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

Water Anomalies

link Phase anomalies (P1-P12) explanations
link Density anomalies (D1-D20) explanations
link Material anomalies (M1-M12) explanations
link Thermodynamic anomalies (T1-T11) explanations

link 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 most atypical 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 local temperature 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-dimensional structures, 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 between molecules, 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) the necessity 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 the water 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 as much 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 it decreases, 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 different bounds [169]. These are shown indicatively opposite as derived from modeling, not experimental data. The Structural bounds indicate where water is more disordered when compressed, the Dynamic bounds indicate where diffusion increases 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 always increases with increasing pressure, a similar relationship holds with pressure along the horizontal axis. Heirarchy of anomalies, based on SPC/E model of Ref. 169. This graph is indicative only and does not show experimental points

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]

Anomalies of water graph

Legend

Some of the anomalies of water related to temperature.

The graph uses data that have been scaled between their maximum 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 those properties that one might deduce from its structure (see for example, [402]). Other tetrahedrally interacting liquids, such as 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 to make 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 solubility prediction, 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; an interesting if somewhat unproductive hypothesis as a sole explanation (as the attribution mixes cause with effect). Water's anomalies 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)

link Density anomalies (D1-D20) explanations
link Material anomalies (M1-M12) explanations
link Thermodynamic anomalies (T1-T11) explanations
link Physical anomalies (F1-F9) explanations

 

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

Phase diagram of water (H2O) showing the melting, boiling and triple points Melting point, 0.00C, 101.325 kPa Boiling point, 100.0C, 101.325 kPa Triple point, 0.01C , 611.657 Pa, 0.99978 g cm-3 Partial phase diagram of water (H2O) showing the melting (M.Pt.), boiling (B.Pt.) and triple (T.Pt) points.a
Melting point comparisons CH4, -182.5C SiH4, -185C GeH4, -164.8C SnH4, -146C H2O, 0C H2S, -85.5C H2Se, -65.7C H2Te, -51C H2Po, -36C
The melting point of water is over 100 K higher than expected by extrapolation of the melting points of other Group 6A hydrides, here above shown compared with Group 4A hydrides. It is also much higher 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 held relatively static. In liquid water, some of the weaker hydrogen bonds must be broken to allow the molecules to move around. 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 (PΔV = -0.166 J mol-1). The free energy change (ΔG=ΔH-TΔS, where ΔH=ΔU+PΔV) must be zero at the melting point. As temperature is increased, the amount of hydrogen bonding in liquid water decreases and its entropy increases. Melting will only occur when there is sufficient entropy change to provide the energy required for the bond breaking. The low entropy (high organization) of liquid water causes this melting point to be high.

Although ice is very difficult to superheat above its (equilibrium) melting point, tiny amounts of ice (Ih) have been superheated 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]. [Backto top of page

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

The boiling point of water is over 150 K higher than expected by extrapolation 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 in high cohesion (water's cohesive energy density is 2.6 times that of methanol), which prevents water molecules from being easily released from the water's surface. Consequentially, the vapor pressure is reduced. As boiling cannot occur until this vapor pressure equals the external pressure, a higher temperature is required.

Boiling point comparisons CH4, -161.6C SiH4, -111C GeH4, -88.1C SnH4, -52C H2O, 100C H2S, -60C H2Se, -41C H2Te, -2C H2Po, 37C

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

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 (but in chains not 3-dimensional) and is much larger and more massive.

The critical point can only be reached when the interactions between the water molecules fall below a certain threshold level. Due to the strength and extent of the hydrogen bonding, much energy is needed to cause this reduction in molecular interaction and this requires higher temperatures. Even close to the critical point, a considerable number of hydrogen bonds remain, albeit bent, elongated and no longer tetrahedrally arranged [92].

Critical point comparisons CH4, -82.7C SiH4, -3.5C GeH4, 34.8C H2O, 374C H2S, 100C H2Se, 138C H2Te, 200C
The critical points (C.Pt.), boiling points (B.Pt.) and melting points (M.Pt.) of the molecules isoelectronic with water shows water to have higher values.
Physical properties of molecules isoelectronic to water Ne, C.Pt. 44.4 K, B.Pt. 27.07 K, M.Pt. 24.56 K HF, -83C HF, 19.5C HF, 188C NH3, -77.7C NH3, -33.4C NH3, 132.2C, 11.339 MPa CH4, -182.5C H2O, 0C CH4, -161.6C H2O, 100C CH4, -82.7C H2O, 374C
 
Ammonia and hydrogen fluoride also have somewhat raised values as they form molecular clustering, albeit with three donor H-atoms and one lone pair acceptor group or one donor H-atom and three lone pair acceptor groups, respectively; giving a maximum of two hydrogen bonds per molecule, on average. Although solid HF forms stronger hydrogen bonds, these form linear zigzag chains with no rings or polygons and hence its three-dimensional structure is weaker. The hydrogen bonds in solid NH3 can form three-dimensional arrangements but are distorted and weakened. Water has two donor H-atoms and two lone pair acceptor groups with close to tetrahedral angles giving the possibility of four hydrogen bonds per molecule with little distortion. [Backto top of page

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]. [Backto top of page

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 thermal conductivity 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]. [Backto top of page

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) ice phases, it is likely that liquid water undergoes a significant change in structure at high pressure (about 200 MPa for liquid water). The pressure-viscosity, self-diffusion, compressibility and structural properties of water change above about 200 MPa. 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 of hydrogen bonded networks at about 200 MPa (at 290 K); interpenetration of hydrogen bonded clusters being preferred over more extreme bending or breaking of the hydrogen bonds. This structuring for liquid water at high pressures is consistent to that found by neutron scattering [1001] and indicates that liquid water structuring at high pressure has similarity to that of its high pressure ice phases [1254]. [Backto top of page

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 low enough temperatures (< -38C) may result in it forming metastable low-density amorphous ice (LDA; although normally it will form hexagonal ice at this temperature). If the pressure on LDA is increased above about 200 MPa then LDA undergoes 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 a second critical point, [45]) as neither of these phases is stable in the presence of liquid water although they may convert into 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] occurring far above the glass-transition temperature, in contrast to many supercooled liquids where this behavior is found only at temperatures just above this transition [1040b]. [Backto top of page

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 melting point as ice is heated whereas freezing of liquid water on cooling involves ice crystal nucleation and crystal growth that generally is initiated a few degrees below the melting point even for pure water. Liquid water below its melting point is supercooled water. It may be expected that the directional hydrogen bonding capacity of water would reduce its tendency 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 with further supercooling possible, in tiny droplets (~5 μm diameter), down to about -41C under normal atmospheric pressure. 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 or hydrophilic 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 never forms a glass as the glass transition temperature (Tg, = ~136 K) for water is far lower, relative to its melting point (Tm, 273 K), than expected; Tm/Tg ~ 2 rather than Tm/Tg ~ 1.3-1.5 as for more typical liquids. Thus supercooled bulk water (i.e. not affected by surfaces or solutes) always crystallizes before its temperature can be sufficiently lowered, whatever the cooling rate [558]. Water glass may only be produced by extremely rapid cooling (105 K s-1) of tiny volumes of water (<~100 μm diameter).

