Water Structure and Science

11/06/2013 Water structure and science

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Water structure and science

(http://www.lsbu.ac.uk/water/anmlies.html)

Water Anomalies

Phase anomalies (P1-P12) explanations Density anomalies (D1-D20) explanations

Material anomalies (M1-M12) explanations

Thermodynamic anomalies (T1-T11) explanations

Physical anomalies (F1-F9) explanations

Water is an apparently simple molecule (H2O) with a highly complex character. As a gas it is one of lightest known, as a

liquid it is much denser than expected and as a solid it is much lighter than expected. Much of the behavior of liquid water

is quite different from what is found with other liquids, giving rise to the term 'the anomalous properties of water'. a

As liquid water is so common-place in our everyday lives, it is often regarded as a typical liquid. In reality water is mostatypical as a liquid, behaving as a quite different material at low temperatures to that when it is hot. It has often been

stated (for example, [127]) that life depends on these anomalous properties of water. In particular, the large heat

capacity, high thermal conductivity and high water content in organisms contribute to thermal regulation and prevent localtemperature fluctuations, thus allowing us to more easily control our body temperature. The high latent heat of evaporation

gives resistance to dehydration and considerable evaporative cooling. Water is an excellent solvent due to its polarity, high

dielectric constant and small size, particularly for polar and ionic compounds and salts.b It has unique hydration properties

towards biological macromolecules (particularly proteins and nucleic acids) that determine their three-dimensionalstructures, and hence their functions, in solution. This hydration forms gels that can reversibly undergo the gel-sol phase

transitions that underlie many cellular mechanisms [351]. Water ionizes and allows easy proton exchange betweenmolecules, so contributing to the richness of the ionic interactions in biology.

At 4C water expands on heating OR cooling. This density maximum together with the low ice density results in (i) thenecessity that all of a body of fresh water (not just its surface) is close to 4C before any freezing can occur, (ii) the

freezing of rivers, lakes and oceans is from the top down, so permitting survival of the bottom ecology, insulating thewater from further freezing, reflecting back sunlight into space and allowing rapid thawing, and (iii) density driven thermal

convection causing seasonal mixing in deeper temperate waters carrying life-providing oxygen into the depths. The large

heat capacity of the oceans and seas allows them to act as heat reservoirs such that sea temperatures vary only a third asmuch as land temperatures and so moderate our climate (for example, the Gulf stream carries tropical warmth to

northwestern Europe). The compressibility of water reduces the sea level by about 40 m giving us 5% more land [65].

Water's high surface tension plus its expansion on freezing encourages the erosion of rocks to give soil for our agriculture.

Notable amongst the anomalies of water are the opposite properties of hot and cold water, with the anomalous behavior

more accentuated at low temperatures where the properties of supercooled water often diverge from those of hexagonal

ice.c As cold liquid water is heated it shrinks, it becomes less easy to compress, its refractive index increases, the speed

of sound within it increases, gases become less soluble and it is easier to heat and conducts heat better. In contrast as hot

liquid water is heated it expands, it becomes easier to compress, its refractive index reduces, the speed of sound within itdecreases, gases become more soluble and it is harder to heat and a poorer conductor of heat. With increasing pressure,

cold water molecules move faster but hot water molecules move slower. Hot water freezes faster than cold water and ice

melts when compressed except at high pressures when liquid water freezes when compressed. No other material is

commonly found as solid, liquid and gas.d

The anomalies of water appear as a heirarchy of effects with
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The anomalies of water appear as a heirarchy of effects with

different bounds [169]. These are shown indicatively opposite asderived from modeling, not experimental data. The Structural

bounds indicate where water is more disordered when

compressed, the Dynamic bounds indicate where diffusionincreases with density, and the Thermodynamic bounds show

where there is a temperature of maximum density; with the data

from [169] shifted upwards 38 K to give the correct temperature

of maximum density under standard pressure. As density alwaysincreases with increasing pressure, a similar relationship holds with

pressure along the horizontal axis.

Water phase anomalies

1. Water has unusually high melting point. [Explanation]2. Water has unusually high boiling point. [Explanation]

3. Water has unusually high critical point. [Explanation]4. Solid water exists in a wider variety of stable (and metastable) crystal and amorphous structures than other

materials. [Explanation]5. The thermal conductivity of ice reduces with increasing pressure. [Explanation]6. The structure of liquid water changes at high pressure. [Explanation]

7. Supercooled water has two phases and a second critical point at about -91C. [Explanation]8. Liquid water is easily supercooled but glassified with difficulty. [Explanation]9. Liquid water exists at very low temperatures and freezes on heating. [Explanation]

10. Liquid water may be easily superheated. [Explanation]11. Hot water may freeze faster than cold water; the Mpemba effect. [Explanation]12. Warm water vibrates longer than cold water. [Explanation]

Water density anomalies

1. The density of ice increases on heating (up to 70 K). [Explanation]2. Water shrinks on melting. [Explanation]

3. Pressure reduces ice's melting point. [Explanation]4. Liquid water has a high density that increases on heating (up to 3.984C). [Explanation]5. Pressure reduces the temperature of maximum density. [Explanation]

6. There is a minimum in the density of supercooled water. [Explanation]7. Water has a low coefficient of expansion (thermal expansivity). [Explanation]

8. Water's thermal expansivity reduces increasingly (becoming negative) at low temperatures. [Explanation]9. Water's thermal expansivity increases with increased pressure. [Explanation]

10. The number of nearest neighbors increases on melting. [Explanation]

11. The number of nearest neighbors increases with temperature. [Explanation]

12. Water has unusually low compressibility. [Explanation]13. The compressibility drops as temperature increases up to 46.5C. [Explanation]

14. There is a maximum in the compressibility-temperature relationship. [Explanation]15. The speed of sound increases with temperature up to 74C. [Explanation]16. The speed of sound may show a minimum. [Explanation]

17. 'Fast sound' is found at high frequencies and shows an discontinuity at higher pressure. [Explanation]18. NMR spin-lattice relaxation time is very small at low temperatures. [Explanation]19. The refractive index of water has a maximum value at just below 0C. [Explanation]

20. The change in volume as liquid changes to gas is very large. [Explanation]



Water material anomalies

1. No aqueous solution is ideal. [Explanation]

2. D2O and T2O differ significantly from H2O in their physical properties. [Explanation]

3. Liquid H2O and D2O differ significantly in their phase behavior. [Explanation]

4. Solutes have varying effects on properties such as density and viscosity. [Explanation]

5. The solubilities of non-polar gases in water decrease with temperature to a minimum and then rise. [Explanation]6. The dielectric constant of water is high. [Explanation]7. The dielectric constant shows a temperature maximum. [Explanation]

8. Proton and hydroxide ion mobilities are anomalously fast in an electric field. [Explanation]9. The electrical conductivity of water rises to a maximum at about 230C. [Explanation]

10. Acidity constants of weak acids show temperature minima. [Explanation]

11. X-ray diffraction shows an unusually detailed structure. [Explanation]12. Under high pressure water molecules move further away from each other with increasing pressure. [Explanation]

Water thermodynamic anomalies

1. The heat of fusion of water with temperature exhibits a maximum at -17C. [Explanation]2. Water has over twice the specific heat capacity of ice or steam. [Explanation]

3. The specific heat capacity (CP and CV) is unusually high. [Explanation]

4. The specific heat capacity CP has a minimum at 36C. [Explanation]

5. The specific heat capacity (CP) has a maximum at about -45C. [Explanation]

6. The specific heat capacity (CP) has a minimum with respect to pressure. [Explanation]

7. The heat capacity (CV) has a maximum. [Explanation]

8. High heat of vaporization. [Explanation]9. High heat of sublimation. [Explanation]

10. High entropy of vaporization. [Explanation]

11. The thermal conductivity of water is high and rises to a maximum at about 130C. [Explanation]

Water physical anomalies

1. Water has unusually high viscosity. [Explanation]2. Large viscosity increase as the temperature is lowered. [Explanation]3. Water's viscosity decreases with pressure below 33C. [Explanation]4. Large diffusion decrease as the temperature is lowered. [Explanation]

5. At low temperatures, the self-diffusion of water increases as the density and pressure increase. [Explanation]

6. The thermal diffusivity rises to a maximum at about 0.8 GPa. [Explanation]7. Water has unusually high surface tension. [Explanation]8. Some salts give a surface tension-concentration minimum; the Jones-Ray effect. [Explanation]9. Some salts prevent the coalescence of small bubbles. [Explanation]

Some of the anomalies of water

related to temperature.



related to temperature.

