l constants—e.g., H e n r y constants—whose m a g n i t u d e is i n d e p e n d e n t of the fitting procedure. ( 3 ) T h e relationships s h o u l d b e e s t a b l i s h e d b e t w e e n these constants a n d s u c h parameters as the t y p e of the z e o l i t e lattice, the t y p e a n d c o n c e n t r a t i o n of cations, the degree of d e c a t i o n i z a t i o n , a n d the structure of the adsorbate m o l e c u l e . A s a result, s e m i e m p i r i c a l relationships m a y b e o b t a i n e d w h i c h c o u l d b e u s e d f o r the p r a c t i c a l c a l c u l a t i o n of the a d s o r p tion equilibrium. ( 4 ) T h e m o l e c u l a r field d i s t r i b u t i o n w i t h i n the channels m u s t b e i n v e s t i g a t e d , t a k i n g i n t o c o n s i d e r a t i o n the structure of the zeolite, a n d the c a l c u l a t i o n of the p o t e n t i a l e n e r g y of i n t e r a c t i o n b e t w e e n the zeolite a n d p a r t i c u l a r m o l e c u l e s m u s t b e m a d e . T h e s e investigations w o u l d b e assisted greatly b y spectroscopic studies w h i c h w o u l d m a k e it p o s s i b l e to e s t a b l i s h the n a t u r e of the zeolite surface, the presence a n d the n a t u r e of s t r u c t u r a l defects, a n d the state of the a d s o r b e d m o l e c u l e s . ( 5 ) T h e statistical c a l c u l a t i o n of t h e r m o d y n a m i c constants f o r the z e o l i t e - a d s o r b a t e system s h o u l d be m a d e . A c o m p a r i s o n of these c o n stants w i t h the e x p e r i m e n t a l values o b t a i n e d i n Stages 2 a n d 3 w o u l d a l l o w the i n t r o d u c t i o n of some c o r r e c t i o n factors for the constants de s c r i b i n g the p o t e n t i a l f u n c t i o n s of the i n t e r a c t i o n . A s a result, a m o r e a c c u r a t e g e n e r a l scheme of m o l e c u l a r - s t a t i s t i c a l c a l c u l a t i o n of the molecule—zeolite system w o u l d be o b t a i n e d . I n the present r e v i e w , an attempt is m a d e to a n a l y z e the e x p e r i m e n t a l d a t a a n d to relate the various aspects i n the d e v e l o p m e n t of the m o l e c u l a r t h e o r y of a d s o r p t i o n as a p p l i e d to zeolites. Selection of the Adsorption

Isotherm

T h e a d s o r p t i o n isotherms w i t h

Equation ( F i g u r e 2)

a n d w i t h o u t (11,

30)

points of i n f l e c t i o n c a n be d e s c r i b e d b y the same e q u a t i o n . T h i s e q u a t i o n necessarily takes into a c c o u n t the a d s o r b a t e - a d s o r b e n t

and

adsorbate-


40

M O L E C U L A R SIEVE

ZEOLITES

II

adsorbate i n t e r a c t i o n . It is b a s e d o n 2 s i m p l i f i e d m o d e l s . A t sufficiently h i g h temperatures, use is m a d e of the m o d e l for n o n l o c a l i z e d a d s o r p t i o n together w i t h the equations of state of the adsorbate.

T h e equations of

the v a n der W a a l s a n d v i r i a l types are r e l a t e d to the isotherms of a d s o r p t i o n of H i l l - d e B o e r (16)

a n d W i l k i n s (1, 11, 28, 40),

respectively. A n

other m o d e l i n v o l v i n g l o c a l i z e d a d s o r p t i o n f o l l o w e d b y association

of

a d s o r b e d molecules leads to i s o t h e r m equations c o n t a i n i n g a t e r m w h i c h i n c l u d e s the i n t e r a c t i o n energy of n e i g h b o r i n g m o l e c u l e s a n d their co o r d i n a t i o n n u m b e r (9)

or the association constant (6, 30).

B o t h models


satisfactorily describe a d s o r p t i o n isotherms w i t h or w i t h o u t a n inflection point. F r o m the p o i n t of v i e w of the m o r e g e n e r a l statistical t h e o r y of a d s o r p t i o n , i f the energy d i s t r i b u t i o n o n the surface is k n o w n w i t h suffi cient a c c u r a c y , there is n o necessity

to use a n y s p e c i a l model—e.g.,

localized adsorption. O n the basis of this g e n e r a l t h e o r y (35, 3 8 ) , the i n i t i a l r e g i o n of the i s o t h e r m is d e s c r i b e d b y a n e x p o n e n t i a l series w i t h v i r i a l coefficients: a ^

G = K

+

l P

K p*

+

2

...

(1)

or b y the reverse series: = KJa

V

+

KJa

2

+

. . .

(la)

H e r e , G is the a d s o r p t i o n p e r g r a m of zeolite (at l o w v a p o r pressure, p, the v a l u e of G is close to the a d s o r p t i o n l e v e l , a);

K

±

a n d Ki

are H e n r y

constants c h a r a c t e r i z i n g the a d s o r b a t e - a d s o r b e n t i n t e r a c t i o n ; K

2

are

constants

c h a r a c t e r i z i n g the

and K '

pair-wise adsorbate-adsorbate

a c t i o n w h i c h is i n f l u e n c e d b y the adsorbent

2

inter

field.

E q u a t i o n l a is a p a r t i c u l a r case ( a t l o w p a n d a)

of the W i l k i n s

equation: V = a exp ( d +

Ca 2

+

C a 3

2

+...)

