Thermodynamics of Adsorption on Zeolites - ACS Publications

26 Thermodynamics of Adsorption on Zeolites W. SCHIRMER, K. FIEDLER, and H. STACH

Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0040.ch026

Zentralinstitut fuer physikalische Chemie der Akademie der Wissenschaften der DDR, Berlin-Adlershof, East Germany

ABSTRACT Comprehensive experimental data on adsorption in zeolites show an influence of structure. Statistical— thermodynamic approaches consider this, the constants of equations are determined by adaption, according to their physical meaning. Empirical correlations within homologous series of chemical compounds represent im portant characteristics of zeolitic adsorption. All observed phenomena can be explained quantitatively. Introduction Although s c i e n t i f i c and t e c h n i c a l a p p l i c a t i o n o f adsorption has s u p p l i e d us, d u r i n g the l a s t t e n y e a r s , w i t h comprehensive experimental data, we, at present, are f a r from being able to formulate a g e n e r a l l y v a l i d theory o f a d s o r p t i o n on microporous s o l i d bodies. Such a theory e s p e c i a l l y , when i t i s a p p l i e d t o z e o l i t e s , must take i n t o account the following structural characteristics: - separate s o r p t i o n c a v i t i e s , a c c e s s i b l e to adsorbed molecules only by c r o s s i n g an a c t i v a t i o n b a r r i e r - s m a l l s i z e o f the c a v i t i e s , l i m i t i n g the number o f adsorbed molecules t o a few and f o r long-chain p a r a f f i n s ) t o one per c a v i t y , so that the i d e a o f a s p e c i a l adsorbed phase can o n l y be used to a very l i m i t e d extent - h e t e r o g e n e i t y o f the f i e l d o f a d s o r p t i o n i n the c a v i t y , causing the e x i s t e n c e o f s p e c i a l molecular arrangements f o r both non-polar molecules ( p a r a f f i ns) and p o l a r molecules (H 0, ΜΗ3)· An examination o f the fundamentals o f the a c t u a l l y p r e v a i l i n g t h e o r e t i c a l approaches, 2

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


306

MOLECULAR SIEVES—II

- the equation of Langmuir [ ] J , - the potential theory of adsorption [2], - the theory of volume f i l l i n g L3], - v i r i a l equations [4,5,6] shows, particularly wifti^regard to molecular sieves, that obviously none of them meets the above-mentioned conditions exactly, A comprehensive theoretical approach could be based i n our opinion, on s t a t i s t i cal thermodynamics. Here we present the f i r s t results of our attempts to derive such an approach* By applying the equations i n a semi-empirical manner we avoid the need for a quantummechanical treatment which i s in principle possible but too d i f f i c u l t for the moment. We present comprehensive experimental material, which we obtained during our research on the adsorption on zeolites of the faujasite type using different classical and modern methods [7,8,9,10]· On the basis of our experiments and the sÎaîistical-thermodynamic approach v/e are able to draw a number of conclusions of a theoretical nature. Experimental Results We investigated the adsorption equilibria of nonpolar, easily polarizable, and polar molecules on zeolites of the types A, X, and Y, which, usually, were not pelletized. Normal-paraffins were chosen as adsorbates because they show the following charact e r i s t i c properties: 1) Carbon-chains of various length permitting us to vary the maximal occupation of one zeolite cavity from ten molecules down to one molecule. 2) P o s s i b i l i t i e s of various conformations leading to new, adapted structures of the adsorbed molecule in the cavity. We further investigated the adsorption of normalolefins, benzene, water, and ammonia [7,1_2]. Figure 1 represents our experimental results on isotherms and isosteres i n a special manner, which in our case represents the data clearly, but may not be appropriate to a l l adsorption systems [13] : the adsorbed quantity a i s plotted against a value ξ , equal to S

T/T RT Eq. (1) i s based on the following known equations 0

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

26.

SCHIRMER

Thermodynamics of Adsorption on Zeolites

E T AL.