As water is cooled, the cluster equilibrium shifts towards the more open structure (e.g. ES ) with higher viscosity. In order for crystallization to occur at least 3 - 4 unit cells worth of water molecules have to come together in the correct orientation.b The formation of whole or part icosahedral clusters interferes with this process whilst not allowing cluster crystallization due to their five fold symmetry. Lowering the temperature further, which should encourage crystallization, is partially counteracted by the increase in icosahedral clustering. The presence of ES clusters is, in principle, in agreement with computer simulation studies requiring the presence of metastable states [216]. Methods that break the hydrogen bonding in these clusters, such as ultrasonics [296], cause the supercooled water to immediately freeze.

There is a recent comprehensive review of the properties of supercooled water [569]. [Backto top of page

P9    Liquid water exists at very low temperatures and freezes on heating

Deeply supercooled liquid water can be produced from glassy amorphous ice between -123C and - 149C [74] and may coexist with cubic ice up to -63C [137]. This behavior is particularly anomalous as the liquid  (deeply supercooled water) is a 'strong' liquid (compared with supercooled water that is a 'fragile' liquid [493]) that changes to crystalline solid (cubic ice) on increasing the temperature whilst keeping the pressure constant. Deeply supercooled water exists in the liquid state where it appears to be too cold to diffuse sufficiently quickly to crystallize noticeably. A possible explanation of this low-temperature-range liquid water may be the formation of strands of icosahedral structures. This model can also explain the high viscosity and strong (that is, low specific heat) liquid behavior of this extremely supercooled water [215]. The unusual behavior of this liquid (that is, deeply supercooled water), by solidifying on heating, has been found with other liquids (for example, methyl cellulose and some cyclodextrin solutions [1026]). [Backto top of page

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 of steam from the superheated water may cause severe injuries. Superheating is also causes the boiling point of water to vary, in much the same way as its freezing point, and of irregular boiling, that is, 'bumping' [1184]. Liquid water may be superheated 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 gas that 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 (i.e. its boiling 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). [Backto top of page

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 first become cold water and therefore the time required for this will always delay its freezing relative to cold water. However experiments show that hot water (for example, 90 C) does often (but by no means always) appear to freeze faster than the 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 the perseverance of Erasto Mpemba a schoolboy at Iringa School, Tanzania, who refused to reject his own evidence, or bow to disbelieving mockery, that he could freeze ice cream faster if he warmed it first. For a recent review of the Mpemba effect, 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 some circumstances, in initially-cold water than initially-hot water. The initially-hot water appears to freeze at a higher temperature (less supercooling) but less of the apparently frozen 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 included liquid water; the lower temperature causing intensive nucleation and a faster crystal growth rate. If the freezing temperature is kept about -6C then the initially-hot water is most likely to (apparently) freeze first. If freezing is continued, initially-cold water always completely freezes before initially-hot water.
Graph showing hot water freezing before cold

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 crystal initiation; 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, if the cooling time is sufficiently short, this will not be fully re-attained before freezing. Experiments on low-density water around macromolecules have shown that such clustering processes may take some time [4]. It is also possible that 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 of dissolved gas on water structure is reported in [294]; re-equilibration taking several days) and (2) increasing the pressure as gas comes out of solution when the water starts to crystallize, so lowering the melting point and reducing the tendency to freeze (see guestbook). Also, the presence of tiny gas bubbles (cavities produced on heating) may increase the rate of nucleation, so reducing supercooling [428]. Recently another possibility has been described depending on changes in dissolved material with temperature (such as the reduction in bicarbonate in heated 'hard' water), but this has not yet been experimentally tested [1014]. The rationale for the Mpemba effect in this case concerns differences in the solute concentration at the ice-liquid interface causing a localized lowering of the melting point [1014]. [Backto top of page

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 the energy and likelihood of interactions with other molecules also both increase. For example, the lifetime of the excited liquid 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 at 358 K [592]. The reason for this is due to the effects of the hydrogen-bonded network. The OH-stretch vibration normally relaxes by transferring energy to an overtone of the H-O-H bending vibration. However, as the temperature increases the hydrogen bonds of water get weaker, which leads to an increase of the frequency of the stretch vibration and a decrease of the frequency of the bending vibration. As a result, the overtone of the bending mode shifts out of resonance with the stretching mode, thereby making the energy transfer less likely. [Backto top of page


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 -5C down to 70 water molecules at -40C [265]. Molecular dynamics studies show that these do not need to form a crystalline 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 at low temperatures. All expand slightly with cooling at all temperatures below about 70 K with a minimum thermal expansivity at about 33 K (expansion coefficient (α) ~ -0.000003 K-1). This appears to be due to alteration in the net bending motion of three tetrahedral hydrogen bonded molecules with temperature, as higher frequency modes are reduced [209]. This is a similar but unrelated phenomenon to the maximum density anomaly that occurs in liquid water. [Backto top of page

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

It is usual for liquids to contract on freezing and expand 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 by about 9% under atmospheric pressure. If the melting point is lowered by increased pressure, the increase in volume on freezing is even greater (for example, 16.8% at -20C [561]). Opposite is shown the molar volumes of ice and water along the melting point curve [561].

 

Changes in the molar volume of water and ice down the melting point curve, data from ref 561

The structure of ice (Ih) is open with a low packing efficiency where all the water molecules are involved in four straight tetrahedrally-oriented hydrogen bonds; for comparison, solid hydrogen sulfide has a face centered cubic closed packed structure 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 silica responsible 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 by expansion.

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 form liquid 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 pressure directly 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 out of (pure water) ice cubes on freezing [564a]. This phenomenon appears to be a general property of any material that expands on freezing [564b]. [Backto top of page

D3    Pressure reduces ice's melting point (13.35 MPa gives a melting point 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 shifts towards a collapsed structure (for example, CS ) with higher entropy. This lowers the melting free energy change (ΔG=ΔH-TΔS) such that it will be zero (that is, at the melting point) at a lower temperature.
Shows how raising the pressure melts water Triple point, 0.01C , 611.657 Pa, 0.99978 g cm-3 Hexagonal ice


 

The minimum temperature that liquid water can exist without ever freezing is -21.985C at 209.9 MPa; at higher pressures water freezes to ice-three, ice-five, ice-six or ice-seven at increasing temperatures. 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 produce sufficient 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 of disorganized and weakly held frozen water (see [1238] for a review).

