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Supercooling capacity of water and the linear crystallization velocity of ice in aqueous solutions
Ref Ser 421 ~ 2 t h no. TT-79 BLDG COPY NO.
NATIONAL
RESEARCH
COUNCIL
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DIVISION OF MECHANICAL ENGINEERING A IRC PUB
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1 4TECHNICAL TRANSLATION NO. TT
-
79THE
SLIPERCOOLING CAPACITY OF WATER AND THE LINEAR
CRYSTALLIZATION VELOCITY OF ICE IN AQLlEOLlS SOLUTIONS
KRISTALLlSATlONSGESCHWlNDlGKElT DES EISES IN WASSR~GEN LOSUNGEN
II
BY G. TAMMANN AND A. BUCHNER
OTTAWA
NATIONAL RESEARCH LABORATORIES Ottawa, Canada TECHNICAL TRANSLATION D i v i s ion. of Mechanical E n g i n e e r i n g Pages
-
P r e f a c e-
2-
Text-
9 F i g u r e s-
8 Tech, T r a n s , TT-79 Date-
26 October, 1948,Lab, Order No,
-
5424AF i l e
-
12-R4-22T i t l e : Die U n t e r r n l u n g s f l t h i g k e i t d e s Wassers und d i e
l i n e a r e Kristallisationsgeschwindigkeit des
E i s e s i n wgssrigen L8sungen0 By: G o Tammann and A o ~ f l c h n e r ,
Reference : Ze i t s c h r i f t f u r a n o r g a n i s c h e und a l l g e m e i n e Chemie ( J o u r n a l f o r I n o r g a n i c and General
C h e m i s t r y ) , Vol, 222, 1935, pp, 371-381, Report o f t h e I n s t i t u t e f o r P h y s i c a l Chemistry,
G8 t t i n g e n ,
S u b j e c t : THE SUPERCOOLING CAPACITY OF WATER AND TIE
L I N E A R CRYSTALLIZATION VELOCITY OF ICE I N AQUEOUS SOLUTIONS, S u b m i t t e d b y : J o Lo O r r , T r a n s l a t e d by: He ad, H o A o G o Nathan, Low Temperature L a b o r a t o r y , Approved by: J o H , P a r k i n , D i r e c t o r , SYNOPSIS Very l i t t l e i s known a b o u t t h e c r y s t a l l i z a t i o n v e l o c i t y of w a t e r and i t s s o l u t i o n s o This r e p o r t s e r v e s t o draw a t t e n t i o n t o a f i e l d of s c i e n c e which h a s s c a r c e l y been touched upon by r e s e a r c h ,
Page
-
( i f ) Te ch, Trans, TT- 99 TABLE OF C O N T E N 2 ----
P The S u p e r c o o l f n g C a p a c i t y of 'JVaterP
1, The S u p e r c o o l i n g Capa- c i t y o f Pure Water 2 2 , The I n f l u e n c e of F o r e i g n S u b s t a n c e s on t h e S u p e r - c o o l i n g C a p a c i t y of Water 3 P I The L i n e a r C r y s t a l l i z a t i o n V e l o c i t y of I c e i n Aqueous Sol.ut io n s 5Page
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lTech, T r a n s , TT-79 THE SUPERCOOLING CAPACITY OF WATER AND TKE
LINEAR CRYSTALLIZATION VELOCITY OF
IC" I N AQUEOUS SOLUTIONS
TH5 SUPERCOOLING CAPACITY OF' WATER
The c r y s t a l l i z a t i o n c e n t r e s of i c e a r i s l n g i n s u p e r c o o l e d w a t e r have
-
even a t s m a l l s u p e r c o o l i n g s-
such g r e a t l i n e a r c r y s t a l P f z a t f o n v e l o c i t i e s t h a t w i t h i n a s h o r t time d e n d r i t f c i c e n e e d l e s a r e s e e n throughout t h e e n t i r e o b s e r v a t i o n v e s s e l , For t h i s r e a s o n t h e observat.ion of t h e f o r m a t i o n of f ' u r t h e r c r y s t a l l i z a t i o n c e n t r e s i s fmpossible, Hence i t i s n o t p o s s i b l e ( b y analogy w i t h o t h e r f l u i d s ) t o determine the s u p e r c o o l i n g c a p a c i t y o f w a t e r a s a f u n c t i o n of t h e s u p e r c o o l i n g , by countfng t h e c r y s t a l l i z a t i o n c e n t r e s which form s p o n t a n e o u s l y w i t h i n a g i v e n time a t a g i v e ns u p e r c o o l i n g , I t i s o n l y p o s s i b l e t o determine t h e appear- ance of t h e f i r s t c r y s t a l l i z a t i o n c e n t r e a s a f u n c t i o n o f t h e time and temperature, This may be done i n two ways, e i t h e r by c o o l i n g t h e w a t e r s l o w l y and determinfng t h e tem- p e r a t u r e a t which t h e c r y s t a l l i z a t i o n b e g i n s o r by c o o l i n g a small q u a n t i t y o f water a s r a p i d l y as p o s s i b l e t o a known temperature and by measuring t h e time u n t i l t h e f i r s t