A H ( a

AS(a,T)=

AS^a.T)

+

P'P

n

+

R


l

AR(aJ)-E

T

- > Τ

"

0

RT

~*

r

R

"

ζ

2

)

(3)

RT

AS~(a,T)

0

(

_ ΔΗ(α,Τ)

0

T/T

307

C4)

'

E Q r e p r e s e n t i n g an average value f o r A H ( a , T ) i S o l v i n g equation (4) y i e l d s the f u n c t i o n α = ί(ξ,Τ)

(5)

,

from which we d e r i v e w i t h the h e l p o f the permutation entropy -R l n a and the decomposition ΔΤ° =-ft in α+Δ$5ό* e

A~H-E

a = e

AS

0

T

*

*

(6)

Eq. (5) has the f o l l o w i n g advantages: I f Δ Η « Ε and AS** * ( * w

(9)

e

which f o r s m a l l values of a leads to

W (0) f

α

do)

=

W (0) depending o n l y on the s i z e of the molecule. Equation (5) permits us to c o r r e l a t e the v a r i o u s r e s u l t s of many authors concerning the a d s o r p t i o n of η-paraffins i n a uniform manner L I 4 , 1 5 , 1 6 ] · F i g u r e 1 shows the adsorption "isotherms of the η-paraffins and the r a r e gases krypton and xenon on z e o l i t e TTaCaA i n the coordinates a = ί(ξ)· every ri-paraffin, the value of E was c a l c u l a t e d by a procedure, explained below, determining the s t a t e of coverage of 1 molecule per c a v i t y (energy of a d s o r p t i o n E^ ). The isotherms of the l i g h t n-alkanes are f a i r l y w e l l represented by a s i n g l e curve, w h i l e l o n g e r - c h a i n η-paraffins show some s c a t t e r i n g f o r h i g h e r coverages. For £-hexane and η-heptane r e s u l t s obtained at h i g h e r temperatures are used. Methane corresponds w e l l to the e x p o n e n t i a l c h a r a c t e r of equation (10). The curve f o r krypton i s the same as f o r methane, p r o v i n g that the s i z e and the symmetric c h a r a c t e r of the p a r t i c l e s are compa r a b l e , see a l s o Ruthven [17]· A l l curves of the Q-paraffines show an e x p o n e n t i a l range, d i m i n i s h i n g w i t h i n c r e a s i n g c h a i n - l e n g t h . For l o n g e r - c h a i n n- p a r a f f i n s , the curves have steps corresponding to an adsorbed q u a n t i t y of approximately one molecule per c a v i t y , \Ve observe c o r r e l a t i o n s between the value of Ç and the number of CH?-groups per c a v i t y which v/e discussed elsewhere [18j# The i s o s t e r e s i n the system n-heptane/zeolite are curved [ 1 9 ] , a f a c t which can~"be explained by the assumption of two d i f f e r e n t groups of s t a t e s of energy f o r the heptane molecules. We observed curved i s o s t e r e s f o r the a d s o r p t i o n of n-hexane, n - c l f NH3, * benzene on A- or X-zeolïtes. We draw the c o n c l u s i o n that d e v i a t i o n s from the l i n e a r c h a r a c t e r o f a d s o r p t i o n i s o s t e r e s may be r a t h e r a common phenomenon, the i n v e s t i g a t i o n of which demands a h i g h accuracy of measurements. We i n t e r p r e t the two groups of s t a t e s of energy as


f

F o r

Q

e c a n e

anc


26.

SCHIRMER

E T AL.


309

1) a group o f s t a t e s o f low energy w i t h l o c a l i s e d p o s i t i o n s near the w a l l o f the c a v i t y 2) a group o f s t a t e s o f h i g h energy, n o n - l o c a l i s e d , s i t u a t e d i n the c e n t r e . Between these two groups o f s t a t e s , a temperature-dependent t r a n s i t i o n o f molecule i s observed, which i s o f h i g h order and may be regarded as q u a s i -Schottky t r a n s i t i o n . The curves c = f ( T ) must t h e r e f o r e go through a maximum, which we indeed detected by c a l o r i m e t r i c measurements. As a r e s u l t o f our experimental work on the adsorption o f water ( t o g e t h e r w i t h Η· P f e i f e r et a l , [ 9 ] ) we observed t h a t , e s p e c i a l l y at low coverage, h i g h values o f enthalpy correspond to low values of entropy, thus p o i n t i n g to s p e c i a l s t a t e s o f a d s o r p t i o n . By the combined a p p l i c a t i o n o f the abovementioned p h y s i c a l methods we found that water-mole c u l e s can be adsorbed i n f a u j a s i t e - c a v i t i e s i n f i v e d i f f e r e n t s t a t e s , s t r o n g l y d i s t i n g u i s h e d by t h e i r c o r r e l a t i o n time t (measured by NMR-pulse- t e c h n i q u e ) . For d e t a i l s see [ 9 ] ·


