34 Analytical Method Applying Polanyi's Theory to Adsorption on Synthetic Zeolites
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J. L. GINOUX, J. C. LANG, and L. BONNETAIN Ecole Nationale Supérieure d'Electrochimie et d'Electrométallurgie de Grenoble, Laboratoire de Chimie Minérale, Domaine Universitaire, 38401 St. Martin d'Hères, Grenoble, France
An analytical method for applying Polanyi's theory at temperatures near the critical temperature of the adsorbate is describ The procedure involves the Cohen-Kisarov equation for the ch acteristic curve as well as extrapolated values from the physic properties of the liquid. This method was adequate for adsorption on various molecular sieves. The range of temperature, where this method is valid, is discussed. The Dubinin-Radushkevich equation was a limiting case of the Cohen-Kisarov's equation. From the value of the integral molar entropy of adsorption, the adsorbed phase appears to have less freedom than the compressed phase of same density. T n t h e field of c h e m i c a l engineering t h e design of a d s o r p t i o n t o w e r s o p e r a t i n g i n a c y c l i c w a y requires a precise k n o w l e d g e of t h e r e l a t i o n s h i p b e t w e e n t h e a m o u n t a d s o r b e d a n d t h e e q u i l i b r i u m t e m p e r a t u r e a n d pressure o v e r a l a r g e r a n g e of these p a r a m e t e r s , w h i c h f r e q u e n t l y i n c l u d e s t h e c r i t i c a l t e m p e r a t u r e of t h e adsorbate. O n a n o t h e r h a n d , P o l a n y i ' s t h e o r y gives a s a t i s f a c t o r y c o r r e l a t i o n between e x p e r i m e n t a l i s o t h e r m s i n t h e range w h e r e t h e p h y s i c a l p r o p e r t i e s of t h e l i q u i d are k n o w n (near t h e n o r m a l b o i l i n g t e m p e r a t u r e ) . H o w e v e r t h e t h e o r y does n o t give t h i s c o r r e l a t i o n i n a n a n a l y t i c a l w a y . I n t h i s paper a n a n a l y t i c a l m e t h o d a p p l i c a b l e a t t e m p e r a t u r e s w h i c h s p a n t h e c r i t i c a l t e m p e r a t u r e of t h e adsorbate is p r e sented. T h i s m e t h o d is b a s e d o n t h e P o l a n y i ' s t h e o r y a n d o n e x t r a p o l a t i o n m e t h o d s of t h e p h y s i c a l properties of t h e l i q u i d i n t h i s r a n g e of t e m p e r a t u r e . A
Theory P o l a n y i ' s T h e o r y . L e t p be t h e s a t u r a t i o n pressure of t h e v a p o r of t h e adsorbate a t a t e m p e r a t u r e T, a n d e the decrease i n G i b b s free energy d u r i n g s
382 In Molecular Sieves; Meier, W., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1973.
34.
GINOUX ET A L .
383
Polanyi's Theory
t h e i s o t h e r m a l passage of one mole of t h e a d s o r b a t e f r o m t h e l i q u i d phase t o t h e a d s o r b e d state e x h i b i t i n g a n e q u i l i b r i u m pressure ρ :
e =
RT
In-
(1)
V
L e t q (expressed i n c m N T P / g r a m of adsorbent) be t h e c o r r e s p o n d i n g a d s o r b e d a m o u n t , ρ ( g r a m / c m ) t h e d e n s i t y of t h e a d s o r b e d phase, a n d V ( c m N T P / g r a m of adsorbate) t h e specific v o l u m e of t h e gaseous phase u n d e r n o r m a l c o n d i t i o n s (1 a t m , 0 ° C ) . T h e v o l u m e W ( c m / g r a m of a d s o r b e n t ) o c c u p i e d b y t h e a d s o r b e d phase is t h e n expressed b y : 3
3
m
3
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3
(2)
P o l a n y i ' s t h e o r y (1) states b a s i c a l l y t h a t t h e e vs. W curve—i.e., t h e so-called c h a r a c t e r i s t i c c u r v e , is t e m p e r a t u r e i n v a r i a n t . C h a r a c t e r i s t i c C u r v e E q u a t i o n . T h e first a n a l y t i c a l e q u a t i o n of t h e c h a r a c t e r i s t i c c u r v e was p r o p o s e d b y D u b i n i n a n d R a d u s h k e v i c h (2) as :
-w.—[-G)"] where W is t h e l i m i t i n g v a l u e of W o b t a i n e d a t s a t u r a t i o n of t h e a d s o r b e n t (e = 0, ρ = ps) w h i c h also corresponds t o t h e w h o l e m i c r o p o r o u s v o l u m e . Θ is t h e degree of filling, a n d Ε is a c o n s t a n t w h i c h depends u p o n t h e a d s o r bate-adsorbent system. 0
E q u a t i o n 3 w a s v e r i f i e d e x p e r i m e n t a l l y (3) o v e r w i d e ranges of t e m p e r a t u r e a n d e q u i l i b r i u m pressure for t h e a d s o r p t i o n of v a r i o u s v a p o r s o n a c t i v e carbons w i t h different p a r a m e t e r s for t h e m i c r o p o r o u s s t r u c t u r e . F o r a d s o r p t i o n o n zeolites, t h i s e q u a t i o n fitted t h e e x p e r i m e n t a l results w e l l o n l y i n t h e r a n g e of h i g h v a l u e s of θ (4, 5, 6, 7). A m o n g other equa t i o n s proposed for t h e c h a r a c t e r i s t i c c u r v e (4, 6, 8, 9, 10) we chose to use t h e C o h e n (4) a n d K i s a r o v ' s (10) e q u a t i o n , w h i c h s t a r t s f r o m t h e f o l l o w i n g adsorption isotherm equation:
