NEUTRON DIFFRACTION STUDIES OF WATER IN THE NORMAL AND SUPER-COOLED LIQUID PHASE

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THE NORMAL AND SUPER-COOLED LIQUID PHASE

J. Dore

To cite this version:

J. Dore. NEUTRON DIFFRACTION STUDIES OF WATER IN THE NORMAL AND SUPER- COOLED LIQUID PHASE. Journal de Physique Colloques, 1984, 45 (C7), pp.C7-49-C7-64.

�10.1051/jphyscol:1984705�. �jpa-00224266�

J O U K N A L

DE PHYSIQUE

Colloque C7, supplément au n09, Tome 45, septembre 1984 page C7-49

NEUTRON DIFFRACTION STUDIES OF WATER

I N

J . C . Dore

Physics Laboratory, University

Kent a t Canterbury, Kent,

Résumé

On décrit ici les progres accomplis récemment dans llutilisation des methodes de diffraction des neutrons permettant l'etude des propriétes micro-

scopiques de l'eau. La détermination de la configuration moleculaire fait res- sortir combien elle s'étire sous l'effet de la liaison hydrogène. Les

études des variations de température indiquent une modification sensible des configurations moléculaires locales qui s'apparentent a la structure en reseau de la glace amorphe. Les études des melanges composes de H29'Q0 peuvent donner des éclaircissements sur les fonctions g(r) partielles mais l'interprétation s'en trouve compliquée du fait de l'apparente non equivalence de H et de D. Des études préliminaires sur l'eau en silice poreuse sont également presentées.

Abstract

Recent advances in the use of neutron diffraction methods for study- ing the microçcopic properties of water are described. The determination of the molecular conformation shows the effective stretching due to hydrogen bond- ing. Temperature variation studies indicate significant re-arrangement of local molecular configurations which are related to the network structure of amorphous ice. Studies of H20/D20 mixtures can give information on partial g(r) functions but the interpretation is complicated by the apparent non-equivalence of H and

Some preliminary studies of water in porous silica are also presented.

1

INTRODUCTION

The detailed structural arrangement of molecules in liquid water has been of funda- mental interest for some considerahle time and significant advances in the quantita-

tive formulation of the structural characteristics have made steady progress over a period spanning the last three decades. During this time there have been several developments in the experimental methodç used to tackle this central problem in liq- uid state physics. It has been recognised from early tintes that hydrogen-bonding plays a major role in both the structural and dynamic properties of water but how this influences the specific behaviour is still open to question, particularly in relation to the 'so-called' anomalous characteristics of the density maximum and the divergent values of several bulk properties in the deeply super-cooled region. These features have been re-emphasised in talks at this 'Workshop' by Stanley Cl1 and, with a more direct relevance to structural arrangements, by Geiger C21. The purpose of the present talk is to give a current s m a r y of the experimental investigation of water "structure" with an emphasis on neutron diffraction results. This is essenti- ally an interim report in a continuing saga involving the characterization of this complex liquid C31.

The basic information on the timer-averaged structure is represented hy the three partial pair-correlation functions g00(r), g o f i ( ' ) and g~~(r). In principle, three independent diffraction measurements can therefore yield the required data but in practice this proves to be extremely difficult (Sec:4) and a definitive set of func- tions have not yet been obtained even at one temperature. The X-ray studies of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984705

Narten and Levy C41 have provided the basic data f o r the g m ( r ) correlations which approximate t o the d i s t r i b u t i o n of molecular centres; the other two p a r t i a l functions e f f e c t i v e l y define the orientational correlations between adjacent molecules and a r e influenced by the d e t a i l e d form of the inter-molecular potential. The expected shape of the g o ~ ( r ) and g m ( r ) functions i s shown in(Fig.1) based on computer simulations and a l s o indicates the molecular configurations responsible f o r t h e main peaks a t low r-values. However, the s t r u c t u r a l d e t a i l s are obviously dependent on the way the hy- drogen-bonding features are incorporated i n t o the p o t e n t i a l and there i s therefore a need f o r accurate experimental data on ' r e a l ' water which can then be compared with predictions from d i f f e r e n t models .

Fig.1 - The p a i r correlation functions g o ~ ( r ) and g ~ ~ ( r ) f o r water obtained from computer simulation, showing the short-range e f f e c t s due t o hydrogen bonding.

0 2 - _1- I -g""

0 ' " ' ~ ' ~ '

0 1 2 3 4 5 6 7 8

DISTANCE BETWEEN ATOMS LA)

2 -

THEORY

a) The Structure Factor

The t h e o r e t i c a l formalism f o r d i f f r a c t i o n studies of molecular liquidç has been presented by Powles C51 and B l u m and Narten C61. We adopt the notation of C51 and w r i t e the l i q u i d s t r u c t u r e f a c t o r SM(Q) as

where

the s c a t t e r i n g vector,

is the number of molecules, b i and bj a r e the coherent s c a t t e r i n g lengths of nuclei

and j a t a separation, r i j ; the summation extends over a l 1 p a i r s

j of nuclei and the

brackets denote an ensemble aver- age.

