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Adsorption systems at temperatures below the freezing point of the
adsorptive
Litvan, G. G.
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781
ADSORPTION SYSTEMS AT TEMPERATURES BELOW
THE FREEZING POINT OF
THE
ADSORPTIVE
by
G.G. utvan
4
Reprinted
from
Advances in Colloid and Interface Science
VoL 9, 1978
p.
253
-
302
BUILDIpJG RESEARCH
1
i
-
LlBRPZRY
-
9
r"
?i
AUG 24
1974
4
i1
C
:
I!DBR Paper No. 781
Division
of Building Research
SOMMAIRE
Des 6tudes portant sur l'adsorption isotherme et la mesure des
variations dimensionnelles au-dessous du point de cong6lation de
l'adsorbat indiquent que les substances adsorb6es dans des solides
poreux ne peuvent geler in situ. Un proc6d6 de d6sorption permet
d161iminer la diffErence entre la pression de la vapeur ou 1'6nergie
libre de l'adsorbat non gel6 et celle de l'adsorbant
511ext6rieur
du systsme poreux; la matisre sujette
5la d6sorption gSle
511ext6rieur du syst2me tandis que la pression de la vapeur de
l'adsorbat dans les pores diminue par formation de mdnisque. La
d6faillance m6canique du syst2me se produit
2
ce moment, lorsque le
cycle de ddsorption ne peut ttre compl6t6 et que 1'6tat d16quilibre
n'est pas atteint.
On a trouv6 que ce m6canisme est valable pour le verre de
silice poreux, le mastic de ciment hydrat6, les briques et mtme
pour des substances biologiques tels les tissus animaux et v6g6taux
et les aliments. Cette recherche a permis la mise au point de
nouvelles m6thodes d'essai de la durabilit6 des mat6riaux de
construction et la clarification de certains probl2mes pos6s par la
m6thode de d6termination de surface BET, en plus de proposer une
explication pour l'action des agents cryoprotecteurs.
Advances in Colloid and Interface Science. 9 (1978) 253-302
O Elsevier Scientific Publishing Company. Amsterdam - Printed in The Netherlands
ADSORPTION SYSTEbIS A T TEMPERATURES BELOW THE FREEZING POINT OF THE ADSORPTIVE
G . G . LITVAN
D i v i s i o n o f B u i l d i n g R e s e a r c h . N a t i o n a l R e s e a r c h C o u n c i l o f Canada. Ottawa. K I A OR6
CONTENTS
...
I I n t r o d u c t i o n 254 I I I11 IVv
VI VII V I I I T h e o r e t i c a l C o n s i d e r a t i o n s...
254 E x p e r i m e n t a l Methods. . .
256 Length Change S t u d i e s. . .
259Ilea7 C o n t e n t and Length Changes
...
260Vapour P r e s s u r e and E x t e n s i o n I s o t h e r m s
...
261 S u r f a c e Area D e t e r m i n a t i o n...
265 I n t e r p r e t a t i o n o f t h e E x t e n s i o n C u r v e s O b t a i n e d i n N o n - e q u i l i b r i u m Temperature C y c l e s...
267 . Length Anomaly i n t h e V i c i n i t y o f 0°C...
267 . F r e e z i n g o r Low T e m p e r a t u r e s...
271 . l n t e r p r e t a t i o n o f t h e E x t e n s i o n I s o s t e r e s...
273Aqueous Sodium C h l o r i d e S o l u t i o n s Adsorbed i n Porous S i l i c a G l a s s
. .
274. Thermograms a n d Length Changes
...
276F r o s t A c t i o n i n Cement and C o n c r e t e
...
279 - Mechanical F a i l u r e...
283 F a c t o r s A f f e c t i n g F r o s t R e s i s t a n c e o f Cement...
285 A g g r a v a t i n g E f f e c t o f D e - i c i n g Agents on t h e F r e e z i n g o f Cement P a s t e 288 T e s t i n g o f F r o s t R e s i s t a n c e...
289 C r y o i n j u r y i n B i o l o g i c a l Systems...
292 Mechanism o f C r y o p r o t e c t i o n...
296 - C o o l i n g R a t e...
296 - P e r m e a b i l i t y...
296 - V i s c o s i t y...
297 - Minimizing Ap...
297 - S a l t B u f f e r i n g...
297 A c t i o n o f C r y o p r o t e c t i v e Agents...
298 C o n c l u s i o n...
300ABSTRACT I s o t h e r m a l a d s o r p t i o n s t u d i e s a n d t h e measurement o f d i m e n s i o n a l c h a n g e s below t h e b u l k f r e e z i n g p o i n t o f t h e a d s o r b a t e i n d i c a t e t h a t s u b s t a n c e s a d s o r b e d i n p o r o u s s o l i d s a r e u n a b l e t o f r e e z e i n s i t u . The d i f f e r e n c e between t h e vapour p r e s s u r e o r f r e e e n e r g y o f t h e u n f r o z e n a d s o r b a t e and t h a t o f t h e b u l k a d s o r p t i v e o u t s i d e o f t h e p o r o u s s y s t e m i s r e s o l v e d by a d e s o r p t i o n p r o c e s s ; t h e d e s o r b e d m a t t e r f r e e z e s o u t s i d e o f t h e s y s t e m w h i l e t h e vapour p r e s s u r e o f t h e a d s o r b a t e r e m a i n i n g i n t h e p o r e s d e c r e a s e s t h r o u g h meniscus f o r m a t i o n .
Mechanical breakdown o f t h e s y s t e m o c c u r s o n l y t h e n , when t h i s p r o c e s s c a n n o t b e c o m p l e t e d a n d a n e q u i l i b r i u m s t a t e i s n o t a t t a i n e d .
T h i s mechanism was found t o b e v a l i d f o r p o r o u s s i l i c a g l a s s , h y d r a t e d cement p a s t e , b r i c k s , and e v e n f o r b i o l o g i c a l s u b s t a n c e s s u c h a s a n i m a l and p l a n t t i s s u e , a n d f o o d s t u f f . T h i s u n d e r s t a n d i n g h a s l e d t o t h e development o f new methods f o r t e s t i n g t h e d u r a b i l i t y o f b u i l d i n g m a t e r i a l s , c l a r i f i c a t i o n o f some problems o f t h e BET s u r f a c e a r e a d e t e r m i n a t i o n method a n d i t s u g g e s t s a n e x p l a n a t i o n f o r t h e a c t i o n o f c r y o p r o t e c t i v e a g e n t s . I . INTRODUCTION A d s o r p t i o n o f vapours o n s o l i d s a t t e m p e r a t u r e s below t h e b u l k t r i p l e - p o i n t o f t h e s u b s t a n c e a n d t h e anomalous b e h a v i o u r e x h i b i t e d by p o r o u s s o l i d - a d s o r b a t e s y s t e m s o n c o o l i n g a r e phenomena o f g r e a t i n t e r e s t . S e v e r a l q u e s t i o n s a r i s e , b u t p e r h a p s t h e two most i m p o r t a n t a r e c o n c e r n e d w i t h : 1 ) t h e p o t e n t i a l m o d i f i - c a t i o n o f t h e a d s o r p t i o n f o r c e s due t o s o l i d i f i c a t i o n o f t h e a d s o r b a t e , and 2) t h e f e a t u r e s o f p h a s e r e l a t i o n s f o r s u b s t a n c e s i n t h e a d s o r b e d s t a t e . Answers a r e s o u g h t n o t o n l y t o s a t i s f y t h e o r e t i c a l c u r i o s i t y b u t f o r p r a c t i c a l a p p l i c a t i o n i n t h e d i v e r s e f i e l d s o f f r o s t h e a v i n g o f s o i l s , f r e e z e - t h a w s u s c e p t i b i l i t y o f p o r o u s b u i l d i n g m a t e r i a l s ( c o n c r e t e , b r i c k , s t o n e ) , w i n t e r h a r d i n e s s o f p l a n t s , and low t e m p e r a t u r e p r e s e r v a t i o n o f f o o d s t u f f and b i o l o g i c a l m a t e r i a l s . Numerous s t u d i e s h a v e b e e n u n d e r t a k e n t o c l a r i f y v a r i o u s a s p e c t s , b u t t h e i n h e r e n t l i n k s among t h e w i d e l y d i v e r s e f i e l d s have n o t b e e n c o n s i d e r e d . T h i s i s t h e p u r p o s e o f t h e p r e s e n t r e v i e w .
