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Melting-Point in Very Narrow Capillaries Kubelka, P.
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PREFACE
The Division of Ruilding Research has been active over a period of years in studying the freezing of
water in both consolidated and non-consolidated systems. The deterioration of building materials containing moisture, due to their exposure to low temperatures, has remained a problem over a long period of tirne but
it is now generally recognized that the mechanism of
this action is related to the depression of the freezing- point of water in the pores of the materials.
This work by P. Kubelka has provided one of the basic approaches towards the depression of the melting- point in very narrow capillaries, and is therefore
published by
DBR/NRC
for the benefit of all who share interest in this work.This translation was prepared by Mr. D.A. Sinclair of the Translations Section of the National Research Council, to whom the Division records its thanks. Ottawa
January 1962
R.F. Legget Director
NATIONAL RESEARCH COUNCIL OF CANADA
Technical Translatfon 1005
Tit 1.e : The melting-point in very narrow capillaries
( h e r den Schmelzpunkt in sehr engen Capillaren)
Author : Paul Kubelka
Reference: Zeitschrift fcr Elektrochemie,
38
(8a) : 611-614, 1932TIIE MELTING-POINT I N VERY NARROW CAPILLARLES The t r i p l e p o i n t of t h e monophase s y s t e m , i . e . t h e m e l t i n g - p o i n t a t t h e n a t u r a l vapour p r e s s u r e , c e a s e s t o be a n i n v a r i a b l e p o i n t as soon as o t h e r e n e r g y p o t e n t i a l s b e s i d e s p r e s s u r e a n d t e m p e r a t u r e a r e i n v o l v e d . I n p r i n c i p l e i t i s p o s s i b l e t h a t t h e m e l t i n g - p o i n t c a n be i n f l u e n c e d by a n e l e c t r i c c h a r g e o r , s a y , by l i g h t r a d i a t i o n s t h a t c a n be a b s o r b e d by t h e s y s t e m . These e f f e c t s have n o t y e t been d e m o n s t r a t e d . O b s e r v a t i o n s a n d t h e o r e t i c a l i n v e s t i g a t i o n s on t h e i n f l u e n c e o f t h e s i z e o f t h e p h a s e boundary s u r f a c e s , i . e . o f t h e boundary s u r f a c e e n e r g y , on t h e m e l t i n g - p o i n t , h a v e i n d e e d been made.
The monophase s y s t e m h a s t h r e e k i n d s of p h a s e boundary
s u r f a c e s , namely c r y s t a l - l i q u i d , c r y s t a l - v a p o u r and l i q u i d - v a p o u r . It h a s s c a r c e l y been n o t e d , h i t h e r t o , t h a t e a c h o f t h e t h r e e boundary s u r f a c e s c a n i n f l u e n c e t h e m e l t i n g - p o i n t , d e p e n d i n g on t h e s p e c i a l a r r a n g e m e n t o f t h e s y s t e m . S i n c e t h e t h r e e t y p e s o f boundary s u r f a c e s p o s s e s s d i f f e r e n t f r e e e n e r g i e s , t h e e x t e n t o f t h e change i n t h e m e l t i n g - p o i n t w i l l depend n o t o n l y on t h e d e g r e e of d i s p e r s i o n , b u t a l s o on t h e s p a t i a l a r r a n g e m e n t of t h e p h a s e s . L e t u s c o n s i d e r t h e f o l l o w i n g a r r a n g e m e n t s : 1. The s o l i d p h a s e i s i n d i r e c t c o n t a c t ( o v e r a l a r g e s p e c i f i c boundary s u r f a c e a r e a ) w i t h t h e l i q u i d p h a s e . The c r y s t a l - l i q u i d boundary s u r f a c e e n e r g y i s h e r e d e c i s i v e f o r t h e change i n t h e m e l t i n g - p o i n t . 2. The s o l i d p h a s e i s d i s p e r s e d i n t h e g a s e o u s p h a s e and i s i n d i r e c b l y ( t h r o u g h t h e g a s e o u s p h a s e ) i n e q u i l i b r i u m w i t h t h e compact l i q u i d p h a s e . Here t h e c r y s t a l - v a p o u r boundary s u r f a c e e n e r g y i s t h e e f f e c t i v e e n e r g y .
3.
