Water structure and science
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, ) 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 . Water ionizes and allows easy proton exchange between molecules, so contributing to the richness of the ionic interactions in biology.
At 4°C 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 4°C 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 . 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
Water phase anomalies
Water density anomalies
Water material anomalies
Water thermodynamic anomalies
Water physical anomalies
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, ). 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  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  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 . 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
Density anomalies (D1-D20) explanations
P1 High melting point (0°C, compare CHCl3 -63°C)
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]. [Back]
P2 High boiling point (100°C, compare CHCl3 61°C)
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 100°C whereas for both H2S and H2Se it is about 25°C. [Back]
P3 High critical point (374°C, compare CH3CH3 32°C)
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 . [Back]
P5 The thermal conductivity of ice reduces with increasing pressure
Hexagonal ice shows anomalous reduction in thermal conductivity with increasing pressure (as do cubic ice and low-density amorphous ice but not high-density amorphous ice ), which behavior is different from most crystals where 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 . [Back]
P6 The structure of liquid water changes at high pressure
In a similar manner to the formation of the high density crystalline (ice-five and ice seven) and amorphous (HDA) 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  and indicates that liquid water structuring at high pressure has similarity to that of its high pressure ice phases . [Back]
P7 Supercooled water has two phases and a second critical point
As water is supercooled it converts mainly into its expanded form (for example, ES) at ambient pressures, which at low enough temperatures (< -38°C) 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 . This phase change cannot continue to higher temperatures (so creating a second critical point, ) 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  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]. [Back]
P8 Liquid water is easily supercooled but glassified with difficulty
Water freezing is not simply the reverse of ice melting . 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 -25°C and with more difficulty down to about -38°C with further supercooling possible, in tiny droplets (~5 μm diameter), down to about -41°C under normal atmospheric pressure. Water, supercooled down to -37.5°C, 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 . Where salts or hydrophilic solutes are present, the homogeneous freezing point reduces about twice as much as the melting point .
Liquid water may be maximally supercooled to about -92°C 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 . 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 . Methods that break the hydrogen bonding in these clusters, such as ultrasonics , cause the supercooled water to immediately freeze.
There is a recent comprehensive review of the properties of supercooled water . [Back]
P9 Liquid water exists at very low temperatures and freezes on heating
Deeply supercooled liquid water can be produced from glassy amorphous ice between -123°C and - 149°C  and may coexist with cubic ice up to -63°C . This behavior is particularly anomalous as the liquid (deeply supercooled water) is a 'strong' liquid (compared with supercooled water that is a 'fragile' liquid ) 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 . 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 ). [Back]
P10 Liquid water may be easily superheated
Liquid water can be easily superheated above its boiling point away from its surface with the atmosphere [1128, 1184]. This may be particularly important when heating foods and drinks in a microwave oven where explosive production 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' . Liquid water may be superheated to about +240°C to +280°C 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 20°C . Superheating is facilitated by dissolved gas that may increase its hydrogen-bonded order  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 .
An interesting, if unrelated effect (the Leidenfrost effect), is that water droplets remain far longer on a hotplate just above 200°C than if the hotplate was just above 100°C. (see  for an amusing scientific answer to how water boils). [Back]
P11 Hot water may freeze faster than cold water; the Mpemba effect
The ability of hot water to freeze faster than cold seems counter-intuitive as it would seem that hot water must 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, 18°C) under otherwise identical conditions . 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 .
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 . 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 ; 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 . 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 . 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 . [Back]
P12 Warm water vibrates longer than cold water
It is expected that the lifetime of an excited molecular vibration should decrease as the temperature increases as 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 . 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. [Back]
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 -5°C down to 70 water molecules at -40°C . Molecular dynamics studies show that these do not need to form a crystalline structure for crystallization to occur . [Back]
Water structure and science
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 . This is a similar but unrelated phenomenon to the maximum density anomaly that occurs in liquid water. [Back]
D2 Water expands on freezing (compare liquid argon shrinks 12% on freezing)
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 . 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 .