Since the sample i s i s o t r o p i c , a spherical average may be taken and it i s convenient t o divide the s m a t i o n i n t o intra-molecular and inter-molecular t e m . This can be conveniently expressed as

where fi(Q) is a molecular form-factor which i s dependent on the conformation of individual molecules and DM(Q) characterises t h e arrangement of the molecules i n the l i q u i d phase. For D20 water, the molecular form-factor may be written as

where r 0 ~ and

a r e the mean intra-molecular distances and the y-factors repre-

sent t h e vibration amplitudes.

b) The cross-section

The differential cross-section d~/&(e,x) in units of barn sterad-1 molecule-]

is measured for the sample corresponding to the intensity of scattering at an angle e for an incident wavelength, A. This experimental quantity is related to the structure factor, SM(Q), where Q is defined for elastic scattering by

~ = 4 "

sin

2 2.4

Within the static approximation, the relation for the coherent scattering may be simply written as

1 ^(bo

2bD12 SM(Q) 2.5

but this is notapplicable for the conditions of most experiments. This factor nece- ssitates a detailed evaluation of procedures to allow for experimental corrections

(container scattering, absorption, multiple scattering) and for analytic corrections (incoherent contributions, inelasticity effects). The technical aspects of these corrections may affect the final results but the details are beyond the scope of this brief report; relevant early references for D20 are presented in work byPowles C5,71 and Narten C6,81. The overall behaviour of the differential cross-se~tion for different wavelengths is shown in(Fig.2) Cg]. For long wavelengths

1.5 A) the

limiting value of Qmax from eqn.2.4 restricts the %ta to relatively low Q-values whereas, the low flwc for short wavelengths

0.5 A) means that the statistical err-

ors may be increased with consequent lack of precision in the diffraction data. The inelasticity corrections are generally reduced for the shorter wavelengthg and the most effective value for reactor neutrons usually falls in the 0.5 - ^{1.0 A range;}

the use of a hot-source in the reactor is therefore advantageous for liquid studies of this kind.

Fig.2 - The neutron scatter- ing cross-section from liquid D20 at different wavelengths.

c) Difference measurements

Structural changes with respect to temperature or pressure, can be conveniently studied by a first-order difference technique which eliniinates many of the problems of systematic uncertainties in the data treatment [IO]. The change in the structure factor relative to that for a reference temperature, To, may be written as

A%(Q,T)

%(Q9T)

Sf,l(Q.To)

DM (Q,T) 2.6

if fl(Q) is temperature-independent. The change in the real-space correlation func- tion is then given by a similar transform relation

This treatment incorporates the effects due to the change of bulk density but a re- finement of the method has been used for water since this exhibits a density maximum and a pair of temperatures may be chosen in which the density is equal. This enables the isochoric temperature derivative @s/~T) to be evaluated C111.

P

d) Partial correlation functions

Any diffraction measurement on H,O (or D,O) water may be used to give a real space-distribution dL(r) which will contain a weighted s m of the three partial pair- correlation functions goo(r), gOH(r) and gW(r), i.e. for a two component system of A and B atoms

where cA, cg and bA, b are the respective concentrations and scattering amplitudes of each component . ltBis therefore possible, in principle, to separate the individ- ual partial functions if three (or more) independent diffraction measurements can be made in which the weighting factors are varied. This method is particularly puwer- ful in the case of aqueous solutions as indicated by Neilson Cl21 where the use of isotopic substitution can give the necessary variation in the relative scattering amplitudes of the different components. The application of a similar method to the study of water, however, leadç to a number of complications which are discussed in Section 4.

3 -

NEUTRON SCATTERING BI' D20 WATER AND AMORPHOUS ICE a) Molecular conformation

In the early studies of Walford and Dore L131, it was noted that the oscillatory part of the diffraction vattern at hiph O-values was not in ~ o o d agreement for dif- ferent incident wavelenGhs. This isuduè to the fact that tce effective maçs of the molecular unit (20 amu) is not large compared with the m a s of the neutron and the complete molecule undergoes a recoil in the scattering process (Fig.3). This molecu- lar recoil effect is yet another aspect of the inelasticity corrections which apply to the interference terms of eqn.2.3. Powles, in a series of papers [141 has de- veloped a theoretical formalism, for handling these corrections in a gas-like (free recoil) approximation; several others have adopted alternative methods. 1151.

Fig.3

A comparison of the uncorrected cross-section data showing the effect

of molecular recoil.