The graph uses data that havebeen scaled between theirmaximum and minimum values(see original data).

a Whether or not the properties of water are seen to be anomalous depends upon which materials water is to be

compared and the interpretation of 'anomalous'. For example, it could well be argued that water possesses exactly thoseproperties that one might deduce from its structure (see for example, [402]). Other tetrahedrally interacting liquids, suchas liquid Si, SiO2 and BeF2 have many similar 'anomalies'. Comparisons between water, liquid sodium, argon and

benzene appear to Franks [112] to indicate several of the properties given above as not being anomalous. However,these materials are perhaps not the most typical of liquids. My list gives the unusual properties generally understood tomake liquid water (and ice) stand out from 'typical' liquids (or solids). See [242] for a review concentrating on the non-

anomalous properties of water; that is, those that are the 'same' as for other liquids. [Back]

b It is therefore very difficult to obtain really pure water (for example, < 5 ng g-1). For a review of aqueous solubilityprediction, see [744]. Note that ice, in contrast, is a very poor solvent and this may be made use of when purifying water(for example, degassing) using successive freeze-thaw cycles. [Back]

c Some scientists attribute the low temperature anomalous nature of water to the presence of a second critical point; aninteresting if somewhat unproductive hypothesis as a sole explanation (as the attribution mixes cause with effect). Water'sanomalies do not require this as an explanation. [Back]

d The temperature range of 'hot' and 'cold' water varies in these examples; see the individual entries for details. [Back]

e The anomalies of water are divided into groups but, clearly, some anomalies may be included under more than one

topic and there may not be universal agreement for the groupings shown. [Back]

Water structure and science(http://www.lsbu.ac.uk/water/explan.html)

Explanation of the Phase Anomalies of Water (P1-P12) Density anomalies (D1-D20) explanations Material anomalies (M1-M12) explanations

Thermodynamic anomalies (T1-T11) explanations Physical anomalies (F1-F9) explanations

P1 High melting point (0C, compare CHCl3 -63C)



Partial phase diagram of water (H2O) showing the melting (M.Pt.),

boiling (B.Pt.) and triple (T.Pt) points.a

The melting point of water is over 100 K higherthan expected by extrapolation of the melting pointsof other Group 6A hydrides, here above showncompared with Group 4A hydrides. It is also muchhigher than O2 (54 K) or H2 (4 K). See also below

for further comparisons.

In ice (Ih), all water molecules participate in four hydrogen bonds (two as donor and two as acceptor) and are heldrelatively static. In liquid water, some of the weaker hydrogen bonds must be broken to allow the molecules to movearound. The large energy required for breaking these bonds must be supplied during the melting process and only a

relatively minor amount of energy is reclaimed from the change in volume (PV = -0.166 J mol-1). The free energy

change (G=H-TS, where H=U+PV) must be zero at the melting point. As temperature is increased, the amountof hydrogen bonding in liquid water decreases and its entropy increases. Melting will only occur when there is sufficiententropy change to provide the energy required for the bond breaking. The low entropy (high organization) of liquid watercauses this melting point to be high.

Although ice is very difficult to superheat above its (equilibrium) melting point, tiny amounts of ice (Ih) have beensuperheated to 290 K (without melting) for very short periods (>250 ps) [954a] with the limit of superheating (>1 ns)

established at about 330 K [954b]. [Back]

P2 High boiling point (100C, compare CHCl3 61C)

The boiling point of water is over 150 K higher than expected byextrapolation of the boiling points of other Group 6A hydrides,here shown compared with Group 4A hydrides. It is also much

higher than O2 (90 K) or H2 (20 K). See also below for further

comparisons.

There is considerable hydrogen bonding in liquid water resulting inhigh cohesion (water's cohesive energy density is 2.6 times that ofmethanol), which prevents water molecules from being easily

released from the water's surface. Consequentially, the vaporpressure is reduced. As boiling cannot occur until this vaporpressure equals the external pressure, a higher temperature isrequired.

The pressure/temperature range of liquidity for water is much larger than for most other materials (for example, underambient pressure the liquid range of water is 100C whereas for both H2S and H2Se it is about 25C. [Back]

P3 High critical point (374C, compare CH3CH3 32C)

The critical point of water is over 250 K higher than expected by extrapolation of the

critical points of other Group 6A hydrides, here shown compared with Group 4A

hydrides. For example, the critical point (647 K, 22.06 MPa 322 kg m-3) is far

higher than ethanol (514 K, 6.14 MPa 276 kg m-3), which also hydrogen bonds (butin chains not 3-dimensional) and is much larger and more massive.

The critical point can only be reached when the interactions between the water
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The critical point can only be reached when the interactions between the watermolecules fall below a certain threshold level. Due to the strength and extent of thehydrogen bonding, much energy is needed to cause this reduction in molecular

interaction and this requires higher temperatures. Even close to the critical point, aconsiderable number of hydrogen bonds remain, albeit bent, elongated and no longertetrahedrally arranged [92].

The critical points (C.Pt.), boiling points (B.Pt.) andmelting points (M.Pt.) of the molecules isoelectronicwith water shows water to have higher values.

Ammonia and hydrogen fluoride also have somewhat raised values

as they form molecular clustering, albeit with three donor H-atomsand one lone pair acceptor group or one donor H-atom and threelone pair acceptor groups, respectively; giving a maximum of twohydrogen bonds per molecule, on average. Although solid HF

forms stronger hydrogen bonds, these form linear zigzag chainswith no rings or polygons and hence its three-dimensional structureis weaker. The hydrogen bonds in solid NH3 can form three-

dimensional arrangements but are distorted and weakened. Waterhas two donor H-atoms and two lone pair acceptor groups withclose to tetrahedral angles giving the possibility of four hydrogenbonds per molecule with little distortion. [Back]

P4 Solid water exists in a wider variety of stable (and metastable)crystal and amorphous structures than other materials.

The ability for water to form extensive networks of hydrogen bonds increases the number of solid phases possible. The

open structure of hexagonal ice (19.65 cm3 mol-1), which contains only about 7.5 cm3 mol-1 of water molecules, gives

plenty of scope for different arrangements of the water molecules as the structure is compressed. For comparison,hydrogen sulfide has only four distinct solid phases [119]. [Back]

P5 The thermal conductivity of ice reduces with increasing pressure

Hexagonal ice shows anomalous reduction in thermal conductivity with increasing pressure (as do cubic ice and low-density amorphous ice but not high-density amorphous ice ), which behavior is different from most crystals where thermalconductivity increases with increasing density. Low-density amorphous ice is the only glass to show this peculiar behavior.This anomaly is due to the pressure-induced bending of the hydrogen bonding decreasing the transverse sound velocity[617]. [Back]

P6 The structure of liquid water changes at high pressure

In a similar manner to the formation of the high density crystalline (ice-five and ice seven) and amorphous (HDA) icephases, it is likely that liquid water undergoes a significant change in structure at high pressure (about 200 MPa for liquidwater). The pressure-viscosity, self-diffusion, compressibility and structural properties of water change above about 200MPa. Other changes also occur around 200 MPa, such as the loss of the density maximum and the discontinuity in fast

sound in liquid water. The explanation for all these effects is that there appears to be an increase in interpenetration ofhydrogen bonded networks at about 200 MPa (at 290 K); interpenetration of hydrogen bonded clusters being preferredover more extreme bending or breaking of the hydrogen bonds. This structuring for liquid water at high pressures isconsistent to that found by neutron scattering [1001] and indicates that liquid water structuring at high pressure hassimilarity to that of its high pressure ice phases [1254]. [Back]

P7 Supercooled water has two phases and a second critical point

As water is supercooled it converts mainly into its expanded form (for example, ES) at ambient pressures, which at lowenough temperatures (< -38C) may result in it forming metastable low-density amorphous ice (LDA; although normally it



enough temperatures (< -38C) may result in it forming metastable low-density amorphous ice (LDA; although normally itwill form hexagonal ice at this temperature). If the pressure on LDA is increased above about 200 MPa then LDAundergoes a 30% collapse forming metastable high-density amorphous ice (HDA) but notably in a continuous process

without breaking the hydrogen bonds [394]. This phase change cannot continue to higher temperatures (so creating asecond critical point, [45]) as neither of these phases is stable in the presence of liquid water although they may convertinto their metastable supercooled liquid forms. The presence of these low- and higher-density forms of liquid(supercooled) water leads to the breakdown of the Stokes-Einstein relationship in supercooled water [1040] occurringfar above the glass-transition temperature, in contrast to many supercooled liquids where this behavior is found only attemperatures just above this transition [1040b]. [Back]

P8 Liquid water is easily supercooled but glassified with difficulty

Water freezing is not simply the reverse of ice melting [1110]. Melting is a single step process that ocurrs at the meltingpoint as ice is heated whereas freezing of liquid water on cooling involves ice crystal nucleation and crystal growth thatgenerally is initiated a few degrees below the melting point even for pure water. Liquid water below its melting point issupercooled water. It may be expected that the directional hydrogen bonding capacity of water would reduce itstendency to supercool as it would encourage the regular structuring in cold liquid that may lead to a crystalline state.Liquid water, however, is easily supercooled down to about -25C and with more difficulty down to about -38C withfurther supercooling possible, in tiny droplets (~5 m diameter), down to about -41C under normal atmosphericpressure. Water, supercooled down to -37.5C, is sustained in storm clouds and the condensed clouds formed by

aircraft at high altitude. Rather strangely, at the limit of this supercooling (also known as the homogeneous freezing point)

the water activity is always 0.305 lower than that of water melting at the same temperature [457]. Where salts orhydrophilic solutes are present, the homogeneous freezing point reduces about twice as much as the melting point [663].

