Investigations of Equilibria and Kinetics of Adsorption of Gases on

1

Investigations of Equilibria and Kinetics of Adsorption of Gases on Zeolites M. M . DUBININ

Downloaded by FUDAN UNIV on March 10, 2017 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0040.ch001

Institute of Physical Chemistry, Academy of Sciences of the U.S.S.R., Union of Soviet Socialists Republic

ABSTRACT A thermodynamic t h e o r y of a d s o r p t i o n equilibr i u m based on the vacancy solution model and the analogy between osmotic and a d s o r p t i o n equilibria has been developed t o d e s c r i b e a d s o r p t i o n on z e o l i t e s over wide ranges of p r e s s u r e and temperature. New methods f o r i n v e s t i g a t i n g the kinetics o f vapor a d s o r p t i o n by microporous adsorbents and f o r theoretical description of these processes on the b a s i s o f a biporous adsorbent model have been proposed. The experimental d a t a agree w i t h t h e o r y . Introduction i^or the subject of the opening l e c t u r e which I have been i n v i t e d t o d e l i v e r , I haven chosen the most important r e s u l t s obtained r e c e n t l y at the S o r p t i o n Processes Department headed by me at the I n s t i t u t e of P h y s i c a l Chemistry of the USSR Academy of S c i e n c e s . These are t h e o r e t i c a l and e x p e r i m e n t a l i n v e s t i g a t i o n s i n t o e q u i l i b r i u m p h y s i c a l a d s o r p t i o n c a r r i e d out by B . P . B e r i n g and V«V»Serpinskii w i t h the p a r t i c i p a t i o n of T.S.Yakubov and A . A . F o m k i n , and s t u d i e s i n t o the k i n e t i c s of p h y s i c a l a d s o r p t i o n f a r b i p o r o u s - s t r u c t u re adsorbents conducted by P . P . Z o l o t a r e v , A . M . V o l o shchuk w i t h the p a r t i c i p a t i o n of I.T#Erashko, V#A#GODl o v , G.Schon arji V . I . U l i n . Based on the s i z e s of t h e i r p o r e s , z e o l i t e s are t y p i c a l microporous adsorbents. The commensurability of the s i z e s of micropores and the molecules adsorbed leads t o a s h a r p l y d e f i n e d e f f e c t o f i n c r e a s e i n a d s o r p t i o n p o t e n t i a l s due t o d i s p e r s i o n f o r c e s . C a t i o n s i n the z e o l i t e v o i d s c o n s i d e r a b l y enhance (owing t o e l e c t r o s t a t i c i n t e r a c t i o n s ) the energy inhomogeneity 1

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


2

MOLECULAR SIEVES—II

o f the a d s o r p t i o n space of the micropores as compar e d w i t h adsorbents of a d i f f e r e n t chemical n a t u r e , such as a c t i v a t e d carbons* Our i n v e s t i g a t i o n s of e q u i l i b r i u m a d s o r p t i o n o f the vapors of v a r i o u s substances i n micropores, have l e a d t o the concept t h a t there was a q u a l i t a t i v e d i f f e r e n c e between a d s o r p t i o n i n micropores and a d s o r p t i o n on the surface of nonr-parous and r e l a t i v e l y l a r g e - p o r e adsorbents of i d e n t i c a l c h e m i c a l nature* As a reasonable approximation f a r d e s c r i b i n g adsorpt i o n i n micropores, we proposed the t h e o r y of volume f i l l i n g of micropores* A survey of these i n v e s t i g a t i o n s i s g i v e n i n (1,2)# I n development of t h i s t h e o r y we meet w i t h some d i f f i c u l t i e s . The t h e o r y i n d i c a t e s o n l y a decrease i n d i f f e r e n t i a l heats o f a d s o r p t i o n w i t h an i n c r e a s e in filling. At tenperature T > T the t h e o r y i s inapplicable. I t f o l l o w s from, the foregoing t h a t i t i s exped i e n t t o search for a more p e r f e c t model o f e q u i l i b r i u m a d s o r p t i o n of gases i n micropores and develop a t h e o r y free from the above drawbacks. B . P . B e r i n g and V . V . S e r p i n s k i i have made a s u c c e s s f u l attempt t o develop and s u b s t a n t i a t e e x p e r i m e n t a l l y a more g e n e r a l thermodynamic t h e o r y of e q u i l i b r i u m a d s o r p t i o n , which was named the osmotic t h e o r y of a d s o r p t i o n . I t s b a s i c p r i n c i p l e s have been p u b l i s h e d o n l y i n Russian Q ) . We w i l l c o n s i d e r the main v e r s i o n o f the t h e o r y as a p p l i e d t o microporous adsorbents,using z e o l i t e s as examples* C