1
1 1 . TllEORETICAL CONSIDERATIONSAccording t o t h e phase r u l e , p u r e b u l k w a t e r h a s one d e g r e e o f freedom when p r e s e n t i n two p h a s e s such a s l i q u i d and v a p o u r . A t t h e t r i p l e - p o i n t t h r e e p h a s e s c o e x i s t a n d t h e s y s t e m i s i n v a r i a n t . I f t h e p h a s e s a r e s e p a r a t e d by c u r v e d i n s t e a d o f p l a n a r s u r f a c e s , t h e phase r u l e i n i t s u s u a l form i s n o l o n g e r v a l i d . The vapour p r e s s u r e o f c u r v e d s u r f a c e s i s d i f f e r e n t from t h a t o f p l a n a r s u r f a c e s and, t h e r e f o r e , e q u i l i b r i u m among t h e t h r e e p h a s e s o f a s i n g l e - c o m p o n e n t
s u b s t a n c e c a n b e a c h i e v e d 'at t e m p e r a t u r e s o t h e r t h a n t h e t r i p l e - p o i n t i f t h e r a d i i o f c u r v a t u r e o f t h e i n t e r f a c e s assume t h e a p p r o p r i a t e v a l u e s .
I The dependence o f t h e t r i p l e - p o i n t o n t h e r a d i i o f c u r v a t u r e was d e r i v e d I b y Defay e t a1 [ I ] f o r a s i n g l e - c o m p o n e n t s y s t e m c o n s i s t i n g o f a d r o p l e t and a c r y s t a l , b o t h s u r r o u n d e d b y v a p o u r . By w r i t i n g t h e Gibbs-Duham e q u a t i o n f o r I each p h a s e , e l i m i n a t i n g t h e p r e s s u r e t e r m s by t h e s u b s t i t u t i o n o f t h e L a p l a c e 1 e q u a t i o n , s i m p l i f i c a t i o n and i n t e g r a t i n g y i e l d s t h e r e l a t i o n I n t h i s e q u a t i o n T d e n o t e s t h e t e m p e r a t u r e , T t h e t r i p l e - p o i n t o f t h e s y s t e m c o m p r i s i n g b u l k p h a s e s ,
n
h t h e h e a t o f f u s i o n , :e'g r a d i u s o f t h e d r o p l e t , rs'g ft h a t o f t h e c r y s t a l , V t h e volume a n d u t h e s u r f a c e t e n s i o n . The new t r i p l e - p o i n t o f t h e s y s t e m may b e e i t h e r below o r above To, depending o n t h e r e l a t i v e s i z e o f t h e d r o p l e t and c r y s t a l . V a r i o u s p o s s i b i l i t i e s can b e s t b e s u r v e y e d by means o f a s c h e m a t i c i l l u s t r a t i o n o f t h e c o e x i s t e n c e c u r v e s o f l i q u i d - v a p o u r and s o l i d - v a p o u r i n t h e c o o r d i n a t e s T and pg ( F i g u r e 1 ) . The v a l u e o f T a t t h e i n t e r s e c t i o n o f t h e c u r v e s i s t h e f r e e z i n g p o i n t . A s h i f t o f e i t h e r o r b o t h c u r v e s t o h i g h e r o r lower pg v a l u e s a l t e r s t h e f r e e z i n g p o i n t . Such a s h i f t o c c u r s i f t h e s u r f a c e o f t h e condensed ,- F i g . 1 . S c h e m a t i c p h a s e diagrams o f w a t e r w i t h p l a n a r and c u r v e d s u r f a c e s .
1
I
I
256
I
phase i s e i t h e r convex o r concave i n s t e a d o f p l a n a r , o r i f t h e c o n c e n t r a t i o n o f I
a new c o n s t i t u e n t i n c r e a s e s from z e r o t o a f i n i t e v a l u e .
E a r l y and even contemporary work [ Z ] u t i l i z e d t h i s c o n c e p t t o e x p l a i n t h e
1
well-known o b s e r v a t i o n t h a t w a t e r i n s o i l s , c o n c r e t e , o r p l a n t s does n o t f r e e z e!
a t O°C, o r a t t h e t e m p e r a t u r e p r e d i c t e d o n t h e b a s i s o f t h e i o n i c s t r e n g t h o f t h e \ s o l u t i o n s , b u t a t a s i g n i f i c a n t l y l o w e r t e m p e r a t u r e . T h i s c o n c e p t , however, c o u l d n o t a c c o u n t f o r t h e o t h e r f e a t u r e s o f t h e f r e e z i n g phenomenon i n porous1
s o l i d s [ 3 ] o r s o l v e t h e many e n g i n e e r i n g problems c a u s e d by i t . N e i t h e r c o u l d u n e q u i v o c a l e x p e r i m e n t a l e v i d e n c e b e found t o s u p p o r t t h e t h e o r y , b u t t h i s may b e a t t r i b u t e d t o t h e i n h e r e n t d i f f i c u l t i e s o f t h e t e c h n i q u e s a p p l i e d , I 1 I . E X P E R I M E N T A L METIIODSVapour p r e s s u r e measurements, d i l a t o m e t r y and c a l o r i m e t r y a r e p e r h a p s t h e most i m p o r t a n t c l a s s i c a l e x p e r i m e n t a l t e c h n i q u e s employed i n t h e s t u d y o f a d s o r b a t e p h a s e t r a n s i t i o n s . U n f o r t u n a t e l y , a l l s u f f e r s e r i o u s d i f f i c u l t i e s . I n conven- t i o n a l d i l a t o m e t r y , t h e p r e s e n c e i n t h e a d s o r p t i o n system o f f l u i d such a s t o l u e n e o r 1 i g r o i n i s o b v i o u s l y u n d e s i r a b l e . I n d e t e r m i n i n g vapour p r e s s u r e , p a r t i c u l a r c a r e h a s t o b e e x e r c i s e d t o a v o i d c o n d e n s a t i o n o f t h e s u b s t a n c e on t h e c e l l w a l l s d u r i n g c o o l i n g . F u r t h e r m o r e , a s t h e maximum vapour p r e s s u r e r e a l i z a b l e e x p e r i m e n t a l l y i s t h a t o f t h e b u l k p h a s e , t h e v a l i d i t y o f t h e h y p o t h e s i s c o n c e r n i n g t h e e l e v a t e d p r e s s u r e o f t h e s o l i d i f i e d a d s o r b a t e can n e v e r b e d i r e c t l y a s s e s s e d . I n c a l o r i m e t r y , t h e s p e c i f i c h e a t d e t e r m i n a t i o n o f t h e a d s o r b a t e i s made d i f f i c u l t by t h e p r e s e n c e o f t h e a d s o r b e n t , t h e mass o f which a c t s a s a h e a t s i n k . The r a t i o o f a d s o r b a t e t o a d s o r b e n t masses i s seldom g r e a t e r t h a n 1 : 4 , b u t i t c a n b e a s s m a l l a s 1 : 2 0 . Because c a l o r i m e t e r s o p e r a t e d i n t h e c o o l i n g mode y i e l d r e s u l t s o f c o n s i d e r a b l e u n c e r t a i n t y , t h e c a l o r i m e t e r was o p e r a t e d i n t h e c o n v e n t i o n a l manner i n a l l t h e work r e p o r t e d i n t h e l i t e r a t u r e , t h u s r e q u i r i n g t h a t t h e s y s t e m b e c o o l e d t o low t e m p e r a t u r e s p r i o r t o t h e e x p e r i m e n t . As w i l l b e d e s c r i b e d , a d s o r p t i o n s y s t e m s e x h i b i t marked h y s t e r e s i s i n low t e m p e r a t u r e c y c l e s w i t h r e s p e c t t o t h e i r d i m e n s i o n a l b e h a v i o u r . C a l o r i m e t r i c measurements t h u s commence n o t from a u n i q u e l y d e f i n e d e q u i l i b r i u m s t a t e b u t from o n e t h a t depends o n t h e p a t h f o l l o w e d t o r e a c h i t .
Another d i f f i c u l t y i s p r e s e n t e d b y t h e e x t r e m e l y l o n g p e r i o d o f t i m e r e q u i r e d t o a t t a i n e q u i l i b r i u m . A t low t e m p e r a t u r e s , t h e r a t e o f change i s s o slow a n d t h e o b s e r v a b l e e f f e c t s o s m a l l t h a t i t i s i n d i s t i n g u i s h a b l e from t h a t c a u s e d b y c a l o r i m e t e r d r i f t . Moreover, i n c a l c u l a t i n g t h e h e a t c a p a c i t y o f t h e a d s o r b a t e t h e h e a t c a p a c i t y o f t h e a d s o r b e n t i s a l w a y s assumed t o b e i t s v a l u e i n t h e p u r e s t a t e . Dimensional c h a n g e s o b s e r v a b l e d u r i n g s u c h measurements i n d i c a t e , how- e v e r , t h a t t h e a d s o r b e n t i s p e r t u r b e d . I t i s v e r y p r o b a b l e t h a t t h e h e a t
c a p a c i t y o f t h e a d s o r b e n t i s a l t e r e d by t h e p r e s e n c e o f an a d s o r b a t e b u t , b e c a u s e
t h e magnitude o f t h e e f f e c t i s unknown, i t h a s t o b e n e g l e c t e d .