c r y s t a l l i z a t i o n c e n t r e forms, Observations were made u s i n g b o t h methods, The r e s u l t s a r e g i v e n below,
For the slow c o o l i n g t e s t s g l a s s t u b e s having an i n n e r d i a m e t e r of 0 , 8 mm, and a w a l l t h i c k n e s s o f 0,4 mm, were u s e d , Each tube was f i l l e d w i t h 0,4 c c , of water and
s e a l e d a t b o t h e n d s , The tubes were p u t i n a b a t h which was c o o l e d by a copper p i p e f i l l e d w i t h d r y i c e , A mechanical s t i r r i n g rod ensured uniform temperature d i s t r i b u t i o n , I n
t h i s b a t h t h e t u b e s were cooled w i t h c o n s t a n t v e l o c i t y b e g i n n i n g a t t h e m e l t i n g p o i n t , The t e m p e r a t u r e a t which
spontaneous c r y s t a l l f z a t f o n began was observed, Normally t h e c o o l i n g r a t e was approximately 0,7 t o 0080C p e r minute, For t h e t e s t s u s i n g t h e r a p i d c o o l i n g method t h e tubes were s i m i l a r b u t heda s m a l l e r w a l l t h i c k n e s s o f o n l y 0 , l mm, The t u b e s were p l a c e d i n a b a t h o f a l c o h o l whose t e m p e r a t u r e was m a i n t a i n e d c o n s t a n t t o w i t h i n O , l e C , The time was measured
from t h e immersion of t h e tube t o t h e b e g i n n i n g o f c r y s t a l - l i z a t i o n ,
Pag?
-
2T e c h Trans. TT-79
1,
The Su-1~ C a p a c i t y of Puce W a t e ~The r e a d i n g s t a k e n fn t h e t e s t s w i t h pure water a r e g i v e n i n Table I ,
Tubes 1 t o 4 c o n t a i n e d o r d i n a r y d i s t i l l e d watek while t u b e s a and b were f i . Z l e w i t h heavy w a t e r c o n t a i n i n g moye than
X P
99,s p e r c e n t D20 The t a b l e g i v e s t h e t e m p e ~ a t u r e s of' the b e g i n n i n g of c r y ~ t a l l i z a t i o n a t v a r i o u s c o o l f n g r a t e s , There a r e d i f f e r e n c e s of s e v e r a l degrees be tween t h e v a r f ous t ~ l b o s , whereas, on r e p e a t i n g t h e measurement f o r e a c h f n d f v i d u a l
t u b e , t h e v a r i a t i o n s amount o n l y t o a few t e n t h s o f a d a g r e e ,
d e s p i t e t h e f a c t t h a t t h e formatlorn o f a c s y s % a l l i a a t l o n c e a t r e IS 8 chance occurInence and conseqilently a P a ~ g c r
v a r i a t i o n would have been expected,
The t e m p e r a t u r e of t h e b e g i n n i n g of c r y s t a l - l i z a t i o n was independent o f tho c o o l i n g r a t e o v e r a wide r a n g e , The formatfon of an i c e n u c l e u s was n e v e r t h e l e s s favoured by sudden c o o l i n g o I n f i v e t e s t s o f tube 1, f o r
example, d u r i n g the c o o l i n g from +20° t o -12°C c r y s t a l l i z a t i o n o c c u r r e d a f t e r 12,0 9 0,8 seconds, and i n t u b e 3, a f t e r
'7,S 2 0,4 seconds, A t slow c o o l i n g , t h e s e two tubes remained a t t e m p e r a t u r e s s e v e r a l d e g r e e s below -12OC f o r 1 6 and 9
minutes r e s p e c t i v e l y , b e f o r e c r y s t a l l f z a t f on s e t i n , I n t h e s e t e s t s , too, an u n e x p e c t e d l y good r e p r o d u c i b i l f t y was n o t e d ,
The s u p e r c o o l i n g c a p a c i t y o f heavy w a t e r w a s found t o be s l i g h t l y l e s s t h a n that. of o r d i n a r y w a t e r , I t w a s a l s o found t h a t t h e dependence of t h e b e g i n n i n g s f cpys-
i.narg w a t e r . Z e i t s c h r i f t f a r anorganfsche und