p

c

Statistical-Thermodynamic

Approach

A t h e o r e t i c a l treatment o f the z e o l i t i c a d s o r p t i o n must be able to d e s c r i b e complicated f u n c t i o n s o f coverage, temperature-dependent molecu l a r t r a n s i t i o n s , and s p e c i a l s t r u c t u r e s o f the adsorbate. The s t a t i s t i c a l thermodynamic treatment developed by H i l l and f i r s t a p p l i e d to z e o l i t i c systems by Bakaev [ 2 0 ] and independently by Ruthven [15] and a l s o by F i e d l e r [21] o f f e r s the most pro mising approach. On the base o f s t a t i s t i c a l thermodynamics and owing to the separate s o r p t i o n c a v i t i e s o f the z e o l i t e s , p a r t i c u l a r l y c h a r a c t e r i s t i c f o r type A, the grand p a r t i t i o n f u n c t i o n Ξ o f the z e o l i t e can be represented as the product o f the grand p a r t i t i o n f u n c t i o n s 2 of the s i n g l e c a v i t i e s (totaj. number = N ) 1

r

(11) Under the c o n d i t i o n , that the c a n o n i c a l p a r t i t i o n function c o n t a i n s the same r e s i d u a l c o n t r i butions o f moments, r o t a t i o n s , and i n t e r n a l motions as the gas we d e r i v e the equation


310

MOLECULAR

Q, λ'=

(p/RT)' 0

SIEVES—II

(12)

i c o n f

In the range o f temperature i n which we measured the a d s o r p t i o n values we r e p l a c e the i n t e g r a l expressions of Q; [6] by f i n i t e sums, whose 1 summations correspond to d i f f e r e n t energy l e v e l s . In t h i s way i t i s p o s s i b l e to d e s c r i b e d i f f e r e n t s t a t e s of energy and t h e i r t r a n s i t i o n s . We put 1=1 f o r a c a v i t y which, f o r a given coverage, i s e n e r g e t i c a l l y homogeneous, w h i l e i n o t h e r cases 1=2 d i f f e r e n t s t a t e s may be regarded as s u f f i c i e n t . The sums are represented by


c o n f

li_L_LL

ο,χ'.,ΙίΕΐ.,·

Γ,'^τ

(13)

4—J7^

T/T Ό n

Sjj° are constants f o r the (T,V ) - s t a n d a r d - d i f f e r e n ces of entropy, Ejj = energy constants of the corresponding l e v e l s . I f the c a v i t y c o n t a i n s o n l y one molecule, we get the value , a l r e a d y used i n figure 1 (E. = ). The isotherm equation α = 3In £/3tnλ transforms i n t o Q

ΣΖΐΟ:λ' 0

s

N

-EL,

c r _ i r 7

c

(H)

θ » Y " i θ;

(15)

=N2li9

i

= N e

i =1 i =1

where

Q λ θ.

=

—

\

1

m

Γ-

,

are v a l i d , c o n s i d e r i n g the s t r u c t u r e ( 1 3 ) · B\ ex presses the p r o b a b i l i t y f o r the e x i s t e n c e of a c a v i t y of an i - f o l d occupation. Equation (14) s u f f i c e s , i n connection w i t h ( 1 3 ) to d e s c r i b e t r a n s i t i o n s of molecules i n the c a v i t y , f o r a given degree of coverage. By a change of Θ*, w i t h temperature i t i s p o s s i b l e to d e s c r i b e another k i n d o f molecular t r a n s i t i o n , t h a t between d i f f e r e n t c a v i t i e s . The d i f f e r e n t i a l s p e c i f i c heat of the s t a t e of coverage i of a c a v i t y , t h e r e f o r e , contains two summations A c j + i (ΔΕ. - Δ Ε

2

) / RT

2


f

(16)

26.

scHiRMER

E T

AL.