Effect of pressure on the melting point of ice

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 volume causes 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. [Backto top of page

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 its cohesiveness. Consequently, the ESreversible arrowCS equilibrium is shifted towards the more-open ES structure. [Backto top of page

D4    Liquid water has a high density that increases on heating (up to 3.984C)

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-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 environments within 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 structural collapse 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 occupy expands 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 above about 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 such as 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 the variation of the molar volume of liquid water with temperature about the density maximum (at 3.984C). Note the unusual and rapid approach of the densities of supercooled water and ice (estimated at -50C, 100 kPa [580]) at about the homogeneous nucleation temperature (~-45C, 101 kPa). This approach moves to lower temperatures at higher pressures, seemingly absent at ~200 MPa [561] (see below, D5). [Backto top of page The variation of the density of ice, liquid water and water vapor, in equilibrium with the liquid, with temperature (the orthobaric density) Liquid water, density minimum ~203 K Liquid water, density maximum at ~4C,  ~1 g cm^-3 Ice, density at 0C,  0.9167 g cm^-3 Critical point, 647.096 K, 22.064 MPa, 322 kg m^-3 Supercooled water density, ref [1325] Minimum molar volume, 18.0157 g mole-1 at 3.984C Liquid water, density minimum Liquid water, density maximum at ~4C,  ~1 g cm^-3 Ice, density at 0C,  0.9167 g cm^-3 Critical point, 647.096 K, 22.064 MPa, 322 kg m^-3 Extrapolated supercooled water density Minimum molar volume, 18.0157 g mole-1 at 3.984C Liquid water, density at 0C,  0.9998 g cm^-3 Ice, density at 0C,  0.9167 g cm^-3 Critical point, 647.096 K, 22.064 MPa, 322 kg m^-3 Extrapolated supercooled water density Minimum molar volume, 18.0157 g mole-1 at 3.984C
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.
Pressure -  temperature relationship at constant volume
Inversely related to changes in densities are the changes 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 a disproportionate 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). Above 28.33 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 in breaking 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 increasing pressure [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; [Backto top of page

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 in simulations [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 hexagonal ice (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) as the 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 the bonds. 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 has been 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. [Backto top of page

D7    Water has a low thermal expansivity (0.00021/C, cf. CCl4 0.00124/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 collapsed structure (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 (αP)
                        αP = [δV/δT]P/V is proportional to <(δV)(δS)>TPN
depends 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). [Backto top of page

D8    Water's thermal expansivity reduces increasingly (becoming negative) 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 cluster equilibrium 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 of the molecules. It should be noted that this behavior requires that the thermodynamic work (dW) equals -pΔV rather than the usual +pΔV (pressure times change in volume) [404]. The behavior expected, if water acted as most other liquids at lower temperatures, is shown as the dashed line opposite. The blue line shows the expansivity of ice. Also, for water and other materials with negative thermal expansivity, both (dS/dV)T and (dS/dV)U are negative [1147] whereas normally both are positive.
Change in themal expansivity with temperature of liquid  and supercooled liquid water, (see ref 68) light blue line gives data for ice 1h

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 greater thermal expansivity than the expanded structure and the increasing pressure shifting the equilibrium towards a more collapsed structure.

Opposite is shown (blue area) the range of temperatures and pressures where the thermal expansion increases with increased pressure. [Backto top of page

The range of temperatures and pressures where the thermal expansion increases with increased pressure

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 hydrogen bonded 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 be found 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. [Backto top of page

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 hexagonal ice) 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 of the 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 found close to each other. [Backto top of page

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 (κT = -[δV/δP]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 is due 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 ESreversible arrowCS 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 the compressibility of the water, as they occupy its clathrate cavities. [Backto top of page

D13    Compressibility drops as temperature increases (up to a minimum 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 due to it favoring the more ordered structure (that is, ΔG for ESreversible arrowCS 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 dependency on density, however, or else the minimum at 46.5C for isothermal (that is, without change in temperature) compressibility 
    κT = -[δV/δP]T/V 
    κT = [δρ/δP]T/ρ is proportional to <(δV)2>TPN
and the minimum at 64C for adiabatic (that is, without loss or gain of heat energy, also called isentropic) compressibility (κS = -[δV/δP]S/V [112]) would both be at the density minimum (4C). Relationships between κT and κS are given elsewhere.
Changes with isothermal compressibility with temperature in liquid water, (see ref 68) Data from [561]
The adiabatic compressibility lies below the isothermal compressibility except at the 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 less apparent [706].

Some other liquids, such as formamide (also extensively hydrogen bonded), show a compressibility minimum. [Backto top of page

D14    There is a maximum in the compressibility-temperature relationship

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 is expected to lie just below the minimum temperature accessible on supercooling (232 K, [215]) close to the temperature of minimum density. [Backto top of page

D15    Speed of sound is slow and increases with temperature (up to a maximum 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 (u) is given by u2 = 1/κSρ =  [δP/δρ]S ~ 1/(<(V)2>) [802] where κS is the adiabatic compressibility, ρ is the density 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 the temperature increases the compressibility drops and goes through a minimum whereas the density goes through a maximum and then drops [67]. Combination of these two properties leads to the maximum in the speed of sound. Increasing the pressure increases the speed of sound and shifts the maximum to higher temperatures, both in line with the effect on the density. The supercooled data has been calculated for the graph, right. Changes in the speed of sound with temperature in liquid water, (see ref 67

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]. [Backto top of page

D16    The speed of sound may show a minimum

Depending on the frequency, there may be a minimum in the speed of sound at low temperatures [568]. Although this may be thought due to compensation in the changes in density decrease and compressibility increase with lowering temperature, this is not apparent in the calculated data above. It is most likely due to the increasing strength of its hydrogen bonding and 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 the increase in speed due to increasing pressure balances the decreasing speed with drop in temperature. Sound waves are trapped and propagate horizontally in this SOFAR channel. [Backto top of page

Deviation of the speed of sound at low temperatures and moderately high frequencies, data from Santucci et al (2006)

D17    'Fast sound' is found at high frequencies and shows an discontinuity 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. [Backto top of page

D18    NMR spin-lattice relaxation time is very small at low temperatures

NMR spin-lattice relaxation time depends on the degree of structure. As the water cluster equilibrium shifts towards a stiffer, 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. [Backto top of page

D19    The refractive index of water has a maximum value at just below 0C.