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]. [Back]
D3 Pressure reduces ice's melting point (13.35 MPa gives a melting point of -1°C)
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 0°C 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 (-21.985°C) is reached at 209.9 MPa.e A recent thermodynamic analysis concludes that ice nucleation cannot arise above -109°C during isochoric cooling , which is close to the upper bound of the realm of deeply supercooled water (-113°C), so it is unclear if ice would ever freeze in such a (unreal) system. [Back]
Melting ice, within a filled and sealed fixed volume, may result in an apparently superheated state where the metastable iso-dense liquid water is stretched, relative to its equilibrium state at the (effectively) negative pressure, due to its cohesiveness. Consequently, the ESCS equilibrium is shifted towards the more-open ES structure. [Back]
D4 Liquid water has a high density that increases on heating (up to 3.984°C)
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 8°C .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 4°C. Thus in water below about 4°C, warmer water sinks whereas when above about 4°C, warmer water rises. As water warms up or cools down through 4°C, 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).
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 0°C (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 -1.33°C. 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 11.185°C at 0.1 MPa) with respect to increasing pressure .
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 , as at very high negative pressures it reduces as the hydrogen bonds are stretched to breaking point; [Back]
D6 There is a minimum in the density of supercooled water
At a temperature below the maximum density anomaly there must be a minimum density anomaly so long as no phase change occurs, as the density increases with reducing temperature at much lower temperatures. This was first seen in simulations  and is expected to lie below the minimum temperature accessible on supercooling (232 K, ) and close to where both maximum ES structuring and compressibility occur, with the liquid density close to that of hexagonal ice (latterly confirmed ). 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 203±5 K . A density minimum at 210 K has been experimentally determined in supercooled D2O contained in 1-D cylindrical pores of mesoporous silica . Although possibly related, density values obtained for confined water cannot be taken as necessarily giving the density minimum for the bulk supercooled liquid however. [Back]
D7 Water has a low thermal expansivity (0.00021/°C, cf. CCl4 0.00124/°C at 20°C)
The thermal expansivity is zero at 3.984°C, being negative below and
positive above (see density and
expansivity anomalies). As the temperature
increases above 3.984°C, 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)
D8 Water's thermal expansivity reduces increasingly (becoming negative) at low temperatures.
It is usual for liquids to expand increasingly with increased temperature.
D9 Water's thermal expansivity 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. [Back]
D11 Nearest neighbors increase with temperature
If a water molecule is in a fully hydrogen-bonded structure with strong and straight hydrogen bonds (such as 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. [Back]
D12 Water has unusually low compressibility (0.46 GPa-1, compare CCl4 1.05 GPa-1, at 25°C)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 Å with increasing or pressure  (and temperature ), 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 10°C but only 2% higher at 40°C ) due its stronger hydrogen bonding producing an ESCS 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. [Back]
D13 Compressibility drops as temperature increases (up to a minimum at about 46.5°C)
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 ESCS becomes more positive). As the water structure is more open at these lower temperatures, the capacity for it to be compressed increases .
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 .
Some other liquids, such as formamide (also extensively hydrogen bonded), show a compressibility minimum. [Back]
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, ) close to the temperature of minimum density. [Back]
D15 Speed of sound is slow and increases with temperature (up to a maximum at 74°C)
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>)  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).
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 . [Back]
D16 The speed of sound may show a minimum
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 20°C . 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  (see above). 'Fast sound' is not a true anomaly as this behavior is what might be expected from a typical liquid, whereas the (hydrodynamic) lower speed of sound (~1500 m s-1) is due to the hydrogen bonding network structure of water. However, there does appear to be a discontinuity anomaly at a density of about 1.12 g cm-1 (in this 'fast sound' only; the discontinuity is less apparent in the hydrodynamic speed of sound) that may indicate a structural rearrangement [644, 655], due to the gradual phase transition to interpenetrating hydrogen bonded networks at the higher pressures, as seen with other anomalies. [Back]
D18 NMR spin-lattice relaxation time is very small at 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. [Back]
D19 The refractive index of water has a maximum value at just below 0°C.