311

the f i r s t one representing t r a n s i t i o n s within a c a v i t y , the second one between the c a v i t i e s . A p p l i c a t i o n of the Approaches Equation (14) depends on the constants Nr, S-J , and Ejj , which are superior to v i r i a l c o e f f i c i e n t s i n that the form of t h e i r dependence on pressure and temperature i s known. The dependence of the coverage a on pressure arid temperature i s expressed e x p l i c i t l y by the s u b s t i t u t i o n of equation (13) i n (14). The values of N , S™ . and Ejj are determined i n the f o l l o w i n g two ways! Ό As they have a concrete p h y s i c a l meaning, they may be c a l c u l a t e d from molecular data on the adsor bents. T i l l now we have had such r e l i a b l e mole c u l a r data f o r only a few systems [ 2 2 ] . We do not know the d e v i a t i o n s from i d e a l values f o r most r e a l systems, so that t h i s way may not f r e q u e n t l y be used. We s h a l l not f o l l o w up i t here. 2) Equation (14) i s adapted to the c h a r a c t e r i s t i c p r o p e r t i e s of the z e o l i t e s . It i s p o s s i b l e to deter mine the values of the constants by means of a method of parameter determination using the measured e q u i l i b r i u m data a(p,T). By t h i s procedure, we f i n a l l y can c a l c u l a t e the thermodynamic functions and other c h a r a c t e r i s t i c q u a n t i t i e s such as the d i s t r i b u t i o n functions θ·, Studies about the r e l a t i o n s of the constants within homologous s e r i e s of chemical compounds and f o r d i f f e r e n t types of z e o l i t e s w i l l give us i n s i g h t i n t o the mechanism of adsorption. Ruthven et al_. considered the free volume under van-der^Waals-conditions i n t r o d u c i n g an a d d i t i o n a l c o r r e l a t i o n between the constants . This i s advantageous f o r small molecules, f o r example f o r short-chain n-alkanes. In using a general form of a r e l a t i o n s whose constants are independent on one another, we are able to treat more complicated z e o l i t i c systems. It i s . however, more d i f f i c u l t to obtain the necessary information data.


c

Results 1) Equation (14) f i t s w e l l the experimental data of the e q u i l i b r i a measured f o r n_-paraffin s of 1-18 C-atoms i n z e o l i t e ^TaCaA, over the whole range of i n v e s t i g a t i o n . The value f o r the quantity of c a v i t i e s , Νς, amounts constantly, within a homolo gous s e r i e s , to approximately 0.80 of the t h e o r e t i c a l


312


value corresponding to an ideal structure of the zeolite* The N -values of different types of zeolites d i f f e r i n the same proportion as the theoretical values. The maximal quantity m of molecules, adsorbed i n one cavity, decreases with increasing length of chain. For ja-alkanes above n-C-jQ * the value for m i s 2, the second molecule only enters the cavity at low temperatures and high pressures. Figure 1 shows d i s t i n c t l y that the adsorption range for one molecule per cavity i s well separated from the two-molecules range. For one molecule i n a cavity equation (14) reduces to the Langmuir equation. This i s the reason why, i n this range, the Langmuir equation can be successfully applied to technical processes. For n - C c to S - C 7 : m = 4; we found m = 6 for the representation of the data for methane to propane. The number of values 1 necessary to describe the levels of energy i s equal to one for each coverage of the cavity except i n the case of û-hexane and η-heptane, where we found 1 = 2. We observed, especially for these two hydrocarbons, curved isosteres, referring to temperature-dependent heats of adsorption. The energy constants E display, as figure 2 shows, a nearly linear dependence on the number of the C-atoms of the η-paraffins. This enables us to extrapolate to long-chain η-paraffins for v/hich adsorption data are not available. A linear depen dence could also be found for E^ -values with i > 1. The curve Ej-j = f ( i ) decreases from an i-value, v/hich corresponds to a total number of 12 C-atoms i n the paraffin molecule adsorbed in one cavity. The curve of the entropy constants S°° begins to decrease beyond η-paraffins with more than 12 C-atoms. This tendency becomes very clear for the adsorption of n-octadecane. In these cases, obviously, strong restrictions i n the p o s s i b i l i t y of display of various conformations are dominating. At high temperatures Τ ( R T » / E J : / ) , the influence of the energy constants Ε,.· on equation (14) and that of Ep on ξ disappear. N and S~ , therefore, alone permit calculation of the temperature-independent curve a=f(Ç) i n figure 1. This shows once more that this curve especially represents the entropie factor of the z e o l i t i c adsorption. The values of S°° determine the character of a=f(Ç), especially in the range of low coverages a. They, therefore, are directly responsible for the shift of the exponential part of the curve i n figure 1 to the right with


c

N

c


26.

scHiRMER E T A L .


