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Amorphous ice

Amorphous Ice and Glassy Water

Solid water can exist in a number of non-crystalline amorphous forms, which have specific physical characteristics.

 

V Supercooled water

V Cold metastable glassy water

V Ultra-viscous water and the glass transition temperature
V Low-density amorphous ice (LDA)
V High-density amorphous ice (HDA)
V Very-high-density amorphous ice (VHDA)

 

'When the (water) vapour was condensed on a surface maintained at a temperature below - 110 °C the condensate was vitreous'

E. F. Burton and W. F. Oliver, 1935    

Cold metastable glassy water

If cooled very rapidly, liquid water forms a glass rather than crystallizing to hexagonal ice, for example, hyperquenched glassy water (HGW, [312e]). HGW is formed by the rapid spraying of a fine jet of μm-sized water droplets into very cold liquefied gas (for example, propane), or onto a very cold solid substrate, about or below 80 K or by cooling capillary tubes containing bulk liquid water (~100 μm diameter) with liquid helium at 4.2 K [1005]. These methods all involve cooling rates of greater than 105 K s-1. The glasses have structural, thermodynamic and density similarity with liquid water at 0 °C, due to their methods of formation and amorphous properties. A similar material is amorphous solid water (ASW), formed from the slow deposition of water vapor, at < 2 nm s-1, onto a very cold metal crystal surface below 120 K [900]. ASW (also called low-density glass, 0.94 g cm-3 solid) may contain considerable voids (up to 230 m2 g-1 [2425]) and dangling hydrogen bonds, which are removed by annealing under vacuum at 120-140 K when the glass converts to material indistinguishable from HGW or low-density amorphous ice (LDA, 0.94 g cm-3) at slightly higher temperatures. High-density glassy water (HDG, 1.1 g cm-3), formed by vapor deposition at 10 K [692] and subject to cosmic ray irradiation, d may be the commonest form of water in the universe. Notably, this 10 K ice had greatly increased numbers of water molecules held at van der Waals distances (~3.3 Å), giving it a higher density, which are not present if the vapor is deposited at 77 K.

 

Recently much interest has been shown in the high-density amorphous ices, high-density ice (HDA, 1.17 g cm-3 at 0.1 MPa) and very-high-density ice (VHDA, 1.26 g cm-3 at 0.1 MPa), formed from LDA or crystalline ices. These last three amorphous ices (LDA, HDA and VHDA) occupy three distinct megabasins in the energy landscape [1719] but are not required to obey the 'ice rules' and may contain a significant number of dangling bonds. Their structures may depend on the preparative method and thermodynamic history with well-relaxed (annealed) samples showing higher thermal stability [1953]. When annealed, they are expected to consist of fully hydrogen-bonded tetrahedral networks. This is borne out by their first-order phase transformation [2968]. The HDA to LDA transformation is a macroscopic phase separation rather than a homogeneous mixing of structures on the molecular scale. It is governed by the restructuring of the oxygen network rather than proton re-organization [2968], but highly dependent on the preparation and any prior relaxation of the LDA [2992].

 

Amorphous ices have been reviewed [1122, 1543, 1719] and their vibrational [1202] and diffraction scattering data compared [1546]. It was found by neutron scattering that ASW, LDA and HGW were structurally very similar [1546], particularly if annealed. The HDA -> LDA phase transition has been examined [1635, 1682].

 

Solid water can thus exist in a number of non-crystalline forms (glasses), which have specific physical characteristics such as density and vibrational spectra. Although often treated as though they are homogeneous, there is no support for this assumption with many natural glasses being clearly heterogeneous on the nano- or micro- scale with two or more separate phases [993]. As amorphous material, they mostly behave as glasses, which act as liquid depending on the time scale of observation. Many, but not all of the transformations, are shown below (mostly from [569]). All the amorphous solids can be recovered to ambient pressure (0.1 MPa) at 77 K (liquid nitrogen) where they are (meta)stable for extended periods. While different preparations of the same density may have similar properties, it is likely that materials prepared by very different routes may differ. Some may simply be mechanically collapsed ice whereas others may have structures related to liquid water [1682], with transformations between these forms on annealing being possible but not obligatory. Using D2O below ∼210 K, but under confined conditions under pressure preventing freezing, two regions are found; a “low-density liquid” phase and a “high-density liquid” phase 16% more dense [2181]. There is no evidence that any of these amorphous ices are actually microcrystalline although they are sometimes proposed as such. There are comprehensive reviews of the amorphous phases of ice and their transitions [569, 2033], an interesting simulation study of this polymorphism [590] and a critical review of the experimental data; particularly the diffraction data [1544]. Similarities to other tetrahedrally arranged substances (e.g. silicon) have also been noted [2392].