Liquid water may be maximally supercooled to about -92C and 210 MPa. It should be noted that bulk water neverforms a glass as the glass transition temperature (7J, = ~136 K) for water is far lower, relative to its melting point (7P,273 K), than expected; 7P/7J~ 2 rather than 7P/7J~ 1.3-1.5 as for more typical liquids. Thus supercooled bulk water(LHnot affected by surfaces or solutes) always crystallizes before its temperature can be sufficiently lowered, whateverthe cooling rate [558]. Water glass may only be produced by extremely rapid cooling (105 K s-1) of tiny volumes ofwater (



liquids (for example, methyl cellulose and some cyclodextrin solutions [1026]). [Back]

P10 Liquid water may be easily superheated

Liquid water can be easily superheated above its boiling point away from its surface with the atmosphere [1128, 1184].This may be particularly important when heating foods and drinks in a microwave oven where explosive production ofsteam from the superheated water may cause severe injuries. Superheating is also causes the boiling point of water tovary, in much the same way as its freezing point, and of irregular boiling, that is, 'bumping' [1184]. Liquid water may besuperheated to about +240C to +280C in capillaries or small droplets within high-boiling immiscible solvents.Superheating is also apparent at low tepertures but at negative pressures (i.e. stretched water). Water may be

superheated by reducing the pressure to below -100 MPa at 20C [1128]. Superheating is facilitated by dissolved gasthat may increase its hydrogen-bonded order [821] but prevented by the presence of gas bubbles or nanobubbles (that is,cavities) that act as initiation sites for vaporization.

Water vapor (gas) may easily be cooled below its condensation temperature (dew point) for its partial pressure (LHitsboiling point ) in the absence of dust, or other, particles or surfaces that help the nucleation process [1184].

An interesting, if unrelated effect (the Leidenfrost effect), is that water droplets remain far longer on a hotplate just above

200C than if the hotplate was just above 100C. (see [960] for an amusing scientific answer to how water boils).[Back]

P11 Hot water may freeze faster than cold water; the Mpemba effect

The ability of hot water to freeze faster than cold seems counter-intuitive as it would seem that hot water must firstbecome cold water and therefore the time required for this will always delay its freezing relative to cold water. Howeverexperiments show that hot water (for example, 90 C) does often (but by no means always) appear to freeze faster thanthe same amount of cold water (for example, 18C) under otherwise identical conditions [158]. This has been recognized

even as far back as Aristotle in the 4th century BC but was brought to the attention of the scientific community by theperseverance of Erasto Mpemba a schoolboy at Iringa School, Tanzania, who refused to reject his own evidence, or bowto disbelieving mockery, that he could freeze ice cream faster if he warmed it first. For a recent review of the Mpembaeffect, see [959].

A number of explanations have been put forward but the most likely scenario(described in [158]) is that the degree of supercooling is greater, under somecircumstances, in initially-cold water than initially-hot water. The initially-hot waterappears to freeze at a higher temperature (less supercooling) but less of the apparentlyfrozen ice is solid and a considerable amount is trapped liquid water. Initially-cold

water freezes at a lower temperature to a more completely solid ice with less includedliquid water; the lower temperature causing intensive nucleation and a faster crystalgrowth rate. If the freezing temperature is kept about -6C then the initially-hot wateris most likely to (apparently) freeze first. If freezing is continued, initially-cold wateralways completely freezes before initially-hot water.

Why initially-cold water supercools more is explained in terms of the gas concentration and the clustering of water.Icosahedral clusters do not readily allow the necessary arrangement of water molecules to enable hexagonal ice crystalinitiation; such clustering is the cause of the facile supercooling of water. Water that is initially-cold will have the maximum(equilibrium) concentration of such icosahedral clustering. Initially-hot water has lost much of its ordered clustering and, ifthe cooling time is sufficiently short, this will not be fully re-attained before freezing. Experiments on low-density wateraround macromolecules have shown that such clustering processes may take some time [4]. It is also possible thatdissolved gases may encourage supercooling by (1) increasing the degree of structuring, by hydrophobic hydration, in the



dissolved gases may encourage supercooling by (1) increasing the degree of structuring, by hydrophobic hydration, in the

previously-cold water relative to the gas-reduced previously-hot water (the critical effect of low concentrations ofdissolved gas on water structure is reported in [294]; re-equilibration taking several days) and (2) increasing the pressureas gas comes out of solution when the water starts to crystallize, so lowering the melting point and reducing the tendencyto freeze (see guestbook). Also, the presence of tiny gas bubbles (cavities produced on heating) may increase the rate ofnucleation, so reducing supercooling [428]. Recently another possibility has been described depending on changes indissolved material with temperature (such as the reduction in bicarbonate in heated 'hard' water), but this has not yet beenexperimentally tested [1014]. The rationale for the Mpemba effect in this case concerns differences in the soluteconcentration at the ice-liquid interface causing a localized lowering of the melting point [1014]. [Back]

P12 Warm water vibrates longer than cold water

It is expected that the lifetime of an excited molecular vibration should decrease as the temperature increases as theenergy and likelihood of interactions with other molecules also both increase. For example, the lifetime of the excitedliquid HCl stretch vibration decreases from 2.1 ns at 173 K to 1.0 ns at 248 K.

In liquid water, the excited OH-stretch vibration has a lifetime of 0.26 ps at 298 K and this lifetime increases to 0.32 ps at358 K [592]. The reason for this is due to the effects of the hydrogen-bonded network. The OH-stretch vibrationnormally relaxes by transferring energy to an overtone of the H-O-H bending vibration. However, as the temperatureincreases the hydrogen bonds of water get weaker, which leads to an increase of the frequency of the stretch vibrationand a decrease of the frequency of the bending vibration. As a result, the overtone of the bending mode shifts out ofresonance with the stretching mode, thereby making the energy transfer less likely. [Back]

Footnotes

a The surface temperature on Mars lies below the triple point of water and its atmospheric pressure is close to this value,such that no liquid water may be found there. [Back]

b Theoretical considerations concerning the ice nucleation site size gives estimates of 45,000 water molecules at -5Cdown to 70 water molecules at -40C [265]. Molecular dynamics studies show that these do not need to form acrystalline structure for crystallization to occur [347]. [Back]

Water structure and science(http://www.lsbu.ac.uk/water/explan2.html)

Explanation of the Density Anomalies of Water (D1-D20)

D1 The density of ice increases on heating (up to 70 K)

Most solids expand and become less dense when heated. Hexagonal, cubic and amorphous ices all become denser atlow temperatures. All expand slightly with cooling at all temperatures below about 70 K with a minimum thermal

expansivity at about 33 K (expansion coefficient () ~ -0.000003 K-1). This appears to be due to alteration in the netbending motion of three tetrahedral hydrogen bonded molecules with temperature, as higher frequency modes arereduced [209]. This is a similar but unrelated phenomenon to the maximum density anomaly that occurs in liquid water.[Back]

D2 Water expands on freezing (compare liquid argon shrinks 12% onfreezing)



It is usual for liquids to contract on freezing andexpand on melting. This is because the molecules

are in fixed positions within the solid but require

more space to move around within the liquid.

When water freezes at 0C its volume increases byabout 9% under atmospheric pressure. If themelting point is lowered by increased pressure, the

increase in volume on freezing is even greater (forexample, 16.8% at -20C [561]). Opposite isshown the molar volumes of ice and water alongthe melting point curve [561].

The structure of ice (Ih) is open with a low packing efficiency where all the water molecules are involved in four straighttetrahedrally-oriented hydrogen bonds; for comparison, solid hydrogen sulfide has a face centered cubic closed packedstructure with each molecule having twelve nearest neighbors [119]. On melting, some of these ice (Ih) bonds break,

others bend and the structure undergoes a partial collapse, like other tetrahedrally arranged solids such as the silicaresponsible for the Earth's crust floating on the outside of our planet. This is different from what happens with most solids,where the extra movement available in the liquid phase requires more space and therefore melting is accompanied byexpansion.

In contrast, it should be noted that the high-pressure ices (ice III, ice V, ice VI and ice VII) all expand on melting to formliquid water (under high pressure). It is the expansion in volume when going from liquid to solid, under ambient pressure,

that causes much of the tissue damage in biological organisms on freezing. In contrast, freezing under high pressuredirectly to the more dense ice VI may cause little structural damage [535].