313

α /Cmmol /gD


a = f(f),NaCaA

5

Figure 1.

10

15

20

ξ/cin

25

Experimental data of the adsorption equilibria of rare gases (Kr, Xe) and η-paraffins on zeolite NaCaA in the plot a vs. $

ο E^/CkJ/mon

; •

S^/CJ/K/molU

NaCaA -50

ο

-100 \

10

15

20

C-number/C1 •

Figure 2. Dependence of the isotherm constants E and S ι / ° ° on the number of C-atoms of the n-paraffins n



314


i n c r e a s i n g c h a i n - l e n g t h o f η-paraffins o r w i t h i n c r e a s i n g atom s i z e f o r the r a r e gases. 2) In f i g u r e 3 we represent r e s u l t s obtained f o r the system n-decane/zeolite NaMgA u s i n g equations (13) and (14)· They d i s t i n c t l y show the changes o f the thermodynamic f u n c t i o n s a f t e r the adsorption of the second molecule i n the c a v i t y . We demonstrate the e f f e c t i v e n e s s o f the equations by e x t r a p o l a t i o n to low temperatures. 3) The i d e a o f the s e p a r a b i l i t y o f the z e o l i t e i s no longer v a l i d when the adsorbate molecules are l a r g e r than the c a v i t i e s o f the 5 A - z e o l i t e s . In such cases, adsorbed molecules f o r i n s t a n c e o f Jl-tetradecane o r n-octadecane, occupy two c a v i t i e s at the same time,"thus reducing the s e p a r a t i o n o f two cages. We considered t h i s f a c t by i n t r o d u c i n g thermodynamic systems c o n s i s t i n g o f c e l l s o f two or f o u r c a v i t i e s . This treatment favours the i n t e r a c t i o n s going on i n the i n t e r i o r o f the system and n e g l e c t s , to a c e r t a i n e x t e n t , the processes on the i n n e r s u r f a c e . This method proved to be v a l u a b l e f o r z e o l i t e ITaX, f o r which the e q u i l i b r i a o f many adsorbates o n l y could be described by l a r g e r c e l l s . We were able to demonstrate s t a t e s f o r n-hexane and benzene i n z e o l i t e NaX. 4) The adsorption o f o l e f i n e s was i n c l u d e d i n the e v a l u a t i o n o f equation (14)· Figure 3 represents some thermodynamic f u n c t i o n s o f the system t r a n s -butene-2/NaX. We see that the heat o f a d s o r p t i o n reaches a maximum at h i g h coverages. 5) F o r the adsorption o f p o l a r molecules, we transform equation (14) i n t o the f o l l o w i n g sum: q

(17) k=1

By means o f t h i s equation we could d e s c r i b e the adsorption o f ammonia and water i n the z e o l i t e s NaCaA and NaMgA. F i g u r e 4 shows some thermodynamic f u n c t i o n s f o r the system NH /NaMgA. A l l values o f m and 1 were placed = 1, so that each summation o f equation (17) was equal to the right-hand s i d e o f a Langmuir equation. The energy constants, h i g h l y d i f f e r e n t f o r v a r i o u s values o f k, are r e s p o n s i b l e f o r the s t e p - l i k e decrease o f the heat o f adsorption. 3

Summarizing our r e s u l t s we s t a t e t h a t the comprehensive experimental m a t e r i a l can be



100-

200

300

100

150 -

/CkJ/molU

e

673 Κ A

Figure 3.

a/CmmoL/g]

a/Cmmol/gl]

1.0

1.0

100

200

H/CkJ/molIl

-^S°/CJ/K/mon

-Δ

• 2

2

a / C mmol /g3

α / C m m o l /g3

I 3

3

Thermodynamic functions of the adsorption of n-decane and trans-butene-2 on zeolites NaMgA and NaX

0.5

0.5

Ο Ο Ο Ο Ο Ο

2 2

-^S /CJ/K/mon

1 0

n-C H ,NaMgA

-ΔΗ


316

MOLECULAR

SIEVES—II

-Δ Η / C k J / m o l D


100

V

NH ,NaMgA 3

173 50 673K

6

J a/Cmmol/gJ

-Δ S°l C J / K / m o i :

NH

id

f

100

NaMgA

3 /

>

6

•

1 ,/

7

3

^

273

1

'/ ι;/ •if

^ 1 7 3

IV

Κ

50 3

1

2

3

4

5

8

6 a/Cmmol/gD

Figure 4.