= a exp

C , a * - ')

(2)

i = 1 T h i s series u s u a l l y converges r a p i d l y . T h u s , the isotherms of a d s o r p t i o n o n the n o n p o r o u s adsorbent ( 5 ) , as w e l l as i n the cavities of zeolite, c a n be d e s c r i b e d satisfactorily—i.e., u p to ^

75%

saturation of z e o l i t e — b y

u s i n g the first 3 or 4 C coefficients ( F i g u r e 3 a ) . t

E q u a t i o n 2 c l e a r l y de

scribes the isotherms, either w i t h or w i t h o u t i n f l e c t i o n , a n d also those i n c l u d i n g a phase t r a n s i t i o n ( F i g u r e 3 b ) . E q u a t i o n 2 describes not o n l y the nonspecific a d s o r p t i o n b y zeolites of m o l e c u l e s of g r o u p A (28, 29)

b u t also the a d s o r p t i o n of q u a d r u p o l e -

t y p e molecules s u c h as C 0 , w i t h respect to w h i c h zeolites are 2

heterogeneous

(1, 11).

T h i s heterogeneity, l i k e the

more

adsorbate-adsorbate

i n t e r a c t i o n , is reflected i n the s i g n a n d m a g n i t u d e of C*. T h u s , E q u a t i o n 2


43.

KISELEV

Vapor Adsorption

41

On Zeolites


a

200

b

400 600 800 1000 P,mmHg

0.00005 0.00010 P,mmHg

Figure 3. Adsorption isotherms of ethane on zeolite LiX a. Experimental points (18) at 25°C are shown with the curves calculated by Equation 2; p = a exp (4.8600 - 0.22166a + 0.10249a 4- 0.009465a ) (A. G. Bezus). Curves 1-4 were calculated using 1, 2, 3, and 4 terms in the exponent, respectively. b. At —150°C; calculated according to Equation 4; constants are indicated in the caption for Figure 6. 2

3

I

2 3 a, m mole /gram Zhurnal Fizicheskoi Khimii

Figure 4. Values of constant C determined by A. G. Bezus from Equation 2 at i = 3 (O) and i = 4 (U) for different ranges of a in experimental adsorption isotherms of ethane on zeolite LiX (14) t

m a y b e u s e d w i t h a d v a n t a g e i n d e s c r i b i n g the v a p o r a d s o r p t i o n b y zeo lites, t h o u g h other a p p r o x i m a t e equations ods o f t a k i n g i n t o a c c o u n t

( i n v o l v i n g the different m e t h

the adsorbate-adsorbate

interaction)

give

satisfactory results f o r c e r t a i n systems (7, 9, 30). U n t i l n o w , E q u a t i o n 2


42


II

has b e e n a p p l i e d to s i m p l e cases w h e r e the a d s o r p t i o n i s o t h e r m contains n o m o r e t h a n one i n f l e c t i o n p o i n t . Treatment of Experimental

Data Using Virial

Equations

V a r i o u s c o m p l e x curves c a n be satisfactorily a p p r o x i m a t e d b y e q u a tions of the l a a n d 2 t y p e . H o w e v e r , the s e c o n d stage i n the d e v e l o p m e n t of the m o l e c u l a r t h e o r y of a d s o r p t i o n concerns the d e t e r m i n a t i o n of K i and K

or C

2

a n d C , w h i c h m u s t d e p e n d o n l y o n the properties of the

1

2


system ( t h e structure of the adsorbent a n d adsorbate m o l e c u l e ) a n d be i n d e p e n d e n t of the fitting p r o c e d u r e . W i t h the a i d of E q u a t i o n 2, there f o r e , one c a n o b t a i n v a l u e s f o r C

and C

1

2

w h i c h are p r a c t i c a l l y i n d e

p e n d e n t of the n u m b e r of terms w i t h i n the series a n d of the i n t e r v a l of e x p e r i m e n t a l values of a ( b e g i n n i n g at a l o w c o v e r a g e ) .

F i g u r e 4 shows

a n e x a m p l e i l l u s t r a t i n g the d e t e r m i n a t i o n of C i . T h e d e p e n d e n c e of C

o n t e m p e r a t u r e is s h o w n i n F i g u r e 5.

x

a p p r o x i m a t e f o r m of these d e p e n d e n c e s is Ci ^ T h e l i n e a r d e p e n d e n c e of C

±

adsorption, Q

u

Bi

-

(=\nKi)

The

(1,6,28):

Qi/RT

(3)

o n 1 / T i m p l i e s that the heat of

at zero coverage i n the p a r t i c u l a r i n t e r v a l of T is i n d e

p e n d e n t of t e m p e r a t u r e .

If the same a s s u m p t i o n is m a d e f o r Q , Q , etc., 2

the d e p e n d e n c e of a o n p a n d . T b e c o m e s (1,6, V =

i i a exp ( £ Bi a* ~ ') exp ( £ i = 1 i = 1

3

28): Q /RT)

(4)

{

F i g u r e 6 gives examples of isotherms that h a v e i n f l e c t i o n p o i n t s a n d also of those that d o not. I n these cases, use w a s m a d e of 4 terms i n E q u a t i o n 4.

It c a n be seen f r o m F i g u r e 6 that E q u a t i o n 2 s a t i s f a c t o r i l y

describes

a d s o r p t i o n o n m i c r o p o r o u s zeolites, as i n the case of a d s o r p t i o n o n n o n porous graphitized carbon black

(6).

It is v e r y i m p o r t a n t to o b t a i n a c c u r a t e l y the first 2 constants and C

2

(Ci

or K i a n d K ) f r o m the e x p e r i m e n t a l d a t a i n o r d e r to c o m p a r e 2

t h e m w i t h those c a l c u l a t e d f r o m the m o l e c u l a r - s t a t i s t i c a l t h e o r y . Ci and C

2

Here,

constants w e r e d e t e r m i n e d f r o m the e x p e r i m e n t a l i s o t h e r m b y

the least squares m e t h o d w i t h the a i d of a c o m p u t e r . H o w e v e r , f o r p r a c t i c a l p u r p o s e s , i t is necessary to d e s c r i b e the isotherms to a h i g h e r a d s o r p t i o n l e v e l . F r o m F i g u r e s 3 a n d 6, i t c a n b e seen that i n o r d e r to r e p r o d u c e the i s o t h e r m u p to >—75% s a t u r a t i o n of the a d s o r b e n t a n d to c a l c u l a t e a at different values of p a n d T, i t is sufficient to d e t e r m i n e o n l y 2 m o r e constants, C

3

and C . 4

Constants Bi a n d Qi i n E q u a t i o n 4 c a n be d e t e r m i n e d either f r o m a d s o r p t i o n measurements of a at v a r i o u s p a n d T or f r o m

measurements



43.

