STUDIES OF SURFACE PROPERTIES OF ICE
USING NUCLEAR MAGNETIC RESONANCE
Y. Mizuno, N. Hanafusa
To cite this version:
Y. Mizuno, N. Hanafusa. STUDIES OF SURFACE PROPERTIES OF ICE USING NUCLEAR
MAGNETIC RESONANCE. Journal de Physique Colloques, 1987, 48 (C1), pp.C1-511-C1-517.
<10.1051/jphyscol:1987170>. <jpa-00226316>
HAL Id: jpa-00226316
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Submitted on 1 Jan 1987
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JOURNAL DE PHYSIQUE
Colloque C 1 , supplgment au n o 3, Tome 48, mars 1987
STUDIES OF SURFACE PROPERTIES OF ICE USING NUCLEAR MAGNETIC RESONANCE
Y.
MIZUNO and N.
HANAFUSA
I n s t i t u t e o f Low Temperature S c i e n c e s , HoWraido U n i v e r s i t y ,
Sapporo 060, J a p a n
R 6 s d - Des e e r i e n c e s de rdsonance magndtique nucldaixe pul&e ont dt6 f a i t e s
sur des p e t i t e s particules de glace ayant un grand rapport surface/volume pour
dtudier l a couche quasi liquide (Q.L.L.)
2 l a surface de l a glace. La &pendance
avec l a t d r a t u r e des caract6ristiques IWN e t l e s propridtds dynamiques t e l l e s que
l e temps de c o r r d l a t i o n pour l e mouvement de r o t a t i o n e t l e c o e f f i c i e n t
d'auto-diffusion de l a Q.L.L. o n t 6td d d c r i t e s . La frdquence du mouvement
moldcaaire rotationnel dans l e Q.L.L. e t l e coefficient d'autc-diffusion sont plus
grands respectivement de 5 et 2 ordres de grandeur que dans l a glace en volume.
Abstract - Pulsed nuclear mgnetic resonance studies were carried out on small i c e
particles with large surface to volume ratios to investigate the so-called quasiliquid layer (Q.L.L.) on an i c e surface. The temperature dependence of features of
the NMR spectra and dynamical properties such as the correlation time for rotational m t i o n and the self diffusion coefficient of the Q.L.L. were described. The
frequency of the rotational mlecular m t i o n and the self diffusion coefficient
were larger than those of bulk i c e by about five orders and by two orders, respectively.
I. I n t r o d u c t i o n
I t i s g e n e r a l l y a c c e p t e d t h a t a mobile p h a s e , t h e s o - c a l l e d q u a s i l i q u i d l a y e r ( Q . L . L . ) on an i c e s u r f a c e , p l a y s an i m p o r t a n t r o l e i n
some phenomena which o c c u r a t t e m p e r a t u r e s n e a r below t h e m e l t i n g
p o i n t , s u c h a s snow metamorphism, s i n t e r i n g , a d h e s i o n , a c c r e t i o n and
c r y s t a l growth.
Many s t u d i e s r e l a t e d t o t h e Q . L . L . have been c a r r i e d
o u t i n t h e p a s t 30 y e a r s t o c l a r i f y i t s e x i s t e n c e and t h e d i s t i n c t i v e
s u r f a c e p r o p e r t i e s of i c e .
Nakaya (1) and Weyl ( 2 ) have i n t e r p r e t e d t h e a d h e s i o n observed between i c e s p h e r e s and r e g e l a t i o n i n terms o f mobile I l l i q u i d - l i k e " s u r face s t r u c t u r e s .
J e l l i n e k ( 3 ) emphasized t h e e x i s t e n c e of t h e mobile
phase b a s e d on e x t e n s i v e s t u d i e s on i c e adhesion and reviewed t h e s u r f a c e p r o p e r t i e s of i c e .
On t h e o t h e r hand, F l e t c h e r ( 4 ) h a s shown t h e o r e t i c a l l y t h e e x i s t e n c e o f t h e p r o p e r s u r f a c e s t r u c t u r e and concluded t h a t a t temperat u r e s above about - 5 ' ~ t h e s u r f a c e of i c e i s covered by t h e Q.L.L.,
whose t h i c k n e s s i n c r e a s e s a s t h e temperature approaches O°C.