Common t o a l l methods
is
t h e d i f f i c u l t y o f p r e v e n t i n g change o f a d s o r b a t e c o n t e n t , i . e . , o f m a i n t a i n i n g i s o s t e r i c c o n d i t i o n s d u r i n g c h a n g e i n c e l l tempera- t u r e s ; seldom, i f e v e r , can mass t r a n s f e r b e r u l e d o u t w i t h c e r t a i n t y . I n i s o s t e r i c measurements, a t e m p e r a t u r e g r a d i e n t a c r o s s t h e c e l l i s c r e a t e d t h a t may c a u s e e v a p o r a t i o n from t h e sample and c o n d e n s a t i o n o n t h e w a l l s o f t h e c o n t a i n e r d u r i n g c o o l i n g . The s y s t e m c a n t h u s b e d e s c r i b e d a s b e i n g i n t h e d e s o r p t i o n b r a n c h o f t h e i s o t h e r m . The r a t e o f mass t r a n s f e r i s d i r e c t l y p r o p o r t i o n a l t o t h e r a t e o f c o o l i n g a n d can b e a v o i d e d o n l y a t i n f i n i t e l y low r a t e o f c o o l i n g , i . e . , a t c o n s t a n t t e m p e r a t u r e . To minimize t h i s e f f e c t i n p r a c t i c e , t h e t e m p e r a t u r e i s changed by v e r y s m a l l i n c r e m e n t s and a l o n g c o n s t a n t - t e m p e r a t u r e p e r i o d i s imposed t o r e - e s t a b l i s h e q u i l i b r i u m . I n some c a s e s i n e r t gas i s added t o t h e c e l l t o r e t a r d d i s t i l l a t i o n ; t h i s a d d i t i o n , o f c o u r s e , p r e c l u d e s vapour p r e s s u r e measurement.The i n h e r e n t d i f f i c u l t y o f c a r r y i n g o u t a n i s o s t e r i c measurement, however, can h a r d l y b e c i r c u m v e n t e d even w i t h t h e g r e a t e s t c a r e . With l o w e r i n g o f t e m p e r a t u r e , t h e vapour p r e s s u r e i n t h e c e l l d e c r e a s e s s o t h a t t h e e x c e s s
!
condenses o n t h e a d s o r b e n t . However s m a l l t h e dead s p a c e i n t h e c e l l , t h e a d s o r b a t e c o n t e n t i n c r e a s e s , r e s u l t i n g i n t h e s y s t e m d e s c r i b e d by t h e a d s o r p t i o n
I
b r a n c h o f t h e i s o t h e r m . On warming, t h e o p p o s i t e e f f e c t , d e s o r p t i o n , o c c u r s a n di
t h e r e l a t i o n b e t w e e n . t h e v a r i a b l e s i s e x p r e s s e d b y t h e d e s o r p t i o n b r a n c h . I t f o l l o w s t h a t a t r e l a t i v e l y h i g h a d s o r b a t e c o n t e n t t h e d i m e n s i o n s o f t h e s y s t e m depend o n t h e s i g n o f t e m p e r a t u r e c h a n g e t h a t o c c u r s when a p a r t i c u l a r s t a t e i s r e a c h e d . I n o r d e r t o t e s t t h i s a s s u m p t i o n t h e f o l l o w i n g e x p e r i m e n t was c a r r i e d o u t [ 3 ] . With a f i x e d amount o f w a t e r a d s o r b e d , t h e l e n g t h o f a porous s i l i c a g l a s s r o d was measured a t +2 .50°C. A f t e r t h e t e m p e r a t u r e o f t h e s y s t e m was changed I ( r a i s e d , l o w e r e d o r b o t h ) , t h e o r i g i n a l t e m p e r a t u r e , 2.5OoC, was r e s t o r e d a sc l o s e l y a s p o s s i b l e ( w i t h i n O.S°C) and t h e l e n g t h measured a g a i n . The r e s u l t s a r e shown i n T a b l e I . I t may b e s e e n t h a t when t h e r e f e r e n c e t e m p e r a t u r e was r e - s t o r e d b y h e a t i n g ( d e s o r p t i o n b r a n c h ) a s i n p o i n t s Nos. 1 , 4 , 8 a n d 11, t h e r o d a p p e a r s t o b e o f t h e same l e n g t h a n d a b o u t A L / L = 1 1 x u n i t s s h o r t e r t h a n i n t h o s e c a s e s where t e m p e r a t u r e was r e s t o r e d by c o o l i n g ( a d s o r p t i o n b r a n c h ) , p o i n t s Nos. 6 and 1 3 . T h i s d i f f e r e n c e i s c o n s i s t e n t w i t h t h e f a c t t h a t t h e d e s o r p t i o n b r a n c h o f t h e e x t e n s i o n i s o t h e r m i s below t h e a d s o r p t i o n b r a n c h . I t i s n o t s u g g e s t e d t h a t t h e r e s u l t s o f t h e i s o s t e r i c e x p e r i m e n t s s h o u l d b e d i s m i s s e d b e c a u s e o f t h e problems a n d s h o r t c o m i n g s o f t h e method. V a l u a b l e i n f o r m a t i o n can b e o b t a i n e d from t h e s e measurements, b u t g r e a t c a r e h a s t o b e e x e r c i s e d t o a v o i d m i s i n t e r p r e t a t i o n . I n a s s e s s i n g r e s u l t s i t h a s t o b e remembered t h a t a d s o r p t i o n s y s t e m s s u b j e c t e d t o t e m p e r a t u r e c y c l i n g a r e n o t a s a r u l e i s o s t e r i c .
258 TABLE I
Length changes due t o temperature v a r i a t i o n w i t h f i x e d amount o f w a t e r [ 3 ]
P o i n t Number Temperature, O C A L / L x 1 + 2.50 0 2 +25 .0 3 - 6 . 5 4 + 2.30 - 1 . 0 1 5 +30.0 6 + 2 . 0 7 + 1 3 . 3 3 7 -31.5 8 + 2.85 - 3.60 9 +22.0 10 0 .0 11 + 2.92 - 0 . 1 2 12 + 2 0 . 0 1 3 + 2.02 +10.25
1
I
t 3 0 + 2 0 + I 0 m0
X5
0 - a -10 I I I 1 I I 1 I-
o
COOLING WARMING-
-._',/P"=
-
I I I I I I I I -175 -150 -125 -100 -75 -50 -25 0 T, OC F i g . 2. Expansion i s o s t e r e o f porous s i l i c a g l a s s c o n t a i n i n g 0.0839 g/g w a t e r a d s o r b e d . (Reproduced by p e r m i s s i o n o f t h e N a t i o n a l Research Council o f Canada from t h e Canadian J o u r n a l o f Chemistry, Volume 4 , p p . 3095-3107, 1963) [ 3 ] .I V . LENGTII CHANGE STUDIES
Work i n t h e f i e l d o f phase c h a n g e s o f a d s o r b a t e s commenced w i t h t h e measure- ment o f d i m e n s i o n a l c h a n g e s . A t f i r s t [ 3 ] a p o r o u s , 96 p e r c e n t , s i l i c a - g l a s s r o d c o n t a i n i n g known amounts o f a d s o r b e d w a t e r was t a k e n i n s t e p s t h r o u g h a t e m p e r a t u r e c y c l e between +5 a n d -16S°C. A t each s t a g e t h e t e m p e r a t u r e was k e p t c o n s t a n t u n t i l changes i n l e n g t h were n o t d e t e c t a b l e w i t h a c a p a c i t a n c e t y p e e x t e n s o m e t e r . R e p r e s e n t a t i v e c u r v e s a r e shown i n F i g u r e s 2 t o 4 , where i t may b e s e e n t h a t t h e l e n g t h o f t h e a d s o r b e n t - a d s o r b a t e s y s t e m does n o t change i n a l i n e a r manner. I n s e v e r a l t e m p e r a t u r e r e g i o n s , anomalous changes i n dimension o c c u r r e d .
The most i m p o r t a n t f i n d i n g s o f t h e e x p e r i m e n t s can b e summarized a s f o l l o w s : 1 . No l e n g t h anomaly can b e d e t e c t e d i f t h e amount o f w a t e r a d s o r b e d i s l e s s t h a n t h a t a t i n c e p t i o n o f t h e h y s t e r e s i s l o o p o f t h e a d s o r p t i o n i s o t h e r m . T h i s c o n d i t i o n i s e q u i v a l e n t t o two a d s o r b e d l a y e r s .