KISELEV

Vapor Adsorption

On Zeolites

3.0

3.5 I0 /T

43

4.0

3

Figure 5. Dependence of constant (see Figure 4) on I/T

a

b

100 P,mm

200

200 P,mm

d

J

1

c

400

200 400 P,mm

e

1

I—

1 2 3 4 a, m mole/gram

O

I

,

f

!

a n d QuQ

2

w h i c h can be used

f o r c o m p a r i s o n w i t h statistical c a l c u l a t i o n s so f a r h a v e b e e n

obtained

o n l y f o r t h e a d s o r p t i o n of gases. F i g u r e 7 shows the dependences of Qi a n d C o n the r a d i u s , r, f o r zeolite X c o n t a i n i n g a l k a l i cations. T h e c o m x

p o s i t i o n of t h e zeolite is d e s c r i b e d b y A v g u l (4).

F o r nonspecific adsorp

t i o n of ethane, Qx g r a d u a l l y increases w i t h the increase i n r. A c c o r d i n g l y , Ci (=

—In K i ) decreases. I n this case, Q

2

increases a n d C

2

F o r specific a d s o r p t i o n of ethylene, the heat of a d s o r p t i o n , Q

Li

0.5

1.0 r, A

1.5

0.5

decreases. on chang-

l9

+

1.0 r, A

1.5

Figure 7. Adsorption of ethane (open circles) and ethylene (solid circles) on zeolites X; dependence of Q and C on the ionic radii, r, of the exchange cations (calculated by A. G. Bezus and Pham Quang Du) t

t


43.

KISELEV

Vapor Adsorption

On

45

Zeolites

i n g f r o m N a X to C s X zeolite, g r a d u a l l y decreases w h i l e C

x

correspond

i n g l y increases; the isotherms of these systems d o n o t e x h i b i t i n f l e c t i o n points ( F i g u r e 6 ) . A s m a l l increase i n Q i f o r ethylene o n g o i n g f r o m L i X to N a X zeolite a n d the c o r r e s p o n d i n g decrease i n C i m a y b e c a u s e d b y a l o w e r ( b y 7 % ) t o t a l c o n c e n t r a t i o n of the L i p l u s N a cations i n this +

p a r t i c u l a r s a m p l e of L i X zeolite (2, 12, For

+

27).

sufficiently strong a d s o r b a t e - a d s o r b a t e

interaction a n d w i t h a

c o r r e s p o n d i n g decrease i n t e m p e r a t u r e , E q u a t i o n 4 leads to a n i s o t h e r m h a v i n g a n i n f l e c t i o n p o i n t b o t h i n the case o f a d s o r p t i o n b y n o n p o r o u s Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch043

adsorbent—e.g., o n g r a p h i t i z e d t h e r m a l c a r b o n b l a c k (6)—and t i o n i n s i d e the zeolite channels.

of a d s o r p

A p p a r e n t l y , these p r o p e r t i e s are pos

sessed b y the system p h o s p h o r u s — z e o l i t e N a X (13),

F i g u r e 2. I n this

case, a r a p i d increase i n the heat of a d s o r p t i o n s h o u l d b e e x p e c t e d i n the r e g i o n of l o w coverage, as w a s o b s e r v e d f o r n o n p o r o u s adsorbent

(15)

( c o m p a r e F i g u r e s 2a a n d 2 c ) . A decrease i n the a d s o r p t i o n l e v e l a n d i n t h e heat of specific a d s o r p t i o n of C 0 has b e e n r e p o r t e d f o r zeolites w i t h a d e c r e a s i n g c o n c e n t r a t i o n 2

of exchange cations (2,12, 27).

T h e r e is a decrease i n the heat of specific

a d s o r p t i o n of b e n z e n e o n c h a n g i n g f r o m N a X z e o l i t e to H Y zeolite

(26).

I n the X - t y p e zeolite, the effect of s u b s t i t u t i o n of N a b y d o u b l y c h a r g e d +

Ca

2 +

32).

o n t h e heat of m o l e c u l a r a d s o r p t i o n also has b e e n i n v e s t i g a t e d

(26,

I n t h e w a l l s of large cavities there a p p e a r n o t o n l y centers o c c u p i e d

by C a

2 +

ions b u t also vacant centers free of a n y cations. A c o m p a r i s o n of

the dependences of the heat of a d s o r p t i o n f o r b e n z e n e f o r zeolites h a v i n g different c o n c e n t r a t i o n o f C a

2 +

indicates that the h i g h e r heat of a d s o r p

t i o n is r e l a t e d to the S - c e n t e r s o c c u p i e d b y C a n

2 +

ions, whereas o n centers

free of cations the heat of a d s o r p t i o n of b e n z e n e lies b e l o w that of the c a t i o n i z e d centers.

Further work should be carried out on deriving

q u a n t i t a t i v e relationships f o r Q

l9

C i and Q , C 2

2

as t h e f u n c t i o n of t h e

A l : S i r a t i o , types a n d c o n c e n t r a t i o n of exchange cations, a n d degree of d e c a t i o n i z a t i o n . T h e examples g i v e n above i n d i c a t e that these p r o b l e m s can be solved. Specific

interaction

molecules at s m a l l a.

causes

greater

l o c a l i z a t i o n of the

adsorbate

I n the case of s t r o n g l y a d s o r b i n g m o l e c u l e s c o n

t a i n i n g s u c h f u n c t i o n a l groups as H O — , H N — , etc., cations i n z e o l i t e 2

c a n a c q u i r e a c e r t a i n m o b i l i t y as a increases.

T h e relationships b e t w e e n

Q a n d a i n these cases b e c o m e v e r y c o m p l e x (see

Figure 1).

Water

molecules are l o c a l i z e d first b y the cations, t h e n they p o s s i b l y f o r m a k i n d of w a t e r cage b y m u t u a l h y d r o g e n b o n d s i n s i d e the zeolite c a v i t y , and

finally

fill

u p the c e n t r a l p a r t of this zeolite a n d w a t e r cage.

process d e p e n d s o n the t y p e o f c a t i o n (4).