D i r e c t evidence of t h e e x i s t e n c e of t h e Q . L . L . on i c e s u r f a c e s h a s
been p r e s e n t e d by many i n v e s t i g a t o r s u s i n g v a r i o u s e x p e r i m e n t a l techn i q u e s : Photoemission by Nason and F l e t c h e r ( 5 1 , p r o t o n c h a n n e l l i n g by
Golecki and J a c c a r d ( 6 ) and n u c l e a r magnetic resonance by Kvlividze e t
a l . ( 7 1 , Anderson ( 8 ) , B e l l e t a 1 . ( 9 ) and Ocampo and K l i n g e r ( 1 0 ) .
A r e c e n t e l l i p s o m e t r i c a l s t u d y by Furukawa e t a l . ( l l ) provided det a i l e d i n f o r m a t i o n on t h e t h i c k n e s s and r e f r a c t i v e i n d e x of t h e l a y e r
T h e i r r e s u l t s on
and i t s dependence on t h e c r y s t a l l o g r a p h i c s u r f a c e .
t h e c r y s t a l l o g r a p h i c s u r f a c e s u p p o r t t h e t h e o r e t i c a l t r e a t m e n t of t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987170
JOURNAL DE PHYSIQUE
C1-512
growth k i n e t i c s o f i c e from t h e vapor phase p r e s e n t e d by Kuroda and
Lacmann ( 12 )
I n f o r m a t i o n on t h e dynamical p r o p e r t i e s o f t h e Q.L.L.,
its d i f f e r e r e n c e from bulk i c e o r i t s " l i q u i d - l i k e v f e a t u r e , i s important t o und e r s t a n d t h e above-mentioned snow and i c e phenomena which a r e c l o s e l y
r e l a t e d t o the surface properties of ice.
. I n t h i s c o n n e c t i o n , t h i s p a p e r d e s c r i b e s t h e dynamical p r o p e r t i e s
of t h e Q.L.L., t h e c o r r e l a t i o n time f o r r o t a t i o n a l molecular motion and
t h e s e l f d i f f u s i o n c o e f f i c i e n t i n t h e Q.L.L. u s i n g p u l s e d n u c l e a r magne t i c resonance.
.
11. Experimental Procedures
I n o r d e r t o o b t a i n t h e NMR s i g n a l due t o i c e s u r f a c e s , s m a l l i c e
p a r t i c l e s o f l e s s t h a n 150 pm i n diameter were p r e p a r e d a t -30°C by
f r e e z i n g supercooled water d r o p l e t s s p r a y e d o u t from a n atomizer on a
clean t e f l o n sheet.
The p a r t i c l e s were p u t i n t o a g l a s s c e l l f o r t h e
NMR s p e c t r o s c o p y .
To p r e v e n t s i n t e r i n g between i c e p a r t i c l e s , t h e
g l a s s c e l l was s t o r e d i n a c o l d chamber whose temperature was k e p t
below -80°C.
T h e NMR measurements were made u s i n g a JEOL FXlOONMR s p e c t r o s c o p e
eqyipped w i t h a s p i n l o c k i n g u n i t and a temperature c o n t r o l l i n g u n i t
and o p e r a t e d a t 100 MHz.
The temperature o f a sample was c o n t r o l l e d
with an accuracy o f * O.l°C, and f o r thermal e q u i l i b r i u m , every measurement performed a t a c e r t a i n temperature w a s s t a r t e d a f t e r keeping
t h e sample f o r more t h a n 30 minutes a t t h a t temperature.
To o b t a i n t h e temperature dependence on both t h e i n t e n s i t y and t h e
l i n e w i d t h , most of t h e measurements were made i n t h e p r o c e s s o f t h e
temperature r i s i n g from - 1 0 O 0 C t o -5°C.
S p i n l a t t i c e r e l a x a t i o n time T I and t h a t i n a r o t a t i n g frame T I P
were measured by t h e i n v e r s i o n recovery and t h e s p i n l o c k i n g methods,
respectively.
111. R e s u l t s
1. NMR s i g n a l due t o s u r f a c e mobile phase
Figure 1 shows NMR s p e c t r a
f o r t h e s u r f a c e mobile phase accumulated 200 times a t t h e v a r i o u s temp e r a t u r e s observed a t 9 9 . 5 MHz, t h e broad s i g n a l due t o c r y s t a l l i n e i c e
i s n o t s e e n w i t h i n t h e range o f o b s e r v a t i o n a l frequency o f 20 kHz.
