MONTE CARLO SIMULATION OF ICE Ih : COMPARISON OF BULK MELTING AT CONSTANT PRESSURE AND STRUCTURE OF ICE LAYERS ON AN ICE NUCLEATING SUBSTRATE

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Submitted on 1 Jan 1987

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MONTE CARLO SIMULATION OF ICE Ih :

COMPARISON OF BULK MELTING AT CONSTANT PRESSURE AND STRUCTURE OF ICE LAYERS ON

AN ICE NUCLEATING SUBSTRATE

B. Hale, K. Han

To cite this version:

B. Hale, K. Han. MONTE CARLO SIMULATION OF ICE Ih : COMPARISON OF BULK MELTING AT CONSTANT PRESSURE AND STRUCTURE OF ICE LAYERS ON AN ICE NUCLEATING SUBSTRATE. Journal de Physique Colloques, 1987, 48 (C1), pp.C1-681-C1-683.

�10.1051/jphyscol:19871107�. �jpa-00226248�

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JOURNAL DE PHYSIQUE

C o l l o q u e C1, s u p p l 6 m e n t a u n o 3 , Tome 4 8 , m a r s 1 9 8 7

MONTE CARL0 SIMULATION OF ICE I h : COMPARISON OF BULK MELTING

AT CONSTANT PRESSURE AND STRUCTURE O F ICE LAYERS ON AN ICE NUCLEATING SUBSTRATE' )

B . N . HALE a n d K.K. HAN

D e p a r t m e n t of P h y s i c s a n d G r a d u a t e C e n t e r of C l o u d P h y s i c s R e s e a r c h . U n i v e r s i t y o f M i s s o u r i - R o l l a , R o l l a , MO 65401, U . S . A .

Abstract : Recently e f f e c t i v e p a i r p o t e n t i a l s (1) and Metropolis m n t e Carlo methods have been used t o study t h e melting of a periodic r i g i d molecule model ice system a t constant volume (2,3) near 290 K. W have extended these s t u d i e s t o exami- e nation of t h e system a t constant pressure and present t h e r e s u l t s f o r approximately 1 atm pressure. I n t h i s approach t h e constant n-r, pressure and temperature (W) ensemble is approximated by t r e a t i n g t h e volume a s an a d d i t i o n a l v a r i a b l e i n t h e Metropolis Monte Carlo procedure (4-7). The u n i t cell for these c a l c u l a t i o n s con-

t a i n s 192 r i g i d c e n t r a l force (1) water molecules and t h e i n i t i a l configurations a r e taken from t h e constant number, volume and temperature (NVT) e q u i l i b r a t e d system (3) a t 260 K. T h i s i n i t i a l ice I h u n i t cell has approximately zero d i p o l e and quadrupole moments and was shown t o remain i n the i c e I h s t r u c t u r e over a range of temperature from 20 K t o about 290 K i n constant NVT ensemble studies. The pressure is found to be extremely s e n s i t i v e to t h e intermolecular i n t e r a c t i o n s and t o t h e instantaneous density of molecules i n t h e u n i t cell. The u n i t cell p r o p e r t i e s (dipole m n t , ice s t r u c t u r e f a c t o r s , s p e c i f i c heat, and p a i r c o r r e l a t i o n functions) w i l l be presented.

A comparison w i l l be made with simulations of two water l a y e r s on a model ice nu- c l e a t i n g s u b s t r a t e (8) a t 200 K and 265 K near zero pressure. A t 200 K t h e s t r u c t u r e of t h e t o p l a y e r of t h i s system shows considerable disorder and liquid- l i k e proper- ties, while t h e water l a y e r adjacent to t h e s u b s t r a t e has a s o l i d ice- l i k e hexago- n a l ring s t r u c t u r e . There appears t o be no preference f o r water d i p o l e o r i e n t a t i o n i n t h e exposed layer of water molecules. The liquid-like p r o p e r t i e s of t h e exposed l a y e r s i n t h i s system a t 200 K and t h e melting of t h e bulk near 290 K a r e c o n s i s t e n t with recent observations t h a t s u r f a c e l a y e r s have noticably reduced solid-liquid t r a n s i t i o n temperatures (9). When these absorbed water l a y e r s a r e subjected to a l a r g e e x t e r n a l electric f i e l d o r constant presure (rv 200 atm) t h e r e appears to no s i g n i f i c a n t change i n t h e exposed l a y e r s t r u c t u r e and l i q u i d - l i k e s t a t e s . Unit cell p r o p e r t i e s f o r t h e l a y e r systems w i l l be discussed. The motivation for these s t u d i e s has been to examine t h e e f f e c t of pressure, temperature and other e x t e r n a l perturba- t i o n s (such a s s u b s t r a t e s t r u c t u r e and s u b s t r a t e d e f e c t s ) on atmospheric ice nucleation.