An interesting phenomenon, due to the expansion on freezing, is the formation of thin ice spikes that occasionally grow outof (pure water) ice cubes on freezing [564a]. This phenomenon appears to be a general property of any material thatexpands on freezing [564b]. [Back]

D3 Pressure reduces ice's melting point (13.35 MPa gives a meltingpoint of -1C)

Increasing pressure normally promotes liquid freezing, shifting the



melting point to higher temperatures. This is shown by a forward

sloping liquid/solid line in the phase diagram. In water, this line is

backward sloping with slope 13 MPa K-1 at 0C, 101.325 kPa.

As the pressure increases, the liquid water equilibrium shiftstowards a collapsed structure (for example, CS ) with higherentropy. This lowers the melting free energy change (G=H-TS) such that it will be zero (that is, at the melting point) at alower temperature.

The minimum temperature that liquid water can exist without everfreezing is -21.985C at 209.9 MPa; at higher pressures waterfreezes to ice-three, ice-five, ice-six or ice-seven at increasingtemperatures. Stretching ice has the reverse effect; ice melting at

+6.5C at about -95 MPa negative pressure within stretched

microscopic aqueous pockets in mineral fluorite [243].a

It should be noted that ice skating (or skiing) does not producesufficient pressure to lower the melting point significantly, except at

very sharp edges, or involving powdered ice on the ice surface.The increase in slipperiness is normally generated by frictional

heating, perhaps initially involving the ultra-thin surface layer ofdisorganized and weakly held frozen water (see [1238] for a

review).

If the increase in volume on freezing is prevented, an increased pressure of up to 25 MPa may be generated in water

pipes; easily capable of bursting them in Winterb. An interesting question concerns what would happen to water cooled

below 0C within a vessel that cannot change its volume (isochoric cooling). Clearly if ice forms, its increased volumecauses an increase in pressure which would lower the freezing point at least until the lowest melting point (-21.985C) is

reached at 209.9 MPa.e A recent thermodynamic analysis concludes that ice nucleation cannot arise above -109C

during isochoric cooling [1053], which is close to the upper bound of the realm of deeply supercooled water (-113C),so it is unclear if ice would ever freeze in such a (unreal) system. [Back]

Melting ice, within a filled and sealed fixed volume, may result in an apparently superheated state where the metastable

iso-dense liquid water is stretched, relative to its equilibrium state at the (effectively) negative pressure, due to itscohesiveness. Consequently, the ES CS equilibrium is shifted towards the more-open ES structure. [Back]

D4 Liquid water has a high density that increases on heating (up to3.984C)

The high density of liquid water is due mainly to the cohesive nature of the hydrogen-bonded network, with each water

molecule capable of forming four hydrogen bonds.g This reduces the free volume and ensures a relatively high-density,

partially compensating for the open nature of the hydrogen-bonded network. Its density, however, is not as great as that

of closely packed, isoelectronic, liquid neon (1207 kg m-3 at 27 K, with molar volume 92.8% of water). It is usual for

liquids to expand when heated, at all temperatures. The change in density is almost mirrored by the size of ortho-



liquids to expand when heated, at all temperatures. The change in density is almost mirrored by the size of ortho-

positronium bubbles,c which are affected by the free volume available and show a minimum at 8C [826].The anomalous

temperature-density behavior of water can be explained as previously [13, 14, 1354] utilizing the range of environmentswithin whole or partially formed clusters with differing degrees of dodecahedral puckering. The density maximum (and

molar volume minimum) is brought about by the opposing effects of increasing temperature, causing both structuralcollapse that increases density and thermal expansion that lowers density. At lower temperatures there is a higher

concentration of ES whereas at higher temperatures there is more CS and fragments, but the volume they occupyexpands with temperature. The change from ES to CS as the temperature rises is accompanied by positive changes in

both entropy and enthalpy due to the less ordered structure and greater hydrogen bond bending respectively.

The change in density with temperature causes an inversion in cold water systems as the temperature is raised aboveabout 4C. Thus in water below about 4C, warmer water sinks whereas when above about 4C, warmer water rises.

As water warms up or cools down through 4C, this process causes considerable mixing with useful consequences suchas increased gas exchange.

Shown below is the variation of the density of ice, liquid water, supercooled water and water vapor, in equilibrium with

the liquid, with temperature (the orthobaric density).

The diagram helps explain why liquid

water cannot exist above the critical

point (C.Pt.). Also shown (inset) is thevariation of the molar volume of liquid

water with temperature about thedensity maximum (at 3.984C). Note

the unusual and rapid approach of thedensities of supercooled water and ice

(estimated at -50C, 100 kPa [580]) atabout the homogeneous nucleation

temperature (~-45C, 101 kPa). Thisapproach moves to lower temperatures

at higher pressures, seemingly absent at

~200 MPa [561] (see below, D5).[Back]

The occurrence of a density maximum, as in water, is sometimes if only rarely found (or predicted) in other liquids , such

as He, Te, Si and SiO2 for a variety of reasons. The effect in liquid He4 is thought due to zero point energy and a similar

reason has been put forward for water [1301] although, in practical terms, this presents a related if alternative approach

to that above.

Inversely related to changes in densities are thechanges in volumes. Opposite are shown pressure-

temperature curves of liquid water at constant

volume; showing the change in pressure that would

occur with temperature using a (theoretically ideal)constant volume container. There is a minimum in

the curve only for volumes greater than 0.986 cm3

g-1. The data were obtained from the IAPWS-95

equations [540].



D5 Increased pressure reduces the temperature of maximum density

Increasing pressure shifts the water equilibrium towards a more collapsed structure (for example, CS). So, although

pressure will increase the density of water at all temperatures (flattening the temperature density curve), there will be adisproportionate effect at lower temperatures. The result is a shift in the temperature of maximum density to lower

temperatures. At high enough pressures the density maximum is shifted to below 0C (at just over 18.84 MPa). Above28.33 MPa it cannot be observed above the melting point (now at 270.97 K) and it cannot be observed at all above

about 200 MPa. A similar effect may be caused by increasing salt concentration, which behaves like increased pressure inbreaking up the low-density clusters. Thus in 0.36 molal NaCl the temperature of freezing and maximum density coincide

at -1.33C. Higher salt concentrations reduce the temperature of maximum density such that it is only accessible in the

supercooled liquid. Lowering the temperature of maximum density is not a colligative property as both the nature and

concentration of the soluted affects the degree of lowering. The stronger and more linear hydrogen bonding in D2O gives

rise to a 25% smaller shift in the temperature of maximum density (from 11.185C at 0.1 MPa) with respect to increasingpressure [726].

Under negative pressure (that is, increased stretching of liquid water) the temperature of maximum density increases.However, the temperature of maximum density shows a maximum with respect to pressure in this negative pressure region

[419], as at very high negative pressures it reduces as the hydrogen bonds are stretched to breaking point; [Back]

D6 There is a minimum in the density of supercooled water

At a temperature below the maximum density anomaly there must be a minimum density anomaly so long as no phase

change occurs, as the density increases with reducing temperature at much lower temperatures. This was first seen insimulations [498] and is expected to lie below the minimum temperature accessible on supercooling (232 K, [215]) and

close to where both maximum ES structuring and compressibility occur, with the liquid density close to that of hexagonalice (latterly confirmed [871]). It is evident that most anomalous behavior must involve a quite sudden discontinuity at

about the homogeneous nucleation temperature (~228 K, where the densities of supercooled water and ice approach) asthe tetrahedrally arranged hydrogen bonding approaches its limit (two acceptor and two donor hydrogen bonds per water

molecule) and no further density reduction is possible without an energetically unfavorable stretching (or breaking) of thebonds. By use of optical scattering data of confined water and a model that divides the liquid water into two forms of low

and high density, the density minimum has been proposed to lie at 2035 K [1325]. A density minimum at 210 K hasbeen experimentally determined in supercooled D2O contained in 1-D cylindrical pores of mesoporous silica [1195].

Although possibly related, density values obtained for confined water cannot be taken as necessarily giving the density

minimum for the bulk supercooled liquid however. [Back]

D7 Water has a low thermal expansivity (0.00021/C, cf. CCl40.00124/C at 20C)

The thermal expansivity is zero at 3.984C, being negative below and positive above (see density and expansivity

anomalies). As the temperature increases above 3.984C, the cluster equilibrium shifts towards the more collapsedstructure (for example, CS), which reduces any increase in volume due to the increased kinetic energy of the molecules.

Normally the higher the volume a molecule occupies, the larger is the disorder (entropy). Thermal expansivity (P)

P = [V/T]P/V TPNdepends on the product of the fluctuations in these factors. In water, however, the more open structure (for example, ES)is also more ordered (that is, as the volume of liquid water increases on lowering the temperature below 3.984C, the

entropy of liquid water reduces). [Back]



entropy of liquid water reduces). [Back]

D8 Water's thermal expansivity reduces increasingly (becomingnegative) at low temperatures.