2 . I f c o n c e n t r a t i o n i s g r e a t e r t h a n two l a y e r s o n c o o l i n g , a n o m a l i e s i n l e n g t h changes a r e o b s e r v a b l e n e a r - 7 a n d -22°C.
3 . The e x a c t t e m p e r a t u r e a t which t h e anomaly o c c u r s depends upon t h e a d s o r b a t e c o n t e n t f o r t h e -7'C t r a n s i t i o n , b u t t h e o t h e r anomaly a l w a y s o c c u r s a t -22°C.
F i g . 3 . Expansion i s o s t e r e o f p o r o u s s i l i c a g l a s s c o n t a i n i n g 0.1389 g / g w a t e r a d s o r b e d . (Reproduced by p e r m i s s i o n o f t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada from t h e Canadian J o u r n a l o f C h e m i s t r y , Volume 41, p p . 3095-3107; 1 9 6 3 . ) [ 3 ]
4 . T r a n s i t i o n s , i f a n o m a l i e s c a n b e a c c e p t e d a s i n d i c a t o r s , a r e n o t s h a r p b u t t a k e p l a c e between 5 a n d 10°C. 5 . Anomalies d u r i n g warming o c c u r a t h i g h e r t e m p e r a t u r e s t h a n d u r i n g c o o l i n g . 6 . A l l i s o s t e r e s e x h i b i t h y s t e r e s i s . 7 . A f t e r c o m p l e t i o n o f a c y c l e , t h e l e n g t h o f t h e a d s o r b e n t i s d i f f e r e n t from i t s i n i t i a l l e n g t h . These r e s u l t s , though i n t e r e s t i n g , a r e i n t h e m s e l v e s i n s u f f i c i e n t t o p r o v i d e I
u n d e r s t a n d i n g o f t h e low t e m p e r a t u r e b e h a v i o u r o f a d s o r p t i o n s y s tems. The a n o m a l i e s c a n n o t b e i n t e r p r e t e d i n terms o f p h y s i c a l e v e n t s w i t h any d e g r e e o f c o n f i d e n c e .
V . HEAT CONTENT AND LENGTH CHANGES
I n o r d e r t o e s t a b l i s h t h e l i n k between l e n g t h a n o m a l i e s and phase c h a n g e s ,
and t o l e a r n more a b o u t t h e n a t u r e o f t h e l a t t e r , s i m u l t a n e o u s measurement o f I
h e a t c o n t e n t and d i m e n s i o n a l changes were u n d e r t a k e n . A c a l o r i m e t e r d e s i g n o r i g i n a l l y d e v e l o p e d by Antoniou [ 4 ] t h a t i n c o r p o r a t e d a n o p t i c a l s t r a i n gauge was u t i l i z e d . R e s u l t s o f t h e e x p e r i m e n t s w i t h p o r o u s s i l i c a g l a s s - w a t e r system,
I
t 2 0-
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a -10 - -20 - 0 COOLING L W A R M I N G -30 --
I I I I I I I I -175 -150 -125 -100 -75 -50 -25 0 T, OC F i g . 4 . Expansion i s o s t e r e o f p o r o u s s i l i c a g l a s s c o n t a i n i n g 0.1754 g / g w a t e r a d s o r b e d . (Reproduced by p e r m i s s i o n o f t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada from t h e Canadian J o u r n a l o f C h e m i s t r y , Volume 41, p p . 3095-3107, 1 9 6 3 . ) [ 3 ]I
T E M P E R A T U R E ." C
F i g . 5 . S p e c i f i c h e a t o f w a t e r a d s o r b e d on p o r o u s s i l i c a g l a s s a s a f u n c t i o n o f t e m p e r a t u r e . Numerical v a l u e s i n d i c a t e t h e w a t e r c o n t e n t o f t h e a d s o r b a t e . (Reproduced by p e r m i s s i o n o f t h e N a t i o n a l Research C o u n c i l o f Canada from t h e Canadian J o u r n a l o f C h e m i s t r y , Volume 44, pp. 2617-2622. 1 9 6 6 . ) [ S ]
shown i n F i g u r e 5 , i n a d d i t i o n t o c o n f i r m i n g t h e f i n d i n g s l i s t e d above [ S ] ,
y i e l d e d t h e f o l l o w i n g c o n c l u s i o n s :
1 . Length a n o m a l i e s do i n d e e d s i g n i f y phase c h a n g e s .
2 . The s p e c i f i c h e a t o f t h e a d s o r b a t e i s , below t h e m e l t i n g anomaly a t - 1 l 0 C , c o n s i s t e n t l y and s i g n i f i c a n t l y more t h a n t h a t o f b u l k i c e ( 0 . 4 5 c a l deg-'). 3 . The h e a t o f f u s i o n o f a d s o r b e d w a t e r i s 5 5 . 5 c a l g - I when t h e w a t e r c o n t e n t i s e q u i v a l e n t t o 7 . 7 m o n o l a y e r s . T h i s v a l u e i s u n c e r t a i n t o t h e e x t e n t t h a t t h e q u a n t i t y o f w a t e r i n v o l v e d i n t h e t r a n s i t i o n i s n o t known. A c c o r d i n g t o c o n c l u s i o n No. 1 ( S e c t i o n I V ) , t h e f i r s t two l a y e r s r e m a i n u n f r o z e n when p r e s e n t i n t h e m s e l v e s , b u t t h e b e h a v i o u r o f t h e s e l a y e r s a t h i g h e r c o n c e n t r a t i o n s c a n o n l y b e s u r m i s e d .
4 . The l e n g t h c u r v e s show good r e p r o d u c i b i l i t y i n a q u a l i t a t i v e s e n s e , b u t v a r y s i g n i f i c a n t l y i n a q u a n t i t a t i v e s e n s e .
VI
.
VAPOUR PRESSURE AND EXTENSION ISOTHERMSI t i s c l e a r t h a t i s o s t e r i c a d s o r p t i o n s t u d i e s s u f f e r from u n c e r t a i n t i e s . T h i s s i t u a t i o n i s most u n f o r t u n a t e b e c a u s e t h e mechanism o f f r o s t a c t i o n c a n n o t
26 2 b e u n d e r s t o o d w i t h o u t knowledge o f a d s o r p t i v e p r o p e r t i e s a t t e m p e r a t u r e s below b u l k f r e e z i n g p o i n t o f t h e a d s o r b a t e . I n t e r e s t i n t h i s f i e l d i s h e i g h t e n e d b y s u r p r i s i n g o b s e r v a t i o n s
.
As t h e h e a t o f a d s o r p t i o n i s e x o t h e r m i c , a n y i n c r e a s e i n t e m p e r a t u r e r e s u l t s i n d i m i n u t i o n o f a d s o r p t i v e c a p a c i t y ; c o o l i n g s h o u l d b r i n g a b o u t a n i n c r e a s e . Although t h i s b e h a v i o u r i s , i n f a c t , found a t t e m p e r a t u r e s above t h e b u l k t r i p l e - p o i n t , i s o t h e r m s d e t e r m i n e d below t h i s t e m p e r a t u r e i n d i c a t e d e c r e a s e d a d s o r p t i v e c a p a c i t y . I n a d d i t i o n , t h e s h a p e s o f t h e vapour p r e s s u r e a n d e x t e n s i o n i s o t h e r m s 1 become d i s t o r t e d a s t e m p e r a t u r e i s l o w e r e d . The r e s u l t s o b t a i n e d w i t h t h e p o r o u s s i l i c a g l a s s - x e n o n s y s t e m shown i n F i g u r e 6 i l l u s t r a t e t h i s p o i n t . To c l a r i f y t h e q u e s t i o n , t h e v a p o u r p r e s s u r e a n d e x t e n s i o n i s o t h e r m s o f t h e p o r o u s s i l i c a g l a s s - w a t e r s y s t e m were d e t e r m i n e d s i m u l t a n e o u s l y a t t e m p e r a t u r e sI
below o O C [ 6 ].