ffundamsntal i n Micropores

of Osmotic Theory of A d s o r p t i o n

As demonstrated by H i l l ( 4 ) , i n d e s c r i b i n g e q u i l i b r i u m between an adsorbent and the gas phase i n p h y s i c a l a d s o r p t i o n , methods of a d s o r p t i o n thermodynamics and of s o l u t i o n thermodynamics can be a p p l i e d w i t h equal s u c c e s s . U s u a l l y , the adsorbent i s a s sumed t o be thermodynamic a l l y i n e r t i n a d s o r p t i o n , and methods of a d s o r p t i o n thermodynamics are u s e d . However the chemical p o t e n t i a l s of the microporous adsorbents and p a r t i c u l a r l y of z e o l i t e s change i n the course o f a d s o r p t i o n (|). Therefore the methods of s o l u t i o n thermodynamics are more expedient i n t h i s c a s e . I n c o n n e c t i o n w i t h t h i s i t was a l s o shown (6) t h a t the l i n e a r dimensions of the z e o l i t e c r y s t a l s change i n the course o f a d s o r p t i o n . T h i s approach t o the d e s c r i p t i o n of a d s o r p t i o n


1.

Adsorption

DUBININ

of Gases on

3

Zeolites

e q u i l i b r i a has proved t o be the most f r u i t f u l , when the t h e o r y was based on the s o l u t i o n model, which was named the vacancy s o l u t i o n . ' . I n t h i s model, one of the s o l u t i o n components i s not a s o l i d adsorbent, as i n ( 5 ) , but s o - c a l l e d " a d s o r p t i o n vacancies * T h i s t e r m means the free elementary volume of the adsorpt i o n space o f the micropores which i s f i l l e d by one adsorbate molecule i n adsorption* Since the adsorpt i o n space of the micropores i s l i m i t e d by t h e i r volume, f o r a u n i t mass of the adsorbent t h e r e i s a maximum number of v a c a n c i e s , which i s equal t o the l i m i t i n g number of the molecules adsorbed. The adsorpt i o n v a l u e tends t o t h i s q u a n t i t y a s y m p t o t i c a l l y w i t h an u n l i m i t e d i n c r e a s e of the e q u i l i b r i u m p r e s s u r e i n the gas phase. At any e q u i l i b r i u m pressure of the adsorbate the a d s o r p t i o n space of the micropores c o n t a i n s adsorbed molecules and a d s o r p t i o n vacancies which form a b i n a r y vacancy s o l u t i o n * At a constant temperature, the dependence of the e q u i l i b r i u m p r e s s u r e i n the gas phase on the molar fraction of the d i s s o l v e d s u b s t a n ce ( a d s o r b a t e ) , i . e . the a d s o r p t i o n v a l u e , r e p r e s e n t s a curve of the p a r t i a l vapor pressure over the v a c a n c y s o l u t i o n , or the a d s o r p t i o n i s o t h e r m . Thus, the a d s o r p t i o n eequilibrium of the adsorbent w i t h the gas phase i s e q u i v a l e n t t o the e q u i l i b r i u m o f the vacancy s o l u t i o n w i t h the same gas phase. I t i s n a t u r a l t o analyse t h i s e q u i l i b r i u m by methods of s o l u t i o n t h e r modynamics. Note t h a t these concepts have proved t o be p a r t i c u l a r l y f r u i t f u l because t h e r e i s a deep, f o r m a l l y thermodynamic, as w e l l as p h y s i c a l , analogy between a d s o r p t i o n e q u i l i b r i u m and osmotic e q u i l i b r i u m . The i d e a of the e x i s t e n c e o f t h i s s i m i l a r i t y i n the s i m p l e s t case o f a d s o r p t i o n on the surface o f a l i q u i d was f i r s t suggested by Erumkin as f a r back as 1925 ( 7 ) i and t h e n was a b s o l u t e l y c l e a r l y formulated by Adam ( 8 ) . I n subsequent y e a r s , however, i t was not developped on a s u f f i c i e n t s c a l e . Consider now the p h y s i c a l background of t h i s anarl o g y . Denote the number o f moles of the substance adsorbed and the number of vacancies per u n i t mass o f the adsorbent by a and d * , r e s p e c t i v e l y . At any equilibrium conditions ,9

1


11

a + a*= a

m

( 1 )

where a i s l i m i t i n g a d s o r p t i o n , which i s assumed t o be temperature i n v a r i a n t . Introduce the concept m


MOLECULAR SIEVES—H

4

of molar f r a c t i o n s of the adsorbate x and of the vacancies x * » i n the vacancy s o l u t i o n :


x= a/a^ ,

x*- aVcim

(2)

We w i l l regard the e q u i l i b r i u m of the microporous adsorbent w i t h the gas phase as e q u i l i b r i u m o f two vacancy s o l u t i o n s of d i f f e r e n t c o n c e n t r a t i o n . One of these s o l u t i o n s i s the vacancy s o l u t i o n i n the micropores, and the o t h e r , the s o l u t i o n formed by the gas molecules i n a vacuum, i n which the r o l e o f the " s o l v e n t " i s p l a y e d by the vacancies i n the gas phase. Two s o l u t i o n s of d i f f e r e n t c o n c e n t r a t i o n formed by u n l i m i t e d s o l u b l e components c a n be at e q u i l i b r i u m o n l y when one of them i s i n the e x t e r n a l p o t e n t i a l f i e l d . I t i s easy t o show t h a t the e f f e c t of t h i s f i e l d i s f o r m a l l y e q u i v a l e n t t o the d i f f e rence of the h y d r o s t a t i c p r e s s u r e s e x i s t i n g i n these s o l u t i o n s . I n the s o l u t i o n t h e o r y the d i f f e r e n c e o f these p r e s s u r e s i s c a l l e d the osmotic p r e s s u r e . We w i l l now w r i t e down the e x p r e s s i o n s f o r the chemical p o t e n t i a l s of the vacancies i n these two s o l u t i o n s , denoting the v a l u e s r e f e r r i n g t o the gas phase by the s u b s c r i p t oC . Note t h a t a vacancy s o l u t i o n corresponding t o the gas phase i s always h i g h ly diluted ( X^c^1 ; X « 1 ) and t h e r e f o r e c a n be regarded as i d e a l o

C

R T ^
i s a c o n s t a n t , or

a =

a jbp Vci +£PVg) (13) Equations o f the type (13) have long been known i n the l i t e r a t u r e as e m p i r i c a l a d s o r p t i o n equations w i t h t h r e e parameters CUv\,j5>t and g (10) /See a l s o (11) and ( 1 2 ) A T h e i r good a p p l i c a b i l i t y over wide ranges of f i l l i n g s , C t / a s u p p o r t s the adopted assuntp t i o n of the constancy of the osmotic c o e f f i c i e n t g • As i s known from a r i g o r o u s thermodynamic anal y s i s of osmotic e q u i l i b r i u m i n b u l k s o l u t i o n s , the osmotic c o e f f i c i e n t g i s a l i n e a r f u n c t i o n o f the r e c i p r o c a l temperature w i t h a constant molar f r a c t i o n of the solvent (13) m

/

m

g= C O - b / T )

(14)

I n developing f u r t h e r the analogy between osmotic e q u i l i b r i u m and a d s o r p t i o n e q u i l i b r i u m , i t i s exped i e n t t o u t i l i z e E q . (14) i n the l a t t e r case as w e l l . For the d i s c u s s e d b i n a r y vacancy s o l u t i o n i n the m i c -


6


ropores the constancy of the molar f r a c t i o n of the vacancies means the constancy of the molar f r a c t i o n of the adsorbate, i . e . of the a d s o r p t i o n v a l u e . Denoting, for b r e v i t y , 4>(CL)= t n [ a / ( a m - a ) ] (15) we o b t a i n from E q . ( 1 2 ) , t n p = g4>(C0-(16) Since *f(0l) = O at a = 0 . 5 a > we apply E q . (16) f o r t h i s case and o b t a i n Downloaded by FUDAN UNIV on March 10, 2017 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0040.ch001

m

where p i s a f u n c t i o n of the temperature a l o n e . To express t h i s dependence, we adopt a second nonthermodynamic assumption t h a t the i s o s t e r e c o r r e s ponding t o a = 0 . 5 a i s l i n e a r : o s

m

^Po. = C 5

a

5

- L

a

5

(18)

/ T

I n E q . ( 1 8 ) , L . s SLD^ C O . S are the slope and the i n t e r c e p t on the* C n p - a x i s , which are temperature invariant. We w i l l o b t a i n a thermal e q u a t i o n (19) of the osmotic t h e o r y of a d s o r p t i o n o f the type f ( a , p / T ) - 0 a f t e r s u b s t i t u t i n g g from (14) and tn. p from (17) and (18) i n t o E q . ( 1 6 ) , t a k i n g i n t o account (15): 0

o s

^ P = C . - Los/T + C (1 - tyl) tn [a/(ct -a)] (19) 0

m

5

T h i s e q u a t i o n c a n be represented as

!np=d ~L/T a

(20)

where

C = a

Cl

a

5

+

Cif(a)

(21)

and L - L . + CL>4>(ct) (22) are temper at ure i n v a r i a n t parajneters. T h e i r r e l a t i o n w i t h the a d s o r p t i o n v a l u e s w i t h an allowance f o r (15} however, i s g i v e n e x p l i c i t form. Thus, on the b a s i s of the p r e v i o u s l y d e r i v e d a d s o r p t i o n i s o t h e r m e q u a t i o n (12), the thermodynamic dependence of the osmotic c o e f f i c i e n t on the temperat u r e ( 1 4 ) , and the assumption (18) as an experimental f a c t , we o b t a i n the "thermal e q u a t i o n of a d s o r p t i o n " (19)» To t h i s e q u a t i o n there corresponds the l i n e a r i t y of the i s o s t e r e s over a wide range o f a d s o r p t i o n v a l u e s . As i s w e l l known, the l i n e a r i t y of t h e a d s o r p t i o n i s o s t e r e s i s one o f t h e v e r y general p r o p e r 0

5



1.