The narrow s i g n a l was n o t d e t e c t e d a t any t e m p e r a t u r e when only
bulk i c e was u s e d , and t h e s i g n a l s a p p e a r i n g i n Fig. 1 were thought t o
be caused by a mobile phase a t an i n t e r f a c e between a i r and c r y s t a l l i n e i c e and/or a t g r a i n boundaries.
A s i s obvious i n t h e f i g u r e , t h e l i n e width and t h e i n t e n s i t y v a r y
w i t h temperature.
I t should be noted t h a t t h e l i n e width of t h e spectrum a t -lO°C is about 7 t i m e s t h a t o f o r d i n a r y water a t +5OC, which i s
shown f o r comparison on t h e l e f t hand s i d e .
The i n t e n s i t y o f t h e
spectrum i s p r o p o r t i o n a l t o t h e number of t h e mobile molecules.
The
r e l a t i v e i n t e n s i t y , which i s normalized w i t h t h e i n t e n s i t y a t -5"C, and
t h e l i n e width v a r i a t i o n w i t h temperature a r e shown i n Fig. 2 .
A s the
s u r f a c e a r e a was reduced by s i n t e r i n g i n o u r experiment, t h e i n t e n s i t y ,
Although t h e r e l a t i v e
e s p e c i a l l y a t -5OC, i s expected t o be l a r g e r .
i n t e n s i t y l a r g e l y changed between -5OC and -lO°C, l i n e width v a r i a t i o n
was q u i t e s m a l l .
2. S p i n - l a t t i c e r e l a x a t i o n time(T1)
The s p i n l a t t i c e r e l a x a t i o n t i m e ,
TI, was measured by t h e i n v e r s i o n recovery method a t v a r i o u s temperatures.
Figure 3 shows t h e r e l a t i o n s between TI and t h e temperature
f o r powder i c e p a r t i c l e s and a r e f r o z e n i c e , where each p o i n t i s an av-
e r a g e o f t h r e e t i m e s measurements i n b o t h c a s e s .
The r e f r o z e n i c e was
made by m e l t i n g t h e powder i c e s l i g h t l y w i t h i n t h e c e l l and t h e r e a f t e r
f r e e z i n g i t r a p i d l y a t below - 3 0 ' ~ .
Microscopical observation reveale d t h a t a l a r g e number o f t i n y b u b b l e s s e v e r a l 10 pm i n d i a m e t e r were
d i s p e r s e d u n i f o r m l y i n t h e sample.
Figure 1. NMR spectra of the Q.L.L. observed a t 99.5 MHz. Signal of liquid
water was taken a t +5OC. Notice the difference in the line w i d t h between liquid
water and the Q.L.L.
Figure 2. Intensity(so1id l i n e ) and
line w i d t h variation(dotted l i n e )
w i t h temperature
The v a r i a n c e i n TI between t h e two samples r e f l e c t s some o f t h e dynamical d i f f e r e n c e s e x p e c t e d t o be c a u s e d mainly by w a t e r vapor p r e s s u r e around t h e i n n e r and t h e o u t e r s u r f a c e s .
However, T I minimum
a p p e a r e d around -35OC i n b o t h samples.
The s p i n l a t t i c e r e l a x a t i o n time T I f o r p r o t o n i s e x p r e s s e d i n t h e
f o l l o w i n g form ( 1 3 ) ,
where, w, = F Ho i s t h e r e s o n a n t f r e q u e n c y , 7f i s t h e gyromagnetic r a t i o ,
r i s t h e s p i n t o s p i n d i s t a n c e and Z i s t h e c o r r e l a t i o n time f o r r o t a t i o n a l m o l e c u l a r motion.
The c o r r e l a t i o n t i m e a t - 3 5 O ~ was e v a l u a t e d
t o be 9 . 6 x 1 0 - ~ ~ s e from
c
t h e c o n d i t i o n t h a t T i i s minimum f o r woZ i s
a b o u t 0.6.
Using t h i s c o r r e l a t i o n t i m e , t h e s p i n t o s p i n d i s t a n c e , r ,
was e v a l u a t e d t o be a b o u t 1 . 6 6 ~ 1 0 - l o m and 1 . 4 1 ~ 1 0 - m~ ~f o r powder and
refrozen i c e , respectively.