U n c e r t a i n t i e s c o n c e r n i n g t h e q u a n t i t y o f a d s o r b e d w a t e r vapour, I I due t o p o t e n t i a l c o n d e n s a t i o n on t h e w a l l s , were a v o i d e d by m e a s u r i n g t h e a d s o r b a t e c o n t e n t g r a v i m e t r i c a l l y w i t h a q u a r t z b a l a n c e . Because o f t h i s a r r a n g e m e n t a companion specimen had t o b e u s e d f o r l e n g t h change measurements. The s m a l l vapour p r e s s u r e s a t low t e m p e r a t u r e s n e c e s s i t a t e d a l l m e t a l and g l a s s c o n s t r u c t i o n o f t h e equipment and b a k e - o u t t o r e d u c e d e g a s s i n g . The i s o t h e r m s0 30(1 600 C! 300 600 0 300 600 0 300 600 - I 0 I I I l 1 I I - 143.43 OC
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I 4 l ' l STP rnl ADSORBED F i g . 6 . A d s o r p t i o n and e x p a n s i o n i s o t h e r m s o f t h e porous g l a s s - x e n o n s y s t e m . (Reproduced by p e r m i s s i o n o f t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada from t h e Canadian J o u r n a l o f C h e m i s t r y , Volume 41, p p . 3095-,3107, 1 9 6 3 . ) [ 3 ] / l l 1 l.
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l i q u i d [ P i ] i n 7 and 8 ( a ) and f o r r e l a t i v e p r e s s u r e b a s e d on t h e v a p o u r
The f o l l o w i n g c o n c l u s i o n s a r e v a l i d :
1 . I f t h e r e l a t i v e p r e s s u r e p/pO i s e x p r e s s e d a s p/p:, t h e amount o f
a d s o r b a t e , a , d e c r e a s e s w i t h d e c r e a s i n g t e m p e r a t u r e .
2 . The i s o t h e r m s can b e s u p e r i m p o s e d i f t h e r e l a t i v e p r e s s u r e i s b a s e d o n
pi.
F i g . 7 . Vapour p r e s s u r e i s o t h e r m s o f t h e p o r o u s g l a s s - w a t e r s y s t e m a t + 1 . 5 ,
- 6 . 4 , - 1 4 . 6 , - 2 5 . 4 a n d -35.3"C (from t o p t o b o t t o m ) . A d s o r p t i o n 0 , d e s o r p t i o n @ .
(Reproduced by p e r m i s s i o n o f The Chemical S o c i e t y from T r a n s a c t i o n s o f t h e
F i g . 8 . Vapour p r e s s u r e i s o t h e r m s superimposed (a)
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-35.3"C. (Reproduced by p e r m i s s i o n o f The Chemical S o c i e t y from T r a n s a c t i o n s o f t h e Faraday S o c i e t y [ 6 ] ) .T h e s e c o n c l u s i o n s a r e c o n s i s t e n t w i t h p r e v i o u s f i n d i n g s c o n c e r n i n g t h e l i q u i d - l i k e n o n - f r o z e n s t a t e o f t h e a d s o r b a t e below t h e normal t r i p l e - p o i n t [7 - 131.
The d e c r e a s e i n a d s o r p t i v e c a p a c i t y was s u g g e s t e d t o b e o n l y a p p a r e n t . I t was a g r e e d t h a t b e c a u s e t h e a d s o r b a t e i s known t o b e i n a l i q u i d - l i k e s t a t e , a d s o r p t i o n i s governed b y t h e magnitude o f p i n r e l a t i o n t o
pi
n o tpz.
As c o n d e n s a t i o n on t h e w a l l s p r e v e n t s t h e r i s e of v a p o u r p r e s s u r e above t h e v a l u e0 '
o f ps, t h i s v a l u e i s t h e upper l i m i t o f t h e e x p e r i m e n t a l l y r e a l i z a b l e p; and R can n e v e r b e a c h i e v e d e x c e p t a t t h e b u l k f r e e z i n g p o i n t . Because
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exceeds p0 by a n i n c r e a s i n g margin a s t h e t e m p e r a t u r e i s l o w e r e d , t h e i s o t h e r m s a r e t e r m i n a t e d a t v a l u e s o fP/Pi
t h a t become p r o g r e s s i v e l y l o w e r a n d always l e s s t h a n u n i t y .On t h e o t h e r hand, i f a , t h e a m u n t o f a d s o r b e d s u b s t a n c e , i s e x p r e s s e d i n terms o f
p/pz,
t h e l i m i t i n g r e l a t i v e p r e s s u r e i s made e q u a l t o u n i t y , i m p l y i n gcomplete s a t u r a t i o n . T h i s method o f p l o t t i n g r e s u l t s i n d i s t o r t i o n o f t h e
c o n s t r u c t e d i s o t h e r m and a n a p p a r e n t r e d u c t i o n o f a f o r a g i v e n
p/pz.
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t h e i s o t h e r m s can b e superimposed ( F i g u r e S ( a ) ) .I
The i s o t h e r m a t -35.3OC ( F i g u r e 7) i s o f s p e c i a l i n t e r e s t . A f t e r o b t a i n i n g by i s o t h e r m a l a d s o r p t i o n t h e p o i n t marked A, w i t h e x c e s s w a t e r on t h e c e l l w a l l s ,
t h e t e m p e r i t u r e was r a i s e d a p p r o x i m a t e l y 2 deg, which r e s u l t e d , a s e x p e c t e d , i n
I f u r t h e r a d s o r p t i o n . R e s t o r a t i o n o f t h e o r i g i n a l t e m p e r a t u r e c a u s e d d e s o r p t i o n ,
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b u t a t t h e o r i g i n a l p r e s s u r e a n e t i n c r e a s e o f a was found ( p o i n t B ) . By I r e p e a t i n g t h i s w a r m i n g / c o o l i n g p r o c e s s , s u c c e s s i v e i n c r e m e n t s o f w a t e r were1
t r a n s f e r r e d t o t h e specimen. The upper l i m i t o f t h e h y s t e r e s i s l o o p , a s e s t a b l i s h e d b y t h e i s o t h e r m a t + l . S ° C , was n o t a t t a i n e d i n t h i s work, b u t i n!
t h e o r y t h e r e i s no r e a s o n why i t s h o u l d n o t b e a c h i e v e d i f a s u f f i c i e n t number o f w a r m i n g / c o o l i n g c y c l e s a r e c a r r i e d o u t . The d e s o r p t i o n p o i n t s o b t a i n e d s u b s e q u e n t l y w e r e a l l i n s t a b l e e q u i l i b r i u m ( a t -35.3') and were above t h o s e o b t a i n e d o n a d s o r p t i o n . Under t h e s e c o n d i t i o n s , t h e a d s o r p t i o n i s o t h e r m i s a v e r t i c a l l i n e a t t h e maximum r e l a t i v e p r e s s u r e t h a t can b e r e a l i z e de x p e r i m e n t a l l y .
Behaviour l e a d i n g t o t h e v e r t i c a l p o r t i o n o f t h e -35.3OC i s o t h e r m i s s i m i l a r t o t h a t d e s c r i b e d by Emmett and C i n e s [9] and c a n b e e x p l a i n e d i n t h e f o l l o w i n g
0 0 .
way. With i n c r e a s i n g t e m p e r a t u r e , p
/
pR I n c r e a s e s , e v e n t u a l l y becoming u n i t y a t 0 ° C . Warming o f t h e c e l l c o n t a i n i n g b u l k i c e c a u s e s a n i n c r e a s e i n a . On c o o l i n g , a d e c r e a s e s , b u t i f t h e s y s t e m i s i n t h e h y s t e r e s i s r e g i o n i t w i l l , on d e s o r p t i o n , f o l l o w a s c a n n i n g c u r v e ( p a t h w i t h i n t h e e x t r e m e b o u n d a r i e s o f t h e h y s t e r e s i s l o o p ) . Thus, a warming c y c l e r e s u l t s i n an i n c r e a s e i n a a n d a c o o l i n g c y c l e i n a d e c r e a s e . Two f i n d i n g s l e n d f u r t h e r s u p p o r t t o t h e c o n c l u s i o n t h a t t h e a d s o r b a t e i s l i q u i d - l i k e : t h e i s o s t e r e s c o n s t r u c t e d from t h e i s o t h e r m s have no b r e a k p o i n t i n d i c a t i v e o f a p h a s e change, and t h e e x t e n s i o n i s o t h e r m s below O°C a r e o f t h e same s h a p e a s t h o s e a b o v e t h i s t e m p e r a t u r e s o t h a t t h e y can b e s u p e r i m p o s e d ( F i g u r e 9 ) .I
V I I.