This

T w o steps i n the p l o t o f Q

vs. a f o r a m m o n i a a d s o r p t i o n o n z e o l i t e C a A w e r e f o u n d i n R e f . 36. T h e


46


coordination of water a n d ammonia around C u

2 +

II

ions a t t h e s a t u r a t i o n

of z e o l i t e s i m i l a r t o that i n s o l u t i o n complexes w e r e f o u n d b y E S R a n d s p e c t r o s c o p i c m e t h o d s ( 3 3 ) . I t is i n f e r r e d thus that at h i g h a d s o r p t i o n l e v e l o f s m a l l s p e c i f i c a l l y a d s o r b e d m o l e c u l e s , t h e o r y m a y a c q u i r e some features s i m i l a r t o t h e t h e o r y o f b u l k solutions. T h u s , t h e d e t e r m i n a t i o n o f Q i a n d C i values o n t h e basis o f measure ments c a r r i e d o u t at o r d i n a r y temperatures i n these cases b e c o m e s diffi cult.

I n s u c h cases, h o w e v e r , o n e c a n a p p r o x i m a t e l y estimate t h e a d d i

tional contribution of the energy

o f specific i n t e r a c t i o n a r i s i n g f r o m


7r-bonds o r t h e f u n c t i o n a l g r o u p s at a s o m e w h a t h i g h e r a—e.g., w h e n values o f a c o r r e s p o n d to 1 m o l e c u l e p e r c a v i t y . A Q c i f i c is d e t e r m i n e d spe

b y s u b t r a c t i n g t h e heat o f a d s o r p t i o n of t h e reference m o l e c u l e ( i n c a p a b l e to specific i n t e r a c t i o n )

f r o m t h e heat o f a d s o r p t i o n o f t h e s p e c i f i c a l l y

a d s o r b e d m o l e c u l e (10, 28-30).

B o t h m o l e c u l e s m u s t h a v e s i m i l a r geome

try, close values o f p o l a r i z a b i l i t y a n d o f heat o f a d s o r p t i o n o n n o n s p e c i f i c adsorbent

(6).

F i g u r e 8 shows t h e r e l a t i o n s h i p s b e t w e e n t h e h e a t o f a d s o r p t i o n a n d the p o l a r i z a b i l i t y o f m o l e c u l e s ethers,

a n d n-alcohols.

AQ

spe

cifi

f o r a h o m o l o g o u s series o f n-alkanes, C

o f t h e f u n c t i o n a l groups — O — a n d

30-

0

2

4 6 8 10 Polarizability oe, A

12

3

Figure 8. Dependence of the heat of adsorption, Q , for zeolite NaX (at a = 1 molecule per cavity) on the polarizability of the molecule a for n-alkanes ( 3 0 ) , ethers ( 4 ) , and n-alcohols (4)


43.

KISELEV

Vapor Adsorption

47

On Zeolites

H O — f o r t h e series o f c o m p o u n d s e x a m i n e d is p r a c t i c a l l y i n d e p e n d e n t o f the l e n g t h o f t h e h y d r o c a r b o n c h a i n i n these m o l e c u l e s . T h e d a t a s u m m a r i z e d i n T a b l e I i l l u s t r a t e h o w values f o r Q a n d AQspecific

d e p e n d o n t h e structure o f t h e adsorbate

molecules.

I n the

series o f g r o u p - B m o l e c u l e s , t h e m a x i m u m e n e r g y o f specific i n t e r a c t i o n is o b s e r v e d f o r n i t r o m e t h a n e a n d a c e t o n i t r i l e , b o t h o f w h i c h h a v e l a r g e dipole

moments.

Even

stronger

specific

interaction

is o b s e r v e d f o r

m o l e c u l e s o f the D - g r o u p , w h i c h c a n f o r m a n a d d i t i o n a l h y d r o g e n b o n d w i t h the n e g a t i v e l y c h a r g e d o x y g e n atoms o f t h e zeolite structure. F o r


the

i n v e s t i g a t e d c o m p o u n d s , t h e r e l a t i v e c o n t r i b u t i o n o f t h e specific

interaction

energy,

AQ

s p e c i f i c

decreases

/Q,

with

t h e increase

length of the hydrocarbon chain of the molecule.

in

T h e larger

the

value

of t h e h e a t o f a d s o r p t i o n f o r t e t r a h y d r o f u r a n c o m p a r e d w i t h that o f furan

(23)

is a t t r i b u t e d m a i n l y t o t h e difference

structure o f these g e o m e t r i c a l l y s i m i l a r m o l e c u l e s .

i n the electronic T h e conjugation of

the electrons o f t h e o x y g e n a t o m w i t h ?r-bonds i n f u r a n causes a m o r e u n i f o r m d i s t r i b u t i o n o f t h e e l e c t r o n d e n s i t y i n this m o l e c u l e . creases t h e d i p o l e m o m e n t a n d

AQ

s p e

cific.

This de

T h e h e a t of a d s o r p t i o n of f u r a n

o n t h e zeolite is thus close to that o f b e n z e n e . The magnitude of A Q

s p e c i f i c

thus o b t a i n e d m a y b e o f p r a c t i c a l v a l u e

f o r e s t i m a t i n g t h e heat o f a d s o r p t i o n f o r h y d r o c a r b o n d e r i v a t i v e s c o n taining functional groups, taking into account the molecule

geometry.