DUBININ

Adsorption

of Gases on

Zeolites

7

t i e s of a d s o r p t i o n e q u i l i b r i u m and i s u s u a l l y w e l l supported by experiment. Note t h a t i n the i n i t i a l p o r t i o n o f the adsorpt i o n i s o t h e r m , when the a d s o r p t i o n values become very l o w , i . e . when p a s s i n g over t o the i d e a l , i n f i n i t e l y d i l u t e d vacancy s o l u t i o n , the osmotic c o e f f i c i e n t g tends t o u n i t y and the parameter b , t o z e r o . T h e r e f o r e , i t should be assumed t h a t i n the i n i t i a l p o r t i o n of any a d s o r p t i o n i s o t h e r m g=1 , and t h e n , as CI i n c r e a s e s , t h i s c o e f f i c i e n t r a p i d l y changes t o a c e r t a i n v a l u e , which remains constant over a wide range of a d s o r p t i o n v a l u e s . Experimental S u b s t a n t i a t i o n of Thermal E q u a t i o n of Osmotic Theory of A d s o r p t i o n The t h e r m a l e q u a t i o n of a d s o r p t i o n (19) c o n t a i n s 5 parameters: C l , Lo.«5iC .s>Cand t> , f o r whose d e t e r m i n a t i o n one must have at l e a s t two e x p e r i m e n t a l a d sorption isotherms. The t h e r m a l e q u a t i o n (19) of the osmotic t h e o r y of ^adsorption d e s c r i b e s w i t h a h i g h accuracy the a d s o r p t i o n e q u i l i b r i u m of gases and vapors on v a r i o u s microporous adsorbents such as z e o l i t e s and a c t i v e carbons over a wide range of temperatures and p r e s s u r e s . To i l l u s t r a t e the agreement between t h e o r y and experiment, we w i l l c o n s i d e r o n l y one t y p i c a l system, namely X e - z e o l i t e N a X which have been s t u d i e d at our L a b o r a t o r y (14)# These i n v e s t i g a t i o n s are o f i n t e r e s t p e r se i n the e x p e r i m e n t a l sense, s i n c e the c o n s t r u c t e d equipment enabled us t o perform r e l i a b l e measurements of a d s o r p t i o n e q u i l i b r i a over a v e r y wide range of p r e s s u r e s from hundredths of T o r r t o hundreds of atm and temperatures from 150 t o 600 K . I n F i g u r e 1, i n c o o r d i n a t e a x e s d - t o g p , the s o l i d l i n e s show the a d s o r p t i o n isotherms of on c r y s t a l s of z e o l i t e NaX, c a l c u l a t e d f o r v a r i o u s temp e r a t u r e s from E q . (19)> for the f o l l o w i n g v a l u e s o f the e q u a t i o n parameters: O L = 4 . 3 0 mmoie/g , L =* m

0

m

= 1225 K , £ .5~ 0

6.76 , C=

5

b=Ho9K.

The e x p e r i m e n t a l p o i n t s are marked by c i r c l e s . W i t h i n the s t u d i e s temperature range from 150 t o 600 K , w h i c h i n c l u d e s the normal c r i t i c a l temperature T = 2 9 0 K, t h e o r y agrees w e l l w i t h experiment i n the range of f i l l i n g a / a f r o m 0.09 t o 0.93* I t i s worth n o t i n g t h a t f o r systems s t u d i e d i n the above-mentioned ranges of CL/Ctmthe a d s o r p t i o n i s o s t e r e s are l i n e a r . The t h e r m a l e q u a t i o n of adsorpt i o n (19) w i t h the same parameter v a l u e s i s e q u a l l y c

m


8


a p p l i c a b l e t o below-and a b o v e - c r i t i c a l temperatures. The good agreement between the c a l c u l a t e d and e x p e r i mental a d s o r p t i o n isotherms and the l i n e a r i t y of the i s o s t e r e s , i n p a r t i c u l a r at a = 0 5 a are d i r e c t exper i m e n t a l c o n f i r m a t i o n s of the main p r i n c i p l e s of the osmotic t h e o r y o f a d s o r p t i o n . Thermodynamic F u n c t i o n s of A d s o r p t i o n E q u i l i b rium On the b a s i s of E q s . (18) and (22) i t i s easy t o o b t a i n expressions f a r the main thermodynamic f u n c t i o n s of a d s o r p t i o n e q u i l i b r i u m f o r the range of p and T i n which the gas phase can be c o n s i d e r e d p r a c t i c a l l y i d e a l . According t o (16) and (17)t G i b b s d i f f e r e n t i a l free energy G i s expressed t h u s :


rtlJ

1

G = R T tn. p = G a 5

fi T4>(a) R

+

(23)