The refractive index of water (λ = 589.26 nm) rises from an estimated 1.33026 at -30C to a maximum value at just below 0C (1.33434) before falling ever increasingly to 1.31854 at 100C [310]. This may be explained by the mixture model [60] applied to the change from ES to CS as the temperature rises; ES possessing a lower refractive index than CS. Most of the effect is due to the density difference between ES and CS. Higher density produces higher refractive index such that the refractive index temperature maximum lies close to the density maximum, with the 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 refractive index (1.31, λ = 589 nm) of any known crystal. [Backto top of page Changes of the refractive index with temperature of liquid water, (see ref 310)

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. [Backto top of page


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 on freezing 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 causing blockage in the pipes at low percentage ice formation. [Back]

c ortho-Positronium consists of a positron - electron pair with parallel spins [826], created here by positron irradiation of water. [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], as discovered 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 to the 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 being greater 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]

Water structure and science
(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 maximum at -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 temperature 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 CSreversible arrowES 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. [Backto top of page

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 the kinetic 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. [Backto top of page

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 gaseous phase. 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. [Backto top of page

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 is raised. CP is the heat capacity at constant pressure defined by
     CP = (δH/δT)P is proportional to <(δS)2>TP is proportional to  <(δH)2>TPN
(that is, equals change in enthalpy with temperature, and proportional to the square of the entropy (or enthalpy) fluctuations). The extra positive δH due to the shift in equilibrium (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 CP at the temperature of maximum density. Usually in liquids CP is more than 20% greater than CV.
Variation of Cp and Cv with temperature

The CV values for supercooled water may be erroneous, being calculated from other data and showing an apparent discontinuity 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 associated with a discontinuity in the Raman depolarization ratio (that is, perpendicular/parallel polarization) data of degassed ultrapure water and hence a weak liquid-liquid phase transition at 34.6C (5.8 kPa) [1044]. [Backto top of page

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 has lower specific heat at very low temperatures. At sufficiently low temperature, there must be a maximum in the specific heat (CP)-temperature relationship, so long as no phase change occurs. This is expected to lie just below the minimum temperature accessible on supercooling (232 K, [215]), although a modeling approach using TIP5P gives ~250 K [1352]. The data opposite for supercooled water (upper red line) is taken from [906]. [Backto top of page
Heat capacity changes for supercooled (amorphous) liquid water and hexagonal ice

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 by its partial build-up, due to interpenetrating hydrogen bonded networks, at the higher pressures. [Backto top of page

T7    The heat capacity (CV) has a maximum.

The CV (the heat capacity at constant volume, CV = (δU/δT)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). The increase 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]. [Backto top of page

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 still considerable hydrogen bonding (~75%) in water at 100C. As effectively all these bonds need to be broken (very few indeed remaining in the gas phase), there is a great deal of energy required to convert the water to gas, where the water molecules are effectively separated. The increased hydrogen bonding at lower temperatures causes higher heats of vaporization (for example, 44.8 kJ mol-1, at 0C). Enthalpies of evaporation and fusion of molecules isoelectronic to water Ne, Fusion 0.34 kJ/mol; evaporation 1.74 kJ/mol HF, 4.56 kJ/mol HF, 25.20 kJ/mol NH3, 7.70 kJ/mol NH3, 17.52 kJ/mol CH4, 8.16 kJ/mol H2O, 6.01 kJ/mol CH4, 0.096 kJ/mol H2O, 40.66 kJ/mol

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. [Backto top of page

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. [Backto top of page

T10    High entropy of vaporization (109 J-1 K mol-1, cf. Trouton's constant 85 J K-1 mol-1).

Water also has anomalously high entropy of vaporization due to the hydrogen-bonded order lost on vaporization in addition 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 (ΔHvap/ΔSvap) is not anomalous.

Interestingly, the entropy of vaporization is inversely related to the absolute temperature from supercooled water to above 400K (that is, ΔSvap is proportional to 1/T). [Backto top of page

T11    The thermal conductivity of water is high and rises to a maximum 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 the increasingly large clusters that occur at lower temperatures. When the thermal energy is increased it shifts the ESreversible arrowCS 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-temperature behavior 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 using TIP5P gives the minimum at ~250 K [1352].

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

The thermal conductivity of water
 
Thermal conductivity along the saturation line (liquid-vapor equilibrium line). Note that the pressure increases with the temperature, see phase diagram. The thermal conductivity becomes infinite at the critical point [IAPWS].

Water structure and science
(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 a homogeneous phase at the molecular level. Local clustering will be effected by the presence of solutes, so changing the nature 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. [Backto top of page

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 a simple 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 a slight 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 oxygen atoms [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 asymmetric vibration and the smaller Bohr radius of D relative to H. This gives rise to small differences in the size and direction of the dipole 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 Equlibrium arrows  2HDO          Keq = 3.82, 25C [609], ΔH = 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 and DOD 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 a consideration 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 differently paired (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, i.e. ~4.4 PBq mol-1 T2O). The β particles travel only about 6 μm 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 H216O 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]. [Backto top of page

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]. [Backto top of page

M4    Solutes have varying effects on properties such as density and viscosity

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. [Backto top of page

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 from their solubility behavior at high temperatures.

The solubilities of the noble gases is shown opposite [IAPWS, 1166] and given below. Their hydration may be considered as the sum of two processes: (A) the endothermic opening of a clathrate pocket in the water, and (B) the exothermic placement of a molecule in that pocket, due to the multiple van der Waals interactions (for example, krypton dissolved in water is surrounded by a clathrate cage with 20 KrOH2 such interactions [1357]). In water at low temperatures, the energy required by process (A) is very small as such pockets may be easily formed within the water clustering (by CS -> ES)f.
Solubilities for the noble gasses in liquid water, http://www.iapws.org/relguide/gassol.pdf, Radon data from ref. 1166

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 noble gases increases considerably as the temperature is lowered. Their enthalpy and entropy of hydration become more negative 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
ΔG of solution in H2O at 25C, kJ mol-1 [1296]
29.41
29.03
26.25
24.80
23.42
 
ΔH of solution in H2O at 25C, kJ mol-1 [1296]
-0.59
-3.80
-11.98
-15.29
-18.99
ΔS 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 ΔH) and (as predicted by Le Chatelier's principle) solubility decreases with temperature rise. At high temperatures (often requiring high pressure) the natural clustering is much reduced causing greater energy to be required for opening of the pocket in the water. The solubilization process therefore becomes endothermic and (as predicted by Le Chatelier's principle) solubility goes through a minimum before increasing with temperature rise (being fully miscible under supercritical conditions).