Page -=. 3 Tech,, T r a n s , TT-79 2 , qnf@aloloeFuSoocr2 C a p a c i t y o f Water The i n v e s t f g a t f o n o f t h e s u p e r c o o l i n g c a p a c i t y o f w a t e r , w!-lich y i e l d e d t o t a l l y d i f f e r e n t v a l u e s f o r t h e v a r i o u s t u b e s b u t gave r e s u l t s t h a t c o u l d e a s i l y b e reprao- duced f o r e a c h i n d i v i d u a l t u b e , seemed t o s u g g e s t t h a t t h e v a r i a t i o n s may b e a t , t r f b u t e d t o t h e i n f l u e n c e o f f o r e i g n substances, e s p s c f a l l y s f n c e t h e t e s t s showed t h a t , a s a r u l e , c r y s t a l l f z a t i o n s e t i n a t t.he same p o i n t s o f t h e t u b e s , It i s a known f a c t t h a t , u n d e r c t h e r w i s e i d e n t i c a l c o n d i t l o n s , f o r e i g n s u b s t a n c e s i n s o l u t i o n have a s t r o n g e f f e c t on t h e number o f c r y s t a l l i z a t i o n c e n t r e s b e i n g formed, But e v e n i n s o l u b l e f o r e i g n s u b s t a n c e s , , s u c
a s powdered s t o n e and m e t a l w i r e s , i n f l u e n c e t h i s numherxf; however, n o d i r e c t dependence o f c r y s t a l l i z a t i o n c e n t r e f o r m a t i o n on t h e p r e s e n c e of s o l i d f o r e i g n s u b s t a n c e was o b s e r v e d , , F u r t h e r m o r e , t h e t e s t s o f J, Meyer and W., p f a f f u ) r e v e a l e d t h a t i n m a t e r i a l s w i t h low n u c l e a r numbers ( s u c h a s thymoP, s ~ l o P , benzophenone, and o t h e r s ) t h e number o f c r y s t a l l i z a t i o n c e n t r e s may b e r e d u c e d c o n s i d e r a b l y b y f i l t r a t i o n ,
The t e s t s u p t o t h o p r e s e n t were made w i t h s u b s t a n c e s h a v i n g Bow c r y s t a l l i z a t i o n v e l o c f t i e s , Water h a s n o t been examined a s y e t f n t h i s r e s p e c t b e c a u s e o f i t s h i g h c r y s t a l l i z a t i o n v e l o c i t y , F o r t h a t r e a s o n t h e i f i -
f l u e n c e o f i r o n wf r e s , powders o f r o c k c r y s t a l , q u a r t z
g l a s s , and corondum was i n v e s t i g a t e d I n f i v e t u b e s for. e a c h c a s e . I n t h e t e s t s w i t h i r o n w i r e s ( T a b l e 1 1 ) t h e tempcsa- t u r e o f t h e b e g i n n i n g o f c r y s t a l l f z a t i o n i n p u r e w a t e r was f f r s t of a l l d e t e r m f n e d , Then e l e c t r o h y t i c i r o n w i r e s ,
5 cm, l o n g and 0.2 rnm, i n d i a m e t e r , a f t e r b e i n g c l e a n e d
w i t h w a t e r and a l c o h o l , were p l a c e d i n t h e w a t e r and r e a d i n g 9 o f t h e t e m p e r a t u r e werd a g a i n t a k e n a t whfch c ~ y s t a l l f z a t f o n began s p o n t a n e o u s l y , F i n a l l y t h e w i r e s were kemoved and t h e
t e m p e r a t u r e o f t h e f o r m a t i o n o f t h e f f r s t n u c l e f was a g a i n d e t e r m i n e d , I t becomes c l e a r that; t h e i r o n w i r e r a f s e s t h e t e m p e r a t u r e of t h e b e g i n n i n g o f i ce f o r m a t i o n c o n s i d e r a b l y t h e r e b y i n c r e a s i n g t h e number o f c r y s t a % l i z a t f o n cen- t r e s , A f t e r t h e removal o f t h e w i r e s t h e ~ e ~ c o o l f n ~ ._4-_1-_Y__
-- -
x ) G, Tammann, 2 , p h y s C h e m , 2 5 (18981, p. 456; P , O t h e r , 2 , a n o r g . Chern, 9 1 (99151, p , 24Boxr) J,
Meyer and W, P f a f f 2 , a n o r g , u , a l l g , Chern. 217 ( 1 9 3 4 ) ~ p. 257.Page
-
4Tech,? T r a n s , TT-79
c a p a s i t y i n c r e a s e d s u b s t a n t i a l l y , i n c o n t r a s t wf t h p i p e r o n a l , d l e ~ e , a c c o r d i n g t o P , Othmer" t e s t t s n l , t h e i n c r e a s e d num- b e r o f r l u c l e l remained even a f t e r removal o f t h e w i r e s ,