SURFACE AREA DETERMINATIONThe f a c t t h a t t h e a d s o r b a t e i s i n a l i q u i d - l i k e s t a t e below t h e b u l k t r i p l e - p o i n t h a s d i r e c t c o n s e q u e n c e s f o r t h e BET s u r f a c e a r e a d e t e r m i n a t i o n . When u s i n g g a s e s o t h e r t h a n n i t r o g e n , f o r example k r y p t o n o r a r g o n , t h e e x p e r i m e n t s a r e u s u a l l y c a r r i e d o u t a t t h e b o i l i n g p o i n t o f n i t r o g e n f o r t h e s a k e o f c o n v e n i e n c e . Because t h i s t e m p e r a t u r e i s 39 d e g below t h e t r i p l e - p o i n t f o r k r y p t o n , a p p l i c a t i o n o f t h e v a p o u r p r e s s u r e o f s o l i d k r y p t o n , p0 would b e S '
j u s t i f i e d i n computing t h e r e s u l t s . T h i s mode o f c a l c u l a t i o n , however, y i e l d s s u r f a c e a r e a s t h a t d i f f e r s i g n i f i c a n t l y from t h o s e c a l c u l a t e d from n i t r o g e n a d s o r p t i o n . The d i s c r e p a n c y v a n i s h e s when i s r e p l a c e d b y
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-35.3'C (from t o p t o b o t t o m ) . Adsorption 0 , d e s o r p t i o n 0 . For s a k e o f c l a r i t y o f p r e s e n t a t i o n t h e measured p o i n t s o f t h e i s o t h e r m a t -35.3'C a r e n o t shown. Arrows i n d i c a t e d i r e c t i o n o f a d s o r p t i o n p a t h , broken l i n e s presumed p a t h between measured p o i n t s . (Reproduced by p e r m i s s i o n o f t h e Chemical S o c i e t y from t h e T r a n s a c t i o n s o f t h e Faraday S o c i e t y [ 6 ] ) .
a n e x t r a p o l a t i o n , which q u a n t i t y i s c o n s i d e r e d t o b e merely an a d j u s t a b l e p a r a - meter whose v a l u e i s i d e n t i c a l t o t h a t o f
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q u a n t i t i e s was thought t o b e f o r t u i t o u s [14, 151. I t i s i m p o r t a n t t o r e a l i z e t h a t t h e use o f
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i s n o t o n l y warranted f o r pragmatic r e a s o n s b u t i s a l s ot h e o r e t i c a l l y c o r r e c t . C o n s e q u e n t l y , t h e a p p l i c a t i o n o f
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i s n o t r e s t r i c t e d t o k r y p t o n a d s o r p t i o n b u t i s r e q u i r e d w i t h a l l o t h e r g a s e s , w i t h no r e g a r d f o r t h e r e l a t i o n o f t h e i r t r i p l e - p o i n t t o t h e t e m p e r a t u r e o f t h e e x p e r i m e n t . I t s h o u l d b e n o t e d t h a t t h e r e s u l t s o f a d s o r p t i o n s t u d i e s c a r r i e d o u t below t h e normal m e l t i n g p o i n t o f t h e a d s o r b a t e w i l l b e d i s t o r t e d a n d l e a d t o e r r o n e o u s c o n c l u s i o n s ; f o r example, a p p a r e n t s u p e r s a t u r a t i o n w i l l b e i n d i c a t e d b y p/pO g r e a t e r t h a n u n i t y , i f t h e a d s o r b a t e i s assumed t o b e s o l i d i f i e d .VII I . INTERPRETATION OF THE EXTENSION CURVES OBTAINED IN NON-EQUILIBRIUM
TEMPERATURE CYCLES
I
I n s i g h t g a i n e d i n i s o t h e r m a l s t u d i e s makes i t p o s s i b l e t o i d e n t i f y some o f t h e p h y s i c a l e v e n t s r e s p o n s i b l e f o r t h e a n o m a l i e s o f t h e d i m e n s i o n a l change c u r v e s o b t a i n e d i n cooling/warming c y c l e s . To t h i s end, e x p e r i m e n t s were c a r r i e d o u t i n n o n - e q u i l i b r i u m t e m p e r a t u r e c y c l e s i n which he.at e f f e c t s were measured by d i f f e r e n t i a l t h e r m a l a n a l y s i s , and s i m u l t a n e o u s l y , t h e l e n g t h c h a n g e s were'
measured w i t h a d i f f e r e n t i a l l i n e a r t r a n s f o r m e r [ 1 6 ] . R e p r e s e n t a t i v e r e s u l t s f o r a p o r o u s s i l i c a g l a s s - w a t e r system a r e shown i n F i g u r e 1 0 .t
Length Anomaly i n t h e V i c i n i t y o f 0°CThe e x t e n s i o n i s o s t e r e s and thermograms o f t h e s a t u r a t e d s a m p l e s ( F i g u r e 1 0 ) show t h a t a n anomalous change i n d i m e n s i o n s , o c c u r r i n g i n t h e r e g i o n between - 0 . 2 a n d -8'C, was accompanied by sudden r e l e a s e o f h e a t . T h i s p r o v e s s o l i d i f i - c a t i o n o f a t l e a s t a f r a c t i o n o f t h e a d s o r b e d w a t e r . I t may b e concluded t h a t i c e formed o n t h e o u t s i d e s u r f a c e o f t h e specimen a n d was i n t h e b u l k s t a t e b e c a u s e ( a ) o n v i s u a l i n s p e c t i o n a t -lO°C, t h e sample was c o v e r e d w i t h i c e ,
(b) t h e e s t a b l i s h e d m e l t i n g p o i n t o f i c e formed a t - 8 . 6 ' ~ was O'C ( F i g u r e l l ) , a n d ( c ) o n f r e e z i n g , t h e r e l e a s e d h e a t warmed t h e s y s t e m t o a b o u t o0C.
When t h e g l a s s sample was immersed i n w a t e r and c o o l e d , t h e s u r r o u n d i n g w a t e r f r o z e a t O°C b u t t h e s u r f a c e w a t e r s o l i d i f i e d o n l y a t -0.4'C, a s i n d i c a t e d by t h e sudden change i n l e n g t h ( F i g u r e 1 2 ) . Because t h e g l a s s was i n c o n t a c t w i t h i c e c r y s t a l s , t h i s r e s u l t i n d i c a t e s t h a t t h e lower f r e e z i n g p o i n t c a n n o t b e a t t r i b u t e d t o u n d e r c o o l i n g . E x p e r i m e n t a l l y e s t a b l i s h e d f a c t s ( t h a t i c e formed o n t h e o u t e r s u r f a c e , below O°C, a n d i n t h e a b s e n c e o f u n d e r c o o l i n g ) s u g g e s t t h a t w a t e r f a i l e d t o s o l i d i f y a t 0°C b e c a u s e i t was l o c a t e d i n p o r e s where i t c o u l d n o t f r e e z e ; a l s o , t h a t a s t h e t e m p e r a t u r e became c o l d e r t h a n 0°C t h e w a t e r m i g r a t e d t o t h e s u r f a c e where i t formed i c e . The c a u s e o f t h i s mechanism i s t h e l i q u i d - l i k e s t a t e o f t h e a d s o r b a t e , a s d i s c u s s e d p r e v i o u s l y . The t e m p e r a t u r e a t which w a t e r becomes a v a i l a b l e f o r f r e e z i n g o n t h e e x t e r n a l s u r f a c e depends on t h e t e m p e r a t u r e a t which t h e a c t u a l a d s o r b a t e c o n t e n t , a , exceeds amax, t h e maximum a d s o r b a t e c o n t e n t d e t e r m i n e d by p:. The o n s e t o f t h i s c o n d i t i o n depends o n t h e s h a p e o f t h e a d s o r p t i o n i s o t h e r m .
I f a = a a t O°C, m i g r a t i o n o f w a t e r w i l l s t a r t a s soon a s t h e t e m p e r a t u r e ma x i s d e c r e a s e d below t h i s v a l u e . When i t r e a c h e s t h e e x t e r n a l s u r f a c e , i t f r e e z e s o r remains i n a s u p e r c o o l e d s t a t e ( F i g u r e 1 2 ) . On t h e o t h e r hand, i f t h e specimen i s p a r t l y s a t u r a t e d a t T > O°C, t h e n a t T = 0 , a < a a n d a e x c e e d s ma x 100 I
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( a ) 2-mm t h i c k g l a s s , w a t e r s a t u r a t e d , c o o l i n g r a t e 0.25"C/min; (b) 5-mm t h i c k Y
g l a s s , w a t e r s a t u r a t e d , 0 . 2 5 O ~ / m i n ; ( c ) 5-mm t h i c k g l a s s , w a t e r s a t u r a t e d , 0.33°C/min. (Reproduced b y p e r m i s s i o n o f t h e Academic P r e s s from J o u r n a l of C o l l o i d a n d I n t e r f a c e S c i e n c e [ 1 6 ] ) .