Thermodynamic functions of the adsorption of NH on zeolite NaMgA


S


26. scHiRMER

E T AL.


317

represented i n a form which allows us to notice the influence of the adsorbent structure. The basic approaches of the s t a t i s t i c a l thermodynamics, considering the principal features of z e o l i t i c sorption, are developed i n a simplified form so that their application becomes possible. The physically established constants are determined by application to experimental data. States of different energy l e v e l , molecular transitions, processes of reorganization of adsorbed molecules and maxima i n the curves of heats of adsorption are explained. A l l observed phenomena can be treated quantitatively. A further development of these approaches seems possible. Nomenclature a, a(p,T) E

adsorbate concentration [mmol/g] estimated or calculated suitable constant for heat of adsorption [kj/mol] E constant for high-energy ( j 1 ) f o r 1 molecule/cavity (i=1 ) [kj/mol] Ejj molar constant for energy (j-th level) for i molecules/cavity [kj/mol] f(Ç T), f(Ç) empirically reduced isotherms [mmol/g] f(i) · empirical function from i [kj/mol] i number of molecules/cavity [1] ί integer for energy level [1] k integer for type of cavity [1] 1 number of energy levels [1] m maximum number of molecules/cavity [1] N, N, number of cavities, type k [1]or[mmol/g] ρ equilibrium adsorbate pressure [Pa] P standard pressure=1 [atm] = 101 325 [Pa] q number of types of cavities [1] Qi canonical partition function for i [1] 0

s

n

f

c

c

k

0

Qjconf

contribution of configuration to

R S S

gas constant = 8.31434 [J/K/mol] d i f f e r e n t i a l entropy adsorbate [J/K/mol] molar entropy of ideal gas [J/K/mol]

gQS

(T,V ) 0


[1]

318

MOLECULAR

S°?

m o l a r

c o n s t a n t

- d i f f e r e n c e Τ

V

s t a n d a r d

0

) - s t a n d a r d -

o f e n t r o p y

[ J / K / m o l ]

v o l u m e

0

f

( a )

W

f

f

( 0 ) f r e e

Ac-,

[ K ]

t e m p e r a t u r e

s t a n d a r d

0

W


Q

t e m p e r a t u r e

T

W

f o r ( T , V

SIEVES—II

v o l u m e

R T

0

/ p

f o r i

ΔΕ-,

m o l a r

i n t e g r a l

f o r

m o l e c u l e s / c a v i t y

T )

d i f f e r e n t i a l

A S ( a , T )


AS™


( a , T )

of A S ° ° *

e n t r o p y

=

- d i f f e r e n c e θ

d i f f .

9

k

'

d i f f .

S - S

of

k

t y p e

3

/ k g ]

[ m

3

/ k g ]

e n e r g y [ k j / m o l ]

o f e n t r o p y

[ k J / m o l ] [ J / K / m o l ]

) - s t a n d a r d - d i f f e r e n c e

Q

g

o f

Q

s

( T , V

r e d u c e d

Q

)

[ J / K / m o l ]

( T , V

Q

) - s t a n d a r d -

o f e n t r o p y

number

[ m

[ k j / m o l ]

o f e n t h a l p y

d i f f . ( T , V

a v e r a g e

/ m o l ]

h e a t

o f e n e r g y

d i f f e r e n c e

n o t p e r m u t a t i o n

l

o f

3

m o l e c u l e s / c a v i t y [ J / K / m o l ]


f

[ m

0

d i f f e r e n c e

Δ I

A H ( a

[ K ]

o f c o n f i g u r a t i o n

i n t e g r a l

c a p a c i t y

i

2 7 3 · 1 5

o f a d s o r p t i o n

v o l u m e

m o l a r

«

«

[ J / K / m o l ]

o f m o l e c u l e s / c a v i t y ,

o f c a v i t i e s

9j

p r o b a b i l i t y

λ

a b s o l u t e

a c t i v i t y

[ 1 ]