T h e heat o f a d s o r p t i o n o f a c o m p l e x m o l e c u l e , c a p a b l e o f specific i n t e r a c t i o n , c a n b e a p p r o x i m a t e l y expressed as t h e s u m of t h e nonspecific heat of a d s o r p t i o n , Q , o f t h e s u i t a b l e r e f e r e n c e m o l e c u l e o f g r o u p A a n d o f A

the c o n t r i b u t i o n o f t h e specific i n t e r a c t i o n energy f o r t h e c o r r e s p o n d i n g functional group,

AQ

s p e C

ific,

t a k e n f r o m T a b l e I. A c c o r d i n g to another

m e t h o d (see T a b l e I I I i n R e f . 4), t h e heat o f a d s o r p t i o n o f a c o m p l e x m o l e c u l e c a n b e expressed as t h e s u m o f t h e i n c r e m e n t s o f the t o t a l h e a t of a d s o r p t i o n f o r e a c h segment o f the m o l e c u l e . F o r these c a l c u l a t i o n s at different a, i t is necessary to s t u d y t h e dependences o f

AQ

s p e

cific

a n d of

increments of Q o n the adsorption level. Potential Energy of Interaction

of Molecules with Zeolite

T h e potential energy of adsorption f o r various cationized X - a n d A - t y p e zeolites has b e e n c a l c u l a t e d b y v a r i o u s authors (9, 12, 30). R e c e n t l y (17, 18), t h e p o t e n t i a l energy of a d s o r p t i o n w a s c a l c u l a t e d i n a large c a v i t y of t h e zeolite t y p e A . A s t h e S i : A l r a t i o is 1:1, i t w a s a s s u m e d that t h e excess o f n e g a t i v e charge o f t h e A 1 0

4 / 2

t e t r a h e d r o n is d i s t r i b u t e d

u n i f o r m l y over a l l t h e o x y g e n atoms. T h u s , a c h a r g e z =

— 0.25e ( h e r e ,

e = e l e m e n t a r y c h a r g e ) w a s assigned to e a c h o x y g e n a t o m . O n the basis of t h e a s s u m p t i o n o f t h e a d d i t i v e p r o p e r t y o f p a i r - w i s e interactions, t h e

American Chemical Society Library

In Molecular Sieve1155 Zeolites-II; E., et al.; 16th Flanigen, St., N.W. Advances in Chemistry; American Chemical Society: Washington, DC, 1971. WashinctofL D i L ?NHfi

48

MOLECULAR

SIEVE ZEOLITES

II

Table I. Heat of Adsorption, Q , and Contribution of the Specific Interaction Energy, A Q i f i c , for N a X Zeolite, Kcal/Mole 0

speC

Properties Which Determine the Specific Nature of Adsorption

A

Adsorbate

Q of Group

Molecules x-bonds, quadrupole moment

C2H4

CeHe N 2


co Dipole moment, ability to form hydrogen bonds through oxygen and nitrogen atoms only

2

(CH ) 0 (C H ) 0 CH N0 CH CN 3

2

2

6

2

3

2

3

0

2

6

3

7

4

9

3

3

B

8.9 18.0 5.0 10.0

3.0 4.5 2.3 6.0

0.34 0.25 0.46 0.55

16.4 21.0 19.9 10.0

7.6 7.6 10.0 11.0

0.46 0.36 0.50 0.58

(15.5) 13.2 13.2 13.2 13.2 (12.5) 11.5

(0.8) 0.72 0.63 0.57 0.51 (0.8) 0.64

18.5 18.4 20.9 23.2 26.0 16.0 18.0

H 0 CH3OH C H OH C H OH n-C H OH NH CH NH 2

[specific

Q

(^specific

of Group D

Molecules Dipole moment, ability to form hydrogen bonds through oxygen or n i t r o g e n a t o m s , as w e l l as t h r o u g h O H or N H hydrogen atoms

A

2

Value of a = 1 molecule per cavity, experimental data

8, 4, 7, 23, 30).

t o t a l p o t e n t i a l energy, V, o f N a d s o r b e d s p h e r i c a l m o l e c u l e s i n t h e field of a large c a v i t y o f z e o l i t e A has t h e f o l l o w i n g f o r m :

V(n,? ,...

,t )

2

N

= I > ( 7 \ - ) + Z * (I"" "I) i =

Here,

1

1
k

k

w h e r e is t h e i n t e r a c t i o n e n e r g y of i t h m o l e c u l e w i t h kih center o f z e o l i t e , a c c o u n t w a s t a k e n o n l y o f t h e cations L i , N a , a n d C a +

+

2 +

i n the various

positions a n d o f t h e o x y g e n atoms b e a r i n g n e g a t i v e c h a r g e z = 0

— 0.25e.

It w a s a s s u m e d that t h e c o n t r i b u t i o n a r i s i n g f r o m t h e charges d i s t r i b u t e d w i t h i n AIO4/2 a n d S i 0 / 2 t e t r a h e d r a c a n b e expressed a p p r o x i m a t e l y b y 4

a charge of z = 0

—0.25e l o c a t e d at t h e centers of t h e o x y g e n atoms. T h e

p o l a r i z a b i l i t y o f o x y g e n i n this state w a s e s t i m a t e d b y B r a u e r et al

(18).

O n t h e other h a n d , h i g h charges o n A l a n d S i w e r e assigned i n R e f . 22.


43.

Vapor Adsorption

KisELEV

On

49

Zeolites

T h e energy Φ ( ^ ) w a s expressed as i n earlier studies (18, 30) as t h e s u m of t h e d i s p e r s i o n , i n d u c t i o n , a n d r e p u l s i o n interactions.

I t w a s as

sumed that:

< ï w (rù =Zc \t-n\-«

(7)

k

induc. (u)

=

-

Φ β ηΐ. (rd = Σ Γ

Ρ

\ a

B

[E

m

Iu -

k

(u)}*

(8)

η |-

(9)

12


k C o n s t a n t C f o r the d i s p e r s i o n a t t r a c t i o n w a s d e t e r m i n e d f r o m the Slaterk

K i r k w o o d equation: Seh ^ where a

m

"

S K

4 χ (m)"* ·

(* /n y* m

m

+

(a*/n*)

1/2

{

W

)

a n d a are t h e p o l a r i z a b i l i t i e s ; η™,η& are t h e effective n u m b e r s k

of electrons f o r the adsorbate m o l e c u l e a n d exchange c a t i o n o r o x y g e n a t o m i n zeolite, r e s p e c t i v e l y ; h is t h e P l a n c k ' s constant a n d m the e l e c t r o n mass.