It is usual for liquids to expand increasingly with increased temperature.

Supercooled and cold (< 3.984C) liquid water both contract

on heating [68]. As the temperature decreases, the clusterequilibrium shifts towards the expanded, more open, structure

(for example, ES), which more than compensates for any

decrease in volume due to the reduction in the kinetic energy ofthe molecules. It should be noted that this behavior requires

that the thermodynamic work (dW) equals -pV rather thanthe usual +pV (pressure times change in volume) [404]. The

behavior expected, if water acted as most other liquids atlower temperatures, is shown as the dashed line opposite. The

blue line shows the expansivity of ice. Also, for water and othermaterials with negative thermal expansivity, both and

are negative [1147] whereas normally both are

positive.

D9 Water's thermal expansivity increases with increased pressure.

The thermal expansion of water increases with increased

pressure up to about 44C in contrast to most other liquids

where thermal expansion decreases with increased pressure.

This is due to the collapsed structure of water having a greaterthermal expansivity than the expanded structure and the

increasing pressure shifting the equilibrium towards a morecollapsed structure.

Opposite is shown (blue area) the range of temperatures andpressures where the thermal expansion increases with

increased pressure. [Back]



D10 The number of nearest neighbors increases on melting

Each water molecule in hexagonal ice has four nearest neighbors. On melting, the partial collapse of the open hydrogenbonded network allows nonbonded molecules to approach more closely so increasing this number. Normally in a liquid

the movement of molecules, and the extra space they find themselves in, means that it becomes less likely that they will befound close to each other; for example, argon has exactly twelve nearest neighbors in the solid state but only an average

of about ten on melting. [Back]

D11 Nearest neighbors increase with temperature

If a water molecule is in a fully hydrogen-bonded structure with strong and straight hydrogen bonds (such as hexagonalice) then it will only have four nearest neighbors. In the liquid phase, molecules approach more closely due to the partial

collapse of the open hydrogen bonded network. As the temperature of liquid water increases, the continuing collapse ofthe hydrogen bonded network allows nonbonded molecules to approach more closely so increasing the number of

nearest neighbors. This is in contrast to normal liquids where the increasing kinetic energy of molecules and space

available due to expansion, as the temperature is raised, means that it becomes less likely that molecules will be foundclose to each other. [Back]

D12 Water has unusually low compressibility (0.46 GPa-1, compare

CCl4 1.05 GPa-1, at 25C)f

It may be thought that water should have a high compressibility (T = -[V/P]T/V) as the large cavities in liquid water

allows plenty of scope for the water structure to collapse under pressure without water molecules approaching close

enough to repel each other. The deformation causes the growth in the radial distribution function peak at about 3.5 with

increasing or pressure [51] (and temperature [50]), due to the collapsing structure. The low compressibility of water isdue to water's high-density, again due to the cohesive nature of the extensive hydrogen bonding. This reduces the free

space (compared with other liquids) to a greater extent than the contained cavities increase it. At low temperatures D2O

has a higher compressibility than H2O (for example, 4% higher at 10C but only 2% higher at 40C [188]) due its

stronger hydrogen bonding producing an ES CS equilibrium shifted towards the more-open ES structure. Also

noteworthy is that solutions of highly compressible liquids, such as diethyl ether (1.88 GPa-1) in water, reduce thecompressibility of the water, as they occupy its clathrate cavities. [Back]

D13 Compressibility drops as temperature increases (up to aminimum at about 46.5C)

In a typical liquid the compressibility decreases as the structure becomes more compact due to lowered temperature. In

water, the cluster equilibrium shifts towards the more open structure (for example, ES ) as the temperature is reduced dueto it favoring the more ordered structure (that is, G for ES CS becomes more positive). As the water structure is

more open at these lower temperatures, the capacity for it to be compressed increases [68].

The effect is not a simple dependencyon density, however, or else the

minimum at 46.5C for isothermal (that

is, without change in temperature)compressibility

T = -[V/P]T/V

T = [/P]T/ TPN

and the minimum at 64C for adiabatic

(that is, without loss or gain of heatenergy, also called isentropic)



energy, also called isentropic)

compressibility (S = -[V/P]S/V

[112]) would both be at the densityminimum (4C). Relationships between

T and S are given elsewhere.The adiabatic compressibility lies below the isothermal compressibility except atthe temperature of maximum density where they are equal.

Compressibility depends on fluctuations in the specific volume and these will be large where water molecules fluctuate

between being associated with a more open structure, or not, and between the different environments within the water

clusters. At high pressures (for example, ~200 MPa) this compressibility anomaly, although still present, is far lessapparent [706].

Some other liquids, such as formamide (also extensively hydrogen bonded), show a compressibility minimum. [Back]

D14 There is a maximum in the compressibility-temperaturerelationship

At sufficiently low temperature, there must be a maximum in this compressibility-temperature relationship, so long as no

phase change occurs, as the compressibility decreases with reducing temperature at much lower temperatures.. This isexpected to lie just below the minimum temperature accessible on supercooling (232 K, [215]) close to the temperature

of minimum density. [Back]

D15 Speed of sound is slow and increases with temperature (up to amaximum at 74C)

Sound is a longitudinal pressure wave, whereby the energy is propagated as deformations in the media but the molecules

then return to their original positions and are not propagated. The propagation of a sound wave depends on the transfer of

vibration from one molecule to another. In a typical liquid, the speed of sound is faster (see fast sound) and decreases as

the temperature increases, at all temperatures. The speed of sound in water is almost five times greater than that in air

(340 m s-1).

The speed (X) is given by X2 = 1/S = [P/]S ~ 1/() [802] where S is the adiabatic compressibility, is thedensity and P the pressure. The anomalous nature of both these physical properties is described above (compressibility,density).

At low temperatures both compressibility and density are

high, so causing a lower speed of sound. As thetemperature increases the compressibility drops and goes

through a minimum whereas the density goes through a

maximum and then drops [67]. Combination of these twoproperties leads to the maximum in the speed of sound.

Increasing the pressure increases the speed of sound andshifts the maximum to higher temperatures, both in line with

the effect on the density. The supercooled data has beencalculated for the graph, right.

The presence of salt causes small shifts in the temperature maximum in line with the Hofmeister series; reducing the

temperature at higher concentrations. Ionic kosmotropes cause a slight increase in the temperature maximum at low

concentrations [921]. [Back]

D16 The speed of sound may show a minimum



Depending on the frequency, there may be a minimum in the speed of soundat low temperatures [568]. Although this may be thought due to

compensation in the changes in density decrease and compressibilityincrease with lowering temperature, this is not apparent in the calculated data

above. It is most likely due to the increasing strength of its hydrogen bondingand consequential transition to 'fast sound' at lower frequencies (see below).

The data opposite is from [1151]

The speed of sound in the oceans has a minimum at about 1000 m where theincrease in speed due to increasing pressure balances the decreasing speed

with drop in temperature. Sound waves are trapped and propagatehorizontally in this SOFAR channel. [Back]

D17 'Fast sound' is found at high frequencies and shows andiscontinuity at higher pressure

Water has a second sound 'anomaly' (called 'fast sound') concerning the speed of sound. Over a range of high frequencies

(> 4 nm-1) liquid water behaves as though it is a glassy solid rather than a liquid and sound travels at about twice its

normal speed (~3200 m s-1; similar to the speed of sound in ice 1h). There is little effect of temperature below 20C[1151]. At lower temperatures the speed of sound increases from its low frequency value towards the high frequency

value (i.e. 'fast sound') at lower frequencies, giving rise to a minimum in the temperature-speed of sound relationship[1151] (see above). 'Fast sound' is not a true anomaly as this behavior is what might be expected from a typical liquid,

whereas the (hydrodynamic) lower speed of sound (~1500 m s-1) is due to the hydrogen bonding network structure of

water. However, there does appear to be a discontinuity anomaly at a density of about 1.12 g cm-1 (in this 'fast sound'only; the discontinuity is less apparent in the hydrodynamic speed of sound) that may indicate a structural rearrangement[644, 655], due to the gradual phase transition to interpenetrating hydrogen bonded networks at the higher pressures, as

seen with other anomalies. [Back]

D18 NMR spin-lattice relaxation time is very small at lowtemperatures

NMR spin-lattice relaxation time depends on the degree of structure. As the water cluster equilibrium shifts towards astiffer, tetrahedrally organized, structure (for example, ES) as the temperature is lowered, the NMR spin-lattice relaxation

time reduces far more than would otherwise be expected [53a]. This effect can be partially reversed by increasing the

pressure, which reduces the degree of structure. [Back]

D19 The refractive index of water has a maximum value at just below0C.