TABLE
--
I1The e f f e c t s f t h e powdelps s f r o c k c ~ y s t a l , q u a r t z - g l a s s , and corundum on t h e s u p e r c o o l f n g c a p a c i t y is shown i n Table 111, B o t h q u a r t z powders cause a consLderable incrbeaee I n t h o nurnbe~ o f n u c l e i , whereas t h e a d d i t i o n o f corundum i s w i t h o u t e f f e c t ,
TABLE
--
I11-z=zz.--
P u ~ o water fl O C
T h e tAir En s o f u t f o n also afP'er:t-s t h e super-
c o o l i n g c apacf tg o f w a t e r , Water c o n t a i n i n g af r c r y s t a l l l i a e s
on an a v e r a g e a t a t e m p e r a t u r e two d e g r e e s h i g h e ? 'than w a t e r
Page tJ 5
Tech, Trans, TT-~79 The r e s u l t s of t h e s e t e s t s make i t seem probable t h a t a s a g e n e r a l r u l e the spontaneous c r y s t a l l i z a t i o n observed was caused by f o r e i g n s u b s t a n c e s , Consequently i t s h o u l d b e p o s s i b l e , a f t e r removfng t h e s e f o ~ e f g n s u b s t a n c e s , t o superq-
c o o l t h e w a t e r t o a temperature lower t h a n -20°C, t h e l o w e s t temperature r e p e a t e d l y observed, The g r e a t e s t s u p e r c o o l i n g e v e r observed t o d a t e f s 2 9 , 5 ° ~ ~ ) ,
I1 THE LINEAR CRYSTALLIZATION VELOCITY -.OF -- ICE I - N - & U u -
l o The measurement o f t h e c r y s t a l l i z a t i o n v e l o c i t y was
c a r r i e d o u t i n U-tubes which had an i n n e r d i a m e t e r of 1,2 mm, and a w a l l t h i c k n e s s o f 0,s mrn, The temperature b a t h c o n s i s - t e d of a l c o h o l cooled by d r y i c e and c o n t a i n e d i n a t r a n s - p a r e n t Dewar f l a s k , A s p i r a l s t i r r i n g rnecha~lism ensured uniform temperature d i s t r i b u t i o n i n t h e b a t h , , The s t a r t o f
c r y s t a l l i z a t i o n was e f f s c t e d by i n o c u l a t i o n w i t h i c e , The p r o g r e s s of t h e c r y s t a l l i z a t i o n was timed between two marks vrhfch had been made on each arm of t h e U-tube 80 mu- a p a r t
thus e n s u r i n g a s t r a i g h t - l i n e measuring d i s t a n c e , A t low v e l o c i t i e s t h e time measurement was made b y means of a 0,2
second watch, and a t v e l o c i t i e s h i g h e r t h a n 1 , 0 0 0 mm, p e r minute, by a Q,02 second stop-watch, The time taken by t h e
c r y s t a l l f z a t f o n boundary t o p a s s upward and downward through t h e d i s t a n c e between two marks, was d e t e r m i r ~ e d , For v e r y low c r y s t a l l i z a t i o n velocf t i e s ( a few m i l l i n ~ e t r e s p e r minute and l e s s ) t h e U-tube was mounted on a g l a s s s c a l e by means of which t;he p r o g r e s s ~ f t h e c r y s t a l l i z a t i o n was 9abserved, The t e m p e r a t u r e o f t h e b a t h waa maintafned c o n s t a n t d u r i n g the measurement t o w i t h f n k O,OEiO, The i c e was added a f t e r t h e U-tubes had remained a t the e x p e r i m e n t a l temperature
f o r a t l e a s t t h r e e m i n u t e s , To p r e v e n t b u r s t i n g o f the t u b e s , t h e y wepa removed from t h e b a t h b e f o r e t h e l e s t few drops of t h e water c o u l d c r y s t a l l i z e ,
2 , The p r e c f p i t a t i n g i c e c r y s t a l l i z e d i n t h e form o f well- developed d e n d r i t e s , The main growth was i n t h e d i r e c t i o n of t h e stem of t h e d e n d r f t e , As a r u l e , t h e r e f o r e , t h e
growth of t h e stem c o i n c i d e d w i t h t h e a x f s o f t h e t u b e , The s t r u c t u r e o f t h e d e n d r i t e i s e a s i l y recognized, e s p e c i a l l y a t t h e c r y s t a l l i z a t i o n boundary formed by one o r s e v e r a l d e n d r f t i c t i p s , F i g u r e 1 shows t h e appearance of such a d e n d r i t f c t i p , The branches make a n angle of 60 d e g r e e s