Assuming r d o e s n o t change w i t h temperat u r e , ~a t e a c h t e m p e r a t u r e c a n be o b t a i n e d by s u b s t i t u t i n g t h e c o r r e sponding T1 i n t o e q . ( 1 ) .
I n t h i s c a s e , woz<<1 i s r e a s o n a b l y c o n s i d e r e d a t h i g h e r t e m p e r a t u r e s and wof;) 1 a t lower t e m p e r a t u r e s compared
t o t h e minimum p o i n t g i v e n i n F i g . 3.
Figure 4 i l l u s t r a t e s the c o r r e l a t i o n time a t v a r i o u s temperatures,
where t h e v a l u e a t O°C was c a l c u l a t e d by u s i n g T i a t o0C, which was
o b t a i n e d by e x t r a p o l a t i n g s e v e r a l p o i n t s a t lower t e m p e r a t u r e s .
JOURNAL DE PHYSIQUE
a: powder ice(o)
b: refrozen ice(.)
0
C
0
Figure 3 . Spin l a t t i c e relaxation time,
T I , VS. inverse temperature
activation energy
a: 28.0 k~.mol.'
Figure 4. Correlation time for rotationa l motion, Z , vs. inverse temperature
The d i f f e r e n c e i n T f o r powder and r e f r o z e n i c e i s c o n s i d e r a b l y
l a r g e n e a r t h e m e l t i n g p o i n t ; however, i t d e c r e a s e s a s t e m p e r a t u r e
f a l l e s , and below -15OC, b o t h samples become a l m o s t e q u a l .
The a c t i v a t i o n energy f o r r o t a t i o n a l motion was 28.0 kJ/mol f o r powder i c e and
59.7 kJ/mol f o r r e f r o z e n i c e i n t h e t e m p e r a t u r e range o f 0 t o -50°C
and 0 t o -15OC, r e s p e c t i v e l y .
A s i s shown i n F i g . 4 , t h e c o r r e l a t i o n time o f t h e Q . L . L . i s i n t h e
o r d e r o f 1 0 -I0 s e c , which i s much c l o s e r t o t h a t o f w a t e r o f 10-l2 s e c
(14) than t h a t of i c e c r y s t a l of
sec(l5).
A s compared w i t h
t h e c o r r e l a t i o n time of t h e Q . L . L . a t O°C and t h a t o f o r d i n a r y w a t e r ,
t h e Q.L.L. i s movable w i t h a f r e q u e n c y o f about 1 / 2 5 o f t h a t i n o r d i n a r y w a t e r a t O°C.
3. D i f f u s i o n c o e f f i c i e n t
For p r o t o n , whose n u c l e u s p o s s e s s e s s p i n
1 / 2 , t h e s p i n l a t t i c e r e l a x a t i o n time i n a r o t a t i n g f r a m e , T l p , i s
r e l a t e d t o w l , t h e r a d i o f r e q u e n c y , and D , t h e s e l f d i f f u s i o n c o e f f i c i e n t , a s follows ( 1 6 ) :
where N i s t h e number d e n s i t y o f r e s o n a n t n u c l e i .
A s i s obvious i n
eq. (21, i n p l o t t i n g l / T l p
v s . ~ $ 1 2 ,t h e s l o p e g i v e s a s e l f d i f f u s i o n
c o e f f i c i e n t , D.
A t y p i c a l r e s u l t a t -lO°C i s shown i n F i g . 5.
We
o b t a i n e d t h e s e l f d i f f u s i o n c o e f f i c i e n t a t t e m p e r a t u r e s between -1.5"C
and-20°C.
TheresultsarelistedinTable 1, whereeveryvalueis
a n a v e r a g e of t h r e e measurements a t e a c h t e m p e r a t u r e .
A c t i v a t i o n e n e r g y f o r d i f f u s i o n by t r a n s l a t i o n a l motion was e v a l u a t e d t o be 2 3 . 5 kJ/mol a s i s shown i n F i g . 6 . F o r comparison, t h e d i f f u s i o n c o e f f i c i e n t i n a s i n g l e c r y s t a l by I t a g a k i ( l 7 ) , i n p o l y c r y s t a l l i n e i c e by Kuhn and T h i i r k a u f ( l 8 ) and i n w a t e r ( l 4 ) a r e a l s o shown i n
t h e same f i g u r e .