The refractive index of water ( = 589.26 nm) rises from anestimated 1.33026 at -30C to a maximum value at just below

0C (1.33434) before falling ever increasingly to 1.31854 at100C [310]. This may be explained by the mixture model [60]

applied to the change from ES to CS as the temperature rises; ESpossessing a lower refractive index than CS. Most of the effect is

due to the density difference between ES and CS. Higher densityproduces higher refractive index such that the refractive index

temperature maximum lies close to the density maximum, with thesmall difference due to the slightly different effect of temperature



small difference due to the slightly different effect of temperature

on the specific refractions of ES and CS. Although not considered

anomalous, it is interesting to note that ice has the lowest refractiveindex (1.31, = 589 nm) of any known crystal. [Back]

D20 The change in volume as liquid changes to gas is very large.

Water is one of the lightest gasses but forms a dense liquid. The volume change is the greatest known (except for metals)at 1603.6 fold, at the boiling point and standard atmospheric pressure. This change in volume allows water to be of great

use in the steam generation of electrical power. [Back]

Footnotes

a There is some dispute over whether such a negative pressure can be reached [917]. [Back]

b Pipes burst due to the rapid formation of a network of feathery dendritic ice enclosing water which then expands onfreezing within a now restricted volume to generate the required pressure [354]. The curious phenomenon of hot water

pipes bursting more often than cold water pipes (see [959]) is due to the differences in this dendritic ice formation causingblockage in the pipes at low percentage ice formation. [Back]

c RUWKR-Positronium consists of a positron - electron pair with parallel spins [826], created here by positron irradiation ofwater. [Back]

d The depression in the temperature of maximum density is linearly related to concentration for most solutes (ethanol and

methanol are exceptional giving a slight increase in the temperature of maximum density at low concentrations) [1037], asdiscovered in 1839 by Despretz. [Back]

e It would be impossible to reach this pressure in a container, unless pressure was also exerted from the outside, due tothe pressure induced expansion of the vessel. [Back]

f Others take a contrary view, stating that water's compressibility is twice that expected [53b]. This difference is down to

the viewpoint and different theoretical expectations. In both cases, water's compressibility is unexpected; either beinggreater than expected due to water's open structure or less than expected (in spite of its open structure) due to the

cohesive nature of its extensive hydrogen bonding. [Back]

g In liquid methanol (CH3OH) the oxygen atoms are 3% closer than they are in liquid water but its density is 21% less

than water, due to methanol only able to form only two hydrogen bonds per molecule. [Back]


(http://www.lsbu.ac.uk/water/explan4.html)

Explanation of the Thermodynamic Anomalies of Water (T1-T11)

T1 The heat of fusion of water with temperature exhibits a maximumat -17C [15].

This strange behavior has been determined from the variation in ice and water specific heat capacities (Cp). It is due to

changes in the structuring of supercooled water. As the temperature is lowered from 0C the hydrogen-bond strength of

ice increases due to the reduction in their vibrational energy and this gives rise to an increasing difference (as temperatureis lowered) between the enthalpy of the water and ice. At low temperatures (below about -17C) the continued shift, with



is lowered) between the enthalpy of the water and ice. At low temperatures (below about -17C) the continued shift, with

lowering temperature, in the supercooled water CS ES equilibrium towards the ES structure reduces the enthalpy of

the liquid water relative to the ice due to the consequent increase in hydrogen-bond strength and this causes the drop in

the heat of fusion with lowering temperature. [Back]

T2 High specific heat capacity; CV and CP, 4.18 J g-1 K-1 at 25C

(compare pentane 1.66 J g-1 K-1).

Water has the highest specific heat of all liquids except ammonia. As water is heated, the increased movement of water

causes the hydrogen bonds to bend and break. As the energy absorbed in these processes is not available to increase thekinetic energy of the water, it takes considerable heat to raise water's temperature. Also, as water is a light molecule there

are more molecules per gram, than most similar molecules, to absorb this energy. Heat absorbed is given out on cooling,

so allowing water to act as a heat reservoir, buffering against changes in temperature. [Back]

T3 Water has about twice the specific heat capacity of ice or steam(compare benzene where CP liquid = 1.03 x CP solid).

At its melting point the CPs of ice-Ih and water are 38 J mol-1 K-1 and 76 J mol-1 K-1 respectively. The CP's of the other

ices may be up to about 40% higher (ice-three) than that of ice-1h but are all significantly lower than liquid water [606].The specific heats of polar molecules do increase considerably on melting but water shows a particularly large increase.

As water is heated, much of the energy is used to bend the hydrogen bonds; a factor not available in the solid or gaseousphase. This extra energy causes the specific heat to be greater in liquid water. The presence of this large specific heat

offers strong support for the extensive nature of the hydrogen-bonded network of liquid water. [Back]

T4 The specific heat capacity (CP) has a minimum at 36C.

It is usual for the specific heats of liquids to increase with increased temperature at all temperatures.

The (isobaric; also called isopiestic) specific heat capacity

(CP) has a shallow minimum at about 36C (D2O ~120C)

with a particularly steep negative slope below 0C [15, 67].The water cluster equilibrium shifts towards less structure

(for example, CS) and higher enthalpy as the temperature israised. CP is the heat capacity at constant pressure defined

by

CP = (H/T)P TP TPN(that is, equals change in enthalpy with temperature, and

proportional to the square of the entropy (or enthalpy)

fluctuations). The extra positive H due to the shift inequilibrium (at low temperatures) as the temperature is

raised causes a higher CP than otherwise, particularly at

supercooling temperatures where a much larger shift occurs[1353]. This addition to the CP, as the temperature is

lowered, is greater than the 'natural' fall expected, so

causing a minimum to be created. Note that CV equals CPat the temperature of maximum density. Usually in liquidsCP is more than 20% greater than CV.

The CV values for supercooled water may be erroneous,

being calculated from other data and showing an apparentdiscontinuity at about -20C.

It is expected that the large specific heat changes with temperature at low temperatures will be reduced at higher

pressures and this specific heat-pressure minimum will shift to lower temperatures. The minimum in CP has been



pressures and this specific heat-pressure minimum will shift to lower temperatures. The minimum in CP has been

associated with a discontinuity in the Raman depolarization ratio (that is, perpendicular/parallel polarization) data ofdegassed ultrapure water and hence a weak liquid-liquid phase transition at 34.6C (5.8 kPa) [1044]. [Back]

T5 The specific heat capacity (CP) has a maximum at about -45C.

There are large specific heat changes with temperature

at low temperatures but deeply supercooled water haslower specific heat at very low temperatures. At

sufficiently low temperature, there must be a maximum inthe specific heat (CP)-temperature relationship, so long

as no phase change occurs. This is expected to lie just

below the minimum temperature accessible onsupercooling (232 K, [215]), although a modeling

approach using TIP5P gives ~250 K [1352]. The dataopposite for supercooled water (upper red line) is taken

from [906]. [Back]

T6 The specific heat capacity (CP) has a minimum with respect to

pressure.

There is a minimum in the heat capacity (CP) of liquid water with respect to pressure; ~400 MPa at 290 K [606]. This

may be explained as due to the break-up of the hydrogen bonding as the pressure increases below 200 MPa followed byits partial build-up, due to interpenetrating hydrogen bonded networks, at the higher pressures. [Back]

T7 The heat capacity (CV) has a maximum.

The CV (the heat capacity at constant volume, CV = (U/T)V) of liquid water is reported as showing an opposite

anomaly, giving a maximum in the supercooled region (this is not shown in the calculated values graphed above). Theincrease in CP in the supercooled region is because most of the anomalous enthalpy change is associated with the

anomalous volume change. The decrease in CV in the supercooled region is reported as due to the decrease in van der

Waals non-bonded interactions, due to water's low density [682]. [Back]

T8 High heat of vaporization (40.7 kJ mol-1, compare H2S 18.7 kJ

mol-1)

Water has the highest heat of vaporization per gram of any

molecular liquid (2257 J g-1 at boiling point). There is stillconsiderable hydrogen bonding (~75%) in water at 100C. As

effectively all these bonds need to be broken (very few indeedremaining in the gas phase), there is a great deal of energy required

to convert the water to gas, where the water molecules are
http://www.lsbu.ac.uk/php-cgiwrap/water/amorph.html#super



to convert the water to gas, where the water molecules are

effectively separated. The increased hydrogen bonding at lowertemperatures causes higher heats of vaporization (for example,

44.8 kJ mol-1, at 0C).

The high heat of vaporization also causes water to have an anomalously low ebullioscopic constant (that is, effect of solute

on boiling point elevation, 0.51 K kg/mol, compare CCl4 4.95 K kg/mol).Also related is the anomalously low cryoscopic

constant of water. [Back]

T9 High heat of sublimation (51.059 kJ mol-1 at 0C).

The high heats of fusion and vaporization combine to give rise to an anomalously high heat of sublimation. [Back]

T10 High entropy of vaporization (109 J-1 K mol-1, FITrouton'sconstant 85 J K-1 mol-1).