T h e electrostatic

field

strength v e c t o r at p o i n t r w a s c a l c u l a t e d {

from the equation: Ε (7*) = where e

k

-

g r a d (Σ

^ ^) €k

(ID

is t h e c a t i o n c h a r g e o r charge of t h e o x y g e n a t o m i n the zeolite.

Constants B

k

w e r e d e t e r m i n e d b y m i n i m i z i n g Φ ( ^ ) at t h e e q u i l i b r i u m

d i s t a n c e b e t w e e n t h e m o l e c u l e a n d t h e c o r r e s p o n d i n g kth center i n t h e w a l l s of t h e c a v i t y . T h e e q u i l i b r i u m distance w a s c a l c u l a t e d f r o m t h e v a n d e r W a a l ' s a n d i o n i c r a d i i o f m o l e c u l e s a n d kth. center. O w i n g to t h e h i g h s y m m e t r y of the lattice f o r the L i A a n d N a A zeo lites, a n analysis w a s m a d e o n l y of t h e section c o m p r i s i n g 1/48 of t h e t o t a l c a v i t y v o l u m e ( F i g u r e 9 ). T h e v o l u m e of the c o r r e s p o n d i n g section f o r C a A zeolite w a s 1 / 2 4 o f t h e t o t a l v o l u m e of t h e c a v i t y . T h e p o t e n t i a l energy w a s c a l c u l a t e d f o r t h e i n n e r c a v i t y of the selected section f o r 16 different d i r e c t i o n s i n t h e case of L i A a n d N a A zeolites a n d f o r 31 d i r e c tions i n t h e case o f t h e C a A zeolite.

F o r e a c h of these d i r e c t i o n s , the

Φ ( u ) w a s c a l c u l a t e d f o r 40 different positions of t h e m o l e c u l e . T h e lattice sums

and



50


II

Figure 9. Elementary, cell of zeolite A containing 8 univalent cations, O, inside six-membered rings and 6 cations, O, in eight-membered rings; a section is shown in which there are 16 selected directions a n d t h e field strength w e r e c a l c u l a t e d i n o r d e r to d e t e r m i n e t h e c o n t r i b u tions a r i s i n g f r o m Φ

2

+

(0.1364 -

(0.0500 -

106.8/7>

+

17.73/T)a ]

(3)

3

I n o r d e r to describe a d s o r p t i o n e q u i l i b r i a f o r ethane o n zeolite L i X f r o m three g i v e n a d s o r p t i o n isotherms f o r temperatures of 2 5 ° , 5 0 ° , a n d 75 ° C , e i g h t constants h a v e to b e d e t e r m i n e d , j u d g i n g b y E q u a t i o n 3. O b v i o u s l y , a d d i t i o n a l e x p e r i m e n t a l d a t a are r e q u i r e d , s u c h as isotherms or d i f f e r e n t i a l heats of a d s o r p t i o n . T h u s , to d e s c r i b e a d s o r p t i o n e q u i l i b r i a b y the m e t h o d p r o p o s e d , one s h o u l d first use, i n o r d e r to d e t e r m i n e the e q u a t i o n constants, s u c h extensive e x p e r i m e n t a l i n f o r m a t i o n as w i l l s u p p l y answers to a l l questions of interest to the p r a c t i c a l w o r k e r . T h e advantage of E q u a t i o n 3 is that it p r o v i d e s a n accurate d e s c r i p t i o n of a d s o r p t i o n e q u i l i b r i a over the ranges of temperatures a n d pres sures u s e d f o r the d e t e r m i n a t i o n of the constants. T h i s m a y b e of interest, f o r e x a m p l e , i n o b t a i n i n g expressions i n a n a n a l y t i c a l f o r m for d i f f e r e n t i a l heats a n d entropies of a d s o r p t i o n most closely c o r r e s p o n d i n g to e x p e r i mental data. T h e coefficient of the first t e r m of the v i r i a l series i n E q u a t i o n 1 is the inverse H e n r y constant for the t e m p e r a t u r e c o n s i d e r e d .

F r o m the

g r a p h of the i s o t h e r m i n F i g u r e 3 of the s u r v e y p a p e r , it f o l l o w s that the l i n e a r i t y of the i n i t i a l section of the a d s o r p t i o n i s o t h e r m of ethane o n z e o l i t e L i X i n a c c o r d a n c e w i t h the c a l c u l a t e d H e n r y constant is o b s e r v e d f o r a d s o r p t i o n values not e x c e e d i n g 0.7 m m o l e / g .

A c c o r d i n g to Κ. N .


64


M i k o s ( 5 ) , d e h y d r a t e d zeolite L i X contains 3.99 χ

10

20

II

large v o i d s p e r

g r a m , c o r r e s p o n d i n g to 0.68 m m o l e / g . T h u s , f o r ethane, the u p p e r b o u n d a r y of the H e n r y r e g i o n corresponds, o n t h e average, to a m a x i m u m o f o n e m o l e c u l e p e r large v o i d of t h e zeolite.

I n t h e case u n d e r c o n s i d e r a t i o n ,

e a c h m o l e c u l e a d s o r b e d w i t h i n the H e n r y r e g i o n occupies a space i n a separate large v o i d of t h e z e o l i t e , w h i c h leads to the constancy of the a d s o r p t i o n energy a n d to t h e absence of i n t e r a c t i o n a m o n g the m o l e c u l e s a d s o r b e d . J u d g i n g b y t h e g r a p h of F i g u r e 6 of the s u r v e y , the d i f f e r e n t i a l heats of a d s o r p t i o n of ethane d o n o t v a r y s i g n i f i c a n t l y i n this r a n g e of Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch043

fillings. T h e increase i n the d i f f e r e n t i a l heats of a d s o r p t i o n w i t h

filling

is

u s u a l l y a t t r i b u t e d to t h e m a n i f e s t a t i o n of i n t e r a c t i o n , n a m e l y of attraction b e t w e e n the molecules a d s o r b e d . T h i s effect is chiefly expressed b y t h e s e c o n d t e r m of the v i r i a l e q u a t i o n . S u c h examples are i l l u s t r a t e d b y the curves of t h e g r a p h i n F i g u r e 6 of t h e s u r v e y p a p e r f o r a d s o r p t i o n of

Of kcrt/ηώ i0'

Active carbon

9

8

•ο—α

7

0

2

6

1

3

kcat/mÀ 10'

9·

δ

7,

0

Figure 1. Dependence of differential heats of adsorption of propane, Q , on adsorption values, a, for active carbon (above) and zeolite NaX (below)


43.