Powles re-anal sis of the data Cl41 in terms of the fl(Q) function gives a value of 0.981

O . M 8 2 for the r O ~ bond-length and a DûD angle of 104

20 . The correspond- ing values for other phases are given in Table 1; this shows a systematic variation in the molecular conformation with the degree of hydrogen-bonding. The rnolecule is apparently 'stretched' by the II-bonding interactions and this phenomenon has now been observed in diffraction studies of a number of other hydrogen-bonded liquids.

C15,161.

Table 1: The intra-molecular bond length for D20 in various phases Phase

liquid 0.98 a- ice 1

ice-Ih 1 .O1 4 7

The effects are present in the specific interactions of neighbouring molecules and therefore have an influence on the normal mode vibrations of the individual molecules.

It is well hown that hydrogen-bonding h a a large effect on the Raman spectra of molecules in the condensed phase and it is only in recent years that progress has been made in understanding the complex behaviour that is seen in the experimental results C161. It can now be appreciated that molecular conformation is an import- ant piece of supplementary information which will be needed to interpret the avail- able data. New facilities C17,181 are likely to provide improved techniques for a more detailed investigation of these features during the next decade.

b) Temperature variation studies

For most molecular liquids that have no association properties the spatial cor- relations are primarily influenced by the overall shape of the molecule Cl91 and the variation of temperature has little effect on the distribution except from minor changes due to the small variation density. In contrast to this, it is found that water and other hydrogen-bonded liquids exhibit substantial changes with respect to

temperature. The classic X-ray experiments of Narten and Levy [41 were made over a wide temperature range and showed a systematic variation in the diffraction pattern.

As stated earlier, the X-ray measurements are mainly dependent on the oxygen corre- lations and give little information on orientational effects. It therefore follows that neutron studies provide necessary complementary information on the structural changes due to temperature variation.

A series of neutron experiinents on D,O water in the normal liquid statehas been made by the UKC group Cl01 and other groups [20,211. The most obviow effect is a systematic displacement in the position of the main diffraction peak as the tempera- ture is varied; it is even possible to measure the approximate temperature of the sanple by this means! The combined results are shown in (Fig.4) including more re- cent results for the super-cooled state. The density maximum for D20 water is llOC

-20 -10 O 10 20 30 40 50 80 70 80 TEMPERATURE 1%

Fig.4

The shift in the pos'ition

of the main diffraction

peak of liquid D20 as a

function of temperature.

(cf 4OC for H20) and the density decrease above this temperature would be expected to shift the peak to a lower(2-value. It is therefore clear that there is a signifi- cant re-arrangement of the local molecular structure.

The detailed behaviour can be conveniently studied by means of the first-orcler dif- ference method. The function A%(Q,T) is shown in (Fig. 5) Ceqn.2.6 of Sec. 2 (c) 1 for several incident neutron wavelengths. The results are in good agreement and show that the variations in the diffraction profile are not restricted to the region of the main peak. Fourier transformation of the data (eqn.2.7) gives the struct-al change in real space, AdL (r,T) and is shown in (Fig .6) . At large r-values ( s 6 A) the changes are consistent with the loss of 'long-range' order as he temperature is raised but the shape of the curves in the intermediate region(3-6 h

indicate that there is a complex change in the local molecular environment. Due to the anomalies exhibited in the deeply super-cooled region it was natural to ask how these changes would be represented as the temperature was reduced below the normal freezing point.

a UKC/Saclay collaboration C221 showed that the systematic trends continued do'm to -150C which was the limiting temperature for the capillary samples used in the ex- periment .

Fig.5 - The function ADM(Q,T) for liquid Fig.6 - The corresponding real-space D20 using a reference temperature funcyion dL (r,T) obtained from

To, of ll°C. Fig.5.

Other work by different groups has resulted in similar conclusions. Egelstaff, Chen and collaborators C201 have brought a refinement to the method by utilizing the fact that the density of the liquid is equal at two temperatures above and below 11%.

It is therefore possible to completely remove the density effect by combining data from equivalent pairs of temperatures and to evaluate the isochoric temperature derivative (aS/aT) as described in Sec.2~. They also show that molecular dynamics cornputations usingPthe MCY potential under-estimate the magnitude of the observed changes.