The a b s o l u t e v a l u e of t h e d i f f u s i o n c o e f f i c i e n t o f t h e Q.L.L. i s
a b o u t f o u r o r d e r s of magnitude s m a l l e r t h a n t h a t o f w a t e r ; however, i t
i s remarkable t h a t t h i s v a l u e i s l a r g e r than t h a t of a s i n g l e c r y s t a l of
i c e by two o r d e r s . I n r e g a r d t o t h e a c t i v a t i o n e n e r g y f o r d i f f u s i o n , t h a t
of t h e Q.L.L.
i s s l i g h t l y l a r g e r t h a n t h a t of l i q u i d w a t e r b u t i s o n l y
a b o u t a t h i r d of a s i n g l e c r y s t a l of i c e .
Temperature
Table 1
Diffusion c o e f f i c i e n t
*rat*, (5-2O.C)
D - Z ~ ~ O - * rnlsec"
18.9 rJ. moi'
'.,'.
'.,
single crystd(ref.17)
63.1 kI.mol1
(065eV)
Figure 5. Tlpvariation with radio frequency at -lO°C; plotted 1/Tlp vs. w:/*
IV.
Figure 6. Diffusion coefficient of the
Q.L.L. vs. inverse temperature
Discussion and Conclusion
The i n t e n s i t y o f t h e NMR s i g n a l was l a r g e l y dependent on t h e p a r t i I n f a c t , i n o u r experiment u s i n g i c e p a r t i c l e s l a r g e r than
cle size.
200 pm i n d i a m e t e r , t h e s i n g n a l was small and f a i n t even a t -lO°C.
However, t h e s i z e of an i n d i v i d u a l c r y s t a l i n an i c e p a r t i c l e was mostl y independent of t h e p a r t i c l e s between 50 and 500 pm i n d i a m e t e r .
Therefore t h e NMR s i g n a l i s c o n s i d e r e d t o be due mainly t o i n n e r o r
o u t e r f r e e s u r f a c e s and t h e c o n t r i b u t i o n from g r a i n . b o u n d a r i e s seems t o
Undoubtedly, t h e e x i s t e n c e of t h e mobile water
be s m a l l i n t h i s c a s e .
phase a t g r a i n boundaries a t v e r y c l o s e t o t h e m e l t i n g p o i n t h a s been
shown by Ohtomo and Wakahama(l9).
F u r t h e r s t u d i e s a r e needed t o c l a r i f y t h e d i f f e r e n c e between t h e dynamical p r o p e r t i e s of a f r e e s u r f a c e
and of a g r a i n boundary, because molecules a t t h e g r a i n boundary a r e
expected t o have a h i g h e r c r y s t a l l i n i t y t h a n t h o s e i n a f r e e s u r f a c e .
A s t h e s u r f a c e a r e a d e c r e a s e s due t o s i n t e r i n g between i c e part i c l e s , t h e i n t e n s i t y v a r i a t i o n w i t h temperature does n o t correspond t o
Regardless o f
t h e t h i c k n e s s v a r i a t i o n o f t h e Q.L.L. w i t h t e m p e r a t u r e .
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JOURNAL D E PHYSIQUE
t h e l a r g e v a r i a t i o n o f t h e i n t e n s i t y between -5OC and -lO°C, t h e l i n e
width d o e s n o t change v e r y much.
This f a c t suggests t h a t t h e thickn e s s o f t h e Q.L.L. changes l a r g e l y w i t h i n t h i s t e m p e r a t u r e range ;
however, v e r y s m a l l changes o c c u r i n t h e dynamical p r o p e r t i e s .
I n o u r e x p e r i m e n t , t h e NMR s i g n a l due t o t h e mobile molecules a t
t h e s u r f a c e was observed even a t a t e m p e r a t u r e o f a s low a s - l O O ° C .
This f i n d i n g i n d i c a t e s t h a t some s u r f a c e molecules can r o t a t e a t a
much h i g h e r f r e q u e n c y t h a n i n b u l k i c e even a t - l O O e C , however, i t
should n o t be c o n s i d e r e d t h a t t h e Q.L.L.
s t i l l remains a t such a low
temperature.