D20 The change in volume as liquid changes to gas is very large.
Water is one of the lightest gasses but forms a dense liquid. The volume change is the greatest known (except for metals) at 1603.6 fold, at the boiling point and standard atmospheric pressure. This change in volume allows water to be of great use in the steam generation of electrical power. [Back]
a There is some dispute over whether such a negative pressure can be reached . [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 . The curious phenomenon of hot water pipes bursting more often than cold water pipes (see ) 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 , 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) , 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
T1 The heat of fusion of water with temperature exhibits a maximum at -17°C .
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 0°C 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 -17°C) the continued shift, with lowering temperature, in the supercooled water CSES equilibrium towards the ES structure reduces the enthalpy of the liquid water relative to the ice due to the consequent increase in hydrogen-bond strength and this causes the drop in the heat of fusion with lowering temperature. [Back]
T2 High specific heat capacity; CV and CP, 4.18 J g-1 K-1 at 25°C (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. [Back]
T3 Water has about twice the specific heat capacity of ice or steam (compare benzene where CP liquid = 1.03 x CP solid).
At its melting point the CPs of ice-Ih and water are 38 J mol-1 K-1 and 76 J mol-1 K-1 respectively. The CP's of the other ices may be up to about 40% higher (ice-three) than that of ice-1h but are all significantly lower than liquid water . 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. [Back]
T4 The specific heat capacity (CP) has a minimum at 36°C.
It is usual for the specific heats of liquids to increase with increased temperature at all temperatures.
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 34.6°C (5.8 kPa) . [Back]
T5 The specific heat capacity (CP) has a maximum at about -45°C.
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 . 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. [Back]
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 . [Back]
T8 High heat of vaporization (40.7 kJ mol-1, compare H2S 18.7 kJ mol-1)
The high heat of vaporization also causes water to have an anomalously low ebullioscopic constant (that is, effect of solute on boiling point elevation, 0.51 K kg/mol, compare CCl4 4.95 K kg/mol).Also related is the anomalously low cryoscopic constant of water. [Back]
T9 High heat of sublimation (51.059 kJ mol-1 at 0°C).
The high heats of fusion and vaporization combine to give rise to an anomalously high heat of sublimation. [Back]
T10 High entropy of vaporization (109 J-1 K mol-1, 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 1/T). [Back]
T11 The thermal conductivity of water is high and rises to a maximum at about 130°C.
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 130°C in liquid water .
Water structure and science
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. [Back]
M2 D2O and T2O differ significantly from H2O in their physical properties
Normally different isotopic forms of compounds behave very similarly to each other. The heavier forms of water (D2O where D = deuterium, 2.0141017780 g mol-1; and T 2O where T = tritium, 3.0160492675 g mol-1) form stronger hydrogen bonds than light water (H2O where H = protium, 1.0078250321 g mol-1) and vibrate less. Hence, they are more ordered than normal water, as shown by their greater molar volumes. This causes many of their properties (such as the viscosity, self-diffusion coefficient, protein solubility and toxicitya ) 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 100°C 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 ; for example, viscosity data has been reconciled if the temperatures are shifted by 6.498°C and 8.766°C for D2O and T2O respectively .b H2O is about four-fold stronger as an acid than D2O at 25°C 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 80°C. 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 . Although the electron densities of the different isotopic forms of liquid water have proved, so far, to be indistinguishable , 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 , 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:
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 . 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 . [Back]
M3 Liquid H2O and D 2O differ significantly in their phase behavior.
The phase behavior of liquid H2O and D2O differ, with the triple point of D2O being 3.82°C and 49 Pa higher than that of H2O, their vapor pressure curves crossing at 221°C and the critical point of D2O being 3.25°C and 393 kPa lower . 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  (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 . [Back]
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. [Back]
M5 The solubilities of non-polar gases in water decrease with increasing temperature to a minimum and then rise.e
Non-polar gases are poorly soluble in water. Most gaseous solutes dissolve more in most solvents as the temperature is raised. However, non-polar gasses are much more soluble in water at low temperatures than would be expected from their solubility behavior at high temperatures.