These experiments demonstrate that water is a "fragile" liquid which is responsive

to relatively minor perturbations caused in changing the temperature by a few de-

grees. This is undoubtedly linked to orientational correlations which are dependent

on the hydrogen-bonding interactions and it is not surprising that existing forms of

the inter-molecular p o t e n t i a l are unable t o adequately reproduce these d e l i c a t e features. The key t o the i n t e r p r e t a t i o n of these r e s u l t s comes from a separate s e t of experiments .

c) The s t r u c t u r e of amorphous i c e

The amorphous o r "glassy" form of water has been known f o r m a n y years. Rice C231 has part'icularly d?awn a t t e n t i o n t o i t s features as a possiblémodel f o r inter- preting the properties of water. X-ray d i f f r a c t i o n r e s u l t s have been given by Narten, Venkatesh and Rice 1241 and a wide-ranging survey, including spectroscopic information, has been presented by Sceats and Rice C251. Neutron d i f f r a c t i o n studies of vapour-deposited D20 i c e have been made by Chowdhury, Dore and Wenzel 1261. The

%(Q) data a r e shown i n (Fig.7), the corresponding DM(Q) and d ( r ) functions a r e given i n (Fig.8) with the equivalent curves f o r water. A s expected, the stronger correlations i n the disordered s o l i d give an increased o s c i l l a t o r y structure and several well-resolved peaks are c l e a r l y i d e n t i f i e d a t s h o r t distances.

Fig. 8

The DM(Q) and d ( r ) functions f o r a-D20 and l i q u i d

1 0 -

0 6

0 4 -

0 2 -

The description of many amorphous materials has been based on the concept of a con- tinuous random network

model C271. There has been a p a r t i c u l a r i n t e r e s t i n four-fold connected networks due t o the importance of amorphous semiconductors such as a-Ge and a-Si. Boutron and Alben C281 have adapted these concepts t o the s t r u c t - ure of amorphouç i c e i n which the oxygen atoms represent the tetrahedrally co-ordi- nated network-and the H (or D) atoms a r e placed a t appropriate positions on the short-range 00 bonds. The p a r t i a l p a i r correlation functions can then be evaluated from the model

comhined (ea,n. 2.8) t o give the composite d ( r ) fimction obtained

O L 12 16 20

~ ( A O ' I

'.

:\

: ^-

:

I , l l , , , , t ,

Fig.7

The s t r u c t u r e f a c t o r Sjq(Q) f o r a-D20 with the molecular form-factor,

f 1

(QI .

from the neutron experiments. The model predictions are shown in (Fig.9) and are in remarkably good agreement with the neutron data. This indicates that a-D20 is formed as a complete random hydrogen-bonded network based on local tetrahedral co- ordination involving two 'donor' and two 'accepter' hydrogen bonds; the structural unit is s h o m in (Fig.9) and is representative of a small part of the ice Ih lattice.

The peaks in d(r) therefore result from the short-range correlations across the tetra- hedral unit but it is interesting to note that theonetwork closure conditions also impose structure in the intermediate range

3-6 A) and this behaviour is of particu- lar significance for the structural relations in water.

0.6

'

iimorpnour D 2 0 - ire

Fig.9

A comparison of d(r) for a-D20 with predictions from the

model based on local tetrahedral col.ordination.

d) Structural variations and the super-cooled state

A comparison of the temperature-variation data, Aci~(r,T) for water with the structural results d(r) for the amorphous solid, a-D20, is highly instructive 1221.

The data given in (Fig.6) are consistent with a tendency to develop increased corre- lations in accordance with the network structure as the temperature is reduced. The composite g(r) curve for two temperatures is shown in (Fig.10) and illustrates an increase in the close overlapping hydrogen-bonding OD and DD distances (Fig.1) which are much broader for the liquid than the well-defined peaks of the solid phase.

However, it is the similar behaviour at larger r-values which is of greater import- ance since this indicates that the changes also affect the second hydrogen-bonded neighbours. These findings suggest that the geometrical features of the network structure are retained in the dynamic disordered state of the liquid phase. In this sense the basic structural information is in agreement with the concepts of hydrogen-bonded "patches" presented by Stanley Cl1 and Teixeira C291 at this meeting.

Fig.10

The g(r) function for D20 in normal liquid, super- cooled liquid and amorphous

o,o r 2 1 t

phases.

O 6 O 4

The r e s u l t s suggest t h a t it is now important t o extend the measurements on the super- l i q u i d t o even lower temperatures. The d i f f r a c t i o n peak f o r a-DnO

a t

;(':Fi-

and the speculative extrapolation of the curve i n (Fig.4) indicates t h a t t h i s point would be reached i n the v i c i n i t y of -400C, i . e . close t o the Ange11 temp- erature, Tc, which r e l a t e s t o the anomalous behaviour a t low terriperatures 1301. Oiie might expect the correlation functions t o show a continuing evolution towards the network s t r u c t u r e as t h e temperature

reduced. One d i f f i c u l t y with t h i s view is t h a t amorphous i c e is unstable above

140 K C311 and t h a t thermodynamic arguments 1321 maybe used t o show there can be no continuity of s t a t e . The s i t u a t i o n there- fore remains paradoxical although recent work has now demonstrated t h a t glassy i c e can be formed d i r e c t l y from the l i q u i d s t a t e . 133,341

There are formidable technical problems i n making neutron d i f f r a c t i o n measurements a t lower temperatures where the metastable s t a t e has a r e l a t i v e l y short lifetime.