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a s a f u n c t i o n o f T . With t h e a i d o f t h e a d s o r p t i o n isotherm, which i s t h e r e l a t i o n between adsorbedTEMPERATURE,
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F i g . 1 1 . Dimensional changes and thermograms o f 5-mm t h i c k porous g l a s s s a t u r a t e d w i t h w a t e r 'during a + 5 t o -lS°C temperature c y c l e (0.33'C/min). (Reproduced by p e r m i s s i o n o f t h e Academic P r e s s from J o u r n a l o f C o l l o i d and I n t e r f a c e S c i e n c e [ 1 6 ] ) .
TEMPERATURE,
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F i g . 1 2 . Dimensional changes of a 5-mm t h i c k porous g l a s s sample immersed i n w a t e r . (Reproduced by p e r m i s s i o n o f t h e Academic P r e s s from J o u r n a l o f C o l l o i d and I n t e r f a c e S c i e n c e 1161).
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amount and r e l a t i v e p r e s s u r e , a c a n b e r e l a t e d t o T f o r t h i s s y s t e m . The
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d e r i v a t i v e o f a w i t h r e s p e c t t o T i s a l s o g i v e n ( F i g u r e 1 4 ( b ) ) . I t c a n b e s e e n
t h a t b e c a u s e o f t h e shape o f t h e i s o t h e r m , a s i g n i f i c a n t amount o f w a t e r moves
o n l y below -5°C. T h i s r e s u l t a g r e e s w e l l w i t h t h e p r e v i o u s l y o b s e r v e d e x t e r n a l
s u r f a c e f r e e z i n g t e m p e r a t u r e o f -7°C.
I n view o f t h e dynamic n a t u r e o f t h e f a c t o r s c a u s i n g e x p a n s i o n , i t i s t o b e e x p e c t e d t h a t , i f t h e c o o l i n g r a t e i s v e r y slow, no anomalous d i m e n s i o n a l c h a n g e s
can b e o b s e r v e d . T h i s e f f e c t , i n f a c t , was found w i t h t h e c e m e n t - w a t e r s y s t e m
[ 1 7 ] a t a c o o l i n g r a t e o f 0 . 0 4 1 7 ~ ~ / m i n . The s u g g e s t e d e x p l a n a t i o n i s n o t s p e c i f i c t o w a t e r a s t h e a d s o r b a t e . The e x t e n s i o n " i s o s t e r e s " of porous g l a s s c o n t a i n i n g a d s o r b a t e s s u c h a s c y c l o h e x a n e , c h l o r o f o r m , x y l e n e , c a r b o n t e t r a -
I
c h l o r i d e , b e n z e n e and o c t a n o l e x h i b i t s i m i l a r f e a t u r e s ( F i g u r e 1 5 ) . I t may b e s e e n t h a t i n e v e r y s y s t e m t h e r e a r e a t l e a s t two f r e e z i n g r a n g e s . The e x i s t e n c e o f t h e anomaly a t t h e h i g h e r t e m p e r a t u r e remained u n d e t e c t e d i n most f o r m e r s t u d i e s b e c a u s e o f e i t h e r e x p e r i m e n t a l d i f f i c u l t i e s o r e r r o n e o u s i n t e r p r e t a t i o n . I(a)
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The v a l u e s e x h i b i t r e m a r k a b l y u n i f o r m b e h a v i o u r . I t a p p e a r s t h a t f i r s t f r e e z i n g o n t h e e x t e r n a l s u r f a c e o c c u r s between 0 . 9 2 and 0 . 9 8 To, where T i s t h e b u l k f r e e z i n g p o i n t o f t h e a d s o r b a t e i n d e g r e e s K e l v i n . The s u g g e s t e d mechanism i s s u p p o r t e d a l s d b y t h e f a c t t h a t m e l t i n g o f t h e a d s o r b a t e a l w a y s o c c u r s a t T
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F r e e z i n g a t Low T e m p e r a t u r e s For t r a n s i t i o n s o c c u r r i n g a t l o w e r t e m p e r a t u r e s , t h e a d s o r b a t e s o l i d i f i e s i n t h e p o r e s . The p r o c e s s i s a s s o c i a t e d w i t h an e x o t h e r m i c h e a t e f f e c t a n d e x p a n s i o n , b o t h e x t e n d i n g o v e r a t e m p e r a t u r e r a n g e o f a p p r o x i m a t e l y 15 d e g r e e s . D e s p i t e t h e g r a d u a l n a t u r e o f t h e t r a n s i t i o n f o r a g i v e n t y p e o f specimen ( e . g . , 5-mm t h i c k p o r o u s g l a s s ) , t h e i n c e p t i o n t e m p e r a t u r e o f t h e p r o c e s s i s c o n s t a n t ( f 0 . 3 O C ) .I
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F i g . 1 4 . ( a ) Maximum r e a l i z a b l e v a p o u r p r e s s u r e o f w a t e r a s a f u n c t i o n o f t e m p e r a t u r e ; (b) Aa/AT x 100 v s T f o r 5-lmn t h i c k porous g l a s s - w a t e r s y s t e m based on i s o t h e r m o f +O.S°C. (Reproduced b y p e r m i s s i o n o f t h e Academic P r e s s from J o u r n a l o f C o l l o i d and I n t e r f a c e S c i e n c e [ 1 6 ] ) .272
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20 ? = : : 0 2 0 -200 120 8 0 4 0 0 T E M P E R A T U R E , "CF i g . 1 5 . Dimensional changes and thermograms of 5 - m m t h i c k porous g l a s s w i t h
v a r i o u s a d s o r b a t e s . (Reproduced by p e r m i s s i o n of t h e Academic P r e s s from
J o u r n a l o f C o l l o i d and I n t e r f a c e S c i e n c e [ 1 6 ] ) . ( a j c h l o r o f o r m , mp -63.S°C; (b) m-xylene -47.g°C; ( c ) c a r b o n t e t r a c h l o r i d e , mp -22.96"C; ( d ) o c t a n o l , mp -16.7"C; (e) b e n z e n e , mp +5.5"C; ( f ) c y c l o h e x a n e mp +6.SoC.
The s i g n o f t h e s p e c i f i c volume change o n f r e e z i n g i n t h e b u l k s t a t e h a s no b e a r i n g o n t h e d i m e n s i o n a l changes o f t h e a d s o r b e n t - a d s o r b a t e s y s t e m . Expansion o c c u r r e d w i t h a l l system? ( F i g u r e I S ) , a l t h o u g h w a t e r i s t h e o n l y s u b s t a n c e i n t h e group t h a t expands on f r e e z i n g i n t h e b u l k s t a t e . I n i s o t h e r m a l a d s o r p t i o n s t u d i e s [ 6 ] , i t was n o t p o s s i b l e t o a c h i e v e s o l i d i - f i c a t i o n of t h e a d s o r b i n g w a t e r i n t h e v o i d s o f porous g l a s s a t e i t h e r -3S°C, a ma x = 0 . 1 2 g / g , o r -2S°C, a ma x = 0 . 1 7 g / g . These r e s u l t s a r e s u r p r i s i n g b e c a u s e e v e n a t -3SoC,
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= 0 . 7 was a t t a i n e d , a n d a t t h i s v a l u e o f t h e r e l a t i v ep r e s s u r e ( a c c o r d i n g t o t h e Kelvin e q u a t i o n ) , p o r e s o f l e s s t h a n 66A d i a m e t e r a r e f i l l e d w i t h w a t e r , which h a s an e s t i m a t e d f r e e z i n g p o i n t a s h i g h a s -13.S°C. On t h e o t h e r hand, a t r a n s i t i o n t o o k p l a c e on " i s o s t e r i c " c o o l i n g w i t h a = 0 . 1 2 g / g [ S ] and even w i t h a = 0 . 0 8 4 g/g [ 3 ] . I f t h e h y p o t h e s i s t h a t c o o l i n g b r i n g s a b o u t d e s o r p t i o n i s c o r r e c t , t h e s e f i n d i n g s imply t h a t f r e e z i n g t a k e s p l a c e o n l y i n s t a t e s d e f i n e d by t h e d e s o r p t i o n b r a n c h o f t h e i s o t h e r m . The t h e o r y t h a t t h e s o l e c a u s e o f f r e e z i n g p o i n t l o w e r i n g i s t h e meniscus e f f e c t , t h e magnitude o f which i s assumed t o b e i n v e r s e l y p r o p o r t i o n a l t o t h e e x t e n t o f t h e vapour p r e s s u r e r e d u c t i o n , a p p e a r s t o b e c o n t r a d i c t e d b y t h i s c o n c l u s i o n ; f o r a g i v e n v a l u e o f a , t h e a d s o r b a t e h a s a l o w e r v a p o u r p r e s s u r e on d e s o r p t i o n t h a n on a d s o r p t i o n , so t h a t t h e l a t t e r s h o u l d h a v e a h i g h e r f r e e z i n g p o i n t . The o p p o s i t e , however, i s t r u e .