The l i q u i d p h a s e i s d i s t r i b u t e d t h r o u g h a n i n e r t , p o r o u s body o f m a t e r i a l d i f f e r i n g from t h e s y s t e m and i s i n e q u i l i b r i u m t h r o u g h t h e g a s e o u s p h a s e w i t h t h e compact s o l i d s u b s t a n c e . Here t h e l i q u i d - v a p o u r boundary s u r f a c e e n e r g y i s d e c i s i v e .A 1 l t h o paper1.? h i t i h e r t o wrj. l;t;eri on M : i s s u b j e c t r e 1 att? t o
c a s e 1. On t h c bas.i n oS J. J. l.'homsonls c o n s i d c r n t i . o r i ~ ( : ~ ~ ) arid t h o s c o f P a v l o v ( )
,
Tnnlrnnnri ( 3 ) and Melssner.(4)
havt: d e r i v e d t h e e q u a t i o nwhere Ta, = s t a n d a r d rr~e:l.ting-po:i.rit, T = a l - t e r c d m e l - t i n g - p o i n t , v =
S n l o l e c u l a r volume o f t h e so1:id p h a s e , r =: r a d i u s o f t h e p a r t i c u l e s assumed s p h e r i - c a l , q
-
l a t e n t h e a t o f me1 t:I.ng p e r m o l e ,a
=s g c r y s t a l - v a . p o u r b o u n d a r y s u r s S a c e t e n s i o n , a = 1.1.quid-vapour bound- a r y s u r f a c e t e n s i - o n . ~ i e '
:'
) a n d H n b c r(6)
f g g i v e t h e equa.tli.or1 T - T w -- - - 2vsT
- 0 03 r q s f 'where asf = c r y s t a l - l : l q u l d b o u n d a r y s u r f ' a c e t e n s r l o n . The d i f f e r e n c e i n t h e two e q u a t i o n s c a n n o t b e due t o t h e f a c t t h a t Tarnnrann a n d
M e i s s n e r a r e c o n s i d e r i . n g meltring i n a n a r r o w c r a c k * . F o r , w h e t h e r w e t t i n g o f t h e c r a c k w a l l b e assumed ( ~ i . ~ . l a . ) o r n o t ( ~ : i . g . l b ) , i r i e i t h e r c a s e o n l y t h e s i z e o f t h e c r y s t a l - 1-i.qu1.d b o u n d a r y s u r f a c e i s i c h a n g e d , j u s t as i n t h e i r i f ' i n i . t e 1iqu:i.d c a s e c o r l s i d e r e d by H a b e r . I f b o t h e q u a t i o n s a r e c o r r e c t , t h e r e f o r e , t h e y must b e i d e n t i c a l , i . e . 0
-
CJ = 0 sf? f f f s f ' T h i s c o n d . i t i o n a c t u a l H y h o l d s f o r t h e rneltrlrig-point ( a n d o n l y f o r t h e m e l t i n g - p o i n t ),
a s t h e f o l _l..owing c o n s i d e r a t i o n s h o w s . I f t h e l i q u i d w e t s t h e cr.ysta.1. ( t h i s was a l w a y s a.ssumetl p r e v i o u s l - y a n d c a n probab1.y be a c c e p t e d ) , t l i e r l e v e n b e l o w t h e me1 t i n g - p o i n t t h e c r y s t a l . must a l r e a d y b e c o a t e d w.:i.th a t h i n S i l n l o f rrielted s u b s t a n c e*
The f a c t t h a t Ivle~i.:.;srier wa.s deal.:i.i?l: w:il;h c r y s t a l p l a t e s w h i c h a r e n o t small. j..n a'll. dircct-i.ori:; h a s b e e n taker1 I n t o a c c o u n t i ne q u a t i o n (1.) b y u s i n g t h e part.i.c:l.e r a d . l u s . i n s t e a d oS t h e p l a t e thickness
.
due t o w e t t i n g a b s o r p t i o n .