Henry's constants for the noble gasses in liquid water, http://www.iapws.org/relguide/gassol.pdf
The more attractive the solute-water van der Waals interactions (due both to atomic number dependency and goodness of fit within the clathrate pocket), the greater the inherent exothermic nature of the process and therefore the higher the temperature minimum (see Table above) and the greater the temperature range of negative temperature solubility coefficient. Similarly Henry's constants (= partial pressure/mole fraction;h represents volatility, see opposite) exhibit increasing maxima with increasing size (the maxima are the same as the solubility minima above).  

The poor solubility of non-polar gases in water, in spite of the negative enthalpy change on dissolution, is due to positive free energy change (+ve ΔG) attributed to the large negative entropy change (-ve TΔS) caused by the structural enhancement of the water (ES) clusters; a conclusion reinforced by the enhanced heat capacity of these solutions (+ve Cp, 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 as ordering the inner dodecahedral water shells surrounding the solute molecules. There is also a reduction in volume (-ve ΔV) showing a reduction in the unoccupied space within the water solvent and also indicative of the gases occupying the pre-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 ('salt out') of the non-polar gases whereas hydrophobic hydrating salts (for example, tetramethylammonium chloride) that increase 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 benzene has 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 free energy 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 as water's dielectric permittivity reduces towards that of common organic solvents as the temperature rises towards its critical 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-thaw operations under reduced pressure for degassing water. [Backto top of page

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 its dielectric 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 dielectric constant. This allows it to act as a solvent for ionic compounds, where the attractive electric field between the oppositely charged ions is reduced by about 80-fold, allowing thermal motion to separate the ions into solution. On cooling, as the water 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, and liquid water becomes far less polar, down to a value of about 6 at the critical point. The dielectric constant similarly reduces if the hydrogen bonding is broken by other means such as strong electric fields but not with pressure. The change in 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 in supercooled water where the dielectric is high and increases (107.7 at -35C) even as the density decreases. Pressure 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 (with higher dipole moments) form liquids also having high dielectric constants (see below). The ratio dielectric constant/(dipole moment)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 dipole moment (e.g. CCl4) have infinite such values.

comparison of dipole moments, dielectric constants and the dielectric constant/(dipole moment)^2 ratio for a number of solvents Shown opposite are the dipole moments (blue triangles below) and dielectric constant/(dipole moment)2 ratios (red diamonds above) relative to the dielectric constants for a range of solvents. The data 1-17 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. [Backto top of page

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 (ε') and/or the imaginary (ε'') part of the complex dielectric constant increase then decrease with increasing temperature. Examples at two close frequencies for liquid (including supercooled) water are shown opposite [588]. This may be understood by noting the shifts with temperature of the maximum frequency of microwave absorption and the dielectric permittivity.

Analysis of the complex permittivity gives a discontinuity at about 30C [1045]. [Backto top of page

Dielectric changes with temperature

M8    Proton and hydroxide ion mobilities are anomalously fast in an electric 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 for hydrogen ions and hydroxide ions, at 349.19 and 199.24 S cm2 mol-1 at 25C [737], are similarly very high compared with values for other small ions such as lithium (38.7 S cm2 mol-1) and fluoride (55.4 S cm2 mol-1) ions. [Backto top of page

M9    The electrical conductivity of water rises to a maximum at about 230C and then falls.

The electrical conductivity of water increases with temperature up to about 230C due mainly to its increased ionization producing higher concentrations of the highly conducting H+ and OH- ions, which reach maximum concentrations at about 250C [IAPWS]. Above this temperature, for liquid water in equilibrium with the vapor, the density is much reduced (for example, 0.7 g cm-3 at 300C) and this reduces the ability for ionization. Proton mobility decreases above 149C due to lowered amounts of 'Zundel' cations (that is, H5O2+) [1061].

Note that the pKw also reaches a maximum value at about 250C in line with that of the hydrogen ion concentration [IAPWS].

Electrical conductivity and hydrogen ion concentration of heated liquid water

Resistivity of water from reference 737

Opposite is shown the great increase in the resistivity (= 1/conductivity) of water at low temperatures [737]; extrapolated values are shown in dashed blue. Interestingly, the electrical conductivity of water increases on degassing [711]. Together these properties support the formation of ES clusters at low temperatures and in the presence of non-polar gases, which involve localized and limited isotropic hydrogen bonding and so prevent lengthy directed proton movements. [Back] to top of page

M10    Acidity constants of weak acids show temperature minima.

An interesting anomaly concerns the changes in the pKa with temperature of many weak acids. As an example, opposite is shown this for the second ionization of phosphoric acid; H2PO4- =H+ + HPO42-. Such changes are due to a combination of factors including changes in the dielectric (high temperatures increasing the pKa) and hydrogen bonding (low temperatures increasing the pKa). [Backto top of page
pKa changes with temperature for the second ionization of phosphoric acid

M11    X-ray diffraction shows an unusually detailed structure

This is shown elsewhere and is simply explained by the presence of ordered clustering within the liquid phase. [Backto top of page

M12   Under high pressure water molecules move further away from each other with increasing pressure. 

When liquid water is put under pressure (below about 200 MPa) the water molecules approach their neighbors more closely, as might be expected from the increase in density. However, if the pressure is increased from about 200 to 400 MPa, the average distance between neighboring water molecules increases [51]. At higher pressures the distances reduce again (but less so) with increasing pressure. A similar and corroborative behavior is seen with the O-H stretch vibration frequency (v1), which increases with pressure between about 200 to 400 MPa [533] whilst reducing with pressure at higher or lower pressures. The O-H stretch data has been confirmed at 23C but not found at 52C, indicating that it requires larger clusters to be recognized [824].  Change in the nearest neighbor O-O distances in liquid water with pressure (see ref 51)

The explanation for all these effects is that there appears to be an increase in interpenetration of hydrogen bonded networks at about 200 MPa (at 290 K); interpenetration of hydrogen bonded clusters being preferred over more extreme bending or breaking of the hydrogen bonds. When liquid water is put under pressure (below about 200 MPa) the water molecules approach their neighbors more closely, as might be expected from the increase in density.