References

(1) S t i l l i n g e r F. and Rahman, A,, J. Chem. Phys. 68, (1978) , 666.

(2) Deutsch, P.W., Hale, B.N., Ward, R.C. and Reago D.A., J r . , J. Chem. Phys. 78, (1983)

.

^5103.

(3) tieutsch P.W., H a l e B.N., Ward R.C. and Reago D.A., J. Phys. Chem. 87, (1983), 4309.

(4) Metropolis M., Rosenbluth A., Rosenbluth M., T e l l e r A. and T e l l e r E., Phys. 21, (19531, 1087. See a l s o Barker J.A. and Watts R.O., Chem. Phys. Lett. 3, (1969), 144.

(5) Wood, W.W., P h y s i c s o f Simple L i q u i d s , E d i t e d by R.N.V. Temperley, F.S.

Rmlinson and G.S. Rushbrooke, North-Holland (1968).

his work is supported in part by National Science Foundation under Grant ATN83-10854

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19871107

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C1-682 JOURNAL DE PHYSIQUE

(6) McDonald I.R., Molec. Phys. 32, (1972) , ^41.

(7) Mezei, M., Molec. Phys., 48, (1983), 1075.

(8) Taylor, J.H. and Hale, B.N., to be p u b l i s h e d .

(9) Frenken J.W.M. and ven der Veen, J.F., Phys. Rev. L e t t e r s 54, (1985), 134.

COMMENTS

N. FUKUTA

It a p p e a r s you modelled w a t e r molecules on t h e b a s a l p l a n e o f AgI. A s you know, t h e r e a r e two k i n d s of t h e s u r f a c e . One is Ag i o n s exposed and t h e o t h e r I i o n s exposed. Which one d i d you model ? What a b o u t t h e e f f e c t o f t h e o t h e r ?

Answer :

We modelled w a t e r l a y e r s on t h e i o d i n e exposed b a s a l f a c e o f AgI. However , we d i d model w a t e r monomer on t h e s i l v e r exposed b a s a l AgI f a c e a r e on a prism AgI f a c e . The h i g h w a t e r monomer b i n d i n g s i t e s on t h e s i l v e r exposed b a s a l AgI f a c e showed a hexagonal symmetry v e r y s i m i l a r t o t h e h i g h monomer bending s i t e s on t h e i o d i n e exposed f a c e . Thus we e x p e c t t h a t t h e s i l v e r exposed b a s a l f a c e would s u p p o r t a n adsorbed H20 l a y e r system which is q u a l i t a t i v e l y t h e same a s t h e r e s u l t s we r e p o r t e d h e r e . There c o u l d be, however, some d i f f e r e n c e s i n t h e p o l a r i z a t i o n o f t h e adsorbed water.

J. DUPUY

What a r e t h e f a c t o r s o r p r o p e r t i e s o f t h e s u b s t r a c t which i n f l u e n c e t h e p r o p e r t i e s o f w a t e r l a y e r s ?

Answer :

L a t t i c e c o n s t a n t , w a t e r - s u b s t r a t e s t r e n g t h o f bonding, p r o p e r t i e s o f t h e r e p u l s i v e c o r e a n d d e p t h o f t h e p o t e n t i a l w e l l s ( d i f f u s i o n b a r r i e r s ) a r e some o f t h e m i c r o s c o p i c p r o p e r t i e s which we e x p e c t w i l l a l t e r t h e s t a b i l i t y and s t r u c t u r e o f t h e adsorbed w a t e r l a y e r s .

P. PISSIS

Your r e s u l t s w i t h AgI show t h e e x i s t e n c e o f a d i p o l e moment # ⁰o f t h e t o p l a y e r . Do you t h i n k t h a t t h i s i s a g e n e r a l p r o p e r t y o f w a t e r l a y e r s on s u b s t r a t e s ?