Water also has anomalously high entropy of vaporization due to the hydrogen-bonded order lost on vaporization inaddition to the order lost by virtue of being a liquid changing into a gas. As the heat of vaporization is also anomalously

high, the ratio (Hvap/Svap) is not anomalous.

Interestingly, the entropy of vaporization is inversely related to the absolute temperature from supercooled water to above400K (that is, Svap 1/T). [Back]

T11 The thermal conductivity of water is high and rises to amaximum at about 130C.

Apart from liquid metals, water has the highest thermal conductivity of any liquid. For most liquids the thermal conductivity

(the rate at which energy is transferred down a temperature gradient) falls with increasing temperature but this occurs only

above about 130C in liquid water [188].

As the temperature of water is lowered, the rate at which

energy is transferred is reduced to an ever-increasing extent.Instead of the energy being transferred between molecules, it is

stored in the hydrogen bonding fluctuations within theincreasingly large clusters that occur at lower temperatures.

When the thermal energy is increased it shifts the ES CS

equilibrium towards the CS structure, which possesses greater

flexibility and has a greater number of bent hydrogen bonds,rather than the transference of kinetic energy. It is likely that

there will be a minimum in the thermal conductivity-temperaturebehavior at about -3015C as the amount of fully expanded

network increases and in line with that indicated by the much

higher value found for ice 1h. A modeling approach usingTIP5P gives the minimum at ~250 K [1352].

If the density is kept constant the thermal conductivity isproportional to the square root of the absolute temperature,between 100C and 400C [614]. [Back]

Thermal conductivity along the saturation line (liquid-

vapor equilibrium line). Note that the pressure increaseswith the temperature, see phase diagram. The thermalconductivity becomes infinite at the critical point[IAPWS].





(http://www.lsbu.ac.uk/water/explan3.html)

Explanation of the Material Anomalies of Water (M1-M12)

M1 No aqueous solution is ideal

Ideality depends on the structure of the solvent being unaffected by the solute. Water is not even close to being ahomogeneous phase at the molecular level. Local clustering will be effected by the presence of solutes, so changing thenature of the water. Even solutions of HDO in H2O do not behave ideally. Although most non-aqueous solutions also

show deviations from ideality at higher concentrations, the deviations that occur in aqueous solutions are generally much

more extensive. [Back]

M2 D2O and T2O differ significantly from H2O in their physical

properties

Normally different isotopic forms of compounds behave very similarly to each other. The heavier forms of water (D2O

where D = deuterium, 2.0141017780 g mol-1; and T 2O where T = tritium, 3.0160492675 g mol-1) form stronger

hydrogen bonds than light water (H2O where H = protium, 1.0078250321 g mol-1) and vibrate less. Hence, they are

more ordered than normal water, as shown by their greater molar volumes. This causes many of their properties (such as

the viscosity, self-diffusion coefficient, protein solubility and toxicitya [424]) to be different from those expected from asimple consideration of their increased mass (for example, the D2O/H2O viscosity ratio rises from about 1.16 at 100C to

around 2.0 in deeply supercooled water [23b]. This difference appears as a shift in the equilibrium position equivalent to aslight increase in temperature [425]; for example, viscosity data has been reconciled if the temperatures are shifted by

6.498C and 8.766C for D2O and T2O respectively [73].b H2O is about four-fold stronger as an acid than D2O at

25C and H3O+ in H2O is 1.5 times as strong an acid as D3O

+ in D2O. Remarkably, the difference in the specific heat

minimum between H2O and D2O is over 80C. Most of the differences between the behavior of H2O and D2O may be

explained as due to the nuclear quantum effectsi inherent in the large mass difference between the hydrogen and oxygenatoms [554]. Although the electron densities of the different isotopic forms of liquid water have proved, so far, to be

indistinguishable [566], it is expected that the O-D bond length is shorter than that of O-H due to its smaller asymmetricvibration and the smaller Bohr radius of D relative to H. This gives rise to small differences in the size and direction of thedipole moment between HDO and H 2O [1174], which further confuses any analysis of the structure of water containing

mixed hydrogen isotopes.

Almost pure H2O and D2O exist but HDO can never be more than about 50% pure, existing only in the presence of both

H2O and D2O. Mixtures of H2O and D2O equilibrate to form HDO:

H2O + D2O 2HDO Keq = 3.82, 25C [609], H = 129.4 J mol-1 [654]

which is close to a total randomization of the hydrogen atoms (that is, equal concentrations of HOH, HOD, DOH andDOD giving Keq = 4) but is reflected in a slight preference for the partitioning of the deuterium-containing species into the

more extensive and stronger hydrogen-bonded clusters. The Keq decreases with decreased temperature [126a] and

increased hydrogen bond cooperativity [985]. Even the properties of HDO deviate from those expected from aconsideration of the properties of H2O and D2O [126b], with the D-atom preferring to be hydrogen bonded over the H-

atom except where the H-bond is particularly short (as in H5O2+) [985]. The vibrational spectrum of HDO is

fundamentally different from either H2O or D2O due to the separation of the two hydroxyl (O-H and O-D) vibrations in

HDO but their combined motion in H2O and D2O. In HDO the H atom is more reactive and more easily dissociated than

the D atom. As hydrogen bonding is a property of at least two water molecules, isotopic mixtures contain many differentlypaired (and more extensive) species each of which may present different properties to those in natural liquid water. It is

clear that care must be taken over extrapolating the properties of H2O/D2O mixtures (often used in neutron scattering and



vibrational spectroscopic studies) to those of normal liquid water (that is, 99.97% H2O). For example, D2O is

preferentially found at hydrophilic interfaces [1342].

Liquid T2O is corrosive due to self-radiolysis (3H 3He + e- + anti-neutrino, ~4.4 x 1015 decays s-1 mol-1 T2O, LH.

~4.4 PBq mol-1 T2O). The particles travel only about 6 m in water and even dilute solutions of HTO produce gaseous

hydrogen (including HT) and redox-active products including highly reactive OH radicals.

Even H218O behaves differently from H2

16O due to reduced quantum translational motions, reducing the size of the first

shell local hydrogen-bonded tetrahedron but leaving the non-bonded water distances almost the same [1035]. Although

D2O has similar mass (only 0.04% heavier than H218O), its behavior much more affected by the isotopic substitution, due

to the altered mass distribution influencing its librations and hence the local environment of both the first and second

aqueous shells [1035]. [Back]

M3 Liquid H2O and D 2O differ significantly in their phase behavior.

The phase behavior of liquid H2O and D2O differ, with the triple point of D2O being 3.82C and 49 Pa higher than that

of H2O, their vapor pressure curves crossing at 221C and the critical point of D2O being 3.25C and 393 kPa lower

[1007]. This isotope effect has its origins in the reduced zero point vibration of D2O that reduces its van der Waals

volume (by about 1%) and its associated repulsive effect within the hydrogen bonds at lower temperatures, so increasing

the D2O-D2O hydrogen bond strength.c At higher temperatures the transition to the excited state is more easily

accomplished in D2O (~2450 cm-1, relative to H2O ~3280 cm

-1). Due to the asymmetry of the vibration, this increases

D2O's effective van der Waals volume and reverses the relative repulsive effect, so reducing the D2O-D2O hydrogen

bond strength at higher temperatures.d

As the Keq decreases with decreased temperature [126a] and increased hydrogen bond cooperativity [985] (see above),

at temperatures close to 0 K this may mean that H2O and D2O may form separate phases and are no longer in

equilibrium [985]. [Back]

M4 Solutes have varying effects on properties such as density andviscosity

Solutes will interfere with the cluster equilibrium by favoring either open or collapsed structures. Any effect will cause the

physical properties of the solution, such as density or viscosity, to change. Solutes have a lower than expected effect on

both the cryoscopic (that is, effect of solute on freezing point depression, 1.86 K kg mol-1, compare CCl4 30 K kg mol-1)

and ebullioscopic constants due to water's low molar mass and high heats of fusion and evaporation respectively. [Back]

M5 The solubilities of non-polar gases in water decrease with

increasing temperature to a minimum and then rise.e

Non-polar gases are poorly soluble in water. Most gaseous solutes dissolve more in most solvents as the temperature is

raised. However, non-polar gasses are much more soluble in water at low temperatures than would be expected fromtheir solubility behavior at high temperatures.

The solubilities of the noble gases is shown opposite[IAPWS, 1166] and given below. Their hydration maybe considered as the sum of two processes: (A) the

endothermic opening of a clathrate pocket in the water,



endothermic opening of a clathrate pocket in the water,and (B) the exothermic placement of a molecule in thatpocket, due to the multiple van der Waals interactions

(for example, krypton dissolved in water is surroundedby a clathrate cage with 20 KrOH2 such interactions

[1357]). In water at low temperatures, the energyrequired by process (A) is very small as such pocketsmay be easily formed within the water clustering (by CS

ES)f.