D i f f e r e n t i a t i n g t h i s e q u a t i o n w i t h r e s p e c t t o T at a - c o n s " t w i t h an allowance f o r the temperature depeiH dence of g according t o ( 1 4 ) , we get the e x p r e s s i o n f o r the d i f f e r e n t i a l entropy of a d s o r p t i o n $ S = - ( a e / a T ) = s - CRIP(CA (24) I f we have an i d e a l e q u i l i b r i u m gas p h a s e , R L — Q , where Q i s the d i f f e r e n t i a l heat o f a d s o r p t i o n . T h e r e f o r e , according t o (22), Q = Q + CbR4>(oO (25) Proceeding from thermodynamic c o n s i d e r a t i o n s we c a n show t h a t the parameter C i n E q . (14) cannot be n e g a t i v e . Therefore i t f o l l o w s from E q . (25) t h a t at T ^ c o n s t t h e dependence o f the heat of a d s o r p t i o n Q. on a i s determined by the s i g n o f the parameter b . When b > 0 , Q i n c r e a s e s w i t h a d s o r p t i o n . F o r b < 0 , Q decreases w i t h i n c r e a s i n g a • Figure 2 compares the dependence of the d i f f e r e n t i a l heat of a d s o r p t i o n on the a d s o r p t i o n value ( s o l i d c u r v e ) , as c a l c u l a t e d by E q . (25)> f o r t h e system X e - N a X i n the range of p where the e q u i l i b r i u m gas phase can p r a c t i c a l l y be considered i d e a l . The c i r c l e s i n d i c a t e the experimental i s o s t e r i c heats of a d s o r p t i o n . C a l c u l a t i o n i s i n good agreement w i t h experiment• Thus, the osmotic t h e o r y of a d s o r p t i o n e q u i l i b r i u m leads t o a thermal equation of a d s o r p t i o n which makes i t p o s s i b l e t o express the i s o t h e r m s , i s o s t e r e ^ and thermodynamic f u n c t i o n s of e q u i l i b r i u m t h r o u g h the same parameters of t h i s e q u a t i o n . a

Q

a

s

S


Adsorption

DUBININ

of Gases on

Zeolites

a MMOle/g


MK

'/65 m %

' 200- '240. '£80. ' 5JO

:

350

Figure 1. Adsorption isotherms of Xe on zeolite NaX. Solid lines calculated from Ref. 19. Circles denote experiment (a, mmole/gr; p, N/m or Pa). 2

Q

kJ/moee

25

20-

15 0. mmoSe/ Figure 2. Dependence of differential heat of adsorption of Xe on zeolite NaX on adsorption values a. Solid line calculated from Ref. 25. Circles denote experimental values.



10

K i n e t i c s of P h y s i c a l A d s o r p t i o n by Microporous Adsorbents According t o the c l a s s i f i c a t i o n based on the mechanisms of a d s o r p t i o n and c a p i l l a r y phenomena o c c u r r i n g i n adsorbent g r a i n s , i t i s expedient t o d i v i d e t h e i r pores i n t o micropores, supermicropores, mesopores and macropores ( 2 1 5 ) « I n many p r a c t i c a l l y important cases i t i s p o s s i b l e t o s l i g h t l y sin5>lify the r e a l s t r u c t u r e of t h e adsorbent and d i s t i n g u i s h o n l y two pore v a r i e t i e s d i f f e r i n g s u b s t a n t i a l l y i n t h e i r p r o p e r t i e s : adsorbi n g pores ( m i c r o - and supermicropores) and t r a n s p o r t pores (meso- and macropores). T h i s biporous adsorbent model, which c h a r a c t e r i z e s , i n p a r t i c u l a r , molded z e o l i t e s , i s presented i n s i m p l i f i e d form i n F i g . 3 . I n r e c e n t y e a r s , i n v e s t i g a t i o n s on the k i n e t i c s of a d s o r p t i o n by biporous adsorbents have been coi>ducted i n the works of a number of authors (16-19) and i n our works (20-27)* We considered the equest i o n s of i n t e r n a l d i f f u s i o n i n biporous adsorbents i n the g e n e r a l case of n o n - l i n e a r a d s o r p t i o n i s o t h e r m s . Then we g e n e r a l i z e d these equations f o r t h e case o f micrcporous zones ( s m a l l c r y s t a l s ) o f v a r i o u s s i z e s t a k i n g i n t o account the f i n i t e d i f f u s i o n r e s i s t a n c e of the e x t e r n a l s u r f a c e o f the c r y s t a l s (21122,25»27). For l i n e a r a d s o r p t i o n i s o t h e r m s , the a p p l i c a t i o n o f the s t a t i s t i c a l moments method made i t p o s s i b l e t o o b t a i n s u f f i c i e n t l y s i n g l e a n a l y t i c a l equations rela?t i n g the c h a r a c t e r i s t i c times of d i f f u s i o n i n adsorbing T and t r a n s p o r t T j pores w i t h the moments of the k i n e t i c curves ( 2 3 , 2 2 ) . I n the case of i n t r o d i f f u s i o n k i n e t i c s and microporous zones of i d e n t i c a l s i z e , k - o r d e r moments have the form