I t is however, possible t o use an emulsion system consisting of sonicated water droplets i n heptane/sorbitan solution. Data have recently been obtained

using the new D4B diffractometer and one scan was successfully completed a t -29oC with only a few droplets having c r y s t a l l i z e d . The second scan showed almost complete c r y s t a l l i z a t i o n a n d w i l l be used i n a detailed analysis of the r e s u l t s ; the s c a t t e r - ed i n t e n s i t y is shown i n (Fig.11). The background s c a t t e r i n g from the heptane does not permit the position of t h e main d i f f r a c t i o n peak t o be extracted from the raw data but comparison with runs a& higher temperatures suggests t h a t it has been fur- ther displaced towards the 1 . 7 A - ~ value f o r amorphous ice. This experiment a l s o demonstrates the advantages of high i n t e n s i t y beams with multi-wire detectors such as t h e D4B diffractometer f o r the study of samples i n metastable conditions.

Fig.11

Raw i n t e n s i t y p l o t s f o r super-cooled water i n emulsion form a t -2g°C;

the f i r s t scan shows only a few droplets have c r y s t a l l i z e d (the main d i f f r a c t i o n peak i n both datasets i s due t o the d-heptane solvent).

4

THE PARTIAL

CORRELATION FUNCTIONS a) I n i t i a l r e s u l t s

I n order t o separate the three p a r t i a l functions, three independent d i f f r a c t i o n measurements a r e required. Palinkas e t a l . [361 were the f i r s t t o produce t h i s in- formation using a combination of X-rayeneutron and electron data. The r e s u l t s are shown i n (Fig.12) with computer predictions using the ST2 p o t e n t i a l ; the short- range f e a t u r ~ s a r e i n reasonable agreement but there are o s c i l l a t i o n s a t larger values (3-6

which a r e not i n agreementwith the simulation r e s u l t s . This

more apparent when the composite curve f o r neutron s c a t t e r i n g i s evaluated as shown i n

(Fig.13) since there a r e apparently two o s c i l l a t o r y terms of similar magnitude which

almost completely cancel and t h i s indicates t h a t the important contributions f o r

t h i s behaviour a r i s e prirnarily from the technically-difficult electron d i f f r a c t i o n

measurements 1371. As a r e s u l t of these d i f f i c u l t i e s the findings of t h i s analysis

have not been generally ciccepted by the s c i e n t i f i c community.

Fig.12

Separation of partial functionç due to Palinkas et al. C361and the comparison with computer pre- dictions.

Fig.13

The decomposition of the composite g(r) curve for neutron scattering from liquid D20 according to the data given in Fig.11.

b) Isoto e substitution

One !O

the particular advantages of neutron diffraction methods is the possibility of changing the scattering length of individual components by isotopic substitution as shown by the study of aqueous solutions by Neilson and Enderby C12,381. The relevant isotopes of water components are given in Table 2.

Table 2: Neutron scattering data for H and O isotopes

Weighting factors for isotopically-pure liquids

HîO: g(r) =0.193 gW(r) -0.492 gOH(r) +0.317gHH(r) D20: g(r) =0.092gm(r) +0.422gOD(r) +0.486gDD(r) T20: g(r)

0.146 gm(r)

0.472 gOT(r)

0.382 gn(r)

Since b~

21bHI, it is convenient to make four measurements for H20/D20 mixtures with variable <bm>

aDbD

(1 - a )b D H z -

<bHD>

i) D,O b~

ii) H20/Dî0 (aD

0.719) lbHl

iii) H20/D20 (aD

0.359) O iv) H20

b~

The difference in the b-values of the oxygen isotopes is clearly insufficient for this technique but there is a large difference between hydrogen and deuterium;

the negative value for b~ arises from a phase difference in the scattering process.

The main difficulty is the large incoherent cross-section of hydrogen which makes it suitable l'or spectroscopic nieasurenients but inappropriate for structural studies.

The use of tritium has been considered but there are obviously difficulties related to sample preparation and containment due to its radiactivity. The only way in which further information can be obtained is through the H/D substitution method

despite the difficulties that this entails.

c) Hydrogenldeuterium substitution

The first attempt to exploite the negative b-value of hydrogen was made in some

~reliminarv measurements of H,]O/D?O mixtures by Powles. Dore and Page C391 which served t g dernonstrate the feâsibility of the hethod but yielded inçufficiently precise values for quantitative treatment. Two further studies were made(at ILL) but the data did not satisfy the stringent criteria of detector stability and high statistical accuracy that are required. However, a third attempt C40lwas successful.