 

Relationships and transformations between the amorphous ices ice VII in ice VIII phase space Ice XII low density amorphous ice ice VIII high density phases intermediate density amorphous ice high density glassy water amorphous solid water hyperquenched glassy water very-high density amorphous ice Ice IV high-density amorphous ice conditions experimentally unobtainable for liquid water Ice Ic Ice Ih keeping the pressure constant

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Ultra-viscous water and the glass transition temperature

Diagram showing the relationship between the metastable phases of water

Nonequilibrium triple point Line of possible second critical point? Second critical point

The metastable phase diagram above based on the few data available plus related D2O work. The 'phases' may be stable for hours or days. Metastable 'phase lines' may move with the direction and time taken for the process. The red dot represents a (disputed) position for the second critical point of water [2119, 2647,] The (dashed) line where there is maximum fluctuations (the 'Widom' line) is disputed but may follow close to the upper bound of 'No man's land' and end in the second critical point at higher temperature and lower pressure than given above. Liquid water also changes its structure at about 200 MPa and possible interference by VHDA is neglected. There is a non-equilibrium 'triple point' where LDA, HDA and liquid water meet [2130], approximately as shown.

There is an excellent review of possible glass-to-liquid transitions of the amorphous ices [2413]. A highly viscous deeply supercooled liquid water phase can be formed from either solid LDA, HDA, and VHDA indicating an extension of 'normal' supercooled liquid water with structural similarities. The transformation occurs on warming amorphous LDA, or compact amorphous solid water (ASW) deposited at 77 K [2593], to about 136 K [74, 137] or heating solid HDA at 1 GPa from approximately 130 K [1770]. On further slow heating above 136 K, the liquid material from compact ASW crystallizes at 144 K [2593].

 

The transformation of HDA is reversible with the low-temperature high-density liquid water phase vitrifying on subsequent cooling [1770]. The use of X-ray photon-correlation spectroscopy (XPCS) in the small-angle X-ray scattering (SAXS) geometry has indicated that a first-order liquid–liquid transition, between low-density liquid and high-density liquid, occurs within the ultra-viscous regime [2930]. X-ray diffraction has shown the transition of ultra-viscous liquid phases of LDA and HDA at about 140 K and 0.2 GPa [1762]. Ultra-viscous liquid HDA can exist down to 116 K under ambient pressure [2048]. A single sample of annealed HDA at 80 K can be warmed through 116 K to produce a high-density ultra-viscous liquid that can be allowed to convert to a low-density ultra-viscous liquid at 136 K and then to LDA if brought down below 136 K. The two distinct ultra-viscous states of water differ by about 25% in density [2048].

 

This ultra-viscous deeply supercooled water has a consistency variously described as "soft toffee" [312c] or "molten sherbet" [868]. It has a viscosity 15 orders of magnitude greater than the normal liquid [1840] but still has a million-fold greater self-diffusion (at the still very low values of 2.2 x 10-19 m2 s-1 at 150 K [334] and ~1 x 10-16 m2 s-1 at 160 K [1840]) than crystalline ice. The hundred-fold higher viscosity than that expected from its diffusivity may indicate the presence of long-lived crystallites within the deeply supercooled liquid [868]. The relationship between these supercooled waters is not easily investigated as there is an unobtainable 'no man's land' in the physical conditions where no liquid or glassy phase can be found and little experimental data exists [1903, 2236]. f ESR. however, indicates that a small fraction of the water molecules may be 'free', coexisting with cubic ice between about 160-230 K [1005]. The very existence of deeply supercooled liquid water, between about 136-160 K, is evidence that the glass transition temperature is the lower of those proposed (136 K, [312]), although characterized by only a small change in specific heat due to the high degree of strong hydrogen bonding in the liquid. It has been proposed that the glass transition is linked with the unfreezing of the reorientation dynamics in a similar manner to the disordered ices I, IV, V, VI, and XII [2601]. Deeply supercooled low-density liquid water is one of the strongest liquids known with heat capacity steps of < 1 J K-1. Deeply supercooled high-density liquid water gives a different glass transition temperature of 116 K [2048].