One may a r g u e t h a t b e c a u s e w a t e r remains i n t h e l i q u i d s t a t e ( b e i n g u n a b l e t o f r e e z e i n t h e pores. i t f i l l e d on i s o t h e r m a l a d s o r p t i o n ) , i t d r a i n s on c o o l i n g i n t o t h e p a r t l y f i l l e d l a r g e r p o r e s when t h e maximum r e a l i z a b l e r e l a t i v e
p r e s s u r e becomes l e s s t h a n t h e vapour p r e s s u r e o f t h e a d s o r b a t e . The s h a r p r i s e of t h e Aa/AT c u r v e i n d i c a t e s t h a t below -1S0C, a l a r g e amount o f w a t e r h a s t o l e a v e t h e p o r o u s s y s t e m . T h i s d e p l e t i o n i s p r o b a b l y seldom p o s s i b l e a t t h i s low t e m p e r a t u r e b e c a u s e o f t h e low v a p o u r p r e s s u r e , h i g h v i s c o s i t y , a n d p a r t l y b l o c k e d p o r e s . E q u i l i b r i u m can b e a t t a i n e d , however, i f t h e t r a p p e d w a t e r f r e e z e s , r e d u c i n g t h e v a p o u r p r e s s u r e t o t h a t o f i c e s o t h a t e q u i l i b r i u m c o n d i - t i o n s a r e a t t a i n e d . The w e l l - e s t a b l i s h e d d i f f e r e n c e between t h e f r e e z i n g and m e l t i n g p o i n t s o f t h e a d s o r b a t e can t h e n b e e x p e c t e d b e c a u s e f r e e z i n g o c c u r s a t t h e t e m p e r a t u r e a t which w a t e r i s t r a n s p o r t e d t o a p o r e i n which i t c a n form i c e ; t h e m e l t i n g p o i n t i s d e t e r m i n e d by t h e c h a r a c t e r i s t i c s o f t h e formed i c e . I n t e r p r e t a t i o n o f t h e E x t e n s i o n I s o s t e r e s On t h e b a s i s o f t h e p r e c e d i n g h y p o t h e s i s , an a t t e m p t c a n b e made t o s p e c i f y t h e p h y s i c a l p r o c e s s e s c a u s i n g a n o m a l i e s i n t h e l e n g t h c h a n g e s . The specimen s a t u r a t e d a t T >
O°C,
p o i n t 0, F i g u r e 1 0 ( b ) , c o n t r a c t s on c o o l i n g a s a r e s u l t of t h e t h e r m a l e f f e c t . A t t h e t e m p e r a t u r e r e p r e s e n t e d by A (because a > a max) 'f r e e z i n g o c c u r s on t h e s u r f a c e and t h e l a t e n t h e a t o f f r e e z i n g warms t h e system t o O°C. P o i n t B r e v e a l s a n e t c o n t r a c t i o n f o r t h i s t e m p e r a t u r e c y c l e r e s u l t i n g
from l o s s o f w a t e r on c o o l i n g t o A . The s y s t e m c o n t r a c t s between B and C a g a i n b e c a u s e o f t h e r m a l c o n t r a c t i o n a n d c o n t i n u o u s l o s s o f w a t e r . A t C, t h e w a t e r i n t h e p o r e s commences t o s o l i d i f y , a p r o c e s s t h a t e x t e n d s t o p o i n t D .
The l a r g e e x p a n s i o n b e t w e e n C and D i s a s s o c i a t e d w i t h f r e e z i n g a n d may b e t h e r e s u l t o f t h e changed i n t e r a c t i o n b e t w e e n t h e g l a s s and t h e s o l i d i f i e d a d s o r b a t e . Dimensional changes n o r m a l l y o c c u r r i n g i n r e s p o n s e t o change i n a m b i e n t c o n d i t i o n s ( t e m p e r a t u r e , v a p o u r p r e s s u r e ) c a n n o t t a k e p l a c e f r e e l y i n
t h e p r e s e n c e o f s o l i d s i n t h e p o r e s , and s t r a i n d e v e l o p s . T h i s e x p a n s i o n a p p e a r s
1
t o b e p a r t l y r e v e r s i b l e ; t h e s y s t e m c o n t r a c t s t o E o n warming, where t h e lowt e m p e r a t u r e m e l t i n g p r o c e s s i s c o m p l e t e d . The n e t i n c r e a s e o f l e n g t h a t t h i s I
I
t e m p e r a t u r e i s a measure o f t h e damage s u f f e r e d between C a n d D . I t must b e
r e c o g n i z e d , however, t h a t t h e d i m e n s i o n s o f t h e a d s o r b e n t a t c o n s t a n t c o v e r a g e I depend a l s o on w h e t h e r i t i s i n a n a d s o r p t i o n o r d e s o r p t i o n s t a t e , a c c o r d i n g t o
1
t h e e x t e n s i o n i s o t h e r m s ( F i g u r e 9 ) . T h i s s i t u a t i o n may w e l l a l s o e x i s t f o rnon- i s o t h e r m a l c o n d i t i o n s .
Expansion between E a n d F i s due t o a d s o r p t i o n b r o u g h t a b o u t b y i n c r e a s i n g r e l a t i v e p r e s s u r e a n d l o s s o f mechanical s t r e n g t h o f t h e g l a s s . T h i s e f f e c t m a n i f e s t s i t s e l f when t h e i c e i n t h e c r e v i c e s m e l t s .
IX. AQUEOUS SODIUM CHLORIDE SOLUTIONS ADSORBED IN POROUS SILICA GLASS
I
Most n a t u r a l s y s t e m s c o n t a i n s o l u t i o n s r a t h e r t h a n p u r e w a t e r , s o t h a t t h e i rf r e e z i n g mechanism i s o f g r e a t i n t e r e s t . I n s t u d y i n g w a t e r a d s o r p t i o n on p o r o u s s i l i c a g l a s s i n t h e p r e s e n c e o f NaCR, specimens were p r e p a r e d by vacuum
i m p r e g n a t i o n w i t h NaCY, s o l u t i o n s o f v a r i o u s c o n c e n t r a t i o n s [ I S ] . The c o n c e n t r a t i o n o f t h e p o r e s o l u t i o n a t c o m p l e t e s a t u r a t i o n c a n b e c a l c u l a - t e d from t h e w a t e r u p t a k e a n d t h e s a l t c o n t e n t o f t h e g l a s s ( d e t e r m i n e d from t h e i n c r e a s e o f t h e d r y w e i g h t due t o i m p r e g n a t i o n . ) The t w e n t y c a l c u l a t e d v a l u e s were s m a l l e r t h a n t h a t o f t h e i m p r e g n a t i n g s o l u t i o n by a p p r o x i m a t e l y 10 p e r c e n t I f , however, t h e c o n c e n t r a t i o n o f t h e a d s o r b e d l i q u i d i s c a l c u l a t e d by assuming t h a t o n e monomolecular l a y e r i s c o m p l e t e l y f r e e o f s a l t , t h e a f o r e m e n t i o n e d d i f f e r e n c e s v a n i s h . T h i s a n a l y s i s i s c o n s i s t e n t w i t h t h e r e p o r t e d s a l t r e j e c t i o n phenomenon i n p o r o u s g l a s s [ I 9 - 231 a n d haemoglobin [ 2 4 , 251, which presumably i s due t o t h e f a c t t h a t t h e s t r u c t u r e d n a t u r e o f t h e f i r s t l a y e r i s u n a v a i l a b l e t o t h e s o l u t e . The a d s o r p t i o n i s o t h e r m s , o b t a i n e d by e x p o s u r e o f s a l t - i m p r e g n a t e d s a m p l e s t o v a r i o u s r e l a t i v e h u m i d i t i e s , a r e shown i n F i g u r e 1 6 . D i s t o r t i o n i s c a u s e d , a t l e a s t i n p a r t , b y t h e c h a n g i n g a d s o r b a t e c o n c e n t r a t i o n i n t h e c o u r s e o f t h e a d s o r p t i o n p r o c e s s , a r e s u l t o f t h e c o n s t a n t s a l t a n d v a r y i n g w a t e r c o n t e n t . I n i t i a l l y , t h e amount o f w a t e r i s i n s u f f i c i e n t t o d i s s o l v e a l l t h e s a l t , s o t h a t s o l i d s a l t and s a t u r a t e d s o l u t i o n a r e p r e s e n t . I n l a t e r s t a g e s when a l l t h e s a l t h a s b e e n d i s s o l v e d , w a t e r u p t a k e l e a d s t o d i l u t i o n o f t h e s o l u t i o n . Only