t h i c k - I n s t y t u t u ~ e t a l u $ ~ j f
Page .- 6 Tech, Trans, TT-5'9 n e s s o f t h e s t e m and t h o b r a n c h e s v a r f e s cor',sfdarzabl.y v i f t k ~ t h e c o n c e n t r a t i o n of t h e s o l u t i o n a n d t h e s u p e ~ ~ c o ~ l f n g , A t s l i g h t s u p e r c o o l f n g , t h i n , b a r e l y r e c o g n i z a b l e f o r m a t i o n s a r f s e ,> A t c o n s i d e r a b l e s u p e r c o o l i n g t h e b ~ a n c h e s a r e o f ten s o t h i c k t h a t t h e y c o l l i d e and t h e d e t a i l s arde no l o n g e r d i s t i n c t , The c r y s t a l l i z a t i o n f r o n t t h e n c o n s i s t s o f one o r more I c e t i p s which, however, always have t h e c l i a r a c t e r i s t i o c u t l i n e of t h e d e n d r i . L i c tip:;, w i t h arL m g l e ( i f appx 3 x l m E t e l y
60 d e g r e e s a t t h e t o p , I n p u r e w a t e r d e n d r i t e s t e m s h a v i n g
a t i i i c k n e a s u p t o 0 , 5 nna,, were o b s o ~ v e d , . 1Vlicroscopic measure- ment o f i n d i v i c i u n l d e r i d r i t e s , which c r y s t a l l f z e d a t losv
c r y s t a l l f z a t i o n v e l o c f t y from a 58 p e r c e n t g l y c e r i n e sc#lu-
t i o n , ; r e v e a l e d a t h i c k n g s s o f a p p c o x f m a t e l y 0,02 mm,, for t h e s t e m s , 0,005 m n i , f o r t h e b r a n c h e s , and 0,001 rim, f o r t h e
f i n e s t twigs, 'The p l a n e o f t h e d e n d r - f t e s lies i n t h e hexa.5 g o n a l g r o u p of i c e , hence t21 d e n d r i t e s c o r r e s p o n d t o one o f
t h e s i x r a y s o f a
snow flak ex^,
I n p u r e wateri a t slight s u p e r z c o o l i n g , . bvf de d e v f a t t o n s f ' m m t h e t u b e a x i s wexye o b s e r v e d i n t h e d i r e c t i o n o f t h e d e r l u r i t e stem&, r o s u l t , I n g i n R con-s i d e r a b l y d e c r e a s e d c r y s t s l l i z a t i o n v e l c c i t y x x ) , I n d i l i ~ t e s u c r o s e s o l u t i . o n s t h e dendrite s t e m and t h e b r b s i e k i e s ~ o ~ ~ l o - tfmes showed a c u r v a t u r e w i t h a r a t i i u s o f a few t e n t h s c s f a
m f l l i m e t r e which r e s u l t e d i n a r e d u c e d c r y s t a % l i z a t f o n v e l o c i t y , , T h i s e x p l a i n s t o a c e r t a i n e x t e n t t h e Z i f f e r e ~ l c e s in t h e v a l u e s found i n t h o l i t e r a t u r e f o r t h e c r g s t a b l i z a t f - o n v e l o c i t y o f f c o from p u r e w a t e r , , U p t o t h e p r a e s e n t t k i s e e d i f f e r e n c e s were a t t r i b u t e d t o v a r y i n g t e s t c o n d . l . t i o n s ( tube d i a m e t e r , t h i c k n e s s of t h e t u b e w a l l s ) ,; ~ i l i c n i : h a l ~ ) , who
made hi8 measurements uricier a1:aost t h e stme c o r l r . l l ? ; i ~ ~ i s ss
t h e a ~ t h o r s o f t h e p r a e s e n t r e p o r t , f c u n d v a l u e s ~ I i f c l i w6re s 1 ~ 1 ~ ~ l P e r by a p p p o x f n l a t e l y s e v e n p e r c e n t , s i n c e h i s t-ubea w e r e b e n t t h r e e t i m e s i n ordon. t o o b t a i n a borlger m e a s u r i n g d l ss=. t a n c e , 3 , F l ~ u r e s 2 t o 4 s h c j w the d e p e n c l e n c ~ o f t h e c r y s t a 2 . l l z a t i o n v e 7 , o ~ ~ i t y o f i c e from v a r i o u s so3ut.Fa3ns on t h e s u p e r c c c ~ l i n g , The numbors g i v e n i n t h e f i g u r e s a r e t h e mo4s s f t h e s u b - s t a n c e s d i s s o l v e d i n 1,000 gm, w a t e r , The c ~ y s t a l l i z a t f o n v o l s c f t y was g e n e r a l l y f o l l o w e d u p a s f a r a s the e r g s t a l - B i z a t i s n c a p a c i t y ~ e m i i t t e d , , The d e c r e a s e i n c r v s t a l l i z a t f o n