KISELEV

Vapor Adsorption

On

Zeolites

65

x e n o n a n d ethane o n zeolite L i X . H o w e v e r , f o r carbonaceous

micro-

p o r o u s adsorbents, f o r w h i c h m i c r o p o r e sizes d e t e r m i n e d b y the s m a l l angle x-ray scattering m e t h o d a r e v e r y close t o those of l a r g e v o i d s of t h e X - t y p e zeolite, the d i f f e r e n t i a l heats of a d s o r p t i o n decrease w i t h

filling

i n t h e r e g i o n of s m a l l a n d m e d i u m fillings. O t h e r examples are the curves of d i f f e r e n t i a l heats of a d s o r p t i o n of p r o p a n e o n active c a r b o n a n d z e o l i t e N a X w h i c h w e r e s t u d i e d i n o u r l a b o r a t o r y ( 2 ) a n d are g i v e n i n the g r a p h of F i g u r e 1. Since p r o p a n e m o l e c u l e s are a p o l a r a n d d i s p e r s i o n i n t e r a c tions b e t w e e n t h e m are p r a c t i c a l l y i n d e p e n d e n t of the o r i e n t a t i o n of the Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch043

m o l e c u l e s , the effect o f attraction b e t w e e n the m o l e c u l e s a d s o r b e d s h o u l d m a n i f e s t itself regardless of the n a t u r e of the adsorbent.

I n a c t u a l fact,

one c a n observe a q u a l i t a t i v e difference i n the curves of d i f f e r e n t i a l heats of a d s o r p t i o n w h i c h calls f o r t h o r o u g h discussion. I b e l i e v e that at this j u n c t u r e elegant ( as regards t h e g e n e r a l scheme ) m o l e c u l a r - s t a t i s t i c a l c a l c u l a t i o n s as a p p l i e d to r e a l a d s o r p t i o n systems are b a s e d o n s u c h n u m e r o u s s i m p l i f i c a t i o n s a n d a p p r o x i m a t i o n s i n c a l c u l a t i o n , i n e s t i m a t i n g a d s o r p t i o n energies a m o n g other things, that t h e i r results are r a t h e r of a q u a l i t a t i v e nature. T h e i r q u a n t i t a t i v e significance should not be overestimated.

T h e m u l t i - c o n s t a n t v i r i a l equations f o l l o w

i n g f r o m these concepts i n e m p i r i c a l d e t e r m i n a t i o n of constants n a t u r a l l y d e s c r i b e a d s o r p t i o n e q u i l i b r i a w i t h a h i g h degree of a c c u r a c y . T h e concepts of a d s o r p t i o n i n m i c r o p o r e s w h i c h are b e i n g d e v e l o p e d b y us a n d are of g e n e r a l i m p o r t a n c e f o r m i c r o p o r o u s adsorbents of v a r i o u s natures are a i m e d at other targets. T h e i r c o m m o n g o a l is a p p r o x i m a t e d e s c r i p t i o n of a d s o r p t i o n e q u i l i b r i a a n d c a l c u l a t i o n of d i f f e r e n t i a l heats a n d entropies of a d s o r p t i o n o v e r sufficiently w i d e ranges of t e m p e r a t u r e a n d pressure o n the basis o f m i n i m u m e x p e r i m e n t a l i n f o r m a t i o n ; f o r i n stance, f r o m a single a d s o r p t i o n i s o t h e r m f o r the m e a n t e m p e r a t u r e .

They

are also a i m e d at substantiating a n a d s o r p t i o n e q u a t i o n w i t h a m i n i m u m n u m b e r of e x p e r i m e n t a l l y d e t e r m i n e d constants; f o r instance, t w o . T h e f o r m o f this e q u a t i o n , w h i c h expresses the d e p e n d e n c e of a d s o r p t i o n o n pressure a n d t e m p e r a t u r e , s h o u l d p e r m i t its a p p l i c a t i o n i n d e v e l o p i n g the f u n d a m e n t a l s of the t h e o r y of kinetics a n d d y n a m i c s of a d s o r p t i o n . W e c o n s i d e r a d i v e r g e n c e of ± 1 0 % b e t w e e n c a l c u l a t e d a n d e x p e r i m e n t a l a d s o r p t i o n values a c c e p t a b l e f o r p r a c t i c a l purposes. O n this basis, c r i t e r i a are established w h i c h d e t e r m i n e the l i m i t s of a p p l i c a b i l i t y of equations. T h e c o n c e p t of v o l u m e filling of m i c r o p o r e s u n d e r r e v i e w is b a s e d o n a r a d i c a l difference of a d s o r p t i o n i n m i c r o p o r e s as a l i m i t i n g case as c o m p a r e d w i t h the opposite l i m i t i n g case of a d s o r p t i o n o n t h e surface of n o n p o r o u s adsorbents of i d e n t i c a l c h e m i c a l n a t u r e .

T h e c o n c e p t of

a d s o r p t i o n i n m i c r o p o r e s is of a t h e r m o d y n a m i c a l nature, a n d its m a i n i n i t i a l p r i n c i p l e , w h i c h has the m e a n i n g of a r a t i o n a l a p p r o x i m a t i o n , c o n -



M O L E C U L A R SIEVE ZEOLITES-

Figure 3. correspond

Characteristic curve of C0 adsorption on LiX; points to experimental adsorption isotherms for temperatures from 273° to 363°K (A, cal/mole) 2


43.

KISELEV

Vapor Adsorption

On Zeolites

67

sists i n t h e a s s u m p t i o n of t e m p e r a t u r e i n v a r i a n c e of the d e p e n d e n c e of the d i f f e r e n t i a l m o l a r w o r k of a d s o r p t i o n or of the v a r i a t i o n i n G i b b s ' free energy o n the degree of filling of t h e m i c r o p o r e s .