The number o f mobile m o l e c u l e s is dependent n o t o n l y on t h e temp e r a t u r e b u t a l s o on t h e degree of t h e p e r f e c t i o n and t h e c r y s t a l l o g raphic o r i e n t a t i o n of the surface.
Our r e s u l t d i f f e r s l a r g e l y from
t h e e l l i p s o m e t r i c a l o b s e r v a t i o n (11) o f t h e t e m p e r a t u r e a t which t h e
mobile phase a p p e a r s .
The d i f f e r e n c e i s c a u s e d mainly by t h e d i f f e r ence i n t h e power o f d e t e c t i o n o f each e x p e r i m e n t a l method t h a n by t h e
d i f f e r e n c e i n t h e sample.
The q u e s t i o n "how many mobile m o l e c u l e s
make t h e s u r f a c e v e r y l i q u i d - l i k e ?I1 can n o t be answered from t h e r e s u l t s o f o u r experiment u s i n g NMR; however, t h i s method does p r o v i d e
i n f o r m a t i o n on t h e s u r f a c e molecule motion.
I t was found t h a t t h e m o l e c u l e s a t t h e s u r f a c e r o t a t e a t a f r e quency o f about f i v e o r d e r s l a r g e r t h a n t h a t o f c r y s t a l l i n e i c e a t
t e m p e r a t u r e s between 0 t o -20°C, and t h i s f r e q u e n c y c o r r e s p o n d s t o
only a b o u t 1 / 2 5 o f t h a t o f a molecule i n l i q u i d w a t e r .
Regarding d i f f u s i o n by t h e t r a n s l a t i o n a l motion, t h e s u r f a c e molec u l e d i f f u s e s a t a r a t e o f a b o u t two o r d e r s l a r g e r t h a n t h a t i n b u l k
ice.
I t can be concluded t h a t t h e s u r f a c e molecule p o s s e s s e s some
p r o p e r t i e s which a r e much c l o s e r t o t h o s e o f l i q u i d w a t e r t h a n t o
t h o s e o f c r y s t a l l i n e i c e , b u t t h e y a r e a p p a r e n t l y d i f f e r e n t from t h o s e
of l i q u i d w a t e r even a t t e m p e r a t u r e s v e r y c l o s e t o t h e m e l t i n g p o i n t .
The a c t i v a t i o n e n e r g y b o t h f o r t h e r o t a t i o n a l and t h e t r a n s l a t i o n a l motion o f t h e s u r f a c e molecule a p p e a r t o be l o c a t e d between
t h o s e o f l i q u i d w a t e r and c r y s t a l l i n e i c e .
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-
COMMENTS
E. OFFENBACHER
Can you estimate the thickness of the Q.L.L.
signals and your sample parameters ?
from the relative intensity of your
Answer :
Yes I can estimate the thickness of the Q.L.L. by assuming the specific surface
area, but in our experiment, especially at higher temperature (-5OC and -lO°C), the
surface area reduces by sintering during experiment and further correction is
required.
P. PISSIS
I think, it is important for such measurements to have a large surface/volume ratio.
I wonder, in this connection, why you don't use emulsified water droplets where you
can easily get droplets of a fewrm in diameter. Is any reason for not using such
systems ?
Answer :
To obtain the MNR signal due to ice surface, the sample with the larger
surface/volume ratio is the better. However the purpose of our study is to know the
properties of the quasi-liquid layer between air and crystalline ice.
So we used rather large ice particle but with free outer surface.
P.L.M.
PLUMMER
I am very pleased to see your very nice results. My interpretation of your results
suggest that since the rotational times of the quasi liquid layer are very similar
to those of liquid water but the diffusion times are between those of liquid and
solid suggest the layer can also be described as quasi-solid amorphous layer with a
high concentration of defects, no long range order and a high degree of rotational
freedom. Do you agree and could you amplify on your opinion of the structure of this
layer implied by your data ?
Answer :
Yes. I agree with you basically. We assume that diffusion takes place with molecular
unit and we evaluated the spin to spin distance to be about 4 8, so some crystalline
structure is expected to be remained in the quasi-liquid layer.
Remark of J.W. GLEN :
Relative to Dr PLUMMERrs comment, the values of D at 10-l2 m2 l's
are about half way between those of water ( N 10-9 m2 s-l) and ice
and the activation energy is more like that of water.
from this paper
m2 s-'1,
( N 10-l5