 

Deeply supercooled liquid water may be formed when amorphous ices are 'annealed' at temperatures above 136 K. This lower density deeply supercooled liquid water is a good solvent for inert gas (Xenon) atoms but a very poor solvent for salt (LiCl) [1120]. In addition, it has an excess entropy(1-2 kJ ˣ mol-1 K-1) much smaller than the entropy difference between liquid water and crystalline ice at 0 °C (22 mol-1 K-1) and an enthalpy of crystallization at 150 K (∼1.35 kJ ˣ mol-1) also much smaller than the heat of crystallization of liquid water (∼6 kJ ˣ mol-1) both indicating a high degree of tetrahedral order via intermolecular hydrogen bonding [1840].These properties indicate ES-like qualities and elsewhere a possible molecular explanation is presented. At higher temperatures (~165 K) LiCl becomes very soluble, and at high concentrations forms a deeply supercooled solution, as its interactions with ultra-viscous water overcome the strong water-water interactions present at lower temperatures [1225]. [Back to Top to top of page]

Low-density amorphous ice (LDA)

Absorption spectrum of LDA ice, crystalline ice and liquid water, [2195]LDA is now considered to include ASW, HGW, LDA-I, and LDA-II [1719] plus a more ordered form [2486]. LDA may be prepared from glassy water, as above, by warming high-density amorphous ice (HDA) to just above 120 K at atmospheric pressure or by heating the high-pressure ice VIII phase at ambient pressure (Note however that some preparations of LDA differ from others; in particular, LDA-I is obtained by isobaric warming of HDA at ambient pressure and LDA-II is obtained by isothermal decompression of VHDA at 143 K). It is stable for months at 77 K and ambient pressure but transforms into cubic ice (probably stacking disordered ice) at about 150-160 K. The structure is unknown but consistent with LDA having an open structure (primarily like ES) and structurally [718, 1284] and thermodynamically related to supercooled liquid water. It has a similar density to ES of 0.94 g cm-3 (LDA of D2O has a density of 1.04 g cm-3 at 0.1 MPa) and has tetrahedrally arranged hydrogen-bonded water molecules with four nearest-neighbors and clathrate cages (evidence presented elsewhere). The dielectric relaxation time for LDA is 100-1000 seconds at 130 K, which is two orders of magnitude greater than that of VHDA, and indicates that the ice rules are preventing more rapid orientational mobility [1447] similar to processes found in the crystalline ices.

Arrhenius diagram of dielectric time constants, data from [2413]

 

The oxygen pair correlation function is similar to that of supercooled liquid water [43], but the thermal conductivity behavior appears to differ [617] with LDA showing behavior more similar to a crystalline material rather than an amorphous glass [617, 1155]. The O-H stretch of 5% HDO in D2O (see above right) shows a broad absorption band due to the disorder in the sample. The peak is red-shifted in LDA from that of liquid water, indicating stronger hydrogen bonds [2195]. The red-shift indicates stronger hydrogen bonds. Although similarities exist, LDA is likely to have a somewhat different structure to ASW or HGW, which both show different glass transition behavior.

 

Dielectric loss spectra (opposite, [2413]) give time constants that correspond to the rates of molecular reorientation. Surprisingly, LDA, HDA and VHDA all give close to parallel lines in their Arrhenius plots with activation energies close to 34 kJ ˣ mol -1 [2048].

 

 

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High-density amorphous ice (HDA)

HDA is considered to include eHDA and uHDA [1719]. HDA may be prepared by submitting low-pressure ices (Ih, Ic, XI a or LDA) to high pressure (~1.0 GPa, ice Ih; ~0.5 GPa, LDA) at low temperatures (for example at 125 K, see below from [1122]). As with LDA some preparations of HDA differ from others. It is stable for months at 77 K and ambient pressure. HDA has a density of 1.17 g cm-3 at 0.1 MPa (1.31 g cm-3 at 1.0 GPa; HDA of D2O has a density of 1.30 g cm-3 at 0.1 MPa). The structure is unknown and varies between preparations and probably consists of a mixture of constrained frozen material. The material appears to be heterogeneous on a length scale of nanometers [995]. However, the available data is not inconsistent with HDA (made from LDA) having primarily the structure of crushed CS; the main feature appearing to be a puckering (collapsing) that increase the number of water molecules in the first coordination shell. b