Meanwhile other groups C41,421 had adopted similar methods, particularly Thiessen and Narten C411 who also adopted the principle of making four measurements so that the three partial functions are effectively over-determined. The four mixtures used by both Oak Ridge and UKC groups are shown at the bottom of Table 2.

It should be emphasises that these are not easy experiments since the coherent con- tribution may be as small as

5% of the total scattering intensity and the inelasti- city corrections are much greater for the lighter hydrogen atom. One important difference in experimental procedure between the two investigations was the use of a thin planar samply by the UKC group which enable the sample thickness to be varied.

in order to reduce possible systematic errors due to multiple scattering effects.

After application of the usual corrections the four datasets can be evaluated as shown in (Fig.14). The overall features are in reasonable agreement but a detailed comparison of the numerical information has not yet been made C421.

14

-

12

-

-L

.D

.

W

'.;: . \.. .. .

[L U

.: +-::--\,-

2 -

Fig .l4

Neutron diffraction measurements on H20/D20 mixtures

a) Narten and Thiessen C411 b) Reed and Dore C40 1.

Narten and Thiessen evaluated the inter-molecuar t e m and determined the separate partial structure factors which were transfonned to give the real-space correlation functions shown in (Fig.15). It is interesting to note the surprisingly sharp girst peak in the gOH(r) function and the absence of any major oscillations beyond 5 A.

- 1

O 2 4 B ' i IO

,

Reed and Dore i401 have adopted a different analysis method by transforming the composite inter-molecular functions and solving for the partial g(r)'s in real space;

the composite dL(r) c rves are shown in (Fig.16) . In this case the oscillatory be- naviour extends ro 8 k but there is negligible structure at higher r-values. Mien the simultaneous equations were solved by four different combinations it was found that the go[.,(r) data were in satisfactory agreement but the gHh(r) curves exhibited systeniatic discrepancies; these curves are çhown in (Figs.17 and 18). The gOIi(r) curve has similar features to those of the Narten and Thiessen data at small r-values, particularly the deep minimum after the first peak which emphasises the strong effects of the hydrogen-bonded interaction. At larger r-values the data show surprisingly good agreement with the oscillatory shape predicted by Palinkas et al.

Return- ing to the temperature variation studies it can readily be appreciated that there must be some structural features in this region to give contributions to the dL(r,T) function. Slore work on the critical comparison of datasets and evaluation of error criteria are obviously needed but this goes beyond the level of this current review.

The composite d(r) functions for

mixtures obtained by the UKC group.

Fig.15 - The partial g(r) func- tions obtained by Narten and Thiessen.

5

4 -

3 -

-

2 2 - 1 -

O

Warn. 25'C

1

1

j jl

Fig.17

The g O H / D ( r ) f u n c t i o n obtained by Fig.18

The g H 0 ( r ) f u n c t i o n ob- Reed and Dore; t h e i l l - c o n d i t i o n e d t a i n e & b y ) ~ e e d and Dore;

combination 3 has been d e l e t e d .

d ) The non-equivalence of H and D

The s y s t e m a t i c d i s c r e p a n c i e s revealed i n (Fig.17) r a i s e a f u r t h e r problem con- cernins t h e i n t e r o r e t a t i o n of t h e d a t a . The H / D method assumes equivalence of t h e hydrogen and deutérium atoms but i t i s apparent from many thermophysical p r o p e r t i e s t h a t t h e r e i s a s h i f t of t h e order

60C between e q u i v a l e n t S t a t e s . Furthermore, t h e previous s e c t i o n s have demonstrated t h e s e n s i t i v i t y of t h e water s t r u c t u r e t o r e l a t i v e l y small temperature s h i f t s . Separate d i f f r a c t i o n measurements on l i q u i d CD30H/D mixtures C441 have a l s o given support t o t h e non-equivalence o f hydrogen and deuteriun. This c o n s i d e r a t i o n adds a new dimension of complexity t o t h e a n a l y s i s and i n t e r p r e t a t i o n of t h e r e s u l t s but i t i s p o s s i b l e t o o b t a i n some i n s i g h t i n t o t h e e f f e c t s by re-evaluating t h e weighting-factors f o r t h e s e p a r a t i o n of t h e p a r t i a l terms. The f u l l f i g u r e s a r e shown i n Table 3. The e v a l u a t i o n of g o ~ ( r ) i s seen t o give s i m i l a r H / D proportions f o r a l 1 combinations whereas g H H ( r ) has widely-varying f r a c t i o n s . These f i g u r e s provide an explanation f o r t h e agreement in(Fig.17)and t h e systematic v a r i a t i o n i n (Fig . 1 8 ) . Much more work i s needed on t h i s , i n t r i c a t e problem but a f u l l e v a l u a t i o n of t h e ' s i m p l e r ' methyl alcohol system w i l l probably be required before t h e d e t a i l e d behaviour of water can be f u l l y unravelled.