t

a

Here, x\ = L*fl+r)D,r / D , r = CL /C L and Y* are the determining dimensions o f t h e granule and the microporous zones, D? and P are t h e c o e f f i c i e n t s of d i f f u s i o n i n the t r a n s p o r t pores and the microporous zones, CX i s the e q u i l i b r i u m a d s o r p t i o n v a l u e , Co i s the adsorptive c o n c e n t r a t i o n at the granule s u r f a c e . The c o e f f i c i e n t s g k depend on the g e o m e t r i c a l shape of the granule and of t h e microporous zones, r e s p e c t i v e l y . T h e i r values f o r g r a n u l e s and microporous zones of v a r i o u s shspe are g i v e n , f a r i n s t a n c e , i n ( 2 £ ) . B e s i d e s , we developed a procedure f o r d e t e r m i n i n g the t r a n s p o r t c o e f f i c i e n t s i n biporous adsorbents based on the s t u d y of adsorp0

a

0

0

a

0

v


0


1.

Adsorption

DUBININ

of Gases on

Zeolites

11

t i v e d i f f u s i o n from one volume t o another through an adsorbent granule ( 2 6 ) . The r e l a t i o n s HTscussed were used by us f o r c a l c u l a t i n g the d i f f u s i o n c o e f f i c i e n t s s e p a r a t e l y i n adsorbing and t r a n s p o r t pores and a n a l y z i n g the c h a r a c t e r of mass t r a n s f e r i n r e a l microporous adsorbents (molded z e o l i t e s , a c t i v e carbons) (25*26).This a n a l y s i s demonstrated the r a t i o n a l i t y o f a p p l i c a t i o n of the biporous model i n studying r e a l microporous adsorbents* Along w i t h the case of l i n e a r a d s o r p t i o n i s o therms the equations of i n t e r n a l d i f f u s i o n i n b i p o rous adsorbents have a l s o been i n v e s t i g a t e d by us t h e o r e t i c a l l y for s h a r p l y convex ( r e c t a n g u l a r ; i s o therms* The case of a c y l i n d r i c a l ( p r i s m a t i c ) adsorbent g r a i n w i t h an impermeable l a t e r a l surface has been c o n s i d e r e d . The v a r i a t i o n i n the l o c a l c o n c e n t r a t i o n of the adsorbate i n the g r a i n , OL(x), at d i f f e r e n t i n s t a n t s of time ( X i s the distance from the g r a i n end f a c e ) and the grain-average r e l a t i v e a d s o r p t i o n , ^ ( " t ) ( k i n e t i c c u r v e s ) , have been i n v e s t i g a t e d . The process p a t t e r n e s s e n t i a l l y depends on the r a t i o o f the c h a r a c t e r i s t i c times t o a d s o r p t i o n e q u i l i b r i u m i n the t r a n s p o r t pores and i n the microporous zones, T? and T . I n the case o f s h a r p l y convex a d s o r p t i o n i s o therms, a p i c t o r i a l p i c t u r e , confirming the r a t i o n a l i t y of the biporous model for molded z e o l i t e s and microporous a c t i v e carbons can be obtained by s t u d y i n g the a d s o r p t i o n k i n e t i c s of the vapors o f X - r a y c o n t r a s t substances by X - r a y technique ( 2 2 , £ £ ) . The advantage of t h i s method i s t h e p o s s i b i l i t y of v i s u a l o b s e r v a t i o n of the formation of the a d s o r p t i o n f r o n t and i t s p r o p a g a t i o n across the g r a i n . Consider a c y l i n d r i c a l z e o l i t e granule whose l a t e r a l surface and one of the end faces are impermeable, and the a d s o r p t i o n of the X - r a y c o n t r a s t s u b stance occurs only from the granule end face ( F i g . 3 ) . I f the a d s o r p t i o n r a t e i s determined by the d i f f u s i o n i n the z e o l i t e c r y s t a l s ( T » tTi ) , the X - r a y p a t t e r n s w i l l show gradual d a r k e n i r g of the e n t i r e a d sorbent granule ( F i g . 3 a ) . I f , however, the p r o c e s s i s l i m i t e d by the t r a n s f e r i n the t r a n s p o r t pores (!:•,» T ) " l a y e r - b y - l a y e r " f i l l i p of the z e o l i t e granule i s t a k i n g p l a c e ( F i g . 3 c ) . I n t h i s case the shape of the a d s o r p t i o n wave q ( x ) i s n e a r - r e c t angulax; and the k i n e t i c curve tf(*t) ~ Vx~. The intermediate case (when the times T - and x a

