3 - Ice and crystalline water

Transcription

1 3 - Ice and crystalline water All ice is not crystalline not all crystalline water is ice H 2 O solid phases (From Savage)

2 Some general comments on the phase diagram All crystalline ice is tetrahedrically coordinated, and the polymorphs differ primarily in H-bond angles and next-nearest neighbour separations. Ice II, VIII and IX cannot be obtained directly from liquid water. Only ice I has a lower density than liquid water. The rich phase diagram is a consequence of the pressure sensitivity following from the open tetrahedral structure of water.

3 Growth of ice from vapour - A function of temperature and supersaturation (From Hallett, Proc. R. Soc. Lond. A247, 440 (1958))

4 Ice Ih ordinary ice Atomic arrangement in ice Ih. H2 positions are half occupied, and H1 positions (filled) indicate positions in the bent hydrogen model. (From Kuhs) Ice Ih is a thoroughly disordered crystalline material, whose translational symmetry is not retained at the unit cell-level. In a time- and space-averaged sense however, the symmetry of ice Ih is very high. Although the oxygen atoms on average forms a regular lattice, this is not the case for the H atoms. Along each O O-axis, there are two equivalent sites, resulting in proton disorder. Averaged molecular geometry (at 223 K for ice) O H O O H O H O O O ρ (Å) (Å) (deg) (deg) (g/cm 3 ) Ice Ih Liquid

5 Proton order and configurational degeneracy Bernal & Fowler (1933) and Pauling (1935) argued that the similarites between ice and water esp. the vibrational spectrum is evidence that H 2 O molecules are intact in ice. This implies the Bernal and Fowler conditions on the arrangement of hydrogen atoms: (1) Each O O line has one and only one H atom. (2) Each O has two H at about 1 Å from its center, and two at about 1.76 Å. Out of the 16 possible ways of arranging H atoms near one particular O atom, there are only 6 consistent with these conditions. The five possible arrangements of hydrogens around a given oxygen. Numbers in brackets indicate the degeneracy. (Adapted from Ben-Naim) Assuming all arrangements are equally likely, how many configurations are there in ice containing N water molecules?

6 The residual entropy With N water molecules, there are N oxygens, 2N hydrogens and 2N O O bonds. Ignoring condition (2), each hydrogen may be placed at either of two sites in each O O bond, thus 2 2N possible arrangements. Some of these are inconsistent with (2); for each oxygen, there is a 6/16 probability of finding an acceptable arrangement, so the total number of possible configurations is Ω = 6 N 2 2N = (3/2) N 16 This can be used to calculate the residual entropy of ice: S 0 = k ln Ω = 3.38 J/mol K in good agreement with the observed 3.41 J/mol K. A classical example of a successful prediction based on an elementary statistical argument! Proton order in ice Ih and disorder in ice VIII. (From Savage)

7 Vibrational constants for water and ice (cm 1 ) Symmetric Asymmetric stretch, ν 1 stretch, ν 2 Bend, ν 3 H 2 O (g) H 2 O (l) Ice Ih Ice II Ice VIII Denser ice forms become liquidlike? Loss of the robust tetrahedral hydrogen bonding (relative to Ih) partially recovers the water-like vibrational nature in denser (high pressure) forms of ice. H-bonded Closest non- ρ O O O Ice O O H-bonded O O (g/cm 3 ) angles Ih II (9) VIII (5)

8 The crystalline ice polymorphs H-bonded Closest non- ρ O O O Hydrogen Ice O O H-bonded O O (g/cm 3 ) angles order Ih Disordered Ic Disordered II (9) Ordered III (1) Disordered IV (9) Disordered V (7) Disordered VI (17) Disordered VII (4) Disordered VIII (5) Ordered IX (1) Ordered X Properties largely unknown (Adapted from Robinson and Savage) All forms have 4 H-bonded nearest neighbours Although denser, most structures have longer nearestneighbour O O distances than ice Ih, due to weakening of the hydrogen bonds. Reduced (non-h-bonded) second-neighbour O O distances cause the density differences. A structural relationship between the phases allow transformations over relatively small energy barriers, which take place primarily by bending, not breaking, H-bonds. X Forms at 440 kbar. Believed to contain symmetric H-bonds with ionic character. Structure uncertain.