xm) G , 'Tamrnann and A , ~ a c h n e r , Yoc, e i t ,
Page -- 7
Tech, ' P r u l s - TT-79
t h e v a r i o u s s u b s t a n c e s a t i d e n t i c a l mol c o n c e n t r b t f on, A s
y e t t h e a v a i l a b l e d a t a a r e n o t s u f f i c i e n t t o g i v e % n f o m ~ a t i o n concerning t h e e f f e c t s of t h e s e v a r i o u s s u b s t a n c e s , The de- c r e a s e i n t h e c r y s t a l l i z a t i o n v e l o c i t y of i c e caused b y
s u c r o s e i s p a r t i c u l a r l y l a r g e , Sucrose f a r exceeds the o t h e r s u b s t a n c e s i n m o l e c u l a r weight and t h e r e f o r e h s s a p a r t i c u - l a r l y low r a t e of d i f f u s i o n , , This probably e x p l a i n s t h e s t r o n g e f f e c t ,
I t was o n l y pcissible t o a t t a i n t h e maximum c r y s t a l l i z a t i o n v e l o c i t y when t h i s was l e s s t h a n 100 mm, p e r minute With s m a l l values of t h e maximum c r y s t a l a b l z a t i o n
v e l o c i t y , l e s s t h a n 1 5 rnm, p e r m i n u t e , marked maxima of t h e c r y s t a l l f z a t f o n velocf t y o c c u r , These maxima l i e , i n t h e p r e s e n t c a s e , between 7" and l b O of s u p e r c o o l i n g f n agreement w i t h t h e f i n d i n g s f o r c h e m i c a l l y pure s u b s t m c e a ,
4 , The dependence of t h e c r y s t a l l f z a t i a n v e l o c i t y on the terriperature may b e r e p r e s e n t e d Tor pure s u b s t a n c e s l i k e o t h e r r e a c t i o n v e l o c f t i e s by an e q u a t i o n of the form:
where T1 and
T2
a r e t h e temperatures a t t h e c r y s t a l l i z a t i o n boundary, For s m a l l v a l u e s of the c r y s t a l l i z a t i o n v e l o c f t yt h e s e temperatures do n o t d i f f e r from t h e t of t h e b a t h , I f t h f s formula i s a p p l i e d t o t h e dependence of t e m p e ~ a t u r e on t h e c r y s t a l l i z a t i o n v e l o c i t y o f s o l u t i o n s , then t h e f a c t must kje t a k e n i n t o account t h a t t h e c ~ y s t a l l i z a t i o n v e l o c i t y i e i n f l u e n c e d n o t o n l y by t h e temperature a t t h e c r y s t a l l i z a t i o n boundary, f ,,e,
,
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 , b u t a l s o by t h e r a t e of d i f f u s i o n of the d i s s o l v e d s u b s t a n c e , The r a t e o f d i f f u s i o n , however, d e c r e a s e s v e r y subs t a n t i a l l y w i t h de-c r e a s i n g temperature, thus r e d u c i n g the c r y s t s l l i z a t - i o n velos= c i t y , For t h i s r e a s o n t h e formula does n o t h o l d f o r l a r g e concent,ration and temperature i n t e r v s l a , For s m a l l ones however, i t i s i n agreement w i t h t h e observations, The l o g a r i t h m of t h e c r y s t a l l f z a t i o n v e l o c i t y i s a l i n e a r f u n c t i o n of t h e c o n c e n t r a t i o n o r of t h e temperature a t t h e c r y s t a l l i z a t i o n boundary, The a d d i t i o n o f f o r e i g n m a t t e r u s u a l l y lowers t h e m e l t i n g p o i n t , The same a p p l i e s t o t h e c r y s t a l l f z a t f o n v e l o c i t y of t h e c r y s t a l s of t h e s o l v e n t a t i d e n t i c a l s u p e r - coolfngs, although t h i s d e c r e a s e i s s u b s t a n t i a l l y l a r g e r and s a t i s f i e s o t h e r laws, In a bilnsry s e r i e s of mfxtukes t h e c r y s t a l l i z a t i o n v e l o c i t y d e c l i n e s w i t h t h e d i s t a n c e from t h e two components, hence f o r f d e n t f c a i i s u p e r c s o l f n g s t h e
Page
-
8Tech, T r a n s , TT-79