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.
Oxygen (O2) and nitrogen (N2) molecules behave similarly (solubility minima at N2 74°C and O2 94°C, 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 5°C, 101,325 Pa ). The greater solubility of O2 over N2, in spite of its lesser clathrate forming ability  has been proposed due to its formation of weak hydrogen bonds to water . 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).
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 . 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 20°C .
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 Å) in the icosahedral network . 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 0°C .
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. [Back]
M6 The dielectric constant of water is high (78.4 at 25°C)
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 (0°C), 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  where the dielectric is low, and in supercooled water where the dielectric is high and increases (107.7 at -35°C) even as the density decreases. Pressure increases the dielectric constant (101.42 at 0°C 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.
M7 The dielectric constant shows a temperature maximum.
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 25°C 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 25°C , 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. [Back]
M9 The electrical conductivity of water rises to a maximum at about 230°C and then falls.
M10 Acidity constants of weak acids show temperature minima.
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. [Back]
M12 Under high pressure water molecules move further away from each other with increasing pressure.
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 O····O 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). [Back]
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 . [Back]
b This method for reconciling the data works poorly at low temperatures . [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 . [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) . [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=O···H-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 . 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 . [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
F1 High viscosity (0.89 cP, compare pentane 0.22 cP, at 25°C)
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 ; all at 0°C and all more than doubling at -30°C). [Back]
F2 Large viscosity increase as the temperature is lowered.
F3 Viscosity decreases with pressure (at temperatures below 33°C)
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.
F4 Large diffusion decrease as the temperature is lowered.
Diffusion may be generally described by the Stokes-Einstein equation for translational diffusion , and the Stokes-Einstein-Debye equation for rotational diffusion, ,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 -35°C and +100°C. 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  caused by the presence of both low and higher density aqueous phases . 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 Å, 25°C)a given that the equations were derived for large spherical particles.
As shown below, this anomalous diffusional behavior is not present when water diffuses in nitromethane in the absence of hydrogen bonding .
F5 At low temperatures, the self-diffusion of water increases as the density and pressure increase.
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). [Back]
F6 The thermal diffusivity rises to a maximum at about 0.8 GPa.
It is likely that there will be a minimum in the thermal diffusivity-temperature behavior at about -30±15°C 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 . [Back]
F7 High surface tension (72.75 mJ/m2, cf. CCl4 26.6 mJ/m2 at 20°C)
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 . 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.
The greater than expected drop in surface tension with temperature increase (0.155 mJ m-2 K-1 at 25°C) is one of the highest known and similar to that of the liquid metals. It has been quantitatively explained using spherically symmetrical water clustering . The thermodynamic change in surface tension with pressure is very high at 25°C . 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 . 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 , 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. [Back]
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 ) may help explain the shallow minima in their surface tension at very low ionic concentrations (that is, the Jones-Ray effect ; 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 . 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 . Similarly to chaotropic ions, hydroxyl radicals also prefer to reside at air-water interfaces ; the radicals donating one hydrogen bond but accepting less than two . 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. [Back]
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 ) 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 . 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  tend to negate the effect of halides . 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 . 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 . A similar phenomenon is the bubble (cavity) attachment to microscopic salt particles used in microflotation, where chaotropic anions encourage bubble formation .
Interestingly, the concentration of salt in our bodies corresponds to the minimum required for optimal prevention of bubble coalescence . As small bubbles are much less harmful than large bubbles, this fact is very useful. [Back]
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 then the water hydrodynamic radius is close to correct at 1.64 Å at 25°C. [Back]
b At temperatures between 100°C and 400°C, the thermal diffusivity scales as the square root of the absolute temperature (Diffusivity/√T density ). [Back]
c A freshly exposed surface of water would be expected to have much higher surface energy (~0.180 J m-2  ). [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 has been shown to equal the change in volume associated with forming more surface, . 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 25°C). The pressure coefficient of the surface tension ( = surface enthalpy/internal+external pressure, = 0.702 nm at 25°C) 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) . 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 ) 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 . 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