9 Ice Ih and ice Ic Ih (left) and Ic (right), perpendicular to c-axis (top) and along the c-axis (bottom). (From Savage) Ice Ic is metastable, and irreversibly converts to ice Ih. Both forms contain similar layers of hexagonal rings, but differs in the way these layers are connected.

10 Temperature dependence Lattice constants for the a and c axes of ice Ih. (From Kuhs)

11 Ice Ih and ice II Ih (top) and II (bottom). The hexagonal rings in ice II are flat, and half the hexagonal tunnel structures along the c- axis are collapsed. The protons in ice II are fully ordered, so the Pauling entropy is absent. (From Savage) H-bonded Closest non- ρ O O O Hydrogen Ice O O H-bonded O O (g/cm 3 ) angles order Ih Disordered II (9) Ordered Without the (proton) ordering, ice II is only slightly less energetically stable than Ih, so that absence of Pauling entropy would likely have led to freezing to the dense II form in the depths of many waters...

12 Ice IX / III Ice IX / III, viewed along the c-axis. Filled bonds show the 5-membered ring in a unit cell. (From Savage) IX and III have the same structure, but H is fully orientationally ordered in IX and fully disordered in III. Contains 5- and 7-membered rings, but no hexagonal rings. H-bonded Closest non- ρ O O O Hydrogen Ice O O H-bonded O O (g/cm 3 ) angles order Ih Disordered III (1) Disordered IX (1) Ordered

13 Ice IV and V O positions in ice IV, filled bonds represent a structural unit (Left). Ice V with the structural unit comprising 4- and 5-membered rings shown separately (Right). (From Savage) IV is a metastable form in the V region of the phase diagram, forming an H-bond through a hexagonal ring. Ice V consists of 4-, 5- and 6-membered rings, with disordered proton structure. H-bonded Closest non- ρ O O O Hydrogen Ice O O H-bonded O O (g/cm 3 ) angles order Ih Disordered IV (9) Disordered V (7) Disordered

14 Ice VI One of the two interpenetrating lattices, with a structural unit marked with filled bonds (left). Both lattices along the c axis of the unit cell (right). (From Savage) The first phase to form two interpenetrating lattices as the pressure is increased. H-bonded Closest non- ρ O O O Hydrogen Ice O O H-bonded O O (g/cm 3 ) angles order Ih Disordered VI (17) Disordered

15 Ice VII and ice VIII VII (left) and VIII (right). (Adapted from Savage) Ices VII and VIII comprise two interpenetrating (ice Ic) lattices with all O O O bond angles close to the tetrahedral value. VIII is fully proton ordered, while VII is disordered. VII has 8 nearest-neighbours at 2.90 Å, of which only 4 are H-bonded. If the H-bonds were not extended, the density of VII would be twice that of Ih. H-bonded Closest non- ρ O O O Hydrogen Ice O O H-bonded O O (g/cm 3 ) angles order Ih Disordered VII (4) Disordered VIII (5) Ordered

16 Amorphous ice I Oxygen-oxygen partial radial distribution functions of lowdensity amorphous ice (LDA), high-density amorphous ice) HDA, liquid water, and ice Ih. HDA appears compressed in a way similar to the way water is collapsed from ice. (From Finney, PRL 88, (2002)). Phase diagram indicating the LDA and HDA regions. (From Science 297, 1289 (2002)).

17 Amorphous ice II Distribution of neighbour water molecules Spatial density functions showing the distribution of neighbour water molecules. Figures in brackets indicate contour levels g(r, Ω). (From Finney, PRL 88, (2002)). LDA has 3.9 nearest neighbours, while HDA has 5; compare with 4 for ice Ih and for liquid water...!

18 Non-solid crystalline water Water structure in coenzyme (Vitamin) B 12 (From Savage)

19 Primary references H. Savage, Water structure in crystalline solids, in Water Science Reviews 2, F. Franks (ed.), Cambridge: CUP G. Wilse Robinson et al., Water in biology, chemistry and physics, Singapore: World Scientific F. W. Kuhs and M. S. Lehmann, The structure of Ice-Ih, in Water Science Reviews 2, F. Franks (ed.), Cambridge: CUP D. Eisenberg and W. Kauzmann, The structure and properties of water, Oxford: OUP A. Ben-Naim, Water and aqueous solutions, New York: Plenum E. Whalley (ed.), Physics and chemistry of ice : papers presented at the symposium on the physics and chemistry of ice held in Ottawa, Canada, August 1972, Ottawa: Royal Society of Canada 1973.