two c u r v e s o f c r y s t a l l i z a t i o n v e l o c i t y i n dependence on t h e c o n c e n t r a t i o n must i n t e r s e c t e x a c t l y a s t h e c u r v e s o f f u s i o n do. However, i t i s n o t requIr3ed t h a t t h e p o i n t o f i n t e r - s e c t i o n o f t h e t w o c u r v e s o f c r y s t a l l f z a t i o n v e l o c i t y s h o u l d l i e a t t h e e u t s c t i c c o n c e n t r a t f o n , A t t h i s p o i n t of' inter- s e c t i o n t h e c r g s t a l l i z a t i o n v e l o c i t i e s sf t h e two components a r e e q u ~ l i f each component c r y s t a l l f z e s s e p a r a t e l y , However, i f b o t h c r y s t u l l i z e t o g e t h e r , t h e n t h e z r y s t a l l l z a t f o n v e l o c i t y
7 1 1 1 g e n e r a l 1 3 i r ~ c r e n u e ~ ? . i z h t l y , coinpared wit21 tth ovvlile of
t,rle ifidividl-l#1 compsnent, 'fie r e a s o n f o r tllis i s Zhht tk?e s e p a r a t i o n o f t h e two s u b s t a n c e s due t o d f f f u s i o n Is f e s i l f - tat;ed b y t h e ex' s t e n c e o f b o t h t y p e s o f c r y s t a l a t tile c r y s t a f =
1 1 z a t l o n frorlt'j, With a m i x t u r e o f t w o components which,
f n t h e pQre ~ t i ~ f ; e have v e r y d f f f c ~ ~ e n t ; c r ~ y s t a l l l z a t i o n velo- c i t i e s , t h e r e a r e c o n c e n t r a t i o n s from whfch e v e n the com- p o n e n t of P a r g s c r y s t a l l f z a t i o n v e l o c i t y c r y s t ; a l l i z e s a t a Power r a t e t h a n t h e p u r e compi>nent o f Power c r y s t a l l i z a t i o n
v e l o c i t y , The i n v e s t i g a t i o n o f g l y c e ~ i n e - w a t e r s o l u t i o n s s e r v e d a s an e x a m p l e , The m a x i m u m c r y s t a l l i z a t i o n vein i t y o f p u r e g l y c e r i n e i s a p p r o x i m a t e l y 0 , l rnm.. p e r m i n u t s m y , Plaom a s o l u t i o 1 1 c o n i ; a l l z l n g 6 0 p e r cant g l y c e r i r i c t h e i c e c r y s t a l l i z e s a t H ~naximui:: c r y s t a l l i z a t i o n v e l o c i t y o f 0,093 rnm, = J e r m i n u t e However, t h e c r y 3 t a l l i z a t i o n v e l o c i t y o f f c o , as
ell as t h a t o f .Qycerint: from 6:) $and 85 p e r c e n t s o 2 u t i s n s , i s a t l e a s t t e n t i m e s s m a k l e ~ ,
5 , Tkle m a g n i t ~ i d e o f t h e c r y s t a l l i z a t i o n v e l o c i t y i s i m p o r t a n t
f o r dec!ding w h e t h e r a s o l u t f o n can b e t ~ a ~ s f o r m e d t o t h e g l a s s - - lf ke s t a t e by r a p i d c o o l i n g , , Small q u a n t f t i e s ( a p p r o x i m a t e l y
Q,'i c e , ) o f e u t e c t i c s o l u t i o n s o f KOH, WaOH, TICB, and CaC12, - whose maximum c r y s t a l l f z a t i o r l v e l o c i t y i s l o w e r than a p p l a ~ x i ' ~ m a t e l y 20 rnrn, p e r m f n u t s , c o u l d b e m a i n t a i n e d g l a s s - l i k e by c o o l i n g i n l i ~ ~ i f d a i r , , 6 , I n t h e concerltzaatforls i n v e v t f g ~ t e d t o d a t e a d d i t i o n s o f d i s s o l v e d for-eii;n r r i 2 t t e ~ r e d u c e t h e c r y s t a l l i z a t i on v e l o c f t y sf i c e , I f , how eve^, t h e e f f e c t of s m a l l q u a n t i t i e s o f d i s - s o l v e d m a t t e r ( s a y l e s s t h a n 0,OB mol p e r 1 S t r e ) i s i n v e s t i - g a t e d , i t i s found that, a s m a l l a d d i t i o n does n o t have a de- c r e a s i n g e f f e c t b u t , on t h e c o n t r a r y , a n i n c r e a s i n g e f f e c t on t h e c r y s t a l l i z a t i o n v e l o c i t y o f i c e , Consequently, a t i d e n t i c a l s u p e r c o o l i n g s , r n a ~ k a d maxima can be f o u n d on t h e c u r v e s r e p r e s e n t i r l g t h e c r y s t a l l i z a t i o n v e l o c i t y a s a f u n c t i o n of t h e c o n c e n t r a t L o n , These c u r v e s f o r s o l u t i o n s o f NaOH,, H C 1 , N a C 1 , and s u c r o s e a r a v e n i n : z a r e s 5 t o 8, The r e -
-
=- ,--= ---=.