we his
h o l d s t r u e , o f c o u r s e , even f o r a macroscopic c r y s t a l . ) The t h i cltness o f t h i s f i l m must I n c r e a s e c o n t l n u o u s l y as we a p p r o a c h t h e m e l t i n g - p o i n t , b e c a u s e t h e vapour p r e s s u r e comes c l o s e r and c l o s e r t o t h e s a t u r a t i o n p r e s s u r e o f t h e l i q u i d p h a s e . When t h e m e l t i n g - p o i n t Is r e a c h e d t h e vapour i s s a t u r a t e d i n r e l a t i o n t o t h e l i q u i d and t h e w e t t i n g f i l m must t h u s have a t t a i n e d i t s maximum t h i c k n e s s . T h i s i s c h a r a c t e r i z e d by t h e f a c t t h a t t h e two boundary s u r f a c e t e n s i o n s ( j u s t as i n t h e c a s e o f , s a y , a t h i c k f i l m of o i l on w a t e r ) have becorne i n d e p e n d e n t of e a c h o t h e r , i . e . t h e y have r e a c h e d t h e i r normal v a l u e s c o r r e s p o n d - i n g t o a macroscopic e x t e n s i o n of t h e l i q u i d p h a s e . The f r e e e n e r g y c o n t e n t a o f a s q u a r e crn of tihe c r y s t a l s u r f a c e i s t h u s st3 made up o f t h e e n e r g y c o n t e n t o f t h e c r y s t a l . - L i q u i d boundary s u r f a c e , O s f Y and t h a t of t h e l i q u i d - v a p o u r boundary s u r f a c e , a f g ' T h e r e f o r e , which i t w a s r e q u i r e d t o p r o v e . I n t h e s e c o n d o f t h e above a r r a n g e m e n t s t h e c r y s t a l i s n o t i n d i r e c t c o n t a c t w i t h t h e l i q u i d d u r i n g t h e m e l - t l n g p r o c e s s , b u t i s s e p a r a t e d from i t by a s p a c e f i l l e d w i t h vapour. I f t h e p a r t i c l - e s a r e small., m e l t i n g t a k e s p l a c e by e v a p o r a t i o n o f t h e s u b s t a n c e from t h e c r y s t a l and c o n d e n s a t i o n on t h e l i q u i d . D u r i n g t h e m e l t i n g p r o c e s s , t h e r e f o r e , t h e s i z e o f t h e c r y s t a l - v a p o u r boundary s u r f a c e changes, b u t o t h e r w i s e c o n d i t i o n s remain e n t i r e l y s i m i l a r t o c a s e 1. The e q u a t i o n w i l l t h e r e f o r e a p p l y . T h i s e q u a t i o n can be d e r i v e d d i r e c t l y by c a l c u l a t i n g t h e vapour p r e s s u r e I n c r e a s e o f t h e c r y s t a l a c c o r d i n gt o W. Thomson
where p = normal v a p o u r p r e s s u r e , 1 = i n c r e a s e v a p o u r p r e s s u r e o f
S p s
t h e c r y s t a l , t h e n introduc-Lng t h e c o n d i t i o n o f m e l t i n g
-
e q u a l i t y of vapour p r e s s u r e s between t h e two p h a s e s-
where p = vapour p r e s s u r e of t h e l i q u i d , and f i n a l l y , c o n n e c t i n g f t h e s e w i t h t h e e q u a t i o n which we o b t a i n by d e v e l o p i n g t h e l a t e n t h e a t of m e l t i n g as t h e d i f f e r e n c e between t h e h e a t s o f e v a p o r a t i n g a n d s u b l i m a t i o n a f t e r C l a u s i u s - C l a p e y r o n a n d i n t e g r a t i n g from T t o Too*. The two a r r a n g e m e n t s d i s c u s s e d r e s u l t , g e n e r a l l y s p e a k i n g , i n i r r e v e r s i b l e , u n s t a b l e e q u i l i b r i a , b e c a u s e t h e s l i g h t e s t change o f t e m p e r a t u r e r e s u l t s i n t h e c o m p l e t e d i s a p p e a r a n c e o f e i t h e r t h e s o l i d o r t h e l i q u i d p h a s e and t h e e a r l i e s t s t a t e ( w i t h r e s p e c t t o t h e d e g r e e of d i s p e r s i o n ) c a n n o t bc r e s t o r e d by r e v e r s i n g t h e t e m p e r a t u r e c h a n g e . Only M e i s s n e r f s s p e c i a l a r r a n g e m e n t s
-
m e l t i n g i n a narrow c r a c k-
r e s u l t i n a p r a c t i c a l l y r e v e r s i b l e e q u i l i b r i u m , s i n c e t h e c r y s t a l , a t l e a s t i n one d i m e n s i o n , i s m e c h a n i c a l l y p r e v e n t e d from e x p a n d i n g beyond t h e w i d t h o f t h e c r a c k . I n p r i n c i p l e t h e s t a b i l - i t y would be cornplete i f M e i s s n e r f s c r a c k were o f c o n s t a n t w i d t h and e n c l o s e d on al.1 s i d e s .The t h i r d a r r a n g e m e n t , where t h e l i q u i d p h a s e i s a b s o r b e d i n a n i n e r t , p o r o u s body a n d by i n t e r v e n t i o n o f t h e g a s e o u s p h a s e i s
*,
N e g l e c t i n g t h e dependence o f t h e h e a t o f m e l t i n g on t h e t e m p e r a t u r e .i n e q u i l i b r i u m with t h e conlpa.c.1; csolic! p h a s e , I.eads t o e q u i l i b r i a t h a t a r e always r c v e r s i b 1 . e . 14elt:i.ng agari-n t a k e s p l a c e by sub1.ima- t i o n from t h e s o l i d . p h a s e and c o n d e n s a t i o n on the 1.iqul.d p h a s e .