Table 3: Relative weighting f a c t o r s f o r d i f f e r e n t combinations from H20/D20 mixtures .

i )

g O H ( r )

1.72 1.78 1.76 1.66

r a t i o of

HH

DO HH

HD

/ Combination

l

Actual f a c t o r s f o r

HH DD H D

I I

5

LiATER I N PORES

Since t h i s conference concerns b i o l o g i c a l i n t e r e s t s it is appropriate t o consider the e f f e c t s of an i n t e r f a c e on the s t r u c t u r e of t h e l i q u i d . Neutron d i f f r a c t i o n mcasurements C451 have been ïeported f o r water i n the high porosity s i l i c a s , Spheris- orb and Gasil. S i l i c a is a hydrophilic substance with a nwnber of s i l o x y l groups on the surface which can r e a d i l y p a r t i c i p a t e i n hydrogen-bonding with the water moleo cules as shown i n (Fig.19). The r e s u l t s f o r Spherisorb with a pore s i z e of

90

.

-

..Deuterium

Fig.19 -

schematic i l l u s t r a t i o n of t h e hydrophilic Si02 surface.

show B i t t l e v a r i a t i o n frornthose of bulk water but f o r Gasil, with a pore s i z e of

%

26 A, t h e r e a r e some small differences. The temperature difference functions, a d ~ ( r , T ) a r e given i n (Fig.20) and a l s o show a corresponding change r e l a t i v e t o bulk water, which indicates t h a t t h e e f f e c t s of the i n t e r f a c e cannot extend more than one o r two molecular layers i n t o the bulk phase. If t h e concept of ' s t r u c t u r e d '

A%(Q,T) function

f o r water i n porous

s i l i c a s ; S

Spheris-

orb and

Gasil.

water at the interfacial layerois to be retained, the data indicate that the layer is restricted to less than 10 A. Other experiments on nucleation in pores reveal a gradua1 process of freezing over a wide temperature range (-15-450C) and the forma- tion of ciihic ice (Tc) in preference to the normal hexagonal Ih formC461. The use of diffraction methods for this type of investigation is relatively new but there are some problems in the precise evaluation of the results due to possible correla- tions across the interface and diffraction broadening effects due to the hetero- genous nature of the material. C453

6

CONCLUSIONS

Although substantial progress has recently been made in the structural investigation of water by diffraction methods, it is apparent that further work is required. It is now possible to examine subtle differences in the molecular configurations by means of difference techniques but the fundamental information on the pair-correla- tion functions is proving to be less,rather than more,accessible as further informa- tion becomes available. ~ 4 2 1 The non-equivalence of H and D represents a consider- able increase in complexity but should eventually lead to a much greater insight into the nature of the hydrogen bond. Even the structural properties of the crystal- line ices are proving to be a fruitful field for new precision studies of isotopic difference effects i471. It seerns quite likely that terms such as 'CO-operativity' and 'quantum corrections' will play a major role in the vocabulary of the next decade - this conunon yet mysterious liquid continues to provide a major challenge to experimentalists and theoreticians alike!

1. H. E. Stanley. this meeting. .

-

A.Geiger, this meeting.

A review of earlier studies has been ~iven in Vol.1 of "Water: A Comprehensive Treatise", F.Franks (ed)

Chap. 9, D. Ï.page (neutron scattering) and* Chap. 8, A.H.Narten and H.A.Levy (X-ray scattering).

A.H.Narten and H.A.Levy, J.Chem.Phys., 55, 2263, (71).

J. G. Powles , Advances in Physics , 22, 1 v 3 ) .

L.Blm and A.H.Narten, Advances iTChem.Phys . , 2, 203 (76).

J.G.Powles, Mol.Phys., g, 757, (81).

L.Blum, M.Rovere and A.H.Narten, J.Chem.Phys., 77, 2647, (82).

Unvublished data from 'Thesis'; G.Walford, University of Kent, 1975.

~.b.~ibson and J.C.Dore, ~ o l . ~ h ~ s . , 48, 1019, (83).

P.A.Eeelstaff. J.A.Polo. J.H.Root. L3.Hahn and S-H.Chen. Phys.Rev.Lett.,

47, 1733, (8lj.

G.W.Neilson, this meeting.

G.Walford, J.H.Clarke and J.C.Dore, Mol.Phys., g , 25 (77).

J.G.Powles, Mol.Phys., 37, 623, (79) and earlier references.

M.Rovere, L.Blm and A.ENarten, J.Chem.Phys . , 73, 3729 (80).

S.Bratos, in NATO Advanced S m e r Inçtitute on Elecular Liquids, Florence, 1983; Barnes and Orville-Thomas (eds), D. Reidel Pub.Co. (pub), 1984.