p
Tamann and A , fSotschwak,Z i a n o r g , u , a l l g o C h e m , 1 5 9 ( 1 9 2 6 ) , p , 27,
G o Tmilann and E , J e n c k e l , 2, a n o r g , u , a l l g . Chem. 193 ( l g a o ) , P O 7 6 ,
Page
-
9 Tech, Trans, TT-79 s p e c t i v e s u p e r c o o l i n g s a r e g i v e n a t t h e r i g h t - h a n d s i d e of each curve, The i n c r e a s e i n t h e c r y s t a l l i z a t f on velocf t y of i c e which i s e v i d e n t d u r i n g t h e f i r s t a d d i t i o n t o t h e water may be interplaeted i n t h e f o l l o w i n g manner, Due t ot h e f o r m a t i o n of i c e t h e c o n c e n t r a t i o n of t h e i c e forming type of molecule w i l l be reduced, The t r a n s i t i o n of the o t h e r molecule types t o t h e i c e forming type i s a c c e l e r a t e d by t h e a d d i t i o n s , I n d i l u t e s o l u t i o n s t h e r e i s a s l i g h t l y h i g h e r c o n c e n t r a t i o n of t h e i c e forming type of molecule
than i n pure w a t e r , causfng an i n c r e a s e i n t h e c r y s t a l l i z a t i o n v e l o c f t y , I n t h e c a s e o f l a r g e r a d d i t i o n s , however, t h e
d e c r e a s e of the c r y s t a l l i z a t i o n v e l o c i t y caused b y t h e de- c r e a s e i n the e q u i l i b r i u m temperature p r e v a i l s , With i n - c r e a s i n g s u p e r c o o l i n g the maximum c r y s t a l l i z a t i on v e l o c i t y becomes more d i s t i n c t , The r a t e of t ~ a n s i t i o n of t h e
molecules of water i n t o the i c e forming type d e c r e a s e s w i t h dropping temperature and t h e a c c e l e r a t i n g e f f e c t of the added substance becomes more pronounced, For t h e a d d i t i o n of NaCl t h e i n c r e a s i n g e f f e c t i s s m a l l e r t h a n f o r a d d i t i o n s o f H C 1 and NaOH, t h u s s h i f t i n g t h e maximum t o s m a l l e r NaCP
c o n c e n t r a t i o n s , Thi s s h i f t i n g i s more pronounced f n t h e c a s e of sucrose,,
FIG.1 ICE DENDRITE v FIG. 1 - 4 T T - 7 9
+
20°FIG. 2 CRYSTALLIZATION VELOCITY
I N MM/MIN PLOTTED
AGAl NST THE SUPERCOOLING.
F IG.3 CRYSTALLIZATION VELOCITY F I G .4 CRYSTALLIZATION VELOCITY
MIN PLOTTED PLOTTED AGAINST THE
t F I G . 5 - 8 T T - 7 9 2 0 0 0 0
1
0 0.1 0.2 0.3 04 0.5 FIG. 5 F I G . 6 MM N ACL+
-+-i\t
O 001 0.02 0.03 0.040
0-01 0.02 003 0.04 0.05 FIG.7 FIG. 8CURVES OF CRYSTALLIZATION VELOCITY AS A FUNCTION OF SOLUTION CONCENTRATION.