F o r t h i s c a s e , as f o r c a s e 2 , t h e fol-1 owing m e l t i n g - p o 5 n t e q ~ a t i o n can be d e r i v e d i n t h e same manner:
where v f = molecul.ar volulne of t h e l i q u i d , = edge a n g l e of t h e l i q u i d r e l a t i v e t o t h e i n e r t body, r = c a p i l l a r y r a d i u s . T h i s a r r a n g e m e n t i s o f s p e c i a l i n t e r e s t b e c a u s e , unl.ike t h e o t h e r two, i t p e r m i t s us t o a t t a i n v e r y c o n s i d e r a b l e l o w e r i n g s o f t h e m e l t i n g - p o i n t experimental1.y. F o r example, t h e i n o r g a n i c g e l s and a c t i v a t e d c h a r c o a l s a r e p o r o u s b o d i e s w i t h c a p i l l a r y d i a m e t e r s of t h e o r d e r of
lo-'
cm, whereas t h e p h a s e s e p a r a t i o n f o r t h e o t h e r two a r r a n g e m e n t s i s l i m i t e d t o a p p r o x i m a t e l y cm. It i s t h u s p o s s i b l e t o o b t a i n e f f e c t s t h a t a r e a t h o u s a n d t i m e s g r e a t e r , 1 . e . i n s t e a d of a m e l - t l n g - p o i n t r e d u c t i o n o f t h e o r d e r o f O . l O , r e d u c t i o n s o f t h e o r d e r of 1 0 0 ° , a s M e l s s n e r h a s f o u n d .The difficulty w i t h t h i s a r r a n g e m e n t , however, l i e s i n t h e f a c t t h a t one c a n n o t d e t e r m i n e by d i r e c t o b s e r v a t i o n w h e t h e r t h e s u b s t a n c e i n t h e s e narrow c a p i l l a r i e s i s l i q u i d o r solrid; t h e
d e t e r m i n a t i o n must be made i n d i r e c t l - y . T h e r e a r e two b a s i c p o s s i - b l l i t i e s f o r d o i n g t h i s . One i s f i r s t t o s o a k t h e p o r o u s s u b s t a n c e above t h e m e l t i n g - p o i n t o f t h e s u b s t a n c e t o be investigated w i t h t h e q u a n t i t y o f l i q u i d c o r r e s p o n d i n g o n l y t o a f r a c t i o n o f i t s
c a p i l l a r y volume, s o t h a t t h e l i q u i d f i l l s t h e n a r r o w e r c a p i l l a r i e s b u t l e a v e s t h e o t h e r s empty. Now, c o o l i n g t h e s y s t c n i and c o n t i n u - o u s l y m e a s u r i n g t h e vapour p r e s s u r e , we r e c o r d t h e vapour p r e s s u r e c u r v e , i . e . t h e i s o s t e r e of t h e l i q u i d , c o n t a i n e d I n t h e c a p i l l a r i e s .
As l o n g as t h e i s o s ' i e r e i s a srnooth c u r v e , t h e subs.1;a.nce I n t h e
c a p i l l a r i e s i s cl.car1.y s t r i l l 1 . i q u i d . C o o l i d g e
( 7 )
o b t a i n e d i s o - s t e r e s of benzene .in a c t i v a t e d c h a r c o a l ~ h i . c h remained srnooth down t o - 3 3 O C , c o r r e s p o n d i n g t o a m e l t i n g - p o i n t loweraing o f a b o u t 40".Actually, Coolidge interpretes his results differently. He assumes that benzene remains liquid below the melting-point, but believes that instead of completely filling the individual capillar- ies, it covers the entire surface of the charcoal with a uniform adsorption or wetting film. He thus believes that the specific effect of the charcoal surface, not the degree of dispersion of the benzene, is responsible for the lowering of the melting-~oint. This interpretation, which assumes that the equilibrium between the benzene and activated charcoal is governed by adsorption and not by capillary condensation stands in contradiction to the condition of 11
covalent pressures
"(81,
which has been proved valid for benzene. Another way is to bring the substance to be investigated below its melting-point, i.e. in solid form, into contact with silica gel, activated charcoal and similar substances and, by weighing, todetermine the quantity of substance that passes over to the porous body. If this experiment is repeated with various kinds of porous substances, then, if the above considerations are correct, all these porous substances must absorb liquid to the extent that all capillaries with diameters below a certain limit, the same for all substances, will be filled up, while all other capillaries remain empty. Then, if the structure of the porous substance, i.e. the distribution of the capillary volume with respect to the individual capillary diameters, is known from previous capillary condensation tests(9), it is merely necessary to convert the quantities of
substance obtained by weighing into parts by volume of liquid and to determine by comparison with the structure curves of the porous substance whether these volumes correspond to the above assumption, i.e. whether in each case the volume of liquid agrees with the
capillary volume up to the given limiting diameter.