This assumption

is f u l f i l l e d a p p r o x i m a t e l y o n l y f o r a d s o r p t i o n i n m i c r o p o r e s .

T h e nature

of the d i s t r i b u t i o n of t h e degree of filling of m i c r o p o r e s over d i f f e r e n t i a l m o l a r w o r k s of a d s o r p t i o n is a p p r o x i m a t e d b y W e i b u l F s statistical e q u a t i o n of d i s t r i b u t i o n . E x a m p l e s of a p p r o x i m a t e observance of the abovem e n t i o n e d t e m p e r a t u r e i n v a r i a n c e a n d of the a n a l y t i c a l expression of t h e d e p e n d e n c e s t u d i e d are i n t h e graphs of F i g u r e s 2 to 4, i n w h i c h t h e Downloaded by PRINCETON UNIV on September 30, 2014 | http://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0102.ch043

e x p e r i m e n t a l p o i n t s c o r r e s p o n d i n g to isotherms f o r different temperatures are d e n o t e d b y different s y m b o l s , w h i l e t h e c o n t i n u o u s curves h a v e b e e n c a l c u l a t e d o n the basis of the parameters of the characteristic f o r e a c h a d s o r p t i o n system. sorption of b e n z e n e

equation

T h e g r a p h of F i g u r e 2 corresponds to a d

o n active c a r b o n C K over the t e m p e r a t u r e

range

f r o m 2 0 ° to 1 4 0 ° C a c c o r d i n g to experiments of E . F . P o l s t y a n o v (4), t h e g r a p h of F i g u r e 3 to a d s o r p t i o n of c a r b o n d i o x i d e o n zeolite L i X a c c o r d i n g to experiments of Ν. N . A v g u l et al. ( I ) over the range f r o m 0 ° to 9 0 ° C , a n d t h e g r a p h o f F i g u r e 4 to a d s o r p t i o n of w a t e r o n zeolite N a X over the range f r o m 2 0 ° to 2 5 0 ° C a c c o r d i n g to experiments of O . K a d l e c

Figure

4.

Characteristic curve of H 0 adsorption on NaX; range from 293° to 523°Κ (A, col/mole) 2

temperature


68


and A . Zukal (3).

II

I n m y p a p e r a n d the i n t r o d u c t i o n to it, I gave examples

of the d e s c r i p t i o n of a d s o r p t i o n e q u i l i b r i a a n d c a l c u l a t i n g of t h e r m o d y n a m i c f u n c t i o n s b a s e d o n the concept of v o l u m e

filling

of m i c r o p o r e s ,

w h i c h is i n most cases a p p l i c a b l e w i t h a satisfactory a c c u r a c y w i t h i n the r a n g e of m i c r o p o r e fillings f r o m 0.2 to 1. N a t u r a l l y , the c o n c e p t of v o l u m e

filling

of m i c r o p o r e s does not re

p l a c e , b u t m e r e l y s u p p l e m e n t s the concepts of a d s o r p t i o n d e v e l o p e d at the s o - c a l l e d " m o l e c u l a r l e v e l , " u s i n g , i n p a r t i c u l a r , the m o l e c u l a r - s t a tistical approach.

We

b e l i e v e that f u r t h e r d e v e l o p m e n t of b o t h

ap


proaches w i l l i n the l o n g r u n result i n the substantiation of the i n i t i a l approximate propositions regarding volume

filling

of m i c r o p o r e s , since

t h e y express the p r i n c i p a l e x p e r i m e n t a l facts. Literature (1) (2) (3) (4) (5)

Cited

Avgul, Ν. N . , Aristov, B. G., Kiselev, Α. V., Kurdyukova, L . Y., Frolova, Ν. N . , Zh. Fiz. Khim. 1968, 42, 2682. Bering, B. P., Zhukovskaya, E . G., Rakhmukov, B. Kh., Serpinsky, V. V., Izv. Akad. Nauk SSSR, Ser. Khim. 1967, 1662. Dubinin, M. M., Kadlec, O . , Zukal, Α., Coll. Czech. Chem. Commun. 1966, 31, 406. Dubinin, M . M . , Polstyanov, E. F., Izv. Akad. Nauk SSSR, Ser. Khim. 1966, 793. Mikos, Κ. N . , thesis, Moscow, 1970. Α . V . K i s e l e v : Zeolites are p o r o u s crystals. T h i s means that w e c a n

find the m o l e c u l a r field d i s t r i b u t i o n i n their channels.

T h e a d v a n t a g e of

d e s c r i b i n g the a d s o r p t i o n o n zeolites u s i n g the m o l e c u l a r t h e o r y consists i n o b t a i n i n g the constants w h i c h h a v e a definite p h y s i c a l m e a n i n g e x a m p l e , the H e n r y constant a n d s e c o n d v i r i a l c o e f f i c i e n t ) .

(for

F u r t h e r de

v e l o p m e n t of the t h e o r y needs a f u r t h e r i m p r o v e m e n t of the m o d e l b a s e d o n the i n v e s t i g a t i o n of the a d s o r b a t e - z e o l i t e systems b y the use of m o d e r n physical methods. T h e other w a y of treating the e x p e r i m e n t a l i s o t h e r m of a d s o r p t i o n is c o n n e c t e d w i t h the P o l a n y i a s s u m p t i o n that the adsorbate has a d e n s i t y w h i c h is close to the d e n s i t y of the c o r r e s p o n d i n g l i q u i d . T h e a d v a n t a g e of this m e t h o d consists i n the p o s s i b i l i t y of c a l c u l a t i n g the i s o t h e r m u s i n g o n l y a f e w constants.

T h e d i s a d v a n t a g e of this c o n c e p t is c o n n e c t e d w i t h

the e m p i r i c a l character of these constants a n d w i t h the i m p o s s i b i l i t y of d e s c r i b i n g b y this m e t h o d the i n i t i a l p a r t of the i s o t h e r m a n d also the isotherms h a v i n g a n i n f l e x i o n p o i n t .


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