ξ

v a r i a b l e

f o r r e p r e s e n t a t i o n

[ 1 ]

^

g r a n d

f o r

p a r t i t i o n

z e o l i t e , f o r

i

[ 1 ]

m o l e c u l e s / c a v i t y

f u n c t i o n s

t h e s i n g l e

f o r

c a v i t y

[ 1 ]

t h e w h o l e t y p e

1

[ 1 ]

Literature Cited [1] FLOOD, Ε. Α., 'The Solid-Gas Interface', Marcel Dekker, New York, 1967 [2] BRUNAUER, S., COUPLAND, L., and KANTRO, D . , in FLOOD, Ε. A., [1] [3] DUBININ, M. M . , 'Adsorption and Porosity' (russ.), Moskau, 1972 [4] BARRER, R. Μ., and GIBBONS, R. Μ., Trans. Faraday Soc. (1963) 59, 2569



26.

SCHIRMER ET AL.


319

[5] BEZUS, A. G . , KISELEV, Α. V., and PHAM QUANG DU, J. Colloid. Interf. Sc. (1972) 40, 223 [6] STEELE, W. Α . , in FLOOD, Ε. Α . , [1 ] [7] KUNATH, D . , SPANGENBERG, H.-J., STACH, Η . , and SCHIRMER, W., Z. Chem. ( 1 9 7 0 ) 10, 11 [8] SPANGENBERG, H.-J., FIEDLER, K . , ORTLIEB, H.-J., and SCHIRMER, W., Z. phys. Chem. Leipzig ( 1 9 7 1 ) 248, 49 [9] PFEIFER, H . , 'NMR-Basic Principles and Progress' 55, Springer-Verlag, Heidelberg-New York, 1972 [10] LOHSE, U . , STACH, Η . , and SCHIRMER, W., Mber. Dt. Akad. Wiss. ( 1 9 7 0 ) 12, 8 1 9 , 828 [11] BARRER, R. Μ., and SUTHERLAND, J. W., Proc. Roy. Soc. A (1956) 237, 439 [12] PEINZE, T . , FIEDLER, Κ., STACH, H.,and SCHIRMER, W., Mber. Dt. Akad. Wiss. ( 1 9 7 0 ) 12, 8 5 5 , 870 [13] FIEDLER, Κ., ORTLIEB, H.-J., and SCHIRMER, W., Festkolloquium zum 8 0 . Geburtstag von Ν. N. Semenev, Moscow, 1976 (in press) [14] RUTHVEN, D. Μ., AIChE. Journal ( 1 9 7 6 ) , 22, 753 [15] RUTHVEN, D. Μ., Nature Phys. Sci.(1971), 232, 70 [16] COUGHLAN, B . , KILMARTIN, S., MeENTEE, J., and SHAW, R. G . , J. C o l l . Interf. S c i . ( 1 9 7 5 ) 5 2 , 386 [17] RUTHVEN, D. M . , J. Phys. Chem. ( 1 9 7 5 ) 7 9 , 856 [18] FIEDLER, Κ., STACH, Η . , and SCHIRMER, W., Publication in preparation [19] SCHIRMER, W., KOELSCH, P . , PETERS, Η . , and STACH, H . , in UYTTERHOEVEN, J. B . , 'Proc. III. Internat. Conf. Molecular Sieves', Leuven Uni versity Press, 1973, p. 285 [20] BAKAEV, V. Α . , Dokl. AN SSSR (1967) 167, 369 [21] FIEDLER, Κ., STACH, Η . , and SCHIRMER, W., 'Entwicklung und Testung von statistisch-thermodynamischen Modellen der energetisch heterogenen Adsorption in Zeolithen',Vortrag auf der Chemiedozententagung der Chem. Ges. der DDR, Freiberg, 1971 [22] KRETSCHMER, R. G . , and FIEDLER, K., Z. phys. Chem. Leipzig (in press)


Thermodynamics of Adsorption on Zeolites - ACS Publications

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