This is similar to what happens in the high density ices where, for example, ice-seven (with two interpenetrating cubic ice lattices) under a pressure of over 2200 MPa (density 1.65 g cm-3) has an average OO nearest neighbor distance about 3.5% greater than that in cubic ice (density 0.92 g cm-3 at 0.1 MPa). Thus the density of ice-seven is somewhat less than twice the density of cubic ice (that is, 2x0.92/(1.035)3 = 1.65 g cm-3). [Backto top of page


Footnotes

a D2O is toxic to many organisms at high levels (20%-100% D2O, where it affects many processes including mitosis and membrane function) but is not generally considered harmful at much lower levels where it is used in human physiological research. There is some evidence to show that artificially reducing its natural abundance in water (0.03% w/w) may have positive effects on the health of organisms [424]. [Back]

b This method for reconciling the data works poorly at low temperatures [1049]. [Back]

c The reduced zero point energy when switching D-atoms for H-atoms from free to hydrogen bonded positions within water clusters has been shown due to the energetic consequences of the lowering of the bend and torsional bond energies which are greater than the raising of the stretching bond energy [986]. [Back]

d Also contributing to this effect are the relative isotopic differences between the zero point energies of the liquid and gaseous phases. Librational vibrations (due to hydrogen bonding) release energy when the phase changes from liquid to gaseous (where they are absent) with H2O librations (being greater) releasing more energy and so increasing the volatility of H2O relative to D2O at lower temperatures. Opposite effects are apparent at higher temperatures where there is less hydrogen bonding but energy still needs to be supplied to provide for the increased zero point vibrational energy of the stretch vibrations (the gaseous stretch vibrations being more energetic than those for the liquid phase) [992]. [Back]

e In many gaseous-solute solvent systems (for example, N2 in CCl4) , the solubility increases with temperature increase. Although solubility decreases with temperature increase is encountered with some other solute-solvent combinations (for example, methane in n-heptane), the behavior is a more general property of water and deserves comment. [Back]

f There is evidence [157, 269, 274] that the first (clathrate) shell possesses stronger hydrogen bonding and this weakens the hydrogen bonding out to the next shell. [Back]

g The formation of O=OH-OH hydrogen bonds may be seen as the first stage in the natural low-level formation of oxygen redox products (for example, H2O2) in water. As the ratio of O2/N2 solubilities has a maximum at 290 K, there is indication that partial clathrate cages may be responsible for the polarization that encourages the hydrogen bond formation. [Back]

h Henry's constant = partial pressure/mole fraction (KH) may be described by the following equation Henrys constant= partial pressure/mole fraction =(RT/molar volume of water)exp(excess chemical potential of hydration/RT). where p is the partial pressure of the solute in the gas, X is the solute mole fraction, R is the gas constant, T is the absolute temperature, VH2O is the molar volume of water and μ is the temperature-dependent excess chemical potential of hydration for the solute [1276]. [Back]

i Nuclear quantum effects concern the different energies of the vibrational states. The bonds involving the deuterium atom (being about twice as heavy as the protium atom) vibrate with less amplitude and frequency. Nuclear quantum effects are seen particularly in differences in their zero point energy; the vibrational energy that remains at close to absolute zero. [Back]

Water structure and science
(http://www.lsbu.ac.uk/water/explan5.html)

Explanation of the Physical Anomalies of Water (P1-P12)

F1    High viscosity (0.89 cP, compare pentane 0.22 cP, at 25C)

The viscosity of a liquid is determined by the ease with which molecules can move relative to each other. It depends on the forces holding the molecules together (cohesiveness). This cohesivity is large in water due to its extensive three-dimensional hydrogen bonding. It should be noted that although the viscosity of water is high, it is not so high that it causes too much difficulty being moved around within organisms. The Arrhenius energy of activation for viscous flow is similar to the hydrogen bond energy  (H2O, 21.5 kJ mol-1; D2O, 24.7 kJ mol-1; T2O, 26.2 kJ mol-1, all calculated from [73]; all at 0C and all more than doubling at -30C).  [Backto top of page

F2    Large viscosity increase as the temperature is lowered.

The increase in the viscosity with lower temperatures is particularly noticeable within supercooled water (see opposite). The water cluster equilibrium shifts towards the more open structure (for example, ES) as the temperature is lowered. This structure is formed by stronger hydrogen bonding. In turn, this creates larger clusters and reduces the ease of movement (increasing viscosity). [Backto top of page
Change in dynamic viscosity with temperature; (see refs 69, 73)

F3    Viscosity decreases with pressure (at temperatures below 33C)

Viscous flow occurs by molecules moving through the voids that exist between them. As the pressure increases, the volume decreases and the volume of these voids reduces, so normally increasing pressure increases the viscosity.

Water's pressure-viscosity behavior [534] can be explained by the increased pressure (up to about 150 MPa) causing deformation, so reducing the strength of the hydrogen-bonded network, which is also partially responsible for the viscosity. This reduction in cohesivity more than compensates for the reduced void volume. It is thus a direct consequence of the balance between hydrogen bonding effects and the van der Waals dispersion forces [558] in water; hydrogen bonding prevailing at lower temperatures and pressures. At higher pressures (and densities), the balance between hydrogen bonding effects and the van der Waals dispersion forces is tipped in favor of the dispersion forces and the remaining hydrogen bonds are stronger due to the closer proximity of the contributing oxygen atoms [655]. Viscosity, then, increases with pressure. The dashed line (opposite) indicates the viscosity minima Liquid water's pressure-viscosity behavior
Liquid water's pressure-(relative)-viscosity behavior The variation of viscosity with pressure and temperature has been used as evidence that the viscosity is determined more by the extent of hydrogen bonding rather than hydrogen bonding strength [824].

Self-diffusion is also affected by pressure where (at low temperatures) both the translational and rotational motion of water anomalously increase as the pressure increases (see below). [Backto top of page

F4    Large diffusion decrease as the temperature is lowered.

Diffusion may be generally described by the Stokes-Einstein equation for translational diffusion [806], Translational diffusivity= (RT/N)x(1/6pi x viscosity x molecular radius) and the Stokes-Einstein-Debye equation for rotational diffusion, Rotational diffusivity= (RT/N)x(1/6pi x viscosity x (molecular radius)^3) ,where Dt and Dr are the translational and rotational diffusivities respectively, R is the gas constant, N is Avogadro's number, η is dynamic viscosity and r is water's molecular radius. The values for self-diffusion are greatly reduced at lower temperatures where they anomalously decrease as the density decreases (see below). This is unsurprising as these diffusion terms are approximately proportional to the reciprocal of the viscosity, and viscosity anomalously increases at lower temperatures. The inverse relationship between water diffusivity and dynamic viscosity, and the ratio of translational to rotational diffusivity, are almost independent of temperature between about -35C and +100C. However there is a strong divergence from these relationships, and their ratio [1040c], at lower, supercooled, temperatures (at 225 K [1040a]) due to the differential effects of clustering [807] caused by the presence of both low and higher density aqueous phases [1040]. Although such behavior is expected of liquids close to their glass transition, that is not the case with water where it occurs well above the glass-transition temperature.

The diffusion equations (above) give unexpectedly good estimates for the radius of the water molecule (r = 1.1 , 25C)a given that the equations were derived for large spherical particles.