Answer :

A t t h i s p o i n t it i s n o t p o s s i b l e t o say. We p l a n t o model a n i c e b a s a l f a c e s u r f a c e and compare t h i s i c e s u r f a c e l a y e r s p r o p e r t i e s w i t h t h o s e o f t h e adsorbed w a t e r l a y e r s on AgI.

J.S. TSE

The s e l f - d i f f u s i o n r a t e o f w a t e r i n i c e c a n , by d e f i n i t i o n , be computed i n e i t h e r iVIC o r MD experiments. However, it may n o t c o r r e s p o n d s t o t h e d i f f u s i o n r a t e observed i n t h e r e a l system where Bjerrum d e f e c t s a r e p r e s e n t . I n p r i n c i p l e , one can a l s o perform s i m u l a t i o n s w i t h Bjerrum d e f e c t s b u i l d i n t o t h e conformation o f t h e w a t e r molecules i n t h e s i m u l a t i o n box.

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Answer :

Yes. U n f o r t u n a t e l y one d e f e c t i n o u r u n i t c e l l f o r t h e b u l k i c e a t low t e m p e r a t u r e would correspond t o a n u n r e a l i s t i c a l l y h i g h c o n c e n t r a t i o n o f d e f e c t s . Only a t high t e m p e r a t u r e s j u s t p r i o r t o m e l t i n g do we s e e e v i d e n c e o f d e f e c t s i n t h e u n i t c e l l .

J.S. TSE

The i n t e r m o l e c u l a r p o t e n t i a l f o r w a t e r i n t e r a c t i o n d o e s n o t a l l o w t h e change o f t h e p o l a r i z a b i l i t y . T h e r e f o r e , t h e s c r e e n i n g e x p e r i e n c e d by t h e second I c e l a y e r i s o n l y a p p r o x i m a t e l y c o r r e c t .

Answer :

Yes, t h e w a t e r molecules a r e r i g i d i n t h i s model. I t would indeed be i n t e r e s t i n g t o a l l o w f o r i n t r a m o l e c u l a r d e f o r m a t i o n s . We p l a n t o i n v e s t i g a t e t h i s e f f e c t .

T. KURODA

You showed t h a t t h e f i r s t l a y e r on AgI s u b s t r a t e is i c e - l i k e . Does t h i s l a y e r melt a t more h i g h e r t e m p e r a t u r e ?

Answer :

We d i d n o t o b s e r v e m e l t i n g o f t h e f i r s t l a y e r below 425K. However, t h i s f i r s t l a y e r shows i n c r e a s i n g d i s o r d e r as t h e t e m p e r a t u r e i n c r e a s e s and pne would e x p e c t t h a t t h i s l a y e r s h o u l d melt a t some t e m p e r a t u r e between 300K and 425K. T h i s is a n e f f e c t which we p l a n t o i n v e s t i g a t e .

J.M. WARMAN

I t i s u s u a l i n d i s c u s s i n g d i f f u s i o n ( a n d m e l t i n g ) i n c r y s t a l l i n e m a t r i c e s t o i n t r o d u c e vacancy o r s e l f i n t e r t i t i a l p o i n t d e f e c t s t o a l l o w f o r mass t r a n s p o r t . Do you s e e any evidence i n your s i m u l a t i o n s o f such d i s c r e t e d e f e c t s a p p e a r i n g under c o n d i t i o n s c o r r e s p o n d i n g t o a system i n which d i f f u s i o n is o c c u r i n g b u t t h e medium h a s n o t y e t melted?

Answer :

Our bulk i c e I h p e r i o d i c u n i t c e l l was i n i t i a l l y c o n s t r u c t e d w i t h o u t d e f e c t s . ( A s i n g l e d e f e c t i n t h e c e l l would have c o r r e s p o n d e d t o an u n r e a l i s t i c a l l h i g h c o n c e n t r a t i o n o f i m p u r i t i e s . ) Oxygen motion i n t h e b u l k i c e s y s t e m s modelled a t low t e m p e r a t u r e s was c o n s i s t e n t w i t h t h e r m a l (harmonic) v i b r a t i o n s i n a s o l i d . However, a t h i g h e r t e m p e r a t u r e s , t h e systems can develop d e f e c t s s i n c e t h e w a t e r m o l e c u l e s have freedom t o t r a n s l a t e and r o t a t e . P r i o r t o m e l t i n g l o c a l i z e d d e f e c t s a r e observed. Without t h e s e d e f e c t s t h e system c o u l d n o t melt.