A Spallation Neutron Source is under construction at the Rutherford Appleton Lab; a general description of the principles has been given by G.Manning in Contemp .Phys . , 2, 505, (78) .

Similar pulsed neutron sources are operative at the Argonne Nat.Lab., (USA), MVR, Los Alamos (USA) and

(Japan) and laboratory reports on scientific activities are generally available.

These principles have been incorporated into the RISM formulation as represented by L.J.Lowden and D. Chandler, J.Chem.Phys. 3, 5228 (74) ; a recent application to tetrahedral molecules is given by D.G.Montague, M.R.Chowdhury, J.C.Dore and J.Reed, blol.Phys., 50, 1, (83).

P.A.kgelstaff and J X R o o t , Chemical Physics , E, ^{405, (83)} .

N.Ohtomo, K.Tokiwano and K.Arakawa, Bull Chem.Soc.Japan, 55, 2788, (82).

L.Bosip, J-Teixeira, J.C.Dore, D.Steytler and P. Chieux, %l.Phys., s, ^{733 (83)}

S.A.Rice, Current Coments in Chemical Physics, 1976.

A.H.Narten, C.G.Venkatesh and S.A.Rice, J.Chem.Phys.,

1106, (76).

M.G.Sceats and S.A.Rice, Chap.2 in Vo1.7 of Water: A Comprehensive Treatise, F.Franks (ed)., Plenum (pub); also earlier references cited therein.

M.R.Chowdhury, J.C.Dore and J.T.Wenze1, J of Non.Cryst.Solids, 23, 247, (82).

W.H.Za&ariasen, J.Chem.Phys., 3, 162, (35).

D.E.Polk, J.Non.Cryst Solids, 27 365, (71).

E.A.Davis, S.R.Elliot, G.N.Greaves and D.P.Jones, p.205, in "Structure of Non-crystalline Materials", 1977, Taylor and Francis (pub).

P.Boutron and R.Alben,'J.Chem.Phys., z, 4848, (75).

J .Teixeira, this meeting.

A.Angel1, Chap.1 in Vo1.7, of Water: A Comprehensive Treatise, F.Franks (ed)., Plenum (pub).

P.Hobbs, 'Ice Physics', 1974, Clarendon Press, Oxford, (pub).

G.P.Johari, Phil..Man.. 35. 1077. (771.

S.A.Rice, ~ . ~ . ~ e r ~ r e n . d . ~ . ~ w i k g l e , - Chem.Phys.Lett., 59, 14, P.llruggeller and E.Mayer, Nature, 1, 569, (81) and - ^{298, 715}

J .Dubochet , this meeting.

L-Bosio, J. Teixeira, MI- bellise sent, J.C.Dore and P.Chieux, recent data (unpublished) .

G.Palinkas, E.Kalman and P.Kovacs, Mol.Phys., 34, 525 (77).

h.Kaïman, G-Palinkas and P.Kovacs, Mol-Phys., 34, 505, (77).

J. h.Enderby and G. W.Neilson, Chap. 1 in Vol. 6 of~ater: A Comprehensive Treat- ise, F.Franks (ed) . , Plenum (pub).

J.G.Powles, J.C.Dore and D.J.Page, Mol.Phys., 24, 1025, (72).

J.Reed, Thesis, University of Kent, 1981.

J.Reed and J.C.Dore, in preparation.

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A.K.Soper and R.N.Silver, Los Alamos Report, LAUR-821173.

The detailed comparison of the datasets is technically difficult due to the different conditions of the measurements and the different treatment of the analytic correction t e m , coupled to a different procedure for solving the simultaneous equations to give the required information; nevertheless, the discrepancies in the final data are disturbing and this task will need to be undertaken when s~if f icient resources are available .

D.G.Montague, J.C.Dore and S.Cummings, submitted to Mol-Phys. and other un- published data.

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J.C.L)ore and P.Chieu, unpublished data.

W.F.Kuhs and M.S.Lehmann, J.Phys.Chem., g , 4312, (83) and private comunica- tion.

Postscript: Implications for biological studies

Neutron diffraction measurements similar to those described in this paper c m be used

to study structural variation in more complex systems provided D,O can be substituted

for the more normal H20 without disrupting the system. Some prelirninary studies on

collagen with varying temperature and humidity were made by G.Jenkin (private communi-

cation) and showed interesting features but the data were not fully processed due to

some experimental difficulties in the control of the sample environment. The work

on water in porous materials indicates some of the basic ideas which could be uti-

lized in biological studies where water is a major constituent of the material under

study. The method would not be suitable for detailed investigation of the role

played by individualwater molecules in stabilizing enzyme structures as it depends

on relatively continuous water volumes.