a

a

Q



12

are comparable) i s c h a r a c t e r i z e d by the formation and p r o p a g a t i o n , across the g r a i n o f an a d s o r p t i o n wave CLteO w i t h a c o n s i d e r a b l y smeared-out fronb P i g . 3 b ) . I n t h i s c a s e , as t h e o r e t i c a l c a l c u l a t i o n s show, #Ct) v a r i e s i n a more complicated way t h a n b y the law Y t . The a c t u a l form o f the dependence #(-t0 i s determined by the type of the k i n e t i c f u n c t i o n o f the f i l l i n g of the microporous zones ( f o r i n s t a n c e , of the s m a l l z e o l i t e c r y s t a l s i n the g r a n u l e ) , T C i : ) ( O ^ P 0 t ) ^ ' 1 ) • I n our o p i n i o n , the approximate i n -


L

t e g r a l e q u a t i o n obtained by us ( f o r t h i s case) f o r the law of motion of the forward front o f the adsorpt i o n wave t

Z

(S) - 2 D S~ [ (CLo/Co) S $ ( S ) + 1/6 ] f

2

(27)

i s of i n r e r e s t . Here, t^(S) and $(s) are the Laplace transformants of the f u n c t i o n f ( t ) and ^ ( t ) • E q u a t i o n (>27) makes i t p o s s i b l e ( i n p r i n c i p l e ) t o determine, on t h e b a s i s o f t h e known law o f motion o f the forward f r o n t of the a d s o r p t i o n wave t("t) , the k i n e t i c s of a d s o r p t i o n i n the microporous zones ^ ( i r ) , and v i c e v e r s a . The same r e l a t i o n can be used f o r c a l c u l a t i n g the d i f f u s i o n c o e f f i c i e n t s . We have a l s o i n v e s t i g a t e d t h e o r e t i c a l l y t h e law of v a r i a t i o n i n the f r o n t w i d t h of the a d s o r p t i o n wave w i t h time i n the intermediate c a s e . For the r e c t a n g u l a r a d s o r p t i o n isotherm, we found t h a t t h i s v a l u e , A("t)t decreases w i t h t i m e . The concrete form o f the decreasing f u n c t i o n A(1f) depends on the nature of the k i n e t i c f u n c t i o n of the f i l l i n g of the m i c r o porous zones, ("t) • I n p a r t i c u l a r , i f 4 (t)=1-exp(-*Ar ) then 2

>

A(t)

G

= ( 5 ^ ) [ ( i ^ - , H i ) - ( i ^ i ) J (») (
0 i s a s m a l l value appearing i n t h e d e f i n i t i o n of the f r o n t w i d t h o f the a b s o r p t i o n wave. The c o n c l u s i o n about the v a r i a t i o n i n the adsorpt i o n wave f r o n t w i d t h , which f o l l o w s from t h e o r e t i c a l a n a l y s i s , c a n be confirmed e x p e r i m e n t a l l y by studying the k i n e t i c s o f a d s o r p t i o n o f X - r a y c o n t r a s t substanrces by X - r a y t e c h n i q u e . T h i s method was used by u s , i n p a r t i c u l a r , when studying t h e k i n e t i c s of adsorpt i o n of e t h y l i o d i d e , e t h y l bromide, and bromobenzene from a n i t r o g e n flow by molded z e o l i t e s CaA, CaX, NaX, and by a c t i v e carbons. F o r X-type z e o l i t e s and a c t i v e carbons, i n a d s o r p t i o n from the c a r r i e r gas flow we observed a c l e a r l y d e f i n e d p a t t e r n of " l a y e r - b y - l a y e r " f i l l i n g of the granules ( F i g . 3 c ) . When studying z e o A



DUBININ

Adsorption

of Gases on

Zeolites

Figure 3. Granule of molded zeolite with impermeable lateral surface and nature of adsorbate distribution in granule of biporous adsorbent

Figure 4.

Distribution of bromobenzene (a) and xenon (b) in active carbon granule in successive time intervals