o ow ever,
if the quantity of substance retained by the porous material isentered in the calculation as
a
volume of solid substance then this agreement will not hold.)Tests which will be reported in detail by the author elsewhere, enable us to prove in the manner indicated here, that iodine in
a p p r o x i m a t e l y 100° below t h e m e l t i n g - p o i n t . Nowhere n e a r s o g r e a t a l o w e r i n g of t h e m e l t i n g - p o i n t as e v e r been o b s e r v e d i n t h e monophase s y s t e m . T h i s o f c o u r s e i s n o t a c a s e of s i m p l e s u p e r - c o o l i n g . It i s a r e v e r s i b l e e q u i l i b r i u m . Summarv 1. The m e l t i n g - p o i n t of d i s p e r s e d monophase s y s t e m s c a n be i n f l u e n c e d n o t o n l y by t h e c r y s t a l - l i q u i d boundary s u r f a c e e n e r g y , b u t a l s o by t h e c r y s t a l - v a p o u r o r l i q u i d - v a p o u r boundary s u r f a c e e n e r g y . Which of t h e t h r e e . b o u n d a r y s u r f a c e e n e r g i e s t a k e s e f f e c t depends on t h e s p a t i a l a r r a n g e m e n t o f t h e s y s t e m . 2 . Two d i f f e r e n t e q u a t i o n s a r e g i v e n i n t h e l i t e r a t u r e f o r t h e i n f l u e n c i n g of t h e m e l t i n g - p o i n t by t h e c r y s t a l - l i q u i d boundary s u r f a c e e n e r g y . With t h e a i d of a newly d e r i v e d r e l a t i o n s h i p
between t h e t h r e e boundary s u r f a c e t e n s i o n s o f t h e monophase s y s t e m i t i s d e m o n s t r a t e d t h a t t h e two e q u a t i o n s a r e i d e n t i c a l .
3 .
The c a s e o f i n f l u e n c i n g t h e m e l t i n g - p o i n t by t h e l i q u i d - vapour boundary s u r f a c e e n e r g y , which a p p l i e d when t h e l i q u i d i s a b s o r b e d by a n i n e r t p o r o u s s u b s t a n c e and i s i n e q u i l i b r i u mt h r o u g h t h e g a s e o u s p h a s e w i t h a compact s o l i d p h a s e , i s d e a l t w i t h more f u l l y . T h i s a r r a n g e m e n t p e r m i t s t h e e x p e r i m e n t a l r e a l i z a t i o n of r e v e r s i b l e r e d u c t i o n s of t h e m e l t i n g - p o i n t of t h e o r d e r of 1 0 0 ° .
References
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F r e u n d l i c h , Kap.i.lla.rchemie, 1: 145 and 4 6 0 ) .Pawlow. 2 . phys. Chem. 65: 1, 1909 e t c . ( c f . F r e u n d l i c h l o c . c i t . ) .
Tarnrnann. 2. anorg. a l l g . Chem. 110: 166, 1920. Meissner. Z . anorg. a l l g . Chem. 110: 169, 1920.
R i e . D i s s e r t a t i o n . Vienna, 1920; 2 . phys. Chem.
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354, 1923.Haber. Ber. Dtsch. chern. Ges. 55: 1722, 1922. Coolidge. J . Am. Chem. Soc.
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c f . Kubelka, P . K o l l ~ l d - 2 . 55: 129,
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Kubelka, P . and Muller, M. K o l l o i d - 2 . 58:
189,
1932.Wetted
L i q u i d Crystal layer Liquid G a s f i l m c r y s t a l wetted layer
F i g . l a F i g . l b
Diagram of t h e m e l t i n g p r o c e s s i n t h e Meissner gap The l i q u i d wets t h e w a l l