The activation energy for this diffusion increases to about the equivalent of two hydrogen bonds (44.4 kJ mol-1) at 238 K where the diffusion coefficient is 1.58 x 10-10 m2 s-1 [653]. The importance of this activation energy disappears above about 315 K, when it appears to be less than the thermal energy [1295]. Thus, the main reason for the low diffusion at low temperatures is the three-dimensional hydrogen bond network.

The diffusion coefficient of deeply supercooled water is 2.2 x 10-19 m2 s-1 at 150 K [334].

Changes in diffusivity with temperature

As shown below, this anomalous diffusional behavior is not present when water diffuses in nitromethane in the absence of hydrogen bonding [652].

Change in diffusivity with temperature of water in nitromethane and in itself
Arrhenius plot of  diffusivity with temperature of water in nitromethane and in itself
 
[Backto top of page

F5    At low temperatures, the self-diffusion of water increases as the density and pressure increase.

The increase in self-diffusion with density (within the range of about 0.9 g cm-3 up to about 1.1 g cm-3, at low temperatures) is in contrast to normal liquids where increasing density decreases self-diffusion as the molecules restrict each other's movements. The density increase may be due to increasing temperature, below 4C, at atmospheric pressure or due to increasing pressure at low temperatures. Liquids normally show reduced self-diffusion when they are squeezed but water at 0C increases its diffusivity by 8% under a pressure of about 200 MPa [226] and the diffusivity of supercooled water at -30C increases by 60% with a similar pressure increase. Further increase in pressure reduces the diffusivity in common with the behavior of other liquids. The movement of water becomes restricted at low temperatures as the more open (lower density) structure produced on cooling (see above) is formed by stronger and more complete hydrogen bonding, which reduces the self-diffusion. The strength of the hydrogen bonding is a controlling influence in this anomalous region, where the hydrogen bond angles and the inter-molecular distances are strongly coupled and this order decreases on compression [169] due to the collapse of ES structures to CS structures. Simulation studies have shown that self-diffusion goes through a minimum as the density of water is reduced below about 0.9 g cm-3 followed by an increase with further density reduction, as might be expected from most liquids [402], due to the disruption of the network at low density as the now-stretched hydrogen bonds are broken [626]. The maximum in the self diffusion is brought about as at even higher pressures there is an increased packing density due to the gradual phase transition to interpenetrating hydrogen bonded networks.

Variation in Diffusivity of water with pressure

Data for these tables was calculated froma the IAPWS viscosity data [540]. The dashed lines indicate the maxima.

Variation in Diffusivity of water with density

For the same reasons, the molecular rotational movement of water (reciprocal rotational relaxation time) also varies in direct proportion to the changes in self-diffusion (translational movement). [Backto top of page

F6    The thermal diffusivity rises to a maximum at about 0.8 GPa.

The thermal diffusivity (=thermal conductivity/(density x specific heat)),b which arises from vibrations in the water network [713], shows less anomalous temperature and pressure behavior than might be expected due to the dependence on the anomalously-behaving, but counteractive, thermal conductivity, density and specific heat capacity. There is, however, a steep increase in thermal diffusivity at low temperatures (see left, 25C) and a maximum in the low-temperature thermal diffusivity - pressure behavior at about 0.8 GPa [614].
Variation of thermal difusivity with pressure

It is likely that there will be a minimum in the thermal diffusivity-temperature behavior at about -3015C at atmospheric pressure in line with changes in the specific heat (CP) and thermal conductivity. A modeling approach using TIP5P gives the minimum at ~250 K [1352]. [Backto top of page

F7    High surface tension (72.75 mJ/m2, cf. CCl4 26.6 mJ/m2 at 20C)

Surface tension (surface free energy, Surface tension =change in free energy per change in surface area at constat temperature and pressure) at a gas liquid interface is produced by the attraction between the molecules being directed away from the surface as surface molecules are more attracted to the molecules within the liquid than they are to molecules of the gas at the surface. In contrast, molecules of water in the bulk are equally attracted in all directions. In order to achieve the greatest possible interaction energy, surface tension causes the maximum number of surface molecules to enter the bulk of the liquid and, hence, the surface area is minimized. Surface tension explanation

Water has an abnormally high surface tensionc and surface enthalpy d with an abnormally tightly packed surface compared to bulk liquid water.e Water molecules at the liquid-gas surface have lost potential hydrogen bonds directed at the gas phase and are pulled towards the underlying bulk liquid water by the remaining stronger hydrogen bonds [214]. Energy is required to increase the surface area (removing a molecule from a well hydrogen bonded interior bulk water to the lesser hydrogen bonded surface), so it is minimized and held under tension. As the forces between the water molecules are several and relatively large on a per-mass basis, compared to those between most other molecules, and the water molecules are very small, the surface tension is large. Lowering the temperature greatly increases the hydrogen bonding in the bulk causing increased surface tension.

Although there is no clear anomaly in the surface tension/temperature behavior [IAPWS], there are inflection points at about -6C [865] and 250C [427]. The inflection in the data at about -6C has been explained by use of a two-state mixture model involving low-density and higher density water clusters [866].

Surface tension changes differently from bulk water properties due to surface enrichment with water clusters.

The surface tension/temperature behavior of liquid water in equilibrium with vapor data from International Assosiation for the Properties of Water and Steam; http://www.iapws.org/relguide/surf.pdf Data for supercooled water from ref [865

The greater than expected drop in surface tension with temperature increase (0.155 mJ m-2 K-1 at 25C) is one of the highest known and similar to that of the liquid metals. It has been quantitatively explained using spherically symmetrical water clustering [376]. The thermodynamic change in surface tension with pressure is very high at 25C [1280]. e

It is interesting to note that surfactants lower the surface tension because they prefer to sit in the surface, attracting the surface water molecules in competition to the bulk water hydrogen bonding and so reducing the net forces away from the surface (that is, the surface tension).