Using the noble gases to investigate the solvation of non-polar gases is useful as they are spherically symmetrical and have

low polarizability, whereas shape and polarizability may confuse the hydration of other gases. The solubility of the noblegases increases considerably as the temperature is lowered. Their enthalpy and entropy of hydration become morenegative as their fit into the water dodecahedral clathrate improves.

He Ne Ar Kr Xe Rn

Atomic number 2 10 18 36 54 86

Atomic radius, [1167] 1.08 1.21 1.64 1.78 1.96 2.11

G of solution in H2O at 25C, kJ mol-1 [1296] 29.41 29.03 26.25 24.80 23.42

H of solution in H2O at 25C, kJ mol-1 [1296] -0.59 -3.80 -11.98 -15.29 -18.99

S of solution in H2O at 25C, J mol-1 K-1 [1296] -100.6 -110.1 -128.2 -134.5 -142.2

Solubility, mM, 5C, 101,325 Pa [1166]H2O 0.41 0.53 2.11 4.20 8.21 18.83

D2O 0.49 0.61 2.38 4.61 8.91 20.41

Solubility minima, C [IAPWS, 678]H2O 30 50 90 108 110

D2O 53 53 98 108 116

Oxygen (O2) and nitrogen (N2) molecules behave similarly (solubility minima at N2 74C and O2 94C, IAPWS),

although their solubilities are low (O2, 1.92 mM in H2O, 2.14 mM in D2O; N2, 0.94 in H2O, 1.05 mM in D2O; all at

5C, 101,325 Pa [1168]). The greater solubility of O2 over N2, in spite of its lesser clathrate forming ability [1168] has

been proposed due to its formation of weak hydrogen bonds to water [1168]. g

The solubilization process is therefore exothermic (that is, has negative H) and (as predicted by Le Chatelier's principle)

solubility decreases with temperature rise. At high temperatures (often requiring high pressure) the natural clustering ismuch reduced causing greater energy to be required for opening of the pocket in the water. The solubilization processtherefore becomes endothermic and (as predicted by Le Chatelier's principle) solubility goes through a minimum beforeincreasing with temperature rise (being fully miscible under supercritical conditions).

The more attractive the solute-water van der Waalsinteractions (due both to atomic number dependency andgoodness of fit within the clathrate pocket), the greater theinherent exothermic nature of the process and therefore the

higher the temperature minimum (see Table above) and thegreater the temperature range of negative temperature solubilitycoefficient. Similarly Henry's constants (= partial pressure/mole

fraction;h represents volatility, see opposite) exhibit increasing



fraction;h represents volatility, see opposite) exhibit increasing

maxima with increasing size (the maxima are the same as thesolubility minima above).

The poor solubility of non-polar gases in water, in spite of the negative enthalpy change on dissolution, is due to positivefree energy change (+ve G) attributed to the large negative entropy change (-ve TS) caused by the structural

enhancement of the water (ES) clusters; a conclusion reinforced by the enhanced heat capacity of these solutions (+veCp, characteristic of a decrease in the degrees of freedom of the water solvent). This structural enhancement may include

the fixing of the cluster centers, preventing the randomizing flickering between clusters otherwise evident, as well asordering the inner dodecahedral water shells surrounding the solute molecules. There is also a reduction in volume (-ve

V) showing a reduction in the unoccupied space within the water solvent and also indicative of the gases occupying thepre-existing, if collapsed, clathrate sites. Counter-intuitively in spite of it forming stronger hydrogen bonds, D2O is a better

solvent than H2O for non-polar gases, as it is a more static molecule and more easily forms the ES water clustering.

Therefore D2O can accommodate the guest molecules more easily without breaking its hydrogen bonds [874]. Addition

of positively hydrating salts (for example, LiCl) that destroy the water low-density ES clustering reduce the solubility ('saltout') of the non-polar gases whereas hydrophobic hydrating salts (for example, tetramethylammonium chloride) thatincrease water low-density ES clustering stability also increase non-polar gas solubility ('salt in'). Small non-polar organic

molecules also behave similarly to non-polar gases, but their increased size alters the clathrate structuring. Thus benzenehas a solubility minimum, at a lower temperature than expected from above, at about 20C [210].

Interestingly, the change in solubility of non-polar gases with respect to their diameters has a maximum (and their freeenergy of hydration has a minimum) when diameters are about the same as that of the dodecahedral cavities (that is, ~4.5) in the icosahedral network [196]. The solubility behavior of larger hydrophobic molecules is discussed briefly

elsewhere. It should also be noted that the solvent properties of liquid superheated water also change with temperature aswater's dielectric permittivity reduces towards that of common organic solvents as the temperature rises towards itscritical point.

Even though the amount of air (that is, N2 + O2 + Ar) dissolved in water is very low, it is sufficient to lower the density of

water by almost 5 ppm (that is, 0.0005%) at 0C [870].

It should be clear from the above discussion that the solubility of non-polar gases, in water at its boiling point, is not zero;an error propagated by some text-books.

The solubility of gases (and other solutes such as salts) in ice is very low. This explains the usefulness of freeze-thawoperations under reduced pressure for degassing water. [Back]

M6 The dielectric constant of water is high (78.4 at 25C)

Polar molecules, where the centers of positive and negative charge are separated, possess dipole moment. This means

that in an applied electric field, polar molecules tend to align themselves with the field. Although water is a polar molecule,its hydrogen-bonded network tends to oppose this alignment. The degree to which a substance does this is called itsdielectric constant (permittivity). Because water possesses a hydrogen bonded network that transmits polarity shifts

extensively through rapid and linked collective changes in the orientation of its hydrogen bonds, it has a high dielectricconstant. This allows it to act as a solvent for ionic compounds, where the attractive electric field between the oppositelycharged ions is reduced by about 80-fold, allowing thermal motion to separate the ions into solution. On cooling, as thewater network strengthens and water's dipole moment increases, the dielectric of liquid water climbs to 87.9 (0C),

increasing on conversion to ice then increasing further as the ice is cooled. On heating, the dielectric constant drops, andliquid water becomes far less polar, down to a value of about 6 at the critical point. The dielectric constant similarlyreduces if the hydrogen bonding is broken by other means such as strong electric fields but not with pressure. The changein dielectric with temperature gives rise to considerable and anomalous changes in its solubilization and partition properties

with temperature, which are particularly noticeable in superheated water [610] where the dielectric is low, and insupercooled water where the dielectric is high and increases (107.7 at -35C) even as the density decreases. Pressureincreases the dielectric constant (101.42 at 0C and 500 MPa), due to its effect on the density.
http://www.lsbu.ac.uk/php-cgiwrap/water/phobic.html#solhttp://www.lsbu.ac.uk/php-cgiwrap/water/magnetic.html



increases the dielectric constant (101.42 at 0C and 500 MPa), due to its effect on the density.

Perhaps the high dielectric constant of water should not be considered anomalous as other small polar molecules (withhigher dipole moments) form liquids also having high dielectric constants (see below).The ratio dielectric constant/(dipolemoment)2 is often also reckoned, by others, to be anomalously high in liquid water (but note that the gas-phase, rather

than liquid, dipole moments are used for comparing these substances). Although high, clearly molecules with zero dipolemoment (HJCCl4) have infinite such values.

Shown opposite are the dipole moments (bluetriangles below) and dielectric constant/(dipole

moment)2 ratios (red diamonds above) relative to the

dielectric constants for a range of solvents. The data1-17 correspond to 1, diethyl ether; 2, chloroform;3, methylene dichloride; 4, methyl ethyl ketone; 5,

acetone; 6, ethanol; 7, methanol; 8, acetonitrile; 9,ethylene glycol; 10, dimethylsulfoxide; 11, hydrazine;12, formic acid; 13, water; 14, sulfuric acid; 15,formamide; 16, hydrogen cyanide; and 17, N-methyl

formamide respectively. [Back]

M7 The dielectric constant shows a temperature maximum.

Anomalous dielectric behavior of water is found over a range

of microwave frequencies between about 2 and 100 GHz

whereby the real (') and/or the imaginary ('') part of thecomplex dielectric constant increase then decrease withincreasing temperature. Examples at two close frequenciesfor liquid (including supercooled) water are shown opposite[588]. This may be understood by noting the shifts with

temperature of the maximum frequency of microwaveabsorption and the dielectric permittivity.

Analysis of the complex permittivity gives a discontinuity atabout 30C [1045]. [Back]

M8 Proton and hydroxide ion mobilities are anomalously fast in anelectric field.

The ionic mobilities of hydrogen ions and hydroxide ions at 361.9 and 206.5 (nm s-1)/(V m-1) at 25C are very high

compared with values for other small ions such as lithium (40.1 (nm s-1)/(V m-1)) and fluoride (57.0 (nm s-1)/(V m-1))

ions. This is explained by the Grotthuss mechanism.



The limiting ionic conductivities are related (= mobility x charge x Faraday) and their values

Water Structure and Science

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