Density of liquid and crystalline water along the phase line and amorphous ice; mouse over for volumes
Note that the liquid water (from the IAPWS-95 equations [540]) and ice data is from the phase line and the temperature varies whereas the amorphous ice line is variation with pressure only.
Effect of pressure on amorphous ices at 125 K, data from ref 1122 Volume of glassyvband crystalline water at anout 100 K

 

The collapsing puckering of convex clathrate-type structures in the LDA -> HDA conversion involves a potential energy barrier which may explain the difficulty of the reverse HDA -> LDA conversion at low temperatures (for example, 77 K) and sometimes put down as a 'lynch pin' effect due to the presence of an extra non-hydrogen bonded water molecule at about 0.345 nm [2895] (compare hydrogen bonded HDA ~0.269 nm and for LDA ~0.274 nm) within the inner O···O coordinated shell. c The HDA -> VHDA conversion involves the presence of a second non-hydrogen bonded water molecule with both at about 0.32 nm [2895] (compare hydrogen bonded VHDA ~0.272 nm) within the inner O···O coordinated shell.

 

Once a clathrate cage has puckered, there exists a larger potential energy barrier to changes in puckering (for example, from a tetrahedral to an octahedral arrangement). Therefore as the initial puckering is expected to vary from site to site dependent on the strength (and weakness) of surrounding hydrogen bonding, HDA formed this way is expected to be somewhat disordered. As HDA's structure appears to vary during annealing [394] (producing intermediate density amorphous ices, IDA [718] and in contrast to several early papers describing a first-order (meaning abrupt and direct) transition between LDA and HDA, see [569]), with preparation method [618b] (particularly with respect to time [618c]) and starting material [618d], data from diffraction and vibrational spectroscopy has to be interpreted carefully. A more stable annealed form of HDA, e-HDA (1.13 g cm3 0.1 MPa), has been prepared by annealing at about 0.2 GPa [1544]. This material appears to be homogeneous, completely converts to ice IX (the low-temperature form of ice III) on warming to ~170 K at 100 MPa, possesses enhanced stability against transition to LDA at ambient pressure and is the best candidate for the solid form of high-density liquid water [2071]. e-HDA, on warming from below 100 K at 0.2 GPa forms ultra-viscous water at about 140 K before crystallizing into ice IX [2348]. An interesting property of HDA is that the thermal conductivity decreases from that of ice Ih, ice Ic or LDA during their pressurized densification, as usually the thermal conductivity of materials increases with increasing pressure [618b].

 

Interestingly, ammonium fluoride (NH4 F), which has a similar hydrogen-bonded hexagonal crystal to hexagonal ice, converts, upon compression at 77 K, to a high-pressure phase isostructural with ice-four. Under the same circumstances, hexagonal ice converts to HDA rather than ice-four. This indicates that at least one form of HDA may be a ‘derailed’ state along the hexagonal ice to ice-four pathway [2861]. [Back to Top to top of page]

Very-high-density amorphous ice (VHDA)

VHDA (first recognized in 2001 [693]) may be prepared by submitting high-density amorphous ice (HDA) at 77 K to isobaric heating to 160 K at 1.15 GPa [421]. On isobaric annealing of HDA between 0.3 and 1.9 GPa (with temperature increasing from 77 K), VHDA appears to have formed at 0.8 GPa with changes in density at higher pressures being due to elastic compression [935]. The LDA=e-HDA=VHDA transitions are reversible [1533]. Certainly, the phase transition from high- (HDA) to very-high-density amorphous ice (VHDA) seems to be continuous rather than sudden (first order) [2665], at least at positive pressures [2895]. D2O behaves similarly to H2O, but with crystallization, to a mixture of high-pressure ices, taking place above 143 K rather than 140 K [1534]. Dielectric spectra indicate that VHDA can form a metastable ultra-viscous water state at 1 GPa and above 140 K [1160], but this liquid has unexpected properties compared with liquid water supercooled past the ice VI phase boundary and may be the high-density equivalent of the deeply supercooled low-density water described earlier. As VHDA is formed from HDA by a process of structural relaxation (also known as rHDA), it has been considered a more stable form of HDA [845] and appears to have a lower chemical potential than HDA for the entire range of pressures [2895]. It shows a greater extent of structuring than HDA and LDA [675] and is stable for months at 77 K and ambient pressure. It has a density of 1.25 g cm-3 at 0.1 MPa (1.37 g cm-3 at 1.4 GPa), which may be indicative of the presence of some ring penetration such as occurs in the similarly dense ice six, although a simulation indicates otherwise [747]. c The dielectric relaxation time for VHDA is a couple of seconds at 130 K, which is two orders of magnitude less than that of LDA, and indicates that the close proximity of non-hydrogen bonded water molecules allows more rapid orientational mobility [1447].