The high surface tension of water endows it with some rather unexpected properties. Thus, water drops may rise up an inclined plate, against gravity, if subjected to symmetrical vibrations of about 100 Hz [1311]. This is due to the unequal changes in contact angle at the top and bottom surfaces, creating upwards forces greater than that due to gravity, and the non-linear friction effects. Also, if a small drop of water (typically 1 mm diameter) is coated in a fine (typically 20 μm diameter) hydrophobic dust then the drop can roll and bounce without leakage [225], and the aqueous spheres can even float on water. Capillarity holds the dust at the air-liquid interface with the elasticity being due to the high surface tension. [Backto top of page

F8    Some salts give a surface tension-concentration minimum; the Jones-Ray effect

The affinity of chaotropic ions for the expanded and weakly hydrogen bonded surface water structure (aided by the excess of 'lone pair' electrons directed towards the bulk [594]) may help explain the shallow minima in their surface tension at very low ionic concentrations (that is, the Jones-Ray effect [674]; first dismissed erroneously as an artifact by Irving Langmuir). For example, at low concentration (< 1 mM) the surface tension of KCl solutions drops (~-0.01% change) with increasing concentration. The increase in surface tension with higher concentrations of salt is thought due to the relative depletion of salt within the surface, which means that when ions do absorb at the surface a depletion layer must be created deeper in. Also, higher concentrations of such salts must disproportionately increase the bulk salt concentration so adding to the attractive forces on the surface water molecules, consequently adding to the increase in the surface tension. Kosmotropic cations and anions prefer to be fully hydrated in the bulk liquid water and so increase the surface tension by the latter mechanism at all concentrations. This partitioning is noticeable in NaCl solutions, such as seawater; the weakly chaotropic Cl- occupying surface sites whereas the weakly kosmotropic Na+ only resides in the bulk water [928]. The polarizability of large chaotropic anions (such as I-) is accentuated due to the asymmetric solvent distribution at the surface and increases the strength of chaotrope-solvent interactions when at the surface [989]. Similarly to chaotropic ions, hydroxyl radicals also prefer to reside at air-water interfaces [939]; the radicals donating one hydrogen bond but accepting less than two [943]. The lesser hydration energy of OH- relative to H3O+, results in OH- preferring the surface over the H3O+, which also has some, but less, preference for the surface [1205,1308], and biases a pure aqueous interface to give it a negative potential [1205c, 1308]. The preference of H3O+ for the surface in acid solution (due to its surface active nature, as its O atom is not hydrogen bonded) is shown by the drop in surface tension with HCl, HNO3 and HClO4 (but not H2SO4) acid concentration. [Backto top of page

F9    Some salts prevent the coalescence of small bubbles.

Higher concentrations (often about 0.1M) of many, but not all, salts prevent the coalescence of small gas bubbles (recently reviewed [672]) in contrast to the expectation from the raised surface tension and reduced surface charge double layer effects (DLVO theory). Higher critical concentrations are required for smaller bubble size [599]. This is the reason behind the foam that is found on the seas (salt water) but not on lakes (fresh water). The salts do not directly follow the Hofmeister effects with both the anion and cation being important with one preferentially closer to the interface than the other; for example, excess hydrogen ions [1205] tend to negate the effect of halides [622]. The explanation for this unexpected phenomenon is that bubble coalescence entails a reduction in the net gas-liquid surface, which acts as a sufficiently more favorable environment for the one out of a pair of ions rather than the bulk when their concentration is higher than a critical value. It has been proposed that anions and cations may be divided into two groups α and β with α cations (Na+, K+, Mg2+) and β anions (ClO4-, CH3CO2-, SCN-) ) avoiding the surface and α anions (OH-, Cl-, SO42-) and β cations (H+, (CH3)4N+) attracted to the interface; αα and ββ anion-cation pairs then cause inhibition of bubble coalescence whereas αβ and βα pairs do not [1305]. These groupings do not behave as bulk-phase ionic kosmotropes and chaotropes, which indicates the different properties of bulk water to that at the gas-liquid surface. It is likely that the ions reside in the interfacial region, between the exterior surface layer and interior bulk water molecules, where the hydrogen bonding is naturally most disrupted [605]. A similar phenomenon is the bubble (cavity) attachment to microscopic salt particles used in microflotation, where chaotropic anions encourage bubble formation [758].

Interestingly, the concentration of salt in our bodies corresponds to the minimum required for optimal prevention of bubble coalescence [622]. As small bubbles are much less harmful than large bubbles, this fact is very useful. [Backto top of page


Footnotes

a If the equation for 'slip boundary' solutes, where the solute diffusion does not involve the fixed shell of solvent molecules assumed in the above equation, is used Diffusivity= (RT/N)x(1/4pi x viscosity x molecular radius) then the water hydrodynamic radius is close to correct at 1.64 at 25C. [Back]

b At temperatures between 100C and 400C, the thermal diffusivity scales as the square root of the absolute temperature (Diffusivity/√T is proportional to density [614]). [Back]

c A freshly exposed surface of water would be expected to have much higher surface energy (~0.180 J m-2 [1255] ). [Back]

d Surface enthalpy (also known as the total surface energy) may be calculated from the binding energy lost per unit surface area (= molecules per surface area x binding energy lost per molecule. If the surface is only half occupied with water molecules that have lost about a third of their hydrogen bonds, the surface enthalpy should be = 0.5 x (1019 molecule m-2) x (1/6.022x1023 mol molecule-1) x 1/3 x (45 kJ mol-1) = ~0.125 J m-2 (compare with the actual value of 0.118 J m-2). [Back]

e The influence of pressure on the surface tension of water, as with other liquids, is not straightforward. There are two clear effects. Firstly, the thermodynamic relationship relating surface tension to pressure Change in surface tension with pressure at constat temperature and surface area has been shown to equal the change in volume associated with forming more surface, (dV/dA)TPn[1283]. (dA/dV)TPn may be taken as a measure of the difference in density of the liquid in the bulk compared with that at its surface and is therefore generally positive (that is, the surface tension should increase with pressure about +0.7 mJ m-2 MPa-1 for water at 25C). The pressure coefficient of the surface tension (Change in surface tension with pressure=change in volume on change in surface area = surface enthalpy/internal+external pressure, = 0.702 nm at 25C) is much generally higher than for other liquids; for example, methanol (0.159 nm), diethyl ether (0.176 nm), benzene (0.178 nm) and even mercury (0.398 nm) [1280]. This high value for water indicates that the density at the surface of water is more similar to the bulk liquid than occurs in most other liquids (see the thermodynamic derivatization). Anomalously amongst liquids, the densities of surface and bulk water are equal at 3.97 C (at atmospheric pressure, as calculated from the equations given in [1280]) and below this temperature the bulk liquid is less dense than the surface liquid.

The thermodynamic relationship does not hold for real liquid-gas systems, however, where the application of pressure will cause water vapor to condense and gas molecules to adsorb on to the liquid-gas interface. The adsorption of gas molecules to the surface of liquid water lowers the surface tension by a greater extent than the thermodynamic effect outlined above (except perhaps for helium). Thus, the surface tension of water, in contact with other molecules in the gas phase, drops with increase in pressure due to the surface activity of surface-absorbed gas molecules [1282]. The extent of this lowering depends upon the gas involved and is much greater for hydrophilic gasses, such as CO2 (-7.7 mJ m-2 MPa-1) , than nonpolar gasses such as N2 and O2 (-0.8 mJ m-2 MPa-1). [Back]

(c) Martin Chaplin 4 January, 2008
(printed 14 January 2008)