14

MOLECULAR SIEVES—Π

l i t e s CaA, which d i f f e r as regards t b e i r b i n d e r s and granule molding c o n d i t i o n s , we observed a l l the p o s s i b l e cases ( F i g * 3 ) * The p a t t e r n t y p i c a l of the i n t e r m e d i a t e case ( T j ^ T a , F i g * 3b) i s observed most c l e a r l y i n s t u d y i n g the k i n e t i c s o f a d s o r p t i o n o f bromobenzene and xenon from a one-component gas phase by microporous a c t i v e carbons w i t h m o l e c u l a r s i e v e p r o p e r t i e s * The e x p e r i m e n t a l r e s u l t s are d e p i c t e d i n P i g . 4 (a -brom-benzene, P=27 P a , T=298K; b-xenon, Ρ =6.5 k p a , Τ=195Κ)· I n a l l the f i g u r e s a t t a c h e d , at the i n i t i a l i n s t a n t s of time one can see a s u b s t a n t i a l l y smearedout a d s o r p t i o n f r o n t , which reduces w i t h t i m e , i n accordance w i t h t h e o r e t i c a l a n a l y s i s , and at s u f f i c i e n t l y large times one observes " l a y e r - b y - l a y e r f i l l i n g of t h e granules* Our i n v e s t i g a t i o n s , as w e l l as those of other a u t h o r s , show t h a t the biporous k i n e t i c model holds much promise f o r s t u d y i n g the k i n e t i c s of a d s o r p t i o n by r e a l adsorbents and, i n the f i r s t p l a c e , by molded z e o l i t e s * I t enables one t o i n t e r p r e t c o r r e c t l y the r e s u l t s of experiments which cannot be s que Θ se d i n t o the framework o f the c l a s s i c a l q u a s i - d i f f u s i o n mo d e l * At the same t i m e , t h i s model r e q u i r e s f u r t h e r e x p e r i m e n t a l s u b s t a n t i a t i o n * T h i s r e f e r s , above a l l , t o the nature of mass t r a n s f e r i n the microporous zones* I n the f i n a l a n a l y s i s , the a p p l i c a t i o n of the biporous model of r e a l adsorbents makes i t p o s s i b l e t o approach more r a t i o n a l l y the c h o i c e o f adsorbents w i t h the most r a t i o n a l porous s t r u c t u r e * 1 1

Literature Cited 1. D u b i n i n Μ.Μ., " C h e m i s t r y and P h y s i c s o f C a r b o n " , Vol.2, p . 5 1 , M.Dekker, New Y o r k , 1966 2. D u b i n i n Μ.Μ., "Progress in Surface and Membrane S c i e n c e " , Vol.9, p . 1 , Academic P r e s s , New Y o r k , 1975 3. B e r i n g B.P., Serpinskii V.V., I z v . A k a d . Nauk SSSR, S e r . Khim. (1974) 2427 4 . Hill T.L., J. Chem. P h y s . , (1950) 18, 246 5. B a r r e r R.M., Calabova I.M., Adv. Chem. S e r i e s (1973) 121, 356 6 . Sarakhov Α.Ι., Kononyuk V.F., D u b i n i n Μ.Μ., Adv. Chem. S e r i e s , (1973) 121, 403 7. Frumkin A.N., Z.phys. Chem., (1925) 116, 466 8. Adam Ν.Κ., "The P h y s i c s and Chemistry of Surfaces" London, 1941



1. Dubinin

Adsorption of Gases on Zeolites

15

9. P r i g o g i n a I., Defay R., "Chemical Thermodynamics", Longmans Green, London, 1954 10.Young D . M . , Crowell A.D., "Physical Adsorption o f Gases", p.110, Butterworths, London, 1962 11.Cohen G., T h e s i s , Grenoble, 1967 12.Kisarov V.N., Z h . Fiz. Khim., (1967) 42, 1037 13.Guggenheim E.A., "Modern Thermodynamics by the Methods of W i l l a r d Gibbs", Methuen and C o . Ltd, London, 1933 14.Fomkin A.A., Dissertacia, Moskva, 1975 15.Dubinin M . M . , A d v . C o l l o i d Interface Sci., (1968) 2, 217 16.Ruckenstein E., Vaidyanathan A.S.,Youngquist G . K . , Chem. Eng. Sci., (1971) 26, 1305 17.Ma Y.H., Mancel C., Adv. Chem. Series, (1973) 121, 392 18.Haynes H.W., Sarma P.N., AIChE J., (1973) 19, 1043 1 9 . K o c h i r j i k M . , Zikanova A., "Adsorbcija i p o r i s t o s t " p. 296, "Nauka", Moskva, 1976 20.Voloshchuk A . M . , Dubinin M . M . , Zolotarev P.P., "Adsorbcija i poristost", p. 285,"Nauka",Moskva, 1976 21.Zolotarev P.P., Dubinin M . M . , D o k l . Akad. Nauk SSSR, (1973) 210, 136 22.Voloshchuk A . M . , D u b i n i n M . M . , D o k l . Akad. Nauk SSSR, (1973) 212, 649 23.Voloshchuk A . M . , Zolotarev P.P., Ulin V.I., Izv. Akad. Nauk SSSR, Ser, Khim., 1974) 1250 24.Zolotarev P.P., U l i n V.I., I z v . Akad. Nauk SSSR, S e r . Khim., (1974) 2367 25.Dubinin M . M . , Erashko I.T., Kadlec O., U l i n V.I., Voloshchuk A . M . , Z o l o t a r e v P.P.,Carbon,(1975),13,198 26.Voloshchuk A . M . , Dubinin M . M . , Nechaeva N . A . , Ulin V.I., D o k l . Akad. Nauk SSSR, (1975) 222, 369 27.Zolotarev P.P., I z v . Akad. Nauk SSSR, Ser. Khim. (1975) 193


Investigations of Equilibria and Kinetics of Adsorption of Gases on

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