 

The Intermolecular partial radial distribution functions of LDA and HDA and VHDA at 80 K, as derived from neutron diffraction, [421, 2303]

Changes from HDA may occur by increased ordering, producing the more dense structure. There is a density-distance paradox with the nearest water-water distances increasing from 2.75 Å to 2.80 Å to 2.83 Å as the density increases for LDA, HDA and VHDA respectively; this increase due to the increase in the number of non-hydrogen-bonded water molecules in the first hydration shell from zero to one to two respectively [421, 1055], these water molecules easing the network outwards in a manner seen in high-density liquid water. The intermolecular partial radial distribution functions of LDA, HDA, and VHDA at 80 K, as derived from neutron diffraction [421, 1546, 2303], are given on the right. The differences were assumed due to an increase in interstitial molecules in the order LDA < HDA < VHDA. HGW and ASW behave very similarly to LDA.

 

Interestingly, when warmed at different pressures between 0.3 and 2 GPa, VHDA recrystallizes into only the proton disordered ices III, IV, V, XII, VI, and VII in order of increasing pressure, but not into the proton ordered phases such as ice II [756] (in apparent contrast to HDA which can form ice IX [932]). Recent molecular dynamics simulation indicates that HDA may evolve continuously into VHDA and densification causes an increase in hydrogen-bonded rings containing 8-10 water molecules, due to more efficient packing [747], like ice-twelve with its 7- and 8- membered rings and similar density. If higher pressure is used (2 - 4 GPa) on HDA then high-pressure ices (ice-seven or ice-eight) are formed. VHDA shows structural similarities to high-pressure cold (>0.2 GPa, < 273 K; cooled and supercooled high-density liquid water) and hot water (to 6.5 GPa and 670 K [1001]) but possesses more extensive ordering. Much has been made of the possibility of a phase transition line between supercooled metastable liquid forms of LDA (called low-density liquid, LDL) and VHDA (called high-density liquid, HDL, and often referred to as the liquid phase of HDA before VHDA was discovered) existing at high pressure. Such a situation is expected to end in a second (metastable) critical point [419, 432, 580, 2665]. The existence of this scenario is difficult to prove, and is disputed, but is capable of (but not necessary for) explaining many of the low-temperature anomalies of liquid water.

 

A high-density two-dimensional form of amorphous water (sometimes referred to as a high-density two-dimensional ice) may be formed under ambient conditions on some surfaces, for example, BaF2 [2344]. [Back to Top to top of page]

 


Footnotes

a   The transformation with pressure of ice XI (and ice VIII) has been modeled [749]. [Back]

 

b   CS has a density of 1.00 and has 1/4 of its water dodecahedra puckered relative to ES (density 0.94 g cm-3). Full puckering of the remaining three water dodecahedra would give a density of 0.94 + 4 x 0.6 = 1.18 g cm-3, which is similar to the density of HDA of 1.17 g cm-3. If this puckering of the water dodecahedra is random with respect to the number of inner water molecules, this would produce a more disordered structure than LDA in line with the thermal conductivity data [617] and the recent finding of HDA's lack of a unique structure [618]. [Back]

 

c   The activation energy for the HDA -> LDA transition has been estimated as equivalent to about one hydrogen bond [792a], with that for the VHDA -> LDA transition being equivalent to about two hydrogen bonds [792b]. The non-hydrogen-bonded water molecules may be due to separate interpenetrating hydrogen bonded networks or a crushed hydrogen bonded structure where nearby water molecules are linked by both hydrogen bonding to third water molecules further away. [Back]

 

d   A similar material may be prepared from low-density glass by lowering the temperature to 12 K when irradiated with 2-3 electron Å-2 at ambient pressure [957]. A glass of intermediate density (1.04 g cm-3) has been found using cooling rates of 110-271 K s-1 on diamond [972] and by modeling [498], and which may be related to the collapsed structure of water (CS) mentioned elsewhere. [Back]

 

f   Liquid water may be studied in aqueous solution within 'no man's land' but only in tiny amounts, with large surface area to volume as nanodrops, within emulsified aqueous solutions, or if confined in nanometer-sized pores [2257]. Under these circumstances it may well not behave as 'bulk' water. [Back]

 

 

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